30^{\\circ}$. We only consider $R \\ge 1$ clusters (with\nmeasured redshifts) since they\nwere defined by Abell (1958) as members of his statistically complete sample.\nRecently, Miller {\\it et al.} (1999a,b) examined similar subsets of $R \\ge 1$ clusters\nfor projection effects, line-of-sight anisotropies, and spatial correlations. We\nsummarize their results below.\n\nThe Abell/ACO $R \\ge 1$ cluster dataset has significant advantages over other cluster\nsamples (including those with $R =0$ clusters as well as APM clusters). With the\nadvent of multi-fiber spectroscopy, nearly all rich Abell/ACO clusters within $z=0.10$ now have\nmultiple galaxy determined redshifts (Slinglend {\\it et al.} 1998; Katgert {\\it et al.}\n1996). Multiple redshifts have allowed for more accurate determinations of the extent\nof projection effects and Miller {\\it et al.} 1999a report that at most, 10\\% of\nAbell/ACO clusters suffer from moderate to severe foreground/background contamination.\nThe lack of projection effects\nfor $R \\ge 1$ clusters is also apparent from the 89\\% X-ray emission\ndetection rate by Voges {\\it et al.} 1999.\nMiller {\\it et al.} (1999a,b) also show that there is very little line-of-sight anisotropy\nin the $R \\ge 1$ Abell/ACO cluster samples - comparable to the APM cluster\ncatalog (Dalton {\\it et al.} 1994)\nThis is in sharp contrast to $R \\ge 0$\nsamples and even some modern X-ray selected/confirmed cluster samples (see e.g. Efstathiou\net al. 1992, Peacock \\& West 1992, and Miller et al. 1999b).\n\nVogeley (1998) recently pointed out how Galactic extinction could\nadd ``false'' power to structure analyses based on large galaxy\nsamples (such as the Sloan Digital Sky Survey). While clusters should\nnot affected as strongly as individual galaxies, it is still worth examining\nextinction effects within our cluster sample.\nIn 1996, Nichol and Connolly used the Stark {\\it et al.} 1992 HI maps to report\nthat some samples of Abell clusters significantly anti-correlate with\nregions of high galactic neutral hydrogen density. \nRecently, Schlegel, Finkbeiner, and Davis (1998) have\ncreated HI extinction maps of the entire sky with much greater resolution than the Stark HI\nmaps. We use these new maps to re-examine\nand confirm the Nichol and Connolly results. We also examine a volume-limited ($z=0.10$) sample\nof Abell/ACO clusters.\nUsing a Kolmogorov-Smirnov (K-S) test, we compare the E(B-V) extinctions for positions\ncentered on the Abell/ACO clusters to E(B-V) extinctions for several thousand randomly\nselection positions. We find that the probability that our clusters were drawn\nfrom a random selection of E(B-V) extinctions is 10\\%. \nIn other words, the average extinction\nwithin our Abell/ACO clusters is smaller than for the random positions, but\nnot significantly so. For comparison, Nichol and Connolly found only a 2\\% probability that the\nPostman, Huchra, and Geller (1992) Abell/ACO clusters (with $|b| \\ge 30^o$ and $R \\ge 1$) were\ndrawn from a random sampling of E(B-V) extinctions. \nThe effect that galactic extinction would have on a power spectrum should not be \nas strong for clusters as it would be for galaxies. Cluster galaxies have\na wide range of magnitudes, and while some dimmer galaxies within a cluster may be missed due\nto extinction, the majority of bright galaxies will still be counted. When we created\nour volume-limited samples, we are including those clusters that appear dim as a result of\ngalactic extinction (as opposed to a magnitude-limited survey which would exclude those\nclusters). The lack of statistically significant evidence that our clusters\nare corrupted by extinction, and the use of a volume-limited sample (with $|b| \\ge 30^o$),\nconvinces us that\nwe can ignore any extinction effects in our analyses.\nHowever, to be certain that extinction is not altering the shape or amplitude of\nour redshift-space power spectrum, we will model the extinction distribution\nof our clusters in our random catalogs for one of our two PS estimation methods (see method (b) below).\n\nAn additional argument for the completeness of $R \\ge 1$ Abell/ACO clusters is\nprovided by their spatial number density as shown in Figure 1. \nWe use clusters of all magnitudes and use the same methods \nas Miller {\\it et al.} (1999a) to calculate and\nbin the cluster number densities. \nNotice in Figure 1 that the sample\nhas a nearly constant density out to $z = 0.10$\nand that the density\nonly drops by a factor of $0.58$ out to $z = 0.14$. \n[Note: The bump in the density at $z \\sim 0.07$ is mostly due to\nthe Corona Borealis Supercluster.]\nIn Figure 1, we fit three different functions to the number density:\na three-parameter number function (as in FKP), a power-law for $z \\ge 0.10$,\nand a step-function. The best-fit produces $\\chi^2_{red} = 2$ for the number function. \n\nUsing cluster redshifts from the literature as well as $\\sim 100$ as yet unpublished\nredshifts from the MX Survey Extension (Miller {\\it et al.} 2000),\nwe have created a sample of 637 $R \\ge 1$ Abell/ACO clusters with $|b| \\ge 30^{\\circ}$.\nThe MX Survey provides a much deeper (in both magnitude and in redshift) catalog\nof Northern Hemisphere cluster redshifts than is currently available for the Southern Hemisphere ACO clusters\n(see e.g. Miller et al. 1999; Katgert et al. 1996).\nTherefore, we exclude any cluster\nbeyond $z = 0.10$ in the south ($\\delta \\le -27^{\\circ}$) and beyond $z = 0.14$ in the\nnorth ($\\delta \\ge -27^{\\circ}$).\nSeveral researchers have noted discrepancies between the richness counts of\nthe Abell and ACO catalogs (see Miller et al. (1999) for a discussion).\nTherefore, we also measure $P(k)$ for a subset of our data that\nexcludes all ACO clusters with\n$N_{gal} < 55 $ (where $N_{gal}$ is the number of galaxies used to determine the richness as\ngiven in ACO and $N_{gal} \\ge 50$ corresponds to $R \\ge 1$). This richness cut excludes\n30 ACO clusters from our sample.\n\nThis is the largest cluster sample compiled to date for large-scale structure analyses.\nThe survey volume covers $1.2\\times10^8h^{-3}$Mpc$^3$ and is nearly four times larger than\nthe APM cluster survey (Dalton {\\it et al.} 1994)\nand the Retzlaff {\\it et al.} (1998) Abell/ACO survey.\nAdditionally, only $\\sim$ 10\\% of our cluster redshifts are\nbased on one measured galaxy redshift.\nWe calculate distances to the clusters using\na Friedmann Universe with $q_0 = 0$ and $H_0 = 100$ km s$^{-1}$ Mpc$^{-1}$. \nThe choice of $q_o$ makes little difference in\nour results (see also Retzlaff {\\it et al.} 1998).\n\n\nWhen a cluster dataset goes as deep as the one used here, and has been\ncreated in a somewhat piecemeal fashion, we must be very \nconfident that the cluster observations used in this sample are more or less isotropic in volume, and that\nwe are not including large sections of the sky that go deeper (in magnitude) than others.\nWe address this concern \nfiguratively in Figure 2, by examining the fraction of observed to total cataloged clusters.\nIn this sky plot (in galactic coordinates), we\nshow Abell clusters with $z=0.10$ (filled circles), Abell clusters within\n$0.10 < z \\le 0.14$ (open circles), and ACO clusters within $z=0.10$ (stars).\nWe can divide the sky into quadrants with two sections in the north\nand two in the south (each separated at $l = 180^{o}$) and examine\nnearby ($z \\le 0.10$) and distant ($0.10 < z \\le 0.14$) clusters\nseparately. From Figure 2, we see\nreasonably fair coverage throughout the entire sky in both redshift\nranges (recall that\nthe southern right quadrant only goes to $z=0.10$).\nQuantitatively, we present in Table 1 the number of clusters available in each\nquadrant cataloged by Abell/ACO, and the number\nof clusters observed in each quadrant. Note that the fractional\ncoverages in each of the sections are very similar. The mean fractional coverage\n(including both near and far quadrants) is $0.138\\pm{0.019}$, so that the\nnumber of clusters within the more distant,\nnorthern right quadrant is only $1.5\\sigma$ smaller than the mean.\nTable 1 provides clear evidence that the sky coverage for our cluster sample is\nnot observationally biased towards certain regions.\n\nAfter accounting for projection effects, line-of-sight anisotropies, X-ray identifications,\nHI column density variations, a constant number density, and fair sky coverage,\nthis is the largest, \nmost complete, and fairly sampled distribution of matter in the local\nUniverse. We assume that clusters are biased tracers of mass (Kaiser 1986; Peacock \\& Dodds 1994) and\nthat in the end, we may compare the shape of our power spectrum to those of typical cosmological models.\n\n\\section{Methods and Analyses}\nWe utilize two different methods to estimate $P(k)$ in redshift-space. Both methods follow\nthe same basic idea: directly sum the plane wave contributions from each cluster, account for\nappropriate weights and the shape of the volume, compute the square of the modulus of each\nmode and subtract off the shot noise. The resultant power spectrum is the estimated variance\nof the density contrast $|\\delta(k)|^2$.\nThe power spectrum is accurate only to some limiting scale, specified by $k_{min}$,\nwhich is constrained by the size and shape of the volume examined.\nThe differences between the two methods arise\nwhen accounting for the weighting scheme and the shape of the volume.\nWe also point out that Tegmark {\\it et al.} (1998) have recently presented\nan alternative method for measuring $P(k)$ for large datasets (such as the Sloan\nDigital Sky Survey). As discussed in detail in Tegmark {\\it et al.}, they\nadvocate the use of standard Fourier techniques on small scales, a pixelized quadratic\nmatrix method on large-scales, and also a Karhunen - Loeve (KL) eigenmode analysis to\nprobe redshift-space anisotropies. While the Tegmark {\\it et al.} power spectrum\nestimation method is undoubtedly\nmore refined than the methods used here, we are more interested in comparing results\nfrom the most commonly used techniques (and also allowing our results to be compared\nto previous cluster $P(k)$ measurements). Also, the methods described in Tegmark et al.\nare designed for large datasets (e.g. several 100,000 points) and we would not expect\na large advantage in our smaller samples.\n\nThe first method we use was originally applied by Vogeley et al. (1992),\nPark et al. (1994) and da Costa et al. (1994) \nto the CfA2 redshift survey (Geller \\& Huchra 1989). This method is also\ndescribed in LCRS and Fisher {\\it et al.} 1993.\nMost recently, this method was used and described by Retzlaff {\\it et al.} (1998) on a \nsample of Abell/ACO clusters. \nBriefly, the estimated power spectrum convolved with\nthe window function can be written as follows:\n\\begin{equation}\n\\hat{P}_{a}(k) = {\\frac{V}{1-|\\hat{W}(k)|^2}}[\\hat{\\Pi}(k) - \\hat{S}].\n\\end{equation}\nThe first factor in Equation 1 accounts for the systematic under-estimation of $P(k)$ at\nsmall values of $k$ due to normalization biases and \nthe shape of the window, also known as large-scale power damping (Peacock \\& Nicholson 1991). \nThe first term in brackets, $\\hat{\\Pi}$ is the squared-modulus of the Fourier transform of the \ndensity contrast, $\\delta(\\bf{r})$, minus the Window Function,\nor the estimated power. $\\hat{\\Pi}$ is a discrete quantity that\nincludes shot noise $\\hat{S}$ which we must subtract off.\nThe estimate of the power, $\\hat{P}_{a}(k)$, is convolved with the\nWindow function, $\\hat{W}(k)$.\n\nIn practice, we calculate $\\hat{W}(k)$ separately for as many points as is feasible (in this case \n$3\\times 10^5$ random points) and average over 1000 directions of $k$. \nThe window function is presented in Figure 3. We calculate $|\\hat{W}(k)|^2$ using points\nrandomly distributed in our volume and also with the same redshift and extinction\ndistribution as our real data (the redshift distribution is smoothed with a Gaussian to remove any\nlarge-scale structure). Figure 3 shows that the shape of $|\\hat{W}(k)|^2$ changes\nvery little as we adjust the random distribution within our volume.\nWe also calculate $|\\hat{W}(k)|^2$ for a volume that\nencompasses only one hemisphere out to $z = 0.14$. We see that, as the volume becomes more asymmetric,\nsignificant\ndifferences betweem the window functions appear.\nThe ``bumps'' seen in $|\\hat{W}(k)|^2$ are a direct result\nof a volume-limited, spherically symmteric survey, and have little effect on the PS estimation,\nso long as their relative heights are much smaller than the largest $|\\hat{W}(k)|^2$ used. \nThese ``bumps'' are an indicator that the survey window is spherically symmetric\nand that averaging over all directions of ${\\bf k}$ is appropriate.\nThis is not typically the case in previous (non-Abell/ACO)\n$P(k)$ analyses (see Tegark (1995) for a good discussion of window functions).\n\nThe smallest $k$ that can be accurately probed depends on the value of $|\\hat{W}(k)|^2$ and\nhow it convolves with the real power spectrum (see Lin et al. 1996). Recall, \n\\begin{equation}\n\\langle P_{estimated}(k) \\rangle \\propto \\int |\\hat{W}({\\bf k} - {\\bf k'})|^2 P_{true}({\\bf k'}) k'^2 dk'.\n\\end{equation}\nIdeally, for all values of $k$ probed, the integrand of Equation (2) will be sharply peaked at $k = k'$.\nIn Figure 4, we plot the integrand of Equation (2) assuming a constant $P(k)$. We find that the\nshape of our volume does not affect our analyses for $k >\\sim 0.015h$Mpc$^{-1}$. For $k$ smaller\nthan this limit, we see that ``leakage'' occurs and power from larger $k$ slips into our measurements.\nFigure 4 also shows that if uncorrelated modes of $P(k)$ are required, we should separate\nour bins by $\\delta k = 0.015$. \nOur choice of $k_{min} =0.015 h$Mpc$^{-1}$ is a conservative\nlimit, since most past analyses of $P(k)$ have stopped where\n$|\\hat{W}(k)|^2 = 0.1$ (e.g. Peacock and Nicholson 1991; Vogeley et al. 1992; Retzlaff et al. 1998).\nThe value of $|\\hat{W}(k)|^2$ for our analysis at $k_{min}$ is only $ 0.05h$Mpc$^{-1}$.\n\nThe weights for each cluster\noriginate in the estimation of the density contrast,\n\\begin {equation}\n\\hat{\\delta}(r)=\\frac{1}{N}\\sum_i{\\frac{\\delta^{3}(\\bf{r}-\\bf{r}_i)}{\\phi(r_i)}} - 1\n\\end{equation}\nwhere $\\phi({\\bf r}) = \\psi(b)\\varphi(z)$ is the selection function which accounts for galactic\nobscuration and redshift selection.\nWe use $\\psi(b) = 10^{\\gamma(1-csc|b|)}$ with $\\gamma = 0.32$ for the latitude selection\nfunction (see Postman, Huchra, and Geller 1992). \n%We use $\\varphi(z) = 1$ for clusters within $z=0.10$ and\n%and $\\varphi = 0.58$ for clusters with $0.10 < z \\le 0.14$.\nThe selection function in $z$ is determined separately for the three different number density models\nused in Figure 1. We find that the choice of number-density fit\nhas little on the PS estimation.\n\nThe second method we use was derived by Feldman, Kaiser, \\& Peacock (1994-hereafter FKP).\nTED96 use a very similar approach in their analysis of APM clusters.\nHere, the\npower spectrum is:\n\\begin{equation}\n\\hat{P}_b(k) = |F({\\bf k})|^2 - P_{shot}\n\\end{equation}\nwhere $F(k)$ is the Fourier transform of the normalized and weighted galaxy fluctuation field:\n\\begin{equation}\nF(\\bf{r})=\\frac{w(r)[n_c(r)-{\\alpha}n_s(r)]}{[\\int d^3r\\bar{n}^2(r)w^2(r)]^{1/2}}\n\\end{equation}\nIn these equations, $n_c$ and $n_s$ represent the number densities of the cluster sample\nand a randomly generated synthetic catalog respectively. \nThe number of\npoints we use in the random catalog is 500 times that of the real data so $\\alpha = \\frac{1}{500}$\n(we note\nthat there is no difference in the power spectrum results for random catalogs with 100\ntimes as many points). $P_{shot}$ is again, the power due to shot noise from a discrete sample and\nis determined as in FKP.\nIn this method, we model the redshift selection of our random catalogs from\nthe redshifts of the real data, smoothed with a Gaussian of width $3000$ km s$^{-1}$.\nThe weights for the individual clusters (real and synthetic) are determined from\n\\begin{equation}\nw_o(r) = \\frac{1}{1+n(r)P_{init}(k)}.\n\\end{equation}\nTo create the extinction adjusted random catalogs, we draw from regions in\nthe sky that have the same extinction distribution as our real data using the Schlegel et al. (1998)\nmaps. We find little difference in our $P(k)$ when we apply no extinction correction.\nTo determine $n(r)$ used in the weighting factor, we use the three different number density\nfits\n(as given in Figure 1). Again, we find that the choice of number density fit has little\neffect on the PS estimation. \n\nThe weighting scheme for $P_{b}(k)$ depends on {\\it a priori} knowledge of $P(k)$ at all\nscales. We choose different values of \n$P_{init}(k)$ ( 5, 10, 30, 60$\\times 10^4h^{-3}$Mpc$^{3}$)\nfor the cluster weights and\nfind that there is little difference in the amplitude ($\\sim 1.5 $ times) \nof $P_{b}(k)$ between\n$P_{init} = 5$ and $60\\times 10^4 h^{-3}$Mpc$^{3}$ and so we adopt \n$P_{init} = 30\\times 10^4 h^{-3}$Mpc$^{3}$ in all further $P_{b}(k)$ results.\nWe calculate errors on $P_{b}(k)$ using those methods of FKP (equation 2.4.6).\n\nIn Figure 5, we compare all of our calculations of $P(k)$.\nIn the top panel of Figure 5, we plot $P_a(k)$ using the three different number density functions.\nWe also measure $P(k)$ for the richness adjusted sample.\nWe plot the same for\n$P_{b}(k)$ in the middle panel of Figure 5. In all cases, we find very little difference in our $P(k)$ estimations.\nIn the bottom panel of Figure 5 we compare $P_a(k)$ to $P_b(k)$ using the number function as our density fit.\nHere, we do see some small differences in the measured power at $k$ less than $0.02h$Mpc$^{-1}$, however\nboth spectra estimates are within the 1 $\\sigma$ error. \nThe lack of difference between $P_a(k)$ and $P_b(k)$ \nis a direct result of the stability of the methods and the\nwell defined number density and \nsymmetric volume of the cluster sample.\n\n\\section{Discussion}\n\nThere are two striking results regarding the power spectrum of rich Abell/ACO clusters. (1) While\nwe do see a dip in power near $k = 0.4h$ Mpc$^{-1}$, it is not statistically significant. \nThe measured power spectrum is essentially featureless and there is \nno narrow peak in the power spectrum as has been\nreported in E97 and Retzlaff {\\it et al.} (1998). (2) The other difference\nis that there is increasing power to very large scales ($k = 0.015h$Mpc$^{-1}$ or $\\sim 400h^{-1}$Mpc).\nIn past analyses of the power spectrum, most\nauthors have reported the (weak) detection of a turnover in the power spectrum (see section 1). However,\nthe turnover has always occurred very near the largest scales accessible in their volumes. \n[Note: other preliminary analyses of the PS on scales $k < 0.05h$Mpc$^{-1}$ are also showing\nthis increase in power (Guzzo et al. 1999; Hamilton and Tegmark 2000; Efstathiou and Moody 2000)].\nThe power spectrum is roughly a power-law on scales $0.02 \\le k < 0.10 h$Mpc$^{-1}$ with $P(k) \\propto k^{-1.4}$.\n\nIn Figure 6, we compare our results to two other cluster sample power spectrum analyses,\nthe APM cluster sample of TED98, and the $R \\ge 0$ Abell/ACO sample of Retzlaff et al. (1998).\nFigure 6 shows that the shapes of $P(k)$ for\nthese three different cluster samples\nare remarkably\nsimilar in the range $ 0.04 \\le k \\le 0.15 h$Mpc$^{-1}$.\nThe higher amplitude for our sample of $R \\ge 1$ clusters is expected according to\nhierarchical clustering schemes (Kaiser 1986) and larger bias found in richer clusters (see\nPeacock and Dodds 1994).\nWe have recalculated the Retzlaff {\\it et al.}\n(1998) Abell/ACO cluster sample using the methods for $P_a(k)$. We do this in part as a check on\nour methods and also to independently confirm their results of a peak near $k = 0.05h$Mpc$^{-1}$\nand a turnover thereafter. The Retzlaff {\\it et al.} sample includes all Abell/ACO clusters\nwithin $240 h^{-1}$Mpc and outside $|b| \\ge 30^{\\circ}$. We find 412 clusters which meet this\ncriteria (compared to their 417 clusters- the difference we attribute to minor variations in\na few cluster redshifts near the survey boundaries). Our results, not surprisingly, are identical\nto those published in Retzlaff {\\it et al.} (1998) since our method for determining $P_a(k)$ is\nidentical to theirs. For this determination of $P_a(k)$ ({\\it i.e.} using $R =0$ clusters and\na much smaller volume), we also see a peak in the power spectrum at $k = 0.05h$Mpc$^{-1}$\nand a turnover thereafter. As pointed out by Retzlaff {\\it et al.}, this peak\nis not statistically significant. As a further examination of this issue, we plot in Figure 6 \n$P_b(k)$ for a smaller cluster sample,\nvolume-limited in the north and south to $z = 0.10$. For this sample, we can only detect power to\n$k_{min} \\sim 0.035h$Mpc$^{-1}$. For $k$ greater than $0.035h$Mpc$^{-1}$\nwe find little difference between this sample and the larger one. But\nwe can no longer probe on the scales where we expect $P(k)$ to continue its rise.\nThus, one could conclude that a turn-over has been found, when in fact a larger (in size and number) sample\nshows that the power continues to rise for $k < 0.03h$Mpc$^{-1}$.\n\n\\subsection{Comparisions to Linear Theory}\nWe also compare our power spectrum results to those of linear theory created by CMBFAST \n(Seljak \\& Zaldarriaga 1996). We consider three Cold Dark Matter (CDM) variants, flat, open and\nwith a vacuum density ($\\Lambda$CDM), and a Mixed Dark Matter (MDM) model.\nFor the CDM cases, we choose $\\Omega_b = 0.02$, in accordance with\nSchramm \\& Turner (1998). For the open case, we choose\n$\\Omega_0=\\Omega_b + \\Omega_{CDM} = 0.2$ in accordance with Bahcall (1997). For the $\\Lambda$CDM\nmodel, we choose $\\Omega_{CDM} = 0.18$ and $\\Omega_{vacuum} = 0.80$ so that\n$\\Omega_b + \\Omega_{CDM} + \\Omega_{vacuum} = 1$. For the MDM model,\nwe choose $H_0 = 50 $km s$^{-1}$Mpc$^{-1}$\nwith $\\Omega_b =0.05$, $\\Omega_{CDM}=0.35$ and $\\Omega_{\\nu}=0.3$\n(where $\\Omega_{\\nu}$ is the massive neutrino density).\nThe CMBFAST package normalizes\nthe amplitude of generated spectra to the Bunn and White (1997) four-year COBE normalization. \nHowever, in this work, we are only concerned with the {\\it shape} of the power spectrum.\nWe are motivated by our assumption that clusters are biased tracers of the mass distribution\nand therefore the shape of the cluster power spectrum should be similar to that of the matter\npower spectrum.\nIn Figure 7, we present the amplitude shifted\nlinear models in comparison to our empirically determined \npower spectra.\nAs a result of the known similarities in the shapes of the $\\Lambda$CDM models and low matter density\nopen CDM models, we find that both fit the shape of the rich\nAbell/ACO cluster power spectrum to $k_{min} = 0.015h$Mpc$^{-1}$ or $400h^{-1}$Mpc extremely\nwell (see Table 2).\nOn the largest scales, the \nMDM model lacks power over a wide range of $k$ ($0.015 \\le $k$ \\le 0.03h$Mpc$^{-1}$) to match\nour cluster data.\nTED98 found that $\\Lambda$CDM linear models did not have\nenough power on large scales to match the APM cluster power spectrum. Instead, they find a much\nbetter fit for\na mixed dark matter (MDM) model.\nWe\npoint out that the $\\Lambda$CDM model in Figure 7 of TED98 does provide an excellent\nfit to the APM cluster data if their last data point at $k = 0.02h$Mpc$^{-1}$ (where\nthe error is rather large) is excluded.\n\n\\section{Conclusion}\nThe agreement between\nthe shapes of $P(k)$ for the four different samples shown in Figure 6 (from $k = 0.05$ to $0.15 $h Mpc$^{-1}$),\nprovides further evidence that clusters are\ntracers of the peaks of the underlying luminous \nmass distribution. While there is a\ngreat deal of volume-overlap in these four samples, they are made up of significantly\ndifferent luminous objects (from very poor APM clusters to the richest Abell clusters).\nFor instance, the Retzlaff et al. (1998) Abell/ACO sample\ncontains at most 253 $R \\ge 1$ clusters, while the remaining 218 are $R \\ge 0$. \nOur sample contains 637 $R \\ge 1$ clusters. The APM sample of 364 clusters, \ncontains even fewer $R \\ge 1$ Abell clusters ($\\sim 40$).\nIf all groups and clusters\ntrace the underlying mass distribution in a similar way, then the we would expect their respective\npower spectra to be similar in shape, and only the amplitude to vary.\n \nPrevious analyses of the cluster power spectrum have been plagued\nby three major problems: (1) uncertainties in the number density, (2) small volumes,\nand (3) irregularly shaped volumes. The sample analyzed in this work greatly improves\nupon each of these difficulties. \nOur Abell/ACO sample has a nearly constant number\ndensity throughout the entire volume. This is in stark contrast to most\nother sparse tracer surveys (such as the QDOT {\\it IRAS} survey power spectrum\nof FKP and the Retzlaff {\\it et al.} Abell/ACO cluster sample).\nAlong with the number density, the large size of the volume\nand the semi-regular shape of the double-cone geometry, all contribute significantly\nto a more accurate determination of $P(k)$ on the largest scales.\nThe reality of the power on scales $200 - 300h^{-1}$Mpc is also becoming evident\nobservationally. Batuski {\\it et al.} 1999\nhave recently discovered two filamentary superclusters in the constellation of Aquarius\nthat are as long as $75h^{-1}$Mpc and $150h^{-1}$Mpc. As we peer out further into the\nlocal Universe, we continue to find structures on very large scales. \n\n\nWe have presented the redshift-space power spectrum for the largest galaxy cluster sample\ncompiled to date. This sample has been examined extensively for projection effects, anisotropies,\nand observational selection effects and found to be a fair and complete sampling of biased\nmatter in the local Universe. The volume and shape of the survey provide accurate and robust\nmeasurements of $P(k)$ over the wavenumber range $0.015 \\le k \\le 0.15 h$Mpc$^{-1}$. From\n$k= 0.15$ down to $k = 0.05 h$Mpc$^{-1}$, we\nfind a similar shape to the power spectrum compared to other cluster samples such as\nthe APM cluster survey and a smaller sample of $R \\ge 0$ Abell/ACO clusters studied by\nRetzlaff {\\it et al.} (1998). At smaller $k$, we do not find\nany statistically significant features in $P(k)$. \nUnlike previous cluster $P(k)$ analyses, we do not find\nany strong evidence for a turnover.\nWe find that $\\Lambda$CDM and\nlow $\\Omega_0$ CDM linear models provide excellent fits to the rich cluster power spectrum.\n\n{\\bf Acknowledgments} The authors wish to thank Adrian Melott and Daniel Eisenstein\nfor helpful conversations. We also would like to acknowledge the role of the\nthe referee, Michael S. Vogeley, for his suggestions on improving the original manuscript. \nWe also thank H. Tadros for supplying the APM cluster PS in electronic form.\nCM was funded in part by NASA-EPSCoR through the\nMaine Science and Technology Foundation.\n\n\\begin{deluxetable}{cccccc}\n%\\tablefontsize{\\footnotesize}\n\\tablenum{1}\n\\tablewidth{0pt}\n\\tablecaption{\\bf Sky Coverage}\n\\tablehead{\n\\colhead{$\\ell$ range} & \\colhead{ $b$ range} & \\colhead{ $z$ range} & \n\\colhead{Number (all z)} & \\colhead{ Number with} & \\colhead{Fraction{\\tablenotemark{a}}} \\nl\n\\colhead{ } & \\colhead{ } & \\colhead{ } &\n\\colhead{cataloged} & \\colhead{observed redshifts} & \\colhead{}}\n\\startdata\n$0^o \\le \\ell < 180^o$ & $30^o \\le b \\le 90^o$ & $z \\le 0.10$ & 636 & 80 & 0.1257 \\nl\n$0^o \\le \\ell < 180^o$ & $30^o \\le b \\le 90^o$ & $0.10 < z \\le 0.14$ & 636 & 86 & 0.1352 \\nl\n$180^o \\le \\ell < 360^o$ & $30^o \\le b \\le 90^o$ &$z \\le 0.10$ & 503 & 78 & 0.1550 \\nl\n$180^o \\le \\ell < 360^o$ & $30^o \\le b \\le 90^o$ &$0.10 < z \\le 0.14$ & 503 & 52 & 0.1034 \\nl\n$0^o \\le \\ell < 180^o$ & $-90^o \\le b \\le -30^o$ &$z \\le 0.10$ &608 & 95 & 0.1563 \\nl\n$0^o \\le \\ell < 180^o$ & $-90^o \\le b \\le -30^o$ &$0.10 < z \\le 0.14$ & 608 & 84 & 0.1382 \\nl\n$180^o \\le \\ell < 360^o$ & $-90^o \\le b \\le -30^o$ &$z \\le 0.10$ & 492 & 75 & 0.1524 \\nl\n\\tablenotetext{a}{Fraction is the Number observed/ Number cataloged.}\n\\enddata\n\\end{deluxetable}\n\n \n\\begin{deluxetable}{ccc}\n%\\tablefontsize{\\footnotesize}\n\\tablenum{2}\n\\tablewidth{0pt}\n\\tablecaption{\\bf Goodness-of-Fit to Linear Models}\n\\tablehead{\n\\colhead{Model} & \\colhead{$\\chi_{reduced}^2$} & \\colhead{DOF}}\n\\startdata\n$\\Lambda$CDM ($H_o = 100$km s$^{-1}$) & 0.65 & 8 \\nl\nOpen CDM ($H_o = 100$km s$^{-1}$) & 0.66 & 8 \\nl\nCDM ($H_o = 100$km s$^{-1}$) & 4.55 & 8 \\nl\nMDM ($H_o = 50$km s$^{-1}$) & 2.19 & 8 \\nl\n\\enddata\n\\end{deluxetable}\n\n\\begin{thebibliography}{}\n\\bibitem[(Abell 1958)]{abe58} Abell, G. 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Turok,\n World Scientific, Singapore, 221\n\\bibitem[(Batuski {\\it et al.} 1999)]{bat99} Batuski, D.J., Miller, C.J., Slinglend, K.A.,\n Balkowski, C., Maurogordato, S., Cayatte, V., Felenbok, P., and Olowin, R. 1999, \\apj, 520, 491\n\\bibitem[(Broadhurst {\\it et al.} 1990)]{brd90} Broadhurst, T.J., Ellis, R.S., Koo, D.C., \\& \n Szalay, A.S. 1990, Nature, 343, 726\n\\bibitem[(Bunn \\& White 1997)]{bun97} Bunn, E.F. \\& White, M. 1997, \\apj, 480, 6\n\\bibitem[(da Costa et al. 1994)]{dac94} da Costa, L.N., Vogeley, M.S., Geller, M.J., Huchra, J.P.,\n \\& Park, C. 1994, \\apj, 437, L1\n\\bibitem[(Dalton {\\it et al.} 1994)]{dal94} Dalton, G.B., Croft, R.A.C.,\n Efstathiou, G., Sutherland, W.J., Maddox, S.J., and Davis, M. 1994, \\mnras,\n 271, 47\n\\bibitem[(Efstathiou {\\it et al.} 1992)]{eft92} Efstathiou, G., Dalton, G.B.,\n Maddox, S.J., \\& Sutherland, W. 1992, \\mnras, ~257, 125\n\\bibitem[(Efstahiou and Moody 2000)]{eft00} Efstathiou, G. and Moody, S.J. 2000, preprint\n ~astro-ph/0010478\n\\bibitem[(Einasto {\\it et al.} 1997)]{ein97} Einasto, J., Einasto, M., Gottl\\\"{o}ber, S.,\n M\\\"{u}ller, V., Saar, V., Starobinsky, A.A., Tago, E., Tucker, D., Andernach, H., \\& \n Frisch, P. 1997, Nature, 385, 139 (E97)\n\\bibitem[(Einasto {\\it et al.} 1999)]{ein99} Einasto, J., Einasto, M., Tago, E.,\n Starobinsky, A.A., Atrio-Barandela, F.,\n M\\\"{u}ller, V., Knebe, A, \\& Cen, R. 1999, \\apj, 519, 469 (E99) \n Frisch, P. 1997, Nature, 385, 139 (E97)\n\\bibitem[(Einasto {\\it et al.} 1994)]{ein94} Einasto, M., Einasto, J., Tago, E., Dalton, G.B.,\n \\& Andernach, H. 1994, \\mnras, 269, 301\n\\bibitem[(Eisenstein and Hu 1998)]{eis98} Eisenstein, D.J., Hu, W., Silk, J., and Szalay, A.S.\n 1998,\\apj, 494, L1\n\\bibitem[(Feldman, Kaiser, \\& Peacock 1994)]{fel94} Feldman, H.A., Kaiser, N. \\& Peacock, J.A.\n 1994, \\apj, 426, 23 (FKP)\n\\bibitem[(Fisher {\\it et al.} 1993)]{fis93} Fisher, K.B., Davis, M., Strauss, M.A.,\n Yahil, A., \\& Huchra, J.P. 1993, \\apj, 402, 42\n\\bibitem[(Gatza\\~{n}aga, \\& Baugh)]{gat98} Gatza\\~{n}aga, E. \\& Baugh, C.M. 1998, \\mnras, 294, 229\n\\bibitem[Geller \\& Huchra(1989)]{1989Sci...246..897G} Geller, M.\\ J.\\ \\& \nHuchra, J.\\ P.\\ 1989, Science, 246, 897 \n\\bibitem[(Gramann \\& Suhhonenko 1999)]{suh99} Gramann, M. \\& Suhhonenko, I. 1999, \\apj, 519, 433\n\\bibitem[(Hamilton and Tegmark 2000)]{hal00} Hamilton, A.J.S. and Tegmark, M. 2000, submitted to \\mnras,\nastroph/0008392\n\\bibitem[(Guzzo 1999)]{guz99} Guzzo, L. 1999, presented at {\\it The Second Coral Sea Cosmology Conference}\n\\bibitem[(Hoyle et al. 1999)]{hoy99} Hoyle, F., Baugh, C. M., Shanks, T., Ratcliffe, A. 1999, \\mnras,\n 309, 659\n\\bibitem[(Jing and Valdarnini 1993)]{jin93} Jing, Y.P. and Valdarnini, R. 1993, \\apj, 406,6\n\\bibitem[(Kaiser 1994)]{kai94} Kaiser, N. 1986, \\mnras, 222,323\n\\bibitem[(Katgert {\\it et al.} 1996)]{kat96} Katgert,P., Mazure, A., Perea, J.,\n den Hartog, R., Moles, M., Le Fevre, O., Dubath, P., Focardi, P., Rhee, G.,\n Jones, B., Escalera, E., Biviano, A., Gerbal, D., Giuricin, G. 1996,\n A \\& A, ~310, 8\n\\bibitem[(Landy {\\it et al.} 1996)]{lan96} Landy, S.D., Shectman, S.A., Lin, H., Kirshner, R.P.,\n Oemler, A.A., \\& Tucker, D. 1996, \\apj, 456, L1\n\\bibitem[(Lin {\\it et al.} 1996)]{lin96} Lin, H., Kirshner, R.P., Shectman, S.A., Landy, S.D.,\n Oemler, A., Tucker, D.L., \\& Schecter, P.L. 1996, \\apj 471, 617 (LCRS)\n\\bibitem[(Miller {\\it et al.} 1999a)]{mi99a} Miller, C.J., Batuski, D.J., Slinglend, K.A., \\&\n Hill, J.M. 1999a, \\apj, 523, 492\n\\bibitem[(Miller {\\it et al.} 1999b)]{mi99b} Miller, C.J., Ledlow, M.J. \\& Batuski, D.J. 1999b,\n \\mnras, submitted\n\\bibitem[(Miller {\\it et al.} 1999c)]{mic99} Miller, C.J., Krughoff, K.S., Slinglend, K.A.,\n Batuski, D.J., \\& Hill, J.M. 1999c (in preparation)\n\\bibitem[(Nichol \\& Connolly 1996)]{nic96} Nichol, R.C. \\& Connolly, A.J. 1996, \\mnras, 279, 521\n\\bibitem[(Park et al. 1994)]{par94} Park, C., Vogeley, M.S., Geller, M.J., \\& Huchra, J.P. 1994,\\apj,431,561\n\\bibitem[(Peacock 1997)]{pea97} Peacock, J.A. 1997, \\mnras, 285, 885\n\\bibitem[(Peacock \\& Dodds 1994)]{pea94} Peacock, J.A. \\& Dodds, S.J. 1994, \\mnras, 267, 1020\n\\bibitem[(Peacock and Nicholson 1991)]{pea91} Peacock, J.A. \\& Nicholson, D. 1991, \\mnras, 253, 307\n\\bibitem[(Peacock \\& West 1992)]{pew92} Peacock, J.A. \\& West, M.J. 1992,\n \\mnras, 259, 494\n\\bibitem[(Postman et al. 1992)]{pos92} Postman, M.,\n Huchra, J. P., \\& Geller, M. J. 1992, \\apj, ~384, 404\n\\bibitem[(Retzlaff {\\it et al.} 1998)]{ret98} Retzlaff, J., Borgani, S., Gottl\\\"{o}ber, S., \n Klypin, A., \\& M\\\"{u}ller, V. 1998, NewA, 3, 631\n\\bibitem[(Schlegel {\\it et al.} 1998)]{sch98} Schlegel, D.J., Finkbeiner, D.P., \\& Davis, M.\n 1998, \\apj, 500, 525\n\\bibitem[(Schramm \\& Turner 1998)]{sch98} Schramm, D.N. \\& Turner, M.S. 1998, Rev. Mod. Phys., 70, 303\n\\bibitem[(Seljak \\& Zaldarriaga 1996)]{sel96} Seljak, U. \\& Zaldarriaga, M. 1996, \\apj, 469, 437\n\\bibitem[(Slinglend {\\it et al.} 1998)]{sli98} Slinglend, K.A., Batuski, D.J,\n Miller, C.M., Haase. S., Michaud, K., \\& Hill, J.M. 1998, \\apjsupp, 115,1\n\\bibitem[(Stark {\\it et al.} 1992)]{sta92} Stark, A.A., Gammie, C.F., Wilson, R.W.,\n Bally, J.L., Linke, R.A., Heiles, C., \\& Hurwitz, M. 1992, \\apjsupp, 79, 77\n\\bibitem[(Sutherland 1988)]{sut88} Sutherland, W. 1988, \\mnras, ~234, 159\n\\bibitem[(Tadros \\& Efstathiou 1996)]{tad96} Tadros, H., \\& Efstathiou, G. 1996, \n \\mnras, 282, 1381 (TE96)\n\\bibitem[(Tadros, Efstathiou \\& Dalton 1998)]{tad98} Tadros, H.,Efstathiou, G., \\& Dalton, G.\n 1998, \\mnras, 296, 995 (TED98)\n\\bibitem[(Tegmark 1995)]{teg95} Tegmark, M. 1995, \\apj, 455, 429\n\\bibitem[(Vogeley 1998)]{vog98} Vogeley, M.S. 1998, in {\\it The Evolving Universe}, \n Kluwer Academic Publishers, p. 395\n\\bibitem[(Vogeley et al. 1992)]{vog92} Vogeley, M.S., Park, C., Geller, M.J., \\& Huchra, J.P. 1992,\n \\apj, 391, L5\n\\bibitem[(Voges, {\\rm et al.} 1999)]{vog99} Voges, W., Ledlow, M.J., Owen, F.N.,\n \\& Burns J.O. 1999, \\aj, submitted \n\n\n\n\\end{thebibliography}\n\n\\begin{figure*}[hl]\n\\plotone{f1.eps}\n\\caption[]{The proper number density as a function of redshift is presented for the Abell/ACO cluster\nsample. The lines are various fits to the data. The solid-line (having the lowest $\\chi^2$) is\na three parameter number function. The dotted-line is for a power-law beyond $z =0.01$. The dashed-line\nis for a step function. We find no significant differences in our PS analysis as a function of\nthe number density function utilized.}\n\\end{figure*}\n\n\\begin{figure*}\n\\plotone{f2.eps}\n\\caption[]{ A Hammer-Aitoff projection sky-plot of all clusters used in the\npower spectrum analysis. Closed circles denote Abell (1958) clusters within $z=0.10$,\nopen circles denote Abell clusters with $0.10 < z \\le 0.14$, and stars indicate\nACO (1989) clusters within $z=0.10$. We have divided our sample into four quadrants\nin latitude/longitude and two bins in $z$, to show that the clusters in our sample\nhave been observed evenly throughout the sky (see Table 1).}\n\\end{figure*}\n\n\n\n\\begin{figure*}\n\\plotone{f3.eps}\n\\caption[]{This is the Fourier window function, $\\langle|\\hat{W}({\\bf k})|^2 \\rangle$ used to calculate $P_a(k)$. We use 300000 points\nand 1000 random directions for each $|k|$ to estimate the Fourier transform of the window function. $k$ is in\nunits of $h$Mpc$^{-1}$. The dashed-line is for a random distribution of points. The solid-line is after\nwe apply the same redshift and extinction distribution as our real data. The dotted-line is for a highly asymmetric\nsurvey (i.e. one hemisphere to $z = 0.14$).\nThe hatched region\nindicates where our window function prevents an accurate determination of $P(k)$.}\n\\end{figure*}\n\n\n\\begin{figure*}[hl]\n\\plotone{f4.eps}\n\\caption[]{The integrand of Equation (2) for constant $P(k)$ with arbitrary normalization.\nWe show three values of $k = 0.01, 0.02, 0.05h$Mpc$^{-1}$. We see that for $ k = 0.01h$Mpc$^{-1}$ there\nis ``leakage'' from large $k$. At $k = 0.02h$Mpc$^{-1}$ this leakage is no longer evident, and\nso we choose $k_{min} = 0.015h$Mpc$^{-1}$ as the largest-scales we can accurately probe.}\n\\end{figure*}\n\n\\begin{figure*}\n\\plotone{f5.eps}\n\\caption[]{In the {\\bf top} panel we show $P_a(k)$ calculated using the three different number density\nfunctions used in Figure 1. Circles are for the step-function, stars are for the power-law fit,\nand squares are for the number function fit. The open circles include all $R \\ge 1$ ACO clusters\nwhile the filled symbols are for ACO clusters with $N_{gal} \\ge 56$. We use a window function\nthat models the real data (e.g. in density and extinction). The errors are estimates based\non scaling the errors from $P_b(k)$.\nIn the {\\bf middle} panel we show $P_b(k)$ using the same symbols as the top panel. We use random\ncatalogs with the same extinction and density distribution as the real data. The error bars\nare determined using the FKP method as mentioned in the text.\nIn the {\\bf bottom} panel, we plot $P_a(k)$ (circles) and $P_b(k)$ (squares). The hatched region\nindicates where our window function prevents an accurate determination of $P(k)$.\n}\n\\end{figure*}\n\n\\begin{figure*}\n\\plotone{f6.eps}\n\\caption[]{We compare $P_b(k)$ for Abell/ACO clusters calculated in this work (solid circles) to the smaller\nAbell/ACO sample used by Retzlaff {\\it et al.} (1998) (triangles) and the APM cluster sample power spectrum\ncalculated by Tadros {\\it et al.} (1998) (stars). The open circles are $R \\ge 1$ Abell/ACO clusters within \n$z=0.10$ (north and south). \n}\n\\end{figure*}\n\n\\begin{figure*}\n\\plotone{f7.eps}\n\\caption[]{\nWe compare $P_b(k)$ to model liner power spectra for a flat CDM \n($\\Omega_b=0.02, \\Omega_{CDM}=0.98$ with $H_0 = 100 $km s$^{-1}$ Mpc$^{-1}$ {\\bf dashed-dot}),\nmixed dark matter\n($\\Omega_b=0.05, \\Omega_{CDM} = 0.65$ and $\\Omega_{\\nu} = 0.3$ with $H_0=50 $km s$^{-1}$ Mpc$^{-1}$\n{\\bf dashed-dot-dot}),\nopen ($\\Omega_b=0.02, \\Omega_{CDM}=0.18$ with $H_0 = 100 $km s$^{-1}$ Mpc$^{-1}$ {\\bf dashed}),\nand lambda \n($\\Omega_b=0.02, \\Omega_{CDM} = 0.18, \\Omega_{vacuum}=0.80$ {\\bf solid}) CDM models. }\n\\end{figure*}\n\n\\end{document}\n"}],"string":"[\n {\n \"name\": \"power2.tex\",\n \"string\": \"\\\\documentstyle[emulateapj]{article}\\n\\\\begin{document}\\n\\\\title{\\\\bf The Power Spectrum of Rich Clusters on Near-Gigaparsec Scales}\\n\\n\\\\author{Christopher J. Miller and David J. Batuski}\\n\\\\affil{Department of Physics \\\\& Astronomy, University of Maine}\\n\\n\\\\begin{abstract} \\nRecently, there have been numerous analyses of the redshift space power spectrum\\nof rich clusters of galaxies. Some of these analyses indicate a \\\\lq\\\\lq bump\\\\rq\\\\rq~\\nin the Abell/ACO cluster power spectrum around $k = 0.05h$Mpc$^{-1}$.\\nSuch a\\nfeature in the power spectrum excludes most standard formation models and indicates\\npossible periodicity in the distribution of large-scale structure. \\nHowever,\\nthe data used in detecting this peak include clusters with estimated redshifts\\nand/or clusters outside of Abell's (1958) statistical sample, {\\\\it i.e.} $R = 0$ clusters. \\nHere, we present estimates of the redshift-space power spectrum for a newly expanded\\nsample of 637 $R \\\\ge 1$ \\nAbell/ACO clusters which has a constant number density to z = 0.10 in the Southern Hemisphere\\nand a nearly constant number density to z = 0.14 in the Northern Hemisphere. \\nThe volume sampled, $\\\\sim 10^8h^{-3}$Mpc$^{3}$, is large\\nenough to accurately calculate the power per mode to scales approaching $10^3h^{-1}$Mpc.\\nWe find the shape of the power spectrum is a power-law on scales $0.02 \\\\le k \\\\le 0.10h$Mpc$^{-1}$,\\nwith\\nenhanced power over less rare clusters such as APM clusters. The power-law here follows $n = -1.4$.\\nThe power spectrum is essentially featureless, \\nalthough we do see a dip near $k = 0.04h$Mpc$^{-1}$ which cannot be considered\\nstatistically significant based on this data alone.\\nWe do not detect a narrow peak at $k \\\\sim 0.05h$Mpc$^{-1}$ and\\nthere is no evidence for a turn-over in the power spectrum as has been previously reported. \\nWe compare the\\nshape of the Abell/ACO rich cluster power spectrum to various linear models.\\n\\n\\\\end{abstract}\\n\\n\\\\section{Introduction}\\nThere has recently been a renewed interest in accurately determining the\\npower spectrum of matter distribution scales greater than 100$h^{-1}$Mpc;\\nin part due to the increased\\nnumber of clusters with measured redshifts and the large volumes they trace.\\nThe power spectrum for\\nthe galaxy distribution has been determined many times for many different classes\\nof galaxies. However, most galaxy surveys lack the volume necessary for the\\naccurate quantification of power on large-scales ({\\\\it e.g.} the Las Campanas Redshift Survey \\n(Lin {\\\\it et al.} 1996-hereafter LCRS) or the Stromlo-APM survey (Tadros \\\\& Efstathiou 1996).\\nA summary of the results from these analyses is that the redshift-space\\npower spectra roughly agree on scales $\\\\lambda$ ($ = 2\\\\pi/k$) $< 100 h^{-1}$Mpc.\\nIn this region, $P(k) \\\\propto k^n$ and $n \\\\sim -2$. (Of course, the amplitude of the\\npower spectra depends on the samples of galaxy examined which provides strong evidence for\\na luminosity bias (see e.g. Vogeley et al. 1992 and Park et al. 1994)).\\nHowever, on scales $\\\\lambda > 100h^{-1}$Mpc, there is much less\\nagreement. For example, some galaxy samples, such as from the LCRS\\nand the Automated Plate Machine (APM) 2d and 3d surveys \\nshow a broad flattening\\naround $k = 0.05 h$Mpc$^{-1}$ although no distinct maximum can be found within\\nconvincing statistical bounds (LCRS;\\nTadros and Efstathiou 1996; Peacock 1997; Gatzanaga \\\\& Baugh 1998).\\nHowever, Landy {\\\\it et al.} (1996) find a distinct peak in $P(k)$ for a 2 dimensional\\nanalysis of the LCRS and Broadhurst {\\\\it et al.} (1990)\\nfind a peak near $\\\\lambda = 130h^{-1}$Mpc in\\na deep pencil beam survey.\\n\\nSome Abell/ACO cluster analyses \\nalso show a peak around\\n$ k \\\\sim 0.05 h$Mpc$^{-1}$ (Retzlaff {\\\\it et al.} 1998; Einasto {\\\\it et al.} 1997-hereafter E97).\\nYet other cluster analyses only show a smooth turnover\\nin the power spectrum to its scale-invariant ($n = 1$) form. For instance,\\nthe APM clusters, examined by Tadros, Efstathiou and Dalton (1998-hereafter TED98)\\nshow a maximum in $P(k)$ at the smaller value of\\n$k \\\\sim 0.03h$Mpc$^{-1}$ and no distinct \\\\lq\\\\lq bump\\\\rq\\\\rq~ at $k = 0.05h$Mpc$^{-1}$.\\nAlso, Peacock \\\\& West (1992) and Jing \\\\& Valdarnini (1993) find a break in the Abell cluster\\npower spectrum near $k = 0.05h$Mpc$^{-1}$, but no distinct peak in power.\\nAn excellent review of the power spectra for different galaxy species can be found in \\nEinasto {\\\\it et al.} (1999-hereafter E99). E99 determine a mean\\npower spectrum for all galaxies for a large range in wavenumber. They do this by \\nusing the APM 2d power spectra on small scales, and by \\naveraging over numerous samples on large scales and then normalizing to the APM 2d power. \\n\\nIf a narrow peak in power near $k \\\\sim 0.05h$Mpc$^{-1}$ is a real feature of the power spectrum\\nin general, most current models of structure formation (in the quasi-linear regime) become invalid\\n(E99). While baryonic signatures can produce features in the power spectrum,\\nthose features are oscillatory and they do not produce a singular, narrow peak as seen\\nin some of the current data. Eisenstein et al. (1998) examined this prospect and found\\nthat no selection of cosmological parameters reproduces the power spectrum as seen in E97.\\nHowever, Gramann \\\\& Suhhonenko (1999) suggest that an inflationary scenario with a scalar field\\nhaving a localized step-like feature can reproduce the power spectrum of clusters.\\nHowever, in this work, we show that the peak in the cluster power spectrum is not\\npresent in larger (in volume and in number)\\ncluster samples after excluding less reliable data (such as $R=0$ Abell/ACO clusters\\nand clusters with estimated redshifts).\\n\\nOur aim in this paper is to provide an estimate for the power spectrum of Abell/ACO\\nclusters that is based on a complete and fair sample. Both Retzlaff {\\\\it et al.} and\\nE97 use $R =0$ clusters in their determination of $P(k)$. \\nEinasto {\\\\it et al.} (1994) have argued that $R =0$ clusters\\ndo not contaminate studies of large-scale structure because the multiplicity of\\nsuperclusters is independent of richness and the mean separation distances for\\n$R =0$ and $R \\\\ge 1$ clusters are very similar.\\nHowever, $R = 0$ clusters were not cataloged in a systematic way and were never \\nmeant to be examined in a statistical manner due to their incompleteness (Abell 1958).\\nIn addition, many researchers have found line-of-sight anisotropies in $R = 0$ cluster\\nsamples (Sutherland 1988; Efstathiou {\\\\it et al.} 1992; Peacock \\\\& West 1992).\\nTherefore, the use of $R =0$ clusters in the determination of $P(k)$\\nis highly suspect. E97 have also used a large\\nnumber (435 out of 1305 clusters) of estimated redshifts in their\\ndetermination of $P(k)$. We also suspect that\\nE97 used a large number of cluster redshifts with only one measured galaxy. Miller {\\\\it et al.}\\n(1999a) show that cluster velocities with one measured galaxy are in error by more than $2500$ km s$^{-1}$\\n14\\\\% of the time.\\nOf course, estimated redshifts are only\\naccurate to at best 25\\\\%. Thus, the statistical certainty of any large-scale structure\\nanalyses based on the cluster samples with a large number of estimated or poorly determined\\nredshifts must also be taken with caution.\\n\\n\\\\section{The Cluster Sample}\\nWe examine Abell/ACO clusters across the entire sky excluding the galactic plane \\n{\\\\it i.e.} $|b| > 30^{\\\\circ}$. We only consider $R \\\\ge 1$ clusters (with\\nmeasured redshifts) since they\\nwere defined by Abell (1958) as members of his statistically complete sample.\\nRecently, Miller {\\\\it et al.} (1999a,b) examined similar subsets of $R \\\\ge 1$ clusters\\nfor projection effects, line-of-sight anisotropies, and spatial correlations. We\\nsummarize their results below.\\n\\nThe Abell/ACO $R \\\\ge 1$ cluster dataset has significant advantages over other cluster\\nsamples (including those with $R =0$ clusters as well as APM clusters). With the\\nadvent of multi-fiber spectroscopy, nearly all rich Abell/ACO clusters within $z=0.10$ now have\\nmultiple galaxy determined redshifts (Slinglend {\\\\it et al.} 1998; Katgert {\\\\it et al.}\\n1996). Multiple redshifts have allowed for more accurate determinations of the extent\\nof projection effects and Miller {\\\\it et al.} 1999a report that at most, 10\\\\% of\\nAbell/ACO clusters suffer from moderate to severe foreground/background contamination.\\nThe lack of projection effects\\nfor $R \\\\ge 1$ clusters is also apparent from the 89\\\\% X-ray emission\\ndetection rate by Voges {\\\\it et al.} 1999.\\nMiller {\\\\it et al.} (1999a,b) also show that there is very little line-of-sight anisotropy\\nin the $R \\\\ge 1$ Abell/ACO cluster samples - comparable to the APM cluster\\ncatalog (Dalton {\\\\it et al.} 1994)\\nThis is in sharp contrast to $R \\\\ge 0$\\nsamples and even some modern X-ray selected/confirmed cluster samples (see e.g. Efstathiou\\net al. 1992, Peacock \\\\& West 1992, and Miller et al. 1999b).\\n\\nVogeley (1998) recently pointed out how Galactic extinction could\\nadd ``false'' power to structure analyses based on large galaxy\\nsamples (such as the Sloan Digital Sky Survey). While clusters should\\nnot affected as strongly as individual galaxies, it is still worth examining\\nextinction effects within our cluster sample.\\nIn 1996, Nichol and Connolly used the Stark {\\\\it et al.} 1992 HI maps to report\\nthat some samples of Abell clusters significantly anti-correlate with\\nregions of high galactic neutral hydrogen density. \\nRecently, Schlegel, Finkbeiner, and Davis (1998) have\\ncreated HI extinction maps of the entire sky with much greater resolution than the Stark HI\\nmaps. We use these new maps to re-examine\\nand confirm the Nichol and Connolly results. We also examine a volume-limited ($z=0.10$) sample\\nof Abell/ACO clusters.\\nUsing a Kolmogorov-Smirnov (K-S) test, we compare the E(B-V) extinctions for positions\\ncentered on the Abell/ACO clusters to E(B-V) extinctions for several thousand randomly\\nselection positions. We find that the probability that our clusters were drawn\\nfrom a random selection of E(B-V) extinctions is 10\\\\%. \\nIn other words, the average extinction\\nwithin our Abell/ACO clusters is smaller than for the random positions, but\\nnot significantly so. For comparison, Nichol and Connolly found only a 2\\\\% probability that the\\nPostman, Huchra, and Geller (1992) Abell/ACO clusters (with $|b| \\\\ge 30^o$ and $R \\\\ge 1$) were\\ndrawn from a random sampling of E(B-V) extinctions. \\nThe effect that galactic extinction would have on a power spectrum should not be \\nas strong for clusters as it would be for galaxies. Cluster galaxies have\\na wide range of magnitudes, and while some dimmer galaxies within a cluster may be missed due\\nto extinction, the majority of bright galaxies will still be counted. When we created\\nour volume-limited samples, we are including those clusters that appear dim as a result of\\ngalactic extinction (as opposed to a magnitude-limited survey which would exclude those\\nclusters). The lack of statistically significant evidence that our clusters\\nare corrupted by extinction, and the use of a volume-limited sample (with $|b| \\\\ge 30^o$),\\nconvinces us that\\nwe can ignore any extinction effects in our analyses.\\nHowever, to be certain that extinction is not altering the shape or amplitude of\\nour redshift-space power spectrum, we will model the extinction distribution\\nof our clusters in our random catalogs for one of our two PS estimation methods (see method (b) below).\\n\\nAn additional argument for the completeness of $R \\\\ge 1$ Abell/ACO clusters is\\nprovided by their spatial number density as shown in Figure 1. \\nWe use clusters of all magnitudes and use the same methods \\nas Miller {\\\\it et al.} (1999a) to calculate and\\nbin the cluster number densities. \\nNotice in Figure 1 that the sample\\nhas a nearly constant density out to $z = 0.10$\\nand that the density\\nonly drops by a factor of $0.58$ out to $z = 0.14$. \\n[Note: The bump in the density at $z \\\\sim 0.07$ is mostly due to\\nthe Corona Borealis Supercluster.]\\nIn Figure 1, we fit three different functions to the number density:\\na three-parameter number function (as in FKP), a power-law for $z \\\\ge 0.10$,\\nand a step-function. The best-fit produces $\\\\chi^2_{red} = 2$ for the number function. \\n\\nUsing cluster redshifts from the literature as well as $\\\\sim 100$ as yet unpublished\\nredshifts from the MX Survey Extension (Miller {\\\\it et al.} 2000),\\nwe have created a sample of 637 $R \\\\ge 1$ Abell/ACO clusters with $|b| \\\\ge 30^{\\\\circ}$.\\nThe MX Survey provides a much deeper (in both magnitude and in redshift) catalog\\nof Northern Hemisphere cluster redshifts than is currently available for the Southern Hemisphere ACO clusters\\n(see e.g. Miller et al. 1999; Katgert et al. 1996).\\nTherefore, we exclude any cluster\\nbeyond $z = 0.10$ in the south ($\\\\delta \\\\le -27^{\\\\circ}$) and beyond $z = 0.14$ in the\\nnorth ($\\\\delta \\\\ge -27^{\\\\circ}$).\\nSeveral researchers have noted discrepancies between the richness counts of\\nthe Abell and ACO catalogs (see Miller et al. (1999) for a discussion).\\nTherefore, we also measure $P(k)$ for a subset of our data that\\nexcludes all ACO clusters with\\n$N_{gal} < 55 $ (where $N_{gal}$ is the number of galaxies used to determine the richness as\\ngiven in ACO and $N_{gal} \\\\ge 50$ corresponds to $R \\\\ge 1$). This richness cut excludes\\n30 ACO clusters from our sample.\\n\\nThis is the largest cluster sample compiled to date for large-scale structure analyses.\\nThe survey volume covers $1.2\\\\times10^8h^{-3}$Mpc$^3$ and is nearly four times larger than\\nthe APM cluster survey (Dalton {\\\\it et al.} 1994)\\nand the Retzlaff {\\\\it et al.} (1998) Abell/ACO survey.\\nAdditionally, only $\\\\sim$ 10\\\\% of our cluster redshifts are\\nbased on one measured galaxy redshift.\\nWe calculate distances to the clusters using\\na Friedmann Universe with $q_0 = 0$ and $H_0 = 100$ km s$^{-1}$ Mpc$^{-1}$. \\nThe choice of $q_o$ makes little difference in\\nour results (see also Retzlaff {\\\\it et al.} 1998).\\n\\n\\nWhen a cluster dataset goes as deep as the one used here, and has been\\ncreated in a somewhat piecemeal fashion, we must be very \\nconfident that the cluster observations used in this sample are more or less isotropic in volume, and that\\nwe are not including large sections of the sky that go deeper (in magnitude) than others.\\nWe address this concern \\nfiguratively in Figure 2, by examining the fraction of observed to total cataloged clusters.\\nIn this sky plot (in galactic coordinates), we\\nshow Abell clusters with $z=0.10$ (filled circles), Abell clusters within\\n$0.10 < z \\\\le 0.14$ (open circles), and ACO clusters within $z=0.10$ (stars).\\nWe can divide the sky into quadrants with two sections in the north\\nand two in the south (each separated at $l = 180^{o}$) and examine\\nnearby ($z \\\\le 0.10$) and distant ($0.10 < z \\\\le 0.14$) clusters\\nseparately. From Figure 2, we see\\nreasonably fair coverage throughout the entire sky in both redshift\\nranges (recall that\\nthe southern right quadrant only goes to $z=0.10$).\\nQuantitatively, we present in Table 1 the number of clusters available in each\\nquadrant cataloged by Abell/ACO, and the number\\nof clusters observed in each quadrant. Note that the fractional\\ncoverages in each of the sections are very similar. The mean fractional coverage\\n(including both near and far quadrants) is $0.138\\\\pm{0.019}$, so that the\\nnumber of clusters within the more distant,\\nnorthern right quadrant is only $1.5\\\\sigma$ smaller than the mean.\\nTable 1 provides clear evidence that the sky coverage for our cluster sample is\\nnot observationally biased towards certain regions.\\n\\nAfter accounting for projection effects, line-of-sight anisotropies, X-ray identifications,\\nHI column density variations, a constant number density, and fair sky coverage,\\nthis is the largest, \\nmost complete, and fairly sampled distribution of matter in the local\\nUniverse. We assume that clusters are biased tracers of mass (Kaiser 1986; Peacock \\\\& Dodds 1994) and\\nthat in the end, we may compare the shape of our power spectrum to those of typical cosmological models.\\n\\n\\\\section{Methods and Analyses}\\nWe utilize two different methods to estimate $P(k)$ in redshift-space. Both methods follow\\nthe same basic idea: directly sum the plane wave contributions from each cluster, account for\\nappropriate weights and the shape of the volume, compute the square of the modulus of each\\nmode and subtract off the shot noise. The resultant power spectrum is the estimated variance\\nof the density contrast $|\\\\delta(k)|^2$.\\nThe power spectrum is accurate only to some limiting scale, specified by $k_{min}$,\\nwhich is constrained by the size and shape of the volume examined.\\nThe differences between the two methods arise\\nwhen accounting for the weighting scheme and the shape of the volume.\\nWe also point out that Tegmark {\\\\it et al.} (1998) have recently presented\\nan alternative method for measuring $P(k)$ for large datasets (such as the Sloan\\nDigital Sky Survey). As discussed in detail in Tegmark {\\\\it et al.}, they\\nadvocate the use of standard Fourier techniques on small scales, a pixelized quadratic\\nmatrix method on large-scales, and also a Karhunen - Loeve (KL) eigenmode analysis to\\nprobe redshift-space anisotropies. While the Tegmark {\\\\it et al.} power spectrum\\nestimation method is undoubtedly\\nmore refined than the methods used here, we are more interested in comparing results\\nfrom the most commonly used techniques (and also allowing our results to be compared\\nto previous cluster $P(k)$ measurements). Also, the methods described in Tegmark et al.\\nare designed for large datasets (e.g. several 100,000 points) and we would not expect\\na large advantage in our smaller samples.\\n\\nThe first method we use was originally applied by Vogeley et al. (1992),\\nPark et al. (1994) and da Costa et al. (1994) \\nto the CfA2 redshift survey (Geller \\\\& Huchra 1989). This method is also\\ndescribed in LCRS and Fisher {\\\\it et al.} 1993.\\nMost recently, this method was used and described by Retzlaff {\\\\it et al.} (1998) on a \\nsample of Abell/ACO clusters. \\nBriefly, the estimated power spectrum convolved with\\nthe window function can be written as follows:\\n\\\\begin{equation}\\n\\\\hat{P}_{a}(k) = {\\\\frac{V}{1-|\\\\hat{W}(k)|^2}}[\\\\hat{\\\\Pi}(k) - \\\\hat{S}].\\n\\\\end{equation}\\nThe first factor in Equation 1 accounts for the systematic under-estimation of $P(k)$ at\\nsmall values of $k$ due to normalization biases and \\nthe shape of the window, also known as large-scale power damping (Peacock \\\\& Nicholson 1991). \\nThe first term in brackets, $\\\\hat{\\\\Pi}$ is the squared-modulus of the Fourier transform of the \\ndensity contrast, $\\\\delta(\\\\bf{r})$, minus the Window Function,\\nor the estimated power. $\\\\hat{\\\\Pi}$ is a discrete quantity that\\nincludes shot noise $\\\\hat{S}$ which we must subtract off.\\nThe estimate of the power, $\\\\hat{P}_{a}(k)$, is convolved with the\\nWindow function, $\\\\hat{W}(k)$.\\n\\nIn practice, we calculate $\\\\hat{W}(k)$ separately for as many points as is feasible (in this case \\n$3\\\\times 10^5$ random points) and average over 1000 directions of $k$. \\nThe window function is presented in Figure 3. We calculate $|\\\\hat{W}(k)|^2$ using points\\nrandomly distributed in our volume and also with the same redshift and extinction\\ndistribution as our real data (the redshift distribution is smoothed with a Gaussian to remove any\\nlarge-scale structure). Figure 3 shows that the shape of $|\\\\hat{W}(k)|^2$ changes\\nvery little as we adjust the random distribution within our volume.\\nWe also calculate $|\\\\hat{W}(k)|^2$ for a volume that\\nencompasses only one hemisphere out to $z = 0.14$. We see that, as the volume becomes more asymmetric,\\nsignificant\\ndifferences betweem the window functions appear.\\nThe ``bumps'' seen in $|\\\\hat{W}(k)|^2$ are a direct result\\nof a volume-limited, spherically symmteric survey, and have little effect on the PS estimation,\\nso long as their relative heights are much smaller than the largest $|\\\\hat{W}(k)|^2$ used. \\nThese ``bumps'' are an indicator that the survey window is spherically symmetric\\nand that averaging over all directions of ${\\\\bf k}$ is appropriate.\\nThis is not typically the case in previous (non-Abell/ACO)\\n$P(k)$ analyses (see Tegark (1995) for a good discussion of window functions).\\n\\nThe smallest $k$ that can be accurately probed depends on the value of $|\\\\hat{W}(k)|^2$ and\\nhow it convolves with the real power spectrum (see Lin et al. 1996). Recall, \\n\\\\begin{equation}\\n\\\\langle P_{estimated}(k) \\\\rangle \\\\propto \\\\int |\\\\hat{W}({\\\\bf k} - {\\\\bf k'})|^2 P_{true}({\\\\bf k'}) k'^2 dk'.\\n\\\\end{equation}\\nIdeally, for all values of $k$ probed, the integrand of Equation (2) will be sharply peaked at $k = k'$.\\nIn Figure 4, we plot the integrand of Equation (2) assuming a constant $P(k)$. We find that the\\nshape of our volume does not affect our analyses for $k >\\\\sim 0.015h$Mpc$^{-1}$. For $k$ smaller\\nthan this limit, we see that ``leakage'' occurs and power from larger $k$ slips into our measurements.\\nFigure 4 also shows that if uncorrelated modes of $P(k)$ are required, we should separate\\nour bins by $\\\\delta k = 0.015$. \\nOur choice of $k_{min} =0.015 h$Mpc$^{-1}$ is a conservative\\nlimit, since most past analyses of $P(k)$ have stopped where\\n$|\\\\hat{W}(k)|^2 = 0.1$ (e.g. Peacock and Nicholson 1991; Vogeley et al. 1992; Retzlaff et al. 1998).\\nThe value of $|\\\\hat{W}(k)|^2$ for our analysis at $k_{min}$ is only $ 0.05h$Mpc$^{-1}$.\\n\\nThe weights for each cluster\\noriginate in the estimation of the density contrast,\\n\\\\begin {equation}\\n\\\\hat{\\\\delta}(r)=\\\\frac{1}{N}\\\\sum_i{\\\\frac{\\\\delta^{3}(\\\\bf{r}-\\\\bf{r}_i)}{\\\\phi(r_i)}} - 1\\n\\\\end{equation}\\nwhere $\\\\phi({\\\\bf r}) = \\\\psi(b)\\\\varphi(z)$ is the selection function which accounts for galactic\\nobscuration and redshift selection.\\nWe use $\\\\psi(b) = 10^{\\\\gamma(1-csc|b|)}$ with $\\\\gamma = 0.32$ for the latitude selection\\nfunction (see Postman, Huchra, and Geller 1992). \\n%We use $\\\\varphi(z) = 1$ for clusters within $z=0.10$ and\\n%and $\\\\varphi = 0.58$ for clusters with $0.10 < z \\\\le 0.14$.\\nThe selection function in $z$ is determined separately for the three different number density models\\nused in Figure 1. We find that the choice of number-density fit\\nhas little on the PS estimation.\\n\\nThe second method we use was derived by Feldman, Kaiser, \\\\& Peacock (1994-hereafter FKP).\\nTED96 use a very similar approach in their analysis of APM clusters.\\nHere, the\\npower spectrum is:\\n\\\\begin{equation}\\n\\\\hat{P}_b(k) = |F({\\\\bf k})|^2 - P_{shot}\\n\\\\end{equation}\\nwhere $F(k)$ is the Fourier transform of the normalized and weighted galaxy fluctuation field:\\n\\\\begin{equation}\\nF(\\\\bf{r})=\\\\frac{w(r)[n_c(r)-{\\\\alpha}n_s(r)]}{[\\\\int d^3r\\\\bar{n}^2(r)w^2(r)]^{1/2}}\\n\\\\end{equation}\\nIn these equations, $n_c$ and $n_s$ represent the number densities of the cluster sample\\nand a randomly generated synthetic catalog respectively. \\nThe number of\\npoints we use in the random catalog is 500 times that of the real data so $\\\\alpha = \\\\frac{1}{500}$\\n(we note\\nthat there is no difference in the power spectrum results for random catalogs with 100\\ntimes as many points). $P_{shot}$ is again, the power due to shot noise from a discrete sample and\\nis determined as in FKP.\\nIn this method, we model the redshift selection of our random catalogs from\\nthe redshifts of the real data, smoothed with a Gaussian of width $3000$ km s$^{-1}$.\\nThe weights for the individual clusters (real and synthetic) are determined from\\n\\\\begin{equation}\\nw_o(r) = \\\\frac{1}{1+n(r)P_{init}(k)}.\\n\\\\end{equation}\\nTo create the extinction adjusted random catalogs, we draw from regions in\\nthe sky that have the same extinction distribution as our real data using the Schlegel et al. (1998)\\nmaps. We find little difference in our $P(k)$ when we apply no extinction correction.\\nTo determine $n(r)$ used in the weighting factor, we use the three different number density\\nfits\\n(as given in Figure 1). Again, we find that the choice of number density fit has little\\neffect on the PS estimation. \\n\\nThe weighting scheme for $P_{b}(k)$ depends on {\\\\it a priori} knowledge of $P(k)$ at all\\nscales. We choose different values of \\n$P_{init}(k)$ ( 5, 10, 30, 60$\\\\times 10^4h^{-3}$Mpc$^{3}$)\\nfor the cluster weights and\\nfind that there is little difference in the amplitude ($\\\\sim 1.5 $ times) \\nof $P_{b}(k)$ between\\n$P_{init} = 5$ and $60\\\\times 10^4 h^{-3}$Mpc$^{3}$ and so we adopt \\n$P_{init} = 30\\\\times 10^4 h^{-3}$Mpc$^{3}$ in all further $P_{b}(k)$ results.\\nWe calculate errors on $P_{b}(k)$ using those methods of FKP (equation 2.4.6).\\n\\nIn Figure 5, we compare all of our calculations of $P(k)$.\\nIn the top panel of Figure 5, we plot $P_a(k)$ using the three different number density functions.\\nWe also measure $P(k)$ for the richness adjusted sample.\\nWe plot the same for\\n$P_{b}(k)$ in the middle panel of Figure 5. In all cases, we find very little difference in our $P(k)$ estimations.\\nIn the bottom panel of Figure 5 we compare $P_a(k)$ to $P_b(k)$ using the number function as our density fit.\\nHere, we do see some small differences in the measured power at $k$ less than $0.02h$Mpc$^{-1}$, however\\nboth spectra estimates are within the 1 $\\\\sigma$ error. \\nThe lack of difference between $P_a(k)$ and $P_b(k)$ \\nis a direct result of the stability of the methods and the\\nwell defined number density and \\nsymmetric volume of the cluster sample.\\n\\n\\\\section{Discussion}\\n\\nThere are two striking results regarding the power spectrum of rich Abell/ACO clusters. (1) While\\nwe do see a dip in power near $k = 0.4h$ Mpc$^{-1}$, it is not statistically significant. \\nThe measured power spectrum is essentially featureless and there is \\nno narrow peak in the power spectrum as has been\\nreported in E97 and Retzlaff {\\\\it et al.} (1998). (2) The other difference\\nis that there is increasing power to very large scales ($k = 0.015h$Mpc$^{-1}$ or $\\\\sim 400h^{-1}$Mpc).\\nIn past analyses of the power spectrum, most\\nauthors have reported the (weak) detection of a turnover in the power spectrum (see section 1). However,\\nthe turnover has always occurred very near the largest scales accessible in their volumes. \\n[Note: other preliminary analyses of the PS on scales $k < 0.05h$Mpc$^{-1}$ are also showing\\nthis increase in power (Guzzo et al. 1999; Hamilton and Tegmark 2000; Efstathiou and Moody 2000)].\\nThe power spectrum is roughly a power-law on scales $0.02 \\\\le k < 0.10 h$Mpc$^{-1}$ with $P(k) \\\\propto k^{-1.4}$.\\n\\nIn Figure 6, we compare our results to two other cluster sample power spectrum analyses,\\nthe APM cluster sample of TED98, and the $R \\\\ge 0$ Abell/ACO sample of Retzlaff et al. (1998).\\nFigure 6 shows that the shapes of $P(k)$ for\\nthese three different cluster samples\\nare remarkably\\nsimilar in the range $ 0.04 \\\\le k \\\\le 0.15 h$Mpc$^{-1}$.\\nThe higher amplitude for our sample of $R \\\\ge 1$ clusters is expected according to\\nhierarchical clustering schemes (Kaiser 1986) and larger bias found in richer clusters (see\\nPeacock and Dodds 1994).\\nWe have recalculated the Retzlaff {\\\\it et al.}\\n(1998) Abell/ACO cluster sample using the methods for $P_a(k)$. We do this in part as a check on\\nour methods and also to independently confirm their results of a peak near $k = 0.05h$Mpc$^{-1}$\\nand a turnover thereafter. The Retzlaff {\\\\it et al.} sample includes all Abell/ACO clusters\\nwithin $240 h^{-1}$Mpc and outside $|b| \\\\ge 30^{\\\\circ}$. We find 412 clusters which meet this\\ncriteria (compared to their 417 clusters- the difference we attribute to minor variations in\\na few cluster redshifts near the survey boundaries). Our results, not surprisingly, are identical\\nto those published in Retzlaff {\\\\it et al.} (1998) since our method for determining $P_a(k)$ is\\nidentical to theirs. For this determination of $P_a(k)$ ({\\\\it i.e.} using $R =0$ clusters and\\na much smaller volume), we also see a peak in the power spectrum at $k = 0.05h$Mpc$^{-1}$\\nand a turnover thereafter. As pointed out by Retzlaff {\\\\it et al.}, this peak\\nis not statistically significant. As a further examination of this issue, we plot in Figure 6 \\n$P_b(k)$ for a smaller cluster sample,\\nvolume-limited in the north and south to $z = 0.10$. For this sample, we can only detect power to\\n$k_{min} \\\\sim 0.035h$Mpc$^{-1}$. For $k$ greater than $0.035h$Mpc$^{-1}$\\nwe find little difference between this sample and the larger one. But\\nwe can no longer probe on the scales where we expect $P(k)$ to continue its rise.\\nThus, one could conclude that a turn-over has been found, when in fact a larger (in size and number) sample\\nshows that the power continues to rise for $k < 0.03h$Mpc$^{-1}$.\\n\\n\\\\subsection{Comparisions to Linear Theory}\\nWe also compare our power spectrum results to those of linear theory created by CMBFAST \\n(Seljak \\\\& Zaldarriaga 1996). We consider three Cold Dark Matter (CDM) variants, flat, open and\\nwith a vacuum density ($\\\\Lambda$CDM), and a Mixed Dark Matter (MDM) model.\\nFor the CDM cases, we choose $\\\\Omega_b = 0.02$, in accordance with\\nSchramm \\\\& Turner (1998). For the open case, we choose\\n$\\\\Omega_0=\\\\Omega_b + \\\\Omega_{CDM} = 0.2$ in accordance with Bahcall (1997). For the $\\\\Lambda$CDM\\nmodel, we choose $\\\\Omega_{CDM} = 0.18$ and $\\\\Omega_{vacuum} = 0.80$ so that\\n$\\\\Omega_b + \\\\Omega_{CDM} + \\\\Omega_{vacuum} = 1$. For the MDM model,\\nwe choose $H_0 = 50 $km s$^{-1}$Mpc$^{-1}$\\nwith $\\\\Omega_b =0.05$, $\\\\Omega_{CDM}=0.35$ and $\\\\Omega_{\\\\nu}=0.3$\\n(where $\\\\Omega_{\\\\nu}$ is the massive neutrino density).\\nThe CMBFAST package normalizes\\nthe amplitude of generated spectra to the Bunn and White (1997) four-year COBE normalization. \\nHowever, in this work, we are only concerned with the {\\\\it shape} of the power spectrum.\\nWe are motivated by our assumption that clusters are biased tracers of the mass distribution\\nand therefore the shape of the cluster power spectrum should be similar to that of the matter\\npower spectrum.\\nIn Figure 7, we present the amplitude shifted\\nlinear models in comparison to our empirically determined \\npower spectra.\\nAs a result of the known similarities in the shapes of the $\\\\Lambda$CDM models and low matter density\\nopen CDM models, we find that both fit the shape of the rich\\nAbell/ACO cluster power spectrum to $k_{min} = 0.015h$Mpc$^{-1}$ or $400h^{-1}$Mpc extremely\\nwell (see Table 2).\\nOn the largest scales, the \\nMDM model lacks power over a wide range of $k$ ($0.015 \\\\le $k$ \\\\le 0.03h$Mpc$^{-1}$) to match\\nour cluster data.\\nTED98 found that $\\\\Lambda$CDM linear models did not have\\nenough power on large scales to match the APM cluster power spectrum. Instead, they find a much\\nbetter fit for\\na mixed dark matter (MDM) model.\\nWe\\npoint out that the $\\\\Lambda$CDM model in Figure 7 of TED98 does provide an excellent\\nfit to the APM cluster data if their last data point at $k = 0.02h$Mpc$^{-1}$ (where\\nthe error is rather large) is excluded.\\n\\n\\\\section{Conclusion}\\nThe agreement between\\nthe shapes of $P(k)$ for the four different samples shown in Figure 6 (from $k = 0.05$ to $0.15 $h Mpc$^{-1}$),\\nprovides further evidence that clusters are\\ntracers of the peaks of the underlying luminous \\nmass distribution. While there is a\\ngreat deal of volume-overlap in these four samples, they are made up of significantly\\ndifferent luminous objects (from very poor APM clusters to the richest Abell clusters).\\nFor instance, the Retzlaff et al. (1998) Abell/ACO sample\\ncontains at most 253 $R \\\\ge 1$ clusters, while the remaining 218 are $R \\\\ge 0$. \\nOur sample contains 637 $R \\\\ge 1$ clusters. The APM sample of 364 clusters, \\ncontains even fewer $R \\\\ge 1$ Abell clusters ($\\\\sim 40$).\\nIf all groups and clusters\\ntrace the underlying mass distribution in a similar way, then the we would expect their respective\\npower spectra to be similar in shape, and only the amplitude to vary.\\n \\nPrevious analyses of the cluster power spectrum have been plagued\\nby three major problems: (1) uncertainties in the number density, (2) small volumes,\\nand (3) irregularly shaped volumes. The sample analyzed in this work greatly improves\\nupon each of these difficulties. \\nOur Abell/ACO sample has a nearly constant number\\ndensity throughout the entire volume. This is in stark contrast to most\\nother sparse tracer surveys (such as the QDOT {\\\\it IRAS} survey power spectrum\\nof FKP and the Retzlaff {\\\\it et al.} Abell/ACO cluster sample).\\nAlong with the number density, the large size of the volume\\nand the semi-regular shape of the double-cone geometry, all contribute significantly\\nto a more accurate determination of $P(k)$ on the largest scales.\\nThe reality of the power on scales $200 - 300h^{-1}$Mpc is also becoming evident\\nobservationally. Batuski {\\\\it et al.} 1999\\nhave recently discovered two filamentary superclusters in the constellation of Aquarius\\nthat are as long as $75h^{-1}$Mpc and $150h^{-1}$Mpc. As we peer out further into the\\nlocal Universe, we continue to find structures on very large scales. \\n\\n\\nWe have presented the redshift-space power spectrum for the largest galaxy cluster sample\\ncompiled to date. This sample has been examined extensively for projection effects, anisotropies,\\nand observational selection effects and found to be a fair and complete sampling of biased\\nmatter in the local Universe. The volume and shape of the survey provide accurate and robust\\nmeasurements of $P(k)$ over the wavenumber range $0.015 \\\\le k \\\\le 0.15 h$Mpc$^{-1}$. From\\n$k= 0.15$ down to $k = 0.05 h$Mpc$^{-1}$, we\\nfind a similar shape to the power spectrum compared to other cluster samples such as\\nthe APM cluster survey and a smaller sample of $R \\\\ge 0$ Abell/ACO clusters studied by\\nRetzlaff {\\\\it et al.} (1998). At smaller $k$, we do not find\\nany statistically significant features in $P(k)$. \\nUnlike previous cluster $P(k)$ analyses, we do not find\\nany strong evidence for a turnover.\\nWe find that $\\\\Lambda$CDM and\\nlow $\\\\Omega_0$ CDM linear models provide excellent fits to the rich cluster power spectrum.\\n\\n{\\\\bf Acknowledgments} The authors wish to thank Adrian Melott and Daniel Eisenstein\\nfor helpful conversations. We also would like to acknowledge the role of the\\nthe referee, Michael S. Vogeley, for his suggestions on improving the original manuscript. \\nWe also thank H. Tadros for supplying the APM cluster PS in electronic form.\\nCM was funded in part by NASA-EPSCoR through the\\nMaine Science and Technology Foundation.\\n\\n\\\\begin{deluxetable}{cccccc}\\n%\\\\tablefontsize{\\\\footnotesize}\\n\\\\tablenum{1}\\n\\\\tablewidth{0pt}\\n\\\\tablecaption{\\\\bf Sky Coverage}\\n\\\\tablehead{\\n\\\\colhead{$\\\\ell$ range} & \\\\colhead{ $b$ range} & \\\\colhead{ $z$ range} & \\n\\\\colhead{Number (all z)} & \\\\colhead{ Number with} & \\\\colhead{Fraction{\\\\tablenotemark{a}}} \\\\nl\\n\\\\colhead{ } & \\\\colhead{ } & \\\\colhead{ } &\\n\\\\colhead{cataloged} & \\\\colhead{observed redshifts} & \\\\colhead{}}\\n\\\\startdata\\n$0^o \\\\le \\\\ell < 180^o$ & $30^o \\\\le b \\\\le 90^o$ & $z \\\\le 0.10$ & 636 & 80 & 0.1257 \\\\nl\\n$0^o \\\\le \\\\ell < 180^o$ & $30^o \\\\le b \\\\le 90^o$ & $0.10 < z \\\\le 0.14$ & 636 & 86 & 0.1352 \\\\nl\\n$180^o \\\\le \\\\ell < 360^o$ & $30^o \\\\le b \\\\le 90^o$ &$z \\\\le 0.10$ & 503 & 78 & 0.1550 \\\\nl\\n$180^o \\\\le \\\\ell < 360^o$ & $30^o \\\\le b \\\\le 90^o$ &$0.10 < z \\\\le 0.14$ & 503 & 52 & 0.1034 \\\\nl\\n$0^o \\\\le \\\\ell < 180^o$ & $-90^o \\\\le b \\\\le -30^o$ &$z \\\\le 0.10$ &608 & 95 & 0.1563 \\\\nl\\n$0^o \\\\le \\\\ell < 180^o$ & $-90^o \\\\le b \\\\le -30^o$ &$0.10 < z \\\\le 0.14$ & 608 & 84 & 0.1382 \\\\nl\\n$180^o \\\\le \\\\ell < 360^o$ & $-90^o \\\\le b \\\\le -30^o$ &$z \\\\le 0.10$ & 492 & 75 & 0.1524 \\\\nl\\n\\\\tablenotetext{a}{Fraction is the Number observed/ Number cataloged.}\\n\\\\enddata\\n\\\\end{deluxetable}\\n\\n \\n\\\\begin{deluxetable}{ccc}\\n%\\\\tablefontsize{\\\\footnotesize}\\n\\\\tablenum{2}\\n\\\\tablewidth{0pt}\\n\\\\tablecaption{\\\\bf Goodness-of-Fit to Linear Models}\\n\\\\tablehead{\\n\\\\colhead{Model} & \\\\colhead{$\\\\chi_{reduced}^2$} & \\\\colhead{DOF}}\\n\\\\startdata\\n$\\\\Lambda$CDM ($H_o = 100$km s$^{-1}$) & 0.65 & 8 \\\\nl\\nOpen CDM ($H_o = 100$km s$^{-1}$) & 0.66 & 8 \\\\nl\\nCDM ($H_o = 100$km s$^{-1}$) & 4.55 & 8 \\\\nl\\nMDM ($H_o = 50$km s$^{-1}$) & 2.19 & 8 \\\\nl\\n\\\\enddata\\n\\\\end{deluxetable}\\n\\n\\\\begin{thebibliography}{}\\n\\\\bibitem[(Abell 1958)]{abe58} Abell, G. O. 1958, \\\\apjsupp, ~ 3, 211\\n\\\\bibitem[(Abell et al. 1989)]{aco89} Abell, G. O.,\\n Corwin, H. G., Olowin, R. P. 1989, \\\\apjsupp, ~70, 1 (ACO)\\n\\\\bibitem[(Bahcall 1997)]{bah97} Bahcall, N. 1997, in {\\\\it Critical Dialogues in Cosmology}, ed. N. Turok,\\n World Scientific, Singapore, 221\\n\\\\bibitem[(Batuski {\\\\it et al.} 1999)]{bat99} Batuski, D.J., Miller, C.J., Slinglend, K.A.,\\n Balkowski, C., Maurogordato, S., Cayatte, V., Felenbok, P., and Olowin, R. 1999, \\\\apj, 520, 491\\n\\\\bibitem[(Broadhurst {\\\\it et al.} 1990)]{brd90} Broadhurst, T.J., Ellis, R.S., Koo, D.C., \\\\& \\n Szalay, A.S. 1990, Nature, 343, 726\\n\\\\bibitem[(Bunn \\\\& White 1997)]{bun97} Bunn, E.F. \\\\& White, M. 1997, \\\\apj, 480, 6\\n\\\\bibitem[(da Costa et al. 1994)]{dac94} da Costa, L.N., Vogeley, M.S., Geller, M.J., Huchra, J.P.,\\n \\\\& Park, C. 1994, \\\\apj, 437, L1\\n\\\\bibitem[(Dalton {\\\\it et al.} 1994)]{dal94} Dalton, G.B., Croft, R.A.C.,\\n Efstathiou, G., Sutherland, W.J., Maddox, S.J., and Davis, M. 1994, \\\\mnras,\\n 271, 47\\n\\\\bibitem[(Efstathiou {\\\\it et al.} 1992)]{eft92} Efstathiou, G., Dalton, G.B.,\\n Maddox, S.J., \\\\& Sutherland, W. 1992, \\\\mnras, ~257, 125\\n\\\\bibitem[(Efstahiou and Moody 2000)]{eft00} Efstathiou, G. and Moody, S.J. 2000, preprint\\n ~astro-ph/0010478\\n\\\\bibitem[(Einasto {\\\\it et al.} 1997)]{ein97} Einasto, J., Einasto, M., Gottl\\\\\\\"{o}ber, S.,\\n M\\\\\\\"{u}ller, V., Saar, V., Starobinsky, A.A., Tago, E., Tucker, D., Andernach, H., \\\\& \\n Frisch, P. 1997, Nature, 385, 139 (E97)\\n\\\\bibitem[(Einasto {\\\\it et al.} 1999)]{ein99} Einasto, J., Einasto, M., Tago, E.,\\n Starobinsky, A.A., Atrio-Barandela, F.,\\n M\\\\\\\"{u}ller, V., Knebe, A, \\\\& Cen, R. 1999, \\\\apj, 519, 469 (E99) \\n Frisch, P. 1997, Nature, 385, 139 (E97)\\n\\\\bibitem[(Einasto {\\\\it et al.} 1994)]{ein94} Einasto, M., Einasto, J., Tago, E., Dalton, G.B.,\\n \\\\& Andernach, H. 1994, \\\\mnras, 269, 301\\n\\\\bibitem[(Eisenstein and Hu 1998)]{eis98} Eisenstein, D.J., Hu, W., Silk, J., and Szalay, A.S.\\n 1998,\\\\apj, 494, L1\\n\\\\bibitem[(Feldman, Kaiser, \\\\& Peacock 1994)]{fel94} Feldman, H.A., Kaiser, N. \\\\& Peacock, J.A.\\n 1994, \\\\apj, 426, 23 (FKP)\\n\\\\bibitem[(Fisher {\\\\it et al.} 1993)]{fis93} Fisher, K.B., Davis, M., Strauss, M.A.,\\n Yahil, A., \\\\& Huchra, J.P. 1993, \\\\apj, 402, 42\\n\\\\bibitem[(Gatza\\\\~{n}aga, \\\\& Baugh)]{gat98} Gatza\\\\~{n}aga, E. \\\\& Baugh, C.M. 1998, \\\\mnras, 294, 229\\n\\\\bibitem[Geller \\\\& Huchra(1989)]{1989Sci...246..897G} Geller, M.\\\\ J.\\\\ \\\\& \\nHuchra, J.\\\\ P.\\\\ 1989, Science, 246, 897 \\n\\\\bibitem[(Gramann \\\\& Suhhonenko 1999)]{suh99} Gramann, M. \\\\& Suhhonenko, I. 1999, \\\\apj, 519, 433\\n\\\\bibitem[(Hamilton and Tegmark 2000)]{hal00} Hamilton, A.J.S. and Tegmark, M. 2000, submitted to \\\\mnras,\\nastroph/0008392\\n\\\\bibitem[(Guzzo 1999)]{guz99} Guzzo, L. 1999, presented at {\\\\it The Second Coral Sea Cosmology Conference}\\n\\\\bibitem[(Hoyle et al. 1999)]{hoy99} Hoyle, F., Baugh, C. M., Shanks, T., Ratcliffe, A. 1999, \\\\mnras,\\n 309, 659\\n\\\\bibitem[(Jing and Valdarnini 1993)]{jin93} Jing, Y.P. and Valdarnini, R. 1993, \\\\apj, 406,6\\n\\\\bibitem[(Kaiser 1994)]{kai94} Kaiser, N. 1986, \\\\mnras, 222,323\\n\\\\bibitem[(Katgert {\\\\it et al.} 1996)]{kat96} Katgert,P., Mazure, A., Perea, J.,\\n den Hartog, R., Moles, M., Le Fevre, O., Dubath, P., Focardi, P., Rhee, G.,\\n Jones, B., Escalera, E., Biviano, A., Gerbal, D., Giuricin, G. 1996,\\n A \\\\& A, ~310, 8\\n\\\\bibitem[(Landy {\\\\it et al.} 1996)]{lan96} Landy, S.D., Shectman, S.A., Lin, H., Kirshner, R.P.,\\n Oemler, A.A., \\\\& Tucker, D. 1996, \\\\apj, 456, L1\\n\\\\bibitem[(Lin {\\\\it et al.} 1996)]{lin96} Lin, H., Kirshner, R.P., Shectman, S.A., Landy, S.D.,\\n Oemler, A., Tucker, D.L., \\\\& Schecter, P.L. 1996, \\\\apj 471, 617 (LCRS)\\n\\\\bibitem[(Miller {\\\\it et al.} 1999a)]{mi99a} Miller, C.J., Batuski, D.J., Slinglend, K.A., \\\\&\\n Hill, J.M. 1999a, \\\\apj, 523, 492\\n\\\\bibitem[(Miller {\\\\it et al.} 1999b)]{mi99b} Miller, C.J., Ledlow, M.J. \\\\& Batuski, D.J. 1999b,\\n \\\\mnras, submitted\\n\\\\bibitem[(Miller {\\\\it et al.} 1999c)]{mic99} Miller, C.J., Krughoff, K.S., Slinglend, K.A.,\\n Batuski, D.J., \\\\& Hill, J.M. 1999c (in preparation)\\n\\\\bibitem[(Nichol \\\\& Connolly 1996)]{nic96} Nichol, R.C. \\\\& Connolly, A.J. 1996, \\\\mnras, 279, 521\\n\\\\bibitem[(Park et al. 1994)]{par94} Park, C., Vogeley, M.S., Geller, M.J., \\\\& Huchra, J.P. 1994,\\\\apj,431,561\\n\\\\bibitem[(Peacock 1997)]{pea97} Peacock, J.A. 1997, \\\\mnras, 285, 885\\n\\\\bibitem[(Peacock \\\\& Dodds 1994)]{pea94} Peacock, J.A. \\\\& Dodds, S.J. 1994, \\\\mnras, 267, 1020\\n\\\\bibitem[(Peacock and Nicholson 1991)]{pea91} Peacock, J.A. \\\\& Nicholson, D. 1991, \\\\mnras, 253, 307\\n\\\\bibitem[(Peacock \\\\& West 1992)]{pew92} Peacock, J.A. \\\\& West, M.J. 1992,\\n \\\\mnras, 259, 494\\n\\\\bibitem[(Postman et al. 1992)]{pos92} Postman, M.,\\n Huchra, J. P., \\\\& Geller, M. J. 1992, \\\\apj, ~384, 404\\n\\\\bibitem[(Retzlaff {\\\\it et al.} 1998)]{ret98} Retzlaff, J., Borgani, S., Gottl\\\\\\\"{o}ber, S., \\n Klypin, A., \\\\& M\\\\\\\"{u}ller, V. 1998, NewA, 3, 631\\n\\\\bibitem[(Schlegel {\\\\it et al.} 1998)]{sch98} Schlegel, D.J., Finkbeiner, D.P., \\\\& Davis, M.\\n 1998, \\\\apj, 500, 525\\n\\\\bibitem[(Schramm \\\\& Turner 1998)]{sch98} Schramm, D.N. \\\\& Turner, M.S. 1998, Rev. Mod. Phys., 70, 303\\n\\\\bibitem[(Seljak \\\\& Zaldarriaga 1996)]{sel96} Seljak, U. \\\\& Zaldarriaga, M. 1996, \\\\apj, 469, 437\\n\\\\bibitem[(Slinglend {\\\\it et al.} 1998)]{sli98} Slinglend, K.A., Batuski, D.J,\\n Miller, C.M., Haase. S., Michaud, K., \\\\& Hill, J.M. 1998, \\\\apjsupp, 115,1\\n\\\\bibitem[(Stark {\\\\it et al.} 1992)]{sta92} Stark, A.A., Gammie, C.F., Wilson, R.W.,\\n Bally, J.L., Linke, R.A., Heiles, C., \\\\& Hurwitz, M. 1992, \\\\apjsupp, 79, 77\\n\\\\bibitem[(Sutherland 1988)]{sut88} Sutherland, W. 1988, \\\\mnras, ~234, 159\\n\\\\bibitem[(Tadros \\\\& Efstathiou 1996)]{tad96} Tadros, H., \\\\& Efstathiou, G. 1996, \\n \\\\mnras, 282, 1381 (TE96)\\n\\\\bibitem[(Tadros, Efstathiou \\\\& Dalton 1998)]{tad98} Tadros, H.,Efstathiou, G., \\\\& Dalton, G.\\n 1998, \\\\mnras, 296, 995 (TED98)\\n\\\\bibitem[(Tegmark 1995)]{teg95} Tegmark, M. 1995, \\\\apj, 455, 429\\n\\\\bibitem[(Vogeley 1998)]{vog98} Vogeley, M.S. 1998, in {\\\\it The Evolving Universe}, \\n Kluwer Academic Publishers, p. 395\\n\\\\bibitem[(Vogeley et al. 1992)]{vog92} Vogeley, M.S., Park, C., Geller, M.J., \\\\& Huchra, J.P. 1992,\\n \\\\apj, 391, L5\\n\\\\bibitem[(Voges, {\\\\rm et al.} 1999)]{vog99} Voges, W., Ledlow, M.J., Owen, F.N.,\\n \\\\& Burns J.O. 1999, \\\\aj, submitted \\n\\n\\n\\n\\\\end{thebibliography}\\n\\n\\\\begin{figure*}[hl]\\n\\\\plotone{f1.eps}\\n\\\\caption[]{The proper number density as a function of redshift is presented for the Abell/ACO cluster\\nsample. The lines are various fits to the data. The solid-line (having the lowest $\\\\chi^2$) is\\na three parameter number function. The dotted-line is for a power-law beyond $z =0.01$. The dashed-line\\nis for a step function. We find no significant differences in our PS analysis as a function of\\nthe number density function utilized.}\\n\\\\end{figure*}\\n\\n\\\\begin{figure*}\\n\\\\plotone{f2.eps}\\n\\\\caption[]{ A Hammer-Aitoff projection sky-plot of all clusters used in the\\npower spectrum analysis. Closed circles denote Abell (1958) clusters within $z=0.10$,\\nopen circles denote Abell clusters with $0.10 < z \\\\le 0.14$, and stars indicate\\nACO (1989) clusters within $z=0.10$. We have divided our sample into four quadrants\\nin latitude/longitude and two bins in $z$, to show that the clusters in our sample\\nhave been observed evenly throughout the sky (see Table 1).}\\n\\\\end{figure*}\\n\\n\\n\\n\\\\begin{figure*}\\n\\\\plotone{f3.eps}\\n\\\\caption[]{This is the Fourier window function, $\\\\langle|\\\\hat{W}({\\\\bf k})|^2 \\\\rangle$ used to calculate $P_a(k)$. We use 300000 points\\nand 1000 random directions for each $|k|$ to estimate the Fourier transform of the window function. $k$ is in\\nunits of $h$Mpc$^{-1}$. The dashed-line is for a random distribution of points. The solid-line is after\\nwe apply the same redshift and extinction distribution as our real data. The dotted-line is for a highly asymmetric\\nsurvey (i.e. one hemisphere to $z = 0.14$).\\nThe hatched region\\nindicates where our window function prevents an accurate determination of $P(k)$.}\\n\\\\end{figure*}\\n\\n\\n\\\\begin{figure*}[hl]\\n\\\\plotone{f4.eps}\\n\\\\caption[]{The integrand of Equation (2) for constant $P(k)$ with arbitrary normalization.\\nWe show three values of $k = 0.01, 0.02, 0.05h$Mpc$^{-1}$. We see that for $ k = 0.01h$Mpc$^{-1}$ there\\nis ``leakage'' from large $k$. At $k = 0.02h$Mpc$^{-1}$ this leakage is no longer evident, and\\nso we choose $k_{min} = 0.015h$Mpc$^{-1}$ as the largest-scales we can accurately probe.}\\n\\\\end{figure*}\\n\\n\\\\begin{figure*}\\n\\\\plotone{f5.eps}\\n\\\\caption[]{In the {\\\\bf top} panel we show $P_a(k)$ calculated using the three different number density\\nfunctions used in Figure 1. Circles are for the step-function, stars are for the power-law fit,\\nand squares are for the number function fit. The open circles include all $R \\\\ge 1$ ACO clusters\\nwhile the filled symbols are for ACO clusters with $N_{gal} \\\\ge 56$. We use a window function\\nthat models the real data (e.g. in density and extinction). The errors are estimates based\\non scaling the errors from $P_b(k)$.\\nIn the {\\\\bf middle} panel we show $P_b(k)$ using the same symbols as the top panel. We use random\\ncatalogs with the same extinction and density distribution as the real data. The error bars\\nare determined using the FKP method as mentioned in the text.\\nIn the {\\\\bf bottom} panel, we plot $P_a(k)$ (circles) and $P_b(k)$ (squares). The hatched region\\nindicates where our window function prevents an accurate determination of $P(k)$.\\n}\\n\\\\end{figure*}\\n\\n\\\\begin{figure*}\\n\\\\plotone{f6.eps}\\n\\\\caption[]{We compare $P_b(k)$ for Abell/ACO clusters calculated in this work (solid circles) to the smaller\\nAbell/ACO sample used by Retzlaff {\\\\it et al.} (1998) (triangles) and the APM cluster sample power spectrum\\ncalculated by Tadros {\\\\it et al.} (1998) (stars). The open circles are $R \\\\ge 1$ Abell/ACO clusters within \\n$z=0.10$ (north and south). \\n}\\n\\\\end{figure*}\\n\\n\\\\begin{figure*}\\n\\\\plotone{f7.eps}\\n\\\\caption[]{\\nWe compare $P_b(k)$ to model liner power spectra for a flat CDM \\n($\\\\Omega_b=0.02, \\\\Omega_{CDM}=0.98$ with $H_0 = 100 $km s$^{-1}$ Mpc$^{-1}$ {\\\\bf dashed-dot}),\\nmixed dark matter\\n($\\\\Omega_b=0.05, \\\\Omega_{CDM} = 0.65$ and $\\\\Omega_{\\\\nu} = 0.3$ with $H_0=50 $km s$^{-1}$ Mpc$^{-1}$\\n{\\\\bf dashed-dot-dot}),\\nopen ($\\\\Omega_b=0.02, \\\\Omega_{CDM}=0.18$ with $H_0 = 100 $km s$^{-1}$ Mpc$^{-1}$ {\\\\bf dashed}),\\nand lambda \\n($\\\\Omega_b=0.02, \\\\Omega_{CDM} = 0.18, \\\\Omega_{vacuum}=0.80$ {\\\\bf solid}) CDM models. }\\n\\\\end{figure*}\\n\\n\\\\end{document}\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002295.extracted_bib","string":"\\begin{thebibliography}{}\n\\bibitem[(Abell 1958)]{abe58} Abell, G. O. 1958, \\apjsupp, ~ 3, 211\n\\bibitem[(Abell et al. 1989)]{aco89} Abell, G. O.,\n Corwin, H. G., Olowin, R. P. 1989, \\apjsupp, ~70, 1 (ACO)\n\\bibitem[(Bahcall 1997)]{bah97} Bahcall, N. 1997, in {\\it Critical Dialogues in Cosmology}, ed. N. Turok,\n World Scientific, Singapore, 221\n\\bibitem[(Batuski {\\it et al.} 1999)]{bat99} Batuski, D.J., Miller, C.J., Slinglend, K.A.,\n Balkowski, C., Maurogordato, S., Cayatte, V., Felenbok, P., and Olowin, R. 1999, \\apj, 520, 491\n\\bibitem[(Broadhurst {\\it et al.} 1990)]{brd90} Broadhurst, T.J., Ellis, R.S., Koo, D.C., \\& \n Szalay, A.S. 1990, Nature, 343, 726\n\\bibitem[(Bunn \\& White 1997)]{bun97} Bunn, E.F. \\& White, M. 1997, \\apj, 480, 6\n\\bibitem[(da Costa et al. 1994)]{dac94} da Costa, L.N., Vogeley, M.S., Geller, M.J., Huchra, J.P.,\n \\& Park, C. 1994, \\apj, 437, L1\n\\bibitem[(Dalton {\\it et al.} 1994)]{dal94} Dalton, G.B., Croft, R.A.C.,\n Efstathiou, G., Sutherland, W.J., Maddox, S.J., and Davis, M. 1994, \\mnras,\n 271, 47\n\\bibitem[(Efstathiou {\\it et al.} 1992)]{eft92} Efstathiou, G., Dalton, G.B.,\n Maddox, S.J., \\& Sutherland, W. 1992, \\mnras, ~257, 125\n\\bibitem[(Efstahiou and Moody 2000)]{eft00} Efstathiou, G. and Moody, S.J. 2000, preprint\n ~astro-ph/0010478\n\\bibitem[(Einasto {\\it et al.} 1997)]{ein97} Einasto, J., Einasto, M., Gottl\\\"{o}ber, S.,\n M\\\"{u}ller, V., Saar, V., Starobinsky, A.A., Tago, E., Tucker, D., Andernach, H., \\& \n Frisch, P. 1997, Nature, 385, 139 (E97)\n\\bibitem[(Einasto {\\it et al.} 1999)]{ein99} Einasto, J., Einasto, M., Tago, E.,\n Starobinsky, A.A., Atrio-Barandela, F.,\n M\\\"{u}ller, V., Knebe, A, \\& Cen, R. 1999, \\apj, 519, 469 (E99) \n Frisch, P. 1997, Nature, 385, 139 (E97)\n\\bibitem[(Einasto {\\it et al.} 1994)]{ein94} Einasto, M., Einasto, J., Tago, E., Dalton, G.B.,\n \\& Andernach, H. 1994, \\mnras, 269, 301\n\\bibitem[(Eisenstein and Hu 1998)]{eis98} Eisenstein, D.J., Hu, W., Silk, J., and Szalay, A.S.\n 1998,\\apj, 494, L1\n\\bibitem[(Feldman, Kaiser, \\& Peacock 1994)]{fel94} Feldman, H.A., Kaiser, N. \\& Peacock, J.A.\n 1994, \\apj, 426, 23 (FKP)\n\\bibitem[(Fisher {\\it et al.} 1993)]{fis93} Fisher, K.B., Davis, M., Strauss, M.A.,\n Yahil, A., \\& Huchra, J.P. 1993, \\apj, 402, 42\n\\bibitem[(Gatza\\~{n}aga, \\& Baugh)]{gat98} Gatza\\~{n}aga, E. \\& Baugh, C.M. 1998, \\mnras, 294, 229\n\\bibitem[Geller \\& Huchra(1989)]{1989Sci...246..897G} Geller, M.\\ J.\\ \\& \nHuchra, J.\\ P.\\ 1989, Science, 246, 897 \n\\bibitem[(Gramann \\& Suhhonenko 1999)]{suh99} Gramann, M. \\& Suhhonenko, I. 1999, \\apj, 519, 433\n\\bibitem[(Hamilton and Tegmark 2000)]{hal00} Hamilton, A.J.S. and Tegmark, M. 2000, submitted to \\mnras,\nastroph/0008392\n\\bibitem[(Guzzo 1999)]{guz99} Guzzo, L. 1999, presented at {\\it The Second Coral Sea Cosmology Conference}\n\\bibitem[(Hoyle et al. 1999)]{hoy99} Hoyle, F., Baugh, C. M., Shanks, T., Ratcliffe, A. 1999, \\mnras,\n 309, 659\n\\bibitem[(Jing and Valdarnini 1993)]{jin93} Jing, Y.P. and Valdarnini, R. 1993, \\apj, 406,6\n\\bibitem[(Kaiser 1994)]{kai94} Kaiser, N. 1986, \\mnras, 222,323\n\\bibitem[(Katgert {\\it et al.} 1996)]{kat96} Katgert,P., Mazure, A., Perea, J.,\n den Hartog, R., Moles, M., Le Fevre, O., Dubath, P., Focardi, P., Rhee, G.,\n Jones, B., Escalera, E., Biviano, A., Gerbal, D., Giuricin, G. 1996,\n A \\& A, ~310, 8\n\\bibitem[(Landy {\\it et al.} 1996)]{lan96} Landy, S.D., Shectman, S.A., Lin, H., Kirshner, R.P.,\n Oemler, A.A., \\& Tucker, D. 1996, \\apj, 456, L1\n\\bibitem[(Lin {\\it et al.} 1996)]{lin96} Lin, H., Kirshner, R.P., Shectman, S.A., Landy, S.D.,\n Oemler, A., Tucker, D.L., \\& Schecter, P.L. 1996, \\apj 471, 617 (LCRS)\n\\bibitem[(Miller {\\it et al.} 1999a)]{mi99a} Miller, C.J., Batuski, D.J., Slinglend, K.A., \\&\n Hill, J.M. 1999a, \\apj, 523, 492\n\\bibitem[(Miller {\\it et al.} 1999b)]{mi99b} Miller, C.J., Ledlow, M.J. \\& Batuski, D.J. 1999b,\n \\mnras, submitted\n\\bibitem[(Miller {\\it et al.} 1999c)]{mic99} Miller, C.J., Krughoff, K.S., Slinglend, K.A.,\n Batuski, D.J., \\& Hill, J.M. 1999c (in preparation)\n\\bibitem[(Nichol \\& Connolly 1996)]{nic96} Nichol, R.C. \\& Connolly, A.J. 1996, \\mnras, 279, 521\n\\bibitem[(Park et al. 1994)]{par94} Park, C., Vogeley, M.S., Geller, M.J., \\& Huchra, J.P. 1994,\\apj,431,561\n\\bibitem[(Peacock 1997)]{pea97} Peacock, J.A. 1997, \\mnras, 285, 885\n\\bibitem[(Peacock \\& Dodds 1994)]{pea94} Peacock, J.A. \\& Dodds, S.J. 1994, \\mnras, 267, 1020\n\\bibitem[(Peacock and Nicholson 1991)]{pea91} Peacock, J.A. \\& Nicholson, D. 1991, \\mnras, 253, 307\n\\bibitem[(Peacock \\& West 1992)]{pew92} Peacock, J.A. \\& West, M.J. 1992,\n \\mnras, 259, 494\n\\bibitem[(Postman et al. 1992)]{pos92} Postman, M.,\n Huchra, J. P., \\& Geller, M. J. 1992, \\apj, ~384, 404\n\\bibitem[(Retzlaff {\\it et al.} 1998)]{ret98} Retzlaff, J., Borgani, S., Gottl\\\"{o}ber, S., \n Klypin, A., \\& M\\\"{u}ller, V. 1998, NewA, 3, 631\n\\bibitem[(Schlegel {\\it et al.} 1998)]{sch98} Schlegel, D.J., Finkbeiner, D.P., \\& Davis, M.\n 1998, \\apj, 500, 525\n\\bibitem[(Schramm \\& Turner 1998)]{sch98} Schramm, D.N. \\& Turner, M.S. 1998, Rev. Mod. Phys., 70, 303\n\\bibitem[(Seljak \\& Zaldarriaga 1996)]{sel96} Seljak, U. \\& Zaldarriaga, M. 1996, \\apj, 469, 437\n\\bibitem[(Slinglend {\\it et al.} 1998)]{sli98} Slinglend, K.A., Batuski, D.J,\n Miller, C.M., Haase. 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M., Shanks, T., Ratcliffe, A. 1999, \\\\mnras,\\n 309, 659\\n\\\\bibitem[(Jing and Valdarnini 1993)]{jin93} Jing, Y.P. and Valdarnini, R. 1993, \\\\apj, 406,6\\n\\\\bibitem[(Kaiser 1994)]{kai94} Kaiser, N. 1986, \\\\mnras, 222,323\\n\\\\bibitem[(Katgert {\\\\it et al.} 1996)]{kat96} Katgert,P., Mazure, A., Perea, J.,\\n den Hartog, R., Moles, M., Le Fevre, O., Dubath, P., Focardi, P., Rhee, G.,\\n Jones, B., Escalera, E., Biviano, A., Gerbal, D., Giuricin, G. 1996,\\n A \\\\& A, ~310, 8\\n\\\\bibitem[(Landy {\\\\it et al.} 1996)]{lan96} Landy, S.D., Shectman, S.A., Lin, H., Kirshner, R.P.,\\n Oemler, A.A., \\\\& Tucker, D. 1996, \\\\apj, 456, L1\\n\\\\bibitem[(Lin {\\\\it et al.} 1996)]{lin96} Lin, H., Kirshner, R.P., Shectman, S.A., Landy, S.D.,\\n Oemler, A., Tucker, D.L., \\\\& Schecter, P.L. 1996, \\\\apj 471, 617 (LCRS)\\n\\\\bibitem[(Miller {\\\\it et al.} 1999a)]{mi99a} Miller, C.J., Batuski, D.J., Slinglend, K.A., \\\\&\\n Hill, J.M. 1999a, \\\\apj, 523, 492\\n\\\\bibitem[(Miller {\\\\it et al.} 1999b)]{mi99b} Miller, C.J., Ledlow, M.J. \\\\& Batuski, D.J. 1999b,\\n \\\\mnras, submitted\\n\\\\bibitem[(Miller {\\\\it et al.} 1999c)]{mic99} Miller, C.J., Krughoff, K.S., Slinglend, K.A.,\\n Batuski, D.J., \\\\& Hill, J.M. 1999c (in preparation)\\n\\\\bibitem[(Nichol \\\\& Connolly 1996)]{nic96} Nichol, R.C. \\\\& Connolly, A.J. 1996, \\\\mnras, 279, 521\\n\\\\bibitem[(Park et al. 1994)]{par94} Park, C., Vogeley, M.S., Geller, M.J., \\\\& Huchra, J.P. 1994,\\\\apj,431,561\\n\\\\bibitem[(Peacock 1997)]{pea97} Peacock, J.A. 1997, \\\\mnras, 285, 885\\n\\\\bibitem[(Peacock \\\\& Dodds 1994)]{pea94} Peacock, J.A. \\\\& Dodds, S.J. 1994, \\\\mnras, 267, 1020\\n\\\\bibitem[(Peacock and Nicholson 1991)]{pea91} Peacock, J.A. \\\\& Nicholson, D. 1991, \\\\mnras, 253, 307\\n\\\\bibitem[(Peacock \\\\& West 1992)]{pew92} Peacock, J.A. \\\\& West, M.J. 1992,\\n \\\\mnras, 259, 494\\n\\\\bibitem[(Postman et al. 1992)]{pos92} Postman, M.,\\n Huchra, J. P., \\\\& Geller, M. J. 1992, \\\\apj, ~384, 404\\n\\\\bibitem[(Retzlaff {\\\\it et al.} 1998)]{ret98} Retzlaff, J., Borgani, S., Gottl\\\\\\\"{o}ber, S., \\n Klypin, A., \\\\& M\\\\\\\"{u}ller, V. 1998, NewA, 3, 631\\n\\\\bibitem[(Schlegel {\\\\it et al.} 1998)]{sch98} Schlegel, D.J., Finkbeiner, D.P., \\\\& Davis, M.\\n 1998, \\\\apj, 500, 525\\n\\\\bibitem[(Schramm \\\\& Turner 1998)]{sch98} Schramm, D.N. \\\\& Turner, M.S. 1998, Rev. Mod. Phys., 70, 303\\n\\\\bibitem[(Seljak \\\\& Zaldarriaga 1996)]{sel96} Seljak, U. \\\\& Zaldarriaga, M. 1996, \\\\apj, 469, 437\\n\\\\bibitem[(Slinglend {\\\\it et al.} 1998)]{sli98} Slinglend, K.A., Batuski, D.J,\\n Miller, C.M., Haase. S., Michaud, K., \\\\& Hill, J.M. 1998, \\\\apjsupp, 115,1\\n\\\\bibitem[(Stark {\\\\it et al.} 1992)]{sta92} Stark, A.A., Gammie, C.F., Wilson, R.W.,\\n Bally, J.L., Linke, R.A., Heiles, C., \\\\& Hurwitz, M. 1992, \\\\apjsupp, 79, 77\\n\\\\bibitem[(Sutherland 1988)]{sut88} Sutherland, W. 1988, \\\\mnras, ~234, 159\\n\\\\bibitem[(Tadros \\\\& Efstathiou 1996)]{tad96} Tadros, H., \\\\& Efstathiou, G. 1996, \\n \\\\mnras, 282, 1381 (TE96)\\n\\\\bibitem[(Tadros, Efstathiou \\\\& Dalton 1998)]{tad98} Tadros, H.,Efstathiou, G., \\\\& Dalton, G.\\n 1998, \\\\mnras, 296, 995 (TED98)\\n\\\\bibitem[(Tegmark 1995)]{teg95} Tegmark, M. 1995, \\\\apj, 455, 429\\n\\\\bibitem[(Vogeley 1998)]{vog98} Vogeley, M.S. 1998, in {\\\\it The Evolving Universe}, \\n Kluwer Academic Publishers, p. 395\\n\\\\bibitem[(Vogeley et al. 1992)]{vog92} Vogeley, M.S., Park, C., Geller, M.J., \\\\& Huchra, J.P. 1992,\\n \\\\apj, 391, L5\\n\\\\bibitem[(Voges, {\\\\rm et al.} 1999)]{vog99} Voges, W., Ledlow, M.J., Owen, F.N.,\\n \\\\& Burns J.O. 1999, \\\\aj, submitted \\n\\n\\n\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":291,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002296"},"title":{"kind":"string","value":"Primordial Nucleosynthesis For The New Millennium"},"authors":{"kind":"list like","value":[{"author":"G. Steigman"}],"string":"[\n {\n \"author\": \"G. Steigman\"\n }\n]"},"abstract":{"kind":"string","value":"The physics of the standard hot big bang cosmology ensures that the early Universe was a primordial nuclear reactor, synthesizing the light nuclides (D, \\3he, \\4he, and \\7li) in the first 20 minutes of its evolution. After an overview of nucleosynthesis in the standard model (SBBN), the primordial abundance yields will be presented, followed by a status report (intended to stimulate further discussion during this symposium) on the progress along the road from observational data to inferred primordial abundances. Theory will be confronted with observations to assess the consistency of SBBN and to constrain cosmology and particle physics. Some of the issues/problems key to SBBN in the new millenium will be highlighted, along with a wish list to challenge theorists and observers alike."},"latex":{"kind":"list like","value":[{"name":"paper.tex","string":"%\\documentstyle[11pt,newpasp,twoside]{article}\n\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n%\\documentstyle[12pt]{article}\n%\\input terry.tex\n\\markboth{G. Steigman}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n% definitions\n%\\def\\la{\\lower0.6ex\\vbox{\\hbox{$ \\buildrel{\\textstyle \n%<}\\over{\\sim}\\ $}}}\n%\\def\\ga{\\lower0.6ex\\vbox{\\hbox{$ \\buildrel{\\textstyle \n%>}\\over{\\sim}\\ $}}}\n\\def\\sun{${\\,_\\odot}$}\n\\def\\msun{${\\,M_\\odot}$}\n\\def\\hii{H\\thinspace{$\\scriptstyle{\\rm II}$}~}\n\\def\\Oii{O\\thinspace{$\\scriptstyle{\\rm II}$}}\n\\def\\Oiii{O\\thinspace{$\\scriptstyle{\\rm III}$}}\n\\def\\Nii{N\\thinspace{$\\scriptstyle{\\rm II}$}}\n\\def\\Sii{S\\thinspace{$\\scriptstyle{\\rm II}$}}\n\\def\\etal{{\\it et al.}~}\n\\def\\ie{{\\it i.e.},~}\n\\def\\eg{{\\it e.g.},~}\n\\def\\3he{$^3$He}\n\\def\\4he{$^4$He}\n\\def\\6li{$^6$Li}\n\\def\\7li{$^7$Li}\n\\def\\3h{$^3$H}\n\\def\\Yp{Y$_{\\rm P}$~}\n\n\n\\begin{document}\n\\title{Primordial Nucleosynthesis For The New Millennium}\n\\author{G. Steigman}\n\\affil{Departments of Physics and Astronomy; The Ohio State University; \n174 West 18th Avenue; Columbus, OH 43210 USA}\n\n\\begin{abstract}\nThe physics of the standard hot big bang cosmology ensures that the early \nUniverse was a primordial nuclear reactor, synthesizing the light nuclides \n(D, \\3he, \\4he, and \\7li) in the first 20 minutes of its evolution. After \nan overview of nucleosynthesis in the standard model (SBBN), the primordial \nabundance yields will be presented, followed by a status report (intended \nto stimulate further discussion during this symposium) on the progress along \nthe road from observational data to inferred primordial abundances. Theory \nwill be confronted with observations to assess the consistency of SBBN and \nto constrain cosmology and particle physics. Some of the issues/problems \nkey to SBBN in the new millenium will be highlighted, along with a wish \nlist to challenge theorists and observers alike.\n\\end{abstract}\n\n\\section{Introduction}\n\nAmong the quantitative, ``hard\" sciences, astronomy has traditionally \nbeen scorned, with particular disdain reserved for cosmology. No more. \nIn the decade of the nineties the combination of an avalanche of high \nquality observational data and theoretical advances driven by enhaced \ncomputer (and brain) power, have succeeded in transforming cosmology to \na precise science. In this introductory lecture to IAU Symposium 198 \non The Light Elements and Their Evolution it is my intent to describe \nprimordial nucleosynthesis in this precision era of cosmology and to \nhighlight the challenges, along with some goals, for the new millennium. \nAfter a brief review of the important physics during the era of primordial \nnucleosynthesis in the standard, hot big bang cosmological model (SBBN), \nI will present an overview of the predicted primordial abundances, \nemphasizing the generally very small theoretical uncertainties. These \nwill then be compared to the present best estimates (including their \nuncertainties) of the primordial abundances inferred from current \nobservational data. After assessing the consistency of SBBN, I will \nexplore what SBBN has to offer to Cosmology and to Particle Physics \nand, what Cosmology may teach us about SBBN. I will conclude with a \nsummary of the key issues/problems confronting SBBN and with a wish \nlist of topics I hope will be addressed during this meeting -- and beyond.\n\n\\section{An Early Universe Chronology}\n\nOur story begins when the Universe is a few tenths of a second old and \nthe temperature of the cosmic background radiation has dropped to a few \nMeV as the Universe expanded and cooled from its denser, hotter infancy. \nAt this time (and earlier) the density and average energy of colliding \nparticles is so high that even the weak interactions occur sufficiently \nrapidly to establish equilibrium. In particular, at this stage all flavors \nof neutrinos ($e, \\mu, \\tau$) are in thermal equilibrium with the cosmic \nbackground radiation (CBR) photons and with the copius electron-position \npairs present ($\\nu_{i} + \\bar{\\nu}_{i} \\leftrightarrow e^{+} + e^{-} \n\\leftrightarrow \\gamma + \\gamma$). However, as the Universe ages beyond \na few tenths of a second and the temperature drops below a few MeV, these \nweak interactions become too slow to keep pace with the rapid expansion of \nthe Universe and the neutrinos decouple from the CBR. The electron-type \nneutrinos continue to play a role in transforming neutrons into protons \nand, vice-versa ($p + e^{-} \\leftrightarrow n + \\nu_{e}$, $n + e^{+} \n\\leftrightarrow p + \\bar{\\nu}_{e}$, $n \\leftrightarrow p + e^{-} + \\bar\n{\\nu}_{e}$). As the temperature continues to drop, less massive protons \nare favored over the more massive neutrons and the $n/p$ ratio falls (roughly \nas $e^{-\\Delta m/kT}$, where $\\Delta m$ is the neutron -- proton mass \ndifference $\\sim 1.3$~MeV). After the temperature drops below 800~keV \nor so, when the Universe is a few seconds old, even these weak interactions \nbecome too slow to keep pace with the expansion and the neutron-to-proton \nratio ``freezes out\" (in fact, the ratio continues to decrease, albeit \nvery slowly). All the while, neutrons and protons have been colliding, \noccasionally forming deuterons ($p + n \\rightarrow D + \\gamma$). However, \nthe deuterons find themselves bathed in a high density background of \nenergetic CBR photons which quickly photodissociate them ($D + \\gamma \n\\rightarrow p + n$) before they can find a proton or neutron and form \nthe more tightly bound, less fragile, \\3h or \\3he nuclei. Since, as we \nshall see, there are roughly nine to ten orders of magnitude more CBR \nphotons than nucleons in the Universe, the deuteron ``stepping-stone\" to \nfurther nucleosynthesis is absent until the temperature drops sufficiently \nlow so that even in the high-energy tail of the black-body spectrum there \nare too few photons to prevent the deuteron from acting as a catalyst for \nprimordial nucleosynthesis. This critical temperature, which is weakly \n(logarithmically) dependent on the nucleon abundance (the nucleon-to-photon \nratio $\\eta$), is roughly 80~keV. Now, at last, when the Universe is a \nfew minutes old, Big Bang Nucleosynthesis finally commences. However, \nthe Universe was a fatally flawed nuclear reactor, cooling and diluting \nrapidly as it aged. When the Universe is some 10 -- 20 minutes old \n($\\sim 1000$~sec) and the temperature has dropped below 30~keV or so, \nthe coulomb barriers preventing nuclear reactions between charged nuclei \nand protons and among charged nuclei become insurmountable (in the short \namount of time available) and primordial nucleosynthesis comes to an \nabrupt end. In this all too brief but shining era there has been time \nto synthesize (in abundances comparable to those observed or observable) \nonly the lightest nuclides: D, \\3he, \\4he, and \\7li. In ``standard\" (a \nhomogeneous Universe, expanding isotropically with the particle content \nof the standard model of particle physics in which there are three flavors \nof light ($m \\ll $~MeV) or massless neutrinos) big bang nucleosynthesis \n(SBBN) the abundances (relative to protons $\\equiv$~ hydrogen) of these \nfour nuclides are determined by only one free parameter, the present epoch \nnucleon-to-photon ratio $\\eta$ ($\\eta \\equiv (n_{\\rm N}/n_{\\gamma})_{0}, \n~\\eta_{10} \\equiv 10^{10}\\eta$).\n\n\\section{SBBN-Predicted Primordial Abundances}\n\nOnce the deuterium photodissociation bottleneck is breached primordial \nnucleosynthesis begins in earnest, quickly burning D to \\3h, \\3he and \n\\4he. The higher the nucleon density, the faster D is destroyed. The \nsame is true of \\3h (which, if it survives will decay to \\3he) and \\3he. \nThus, the primordial abundances of D and \\3he are determined by the \ncompetition between the nuclear reaction rates and the universal expansion \nrate. The former rate depends on the overall density of the reactants -- \nthe nucleon density. Since all densities decrease as the Universe expands, \nit is convenient to quantify the nucleon density by specifying the {\\it \nratio} of the nucleon density to the photon density (measured after $e^{+}\ne^{-}$ annihilation which enhances the Universe's photon budget) $\\eta$. \nSince observations of the cosmic background radiation (CBR) temperature \n(T = 2.73~K) determine the present density of CBR photons, a knowledge \nof $\\eta$ is equivalent to a determination of the present mass density \nin nucleons (``baryons\" $\\equiv $~B). In terms of the density parameter\n$\\Omega_{\\rm B}$ (the ratio of the mass density to the critical mass density)\nand the present value of the Hubble parameter (H$_{0} \\equiv 100h$~km/s/Mpc),\n$\\eta_{10} = 273\\Omega_{\\rm B}h^{2}$. As $\\eta$ increases the surviving \nabundances of D and \\3he decrease; since the \\3he nucleus is more tightly \nbound than the deuteron, the decrease of the \\3he/H ratio with $\\eta$ is \nless rapid than that of D/H. \n\nIn contrast to D and \\3he, the primordial abundance of \\4he is not reaction \nrate limited since the nuclear reactions building helium-4 are so rapid \nthat virtually all neutrons available when BBN commences are incorporated \ninto \\4he. As a result the \\4he abundance, conventionally presented as \nthe mass fraction of all nucleons which are in \\4he, Y$_{\\rm P}$, is {\\it \nneutron limited}. Since the neutron-to-proton ratio is determined by the \ncompetition between the (charged-current) weak interactions which mediate \nthe transformation of neutrons into protons (and, vice-versa) and the \nuniversal expansion rate, \\Yp is sensitive to the universal expansion \nrate at the time the $n/p$ ratio ``freezes\" and when the deuterium \nphotodissociation barrier disappears. Since the universal expansion rate \nis controlled by the total energy density, \\Yp provides an important test \nof cosmology and of particle physics in the early Universe (Steigman, \nSchramm \\& Gunn 1977). It should be noted that \\Yp is not entirely \ninsensitive to the nucleon density since the higher $\\eta$, the earlier \nthe photodissociation barrier is overcome. At earlier times when the \ntemperature is higher, fewer neutrons have been transformed into protons \nand are available for incorporation into \\4he. As a result, \\Yp increases \nlogarithmically with $\\eta$.\n\nThere is no stable nucleus at mass-5 and this presents a gap in the \nroad to the synthesis of nuclei heavier than \\4he. In order to bridge \nthe gap nuclear reactions must occur among nuclei with two or more \nnucleons. But, the abundances of D, \\3h, and \\3he are small and the \ncoulomb barriers (especially between \\3he and \\4he and between \\4he \nand \\4he) suppress these reactions as the Universe expands and cools. \nAs a result, there is very little ``leakage\" to nuclei beyond mass-4; \nas a corollary, virtually all the \\4he formed, survives. The only \nheavier nucleus produced primordially in an abundance comparable to \nthat observed (or, even, observable with current technology) is \\7li, \nwhose BBN abundance is some 4 -- 5 orders of magnitude smaller than \nthat of D and \\3he. The absence of a stable nucleus at mass-8 provides \nanother gap preventing the production of astrophysically interesting \nabundances of any heavier nuclei.\n\nAs will become clear in our subsequent discussion, the ``interesting\" \nrange of $\\eta$ is $\\eta_{10} = 1 - 10$ ($\\Omega_{\\rm B}h^{2} = 0.004 \n- 0.037$), so we focus our discussion here on values of $\\eta$ in this \nrange. In the current precision era of BBN {\\it most} of the nuclear\nreactions relevant to the synthesis of the light elements have been\nmeasured to reasonable accuracy at energies directly comparable to the\nthermal energies at the time of primordial nucleosynthesis (\\eg see \nNollett, this volume). As a result, the theoretical uncertainties in\nthe BBN-predicted abundances are generally quite small. For $\\eta$ in\nthe above range, the 1$\\sigma$ uncertainties in D/H and \\3he/H vary\nfrom 8 -- 10\\%. Since \\4he is most sensitive to the very well measured\nweak interaction rates, the error in SBBN-predicted \\Yp is very small \n(0.2 -- 0.5\\% or, $\\sigma_{\\rm Y}$ = 0.0005 -- 0.0011). In contrast,\nlarger uncertainties, of order 12 -- 21\\%, afflict the predicted \nprimordial abundance of \\7li. \n\nSince this Symposium devoted much discussion to \\7li, and space-limitations\nhere prevent me from discussing all the light elements in detail, I will\nconcentrate in the following on the two key light elements, deuterium and \nhelium-4. In Figure 1 is shown the relation between the BBN-predicted\nabundances of D and \\4he. The band going from upper left to lower right\nrepresents the $\\pm 2\\sigma$ range of uncertainties in the primordial \nabundances ((D/H)$_{\\rm P}$ and Y$_{\\rm P}$). Low D/H (high $\\eta$) \ncorresponds to high \\Yp and high D/H (low $\\eta$) corresponds to low \nY$_{\\rm P}$. This anticorrelation will be very important when we \nconfront the predictions of SBBN with the observational data.\n\n\\section{Precise (Accurate?) Primordial Abundances}\n\nTo test SBBN and fully exploit the opportunities it offers to constrain\ncosmology (e.g., the baryon density) and particle physics (e.g., new\nparticles with weak or weaker-than-weak interactions) requires that \nobservational data be used to pin down the primordial abundances of the\nlight elements to precisions as good as (or, better than) those of the\nSBBN predictions. As we approach the new millennium there is good news\nalong with some bad news. The good news is that new detectors on ever\nlarger telescopes which cover the spectrum from radio to x-ray energies\nand beyond are providing very high quality data, leading to inferred\nabundances of high statistical accuracy. Furthermore, the abundances \nof the light elements are determined from observations which differ \nfrom element to element in the telescopes and techniques employed as \nwell as in the astrophysical sites explored. As a result, insidious \ncorrelated errors between and among the various element abundances are \nunlikely to be a problem. The good news is also responsible for the \nbad news. Since the statistical errors have become so small, systematic \nerrors now tend to dominate the uncertainties in the derived primordial \nabundances. As Bob Rood has said during this Symposium, estimating \nsystematic errors is an oxymoron. When a potential source of systematic \nerror is identified, observations can (and should) be designed to \neliminate or bound its contribution to the error budget. It is a \npointless and potentially misleading exercise to ``estimate\" the magnitude \nof unidentified systematic errors. In part to remind us that our precise \nabundance determinations may not be accurate, and in part to challenge \nour observational colleagues who have done such a magnificent job of \nreducing the statistical errors, I will try to focus on the potential \nsources of systematic uncertainty (when I can identify them) in the \nfollowing overview of the current observational status.\n\n\\subsection{Deuterium}\n\nAs J. Linsky (this volume) has reminded us, the deuterium abundance \nin the local interstellar medium (the local interstellar cloud: LIC) \nis known very accurately: (D/H)$_{\\rm LIC} = 1.5 \\pm 0.1 \\times \n10^{-5}$ (Linsky 1998). Since deuterium is only destroyed during \nthe evolution of the Galaxy (Epstein, Lattimer \\& Schramm 1976), the \nLIC abundance provides a lower bound to its primordial (pre-Galactic) \nvalue. This bound is strong enough to bound the nucleon density from \nabove ($\\eta_{10} \\la 10$; $\\Omega_{\\rm B}h^{2} \\la 0.04$), ensuring \nthat baryons cannot ``close\" the Universe ($\\Omega_{\\rm B} \\ll 1$), \nnor even dominate its present mass density ($\\Omega_{\\rm B} \\ll \n\\Omega_{\\rm M} \\approx 0.3 - 0.4$). Thus, local observations of \ndeuterium, combined with the {\\it assumption} of the correctness \nof SBBN (which we must test), already reaps great rewards: the \nmass-energy density of the Universe must be dominated by unseen \n(``dark\") non-baryonic matter. To go beyond (in the quest for the \nprimordial deuterium abundance) we must look for observing targets \nwhich are less evolved than the LIC. The presolar nebula is one such \nsite. From solar system observations of \\3he reported by G. Gloeckler \n(this volume), it is possible to infer the presolar deuterium abundance \n(Geiss \\& Reeves 1972; Geiss \\& Gloecker 1998): (D/H)$_{\\odot} = 1.9 \n\\pm 0.5 \\times 10^{-5}$. Although marginally higher than the LIC \nabundance, the larger errors prevent us from using this determination \nto improve on our previous bounds from the LIC. What this result does \nindicate is that there has been very little (if any) evolution in the \nD-abundance in the solar vicinity of the Galaxy in the last 4.5~Gyr. \nThis is consistent with a large class of Galactic chemical evolution \nmodels discussed by M. Tosi (this volume) which point to only a modest \noverall destruction of primordial deuterium by a factor of 2 -- 3 \n(Tosi et al. 1998). If this theoretical estimate is combined with the \nLIC abundance, we may estimate the primordial abundance: (D/H)$_{\\rm P} \n\\approx 2.6 - 5.1 \\times 10^{-5}$ ($\\sim 2\\sigma$). Although possibly \nmodel dependent, this estimate is in remarkable agreement with the \n2 -- 3 determinations of D/H in high-redshift, low-metallicity (hence \nvery nearly primordial) Ly-$\\alpha$ absorbers illuminated by background \nQSOs described by D. Tytler and S. Levshakov (this volume). The \ndata and analysis of Burles \\& Tytler (1998a,b: BT) suggests that \n(D/H)$_{\\rm P} = 2.9 - 4.0 \\times 10^{-5}$ ($\\sim 2\\sigma$). Notice \nthat the 1$\\sigma$ uncertainty in the observationally determined \nprimordial abundance, $\\sim 8$\\%, is impedance-matched to the \n$\\sim 8$\\% SBBN theoretical uncertainty cited earlier. However, \nlest we risk dislocating a shoulder while patting ourselves on the \nback at the triumph of such wonderful data, we should not ignore \nthe claim (Webb et al. 1997; Tytler et al. 1999) that the deuterium \nabundance in at least one Ly-$\\alpha$ absorption system may be much \nhigher. This is a reminder that while any determination of the \ndeuterium abundance anywhere in the Universe (LIC, solar system, \nLy-$\\alpha$ absorbers, etc.) provides a {\\it lower} bound to primordial \ndeuterium, finding an upper bound is more problematic. Indeed, in \nsome absorbing systems it may be impossible to distinguish D-absorption \nfrom that due to hydrogen in an interloping, low column density, \n``wrong-velocity\" system. Thus, the deuterium abundance inferred \nfrom absorption-line data may only provide an {\\it upper} bound to \nthe true deuterium abundance. Since the low-Z, high-z QSO absorbing \nsystems hold the greatest promise of revealing for us nearly unevolved, \nnearly primordial material, we look forward to the time when we can \nuse the {\\it distribution} of D/H values from more than a handful of \nsuch systems to eliminate -- statistically -- the uninvited contribution \nto the inferred primordial deuterium abundance from such interlopers. \nKeeping this in mind, in the following I will, nevertheless, use the \nBT determination when confronting theory with data. \n\n\\subsection{Helium-4}\n\nIn contrast to deuterium whose primordial abundance only decreases \nas pristine gas is incorporated into stars, stars burn hydrogen to \nhelium. As a result, the \\4he observed anywhere in the Universe is \nan unknown mixture of primordial and stellar-produced helium. It has \nlong been appreciated that to minimize the uncertain correction due \nto the debris of stellar evolution, it is best to concentrate on \\4he \nabundance determinations in the lowest-metallicity regions available. \nThese are the low-Z, extragalactic \\hii regions which have been discussed \nby K. Olive, T. Thuan, and S. M. Viegas at this Symposium (this volume). \nThe reader is urged to consult their papers for details; here I will \nmerely summarize my view of the current status of the determination \nof the primordial \\4he mass fraction Y$_{\\rm P}$. Several years ago \nOlive \\& Steigman (1995: OS) gathered together the data from the literature \n(dominated by the data assembled by Pagel et al. 1992). More recently \nOlive, Skillman \\& Steigman (1997: OSS) supplemented this with newer \ndata (some of it, unfortunately, still unpublished). Using a variety \nof approaches such as the regression of Y on the oxygen and/or nitrogen\nabundances and the weighted means of Y in the lowest metal-abundance \n\\hii regions, OSS concluded that \\Yp = 0.234 $\\pm$ 0.003 (note that, \nin contrast to the published (OSS) result, this value is obtained when \nthe NW region of IZw18, suspected of being contaminated by underlying \nstellar absorption, is excluded from the fit, and the newer data of \nIzotov, Thuan and collaborators is not included). Izotov, Thuan \nand their collaborators (Izotov, Thuan, \\& Lipovetsky 1994, 1997; \nIzotov \\& Thuan 1998(IT); Thuan, this volume) have been systematically \nobserving a mostly independent set of \\hii regions. Although, as \nwith the data employed in the OS and OSS studies, they ignore the \nionization correction ($icf \\equiv 1$), they take special care with \nthe correction for collisional excitation. IT (also Thuan, this volume) \nfind Y$_{\\rm P}({\\rm IT}) = 0.244~\\pm$ 0.002. Comparing the IT and OSS \nestimates of \\Yp we find that difference between the two \\Yp estimates \nfar exceeds the statistical errors, suggesting systematic differences \nin the acquisition and/or analysis of the data samples. In a recent \ndiscussion which attempted to account for these unidentified systematic \ndifferences, Olive, Steigman \\& Walker (1999: OSW) combined the 2$\\sigma$ \nranges for each determination to conclude: \\Yp = 0.238 $\\pm$ 0.005; at \nthe 2$\\sigma$ level, \\Yp $\\leq 0.248$. Note, that this is also the \n2$\\sigma$ upper bound to the IT data alone. Since, as we shall see \nshortly, it is the upper bound which is crucial to testing the consistency \nof SBBN, in the following we shall adopt the IT value (and error estimate) \nfor the primordial abundance of \\4he. \n\nRecently, Viegas, Gruenwald \\& Steigman (1999: VGS; see Viegas \\& \nGruenwald, this volume) have emphasized the importance of the ionization \ncorrection which has heretofore been ignored. VGS suggest that the \nIT helium abundance (Y$_{\\rm P}$) should be reduced by 0.003 to account \nfor unseen neutral hydrogen in regions where the helium is still ionized \nin \\hii regions ionized by young, hot, metal-poor stars. In subsequent \ncomparisons I shall explore the implications of adopting Y$_{\\rm P}({\\rm \nVGS}) = 0.241~\\pm$ 0.002.\n\n\\subsection{Helium-3 and Lithium-7}\n\nThe cosmic history of the two other light nuclides produced in\nastrophysically interesting abundances during SBBN, \\3he and \n\\7li, is considerably more complex than that of D or \\4he, which \nlimits their utility as probes of the consistency of SBBN. \\3he \nis destroyed in the hotter interiors of all stars, but some \\3he \ndoes survive in the cooler, outer layers. For lower mass stars \nthis \\3he survival layer increases and, indeed, newly synthesized \n\\3he is produced by incomplete hydrogen burning. The competition \nbetween destruction, survival, and synthesis complicates the Galactic\nhistory of the \\3he abundance. Nonetheless, since any deuterium \nincorporated into stars is first burned to \\3he, the apparent lack \nof enhanced \\3he (see Bania \\& Rood, this volume) argues against \na very large pre-Galactic abundance of deuterium (Steigman \\& Tosi \n1995). For further discussion of the evolution of \\3he see Bania \n\\& Rood (this volume).\n\nAs with \\3he, any \\7li incorporated into stars is quickly burned \naway. However, fusion and spallation reactions between cosmic ray \nnuclei and those in the interstellar medium are a potent source of \n\\7li (as well as of \\6li, $^7$Be, $^{10}$B, and $^{11}$B). It is\nalso likely that there are stellar sources of \\7li as indicated \nby the sample of lithium-rich red giants (V. Smith, this volume). \nSince the abundance of lithium in the solar system and in the \ninterstellar medium (``here and now\") greatly exceeds that in the \nvery metal-poor halo stars (T. Beers \\& S. Ryan, this volume), the \nlatter likely provide the closest approach to a nearly primordial \nsample. Since a significant fraction of this Symposium is devoted \nto lithium, I will defer here to those other discussions except to \ncomment that, within the theoretical and observational uncertainties, \nthe primordial abundances inferred from the observational data are \nconsistent with SBBN constrained by the confrontation with D and \\4he.\n\n\\section{Confrontation Of SBBN With Data}\n\nAlthough SBBN does lead to the prediction of the abundances of D, \n\\3he, \\4he, and \\7li, the currently best-constrained primordial \nabundances are those of deuterium and helium-4 which we are \nconcentrating on in this status report. For each value of $\\eta$, \nSBBN predicts a pair of (D/H)$_{\\rm P}$ and \\Yp values. Therefore, \nin SBBN there is a unique connection between (D/H)$_{\\rm P}$ and \n\\Yp which, allowing for the theoretical uncertainties discussed \nabove, is shown as the band (solid lines) in Figure 1 going from \nthe upper left to the lower right (2$\\sigma$ uncertainties). Note \nthat high-helium correlates with low-deuterium and, vice-versa. \nAlso shown as the dotted ellipse in Figure 1 is the contour of the \n(independent) 2$\\sigma$ uncertainties in the BT deuterium abundance \nand the IT helium-4 mass fraction. \n\n\\begin{figure}\n\\vspace{1.in}\n%\\plotone{fig1.eps}\n\\plotfiddle{fig1.eps}{1in}{0}{30}{30}{-100}{-50}\n\\caption{The SBBN-predicted \\4he mass fraction \\Yp as a function \nof the SBBN-predicted primordial deuterium-to-hydrogen ratio D/H \nis shown (at the $\\pm 2\\sigma$ level) by the solid lines. The \ndotted ellipse is the 95\\% contour of the BT deuterium abundance \nand the IT \\4he mass fraction (see the text).}\n\\end{figure}\n\nAlthough the overlap between theory and data is not complete, \nFigure 1 shows that, at the $\\sim 2\\sigma$ level, the predictions \nof SBBN are consistent with current observational data. This is \na dramatic success for the standard hot, big bang cosmological \nmodel. Of course it is not at all surprising that some value \nof $\\eta$ may be found to provide consistency with the inferred \nprimordial deuterium abundance. But there was no guarantee at \nall that the helium-4 abundance corresponding to this choice would \nbear any relation to its inferred primordial value. Consistency \nwith the BT D-abundance limits the nucleon abundance to the range \n(2$\\sigma$) $\\eta_{10} = 4.4 - 5.9$ or, $\\Omega_{\\rm B}h^{2} = \n0.016 - 0.022$. For $\\eta$ in this range there is consistency, \nwithin the theoretical and observational uncertainties, between \nthe SBBN-predicted and observationally inferred primordial abundances \nof \\3he and \\7li as well. Four for the price of one! There is, \nof course, one more test -- and opportunity -- offered by this \nresult. This SBBN-inferred nucleon abundance must also be \nconsistent with present epoch estimates of the baryon density. \nIndeed, the SBBN-determined value of $\\Omega_{\\rm B}$ is {\\it \nlarger} than estimates (Persic \\& Salucci 1992) of the ``luminous\" \nmatter in the Universe suggesting that the majority of baryons \nare ``dark\". This is good ($\\Omega_{\\rm B} > \\Omega_{\\rm LUM}$); \nthe opposite would have been a disaster. This early-Universe \nestimate of the baryon density is in good agreement with that \ninferred from the X-ray cluster baryon fraction (Steigman, Hata \n\\& Felten 1999) and with the independent estimate from the \nLy-$\\alpha$ forest (Weinberg et al. 1997) discussed below.\n\n\\subsection{What BBN May Do For Cosmology}\n\nX-ray clusters likely provide a ``fair\" sample of the universal\nbaryon {\\it fraction} $f_{\\rm B}$ (White et al. 1993; Steigman \n\\& Felten 1995; Evrard, Metzler, \\& Navarro 1996) which, when \ncombined with the SBBN-inferred baryon density $\\Omega_{\\rm B}$, \nleads to a ``clean\" prediction, independent of detailed cosmological \nmodels, of the overall matter density $\\Omega_{\\rm M}$. If the \nresults presented here are combined with the determination of \n$f_{\\rm B}$ from Evrard (1997), and with a Hubble parameter $h \n= 0.70 \\pm 0.07$ (Mould et al. 1999), we predict $\\Omega_{\\rm M} \n= 0.35 \\pm 0.08$, in excellent agreement with several other recent, \nindependent determinations. For example, a lower bound to the cosmic \nbaryon density follows from the requirement that the high-redshift \nintergalactic medium contain enough neutral hydrogen to produce\nthe Ly-$\\alpha$ absorption observed in quasar spectra. According\nto Weinberg et al. (1997), depending on estimates of the quasar\nUV background intensity, this lower bound corresponds to $\\eta_{10}\n\\ga 3.4 - 4.9$, in excellent agreement with the SBBN prediction\nbased on the BT deuterium determination. Note that this lower\nbound from the Ly-$\\alpha$ absorption forbids (in the context of\nSBBN) the primordial deuterium abundance to be any larger than\n$\\sim 8 \\times 10^{-5}$, largely excluding the one surviving\nclaim of high D (Webb et al. 1997).\n\nIndeed, if the SBBN results are combined with the magnitude-redshift \ndata from surveys of high-redshift Type Ia supernovae (Garnavich et \nal. 1998; Perlmutter et al. 1999) which bound a linear combination \nof $\\Omega_{\\rm M}$ and the cosmological constant $\\Omega_{\\Lambda} \n\\equiv \\Lambda/3$H$_{0}^{2}$, we may also constrain the cosmological \nconstant ($\\Omega_{\\Lambda} = 0.80 \\pm 0.20$), the curvature \n($\\Omega_{k} \\equiv 1 - (\\Omega_{\\rm M} + \\Omega_{\\Lambda}) = \n-0.15 \\pm 0.25$), and the deceleration parameter ($q_{0} = \n\\Omega_{\\rm M}/2 - \\Omega_{\\Lambda} = -0.62 \\pm 0.18$).\n\n\\subsection{What Cosmology May Do For BBN}\n\nAs we have just seen, the SBBN-determined baryon density is \nconsistent with that determined or constrained by observations \nof the Universe during its present or recent evolution. We \nmay turn the argument around and ask what baryon density is \nsuggested by non-BBN contraints, and then compare the light \nelement abundances which correspond to that density with those \ninferred from the observational data. As an exercise of this \nsort, suppose (for reasons of ``naturalness\" or inflation) that \nthe Universe is ``flat\": $\\Omega_{\\rm M} + \\Omega_{\\Lambda} \n= 1$. When combined with the SN Ia magnitude-redshift data \n(Perlmutter et al. 1999), this suggests that $\\Omega_{\\rm M} \n= 0.29 \\pm 0.07$ (and $\\Omega_{\\Lambda} = 0.71 \\pm 0.07$).\nNow, if this mass density estimate ($\\Omega_{\\rm M}$) is \ncombined with with the X-ray determined cluster baryon fraction \n$f_{\\rm B}$ (Evrard 1997; Steigman, Hata \\& Felten 1999), \nthe resulting nucleon abundance is $\\eta_{10} = 4.5 \\pm 1.5$. \nAlthough the uncertainty is large, it is reassuring that this \nnon-BBN estimate has significant overlap with our SBBN estimate.\nIndeed, for the baryon density in this range SBBN predicts:\n(D/H)$_{\\rm P} = 4.3 \\pm 2.3 \\times 10^{-5}$ and Y$_{\\rm P} \n= 0.245 \\pm 0.004$. \n\n\\subsection{What SBBN May Do For Particle Physics}\n\nThe expansion rate of the early Universe is controlled by the\ndensity of the relativistic particles present. In the standard\nmodel at the time of BBN these are: photons, electron-positron\npairs (when T $ \\ga m_{e}$) and three ``flavors\" of neutrinos\n($\\nu_{e}$, $\\nu_{\\mu}$, $\\nu_{\\tau}$) which, if ``light\" ($m_{\\nu}\n\\ll 1$~MeV), are relativistic at BBN even if one or more of them\nmay contribute to the present density of non-relativistic (``hot\")\ndark matter. If ``new\" particles were to contribute to the energy \ndensity at BBN, the increase in the density would result in an\nincrease in the universal expansion rate, leaving less time for\nneutrons to transform into protons. The higher $n/p$ ratio at BBN\nwould result in the production of more primordial \\4he (Steigman,\nSchramm \\& Gunn 1977). It is convenient (and conventional) to\ncharacterize such additional contributions to the energy density\nby comparing their effects to that of an additional ``flavor\" of\n(light) neutrino: $\\Delta\\rho \\equiv \\Delta N_{\\nu}\\rho_{\\nu}$.\nFor $\\Delta N_{\\nu}$ small, $\\Delta $Y $ \\approx 0.01\\Delta N_{\\nu}$.\nNotice in Figure 1 that the predicted \\4he abundance is a little\nhigh for perfect overlap with the observations. If $\\Delta N_{\\nu}$ \nwere $ < 0$, (N$_{\\nu} \\approx 2.8$) the overlap would improve (e.g., \nHata et al. 1995), while if $\\Delta N_{\\nu} > 0$, the overlap would \nbe reduced until it disappeared. This is illustrated in Figure 2 \nwhich shows the Y versus D/H BBN band that would result if $\\Delta \nN_{\\nu} = 0.2$ (i.e., $N_{\\nu} = 3.2$, in contrast to the SBBN value \nof 3.0). Notice that due to the faster expansion, more deuterium \nsurvives being burnt away so that, for fixed $\\eta$, the D-abundance \nalso increases; however since D/H is a much more sensitive function \nof $\\eta$, this has a much smaller effect on the Y versus D/H relation \nthan does the increase in Y.\n\n\\begin{figure}\n\\vspace{1.in}\n%\\plotone{fig2.eps}\n\\plotfiddle{fig2.eps}{1in}{0}{30}{30}{-100}{-50}\n\\caption{As Figure 1, but for $N_{\\nu} = 3.2$}\n\\end{figure}\n\n\\section{Conclusions And Outlook}\n\nThe study of the early evolution of the Universe and, in\nparticular primordial nucleosynthesis, has truly entered\nthe precision era of cosmology. Precise abundances of the \nlight nuclides are predicted and inferred from observations\nand the two are -- apparently -- in excellent agreement.\nAs pleased as we may be at this success, it behooves us\nto avoid the temptation to rest on our laurels and to\ntest this consistency ever more carefully. To this end,\nit doesn't take much contemplation to identify several\nclouds looming on the horizon. What follows is my\npersonal list of some problems/issues I would like \nto see addressed at this Symposium and beyond.\n\n\\subsection{Problems/Issues}\n\nFirst consider deuterium. On the one hand, any determination\nof the D/H ratio anywhere, anytime provides a {\\it lower}\nbound to the primordial abundance. On the other hand, since\n``wrong\" velocity hydrogen can masquerade as deuterium, any\nobservation of ``deuterium\" is really an {\\it upper} bound \nto its true abundance. More data tracking the velocity\nstructure of the absorbing features used to identify D \nand H and exploring variations in D/H in material with \nsimilar histories will be very valuable. More data at \nhigh-redshift and low-metallicity will be very valuable. \nAfter all, at present we are drawing profound conclusions \non the basis of only two such systems.\n\nMuch remains to be done concerning the primordial abundance\nof \\4he. For the most part, the \\hii regions from which\nthe helium abundance is inferred have been modelled as\nhomogeneous spheres or plane-parallel slabs. A glance at \nthe beautiful HST images of real \\hii regions reveals that \nthey are anything but such idealizations. What are the effects \nof temperature and/or density inhomogeneities, and how large \nmay they be? What of underlying stellar absorption which, if \npresent but neglected, would lead to an {\\it under}estimate \nof the helium abundance. And, what of the usually neglected\nionization correction for neutral hydrogen and helium (Viegas, \nGruenwald \\& Steigman 1999; see Viegas \\& Gruenwald, this \nvolume)? Considering this latter work, where models of \\hii \nregions ionized by realistic spectra of young star clusters \nwere used in a reanalysis of the IT data, a {\\it reduction} \nin \\Yp of order 0.003 was suggested. A comparison with Figure \n1 shows that if \\Yp were reduced by this amount, the overlap \nbetween theory and data would, in fact, disappear.\n\n\\subsection{Wish List}\n\nGiven the setting of this Symposium (Natal) and the proximity\nto the Christmas season, I'd like to conclude with my personal\nwish list. To avoid being greedy, I'll only ask for two gifts.\n\nA half-dozen or so observations of deuterium in high-z, low-Z \nsystems along the lines-of-sight to distant quasars, with D/H \ndetermined in each (on average) to 10\\% or better. With such \na gift, I could determine $\\eta$ to better than 4\\%, predict\n\\Yp to $\\la 0.0007$, and constrain $\\Delta N_{\\nu}$ to an \nuncertainty less than $\\pm$~0.05. I'd be a very happy \ncosmologist indeed.\n\nMy second wish is for \\4he measured to 3\\% accuracy (or better)\nin each of about a dozen low-metallicity, extragalactic \\hii \nregions, with care taken to address the several problems outlined \nabove. With such data, \\Yp could be fixed to better than the \ncurrent level of $\\pm 0.002$, permitting \\4he to be used as a \nbaryometer ($\\Delta\\eta/\\eta~\\la 20\\%$).\n\n%\\end{document} \n\n\\acknowledgments\n\nMuch of what I know about this subject I have learned from my \ncollaborators and I would be remiss if I failed to thank them \nfor their contributions. In particular, I wish to acknowledge\nR. Gruenwald, K. Olive, E. Skillman, M. Tosi, and S. M. Viegas \nand, of course, my late friend Dave Schramm. L. da Silva, M. \nSpite and the Scientific and Local Organizing committees deserve \ngreat credit for their efficient organization of a very enjoyable \nand successful meeting. In part, this work is supported at The \nOhio State University by DOE grant DE--AC02--76ER--01545. \n\n\\begin{references}\n\n\\reference Burles, S., \\& Tytler, D. 1998a, \\apj, 499, 699 (BT)\n\n\\reference Burles, S., \\& Tytler, D. 1998b, \\apj, 507, 732 (BT)\n\n\\reference Epstein, R. Lattimer, J., \\& Schramm, D. N. 1976, \nNature, 263, 198\n\n\\reference Evrard, A. E. 1997, \\mnras, 292, 289 \n\n\\reference Evrard, A. E., Metzler, C. A., \\& Navarro, J. F. 1996,\n\\apj, 469, 494\n\n\\reference Garnavich, P. M. et al. 1998, \\apj, 509, 74\n \n\\reference Geiss, J., \\& Reeves, H. 1972, \\aap, 18, 126\n\n\\reference Geiss, J., \\& Gloeckler, G. 1998, \\ssr, 84, 239\n\n\\reference Hata, N., Scherrer, R. J., Steigman, G., Thomas, D., \nWalker, T. P., Bludman, S., \\& Langacker P. 1995, \\prl, 75, 3977\n\n\\reference Linsky, J. L. 1998, \\ssr, 84, 285\n \n\\reference Izotov, Y. I., Thuan, T. X., \\& Lipovetsky, V. A. 1994, \n\\apj, 435, 647\n\n\\reference Izotov, Y. I., Thuan, T. X., \\& Lipovetsky, V. A. 1997, \n\\apjs, 108, 1\n\n\\reference Izotov, Y. I., \\& Thuan, T. X. 1998, \\apj, 500, 188 (IT)\n\n\\reference Mould, J. R. et al. 1999, \\apj, submitted (astro-ph/9909260)\n\n\\reference Olive, K. A., Skillman, E., \\& Steigman, G. 1997, \\apj, 483, \n788 (OSS)\n\n\\reference Olive, K. A., \\&, Steigman, G. 1995, \\apjs, 97, 49 (OS)\n\n\\reference Olive, K. A., \\&, Steigman, G., \\& Walker, T. P. 1999, Physics\nReports, in press (astro-ph/9905320) (OSW)\n\n\\reference Pagel, B. E. J., Simonson, E. A., Terlevich, R. J. \\& Edmunds, \nM. 1992, \\mnras, 255, 325\n\n\\reference Perlmutter, S. et al. 1999, \\apj, 517, 565 \n\n\\reference Persic, M., \\& Salucci, P. 1992, \\mnras, 258, 14P\n\n\\reference Steigman, G., Schramm, D. N., \\& Gunn, J. E. 1977, Phys. Lett.,\nB66, 202\n\n\\reference Steigman, G., \\& Felten, J. E. 1995, \\ssr, 74, 245\n\n\\reference Steigman, G., Hata, N., \\& Felten, J. E. 1999, \\apj, 510, 564\n\n\\reference Steigman, G., \\& Tosi, M. 1995, \\apj, 453, 173\n\n\\reference Tosi, M., Steigman, G., Matteucci, F., \\& Chiappini, C. 1998,\n\\apj, 498, 226\n\n\\reference Tytler, D., Burles, S., Lu, L., Fan, X. M., Wolfe, A., \\&\nSavage, B. D. 1999, \\aj, 117, 63\n \n\\reference Viegas, S.M., Gruenwald, R., \\& Steigman, G. 1999, \\apj, 532 \n(in press, March 20, 2000; astro-ph/9909213)\n\n%\\reference Vilchez, J.M. \\& Pagel, B.E.J. 1988, MNRAS, 231, 257\n\n\\reference Webb, J. K., Carswell, R. F., Lanzetta, K. M., Ferlet, R., \nLemoine, M., Vidal-Madjar, A., \\& Bowen, D. V. 1997, Nature, 388, 250\n\n\\reference Weinberg, D. H., Miralda-Escud$\\acute{\\rm e}$, J., Hernquist, \nL., \\& Katz, N. 1997, \\apj 490, 564\n\n\\reference White, S. D. M., Navarro, J. F., Evrard, A. E., \\& Frenk,\nC. S. 1993, Nature, 366, 429\n\n\\end{references}\n\n\n\\end{document}\n\n\n\n"}],"string":"[\n {\n \"name\": \"paper.tex\",\n \"string\": \"%\\\\documentstyle[11pt,newpasp,twoside]{article}\\n\\\\documentstyle[11pt,newpasp,twoside,epsf]{article}\\n%\\\\documentstyle[12pt]{article}\\n%\\\\input terry.tex\\n\\\\markboth{G. Steigman}{APS Conf. Ser. Style}\\n\\\\pagestyle{myheadings}\\n\\\\nofiles\\n\\n% Some definitions I use in these instructions.\\n\\n\\\\def\\\\emphasize#1{{\\\\sl#1\\\\/}}\\n\\\\def\\\\arg#1{{\\\\it#1\\\\/}}\\n\\\\let\\\\prog=\\\\arg\\n\\n\\\\def\\\\edcomment#1{\\\\iffalse\\\\marginpar{\\\\raggedright\\\\sl#1\\\\/}\\\\else\\\\relax\\\\fi}\\n\\\\marginparwidth 1.25in\\n\\\\marginparsep .125in\\n\\\\marginparpush .25in\\n\\\\reversemarginpar\\n% definitions\\n%\\\\def\\\\la{\\\\lower0.6ex\\\\vbox{\\\\hbox{$ \\\\buildrel{\\\\textstyle \\n%<}\\\\over{\\\\sim}\\\\ $}}}\\n%\\\\def\\\\ga{\\\\lower0.6ex\\\\vbox{\\\\hbox{$ \\\\buildrel{\\\\textstyle \\n%>}\\\\over{\\\\sim}\\\\ $}}}\\n\\\\def\\\\sun{${\\\\,_\\\\odot}$}\\n\\\\def\\\\msun{${\\\\,M_\\\\odot}$}\\n\\\\def\\\\hii{H\\\\thinspace{$\\\\scriptstyle{\\\\rm II}$}~}\\n\\\\def\\\\Oii{O\\\\thinspace{$\\\\scriptstyle{\\\\rm II}$}}\\n\\\\def\\\\Oiii{O\\\\thinspace{$\\\\scriptstyle{\\\\rm III}$}}\\n\\\\def\\\\Nii{N\\\\thinspace{$\\\\scriptstyle{\\\\rm II}$}}\\n\\\\def\\\\Sii{S\\\\thinspace{$\\\\scriptstyle{\\\\rm II}$}}\\n\\\\def\\\\etal{{\\\\it et al.}~}\\n\\\\def\\\\ie{{\\\\it i.e.},~}\\n\\\\def\\\\eg{{\\\\it e.g.},~}\\n\\\\def\\\\3he{$^3$He}\\n\\\\def\\\\4he{$^4$He}\\n\\\\def\\\\6li{$^6$Li}\\n\\\\def\\\\7li{$^7$Li}\\n\\\\def\\\\3h{$^3$H}\\n\\\\def\\\\Yp{Y$_{\\\\rm P}$~}\\n\\n\\n\\\\begin{document}\\n\\\\title{Primordial Nucleosynthesis For The New Millennium}\\n\\\\author{G. Steigman}\\n\\\\affil{Departments of Physics and Astronomy; The Ohio State University; \\n174 West 18th Avenue; Columbus, OH 43210 USA}\\n\\n\\\\begin{abstract}\\nThe physics of the standard hot big bang cosmology ensures that the early \\nUniverse was a primordial nuclear reactor, synthesizing the light nuclides \\n(D, \\\\3he, \\\\4he, and \\\\7li) in the first 20 minutes of its evolution. After \\nan overview of nucleosynthesis in the standard model (SBBN), the primordial \\nabundance yields will be presented, followed by a status report (intended \\nto stimulate further discussion during this symposium) on the progress along \\nthe road from observational data to inferred primordial abundances. Theory \\nwill be confronted with observations to assess the consistency of SBBN and \\nto constrain cosmology and particle physics. Some of the issues/problems \\nkey to SBBN in the new millenium will be highlighted, along with a wish \\nlist to challenge theorists and observers alike.\\n\\\\end{abstract}\\n\\n\\\\section{Introduction}\\n\\nAmong the quantitative, ``hard\\\" sciences, astronomy has traditionally \\nbeen scorned, with particular disdain reserved for cosmology. No more. \\nIn the decade of the nineties the combination of an avalanche of high \\nquality observational data and theoretical advances driven by enhaced \\ncomputer (and brain) power, have succeeded in transforming cosmology to \\na precise science. In this introductory lecture to IAU Symposium 198 \\non The Light Elements and Their Evolution it is my intent to describe \\nprimordial nucleosynthesis in this precision era of cosmology and to \\nhighlight the challenges, along with some goals, for the new millennium. \\nAfter a brief review of the important physics during the era of primordial \\nnucleosynthesis in the standard, hot big bang cosmological model (SBBN), \\nI will present an overview of the predicted primordial abundances, \\nemphasizing the generally very small theoretical uncertainties. These \\nwill then be compared to the present best estimates (including their \\nuncertainties) of the primordial abundances inferred from current \\nobservational data. After assessing the consistency of SBBN, I will \\nexplore what SBBN has to offer to Cosmology and to Particle Physics \\nand, what Cosmology may teach us about SBBN. I will conclude with a \\nsummary of the key issues/problems confronting SBBN and with a wish \\nlist of topics I hope will be addressed during this meeting -- and beyond.\\n\\n\\\\section{An Early Universe Chronology}\\n\\nOur story begins when the Universe is a few tenths of a second old and \\nthe temperature of the cosmic background radiation has dropped to a few \\nMeV as the Universe expanded and cooled from its denser, hotter infancy. \\nAt this time (and earlier) the density and average energy of colliding \\nparticles is so high that even the weak interactions occur sufficiently \\nrapidly to establish equilibrium. In particular, at this stage all flavors \\nof neutrinos ($e, \\\\mu, \\\\tau$) are in thermal equilibrium with the cosmic \\nbackground radiation (CBR) photons and with the copius electron-position \\npairs present ($\\\\nu_{i} + \\\\bar{\\\\nu}_{i} \\\\leftrightarrow e^{+} + e^{-} \\n\\\\leftrightarrow \\\\gamma + \\\\gamma$). However, as the Universe ages beyond \\na few tenths of a second and the temperature drops below a few MeV, these \\nweak interactions become too slow to keep pace with the rapid expansion of \\nthe Universe and the neutrinos decouple from the CBR. The electron-type \\nneutrinos continue to play a role in transforming neutrons into protons \\nand, vice-versa ($p + e^{-} \\\\leftrightarrow n + \\\\nu_{e}$, $n + e^{+} \\n\\\\leftrightarrow p + \\\\bar{\\\\nu}_{e}$, $n \\\\leftrightarrow p + e^{-} + \\\\bar\\n{\\\\nu}_{e}$). As the temperature continues to drop, less massive protons \\nare favored over the more massive neutrons and the $n/p$ ratio falls (roughly \\nas $e^{-\\\\Delta m/kT}$, where $\\\\Delta m$ is the neutron -- proton mass \\ndifference $\\\\sim 1.3$~MeV). After the temperature drops below 800~keV \\nor so, when the Universe is a few seconds old, even these weak interactions \\nbecome too slow to keep pace with the expansion and the neutron-to-proton \\nratio ``freezes out\\\" (in fact, the ratio continues to decrease, albeit \\nvery slowly). All the while, neutrons and protons have been colliding, \\noccasionally forming deuterons ($p + n \\\\rightarrow D + \\\\gamma$). However, \\nthe deuterons find themselves bathed in a high density background of \\nenergetic CBR photons which quickly photodissociate them ($D + \\\\gamma \\n\\\\rightarrow p + n$) before they can find a proton or neutron and form \\nthe more tightly bound, less fragile, \\\\3h or \\\\3he nuclei. Since, as we \\nshall see, there are roughly nine to ten orders of magnitude more CBR \\nphotons than nucleons in the Universe, the deuteron ``stepping-stone\\\" to \\nfurther nucleosynthesis is absent until the temperature drops sufficiently \\nlow so that even in the high-energy tail of the black-body spectrum there \\nare too few photons to prevent the deuteron from acting as a catalyst for \\nprimordial nucleosynthesis. This critical temperature, which is weakly \\n(logarithmically) dependent on the nucleon abundance (the nucleon-to-photon \\nratio $\\\\eta$), is roughly 80~keV. Now, at last, when the Universe is a \\nfew minutes old, Big Bang Nucleosynthesis finally commences. However, \\nthe Universe was a fatally flawed nuclear reactor, cooling and diluting \\nrapidly as it aged. When the Universe is some 10 -- 20 minutes old \\n($\\\\sim 1000$~sec) and the temperature has dropped below 30~keV or so, \\nthe coulomb barriers preventing nuclear reactions between charged nuclei \\nand protons and among charged nuclei become insurmountable (in the short \\namount of time available) and primordial nucleosynthesis comes to an \\nabrupt end. In this all too brief but shining era there has been time \\nto synthesize (in abundances comparable to those observed or observable) \\nonly the lightest nuclides: D, \\\\3he, \\\\4he, and \\\\7li. In ``standard\\\" (a \\nhomogeneous Universe, expanding isotropically with the particle content \\nof the standard model of particle physics in which there are three flavors \\nof light ($m \\\\ll $~MeV) or massless neutrinos) big bang nucleosynthesis \\n(SBBN) the abundances (relative to protons $\\\\equiv$~ hydrogen) of these \\nfour nuclides are determined by only one free parameter, the present epoch \\nnucleon-to-photon ratio $\\\\eta$ ($\\\\eta \\\\equiv (n_{\\\\rm N}/n_{\\\\gamma})_{0}, \\n~\\\\eta_{10} \\\\equiv 10^{10}\\\\eta$).\\n\\n\\\\section{SBBN-Predicted Primordial Abundances}\\n\\nOnce the deuterium photodissociation bottleneck is breached primordial \\nnucleosynthesis begins in earnest, quickly burning D to \\\\3h, \\\\3he and \\n\\\\4he. The higher the nucleon density, the faster D is destroyed. The \\nsame is true of \\\\3h (which, if it survives will decay to \\\\3he) and \\\\3he. \\nThus, the primordial abundances of D and \\\\3he are determined by the \\ncompetition between the nuclear reaction rates and the universal expansion \\nrate. The former rate depends on the overall density of the reactants -- \\nthe nucleon density. Since all densities decrease as the Universe expands, \\nit is convenient to quantify the nucleon density by specifying the {\\\\it \\nratio} of the nucleon density to the photon density (measured after $e^{+}\\ne^{-}$ annihilation which enhances the Universe's photon budget) $\\\\eta$. \\nSince observations of the cosmic background radiation (CBR) temperature \\n(T = 2.73~K) determine the present density of CBR photons, a knowledge \\nof $\\\\eta$ is equivalent to a determination of the present mass density \\nin nucleons (``baryons\\\" $\\\\equiv $~B). In terms of the density parameter\\n$\\\\Omega_{\\\\rm B}$ (the ratio of the mass density to the critical mass density)\\nand the present value of the Hubble parameter (H$_{0} \\\\equiv 100h$~km/s/Mpc),\\n$\\\\eta_{10} = 273\\\\Omega_{\\\\rm B}h^{2}$. As $\\\\eta$ increases the surviving \\nabundances of D and \\\\3he decrease; since the \\\\3he nucleus is more tightly \\nbound than the deuteron, the decrease of the \\\\3he/H ratio with $\\\\eta$ is \\nless rapid than that of D/H. \\n\\nIn contrast to D and \\\\3he, the primordial abundance of \\\\4he is not reaction \\nrate limited since the nuclear reactions building helium-4 are so rapid \\nthat virtually all neutrons available when BBN commences are incorporated \\ninto \\\\4he. As a result the \\\\4he abundance, conventionally presented as \\nthe mass fraction of all nucleons which are in \\\\4he, Y$_{\\\\rm P}$, is {\\\\it \\nneutron limited}. Since the neutron-to-proton ratio is determined by the \\ncompetition between the (charged-current) weak interactions which mediate \\nthe transformation of neutrons into protons (and, vice-versa) and the \\nuniversal expansion rate, \\\\Yp is sensitive to the universal expansion \\nrate at the time the $n/p$ ratio ``freezes\\\" and when the deuterium \\nphotodissociation barrier disappears. Since the universal expansion rate \\nis controlled by the total energy density, \\\\Yp provides an important test \\nof cosmology and of particle physics in the early Universe (Steigman, \\nSchramm \\\\& Gunn 1977). It should be noted that \\\\Yp is not entirely \\ninsensitive to the nucleon density since the higher $\\\\eta$, the earlier \\nthe photodissociation barrier is overcome. At earlier times when the \\ntemperature is higher, fewer neutrons have been transformed into protons \\nand are available for incorporation into \\\\4he. As a result, \\\\Yp increases \\nlogarithmically with $\\\\eta$.\\n\\nThere is no stable nucleus at mass-5 and this presents a gap in the \\nroad to the synthesis of nuclei heavier than \\\\4he. In order to bridge \\nthe gap nuclear reactions must occur among nuclei with two or more \\nnucleons. But, the abundances of D, \\\\3h, and \\\\3he are small and the \\ncoulomb barriers (especially between \\\\3he and \\\\4he and between \\\\4he \\nand \\\\4he) suppress these reactions as the Universe expands and cools. \\nAs a result, there is very little ``leakage\\\" to nuclei beyond mass-4; \\nas a corollary, virtually all the \\\\4he formed, survives. The only \\nheavier nucleus produced primordially in an abundance comparable to \\nthat observed (or, even, observable with current technology) is \\\\7li, \\nwhose BBN abundance is some 4 -- 5 orders of magnitude smaller than \\nthat of D and \\\\3he. The absence of a stable nucleus at mass-8 provides \\nanother gap preventing the production of astrophysically interesting \\nabundances of any heavier nuclei.\\n\\nAs will become clear in our subsequent discussion, the ``interesting\\\" \\nrange of $\\\\eta$ is $\\\\eta_{10} = 1 - 10$ ($\\\\Omega_{\\\\rm B}h^{2} = 0.004 \\n- 0.037$), so we focus our discussion here on values of $\\\\eta$ in this \\nrange. In the current precision era of BBN {\\\\it most} of the nuclear\\nreactions relevant to the synthesis of the light elements have been\\nmeasured to reasonable accuracy at energies directly comparable to the\\nthermal energies at the time of primordial nucleosynthesis (\\\\eg see \\nNollett, this volume). As a result, the theoretical uncertainties in\\nthe BBN-predicted abundances are generally quite small. For $\\\\eta$ in\\nthe above range, the 1$\\\\sigma$ uncertainties in D/H and \\\\3he/H vary\\nfrom 8 -- 10\\\\%. Since \\\\4he is most sensitive to the very well measured\\nweak interaction rates, the error in SBBN-predicted \\\\Yp is very small \\n(0.2 -- 0.5\\\\% or, $\\\\sigma_{\\\\rm Y}$ = 0.0005 -- 0.0011). In contrast,\\nlarger uncertainties, of order 12 -- 21\\\\%, afflict the predicted \\nprimordial abundance of \\\\7li. \\n\\nSince this Symposium devoted much discussion to \\\\7li, and space-limitations\\nhere prevent me from discussing all the light elements in detail, I will\\nconcentrate in the following on the two key light elements, deuterium and \\nhelium-4. In Figure 1 is shown the relation between the BBN-predicted\\nabundances of D and \\\\4he. The band going from upper left to lower right\\nrepresents the $\\\\pm 2\\\\sigma$ range of uncertainties in the primordial \\nabundances ((D/H)$_{\\\\rm P}$ and Y$_{\\\\rm P}$). Low D/H (high $\\\\eta$) \\ncorresponds to high \\\\Yp and high D/H (low $\\\\eta$) corresponds to low \\nY$_{\\\\rm P}$. This anticorrelation will be very important when we \\nconfront the predictions of SBBN with the observational data.\\n\\n\\\\section{Precise (Accurate?) Primordial Abundances}\\n\\nTo test SBBN and fully exploit the opportunities it offers to constrain\\ncosmology (e.g., the baryon density) and particle physics (e.g., new\\nparticles with weak or weaker-than-weak interactions) requires that \\nobservational data be used to pin down the primordial abundances of the\\nlight elements to precisions as good as (or, better than) those of the\\nSBBN predictions. As we approach the new millennium there is good news\\nalong with some bad news. The good news is that new detectors on ever\\nlarger telescopes which cover the spectrum from radio to x-ray energies\\nand beyond are providing very high quality data, leading to inferred\\nabundances of high statistical accuracy. Furthermore, the abundances \\nof the light elements are determined from observations which differ \\nfrom element to element in the telescopes and techniques employed as \\nwell as in the astrophysical sites explored. As a result, insidious \\ncorrelated errors between and among the various element abundances are \\nunlikely to be a problem. The good news is also responsible for the \\nbad news. Since the statistical errors have become so small, systematic \\nerrors now tend to dominate the uncertainties in the derived primordial \\nabundances. As Bob Rood has said during this Symposium, estimating \\nsystematic errors is an oxymoron. When a potential source of systematic \\nerror is identified, observations can (and should) be designed to \\neliminate or bound its contribution to the error budget. It is a \\npointless and potentially misleading exercise to ``estimate\\\" the magnitude \\nof unidentified systematic errors. In part to remind us that our precise \\nabundance determinations may not be accurate, and in part to challenge \\nour observational colleagues who have done such a magnificent job of \\nreducing the statistical errors, I will try to focus on the potential \\nsources of systematic uncertainty (when I can identify them) in the \\nfollowing overview of the current observational status.\\n\\n\\\\subsection{Deuterium}\\n\\nAs J. Linsky (this volume) has reminded us, the deuterium abundance \\nin the local interstellar medium (the local interstellar cloud: LIC) \\nis known very accurately: (D/H)$_{\\\\rm LIC} = 1.5 \\\\pm 0.1 \\\\times \\n10^{-5}$ (Linsky 1998). Since deuterium is only destroyed during \\nthe evolution of the Galaxy (Epstein, Lattimer \\\\& Schramm 1976), the \\nLIC abundance provides a lower bound to its primordial (pre-Galactic) \\nvalue. This bound is strong enough to bound the nucleon density from \\nabove ($\\\\eta_{10} \\\\la 10$; $\\\\Omega_{\\\\rm B}h^{2} \\\\la 0.04$), ensuring \\nthat baryons cannot ``close\\\" the Universe ($\\\\Omega_{\\\\rm B} \\\\ll 1$), \\nnor even dominate its present mass density ($\\\\Omega_{\\\\rm B} \\\\ll \\n\\\\Omega_{\\\\rm M} \\\\approx 0.3 - 0.4$). Thus, local observations of \\ndeuterium, combined with the {\\\\it assumption} of the correctness \\nof SBBN (which we must test), already reaps great rewards: the \\nmass-energy density of the Universe must be dominated by unseen \\n(``dark\\\") non-baryonic matter. To go beyond (in the quest for the \\nprimordial deuterium abundance) we must look for observing targets \\nwhich are less evolved than the LIC. The presolar nebula is one such \\nsite. From solar system observations of \\\\3he reported by G. Gloeckler \\n(this volume), it is possible to infer the presolar deuterium abundance \\n(Geiss \\\\& Reeves 1972; Geiss \\\\& Gloecker 1998): (D/H)$_{\\\\odot} = 1.9 \\n\\\\pm 0.5 \\\\times 10^{-5}$. Although marginally higher than the LIC \\nabundance, the larger errors prevent us from using this determination \\nto improve on our previous bounds from the LIC. What this result does \\nindicate is that there has been very little (if any) evolution in the \\nD-abundance in the solar vicinity of the Galaxy in the last 4.5~Gyr. \\nThis is consistent with a large class of Galactic chemical evolution \\nmodels discussed by M. Tosi (this volume) which point to only a modest \\noverall destruction of primordial deuterium by a factor of 2 -- 3 \\n(Tosi et al. 1998). If this theoretical estimate is combined with the \\nLIC abundance, we may estimate the primordial abundance: (D/H)$_{\\\\rm P} \\n\\\\approx 2.6 - 5.1 \\\\times 10^{-5}$ ($\\\\sim 2\\\\sigma$). Although possibly \\nmodel dependent, this estimate is in remarkable agreement with the \\n2 -- 3 determinations of D/H in high-redshift, low-metallicity (hence \\nvery nearly primordial) Ly-$\\\\alpha$ absorbers illuminated by background \\nQSOs described by D. Tytler and S. Levshakov (this volume). The \\ndata and analysis of Burles \\\\& Tytler (1998a,b: BT) suggests that \\n(D/H)$_{\\\\rm P} = 2.9 - 4.0 \\\\times 10^{-5}$ ($\\\\sim 2\\\\sigma$). Notice \\nthat the 1$\\\\sigma$ uncertainty in the observationally determined \\nprimordial abundance, $\\\\sim 8$\\\\%, is impedance-matched to the \\n$\\\\sim 8$\\\\% SBBN theoretical uncertainty cited earlier. However, \\nlest we risk dislocating a shoulder while patting ourselves on the \\nback at the triumph of such wonderful data, we should not ignore \\nthe claim (Webb et al. 1997; Tytler et al. 1999) that the deuterium \\nabundance in at least one Ly-$\\\\alpha$ absorption system may be much \\nhigher. This is a reminder that while any determination of the \\ndeuterium abundance anywhere in the Universe (LIC, solar system, \\nLy-$\\\\alpha$ absorbers, etc.) provides a {\\\\it lower} bound to primordial \\ndeuterium, finding an upper bound is more problematic. Indeed, in \\nsome absorbing systems it may be impossible to distinguish D-absorption \\nfrom that due to hydrogen in an interloping, low column density, \\n``wrong-velocity\\\" system. Thus, the deuterium abundance inferred \\nfrom absorption-line data may only provide an {\\\\it upper} bound to \\nthe true deuterium abundance. Since the low-Z, high-z QSO absorbing \\nsystems hold the greatest promise of revealing for us nearly unevolved, \\nnearly primordial material, we look forward to the time when we can \\nuse the {\\\\it distribution} of D/H values from more than a handful of \\nsuch systems to eliminate -- statistically -- the uninvited contribution \\nto the inferred primordial deuterium abundance from such interlopers. \\nKeeping this in mind, in the following I will, nevertheless, use the \\nBT determination when confronting theory with data. \\n\\n\\\\subsection{Helium-4}\\n\\nIn contrast to deuterium whose primordial abundance only decreases \\nas pristine gas is incorporated into stars, stars burn hydrogen to \\nhelium. As a result, the \\\\4he observed anywhere in the Universe is \\nan unknown mixture of primordial and stellar-produced helium. It has \\nlong been appreciated that to minimize the uncertain correction due \\nto the debris of stellar evolution, it is best to concentrate on \\\\4he \\nabundance determinations in the lowest-metallicity regions available. \\nThese are the low-Z, extragalactic \\\\hii regions which have been discussed \\nby K. Olive, T. Thuan, and S. M. Viegas at this Symposium (this volume). \\nThe reader is urged to consult their papers for details; here I will \\nmerely summarize my view of the current status of the determination \\nof the primordial \\\\4he mass fraction Y$_{\\\\rm P}$. Several years ago \\nOlive \\\\& Steigman (1995: OS) gathered together the data from the literature \\n(dominated by the data assembled by Pagel et al. 1992). More recently \\nOlive, Skillman \\\\& Steigman (1997: OSS) supplemented this with newer \\ndata (some of it, unfortunately, still unpublished). Using a variety \\nof approaches such as the regression of Y on the oxygen and/or nitrogen\\nabundances and the weighted means of Y in the lowest metal-abundance \\n\\\\hii regions, OSS concluded that \\\\Yp = 0.234 $\\\\pm$ 0.003 (note that, \\nin contrast to the published (OSS) result, this value is obtained when \\nthe NW region of IZw18, suspected of being contaminated by underlying \\nstellar absorption, is excluded from the fit, and the newer data of \\nIzotov, Thuan and collaborators is not included). Izotov, Thuan \\nand their collaborators (Izotov, Thuan, \\\\& Lipovetsky 1994, 1997; \\nIzotov \\\\& Thuan 1998(IT); Thuan, this volume) have been systematically \\nobserving a mostly independent set of \\\\hii regions. Although, as \\nwith the data employed in the OS and OSS studies, they ignore the \\nionization correction ($icf \\\\equiv 1$), they take special care with \\nthe correction for collisional excitation. IT (also Thuan, this volume) \\nfind Y$_{\\\\rm P}({\\\\rm IT}) = 0.244~\\\\pm$ 0.002. Comparing the IT and OSS \\nestimates of \\\\Yp we find that difference between the two \\\\Yp estimates \\nfar exceeds the statistical errors, suggesting systematic differences \\nin the acquisition and/or analysis of the data samples. In a recent \\ndiscussion which attempted to account for these unidentified systematic \\ndifferences, Olive, Steigman \\\\& Walker (1999: OSW) combined the 2$\\\\sigma$ \\nranges for each determination to conclude: \\\\Yp = 0.238 $\\\\pm$ 0.005; at \\nthe 2$\\\\sigma$ level, \\\\Yp $\\\\leq 0.248$. Note, that this is also the \\n2$\\\\sigma$ upper bound to the IT data alone. Since, as we shall see \\nshortly, it is the upper bound which is crucial to testing the consistency \\nof SBBN, in the following we shall adopt the IT value (and error estimate) \\nfor the primordial abundance of \\\\4he. \\n\\nRecently, Viegas, Gruenwald \\\\& Steigman (1999: VGS; see Viegas \\\\& \\nGruenwald, this volume) have emphasized the importance of the ionization \\ncorrection which has heretofore been ignored. VGS suggest that the \\nIT helium abundance (Y$_{\\\\rm P}$) should be reduced by 0.003 to account \\nfor unseen neutral hydrogen in regions where the helium is still ionized \\nin \\\\hii regions ionized by young, hot, metal-poor stars. In subsequent \\ncomparisons I shall explore the implications of adopting Y$_{\\\\rm P}({\\\\rm \\nVGS}) = 0.241~\\\\pm$ 0.002.\\n\\n\\\\subsection{Helium-3 and Lithium-7}\\n\\nThe cosmic history of the two other light nuclides produced in\\nastrophysically interesting abundances during SBBN, \\\\3he and \\n\\\\7li, is considerably more complex than that of D or \\\\4he, which \\nlimits their utility as probes of the consistency of SBBN. \\\\3he \\nis destroyed in the hotter interiors of all stars, but some \\\\3he \\ndoes survive in the cooler, outer layers. For lower mass stars \\nthis \\\\3he survival layer increases and, indeed, newly synthesized \\n\\\\3he is produced by incomplete hydrogen burning. The competition \\nbetween destruction, survival, and synthesis complicates the Galactic\\nhistory of the \\\\3he abundance. Nonetheless, since any deuterium \\nincorporated into stars is first burned to \\\\3he, the apparent lack \\nof enhanced \\\\3he (see Bania \\\\& Rood, this volume) argues against \\na very large pre-Galactic abundance of deuterium (Steigman \\\\& Tosi \\n1995). For further discussion of the evolution of \\\\3he see Bania \\n\\\\& Rood (this volume).\\n\\nAs with \\\\3he, any \\\\7li incorporated into stars is quickly burned \\naway. However, fusion and spallation reactions between cosmic ray \\nnuclei and those in the interstellar medium are a potent source of \\n\\\\7li (as well as of \\\\6li, $^7$Be, $^{10}$B, and $^{11}$B). It is\\nalso likely that there are stellar sources of \\\\7li as indicated \\nby the sample of lithium-rich red giants (V. Smith, this volume). \\nSince the abundance of lithium in the solar system and in the \\ninterstellar medium (``here and now\\\") greatly exceeds that in the \\nvery metal-poor halo stars (T. Beers \\\\& S. Ryan, this volume), the \\nlatter likely provide the closest approach to a nearly primordial \\nsample. Since a significant fraction of this Symposium is devoted \\nto lithium, I will defer here to those other discussions except to \\ncomment that, within the theoretical and observational uncertainties, \\nthe primordial abundances inferred from the observational data are \\nconsistent with SBBN constrained by the confrontation with D and \\\\4he.\\n\\n\\\\section{Confrontation Of SBBN With Data}\\n\\nAlthough SBBN does lead to the prediction of the abundances of D, \\n\\\\3he, \\\\4he, and \\\\7li, the currently best-constrained primordial \\nabundances are those of deuterium and helium-4 which we are \\nconcentrating on in this status report. For each value of $\\\\eta$, \\nSBBN predicts a pair of (D/H)$_{\\\\rm P}$ and \\\\Yp values. Therefore, \\nin SBBN there is a unique connection between (D/H)$_{\\\\rm P}$ and \\n\\\\Yp which, allowing for the theoretical uncertainties discussed \\nabove, is shown as the band (solid lines) in Figure 1 going from \\nthe upper left to the lower right (2$\\\\sigma$ uncertainties). Note \\nthat high-helium correlates with low-deuterium and, vice-versa. \\nAlso shown as the dotted ellipse in Figure 1 is the contour of the \\n(independent) 2$\\\\sigma$ uncertainties in the BT deuterium abundance \\nand the IT helium-4 mass fraction. \\n\\n\\\\begin{figure}\\n\\\\vspace{1.in}\\n%\\\\plotone{fig1.eps}\\n\\\\plotfiddle{fig1.eps}{1in}{0}{30}{30}{-100}{-50}\\n\\\\caption{The SBBN-predicted \\\\4he mass fraction \\\\Yp as a function \\nof the SBBN-predicted primordial deuterium-to-hydrogen ratio D/H \\nis shown (at the $\\\\pm 2\\\\sigma$ level) by the solid lines. The \\ndotted ellipse is the 95\\\\% contour of the BT deuterium abundance \\nand the IT \\\\4he mass fraction (see the text).}\\n\\\\end{figure}\\n\\nAlthough the overlap between theory and data is not complete, \\nFigure 1 shows that, at the $\\\\sim 2\\\\sigma$ level, the predictions \\nof SBBN are consistent with current observational data. This is \\na dramatic success for the standard hot, big bang cosmological \\nmodel. Of course it is not at all surprising that some value \\nof $\\\\eta$ may be found to provide consistency with the inferred \\nprimordial deuterium abundance. But there was no guarantee at \\nall that the helium-4 abundance corresponding to this choice would \\nbear any relation to its inferred primordial value. Consistency \\nwith the BT D-abundance limits the nucleon abundance to the range \\n(2$\\\\sigma$) $\\\\eta_{10} = 4.4 - 5.9$ or, $\\\\Omega_{\\\\rm B}h^{2} = \\n0.016 - 0.022$. For $\\\\eta$ in this range there is consistency, \\nwithin the theoretical and observational uncertainties, between \\nthe SBBN-predicted and observationally inferred primordial abundances \\nof \\\\3he and \\\\7li as well. Four for the price of one! There is, \\nof course, one more test -- and opportunity -- offered by this \\nresult. This SBBN-inferred nucleon abundance must also be \\nconsistent with present epoch estimates of the baryon density. \\nIndeed, the SBBN-determined value of $\\\\Omega_{\\\\rm B}$ is {\\\\it \\nlarger} than estimates (Persic \\\\& Salucci 1992) of the ``luminous\\\" \\nmatter in the Universe suggesting that the majority of baryons \\nare ``dark\\\". This is good ($\\\\Omega_{\\\\rm B} > \\\\Omega_{\\\\rm LUM}$); \\nthe opposite would have been a disaster. This early-Universe \\nestimate of the baryon density is in good agreement with that \\ninferred from the X-ray cluster baryon fraction (Steigman, Hata \\n\\\\& Felten 1999) and with the independent estimate from the \\nLy-$\\\\alpha$ forest (Weinberg et al. 1997) discussed below.\\n\\n\\\\subsection{What BBN May Do For Cosmology}\\n\\nX-ray clusters likely provide a ``fair\\\" sample of the universal\\nbaryon {\\\\it fraction} $f_{\\\\rm B}$ (White et al. 1993; Steigman \\n\\\\& Felten 1995; Evrard, Metzler, \\\\& Navarro 1996) which, when \\ncombined with the SBBN-inferred baryon density $\\\\Omega_{\\\\rm B}$, \\nleads to a ``clean\\\" prediction, independent of detailed cosmological \\nmodels, of the overall matter density $\\\\Omega_{\\\\rm M}$. If the \\nresults presented here are combined with the determination of \\n$f_{\\\\rm B}$ from Evrard (1997), and with a Hubble parameter $h \\n= 0.70 \\\\pm 0.07$ (Mould et al. 1999), we predict $\\\\Omega_{\\\\rm M} \\n= 0.35 \\\\pm 0.08$, in excellent agreement with several other recent, \\nindependent determinations. For example, a lower bound to the cosmic \\nbaryon density follows from the requirement that the high-redshift \\nintergalactic medium contain enough neutral hydrogen to produce\\nthe Ly-$\\\\alpha$ absorption observed in quasar spectra. According\\nto Weinberg et al. (1997), depending on estimates of the quasar\\nUV background intensity, this lower bound corresponds to $\\\\eta_{10}\\n\\\\ga 3.4 - 4.9$, in excellent agreement with the SBBN prediction\\nbased on the BT deuterium determination. Note that this lower\\nbound from the Ly-$\\\\alpha$ absorption forbids (in the context of\\nSBBN) the primordial deuterium abundance to be any larger than\\n$\\\\sim 8 \\\\times 10^{-5}$, largely excluding the one surviving\\nclaim of high D (Webb et al. 1997).\\n\\nIndeed, if the SBBN results are combined with the magnitude-redshift \\ndata from surveys of high-redshift Type Ia supernovae (Garnavich et \\nal. 1998; Perlmutter et al. 1999) which bound a linear combination \\nof $\\\\Omega_{\\\\rm M}$ and the cosmological constant $\\\\Omega_{\\\\Lambda} \\n\\\\equiv \\\\Lambda/3$H$_{0}^{2}$, we may also constrain the cosmological \\nconstant ($\\\\Omega_{\\\\Lambda} = 0.80 \\\\pm 0.20$), the curvature \\n($\\\\Omega_{k} \\\\equiv 1 - (\\\\Omega_{\\\\rm M} + \\\\Omega_{\\\\Lambda}) = \\n-0.15 \\\\pm 0.25$), and the deceleration parameter ($q_{0} = \\n\\\\Omega_{\\\\rm M}/2 - \\\\Omega_{\\\\Lambda} = -0.62 \\\\pm 0.18$).\\n\\n\\\\subsection{What Cosmology May Do For BBN}\\n\\nAs we have just seen, the SBBN-determined baryon density is \\nconsistent with that determined or constrained by observations \\nof the Universe during its present or recent evolution. We \\nmay turn the argument around and ask what baryon density is \\nsuggested by non-BBN contraints, and then compare the light \\nelement abundances which correspond to that density with those \\ninferred from the observational data. As an exercise of this \\nsort, suppose (for reasons of ``naturalness\\\" or inflation) that \\nthe Universe is ``flat\\\": $\\\\Omega_{\\\\rm M} + \\\\Omega_{\\\\Lambda} \\n= 1$. When combined with the SN Ia magnitude-redshift data \\n(Perlmutter et al. 1999), this suggests that $\\\\Omega_{\\\\rm M} \\n= 0.29 \\\\pm 0.07$ (and $\\\\Omega_{\\\\Lambda} = 0.71 \\\\pm 0.07$).\\nNow, if this mass density estimate ($\\\\Omega_{\\\\rm M}$) is \\ncombined with with the X-ray determined cluster baryon fraction \\n$f_{\\\\rm B}$ (Evrard 1997; Steigman, Hata \\\\& Felten 1999), \\nthe resulting nucleon abundance is $\\\\eta_{10} = 4.5 \\\\pm 1.5$. \\nAlthough the uncertainty is large, it is reassuring that this \\nnon-BBN estimate has significant overlap with our SBBN estimate.\\nIndeed, for the baryon density in this range SBBN predicts:\\n(D/H)$_{\\\\rm P} = 4.3 \\\\pm 2.3 \\\\times 10^{-5}$ and Y$_{\\\\rm P} \\n= 0.245 \\\\pm 0.004$. \\n\\n\\\\subsection{What SBBN May Do For Particle Physics}\\n\\nThe expansion rate of the early Universe is controlled by the\\ndensity of the relativistic particles present. In the standard\\nmodel at the time of BBN these are: photons, electron-positron\\npairs (when T $ \\\\ga m_{e}$) and three ``flavors\\\" of neutrinos\\n($\\\\nu_{e}$, $\\\\nu_{\\\\mu}$, $\\\\nu_{\\\\tau}$) which, if ``light\\\" ($m_{\\\\nu}\\n\\\\ll 1$~MeV), are relativistic at BBN even if one or more of them\\nmay contribute to the present density of non-relativistic (``hot\\\")\\ndark matter. If ``new\\\" particles were to contribute to the energy \\ndensity at BBN, the increase in the density would result in an\\nincrease in the universal expansion rate, leaving less time for\\nneutrons to transform into protons. The higher $n/p$ ratio at BBN\\nwould result in the production of more primordial \\\\4he (Steigman,\\nSchramm \\\\& Gunn 1977). It is convenient (and conventional) to\\ncharacterize such additional contributions to the energy density\\nby comparing their effects to that of an additional ``flavor\\\" of\\n(light) neutrino: $\\\\Delta\\\\rho \\\\equiv \\\\Delta N_{\\\\nu}\\\\rho_{\\\\nu}$.\\nFor $\\\\Delta N_{\\\\nu}$ small, $\\\\Delta $Y $ \\\\approx 0.01\\\\Delta N_{\\\\nu}$.\\nNotice in Figure 1 that the predicted \\\\4he abundance is a little\\nhigh for perfect overlap with the observations. If $\\\\Delta N_{\\\\nu}$ \\nwere $ < 0$, (N$_{\\\\nu} \\\\approx 2.8$) the overlap would improve (e.g., \\nHata et al. 1995), while if $\\\\Delta N_{\\\\nu} > 0$, the overlap would \\nbe reduced until it disappeared. This is illustrated in Figure 2 \\nwhich shows the Y versus D/H BBN band that would result if $\\\\Delta \\nN_{\\\\nu} = 0.2$ (i.e., $N_{\\\\nu} = 3.2$, in contrast to the SBBN value \\nof 3.0). Notice that due to the faster expansion, more deuterium \\nsurvives being burnt away so that, for fixed $\\\\eta$, the D-abundance \\nalso increases; however since D/H is a much more sensitive function \\nof $\\\\eta$, this has a much smaller effect on the Y versus D/H relation \\nthan does the increase in Y.\\n\\n\\\\begin{figure}\\n\\\\vspace{1.in}\\n%\\\\plotone{fig2.eps}\\n\\\\plotfiddle{fig2.eps}{1in}{0}{30}{30}{-100}{-50}\\n\\\\caption{As Figure 1, but for $N_{\\\\nu} = 3.2$}\\n\\\\end{figure}\\n\\n\\\\section{Conclusions And Outlook}\\n\\nThe study of the early evolution of the Universe and, in\\nparticular primordial nucleosynthesis, has truly entered\\nthe precision era of cosmology. Precise abundances of the \\nlight nuclides are predicted and inferred from observations\\nand the two are -- apparently -- in excellent agreement.\\nAs pleased as we may be at this success, it behooves us\\nto avoid the temptation to rest on our laurels and to\\ntest this consistency ever more carefully. To this end,\\nit doesn't take much contemplation to identify several\\nclouds looming on the horizon. What follows is my\\npersonal list of some problems/issues I would like \\nto see addressed at this Symposium and beyond.\\n\\n\\\\subsection{Problems/Issues}\\n\\nFirst consider deuterium. On the one hand, any determination\\nof the D/H ratio anywhere, anytime provides a {\\\\it lower}\\nbound to the primordial abundance. On the other hand, since\\n``wrong\\\" velocity hydrogen can masquerade as deuterium, any\\nobservation of ``deuterium\\\" is really an {\\\\it upper} bound \\nto its true abundance. More data tracking the velocity\\nstructure of the absorbing features used to identify D \\nand H and exploring variations in D/H in material with \\nsimilar histories will be very valuable. More data at \\nhigh-redshift and low-metallicity will be very valuable. \\nAfter all, at present we are drawing profound conclusions \\non the basis of only two such systems.\\n\\nMuch remains to be done concerning the primordial abundance\\nof \\\\4he. For the most part, the \\\\hii regions from which\\nthe helium abundance is inferred have been modelled as\\nhomogeneous spheres or plane-parallel slabs. A glance at \\nthe beautiful HST images of real \\\\hii regions reveals that \\nthey are anything but such idealizations. What are the effects \\nof temperature and/or density inhomogeneities, and how large \\nmay they be? What of underlying stellar absorption which, if \\npresent but neglected, would lead to an {\\\\it under}estimate \\nof the helium abundance. And, what of the usually neglected\\nionization correction for neutral hydrogen and helium (Viegas, \\nGruenwald \\\\& Steigman 1999; see Viegas \\\\& Gruenwald, this \\nvolume)? Considering this latter work, where models of \\\\hii \\nregions ionized by realistic spectra of young star clusters \\nwere used in a reanalysis of the IT data, a {\\\\it reduction} \\nin \\\\Yp of order 0.003 was suggested. A comparison with Figure \\n1 shows that if \\\\Yp were reduced by this amount, the overlap \\nbetween theory and data would, in fact, disappear.\\n\\n\\\\subsection{Wish List}\\n\\nGiven the setting of this Symposium (Natal) and the proximity\\nto the Christmas season, I'd like to conclude with my personal\\nwish list. To avoid being greedy, I'll only ask for two gifts.\\n\\nA half-dozen or so observations of deuterium in high-z, low-Z \\nsystems along the lines-of-sight to distant quasars, with D/H \\ndetermined in each (on average) to 10\\\\% or better. With such \\na gift, I could determine $\\\\eta$ to better than 4\\\\%, predict\\n\\\\Yp to $\\\\la 0.0007$, and constrain $\\\\Delta N_{\\\\nu}$ to an \\nuncertainty less than $\\\\pm$~0.05. I'd be a very happy \\ncosmologist indeed.\\n\\nMy second wish is for \\\\4he measured to 3\\\\% accuracy (or better)\\nin each of about a dozen low-metallicity, extragalactic \\\\hii \\nregions, with care taken to address the several problems outlined \\nabove. With such data, \\\\Yp could be fixed to better than the \\ncurrent level of $\\\\pm 0.002$, permitting \\\\4he to be used as a \\nbaryometer ($\\\\Delta\\\\eta/\\\\eta~\\\\la 20\\\\%$).\\n\\n%\\\\end{document} \\n\\n\\\\acknowledgments\\n\\nMuch of what I know about this subject I have learned from my \\ncollaborators and I would be remiss if I failed to thank them \\nfor their contributions. In particular, I wish to acknowledge\\nR. Gruenwald, K. Olive, E. Skillman, M. Tosi, and S. M. Viegas \\nand, of course, my late friend Dave Schramm. L. da Silva, M. \\nSpite and the Scientific and Local Organizing committees deserve \\ngreat credit for their efficient organization of a very enjoyable \\nand successful meeting. In part, this work is supported at The \\nOhio State University by DOE grant DE--AC02--76ER--01545. \\n\\n\\\\begin{references}\\n\\n\\\\reference Burles, S., \\\\& Tytler, D. 1998a, \\\\apj, 499, 699 (BT)\\n\\n\\\\reference Burles, S., \\\\& Tytler, D. 1998b, \\\\apj, 507, 732 (BT)\\n\\n\\\\reference Epstein, R. Lattimer, J., \\\\& Schramm, D. N. 1976, \\nNature, 263, 198\\n\\n\\\\reference Evrard, A. E. 1997, \\\\mnras, 292, 289 \\n\\n\\\\reference Evrard, A. E., Metzler, C. A., \\\\& Navarro, J. F. 1996,\\n\\\\apj, 469, 494\\n\\n\\\\reference Garnavich, P. M. et al. 1998, \\\\apj, 509, 74\\n \\n\\\\reference Geiss, J., \\\\& Reeves, H. 1972, \\\\aap, 18, 126\\n\\n\\\\reference Geiss, J., \\\\& Gloeckler, G. 1998, \\\\ssr, 84, 239\\n\\n\\\\reference Hata, N., Scherrer, R. J., Steigman, G., Thomas, D., \\nWalker, T. P., Bludman, S., \\\\& Langacker P. 1995, \\\\prl, 75, 3977\\n\\n\\\\reference Linsky, J. L. 1998, \\\\ssr, 84, 285\\n \\n\\\\reference Izotov, Y. I., Thuan, T. X., \\\\& Lipovetsky, V. A. 1994, \\n\\\\apj, 435, 647\\n\\n\\\\reference Izotov, Y. I., Thuan, T. X., \\\\& Lipovetsky, V. A. 1997, \\n\\\\apjs, 108, 1\\n\\n\\\\reference Izotov, Y. I., \\\\& Thuan, T. X. 1998, \\\\apj, 500, 188 (IT)\\n\\n\\\\reference Mould, J. R. et al. 1999, \\\\apj, submitted (astro-ph/9909260)\\n\\n\\\\reference Olive, K. A., Skillman, E., \\\\& Steigman, G. 1997, \\\\apj, 483, \\n788 (OSS)\\n\\n\\\\reference Olive, K. A., \\\\&, Steigman, G. 1995, \\\\apjs, 97, 49 (OS)\\n\\n\\\\reference Olive, K. A., \\\\&, Steigman, G., \\\\& Walker, T. P. 1999, Physics\\nReports, in press (astro-ph/9905320) (OSW)\\n\\n\\\\reference Pagel, B. E. J., Simonson, E. A., Terlevich, R. J. \\\\& Edmunds, \\nM. 1992, \\\\mnras, 255, 325\\n\\n\\\\reference Perlmutter, S. et al. 1999, \\\\apj, 517, 565 \\n\\n\\\\reference Persic, M., \\\\& Salucci, P. 1992, \\\\mnras, 258, 14P\\n\\n\\\\reference Steigman, G., Schramm, D. N., \\\\& Gunn, J. E. 1977, Phys. Lett.,\\nB66, 202\\n\\n\\\\reference Steigman, G., \\\\& Felten, J. E. 1995, \\\\ssr, 74, 245\\n\\n\\\\reference Steigman, G., Hata, N., \\\\& Felten, J. E. 1999, \\\\apj, 510, 564\\n\\n\\\\reference Steigman, G., \\\\& Tosi, M. 1995, \\\\apj, 453, 173\\n\\n\\\\reference Tosi, M., Steigman, G., Matteucci, F., \\\\& Chiappini, C. 1998,\\n\\\\apj, 498, 226\\n\\n\\\\reference Tytler, D., Burles, S., Lu, L., Fan, X. M., Wolfe, A., \\\\&\\nSavage, B. D. 1999, \\\\aj, 117, 63\\n \\n\\\\reference Viegas, S.M., Gruenwald, R., \\\\& Steigman, G. 1999, \\\\apj, 532 \\n(in press, March 20, 2000; astro-ph/9909213)\\n\\n%\\\\reference Vilchez, J.M. \\\\& Pagel, B.E.J. 1988, MNRAS, 231, 257\\n\\n\\\\reference Webb, J. K., Carswell, R. F., Lanzetta, K. M., Ferlet, R., \\nLemoine, M., Vidal-Madjar, A., \\\\& Bowen, D. V. 1997, Nature, 388, 250\\n\\n\\\\reference Weinberg, D. H., Miralda-Escud$\\\\acute{\\\\rm e}$, J., Hernquist, \\nL., \\\\& Katz, N. 1997, \\\\apj 490, 564\\n\\n\\\\reference White, S. D. M., Navarro, J. F., Evrard, A. E., \\\\& Frenk,\\nC. S. 1993, Nature, 366, 429\\n\\n\\\\end{references}\\n\\n\\n\\\\end{document}\\n\\n\\n\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[],"string":"[]"}}},{"rowIdx":292,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002297"},"title":{"kind":"string","value":"A Sample of 669 Ultra Steep Spectrum Radio Sources to Find High Redshift Radio Galaxies \\thanks{Tables A.1, A.2 and A.3 are also and appendices B, C and D are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html }"},"authors":{"kind":"list like","value":[{"author":"Carlos De Breuck \\inst{1,2}"},{"author":"Wil van Breugel \\inst{2}"},{"author":"Huub J. A. R\\\"ottgering \\inst{1}"},{"author":"George Miley \\inst{1}"}],"string":"[\n {\n \"author\": \"Carlos De Breuck \\\\inst{1,2}\"\n },\n {\n \"author\": \"Wil van Breugel \\\\inst{2}\"\n },\n {\n \"author\": \"Huub J. A. R\\\\\\\"ottgering \\\\inst{1}\"\n },\n {\n \"author\": \"George Miley \\\\inst{1}\"\n }\n]"},"abstract":{"kind":"string","value":"Since radio sources with Ultra Steep Spectra (USS; $\\alpha \\lesssim -1.30; S \\propto \\nu^{\\alpha}$) are efficient tracers of high redshift radio galaxies (HzRGs), we have defined three samples of such USS sources using the recently completed WENSS, TEXAS, MRC, NVSS and PMN radio-surveys. Our combined sample contains 669 sources with $S_{1400} > 10$~mJy and covers virtually the entire sky outside the Galactic plane ($|b|>15$\\arcdeg). For our 2 largest samples, covering $\\delta > -35\\arcdeg$, we selected only sources with angular sizes $\\Theta < 1\\arcmin$. For 410 sources, we present radio-maps with 0\\farcs3 to $\\sim$5\\arcsec\\ resolution from VLA and ATCA observations or from the FIRST survey, which allows the optical identification of these radio sources. Comparison with spectrally unbiased samples at similar flux density levels, shows that our spectral index, flux density, and angular size selections do not affect the angular size distribution of the sample, but do avoid significant contributions by faint foreground spiral galaxies. We find that the spectral index distribution of 143,000 sources from the WENSS and NVSS consists of a steep spectrum galaxy and a flat spectrum quasar population, with the relative contribution of flat spectrum sources doubling from $S_{1400}>0.1$~Jy to $S_{1400}>2.5$~Jy. The identification fraction of our USS sources on the POSS ($R \\lesssim 20$) is as low as 15\\%, independent of spectral index $\\alpha < -1.30$. We further show that 85\\% of the USS sources that can be identified with an X-ray source are probably contained in galaxy clusters, and that $\\alpha < -1.6$ sources are excellent Galactic pulsar candidates, because the percentage of these sources is four times higher in the Galactic plane. Our sample has been constructed to start an intensive campaign to obtain a large sample of high redshift objects ($z>3$) that is selected in a way that does not suffer from dust extinction or any other optical bias. \\keywords{Surveys --- Galaxies: active --- Radio continuum: galaxies}"},"latex":{"kind":"list like","value":[{"name":"ds1811.tex","string":"%\\documentclass[referee]{aa} % for a referee version\n%\n\\documentclass{aa}\n\\usepackage{psfig}\n%\n \n\\newcommand\\eg{{\\it e.g.} }\n\\newcommand\\etal{et~al.}\n\\newcommand\\ie{{\\it i.e.~}\\ }\n\\newcommand\\lya{Ly$\\alpha$}\n\\newcommand\\Lya{Ly$\\alpha$}\n\\font\\aipsfont = cmsy9 scaled\\magstep1\n\\font\\smallaipsfont = cmsy5 scaled\\magstep1\n\\newcommand\\aips {{\\aipsfont AIPS}}\n\\newcommand\\Lh {{\\aipsfont L$\\;$}}\n\\newcommand\\minpoint{$^{\\prime}\\mskip-4.7mu.\\mskip0.8mu$}\n\\newcommand\\araa{{ARA\\&A}}\n\\newcommand\\aap{{A\\&A}}\n\\newcommand\\aasup{{A\\&AS}}\n\\newcommand\\aaps{{A\\&AS}}\n\\newcommand\\aj{{AJ}}\n\\newcommand\\apj{{ApJ}}\n\\newcommand\\apjl{{ApJ}}\n\\newcommand\\apjs{{ApJS}}\n\\newcommand\\iaucirc{{IAU Circ.}}\n\\newcommand\\mnras{{MNRAS}}\n\\newcommand\\nature{{Nature}}\n\\newcommand\\nat{{Nature}}\n\\newcommand\\pasp{{PASP}}\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\newcommand\\simlt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}}\n\\newcommand\\lesssim{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}}\n\\newcommand\\simgt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}}\n\\newcommand\\gtrsim{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}}\n\\newcommand\\arcdeg{\\degr}\n\\newcommand\\nodata{...}\n\\includeonly{wntable,tnmptable}\n\n\\begin{document}\n\n\\thesaurus{04.19.1; 11.01.2; 13.18.1}\n\n\\title{A Sample of 669 Ultra Steep Spectrum Radio Sources to Find High Redshift Radio Galaxies \\thanks{Tables A.1, A.2 and A.3 are also and appendices B, C and D are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html }}\n\\subtitle{}\n\\titlerunning{A sample of 669 USS sources}\n\n\\author{Carlos De Breuck \\inst{1,2} \\and Wil van Breugel \\inst{2} \\and Huub J. A. R\\\"ottgering \\inst{1} \\and George Miley \\inst{1}}\n\n\\authorrunning{Carlos De Breuck \\etal}\n\n\\offprints{Carlos De Breuck}\n\n\\institute{Sterrewacht Leiden, Postbus 9513, 2300 RA Leiden, The\n Netherlands; debreuck,miley,rottgeri@strw.leidenuniv.nl\n \\and Institute of Geophysics and Planetary Physics,\n Lawrence Livermore National Laboratory, L-413, Livermore,\n CA 94550, U.S.A.; wil@igpp.llnl.gov}\n\n\\date{Received 1999 November 5; accepted 2000 February 10}\n\n\\maketitle\n\n\\begin{abstract}\nSince radio sources with Ultra Steep Spectra (USS; $\\alpha \\lesssim -1.30; S \\propto \\nu^{\\alpha}$) are efficient tracers of high redshift radio galaxies (HzRGs), we have defined three samples of such USS sources using the recently completed WENSS, TEXAS, MRC, NVSS and PMN radio-surveys. Our combined sample contains 669 sources with $S_{1400} > 10$~mJy and covers virtually the entire sky outside the Galactic plane ($|b|>15$\\arcdeg). For our 2 largest samples, covering $\\delta > -35\\arcdeg$, we selected only sources with angular sizes $\\Theta < 1\\arcmin$. For 410 sources, we present radio-maps with 0\\farcs3 to $\\sim$5\\arcsec\\ resolution from VLA and ATCA observations or from the FIRST survey, which allows the optical identification of these radio sources.\n\nComparison with spectrally unbiased samples at similar flux density levels, shows that our spectral index, flux density, and angular size selections do not affect the angular size distribution of the sample, but do avoid significant contributions by faint foreground spiral galaxies.\nWe find that the spectral index distribution of 143,000 sources from the WENSS and NVSS consists of a steep spectrum galaxy and a flat spectrum quasar population, with the relative contribution of flat spectrum sources doubling from $S_{1400}>0.1$~Jy to $S_{1400}>2.5$~Jy.\nThe identification fraction of our USS sources on the POSS ($R \\lesssim 20$) is as low as 15\\%, independent of spectral index $\\alpha < -1.30$. We further show that 85\\% of the USS sources that can be identified with an X-ray source are probably contained in galaxy clusters, and that $\\alpha < -1.6$ sources are excellent Galactic pulsar candidates, because the percentage of these sources is four times higher in the Galactic plane.\n\nOur sample has been constructed to start an intensive campaign to obtain a large sample of high redshift objects ($z>3$) that is selected in a way that does not suffer from dust extinction or any other optical bias.\n\n\\keywords{Surveys --- Galaxies: active --- Radio continuum: galaxies}\n\n\\end{abstract}\n \n\\section{Introduction}\nRadio galaxies have now been found out to redshifts of $z=5.19$ (\\cite{wvb99b}) and radio-loud quasars out to $z=4.72$ (\\cite{hoo98}). Although new optical selection techniques such as color-dropouts, deep spectroscopy of blank fields, and narrow-band \\Lya\\ imaging have now found galaxies at similar (\\cite{ste99}) and even higher redshifts (up to $z \\sim 5.75$; \\cite{dey98}; \\cite{wey98}; \\cite{spi98}, \\cite{hu99}), radio sources are still the only objects that can be selected uniformly over all redshift ranges, and in a way that does not suffer from optical biases such as dust extinction, which is known to be important at these high redshifts (\\eg\\ \\cite{hug98}; \\cite{ivi98}; \\cite{dic98}).\n\nAt low to moderate redshift ($z \\lesssim 1$), powerful radio sources are uniquely identified with massive ellipticals (\\cite{lil84}; \\cite{owe89}; \\cite{bes98}; \\cite{mcl00}). The strongest indications that this is also true at higher redshifts comes from the near-IR Hubble $K-z$ diagram of radio galaxies which shows a remarkably close correlation from the present out to $z=5.19$ (\\cite{lil89}; \\cite{eal97}; \\cite{wvb98}, \\cite{wvb99b}). This suggests that we can use radio galaxies to study the formation and evolution of the most massive galaxies, which, by their implied star-formation history, can put important constraints on galaxy formation models, and even on cosmological parameters (\\eg \\cite{dun96}; \\cite{spi97}).\nAlthough the unification model for radio galaxies and quasars (\\eg \\cite{bar89}) suggests we could also use quasars as tracers, a detailed stellar population study of quasar host galaxies is almost impossible due to the extreme luminosity of the AGN. Furthermore, samples of radio sources designed to find large quantities of quasars require additional optical selections (\\eg\\ \\cite{gre96}, \\cite{hoo98}, \\cite{whi00}).\n\n%---------------------------------------------------------- zalpha\n\\begin{figure}\n\\psfig{file=ds1811f1.eps,width=8.8cm}\n\\caption[zalpha.ps]{$\\alpha_{1400}^{325}$ against $z$ for 2 samples\nwithout spectral index selection (3CR, \\cite{spi85} and MRC,\n\\cite{mcc96}), and 2 USS samples (4C, \\cite{cha96a} and our new WN/TN\nsamples, as defined in this paper). Note that the correlation is\npresent in the spectrally unbiased 3CR and MRC, and that the 4C and\nour new USS samples are finding three to five times more $z>2$ radio\ngalaxies than the MRC. The horizontal dotted line indicates the\n$\\alpha_{1400}^{325} < -1.3$ cutoff used in our USS\nsample. \\label{zalpha}}\n\\end{figure}\n%______________________________________________________________\n\nConsiderable effort has been spent over the last decade to find these high redshift radio galaxies (HzRGs), which has lead to the discovery of more than 140 radio galaxies at redshifts $z>2$ (see \\eg \\cite{deb98a} for a recent summary). However by $z>3$, their numbers become increasingly sparse, and using flux limited radio surveys such as the 3CR ($S_{178} > 10$~Jy; \\cite{lai83}), or the MRC strip ($S_{408} > 0.95$~Jy; \\cite{mcc96}), the highest redshift radio galaxy found so far is at $z\\sim 3.2$ (Fig. \\ref{zalpha}; \\cite{raw90}; \\cite{mcc96}). This redshift limit arises because radio power is correlated with redshift in bright flux limited samples, and an upper limit exists in the radio luminosity. Lowering the flux limit would not only substantially increase the number of sources in these samples, but at the same time the fraction of luminous very high redshift radio galaxies would decrease (\\cite{blu98}, \\cite{jar99}). This fractional decrease would arise even if there is no decrease in co-moving space density at $z \\sim 2.5$. Such a redshift cutoff has been suggested by Bremer \\etal (1998), but recently Jarvis \\etal (1999) rule out a break at $z\\lesssim 2.5$. To efficiently find large numbers of HzRGs in acceptable observing times, it is therefore necessary to apply additional selection criteria, at the expense of completeness.\n\nBy far the most successful selection criterion has been the ultra steep spectrum criterion (\\eg \\cite{rot94}; \\cite{cha96a}; \\cite{blu98}). Selecting sources with very steep radio spectra increases dramatically the chance of finding $z>2$ radio galaxies (Fig. \\ref{zalpha}). This technique is based on the results of Tielens \\etal\\ (1979) \\nocite{tie79} and Blumenthal \\& Miley (1979)\\nocite{blu79}, who found that the identification fraction on the POSS ($R \\lesssim 20$) decreases with steepening spectral index, consistent with the steeper sources being at higher redshifts. It is now getting clear that this correlation can be explained by a combination of a K-correction of a concave radio spectrum and an increasing spectral curvature with redshift (\\cite{kro91}, \\cite{car99}; \\cite{wvb99a}). To further investigate the $z - \\alpha$ correlation, we have calculated spectral indices using the flux densities from the WENSS (\\cite{ren97}) and NVSS (\\cite{con98}) catalogs for four different samples: the flux density limited 3CR (\\cite{spi85}) and MRC (\\cite{mcc96}) surveys, and the USS samples from the 4C (\\cite{cha96a}) and the one presented in this paper.\nThe results (Fig. \\ref{zalpha}) show a trend for steeper spectral index sources to have higher redshifts in flux limited, spectrally unbiased samples, confirming the empirical relation out to the highest redshifts. The efficiency of the USS criterion is clearly illustrated by the fact that the 4C USS sample (\\cite{cha96a}) contains 50\\% $z>2$ sources, and by the early spectroscopic results on the USS samples presented in this paper, which indicate that $\\sim$2/3 of our sources have $z>2$. It is even more impressive to note that 13 of the 14 radio galaxies at $z>3.5$ we know of have been found from samples with a steep spectral index selection\\footnote{The only exception is VLA J123642+6213 (\\cite{wad99}), which has been identified in the HDF, but it does have a steep spectral index ($\\alpha_{1400}^{8500}=-0.94$).}! The limitation of this technique is that the steepest spectrum sources are rare, comprising typically only 0.5\\% (at $\\alpha < -1.30$) of a complete low frequency sample; therefore, large and deep all sky surveys are needed to obtain a significant sample of USS sources.\n\nWith the advent of several new deep all-sky surveys (\\S 2), it is now possible for the first time to construct a well defined all-sky USS sample with optimized selection criteria to find large numbers of $z>3$ radio galaxies. In this paper, we describe the construction of such a sample, and present high resolution radio observations needed to determine accurate positions and morphologies. This information is essential for the optical and near-IR identifications, and subsequent optical spectroscopy of a significant sub-set of our sample, which will be described in a future papers. \nThe organization of the paper is as follows: we describe the radio surveys we used in \\S 2 and define our samples in \\S 3. We present and discuss our radio observations in \\S 4, and present our conclusions in \\S 5. \n%Throughout the paper, we use $H_0 = 50$ km s$^{-1}$ Mpc$^{-1}$, $q_0 = 0$ and $\\Lambda = 0$.\n\\begin{table*}\n\\centerline{\\bf Table 1: Radio Surveys}\n\n\\footnotesize\n\\begin{tabular}{lccc}\n\\hline\n\\\\\n & WENSS & TEXAS & MRC \\\\\n\\\\\n\\hline\n\\\\\nFrequency (MHz) & 325 & 365 & 408 \\\\\nSky region (J2000) & $\\delta >$ +29\\arcdeg & $-$35\\fdg7 $< \\delta <$ +71\\fdg5 & $-$85\\arcdeg $< \\delta <$ +18\\fdg5 \\\\\n\\# of sources & 229,576 & 67,551 & 12,141 \\\\\nResolution & $ 54\\arcsec \\times$ 54\\arcsec cosec$\\delta$ & 10\\arcsec$^a$ & $2\\farcm62 \\times 2\\farcm86 \\sec (\\delta - 35\\fdg5)$ \\\\\nPosition uncertainty & 1\\farcs5 & 0\\farcs5---1\\arcsec & 8\\arcsec \\\\\n(strong sources) & & & \\\\\nRMS noise & $\\sim$4 mJy & 20 mJy & 70 mJy \\\\\nFlux density limit & 18 mJy & 150 mJy & 670 mJy \\\\\nReference & \\cite{ren97} & \\cite{dou96} & \\cite{lar81} \\\\\n\\\\\n\\hline\n\\hline\n\\\\\n & NVSS & FIRST & PMN \\\\\n\\\\\n\\hline\n\\\\\nFrequency (MHz) & 1400 & 1400 & 4850 \\\\\nSky region (J2000) & $\\delta > -$40\\arcdeg$^b$ & $7^h20^m < \\alpha < 17^h20^m$; +22\\fdg2 $< \\delta <$ +57\\fdg5 & $-$87\\fdg5 $< \\delta <$ +10\\arcdeg \\\\\n & & $21^h20^m < \\alpha < 3^h20^m$; $-$2\\fdg5 $< \\delta <$ +1\\fdg6 \\\\\n\\# of sources & 1,689,515 & 437,429 & 50,814 \\\\\nResolution & 45\\arcsec $\\times$ 45\\arcsec & 5\\arcsec $\\times$ 5\\arcsec & 4\\minpoint2 \\\\\nPosition uncertainty & 1\\arcsec & 0\\farcs1 & $\\sim$45\\arcsec \\\\\n(strong sources) & & & \\\\\nRMS noise & 0.5 mJy & 0.15 mJy & $\\sim$8 mJy \\\\\nFlux density limit & 2.5 mJy & 1 mJy & 20 mJy \\\\\nReference & \\cite{con98} & \\cite{bec95} & \\cite{gri93} \\\\\n\\hline\n\\end{tabular}\n\n$^a$ The Texas interferometer has a complicated beam. However, sources with separations between 10\\arcsec\\ and 2\\arcmin\\ can be successfully modeled as doubles, and will have a single entry in the catalog. See \\cite{dou96} for details.\n\n$^b$ Some small gaps are not covered. They are listed on the NVSS homepage (1998 January 19 version).\n\\end{table*}\n\n\n\\section{Description of the Radio Surveys}\n\n%---------------------------------------------------------- surveylimits\n\\begin{figure}[t]\n\\psfig{file=ds1811f2.eps,width=8.6cm}\n\\caption[surveylimits.ps]{Limiting flux density plotted for all major radio surveys. Lines are of constant spectral indices of $-1.3$. Note that WENSS, NVSS and FIRST have flux density limits $\\sim 100$ times deeper than previous surveys at comparable wavelengths. \\label{surveylimits}}\n\\end{figure}\n%______________________________________________________________\n\nDuring the past years, several all-sky radio-surveys have become available (Table 1), which are 1--2 orders of magnitude more sensitive than previous surveys at similar frequencies (Fig.\\ \\ref{surveylimits}). The combination of these new surveys allows us to define for the first time a large sample of USS sources that covers the whole sky\\footnote{To facilitate optical follow-up, we will exclude the Galactic plane at $|b|<15$\\degr} in both hemispheres. We list the main survey parameters in Table 1. In this section, we will briefly discuss the usefulness of these new radio surveys for the construction of USS samples. \n\n\\subsection{WENSS}\nThe Westerbork Northern Sky Survey (WENSS; \\cite{ren97}) at 325~MHz is the deepest low-frequency survey with a large sky coverage (3.14 sr). We used the WENSS to define the largest, and most complete USS sample to date, covering the entire sky North of declination 29\\arcdeg. We used version 1.0 of the main and polar WENSS catalogs. A small area is covered by both these catalogs; we selected only the sources from the main catalog in this overlapping area.\n\n\\subsection{Texas}\n%---------------------------------------------------------- texasppp\n\\begin{figure}\n\\psfig{file=ds1811f3.eps,width=9cm}\n\\caption[texasppp.ps]{Fraction of sources with '+++'\\ flag in the Texas catalog (see text) as a function of Texas $S_{365}$ flux density. Note that the selection of '+++' sources excludes primarily sources with $S_{365} \\lesssim 700$~mJy. \\label{texasppp}}\n\\end{figure}\n%______________________________________________________________\n\nThe Texas survey, made with the Texas interferometer from 1974 to 1983 (\\cite{dou96}), covers 9.63 steradians at a frequency of 365~MHz with a limiting flux density about ten times higher than that of the WENSS. The Texas interferometer's 3.5~km maximum baseline provides $<$1\\arcsec\\ positional accuracy, but its poor uv-coverage leads to irregular beamshapes and lobe-shifts, hampering accurate modeling of extended sources. A detailed discussion of these complications can be found in Douglas \\etal\\ (1996).\nTo minimize these problems, we have selected only the 40.9\\% sources that are well modeled (listed with a '+++' flag in the catalog). This selection excludes primarily $S_{365} \\lesssim 700$~mJy sources (Fig. \\ref{texasppp}), but even at $S_{365} \\gtrsim 700$~mJy, one out of three sources is excluded by this criterion.\n\\cite{dou96} have calculated the completeness above flux density S of the Texas catalog (defined as the fraction of sources with true flux density greater than S which appear in the catalog) by comparing the Texas with the MRC (\\cite{lar81}) and a variety of other low-frequency catalogs. They found that the completeness varies with declination (because the survey was done in declination strips over a large time span), and an expected increase in completeness at higher flux densities. In Table 2, we reproduce their completeness table, extended with the values after the '+++' selection.\n\n\\begin{table}\n\\centerline{\\bf Table 2: Completeness of the Texas survey}\n\\begin{tabular}{lcc}\n\\hline\nLimiting flux density & all sources & '+++' sources \\\\\n\\hline\n250 mJy & 0.8 & 0.2 \\\\\n350 mJy & 0.88 & 0.28 \\\\\n500 mJy & 0.92 & 0.40 \\\\\n750 mJy & 0.96 & 0.51 \\\\\n1 Jy & 0.96 & 0.50 \\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\n%---------------------------------------------------------- wtratio\n\\begin{figure}\n\\psfig{file=ds1811f4.eps,width=8.6cm}\n\\caption[wtratio.ps]{Ratio of integrated Texas over WENSS flux density against integrated WENSS flux density. Only Texas '+++' sources are plotted. The horizontal line is the expected ratio 0.865 due to the 40 MHz difference in central frequency, and assuming a spectral index of $\\alpha_{365}^{1400}=-0.88$. The curved line indicates a 150 mJy flux density limit in the Texas catalog. Note the increasing amount of overestimated Texas flux densities with decreasing flux density $S_{WENSS} < 400$~mJy. \\label{wtratio}}\n\\end{figure}\n%______________________________________________________________\n\nTo examine the reliability of the listed flux densities, and to check to what extent the '+++' selection has removed the spurious sources from the catalog, we have correlated the Texas '+++' sources with WENSS, NVSS and FIRST.\nIn Figure \\ref{wtratio}, we compare the Texas flux densities with those of the WENSS. At $S_{325} \\gtrsim 500$~mJy, the ratio of the flux densities is closely distributed around 0.9. This ratio is what we expect due to the 40 MHz central frequency difference between the two surveys and assuming a spectral index $\\alpha_{365}^{1400} = -0.879$ (the median of the Texas-NVSS spectral indices).\nAt $S_{325} \\lesssim 500$~mJy, the number of sources in the Texas catalog which are brighter than in WENSS catalog increases with decreasing flux density. This can be explained by the 'up-scattering' of sources near the flux limit of the Texas catalog (\\ie only sources intrinsically brighter than $S_{365} = 150$~mJy will be detected, but no $S_{365} < 150$~mJy sources with a large positive flux density measurement error). The result of this on a USS sample based on the Texas survey and correlated with a higher frequency survey (such as the NVSS), will be that with lower $S_{365}$, we will find more sources whose spectral indices appear steeper than they really are.\n\nWe also examined the dependence of the ratio Texas/WENSS flux density on angular size, determined from the FIRST survey (see \\S 2.1.4). We found no significant residual variation of the flux density ratio at sizes between 5\\arcsec\\ and 2\\arcmin.\n\nIn Figure \\ref{usssr}b, we plot the density of NVSS sources around a Texas source (see also \\S 2.2.5). The width of the over-density peak ($\\sim 10$\\arcsec) is due to the positional inaccuracies in the Texas and NVSS catalogues. However, the very broad tail of sources between 20\\arcsec\\ and 110\\arcsec\\ and the secondary peak coinciding with the fringe separation at 73\\arcsec\\ indicates that the '+++' selection did not remove all spurious sources from the catalog.\n\nIn summary, after the selection of '+++' sources, the Texas catalog still contains $<5$\\% spurious sources (\\cite{dou96}), probably due to residual lobe-shifted sources. Our comparison of the Texas flux densities with those of the WENSS survey shows that the differences are consistent with the errors quoted in the catalog. The selection of the Texas catalog with only '+++' sources is thus $>$95\\% reliable, but only $\\sim$40\\% complete.\n\n\\subsection{NVSS}\nThe NRAO VLA Sky Survey (NVSS; \\cite{con98}) covers the 10.3 steradians north of $-$40\\arcdeg\\ at 1.4~GHz, and reaches a 50 times lower limiting flux density than previous large area 1.4~GHz surveys. At the flux density levels we are using ($S_{1400}>10$~mJy), the catalog is virtually complete.\nBecause the NVSS resolution is comparable to that of the WENSS and Texas surveys, and its sky coverage is large, we use the NVSS to determine the spectral indices in our USS samples based on the WENSS and Texas surveys.\nThe final NVSS catalog was not yet completed at the time of our USS sample construction. For our final sample, presented in this paper, we use the 1998 January 19 version. This version still lacks data in a small number of regions of the sky (listed on the NVSS homepage). As a result, the sky coverage of the area listed in Table 3 is only 99.77\\%.\n\n\\subsection{FIRST}\nThe Faint Images of Radio Sky at Twenty centimeters (FIRST, \\cite{bec95}) survey is currently being made with the VLA in the B-array at 1.4~GHz, and has a limiting flux density three times deeper than the NVSS. We used the 1998 February 4 version of the catalog, covering 1.45~steradians. As noted by Becker \\etal\\ (1995), the photometry for extended sources in FIRST might be less reliable than that of the NVSS, due to the $9 \\times$ higher resolution, which could underestimate large-scale diffuse radio emission. As the FIRST area is completely covered by the NVSS, we will consistently use NVSS flux densities for our spectral index calculation. The main advantages of FIRST over NVSS for our purposes are the much better positional accuracy ($<$~0\\farcs5) and the higher (5\\arcsec) resolution. This combination allows the identification of even the very faint ($R > 20$) optical counterparts of radio sources. Additionally, the fainter detection limit of the FIRST allows an extra check on the flux densities of compact sources.\n\n\\subsection{MRC}\nThe Molonglo Reference Catalog of radio sources (\\cite{lar81}) at 408~MHz is presently the most sensitive low-frequency catalog with reasonable positional accuracy that covers the deep southern hemisphere, $\\delta < -35$\\arcdeg. We will use this catalog in combination with the PMN survey (see below) to define the first USS sample at $\\delta < -40\\arcdeg$.\n\n\\subsection{PMN}\nThe Parkes-MIT-NRAO (PMN) survey is a combination of 4 strips observed with the Parkes telescope at 4.85~GHz. The strips cover different parts of the sky, each with a slightly different limiting flux density. The regions are: southern ($-87\\fdg5 < \\delta < -37\\arcdeg$, \\cite{wri94}), zenith ($-37\\arcdeg < \\delta < -29\\arcdeg$, \\cite{wri96}), tropical ($-29\\arcdeg < \\delta < -9\\fdg5$, \\cite{gri94}), and equatorial ($-9\\fdg5 < \\delta < +10\\arcdeg$, \\cite{gri95}). For our southern hemisphere sample, we have used the southern and zenith catalogs to find USS sources at $\\delta < -30\\arcdeg$.\n\n%---------------------------------------------------------- usssky\n\\begin{figure}\n\\psfig{file=ds1811f6.eps,width=8.8cm}\n\\caption[usssky.ps]{Sky coverage of our 3 USS samples. Constant declination lines denote the boundaries between our the WN and TN and between the TN and MP samples, as indicated on the right. Note the difference in source density and the exclusion of the Galactic Plane. \\label{usssky}}\n\\end{figure}\n%______________________________________________________________\n\n\\section{USS Samples}\n\n%---------------------------------------------------------- usssr\n\\begin{figure*}\n\\psfig{file=ds1811f5.eps,width=18cm}\n\\caption[usssr.ps]{The density of sources from the high frequency catalog used in the correlation (NVSS or PMN) around sources from the low frequency catalog (WENSS, Texas or MRC) as a function of search radius. The dotted line represents the distribution of confusion sources (see text). The apparent under-density of WENSS--NVSS sources at search radii $\\simgt 60\\arcsec$ is due to the grouping of multiple component sources in the $\\sim$1\\arcmin\\ resolution WENSS. Note the plateau and secondary peak around the 73\\arcsec\\ Texas fringe separation in the Texas--NVSS correlation and the much larger uncertainty in the MRC--PMN correlation.\\label{usssr}}\n\\end{figure*}\n%______________________________________________________________\n\nFigure \\ref{surveylimits} shows that the surveys described above have very compatible flux density limits for defining samples of USS sources. At the same time, their sky coverage is larger and more uniform than previous surveys used for USS sample construction (\\cite{wie92}, \\cite{rot94}; \\cite{cha96a}, \\cite{blu98}; \\cite{ren98}, \\cite{pur99}, \\cite{ped99}, \\cite{and00}). We selected the deepest low and high frequency survey available at each part of the sky. For a small region $-35\\arcdeg < \\delta < -30\\arcdeg$ which is covered by both Texas and MRC, we used both surveys. This resulted in a more complete samples since the lower sensitivity of the PMN survey in the zenith strip (see \\S2.6) is partly compensated by the (albeit incomplete) Texas survey.\nTo avoid problems with high Galactic extinction during optical imaging and spectroscopy, all regions at Galactic latitude $|b| <$ 15\\arcdeg\\ were excluded\\footnote{This also reduces the number of Galactic pulsars in our sample (see \\S4.7.2).}, as well as the area within 7\\arcdeg of the LMC and SMC. This resulted in three USS samples that cover a total of 9.4 steradians (Fig. \\ref{usssky}).\n\nWe designate the USS samples by a two-letter name, using the first letter of their low- and high-frequency contributing surveys. Sources from these samples are named with this 2-letter prefix followed by their IAU J2000-names using the positions from the NVSS catalog (WN and TN samples) or the MRC catalog (MP sample). We did not rename the sources after a more accurate position from our radio observations or from the FIRST survey. The sample definitions are summarized in Table 3.\n\n\\subsection{Survey combination issues}\nWe first discuss the problems that arise when combining radio surveys with different resolutions and positional uncertainties.\n\\subsubsection{Correlation search radius}\nDue to the positional uncertainties and resolution differences between radio surveys, in general the same source will be listed with slightly different positions in the catalogs.\n\nTo empirically determine the search radius within which to accept sources in 2 catalogs to be the same, we compared the density of objects around the position listed in the low-frequency survey (which has lower resolution) with the expected number of random correlations in each sample ($\\equiv$ confusion sources). To determine this number as a function of distance from the position in the most accurate catalog, we created a random position catalog by shifting one of the input catalogs by 1\\arcdeg\\ in declination, and made a correlation with this shifted catalog. The density of sources as a function of distance from the un-shifted catalog then represents the expected number of confusing sources as a function of radial distance. In Figure \\ref{usssr}, we plot for each of our three samples the observed density around these sources with this confusing distribution over-plotted. The correlation search radius should thus be chosen at a distance small enough for the density of confusion sources to be negligible.\n\nWe decided to adopt the radius where the density of real sources is at least ten times higher that the density of confusion sources as the search radius for our sample construction, except for the WN sample (would be 15\\arcsec) where we chose the same radius as for the TN sample (10\\arcsec). The later was done for consistency between both samples. Because of the five times lower resolution and source densities in the MRC and PMN surveys, the search radius of the MP sample is eight times larger. Summarized, the search radii we used are 10\\arcsec\\ for WN and TN, and 80\\arcsec\\ for MP.\n\\begin{table*}\n\\centerline{\\bf Table 3: USS samples}\n\\scriptsize\n\\begin{tabular}{lrccccccc}\n\\hline\nSample & Sky Area$\\qquad\\quad$ & Density & Spectral Index & Search Radius & Flux Limit & C$^a$ & R$^a$ & \\# of Sources \\\\\n & & sr$^{-1}$ & & & mJy & &\\\\\n\\hline\nWN & 29\\arcdeg $< \\delta <$ 75\\arcdeg, $|b| >$ 15\\arcdeg$^b$ & 151 & $\\alpha_{325}^{1400} \\le -1.30$ & 10\\arcsec & $S_{1400} >$ 10 & 96\\% & 90\\% & 343 \\\\\nTN & $-$35\\arcdeg $< \\delta <$ 29\\arcdeg, $|b| >$ 15\\arcdeg$^b$ & 48$^c$ & $\\alpha_{365}^{1400} \\le -1.30$ & 10\\arcsec & $S_{1400} >$ 10 & 97\\%$^c$ & 93\\% & 268 \\\\\nMP & $\\delta < -$30\\arcdeg, $|b| >$ 15\\arcdeg & 26 & $\\alpha_{408}^{4800} \\le -1.20$ & 80\\arcsec & S$_{408} > 700$; S$_{4850} > 35$ & 100\\% & 100\\% & 58 \\\\\n\\hline\n\\end{tabular}\n\n$^a$ C=completeness and R=reliability accounting only for scattering across the spectral index limit (see \\S3.3.1).\n\n$^b$ coverage is only 99.7\\% because some small patches of sky we not covered at the time of writing. They are listed on the NVSS homepage \\\\(1998 January 19 version).\n\n$^c$ Because we selected only problem free sources from the Texas survey, the effective completness of the TN sample is $\\sim 30\\%$.\n\\end{table*}\n\n\\subsubsection{Angular size}\nIn order to minimize errors in the spectral indices due to different resolutions and missing flux on large angular scales in the composing surveys, we have only considered sources which are not resolved into different components in the composing surveys. Effectively, this imposes an angular size cutoff of $\\sim$1\\arcmin\\ to the WN, $\\sim$2\\arcmin\\ to the TN sample and $\\sim$4\\arcmin\\ to the MP sample.\nWe deliberately did not choose a smaller angular size cutoff (as \\eg Blundell \\etal\\ (1998) did for the 6C$^*$ sample), because (1) higher resolution angular size information is only available in the area covered by the FIRST survey, and (2) even a 15\\arcsec\\ cutoff would only reduce the number of sources by 30\\%, while it would definitely exclude several HzRGs from the sample. For example, in the 4C USS sample (\\cite{cha96b}), three out of eight $z>2$ radio galaxies have angular sizes $>$15\\arcsec.\n\nWe think that our $\\sim$1\\arcmin\\ angular size cutoff will exclude almost no HzRGs, because the largest angular size for $z > 2$ radio galaxies in the literature is 53\\arcsec\\ (4C~23.56 at $z = 2.479$; \\cite{cha96a}, \\cite{car97}), while all 45 $z > 2.5$ radio galaxies with good radio maps are $<$~35\\arcsec\\ (\\cite{car97}). Although the sample of known $z>2$ radio galaxies is affected by angular size selection effects, very few HzRGs larger than 1\\arcmin\\ would be expected.\n\nThe main incompleteness of our USS sample stems from the spectral index cutoff and the flux limit (\\S3.2). However, our flux limit ($S_{1400}$=10~mJy) is low enough to break most of the redshift-radio power degeneracy at $z>2$. To achieve this with flux limited samples, multiple samples are needed (\\eg \\cite{blu99}).\n\n\\subsection{Sample definition}\n\n\\subsubsection{WENSS-NVSS (WN) sample}\nA correlation of the WENSS and NVSS catalogs with a search radius of 10\\arcsec\\ centered on the WENSS position (see \\S 3.1.1) provides spectral indices for $\\sim 143,000$ sources. Even with a very steep $\\alpha_{325}^{1400} \\le -1.30$ spectral index criterion, we would still have 768 sources in our sample.\nTo facilitate follow-up radio observations, and to increase the accuracy of the derived spectral indices (see \\S 3.3.1), we have selected only NVSS sources with $S_{1400} > 10$~mJy. Because the space density of the highest redshift galaxies is low, it is important not to limit the sample area (see \\eg \\cite{raw98}) to further reduce the number of sources in our sample.\nBecause the NVSS has a slightly higher resolution than the WENSS (45\\arcsec\\ compared to $54\\arcsec \\times 54\\arcsec $cosec$~\\delta$), some WENSS sources have more than one associated NVSS source. We have rejected the 11 WN sources that have a second NVSS source within one WENSS beam. Instead of the nominal WENSS beam ($54\\arcsec \\times 54\\arcsec$cosec$\\delta$), we have used a circular 72\\arcsec\\ WENSS beam, corresponding to the major axis of the beam at $\\delta = 48\\arcdeg$, the position that divides the WN sample into equal numbers to the North and South. \nThe final WN sample contains 343 sources.\n\n\\subsubsection{Texas-NVSS (TN) sample}\nBecause the Texas and NVSS both have a large sky-coverage, the area covered by the TN sample includes 90\\% of the WN area. In the region $\\delta >29\\arcdeg$, we have based our sample on the WENSS, since it does not suffer from lobe-shift problems and reaches ten times lower flux densities than the Texas survey (\\S 2.2).\nIn the remaining 5.28 steradians South of declination +29\\arcdeg, we have spectral indices for $\\sim 25,200$ sources. Again, we used a 10\\arcsec\\ search radius (see \\S 3.1.1), and for the same reason as in the WN sample we selected only NVSS sources with $S_{1400} > 10$~mJy. Combined with the $\\alpha_{365}^{1400} \\le -1.30$ criterion, the number of USS TN sources is 285.\nAs for the WN sample, we further excluded sources with more than one $S_{1400}>$10~mJy NVSS source within 60\\arcsec\\ around the TEXAS position, leaving 268 sources in the final TN sample. We remind (see \\S 2.2) that the selection of the TEXAS survey we used is only $\\sim$40\\% complete with a strong dependence on flux density. Using the values from table 2, we estimate that the completeness of our TN sample is $\\sim$30\\%.\n\n\\subsubsection{MRC-PMN (MP) sample}\nIn the overlapping area, we preferred the TN over the MP sample for the superior positional accuracies and resolutions of both Texas and NVSS compared to MRC or PMN. Because the MRC survey has a low source density, we would have only 13 MP sources with $\\alpha_{408}^{4850} \\le -1.30$. We therefore relaxed this selection criterion to $\\alpha_{408}^{4850} \\le -1.20$, yielding a total sample of 58 sources in the deep South ($\\delta < -30$\\arcdeg).\n%---------------------------------------------------------- wn3spixhis\n\\begin{figure*}\n\\centerline{\\psfig{file=ds1811f7.eps,width=15cm}}\n\\caption[wn3his.ps]{Spectral index distributions from the WENSS-NVSS correlation. The left and right panels show the variation with 325~MHz and 1.4~GHz flux density. A low frequency selected sample is more appropriate to study the steep-spectrum population. The parameters of a two-component Gaussian fit (dotted line = steep, dashed line = flat) are shown in each panel. The solid line is the sum of both Gaussians. \\label{wn3spixhis}}\n\\end{figure*}\n%______________________________________________________________\n\n\\subsection{Discussion}\n\n\\subsubsection{Spectral index errors}\nWe have listed the errors in the spectral indices due to flux density errors in the catalogs in Tables A.1 to A.3. The WN and TN samples have the most accurate spectral indices: the median spectral index errors are $\\Delta\\bar{\\alpha}_{325}^{1400} = 0.04$ for WN sources and $\\Delta\\bar{\\alpha}_{365}^{1400} = 0.04$ ($S_{365} >$ 1~Jy) to 0.07 ($S_{365} >$ 150~mJy) for TN sources. For the MP sample, $\\Delta\\bar{\\alpha}_{408}^{4850} \\approx 0.1$, with little dependence on flux density (S$_{408} > 750$mJy).\n\nBecause our sample selects the sources in the steep tail of the spectral index distribution (Fig. \\ref{wn3spixhis} and \\ref{spixhis}), there will be more sources with an intrinsic spectral index flatter than our cutoff spectral index that get scattered into our sample by measurement errors than there will be sources with intrinsic spectral index steeper than the cutoff that get scattered out of our sample. \n\nFollowing the method of \\cite{ren98}, we fitted the steep tail between $-1.60 < \\alpha < -1.0$ with a Gaussian function. For each of our three samples, we generated a mock sample drawn from this distribution, and added measurement errors by convolving this true spectral index distribution with a Gaussian distribution with as standard deviation the mean error of the spectral indices. The WN mock sample predicts that 13 $\\alpha_{325}^{1400} < -1.30$ sources get scattered out of the sample while 36 $\\alpha_{325}^{1400} > -1.30$ sources get scattered into the USS sample.\nThus, the WN sample is 96\\% complete and 90\\% reliable. For the TN sample, we expect to loose 7 $\\alpha_{365}^{1400} < -1.30$ sources\\footnote{only due to the spectral index cutoff, the sample has more important incompleteness factors; see \\S 2.2}, and have 18 contaminating $\\alpha_{365}^{1400} > -1.30$ sources. The completeness is thus 97\\% and the reliability 93\\%. For the MP sample, this spectral index scattering is negligible, because there are too few sources in the steep spectral index tail.\n\nOur reliability and completeness are significantly better than the values of $\\sim$75\\% and $\\sim$50\\% of \\cite{ren98} because (1) our spectral indices are more accurate because they were determined from a wider frequency interval than the 325--610~MHz used by \\cite{ren98}, and (2) our sample has a steeper cutoff spectral index, where the spectral index distribution function contains fewer sources and has a shallower slope, leading to fewer sources that can scatter in or out of the sample.\n\n\\subsubsection{Spectral index distributions}\nUsing the 143,000 spectral indices from the WENSS-NVSS correlation, we examined the flux density dependence of the steep and flat spectrum sources. Selecting sources with $S_{325}>50$~mJy or $S_{1400}>100$~mJy assures that we will detect all sources with $\\alpha_{325}^{1400}>{\\frac{\\ln(S_{NVSS}^{lim}/50)}{\\ln(325/1400)}}=-1.82$ or $\\alpha_{325}^{1400}<{\\frac{\\ln(S_{WENSS}^{lim}/100)}{\\ln(325/1400)}}=0.82$ respectively, where $S_{NVSS}^{lim}=3.5$~mJy and $S_{WENSS}^{lim}=30$~mJy are the lowest flux densities where the NVSS and WENSS are complete (\\cite{con98}, \\cite{ren97}). The results shown in Figure \\ref{wn3spixhis} therefore reflect only the effect of a different selection frequency. Two populations are present in both the $S_{325}$ and $S_{1400}$ selected distributions. The peaks of the steep and flat populations at $\\bar{\\alpha}_{325}^{1400} \\approx -0.8$ and $\\bar{\\alpha}_{325}^{1400} \\approx -0.4$ do not show significant shifts over three orders of magnitude in flux density. This is consistent with the results that have been found at 4.8~GHz (\\cite{wit79}, \\cite{mac81}, \\cite{owe83}), with the exception that their $\\bar{\\alpha}_{1400}^{4800} \\approx 0.0$ for the flat spectrum component is flatter than the $\\bar{\\alpha}_{325}^{1400} \\approx -0.4$ we found. However, we find that the relative contribution of the flat spectrum component increases from 25\\% at $S_{1400}>0.1$~Jy to 50\\% at $S_{1400}>2.5$~Jy\n\nBecause the steep- and flat-spectrum populations are best separated in the $S_{1400}>$2.5~Jy bin, we have searched the literature for identifications of all 58 $S_{1400} > 2.5$~Jy sources to determine the nature of both populations. All but one (3C 399, \\cite{mar98}) of the objects outside of the Galactic plane ($|b| > 15\\arcdeg$) were optically identified. Of the 30 steep spectrum ($\\alpha_{325}^{1400} < -0.6$) sources, two thirds were galaxies, while the rest were quasars. Half of the flat spectrum ($\\alpha_{325}^{1400} > -0.6$) sources were quasars, 20\\% blazars, and 30\\% galaxies. Figure \\ref{wn3spixhis} therefore confirms that the steep and flat spectral index populations are dominated by radio galaxies and quasars respectively. We also find that while the relative strength between the steep and flat spectrum populations changes due to the selection frequency, the median spectral index and width of the population does not change significantly over three orders in magnitude of flux density. Even fainter studies would eventually start to get contamination from the faint blue galaxy population (see \\eg\\ \\cite{win85}).\n%---------------------------------------------------------- spixhis\n\\begin{figure}\n\\psfig{file=ds1811f8.eps,width=9cm}\n\\caption[spixhis.ps]{ Logarithmic spectral index distribution for WENSS-NVSS (full line), Texas-NVSS (dot-dash line) and MRC-PMN (dotted line). The vertical line indicates the -1.3 cutoff used in our spectral index selection. Note the difference in number density and the sharper fall-off on the flat-end part of the TN and MP compared to the WN. \\label{spixhis}}\n\\end{figure}\n%______________________________________________________________\n\n\\begin{table*}\n\\centerline{\\bf Table 4: Radio Observations}\n\\begin{center}\n\\begin{tabular}{lrrrcr}\n\\hline\nUT Date & Telescope & Config. & Frequency & Resolution & \\# of sources \\\\\n\\hline\n1996 October 28 & VLA & A & 4.86 GHz & 0\\farcs3 & 90 WN, 25 TN \\\\\n1997 January 25 & VLA & BnA& 4.86 GHz & 0\\farcs6 & 29 TN \\\\\n1997 March 10 & VLA & BnA & 4.885 GHz & 0\\farcs6 & 8 TN \\\\\n1997 December 15 & ATCA & 6C & 1.420 GHz & 6\\arcsec $\\times$ 6\\arcsec\\ cosec$\\delta$ & 41 MP, 32 TN \\\\\n1998 August 12+17 & VLA & B & 4.86 GHz & 1\\farcs0 & 151 WN \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\subsubsection{Consistency of the three USS samples}\nWe compare the spectral index distributions of our three USS samples in logarithmic histograms (Fig. \\ref{spixhis}). The distributions are different in two ways. First, the WENSS-NVSS correlation contains nine times more sources than the Texas-NVSS, and 14 times more than the MRC-PMN correlation. Second, the shapes of the distributions are different: while the steep side of the TN sample coincides with that of the WN, its flat end part falls off much faster. The effect is so strong that it even shifts the TN peak steep-wards by $\\sim0.15$. For the MP sample, the same effect is less pronounced, though still present.\n\nBoth effects are due to the different flux density limits of the catalogs. The deeper WENSS catalog obviously contains more sources than the TEXAS or MRC catalogs, shifting the distributions vertically in Figure \\ref{surveylimits}. The relative 'shortage' of flat spectrum sources in the Texas-NVSS and MRC-PMN correlations can be explained as follows. A source at the flux density limit in both WENSS and NVSS would have a spectral index of $\\alpha_{325}^{1400} = -1.3$, while for Texas and NVSS this would be $\\alpha_{365}^{1400} = -1.7$ (see Fig. \\ref{surveylimits}). Faint NVSS sources with spectral indices flatter than these limits will thus more often get missed in the TEXAS catalog than in the WENSS catalog. This effect is even strengthened by the lower completeness at low flux densities of the Texas catalog. However, very few USS sources will be missed in either the WENSS-NVSS or Texas-NVSS correlations\\footnote{The TN sample will have more spurious sources at low flux density levels; see \\S2.2}. The parallel slope also indicates that the USS sources from both the WENSS-NVSS and Texas-NVSS correlations were drawn from the same population of radio sources. We therefore expect a similar efficiency in finding HzRGs from both samples.\n\nThe MP sample has been defined using a spectral index with a much wider frequency difference. However, the observed ATCA 1.420 GHz flux densities can be used to construct $\\alpha_{408}^{1420}$. An 'a posteriori' selection using $\\alpha_{408}^{1420} \\le -1.30$ from out ATCA observations (see \\S 4.2) would keep $\\sim$60\\% of the MP sources in a WN/TN USS sample.\n\n\\section{Radio Observations}\nOf all the major radio surveys described in \\S 2, only FIRST has sufficient positional accuracy and resolution for the optical identification of $R > 20$ objects. We present FIRST maps of 139 WN and 8 TN sources in appendices B.2 and B.4.\n\nOutside the area covered by FIRST, we have observed all the remaining WN sources, 30\\% of the TN sample, and 71\\% of the MP sources at 0\\farcs3 to 5\\arcsec\\ resolution using the Very Large Array (VLA; \\cite{nap83}) and Australia Telescope Compact Array (ATCA; \\cite{fra92}) telescopes.\nA log of the radio observations is given in Table 4. We observed targets for our VLA runs on the basis of declination (A-array for $\\delta >$ 0\\arcdeg\\ and BnA-array for $\\delta <$ 0\\arcdeg) and sky coverage of the WN and TN samples, which were still incomplete at the time of the 1996 observations. We observed all WN, and most TN sources with the VLA, and all MP sources with the ATCA. We observed TN sources between $-31$\\arcdeg $< \\delta < -10$\\arcdeg\\ with either VLA or ATCA, depending on the progress of the NVSS at the time of the observations.\n\n\\subsection{VLA observations and data reduction}\n\nWe observed all sources in the standard 4.86 GHz C-band with a 50 MHz bandwidth, resulting in a resolution of $\\sim$0\\farcs3 in the A-array and $\\sim$1\\arcsec\\ in the BnA-array. We spent 5 minutes on each source, implying a theoretical rms level of 75 $\\mu$Jy, or a ratio of total integrated signal over map noise of 110 for the weakest sources, assuming no spectral curvature beyond 1.4 GHz.\nWe performed calibration and data editing in \\aips, the Astronomical Image Processing System from NRAO.\nWe used 3C286 as the primary flux calibrator in all runs. Comparison of the flux density of 3C48 with the predicted values indicated the absolute flux density scale was accurate up to 2\\%. We observed nearby (within 15\\arcdeg) secondary flux calibrators every 15 to 20 minutes to calibrate the phases. After flagging of bad data, we spilt the uv-data up into separate data sets for imaging and self-calibration in DIFMAP, the Caltech difference mapping program (\\cite{she97}).\nWe used field sizes of 164\\arcsec\\ (A$-$array) or 256\\arcsec\\ (BnA$-$array) with pixel scales of 0\\farcs08 / pixel (A$-$array) or 0\\farcs25 / pixel (BnA$-$array). Even the smallest field of view is still four times larger than the resolution of the NVSS, so all components of an unresolved NVSS source will be covered.\n\nWe cleaned each source brighter than the 5$\\sigma$ level, followed by a phase-only self-calibration. We repeated the latter for all sources in the field of a source. Next, we made a new model from the (self-calibrated) uv-data, and subsequently cleaned to the level reached before. The last stage in the mapping routine was a deep clean with a 1\\% gain factor over the entire field. Most of the resulting maps have noise levels in the range 75 to 100 $\\mu$Jy, as expected.\n\n\\subsection{ATCA observations and data reduction}\nWe used the ATCA in the 6C configuration, which has a largest baseline of 6km. We observed at a central frequency of 1.384 GHz, which was selected to avoid local interference. We used 21 of the 30 frequency channels that had high enough signal, which resulted in an effective central frequency of 1.420 GHz, with a 84 MHz bandwidth. In order to obtain a good uv-coverage, we observed each source eight to ten times for three minutes, spread in hour angle. The primary flux calibrator was the source 1934-648; we used secondary flux calibrators within 20\\arcdeg\\ of the sources to calibrate the phases.\nWe performed editing and calibration in \\aips, following standard procedures. We made maps using the automated mapping/self-calibration procedure MAPIT in \\aips. The resulting 1.420 GHz maps (Fig. \\ref{mpatca}) have noise levels of $\\sim$5 mJy.\n\n\\subsection{Results}\nOf all 343 WN sources, 139 have FIRST maps (appendix B.2). All remaining 204 sources were observed, and 141 were detected. The remaining 30\\% were too faint at 4.86~GHz to be detected in 5~min snapshots, because their high frequency spectral index steepens more than expected, or they were over-resolved. Because they are significantly brighter, all the observed 89 TN and 41 MP sources were detected.\nWe present contour maps of all the detections in Appendices B.1, B.3, B.5, and B.6 and list the source parameters in Tables A.1 to A.3.\n\nWe have subdivided our sources into 5 morphological classes, using a classification similar to that used by R\\\"ottgering \\etal\\ (1994). Note that this classification is inevitably a strong function of the resolution, which varies by a factor of 20 between the VLA A-array and the ATCA observations. \n\nWe have determined the source parameters by fitting two-dimensional Gaussian profile to all the components of a source. The results are listed in Tables A.1 to A.3 which contain:\n\n\\begin{description}\n\\item[Col 1:]{Name of the source in IAU J2000 format. The 2-letter prefix indicates the sample: WN: WENSS--NVSS, TN: Texas--NVSS, MP: MRC--PMN.}\n\\item[Col 2:]{The integrated flux density from the low-frequency catalog.}\n\\item[Col 3:]{The integrated flux density at the intermediate frequency, determined from the NVSS for WN and TN, or from the 1.420~GHz ATCA observations for the MP sample.}\n\\item[Col 4:]{The integrated flux density at 4.86 GHz, determined from the VLA observations for WN and TN, and from the PMN survey for the MP sample.}\n\\item[Col 5:]{The lower frequency two-point spectral index. This is the spectral index used to define the WN and TN samples.}\n\\item[Col 6:]{The higher frequency two-point spectral index. This is the spectral index used to define the MP sample.}\n\\item[Col 7:]{Morphological classification code: single (S), double (D), triple (T) and multiple (M) component sources, and irregularly shaped diffuse (DF) sources.}\n\\item[Col 8:]{Largest angular size. For single component sources, this is the de-convolved major axis of the elliptical Gaussian, or, for unresolved sources (preceded with $<$), an upper limit is given by the resolution. For double, triple and multiple component sources, this is the largest separation between their components. For diffuse sources this is the maximum distance between the source boundaries defined by three times the map rms noise.}\n\\item[Col 9:]{De-convolved position angle of the radio structure, measured North through East}\n\\item[Col 10 -- 11:]{J2000 coordinates, determined from the map with position code listed in col. 12. The positions in the VLA and ATCA maps have been fitted with a single two-dimensional elliptical Gaussian. For double (D) sources, the geometric midpoint is given; for triples (T) and multiples (M), the core position is listed. For diffuse (DF) sources we list the center as determined by eye.}\n\\item[Col 12:]{Position code, indicating the origin of the morphological and positional data in column 7 to 11: A=ATCA, F=FIRST, M=MRC, N=NVSS, and V=VLA}.\n\\end{description}\n\n\\subsection{Notes on individual sources}\n\\noindent{\\bf WN~J0043+4719:} The source 18\\arcsec\\ north of the NVSS position is not detected in the NVSS. This is therefore not a real USS source because the NVSS flux density was underestimated.\n\n\\noindent{\\bf WN~J0048+4137:} Our VLA map probably doesn't go deep enough to detect all the flux of this source.\n\n\\noindent{\\bf WN~J0727+3020:} The higher resolution FIRST map shows that both components of this object are indeed identified on the POSS, even though the NVSS position is too far off to satisfy our identification criterion.\n\n\\noindent{\\bf WN~J0717+4611:} Optical and near-IR spectroscopy revealed this object as a red quasar at $z=1.462$ (\\cite{deb98b}).\n\n\\noindent{\\bf WN~J0725+4123:} The extended POSS identification suggest this source is located in a galaxy cluster.\n\n\\noindent{\\bf WN~J0829+3834:} The NVSS position of this unresolved source is 7\\arcsec\\ ($3\\sigma$) from the FIRST position, which itself is only at 2\\arcsec\\ from the WENSS position.\n\n\\noindent{\\bf WN~J0850+4830:} The difference with the NVSS position indicates that our VLA observations are not deep enough to detect a probable north-eastern component.\n\n\\noindent{\\bf WN~J0901+6547:} This 38\\arcsec\\ large source is over-resolved in our VLA observations, and probably even misses flux in the NVSS, and is therefore not a real USS source.\n\n\\noindent{\\bf WN~J1012+3334:} The bend morphology and bright optical sources to the east indicate this object is probably located in a galaxy cluster.\n\n\\noindent{\\bf WN~J1101+3520:} The faint FIRST component 20\\arcsec\\ north of the brighter Southern component is not listed in the FIRST catalog, but is within 1\\arcsec\\ of a faint optical object. This might be the core of a 70\\arcsec\\ triple source.\n\n\\noindent{\\bf WN~J1152+3732:} The distorted radio morphology and bright, extended POSS identification suggest this source is located in a galaxy cluster.\n\n\\noindent{\\bf WN~J1232+4621:} This optically identified and diffuse radio source suggest this source is located in a galaxy cluster.\n\n\\noindent{\\bf WN~J1314+3515:} The diffuse radio source appears marginally detected on the POSS.\n\n\\noindent{\\bf WN~J1329+3046A,B, WN~J1330+3037, WN~J1332+3009 \\& WN~J1333+3037:} The noise in the FIRST image is almost ten times higher than average due to the proximity of the $S_{1400}$=15~Jy source 3C~286.\n\n\\noindent{\\bf WN~J1330+5344:} The difference with the NVSS position indicates that our VLA observations are not deep enough to detect a probable south-eastern component.\n\n\\noindent{\\bf WN~J1335+3222:} Although the source appears much like the hotspot of a larger source with the core 90\\arcsec\\ to the east, no other hotspot is detected in the FIRST within 5\\arcmin.\n\n\\noindent{\\bf WN~J1359+7446:} The extended POSS identification suggests this source is located in a galaxy cluster.\n\n\\noindent{\\bf WN~J1440+3707:} The equally bright galaxy 30\\arcsec\\ south of the POSS identification suggests that this source is located in a galaxy cluster.\n\n\\noindent{\\bf WN~J1509+5905:} The difference with the NVSS position indicates that our VLA observations are not deep enough to detect a probable western component.\n\n\\noindent{\\bf WN~J1628+3932:} This is the well studied galaxy NGC~6166 in the galaxy cluster Abell 2199 (\\eg \\cite{zab93}.\n\n\\noindent{\\bf WN~J1509+5905:} The difference with the NVSS position indicates that our VLA observations are not deep enough to detect a probable west-south-western component.\n\n\\noindent{\\bf WN~J1821+3601:} The source 35\\arcsec\\ south-west of the NVSS position is not detected in the NVSS. This is therefore not a real USS source because the NVSS flux density was underestimated.\n\n\\noindent{\\bf WN~J1832+5354:} The source 19\\arcsec\\ north-east of the NVSS position is not detected in the NVSS. This is therefore not a real USS source because the NVSS flux density was underestimated.\n\n\\noindent{\\bf WN~J1852+5711:} The extended POSS identification suggests this source is located in a galaxy cluster.\n\n\\noindent{\\bf WN~J2313+3842:} The extended POSS identification suggests this source is located in a galaxy cluster.\n\n\\noindent{\\bf TN~J0233+2349:} This is probably the north-western hotspot of a 35\\arcsec\\ source, with the south-eastern component barely detected in our VLA map. \n\n\\noindent{\\bf TN~J0309-2425:} We have classified this source as a 13\\arcsec\\ double, but the western component might also be the core of a 45\\arcsec\\ source, with the other hotspot around $\\alpha = 3^h9^m10^s, \\delta=-24\\arcdeg25\\arcmin50\\arcsec$.\n\n\\noindent{\\bf TN~J0349-1207:} The core-dominated structure is reminiscent of the red quasar WN~J0717+4611.\n\n\\noindent{\\bf TN~J0352-0355:} This is probably the south-western hotspot of a 30\\arcsec\\ source.\n\n\\noindent{\\bf TN~J0837-1053:} Given the 10\\arcsec\\ difference between the positions of the NVSS and diffuse VLA source, this is probably the northern component of a larger source.\n\n\\noindent{\\bf TN~J0408-2418:} This is the z=2.44 source MRC 0406-244 (\\cite{mcc96}). The bright object on the POSS is a foreground star to the north-east of the R=22.7 galaxy.\n\n\\noindent{\\bf TN~J0443-1212:} Using the higher resolution VLA image, we can identify this radio source with a faint object on the POSS.\n\n\\noindent{\\bf TN~J2106-2405:} This is the z=2.491 source MRC 2104-242 (\\cite{mcc96}). The identification is an R=22.7 object, not the star to the north-north-west of the NVSS position.\n%---------------------------------------------------------- wnspeccurv\n\\begin{figure}\n\\psfig{file=ds1811f9.eps,width=9cm,angle=90}\n\\caption[wnspeccurv]{Radio ``color-color'' plots for the WN sample. The abscissa is the $\\alpha_{325}^{1400}$ spectral index used to construct the sample. The ordinates are the low-frequency spectral indices determined from the 8C (38 MHz, \\cite{ree90}) or 6C (151 MHz, \\cite{hal93}) and the 325~MHz WENSS (left panel), and the high frequency spectral index determined between the 1.4~GHz NVSS and our 4.86~GHz VLA observations (right panel). The line in each panel indicates a straight power law spectrum. Note the unequal number of points on either side of these lines, indicating substantial spectral curvature. \\label{wnspeccurv}}\n\\end{figure}\n%______________________________________________________________\n\n\\subsection{Radio spectra and spectral curvature}\n\nWe have used the CATS database at the Special Astronomical Observatory (\\cite{ver97}) to search for all published radio measurements of the sources in our samples. In Appendix C, we show the radio spectra for all sources with flux density information for more than two frequencies (the $S_{4860}$ points from our VLA observations are also included). These figures show that most radio spectra have curved spectra, with flatter spectral indices below our selection frequencies, as has been seen in previous USS studies (see \\eg\\ \\cite{rot94}, \\cite{blu98}). \n\nThis low frequency flattening and high frequency steepening is obvious in the radio 'color-color diagrams' of the WN sample (Fig. \\ref{wnspeccurv}). The median spectral index at low frequencies ($\\nu < 325$~MHz) is $-1.16$, while the median $\\bar{\\alpha}_{325}^{1400} = -1.38$. At higher frequencies ($\\nu > 1400$~MHz), the steepening continues to a median $\\bar{\\alpha}_{1400}^{4850} = -1.44$. Note that the real value of the latter is probably even steeper, as 30\\% of the WN sources were not detected in our 4.86~GHz VLA observations, and may therefore have even more steepened high-frequency spectral indices.\n\n\\subsection{Radio source properties}\n\\subsubsection{Radio source structure and angular size}\n\nIn Table 5, we give the distribution of the radio structures of the 410 USS sources for which we have good radio-maps. At first sight, all three our samples have basically the same percentage of resolved sources, but the similar value for the MP sample is misleading, as it was observed at much lower resolution.\n\n\\begin{table}\n\\centerline{\\bf Table 5: Radio Structure Distribution}\n\\tiny\n\\begin{center}\n\\begin{tabular}{lrrrr}\n\\\\\n & \\multicolumn{4}{c}{USS Samples} \\\\\n\\cline{2-5} \\\\\nMorphology & WN$\\qquad$ & TN$\\qquad$ & MP$\\qquad$ & Combined$\\quad$\\\\\n\\hline\nSingle & 157 (56$\\pm$4\\%) & 43 (48$\\pm$7\\%) & 23 (56$\\pm$12\\%) & 223 (54$\\pm$4\\%) \\\\\nDouble & 81 (29$\\pm$3\\%) & 28 (31$\\pm$6\\%) & 16 (39$\\pm$10\\%) & 125 (31$\\pm$3\\%) \\\\\nTriple & 22 ( 8$\\pm$2\\%) & 9 (10$\\pm$3\\%) & 0 ( 0$\\pm$ 0\\%) & 31 ( 8$\\pm$1\\%) \\\\\nMultiple & 2 ( 1$\\pm$1\\%) & 4 ( 5$\\pm$2\\%) & 0 ( 0$\\pm$ 0\\%) & 6 ( 1$\\pm$1\\%) \\\\\nDiffuse & 18 ( 6$\\pm$2\\%) & 5 ( 6$\\pm$3\\%) & 2 ( 5$\\pm$ 3\\%) & 25 ( 6$\\pm$1\\%) \\\\\n\\hline\n\\# Observed & 280 & 89 & 41 & 410 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n%---------------------------------------------------------- slas\n\\begin{figure}\n\\psfig{file=ds1811f10.eps,width=9cm}\n\\caption[slas]{Median angular size for the flux density limited, spectrally unbiased WSRT samples of \\cite{oor88} (open triangles), and for our combined USS samples (filled squares). The sources have been binned in equal number bins, and errors represent the 35\\% and 65\\% levels of the distribution. Note that our USS selection does not affect the value of the median, and that our USS samples also exclude sources that fall below the break at $S_{1400} \\lesssim 10$~mJy. \\label{slas}}\n\\end{figure}\n%______________________________________________________________\n\nOur results are different from the USS sample of R\\\"ottgering \\etal\\ (1994), which contains only 18\\% unresolved sources at comparable resolution (1\\farcs5). To check if this effect is due to the fainter sources in our sample, we compared our sample with the deep high resolution VLA observations of spectrally unbiased sources (\\cite{oor88}; \\cite{col85}).\nThe resolution of our observations is significantly better than the median angular size for $S_{1400} > 1$~mJy sources, allowing us to accurately determine the median angular sizes in our samples.\nWe find that our USS sources have a constant median angular size of $\\sim6$\\arcsec\\ between 10~mJy and 1~Jy (Fig. \\ref{slas}). This is indistinguishable from the results from samples without spectral index selection. It indicates that our USS selection of sources with $\\alpha < -1.3$ and $\\Theta < 1\\arcmin$ does not bias the angular size distribution in the resulting sample. The 'downturn' in angular sizes that occurs at $\\sim$1~mJy is probably due to a different radio source population, which consist of lower redshift sources in spiral galaxies (see \\eg, \\cite{col85}, \\cite{oor87}, \\cite{ben93}). By selecting only sources with $S_{1400} > 10$~mJy, we have avoided ``contamination'' of our sample by these foreground sources.\n\nWe have searched for further correlations between spectral index or spectral curvatures and angular size or flux density, but found no significant results, except for a trend for more extended sources to have lower than expected 4.86~GHz flux densities, but this effect can be explained by missing flux at large scales in our VLA observations.\n\n\\subsection{Identifications}\n\\subsubsection{POSS}\nWe have searched for optical identifications of our USS sources on the digitized POSS-I. We used the likelihood ratio identification criterion as described by \\eg de Ruiter \\etal\\ (1977). In short, this criterion compares the probability that a radio and optical source with a certain positional difference are really associated with the probability that this positional difference is due to confusion with a field object (mostly a foreground star), thereby incorporating positional uncertainties in both radio and optical positions. The ratio of these probabilities is expressed as the likelihood ratio $LR$. \nIn the calculation, we have assumed a density of POSS objects $\\rho = 4 \\times 10^{-4}$ \\arcsec$^{-2}$, independent of galactic latitude $b$. \nWe have adopted a likelihood ratio cutoff \\Lh=1.0, slightly lower than the values used by de Ruiter \\etal\\ (1977) and R\\\"ottgering \\etal\\ (1994). We list sources with $LR >$ 1.0 for our USS samples in Tables A.4 to A.6. We have included four WN sources (WN~J0704+6318, WN~J1259+3121, WN~J1628+3932 and WN~J2313+3842), two TN sources (TN~J0510-1838 and TN~J1521+0741) and four MP sources (MP~J0003-3556, MP~J1921-5431, MP~J1943-4030 and MP~J2357-3445) as identifications because both their optical and radio morphologies are diffuse and overlapping, making it impossible to measure a common radio and optical component, while they are very likely to be associated.\n\n%---------------------------------------------------------- idfraction\n\\begin{figure}\n\\psfig{file=ds1811f11.eps,width=9cm}\n\\caption[idfraction]{Identification fraction on the POSS as a function of spectral index for the combined WN and TN sample. Note the absence of a further decrease in the identification fraction with steepening spectral index. \\label{idfraction}}\n\\end{figure}\n%______________________________________________________________\n\nFigure \\ref{idfraction} shows the identification fraction of USS sources on the POSS ($R \\lesssim 20$). Because the distributions for the WN and TN are very similar, we have combined both samples to calculate the identification fraction. Unlike the results for 4C USS (\\cite{tie79,blu79}), we do not detect a decrease of the identification fraction with steepening spectral index\\footnote{In the Westerbork faint USS (\\cite{wie92}) or the USS sample from R\\\"ottgering \\etal\\ (1994), there is also a decrease in the identification fraction, even at limiting magnitudes of $R=22.5$ and $R=23.7$, indicating that this trend continues out to fainter magnitudes and radio fluxes}. We interpret the constant $\\sim$15\\% identification fraction from our sample as a combined population of foreground objects, primarily consisting of clusters (see next section). Our extremely steep spectral index criterion would then selected only radio galaxies too distant to be detected on the POSS ($R \\simgt 20.0$).\n\n\\subsubsection{Literature}\nUsing the NASA Extragalactic Database (NED), the SIMBAD database and the W$^3$Browse at the High Energy Astrophysics Science Archive Research Center, we have searched for known optical and X-ray identifications of sources in our samples (see appendices A.7 to A.9). Of the bright optical ($R \\lesssim 20$) identifications, only one source is a known as a K0-star, three (TN~J0055$+$2624, TN~J0102$-$2152, and TN~J1521$+$0742) are ``Relic radio galaxies'' (\\cite{kom94}, \\cite{gio99}), while all others are known galaxy clusters. \n\nAll optical cluster identifications, except MP~J1943-4030, are also detected in the ROSAT All-Sky survey Bright Source Catalogue (RASS-BSC; \\cite{vog99}). Conversely, of the 23 X-ray sources, seven are known galaxy clusters, and three known galaxies. The remaining 13 sources are good galaxy cluster candidates because they either show a clear over-density of galaxies on the POSS (eight sources), or they have low X-ray count rates ($<$ 0.02 counts s$^{-1}$), suggesting that these might be more distant galaxy clusters too faint to be detected on the POSS. We conclude that probably $>$3\\% of our USS sources are associated with galaxy clusters, and that the combined USS + X-ray selection is an efficient (up to 85\\%) selection technique to find galaxy clusters\\footnote{In the RASS-BSC, only 14\\% of the extra-galactic sources are identified with galaxy clusters (\\cite{vog99}).}.\n\nThree of our USS sources (WN~J2313+4253, TN~J0630-2834 and TN~J1136+1551) are previously known pulsars (\\cite{kap98}). It is worth noting that two out of nine sources in our USS samples with $\\alpha < -2$ are known pulsars. Because Lorimer \\etal\\ (1995) \\nocite{lor95} found the median spectral index of pulsars to be $\\sim -1.6$, we examined the distribution of spectral indices as a function of Galactic latitude. In figure \\ref{pulsargb}, we plot the percentage of $\\alpha_{325}^{1400} < -1.60$ pulsar candidates as a function of Galactic latitude. The four times higher density near the Galactic plane strongly suggests that the majority of these $\\alpha_{325}^{1400} < -1.60$ sources are indeed pulsars, which are confined to our Galaxy. A sample of such $\\alpha_{325}^{1400} < -1.60$ sources at $|b|<15$\\degr\\ would be an efficient pulsar search method.\n\n%---------------------------------------------------------- pulsargb\n\\begin{figure}\n\\psfig{file=ds1811f12.eps,width=9cm}\n\\caption[pulsargb]{Percentage of $\\alpha_{325}^{1400} < -1.60$ radio sources from a WENSS--NVSS correlation as a function of Galactic latitude. Note the clear peak near the Galactic plane, indicating that these $\\alpha_{325}^{1400} < -1.60$ objects might well be Galactic pulsars. \\label{pulsargb}}\n\\end{figure}\n%______________________________________________________________\n\nWe also note that no known quasars are present in our sample. Preliminary results from our optical spectroscopy campaign (De Breuck \\etal\\ 1998b, 2000) indicate that $\\sim$10\\% of our sample are quasars. We interpret this lack of previously known quasars are a selection bias in quasar samples against USS sources.\n\nAt $R \\simgt 20$, all five USS sources with known redshift are HzRGs, indicating a selection of sources without detections on the POSS strongly increases our chances of finding HzRGs.\n\n\\section{Conclusions}\nWe have constructed three spatially separated samples of USS sources containing a total of 669 objects. High-resolution radio observations of more than half of these show that the median size is $\\sim$6\\arcsec, independent of 1.4 GHz flux density, which is consistent with results of similar resolution surveys of samples without spectral index selection. The absence of a downturn in angular size at the lowest fluxes indicates that we do not include significant numbers of spiral galaxies in our sample. A USS sample fainter than ours would therefore include more of these foreground sources, and be less efficient to find HzRGs. \n\nThe identification fraction on the POSS is $\\sim$15\\%, with no clear dependence on spectral index, indicating that the HzRGs in the sample are all too distant to be detected, and the POSS detections consist of different classes of objects. A correlation of our USS samples with X-ray catalogs showed that at least 85\\% of the X-ray identifications seem to be galaxy clusters known from the literature or by inspection of the POSS. We conclude that (1) the majority of the 'non HzRG' USS sources in our sample are clusters, and (2) the combined selection of USS and X-ray sources is an extremely efficient technique to select galaxy clusters.\n\nThe above results indicate that up to 85\\% of our USS sample might be HzRGs. To identify these objects, we have started an intensive program of R- and K-band imaging on 3--10m class telescopes.\nInitial results from optical spectroscopy indicate that 2/3 are indeed $z>2$ radio galaxies (\\cite{deb98a}), and K-band imaging of optically undetected ($R > 25$) sources (see \\eg, \\cite{wvb99a}) has already lead to the discovery of the first radio galaxy at $z>5$ (\\cite{wvb99b}). \n\n\\begin{acknowledgements}\n\nWe are grateful for the excellent help provided by the staff of the\nVLA and ATCA observatories, with special thanks to Chris Carilli and\nGreg Taylor (NRAO), and Ray Norris and Kate Brooks (ATNF) for help in\nwith observation planning and data reduction. We thank Hien ``Napkin''\nTran for his comments on the manuscript. The VLA is a facility of the\nNational Radio Astronomy Observatory, which is operated by Associated\nUniversities Inc. under cooperative agreement with the National\nScience Foundation. The Australia Telescope is funded by the\nCommonwealth of Australia for operation as a National Facility managed\nby CSIRO. The authors made use of the database CATS (\\cite{ver97}) of\nthe Special Astrophysical Observatory, the NASA/IPAC Extragalactic\nDatabase (NED) which is operated by the Jet Propulsion Laboratory,\nCalifornia Institute of Technology, under contract with the National\nAeronautics and Space Administration, and the High Energy Astrophysics\nScience Archive Research Center Online Service, provided by the\nNASA/Goddard Space Flight Center. Work performed at the Lawrence\nLivermore National Laboratory is supported by the DOE under contract\nW7405-ENG-48.\n\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\\bibitem[Abell \\etal\\ 1989]{abe89} Abell, G. O., Corwin, H. G. Jr., \\& Olowin, R. 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Morganti, Sydney, p.\\ 236\n\\bibitem[van Breugel \\etal\\ 1999b]{wvb99b} van Breugel, W., De Breuck, C., Stanford\n, S. A., Stern, D., R\\\"ottgering, H., \\& Miley, G. 1999, \\apj, 518, 61\n\\bibitem[Verkhodanov \\etal\\ 1997]{ver97} Verkhodanov O. V., Trushkin S. A., Andernach H., Chernenkov V. N. 1997, in \"Astronomical Data Analysis Software and Systems VI\", ed.: G. Hunt and H. E. Payne, ASP Conference Series, Vol. 125, p.\\ 322-325.\n\\bibitem[Vigotti \\etal\\ 1989]{vig89} Vigotti, M., Grueff, G., Perley, R., Clark, B. G., \\& Bridle, A. 1989, \\aj, 98, 419\n\\bibitem[Voges \\etal\\ 1999]{vog99} Voges, W., \\etal\\ 1999, \\aap, 349, 389 \n\\bibitem[Waddington \\etal\\ 1999]{wad99} Waddington, I., Windhorst, R., Cohen, S., Partridge, R., Spinrad, H., \\& Stern, D. 1999, \\apjl, 526, L77 \n\\bibitem[Weymann et al. 1998]{wey98} Weymann, R. \\etal\\ 1998, \\apjl, 505, L95 \n\\bibitem[White, Giommi \\& Angelini 1994]{whi94} White, N. E., Giommi, P. \\& Angelini, L. 1994, \\iaucirc, 6100, 1\n\\bibitem[White \\etal\\ 1997]{whi97} White, R. L., Becker, R. H., Helfand, D. J., \\& Gregg, M. D. 1997, \\apj, 475, 479\n\\bibitem[White \\etal\\ 2000]{whi00} White, R. L. \\etal 2000, \\apjs, in press, astro-ph/9912215\n\\bibitem[Wieringa 1991]{wie91} Wieringa, M. H., Ph. D. thesis, Rijksuniversiteit Leiden\n\\bibitem[Wieringa \\& Katgert 1992]{wie92} Wieringa, M. H., \\& Katgert, P. 1992, \\aasup, 93, 399\n\\bibitem[Windhorst \\etal\\ 1985]{win85} Windhorst, R. A., Miley, G. K., Owen, F. N., Kron, R. G., \\& Koo, D. C. 1985, \\apj, 289, 494\n\\bibitem[Witzel \\etal\\ 1979]{wit79} Witzel, A., Schmidt, J., Pauliny-Toth, I. I. K., \\& Nauber, U. 1979, \\aj, 84, 942\n\\bibitem[Wright \\etal\\ 1994]{wri94} Wright, A. E., Griffith, M. R., Burke, B. F., \\& Ekers, R. D. 1994, \\apjs, 91, 111\n\\bibitem[Wright \\etal\\ 1996]{wri96} Wright, A. E., Griffith, M. R., Troup, E., Hunt, A., Burke, B. F., \\& Ekers, R. D. 1996, \\apjs, 103, 145\n\\bibitem[Zabludoff \\etal\\ 1993]{zab93} Zabuldoff, A. I., Geller, M. J., Huchra, J. P., \\& Vogeley, M. S. 1993, \\aj, 106, 1273\n\\end{thebibliography}\n\n\\appendix\n\\section{Source Lists}\n\\include{wntable}\n\\include{tnmptable}\n\n\\begin{table}\n\\footnotesize\n\\centerline{\\bf Table A.4: WN POSS identifications}\n\\begin{tabular}{rrrrr}\nName & $S_{1400}$ & $\\alpha_{325}^{1400}$ & LAS & LR$^a$ \\\\\n & mJy & & \\arcsec & \\\\\n\\hline\nWN J0029$+$3439 & 40.9 & $-$1.34 & 12.8 & 4.2 \\\\\nWN J0121$+$4305 & 50.8 & $-$1.39 & \\nodata & 7.1 \\\\\nWN J0315$+$3757 & 13.3 & $-$1.35 & 1.7 & 14.8 \\\\\nWN J0559$+$6926 & 12.9 & $-$1.31 & 0.3 & 4.6 \\\\\nWN J0641$+$4325 & 15.6 & $-$1.57 & \\nodata & 195.6 \\\\\nWN J0725$+$4123 & 35.5 & $-$1.39 & 8.3 & 183.0 \\\\\nWN J0756$+$5010 & 29.9 & $-$1.31 & 1.7 & 127.3 \\\\\nWN J0830$+$3018 & 13.9 & $-$1.41 & 3.5 & 27.3 \\\\\nWN J0835$+$3439 & 19.1 & $-$1.38 & 58.0 & 24.6 \\\\\nWN J0923$+$4602 & 12.1 & $-$1.49 & 21.6 & 17.0 \\\\\nWN J0952$+$5153 & 16.1 & $-$1.76 & 2.7 & 194.1 \\\\\nWN J0955$+$6023 & 10.9 & $-$1.54 & 3.1 & 1.0 \\\\\nWN J1014$+$7407 & 21.8 & $-$1.41 & 2.2 & 147.7 \\\\\nWN J1026$+$2943 & 12.0 & $-$1.31 & 11.9 & 136.5 \\\\\nWN J1030$+$5415 & 29.2 & $-$1.39 & 6.1 & 16.4 \\\\\nWN J1052$+$4826 & 154.2 & $-$1.31 & 10.0 & 38.1 \\\\\nWN J1124$+$3228 & 38.9 & $-$1.31 & 5.7 & 101.2 \\\\\nWN J1130$+$4911 & 18.9 & $-$1.34 & 37.0 & 18.9 \\\\\nWN J1141$+$6924 & 11.8 & $-$1.32 & \\nodata & 1.4 \\\\\nWN J1148$+$5116 & 20.5 & $-$1.35 & 6.7 & 1.0 \\\\\nWN J1152$+$3732 & 17.1 & $-$2.18 & 15.0 & 159.9 \\\\\nWN J1232$+$4621 & 19.8 & $-$1.30 & 12.5 & 42.9 \\\\\nWN J1258$+$5041 & 28.8 & $-$1.42 & 44.9 & 3.7 \\\\\nWN J1259$+$3121 & 34.0 & $-$1.41 & 20.6 & 0.0 \\\\\nWN J1330$+$6505 & 10.5 & $-$1.34 & 1.8 & 21.5 \\\\\nWN J1353$+$3336 & 15.9 & $-$1.31 & \\nodata & 3.3 \\\\\nWN J1400$+$4348 & 20.2 & $-$1.49 & 6.4 & 29.2 \\\\\nWN J1403$+$3109 & 45.7 & $-$1.35 & 11.0 & 148.5 \\\\\nWN J1410$+$4615 & 14.2 & $-$1.36 & 4.4 & 42.5 \\\\\nWN J1440$+$3707 & 16.7 & $-$1.76 & 7.4 & 182.0 \\\\\nWN J1459$+$4947 & 18.7 & $-$1.53 & 3.0 & 47.2 \\\\\nWN J1558$+$7028 & 15.7 & $-$1.36 & 2.1 & 2.8 \\\\\nWN J1624$+$4202 & 11.0 & $-$1.31 & 24.4 & 182.2 \\\\\nWN J1628$+$3932 & 3680.7 & $-$1.36 & 48.8 & 0.0 \\\\\nWN J1717$+$3828 & 35.8 & $-$1.60 & 33.6 & 141.4 \\\\\nWN J1752$+$2949 & 16.9 & $-$1.42 & 3.2 & 3.4 \\\\\nWN J1801$+$3336 & 11.6 & $-$1.69 & 2.5 & 1.5 \\\\\nWN J1815$+$3656 & 17.6 & $-$1.34 & 1.6 & 195.0 \\\\\nWN J1819$+$6213 & 12.7 & $-$1.45 & 1.6 & 122.9 \\\\\nWN J1852$+$5711 & 53.4 & $-$1.36 & \\nodata & 145.4 \\\\\nWN J1927$+$6436 & 80.3 & $-$1.44 & 20.1 & 6.2 \\\\\nWN J1944$+$6552 & 147.2 & $-$1.53 & 1.8 & 147.5 \\\\\nWN J2146$+$3330 & 10.8 & $-$1.56 & \\nodata & 4.6 \\\\\nWN J2147$+$3137 & 25.4 & $-$1.46 & \\nodata & 31.9 \\\\\nWN J2313$+$3842 & 11.3 & $-$1.50 & \\nodata & 0.0 \\\\\nWN J2313$+$4053 & 40.2 & $-$1.42 & 1.5 & 36.4 \\\\\n\\hline\n\\end{tabular}\n\n$^a$ Likelihood Ratio, see text\n\\vspace{1cm}\n\\end{table}\n\n\\begin{table}\n\\footnotesize\n\\centerline{\\bf Table A.5: TN POSS identifications}\n\\begin{tabular}{rrrrr}\nName & $S_{1400}$ & $\\alpha_{365}^{1400}$ & LAS & LR$^a$ \\\\\n & mJy & & \\arcsec & \\\\\n\\hline\nTN J0244$+$0327 & 84.8 & $-$1.38 & \\nodata & 6.9 \\\\\nTN J0245$+$2700 & 54.0 & $-$1.47 & \\nodata & 30.5 \\\\\nTN J0250$+$0130 & 39.1 & $-$1.45 & \\nodata & 14.7 \\\\\nTN J0256$-$2717 & 177.9 & $-$1.32 & \\nodata & 126.6 \\\\\nTN J0301$+$0155 & 402.7 & $-$1.70 & \\nodata & 21.3 \\\\\nTN J0433$+$0717 & 33.1 & $-$1.44 & \\nodata & 29.9 \\\\\nTN J0443$-$1212 & 56.8 & $-$1.47 & 20.2 & 162.1 \\\\\nTN J0510$-$1838 & 641.3 & $-$1.76 & 36.1 & 0.0 \\\\\nTN J0729$+$2436 & 68.9 & $-$2.03 & 19.4 & 129.0 \\\\\nTN J0812$+$0915 & 43.4 & $-$1.38 & \\nodata & 37.7 \\\\\nTN J0818$-$0741 & 59.3 & $-$1.38 & \\nodata & 96.5 \\\\\nTN J0958$-$1103 & 70.6 & $-$1.35 & \\nodata & 181.8 \\\\\nTN J1043$+$2404 & 52.0 & $-$1.59 & 3.7 & 167.8 \\\\\nTN J1053$-$1518 & 63.7 & $-$1.33 & \\nodata & 1.8 \\\\\nTN J1117$-$1409 & 134.5 & $-$1.31 & \\nodata & 128.0 \\\\\nTN J1220$+$0604 & 65.1 & $-$1.50 & \\nodata & 189.4 \\\\\nTN J1239$+$1005 & 79.3 & $-$1.75 & \\nodata & 180.7 \\\\\nTN J1245$-$1127 & 88.0 & $-$1.32 & \\nodata & 146.1 \\\\\nTN J1326$-$2330 & 83.2 & $-$1.37 & \\nodata & 190.1 \\\\\nTN J1408$-$0855 & 114.3 & $-$1.34 & \\nodata & 160.9 \\\\\nTN J1418$-$2256 & 82.0 & $-$1.38 & 7.6 & 85.4 \\\\\nTN J1513$-$2417 & 83.6 & $-$1.34 & \\nodata & 2.5 \\\\\nTN J1521$+$0741 & 105.6 & $-$2.10 & \\nodata & 0.0 \\\\\nTN J1531$-$3234 & 80.6 & $-$1.39 & 4.8 & 172.5 \\\\\nTN J1547$-$2218 & 72.4 & $-$1.32 & \\nodata & 7.1 \\\\\nTN J1556$-$2759 & 66.4 & $-$1.65 & \\nodata & 9.2 \\\\\nTN J1628$+$1604 & 55.5 & $-$1.77 & \\nodata & 153.7 \\\\\nTN J1646$-$1328 & 102.5 & $-$1.32 & \\nodata & 119.7 \\\\\nTN J1701$+$0252 & 57.1 & $-$1.36 & \\nodata & 19.4 \\\\\nTN J1707$-$1120 & 54.2 & $-$1.53 & \\nodata & 85.5 \\\\\nTN J1710$-$0826 & 69.2 & $-$1.38 & \\nodata & 8.8 \\\\\nTN J1953$-$0541 & 59.0 & $-$1.56 & \\nodata & 71.3 \\\\\nTN J2028$+$0811 & 74.8 & $-$1.34 & \\nodata & 33.1 \\\\\nTN J2155$-$2109 & 77.2 & $-$1.31 & \\nodata & 184.6 \\\\\nTN J2335$+$0634 & 84.3 & $-$1.33 & \\nodata & 189.2 \\\\\n\\hline\n\\end{tabular}\n\n$^a$ Likelihood Ratio, see text\n\\vspace{1cm}\n\\end{table}\n\n\\begin{table}\n\\footnotesize\n\\centerline{\\bf Table A.6: MP UKST identifications}\n\\begin{tabular}{rrrrr}\nName & $S_{408}$ & $\\alpha_{408}^{4850}$ & LAS & LR$^a$ \\\\\n & mJy & & \\arcsec & \\\\\n\\hline\nMP J0003$-$3556 & 2440 & $-$1.28 & \\nodata & 0.0 \\\\\nMP J0103$-$3225 & 2290 & $-$1.29 & \\nodata & 88.1 \\\\\nMP J0618$-$7340 & 750 & $-$1.37 & \\nodata & 7.5 \\\\\nMP J1033$-$3418 & 5590 & $-$1.23 & \\nodata & 81.7 \\\\\nMP J1250$-$4026 & 1350 & $-$1.24 & 7.4 & 131.0 \\\\\nMP J1921$-$5431 & 4590 & $-$1.71 & \\nodata & 0.0 \\\\\nMP J1943$-$4030 & 4400 & $-$1.36 & \\nodata & 0.0 \\\\\nMP J2313$-$4243 & 1390 & $-$1.28 & \\nodata & 95.5 \\\\\nMP J2357$-$3445 & 8700 & $-$1.74 & \\nodata & 0.0 \\\\\n\\hline\n\\end{tabular}\n\n$^a$ Likelihood Ratio, see text\n\\vspace{1cm}\n\\end{table}\n\n\\begin{table*}\n\\centerline{\\bf Table A.7: WN identifications from the literature}\n\\begin{tabular}{rrrrrr}\nName & $z$ & $R$[mag] & $F_X^a$ & Identification & Reference \\\\\n\\hline\nWN J0633$+$4653 & \\nodata & 23.6 & \\nodata & 4C +46.12 & \\cite{cha96a} \\\\\nWN J0648$+$4309 & \\nodata & 23.0 & \\nodata & B3 0644+432 & \\cite{wie92} \\\\\nWN J0658$+$4444 & \\nodata & 23.4 & \\nodata & B3 0654+448 & \\cite{wie92} \\\\\nWN J0717$+$4611 & 1.462 & 21.6 & \\nodata & B3 0714+462 & \\cite{deb98b} \\\\\nWN J0725$+$4123 & \\nodata & \\nodata & 0.1137 & 1RXS J072600.0+4 & \\cite{vog99} \\\\\nWN J0923$+$4602 & \\nodata & \\nodata & 0.0242 & 1WGA J0923.1+460 & \\cite{whi94}\\\\\nWN J0952$+$5153 & 0.214 & \\nodata & 0.2413 & ZwCl 0949.6+5207 & \\cite{vog99} \\\\\nWN J1148$+$5116 & \\nodata & \\nodata & 0.0508 & 1RXS J114802.7+5 & \\cite{vog99} \\\\\nWN J1152$+$3732 & \\nodata & \\nodata & 0.0192 & 1WGA J1152.5+373 & \\cite{whi94} \\\\\nWN J1259$+$3121 & \\nodata & 16.2 & \\nodata & NGP9 F323-0140639 & \\cite{ode96} \\\\\nWN J1332$+$3009 & \\nodata & 19.8 & \\nodata & NGP9 F324-0235590 & \\cite{ode96} \\\\\nWN J1352$+$4259 & \\nodata & 21.7 & \\nodata & 4C +43.31 & \\cite{vig89} \\\\\nWN J1359$+$7447 & \\nodata & \\nodata & 0.07485 & 1RXS J135916.0+7 & \\cite{vog99} \\\\\nWN J1400$+$4348 & \\nodata & 8.2 & & HD122441 & SIMBAD \\\\\nWN J1410$+$4615 & \\nodata & \\nodata & & SHK 010 & \\cite{sha73} \\\\\nWN J1436$+$6319 & 4.261 & 24.1 & \\nodata & 4C +63.20 & \\cite{lac94} \\\\\nWN J1440$+$3707 & \\nodata & \\nodata & 0.07944 & 1RXS J144005.4+3 & \\cite{vog99} \\\\\nWN J1628$+$3932 & 0.031 & 13.1 & 4.5 & NGC 6166 & \\cite{zab93} \\\\\nWN J1736$+$6502 & \\nodata & 22.2 & \\nodata & 8C 1736+650 & \\cite{lac93} \\\\\nWN J1829$+$6913 & \\nodata & \\nodata & 0.05765 & 1RXS J182903.8+6 & \\cite{vog99} \\\\\nWN J1852$+$5711 & \\nodata & \\nodata & 0.1466 & 1RXS J185209.4+5 & \\cite{vog99} \\\\\nWN J1944$+$6552 & \\nodata & \\nodata & 0.1118 & 1RXS J194423.1+6 & \\cite{vog99} \\\\\nWN J2319$+$4251 & \\nodata & \\nodata & 0.1255 & 1RXS J231947.4+4 & \\cite{vog99} \\\\\n\\hline\n\\end{tabular}\n\n$^a$F$_X$ is the number of X-ray counts s$^{-1}$ as listed in the cited catalogs.\n\n\\vspace{1cm}\n\\end{table*}\n\n\\begin{table*}\n\\centerline{\\bf Table A.8: TN identifications from the literature}\n\\begin{tabular}{rrrrrr}\nName & $z$ & $R$[mag] & $F_X^a$ & Identification & Reference \\\\\n\\hline\nTN J0055$+$2624 & 0.1971 & \\nodata & \\nodata & ABELL 85 & \\cite{gio99} \\\\\nTN J0102$-$2152 & 0.0604 & \\nodata & \\nodata & ABELL 133 & \\cite{kom94} \\\\\nTN J0245$+$2700 & \\nodata & \\nodata & 0.0782 & 1RXS J024521.0+2 & \\cite{bad98} \\\\\nTN J0256$-$2717 & 0.480 & 19.2 & \\nodata & MRC 0254-27 & \\cite{mcc96} \\\\\nTN J0301$+$0155 & 0.170 & \\nodata & 0.2053 & ZwCl 0258.9+0142 & \\cite{cra95} \\\\\nTN J0408$-$2418 & 2.440 & 22.7 & \\nodata & MRC 0406-244 & \\cite{mcc96} \\\\\nTN J0510$-$1838 & \\nodata & 19.5 & 0.00314 & 1RXS J051032.4-1 & \\cite{vog99} \\\\\nTN J0630$-$2834 & \\nodata & \\nodata & 0.00314 & 1WGA J0630.8-283 & \\cite{whi94} \\\\\nTN J0729$+$2436 & \\nodata & \\nodata & 0.1752 & 1RXS J072927.4+2 & \\cite{vog99} \\\\\nTN J0936$-$2243 & 1.339 & 23.0 & \\nodata & 3C 222 & \\cite{hec94} \\\\\nTN J0958$-$1103 & 0.153 & \\nodata & 1.64 & ABELL 0907 & \\cite{mcc96} \\\\\nTN J1521$+$0742 & 0.045 & 14.5 & 1.64 & NGC 5920 & \\cite{kom94} \\\\\nTN J2106$-$2405 & 2.491 & 22.7 & \\nodata & MRC 2104-242 & \\cite{mcc96} \\\\\nTN J2239$-$0429 & \\nodata & 18.8 & \\nodata & 4C -04.85 & \\cite{rot95} \\\\\nTN J2320$+$1222 & \\nodata & 22.9 & \\nodata & MRC 2317+120 & \\cite{rot95} \\\\\n\\hline\n\\end{tabular}\n\n$^a$F$_X$ is the number of X-ray counts s$^{-1}$ as listed in the cited catalogs.\n\n\\vspace{1cm}\n\\end{table*}\n\n\\begin{table*}\n\\centerline{\\bf Table A.9: MP identifications from the literature}\n\\begin{tabular}{rrrrrr}\nName & $z$ & $R$[mag] & $F_X^a$ & Identification & Reference \\\\\n\\hline\nMP J0003$-$3556 & 0.0497 & 13.2 & 0.5206 & ABELL 2717 & \\cite{col95} \\\\\nMP J0103$-$3225 & \\nodata & 19.0 & & IRAS F01009-3241 & \\cite{con95} \\\\\nMP J1250$-$4026 & \\nodata & \\nodata & 0.000595 & 1RXP J125006-402 & \\cite{vog99} \\\\\nMP J1943$-$4030 & \\nodata & 17.3 & & ABELL 3646 & \\cite{abe89} \\\\\nMP J2313$-$4243 & 0.0564 & 14.6 & 2.024 & ABELL S1101 & \\cite{sto91} \\\\\nMP J2357$-$3445 & 0.0490 & 13.7 & 2.27 & ABELL 4059 & \\cite{pos95} \\\\\n\\hline\n\\end{tabular}\n\n$^a$F$_X$ is the number of X-ray counts s$^{-1}$ as listed in the cited catalogs.\n\n\\end{table*}\n\n\\clearpage\n\n\\section{Radio Maps}\n\\subsection{VLA Maps of the WN Sample}\n\n\\small{VLA maps of the WN sample. The contour scheme is a geometric progression in $\\sqrt 2$, which implies a factor 2 change in surface brightness every 2 contours. The first contour level, indicated above each plot, is at $3\\sigma_{rms}$, where $\\sigma_{rms}$ is the rms noise determined around the sources. The restoring beams are indicated in the lower left corner of the plots. Two maps are given for each source, one showing a 6\\arcmin\\ field of view to show possible related components, and a smaller blow-up of the source to show its morphology. The open cross indicates the NVSS position. Sources identified on the POSS have been marked in the top right corner. \\label{wnvla}}\n\n\\subsection{FIRST Maps of the WN Sample}\n\n\\small{FIRST maps of the WN sample.Contours are as in section \\ref{wnvla} \\label{wnfirst}}\n\n\\subsection{VLA Maps of the TN Sample}\n\n\\small{VLA maps of the TN sample. Contours are as in section \\ref{wnvla} \\label{tnvla}}\n \n\\subsection{FIRST Maps of the TN Sample}\n\n\\small{FIRST maps of the TN sample. Contours are as in section \\ref{wnvla}. \\label{tnfirst}}\n\n\\subsection{ATCA Maps of the TN Sample}\n\n\\small{ATCA maps of the TN sample. Contours are as in section \\ref{wnvla}. \\label{tnatca}}\n\n\\subsection{ATCA Maps of the MP Sample}\n\n\\small{ATCA maps of the MP sample. Contours are as in section \\ref{wnvla}. \\label{mpatca}}\n\n\\section{Radio Spectra}\n\\subsection{Radio Spectra for the WN Sample}\n\n\\small{Radio spectra of the WN sample using data from the literature. The two connected flux points indicate the spectral index used to select the source in the USS sample. Note the steeper spectra with higher frequency in most objects. \\label{wnradiospectra}}\n\n\\subsection{Radio Spectra for the TN Sample}\n\n\\small{Radio spectra of the TN sample using data from the literature. The two connected flux points indicate the spectral index used to select the source in the USS sample. Note the steeper spectra with higher frequency in most objects. \\label{tnradiospectra}}\n\n\\subsection{Radio Spectra for the MP Sample}\n\n\\small{Radio spectra of the MP sample using data from the literature and our ATCA observations (diamonds). The two connected flux points indicate the spectral index used to select the source in the USS sample. Note the steeper spectra with higher frequency in most objects. \\label{mpradiospectra}}\n\n\\section{POSS Finding Charts}\n\\subsection{POSS Finding Charts for the WN Sample}\n\n\\small{POSS finding charts of the WN sample. The open cross indicates the NVSS position.}\n\n\\subsection{POSS Finding Charts for the TN Sample}\n\n\\small{POSS finding charts of the TN sample. The open cross indicates the NVSS position.}\n\n\\subsection{POSS Finding Charts for the MP Sample}\n\n\\small{POSS finding charts of the MP sample. The open cross indicates the MRC position.}\n\n\\end{document}\n"},{"name":"tnmptable.tex","string":"\\begin{table*}\n\\centerline{\\bf Table A.2: TN sample}\n\\tiny\n\\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{365}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{365}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nTN J0008-0912 & 638$\\pm$ 64 & 100.2$\\pm$ 4.4 & \\nodata & $-1.38\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 00 08 52.43 & $-$09 12 01.4 & N \\\\\nTN J0018+1904 & 498$\\pm$ 30 & 84.5$\\pm$ 3.8 & \\nodata & $-1.32\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 00 18 07.35 & $+$19 04 50.0 & N \\\\\nTN J0026+1501 & 241$\\pm$ 26 & 39.4$\\pm$ 2.0 & \\nodata & $-1.35\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 00 26 03.31 & $+$15 01 29.2 & N \\\\\nTN J0027+0059 & 735$\\pm$ 55 & 98.0$\\pm$ 4.4 & \\nodata & $-1.50\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 00 27 39.36 & $+$00 59 53.6 & N \\\\\nTN J0033-2731 & 512$\\pm$ 41 & 66.1$\\pm$ 3.0 & \\nodata & $-1.52\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 00 33 24.28 & $-$27 31 48.1 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0037+2629 & 442$\\pm$ 35 & 70.8$\\pm$ 3.2 & \\nodata & $-1.36\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 00 37 10.05 & $+$26 29 42.3 & N \\\\\nTN J0038-1540 & 471$\\pm$ 33 & 63.9$\\pm$ 1.4 & $10.8\\pm0.6$ & $-1.49\\pm$0.06 & $-1.43\\pm0.05$ & D & 3.2 & 18 & 00 38 47.19 & $-$15 40 06.6 & V \\\\\nTN J0040+1417 & 435$\\pm$ 41 & 71.1$\\pm$ 1.5 & \\nodata & $-1.35\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 00 40 37.04 & $+$14 17 14.6 & N \\\\\nTN J0041+1250 & 451$\\pm$ 65 & 71.0$\\pm$ 3.3 & $21.0\\pm1.1$ & $-1.38\\pm$0.11 & $-0.98\\pm0.06$ & D & 10.7 & 103 & 00 41 31.27 & $+$12 50 32.3 & V \\\\\nTN J0042+2649 & 484$\\pm$ 57 & 69.6$\\pm$ 3.2 & \\nodata & $-1.44\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 00 42 32.46 & $+$26 49 06.2 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0055+2624 & 8670$\\pm$457 & 1375.5$\\pm$56.2 & \\nodata & $-1.37\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 00 55 50.38 & $+$26 24 35.8 & N \\\\\nTN J0102-1055 & 775$\\pm$ 41 & 110.4$\\pm$ 4.9 & $16.4\\pm0.9$ & $-1.45\\pm$0.05 & $-1.53\\pm0.06$ & D & 1.5 & 136 & 01 01 59.99 & $-$10 55 56.0 & V \\\\\nTN J0102-2152 & 1900$\\pm$ 88 & 168.3$\\pm$ 6.7 & \\nodata & $-1.80\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 01 02 41.09 & $-$21 52 30.2 & N \\\\\nTN J0114-0333 & 367$\\pm$ 36 & 54.7$\\pm$ 2.6 & $12.9\\pm0.7$ & $-1.42\\pm$0.08 & $-1.16\\pm0.06$ & T & 2.4 & 146 & 01 14 42.50 & $-$03 33 58.8 & V \\\\\nTN J0119-2054 & 522$\\pm$ 60 & 87.8$\\pm$ 4.0 & \\nodata & $-1.33\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 01 19 47.65 & $-$20 54 46.8 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0121+1320 & 348$\\pm$ 33 & 57.3$\\pm$ 2.7 & $ 8.4\\pm0.5$ & $-1.34\\pm$0.08 & $-1.55\\pm0.06$ & S & 0.3 & 89 & 01 21 42.74 & $+$13 20 58.3 & V \\\\\nTN J0154+0044 & 465$\\pm$ 29 & 78.6$\\pm$ 3.6 & \\nodata & $-1.32\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 01 54 38.48 & $+$00 44 37.7 & N \\\\\nTN J0156+1619 & 437$\\pm$ 45 & 62.9$\\pm$ 2.9 & \\nodata & $-1.44\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 01 56 18.01 & $+$16 19 52.5 & N \\\\\nTN J0201-1302 & 360$\\pm$ 33 & 57.0$\\pm$ 2.7 & $11.0\\pm0.6$ & $-1.37\\pm$0.08 & $-1.32\\pm0.06$ & S & $<$ 1.3 & 0 & 02 01 15.80 & $-$13 02 19.4 & V \\\\\nTN J0205+2242 & 381$\\pm$ 26 & 60.4$\\pm$ 2.8 & $ 8.8\\pm0.5$ & $-1.37\\pm$0.06 & $-1.55\\pm0.06$ & D & 2.7 & 148 & 02 05 10.69 & $+$22 42 50.2 & V \\\\\n&&&&&&&&&&&\\\\\nTN J0208+1305 & 403$\\pm$ 61 & 68.3$\\pm$ 3.1 & \\nodata & $-1.32\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 02 08 32.45 & $+$13 05 53.0 & N \\\\\nTN J0215+2651 & 431$\\pm$ 49 & 69.3$\\pm$ 3.2 & \\nodata & $-1.36\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 02 15 45.31 & $+$26 51 12.3 & N \\\\\nTN J0218+0844 & 395$\\pm$ 32 & 61.8$\\pm$ 1.3 & $ 8.8\\pm0.5$ & $-1.38\\pm$0.06 & $-1.56\\pm0.05$ & S & 0.4 & 169 & 02 18 25.56 & $+$08 44 31.3 & V \\\\\nTN J0230-0255 & 573$\\pm$ 56 & 90.1$\\pm$ 4.0 & $22.5\\pm1.2$ & $-1.38\\pm$0.08 & $-1.12\\pm0.06$ & M & 6.7 & 156 & 02 30 21.97 & $-$02 55 05.1 & V \\\\\nTN J0230-2001 & 380$\\pm$ 33 & 57.8$\\pm$ 2.7 & \\nodata & $-1.40\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 02 30 45.73 & $-$20 01 19.0 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0233+2349$^*$ & 1075$\\pm$ 86 & 176.8$\\pm$ 7.8 & $43.5\\pm2.3$ & $-1.34\\pm$0.07 & $-1.13\\pm0.06$ & DF & 4.0 & 116 & 02 33 10.32 & $+$23 49 52.2 & V \\\\\nTN J0234-1215 & 451$\\pm$ 46 & 64.2$\\pm$ 2.9 & \\nodata & $-1.45\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 02 34 57.31 & $-$12 15 21.7 & N \\\\\nTN J0243+1405 & 395$\\pm$ 51 & 58.4$\\pm$ 1.3 & $26.2\\pm1.4$ & $-1.42\\pm$0.10 & $-0.64\\pm0.05$ & T & 3.1 & 126 & 02 43 10.52 & $+$14 05 36.9 & V \\\\\nTN J0244+0327 & 542$\\pm$ 62 & 84.8$\\pm$ 3.8 & \\nodata & $-1.38\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 02 44 53.97 & $+$03 27 46.8 & N \\\\\nTN J0245+2700 & 388$\\pm$ 53 & 54.0$\\pm$ 2.5 & \\nodata & $-1.47\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 02 45 22.27 & $+$27 00 06.3 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0250+0130 & 275$\\pm$ 25 & 39.1$\\pm$ 2.0 & \\nodata & $-1.45\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 02 50 20.94 & $+$01 30 24.9 & N \\\\\nTN J0254-1039 & 421$\\pm$ 60 & 68.1$\\pm$ 3.1 & $25.5\\pm1.4$ & $-1.36\\pm$0.11 & $-0.79\\pm0.06$ & D & 11.7 & 129 & 02 54 59.89 & $-$10 39 49.2 & V \\\\\nTN J0256-2717 & 1045$\\pm$ 70 & 177.9$\\pm$ 7.4 & \\nodata & $-1.32\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 02 56 51.44 & $-$27 17 56.5 & N \\\\\nTN J0301+0155 & 3950$\\pm$180 & 402.7$\\pm$17.3 & \\nodata & $-1.70\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 03 01 38.49 & $+$01 55 14.9 & N \\\\\nTN J0306+0524 & 909$\\pm$ 76 & 155.1$\\pm$ 6.3 & \\nodata & $-1.32\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 03 06 08.10 & $+$05 24 23.8 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0309-2425$^*$ & 483$\\pm$ 53 & 62.6$\\pm$ 2.9 & $14.8\\pm0.9$ & $-1.52\\pm$0.09 & $-1.16\\pm0.06$ & D & 12.9 & 23 & 03 09 09.26 & $-$24 25 11.7 & V \\\\\nTN J0310+0814 & 593$\\pm$ 67 & 96.8$\\pm$ 4.3 & \\nodata & $-1.35\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 03 10 37.37 & $+$08 14 59.2 & N \\\\\nTN J0311-2553 & 1102$\\pm$ 66 & 174.1$\\pm$ 7.5 & \\nodata & $-1.37\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 03 11 47.40 & $-$25 53 21.1 & N \\\\\nTN J0312-2622 & 442$\\pm$ 41 & 46.4$\\pm$ 2.3 & \\nodata & $-1.68\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 03 12 34.19 & $-$26 22 23.9 & N \\\\\nTN J0316-0815 & 1950$\\pm$ 92 & 305.1$\\pm$13.4 & $42.2\\pm2.2$ & $-1.38\\pm$0.05 & $-1.59\\pm0.05$ & T & 3.2 & 34 & 03 16 18.59 & $-$08 15 54.8 & V \\\\\n&&&&&&&&&&&\\\\\nTN J0321+1631 & 1084$\\pm$ 85 & 175.7$\\pm$ 7.7 & \\nodata & $-1.35\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 03 21 36.86 & $+$16 31 55.8 & N \\\\\nTN J0327-0948 & 281$\\pm$ 30 & 39.0$\\pm$ 2.0 & \\nodata & $-1.47\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 03 27 00.55 & $-$09 48 05.2 & N \\\\\nTN J0344+1903 & 297$\\pm$ 22 & 50.7$\\pm$ 2.4 & \\nodata & $-1.32\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 03 44 00.12 & $+$19 03 53.1 & N \\\\\nTN J0344-2029 & 538$\\pm$ 71 & 74.0$\\pm$ 1.6 & $19.2\\pm1.1$ & $-1.48\\pm$0.10 & $-1.08\\pm0.05$ & D & 6.5 & 42 & 03 44 37.88 & $-$20 29 03.8 & V \\\\\nTN J0349-1207$^*$ & 460$\\pm$ 61 & 77.5$\\pm$ 3.5 & $23.3\\pm1.3$ & $-1.32\\pm$0.11 & $-0.97\\pm0.06$ & T & 9.4 & 101 & 03 49 49.22 & $-$12 07 10.6 & V \\\\\n&&&&&&&&&&&\\\\\nTN J0351-1947 & 642$\\pm$ 86 & 111.4$\\pm$ 4.9 & \\nodata & $-1.30\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 03 51 33.13 & $-$19 47 10.5 & N \\\\\nTN J0352-0355$^*$ & 681$\\pm$ 63 & 114.9$\\pm$ 4.8 & $13.5\\pm0.8$ & $-1.32\\pm$0.08 & $-1.65\\pm0.06$ & DF & \\nodata & 0 & 03 52 32.04 & $-$03 55 47.2 & V \\\\\nTN J0355+0440 & 2015$\\pm$119 & 262.0$\\pm$11.5 & \\nodata & $-1.52\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 03 55 12.79 & $+$04 40 41.0 & N \\\\\nTN J0356-3028 & 1030$\\pm$ 65 & 167.5$\\pm$ 7.3 & $34.1\\pm1.8$ & $-1.35\\pm$0.06 & $-1.28\\pm0.06$ & D & 3.1 & 86 & 03 56 45.54 & $-$30 28 36.9 & V \\\\\nTN J0401-0156 & 1001$\\pm$ 65 & 172.8$\\pm$ 7.1 & \\nodata & $-1.31\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 04 01 08.43 & $-$01 56 08.9 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0402+1007 & 479$\\pm$ 54 & 74.6$\\pm$ 3.4 & $13.4\\pm0.8$ & $-1.38\\pm$0.09 & $-1.38\\pm0.06$ & D & 0.8 & 67 & 04 02 34.44 & $+$10 07 14.9 & V \\\\\nTN J0404-0541 & 666$\\pm$ 69 & 114.1$\\pm$ 5.1 & \\nodata & $-1.31\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 04 04 09.66 & $-$05 41 07.3 & N \\\\\nTN J0408-2418$^*$ & 3881$\\pm$172 & 647.7$\\pm$28.1 & \\nodata & $-1.33\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 04 08 51.38 & $-$24 18 15.5 & N \\\\\nTN J0410+1019 & 1185$\\pm$ 88 & 166.9$\\pm$ 3.4 & $26.5\\pm1.4$ & $-1.46\\pm$0.06 & $-1.26\\pm0.05$ & S & 0.2 & 109 & 04 10 40.52 & $+$10 19 13.6 & V \\\\\nTN J0429-2118 & 561$\\pm$ 58 & 95.5$\\pm$ 4.3 & \\nodata & $-1.32\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 04 29 39.79 & $-$21 18 01.7 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0431+0725 & 175$\\pm$ 24 & 30.4$\\pm$ 0.7 & \\nodata & $-1.30\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 04 31 54.21 & $+$07 25 13.8 & N \\\\\nTN J0433+0717 & 229$\\pm$ 27 & 33.1$\\pm$ 1.8 & \\nodata & $-1.44\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 04 33 05.61 & $+$07 17 55.2 & N \\\\\nTN J0435-0736 & 358$\\pm$ 71 & 47.0$\\pm$ 2.3 & $16.6\\pm0.9$ & $-1.51\\pm$0.15 & $-0.84\\pm0.06$ & T & 11.9 & 59 & 04 35 32.20 & $-$07 36 12.3 & V \\\\\nTN J0437+0259 & 410$\\pm$ 54 & 71.1$\\pm$ 3.3 & \\nodata & $-1.30\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 04 37 33.04 & $+$02 59 06.2 & N \\\\\nTN J0443-1212$^*$ & 412$\\pm$ 59 & 56.8$\\pm$ 2.7 & $14.6\\pm0.8$ & $-1.47\\pm$0.11 & $-1.09\\pm0.06$ & M & 20.2 & 25 & 04 43 53.72 & $-$12 12 46.7 & V \\\\\n&&&&&&&&&&&\\\\\nTN J0452-1737 & 747$\\pm$ 73 & 118.1$\\pm$ 2.5 & $23.7\\pm1.3$ & $-1.37\\pm$0.07 & $-1.29\\pm0.05$ & D & 2.4 & 176 & 04 52 26.66 & $-$17 37 54.0 & V \\\\\nTN J0510-1838 & 6801$\\pm$325 & 641.3$\\pm$25.6 & \\nodata & $-1.76\\pm$0.05 & \\nodata & D & 36.1 & 63 & 05 10 32.30 & $-$18 38 41.4 & A \\\\\nTN J0515-3410 & 589$\\pm$ 52 & 97.4$\\pm$ 4.4 & \\nodata & $-1.34\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 05 15 18.86 & $-$34 10 09.5 & N \\\\\nTN J0517-0641 & 285$\\pm$ 30 & 40.0$\\pm$ 0.9 & $ 6.8\\pm0.4$ & $-1.46\\pm$0.08 & $-1.43\\pm0.05$ & S & 1.0 & 0 & 05 17 36.89 & $-$06 41 14.6 & V \\\\\nTN J0525-1832 & 549$\\pm$ 73 & 86.4$\\pm$ 3.9 & $24.1\\pm1.3$ & $-1.38\\pm$0.11 & $-1.02\\pm0.06$ & T & 8.1 & 172 & 05 25 54.85 & $-$18 32 32.5 & V \\\\\n&&&&&&&&&&&\\\\\nTN J0547-0706 & 2552$\\pm$156 & 362.6$\\pm$16.0 & \\nodata & $-1.45\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 05 47 27.57 & $-$07 06 35.0 & N \\\\\nTN J0549-2459 & 427$\\pm$ 55 & 58.0$\\pm$ 1.3 & \\nodata & $-1.49\\pm$0.10 & \\nodata & S & 23.5 & 8 & 05 49 28.61 & $-$24 59 15.2 & A \\\\\nTN J0551-0756 & 473$\\pm$ 71 & 68.5$\\pm$ 3.2 & \\nodata & $-1.44\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 05 51 30.37 & $-$07 56 17.5 & N \\\\\nTN J0552-0433 & 1618$\\pm$ 83 & 269.7$\\pm$11.8 & $37.7\\pm2.0$ & $-1.33\\pm$0.05 & $-1.56\\pm0.06$ & D & 4.3 & 152 & 05 52 14.38 & $-$04 33 28.8 & V \\\\\nTN J0553-2033 & 887$\\pm$ 80 & 148.0$\\pm$ 6.2 & \\nodata & $-1.33\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 05 53 37.24 & $-$20 33 07.6 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0558-1358 & 425$\\pm$ 54 & 73.4$\\pm$ 3.4 & \\nodata & $-1.31\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 05 58 39.43 & $-$13 58 45.5 & N \\\\\nTN J0559-3406 & 773$\\pm$ 69 & 123.5$\\pm$ 5.4 & \\nodata & $-1.36\\pm$0.07 & \\nodata & S & 4.6 & 8 & 05 59 14.30 & $-$34 06 51.0 & A \\\\\nTN J0602-2741 & 810$\\pm$ 54 & 117.2$\\pm$ 5.2 & $20.7\\pm1.2$ & $-1.44\\pm$0.06 & $-1.39\\pm0.06$ & T & 4.3 & 88 & 06 02 41.32 & $-$27 41 10.1 & V \\\\\nTN J0630-2834 & 343$\\pm$ 29 & 14.3$\\pm$ 0.5 & \\nodata & $-2.36\\pm$0.07 & \\nodata & S & 13.5 & 2 & 06 30 49.49 & $-$28 34 40.4 & A \\\\\nTN J0634-3232 & 394$\\pm$ 63 & 67.7$\\pm$ 3.1 & \\nodata & $-1.31\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 06 34 17.10 & $-$32 32 34.1 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0729+2436 & 1062$\\pm$ 87 & 68.9$\\pm$ 3.1 & \\nodata & $-2.03\\pm$0.07 & \\nodata & D & 19.4 & 72 & 07 29 28.65 & $+$24 36 26.2 & F \\\\\nTN J0733+1753 & 291$\\pm$ 45 & 46.1$\\pm$ 2.3 & \\nodata & $-1.37\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 07 33 17.53 & $+$17 53 28.4 & N \\\\\nTN J0805+2738 & 987$\\pm$ 79 & 153.0$\\pm$ 6.7 & \\nodata & $-1.39\\pm$0.07 & \\nodata & T & 71.3 & 119 & 08 05 15.50 & $+$27 38 01.2 & F \\\\\nTN J0806+0401 & 560$\\pm$ 53 & 92.1$\\pm$ 2.0 & \\nodata & $-1.34\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 08 06 32.25 & $+$04 01 37.7 & N \\\\\nTN J0812+0915 & 277$\\pm$ 46 & 43.4$\\pm$ 2.2 & \\nodata & $-1.38\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 08 12 16.84 & $+$09 15 43.7 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0818-0741 & 381$\\pm$ 48 & 59.3$\\pm$ 2.8 & \\nodata & $-1.38\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 08 18 51.89 & $-$07 41 48.2 & N \\\\\nTN J0831+0046 & 451$\\pm$ 55 & 72.8$\\pm$ 3.3 & \\nodata & $-1.36\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 08 31 39.92 & $+$00 46 56.5 & N \\\\\nTN J0831+0851 & 567$\\pm$ 53 & 83.8$\\pm$ 3.8 & $98.3\\pm5.2$ & $-1.42\\pm$0.08 & $ 0.13\\pm0.06$ & DF & 3.0 & 2 & 08 31 52.74 & $+$08 51 14.1 & V \\\\\nTN J0837-1053$^*$ & 450$\\pm$ 81 & 69.2$\\pm$ 3.1 & $11.6\\pm0.7$ & $-1.39\\pm$0.14 & $-1.43\\pm0.06$ & D & 23.5 & 11 & 08 37 41.62 & $-$10 53 46.0 & V \\\\\nTN J0855-0000 & 416$\\pm$ 57 & 65.9$\\pm$ 3.0 & $13.8\\pm0.8$ & $-1.37\\pm$0.11 & $-1.26\\pm0.06$ & D & 3.8 & 85 & 08 55 57.26 & $-$00 00 58.2 & V \\\\\n\\end{tabular}\n\\end{table*}\n\\begin{table*}\n\\tiny\n\\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{365}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{365}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nTN J0856-1510 & 469$\\pm$ 68 & 70.0$\\pm$ 3.2 & $ 3.7\\pm0.3$ & $-1.41\\pm$0.11 & $-2.01\\pm0.07$ & S & 1.0 & 14 & 08 56 12.44 & $-$15 10 35.7 & V \\\\\nTN J0902+1809 & 491$\\pm$ 37 & 55.5$\\pm$ 2.6 & \\nodata & $-1.62\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 09 02 00.00 & $+$18 09 03.4 & N \\\\\nTN J0906-0701 & 939$\\pm$101 & 142.5$\\pm$ 5.8 & \\nodata & $-1.40\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 09 06 40.23 & $-$07 01 12.4 & N \\\\\nTN J0910-2228 & 465$\\pm$ 32 & 55.3$\\pm$ 2.6 & $ 4.0\\pm0.3$ & $-1.58\\pm$0.06 & $-2.11\\pm0.07$ & S & 2.0 & 0 & 09 10 34.15 & $-$22 28 47.4 & V \\\\\nTN J0914+1119 & 343$\\pm$ 53 & 49.5$\\pm$ 1.1 & \\nodata & $-1.44\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 09 14 30.81 & $+$11 19 08.0 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0919+1845 & 522$\\pm$ 50 & 90.0$\\pm$ 4.0 & \\nodata & $-1.31\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 09 19 33.25 & $+$18 45 51.2 & N \\\\\nTN J0920-0712 & 760$\\pm$ 53 & 100.4$\\pm$ 4.5 & $16.3\\pm0.9$ & $-1.51\\pm$0.06 & $-1.46\\pm0.06$ & S & 1.4 & 135 & 09 20 22.43 & $-$07 12 17.6 & V \\\\\nTN J0920-1405 & 842$\\pm$ 88 & 133.6$\\pm$ 5.5 & \\nodata & $-1.37\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 09 20 37.77 & $-$14 05 56.3 & N \\\\\nTN J0924-2201 & 656$\\pm$ 72 & 73.3$\\pm$ 1.5 & $ 8.6\\pm0.5$ & $-1.63\\pm$0.08 & $-1.72\\pm0.05$ & D & 1.2 & 74 & 09 24 19.92 & $-$22 01 41.5 & V \\\\\nTN J0936+0422 & 6025$\\pm$362 & 992.0$\\pm$42.5 & \\nodata & $-1.34\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 09 36 32.02 & $+$04 22 10.7 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0936-2243 & 488$\\pm$ 63 & 69.1$\\pm$ 3.2 & $18.5\\pm1.0$ & $-1.45\\pm$0.10 & $-1.06\\pm0.06$ & D & 8.1 & 77 & 09 36 32.53 & $-$22 43 04.9 & V \\\\\nTN J0941-1628 & 1810$\\pm$115 & 304.4$\\pm$13.4 & $64.7\\pm3.8$ & $-1.33\\pm$0.06 & $-1.24\\pm0.06$ & D & 1.9 & 175 & 09 41 07.43 & $-$16 28 02.5 & V \\\\\nTN J0946-0306 & 238$\\pm$ 24 & 38.2$\\pm$ 2.0 & \\nodata & $-1.36\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 09 46 00.88 & $-$03 06 26.2 & N \\\\\nTN J0954-1635 & 1531$\\pm$ 98 & 260.0$\\pm$11.4 & \\nodata & $-1.32\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 09 54 52.30 & $-$16 35 35.1 & N \\\\\nTN J0956-1500 & 505$\\pm$ 49 & 68.9$\\pm$ 1.5 & \\nodata & $-1.48\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 09 56 01.46 & $-$15 00 21.6 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0958-1103 & 431$\\pm$ 63 & 70.6$\\pm$ 3.2 & \\nodata & $-1.35\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 09 58 21.84 & $-$11 03 47.5 & N \\\\\nTN J1000+0549 & 410$\\pm$ 55 & 67.3$\\pm$ 3.1 & \\nodata & $-1.34\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 10 00 44.58 & $+$05 49 31.1 & N \\\\\nTN J1002+2225 & 343$\\pm$ 41 & 54.2$\\pm$ 2.6 & $12.2\\pm0.7$ & $-1.37\\pm$0.10 & $-1.20\\pm0.06$ & D & 11.2 & 10 & 10 02 54.08 & $+$22 25 21.9 & V \\\\\nTN J1026-2116 & 399$\\pm$ 29 & 61.5$\\pm$ 1.3 & $ 8.5\\pm0.5$ & $-1.39\\pm$0.06 & $-1.59\\pm0.05$ & S & 1.0 & 0 & 10 26 22.37 & $-$21 16 07.7 & V \\\\\nTN J1028+1114 & 459$\\pm$ 56 & 79.7$\\pm$ 3.6 & \\nodata & $-1.30\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 10 28 24.31 & $+$11 14 52.4 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1031+0259 & 416$\\pm$ 62 & 60.0$\\pm$ 1.3 & \\nodata & $-1.44\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 10 31 13.36 & $+$02 59 05.3 & N \\\\\nTN J1033-1339 & 981$\\pm$ 75 & 153.8$\\pm$ 6.8 & $26.0\\pm1.4$ & $-1.38\\pm$0.07 & $-1.43\\pm0.06$ & S & 2.0 & 107 & 10 33 10.70 & $-$13 39 52.0 & V \\\\\nTN J1043-1718 & 578$\\pm$ 70 & 91.0$\\pm$ 3.9 & $18.9\\pm1.0$ & $-1.38\\pm$0.10 & $-1.26\\pm0.06$ & D & 34.7 & 63 & 10 43 19.42 & $-$17 18 53.5 & V \\\\\nTN J1043+2404 & 439$\\pm$ 34 & 52.0$\\pm$ 2.5 & \\nodata & $-1.59\\pm$0.07 & \\nodata & S & 3.7 & 90 & 10 43 43.28 & $+$24 04 47.3 & F \\\\\nTN J1045+1832 & 348$\\pm$ 27 & 53.6$\\pm$ 1.2 & \\nodata & $-1.39\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 10 45 42.93 & $+$18 32 37.5 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1049-1258 & 818$\\pm$ 56 & 112.2$\\pm$ 5.0 & $17.2\\pm0.9$ & $-1.48\\pm$0.06 & $-1.50\\pm0.06$ & M & 10.1 & 104 & 10 49 06.22 & $-$12 58 18.3 & V \\\\\nTN J1053-1518 & 383$\\pm$ 62 & 63.7$\\pm$ 2.9 & \\nodata & $-1.33\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 10 53 44.52 & $-$15 18 29.8 & N \\\\\nTN J1056-0400 & 449$\\pm$ 57 & 57.2$\\pm$ 2.7 & \\nodata & $-1.53\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 10 56 52.64 & $-$04 00 15.9 & N \\\\\nTN J1102+1029 & 3713$\\pm$224 & 633.6$\\pm$27.8 & \\nodata & $-1.32\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 11 02 17.47 & $+$10 29 08.0 & N \\\\\nTN J1102-1651 & 688$\\pm$ 68 & 112.5$\\pm$ 5.0 & $20.2\\pm1.1$ & $-1.35\\pm$0.08 & $-1.38\\pm0.06$ & D & 3.0 & 70 & 11 02 47.13 & $-$16 51 34.4 & V \\\\\n&&&&&&&&&&&\\\\\nTN J1112-2948 & 663$\\pm$ 51 & 101.0$\\pm$ 4.5 & $16.6\\pm0.9$ & $-1.40\\pm$0.07 & $-1.45\\pm0.06$ & D & 9.1 & 119 & 11 12 23.86 & $-$29 48 06.4 & V \\\\\nTN J1114-2221 & 386$\\pm$ 53 & 64.9$\\pm$ 3.0 & \\nodata & $-1.33\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 11 14 04.82 & $-$22 21 26.6 & N \\\\\nTN J1117-1409 & 785$\\pm$ 69 & 134.5$\\pm$ 5.9 & \\nodata & $-1.31\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 11 17 23.00 & $-$14 09 09.5 & N \\\\\nTN J1118-2612 & 514$\\pm$ 44 & 62.3$\\pm$ 2.9 & \\nodata & $-1.57\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 11 18 54.08 & $-$26 12 20.6 & N \\\\\nTN J1121-1155 & 332$\\pm$ 65 & 50.1$\\pm$ 2.4 & \\nodata & $-1.41\\pm$0.15 & \\nodata & \\nodata & \\nodata & \\nodata & 11 21 32.75 & $-$11 55 03.2 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1121+1706 & 1156$\\pm$ 83 & 196.8$\\pm$ 8.4 & \\nodata & $-1.32\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 11 21 39.89 & $+$17 06 14.8 & N \\\\\nTN J1123-2154 & 407$\\pm$ 64 & 50.6$\\pm$ 2.4 & $ 8.5\\pm0.5$ & $-1.55\\pm$0.12 & $-1.43\\pm0.06$ & S & 0.8 & 29 & 11 23 10.15 & $-$21 54 05.3 & V \\\\\nTN J1125-0342 & 354$\\pm$ 52 & 61.4$\\pm$ 2.9 & \\nodata & $-1.30\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 11 25 57.41 & $-$03 42 04.0 & N \\\\\nTN J1133-2715 & 2938$\\pm$125 & 447.9$\\pm$ 9.2 & \\nodata & $-1.40\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 11 33 31.53 & $-$27 15 22.9 & N \\\\\nTN J1136+1551 & 384$\\pm$ 33 & 21.7$\\pm$ 0.6 & \\nodata & $-2.14\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 11 36 03.28 & $+$15 51 06.7 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1136+0610 & 698$\\pm$ 50 & 118.8$\\pm$ 5.3 & \\nodata & $-1.32\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 11 36 38.91 & $+$06 10 26.8 & N \\\\\nTN J1139+0935 & 508$\\pm$ 58 & 87.3$\\pm$ 3.9 & \\nodata & $-1.31\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 11 39 22.75 & $+$09 35 26.1 & N \\\\\nTN J1146-1052 & 843$\\pm$ 79 & 120.9$\\pm$ 5.4 & \\nodata & $-1.44\\pm$0.08 & \\nodata & S & 8.8 & 1 & 11 46 07.21 & $-$10 52 08.6 & A \\\\\nTN J1148-0901 & 571$\\pm$ 67 & 80.4$\\pm$ 3.7 & \\nodata & $-1.46\\pm$0.09 & \\nodata & S & $<$ 6.0 & 5 & 11 48 39.90 & $-$09 01 48.8 & A \\\\\nTN J1149+1844 & 457$\\pm$ 39 & 77.6$\\pm$ 1.6 & \\nodata & $-1.32\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 11 49 36.78 & $+$18 44 21.5 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1151-3013 & 435$\\pm$ 28 & 52.7$\\pm$ 1.2 & $ 7.0\\pm0.4$ & $-1.57\\pm$0.05 & $-1.62\\pm0.05$ & S & 1.0 & 0 & 11 51 59.42 & $-$30 13 40.8 & V \\\\\nTN J1156-3105 & 317$\\pm$ 48 & 48.3$\\pm$ 2.3 & \\nodata & $-1.40\\pm$0.12 & \\nodata & S & 10.7 & 167 & 11 56 25.60 & $-$31 05 40.0 & A \\\\\nTN J1159-1629 & 324$\\pm$ 34 & 52.9$\\pm$ 1.2 & $10.4\\pm0.6$ & $-1.35\\pm$0.08 & $-1.30\\pm0.05$ & D & 1.4 & 38 & 11 59 53.25 & $-$16 29 48.2 & V \\\\\nTN J1204+1630 & 804$\\pm$ 56 & 129.7$\\pm$ 5.8 & \\nodata & $-1.36\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 12 04 20.49 & $+$16 30 49.5 & N \\\\\nTN J1210+1738 & 397$\\pm$ 50 & 68.1$\\pm$ 3.2 & \\nodata & $-1.31\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 12 10 36.00 & $+$17 38 27.8 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1216+1944 & 546$\\pm$ 44 & 91.7$\\pm$ 4.1 & \\nodata & $-1.33\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 12 16 01.76 & $+$19 44 43.3 & N \\\\\nTN J1216-2850 & 870$\\pm$ 43 & 145.2$\\pm$ 6.4 & \\nodata & $-1.33\\pm$0.05 & \\nodata & S & $<$ 7.0 & 163 & 12 16 17.38 & $-$28 50 48.7 & A \\\\\nTN J1220+0604 & 491$\\pm$ 61 & 65.1$\\pm$ 3.0 & \\nodata & $-1.50\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 12 20 07.82 & $+$06 04 16.5 & N \\\\\nTN J1221-2646 & 1403$\\pm$ 82 & 217.1$\\pm$ 9.5 & \\nodata & $-1.39\\pm$0.05 & \\nodata & S & 8.3 & 162 & 12 21 42.91 & $-$26 46 37.7 & A \\\\\nTN J1227-2255 & 271$\\pm$ 27 & 44.0$\\pm$ 2.2 & \\nodata & $-1.35\\pm$0.08 & \\nodata & S & $<$ 7.0 & 158 & 12 27 47.23 & $-$22 55 35.1 & A \\\\\n&&&&&&&&&&&\\\\\nTN J1239+1005 & 830$\\pm$ 89 & 79.3$\\pm$ 1.7 & \\nodata & $-1.75\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 12 39 02.08 & $+$10 05 49.2 & N \\\\\nTN J1239+1043 & 569$\\pm$ 63 & 87.1$\\pm$ 3.8 & \\nodata & $-1.40\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 12 39 31.67 & $+$10 43 22.9 & N \\\\\nTN J1239-0319 & 1629$\\pm$ 74 & 277.3$\\pm$12.2 & \\nodata & $-1.32\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 12 39 38.91 & $-$03 19 02.2 & N \\\\\nTN J1245-1127 & 518$\\pm$ 62 & 88.0$\\pm$ 4.0 & \\nodata & $-1.32\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 12 45 02.47 & $-$11 27 25.9 & N \\\\\nTN J1247+1547 & 405$\\pm$ 44 & 70.1$\\pm$ 3.2 & \\nodata & $-1.30\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 12 47 04.84 & $+$15 47 38.9 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1251-2714 & 609$\\pm$ 53 & 96.5$\\pm$ 4.3 & \\nodata & $-1.37\\pm$0.07 & \\nodata & S & $<$ 7.0 & 158 & 12 51 14.86 & $-$27 14 19.9 & A \\\\\nTN J1256-0911 & 457$\\pm$ 38 & 76.4$\\pm$ 3.5 & \\nodata & $-1.33\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 12 56 19.48 & $-$09 11 24.8 & N \\\\\nTN J1303-3349 & 2431$\\pm$108 & 360.8$\\pm$ 7.7 & \\nodata & $-1.42\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 13 03 02.67 & $-$33 49 15.5 & N \\\\\nTN J1306-0436 & 331$\\pm$ 57 & 55.2$\\pm$ 2.6 & \\nodata & $-1.33\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 13 06 36.11 & $-$04 36 17.4 & N \\\\\nTN J1313-0459 & 369$\\pm$ 34 & 58.1$\\pm$ 2.7 & \\nodata & $-1.38\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 13 13 34.37 & $-$04 59 30.0 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1317+0339 & 399$\\pm$ 62 & 39.8$\\pm$ 2.0 & \\nodata & $-1.71\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 13 17 48.12 & $+$03 39 12.3 & N \\\\\nTN J1323-2604 & 564$\\pm$ 60 & 97.3$\\pm$ 2.0 & \\nodata & $-1.31\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 13 23 32.43 & $-$26 04 04.7 & N \\\\\nTN J1326-2330 & 523$\\pm$ 33 & 83.2$\\pm$ 3.8 & \\nodata & $-1.37\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 13 26 25.24 & $-$23 30 23.5 & N \\\\\nTN J1327+1437 & 788$\\pm$ 68 & 115.0$\\pm$ 5.1 & \\nodata & $-1.43\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 13 27 23.93 & $+$14 37 00.4 & N \\\\\nTN J1336+2450 & 358$\\pm$ 71 & 51.3$\\pm$ 2.5 & \\nodata & $-1.45\\pm$0.15 & \\nodata & M & 54.4 & 100 & 13 36 15.12 & $+$24 50 05.4 & F \\\\\n&&&&&&&&&&&\\\\\nTN J1338-1942 & 718$\\pm$ 63 & 122.9$\\pm$ 5.4 & $22.1\\pm1.2$ & $-1.31\\pm$0.07 & $-1.34\\pm0.06$ & S & 1.4 & 152 & 13 38 26.06 & $-$19 42 30.1 & V \\\\\nTN J1339-0114 & 349$\\pm$ 51 & 59.5$\\pm$ 1.3 & \\nodata & $-1.32\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 13 39 55.26 & $-$01 14 10.8 & N \\\\\nTN J1340+2723 & 827$\\pm$ 93 & 137.8$\\pm$ 6.1 & $24.8\\pm1.4$ & $-1.33\\pm$0.09 & $-1.38\\pm0.06$ & DF & 1.7 & 0 & 13 40 29.38 & $+$27 23 25.0 & V \\\\\nTN J1346-1004 & 363$\\pm$ 59 & 49.6$\\pm$ 2.4 & \\nodata & $-1.48\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 13 46 16.84 & $-$10 04 57.2 & N \\\\\nTN J1351+1328 & 662$\\pm$ 54 & 93.8$\\pm$ 4.2 & \\nodata & $-1.45\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 13 51 54.72 & $+$13 28 38.1 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1352-0800 & 554$\\pm$ 88 & 95.6$\\pm$ 4.3 & \\nodata & $-1.31\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 13 52 55.32 & $-$08 00 14.1 & N \\\\\nTN J1353+2302 & 403$\\pm$ 38 & 59.5$\\pm$ 1.3 & $23.3\\pm1.3$ & $-1.42\\pm$0.07 & $-0.75\\pm0.05$ & DF & 2.5 & 44 & 13 53 42.26 & $+$23 02 50.9 & V \\\\\nTN J1358+2003 & 227$\\pm$ 42 & 35.0$\\pm$ 1.8 & \\nodata & $-1.39\\pm$0.14 & \\nodata & \\nodata & \\nodata & \\nodata & 13 58 29.63 & $+$20 03 13.4 & N \\\\\nTN J1403-1223 & 396$\\pm$ 69 & 65.8$\\pm$ 3.0 & \\nodata & $-1.34\\pm$0.14 & \\nodata & S & 30.6 & 169 & 14 03 37.33 & $-$12 23 57.3 & A \\\\\nTN J1408-0855 & 694$\\pm$ 73 & 114.3$\\pm$ 5.1 & \\nodata & $-1.34\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 14 08 18.46 & $-$08 55 38.5 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1411-0824 & 542$\\pm$ 71 & 76.1$\\pm$ 3.5 & \\nodata & $-1.46\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 14 11 53.33 & $-$08 24 02.9 & N \\\\\nTN J1412-2548 & 452$\\pm$ 59 & 78.0$\\pm$ 3.6 & \\nodata & $-1.31\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 14 12 51.27 & $-$25 48 05.5 & N \\\\\nTN J1418-2256 & 527$\\pm$ 59 & 82.0$\\pm$ 3.7 & \\nodata & $-1.38\\pm$0.09 & \\nodata & S & 7.6 & 148 & 14 18 16.65 & $-$22 56 58.6 & A \\\\\nTN J1428+2425 & 411$\\pm$ 34 & 69.1$\\pm$ 1.5 & \\nodata & $-1.33\\pm$0.07 & \\nodata & S & 1.0 & 0 & 14 28 10.20 & $+$24 25 11.3 & F \\\\\nTN J1438+2334 & 564$\\pm$ 69 & 96.5$\\pm$ 4.2 & \\nodata & $-1.31\\pm$0.10 & \\nodata & D & 21.1 & 157 & 14 38 56.52 & $+$23 34 25.6 & F \\\\\n\\end{tabular}\n\\end{table*}\n\\begin{table*}\n\\tiny\n\\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{365}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{365}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nTN J1439-3226 & 622$\\pm$ 65 & 90.7$\\pm$ 1.9 & \\nodata & $-1.43\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 14 39 02.87 & $-$32 26 46.6 & N \\\\\nTN J1449+1440 & 464$\\pm$ 50 & 80.3$\\pm$ 3.7 & \\nodata & $-1.30\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 14 49 02.50 & $+$14 40 42.2 & N \\\\\nTN J1451+2351 & 595$\\pm$ 44 & 93.2$\\pm$ 4.2 & \\nodata & $-1.38\\pm$0.07 & \\nodata & D & 12.6 & 109 & 14 51 10.71 & $+$23 51 38.8 & F \\\\\nTN J1452-1113 & 344$\\pm$ 55 & 53.9$\\pm$ 2.6 & \\nodata & $-1.38\\pm$0.13 & \\nodata & S & $<$ 7.5 & 2 & 14 52 04.88 & $-$11 13 35.7 & A \\\\\nTN J1452+2013 & 291$\\pm$ 40 & 43.4$\\pm$ 1.0 & \\nodata & $-1.42\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 14 52 22.93 & $+$20 13 09.8 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1453+1106 & 833$\\pm$ 56 & 144.9$\\pm$ 6.4 & \\nodata & $-1.30\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 14 53 21.97 & $+$11 06 04.9 & N \\\\\nTN J1454+0017 & 1309$\\pm$ 88 & 214.8$\\pm$ 9.2 & \\nodata & $-1.34\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 14 54 40.87 & $+$00 17 41.9 & N \\\\\nTN J1459-2730 & 321$\\pm$ 40 & 52.5$\\pm$ 2.5 & \\nodata & $-1.35\\pm$0.10 & \\nodata & S & 6.5 & 143 & 14 59 34.96 & $-$27 30 08.3 & A \\\\\nTN J1506+2728 & 360$\\pm$ 58 & 60.7$\\pm$ 1.3 & $15.9\\pm0.9$ & $-1.32\\pm$0.12 & $-1.07\\pm0.05$ & D & 1.1 & 131 & 15 06 35.41 & $+$27 28 55.6 & V \\\\\nTN J1513-2417 & 504$\\pm$ 33 & 83.6$\\pm$ 3.7 & \\nodata & $-1.34\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 15 13 31.67 & $-$24 17 55.3 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1513-1801 & 534$\\pm$ 36 & 85.3$\\pm$ 3.9 & \\nodata & $-1.36\\pm$0.06 & \\nodata & S & $<$ 7.5 & 4 & 15 13 55.31 & $-$18 01 07.9 & A \\\\\nTN J1515-2651 & 352$\\pm$ 44 & 58.0$\\pm$ 2.7 & \\nodata & $-1.34\\pm$0.10 & \\nodata & S & 6.5 & 9 & 15 15 59.29 & $-$26 51 14.9 & A \\\\\nTN J1520+1410 & 478$\\pm$ 55 & 66.0$\\pm$ 1.4 & \\nodata & $-1.47\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 15 20 53.36 & $+$14 10 45.5 & N \\\\\nTN J1521+0741 & 1777$\\pm$123 & 105.6$\\pm$ 4.5 & \\nodata & $-2.10\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 15 21 50.75 & $+$07 41 41.1 & N \\\\\nTN J1522-2540 & 464$\\pm$ 63 & 54.1$\\pm$ 2.6 & \\nodata & $-1.60\\pm$0.11 & \\nodata & S & 8.2 & 10 & 15 22 23.28 & $-$25 40 07.1 & A \\\\\n&&&&&&&&&&&\\\\\nTN J1524+0642 & 479$\\pm$ 55 & 82.9$\\pm$ 1.7 & \\nodata & $-1.30\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 15 24 06.39 & $+$06 42 15.9 & N \\\\\nTN J1531-3234 & 522$\\pm$ 59 & 80.6$\\pm$ 3.6 & \\nodata & $-1.39\\pm$0.09 & \\nodata & S & 4.8 & 27 & 15 31 33.59 & $-$32 34 01.7 & A \\\\\nTN J1547-2218 & 427$\\pm$ 62 & 72.4$\\pm$ 3.3 & \\nodata & $-1.32\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 15 47 49.95 & $-$22 18 25.6 & N \\\\\nTN J1556-2759 & 612$\\pm$ 56 & 66.4$\\pm$ 3.1 & \\nodata & $-1.65\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 15 56 43.63 & $-$27 59 43.1 & N \\\\\nTN J1559-1727 & 575$\\pm$ 71 & 97.4$\\pm$ 4.3 & \\nodata & $-1.32\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 15 59 34.08 & $-$17 27 41.6 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1604-0248 & 345$\\pm$ 33 & 46.8$\\pm$ 1.0 & \\nodata & $-1.49\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 16 04 59.59 & $-$02 48 47.9 & N \\\\\nTN J1621+2043 & 539$\\pm$ 48 & 61.4$\\pm$ 2.9 & \\nodata & $-1.62\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 16 21 06.18 & $+$20 43 36.4 & N \\\\\nTN J1628+1604 & 602$\\pm$ 44 & 55.5$\\pm$ 2.6 & \\nodata & $-1.77\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 16 28 19.16 & $+$16 04 00.0 & N \\\\\nTN J1634-2222 & 4714$\\pm$214 & 809.2$\\pm$35.4 & \\nodata & $-1.31\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 16 34 49.79 & $-$22 22 12.7 & N \\\\\nTN J1637-1931 & 432$\\pm$ 40 & 36.8$\\pm$ 0.9 & \\nodata & $-1.83\\pm$0.07 & \\nodata & S & 10.8 & 6 & 16 37 44.80 & $-$19 31 24.8 & A \\\\\n&&&&&&&&&&&\\\\\nTN J1646-1328 & 608$\\pm$ 63 & 102.5$\\pm$ 4.6 & \\nodata & $-1.32\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 16 46 51.67 & $-$13 28 49.1 & N \\\\\nTN J1652-1339 & 328$\\pm$ 33 & 56.5$\\pm$ 1.3 & \\nodata & $-1.31\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 16 52 24.29 & $-$13 39 04.3 & N \\\\\nTN J1653-1155 & 1131$\\pm$ 60 & 197.0$\\pm$ 8.7 & \\nodata & $-1.30\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 16 53 52.81 & $-$11 55 59.2 & N \\\\\nTN J1656-1521 & 587$\\pm$ 79 & 93.9$\\pm$ 4.2 & \\nodata & $-1.36\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 16 56 03.77 & $-$15 21 23.3 & N \\\\\nTN J1701-0101 & 999$\\pm$ 55 & 172.2$\\pm$ 7.6 & \\nodata & $-1.31\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 17 01 37.58 & $-$01 01 13.6 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1701+0252 & 356$\\pm$ 38 & 57.1$\\pm$ 2.7 & \\nodata & $-1.36\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 17 01 54.89 & $+$02 52 13.4 & N \\\\\nTN J1702-0811 & 436$\\pm$ 38 & 69.9$\\pm$ 3.2 & \\nodata & $-1.36\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 17 02 04.71 & $-$08 11 07.5 & N \\\\\nTN J1702+2015 & 322$\\pm$ 48 & 43.4$\\pm$ 2.1 & \\nodata & $-1.49\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 17 02 23.02 & $+$20 15 34.2 & N \\\\\nTN J1702-0145 & 808$\\pm$ 74 & 135.6$\\pm$ 6.0 & \\nodata & $-1.33\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 17 02 43.11 & $-$01 45 54.0 & N \\\\\nTN J1707-1120 & 425$\\pm$ 72 & 54.2$\\pm$ 2.6 & \\nodata & $-1.53\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 17 07 51.37 & $-$11 20 21.0 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1710-0826 & 445$\\pm$ 74 & 69.2$\\pm$ 3.2 & \\nodata & $-1.38\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 17 10 20.36 & $-$08 26 40.3 & N \\\\\nTN J1714+2226 & 285$\\pm$ 48 & 43.3$\\pm$ 1.0 & \\nodata & $-1.40\\pm$0.13 & \\nodata & S & 1.6 & 38 & 17 14 53.42 & $+$22 26 18.5 & F \\\\\nTN J1821+2433 & 1416$\\pm$ 95 & 227.5$\\pm$ 4.7 & \\nodata & $-1.36\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 18 21 37.07 & $+$24 33 13.8 & N \\\\\nTN J1855-3430 & 654$\\pm$ 85 & 87.8$\\pm$ 3.8 & \\nodata & $-1.49\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 18 55 24.12 & $-$34 30 27.7 & N \\\\\nTN J1905-3520 & 799$\\pm$ 75 & 131.3$\\pm$ 5.4 & \\nodata & $-1.34\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 19 05 22.67 & $-$35 20 50.9 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1932-1931 & 5678$\\pm$335 & 813.6$\\pm$35.5 & \\nodata & $-1.45\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 19 32 07.22 & $-$19 31 49.7 & N \\\\\nTN J1941-1952 & 1194$\\pm$103 & 183.0$\\pm$ 3.8 & \\nodata & $-1.40\\pm$0.07 & \\nodata & S & 7.9 & 164 & 19 41 00.07 & $-$19 52 14.0 & A \\\\\nTN J1953-0541 & 478$\\pm$ 83 & 59.0$\\pm$ 2.8 & \\nodata & $-1.56\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 19 53 27.04 & $-$05 41 28.5 & N \\\\\nTN J1954-1207 & 657$\\pm$ 67 & 102.8$\\pm$ 4.6 & \\nodata & $-1.38\\pm$0.08 & \\nodata & S & $<$ 7.0 & 177 & 19 54 24.15 & $-$12 07 48.7 & A \\\\\nTN J2007-1316 & 777$\\pm$ 46 & 115.4$\\pm$ 5.2 & \\nodata & $-1.42\\pm$0.06 & \\nodata & S & 7.2 & 174 & 20 07 53.23 & $-$13 16 43.6 & A \\\\\n&&&&&&&&&&&\\\\\nTN J2008-1344 & 798$\\pm$ 71 & 132.3$\\pm$ 2.7 & \\nodata & $-1.34\\pm$0.07 & \\nodata & S & 8.2 & 176 & 20 08 07.48 & $-$13 44 17.8 & A \\\\\nTN J2009-3040 & 409$\\pm$ 65 & 65.3$\\pm$ 3.0 & \\nodata & $-1.36\\pm$0.12 & \\nodata & S & $<$ 7.0 & 144 & 20 09 48.13 & $-$30 40 07.0 & A \\\\\nTN J2014-2115 & 348$\\pm$ 33 & 48.0$\\pm$ 1.1 & \\nodata & $-1.47\\pm$0.07 & \\nodata & D & 56.4 & 11 & 20 14 31.96 & $-$21 14 36.7 & A \\\\\nTN J2021+0839 & 880$\\pm$ 72 & 145.4$\\pm$ 6.4 & \\nodata & $-1.34\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 20 21 33.11 & $+$08 39 09.2 & N \\\\\nTN J2028+0811 & 455$\\pm$ 58 & 74.8$\\pm$ 1.6 & \\nodata & $-1.34\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 20 28 37.12 & $+$08 11 21.4 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2028-1934 & 814$\\pm$ 88 & 134.4$\\pm$ 5.8 & \\nodata & $-1.34\\pm$0.09 & \\nodata & S & 19.2 & 169 & 20 28 48.57 & $-$19 34 03.2 & A \\\\\nTN J2029-0858 & 396$\\pm$ 34 & 47.2$\\pm$ 2.3 & \\nodata & $-1.58\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 20 29 49.60 & $-$08 58 48.5 & N \\\\\nTN J2034-2735 & 510$\\pm$ 70 & 67.4$\\pm$ 1.5 & \\nodata & $-1.51\\pm$0.10 & \\nodata & S & $<$ 8.0 & 163 & 20 34 15.74 & $-$27 35 45.6 & A \\\\\nTN J2042+1354 & 281$\\pm$ 45 & 42.0$\\pm$ 1.0 & \\nodata & $-1.41\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 20 42 07.25 & $+$13 54 16.6 & N \\\\\nTN J2048-0618 & 881$\\pm$ 99 & 150.7$\\pm$ 6.6 & \\nodata & $-1.31\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 20 48 06.24 & $-$06 18 40.5 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2049-2223 & 823$\\pm$ 86 & 126.1$\\pm$ 5.6 & \\nodata & $-1.40\\pm$0.08 & \\nodata & D & 95.0 & 97 & 20 49 43.04 & $-$22 22 56.3 & A \\\\\nTN J2051-0527 & 377$\\pm$ 79 & 54.7$\\pm$ 1.2 & \\nodata & $-1.44\\pm$0.16 & \\nodata & \\nodata & \\nodata & \\nodata & 20 51 13.39 & $-$05 27 06.1 & N \\\\\nTN J2051+0133 & 391$\\pm$ 33 & 66.6$\\pm$ 3.1 & \\nodata & $-1.32\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 20 51 32.31 & $+$01 33 34.9 & N \\\\\nTN J2052-0555 & 321$\\pm$ 35 & 41.5$\\pm$ 0.9 & \\nodata & $-1.52\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 20 52 49.93 & $-$05 55 49.1 & N \\\\\nTN J2102+2158 & 483$\\pm$ 52 & 73.5$\\pm$ 1.6 & \\nodata & $-1.40\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 21 02 52.80 & $+$21 58 35.1 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2103-1917 & 1410$\\pm$109 & 228.6$\\pm$10.1 & \\nodata & $-1.35\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 21 03 42.91 & $-$19 17 47.7 & N \\\\\nTN J2106-2405$^*$ & 2232$\\pm$150 & 366.3$\\pm$15.9 & \\nodata & $-1.34\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 21 06 58.42 & $-$24 05 04.2 & N \\\\\nTN J2107+0933 & 476$\\pm$ 56 & 68.0$\\pm$ 3.1 & \\nodata & $-1.45\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 21 07 10.61 & $+$09 33 32.5 & N \\\\\nTN J2108+0249 & 573$\\pm$ 41 & 65.8$\\pm$ 3.1 & \\nodata & $-1.61\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 21 08 26.75 & $+$02 49 46.3 & N \\\\\nTN J2113+0111 & 553$\\pm$ 68 & 90.8$\\pm$ 4.1 & \\nodata & $-1.34\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 21 13 50.43 & $+$01 11 22.3 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2125+2013 & 352$\\pm$ 45 & 51.9$\\pm$ 2.5 & \\nodata & $-1.42\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 21 25 51.74 & $+$20 13 39.8 & N \\\\\nTN J2133+1629 & 1737$\\pm$123 & 283.4$\\pm$12.4 & \\nodata & $-1.35\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 21 33 29.32 & $+$16 29 19.4 & N \\\\\nTN J2134+0946 & 351$\\pm$ 47 & 48.0$\\pm$ 2.3 & \\nodata & $-1.48\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 21 34 42.85 & $+$09 46 56.6 & N \\\\\nTN J2136+0947 & 426$\\pm$ 60 & 66.9$\\pm$ 3.1 & \\nodata & $-1.38\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 21 36 36.29 & $+$09 47 22.8 & N \\\\\nTN J2147-0645 & 382$\\pm$ 63 & 57.3$\\pm$ 2.7 & \\nodata & $-1.41\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 21 47 57.13 & $-$06 45 48.8 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2155-2109 & 449$\\pm$ 87 & 77.2$\\pm$ 1.6 & \\nodata & $-1.31\\pm$0.15 & \\nodata & \\nodata & \\nodata & \\nodata & 21 55 50.90 & $-$21 09 30.0 & N \\\\\nTN J2158-2516 & 1225$\\pm$ 59 & 200.9$\\pm$ 8.9 & \\nodata & $-1.34\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 21 58 11.14 & $-$25 16 01.5 & N \\\\\nTN J2201-2822 & 703$\\pm$ 54 & 120.5$\\pm$ 5.1 & \\nodata & $-1.31\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 22 01 22.94 & $-$28 22 14.0 & N \\\\\nTN J2204+1621 & 381$\\pm$ 42 & 57.3$\\pm$ 2.7 & \\nodata & $-1.41\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 22 04 14.18 & $+$16 21 43.7 & N \\\\\nTN J2205-3201 & 430$\\pm$ 60 & 65.7$\\pm$ 3.1 & \\nodata & $-1.40\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 22 05 27.56 & $-$32 01 23.9 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2217-1913 & 321$\\pm$ 34 & 40.5$\\pm$ 2.0 & \\nodata & $-1.54\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 22 17 28.22 & $-$19 13 21.1 & N \\\\\nTN J2219-1648 & 301$\\pm$ 53 & 32.0$\\pm$ 0.8 & \\nodata & $-1.67\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 22 19 40.06 & $-$16 48 03.1 & N \\\\\nTN J2232-2917 & 528$\\pm$ 59 & 91.7$\\pm$ 1.9 & \\nodata & $-1.30\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 22 32 57.25 & $-$29 17 56.5 & N \\\\\nTN J2237-0242 & 727$\\pm$ 48 & 125.0$\\pm$ 2.6 & \\nodata & $-1.31\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 22 37 22.60 & $-$02 42 23.0 & N \\\\\nTN J2239-0429 & 3807$\\pm$177 & 571.4$\\pm$24.9 & \\nodata & $-1.41\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 22 39 32.85 & $-$04 29 33.9 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2245+0007 & 297$\\pm$ 53 & 51.6$\\pm$ 1.1 & \\nodata & $-1.30\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 22 45 44.99 & $+$00 07 11.3 & N \\\\\nTN J2251-1634 & 551$\\pm$ 64 & 60.6$\\pm$ 1.3 & \\nodata & $-1.64\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 22 51 14.06 & $-$16 34 03.2 & N \\\\\nTN J2251-1034 & 862$\\pm$ 72 & 138.8$\\pm$ 5.9 & \\nodata & $-1.36\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 22 51 22.01 & $-$10 34 18.0 & N \\\\\nTN J2252-1618 & 397$\\pm$ 60 & 51.6$\\pm$ 2.5 & \\nodata & $-1.52\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 22 52 20.15 & $-$16 18 14.9 & N \\\\\nTN J2253-2156 & 425$\\pm$ 72 & 59.3$\\pm$ 2.8 & \\nodata & $-1.47\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 22 53 17.03 & $-$21 56 38.0 & N \\\\\n\\end{tabular}\n\\end{table*}\n\\begin{table*}\n\\tiny\n\\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{365}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{365}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nTN J2301+0555 & 484$\\pm$ 62 & 74.1$\\pm$ 3.3 & \\nodata & $-1.40\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 23 01 18.11 & $+$05 55 01.0 & N \\\\\nTN J2303-0251 & 405$\\pm$ 56 & 66.5$\\pm$ 3.1 & \\nodata & $-1.34\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 23 03 55.67 & $-$02 51 08.6 & N \\\\\nTN J2310+1358 & 1497$\\pm$102 & 251.9$\\pm$ 5.2 & \\nodata & $-1.33\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 23 10 52.32 & $+$13 58 20.5 & N \\\\\nTN J2312-0040 & 293$\\pm$ 25 & 45.5$\\pm$ 1.0 & \\nodata & $-1.39\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 23 12 46.90 & $-$00 40 53.0 & N \\\\\nTN J2312-0208 & 1295$\\pm$ 80 & 194.8$\\pm$ 8.6 & \\nodata & $-1.41\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 23 12 55.71 & $-$02 08 39.9 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2314+2053 & 386$\\pm$ 27 & 46.8$\\pm$ 2.3 & $ 5.9\\pm0.4$ & $-1.57\\pm$0.06 & $-1.67\\pm0.07$ & S & 0.3 & 129 & 23 14 56.04 & $+$20 53 37.4 & V \\\\\nTN J2320+1222 & 1566$\\pm$ 93 & 264.3$\\pm$ 5.4 & \\nodata & $-1.32\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 23 20 07.79 & $+$12 22 06.6 & N \\\\\nTN J2333-1508 & 504$\\pm$ 68 & 70.2$\\pm$ 3.3 & \\nodata & $-1.47\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 23 33 06.99 & $-$15 08 12.8 & N \\\\\nTN J2335+0634 & 507$\\pm$ 58 & 84.3$\\pm$ 3.8 & \\nodata & $-1.33\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 23 35 06.42 & $+$06 34 38.8 & N \\\\\nTN J2350-1321 & 419$\\pm$ 35 & 56.1$\\pm$ 1.2 & \\nodata & $-1.50\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 23 50 15.92 & $-$13 21 16.0 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2352+0814 & 498$\\pm$ 50 & 71.0$\\pm$ 3.2 & \\nodata & $-1.45\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 23 52 10.44 & $+$08 14 50.0 & N \\\\\nTN J2352+0450 & 398$\\pm$ 59 & 60.5$\\pm$ 2.8 & \\nodata & $-1.40\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 23 52 32.20 & $+$04 50 30.1 & N \\\\\nTN J2352-3139 & 573$\\pm$ 87 & 85.8$\\pm$ 3.8 & $29.0\\pm1.5$ & $-1.41\\pm$0.12 & $-0.87\\pm0.06$ & T & 21.1 & 170 & 23 52 46.79 & $-$31 39 36.9 & V \\\\\n\\hline\n\\end{tabular}\n\n$^{\\dag}$ Not a real USS source; see notes\n\n$^*$ See notes\n\\vspace{1cm}\n\\end{table*}\n\\begin{table*}\n\\centerline{\\bf Table A.3: MP sample}\n\\tiny\n\\begin{tabular}{rrrrrrrrrrrrr}\nName & $S_{408}$ & $S_{1420}$ & $S_{4850}$ & $\\alpha_{408}^{1420}$ & $\\alpha_{408}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos\\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$\\arcsec$\\;$ & \\\\\n\\hline\nMP J0003-3556 & 2440$\\pm$ 80 & \\nodata & 103.0$\\pm$13.0 & \\nodata & $-1.28\\pm$0.05 & \\nodata & \\nodata & \\nodata & 00 03 13.11 & $-$35 56 33.8 & M \\\\\nMP J0028-5523 & 1910$\\pm$ 80 & $ 389\\pm 38$ & 86.0$\\pm$ 9.0 & $-1.28\\pm0.10$ & $-1.25\\pm$0.05 & S & 3.7 & 57 & 00 28 53.76 & $-$55 23 28.5 & A \\\\\nMP J0100-6403 & 1410$\\pm$150 & $ 247\\pm 24$ & 56.0$\\pm$ 7.0 & $-1.40\\pm0.11$ & $-1.30\\pm$0.07 & S & 4.2 & 100 & 01 00 32.42 & $-$64 03 13.6 & A \\\\\nMP J0103-3225 & 2290$\\pm$ 80 & \\nodata & 93.0$\\pm$13.0 & \\nodata & $-1.29\\pm$0.06 & \\nodata & \\nodata & \\nodata & 01 03 17.10 & $-$32 25 53.3 & M \\\\\nMP J0114-3302 & 1590$\\pm$ 90 & $ 396\\pm 39$ & 76.0$\\pm$12.0 & $-1.11\\pm0.14$ & $-1.23\\pm$0.07 & D & 22.0 & 119 & 01 14 37.06 & $-$33 02 10.2 & A \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J0118-6331 & 1040$\\pm$ 90 & $ 264\\pm 26$ & 50.0$\\pm$ 7.0 & $-1.10\\pm0.09$ & $-1.23\\pm$0.07 & S & 4.1 & 48 & 01 18 07.54 & $-$63 31 43.2 & A \\\\\nMP J0130-8352 & 950$\\pm$ 50 & $ 159\\pm 15$ & 23.0$\\pm$ 5.0 & $-1.43\\pm0.11$ & $-1.50\\pm$0.09 & S & 3.2 & 66 & 01 30 07.45 & $-$83 52 29.6 & A \\\\\nMP J0141-4421 & 1400$\\pm$ 60 & $ 295\\pm 29$ & 56.0$\\pm$ 9.0 & $-1.25\\pm0.10$ & $-1.30\\pm$0.07 & D & 29.9 & 95 & 01 41 13.57 & $-$44 21 10.8 & A \\\\\nMP J0141-6941 & 3980$\\pm$320 & $ 755\\pm 75$ & 179.0$\\pm$11.0 & $-1.33\\pm0.09$ & $-1.25\\pm$0.04 & D & 16.1 & 153 & 01 41 55.18 & $-$69 41 33.1 & A \\\\\nMP J0155-8521 & 830$\\pm$ 70 & \\nodata & 38.0$\\pm$ 5.0 & \\nodata & $-1.25\\pm$0.06 & \\nodata & \\nodata & \\nodata & 01 55 16.98 & $-$85 21 07.4 & M \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J0202-5425 & 820$\\pm$ 70 & $ 186\\pm 18$ & 41.0$\\pm$ 8.0 & $-1.19\\pm0.09$ & $-1.21\\pm$0.09 & D & 14.5 & 5 & 02 02 56.25 & $-$54 25 13.3 & A \\\\\nMP J0211-5146 & 900$\\pm$ 40 & $ 160\\pm 16$ & 43.0$\\pm$ 8.0 & $-1.38\\pm0.08$ & $-1.23\\pm$0.08 & S & 11.1 & 50 & 02 11 44.92 & $-$51 46 47.0 & A \\\\\nMP J0249-4145 & 1100$\\pm$ 50 & $ 242\\pm 24$ & 48.0$\\pm$ 9.0 & $-1.21\\pm0.08$ & $-1.27\\pm$0.08 & S & 8.2 & 49 & 02 49 10.08 & $-$41 45 36.3 & A \\\\\nMP J0339-4018 & 3610$\\pm$140 & $ 759\\pm 75$ & 174.0$\\pm$13.0 & $-1.25\\pm0.09$ & $-1.22\\pm$0.03 & S & 5.6 & 33 & 03 39 48.18 & $-$40 18 22.1 & A \\\\\nMP J0340-6507 & 1640$\\pm$ 50 & $ 383\\pm 38$ & 81.0$\\pm$ 8.0 & $-1.17\\pm0.10$ & $-1.22\\pm$0.04 & D & 14.0 & 18 & 03 40 44.92 & $-$65 07 07.3 & A \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J0446-3305 & 1910$\\pm$100 & $ 448\\pm 44$ & 82.0$\\pm$12.0 & $-1.16\\pm0.10$ & $-1.27\\pm$0.06 & D & 58.8 & 6 & 04 46 00.21 & $-$33 05 18.3 & A \\\\\nMP J0449-5449 & 900$\\pm$ 70 & $ 200\\pm 20$ & 46.0$\\pm$ 8.0 & $-1.20\\pm0.09$ & $-1.20\\pm$0.08 & S & 4.3 & 56 & 04 49 04.66 & $-$54 49 10.1 & A \\\\\nMP J0601-3926 & 2270$\\pm$320 & $ 451\\pm 45$ & 97.0$\\pm$10.0 & $-1.29\\pm0.09$ & $-1.27\\pm$0.07 & S & 6.2 & 43 & 06 01 00.77 & $-$39 26 18.1 & A \\\\\nMP J0605-5036 & 1040$\\pm$ 70 & $ 358\\pm 35$ & 43.0$\\pm$ 8.0 & $-0.85\\pm0.10$ & $-1.29\\pm$0.08 & D & 9.4 & 105 & 06 05 47.25 & $-$50 36 41.7 & A \\\\\nMP J0618-7340 & 750$\\pm$ 50 & \\nodata & 25.0$\\pm$ 6.0 & \\nodata & $-1.37\\pm$0.10 & \\nodata & \\nodata & \\nodata & 06 18 47.54 & $-$73 40 40.8 & M \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J0648-7118 & 1000$\\pm$ 50 & $ 300\\pm 30$ & 42.0$\\pm$ 7.0 & $-0.96\\pm0.09$ & $-1.28\\pm$0.07 & S & 2.5 & 45 & 06 48 37.38 & $-$71 18 26.4 & A \\\\\nMP J0731-6621 & 870$\\pm$ 40 & \\nodata & 40.0$\\pm$ 7.0 & \\nodata & $-1.24\\pm$0.07 & \\nodata & \\nodata & \\nodata & 07 31 47.00 & $-$66 21 30.3 & M \\\\\nMP J0839-7359 & 1450$\\pm$ 60 & \\nodata & 69.0$\\pm$ 7.0 & \\nodata & $-1.23\\pm$0.04 & DF & \\nodata & \\nodata & 08 39 33.28 & $-$73 59 37.4 & M \\\\\nMP J1033-3418 & 5590$\\pm$250 & \\nodata & 268.0$\\pm$22.0 & \\nodata & $-1.23\\pm$0.04 & \\nodata & \\nodata & \\nodata & 10 33 13.04 & $-$34 18 48.4 & M \\\\\nMP J1119-3631 & 2440$\\pm$ 70 & $ 542\\pm 54$ & 113.0$\\pm$14.0 & $-1.21\\pm0.10$ & $-1.24\\pm$0.05 & S & 4.8 & 166 & 11 19 21.81 & $-$36 31 39.5 & A \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J1208-3403 & 4650$\\pm$210 & \\nodata & 198.0$\\pm$18.0 & \\nodata & $-1.28\\pm$0.04 & \\nodata & \\nodata & \\nodata & 12 08 39.17 & $-$34 03 10.7 & M \\\\\nMP J1250-4026 & 6030$\\pm$180 & \\nodata & 299.0$\\pm$18.0 & \\nodata & $-1.21\\pm$0.03 & \\nodata & \\nodata & \\nodata & 12 50 05.68 & $-$40 26 28.7 & M \\\\\nMP J1250-4119 & 1350$\\pm$ 60 & $ 167\\pm 16$ & 63.0$\\pm$ 9.0 & $-1.67\\pm0.09$ & $-1.24\\pm$0.06 & S & 7.4 & 123 & 12 50 46.49 & $-$41 19 35.7 & A \\\\\nMP J1355-7806 & 1690$\\pm$ 90 & \\nodata & 44.0$\\pm$ 6.0 & \\nodata & $-1.47\\pm$0.06 & DF & \\nodata & \\nodata & 13 55 35.57 & $-$78 06 43.7 & M \\\\\nMP J1657-7423 & 1080$\\pm$ 50 & \\nodata & 50.0$\\pm$ 7.0 & \\nodata & $-1.24\\pm$0.06 & \\nodata & \\nodata & \\nodata & 16 57 44.73 & $-$74 23 09.3 & M \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J1710-7343 & 910$\\pm$ 70 & $ 47\\pm 4$ & 26.0$\\pm$ 6.0 & $-2.37\\pm0.10$ & $-1.44\\pm$0.10 & S & \\nodata & 149 & 17 10 17.73 & $-$73 43 19.1 & A \\\\\nMP J1733-8342 & 4630$\\pm$210 & \\nodata & 198.0$\\pm$12.0 & \\nodata & $-1.27\\pm$0.03 & \\nodata & \\nodata & \\nodata & 17 33 55.38 & $-$83 42 48.0 & M \\\\\nMP J1755-6916 & 1580$\\pm$ 90 & $ 486\\pm 48$ & 71.0$\\pm$ 7.0 & $-0.94\\pm0.09$ & $-1.25\\pm$0.05 & D & 0.5 & 90 & 17 55 30.23 & $-$69 16 49.8 & A \\\\\nMP J1758-6738 & 3000$\\pm$140 & $ 478\\pm 47$ & 112.0$\\pm$ 9.0 & $-1.47\\pm0.09$ & $-1.33\\pm$0.04 & D & 31.2 & 119 & 17 58 51.25 & $-$67 38 30.5 & A \\\\\nMP J1821-7457 & 2190$\\pm$110 & \\nodata & 77.0$\\pm$ 7.0 & \\nodata & $-1.35\\pm$0.04 & \\nodata & \\nodata & \\nodata & 18 21 59.83 & $-$74 57 47.5 & M \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J1909-7755 & 900$\\pm$ 70 & $ 182\\pm 18$ & 41.0$\\pm$ 6.0 & $-1.28\\pm0.09$ & $-1.25\\pm$0.07 & D & 27.9 & 81 & 19 09 57.19 & $-$77 56 01.5 & A \\\\\nMP J1912-5349 & 1110$\\pm$ 70 & $ 441\\pm 44$ & 56.0$\\pm$ 8.0 & $-0.74\\pm0.09$ & $-1.21\\pm$0.06 & D & 17.0 & 45 & 19 12 20.77 & $-$53 49 01.3 & A \\\\\nMP J1921-6217 & 2110$\\pm$ 40 & $ 400\\pm 40$ & 79.0$\\pm$ 8.0 & $-1.33\\pm0.08$ & $-1.33\\pm$0.04 & S & 3.4 & 113 & 19 21 03.06 & $-$62 17 25.2 & A \\\\\nMP J1921-5431 & 4590$\\pm$210 & \\nodata & 66.0$\\pm$ 8.0 & \\nodata & $-1.71\\pm$0.05 & \\nodata & \\nodata & \\nodata & 19 21 52.92 & $-$54 31 51.8 & M \\\\\nMP J1929-3732 & 3260$\\pm$110 & $ 806\\pm 80$ & 135.0$\\pm$12.0 & $-1.12\\pm0.09$ & $-1.29\\pm$0.04 & S & 3.7 & 14 & 19 29 08.51 & $-$37 32 48.8 & A \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J1940-4236 & 1340$\\pm$ 70 & \\nodata & 64.0$\\pm$ 9.0 & \\nodata & $-1.23\\pm$0.06 & \\nodata & \\nodata & \\nodata & 19 40 58.04 & $-$42 36 49.5 & M \\\\\nMP J1942-5553 & 2120$\\pm$110 & $ 385\\pm 38$ & 74.0$\\pm$ 8.0 & $-1.37\\pm0.08$ & $-1.36\\pm$0.05 & S & 6.7 & 176 & 19 42 06.97 & $-$55 53 32.6 & A \\\\\nMP J1943-4030 & 4400$\\pm$140 & \\nodata & 153.0$\\pm$12.0 & \\nodata & $-1.36\\pm$0.03 & DF & \\nodata & \\nodata & 19 43 52.33 & $-$40 30 10.9 & M \\\\\nMP J1953-4852 & 860$\\pm$ 30 & $ 143\\pm 14$ & 42.0$\\pm$ 8.0 & $-1.44\\pm0.09$ & $-1.22\\pm$0.08 & S & 4.7 & 115 & 19 53 39.88 & $-$48 52 13.8 & A \\\\\nMP J2002-5252 & 2730$\\pm$130 & $ 411\\pm 41$ & 76.0$\\pm$ 9.0 & $-1.52\\pm0.09$ & $-1.45\\pm$0.05 & S & 4.5 & 29 & 20 02 22.89 & $-$52 52 51.8 & A \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J2003-8340 & 1600$\\pm$ 80 & $ 253\\pm 25$ & 67.0$\\pm$ 6.0 & $-1.48\\pm0.09$ & $-1.28\\pm$0.04 & S & 3.5 & 106 & 20 03 30.73 & $-$83 41 00.0 & A \\\\\nMP J2017-5747 & 1860$\\pm$160 & $ 287\\pm 28$ & 79.0$\\pm$ 8.0 & $-1.50\\pm0.08$ & $-1.28\\pm$0.05 & S & 11.8 & 28 & 20 17 48.11 & $-$57 47 11.9 & A \\\\\nMP J2045-6018 & 11160$\\pm$340 & $2105\\pm210$ & 447.0$\\pm$24.0 & $-1.34\\pm0.09$ & $-1.30\\pm$0.02 & D & 41.6 & 44 & 20 45 21.82 & $-$60 18 51.5 & A \\\\\nMP J2048-5750 & 2810$\\pm$130 & $ 494\\pm 49$ & 137.0$\\pm$10.0 & $-1.39\\pm0.09$ & $-1.22\\pm$0.03 & S & 5.7 & 18 & 20 48 36.64 & $-$57 50 47.6 & A \\\\\nMP J2126-5439 & 1180$\\pm$ 80 & $ 282\\pm 28$ & 57.0$\\pm$ 8.0 & $-1.15\\pm0.12$ & $-1.22\\pm$0.06 & D & 17.1 & 147 & 21 26 53.65 & $-$54 39 36.0 & A \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J2204-5831 & 900$\\pm$ 70 & $ 148\\pm 14$ & 44.0$\\pm$ 8.0 & $-1.45\\pm0.08$ & $-1.22\\pm$0.08 & S & 10.5 & 11 & 22 04 05.48 & $-$58 31 38.3 & A \\\\\nMP J2222-4723 & 910$\\pm$ 70 & $ 509\\pm 50$ & 45.0$\\pm$ 9.0 & $-0.47\\pm0.09$ & $-1.21\\pm$0.09 & D & 9.1 & 148 & 22 22 53.71 & $-$47 23 12.1 & A \\\\\nMP J2226-7654 & 900$\\pm$ 60 & $ 203\\pm 20$ & 35.0$\\pm$ 6.0 & $-1.19\\pm0.09$ & $-1.31\\pm$0.07 & S & 4.1 & 107 & 22 26 56.90 & $-$76 54 48.0 & A \\\\\nMP J2229-3824 & 8210$\\pm$210 & \\nodata & 412.0$\\pm$23.0 & \\nodata & $-1.21\\pm$0.02 & \\nodata & \\nodata & \\nodata & 22 29 46.94 & $-$38 24 02.9 & M \\\\\nMP J2308-6423 & 1750$\\pm$ 90 & $ 301\\pm 30$ & 39.0$\\pm$ 7.0 & $-1.41\\pm0.09$ & $-1.54\\pm$0.08 & D & 14.3 & 7 & 23 08 45.21 & $-$64 23 33.3 & A \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J2313-4243 & 1390$\\pm$ 60 & \\nodata & 58.0$\\pm$ 9.0 & \\nodata & $-1.28\\pm$0.07 & \\nodata & \\nodata & \\nodata & 23 13 58.76 & $-$42 43 38.1 & M \\\\\nMP J2352-6154 & 1450$\\pm$ 40 & $ 311\\pm 31$ & 69.0$\\pm$ 8.0 & $-1.23\\pm0.10$ & $-1.23\\pm$0.05 & D & 56.1 & 148 & 23 52 55.52 & $-$61 54 06.9 & A \\\\\nMP J2357-3445 & 8700$\\pm$350 & \\nodata & 117.0$\\pm$14.0 & \\nodata & $-1.74\\pm$0.05 & \\nodata & \\nodata & \\nodata & 23 57 01.09 & $-$34 45 38.9 & M \\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n"},{"name":"wntable.tex","string":"\\begin{table*}\n\\centerline{\\bf Table A.1: WN sample}\n\\tiny\n \\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{325}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{325}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nWN J0000+4654 & 204$\\pm$ 9 & 21.1$\\pm$ 1.4 & $ 2.97\\pm0.13$ & $-1.55\\pm$0.06 & $-1.58\\pm0.06$ & D & 3.6 & 173 & 00 00 28.88 & +46 54 40.7 & V \\\\\nWN J0007+3641 & 447$\\pm$18 & 28.8$\\pm$ 1.7 & $ 2.51\\pm0.11$ & $-1.88\\pm$0.05 & $-1.96\\pm0.06$ & S & 1.7 & 67 & 00 07 02.92 & +36 41 55.9 & V \\\\\nWN J0007+4615 & 144$\\pm$ 7 & 16.9$\\pm$ 0.5 & \\nodata & $-1.47\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 00 07 15.05 & +46 15 40.8 & N \\\\\nWN J0016+4311 & 105$\\pm$ 6 & 15.7$\\pm$ 1.5 & \\nodata & $-1.30\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 00 16 40.63 & +43 11 03.5 & N \\\\\nWN J0029+3439 & 288$\\pm$12 & 40.9$\\pm$ 2.0 & $ 44.76\\pm1.05$ & $-1.34\\pm$0.04 & $ 0.07\\pm0.04$ & DF & 12.8 & 80 & 00 29 01.61 & +34 39 34.7 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0034+4142 & 84$\\pm$ 6 & 11.0$\\pm$ 0.5 & $ 2.50\\pm0.12$ & $-1.39\\pm$0.05 & $-1.19\\pm0.05$ & D & 23.7 & 154 & 00 34 29.21 & +41 42 09.5 & V \\\\\nWN J0034+3238 & 120$\\pm$ 9 & 16.4$\\pm$ 0.5 & \\nodata & $-1.36\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 00 34 56.36 & +32 38 36.4 & N \\\\\nWN J0038+7859 & 109$\\pm$ 6 & 15.1$\\pm$ 0.5 & $ 1.30\\pm0.09$ & $-1.35\\pm$0.04 & $-1.97\\pm0.06$ & S & 2.5 & 159 & 00 38 01.96 & +78 59 51.5 & V \\\\\nWN J0040+3857 & 127$\\pm$ 7 & 17.5$\\pm$ 0.5 & $ 3.13\\pm0.14$ & $-1.36\\pm$0.04 & $-1.38\\pm0.04$ & S & 1.4 & 31 & 00 40 56.23 & +38 57 30.0 & V \\\\\nWN J0043+4719$^{\\dag}$ & 99$\\pm$ 6 & 14.2$\\pm$ 1.3 & $ 41.81\\pm1.01$ & $-1.33\\pm$0.08 & $ 0.87\\pm0.08$ & T & 18.5 & 157 & 00 43 53.13 & +47 19 48.3 & V \\\\\n&&&&&&&&&&&\\\\\nWN J0048+4137$^*$ & 277$\\pm$11 & 34.5$\\pm$ 1.9 & $ 1.75\\pm0.10$ & $-1.43\\pm$0.05 & $-2.40\\pm0.06$ & S & 2.5 & 17 & 00 48 46.34 & +41 37 20.8 & V \\\\\nWN J0059+3958 & 152$\\pm$ 7 & 11.4$\\pm$ 1.4 & \\nodata & $-1.77\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 00 59 51.07 & +39 58 46.5 & N \\\\\nWN J0112+4039 & 111$\\pm$ 7 & 15.4$\\pm$ 0.5 & \\nodata & $-1.35\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 01 12 26.31 & +40 39 30.1 & N \\\\\nWN J0117+3715 & 165$\\pm$ 8 & 22.5$\\pm$ 0.6 & $ 6.62\\pm0.21$ & $-1.36\\pm$0.04 & $-0.98\\pm0.03$ & S & 1.4 & 71 & 01 17 10.02 & +37 15 16.3 & V \\\\\nWN J0121+4305 & 389$\\pm$16 & 50.8$\\pm$ 2.5 & \\nodata & $-1.39\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 01 21 10.71 & +43 05 18.3 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0135+3303 & 94$\\pm$ 6 & 12.1$\\pm$ 0.5 & $ 10.22\\pm0.28$ & $-1.40\\pm$0.06 & $-0.14\\pm0.04$ & T & 1.8 & 18 & 01 35 07.24 & +33 03 47.4 & V \\\\\nWN J0137+3250 & 177$\\pm$ 9 & 23.8$\\pm$ 1.6 & $ 16.06\\pm0.40$ & $-1.37\\pm$0.06 & $-0.32\\pm0.06$ & T & 27.9 & 104 & 01 36 59.85 & +32 50 40.7 & V \\\\\nWN J0155+8036 & 338$\\pm$14 & 38.0$\\pm$ 0.9 & $ 6.87\\pm0.21$ & $-1.50\\pm$0.03 & $-1.38\\pm0.03$ & D & 4.6 & 159 & 01 55 43.77 & +80 36 48.1 & V \\\\\nWN J0207+3655 & 118$\\pm$ 6 & 17.5$\\pm$ 1.4 & \\nodata & $-1.31\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 02 07 22.59 & +36 55 16.0 & N \\\\\nWN J0231+3600 & 303$\\pm$13 & 45.2$\\pm$ 2.2 & $ 7.66\\pm0.22$ & $-1.30\\pm$0.04 & $-1.43\\pm0.05$ & D & 14.8 & 59 & 02 31 11.48 & +36 00 26.6 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0240+3526 & 79$\\pm$ 5 & 10.2$\\pm$ 0.5 & \\nodata & $-1.40\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 02 40 31.10 & +35 26 55.1 & N \\\\\nWN J0303+3733 & 1071$\\pm$43 & 127.9$\\pm$ 5.7 & $ 17.32\\pm0.43$ & $-1.46\\pm$0.04 & $-1.61\\pm0.04$ & D & 4.4 & 3 & 03 03 26.01 & +37 33 41.6 & V \\\\\nWN J0303+3629 & 117$\\pm$ 6 & 17.1$\\pm$ 0.5 & \\nodata & $-1.32\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 03 03 29.87 & +36 29 56.1 & N \\\\\nWN J0305+3525 & 110$\\pm$ 6 & 15.8$\\pm$ 1.3 & $ 3.74\\pm0.15$ & $-1.33\\pm$0.07 & $-1.16\\pm0.07$ & S & 1.9 & 64 & 03 05 47.42 & +35 25 13.4 & V \\\\\nWN J0310+3644 & 289$\\pm$11 & 24.2$\\pm$ 0.6 & $ 2.45\\pm0.12$ & $-1.70\\pm$0.03 & $-1.84\\pm0.05$ & S & 2.0 & 118 & 03 10 54.80 & +36 44 02.5 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0315+3757 & 95$\\pm$ 5 & 13.3$\\pm$ 0.5 & $ 4.74\\pm0.17$ & $-1.35\\pm$0.05 & $-0.83\\pm0.04$ & S & 1.7 & 53 & 03 15 17.29 & +37 57 05.0 & V \\\\\nWN J0323+3738 & 205$\\pm$ 9 & 22.6$\\pm$ 1.5 & $ 8.11\\pm0.25$ & $-1.51\\pm$0.06 & $-0.83\\pm0.06$ & DF & 9.7 & 100 & 03 23 38.24 & +37 38 39.3 & V \\\\\nWN J0343+7540 & 118$\\pm$ 6 & 12.5$\\pm$ 1.6 & \\nodata & $-1.54\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 03 43 39.77 & +75 40 43.2 & N \\\\\nWN J0346+3039 & 286$\\pm$12 & 35.6$\\pm$ 1.9 & $ 4.95\\pm0.18$ & $-1.43\\pm$0.05 & $-1.59\\pm0.05$ & D & 0.4 & 89 & 03 46 42.60 & +30 39 51.0 & V \\\\\nWN J0352+3143 & 154$\\pm$ 7 & 21.8$\\pm$ 1.5 & \\nodata & $-1.34\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 03 52 24.49 & +31 43 03.1 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0359+3000 & 88$\\pm$ 6 & 12.1$\\pm$ 0.5 & \\nodata & $-1.36\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 03 59 12.86 & +30 00 51.7 & N \\\\\nWN J0528+6549 & 96$\\pm$ 6 & 10.6$\\pm$ 2.4 & $ 1.08\\pm0.09$ & $-1.51\\pm$0.16 & $-1.84\\pm0.19$ & S & 1.9 & 108 & 05 28 46.07 & +65 49 57.3 & V \\\\\nWN J0533+7205 & 117$\\pm$ 7 & 17.4$\\pm$ 1.6 & $ 2.42\\pm0.12$ & $-1.30\\pm$0.08 & $-1.59\\pm0.08$ & D & 2.9 & 140 & 05 33 38.64 & +72 05 52.7 & V \\\\\nWN J0538+7348 & 132$\\pm$ 7 & 18.1$\\pm$ 0.5 & $ 3.20\\pm0.14$ & $-1.36\\pm$0.04 & $-1.39\\pm0.04$ & S & 2.1 & 113 & 05 38 25.59 & +73 48 39.6 & V \\\\\nWN J0559+6926 & 87$\\pm$ 5 & 12.9$\\pm$ 0.5 & $ 1.88\\pm0.13$ & $-1.31\\pm$0.06 & $-1.55\\pm0.06$ & S & 0.3 & 85 & 05 59 06.04 & +69 26 37.8 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0610+6611 & 98$\\pm$ 6 & 12.5$\\pm$ 1.9 & $ 1.19\\pm0.09$ & $-1.41\\pm$0.11 & $-1.89\\pm0.14$ & S & 2.2 & 114 & 06 10 08.59 & +66 11 43.1 & V \\\\\nWN J0617+5012 & 196$\\pm$ 9 & 26.5$\\pm$ 0.7 & $ 6.80\\pm0.23$ & $-1.37\\pm$0.04 & $-1.09\\pm0.03$ & D & 3.4 & 11 & 06 17 39.37 & +50 12 54.7 & V \\\\\nWN J0625+5708 & 71$\\pm$ 4 & 10.3$\\pm$ 0.5 & $ 1.54\\pm0.10$ & $-1.32\\pm$0.07 & $-1.53\\pm0.06$ & D & 7.3 & 18 & 06 25 01.67 & +57 08 26.1 & V \\\\\nWN J0627+7311 & 470$\\pm$19 & 61.9$\\pm$ 2.9 & $ 4.00\\pm0.17$ & $-1.39\\pm$0.04 & $-2.20\\pm0.05$ & S & $<0.3$ & 0 & 06 27 03.64 & +73 11 54.2 & V \\\\\nWN J0633+6024 & 115$\\pm$ 6 & 13.4$\\pm$ 2.8 & $ 2.07\\pm0.11$ & $-1.47\\pm$0.15 & $-1.50\\pm0.17$ & S & 2.2 & 118 & 06 33 19.70 & +60 24 37.1 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0633+4653 & 3661$\\pm$146 & 520.1$\\pm$22.8 & $ 80.88\\pm1.74$ & $-1.34\\pm$0.04 & $-1.50\\pm0.04$ & T & 4.0 & 19 & 06 33 52.18 & +46 53 40.5 & V \\\\\nWN J0641+4325 & 154$\\pm$ 7 & 15.6$\\pm$ 0.5 & \\nodata & $-1.57\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 06 41 08.23 & +43 25 00.3 & N \\\\\nWN J0646+3912 & 166$\\pm$ 8 & 20.5$\\pm$ 2.4 & \\nodata & $-1.43\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 06 46 34.97 & +39 12 00.3 & N \\\\\nWN J0648+4309 & 215$\\pm$ 9 & 30.4$\\pm$ 1.7 & $ 5.00\\pm0.19$ & $-1.34\\pm$0.05 & $-1.45\\pm0.05$ & DF & 1.5 & 151 & 06 48 01.10 & +43 09 47.8 & V \\\\\nWN J0648+4137 & 91$\\pm$ 5 & 10.9$\\pm$ 1.5 & $ 1.69\\pm0.11$ & $-1.45\\pm$0.11 & $-1.50\\pm0.12$ & S & 13.2 & 94 & 06 48 14.58 & +41 37 18.8 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0650+4106 & 393$\\pm$16 & 53.5$\\pm$ 1.2 & $ 15.04\\pm0.41$ & $-1.37\\pm$0.03 & $-1.02\\pm0.03$ & DF & 3.0 & 26 & 06 50 41.66 & +41 06 39.1 & V \\\\\nWN J0653+4434 & 115$\\pm$ 6 & 13.1$\\pm$ 0.5 & \\nodata & $-1.49\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 06 53 23.84 & +44 34 55.4 & N \\\\\nWN J0656+5301 & 137$\\pm$ 7 & 18.7$\\pm$ 1.5 & \\nodata & $-1.36\\pm$0.07 & \\nodata & D & 56.1 & 88 & 06 56 38.40 & +53 01 18.1 & F \\\\\nWN J0658+4444 & 407$\\pm$17 & 50.6$\\pm$ 2.4 & $ 13.91\\pm0.35$ & $-1.43\\pm$0.04 & $-1.04\\pm0.04$ & S & 1.7 & 73 & 06 58 27.43 & +44 44 16.4 & V \\\\\nWN J0702+4448 & 147$\\pm$ 7 & 17.0$\\pm$ 0.5 & \\nodata & $-1.48\\pm$0.04 & \\nodata & S & 7.8 & 119 & 07 02 16.79 & +44 48 59.7 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0711+4242 & 140$\\pm$ 6 & 16.0$\\pm$ 0.5 & \\nodata & $-1.49\\pm$0.04 & \\nodata & S & 3.3 & 17 & 07 11 40.25 & +42 42 09.6 & F \\\\\nWN J0715+4655 & 89$\\pm$ 6 & 10.4$\\pm$ 0.5 & $ 1.86\\pm0.13$ & $-1.47\\pm$0.06 & $-1.38\\pm0.07$ & S & 0.2 & 114 & 07 15 02.03 & +46 55 26.3 & V \\\\\nWN J0716+5107 & 204$\\pm$ 9 & 28.4$\\pm$ 0.7 & $ 4.54\\pm0.18$ & $-1.35\\pm$0.04 & $-1.47\\pm0.04$ & D & 1.2 & 8 & 07 16 40.50 & +51 07 04.7 & V \\\\\nWN J0717+4611$^*$ & 724$\\pm$29 & 107.8$\\pm$ 4.8 & $ 45.30\\pm1.00$ & $-1.30\\pm$0.04 & $-0.70\\pm0.04$ & T & 6.2 & 16 & 07 17 58.49 & +46 11 39.1 & V \\\\\nWN J0720+5140 & 95$\\pm$ 6 & 11.6$\\pm$ 0.5 & \\nodata & $-1.44\\pm$0.05 & \\nodata & S & 3.2 & 101 & 07 20 00.20 & +51 40 28.5 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0720+5758 & 93$\\pm$ 7 & 13.9$\\pm$ 0.5 & $ 2.37\\pm0.12$ & $-1.30\\pm$0.05 & $-1.42\\pm0.05$ & S & 2.0 & 109 & 07 20 09.56 & +57 58 32.9 & V \\\\\nWN J0721+3324 & 313$\\pm$13 & 36.8$\\pm$ 1.9 & $ 2.35\\pm0.13$ & $-1.47\\pm$0.05 & $-2.21\\pm0.06$ & DF & 2.0 & 143 & 07 21 56.85 & +33 24 53.8 & V \\\\\nWN J0725+4123$^*$ & 272$\\pm$12 & 35.5$\\pm$ 1.9 & \\nodata & $-1.39\\pm$0.05 & \\nodata & S & 8.3 & 156 & 07 25 57.08 & +41 23 05.1 & F \\\\\nWN J0727+3020$^*$ & 93$\\pm$ 6 & 12.8$\\pm$ 1.9 & \\nodata & $-1.36\\pm$0.11 & \\nodata & D & 34.8 & 103 & 07 27 48.50 & +30 21 00.7 & F \\\\\nWN J0736+6845 & 84$\\pm$ 5 & 12.4$\\pm$ 0.5 & \\nodata & $-1.31\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 07 36 36.42 & +68 45 56.8 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0737+7146 & 79$\\pm$ 5 & 10.3$\\pm$ 0.5 & \\nodata & $-1.40\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 07 37 09.93 & +71 46 29.3 & N \\\\\nWN J0740+6319 & 254$\\pm$11 & 26.1$\\pm$ 1.7 & \\nodata & $-1.56\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 07 40 27.01 & +63 19 55.2 & N \\\\\nWN J0741+5611 & 313$\\pm$13 & 44.4$\\pm$ 1.0 & $ 7.08\\pm0.24$ & $-1.34\\pm$0.03 & $-1.48\\pm0.03$ & S & 0.5 & 20 & 07 41 15.38 & +56 11 35.9 & V \\\\\nWN J0747+3654 & 289$\\pm$12 & 36.8$\\pm$ 0.8 & \\nodata & $-1.41\\pm$0.03 & \\nodata & S & 2.1 & 2 & 07 47 29.38 & +36 54 38.1 & F \\\\\nWN J0747+4527 & 138$\\pm$ 7 & 19.1$\\pm$ 2.2 & \\nodata & $-1.35\\pm$0.09 & \\nodata & S & 3.5 & 109 & 07 47 29.56 & +45 27 16.3 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0751+3300 & 98$\\pm$ 7 & 11.5$\\pm$ 0.5 & $ 1.90\\pm0.12$ & $-1.47\\pm$0.05 & $-1.44\\pm0.06$ & S & 0.4 & 139 & 07 51 48.04 & +33 00 07.1 & V \\\\\nWN J0756+5010 & 204$\\pm$ 9 & 29.9$\\pm$ 0.7 & \\nodata & $-1.31\\pm$0.04 & \\nodata & S & 1.7 & 93 & 07 56 24.63 & +50 10 12.5 & F \\\\\nWN J0801+7134 & 120$\\pm$ 6 & 13.5$\\pm$ 2.3 & \\nodata & $-1.50\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 08 01 18.68 & +71 34 01.6 & N \\\\\nWN J0809+6624 & 257$\\pm$11 & 32.2$\\pm$ 2.3 & \\nodata & $-1.42\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 08 09 19.28 & +66 24 09.5 & N \\\\\nWN J0810+4948 & 146$\\pm$ 7 & 18.1$\\pm$ 1.4 & $ 2.16\\pm0.13$ & $-1.43\\pm$0.07 & $-1.74\\pm0.08$ & S & $<0.3$ & 0 & 08 10 34.92 & +49 48 37.5 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0812+3424 & 160$\\pm$ 8 & 19.9$\\pm$ 1.4 & \\nodata & $-1.43\\pm$0.06 & \\nodata & D & 6.6 & 58 & 08 12 14.43 & +34 24 09.3 & F \\\\\nWN J0813+4828 & 184$\\pm$ 9 & 23.3$\\pm$ 1.7 & $ 15.20\\pm0.40$ & $-1.42\\pm$0.06 & $-0.32\\pm0.06$ & D & 0.9 & 173 & 08 13 38.10 & +48 28 41.5 & V \\\\\nWN J0819+5628 & 95$\\pm$ 6 & 11.7$\\pm$ 0.5 & \\nodata & $-1.43\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 08 19 33.65 & +56 28 38.1 & N \\\\\nWN J0829+3834$^*$ & 112$\\pm$ 6 & 12.7$\\pm$ 1.3 & \\nodata & $-1.49\\pm$0.08 & \\nodata & S & 1.6 & 0 & 08 29 17.35 & +38 34 52.6 & F \\\\\nWN J0830+3018 & 109$\\pm$ 6 & 13.9$\\pm$ 1.2 & \\nodata & $-1.41\\pm$0.07 & \\nodata & S & 3.5 & 89 & 08 30 36.91 & +30 18 11.8 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0834+4820 & 128$\\pm$ 7 & 17.9$\\pm$ 0.5 & $ 3.65\\pm0.18$ & $-1.35\\pm$0.04 & $-1.27\\pm0.04$ & S & 0.4 & 99 & 08 34 25.85 & +48 20 00.8 & V \\\\\nWN J0835+3439 & 143$\\pm$ 7 & 19.1$\\pm$ 1.3 & \\nodata & $-1.38\\pm$0.06 & \\nodata & D & 58.0 & 168 & 08 35 22.92 & +34 39 49.8 & F \\\\\nWN J0842+3540 & 110$\\pm$ 6 & 15.0$\\pm$ 0.5 & \\nodata & $-1.36\\pm$0.04 & \\nodata & S & 1.1 & 0 & 08 42 10.82 & +35 40 42.2 & F \\\\\nWN J0842+3101 & 76$\\pm$ 5 & 10.5$\\pm$ 3.6 & \\nodata & $-1.36\\pm$0.24 & \\nodata & \\nodata & \\nodata & \\nodata & 08 42 16.35 & +31 01 11.6 & N \\\\\nWN J0843+3723 & 290$\\pm$13 & 35.8$\\pm$ 1.9 & \\nodata & $-1.43\\pm$0.05 & \\nodata & S & 1.1 & 5 & 08 43 02.09 & +37 23 18.1 & F \\\\\n&&&&&&&&&&&\\\\\nWN J0850+4830$^*$ & 192$\\pm$ 9 & 18.9$\\pm$ 1.4 & $ 1.53\\pm0.13$ & $-1.59\\pm$0.06 & $-2.02\\pm0.09$ & S & 0.3 & 52 & 08 50 56.50 & +48 30 46.2 & V \\\\\nWN J0852+3311 & 179$\\pm$ 8 & 24.6$\\pm$ 1.5 & \\nodata & $-1.36\\pm$0.05 & \\nodata & D & 6.1 & 13 & 08 52 50.55 & +33 11 41.0 & F \\\\\nWN J0901+6547$^{\\dag}$ & 140$\\pm$ 7 & 19.0$\\pm$ 0.5 & $ 71.60\\pm1.57$ & $-1.37\\pm$0.04 & $ 1.07\\pm0.03$ & D & 37.6 & 117 & 09 01 27.69 & +65 47 25.8 & V \\\\\nWN J0901+3151 & 135$\\pm$ 8 & 20.1$\\pm$ 1.4 & \\nodata & $-1.30\\pm$0.06 & \\nodata & D & 20.1 & 109 & 09 01 48.50 & +31 51 59.4 & F \\\\\nWN J0903+8246 & 112$\\pm$ 6 & 15.5$\\pm$ 0.5 & \\nodata & $-1.35\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 09 03 44.81 & +82 46 02.0 & N \\\\\n\\end{tabular}\n\\end{table*}\n\n\\begin{table*}\n\\tiny\n\\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{325}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{325}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nWN J0911+6306 & 118$\\pm$ 6 & 12.9$\\pm$ 1.3 & \\nodata & $-1.52\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 09 11 34.24 & +63 06 21.7 & N \\\\\nWN J0913+6104 & 297$\\pm$12 & 33.8$\\pm$ 1.8 & \\nodata & $-1.49\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 09 13 05.21 & +61 04 11.7 & N \\\\\nWN J0915+8133 & 127$\\pm$ 5 & 18.6$\\pm$ 0.6 & $ 2.99\\pm0.13$ & $-1.32\\pm$0.04 & $-1.47\\pm0.04$ & S & 2.3 & 127 & 09 15 09.29 & +81 33 34.1 & V \\\\\nWN J0920+5544 & 142$\\pm$ 7 & 13.5$\\pm$ 1.2 & \\nodata & $-1.61\\pm$0.07 & \\nodata & D & 8.9 & 129 & 09 20 46.78 & +55 44 21.8 & F \\\\\nWN J0923+4602 & 107$\\pm$ 5 & 12.1$\\pm$ 0.5 & \\nodata & $-1.49\\pm$0.06 & \\nodata & D & 21.6 & 172 & 09 23 10.44 & +46 02 59.0 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0928+6003 & 119$\\pm$ 6 & 11.0$\\pm$ 0.5 & $ 2.14\\pm0.11$ & $-1.63\\pm$0.05 & $-1.32\\pm0.06$ & S & 3.4 & 128 & 09 28 44.58 & +60 03 01.7 & V \\\\\nWN J0930+4358 & 118$\\pm$ 7 & 12.0$\\pm$ 0.5 & \\nodata & $-1.57\\pm$0.05 & \\nodata & S & 3.1 & 88 & 09 30 12.14 & +43 58 27.2 & F \\\\\nWN J0930+3207 & 218$\\pm$ 9 & 31.1$\\pm$ 1.7 & \\nodata & $-1.33\\pm$0.05 & \\nodata & S & 11.7 & 58 & 09 30 53.32 & +32 07 20.8 & F \\\\\nWN J0939+6323 & 268$\\pm$11 & 39.7$\\pm$ 2.0 & $ 10.86\\pm0.29$ & $-1.31\\pm$0.05 & $-1.04\\pm0.05$ & T & 30.3 & 27 & 09 39 54.89 & +63 23 31.9 & V \\\\\nWN J0940+3838 & 108$\\pm$ 6 & 11.8$\\pm$ 1.6 & \\nodata & $-1.52\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 09 40 26.15 & +38 38 35.0 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0946+6726 & 632$\\pm$25 & 84.7$\\pm$ 3.7 & $ 40.19\\pm0.88$ & $-1.38\\pm$0.04 & $-0.60\\pm0.04$ & T & 44.8 & 114 & 09 46 44.25 & +67 26 41.8 & V \\\\\nWN J0948+6305 & 731$\\pm$29 & 90.5$\\pm$ 1.9 & $ 14.46\\pm0.38$ & $-1.43\\pm$0.03 & $-1.48\\pm0.03$ & D & 3.1 & 134 & 09 48 40.83 & +63 05 42.0 & V \\\\\nWN J0952+5153 & 211$\\pm$10 & 16.1$\\pm$ 1.3 & \\nodata & $-1.76\\pm$0.06 & \\nodata & S & 2.7 & 166 & 09 52 49.14 & +51 53 05.0 & F \\\\\nWN J0955+6023 & 103$\\pm$ 6 & 10.9$\\pm$ 1.6 & $ 4.32\\pm0.15$ & $-1.54\\pm$0.11 & $-0.75\\pm0.12$ & DF & 3.1 & 129 & 09 55 30.01 & +60 23 17.1 & V \\\\\nWN J1002+5512 & 119$\\pm$ 5 & 17.7$\\pm$ 0.5 & \\nodata & $-1.30\\pm$0.05 & \\nodata & S & 10.4 & 58 & 10 02 39.24 & +55 12 55.5 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1003+4448 & 94$\\pm$ 5 & 13.9$\\pm$ 2.0 & \\nodata & $-1.31\\pm$0.11 & \\nodata & DF & 17.2 & 93 & 10 03 30.22 & +44 48 16.2 & F \\\\\nWN J1012+3334$^*$ & 168$\\pm$ 8 & 16.4$\\pm$ 1.6 & \\nodata & $-1.59\\pm$0.07 & \\nodata & D & 22.1 & 6 & 10 12 00.43 & +33 35 00.9 & F \\\\\nWN J1013+3254 & 102$\\pm$ 7 & 14.2$\\pm$ 0.5 & \\nodata & $-1.35\\pm$0.05 & \\nodata & S & $<0.3$ & 89 & 10 13 06.54 & +32 54 33.2 & F \\\\\nWN J1014+7407 & 170$\\pm$ 8 & 21.8$\\pm$ 0.6 & $ 3.76\\pm0.14$ & $-1.41\\pm$0.04 & $-1.41\\pm0.04$ & S & 2.2 & 150 & 10 14 15.75 & +74 07 56.2 & V \\\\\nWN J1015+3038 & 285$\\pm$12 & 38.0$\\pm$ 1.9 & \\nodata & $-1.38\\pm$0.04 & \\nodata & D & 12.8 & 151 & 10 15 08.92 & +30 38 02.0 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1015+7432 & 146$\\pm$ 7 & 21.4$\\pm$ 0.6 & \\nodata & $-1.31\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 10 15 52.49 & +74 32 20.0 & N \\\\\nWN J1018+3634 & 137$\\pm$ 7 & 20.0$\\pm$ 1.4 & \\nodata & $-1.32\\pm$0.06 & \\nodata & S & $<0.3$ & 180 & 10 18 03.13 & +36 34 43.2 & F \\\\\nWN J1019+5244 & 85$\\pm$ 5 & 10.5$\\pm$ 0.4 & \\nodata & $-1.43\\pm$0.06 & \\nodata & D & 16.5 & 145 & 10 19 20.59 & +52 44 33.2 & F \\\\\nWN J1022+3308 & 90$\\pm$ 5 & 10.1$\\pm$ 0.4 & \\nodata & $-1.50\\pm$0.05 & \\nodata & S & 7.8 & 136 & 10 22 37.44 & +33 08 43.6 & F \\\\\nWN J1026+2943 & 81$\\pm$ 6 & 12.0$\\pm$ 1.2 & \\nodata & $-1.31\\pm$0.08 & \\nodata & S & 11.9 & 20 & 10 26 12.04 & +29 43 48.0 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1029+4838 & 118$\\pm$ 8 & 17.2$\\pm$ 1.4 & $ 2.80\\pm0.16$ & $-1.32\\pm$0.07 & $-1.46\\pm0.08$ & S & 2.0 & 131 & 10 29 32.99 & +48 38 09.0 & V \\\\\nWN J1030+5415 & 223$\\pm$10 & 29.2$\\pm$ 1.6 & \\nodata & $-1.39\\pm$0.05 & \\nodata & S & 6.1 & 44 & 10 30 42.94 & +54 15 35.9 & F \\\\\nWN J1036+3936 & 153$\\pm$ 7 & 16.7$\\pm$ 0.5 & \\nodata & $-1.52\\pm$0.04 & \\nodata & T & 17.5 & 107 & 10 36 21.29 & +39 36 59.4 & F \\\\\nWN J1038+4229 & 816$\\pm$33 & 114.0$\\pm$ 5.1 & \\nodata & $-1.35\\pm$0.04 & \\nodata & S & 1.2 & 3 & 10 38 41.04 & +42 29 51.5 & F \\\\\nWN J1041+5859 & 193$\\pm$ 9 & 25.2$\\pm$ 0.6 & $ 6.96\\pm0.22$ & $-1.39\\pm$0.04 & $-1.04\\pm0.03$ & D & 11.2 & 119 & 10 41 29.64 & +58 59 23.5 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1043+3953 & 95$\\pm$ 8 & 13.9$\\pm$ 0.5 & \\nodata & $-1.32\\pm$0.05 & \\nodata & S & $<0.3$ & 79 & 10 43 32.24 & +39 53 46.8 & F \\\\\nWN J1052+4826 & 1039$\\pm$41 & 154.2$\\pm$ 6.8 & \\nodata & $-1.31\\pm$0.04 & \\nodata & D & 10.0 & 108 & 10 52 53.05 & +48 26 33.8 & F \\\\\nWN J1053+5424 & 467$\\pm$20 & 66.4$\\pm$ 1.4 & $ 7.94\\pm0.25$ & $-1.34\\pm$0.03 & $-1.70\\pm0.03$ & D & 1.1 & 34 & 10 53 36.31 & +54 24 42.1 & V \\\\\nWN J1055+3047 & 342$\\pm$14 & 39.0$\\pm$ 2.0 & \\nodata & $-1.49\\pm$0.05 & \\nodata & S & 7.1 & 147 & 10 55 18.52 & +30 47 23.2 & F \\\\\nWN J1057+3156 & 221$\\pm$10 & 22.2$\\pm$ 1.5 & \\nodata & $-1.57\\pm$0.06 & \\nodata & T & 28.7 & 20 & 10 57 56.56 & +31 56 21.0 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1057+3007 & 276$\\pm$12 & 39.5$\\pm$ 2.0 & \\nodata & $-1.33\\pm$0.05 & \\nodata & D & 24.6 & 90 & 10 57 57.45 & +30 07 02.9 & F \\\\\nWN J1058+3506 & 205$\\pm$10 & 24.0$\\pm$ 1.5 & \\nodata & $-1.47\\pm$0.05 & \\nodata & S & 1.3 & 126 & 10 58 14.74 & +35 06 40.9 & F \\\\\nWN J1058+7003 & 82$\\pm$ 4 & 10.5$\\pm$ 0.5 & \\nodata & $-1.41\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 10 58 34.95 & +70 03 17.6 & N \\\\\nWN J1059+4341 & 99$\\pm$ 8 & 12.3$\\pm$ 1.6 & \\nodata & $-1.43\\pm$0.10 & \\nodata & D & 29.1 & 66 & 10 59 43.88 & +43 41 05.2 & F \\\\\nWN J1101+3520$^*$ & 120$\\pm$ 7 & 17.5$\\pm$ 2.1 & \\nodata & $-1.32\\pm$0.09 & \\nodata & S & 8.1 & 1 & 11 01 14.35 & +35 20 12.7 & F \\\\\n&&&&&&&&&&&\\\\\nWN J1111+3311 & 92$\\pm$ 6 & 13.3$\\pm$ 0.5 & \\nodata & $-1.32\\pm$0.05 & \\nodata & S & 6.7 & 16 & 11 11 40.79 & +33 12 00.9 & F \\\\\nWN J1115+5016 & 232$\\pm$10 & 33.9$\\pm$ 0.8 & $ 5.47\\pm0.22$ & $-1.32\\pm$0.03 & $-1.46\\pm0.04$ & D & 0.2 & 117 & 11 15 06.87 & +50 16 23.9 & V \\\\\nWN J1117+5251 & 1439$\\pm$57 & 198.7$\\pm$ 8.7 & \\nodata & $-1.36\\pm$0.04 & \\nodata & D & 9.5 & 6 & 11 17 24.37 & +52 51 54.6 & F \\\\\nWN J1122+3239 & 143$\\pm$ 7 & 19.5$\\pm$ 1.4 & \\nodata & $-1.36\\pm$0.06 & \\nodata & S & 4.2 & 89 & 11 22 33.53 & +32 39 40.9 & F \\\\\nWN J1123+3141 & 623$\\pm$25 & 74.0$\\pm$ 3.3 & \\nodata & $-1.46\\pm$0.04 & \\nodata & T & 25.8 & 83 & 11 23 55.85 & +31 41 26.1 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1124+3228 & 263$\\pm$11 & 38.9$\\pm$ 0.9 & \\nodata & $-1.31\\pm$0.03 & \\nodata & S & 5.7 & 165 & 11 24 34.17 & +32 28 19.6 & F \\\\\nWN J1126+8318 & 175$\\pm$ 8 & 25.8$\\pm$ 1.6 & \\nodata & $-1.31\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 11 26 26.48 & +83 18 23.8 & N \\\\\nWN J1128+4822 & 280$\\pm$12 & 29.9$\\pm$ 0.7 & \\nodata & $-1.53\\pm$0.03 & \\nodata & S & 1.2 & 171 & 11 28 05.19 & +48 22 56.6 & F \\\\\nWN J1128+6416 & 257$\\pm$11 & 31.0$\\pm$ 1.7 & $ 3.20\\pm0.17$ & $-1.45\\pm$0.05 & $-1.82\\pm0.06$ & S & 0.8 & 116 & 11 28 12.10 & +64 16 25.3 & V \\\\\nWN J1130+4911 & 134$\\pm$ 6 & 18.9$\\pm$ 1.5 & \\nodata & $-1.34\\pm$0.07 & \\nodata & T & 37.0 & 145 & 11 30 17.53 & +49 11 17.7 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1139+3048 & 819$\\pm$33 & 119.6$\\pm$ 5.3 & \\nodata & $-1.32\\pm$0.04 & \\nodata & D & 9.0 & 40 & 11 39 14.34 & +30 48 50.7 & F \\\\\nWN J1139+3706 & 139$\\pm$ 8 & 16.7$\\pm$ 1.4 & \\nodata & $-1.45\\pm$0.07 & \\nodata & S & 3.5 & 32 & 11 39 43.04 & +37 06 55.7 & F \\\\\nWN J1141+6924 & 81$\\pm$ 5 & 11.8$\\pm$ 0.5 & \\nodata & $-1.32\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 11 41 09.71 & +69 24 16.3 & N \\\\\nWN J1148+5116 & 148$\\pm$ 7 & 20.5$\\pm$ 1.7 & \\nodata & $-1.35\\pm$0.07 & \\nodata & D & 6.7 & 50 & 11 48 01.92 & +51 16 29.6 & F \\\\\nWN J1148+6233 & 98$\\pm$ 5 & 14.1$\\pm$ 0.5 & $ 1.37\\pm0.09$ & $-1.33\\pm$0.05 & $-1.88\\pm0.06$ & S & 2.4 & 144 & 11 48 44.42 & +62 33 24.6 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1148+3519 & 114$\\pm$ 7 & 13.9$\\pm$ 1.7 & \\nodata & $-1.44\\pm$0.09 & \\nodata & D & 20.0 & 7 & 11 48 54.29 & +35 19 10.1 & F \\\\\nWN J1151+4436 & 78$\\pm$ 5 & 11.1$\\pm$ 0.5 & \\nodata & $-1.34\\pm$0.06 & \\nodata & D & 15.1 & 20 & 11 51 16.80 & +44 36 10.0 & F \\\\\nWN J1152+3732$^*$ & 414$\\pm$17 & 17.1$\\pm$ 1.4 & \\nodata & $-2.18\\pm$0.06 & \\nodata & S & 15.0 & 119 & 11 52 36.34 & +37 32 43.9 & F \\\\\nWN J1154+5415 & 153$\\pm$ 7 & 19.1$\\pm$ 0.5 & $ 1.05\\pm0.10$ & $-1.42\\pm$0.04 & $-2.33\\pm0.08$ & S & $<0.3$ & 0 & 11 54 18.97 & +54 15 11.4 & V \\\\\nWN J1203+8350 & 132$\\pm$ 6 & 18.5$\\pm$ 0.5 & \\nodata & $-1.35\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 12 03 30.63 & +83 50 37.1 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1204+5014 & 94$\\pm$ 5 & 11.3$\\pm$ 1.7 & \\nodata & $-1.45\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 12 04 31.11 & +50 14 49.8 & N \\\\\nWN J1206+3136 & 167$\\pm$ 9 & 22.2$\\pm$ 1.5 & \\nodata & $-1.38\\pm$0.06 & \\nodata & D & 16.6 & 53 & 12 06 48.10 & +31 36 50.9 & F \\\\\nWN J1208+4301 & 162$\\pm$ 8 & 13.9$\\pm$ 1.4 & \\nodata & $-1.68\\pm$0.08 & \\nodata & T & 8.0 & 27 & 12 08 42.77 & +43 01 42.3 & F \\\\\nWN J1216+4446 & 191$\\pm$ 8 & 13.6$\\pm$ 0.5 & \\nodata & $-1.81\\pm$0.04 & \\nodata & S & 6.1 & 98 & 12 16 46.84 & +44 46 51.3 & F \\\\\nWN J1218+3143 & 1906$\\pm$76 & 281.5$\\pm$12.4 & \\nodata & $-1.31\\pm$0.04 & \\nodata & S & 5.6 & 65 & 12 18 31.47 & +31 43 41.7 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1219+4644 & 140$\\pm$ 8 & 20.9$\\pm$ 0.6 & $ 2.84\\pm0.14$ & $-1.30\\pm$0.04 & $-1.59\\pm0.05$ & S & 0.2 & 157 & 12 19 31.79 & +46 44 49.6 & V \\\\\nWN J1223+4256 & 116$\\pm$ 6 & 17.2$\\pm$ 0.5 & \\nodata & $-1.31\\pm$0.04 & \\nodata & S & 4.3 & 179 & 12 23 11.32 & +42 56 57.3 & F \\\\\nWN J1224+4956 & 145$\\pm$ 7 & 21.4$\\pm$ 1.6 & \\nodata & $-1.31\\pm$0.06 & \\nodata & T & 39.6 & 66 & 12 24 21.03 & +49 56 49.2 & F \\\\\nWN J1224+5436 & 790$\\pm$31 & 69.1$\\pm$ 1.5 & $ 6.30\\pm0.20$ & $-1.67\\pm$0.03 & $-1.92\\pm0.03$ & D & 0.9 & 16 & 12 24 52.35 & +54 36 39.9 & V \\\\\nWN J1226+4836 & 155$\\pm$ 8 & 17.0$\\pm$ 0.5 & \\nodata & $-1.51\\pm$0.04 & \\nodata & S & 4.8 & 115 & 12 26 22.45 & +48 36 39.6 & F \\\\\n&&&&&&&&&&&\\\\\nWN J1232+4621$^*$ & 133$\\pm$ 6 & 19.8$\\pm$ 1.8 & \\nodata & $-1.30\\pm$0.07 & \\nodata & DF & 12.5 & 156 & 12 32 39.79 & +46 21 48.1 & F \\\\\nWN J1242+3915 & 549$\\pm$22 & 78.4$\\pm$ 1.7 & \\nodata & $-1.33\\pm$0.03 & \\nodata & D & 11.2 & 51 & 12 42 53.09 & +39 15 48.6 & F \\\\\nWN J1247+6121 & 103$\\pm$ 5 & 15.4$\\pm$ 2.4 & \\nodata & $-1.30\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 12 47 45.31 & +61 21 23.3 & N \\\\\nWN J1249+4043 & 160$\\pm$ 7 & 22.8$\\pm$ 1.4 & \\nodata & $-1.33\\pm$0.05 & \\nodata & D & 37.0 & 80 & 12 49 27.43 & +40 43 49.3 & F \\\\\nWN J1258+3212 & 182$\\pm$12 & 19.9$\\pm$ 1.5 & \\nodata & $-1.52\\pm$0.06 & \\nodata & S & 6.7 & 131 & 12 58 23.62 & +32 12 42.4 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1258+5041 & 230$\\pm$11 & 28.8$\\pm$ 2.0 & \\nodata & $-1.42\\pm$0.06 & \\nodata & T & 44.9 & 58 & 12 58 50.96 & +50 41 42.3 & F \\\\\nWN J1259+3121 & 268$\\pm$11 & 34.0$\\pm$ 1.8 & \\nodata & $-1.41\\pm$0.05 & \\nodata & DF & 20.6 & 1 & 12 59 51.96 & +31 21 05.6 & F \\\\\nWN J1300+5311 & 157$\\pm$ 7 & 19.2$\\pm$ 0.5 & $ 2.70\\pm0.16$ & $-1.44\\pm$0.04 & $-1.58\\pm0.05$ & S & 0.3 & 7 & 13 00 36.25 & +53 11 52.4 & V \\\\\nWN J1302+3206 & 383$\\pm$16 & 54.0$\\pm$ 1.2 & \\nodata & $-1.34\\pm$0.03 & \\nodata & S & 4.7 & 102 & 13 02 03.07 & +32 06 35.6 & F \\\\\nWN J1303+8024 & 165$\\pm$ 7 & 22.2$\\pm$ 0.6 & $ 5.05\\pm0.18$ & $-1.37\\pm$0.03 & $-1.19\\pm0.04$ & D & 4.1 & 145 & 13 03 33.92 & +80 24 42.2 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1303+5437 & 145$\\pm$ 7 & 15.4$\\pm$ 1.4 & \\nodata & $-1.54\\pm$0.07 & \\nodata & D & 16.5 & 88 & 13 03 45.48 & +54 37 28.9 & F \\\\\nWN J1306+4726 & 100$\\pm$ 7 & 13.1$\\pm$ 0.5 & \\nodata & $-1.39\\pm$0.05 & \\nodata & S & 10.2 & 40 & 13 06 35.99 & +47 26 10.1 & F \\\\\nWN J1310+5706 & 112$\\pm$ 6 & 15.9$\\pm$ 0.5 & \\nodata & $-1.34\\pm$0.04 & \\nodata & S & 4.2 & 99 & 13 10 22.96 & +57 06 57.9 & F \\\\\nWN J1310+3820 & 69$\\pm$ 4 & 10.3$\\pm$ 1.5 & \\nodata & $-1.30\\pm$0.12 & \\nodata & S & 4.4 & 18 & 13 10 24.08 & +38 20 44.1 & F \\\\\nWN J1312+6646 & 291$\\pm$12 & 41.6$\\pm$ 0.9 & $ 8.56\\pm0.24$ & $-1.33\\pm$0.03 & $-1.27\\pm0.03$ & D & 6.3 & 118 & 13 12 45.59 & +66 46 36.1 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1314+3649 & 286$\\pm$11 & 36.4$\\pm$ 0.8 & \\nodata & $-1.41\\pm$0.03 & \\nodata & S & 1.3 & 90 & 13 14 17.86 & +36 49 14.6 & F \\\\\nWN J1314+3515$^*$ & 169$\\pm$ 7 & 20.2$\\pm$ 1.7 & \\nodata & $-1.45\\pm$0.07 & \\nodata & DF & 34.2 & 47 & 13 14 25.00 & +35 15 53.9 & F \\\\\nWN J1315+4337 & 149$\\pm$ 8 & 16.3$\\pm$ 0.5 & \\nodata & $-1.52\\pm$0.04 & \\nodata & S & 1.3 & 152 & 13 15 19.05 & +43 37 57.1 & F \\\\\nWN J1321+3311 & 141$\\pm$ 8 & 19.0$\\pm$ 0.6 & \\nodata & $-1.37\\pm$0.04 & \\nodata & D & 14.7 & 63 & 13 21 13.55 & +33 11 31.2 & F \\\\\nWN J1323+4713 & 106$\\pm$ 5 & 14.9$\\pm$ 0.5 & \\nodata & $-1.34\\pm$0.04 & \\nodata & S & 2.5 & 139 & 13 23 08.31 & +47 13 10.7 & F \\\\\n\\end{tabular}\n\\end{table*}\n\n\\begin{table*}\n\\tiny\n\\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{325}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{325}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nWN J1327+5341 & 196$\\pm$ 9 & 27.4$\\pm$ 0.7 & \\nodata & $-1.35\\pm$0.04 & \\nodata & S & 0.6 & 162 & 13 27 12.77 & +53 41 20.6 & F \\\\\nWN J1327+5332 & 163$\\pm$ 7 & 20.5$\\pm$ 0.6 & $ 2.70\\pm0.17$ & $-1.42\\pm$0.04 & $-1.61\\pm0.06$ & D & 0.3 & 89 & 13 27 37.86 & +53 32 10.8 & V \\\\\nWN J1329+3046$^*$ & 86$\\pm$ 5 & 11.7$\\pm$ 1.7 & \\nodata & $-1.37\\pm$0.11 & \\nodata & S & 1.6 & 6 & 13 29 31.75 & +30 46 13.6 & F \\\\\nWN J1329+3046$^*$ & 88$\\pm$ 5 & 12.1$\\pm$ 2.0 & \\nodata & $-1.36\\pm$0.13 & \\nodata & S & 3.6 & 129 & 13 29 55.12 & +30 46 51.2 & F \\\\\nWN J1330+6505 & 74$\\pm$ 6 & 10.5$\\pm$ 0.5 & $ 2.34\\pm0.12$ & $-1.34\\pm$0.06 & $-1.21\\pm0.06$ & S & 1.8 & 5 & 13 30 02.77 & +65 04 59.3 & V \\\\\n&&&&&&&&&&&\\\\\nWN J1330+3037$^*$ & 496$\\pm$20 & 64.5$\\pm$ 2.9 & \\nodata & $-1.40\\pm$0.04 & \\nodata & D & 25.5 & 140 & 13 30 53.67 & +30 37 59.1 & F \\\\\nWN J1330+3604 & 103$\\pm$ 5 & 15.1$\\pm$ 0.5 & \\nodata & $-1.31\\pm$0.05 & \\nodata & D & 9.6 & 0 & 13 30 56.83 & +36 04 01.6 & F \\\\\nWN J1330+5344$^*$ & 525$\\pm$21 & 71.0$\\pm$ 3.2 & $ 8.10\\pm0.29$ & $-1.37\\pm$0.04 & $-1.74\\pm0.05$ & DF & 2.5 & 173 & 13 30 58.90 & +53 44 07.8 & V \\\\\nWN J1331+2937 & 93$\\pm$ 5 & 12.5$\\pm$ 1.3 & $ 3.44\\pm0.13$ & $-1.37\\pm$0.09 & $-1.04\\pm0.09$ & S & 2.7 & 40 & 13 31 21.58 & +29 37 12.6 & V \\\\\nWN J1332+3009$^*$ & 239$\\pm$10 & 35.3$\\pm$ 2.0 & \\nodata & $-1.31\\pm$0.05 & \\nodata & D & 39.2 & 161 & 13 32 45.73 & +30 09 59.9 & F \\\\\n&&&&&&&&&&&\\\\\nWN J1333+3037$^*$ & 423$\\pm$17 & 21.5$\\pm$ 0.6 & \\nodata & $-2.04\\pm$0.03 & \\nodata & S & 0.4 & 179 & 13 33 21.20 & +30 37 35.1 & F \\\\\nWN J1333+4913 & 149$\\pm$ 7 & 22.2$\\pm$ 0.6 & $ 4.78\\pm0.23$ & $-1.30\\pm$0.04 & $-1.22\\pm0.04$ & T & 5.4 & 40 & 13 33 56.42 & +49 13 27.1 & V \\\\\nWN J1335+3222$^*$ & 150$\\pm$ 7 & 18.3$\\pm$ 1.4 & \\nodata & $-1.44\\pm$0.06 & \\nodata & D & 8.8 & 85 & 13 35 35.44 & +32 22 48.7 & F \\\\\nWN J1336+3820 & 116$\\pm$ 6 & 15.6$\\pm$ 0.5 & \\nodata & $-1.37\\pm$0.04 & \\nodata & S & 3.4 & 61 & 13 36 40.88 & +38 20 02.2 & F \\\\\nWN J1337+3149 & 142$\\pm$ 7 & 19.6$\\pm$ 1.9 & \\nodata & $-1.36\\pm$0.08 & \\nodata & D & 35.2 & 21 & 13 37 02.46 & +31 49 49.2 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1337+3401 & 109$\\pm$ 8 & 14.3$\\pm$ 0.5 & \\nodata & $-1.39\\pm$0.04 & \\nodata & S & 3.5 & 56 & 13 37 10.50 & +34 01 26.8 & F \\\\\nWN J1339+5320 & 104$\\pm$ 5 & 13.9$\\pm$ 0.5 & $ 1.80\\pm0.15$ & $-1.38\\pm$0.05 & $-1.63\\pm0.07$ & D & 0.1 & 138 & 13 39 59.25 & +53 20 07.8 & V \\\\\nWN J1341+4953 & 153$\\pm$ 8 & 16.4$\\pm$ 1.4 & \\nodata & $-1.53\\pm$0.07 & \\nodata & D & 18.6 & 160 & 13 41 25.70 & +49 53 41.8 & F \\\\\nWN J1346+6736 & 107$\\pm$ 6 & 14.5$\\pm$ 0.5 & $ 2.82\\pm0.16$ & $-1.37\\pm$0.04 & $-1.32\\pm0.05$ & S & $<0.3$ & 0 & 13 46 37.02 & +67 36 21.7 & V \\\\\nWN J1347+3033 & 341$\\pm$14 & 42.4$\\pm$ 2.2 & \\nodata & $-1.43\\pm$0.05 & \\nodata & D & 37.3 & 151 & 13 47 16.09 & +30 33 07.6 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1352+4259 & 1213$\\pm$48 & 173.9$\\pm$ 7.7 & \\nodata & $-1.33\\pm$0.04 & \\nodata & D & 12.1 & 19 & 13 52 28.39 & +42 59 18.1 & F \\\\\nWN J1353+3336 & 107$\\pm$ 6 & 15.9$\\pm$ 1.9 & \\nodata & $-1.31\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 13 53 07.46 & +33 36 24.6 & N \\\\\nWN J1355+3848 & 204$\\pm$ 8 & 25.6$\\pm$ 0.6 & \\nodata & $-1.42\\pm$0.03 & \\nodata & S & 2.3 & 59 & 13 55 29.50 & +38 48 11.1 & F \\\\\nWN J1359+7446$^*$ & 214$\\pm$ 9 & 12.9$\\pm$ 0.5 & $ 1.26\\pm0.10$ & $-1.92\\pm$0.05 & $-1.87\\pm0.07$ & S & 2.5 & 12 & 13 59 16.90 & +74 46 42.6 & V \\\\\nWN J1400+4348 & 178$\\pm$ 7 & 20.2$\\pm$ 1.5 & \\nodata & $-1.49\\pm$0.06 & \\nodata & S & 6.4 & 93 & 14 00 51.84 & +43 48 07.2 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1403+3109 & 328$\\pm$13 & 45.7$\\pm$ 2.2 & \\nodata & $-1.35\\pm$0.04 & \\nodata & S & 11.0 & 25 & 14 03 39.47 & +31 09 11.4 & F \\\\\nWN J1410+4615 & 103$\\pm$ 5 & 14.2$\\pm$ 1.4 & \\nodata & $-1.36\\pm$0.08 & \\nodata & S & 4.4 & 79 & 14 10 48.17 & +46 15 57.5 & F \\\\\nWN J1416+3821 & 94$\\pm$ 6 & 13.1$\\pm$ 0.5 & \\nodata & $-1.35\\pm$0.05 & \\nodata & D & 7.6 & 14 & 14 16 13.21 & +38 21 56.7 & F \\\\\nWN J1418+4546 & 186$\\pm$ 8 & 17.9$\\pm$ 0.5 & $ 2.70\\pm0.14$ & $-1.60\\pm$0.04 & $-1.52\\pm0.05$ & S & 0.5 & 18 & 14 18 38.40 & +45 46 38.4 & V \\\\\nWN J1420+6735 & 382$\\pm$15 & 33.1$\\pm$ 1.7 & $ 1.22\\pm0.09$ & $-1.67\\pm$0.05 & $-2.65\\pm0.07$ & S & 2.0 & 173 & 14 20 03.34 & +67 35 07.5 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1420+4126 & 128$\\pm$ 6 & 18.7$\\pm$ 0.6 & \\nodata & $-1.32\\pm$0.04 & \\nodata & S & 5.3 & 65 & 14 20 50.23 & +41 26 26.1 & F \\\\\nWN J1421+3103 & 110$\\pm$ 5 & 13.6$\\pm$ 0.5 & \\nodata & $-1.43\\pm$0.05 & \\nodata & S & 0.4 & 127 & 14 21 07.69 & +31 03 03.9 & F \\\\\nWN J1422+3452 & 163$\\pm$ 7 & 10.7$\\pm$ 1.3 & \\nodata & $-1.86\\pm$0.09 & \\nodata & S & 13.3 & 151 & 14 22 05.17 & +34 52 14.4 & F \\\\\nWN J1422+4212 & 258$\\pm$10 & 35.4$\\pm$ 1.8 & \\nodata & $-1.36\\pm$0.05 & \\nodata & S & 5.1 & 164 & 14 22 44.38 & +42 12 00.2 & F \\\\\nWN J1426+3522 & 89$\\pm$ 5 & 11.5$\\pm$ 1.6 & \\nodata & $-1.40\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 14 26 56.32 & +35 22 34.7 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1431+3015 & 101$\\pm$ 5 & 14.3$\\pm$ 1.5 & \\nodata & $-1.34\\pm$0.09 & \\nodata & D & 28.9 & 158 & 14 31 17.77 & +30 15 00.2 & F \\\\\nWN J1431+7317 & 129$\\pm$ 6 & 17.9$\\pm$ 1.3 & $ 4.65\\pm0.19$ & $-1.35\\pm$0.06 & $-1.08\\pm0.07$ & D & 11.2 & 47 & 14 31 28.01 & +73 17 29.7 & V \\\\\nWN J1433+3044 & 144$\\pm$ 6 & 16.7$\\pm$ 1.3 & \\nodata & $-1.48\\pm$0.06 & \\nodata & D & 14.5 & 100 & 14 33 56.51 & +30 44 25.5 & F \\\\\nWN J1435+3523 & 160$\\pm$ 7 & 22.3$\\pm$ 1.6 & \\nodata & $-1.35\\pm$0.06 & \\nodata & S & 8.0 & 64 & 14 35 53.99 & +35 24 06.8 & F \\\\\nWN J1436+6319 & 3507$\\pm$140 & 514.0$\\pm$22.4 & $ 64.84\\pm1.39$ & $-1.31\\pm$0.04 & $-1.67\\pm0.04$ & D & 3.8 & 154 & 14 36 37.28 & +63 19 13.9 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1437+7409 & 111$\\pm$ 5 & 16.4$\\pm$ 0.5 & $ 1.32\\pm0.11$ & $-1.31\\pm$0.05 & $-2.02\\pm0.07$ & S & $<0.3$ & 0 & 14 37 35.89 & +74 09 22.2 & V \\\\\nWN J1439+3729 & 142$\\pm$ 7 & 17.1$\\pm$ 0.5 & \\nodata & $-1.45\\pm$0.04 & \\nodata & D & 7.2 & 157 & 14 39 49.99 & +37 29 03.4 & F \\\\\nWN J1440+3707$^*$ & 219$\\pm$ 9 & 16.7$\\pm$ 1.3 & \\nodata & $-1.76\\pm$0.06 & \\nodata & S & 7.4 & 61 & 14 40 03.63 & +37 07 27.4 & F \\\\\nWN J1444+4114 & 97$\\pm$ 5 & 13.2$\\pm$ 1.4 & \\nodata & $-1.37\\pm$0.09 & \\nodata & D & 30.1 & 151 & 14 44 27.65 & +41 14 38.3 & F \\\\\nWN J1444+4112 & 109$\\pm$ 6 & 13.1$\\pm$ 0.5 & \\nodata & $-1.45\\pm$0.05 & \\nodata & D & 12.6 & 96 & 14 44 48.82 & +41 12 25.5 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1447+5423 & 97$\\pm$ 6 & 13.3$\\pm$ 0.5 & \\nodata & $-1.36\\pm$0.05 & \\nodata & S & 11.0 & 174 & 14 47 54.36 & +54 23 25.2 & F \\\\\nWN J1450+3534 & 95$\\pm$ 5 & 10.2$\\pm$ 0.4 & \\nodata & $-1.53\\pm$0.05 & \\nodata & S & 3.3 & 62 & 14 50 20.69 & +35 34 46.5 & F \\\\\nWN J1451+3649 & 254$\\pm$10 & 29.8$\\pm$ 2.3 & \\nodata & $-1.47\\pm$0.06 & \\nodata & T & 50.7 & 101 & 14 51 11.62 & +36 49 34.4 & F \\\\\nWN J1454+3210 & 264$\\pm$11 & 37.6$\\pm$ 0.9 & \\nodata & $-1.33\\pm$0.03 & \\nodata & S & 3.0 & 22 & 14 54 11.64 & +32 10 16.8 & F \\\\\nWN J1459+6405 & 339$\\pm$14 & 40.0$\\pm$ 3.6 & \\nodata & $-1.46\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 14 59 33.34 & +64 05 58.0 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1459+4947 & 175$\\pm$ 8 & 18.7$\\pm$ 0.5 & \\nodata & $-1.53\\pm$0.04 & \\nodata & S & 3.0 & 109 & 14 59 43.19 & +49 47 15.9 & F \\\\\nWN J1500+3613 & 390$\\pm$16 & 52.9$\\pm$ 2.5 & \\nodata & $-1.37\\pm$0.04 & \\nodata & S & 2.2 & 76 & 15 00 09.01 & +36 13 25.8 & F \\\\\nWN J1502+4756 & 221$\\pm$ 9 & 19.1$\\pm$ 1.5 & \\nodata & $-1.68\\pm$0.06 & \\nodata & D & 12.3 & 37 & 15 02 03.58 & +47 56 34.7 & F \\\\\nWN J1508+5839 & 122$\\pm$ 6 & 12.5$\\pm$ 0.5 & $ 1.37\\pm0.09$ & $-1.56\\pm$0.05 & $-1.78\\pm0.06$ & D & 35.2 & 128 & 15 08 08.17 & +58 39 13.3 & V \\\\\nWN J1509+5905$^*$ & 752$\\pm$30 & 107.3$\\pm$ 4.6 & $ 8.60\\pm0.26$ & $-1.33\\pm$0.04 & $-2.03\\pm0.04$ & DF & 1.8 & 74 & 15 09 32.34 & +59 05 24.5 & V \\\\\n&&&&&&&&&&&\\\\\nWN J1525+3010 & 145$\\pm$ 7 & 17.2$\\pm$ 0.5 & \\nodata & $-1.46\\pm$0.04 & \\nodata & S & 1.2 & 123 & 15 25 01.21 & +30 10 30.2 & F \\\\\nWN J1525+5130 & 94$\\pm$ 5 & 10.7$\\pm$ 0.5 & $ 2.02\\pm0.13$ & $-1.49\\pm$0.06 & $-1.34\\pm0.06$ & S & 0.8 & 7 & 15 25 12.93 & +51 30 06.1 & V \\\\\nWN J1528+6317 & 332$\\pm$14 & 40.0$\\pm$ 2.0 & $ 20.80\\pm0.52$ & $-1.45\\pm$0.04 & $-0.53\\pm0.05$ & DF & 6.0 & 121 & 15 28 06.47 & +63 17 40.2 & V \\\\\nWN J1529+3454 & 124$\\pm$ 6 & 13.0$\\pm$ 0.5 & \\nodata & $-1.54\\pm$0.05 & \\nodata & S & 2.3 & 35 & 15 29 41.52 & +34 54 31.3 & F \\\\\nWN J1537+3402 & 83$\\pm$ 5 & 11.6$\\pm$ 0.5 & \\nodata & $-1.35\\pm$0.05 & \\nodata & S & 1.7 & 31 & 15 37 50.57 & +34 02 33.3 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1543+3512 & 231$\\pm$10 & 23.6$\\pm$ 1.5 & \\nodata & $-1.56\\pm$0.05 & \\nodata & D & 9.2 & 0 & 15 43 29.49 & +35 12 29.7 & F \\\\\nWN J1546+3935 & 155$\\pm$ 7 & 13.7$\\pm$ 0.5 & \\nodata & $-1.66\\pm$0.04 & \\nodata & D & 8.5 & 102 & 15 46 41.95 & +39 35 52.7 & F \\\\\nWN J1546+3005 & 92$\\pm$ 6 & 13.0$\\pm$ 0.5 & \\nodata & $-1.34\\pm$0.05 & \\nodata & S & 2.3 & 144 & 15 46 57.65 & +30 05 38.1 & F \\\\\nWN J1550+3830 & 229$\\pm$10 & 32.9$\\pm$ 1.7 & \\nodata & $-1.33\\pm$0.05 & \\nodata & S & 4.2 & 178 & 15 50 19.42 & +38 30 14.8 & F \\\\\nWN J1552+3715 & 546$\\pm$22 & 27.3$\\pm$ 1.6 & \\nodata & $-2.05\\pm$0.05 & \\nodata & D & 18.6 & 120 & 15 52 07.07 & +37 15 07.1 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1555+4011 & 359$\\pm$14 & 50.9$\\pm$ 2.4 & \\nodata & $-1.34\\pm$0.04 & \\nodata & S & 1.1 & 90 & 15 55 02.50 & +40 11 58.2 & F \\\\\nWN J1558+7028 & 114$\\pm$ 6 & 15.7$\\pm$ 2.1 & $ 1.68\\pm0.11$ & $-1.36\\pm$0.11 & $-1.80\\pm0.12$ & S & 2.1 & 38 & 15 58 37.92 & +70 28 11.2 & V \\\\\nWN J1559+6110 & 130$\\pm$ 6 & 18.3$\\pm$ 1.3 & $ 3.47\\pm0.14$ & $-1.34\\pm$0.06 & $-1.34\\pm0.07$ & S & 0.3 & 20 & 15 59 50.65 & +61 10 57.8 & V \\\\\nWN J1559+5926 & 116$\\pm$ 6 & 15.3$\\pm$ 1.3 & $ 41.70\\pm0.92$ & $-1.39\\pm$0.07 & \\nodata & D & 31.0 & 60 & 15 59 54.42 & +59 26 35.3 & V \\\\\nWN J1604+5505 & 142$\\pm$ 7 & 20.7$\\pm$ 0.6 & \\nodata & $-1.32\\pm$0.04 & \\nodata & S & 1.1 & 15 & 16 04 21.91 & +55 05 45.4 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1606+6346 & 130$\\pm$ 6 & 19.0$\\pm$ 0.6 & $ 5.60\\pm0.19$ & $-1.32\\pm$0.04 & $-0.98\\pm0.04$ & D & 5.6 & 14 & 16 06 12.44 & +63 47 06.1 & V \\\\\nWN J1606+4142 & 83$\\pm$ 5 & 12.3$\\pm$ 0.5 & \\nodata & $-1.31\\pm$0.05 & \\nodata & S & 3.2 & 145 & 16 06 30.58 & +41 42 10.8 & F \\\\\nWN J1609+5725 & 70$\\pm$ 5 & 10.2$\\pm$ 0.5 & $ 2.13\\pm0.11$ & $-1.32\\pm$0.07 & $-1.26\\pm0.06$ & S & 1.7 & 60 & 16 09 28.14 & +57 25 02.8 & V \\\\\nWN J1618+5736 & 233$\\pm$10 & 33.5$\\pm$ 1.8 & $ 6.38\\pm0.20$ & $-1.33\\pm$0.05 & $-1.34\\pm0.05$ & S & 2.1 & 102 & 16 18 07.35 & +57 36 11.7 & V \\\\\nWN J1622+3447 & 156$\\pm$ 7 & 21.1$\\pm$ 0.6 & \\nodata & $-1.37\\pm$0.04 & \\nodata & S & 1.6 & 0 & 16 22 10.93 & +34 47 44.6 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1623+8213 & 166$\\pm$ 7 & 19.8$\\pm$ 0.6 & \\nodata & $-1.46\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 16 23 01.71 & +82 13 17.4 & N \\\\\nWN J1624+4202 & 75$\\pm$ 5 & 11.0$\\pm$ 1.7 & \\nodata & $-1.31\\pm$0.12 & \\nodata & D & 24.4 & 19 & 16 24 37.86 & +42 02 10.5 & F \\\\\nWN J1627+5430 & 146$\\pm$ 7 & 20.9$\\pm$ 0.6 & \\nodata & $-1.33\\pm$0.04 & \\nodata & S & 1.6 & 176 & 16 27 24.09 & +54 30 55.2 & F \\\\\nWN J1628+3932 & 26737$\\pm$1069 & 3680.7$\\pm$35.1 & \\nodata & $-1.36\\pm$0.03 & \\nodata & M & 48.8 & 77 & 16 28 38.56 & +39 33 00.1 & F \\\\\nWN J1633+7351 & 75$\\pm$ 5 & 10.1$\\pm$ 1.3 & $ 23.88\\pm0.55$ & $-1.37\\pm$0.11 & $ 0.69\\pm0.11$ & DF & 21.8 & 90 & 16 33 07.45 & +73 51 38.1 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1645+4413 & 135$\\pm$ 6 & 18.9$\\pm$ 0.6 & \\nodata & $-1.35\\pm$0.04 & \\nodata & S & 1.1 & 56 & 16 45 35.69 & +44 13 42.1 & F \\\\\nWN J1704+3839 & 335$\\pm$14 & 34.5$\\pm$ 1.8 & \\nodata & $-1.56\\pm$0.05 & \\nodata & D & 23.8 & 145 & 17 04 00.50 & +38 39 56.7 & F \\\\\nWN J1713+3656 & 116$\\pm$ 6 & 14.8$\\pm$ 0.5 & \\nodata & $-1.41\\pm$0.04 & \\nodata & S & 1.1 & 169 & 17 13 55.63 & +36 56 34.5 & F \\\\\nWN J1714+7031 & 132$\\pm$ 6 & 14.2$\\pm$ 1.4 & $ 0.95\\pm0.09$ & $-1.53\\pm$0.08 & $-2.18\\pm0.11$ & S & 2.4 & 46 & 17 14 35.18 & +70 31 30.7 & V \\\\\nWN J1714+5251 & 262$\\pm$11 & 37.9$\\pm$ 2.0 & \\nodata & $-1.32\\pm$0.05 & \\nodata & D & 26.6 & 80 & 17 14 37.93 & +52 51 30.1 & F \\\\\n\\end{tabular}\n\\end{table*}\n\n\\begin{table*}\n\\tiny\n\\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{325}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{325}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nWN J1717+3828 & 368$\\pm$15 & 35.8$\\pm$ 2.0 & \\nodata & $-1.60\\pm$0.05 & \\nodata & M & 33.6 & 156 & 17 17 16.22 & +38 28 16.5 & F \\\\\nWN J1718+5823 & 1098$\\pm$44 & 133.2$\\pm$ 2.7 & $ 11.26\\pm0.32$ & $-1.44\\pm$0.03 & $-1.98\\pm0.03$ & S & 0.3 & 107 & 17 18 18.51 & +58 23 21.8 & V \\\\\nWN J1723+5822 & 88$\\pm$ 6 & 10.4$\\pm$ 0.5 & $ 2.27\\pm0.11$ & $-1.46\\pm$0.06 & $-1.23\\pm0.06$ & S & 4.7 & 103 & 17 23 01.98 & +58 22 44.0 & V \\\\\nWN J1723+6844 & 105$\\pm$ 6 & 15.7$\\pm$ 1.3 & \\nodata & $-1.30\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 17 23 05.64 & +68 44 17.7 & N \\\\\nWN J1731+4640 & 200$\\pm$ 9 & 15.7$\\pm$ 0.5 & \\nodata & $-1.74\\pm$0.04 & \\nodata & D & 11.6 & 106 & 17 31 46.10 & +46 40 03.1 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1731+4654 & 323$\\pm$13 & 42.0$\\pm$ 2.1 & \\nodata & $-1.40\\pm$0.05 & \\nodata & S & 1.9 & 176 & 17 31 59.63 & +46 54 00.2 & F \\\\\nWN J1732+6757 & 85$\\pm$ 5 & 11.9$\\pm$ 0.5 & $ 2.31\\pm0.11$ & $-1.35\\pm$0.05 & $-1.32\\pm0.05$ & D & 1.5 & 178 & 17 32 30.61 & +67 57 02.5 & V \\\\\nWN J1733+4037 & 80$\\pm$ 5 & 11.2$\\pm$ 2.0 & \\nodata & $-1.35\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 17 33 31.13 & +40 37 00.6 & N \\\\\nWN J1734+4527 & 87$\\pm$ 5 & 11.0$\\pm$ 0.5 & \\nodata & $-1.42\\pm$0.06 & \\nodata & D & 10.4 & 174 & 17 34 07.58 & +45 27 25.6 & F \\\\\nWN J1734+3606 & 69$\\pm$ 3 & 10.2$\\pm$ 3.2 & $ 3.12\\pm0.13$ & $-1.31\\pm$0.22 & $-0.95\\pm0.25$ & S & 2.1 & 137 & 17 34 24.13 & +36 06 38.8 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1736+6502 & 193$\\pm$ 8 & 27.4$\\pm$ 1.6 & $ 4.40\\pm0.16$ & $-1.34\\pm$0.05 & $-1.47\\pm0.06$ & D & 16.0 & 159 & 17 36 37.50 & +65 02 28.7 & V \\\\\nWN J1739+5309 & 78$\\pm$ 5 & 11.3$\\pm$ 0.5 & \\nodata & $-1.32\\pm$0.06 & \\nodata & S & 7.3 & 114 & 17 39 28.39 & +53 09 41.8 & F \\\\\nWN J1749+5659 & 124$\\pm$ 7 & 15.9$\\pm$ 1.6 & \\nodata & $-1.41\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 17 49 21.19 & +56 59 59.6 & N \\\\\nWN J1749+6248 & 104$\\pm$ 6 & 13.3$\\pm$ 0.5 & $ 2.93\\pm0.12$ & $-1.41\\pm$0.05 & $-1.22\\pm0.05$ & S & 1.7 & 48 & 17 49 27.04 & +62 48 54.0 & V \\\\\nWN J1752+2949 & 135$\\pm$ 6 & 16.9$\\pm$ 0.5 & $ 2.29\\pm0.14$ & $-1.42\\pm$0.04 & $-1.61\\pm0.05$ & S & 3.2 & 102 & 17 52 56.67 & +29 49 28.3 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1801+3336 & 136$\\pm$ 6 & 11.6$\\pm$ 0.5 & $ 1.26\\pm0.12$ & $-1.69\\pm$0.05 & $-1.78\\pm0.08$ & S & 2.5 & 34 & 18 01 07.26 & +33 36 40.4 & V \\\\\nWN J1802+3948 & 1102$\\pm$44 & 157.3$\\pm$ 6.8 & $ 27.67\\pm0.62$ & $-1.33\\pm$0.04 & $-1.40\\pm0.04$ & T & 19.2 & 13 & 18 02 31.65 & +39 48 59.6 & V \\\\\nWN J1804+5547 & 173$\\pm$ 8 & 22.9$\\pm$ 1.7 & \\nodata & $-1.38\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 18 04 15.35 & +55 47 16.3 & N \\\\\nWN J1804+3048 & 192$\\pm$ 8 & 27.7$\\pm$ 0.7 & $ 5.88\\pm0.18$ & $-1.33\\pm$0.04 & $-1.25\\pm0.03$ & S & 2.0 & 84 & 18 04 42.01 & +30 48 45.0 & V \\\\\nWN J1806+6332 & 138$\\pm$ 7 & 17.7$\\pm$ 0.5 & \\nodata & $-1.41\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 18 06 23.66 & +63 32 07.9 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1807+5027 & 483$\\pm$19 & 71.4$\\pm$ 3.3 & $ 11.67\\pm0.31$ & $-1.31\\pm$0.04 & $-1.46\\pm0.04$ & D & 3.7 & 173 & 18 07 07.39 & +50 27 25.8 & V \\\\\nWN J1807+6628 & 76$\\pm$ 5 & 10.9$\\pm$ 1.4 & $ 1.20\\pm0.11$ & $-1.33\\pm$0.10 & $-1.78\\pm0.13$ & S & 0.3 & 103 & 18 07 29.75 & +66 28 33.4 & V \\\\\nWN J1810+6635 & 115$\\pm$ 8 & 14.1$\\pm$ 0.5 & $ 2.62\\pm0.12$ & $-1.44\\pm$0.04 & $-1.36\\pm0.05$ & S & 1.6 & 15 & 18 10 28.41 & +66 35 15.1 & V \\\\\nWN J1811+6008 & 160$\\pm$ 7 & 17.8$\\pm$ 0.5 & $ 7.87\\pm0.24$ & $-1.50\\pm$0.04 & $-0.66\\pm0.03$ & DF & 3.5 & 31 & 18 11 18.38 & +60 08 42.9 & V \\\\\nWN J1813+4847 & 92$\\pm$ 5 & 12.1$\\pm$ 0.5 & \\nodata & $-1.39\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 18 13 16.68 & +48 47 50.1 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1814+5009 & 120$\\pm$ 7 & 16.7$\\pm$ 0.5 & \\nodata & $-1.35\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 18 14 01.40 & +50 09 58.0 & N \\\\\nWN J1815+3656 & 124$\\pm$ 6 & 17.6$\\pm$ 0.6 & $ 2.96\\pm0.14$ & $-1.34\\pm$0.04 & $-1.43\\pm0.05$ & S & 1.6 & 48 & 18 15 23.11 & +36 56 00.9 & V \\\\\nWN J1816+3840 & 186$\\pm$ 8 & 27.3$\\pm$ 1.6 & \\nodata & $-1.31\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 18 16 26.11 & +38 40 53.0 & N \\\\\nWN J1818+7042 & 1624$\\pm$65 & 199.6$\\pm$ 8.8 & $ 30.50\\pm0.74$ & $-1.44\\pm$0.04 & $-1.51\\pm0.04$ & D & 1.4 & 10 & 18 18 04.24 & +70 42 59.5 & V \\\\\nWN J1818+3852 & 105$\\pm$ 6 & 12.6$\\pm$ 0.5 & $ 1.29\\pm0.09$ & $-1.45\\pm$0.05 & $-1.84\\pm0.07$ & S & 2.6 & 64 & 18 18 42.17 & +38 52 20.4 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1818+3428 & 167$\\pm$ 7 & 23.7$\\pm$ 0.6 & $ 5.68\\pm0.19$ & $-1.34\\pm$0.04 & $-1.15\\pm0.03$ & T & 7.5 & 103 & 18 18 47.90 & +34 28 24.0 & V \\\\\nWN J1818+6144 & 149$\\pm$ 6 & 21.9$\\pm$ 1.5 & $ 1.11\\pm0.10$ & $-1.31\\pm$0.06 & $-2.40\\pm0.09$ & S & 1.6 & 11 & 18 18 50.55 & +61 44 18.4 & V \\\\\nWN J1819+3122 & 77$\\pm$ 5 & 10.5$\\pm$ 0.5 & \\nodata & $-1.36\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 18 19 28.60 & +31 22 19.3 & N \\\\\nWN J1819+6213 & 106$\\pm$ 6 & 12.7$\\pm$ 0.5 & $ 0.47\\pm0.08$ & $-1.45\\pm$0.05 & $-2.66\\pm0.14$ & S & 1.6 & 41 & 18 19 52.26 & +62 13 58.0 & V \\\\\nWN J1820+5711 & 136$\\pm$ 7 & 20.3$\\pm$ 1.5 & \\nodata & $-1.30\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 18 20 51.14 & +57 11 06.5 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1821+3602 & 3398$\\pm$136 & 99.0$\\pm$ 4.2 & $233.33\\pm4.90$ & $-2.42\\pm$0.04 & $ 0.69\\pm0.04$ & T & 35.0 & 55 & 18 21 02.20 & +36 02 15.7 & V \\\\\nWN J1821+3601$^{\\dag}$ & 151$\\pm$ 6 & 10.2$\\pm$ 1.5 & $105.26\\pm2.53$ & $-1.85\\pm$0.11 & $ 1.88\\pm0.12$ & D & 34.9 & 55 & 18 21 22.59 & +36 01 03.3 & V \\\\\nWN J1829+6914 & 207$\\pm$ 9 & 13.0$\\pm$ 1.3 & $ 2.25\\pm0.12$ & $-1.90\\pm$0.08 & $-1.41\\pm0.09$ & S & 1.8 & 22 & 18 29 05.68 & +69 14 06.1 & V \\\\\nWN J1829+4919 & 98$\\pm$ 6 & 14.2$\\pm$ 0.5 & $ 7.95\\pm0.24$ & $-1.32\\pm$0.06 & $-0.47\\pm0.04$ & D & 12.5 & 173 & 18 29 33.74 & +49 19 55.6 & V \\\\\nWN J1829+5945 & 346$\\pm$14 & 50.4$\\pm$ 2.4 & $ 8.82\\pm0.25$ & $-1.32\\pm$0.04 & $-1.40\\pm0.04$ & S & 1.7 & 26 & 18 29 57.26 & +59 45 03.2 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1830+6422 & 70$\\pm$ 3 & 10.3$\\pm$ 0.5 & \\nodata & $-1.31\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 18 30 45.82 & +64 22 26.3 & N \\\\\nWN J1832+5354$^{\\dag}$ & 226$\\pm$10 & 28.7$\\pm$ 1.6 & $ 23.82\\pm0.59$ & $-1.41\\pm$0.05 & $-0.15\\pm0.05$ & D & 19.4 & 56 & 18 32 41.16 & +53 54 34.0 & V \\\\\nWN J1836+5210 & 191$\\pm$ 9 & 24.2$\\pm$ 1.5 & $ 3.54\\pm0.15$ & $-1.41\\pm$0.05 & $-1.55\\pm0.06$ & S & 1.4 & 10 & 18 36 23.22 & +52 10 28.4 & V \\\\\nWN J1839+4710 & 176$\\pm$ 8 & 22.8$\\pm$ 1.6 & \\nodata & $-1.40\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 18 39 14.54 & +47 10 59.4 & N \\\\\nWN J1843+5932 & 998$\\pm$40 & 148.2$\\pm$ 6.6 & $ 30.87\\pm0.70$ & $-1.31\\pm$0.04 & $-1.26\\pm0.04$ & T & 7.7 & 64 & 18 43 31.70 & +59 32 59.3 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1847+5423 & 108$\\pm$ 6 & 15.8$\\pm$ 1.3 & $ 6.67\\pm0.23$ & $-1.32\\pm$0.07 & $-0.69\\pm0.07$ & DF & 2.9 & 67 & 18 47 04.03 & +54 23 06.6 & V \\\\\nWN J1852+5711$^*$ & 387$\\pm$16 & 53.4$\\pm$ 2.5 & \\nodata & $-1.36\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 18 52 08.35 & +57 11 42.7 & N \\\\\nWN J1857+7411 & 160$\\pm$ 7 & 19.9$\\pm$ 0.6 & \\nodata & $-1.43\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 18 57 03.60 & +74 11 31.2 & N \\\\\nWN J1859+5900 & 98$\\pm$ 6 & 11.7$\\pm$ 0.5 & $ 1.64\\pm0.12$ & $-1.46\\pm$0.06 & $-1.56\\pm0.07$ & S & 0.5 & 171 & 18 59 40.34 & +59 00 36.8 & V \\\\\nWN J1859+5416 & 81$\\pm$ 4 & 10.1$\\pm$ 1.6 & $ 2.70\\pm0.14$ & $-1.43\\pm$0.12 & $-1.06\\pm0.13$ & S & 1.7 & 17 & 18 59 57.65 & +54 16 21.8 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1907+8532 & 69$\\pm$ 4 & 10.2$\\pm$ 0.4 & \\nodata & $-1.31\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 19 07 26.54 & +85 32 35.2 & N \\\\\nWN J1911+6342 & 185$\\pm$10 & 23.3$\\pm$ 1.5 & $ 3.37\\pm0.14$ & $-1.42\\pm$0.05 & $-1.56\\pm0.06$ & S & 1.8 & 7 & 19 11 49.54 & +63 42 09.6 & V \\\\\nWN J1912+8627 & 126$\\pm$ 7 & 18.8$\\pm$ 1.2 & $ 2.55\\pm0.13$ & $-1.30\\pm$0.05 & $-1.61\\pm0.07$ & S & 2.4 & 178 & 19 12 06.26 & +86 27 10.1 & V \\\\\nWN J1917+6635 & 75$\\pm$ 5 & 11.2$\\pm$ 0.5 & $ 2.37\\pm0.12$ & $-1.30\\pm$0.06 & $-1.25\\pm0.06$ & S & 1.9 & 152 & 19 17 35.50 & +66 35 38.5 & V \\\\\nWN J1917+7149 & 280$\\pm$12 & 40.4$\\pm$ 2.1 & \\nodata & $-1.33\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 19 17 56.11 & +71 49 19.7 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1923+6047 & 83$\\pm$ 5 & 12.4$\\pm$ 0.5 & $ 2.56\\pm0.13$ & $-1.30\\pm$0.06 & $-1.27\\pm0.05$ & S & 2.4 & 91 & 19 23 33.18 & +60 47 56.8 & V \\\\\nWN J1925+5203 & 199$\\pm$ 9 & 27.5$\\pm$ 1.7 & $ 4.30\\pm0.16$ & $-1.36\\pm$0.05 & $-1.49\\pm0.06$ & D & 8.6 & 52 & 19 25 16.97 & +52 03 34.4 & V \\\\\nWN J1925+5742 & 100$\\pm$ 6 & 14.5$\\pm$ 0.5 & $ 1.58\\pm0.11$ & $-1.32\\pm$0.06 & $-1.78\\pm0.06$ & S & 2.0 & 9 & 19 25 22.22 & +57 42 27.3 & V \\\\\nWN J1926+5710 & 136$\\pm$ 7 & 20.2$\\pm$ 0.6 & $ 4.55\\pm0.18$ & $-1.31\\pm$0.04 & $-1.20\\pm0.04$ & S & 1.8 & 161 & 19 26 43.85 & +57 10 00.5 & V \\\\\nWN J1927+6436 & 661$\\pm$26 & 80.3$\\pm$ 3.5 & $ 6.62\\pm0.21$ & $-1.44\\pm$0.04 & $-2.01\\pm0.04$ & D & 20.1 & 120 & 19 27 22.83 & +64 36 02.6 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1944+6552 & 1367$\\pm$55 & 147.2$\\pm$ 6.5 & $ 19.45\\pm0.47$ & $-1.53\\pm$0.04 & $-1.63\\pm0.04$ & S & 1.8 & 165 & 19 44 23.99 & +65 52 23.8 & V \\\\\nWN J1953+7052 & 75$\\pm$ 7 & 10.3$\\pm$ 0.5 & $ 3.22\\pm0.15$ & $-1.36\\pm$0.07 & $-0.94\\pm0.05$ & D & 14.4 & 150 & 19 53 21.10 & +70 52 19.8 & V \\\\\nWN J1954+7011 & 460$\\pm$19 & 63.4$\\pm$ 2.9 & \\nodata & $-1.36\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 19 54 30.53 & +70 11 33.5 & N \\\\\nWN J2044+7044 & 311$\\pm$13 & 41.7$\\pm$ 0.9 & $ 7.18\\pm0.22$ & $-1.38\\pm$0.03 & $-1.42\\pm0.03$ & D & 1.3 & 83 & 20 44 57.80 & +70 44 03.8 & V \\\\\nWN J2052+6925 & 113$\\pm$ 6 & 16.1$\\pm$ 1.3 & \\nodata & $-1.33\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 20 52 33.78 & +69 25 09.3 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J2053+6849 & 109$\\pm$ 5 & 15.8$\\pm$ 0.5 & $ 2.59\\pm0.13$ & $-1.32\\pm$0.05 & $-1.45\\pm0.05$ & S & 2.8 & 13 & 20 53 38.68 & +68 48 54.7 & V \\\\\nWN J2139+3125 & 249$\\pm$10 & 28.0$\\pm$ 0.7 & \\nodata & $-1.50\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 21 39 32.31 & +31 25 18.7 & N \\\\\nWN J2146+3330 & 105$\\pm$ 6 & 10.8$\\pm$ 0.5 & \\nodata & $-1.56\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 21 46 55.47 & +33 30 01.7 & N \\\\\nWN J2147+3137 & 215$\\pm$ 9 & 25.4$\\pm$ 1.6 & \\nodata & $-1.46\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 21 47 35.21 & +31 37 58.9 & N \\\\\nWN J2158+3424 & 182$\\pm$ 8 & 25.3$\\pm$ 0.7 & $ 4.48\\pm0.17$ & $-1.35\\pm$0.04 & $-1.39\\pm0.04$ & T & 7.9 & 163 & 21 58 54.14 & +34 24 47.8 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J2213+3411 & 320$\\pm$13 & 29.8$\\pm$ 2.2 & \\nodata & $-1.63\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 22 13 12.48 & +34 11 42.8 & N \\\\\nWN J2219+2951 & 151$\\pm$10 & 13.2$\\pm$ 0.5 & \\nodata & $-1.67\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 22 19 28.65 & +29 51 57.4 & N \\\\\nWN J2221+3800 & 99$\\pm$ 6 & 14.4$\\pm$ 0.5 & $ 2.18\\pm0.11$ & $-1.32\\pm$0.05 & $-1.52\\pm0.05$ & S & 1.4 & 5 & 22 21 49.53 & +38 00 38.4 & V \\\\\nWN J2222+3305 & 232$\\pm$10 & 30.4$\\pm$ 1.7 & $ 3.53\\pm0.14$ & $-1.39\\pm$0.05 & $-1.73\\pm0.05$ & S & 1.4 & 13 & 22 22 15.19 & +33 05 44.1 & V \\\\\nWN J2245+3937 & 204$\\pm$ 8 & 15.5$\\pm$ 1.3 & $ 5.65\\pm0.21$ & $-1.76\\pm$0.07 & $-0.81\\pm0.07$ & DF & 4.0 & 168 & 22 45 02.74 & +39 37 27.9 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J2250+4131 & 128$\\pm$ 7 & 15.2$\\pm$ 1.4 & $ 2.03\\pm0.11$ & $-1.46\\pm$0.07 & $-1.62\\pm0.09$ & S & 1.5 & 25 & 22 50 51.16 & +41 31 16.4 & V \\\\\nWN J2313+4053 & 101$\\pm$ 6 & 11.3$\\pm$ 1.4 & \\nodata & $-1.50\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 23 13 06.34 & +40 53 40.6 & N \\\\\nWN J2313+4253 & 94$\\pm$ 7 & 13.4$\\pm$ 1.5 & $ 3.41\\pm0.14$ & $-1.33\\pm$0.09 & $-1.10\\pm0.10$ & S & 1.4 & 13 & 23 13 08.62 & +42 53 13.0 & V \\\\\nWN J2313+3842$^*$ & 304$\\pm$13 & 13.2$\\pm$ 2.6 & \\nodata & $-2.15\\pm$0.14 & \\nodata & \\nodata & \\nodata & \\nodata & 23 13 47.75 & +38 42 26.2 & N \\\\\nWN J2319+4251 & 321$\\pm$14 & 40.2$\\pm$ 2.9 & $ 3.88\\pm0.14$ & $-1.42\\pm$0.06 & $-1.88\\pm0.07$ & S & 1.5 & 20 & 23 19 47.25 & +42 51 09.2 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J2337+3421 & 84$\\pm$ 4 & 12.4$\\pm$ 1.3 & \\nodata & $-1.31\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 23 37 23.43 & +34 21 51.5 & N \\\\\nWN J2338+4047 & 115$\\pm$ 6 & 16.9$\\pm$ 0.5 & $ 5.06\\pm0.18$ & $-1.31\\pm$0.04 & $-0.97\\pm0.04$ & D & 15.7 & 8 & 23 38 11.10 & +40 47 19.6 & V \\\\\nWN J2350+3631 & 196$\\pm$ 8 & 22.8$\\pm$ 0.6 & $ 2.20\\pm0.11$ & $-1.47\\pm$0.04 & $-1.88\\pm0.04$ & DF & 2.7 & 165 & 23 50 25.69 & +36 31 27.6 & V \\\\\n\\hline\n\\end{tabular}\n\n$^{\\dag}$ Not a real USS source; see notes\n\n$^*$ See notes\n\n\\end{table*}\n"}],"string":"[\n {\n \"name\": \"ds1811.tex\",\n \"string\": \"%\\\\documentclass[referee]{aa} % for a referee version\\n%\\n\\\\documentclass{aa}\\n\\\\usepackage{psfig}\\n%\\n \\n\\\\newcommand\\\\eg{{\\\\it e.g.} }\\n\\\\newcommand\\\\etal{et~al.}\\n\\\\newcommand\\\\ie{{\\\\it i.e.~}\\\\ }\\n\\\\newcommand\\\\lya{Ly$\\\\alpha$}\\n\\\\newcommand\\\\Lya{Ly$\\\\alpha$}\\n\\\\font\\\\aipsfont = cmsy9 scaled\\\\magstep1\\n\\\\font\\\\smallaipsfont = cmsy5 scaled\\\\magstep1\\n\\\\newcommand\\\\aips {{\\\\aipsfont AIPS}}\\n\\\\newcommand\\\\Lh {{\\\\aipsfont L$\\\\;$}}\\n\\\\newcommand\\\\minpoint{$^{\\\\prime}\\\\mskip-4.7mu.\\\\mskip0.8mu$}\\n\\\\newcommand\\\\araa{{ARA\\\\&A}}\\n\\\\newcommand\\\\aap{{A\\\\&A}}\\n\\\\newcommand\\\\aasup{{A\\\\&AS}}\\n\\\\newcommand\\\\aaps{{A\\\\&AS}}\\n\\\\newcommand\\\\aj{{AJ}}\\n\\\\newcommand\\\\apj{{ApJ}}\\n\\\\newcommand\\\\apjl{{ApJ}}\\n\\\\newcommand\\\\apjs{{ApJS}}\\n\\\\newcommand\\\\iaucirc{{IAU Circ.}}\\n\\\\newcommand\\\\mnras{{MNRAS}}\\n\\\\newcommand\\\\nature{{Nature}}\\n\\\\newcommand\\\\nat{{Nature}}\\n\\\\newcommand\\\\pasp{{PASP}}\\n\\\\def\\\\spose#1{\\\\hbox to 0pt{#1\\\\hss}}\\n\\\\newcommand\\\\simlt{\\\\mathrel{\\\\spose{\\\\lower 3pt\\\\hbox{$\\\\mathchar\\\"218$}}\\n \\\\raise 2.0pt\\\\hbox{$\\\\mathchar\\\"13C$}}}\\n\\\\newcommand\\\\lesssim{\\\\mathrel{\\\\spose{\\\\lower 3pt\\\\hbox{$\\\\mathchar\\\"218$}}\\n \\\\raise 2.0pt\\\\hbox{$\\\\mathchar\\\"13C$}}}\\n\\\\newcommand\\\\simgt{\\\\mathrel{\\\\spose{\\\\lower 3pt\\\\hbox{$\\\\mathchar\\\"218$}}\\n \\\\raise 2.0pt\\\\hbox{$\\\\mathchar\\\"13E$}}}\\n\\\\newcommand\\\\gtrsim{\\\\mathrel{\\\\spose{\\\\lower 3pt\\\\hbox{$\\\\mathchar\\\"218$}}\\n \\\\raise 2.0pt\\\\hbox{$\\\\mathchar\\\"13E$}}}\\n\\\\newcommand\\\\arcdeg{\\\\degr}\\n\\\\newcommand\\\\nodata{...}\\n\\\\includeonly{wntable,tnmptable}\\n\\n\\\\begin{document}\\n\\n\\\\thesaurus{04.19.1; 11.01.2; 13.18.1}\\n\\n\\\\title{A Sample of 669 Ultra Steep Spectrum Radio Sources to Find High Redshift Radio Galaxies \\\\thanks{Tables A.1, A.2 and A.3 are also and appendices B, C and D are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html }}\\n\\\\subtitle{}\\n\\\\titlerunning{A sample of 669 USS sources}\\n\\n\\\\author{Carlos De Breuck \\\\inst{1,2} \\\\and Wil van Breugel \\\\inst{2} \\\\and Huub J. A. R\\\\\\\"ottgering \\\\inst{1} \\\\and George Miley \\\\inst{1}}\\n\\n\\\\authorrunning{Carlos De Breuck \\\\etal}\\n\\n\\\\offprints{Carlos De Breuck}\\n\\n\\\\institute{Sterrewacht Leiden, Postbus 9513, 2300 RA Leiden, The\\n Netherlands; debreuck,miley,rottgeri@strw.leidenuniv.nl\\n \\\\and Institute of Geophysics and Planetary Physics,\\n Lawrence Livermore National Laboratory, L-413, Livermore,\\n CA 94550, U.S.A.; wil@igpp.llnl.gov}\\n\\n\\\\date{Received 1999 November 5; accepted 2000 February 10}\\n\\n\\\\maketitle\\n\\n\\\\begin{abstract}\\nSince radio sources with Ultra Steep Spectra (USS; $\\\\alpha \\\\lesssim -1.30; S \\\\propto \\\\nu^{\\\\alpha}$) are efficient tracers of high redshift radio galaxies (HzRGs), we have defined three samples of such USS sources using the recently completed WENSS, TEXAS, MRC, NVSS and PMN radio-surveys. Our combined sample contains 669 sources with $S_{1400} > 10$~mJy and covers virtually the entire sky outside the Galactic plane ($|b|>15$\\\\arcdeg). For our 2 largest samples, covering $\\\\delta > -35\\\\arcdeg$, we selected only sources with angular sizes $\\\\Theta < 1\\\\arcmin$. For 410 sources, we present radio-maps with 0\\\\farcs3 to $\\\\sim$5\\\\arcsec\\\\ resolution from VLA and ATCA observations or from the FIRST survey, which allows the optical identification of these radio sources.\\n\\nComparison with spectrally unbiased samples at similar flux density levels, shows that our spectral index, flux density, and angular size selections do not affect the angular size distribution of the sample, but do avoid significant contributions by faint foreground spiral galaxies.\\nWe find that the spectral index distribution of 143,000 sources from the WENSS and NVSS consists of a steep spectrum galaxy and a flat spectrum quasar population, with the relative contribution of flat spectrum sources doubling from $S_{1400}>0.1$~Jy to $S_{1400}>2.5$~Jy.\\nThe identification fraction of our USS sources on the POSS ($R \\\\lesssim 20$) is as low as 15\\\\%, independent of spectral index $\\\\alpha < -1.30$. We further show that 85\\\\% of the USS sources that can be identified with an X-ray source are probably contained in galaxy clusters, and that $\\\\alpha < -1.6$ sources are excellent Galactic pulsar candidates, because the percentage of these sources is four times higher in the Galactic plane.\\n\\nOur sample has been constructed to start an intensive campaign to obtain a large sample of high redshift objects ($z>3$) that is selected in a way that does not suffer from dust extinction or any other optical bias.\\n\\n\\\\keywords{Surveys --- Galaxies: active --- Radio continuum: galaxies}\\n\\n\\\\end{abstract}\\n \\n\\\\section{Introduction}\\nRadio galaxies have now been found out to redshifts of $z=5.19$ (\\\\cite{wvb99b}) and radio-loud quasars out to $z=4.72$ (\\\\cite{hoo98}). Although new optical selection techniques such as color-dropouts, deep spectroscopy of blank fields, and narrow-band \\\\Lya\\\\ imaging have now found galaxies at similar (\\\\cite{ste99}) and even higher redshifts (up to $z \\\\sim 5.75$; \\\\cite{dey98}; \\\\cite{wey98}; \\\\cite{spi98}, \\\\cite{hu99}), radio sources are still the only objects that can be selected uniformly over all redshift ranges, and in a way that does not suffer from optical biases such as dust extinction, which is known to be important at these high redshifts (\\\\eg\\\\ \\\\cite{hug98}; \\\\cite{ivi98}; \\\\cite{dic98}).\\n\\nAt low to moderate redshift ($z \\\\lesssim 1$), powerful radio sources are uniquely identified with massive ellipticals (\\\\cite{lil84}; \\\\cite{owe89}; \\\\cite{bes98}; \\\\cite{mcl00}). The strongest indications that this is also true at higher redshifts comes from the near-IR Hubble $K-z$ diagram of radio galaxies which shows a remarkably close correlation from the present out to $z=5.19$ (\\\\cite{lil89}; \\\\cite{eal97}; \\\\cite{wvb98}, \\\\cite{wvb99b}). This suggests that we can use radio galaxies to study the formation and evolution of the most massive galaxies, which, by their implied star-formation history, can put important constraints on galaxy formation models, and even on cosmological parameters (\\\\eg \\\\cite{dun96}; \\\\cite{spi97}).\\nAlthough the unification model for radio galaxies and quasars (\\\\eg \\\\cite{bar89}) suggests we could also use quasars as tracers, a detailed stellar population study of quasar host galaxies is almost impossible due to the extreme luminosity of the AGN. Furthermore, samples of radio sources designed to find large quantities of quasars require additional optical selections (\\\\eg\\\\ \\\\cite{gre96}, \\\\cite{hoo98}, \\\\cite{whi00}).\\n\\n%---------------------------------------------------------- zalpha\\n\\\\begin{figure}\\n\\\\psfig{file=ds1811f1.eps,width=8.8cm}\\n\\\\caption[zalpha.ps]{$\\\\alpha_{1400}^{325}$ against $z$ for 2 samples\\nwithout spectral index selection (3CR, \\\\cite{spi85} and MRC,\\n\\\\cite{mcc96}), and 2 USS samples (4C, \\\\cite{cha96a} and our new WN/TN\\nsamples, as defined in this paper). Note that the correlation is\\npresent in the spectrally unbiased 3CR and MRC, and that the 4C and\\nour new USS samples are finding three to five times more $z>2$ radio\\ngalaxies than the MRC. The horizontal dotted line indicates the\\n$\\\\alpha_{1400}^{325} < -1.3$ cutoff used in our USS\\nsample. \\\\label{zalpha}}\\n\\\\end{figure}\\n%______________________________________________________________\\n\\nConsiderable effort has been spent over the last decade to find these high redshift radio galaxies (HzRGs), which has lead to the discovery of more than 140 radio galaxies at redshifts $z>2$ (see \\\\eg \\\\cite{deb98a} for a recent summary). However by $z>3$, their numbers become increasingly sparse, and using flux limited radio surveys such as the 3CR ($S_{178} > 10$~Jy; \\\\cite{lai83}), or the MRC strip ($S_{408} > 0.95$~Jy; \\\\cite{mcc96}), the highest redshift radio galaxy found so far is at $z\\\\sim 3.2$ (Fig. \\\\ref{zalpha}; \\\\cite{raw90}; \\\\cite{mcc96}). This redshift limit arises because radio power is correlated with redshift in bright flux limited samples, and an upper limit exists in the radio luminosity. Lowering the flux limit would not only substantially increase the number of sources in these samples, but at the same time the fraction of luminous very high redshift radio galaxies would decrease (\\\\cite{blu98}, \\\\cite{jar99}). This fractional decrease would arise even if there is no decrease in co-moving space density at $z \\\\sim 2.5$. Such a redshift cutoff has been suggested by Bremer \\\\etal (1998), but recently Jarvis \\\\etal (1999) rule out a break at $z\\\\lesssim 2.5$. To efficiently find large numbers of HzRGs in acceptable observing times, it is therefore necessary to apply additional selection criteria, at the expense of completeness.\\n\\nBy far the most successful selection criterion has been the ultra steep spectrum criterion (\\\\eg \\\\cite{rot94}; \\\\cite{cha96a}; \\\\cite{blu98}). Selecting sources with very steep radio spectra increases dramatically the chance of finding $z>2$ radio galaxies (Fig. \\\\ref{zalpha}). This technique is based on the results of Tielens \\\\etal\\\\ (1979) \\\\nocite{tie79} and Blumenthal \\\\& Miley (1979)\\\\nocite{blu79}, who found that the identification fraction on the POSS ($R \\\\lesssim 20$) decreases with steepening spectral index, consistent with the steeper sources being at higher redshifts. It is now getting clear that this correlation can be explained by a combination of a K-correction of a concave radio spectrum and an increasing spectral curvature with redshift (\\\\cite{kro91}, \\\\cite{car99}; \\\\cite{wvb99a}). To further investigate the $z - \\\\alpha$ correlation, we have calculated spectral indices using the flux densities from the WENSS (\\\\cite{ren97}) and NVSS (\\\\cite{con98}) catalogs for four different samples: the flux density limited 3CR (\\\\cite{spi85}) and MRC (\\\\cite{mcc96}) surveys, and the USS samples from the 4C (\\\\cite{cha96a}) and the one presented in this paper.\\nThe results (Fig. \\\\ref{zalpha}) show a trend for steeper spectral index sources to have higher redshifts in flux limited, spectrally unbiased samples, confirming the empirical relation out to the highest redshifts. The efficiency of the USS criterion is clearly illustrated by the fact that the 4C USS sample (\\\\cite{cha96a}) contains 50\\\\% $z>2$ sources, and by the early spectroscopic results on the USS samples presented in this paper, which indicate that $\\\\sim$2/3 of our sources have $z>2$. It is even more impressive to note that 13 of the 14 radio galaxies at $z>3.5$ we know of have been found from samples with a steep spectral index selection\\\\footnote{The only exception is VLA J123642+6213 (\\\\cite{wad99}), which has been identified in the HDF, but it does have a steep spectral index ($\\\\alpha_{1400}^{8500}=-0.94$).}! The limitation of this technique is that the steepest spectrum sources are rare, comprising typically only 0.5\\\\% (at $\\\\alpha < -1.30$) of a complete low frequency sample; therefore, large and deep all sky surveys are needed to obtain a significant sample of USS sources.\\n\\nWith the advent of several new deep all-sky surveys (\\\\S 2), it is now possible for the first time to construct a well defined all-sky USS sample with optimized selection criteria to find large numbers of $z>3$ radio galaxies. In this paper, we describe the construction of such a sample, and present high resolution radio observations needed to determine accurate positions and morphologies. This information is essential for the optical and near-IR identifications, and subsequent optical spectroscopy of a significant sub-set of our sample, which will be described in a future papers. \\nThe organization of the paper is as follows: we describe the radio surveys we used in \\\\S 2 and define our samples in \\\\S 3. We present and discuss our radio observations in \\\\S 4, and present our conclusions in \\\\S 5. \\n%Throughout the paper, we use $H_0 = 50$ km s$^{-1}$ Mpc$^{-1}$, $q_0 = 0$ and $\\\\Lambda = 0$.\\n\\\\begin{table*}\\n\\\\centerline{\\\\bf Table 1: Radio Surveys}\\n\\n\\\\footnotesize\\n\\\\begin{tabular}{lccc}\\n\\\\hline\\n\\\\\\\\\\n & WENSS & TEXAS & MRC \\\\\\\\\\n\\\\\\\\\\n\\\\hline\\n\\\\\\\\\\nFrequency (MHz) & 325 & 365 & 408 \\\\\\\\\\nSky region (J2000) & $\\\\delta >$ +29\\\\arcdeg & $-$35\\\\fdg7 $< \\\\delta <$ +71\\\\fdg5 & $-$85\\\\arcdeg $< \\\\delta <$ +18\\\\fdg5 \\\\\\\\\\n\\\\# of sources & 229,576 & 67,551 & 12,141 \\\\\\\\\\nResolution & $ 54\\\\arcsec \\\\times$ 54\\\\arcsec cosec$\\\\delta$ & 10\\\\arcsec$^a$ & $2\\\\farcm62 \\\\times 2\\\\farcm86 \\\\sec (\\\\delta - 35\\\\fdg5)$ \\\\\\\\\\nPosition uncertainty & 1\\\\farcs5 & 0\\\\farcs5---1\\\\arcsec & 8\\\\arcsec \\\\\\\\\\n(strong sources) & & & \\\\\\\\\\nRMS noise & $\\\\sim$4 mJy & 20 mJy & 70 mJy \\\\\\\\\\nFlux density limit & 18 mJy & 150 mJy & 670 mJy \\\\\\\\\\nReference & \\\\cite{ren97} & \\\\cite{dou96} & \\\\cite{lar81} \\\\\\\\\\n\\\\\\\\\\n\\\\hline\\n\\\\hline\\n\\\\\\\\\\n & NVSS & FIRST & PMN \\\\\\\\\\n\\\\\\\\\\n\\\\hline\\n\\\\\\\\\\nFrequency (MHz) & 1400 & 1400 & 4850 \\\\\\\\\\nSky region (J2000) & $\\\\delta > -$40\\\\arcdeg$^b$ & $7^h20^m < \\\\alpha < 17^h20^m$; +22\\\\fdg2 $< \\\\delta <$ +57\\\\fdg5 & $-$87\\\\fdg5 $< \\\\delta <$ +10\\\\arcdeg \\\\\\\\\\n & & $21^h20^m < \\\\alpha < 3^h20^m$; $-$2\\\\fdg5 $< \\\\delta <$ +1\\\\fdg6 \\\\\\\\\\n\\\\# of sources & 1,689,515 & 437,429 & 50,814 \\\\\\\\\\nResolution & 45\\\\arcsec $\\\\times$ 45\\\\arcsec & 5\\\\arcsec $\\\\times$ 5\\\\arcsec & 4\\\\minpoint2 \\\\\\\\\\nPosition uncertainty & 1\\\\arcsec & 0\\\\farcs1 & $\\\\sim$45\\\\arcsec \\\\\\\\\\n(strong sources) & & & \\\\\\\\\\nRMS noise & 0.5 mJy & 0.15 mJy & $\\\\sim$8 mJy \\\\\\\\\\nFlux density limit & 2.5 mJy & 1 mJy & 20 mJy \\\\\\\\\\nReference & \\\\cite{con98} & \\\\cite{bec95} & \\\\cite{gri93} \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\n$^a$ The Texas interferometer has a complicated beam. However, sources with separations between 10\\\\arcsec\\\\ and 2\\\\arcmin\\\\ can be successfully modeled as doubles, and will have a single entry in the catalog. See \\\\cite{dou96} for details.\\n\\n$^b$ Some small gaps are not covered. They are listed on the NVSS homepage (1998 January 19 version).\\n\\\\end{table*}\\n\\n\\n\\\\section{Description of the Radio Surveys}\\n\\n%---------------------------------------------------------- surveylimits\\n\\\\begin{figure}[t]\\n\\\\psfig{file=ds1811f2.eps,width=8.6cm}\\n\\\\caption[surveylimits.ps]{Limiting flux density plotted for all major radio surveys. Lines are of constant spectral indices of $-1.3$. Note that WENSS, NVSS and FIRST have flux density limits $\\\\sim 100$ times deeper than previous surveys at comparable wavelengths. \\\\label{surveylimits}}\\n\\\\end{figure}\\n%______________________________________________________________\\n\\nDuring the past years, several all-sky radio-surveys have become available (Table 1), which are 1--2 orders of magnitude more sensitive than previous surveys at similar frequencies (Fig.\\\\ \\\\ref{surveylimits}). The combination of these new surveys allows us to define for the first time a large sample of USS sources that covers the whole sky\\\\footnote{To facilitate optical follow-up, we will exclude the Galactic plane at $|b|<15$\\\\degr} in both hemispheres. We list the main survey parameters in Table 1. In this section, we will briefly discuss the usefulness of these new radio surveys for the construction of USS samples. \\n\\n\\\\subsection{WENSS}\\nThe Westerbork Northern Sky Survey (WENSS; \\\\cite{ren97}) at 325~MHz is the deepest low-frequency survey with a large sky coverage (3.14 sr). We used the WENSS to define the largest, and most complete USS sample to date, covering the entire sky North of declination 29\\\\arcdeg. We used version 1.0 of the main and polar WENSS catalogs. A small area is covered by both these catalogs; we selected only the sources from the main catalog in this overlapping area.\\n\\n\\\\subsection{Texas}\\n%---------------------------------------------------------- texasppp\\n\\\\begin{figure}\\n\\\\psfig{file=ds1811f3.eps,width=9cm}\\n\\\\caption[texasppp.ps]{Fraction of sources with '+++'\\\\ flag in the Texas catalog (see text) as a function of Texas $S_{365}$ flux density. Note that the selection of '+++' sources excludes primarily sources with $S_{365} \\\\lesssim 700$~mJy. \\\\label{texasppp}}\\n\\\\end{figure}\\n%______________________________________________________________\\n\\nThe Texas survey, made with the Texas interferometer from 1974 to 1983 (\\\\cite{dou96}), covers 9.63 steradians at a frequency of 365~MHz with a limiting flux density about ten times higher than that of the WENSS. The Texas interferometer's 3.5~km maximum baseline provides $<$1\\\\arcsec\\\\ positional accuracy, but its poor uv-coverage leads to irregular beamshapes and lobe-shifts, hampering accurate modeling of extended sources. A detailed discussion of these complications can be found in Douglas \\\\etal\\\\ (1996).\\nTo minimize these problems, we have selected only the 40.9\\\\% sources that are well modeled (listed with a '+++' flag in the catalog). This selection excludes primarily $S_{365} \\\\lesssim 700$~mJy sources (Fig. \\\\ref{texasppp}), but even at $S_{365} \\\\gtrsim 700$~mJy, one out of three sources is excluded by this criterion.\\n\\\\cite{dou96} have calculated the completeness above flux density S of the Texas catalog (defined as the fraction of sources with true flux density greater than S which appear in the catalog) by comparing the Texas with the MRC (\\\\cite{lar81}) and a variety of other low-frequency catalogs. They found that the completeness varies with declination (because the survey was done in declination strips over a large time span), and an expected increase in completeness at higher flux densities. In Table 2, we reproduce their completeness table, extended with the values after the '+++' selection.\\n\\n\\\\begin{table}\\n\\\\centerline{\\\\bf Table 2: Completeness of the Texas survey}\\n\\\\begin{tabular}{lcc}\\n\\\\hline\\nLimiting flux density & all sources & '+++' sources \\\\\\\\\\n\\\\hline\\n250 mJy & 0.8 & 0.2 \\\\\\\\\\n350 mJy & 0.88 & 0.28 \\\\\\\\\\n500 mJy & 0.92 & 0.40 \\\\\\\\\\n750 mJy & 0.96 & 0.51 \\\\\\\\\\n1 Jy & 0.96 & 0.50 \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\\\end{table}\\n\\n%---------------------------------------------------------- wtratio\\n\\\\begin{figure}\\n\\\\psfig{file=ds1811f4.eps,width=8.6cm}\\n\\\\caption[wtratio.ps]{Ratio of integrated Texas over WENSS flux density against integrated WENSS flux density. Only Texas '+++' sources are plotted. The horizontal line is the expected ratio 0.865 due to the 40 MHz difference in central frequency, and assuming a spectral index of $\\\\alpha_{365}^{1400}=-0.88$. The curved line indicates a 150 mJy flux density limit in the Texas catalog. Note the increasing amount of overestimated Texas flux densities with decreasing flux density $S_{WENSS} < 400$~mJy. \\\\label{wtratio}}\\n\\\\end{figure}\\n%______________________________________________________________\\n\\nTo examine the reliability of the listed flux densities, and to check to what extent the '+++' selection has removed the spurious sources from the catalog, we have correlated the Texas '+++' sources with WENSS, NVSS and FIRST.\\nIn Figure \\\\ref{wtratio}, we compare the Texas flux densities with those of the WENSS. At $S_{325} \\\\gtrsim 500$~mJy, the ratio of the flux densities is closely distributed around 0.9. This ratio is what we expect due to the 40 MHz central frequency difference between the two surveys and assuming a spectral index $\\\\alpha_{365}^{1400} = -0.879$ (the median of the Texas-NVSS spectral indices).\\nAt $S_{325} \\\\lesssim 500$~mJy, the number of sources in the Texas catalog which are brighter than in WENSS catalog increases with decreasing flux density. This can be explained by the 'up-scattering' of sources near the flux limit of the Texas catalog (\\\\ie only sources intrinsically brighter than $S_{365} = 150$~mJy will be detected, but no $S_{365} < 150$~mJy sources with a large positive flux density measurement error). The result of this on a USS sample based on the Texas survey and correlated with a higher frequency survey (such as the NVSS), will be that with lower $S_{365}$, we will find more sources whose spectral indices appear steeper than they really are.\\n\\nWe also examined the dependence of the ratio Texas/WENSS flux density on angular size, determined from the FIRST survey (see \\\\S 2.1.4). We found no significant residual variation of the flux density ratio at sizes between 5\\\\arcsec\\\\ and 2\\\\arcmin.\\n\\nIn Figure \\\\ref{usssr}b, we plot the density of NVSS sources around a Texas source (see also \\\\S 2.2.5). The width of the over-density peak ($\\\\sim 10$\\\\arcsec) is due to the positional inaccuracies in the Texas and NVSS catalogues. However, the very broad tail of sources between 20\\\\arcsec\\\\ and 110\\\\arcsec\\\\ and the secondary peak coinciding with the fringe separation at 73\\\\arcsec\\\\ indicates that the '+++' selection did not remove all spurious sources from the catalog.\\n\\nIn summary, after the selection of '+++' sources, the Texas catalog still contains $<5$\\\\% spurious sources (\\\\cite{dou96}), probably due to residual lobe-shifted sources. Our comparison of the Texas flux densities with those of the WENSS survey shows that the differences are consistent with the errors quoted in the catalog. The selection of the Texas catalog with only '+++' sources is thus $>$95\\\\% reliable, but only $\\\\sim$40\\\\% complete.\\n\\n\\\\subsection{NVSS}\\nThe NRAO VLA Sky Survey (NVSS; \\\\cite{con98}) covers the 10.3 steradians north of $-$40\\\\arcdeg\\\\ at 1.4~GHz, and reaches a 50 times lower limiting flux density than previous large area 1.4~GHz surveys. At the flux density levels we are using ($S_{1400}>10$~mJy), the catalog is virtually complete.\\nBecause the NVSS resolution is comparable to that of the WENSS and Texas surveys, and its sky coverage is large, we use the NVSS to determine the spectral indices in our USS samples based on the WENSS and Texas surveys.\\nThe final NVSS catalog was not yet completed at the time of our USS sample construction. For our final sample, presented in this paper, we use the 1998 January 19 version. This version still lacks data in a small number of regions of the sky (listed on the NVSS homepage). As a result, the sky coverage of the area listed in Table 3 is only 99.77\\\\%.\\n\\n\\\\subsection{FIRST}\\nThe Faint Images of Radio Sky at Twenty centimeters (FIRST, \\\\cite{bec95}) survey is currently being made with the VLA in the B-array at 1.4~GHz, and has a limiting flux density three times deeper than the NVSS. We used the 1998 February 4 version of the catalog, covering 1.45~steradians. As noted by Becker \\\\etal\\\\ (1995), the photometry for extended sources in FIRST might be less reliable than that of the NVSS, due to the $9 \\\\times$ higher resolution, which could underestimate large-scale diffuse radio emission. As the FIRST area is completely covered by the NVSS, we will consistently use NVSS flux densities for our spectral index calculation. The main advantages of FIRST over NVSS for our purposes are the much better positional accuracy ($<$~0\\\\farcs5) and the higher (5\\\\arcsec) resolution. This combination allows the identification of even the very faint ($R > 20$) optical counterparts of radio sources. Additionally, the fainter detection limit of the FIRST allows an extra check on the flux densities of compact sources.\\n\\n\\\\subsection{MRC}\\nThe Molonglo Reference Catalog of radio sources (\\\\cite{lar81}) at 408~MHz is presently the most sensitive low-frequency catalog with reasonable positional accuracy that covers the deep southern hemisphere, $\\\\delta < -35$\\\\arcdeg. We will use this catalog in combination with the PMN survey (see below) to define the first USS sample at $\\\\delta < -40\\\\arcdeg$.\\n\\n\\\\subsection{PMN}\\nThe Parkes-MIT-NRAO (PMN) survey is a combination of 4 strips observed with the Parkes telescope at 4.85~GHz. The strips cover different parts of the sky, each with a slightly different limiting flux density. The regions are: southern ($-87\\\\fdg5 < \\\\delta < -37\\\\arcdeg$, \\\\cite{wri94}), zenith ($-37\\\\arcdeg < \\\\delta < -29\\\\arcdeg$, \\\\cite{wri96}), tropical ($-29\\\\arcdeg < \\\\delta < -9\\\\fdg5$, \\\\cite{gri94}), and equatorial ($-9\\\\fdg5 < \\\\delta < +10\\\\arcdeg$, \\\\cite{gri95}). For our southern hemisphere sample, we have used the southern and zenith catalogs to find USS sources at $\\\\delta < -30\\\\arcdeg$.\\n\\n%---------------------------------------------------------- usssky\\n\\\\begin{figure}\\n\\\\psfig{file=ds1811f6.eps,width=8.8cm}\\n\\\\caption[usssky.ps]{Sky coverage of our 3 USS samples. Constant declination lines denote the boundaries between our the WN and TN and between the TN and MP samples, as indicated on the right. Note the difference in source density and the exclusion of the Galactic Plane. \\\\label{usssky}}\\n\\\\end{figure}\\n%______________________________________________________________\\n\\n\\\\section{USS Samples}\\n\\n%---------------------------------------------------------- usssr\\n\\\\begin{figure*}\\n\\\\psfig{file=ds1811f5.eps,width=18cm}\\n\\\\caption[usssr.ps]{The density of sources from the high frequency catalog used in the correlation (NVSS or PMN) around sources from the low frequency catalog (WENSS, Texas or MRC) as a function of search radius. The dotted line represents the distribution of confusion sources (see text). The apparent under-density of WENSS--NVSS sources at search radii $\\\\simgt 60\\\\arcsec$ is due to the grouping of multiple component sources in the $\\\\sim$1\\\\arcmin\\\\ resolution WENSS. Note the plateau and secondary peak around the 73\\\\arcsec\\\\ Texas fringe separation in the Texas--NVSS correlation and the much larger uncertainty in the MRC--PMN correlation.\\\\label{usssr}}\\n\\\\end{figure*}\\n%______________________________________________________________\\n\\nFigure \\\\ref{surveylimits} shows that the surveys described above have very compatible flux density limits for defining samples of USS sources. At the same time, their sky coverage is larger and more uniform than previous surveys used for USS sample construction (\\\\cite{wie92}, \\\\cite{rot94}; \\\\cite{cha96a}, \\\\cite{blu98}; \\\\cite{ren98}, \\\\cite{pur99}, \\\\cite{ped99}, \\\\cite{and00}). We selected the deepest low and high frequency survey available at each part of the sky. For a small region $-35\\\\arcdeg < \\\\delta < -30\\\\arcdeg$ which is covered by both Texas and MRC, we used both surveys. This resulted in a more complete samples since the lower sensitivity of the PMN survey in the zenith strip (see \\\\S2.6) is partly compensated by the (albeit incomplete) Texas survey.\\nTo avoid problems with high Galactic extinction during optical imaging and spectroscopy, all regions at Galactic latitude $|b| <$ 15\\\\arcdeg\\\\ were excluded\\\\footnote{This also reduces the number of Galactic pulsars in our sample (see \\\\S4.7.2).}, as well as the area within 7\\\\arcdeg of the LMC and SMC. This resulted in three USS samples that cover a total of 9.4 steradians (Fig. \\\\ref{usssky}).\\n\\nWe designate the USS samples by a two-letter name, using the first letter of their low- and high-frequency contributing surveys. Sources from these samples are named with this 2-letter prefix followed by their IAU J2000-names using the positions from the NVSS catalog (WN and TN samples) or the MRC catalog (MP sample). We did not rename the sources after a more accurate position from our radio observations or from the FIRST survey. The sample definitions are summarized in Table 3.\\n\\n\\\\subsection{Survey combination issues}\\nWe first discuss the problems that arise when combining radio surveys with different resolutions and positional uncertainties.\\n\\\\subsubsection{Correlation search radius}\\nDue to the positional uncertainties and resolution differences between radio surveys, in general the same source will be listed with slightly different positions in the catalogs.\\n\\nTo empirically determine the search radius within which to accept sources in 2 catalogs to be the same, we compared the density of objects around the position listed in the low-frequency survey (which has lower resolution) with the expected number of random correlations in each sample ($\\\\equiv$ confusion sources). To determine this number as a function of distance from the position in the most accurate catalog, we created a random position catalog by shifting one of the input catalogs by 1\\\\arcdeg\\\\ in declination, and made a correlation with this shifted catalog. The density of sources as a function of distance from the un-shifted catalog then represents the expected number of confusing sources as a function of radial distance. In Figure \\\\ref{usssr}, we plot for each of our three samples the observed density around these sources with this confusing distribution over-plotted. The correlation search radius should thus be chosen at a distance small enough for the density of confusion sources to be negligible.\\n\\nWe decided to adopt the radius where the density of real sources is at least ten times higher that the density of confusion sources as the search radius for our sample construction, except for the WN sample (would be 15\\\\arcsec) where we chose the same radius as for the TN sample (10\\\\arcsec). The later was done for consistency between both samples. Because of the five times lower resolution and source densities in the MRC and PMN surveys, the search radius of the MP sample is eight times larger. Summarized, the search radii we used are 10\\\\arcsec\\\\ for WN and TN, and 80\\\\arcsec\\\\ for MP.\\n\\\\begin{table*}\\n\\\\centerline{\\\\bf Table 3: USS samples}\\n\\\\scriptsize\\n\\\\begin{tabular}{lrccccccc}\\n\\\\hline\\nSample & Sky Area$\\\\qquad\\\\quad$ & Density & Spectral Index & Search Radius & Flux Limit & C$^a$ & R$^a$ & \\\\# of Sources \\\\\\\\\\n & & sr$^{-1}$ & & & mJy & &\\\\\\\\\\n\\\\hline\\nWN & 29\\\\arcdeg $< \\\\delta <$ 75\\\\arcdeg, $|b| >$ 15\\\\arcdeg$^b$ & 151 & $\\\\alpha_{325}^{1400} \\\\le -1.30$ & 10\\\\arcsec & $S_{1400} >$ 10 & 96\\\\% & 90\\\\% & 343 \\\\\\\\\\nTN & $-$35\\\\arcdeg $< \\\\delta <$ 29\\\\arcdeg, $|b| >$ 15\\\\arcdeg$^b$ & 48$^c$ & $\\\\alpha_{365}^{1400} \\\\le -1.30$ & 10\\\\arcsec & $S_{1400} >$ 10 & 97\\\\%$^c$ & 93\\\\% & 268 \\\\\\\\\\nMP & $\\\\delta < -$30\\\\arcdeg, $|b| >$ 15\\\\arcdeg & 26 & $\\\\alpha_{408}^{4800} \\\\le -1.20$ & 80\\\\arcsec & S$_{408} > 700$; S$_{4850} > 35$ & 100\\\\% & 100\\\\% & 58 \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\n$^a$ C=completeness and R=reliability accounting only for scattering across the spectral index limit (see \\\\S3.3.1).\\n\\n$^b$ coverage is only 99.7\\\\% because some small patches of sky we not covered at the time of writing. They are listed on the NVSS homepage \\\\\\\\(1998 January 19 version).\\n\\n$^c$ Because we selected only problem free sources from the Texas survey, the effective completness of the TN sample is $\\\\sim 30\\\\%$.\\n\\\\end{table*}\\n\\n\\\\subsubsection{Angular size}\\nIn order to minimize errors in the spectral indices due to different resolutions and missing flux on large angular scales in the composing surveys, we have only considered sources which are not resolved into different components in the composing surveys. Effectively, this imposes an angular size cutoff of $\\\\sim$1\\\\arcmin\\\\ to the WN, $\\\\sim$2\\\\arcmin\\\\ to the TN sample and $\\\\sim$4\\\\arcmin\\\\ to the MP sample.\\nWe deliberately did not choose a smaller angular size cutoff (as \\\\eg Blundell \\\\etal\\\\ (1998) did for the 6C$^*$ sample), because (1) higher resolution angular size information is only available in the area covered by the FIRST survey, and (2) even a 15\\\\arcsec\\\\ cutoff would only reduce the number of sources by 30\\\\%, while it would definitely exclude several HzRGs from the sample. For example, in the 4C USS sample (\\\\cite{cha96b}), three out of eight $z>2$ radio galaxies have angular sizes $>$15\\\\arcsec.\\n\\nWe think that our $\\\\sim$1\\\\arcmin\\\\ angular size cutoff will exclude almost no HzRGs, because the largest angular size for $z > 2$ radio galaxies in the literature is 53\\\\arcsec\\\\ (4C~23.56 at $z = 2.479$; \\\\cite{cha96a}, \\\\cite{car97}), while all 45 $z > 2.5$ radio galaxies with good radio maps are $<$~35\\\\arcsec\\\\ (\\\\cite{car97}). Although the sample of known $z>2$ radio galaxies is affected by angular size selection effects, very few HzRGs larger than 1\\\\arcmin\\\\ would be expected.\\n\\nThe main incompleteness of our USS sample stems from the spectral index cutoff and the flux limit (\\\\S3.2). However, our flux limit ($S_{1400}$=10~mJy) is low enough to break most of the redshift-radio power degeneracy at $z>2$. To achieve this with flux limited samples, multiple samples are needed (\\\\eg \\\\cite{blu99}).\\n\\n\\\\subsection{Sample definition}\\n\\n\\\\subsubsection{WENSS-NVSS (WN) sample}\\nA correlation of the WENSS and NVSS catalogs with a search radius of 10\\\\arcsec\\\\ centered on the WENSS position (see \\\\S 3.1.1) provides spectral indices for $\\\\sim 143,000$ sources. Even with a very steep $\\\\alpha_{325}^{1400} \\\\le -1.30$ spectral index criterion, we would still have 768 sources in our sample.\\nTo facilitate follow-up radio observations, and to increase the accuracy of the derived spectral indices (see \\\\S 3.3.1), we have selected only NVSS sources with $S_{1400} > 10$~mJy. Because the space density of the highest redshift galaxies is low, it is important not to limit the sample area (see \\\\eg \\\\cite{raw98}) to further reduce the number of sources in our sample.\\nBecause the NVSS has a slightly higher resolution than the WENSS (45\\\\arcsec\\\\ compared to $54\\\\arcsec \\\\times 54\\\\arcsec $cosec$~\\\\delta$), some WENSS sources have more than one associated NVSS source. We have rejected the 11 WN sources that have a second NVSS source within one WENSS beam. Instead of the nominal WENSS beam ($54\\\\arcsec \\\\times 54\\\\arcsec$cosec$\\\\delta$), we have used a circular 72\\\\arcsec\\\\ WENSS beam, corresponding to the major axis of the beam at $\\\\delta = 48\\\\arcdeg$, the position that divides the WN sample into equal numbers to the North and South. \\nThe final WN sample contains 343 sources.\\n\\n\\\\subsubsection{Texas-NVSS (TN) sample}\\nBecause the Texas and NVSS both have a large sky-coverage, the area covered by the TN sample includes 90\\\\% of the WN area. In the region $\\\\delta >29\\\\arcdeg$, we have based our sample on the WENSS, since it does not suffer from lobe-shift problems and reaches ten times lower flux densities than the Texas survey (\\\\S 2.2).\\nIn the remaining 5.28 steradians South of declination +29\\\\arcdeg, we have spectral indices for $\\\\sim 25,200$ sources. Again, we used a 10\\\\arcsec\\\\ search radius (see \\\\S 3.1.1), and for the same reason as in the WN sample we selected only NVSS sources with $S_{1400} > 10$~mJy. Combined with the $\\\\alpha_{365}^{1400} \\\\le -1.30$ criterion, the number of USS TN sources is 285.\\nAs for the WN sample, we further excluded sources with more than one $S_{1400}>$10~mJy NVSS source within 60\\\\arcsec\\\\ around the TEXAS position, leaving 268 sources in the final TN sample. We remind (see \\\\S 2.2) that the selection of the TEXAS survey we used is only $\\\\sim$40\\\\% complete with a strong dependence on flux density. Using the values from table 2, we estimate that the completeness of our TN sample is $\\\\sim$30\\\\%.\\n\\n\\\\subsubsection{MRC-PMN (MP) sample}\\nIn the overlapping area, we preferred the TN over the MP sample for the superior positional accuracies and resolutions of both Texas and NVSS compared to MRC or PMN. Because the MRC survey has a low source density, we would have only 13 MP sources with $\\\\alpha_{408}^{4850} \\\\le -1.30$. We therefore relaxed this selection criterion to $\\\\alpha_{408}^{4850} \\\\le -1.20$, yielding a total sample of 58 sources in the deep South ($\\\\delta < -30$\\\\arcdeg).\\n%---------------------------------------------------------- wn3spixhis\\n\\\\begin{figure*}\\n\\\\centerline{\\\\psfig{file=ds1811f7.eps,width=15cm}}\\n\\\\caption[wn3his.ps]{Spectral index distributions from the WENSS-NVSS correlation. The left and right panels show the variation with 325~MHz and 1.4~GHz flux density. A low frequency selected sample is more appropriate to study the steep-spectrum population. The parameters of a two-component Gaussian fit (dotted line = steep, dashed line = flat) are shown in each panel. The solid line is the sum of both Gaussians. \\\\label{wn3spixhis}}\\n\\\\end{figure*}\\n%______________________________________________________________\\n\\n\\\\subsection{Discussion}\\n\\n\\\\subsubsection{Spectral index errors}\\nWe have listed the errors in the spectral indices due to flux density errors in the catalogs in Tables A.1 to A.3. The WN and TN samples have the most accurate spectral indices: the median spectral index errors are $\\\\Delta\\\\bar{\\\\alpha}_{325}^{1400} = 0.04$ for WN sources and $\\\\Delta\\\\bar{\\\\alpha}_{365}^{1400} = 0.04$ ($S_{365} >$ 1~Jy) to 0.07 ($S_{365} >$ 150~mJy) for TN sources. For the MP sample, $\\\\Delta\\\\bar{\\\\alpha}_{408}^{4850} \\\\approx 0.1$, with little dependence on flux density (S$_{408} > 750$mJy).\\n\\nBecause our sample selects the sources in the steep tail of the spectral index distribution (Fig. \\\\ref{wn3spixhis} and \\\\ref{spixhis}), there will be more sources with an intrinsic spectral index flatter than our cutoff spectral index that get scattered into our sample by measurement errors than there will be sources with intrinsic spectral index steeper than the cutoff that get scattered out of our sample. \\n\\nFollowing the method of \\\\cite{ren98}, we fitted the steep tail between $-1.60 < \\\\alpha < -1.0$ with a Gaussian function. For each of our three samples, we generated a mock sample drawn from this distribution, and added measurement errors by convolving this true spectral index distribution with a Gaussian distribution with as standard deviation the mean error of the spectral indices. The WN mock sample predicts that 13 $\\\\alpha_{325}^{1400} < -1.30$ sources get scattered out of the sample while 36 $\\\\alpha_{325}^{1400} > -1.30$ sources get scattered into the USS sample.\\nThus, the WN sample is 96\\\\% complete and 90\\\\% reliable. For the TN sample, we expect to loose 7 $\\\\alpha_{365}^{1400} < -1.30$ sources\\\\footnote{only due to the spectral index cutoff, the sample has more important incompleteness factors; see \\\\S 2.2}, and have 18 contaminating $\\\\alpha_{365}^{1400} > -1.30$ sources. The completeness is thus 97\\\\% and the reliability 93\\\\%. For the MP sample, this spectral index scattering is negligible, because there are too few sources in the steep spectral index tail.\\n\\nOur reliability and completeness are significantly better than the values of $\\\\sim$75\\\\% and $\\\\sim$50\\\\% of \\\\cite{ren98} because (1) our spectral indices are more accurate because they were determined from a wider frequency interval than the 325--610~MHz used by \\\\cite{ren98}, and (2) our sample has a steeper cutoff spectral index, where the spectral index distribution function contains fewer sources and has a shallower slope, leading to fewer sources that can scatter in or out of the sample.\\n\\n\\\\subsubsection{Spectral index distributions}\\nUsing the 143,000 spectral indices from the WENSS-NVSS correlation, we examined the flux density dependence of the steep and flat spectrum sources. Selecting sources with $S_{325}>50$~mJy or $S_{1400}>100$~mJy assures that we will detect all sources with $\\\\alpha_{325}^{1400}>{\\\\frac{\\\\ln(S_{NVSS}^{lim}/50)}{\\\\ln(325/1400)}}=-1.82$ or $\\\\alpha_{325}^{1400}<{\\\\frac{\\\\ln(S_{WENSS}^{lim}/100)}{\\\\ln(325/1400)}}=0.82$ respectively, where $S_{NVSS}^{lim}=3.5$~mJy and $S_{WENSS}^{lim}=30$~mJy are the lowest flux densities where the NVSS and WENSS are complete (\\\\cite{con98}, \\\\cite{ren97}). The results shown in Figure \\\\ref{wn3spixhis} therefore reflect only the effect of a different selection frequency. Two populations are present in both the $S_{325}$ and $S_{1400}$ selected distributions. The peaks of the steep and flat populations at $\\\\bar{\\\\alpha}_{325}^{1400} \\\\approx -0.8$ and $\\\\bar{\\\\alpha}_{325}^{1400} \\\\approx -0.4$ do not show significant shifts over three orders of magnitude in flux density. This is consistent with the results that have been found at 4.8~GHz (\\\\cite{wit79}, \\\\cite{mac81}, \\\\cite{owe83}), with the exception that their $\\\\bar{\\\\alpha}_{1400}^{4800} \\\\approx 0.0$ for the flat spectrum component is flatter than the $\\\\bar{\\\\alpha}_{325}^{1400} \\\\approx -0.4$ we found. However, we find that the relative contribution of the flat spectrum component increases from 25\\\\% at $S_{1400}>0.1$~Jy to 50\\\\% at $S_{1400}>2.5$~Jy\\n\\nBecause the steep- and flat-spectrum populations are best separated in the $S_{1400}>$2.5~Jy bin, we have searched the literature for identifications of all 58 $S_{1400} > 2.5$~Jy sources to determine the nature of both populations. All but one (3C 399, \\\\cite{mar98}) of the objects outside of the Galactic plane ($|b| > 15\\\\arcdeg$) were optically identified. Of the 30 steep spectrum ($\\\\alpha_{325}^{1400} < -0.6$) sources, two thirds were galaxies, while the rest were quasars. Half of the flat spectrum ($\\\\alpha_{325}^{1400} > -0.6$) sources were quasars, 20\\\\% blazars, and 30\\\\% galaxies. Figure \\\\ref{wn3spixhis} therefore confirms that the steep and flat spectral index populations are dominated by radio galaxies and quasars respectively. We also find that while the relative strength between the steep and flat spectrum populations changes due to the selection frequency, the median spectral index and width of the population does not change significantly over three orders in magnitude of flux density. Even fainter studies would eventually start to get contamination from the faint blue galaxy population (see \\\\eg\\\\ \\\\cite{win85}).\\n%---------------------------------------------------------- spixhis\\n\\\\begin{figure}\\n\\\\psfig{file=ds1811f8.eps,width=9cm}\\n\\\\caption[spixhis.ps]{ Logarithmic spectral index distribution for WENSS-NVSS (full line), Texas-NVSS (dot-dash line) and MRC-PMN (dotted line). The vertical line indicates the -1.3 cutoff used in our spectral index selection. Note the difference in number density and the sharper fall-off on the flat-end part of the TN and MP compared to the WN. \\\\label{spixhis}}\\n\\\\end{figure}\\n%______________________________________________________________\\n\\n\\\\begin{table*}\\n\\\\centerline{\\\\bf Table 4: Radio Observations}\\n\\\\begin{center}\\n\\\\begin{tabular}{lrrrcr}\\n\\\\hline\\nUT Date & Telescope & Config. & Frequency & Resolution & \\\\# of sources \\\\\\\\\\n\\\\hline\\n1996 October 28 & VLA & A & 4.86 GHz & 0\\\\farcs3 & 90 WN, 25 TN \\\\\\\\\\n1997 January 25 & VLA & BnA& 4.86 GHz & 0\\\\farcs6 & 29 TN \\\\\\\\\\n1997 March 10 & VLA & BnA & 4.885 GHz & 0\\\\farcs6 & 8 TN \\\\\\\\\\n1997 December 15 & ATCA & 6C & 1.420 GHz & 6\\\\arcsec $\\\\times$ 6\\\\arcsec\\\\ cosec$\\\\delta$ & 41 MP, 32 TN \\\\\\\\\\n1998 August 12+17 & VLA & B & 4.86 GHz & 1\\\\farcs0 & 151 WN \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\end{table*}\\n\\n\\\\subsubsection{Consistency of the three USS samples}\\nWe compare the spectral index distributions of our three USS samples in logarithmic histograms (Fig. \\\\ref{spixhis}). The distributions are different in two ways. First, the WENSS-NVSS correlation contains nine times more sources than the Texas-NVSS, and 14 times more than the MRC-PMN correlation. Second, the shapes of the distributions are different: while the steep side of the TN sample coincides with that of the WN, its flat end part falls off much faster. The effect is so strong that it even shifts the TN peak steep-wards by $\\\\sim0.15$. For the MP sample, the same effect is less pronounced, though still present.\\n\\nBoth effects are due to the different flux density limits of the catalogs. The deeper WENSS catalog obviously contains more sources than the TEXAS or MRC catalogs, shifting the distributions vertically in Figure \\\\ref{surveylimits}. The relative 'shortage' of flat spectrum sources in the Texas-NVSS and MRC-PMN correlations can be explained as follows. A source at the flux density limit in both WENSS and NVSS would have a spectral index of $\\\\alpha_{325}^{1400} = -1.3$, while for Texas and NVSS this would be $\\\\alpha_{365}^{1400} = -1.7$ (see Fig. \\\\ref{surveylimits}). Faint NVSS sources with spectral indices flatter than these limits will thus more often get missed in the TEXAS catalog than in the WENSS catalog. This effect is even strengthened by the lower completeness at low flux densities of the Texas catalog. However, very few USS sources will be missed in either the WENSS-NVSS or Texas-NVSS correlations\\\\footnote{The TN sample will have more spurious sources at low flux density levels; see \\\\S2.2}. The parallel slope also indicates that the USS sources from both the WENSS-NVSS and Texas-NVSS correlations were drawn from the same population of radio sources. We therefore expect a similar efficiency in finding HzRGs from both samples.\\n\\nThe MP sample has been defined using a spectral index with a much wider frequency difference. However, the observed ATCA 1.420 GHz flux densities can be used to construct $\\\\alpha_{408}^{1420}$. An 'a posteriori' selection using $\\\\alpha_{408}^{1420} \\\\le -1.30$ from out ATCA observations (see \\\\S 4.2) would keep $\\\\sim$60\\\\% of the MP sources in a WN/TN USS sample.\\n\\n\\\\section{Radio Observations}\\nOf all the major radio surveys described in \\\\S 2, only FIRST has sufficient positional accuracy and resolution for the optical identification of $R > 20$ objects. We present FIRST maps of 139 WN and 8 TN sources in appendices B.2 and B.4.\\n\\nOutside the area covered by FIRST, we have observed all the remaining WN sources, 30\\\\% of the TN sample, and 71\\\\% of the MP sources at 0\\\\farcs3 to 5\\\\arcsec\\\\ resolution using the Very Large Array (VLA; \\\\cite{nap83}) and Australia Telescope Compact Array (ATCA; \\\\cite{fra92}) telescopes.\\nA log of the radio observations is given in Table 4. We observed targets for our VLA runs on the basis of declination (A-array for $\\\\delta >$ 0\\\\arcdeg\\\\ and BnA-array for $\\\\delta <$ 0\\\\arcdeg) and sky coverage of the WN and TN samples, which were still incomplete at the time of the 1996 observations. We observed all WN, and most TN sources with the VLA, and all MP sources with the ATCA. We observed TN sources between $-31$\\\\arcdeg $< \\\\delta < -10$\\\\arcdeg\\\\ with either VLA or ATCA, depending on the progress of the NVSS at the time of the observations.\\n\\n\\\\subsection{VLA observations and data reduction}\\n\\nWe observed all sources in the standard 4.86 GHz C-band with a 50 MHz bandwidth, resulting in a resolution of $\\\\sim$0\\\\farcs3 in the A-array and $\\\\sim$1\\\\arcsec\\\\ in the BnA-array. We spent 5 minutes on each source, implying a theoretical rms level of 75 $\\\\mu$Jy, or a ratio of total integrated signal over map noise of 110 for the weakest sources, assuming no spectral curvature beyond 1.4 GHz.\\nWe performed calibration and data editing in \\\\aips, the Astronomical Image Processing System from NRAO.\\nWe used 3C286 as the primary flux calibrator in all runs. Comparison of the flux density of 3C48 with the predicted values indicated the absolute flux density scale was accurate up to 2\\\\%. We observed nearby (within 15\\\\arcdeg) secondary flux calibrators every 15 to 20 minutes to calibrate the phases. After flagging of bad data, we spilt the uv-data up into separate data sets for imaging and self-calibration in DIFMAP, the Caltech difference mapping program (\\\\cite{she97}).\\nWe used field sizes of 164\\\\arcsec\\\\ (A$-$array) or 256\\\\arcsec\\\\ (BnA$-$array) with pixel scales of 0\\\\farcs08 / pixel (A$-$array) or 0\\\\farcs25 / pixel (BnA$-$array). Even the smallest field of view is still four times larger than the resolution of the NVSS, so all components of an unresolved NVSS source will be covered.\\n\\nWe cleaned each source brighter than the 5$\\\\sigma$ level, followed by a phase-only self-calibration. We repeated the latter for all sources in the field of a source. Next, we made a new model from the (self-calibrated) uv-data, and subsequently cleaned to the level reached before. The last stage in the mapping routine was a deep clean with a 1\\\\% gain factor over the entire field. Most of the resulting maps have noise levels in the range 75 to 100 $\\\\mu$Jy, as expected.\\n\\n\\\\subsection{ATCA observations and data reduction}\\nWe used the ATCA in the 6C configuration, which has a largest baseline of 6km. We observed at a central frequency of 1.384 GHz, which was selected to avoid local interference. We used 21 of the 30 frequency channels that had high enough signal, which resulted in an effective central frequency of 1.420 GHz, with a 84 MHz bandwidth. In order to obtain a good uv-coverage, we observed each source eight to ten times for three minutes, spread in hour angle. The primary flux calibrator was the source 1934-648; we used secondary flux calibrators within 20\\\\arcdeg\\\\ of the sources to calibrate the phases.\\nWe performed editing and calibration in \\\\aips, following standard procedures. We made maps using the automated mapping/self-calibration procedure MAPIT in \\\\aips. The resulting 1.420 GHz maps (Fig. \\\\ref{mpatca}) have noise levels of $\\\\sim$5 mJy.\\n\\n\\\\subsection{Results}\\nOf all 343 WN sources, 139 have FIRST maps (appendix B.2). All remaining 204 sources were observed, and 141 were detected. The remaining 30\\\\% were too faint at 4.86~GHz to be detected in 5~min snapshots, because their high frequency spectral index steepens more than expected, or they were over-resolved. Because they are significantly brighter, all the observed 89 TN and 41 MP sources were detected.\\nWe present contour maps of all the detections in Appendices B.1, B.3, B.5, and B.6 and list the source parameters in Tables A.1 to A.3.\\n\\nWe have subdivided our sources into 5 morphological classes, using a classification similar to that used by R\\\\\\\"ottgering \\\\etal\\\\ (1994). Note that this classification is inevitably a strong function of the resolution, which varies by a factor of 20 between the VLA A-array and the ATCA observations. \\n\\nWe have determined the source parameters by fitting two-dimensional Gaussian profile to all the components of a source. The results are listed in Tables A.1 to A.3 which contain:\\n\\n\\\\begin{description}\\n\\\\item[Col 1:]{Name of the source in IAU J2000 format. The 2-letter prefix indicates the sample: WN: WENSS--NVSS, TN: Texas--NVSS, MP: MRC--PMN.}\\n\\\\item[Col 2:]{The integrated flux density from the low-frequency catalog.}\\n\\\\item[Col 3:]{The integrated flux density at the intermediate frequency, determined from the NVSS for WN and TN, or from the 1.420~GHz ATCA observations for the MP sample.}\\n\\\\item[Col 4:]{The integrated flux density at 4.86 GHz, determined from the VLA observations for WN and TN, and from the PMN survey for the MP sample.}\\n\\\\item[Col 5:]{The lower frequency two-point spectral index. This is the spectral index used to define the WN and TN samples.}\\n\\\\item[Col 6:]{The higher frequency two-point spectral index. This is the spectral index used to define the MP sample.}\\n\\\\item[Col 7:]{Morphological classification code: single (S), double (D), triple (T) and multiple (M) component sources, and irregularly shaped diffuse (DF) sources.}\\n\\\\item[Col 8:]{Largest angular size. For single component sources, this is the de-convolved major axis of the elliptical Gaussian, or, for unresolved sources (preceded with $<$), an upper limit is given by the resolution. For double, triple and multiple component sources, this is the largest separation between their components. For diffuse sources this is the maximum distance between the source boundaries defined by three times the map rms noise.}\\n\\\\item[Col 9:]{De-convolved position angle of the radio structure, measured North through East}\\n\\\\item[Col 10 -- 11:]{J2000 coordinates, determined from the map with position code listed in col. 12. The positions in the VLA and ATCA maps have been fitted with a single two-dimensional elliptical Gaussian. For double (D) sources, the geometric midpoint is given; for triples (T) and multiples (M), the core position is listed. For diffuse (DF) sources we list the center as determined by eye.}\\n\\\\item[Col 12:]{Position code, indicating the origin of the morphological and positional data in column 7 to 11: A=ATCA, F=FIRST, M=MRC, N=NVSS, and V=VLA}.\\n\\\\end{description}\\n\\n\\\\subsection{Notes on individual sources}\\n\\\\noindent{\\\\bf WN~J0043+4719:} The source 18\\\\arcsec\\\\ north of the NVSS position is not detected in the NVSS. This is therefore not a real USS source because the NVSS flux density was underestimated.\\n\\n\\\\noindent{\\\\bf WN~J0048+4137:} Our VLA map probably doesn't go deep enough to detect all the flux of this source.\\n\\n\\\\noindent{\\\\bf WN~J0727+3020:} The higher resolution FIRST map shows that both components of this object are indeed identified on the POSS, even though the NVSS position is too far off to satisfy our identification criterion.\\n\\n\\\\noindent{\\\\bf WN~J0717+4611:} Optical and near-IR spectroscopy revealed this object as a red quasar at $z=1.462$ (\\\\cite{deb98b}).\\n\\n\\\\noindent{\\\\bf WN~J0725+4123:} The extended POSS identification suggest this source is located in a galaxy cluster.\\n\\n\\\\noindent{\\\\bf WN~J0829+3834:} The NVSS position of this unresolved source is 7\\\\arcsec\\\\ ($3\\\\sigma$) from the FIRST position, which itself is only at 2\\\\arcsec\\\\ from the WENSS position.\\n\\n\\\\noindent{\\\\bf WN~J0850+4830:} The difference with the NVSS position indicates that our VLA observations are not deep enough to detect a probable north-eastern component.\\n\\n\\\\noindent{\\\\bf WN~J0901+6547:} This 38\\\\arcsec\\\\ large source is over-resolved in our VLA observations, and probably even misses flux in the NVSS, and is therefore not a real USS source.\\n\\n\\\\noindent{\\\\bf WN~J1012+3334:} The bend morphology and bright optical sources to the east indicate this object is probably located in a galaxy cluster.\\n\\n\\\\noindent{\\\\bf WN~J1101+3520:} The faint FIRST component 20\\\\arcsec\\\\ north of the brighter Southern component is not listed in the FIRST catalog, but is within 1\\\\arcsec\\\\ of a faint optical object. This might be the core of a 70\\\\arcsec\\\\ triple source.\\n\\n\\\\noindent{\\\\bf WN~J1152+3732:} The distorted radio morphology and bright, extended POSS identification suggest this source is located in a galaxy cluster.\\n\\n\\\\noindent{\\\\bf WN~J1232+4621:} This optically identified and diffuse radio source suggest this source is located in a galaxy cluster.\\n\\n\\\\noindent{\\\\bf WN~J1314+3515:} The diffuse radio source appears marginally detected on the POSS.\\n\\n\\\\noindent{\\\\bf WN~J1329+3046A,B, WN~J1330+3037, WN~J1332+3009 \\\\& WN~J1333+3037:} The noise in the FIRST image is almost ten times higher than average due to the proximity of the $S_{1400}$=15~Jy source 3C~286.\\n\\n\\\\noindent{\\\\bf WN~J1330+5344:} The difference with the NVSS position indicates that our VLA observations are not deep enough to detect a probable south-eastern component.\\n\\n\\\\noindent{\\\\bf WN~J1335+3222:} Although the source appears much like the hotspot of a larger source with the core 90\\\\arcsec\\\\ to the east, no other hotspot is detected in the FIRST within 5\\\\arcmin.\\n\\n\\\\noindent{\\\\bf WN~J1359+7446:} The extended POSS identification suggests this source is located in a galaxy cluster.\\n\\n\\\\noindent{\\\\bf WN~J1440+3707:} The equally bright galaxy 30\\\\arcsec\\\\ south of the POSS identification suggests that this source is located in a galaxy cluster.\\n\\n\\\\noindent{\\\\bf WN~J1509+5905:} The difference with the NVSS position indicates that our VLA observations are not deep enough to detect a probable western component.\\n\\n\\\\noindent{\\\\bf WN~J1628+3932:} This is the well studied galaxy NGC~6166 in the galaxy cluster Abell 2199 (\\\\eg \\\\cite{zab93}.\\n\\n\\\\noindent{\\\\bf WN~J1509+5905:} The difference with the NVSS position indicates that our VLA observations are not deep enough to detect a probable west-south-western component.\\n\\n\\\\noindent{\\\\bf WN~J1821+3601:} The source 35\\\\arcsec\\\\ south-west of the NVSS position is not detected in the NVSS. This is therefore not a real USS source because the NVSS flux density was underestimated.\\n\\n\\\\noindent{\\\\bf WN~J1832+5354:} The source 19\\\\arcsec\\\\ north-east of the NVSS position is not detected in the NVSS. This is therefore not a real USS source because the NVSS flux density was underestimated.\\n\\n\\\\noindent{\\\\bf WN~J1852+5711:} The extended POSS identification suggests this source is located in a galaxy cluster.\\n\\n\\\\noindent{\\\\bf WN~J2313+3842:} The extended POSS identification suggests this source is located in a galaxy cluster.\\n\\n\\\\noindent{\\\\bf TN~J0233+2349:} This is probably the north-western hotspot of a 35\\\\arcsec\\\\ source, with the south-eastern component barely detected in our VLA map. \\n\\n\\\\noindent{\\\\bf TN~J0309-2425:} We have classified this source as a 13\\\\arcsec\\\\ double, but the western component might also be the core of a 45\\\\arcsec\\\\ source, with the other hotspot around $\\\\alpha = 3^h9^m10^s, \\\\delta=-24\\\\arcdeg25\\\\arcmin50\\\\arcsec$.\\n\\n\\\\noindent{\\\\bf TN~J0349-1207:} The core-dominated structure is reminiscent of the red quasar WN~J0717+4611.\\n\\n\\\\noindent{\\\\bf TN~J0352-0355:} This is probably the south-western hotspot of a 30\\\\arcsec\\\\ source.\\n\\n\\\\noindent{\\\\bf TN~J0837-1053:} Given the 10\\\\arcsec\\\\ difference between the positions of the NVSS and diffuse VLA source, this is probably the northern component of a larger source.\\n\\n\\\\noindent{\\\\bf TN~J0408-2418:} This is the z=2.44 source MRC 0406-244 (\\\\cite{mcc96}). The bright object on the POSS is a foreground star to the north-east of the R=22.7 galaxy.\\n\\n\\\\noindent{\\\\bf TN~J0443-1212:} Using the higher resolution VLA image, we can identify this radio source with a faint object on the POSS.\\n\\n\\\\noindent{\\\\bf TN~J2106-2405:} This is the z=2.491 source MRC 2104-242 (\\\\cite{mcc96}). The identification is an R=22.7 object, not the star to the north-north-west of the NVSS position.\\n%---------------------------------------------------------- wnspeccurv\\n\\\\begin{figure}\\n\\\\psfig{file=ds1811f9.eps,width=9cm,angle=90}\\n\\\\caption[wnspeccurv]{Radio ``color-color'' plots for the WN sample. The abscissa is the $\\\\alpha_{325}^{1400}$ spectral index used to construct the sample. The ordinates are the low-frequency spectral indices determined from the 8C (38 MHz, \\\\cite{ree90}) or 6C (151 MHz, \\\\cite{hal93}) and the 325~MHz WENSS (left panel), and the high frequency spectral index determined between the 1.4~GHz NVSS and our 4.86~GHz VLA observations (right panel). The line in each panel indicates a straight power law spectrum. Note the unequal number of points on either side of these lines, indicating substantial spectral curvature. \\\\label{wnspeccurv}}\\n\\\\end{figure}\\n%______________________________________________________________\\n\\n\\\\subsection{Radio spectra and spectral curvature}\\n\\nWe have used the CATS database at the Special Astronomical Observatory (\\\\cite{ver97}) to search for all published radio measurements of the sources in our samples. In Appendix C, we show the radio spectra for all sources with flux density information for more than two frequencies (the $S_{4860}$ points from our VLA observations are also included). These figures show that most radio spectra have curved spectra, with flatter spectral indices below our selection frequencies, as has been seen in previous USS studies (see \\\\eg\\\\ \\\\cite{rot94}, \\\\cite{blu98}). \\n\\nThis low frequency flattening and high frequency steepening is obvious in the radio 'color-color diagrams' of the WN sample (Fig. \\\\ref{wnspeccurv}). The median spectral index at low frequencies ($\\\\nu < 325$~MHz) is $-1.16$, while the median $\\\\bar{\\\\alpha}_{325}^{1400} = -1.38$. At higher frequencies ($\\\\nu > 1400$~MHz), the steepening continues to a median $\\\\bar{\\\\alpha}_{1400}^{4850} = -1.44$. Note that the real value of the latter is probably even steeper, as 30\\\\% of the WN sources were not detected in our 4.86~GHz VLA observations, and may therefore have even more steepened high-frequency spectral indices.\\n\\n\\\\subsection{Radio source properties}\\n\\\\subsubsection{Radio source structure and angular size}\\n\\nIn Table 5, we give the distribution of the radio structures of the 410 USS sources for which we have good radio-maps. At first sight, all three our samples have basically the same percentage of resolved sources, but the similar value for the MP sample is misleading, as it was observed at much lower resolution.\\n\\n\\\\begin{table}\\n\\\\centerline{\\\\bf Table 5: Radio Structure Distribution}\\n\\\\tiny\\n\\\\begin{center}\\n\\\\begin{tabular}{lrrrr}\\n\\\\\\\\\\n & \\\\multicolumn{4}{c}{USS Samples} \\\\\\\\\\n\\\\cline{2-5} \\\\\\\\\\nMorphology & WN$\\\\qquad$ & TN$\\\\qquad$ & MP$\\\\qquad$ & Combined$\\\\quad$\\\\\\\\\\n\\\\hline\\nSingle & 157 (56$\\\\pm$4\\\\%) & 43 (48$\\\\pm$7\\\\%) & 23 (56$\\\\pm$12\\\\%) & 223 (54$\\\\pm$4\\\\%) \\\\\\\\\\nDouble & 81 (29$\\\\pm$3\\\\%) & 28 (31$\\\\pm$6\\\\%) & 16 (39$\\\\pm$10\\\\%) & 125 (31$\\\\pm$3\\\\%) \\\\\\\\\\nTriple & 22 ( 8$\\\\pm$2\\\\%) & 9 (10$\\\\pm$3\\\\%) & 0 ( 0$\\\\pm$ 0\\\\%) & 31 ( 8$\\\\pm$1\\\\%) \\\\\\\\\\nMultiple & 2 ( 1$\\\\pm$1\\\\%) & 4 ( 5$\\\\pm$2\\\\%) & 0 ( 0$\\\\pm$ 0\\\\%) & 6 ( 1$\\\\pm$1\\\\%) \\\\\\\\\\nDiffuse & 18 ( 6$\\\\pm$2\\\\%) & 5 ( 6$\\\\pm$3\\\\%) & 2 ( 5$\\\\pm$ 3\\\\%) & 25 ( 6$\\\\pm$1\\\\%) \\\\\\\\\\n\\\\hline\\n\\\\# Observed & 280 & 89 & 41 & 410 \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\\\end{center}\\n\\\\end{table}\\n\\n%---------------------------------------------------------- slas\\n\\\\begin{figure}\\n\\\\psfig{file=ds1811f10.eps,width=9cm}\\n\\\\caption[slas]{Median angular size for the flux density limited, spectrally unbiased WSRT samples of \\\\cite{oor88} (open triangles), and for our combined USS samples (filled squares). The sources have been binned in equal number bins, and errors represent the 35\\\\% and 65\\\\% levels of the distribution. Note that our USS selection does not affect the value of the median, and that our USS samples also exclude sources that fall below the break at $S_{1400} \\\\lesssim 10$~mJy. \\\\label{slas}}\\n\\\\end{figure}\\n%______________________________________________________________\\n\\nOur results are different from the USS sample of R\\\\\\\"ottgering \\\\etal\\\\ (1994), which contains only 18\\\\% unresolved sources at comparable resolution (1\\\\farcs5). To check if this effect is due to the fainter sources in our sample, we compared our sample with the deep high resolution VLA observations of spectrally unbiased sources (\\\\cite{oor88}; \\\\cite{col85}).\\nThe resolution of our observations is significantly better than the median angular size for $S_{1400} > 1$~mJy sources, allowing us to accurately determine the median angular sizes in our samples.\\nWe find that our USS sources have a constant median angular size of $\\\\sim6$\\\\arcsec\\\\ between 10~mJy and 1~Jy (Fig. \\\\ref{slas}). This is indistinguishable from the results from samples without spectral index selection. It indicates that our USS selection of sources with $\\\\alpha < -1.3$ and $\\\\Theta < 1\\\\arcmin$ does not bias the angular size distribution in the resulting sample. The 'downturn' in angular sizes that occurs at $\\\\sim$1~mJy is probably due to a different radio source population, which consist of lower redshift sources in spiral galaxies (see \\\\eg, \\\\cite{col85}, \\\\cite{oor87}, \\\\cite{ben93}). By selecting only sources with $S_{1400} > 10$~mJy, we have avoided ``contamination'' of our sample by these foreground sources.\\n\\nWe have searched for further correlations between spectral index or spectral curvatures and angular size or flux density, but found no significant results, except for a trend for more extended sources to have lower than expected 4.86~GHz flux densities, but this effect can be explained by missing flux at large scales in our VLA observations.\\n\\n\\\\subsection{Identifications}\\n\\\\subsubsection{POSS}\\nWe have searched for optical identifications of our USS sources on the digitized POSS-I. We used the likelihood ratio identification criterion as described by \\\\eg de Ruiter \\\\etal\\\\ (1977). In short, this criterion compares the probability that a radio and optical source with a certain positional difference are really associated with the probability that this positional difference is due to confusion with a field object (mostly a foreground star), thereby incorporating positional uncertainties in both radio and optical positions. The ratio of these probabilities is expressed as the likelihood ratio $LR$. \\nIn the calculation, we have assumed a density of POSS objects $\\\\rho = 4 \\\\times 10^{-4}$ \\\\arcsec$^{-2}$, independent of galactic latitude $b$. \\nWe have adopted a likelihood ratio cutoff \\\\Lh=1.0, slightly lower than the values used by de Ruiter \\\\etal\\\\ (1977) and R\\\\\\\"ottgering \\\\etal\\\\ (1994). We list sources with $LR >$ 1.0 for our USS samples in Tables A.4 to A.6. We have included four WN sources (WN~J0704+6318, WN~J1259+3121, WN~J1628+3932 and WN~J2313+3842), two TN sources (TN~J0510-1838 and TN~J1521+0741) and four MP sources (MP~J0003-3556, MP~J1921-5431, MP~J1943-4030 and MP~J2357-3445) as identifications because both their optical and radio morphologies are diffuse and overlapping, making it impossible to measure a common radio and optical component, while they are very likely to be associated.\\n\\n%---------------------------------------------------------- idfraction\\n\\\\begin{figure}\\n\\\\psfig{file=ds1811f11.eps,width=9cm}\\n\\\\caption[idfraction]{Identification fraction on the POSS as a function of spectral index for the combined WN and TN sample. Note the absence of a further decrease in the identification fraction with steepening spectral index. \\\\label{idfraction}}\\n\\\\end{figure}\\n%______________________________________________________________\\n\\nFigure \\\\ref{idfraction} shows the identification fraction of USS sources on the POSS ($R \\\\lesssim 20$). Because the distributions for the WN and TN are very similar, we have combined both samples to calculate the identification fraction. Unlike the results for 4C USS (\\\\cite{tie79,blu79}), we do not detect a decrease of the identification fraction with steepening spectral index\\\\footnote{In the Westerbork faint USS (\\\\cite{wie92}) or the USS sample from R\\\\\\\"ottgering \\\\etal\\\\ (1994), there is also a decrease in the identification fraction, even at limiting magnitudes of $R=22.5$ and $R=23.7$, indicating that this trend continues out to fainter magnitudes and radio fluxes}. We interpret the constant $\\\\sim$15\\\\% identification fraction from our sample as a combined population of foreground objects, primarily consisting of clusters (see next section). Our extremely steep spectral index criterion would then selected only radio galaxies too distant to be detected on the POSS ($R \\\\simgt 20.0$).\\n\\n\\\\subsubsection{Literature}\\nUsing the NASA Extragalactic Database (NED), the SIMBAD database and the W$^3$Browse at the High Energy Astrophysics Science Archive Research Center, we have searched for known optical and X-ray identifications of sources in our samples (see appendices A.7 to A.9). Of the bright optical ($R \\\\lesssim 20$) identifications, only one source is a known as a K0-star, three (TN~J0055$+$2624, TN~J0102$-$2152, and TN~J1521$+$0742) are ``Relic radio galaxies'' (\\\\cite{kom94}, \\\\cite{gio99}), while all others are known galaxy clusters. \\n\\nAll optical cluster identifications, except MP~J1943-4030, are also detected in the ROSAT All-Sky survey Bright Source Catalogue (RASS-BSC; \\\\cite{vog99}). Conversely, of the 23 X-ray sources, seven are known galaxy clusters, and three known galaxies. The remaining 13 sources are good galaxy cluster candidates because they either show a clear over-density of galaxies on the POSS (eight sources), or they have low X-ray count rates ($<$ 0.02 counts s$^{-1}$), suggesting that these might be more distant galaxy clusters too faint to be detected on the POSS. We conclude that probably $>$3\\\\% of our USS sources are associated with galaxy clusters, and that the combined USS + X-ray selection is an efficient (up to 85\\\\%) selection technique to find galaxy clusters\\\\footnote{In the RASS-BSC, only 14\\\\% of the extra-galactic sources are identified with galaxy clusters (\\\\cite{vog99}).}.\\n\\nThree of our USS sources (WN~J2313+4253, TN~J0630-2834 and TN~J1136+1551) are previously known pulsars (\\\\cite{kap98}). It is worth noting that two out of nine sources in our USS samples with $\\\\alpha < -2$ are known pulsars. Because Lorimer \\\\etal\\\\ (1995) \\\\nocite{lor95} found the median spectral index of pulsars to be $\\\\sim -1.6$, we examined the distribution of spectral indices as a function of Galactic latitude. In figure \\\\ref{pulsargb}, we plot the percentage of $\\\\alpha_{325}^{1400} < -1.60$ pulsar candidates as a function of Galactic latitude. The four times higher density near the Galactic plane strongly suggests that the majority of these $\\\\alpha_{325}^{1400} < -1.60$ sources are indeed pulsars, which are confined to our Galaxy. A sample of such $\\\\alpha_{325}^{1400} < -1.60$ sources at $|b|<15$\\\\degr\\\\ would be an efficient pulsar search method.\\n\\n%---------------------------------------------------------- pulsargb\\n\\\\begin{figure}\\n\\\\psfig{file=ds1811f12.eps,width=9cm}\\n\\\\caption[pulsargb]{Percentage of $\\\\alpha_{325}^{1400} < -1.60$ radio sources from a WENSS--NVSS correlation as a function of Galactic latitude. Note the clear peak near the Galactic plane, indicating that these $\\\\alpha_{325}^{1400} < -1.60$ objects might well be Galactic pulsars. \\\\label{pulsargb}}\\n\\\\end{figure}\\n%______________________________________________________________\\n\\nWe also note that no known quasars are present in our sample. Preliminary results from our optical spectroscopy campaign (De Breuck \\\\etal\\\\ 1998b, 2000) indicate that $\\\\sim$10\\\\% of our sample are quasars. We interpret this lack of previously known quasars are a selection bias in quasar samples against USS sources.\\n\\nAt $R \\\\simgt 20$, all five USS sources with known redshift are HzRGs, indicating a selection of sources without detections on the POSS strongly increases our chances of finding HzRGs.\\n\\n\\\\section{Conclusions}\\nWe have constructed three spatially separated samples of USS sources containing a total of 669 objects. High-resolution radio observations of more than half of these show that the median size is $\\\\sim$6\\\\arcsec, independent of 1.4 GHz flux density, which is consistent with results of similar resolution surveys of samples without spectral index selection. The absence of a downturn in angular size at the lowest fluxes indicates that we do not include significant numbers of spiral galaxies in our sample. A USS sample fainter than ours would therefore include more of these foreground sources, and be less efficient to find HzRGs. \\n\\nThe identification fraction on the POSS is $\\\\sim$15\\\\%, with no clear dependence on spectral index, indicating that the HzRGs in the sample are all too distant to be detected, and the POSS detections consist of different classes of objects. A correlation of our USS samples with X-ray catalogs showed that at least 85\\\\% of the X-ray identifications seem to be galaxy clusters known from the literature or by inspection of the POSS. We conclude that (1) the majority of the 'non HzRG' USS sources in our sample are clusters, and (2) the combined selection of USS and X-ray sources is an extremely efficient technique to select galaxy clusters.\\n\\nThe above results indicate that up to 85\\\\% of our USS sample might be HzRGs. To identify these objects, we have started an intensive program of R- and K-band imaging on 3--10m class telescopes.\\nInitial results from optical spectroscopy indicate that 2/3 are indeed $z>2$ radio galaxies (\\\\cite{deb98a}), and K-band imaging of optically undetected ($R > 25$) sources (see \\\\eg, \\\\cite{wvb99a}) has already lead to the discovery of the first radio galaxy at $z>5$ (\\\\cite{wvb99b}). \\n\\n\\\\begin{acknowledgements}\\n\\nWe are grateful for the excellent help provided by the staff of the\\nVLA and ATCA observatories, with special thanks to Chris Carilli and\\nGreg Taylor (NRAO), and Ray Norris and Kate Brooks (ATNF) for help in\\nwith observation planning and data reduction. We thank Hien ``Napkin''\\nTran for his comments on the manuscript. The VLA is a facility of the\\nNational Radio Astronomy Observatory, which is operated by Associated\\nUniversities Inc. under cooperative agreement with the National\\nScience Foundation. The Australia Telescope is funded by the\\nCommonwealth of Australia for operation as a National Facility managed\\nby CSIRO. The authors made use of the database CATS (\\\\cite{ver97}) of\\nthe Special Astrophysical Observatory, the NASA/IPAC Extragalactic\\nDatabase (NED) which is operated by the Jet Propulsion Laboratory,\\nCalifornia Institute of Technology, under contract with the National\\nAeronautics and Space Administration, and the High Energy Astrophysics\\nScience Archive Research Center Online Service, provided by the\\nNASA/Goddard Space Flight Center. Work performed at the Lawrence\\nLivermore National Laboratory is supported by the DOE under contract\\nW7405-ENG-48.\\n\\n\\\\end{acknowledgements}\\n\\n\\\\begin{thebibliography}{}\\n\\\\bibitem[Abell \\\\etal\\\\ 1989]{abe89} Abell, G. O., Corwin, H. G. Jr., \\\\& Olowin, R. 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S. 1993, \\\\aj, 106, 1273\\n\\\\end{thebibliography}\\n\\n\\\\appendix\\n\\\\section{Source Lists}\\n\\\\include{wntable}\\n\\\\include{tnmptable}\\n\\n\\\\begin{table}\\n\\\\footnotesize\\n\\\\centerline{\\\\bf Table A.4: WN POSS identifications}\\n\\\\begin{tabular}{rrrrr}\\nName & $S_{1400}$ & $\\\\alpha_{325}^{1400}$ & LAS & LR$^a$ \\\\\\\\\\n & mJy & & \\\\arcsec & \\\\\\\\\\n\\\\hline\\nWN J0029$+$3439 & 40.9 & $-$1.34 & 12.8 & 4.2 \\\\\\\\\\nWN J0121$+$4305 & 50.8 & $-$1.39 & \\\\nodata & 7.1 \\\\\\\\\\nWN J0315$+$3757 & 13.3 & $-$1.35 & 1.7 & 14.8 \\\\\\\\\\nWN J0559$+$6926 & 12.9 & $-$1.31 & 0.3 & 4.6 \\\\\\\\\\nWN J0641$+$4325 & 15.6 & $-$1.57 & \\\\nodata & 195.6 \\\\\\\\\\nWN J0725$+$4123 & 35.5 & $-$1.39 & 8.3 & 183.0 \\\\\\\\\\nWN J0756$+$5010 & 29.9 & $-$1.31 & 1.7 & 127.3 \\\\\\\\\\nWN J0830$+$3018 & 13.9 & $-$1.41 & 3.5 & 27.3 \\\\\\\\\\nWN J0835$+$3439 & 19.1 & $-$1.38 & 58.0 & 24.6 \\\\\\\\\\nWN J0923$+$4602 & 12.1 & $-$1.49 & 21.6 & 17.0 \\\\\\\\\\nWN J0952$+$5153 & 16.1 & $-$1.76 & 2.7 & 194.1 \\\\\\\\\\nWN J0955$+$6023 & 10.9 & $-$1.54 & 3.1 & 1.0 \\\\\\\\\\nWN J1014$+$7407 & 21.8 & $-$1.41 & 2.2 & 147.7 \\\\\\\\\\nWN J1026$+$2943 & 12.0 & $-$1.31 & 11.9 & 136.5 \\\\\\\\\\nWN J1030$+$5415 & 29.2 & $-$1.39 & 6.1 & 16.4 \\\\\\\\\\nWN J1052$+$4826 & 154.2 & $-$1.31 & 10.0 & 38.1 \\\\\\\\\\nWN J1124$+$3228 & 38.9 & $-$1.31 & 5.7 & 101.2 \\\\\\\\\\nWN J1130$+$4911 & 18.9 & $-$1.34 & 37.0 & 18.9 \\\\\\\\\\nWN J1141$+$6924 & 11.8 & $-$1.32 & \\\\nodata & 1.4 \\\\\\\\\\nWN J1148$+$5116 & 20.5 & $-$1.35 & 6.7 & 1.0 \\\\\\\\\\nWN J1152$+$3732 & 17.1 & $-$2.18 & 15.0 & 159.9 \\\\\\\\\\nWN J1232$+$4621 & 19.8 & $-$1.30 & 12.5 & 42.9 \\\\\\\\\\nWN J1258$+$5041 & 28.8 & $-$1.42 & 44.9 & 3.7 \\\\\\\\\\nWN J1259$+$3121 & 34.0 & $-$1.41 & 20.6 & 0.0 \\\\\\\\\\nWN J1330$+$6505 & 10.5 & $-$1.34 & 1.8 & 21.5 \\\\\\\\\\nWN J1353$+$3336 & 15.9 & $-$1.31 & \\\\nodata & 3.3 \\\\\\\\\\nWN J1400$+$4348 & 20.2 & $-$1.49 & 6.4 & 29.2 \\\\\\\\\\nWN J1403$+$3109 & 45.7 & $-$1.35 & 11.0 & 148.5 \\\\\\\\\\nWN J1410$+$4615 & 14.2 & $-$1.36 & 4.4 & 42.5 \\\\\\\\\\nWN J1440$+$3707 & 16.7 & $-$1.76 & 7.4 & 182.0 \\\\\\\\\\nWN J1459$+$4947 & 18.7 & $-$1.53 & 3.0 & 47.2 \\\\\\\\\\nWN J1558$+$7028 & 15.7 & $-$1.36 & 2.1 & 2.8 \\\\\\\\\\nWN J1624$+$4202 & 11.0 & $-$1.31 & 24.4 & 182.2 \\\\\\\\\\nWN J1628$+$3932 & 3680.7 & $-$1.36 & 48.8 & 0.0 \\\\\\\\\\nWN J1717$+$3828 & 35.8 & $-$1.60 & 33.6 & 141.4 \\\\\\\\\\nWN J1752$+$2949 & 16.9 & $-$1.42 & 3.2 & 3.4 \\\\\\\\\\nWN J1801$+$3336 & 11.6 & $-$1.69 & 2.5 & 1.5 \\\\\\\\\\nWN J1815$+$3656 & 17.6 & $-$1.34 & 1.6 & 195.0 \\\\\\\\\\nWN J1819$+$6213 & 12.7 & $-$1.45 & 1.6 & 122.9 \\\\\\\\\\nWN J1852$+$5711 & 53.4 & $-$1.36 & \\\\nodata & 145.4 \\\\\\\\\\nWN J1927$+$6436 & 80.3 & $-$1.44 & 20.1 & 6.2 \\\\\\\\\\nWN J1944$+$6552 & 147.2 & $-$1.53 & 1.8 & 147.5 \\\\\\\\\\nWN J2146$+$3330 & 10.8 & $-$1.56 & \\\\nodata & 4.6 \\\\\\\\\\nWN J2147$+$3137 & 25.4 & $-$1.46 & \\\\nodata & 31.9 \\\\\\\\\\nWN J2313$+$3842 & 11.3 & $-$1.50 & \\\\nodata & 0.0 \\\\\\\\\\nWN J2313$+$4053 & 40.2 & $-$1.42 & 1.5 & 36.4 \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\n$^a$ Likelihood Ratio, see text\\n\\\\vspace{1cm}\\n\\\\end{table}\\n\\n\\\\begin{table}\\n\\\\footnotesize\\n\\\\centerline{\\\\bf Table A.5: TN POSS identifications}\\n\\\\begin{tabular}{rrrrr}\\nName & $S_{1400}$ & $\\\\alpha_{365}^{1400}$ & LAS & LR$^a$ \\\\\\\\\\n & mJy & & \\\\arcsec & \\\\\\\\\\n\\\\hline\\nTN J0244$+$0327 & 84.8 & $-$1.38 & \\\\nodata & 6.9 \\\\\\\\\\nTN J0245$+$2700 & 54.0 & $-$1.47 & \\\\nodata & 30.5 \\\\\\\\\\nTN J0250$+$0130 & 39.1 & $-$1.45 & \\\\nodata & 14.7 \\\\\\\\\\nTN J0256$-$2717 & 177.9 & $-$1.32 & \\\\nodata & 126.6 \\\\\\\\\\nTN J0301$+$0155 & 402.7 & $-$1.70 & \\\\nodata & 21.3 \\\\\\\\\\nTN J0433$+$0717 & 33.1 & $-$1.44 & \\\\nodata & 29.9 \\\\\\\\\\nTN J0443$-$1212 & 56.8 & $-$1.47 & 20.2 & 162.1 \\\\\\\\\\nTN J0510$-$1838 & 641.3 & $-$1.76 & 36.1 & 0.0 \\\\\\\\\\nTN J0729$+$2436 & 68.9 & $-$2.03 & 19.4 & 129.0 \\\\\\\\\\nTN J0812$+$0915 & 43.4 & $-$1.38 & \\\\nodata & 37.7 \\\\\\\\\\nTN J0818$-$0741 & 59.3 & $-$1.38 & \\\\nodata & 96.5 \\\\\\\\\\nTN J0958$-$1103 & 70.6 & $-$1.35 & \\\\nodata & 181.8 \\\\\\\\\\nTN J1043$+$2404 & 52.0 & $-$1.59 & 3.7 & 167.8 \\\\\\\\\\nTN J1053$-$1518 & 63.7 & $-$1.33 & \\\\nodata & 1.8 \\\\\\\\\\nTN J1117$-$1409 & 134.5 & $-$1.31 & \\\\nodata & 128.0 \\\\\\\\\\nTN J1220$+$0604 & 65.1 & $-$1.50 & \\\\nodata & 189.4 \\\\\\\\\\nTN J1239$+$1005 & 79.3 & $-$1.75 & \\\\nodata & 180.7 \\\\\\\\\\nTN J1245$-$1127 & 88.0 & $-$1.32 & \\\\nodata & 146.1 \\\\\\\\\\nTN J1326$-$2330 & 83.2 & $-$1.37 & \\\\nodata & 190.1 \\\\\\\\\\nTN J1408$-$0855 & 114.3 & $-$1.34 & \\\\nodata & 160.9 \\\\\\\\\\nTN J1418$-$2256 & 82.0 & $-$1.38 & 7.6 & 85.4 \\\\\\\\\\nTN J1513$-$2417 & 83.6 & $-$1.34 & \\\\nodata & 2.5 \\\\\\\\\\nTN J1521$+$0741 & 105.6 & $-$2.10 & \\\\nodata & 0.0 \\\\\\\\\\nTN J1531$-$3234 & 80.6 & $-$1.39 & 4.8 & 172.5 \\\\\\\\\\nTN J1547$-$2218 & 72.4 & $-$1.32 & \\\\nodata & 7.1 \\\\\\\\\\nTN J1556$-$2759 & 66.4 & $-$1.65 & \\\\nodata & 9.2 \\\\\\\\\\nTN J1628$+$1604 & 55.5 & $-$1.77 & \\\\nodata & 153.7 \\\\\\\\\\nTN J1646$-$1328 & 102.5 & $-$1.32 & \\\\nodata & 119.7 \\\\\\\\\\nTN J1701$+$0252 & 57.1 & $-$1.36 & \\\\nodata & 19.4 \\\\\\\\\\nTN J1707$-$1120 & 54.2 & $-$1.53 & \\\\nodata & 85.5 \\\\\\\\\\nTN J1710$-$0826 & 69.2 & $-$1.38 & \\\\nodata & 8.8 \\\\\\\\\\nTN J1953$-$0541 & 59.0 & $-$1.56 & \\\\nodata & 71.3 \\\\\\\\\\nTN J2028$+$0811 & 74.8 & $-$1.34 & \\\\nodata & 33.1 \\\\\\\\\\nTN J2155$-$2109 & 77.2 & $-$1.31 & \\\\nodata & 184.6 \\\\\\\\\\nTN J2335$+$0634 & 84.3 & $-$1.33 & \\\\nodata & 189.2 \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\n$^a$ Likelihood Ratio, see text\\n\\\\vspace{1cm}\\n\\\\end{table}\\n\\n\\\\begin{table}\\n\\\\footnotesize\\n\\\\centerline{\\\\bf Table A.6: MP UKST identifications}\\n\\\\begin{tabular}{rrrrr}\\nName & $S_{408}$ & $\\\\alpha_{408}^{4850}$ & LAS & LR$^a$ \\\\\\\\\\n & mJy & & \\\\arcsec & \\\\\\\\\\n\\\\hline\\nMP J0003$-$3556 & 2440 & $-$1.28 & \\\\nodata & 0.0 \\\\\\\\\\nMP J0103$-$3225 & 2290 & $-$1.29 & \\\\nodata & 88.1 \\\\\\\\\\nMP J0618$-$7340 & 750 & $-$1.37 & \\\\nodata & 7.5 \\\\\\\\\\nMP J1033$-$3418 & 5590 & $-$1.23 & \\\\nodata & 81.7 \\\\\\\\\\nMP J1250$-$4026 & 1350 & $-$1.24 & 7.4 & 131.0 \\\\\\\\\\nMP J1921$-$5431 & 4590 & $-$1.71 & \\\\nodata & 0.0 \\\\\\\\\\nMP J1943$-$4030 & 4400 & $-$1.36 & \\\\nodata & 0.0 \\\\\\\\\\nMP J2313$-$4243 & 1390 & $-$1.28 & \\\\nodata & 95.5 \\\\\\\\\\nMP J2357$-$3445 & 8700 & $-$1.74 & \\\\nodata & 0.0 \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\n$^a$ Likelihood Ratio, see text\\n\\\\vspace{1cm}\\n\\\\end{table}\\n\\n\\\\begin{table*}\\n\\\\centerline{\\\\bf Table A.7: WN identifications from the literature}\\n\\\\begin{tabular}{rrrrrr}\\nName & $z$ & $R$[mag] & $F_X^a$ & Identification & Reference \\\\\\\\\\n\\\\hline\\nWN J0633$+$4653 & \\\\nodata & 23.6 & \\\\nodata & 4C +46.12 & \\\\cite{cha96a} \\\\\\\\\\nWN J0648$+$4309 & \\\\nodata & 23.0 & \\\\nodata & B3 0644+432 & \\\\cite{wie92} \\\\\\\\\\nWN J0658$+$4444 & \\\\nodata & 23.4 & \\\\nodata & B3 0654+448 & \\\\cite{wie92} \\\\\\\\\\nWN J0717$+$4611 & 1.462 & 21.6 & \\\\nodata & B3 0714+462 & \\\\cite{deb98b} \\\\\\\\\\nWN J0725$+$4123 & \\\\nodata & \\\\nodata & 0.1137 & 1RXS J072600.0+4 & \\\\cite{vog99} \\\\\\\\\\nWN J0923$+$4602 & \\\\nodata & \\\\nodata & 0.0242 & 1WGA J0923.1+460 & \\\\cite{whi94}\\\\\\\\\\nWN J0952$+$5153 & 0.214 & \\\\nodata & 0.2413 & ZwCl 0949.6+5207 & \\\\cite{vog99} \\\\\\\\\\nWN J1148$+$5116 & \\\\nodata & \\\\nodata & 0.0508 & 1RXS J114802.7+5 & \\\\cite{vog99} \\\\\\\\\\nWN J1152$+$3732 & \\\\nodata & \\\\nodata & 0.0192 & 1WGA J1152.5+373 & \\\\cite{whi94} \\\\\\\\\\nWN J1259$+$3121 & \\\\nodata & 16.2 & \\\\nodata & NGP9 F323-0140639 & \\\\cite{ode96} \\\\\\\\\\nWN J1332$+$3009 & \\\\nodata & 19.8 & \\\\nodata & NGP9 F324-0235590 & \\\\cite{ode96} \\\\\\\\\\nWN J1352$+$4259 & \\\\nodata & 21.7 & \\\\nodata & 4C +43.31 & \\\\cite{vig89} \\\\\\\\\\nWN J1359$+$7447 & \\\\nodata & \\\\nodata & 0.07485 & 1RXS J135916.0+7 & \\\\cite{vog99} \\\\\\\\\\nWN J1400$+$4348 & \\\\nodata & 8.2 & & HD122441 & SIMBAD \\\\\\\\\\nWN J1410$+$4615 & \\\\nodata & \\\\nodata & & SHK 010 & \\\\cite{sha73} \\\\\\\\\\nWN J1436$+$6319 & 4.261 & 24.1 & \\\\nodata & 4C +63.20 & \\\\cite{lac94} \\\\\\\\\\nWN J1440$+$3707 & \\\\nodata & \\\\nodata & 0.07944 & 1RXS J144005.4+3 & \\\\cite{vog99} \\\\\\\\\\nWN J1628$+$3932 & 0.031 & 13.1 & 4.5 & NGC 6166 & \\\\cite{zab93} \\\\\\\\\\nWN J1736$+$6502 & \\\\nodata & 22.2 & \\\\nodata & 8C 1736+650 & \\\\cite{lac93} \\\\\\\\\\nWN J1829$+$6913 & \\\\nodata & \\\\nodata & 0.05765 & 1RXS J182903.8+6 & \\\\cite{vog99} \\\\\\\\\\nWN J1852$+$5711 & \\\\nodata & \\\\nodata & 0.1466 & 1RXS J185209.4+5 & \\\\cite{vog99} \\\\\\\\\\nWN J1944$+$6552 & \\\\nodata & \\\\nodata & 0.1118 & 1RXS J194423.1+6 & \\\\cite{vog99} \\\\\\\\\\nWN J2319$+$4251 & \\\\nodata & \\\\nodata & 0.1255 & 1RXS J231947.4+4 & \\\\cite{vog99} \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\n$^a$F$_X$ is the number of X-ray counts s$^{-1}$ as listed in the cited catalogs.\\n\\n\\\\vspace{1cm}\\n\\\\end{table*}\\n\\n\\\\begin{table*}\\n\\\\centerline{\\\\bf Table A.8: TN identifications from the literature}\\n\\\\begin{tabular}{rrrrrr}\\nName & $z$ & $R$[mag] & $F_X^a$ & Identification & Reference \\\\\\\\\\n\\\\hline\\nTN J0055$+$2624 & 0.1971 & \\\\nodata & \\\\nodata & ABELL 85 & \\\\cite{gio99} \\\\\\\\\\nTN J0102$-$2152 & 0.0604 & \\\\nodata & \\\\nodata & ABELL 133 & \\\\cite{kom94} \\\\\\\\\\nTN J0245$+$2700 & \\\\nodata & \\\\nodata & 0.0782 & 1RXS J024521.0+2 & \\\\cite{bad98} \\\\\\\\\\nTN J0256$-$2717 & 0.480 & 19.2 & \\\\nodata & MRC 0254-27 & \\\\cite{mcc96} \\\\\\\\\\nTN J0301$+$0155 & 0.170 & \\\\nodata & 0.2053 & ZwCl 0258.9+0142 & \\\\cite{cra95} \\\\\\\\\\nTN J0408$-$2418 & 2.440 & 22.7 & \\\\nodata & MRC 0406-244 & \\\\cite{mcc96} \\\\\\\\\\nTN J0510$-$1838 & \\\\nodata & 19.5 & 0.00314 & 1RXS J051032.4-1 & \\\\cite{vog99} \\\\\\\\\\nTN J0630$-$2834 & \\\\nodata & \\\\nodata & 0.00314 & 1WGA J0630.8-283 & \\\\cite{whi94} \\\\\\\\\\nTN J0729$+$2436 & \\\\nodata & \\\\nodata & 0.1752 & 1RXS J072927.4+2 & \\\\cite{vog99} \\\\\\\\\\nTN J0936$-$2243 & 1.339 & 23.0 & \\\\nodata & 3C 222 & \\\\cite{hec94} \\\\\\\\\\nTN J0958$-$1103 & 0.153 & \\\\nodata & 1.64 & ABELL 0907 & \\\\cite{mcc96} \\\\\\\\\\nTN J1521$+$0742 & 0.045 & 14.5 & 1.64 & NGC 5920 & \\\\cite{kom94} \\\\\\\\\\nTN J2106$-$2405 & 2.491 & 22.7 & \\\\nodata & MRC 2104-242 & \\\\cite{mcc96} \\\\\\\\\\nTN J2239$-$0429 & \\\\nodata & 18.8 & \\\\nodata & 4C -04.85 & \\\\cite{rot95} \\\\\\\\\\nTN J2320$+$1222 & \\\\nodata & 22.9 & \\\\nodata & MRC 2317+120 & \\\\cite{rot95} \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\n$^a$F$_X$ is the number of X-ray counts s$^{-1}$ as listed in the cited catalogs.\\n\\n\\\\vspace{1cm}\\n\\\\end{table*}\\n\\n\\\\begin{table*}\\n\\\\centerline{\\\\bf Table A.9: MP identifications from the literature}\\n\\\\begin{tabular}{rrrrrr}\\nName & $z$ & $R$[mag] & $F_X^a$ & Identification & Reference \\\\\\\\\\n\\\\hline\\nMP J0003$-$3556 & 0.0497 & 13.2 & 0.5206 & ABELL 2717 & \\\\cite{col95} \\\\\\\\\\nMP J0103$-$3225 & \\\\nodata & 19.0 & & IRAS F01009-3241 & \\\\cite{con95} \\\\\\\\\\nMP J1250$-$4026 & \\\\nodata & \\\\nodata & 0.000595 & 1RXP J125006-402 & \\\\cite{vog99} \\\\\\\\\\nMP J1943$-$4030 & \\\\nodata & 17.3 & & ABELL 3646 & \\\\cite{abe89} \\\\\\\\\\nMP J2313$-$4243 & 0.0564 & 14.6 & 2.024 & ABELL S1101 & \\\\cite{sto91} \\\\\\\\\\nMP J2357$-$3445 & 0.0490 & 13.7 & 2.27 & ABELL 4059 & \\\\cite{pos95} \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\n$^a$F$_X$ is the number of X-ray counts s$^{-1}$ as listed in the cited catalogs.\\n\\n\\\\end{table*}\\n\\n\\\\clearpage\\n\\n\\\\section{Radio Maps}\\n\\\\subsection{VLA Maps of the WN Sample}\\n\\n\\\\small{VLA maps of the WN sample. The contour scheme is a geometric progression in $\\\\sqrt 2$, which implies a factor 2 change in surface brightness every 2 contours. The first contour level, indicated above each plot, is at $3\\\\sigma_{rms}$, where $\\\\sigma_{rms}$ is the rms noise determined around the sources. The restoring beams are indicated in the lower left corner of the plots. Two maps are given for each source, one showing a 6\\\\arcmin\\\\ field of view to show possible related components, and a smaller blow-up of the source to show its morphology. The open cross indicates the NVSS position. Sources identified on the POSS have been marked in the top right corner. \\\\label{wnvla}}\\n\\n\\\\subsection{FIRST Maps of the WN Sample}\\n\\n\\\\small{FIRST maps of the WN sample.Contours are as in section \\\\ref{wnvla} \\\\label{wnfirst}}\\n\\n\\\\subsection{VLA Maps of the TN Sample}\\n\\n\\\\small{VLA maps of the TN sample. Contours are as in section \\\\ref{wnvla} \\\\label{tnvla}}\\n \\n\\\\subsection{FIRST Maps of the TN Sample}\\n\\n\\\\small{FIRST maps of the TN sample. Contours are as in section \\\\ref{wnvla}. \\\\label{tnfirst}}\\n\\n\\\\subsection{ATCA Maps of the TN Sample}\\n\\n\\\\small{ATCA maps of the TN sample. Contours are as in section \\\\ref{wnvla}. \\\\label{tnatca}}\\n\\n\\\\subsection{ATCA Maps of the MP Sample}\\n\\n\\\\small{ATCA maps of the MP sample. Contours are as in section \\\\ref{wnvla}. \\\\label{mpatca}}\\n\\n\\\\section{Radio Spectra}\\n\\\\subsection{Radio Spectra for the WN Sample}\\n\\n\\\\small{Radio spectra of the WN sample using data from the literature. The two connected flux points indicate the spectral index used to select the source in the USS sample. Note the steeper spectra with higher frequency in most objects. \\\\label{wnradiospectra}}\\n\\n\\\\subsection{Radio Spectra for the TN Sample}\\n\\n\\\\small{Radio spectra of the TN sample using data from the literature. The two connected flux points indicate the spectral index used to select the source in the USS sample. Note the steeper spectra with higher frequency in most objects. \\\\label{tnradiospectra}}\\n\\n\\\\subsection{Radio Spectra for the MP Sample}\\n\\n\\\\small{Radio spectra of the MP sample using data from the literature and our ATCA observations (diamonds). The two connected flux points indicate the spectral index used to select the source in the USS sample. Note the steeper spectra with higher frequency in most objects. \\\\label{mpradiospectra}}\\n\\n\\\\section{POSS Finding Charts}\\n\\\\subsection{POSS Finding Charts for the WN Sample}\\n\\n\\\\small{POSS finding charts of the WN sample. The open cross indicates the NVSS position.}\\n\\n\\\\subsection{POSS Finding Charts for the TN Sample}\\n\\n\\\\small{POSS finding charts of the TN sample. The open cross indicates the NVSS position.}\\n\\n\\\\subsection{POSS Finding Charts for the MP Sample}\\n\\n\\\\small{POSS finding charts of the MP sample. The open cross indicates the MRC position.}\\n\\n\\\\end{document}\\n\"\n },\n {\n \"name\": \"tnmptable.tex\",\n \"string\": \"\\\\begin{table*}\\n\\\\centerline{\\\\bf Table A.2: TN sample}\\n\\\\tiny\\n\\\\begin{tabular}{lrrrrrrrrrrrr}\\nName & $S_{365}$ & $S_{1400}$ & S$_{4850}$ & $\\\\alpha_{365}^{1400}$ & $\\\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\\\alpha_{J2000}$ & $\\\\delta_{J2000}$ & Pos \\\\\\\\\\n & mJy & mJy & mJy & & & & \\\\arcsec & $\\\\arcdeg$ & $^h\\\\;\\\\;$$^m\\\\;\\\\;\\\\;\\\\;$$^s\\\\;\\\\;\\\\,$ & \\\\arcdeg$\\\\;\\\\;\\\\;$ \\\\arcmin$\\\\;\\\\;\\\\;$ \\\\arcsec$\\\\;$ & \\\\\\\\\\n\\\\hline\\nTN J0008-0912 & 638$\\\\pm$ 64 & 100.2$\\\\pm$ 4.4 & \\\\nodata & $-1.38\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 00 08 52.43 & $-$09 12 01.4 & N \\\\\\\\\\nTN J0018+1904 & 498$\\\\pm$ 30 & 84.5$\\\\pm$ 3.8 & \\\\nodata & $-1.32\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 00 18 07.35 & $+$19 04 50.0 & N \\\\\\\\\\nTN J0026+1501 & 241$\\\\pm$ 26 & 39.4$\\\\pm$ 2.0 & \\\\nodata & $-1.35\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 00 26 03.31 & $+$15 01 29.2 & N \\\\\\\\\\nTN J0027+0059 & 735$\\\\pm$ 55 & 98.0$\\\\pm$ 4.4 & \\\\nodata & $-1.50\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 00 27 39.36 & $+$00 59 53.6 & N \\\\\\\\\\nTN J0033-2731 & 512$\\\\pm$ 41 & 66.1$\\\\pm$ 3.0 & \\\\nodata & $-1.52\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 00 33 24.28 & $-$27 31 48.1 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0037+2629 & 442$\\\\pm$ 35 & 70.8$\\\\pm$ 3.2 & \\\\nodata & $-1.36\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 00 37 10.05 & $+$26 29 42.3 & N \\\\\\\\\\nTN J0038-1540 & 471$\\\\pm$ 33 & 63.9$\\\\pm$ 1.4 & $10.8\\\\pm0.6$ & $-1.49\\\\pm$0.06 & $-1.43\\\\pm0.05$ & D & 3.2 & 18 & 00 38 47.19 & $-$15 40 06.6 & V \\\\\\\\\\nTN J0040+1417 & 435$\\\\pm$ 41 & 71.1$\\\\pm$ 1.5 & \\\\nodata & $-1.35\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 00 40 37.04 & $+$14 17 14.6 & N \\\\\\\\\\nTN J0041+1250 & 451$\\\\pm$ 65 & 71.0$\\\\pm$ 3.3 & $21.0\\\\pm1.1$ & $-1.38\\\\pm$0.11 & $-0.98\\\\pm0.06$ & D & 10.7 & 103 & 00 41 31.27 & $+$12 50 32.3 & V \\\\\\\\\\nTN J0042+2649 & 484$\\\\pm$ 57 & 69.6$\\\\pm$ 3.2 & \\\\nodata & $-1.44\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 00 42 32.46 & $+$26 49 06.2 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0055+2624 & 8670$\\\\pm$457 & 1375.5$\\\\pm$56.2 & \\\\nodata & $-1.37\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 00 55 50.38 & $+$26 24 35.8 & N \\\\\\\\\\nTN J0102-1055 & 775$\\\\pm$ 41 & 110.4$\\\\pm$ 4.9 & $16.4\\\\pm0.9$ & $-1.45\\\\pm$0.05 & $-1.53\\\\pm0.06$ & D & 1.5 & 136 & 01 01 59.99 & $-$10 55 56.0 & V \\\\\\\\\\nTN J0102-2152 & 1900$\\\\pm$ 88 & 168.3$\\\\pm$ 6.7 & \\\\nodata & $-1.80\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 01 02 41.09 & $-$21 52 30.2 & N \\\\\\\\\\nTN J0114-0333 & 367$\\\\pm$ 36 & 54.7$\\\\pm$ 2.6 & $12.9\\\\pm0.7$ & $-1.42\\\\pm$0.08 & $-1.16\\\\pm0.06$ & T & 2.4 & 146 & 01 14 42.50 & $-$03 33 58.8 & V \\\\\\\\\\nTN J0119-2054 & 522$\\\\pm$ 60 & 87.8$\\\\pm$ 4.0 & \\\\nodata & $-1.33\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 01 19 47.65 & $-$20 54 46.8 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0121+1320 & 348$\\\\pm$ 33 & 57.3$\\\\pm$ 2.7 & $ 8.4\\\\pm0.5$ & $-1.34\\\\pm$0.08 & $-1.55\\\\pm0.06$ & S & 0.3 & 89 & 01 21 42.74 & $+$13 20 58.3 & V \\\\\\\\\\nTN J0154+0044 & 465$\\\\pm$ 29 & 78.6$\\\\pm$ 3.6 & \\\\nodata & $-1.32\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 01 54 38.48 & $+$00 44 37.7 & N \\\\\\\\\\nTN J0156+1619 & 437$\\\\pm$ 45 & 62.9$\\\\pm$ 2.9 & \\\\nodata & $-1.44\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 01 56 18.01 & $+$16 19 52.5 & N \\\\\\\\\\nTN J0201-1302 & 360$\\\\pm$ 33 & 57.0$\\\\pm$ 2.7 & $11.0\\\\pm0.6$ & $-1.37\\\\pm$0.08 & $-1.32\\\\pm0.06$ & S & $<$ 1.3 & 0 & 02 01 15.80 & $-$13 02 19.4 & V \\\\\\\\\\nTN J0205+2242 & 381$\\\\pm$ 26 & 60.4$\\\\pm$ 2.8 & $ 8.8\\\\pm0.5$ & $-1.37\\\\pm$0.06 & $-1.55\\\\pm0.06$ & D & 2.7 & 148 & 02 05 10.69 & $+$22 42 50.2 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0208+1305 & 403$\\\\pm$ 61 & 68.3$\\\\pm$ 3.1 & \\\\nodata & $-1.32\\\\pm$0.12 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 02 08 32.45 & $+$13 05 53.0 & N \\\\\\\\\\nTN J0215+2651 & 431$\\\\pm$ 49 & 69.3$\\\\pm$ 3.2 & \\\\nodata & $-1.36\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 02 15 45.31 & $+$26 51 12.3 & N \\\\\\\\\\nTN J0218+0844 & 395$\\\\pm$ 32 & 61.8$\\\\pm$ 1.3 & $ 8.8\\\\pm0.5$ & $-1.38\\\\pm$0.06 & $-1.56\\\\pm0.05$ & S & 0.4 & 169 & 02 18 25.56 & $+$08 44 31.3 & V \\\\\\\\\\nTN J0230-0255 & 573$\\\\pm$ 56 & 90.1$\\\\pm$ 4.0 & $22.5\\\\pm1.2$ & $-1.38\\\\pm$0.08 & $-1.12\\\\pm0.06$ & M & 6.7 & 156 & 02 30 21.97 & $-$02 55 05.1 & V \\\\\\\\\\nTN J0230-2001 & 380$\\\\pm$ 33 & 57.8$\\\\pm$ 2.7 & \\\\nodata & $-1.40\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 02 30 45.73 & $-$20 01 19.0 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0233+2349$^*$ & 1075$\\\\pm$ 86 & 176.8$\\\\pm$ 7.8 & $43.5\\\\pm2.3$ & $-1.34\\\\pm$0.07 & $-1.13\\\\pm0.06$ & DF & 4.0 & 116 & 02 33 10.32 & $+$23 49 52.2 & V \\\\\\\\\\nTN J0234-1215 & 451$\\\\pm$ 46 & 64.2$\\\\pm$ 2.9 & \\\\nodata & $-1.45\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 02 34 57.31 & $-$12 15 21.7 & N \\\\\\\\\\nTN J0243+1405 & 395$\\\\pm$ 51 & 58.4$\\\\pm$ 1.3 & $26.2\\\\pm1.4$ & $-1.42\\\\pm$0.10 & $-0.64\\\\pm0.05$ & T & 3.1 & 126 & 02 43 10.52 & $+$14 05 36.9 & V \\\\\\\\\\nTN J0244+0327 & 542$\\\\pm$ 62 & 84.8$\\\\pm$ 3.8 & \\\\nodata & $-1.38\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 02 44 53.97 & $+$03 27 46.8 & N \\\\\\\\\\nTN J0245+2700 & 388$\\\\pm$ 53 & 54.0$\\\\pm$ 2.5 & \\\\nodata & $-1.47\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 02 45 22.27 & $+$27 00 06.3 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0250+0130 & 275$\\\\pm$ 25 & 39.1$\\\\pm$ 2.0 & \\\\nodata & $-1.45\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 02 50 20.94 & $+$01 30 24.9 & N \\\\\\\\\\nTN J0254-1039 & 421$\\\\pm$ 60 & 68.1$\\\\pm$ 3.1 & $25.5\\\\pm1.4$ & $-1.36\\\\pm$0.11 & $-0.79\\\\pm0.06$ & D & 11.7 & 129 & 02 54 59.89 & $-$10 39 49.2 & V \\\\\\\\\\nTN J0256-2717 & 1045$\\\\pm$ 70 & 177.9$\\\\pm$ 7.4 & \\\\nodata & $-1.32\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 02 56 51.44 & $-$27 17 56.5 & N \\\\\\\\\\nTN J0301+0155 & 3950$\\\\pm$180 & 402.7$\\\\pm$17.3 & \\\\nodata & $-1.70\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 03 01 38.49 & $+$01 55 14.9 & N \\\\\\\\\\nTN J0306+0524 & 909$\\\\pm$ 76 & 155.1$\\\\pm$ 6.3 & \\\\nodata & $-1.32\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 03 06 08.10 & $+$05 24 23.8 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0309-2425$^*$ & 483$\\\\pm$ 53 & 62.6$\\\\pm$ 2.9 & $14.8\\\\pm0.9$ & $-1.52\\\\pm$0.09 & $-1.16\\\\pm0.06$ & D & 12.9 & 23 & 03 09 09.26 & $-$24 25 11.7 & V \\\\\\\\\\nTN J0310+0814 & 593$\\\\pm$ 67 & 96.8$\\\\pm$ 4.3 & \\\\nodata & $-1.35\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 03 10 37.37 & $+$08 14 59.2 & N \\\\\\\\\\nTN J0311-2553 & 1102$\\\\pm$ 66 & 174.1$\\\\pm$ 7.5 & \\\\nodata & $-1.37\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 03 11 47.40 & $-$25 53 21.1 & N \\\\\\\\\\nTN J0312-2622 & 442$\\\\pm$ 41 & 46.4$\\\\pm$ 2.3 & \\\\nodata & $-1.68\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 03 12 34.19 & $-$26 22 23.9 & N \\\\\\\\\\nTN J0316-0815 & 1950$\\\\pm$ 92 & 305.1$\\\\pm$13.4 & $42.2\\\\pm2.2$ & $-1.38\\\\pm$0.05 & $-1.59\\\\pm0.05$ & T & 3.2 & 34 & 03 16 18.59 & $-$08 15 54.8 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0321+1631 & 1084$\\\\pm$ 85 & 175.7$\\\\pm$ 7.7 & \\\\nodata & $-1.35\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 03 21 36.86 & $+$16 31 55.8 & N \\\\\\\\\\nTN J0327-0948 & 281$\\\\pm$ 30 & 39.0$\\\\pm$ 2.0 & \\\\nodata & $-1.47\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 03 27 00.55 & $-$09 48 05.2 & N \\\\\\\\\\nTN J0344+1903 & 297$\\\\pm$ 22 & 50.7$\\\\pm$ 2.4 & \\\\nodata & $-1.32\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 03 44 00.12 & $+$19 03 53.1 & N \\\\\\\\\\nTN J0344-2029 & 538$\\\\pm$ 71 & 74.0$\\\\pm$ 1.6 & $19.2\\\\pm1.1$ & $-1.48\\\\pm$0.10 & $-1.08\\\\pm0.05$ & D & 6.5 & 42 & 03 44 37.88 & $-$20 29 03.8 & V \\\\\\\\\\nTN J0349-1207$^*$ & 460$\\\\pm$ 61 & 77.5$\\\\pm$ 3.5 & $23.3\\\\pm1.3$ & $-1.32\\\\pm$0.11 & $-0.97\\\\pm0.06$ & T & 9.4 & 101 & 03 49 49.22 & $-$12 07 10.6 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0351-1947 & 642$\\\\pm$ 86 & 111.4$\\\\pm$ 4.9 & \\\\nodata & $-1.30\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 03 51 33.13 & $-$19 47 10.5 & N \\\\\\\\\\nTN J0352-0355$^*$ & 681$\\\\pm$ 63 & 114.9$\\\\pm$ 4.8 & $13.5\\\\pm0.8$ & $-1.32\\\\pm$0.08 & $-1.65\\\\pm0.06$ & DF & \\\\nodata & 0 & 03 52 32.04 & $-$03 55 47.2 & V \\\\\\\\\\nTN J0355+0440 & 2015$\\\\pm$119 & 262.0$\\\\pm$11.5 & \\\\nodata & $-1.52\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 03 55 12.79 & $+$04 40 41.0 & N \\\\\\\\\\nTN J0356-3028 & 1030$\\\\pm$ 65 & 167.5$\\\\pm$ 7.3 & $34.1\\\\pm1.8$ & $-1.35\\\\pm$0.06 & $-1.28\\\\pm0.06$ & D & 3.1 & 86 & 03 56 45.54 & $-$30 28 36.9 & V \\\\\\\\\\nTN J0401-0156 & 1001$\\\\pm$ 65 & 172.8$\\\\pm$ 7.1 & \\\\nodata & $-1.31\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 04 01 08.43 & $-$01 56 08.9 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0402+1007 & 479$\\\\pm$ 54 & 74.6$\\\\pm$ 3.4 & $13.4\\\\pm0.8$ & $-1.38\\\\pm$0.09 & $-1.38\\\\pm0.06$ & D & 0.8 & 67 & 04 02 34.44 & $+$10 07 14.9 & V \\\\\\\\\\nTN J0404-0541 & 666$\\\\pm$ 69 & 114.1$\\\\pm$ 5.1 & \\\\nodata & $-1.31\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 04 04 09.66 & $-$05 41 07.3 & N \\\\\\\\\\nTN J0408-2418$^*$ & 3881$\\\\pm$172 & 647.7$\\\\pm$28.1 & \\\\nodata & $-1.33\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 04 08 51.38 & $-$24 18 15.5 & N \\\\\\\\\\nTN J0410+1019 & 1185$\\\\pm$ 88 & 166.9$\\\\pm$ 3.4 & $26.5\\\\pm1.4$ & $-1.46\\\\pm$0.06 & $-1.26\\\\pm0.05$ & S & 0.2 & 109 & 04 10 40.52 & $+$10 19 13.6 & V \\\\\\\\\\nTN J0429-2118 & 561$\\\\pm$ 58 & 95.5$\\\\pm$ 4.3 & \\\\nodata & $-1.32\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 04 29 39.79 & $-$21 18 01.7 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0431+0725 & 175$\\\\pm$ 24 & 30.4$\\\\pm$ 0.7 & \\\\nodata & $-1.30\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 04 31 54.21 & $+$07 25 13.8 & N \\\\\\\\\\nTN J0433+0717 & 229$\\\\pm$ 27 & 33.1$\\\\pm$ 1.8 & \\\\nodata & $-1.44\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 04 33 05.61 & $+$07 17 55.2 & N \\\\\\\\\\nTN J0435-0736 & 358$\\\\pm$ 71 & 47.0$\\\\pm$ 2.3 & $16.6\\\\pm0.9$ & $-1.51\\\\pm$0.15 & $-0.84\\\\pm0.06$ & T & 11.9 & 59 & 04 35 32.20 & $-$07 36 12.3 & V \\\\\\\\\\nTN J0437+0259 & 410$\\\\pm$ 54 & 71.1$\\\\pm$ 3.3 & \\\\nodata & $-1.30\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 04 37 33.04 & $+$02 59 06.2 & N \\\\\\\\\\nTN J0443-1212$^*$ & 412$\\\\pm$ 59 & 56.8$\\\\pm$ 2.7 & $14.6\\\\pm0.8$ & $-1.47\\\\pm$0.11 & $-1.09\\\\pm0.06$ & M & 20.2 & 25 & 04 43 53.72 & $-$12 12 46.7 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0452-1737 & 747$\\\\pm$ 73 & 118.1$\\\\pm$ 2.5 & $23.7\\\\pm1.3$ & $-1.37\\\\pm$0.07 & $-1.29\\\\pm0.05$ & D & 2.4 & 176 & 04 52 26.66 & $-$17 37 54.0 & V \\\\\\\\\\nTN J0510-1838 & 6801$\\\\pm$325 & 641.3$\\\\pm$25.6 & \\\\nodata & $-1.76\\\\pm$0.05 & \\\\nodata & D & 36.1 & 63 & 05 10 32.30 & $-$18 38 41.4 & A \\\\\\\\\\nTN J0515-3410 & 589$\\\\pm$ 52 & 97.4$\\\\pm$ 4.4 & \\\\nodata & $-1.34\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 05 15 18.86 & $-$34 10 09.5 & N \\\\\\\\\\nTN J0517-0641 & 285$\\\\pm$ 30 & 40.0$\\\\pm$ 0.9 & $ 6.8\\\\pm0.4$ & $-1.46\\\\pm$0.08 & $-1.43\\\\pm0.05$ & S & 1.0 & 0 & 05 17 36.89 & $-$06 41 14.6 & V \\\\\\\\\\nTN J0525-1832 & 549$\\\\pm$ 73 & 86.4$\\\\pm$ 3.9 & $24.1\\\\pm1.3$ & $-1.38\\\\pm$0.11 & $-1.02\\\\pm0.06$ & T & 8.1 & 172 & 05 25 54.85 & $-$18 32 32.5 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0547-0706 & 2552$\\\\pm$156 & 362.6$\\\\pm$16.0 & \\\\nodata & $-1.45\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 05 47 27.57 & $-$07 06 35.0 & N \\\\\\\\\\nTN J0549-2459 & 427$\\\\pm$ 55 & 58.0$\\\\pm$ 1.3 & \\\\nodata & $-1.49\\\\pm$0.10 & \\\\nodata & S & 23.5 & 8 & 05 49 28.61 & $-$24 59 15.2 & A \\\\\\\\\\nTN J0551-0756 & 473$\\\\pm$ 71 & 68.5$\\\\pm$ 3.2 & \\\\nodata & $-1.44\\\\pm$0.12 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 05 51 30.37 & $-$07 56 17.5 & N \\\\\\\\\\nTN J0552-0433 & 1618$\\\\pm$ 83 & 269.7$\\\\pm$11.8 & $37.7\\\\pm2.0$ & $-1.33\\\\pm$0.05 & $-1.56\\\\pm0.06$ & D & 4.3 & 152 & 05 52 14.38 & $-$04 33 28.8 & V \\\\\\\\\\nTN J0553-2033 & 887$\\\\pm$ 80 & 148.0$\\\\pm$ 6.2 & \\\\nodata & $-1.33\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 05 53 37.24 & $-$20 33 07.6 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0558-1358 & 425$\\\\pm$ 54 & 73.4$\\\\pm$ 3.4 & \\\\nodata & $-1.31\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 05 58 39.43 & $-$13 58 45.5 & N \\\\\\\\\\nTN J0559-3406 & 773$\\\\pm$ 69 & 123.5$\\\\pm$ 5.4 & \\\\nodata & $-1.36\\\\pm$0.07 & \\\\nodata & S & 4.6 & 8 & 05 59 14.30 & $-$34 06 51.0 & A \\\\\\\\\\nTN J0602-2741 & 810$\\\\pm$ 54 & 117.2$\\\\pm$ 5.2 & $20.7\\\\pm1.2$ & $-1.44\\\\pm$0.06 & $-1.39\\\\pm0.06$ & T & 4.3 & 88 & 06 02 41.32 & $-$27 41 10.1 & V \\\\\\\\\\nTN J0630-2834 & 343$\\\\pm$ 29 & 14.3$\\\\pm$ 0.5 & \\\\nodata & $-2.36\\\\pm$0.07 & \\\\nodata & S & 13.5 & 2 & 06 30 49.49 & $-$28 34 40.4 & A \\\\\\\\\\nTN J0634-3232 & 394$\\\\pm$ 63 & 67.7$\\\\pm$ 3.1 & \\\\nodata & $-1.31\\\\pm$0.12 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 06 34 17.10 & $-$32 32 34.1 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0729+2436 & 1062$\\\\pm$ 87 & 68.9$\\\\pm$ 3.1 & \\\\nodata & $-2.03\\\\pm$0.07 & \\\\nodata & D & 19.4 & 72 & 07 29 28.65 & $+$24 36 26.2 & F \\\\\\\\\\nTN J0733+1753 & 291$\\\\pm$ 45 & 46.1$\\\\pm$ 2.3 & \\\\nodata & $-1.37\\\\pm$0.12 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 07 33 17.53 & $+$17 53 28.4 & N \\\\\\\\\\nTN J0805+2738 & 987$\\\\pm$ 79 & 153.0$\\\\pm$ 6.7 & \\\\nodata & $-1.39\\\\pm$0.07 & \\\\nodata & T & 71.3 & 119 & 08 05 15.50 & $+$27 38 01.2 & F \\\\\\\\\\nTN J0806+0401 & 560$\\\\pm$ 53 & 92.1$\\\\pm$ 2.0 & \\\\nodata & $-1.34\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 08 06 32.25 & $+$04 01 37.7 & N \\\\\\\\\\nTN J0812+0915 & 277$\\\\pm$ 46 & 43.4$\\\\pm$ 2.2 & \\\\nodata & $-1.38\\\\pm$0.13 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 08 12 16.84 & $+$09 15 43.7 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0818-0741 & 381$\\\\pm$ 48 & 59.3$\\\\pm$ 2.8 & \\\\nodata & $-1.38\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 08 18 51.89 & $-$07 41 48.2 & N \\\\\\\\\\nTN J0831+0046 & 451$\\\\pm$ 55 & 72.8$\\\\pm$ 3.3 & \\\\nodata & $-1.36\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 08 31 39.92 & $+$00 46 56.5 & N \\\\\\\\\\nTN J0831+0851 & 567$\\\\pm$ 53 & 83.8$\\\\pm$ 3.8 & $98.3\\\\pm5.2$ & $-1.42\\\\pm$0.08 & $ 0.13\\\\pm0.06$ & DF & 3.0 & 2 & 08 31 52.74 & $+$08 51 14.1 & V \\\\\\\\\\nTN J0837-1053$^*$ & 450$\\\\pm$ 81 & 69.2$\\\\pm$ 3.1 & $11.6\\\\pm0.7$ & $-1.39\\\\pm$0.14 & $-1.43\\\\pm0.06$ & D & 23.5 & 11 & 08 37 41.62 & $-$10 53 46.0 & V \\\\\\\\\\nTN J0855-0000 & 416$\\\\pm$ 57 & 65.9$\\\\pm$ 3.0 & $13.8\\\\pm0.8$ & $-1.37\\\\pm$0.11 & $-1.26\\\\pm0.06$ & D & 3.8 & 85 & 08 55 57.26 & $-$00 00 58.2 & V \\\\\\\\\\n\\\\end{tabular}\\n\\\\end{table*}\\n\\\\begin{table*}\\n\\\\tiny\\n\\\\begin{tabular}{lrrrrrrrrrrrr}\\nName & $S_{365}$ & $S_{1400}$ & S$_{4850}$ & $\\\\alpha_{365}^{1400}$ & $\\\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\\\alpha_{J2000}$ & $\\\\delta_{J2000}$ & Pos \\\\\\\\\\n & mJy & mJy & mJy & & & & \\\\arcsec & $\\\\arcdeg$ & $^h\\\\;\\\\;$$^m\\\\;\\\\;\\\\;\\\\;$$^s\\\\;\\\\;\\\\,$ & \\\\arcdeg$\\\\;\\\\;\\\\;$ \\\\arcmin$\\\\;\\\\;\\\\;$ \\\\arcsec$\\\\;$ & \\\\\\\\\\n\\\\hline\\nTN J0856-1510 & 469$\\\\pm$ 68 & 70.0$\\\\pm$ 3.2 & $ 3.7\\\\pm0.3$ & $-1.41\\\\pm$0.11 & $-2.01\\\\pm0.07$ & S & 1.0 & 14 & 08 56 12.44 & $-$15 10 35.7 & V \\\\\\\\\\nTN J0902+1809 & 491$\\\\pm$ 37 & 55.5$\\\\pm$ 2.6 & \\\\nodata & $-1.62\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 09 02 00.00 & $+$18 09 03.4 & N \\\\\\\\\\nTN J0906-0701 & 939$\\\\pm$101 & 142.5$\\\\pm$ 5.8 & \\\\nodata & $-1.40\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 09 06 40.23 & $-$07 01 12.4 & N \\\\\\\\\\nTN J0910-2228 & 465$\\\\pm$ 32 & 55.3$\\\\pm$ 2.6 & $ 4.0\\\\pm0.3$ & $-1.58\\\\pm$0.06 & $-2.11\\\\pm0.07$ & S & 2.0 & 0 & 09 10 34.15 & $-$22 28 47.4 & V \\\\\\\\\\nTN J0914+1119 & 343$\\\\pm$ 53 & 49.5$\\\\pm$ 1.1 & \\\\nodata & $-1.44\\\\pm$0.12 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 09 14 30.81 & $+$11 19 08.0 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0919+1845 & 522$\\\\pm$ 50 & 90.0$\\\\pm$ 4.0 & \\\\nodata & $-1.31\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 09 19 33.25 & $+$18 45 51.2 & N \\\\\\\\\\nTN J0920-0712 & 760$\\\\pm$ 53 & 100.4$\\\\pm$ 4.5 & $16.3\\\\pm0.9$ & $-1.51\\\\pm$0.06 & $-1.46\\\\pm0.06$ & S & 1.4 & 135 & 09 20 22.43 & $-$07 12 17.6 & V \\\\\\\\\\nTN J0920-1405 & 842$\\\\pm$ 88 & 133.6$\\\\pm$ 5.5 & \\\\nodata & $-1.37\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 09 20 37.77 & $-$14 05 56.3 & N \\\\\\\\\\nTN J0924-2201 & 656$\\\\pm$ 72 & 73.3$\\\\pm$ 1.5 & $ 8.6\\\\pm0.5$ & $-1.63\\\\pm$0.08 & $-1.72\\\\pm0.05$ & D & 1.2 & 74 & 09 24 19.92 & $-$22 01 41.5 & V \\\\\\\\\\nTN J0936+0422 & 6025$\\\\pm$362 & 992.0$\\\\pm$42.5 & \\\\nodata & $-1.34\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 09 36 32.02 & $+$04 22 10.7 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0936-2243 & 488$\\\\pm$ 63 & 69.1$\\\\pm$ 3.2 & $18.5\\\\pm1.0$ & $-1.45\\\\pm$0.10 & $-1.06\\\\pm0.06$ & D & 8.1 & 77 & 09 36 32.53 & $-$22 43 04.9 & V \\\\\\\\\\nTN J0941-1628 & 1810$\\\\pm$115 & 304.4$\\\\pm$13.4 & $64.7\\\\pm3.8$ & $-1.33\\\\pm$0.06 & $-1.24\\\\pm0.06$ & D & 1.9 & 175 & 09 41 07.43 & $-$16 28 02.5 & V \\\\\\\\\\nTN J0946-0306 & 238$\\\\pm$ 24 & 38.2$\\\\pm$ 2.0 & \\\\nodata & $-1.36\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 09 46 00.88 & $-$03 06 26.2 & N \\\\\\\\\\nTN J0954-1635 & 1531$\\\\pm$ 98 & 260.0$\\\\pm$11.4 & \\\\nodata & $-1.32\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 09 54 52.30 & $-$16 35 35.1 & N \\\\\\\\\\nTN J0956-1500 & 505$\\\\pm$ 49 & 68.9$\\\\pm$ 1.5 & \\\\nodata & $-1.48\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 09 56 01.46 & $-$15 00 21.6 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J0958-1103 & 431$\\\\pm$ 63 & 70.6$\\\\pm$ 3.2 & \\\\nodata & $-1.35\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 09 58 21.84 & $-$11 03 47.5 & N \\\\\\\\\\nTN J1000+0549 & 410$\\\\pm$ 55 & 67.3$\\\\pm$ 3.1 & \\\\nodata & $-1.34\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 10 00 44.58 & $+$05 49 31.1 & N \\\\\\\\\\nTN J1002+2225 & 343$\\\\pm$ 41 & 54.2$\\\\pm$ 2.6 & $12.2\\\\pm0.7$ & $-1.37\\\\pm$0.10 & $-1.20\\\\pm0.06$ & D & 11.2 & 10 & 10 02 54.08 & $+$22 25 21.9 & V \\\\\\\\\\nTN J1026-2116 & 399$\\\\pm$ 29 & 61.5$\\\\pm$ 1.3 & $ 8.5\\\\pm0.5$ & $-1.39\\\\pm$0.06 & $-1.59\\\\pm0.05$ & S & 1.0 & 0 & 10 26 22.37 & $-$21 16 07.7 & V \\\\\\\\\\nTN J1028+1114 & 459$\\\\pm$ 56 & 79.7$\\\\pm$ 3.6 & \\\\nodata & $-1.30\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 10 28 24.31 & $+$11 14 52.4 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1031+0259 & 416$\\\\pm$ 62 & 60.0$\\\\pm$ 1.3 & \\\\nodata & $-1.44\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 10 31 13.36 & $+$02 59 05.3 & N \\\\\\\\\\nTN J1033-1339 & 981$\\\\pm$ 75 & 153.8$\\\\pm$ 6.8 & $26.0\\\\pm1.4$ & $-1.38\\\\pm$0.07 & $-1.43\\\\pm0.06$ & S & 2.0 & 107 & 10 33 10.70 & $-$13 39 52.0 & V \\\\\\\\\\nTN J1043-1718 & 578$\\\\pm$ 70 & 91.0$\\\\pm$ 3.9 & $18.9\\\\pm1.0$ & $-1.38\\\\pm$0.10 & $-1.26\\\\pm0.06$ & D & 34.7 & 63 & 10 43 19.42 & $-$17 18 53.5 & V \\\\\\\\\\nTN J1043+2404 & 439$\\\\pm$ 34 & 52.0$\\\\pm$ 2.5 & \\\\nodata & $-1.59\\\\pm$0.07 & \\\\nodata & S & 3.7 & 90 & 10 43 43.28 & $+$24 04 47.3 & F \\\\\\\\\\nTN J1045+1832 & 348$\\\\pm$ 27 & 53.6$\\\\pm$ 1.2 & \\\\nodata & $-1.39\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 10 45 42.93 & $+$18 32 37.5 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1049-1258 & 818$\\\\pm$ 56 & 112.2$\\\\pm$ 5.0 & $17.2\\\\pm0.9$ & $-1.48\\\\pm$0.06 & $-1.50\\\\pm0.06$ & M & 10.1 & 104 & 10 49 06.22 & $-$12 58 18.3 & V \\\\\\\\\\nTN J1053-1518 & 383$\\\\pm$ 62 & 63.7$\\\\pm$ 2.9 & \\\\nodata & $-1.33\\\\pm$0.13 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 10 53 44.52 & $-$15 18 29.8 & N \\\\\\\\\\nTN J1056-0400 & 449$\\\\pm$ 57 & 57.2$\\\\pm$ 2.7 & \\\\nodata & $-1.53\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 10 56 52.64 & $-$04 00 15.9 & N \\\\\\\\\\nTN J1102+1029 & 3713$\\\\pm$224 & 633.6$\\\\pm$27.8 & \\\\nodata & $-1.32\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 11 02 17.47 & $+$10 29 08.0 & N \\\\\\\\\\nTN J1102-1651 & 688$\\\\pm$ 68 & 112.5$\\\\pm$ 5.0 & $20.2\\\\pm1.1$ & $-1.35\\\\pm$0.08 & $-1.38\\\\pm0.06$ & D & 3.0 & 70 & 11 02 47.13 & $-$16 51 34.4 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1112-2948 & 663$\\\\pm$ 51 & 101.0$\\\\pm$ 4.5 & $16.6\\\\pm0.9$ & $-1.40\\\\pm$0.07 & $-1.45\\\\pm0.06$ & D & 9.1 & 119 & 11 12 23.86 & $-$29 48 06.4 & V \\\\\\\\\\nTN J1114-2221 & 386$\\\\pm$ 53 & 64.9$\\\\pm$ 3.0 & \\\\nodata & $-1.33\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 11 14 04.82 & $-$22 21 26.6 & N \\\\\\\\\\nTN J1117-1409 & 785$\\\\pm$ 69 & 134.5$\\\\pm$ 5.9 & \\\\nodata & $-1.31\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 11 17 23.00 & $-$14 09 09.5 & N \\\\\\\\\\nTN J1118-2612 & 514$\\\\pm$ 44 & 62.3$\\\\pm$ 2.9 & \\\\nodata & $-1.57\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 11 18 54.08 & $-$26 12 20.6 & N \\\\\\\\\\nTN J1121-1155 & 332$\\\\pm$ 65 & 50.1$\\\\pm$ 2.4 & \\\\nodata & $-1.41\\\\pm$0.15 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 11 21 32.75 & $-$11 55 03.2 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1121+1706 & 1156$\\\\pm$ 83 & 196.8$\\\\pm$ 8.4 & \\\\nodata & $-1.32\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 11 21 39.89 & $+$17 06 14.8 & N \\\\\\\\\\nTN J1123-2154 & 407$\\\\pm$ 64 & 50.6$\\\\pm$ 2.4 & $ 8.5\\\\pm0.5$ & $-1.55\\\\pm$0.12 & $-1.43\\\\pm0.06$ & S & 0.8 & 29 & 11 23 10.15 & $-$21 54 05.3 & V \\\\\\\\\\nTN J1125-0342 & 354$\\\\pm$ 52 & 61.4$\\\\pm$ 2.9 & \\\\nodata & $-1.30\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 11 25 57.41 & $-$03 42 04.0 & N \\\\\\\\\\nTN J1133-2715 & 2938$\\\\pm$125 & 447.9$\\\\pm$ 9.2 & \\\\nodata & $-1.40\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 11 33 31.53 & $-$27 15 22.9 & N \\\\\\\\\\nTN J1136+1551 & 384$\\\\pm$ 33 & 21.7$\\\\pm$ 0.6 & \\\\nodata & $-2.14\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 11 36 03.28 & $+$15 51 06.7 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1136+0610 & 698$\\\\pm$ 50 & 118.8$\\\\pm$ 5.3 & \\\\nodata & $-1.32\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 11 36 38.91 & $+$06 10 26.8 & N \\\\\\\\\\nTN J1139+0935 & 508$\\\\pm$ 58 & 87.3$\\\\pm$ 3.9 & \\\\nodata & $-1.31\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 11 39 22.75 & $+$09 35 26.1 & N \\\\\\\\\\nTN J1146-1052 & 843$\\\\pm$ 79 & 120.9$\\\\pm$ 5.4 & \\\\nodata & $-1.44\\\\pm$0.08 & \\\\nodata & S & 8.8 & 1 & 11 46 07.21 & $-$10 52 08.6 & A \\\\\\\\\\nTN J1148-0901 & 571$\\\\pm$ 67 & 80.4$\\\\pm$ 3.7 & \\\\nodata & $-1.46\\\\pm$0.09 & \\\\nodata & S & $<$ 6.0 & 5 & 11 48 39.90 & $-$09 01 48.8 & A \\\\\\\\\\nTN J1149+1844 & 457$\\\\pm$ 39 & 77.6$\\\\pm$ 1.6 & \\\\nodata & $-1.32\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 11 49 36.78 & $+$18 44 21.5 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1151-3013 & 435$\\\\pm$ 28 & 52.7$\\\\pm$ 1.2 & $ 7.0\\\\pm0.4$ & $-1.57\\\\pm$0.05 & $-1.62\\\\pm0.05$ & S & 1.0 & 0 & 11 51 59.42 & $-$30 13 40.8 & V \\\\\\\\\\nTN J1156-3105 & 317$\\\\pm$ 48 & 48.3$\\\\pm$ 2.3 & \\\\nodata & $-1.40\\\\pm$0.12 & \\\\nodata & S & 10.7 & 167 & 11 56 25.60 & $-$31 05 40.0 & A \\\\\\\\\\nTN J1159-1629 & 324$\\\\pm$ 34 & 52.9$\\\\pm$ 1.2 & $10.4\\\\pm0.6$ & $-1.35\\\\pm$0.08 & $-1.30\\\\pm0.05$ & D & 1.4 & 38 & 11 59 53.25 & $-$16 29 48.2 & V \\\\\\\\\\nTN J1204+1630 & 804$\\\\pm$ 56 & 129.7$\\\\pm$ 5.8 & \\\\nodata & $-1.36\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 12 04 20.49 & $+$16 30 49.5 & N \\\\\\\\\\nTN J1210+1738 & 397$\\\\pm$ 50 & 68.1$\\\\pm$ 3.2 & \\\\nodata & $-1.31\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 12 10 36.00 & $+$17 38 27.8 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1216+1944 & 546$\\\\pm$ 44 & 91.7$\\\\pm$ 4.1 & \\\\nodata & $-1.33\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 12 16 01.76 & $+$19 44 43.3 & N \\\\\\\\\\nTN J1216-2850 & 870$\\\\pm$ 43 & 145.2$\\\\pm$ 6.4 & \\\\nodata & $-1.33\\\\pm$0.05 & \\\\nodata & S & $<$ 7.0 & 163 & 12 16 17.38 & $-$28 50 48.7 & A \\\\\\\\\\nTN J1220+0604 & 491$\\\\pm$ 61 & 65.1$\\\\pm$ 3.0 & \\\\nodata & $-1.50\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 12 20 07.82 & $+$06 04 16.5 & N \\\\\\\\\\nTN J1221-2646 & 1403$\\\\pm$ 82 & 217.1$\\\\pm$ 9.5 & \\\\nodata & $-1.39\\\\pm$0.05 & \\\\nodata & S & 8.3 & 162 & 12 21 42.91 & $-$26 46 37.7 & A \\\\\\\\\\nTN J1227-2255 & 271$\\\\pm$ 27 & 44.0$\\\\pm$ 2.2 & \\\\nodata & $-1.35\\\\pm$0.08 & \\\\nodata & S & $<$ 7.0 & 158 & 12 27 47.23 & $-$22 55 35.1 & A \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1239+1005 & 830$\\\\pm$ 89 & 79.3$\\\\pm$ 1.7 & \\\\nodata & $-1.75\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 12 39 02.08 & $+$10 05 49.2 & N \\\\\\\\\\nTN J1239+1043 & 569$\\\\pm$ 63 & 87.1$\\\\pm$ 3.8 & \\\\nodata & $-1.40\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 12 39 31.67 & $+$10 43 22.9 & N \\\\\\\\\\nTN J1239-0319 & 1629$\\\\pm$ 74 & 277.3$\\\\pm$12.2 & \\\\nodata & $-1.32\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 12 39 38.91 & $-$03 19 02.2 & N \\\\\\\\\\nTN J1245-1127 & 518$\\\\pm$ 62 & 88.0$\\\\pm$ 4.0 & \\\\nodata & $-1.32\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 12 45 02.47 & $-$11 27 25.9 & N \\\\\\\\\\nTN J1247+1547 & 405$\\\\pm$ 44 & 70.1$\\\\pm$ 3.2 & \\\\nodata & $-1.30\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 12 47 04.84 & $+$15 47 38.9 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1251-2714 & 609$\\\\pm$ 53 & 96.5$\\\\pm$ 4.3 & \\\\nodata & $-1.37\\\\pm$0.07 & \\\\nodata & S & $<$ 7.0 & 158 & 12 51 14.86 & $-$27 14 19.9 & A \\\\\\\\\\nTN J1256-0911 & 457$\\\\pm$ 38 & 76.4$\\\\pm$ 3.5 & \\\\nodata & $-1.33\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 12 56 19.48 & $-$09 11 24.8 & N \\\\\\\\\\nTN J1303-3349 & 2431$\\\\pm$108 & 360.8$\\\\pm$ 7.7 & \\\\nodata & $-1.42\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 13 03 02.67 & $-$33 49 15.5 & N \\\\\\\\\\nTN J1306-0436 & 331$\\\\pm$ 57 & 55.2$\\\\pm$ 2.6 & \\\\nodata & $-1.33\\\\pm$0.13 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 13 06 36.11 & $-$04 36 17.4 & N \\\\\\\\\\nTN J1313-0459 & 369$\\\\pm$ 34 & 58.1$\\\\pm$ 2.7 & \\\\nodata & $-1.38\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 13 13 34.37 & $-$04 59 30.0 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1317+0339 & 399$\\\\pm$ 62 & 39.8$\\\\pm$ 2.0 & \\\\nodata & $-1.71\\\\pm$0.12 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 13 17 48.12 & $+$03 39 12.3 & N \\\\\\\\\\nTN J1323-2604 & 564$\\\\pm$ 60 & 97.3$\\\\pm$ 2.0 & \\\\nodata & $-1.31\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 13 23 32.43 & $-$26 04 04.7 & N \\\\\\\\\\nTN J1326-2330 & 523$\\\\pm$ 33 & 83.2$\\\\pm$ 3.8 & \\\\nodata & $-1.37\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 13 26 25.24 & $-$23 30 23.5 & N \\\\\\\\\\nTN J1327+1437 & 788$\\\\pm$ 68 & 115.0$\\\\pm$ 5.1 & \\\\nodata & $-1.43\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 13 27 23.93 & $+$14 37 00.4 & N \\\\\\\\\\nTN J1336+2450 & 358$\\\\pm$ 71 & 51.3$\\\\pm$ 2.5 & \\\\nodata & $-1.45\\\\pm$0.15 & \\\\nodata & M & 54.4 & 100 & 13 36 15.12 & $+$24 50 05.4 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1338-1942 & 718$\\\\pm$ 63 & 122.9$\\\\pm$ 5.4 & $22.1\\\\pm1.2$ & $-1.31\\\\pm$0.07 & $-1.34\\\\pm0.06$ & S & 1.4 & 152 & 13 38 26.06 & $-$19 42 30.1 & V \\\\\\\\\\nTN J1339-0114 & 349$\\\\pm$ 51 & 59.5$\\\\pm$ 1.3 & \\\\nodata & $-1.32\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 13 39 55.26 & $-$01 14 10.8 & N \\\\\\\\\\nTN J1340+2723 & 827$\\\\pm$ 93 & 137.8$\\\\pm$ 6.1 & $24.8\\\\pm1.4$ & $-1.33\\\\pm$0.09 & $-1.38\\\\pm0.06$ & DF & 1.7 & 0 & 13 40 29.38 & $+$27 23 25.0 & V \\\\\\\\\\nTN J1346-1004 & 363$\\\\pm$ 59 & 49.6$\\\\pm$ 2.4 & \\\\nodata & $-1.48\\\\pm$0.13 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 13 46 16.84 & $-$10 04 57.2 & N \\\\\\\\\\nTN J1351+1328 & 662$\\\\pm$ 54 & 93.8$\\\\pm$ 4.2 & \\\\nodata & $-1.45\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 13 51 54.72 & $+$13 28 38.1 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1352-0800 & 554$\\\\pm$ 88 & 95.6$\\\\pm$ 4.3 & \\\\nodata & $-1.31\\\\pm$0.12 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 13 52 55.32 & $-$08 00 14.1 & N \\\\\\\\\\nTN J1353+2302 & 403$\\\\pm$ 38 & 59.5$\\\\pm$ 1.3 & $23.3\\\\pm1.3$ & $-1.42\\\\pm$0.07 & $-0.75\\\\pm0.05$ & DF & 2.5 & 44 & 13 53 42.26 & $+$23 02 50.9 & V \\\\\\\\\\nTN J1358+2003 & 227$\\\\pm$ 42 & 35.0$\\\\pm$ 1.8 & \\\\nodata & $-1.39\\\\pm$0.14 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 13 58 29.63 & $+$20 03 13.4 & N \\\\\\\\\\nTN J1403-1223 & 396$\\\\pm$ 69 & 65.8$\\\\pm$ 3.0 & \\\\nodata & $-1.34\\\\pm$0.14 & \\\\nodata & S & 30.6 & 169 & 14 03 37.33 & $-$12 23 57.3 & A \\\\\\\\\\nTN J1408-0855 & 694$\\\\pm$ 73 & 114.3$\\\\pm$ 5.1 & \\\\nodata & $-1.34\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 14 08 18.46 & $-$08 55 38.5 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1411-0824 & 542$\\\\pm$ 71 & 76.1$\\\\pm$ 3.5 & \\\\nodata & $-1.46\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 14 11 53.33 & $-$08 24 02.9 & N \\\\\\\\\\nTN J1412-2548 & 452$\\\\pm$ 59 & 78.0$\\\\pm$ 3.6 & \\\\nodata & $-1.31\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 14 12 51.27 & $-$25 48 05.5 & N \\\\\\\\\\nTN J1418-2256 & 527$\\\\pm$ 59 & 82.0$\\\\pm$ 3.7 & \\\\nodata & $-1.38\\\\pm$0.09 & \\\\nodata & S & 7.6 & 148 & 14 18 16.65 & $-$22 56 58.6 & A \\\\\\\\\\nTN J1428+2425 & 411$\\\\pm$ 34 & 69.1$\\\\pm$ 1.5 & \\\\nodata & $-1.33\\\\pm$0.07 & \\\\nodata & S & 1.0 & 0 & 14 28 10.20 & $+$24 25 11.3 & F \\\\\\\\\\nTN J1438+2334 & 564$\\\\pm$ 69 & 96.5$\\\\pm$ 4.2 & \\\\nodata & $-1.31\\\\pm$0.10 & \\\\nodata & D & 21.1 & 157 & 14 38 56.52 & $+$23 34 25.6 & F \\\\\\\\\\n\\\\end{tabular}\\n\\\\end{table*}\\n\\\\begin{table*}\\n\\\\tiny\\n\\\\begin{tabular}{lrrrrrrrrrrrr}\\nName & $S_{365}$ & $S_{1400}$ & S$_{4850}$ & $\\\\alpha_{365}^{1400}$ & $\\\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\\\alpha_{J2000}$ & $\\\\delta_{J2000}$ & Pos \\\\\\\\\\n & mJy & mJy & mJy & & & & \\\\arcsec & $\\\\arcdeg$ & $^h\\\\;\\\\;$$^m\\\\;\\\\;\\\\;\\\\;$$^s\\\\;\\\\;\\\\,$ & \\\\arcdeg$\\\\;\\\\;\\\\;$ \\\\arcmin$\\\\;\\\\;\\\\;$ \\\\arcsec$\\\\;$ & \\\\\\\\\\n\\\\hline\\nTN J1439-3226 & 622$\\\\pm$ 65 & 90.7$\\\\pm$ 1.9 & \\\\nodata & $-1.43\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 14 39 02.87 & $-$32 26 46.6 & N \\\\\\\\\\nTN J1449+1440 & 464$\\\\pm$ 50 & 80.3$\\\\pm$ 3.7 & \\\\nodata & $-1.30\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 14 49 02.50 & $+$14 40 42.2 & N \\\\\\\\\\nTN J1451+2351 & 595$\\\\pm$ 44 & 93.2$\\\\pm$ 4.2 & \\\\nodata & $-1.38\\\\pm$0.07 & \\\\nodata & D & 12.6 & 109 & 14 51 10.71 & $+$23 51 38.8 & F \\\\\\\\\\nTN J1452-1113 & 344$\\\\pm$ 55 & 53.9$\\\\pm$ 2.6 & \\\\nodata & $-1.38\\\\pm$0.13 & \\\\nodata & S & $<$ 7.5 & 2 & 14 52 04.88 & $-$11 13 35.7 & A \\\\\\\\\\nTN J1452+2013 & 291$\\\\pm$ 40 & 43.4$\\\\pm$ 1.0 & \\\\nodata & $-1.42\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 14 52 22.93 & $+$20 13 09.8 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1453+1106 & 833$\\\\pm$ 56 & 144.9$\\\\pm$ 6.4 & \\\\nodata & $-1.30\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 14 53 21.97 & $+$11 06 04.9 & N \\\\\\\\\\nTN J1454+0017 & 1309$\\\\pm$ 88 & 214.8$\\\\pm$ 9.2 & \\\\nodata & $-1.34\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 14 54 40.87 & $+$00 17 41.9 & N \\\\\\\\\\nTN J1459-2730 & 321$\\\\pm$ 40 & 52.5$\\\\pm$ 2.5 & \\\\nodata & $-1.35\\\\pm$0.10 & \\\\nodata & S & 6.5 & 143 & 14 59 34.96 & $-$27 30 08.3 & A \\\\\\\\\\nTN J1506+2728 & 360$\\\\pm$ 58 & 60.7$\\\\pm$ 1.3 & $15.9\\\\pm0.9$ & $-1.32\\\\pm$0.12 & $-1.07\\\\pm0.05$ & D & 1.1 & 131 & 15 06 35.41 & $+$27 28 55.6 & V \\\\\\\\\\nTN J1513-2417 & 504$\\\\pm$ 33 & 83.6$\\\\pm$ 3.7 & \\\\nodata & $-1.34\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 15 13 31.67 & $-$24 17 55.3 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1513-1801 & 534$\\\\pm$ 36 & 85.3$\\\\pm$ 3.9 & \\\\nodata & $-1.36\\\\pm$0.06 & \\\\nodata & S & $<$ 7.5 & 4 & 15 13 55.31 & $-$18 01 07.9 & A \\\\\\\\\\nTN J1515-2651 & 352$\\\\pm$ 44 & 58.0$\\\\pm$ 2.7 & \\\\nodata & $-1.34\\\\pm$0.10 & \\\\nodata & S & 6.5 & 9 & 15 15 59.29 & $-$26 51 14.9 & A \\\\\\\\\\nTN J1520+1410 & 478$\\\\pm$ 55 & 66.0$\\\\pm$ 1.4 & \\\\nodata & $-1.47\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 15 20 53.36 & $+$14 10 45.5 & N \\\\\\\\\\nTN J1521+0741 & 1777$\\\\pm$123 & 105.6$\\\\pm$ 4.5 & \\\\nodata & $-2.10\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 15 21 50.75 & $+$07 41 41.1 & N \\\\\\\\\\nTN J1522-2540 & 464$\\\\pm$ 63 & 54.1$\\\\pm$ 2.6 & \\\\nodata & $-1.60\\\\pm$0.11 & \\\\nodata & S & 8.2 & 10 & 15 22 23.28 & $-$25 40 07.1 & A \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1524+0642 & 479$\\\\pm$ 55 & 82.9$\\\\pm$ 1.7 & \\\\nodata & $-1.30\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 15 24 06.39 & $+$06 42 15.9 & N \\\\\\\\\\nTN J1531-3234 & 522$\\\\pm$ 59 & 80.6$\\\\pm$ 3.6 & \\\\nodata & $-1.39\\\\pm$0.09 & \\\\nodata & S & 4.8 & 27 & 15 31 33.59 & $-$32 34 01.7 & A \\\\\\\\\\nTN J1547-2218 & 427$\\\\pm$ 62 & 72.4$\\\\pm$ 3.3 & \\\\nodata & $-1.32\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 15 47 49.95 & $-$22 18 25.6 & N \\\\\\\\\\nTN J1556-2759 & 612$\\\\pm$ 56 & 66.4$\\\\pm$ 3.1 & \\\\nodata & $-1.65\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 15 56 43.63 & $-$27 59 43.1 & N \\\\\\\\\\nTN J1559-1727 & 575$\\\\pm$ 71 & 97.4$\\\\pm$ 4.3 & \\\\nodata & $-1.32\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 15 59 34.08 & $-$17 27 41.6 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1604-0248 & 345$\\\\pm$ 33 & 46.8$\\\\pm$ 1.0 & \\\\nodata & $-1.49\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 16 04 59.59 & $-$02 48 47.9 & N \\\\\\\\\\nTN J1621+2043 & 539$\\\\pm$ 48 & 61.4$\\\\pm$ 2.9 & \\\\nodata & $-1.62\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 16 21 06.18 & $+$20 43 36.4 & N \\\\\\\\\\nTN J1628+1604 & 602$\\\\pm$ 44 & 55.5$\\\\pm$ 2.6 & \\\\nodata & $-1.77\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 16 28 19.16 & $+$16 04 00.0 & N \\\\\\\\\\nTN J1634-2222 & 4714$\\\\pm$214 & 809.2$\\\\pm$35.4 & \\\\nodata & $-1.31\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 16 34 49.79 & $-$22 22 12.7 & N \\\\\\\\\\nTN J1637-1931 & 432$\\\\pm$ 40 & 36.8$\\\\pm$ 0.9 & \\\\nodata & $-1.83\\\\pm$0.07 & \\\\nodata & S & 10.8 & 6 & 16 37 44.80 & $-$19 31 24.8 & A \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1646-1328 & 608$\\\\pm$ 63 & 102.5$\\\\pm$ 4.6 & \\\\nodata & $-1.32\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 16 46 51.67 & $-$13 28 49.1 & N \\\\\\\\\\nTN J1652-1339 & 328$\\\\pm$ 33 & 56.5$\\\\pm$ 1.3 & \\\\nodata & $-1.31\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 16 52 24.29 & $-$13 39 04.3 & N \\\\\\\\\\nTN J1653-1155 & 1131$\\\\pm$ 60 & 197.0$\\\\pm$ 8.7 & \\\\nodata & $-1.30\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 16 53 52.81 & $-$11 55 59.2 & N \\\\\\\\\\nTN J1656-1521 & 587$\\\\pm$ 79 & 93.9$\\\\pm$ 4.2 & \\\\nodata & $-1.36\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 16 56 03.77 & $-$15 21 23.3 & N \\\\\\\\\\nTN J1701-0101 & 999$\\\\pm$ 55 & 172.2$\\\\pm$ 7.6 & \\\\nodata & $-1.31\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 17 01 37.58 & $-$01 01 13.6 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1701+0252 & 356$\\\\pm$ 38 & 57.1$\\\\pm$ 2.7 & \\\\nodata & $-1.36\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 17 01 54.89 & $+$02 52 13.4 & N \\\\\\\\\\nTN J1702-0811 & 436$\\\\pm$ 38 & 69.9$\\\\pm$ 3.2 & \\\\nodata & $-1.36\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 17 02 04.71 & $-$08 11 07.5 & N \\\\\\\\\\nTN J1702+2015 & 322$\\\\pm$ 48 & 43.4$\\\\pm$ 2.1 & \\\\nodata & $-1.49\\\\pm$0.12 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 17 02 23.02 & $+$20 15 34.2 & N \\\\\\\\\\nTN J1702-0145 & 808$\\\\pm$ 74 & 135.6$\\\\pm$ 6.0 & \\\\nodata & $-1.33\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 17 02 43.11 & $-$01 45 54.0 & N \\\\\\\\\\nTN J1707-1120 & 425$\\\\pm$ 72 & 54.2$\\\\pm$ 2.6 & \\\\nodata & $-1.53\\\\pm$0.13 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 17 07 51.37 & $-$11 20 21.0 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1710-0826 & 445$\\\\pm$ 74 & 69.2$\\\\pm$ 3.2 & \\\\nodata & $-1.38\\\\pm$0.13 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 17 10 20.36 & $-$08 26 40.3 & N \\\\\\\\\\nTN J1714+2226 & 285$\\\\pm$ 48 & 43.3$\\\\pm$ 1.0 & \\\\nodata & $-1.40\\\\pm$0.13 & \\\\nodata & S & 1.6 & 38 & 17 14 53.42 & $+$22 26 18.5 & F \\\\\\\\\\nTN J1821+2433 & 1416$\\\\pm$ 95 & 227.5$\\\\pm$ 4.7 & \\\\nodata & $-1.36\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 18 21 37.07 & $+$24 33 13.8 & N \\\\\\\\\\nTN J1855-3430 & 654$\\\\pm$ 85 & 87.8$\\\\pm$ 3.8 & \\\\nodata & $-1.49\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 18 55 24.12 & $-$34 30 27.7 & N \\\\\\\\\\nTN J1905-3520 & 799$\\\\pm$ 75 & 131.3$\\\\pm$ 5.4 & \\\\nodata & $-1.34\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 19 05 22.67 & $-$35 20 50.9 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J1932-1931 & 5678$\\\\pm$335 & 813.6$\\\\pm$35.5 & \\\\nodata & $-1.45\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 19 32 07.22 & $-$19 31 49.7 & N \\\\\\\\\\nTN J1941-1952 & 1194$\\\\pm$103 & 183.0$\\\\pm$ 3.8 & \\\\nodata & $-1.40\\\\pm$0.07 & \\\\nodata & S & 7.9 & 164 & 19 41 00.07 & $-$19 52 14.0 & A \\\\\\\\\\nTN J1953-0541 & 478$\\\\pm$ 83 & 59.0$\\\\pm$ 2.8 & \\\\nodata & $-1.56\\\\pm$0.13 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 19 53 27.04 & $-$05 41 28.5 & N \\\\\\\\\\nTN J1954-1207 & 657$\\\\pm$ 67 & 102.8$\\\\pm$ 4.6 & \\\\nodata & $-1.38\\\\pm$0.08 & \\\\nodata & S & $<$ 7.0 & 177 & 19 54 24.15 & $-$12 07 48.7 & A \\\\\\\\\\nTN J2007-1316 & 777$\\\\pm$ 46 & 115.4$\\\\pm$ 5.2 & \\\\nodata & $-1.42\\\\pm$0.06 & \\\\nodata & S & 7.2 & 174 & 20 07 53.23 & $-$13 16 43.6 & A \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J2008-1344 & 798$\\\\pm$ 71 & 132.3$\\\\pm$ 2.7 & \\\\nodata & $-1.34\\\\pm$0.07 & \\\\nodata & S & 8.2 & 176 & 20 08 07.48 & $-$13 44 17.8 & A \\\\\\\\\\nTN J2009-3040 & 409$\\\\pm$ 65 & 65.3$\\\\pm$ 3.0 & \\\\nodata & $-1.36\\\\pm$0.12 & \\\\nodata & S & $<$ 7.0 & 144 & 20 09 48.13 & $-$30 40 07.0 & A \\\\\\\\\\nTN J2014-2115 & 348$\\\\pm$ 33 & 48.0$\\\\pm$ 1.1 & \\\\nodata & $-1.47\\\\pm$0.07 & \\\\nodata & D & 56.4 & 11 & 20 14 31.96 & $-$21 14 36.7 & A \\\\\\\\\\nTN J2021+0839 & 880$\\\\pm$ 72 & 145.4$\\\\pm$ 6.4 & \\\\nodata & $-1.34\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 20 21 33.11 & $+$08 39 09.2 & N \\\\\\\\\\nTN J2028+0811 & 455$\\\\pm$ 58 & 74.8$\\\\pm$ 1.6 & \\\\nodata & $-1.34\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 20 28 37.12 & $+$08 11 21.4 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J2028-1934 & 814$\\\\pm$ 88 & 134.4$\\\\pm$ 5.8 & \\\\nodata & $-1.34\\\\pm$0.09 & \\\\nodata & S & 19.2 & 169 & 20 28 48.57 & $-$19 34 03.2 & A \\\\\\\\\\nTN J2029-0858 & 396$\\\\pm$ 34 & 47.2$\\\\pm$ 2.3 & \\\\nodata & $-1.58\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 20 29 49.60 & $-$08 58 48.5 & N \\\\\\\\\\nTN J2034-2735 & 510$\\\\pm$ 70 & 67.4$\\\\pm$ 1.5 & \\\\nodata & $-1.51\\\\pm$0.10 & \\\\nodata & S & $<$ 8.0 & 163 & 20 34 15.74 & $-$27 35 45.6 & A \\\\\\\\\\nTN J2042+1354 & 281$\\\\pm$ 45 & 42.0$\\\\pm$ 1.0 & \\\\nodata & $-1.41\\\\pm$0.12 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 20 42 07.25 & $+$13 54 16.6 & N \\\\\\\\\\nTN J2048-0618 & 881$\\\\pm$ 99 & 150.7$\\\\pm$ 6.6 & \\\\nodata & $-1.31\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 20 48 06.24 & $-$06 18 40.5 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J2049-2223 & 823$\\\\pm$ 86 & 126.1$\\\\pm$ 5.6 & \\\\nodata & $-1.40\\\\pm$0.08 & \\\\nodata & D & 95.0 & 97 & 20 49 43.04 & $-$22 22 56.3 & A \\\\\\\\\\nTN J2051-0527 & 377$\\\\pm$ 79 & 54.7$\\\\pm$ 1.2 & \\\\nodata & $-1.44\\\\pm$0.16 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 20 51 13.39 & $-$05 27 06.1 & N \\\\\\\\\\nTN J2051+0133 & 391$\\\\pm$ 33 & 66.6$\\\\pm$ 3.1 & \\\\nodata & $-1.32\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 20 51 32.31 & $+$01 33 34.9 & N \\\\\\\\\\nTN J2052-0555 & 321$\\\\pm$ 35 & 41.5$\\\\pm$ 0.9 & \\\\nodata & $-1.52\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 20 52 49.93 & $-$05 55 49.1 & N \\\\\\\\\\nTN J2102+2158 & 483$\\\\pm$ 52 & 73.5$\\\\pm$ 1.6 & \\\\nodata & $-1.40\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 02 52.80 & $+$21 58 35.1 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J2103-1917 & 1410$\\\\pm$109 & 228.6$\\\\pm$10.1 & \\\\nodata & $-1.35\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 03 42.91 & $-$19 17 47.7 & N \\\\\\\\\\nTN J2106-2405$^*$ & 2232$\\\\pm$150 & 366.3$\\\\pm$15.9 & \\\\nodata & $-1.34\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 06 58.42 & $-$24 05 04.2 & N \\\\\\\\\\nTN J2107+0933 & 476$\\\\pm$ 56 & 68.0$\\\\pm$ 3.1 & \\\\nodata & $-1.45\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 07 10.61 & $+$09 33 32.5 & N \\\\\\\\\\nTN J2108+0249 & 573$\\\\pm$ 41 & 65.8$\\\\pm$ 3.1 & \\\\nodata & $-1.61\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 08 26.75 & $+$02 49 46.3 & N \\\\\\\\\\nTN J2113+0111 & 553$\\\\pm$ 68 & 90.8$\\\\pm$ 4.1 & \\\\nodata & $-1.34\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 13 50.43 & $+$01 11 22.3 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J2125+2013 & 352$\\\\pm$ 45 & 51.9$\\\\pm$ 2.5 & \\\\nodata & $-1.42\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 25 51.74 & $+$20 13 39.8 & N \\\\\\\\\\nTN J2133+1629 & 1737$\\\\pm$123 & 283.4$\\\\pm$12.4 & \\\\nodata & $-1.35\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 33 29.32 & $+$16 29 19.4 & N \\\\\\\\\\nTN J2134+0946 & 351$\\\\pm$ 47 & 48.0$\\\\pm$ 2.3 & \\\\nodata & $-1.48\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 34 42.85 & $+$09 46 56.6 & N \\\\\\\\\\nTN J2136+0947 & 426$\\\\pm$ 60 & 66.9$\\\\pm$ 3.1 & \\\\nodata & $-1.38\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 36 36.29 & $+$09 47 22.8 & N \\\\\\\\\\nTN J2147-0645 & 382$\\\\pm$ 63 & 57.3$\\\\pm$ 2.7 & \\\\nodata & $-1.41\\\\pm$0.13 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 47 57.13 & $-$06 45 48.8 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J2155-2109 & 449$\\\\pm$ 87 & 77.2$\\\\pm$ 1.6 & \\\\nodata & $-1.31\\\\pm$0.15 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 55 50.90 & $-$21 09 30.0 & N \\\\\\\\\\nTN J2158-2516 & 1225$\\\\pm$ 59 & 200.9$\\\\pm$ 8.9 & \\\\nodata & $-1.34\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 58 11.14 & $-$25 16 01.5 & N \\\\\\\\\\nTN J2201-2822 & 703$\\\\pm$ 54 & 120.5$\\\\pm$ 5.1 & \\\\nodata & $-1.31\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 01 22.94 & $-$28 22 14.0 & N \\\\\\\\\\nTN J2204+1621 & 381$\\\\pm$ 42 & 57.3$\\\\pm$ 2.7 & \\\\nodata & $-1.41\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 04 14.18 & $+$16 21 43.7 & N \\\\\\\\\\nTN J2205-3201 & 430$\\\\pm$ 60 & 65.7$\\\\pm$ 3.1 & \\\\nodata & $-1.40\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 05 27.56 & $-$32 01 23.9 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J2217-1913 & 321$\\\\pm$ 34 & 40.5$\\\\pm$ 2.0 & \\\\nodata & $-1.54\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 17 28.22 & $-$19 13 21.1 & N \\\\\\\\\\nTN J2219-1648 & 301$\\\\pm$ 53 & 32.0$\\\\pm$ 0.8 & \\\\nodata & $-1.67\\\\pm$0.13 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 19 40.06 & $-$16 48 03.1 & N \\\\\\\\\\nTN J2232-2917 & 528$\\\\pm$ 59 & 91.7$\\\\pm$ 1.9 & \\\\nodata & $-1.30\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 32 57.25 & $-$29 17 56.5 & N \\\\\\\\\\nTN J2237-0242 & 727$\\\\pm$ 48 & 125.0$\\\\pm$ 2.6 & \\\\nodata & $-1.31\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 37 22.60 & $-$02 42 23.0 & N \\\\\\\\\\nTN J2239-0429 & 3807$\\\\pm$177 & 571.4$\\\\pm$24.9 & \\\\nodata & $-1.41\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 39 32.85 & $-$04 29 33.9 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J2245+0007 & 297$\\\\pm$ 53 & 51.6$\\\\pm$ 1.1 & \\\\nodata & $-1.30\\\\pm$0.13 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 45 44.99 & $+$00 07 11.3 & N \\\\\\\\\\nTN J2251-1634 & 551$\\\\pm$ 64 & 60.6$\\\\pm$ 1.3 & \\\\nodata & $-1.64\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 51 14.06 & $-$16 34 03.2 & N \\\\\\\\\\nTN J2251-1034 & 862$\\\\pm$ 72 & 138.8$\\\\pm$ 5.9 & \\\\nodata & $-1.36\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 51 22.01 & $-$10 34 18.0 & N \\\\\\\\\\nTN J2252-1618 & 397$\\\\pm$ 60 & 51.6$\\\\pm$ 2.5 & \\\\nodata & $-1.52\\\\pm$0.12 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 52 20.15 & $-$16 18 14.9 & N \\\\\\\\\\nTN J2253-2156 & 425$\\\\pm$ 72 & 59.3$\\\\pm$ 2.8 & \\\\nodata & $-1.47\\\\pm$0.13 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 53 17.03 & $-$21 56 38.0 & N \\\\\\\\\\n\\\\end{tabular}\\n\\\\end{table*}\\n\\\\begin{table*}\\n\\\\tiny\\n\\\\begin{tabular}{lrrrrrrrrrrrr}\\nName & $S_{365}$ & $S_{1400}$ & S$_{4850}$ & $\\\\alpha_{365}^{1400}$ & $\\\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\\\alpha_{J2000}$ & $\\\\delta_{J2000}$ & Pos \\\\\\\\\\n & mJy & mJy & mJy & & & & \\\\arcsec & $\\\\arcdeg$ & $^h\\\\;\\\\;$$^m\\\\;\\\\;\\\\;\\\\;$$^s\\\\;\\\\;\\\\,$ & \\\\arcdeg$\\\\;\\\\;\\\\;$ \\\\arcmin$\\\\;\\\\;\\\\;$ \\\\arcsec$\\\\;$ & \\\\\\\\\\n\\\\hline\\nTN J2301+0555 & 484$\\\\pm$ 62 & 74.1$\\\\pm$ 3.3 & \\\\nodata & $-1.40\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 23 01 18.11 & $+$05 55 01.0 & N \\\\\\\\\\nTN J2303-0251 & 405$\\\\pm$ 56 & 66.5$\\\\pm$ 3.1 & \\\\nodata & $-1.34\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 23 03 55.67 & $-$02 51 08.6 & N \\\\\\\\\\nTN J2310+1358 & 1497$\\\\pm$102 & 251.9$\\\\pm$ 5.2 & \\\\nodata & $-1.33\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 23 10 52.32 & $+$13 58 20.5 & N \\\\\\\\\\nTN J2312-0040 & 293$\\\\pm$ 25 & 45.5$\\\\pm$ 1.0 & \\\\nodata & $-1.39\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 23 12 46.90 & $-$00 40 53.0 & N \\\\\\\\\\nTN J2312-0208 & 1295$\\\\pm$ 80 & 194.8$\\\\pm$ 8.6 & \\\\nodata & $-1.41\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 23 12 55.71 & $-$02 08 39.9 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J2314+2053 & 386$\\\\pm$ 27 & 46.8$\\\\pm$ 2.3 & $ 5.9\\\\pm0.4$ & $-1.57\\\\pm$0.06 & $-1.67\\\\pm0.07$ & S & 0.3 & 129 & 23 14 56.04 & $+$20 53 37.4 & V \\\\\\\\\\nTN J2320+1222 & 1566$\\\\pm$ 93 & 264.3$\\\\pm$ 5.4 & \\\\nodata & $-1.32\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 23 20 07.79 & $+$12 22 06.6 & N \\\\\\\\\\nTN J2333-1508 & 504$\\\\pm$ 68 & 70.2$\\\\pm$ 3.3 & \\\\nodata & $-1.47\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 23 33 06.99 & $-$15 08 12.8 & N \\\\\\\\\\nTN J2335+0634 & 507$\\\\pm$ 58 & 84.3$\\\\pm$ 3.8 & \\\\nodata & $-1.33\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 23 35 06.42 & $+$06 34 38.8 & N \\\\\\\\\\nTN J2350-1321 & 419$\\\\pm$ 35 & 56.1$\\\\pm$ 1.2 & \\\\nodata & $-1.50\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 23 50 15.92 & $-$13 21 16.0 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nTN J2352+0814 & 498$\\\\pm$ 50 & 71.0$\\\\pm$ 3.2 & \\\\nodata & $-1.45\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 23 52 10.44 & $+$08 14 50.0 & N \\\\\\\\\\nTN J2352+0450 & 398$\\\\pm$ 59 & 60.5$\\\\pm$ 2.8 & \\\\nodata & $-1.40\\\\pm$0.12 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 23 52 32.20 & $+$04 50 30.1 & N \\\\\\\\\\nTN J2352-3139 & 573$\\\\pm$ 87 & 85.8$\\\\pm$ 3.8 & $29.0\\\\pm1.5$ & $-1.41\\\\pm$0.12 & $-0.87\\\\pm0.06$ & T & 21.1 & 170 & 23 52 46.79 & $-$31 39 36.9 & V \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\n$^{\\\\dag}$ Not a real USS source; see notes\\n\\n$^*$ See notes\\n\\\\vspace{1cm}\\n\\\\end{table*}\\n\\\\begin{table*}\\n\\\\centerline{\\\\bf Table A.3: MP sample}\\n\\\\tiny\\n\\\\begin{tabular}{rrrrrrrrrrrrr}\\nName & $S_{408}$ & $S_{1420}$ & $S_{4850}$ & $\\\\alpha_{408}^{1420}$ & $\\\\alpha_{408}^{4850}$ & Str & LAS & PA & $\\\\alpha_{J2000}$ & $\\\\delta_{J2000}$ & Pos\\\\\\\\\\n & mJy & mJy & mJy & & & & \\\\arcsec & $\\\\arcdeg$ & $^h\\\\;\\\\;$$^m\\\\;\\\\;\\\\;\\\\;$$^s\\\\;\\\\;\\\\,$ & \\\\arcdeg$\\\\;\\\\;\\\\;$ \\\\arcmin$\\\\;\\\\;\\\\;$\\\\arcsec$\\\\;$ & \\\\\\\\\\n\\\\hline\\nMP J0003-3556 & 2440$\\\\pm$ 80 & \\\\nodata & 103.0$\\\\pm$13.0 & \\\\nodata & $-1.28\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & 00 03 13.11 & $-$35 56 33.8 & M \\\\\\\\\\nMP J0028-5523 & 1910$\\\\pm$ 80 & $ 389\\\\pm 38$ & 86.0$\\\\pm$ 9.0 & $-1.28\\\\pm0.10$ & $-1.25\\\\pm$0.05 & S & 3.7 & 57 & 00 28 53.76 & $-$55 23 28.5 & A \\\\\\\\\\nMP J0100-6403 & 1410$\\\\pm$150 & $ 247\\\\pm 24$ & 56.0$\\\\pm$ 7.0 & $-1.40\\\\pm0.11$ & $-1.30\\\\pm$0.07 & S & 4.2 & 100 & 01 00 32.42 & $-$64 03 13.6 & A \\\\\\\\\\nMP J0103-3225 & 2290$\\\\pm$ 80 & \\\\nodata & 93.0$\\\\pm$13.0 & \\\\nodata & $-1.29\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & 01 03 17.10 & $-$32 25 53.3 & M \\\\\\\\\\nMP J0114-3302 & 1590$\\\\pm$ 90 & $ 396\\\\pm 39$ & 76.0$\\\\pm$12.0 & $-1.11\\\\pm0.14$ & $-1.23\\\\pm$0.07 & D & 22.0 & 119 & 01 14 37.06 & $-$33 02 10.2 & A \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nMP J0118-6331 & 1040$\\\\pm$ 90 & $ 264\\\\pm 26$ & 50.0$\\\\pm$ 7.0 & $-1.10\\\\pm0.09$ & $-1.23\\\\pm$0.07 & S & 4.1 & 48 & 01 18 07.54 & $-$63 31 43.2 & A \\\\\\\\\\nMP J0130-8352 & 950$\\\\pm$ 50 & $ 159\\\\pm 15$ & 23.0$\\\\pm$ 5.0 & $-1.43\\\\pm0.11$ & $-1.50\\\\pm$0.09 & S & 3.2 & 66 & 01 30 07.45 & $-$83 52 29.6 & A \\\\\\\\\\nMP J0141-4421 & 1400$\\\\pm$ 60 & $ 295\\\\pm 29$ & 56.0$\\\\pm$ 9.0 & $-1.25\\\\pm0.10$ & $-1.30\\\\pm$0.07 & D & 29.9 & 95 & 01 41 13.57 & $-$44 21 10.8 & A \\\\\\\\\\nMP J0141-6941 & 3980$\\\\pm$320 & $ 755\\\\pm 75$ & 179.0$\\\\pm$11.0 & $-1.33\\\\pm0.09$ & $-1.25\\\\pm$0.04 & D & 16.1 & 153 & 01 41 55.18 & $-$69 41 33.1 & A \\\\\\\\\\nMP J0155-8521 & 830$\\\\pm$ 70 & \\\\nodata & 38.0$\\\\pm$ 5.0 & \\\\nodata & $-1.25\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & 01 55 16.98 & $-$85 21 07.4 & M \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nMP J0202-5425 & 820$\\\\pm$ 70 & $ 186\\\\pm 18$ & 41.0$\\\\pm$ 8.0 & $-1.19\\\\pm0.09$ & $-1.21\\\\pm$0.09 & D & 14.5 & 5 & 02 02 56.25 & $-$54 25 13.3 & A \\\\\\\\\\nMP J0211-5146 & 900$\\\\pm$ 40 & $ 160\\\\pm 16$ & 43.0$\\\\pm$ 8.0 & $-1.38\\\\pm0.08$ & $-1.23\\\\pm$0.08 & S & 11.1 & 50 & 02 11 44.92 & $-$51 46 47.0 & A \\\\\\\\\\nMP J0249-4145 & 1100$\\\\pm$ 50 & $ 242\\\\pm 24$ & 48.0$\\\\pm$ 9.0 & $-1.21\\\\pm0.08$ & $-1.27\\\\pm$0.08 & S & 8.2 & 49 & 02 49 10.08 & $-$41 45 36.3 & A \\\\\\\\\\nMP J0339-4018 & 3610$\\\\pm$140 & $ 759\\\\pm 75$ & 174.0$\\\\pm$13.0 & $-1.25\\\\pm0.09$ & $-1.22\\\\pm$0.03 & S & 5.6 & 33 & 03 39 48.18 & $-$40 18 22.1 & A \\\\\\\\\\nMP J0340-6507 & 1640$\\\\pm$ 50 & $ 383\\\\pm 38$ & 81.0$\\\\pm$ 8.0 & $-1.17\\\\pm0.10$ & $-1.22\\\\pm$0.04 & D & 14.0 & 18 & 03 40 44.92 & $-$65 07 07.3 & A \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nMP J0446-3305 & 1910$\\\\pm$100 & $ 448\\\\pm 44$ & 82.0$\\\\pm$12.0 & $-1.16\\\\pm0.10$ & $-1.27\\\\pm$0.06 & D & 58.8 & 6 & 04 46 00.21 & $-$33 05 18.3 & A \\\\\\\\\\nMP J0449-5449 & 900$\\\\pm$ 70 & $ 200\\\\pm 20$ & 46.0$\\\\pm$ 8.0 & $-1.20\\\\pm0.09$ & $-1.20\\\\pm$0.08 & S & 4.3 & 56 & 04 49 04.66 & $-$54 49 10.1 & A \\\\\\\\\\nMP J0601-3926 & 2270$\\\\pm$320 & $ 451\\\\pm 45$ & 97.0$\\\\pm$10.0 & $-1.29\\\\pm0.09$ & $-1.27\\\\pm$0.07 & S & 6.2 & 43 & 06 01 00.77 & $-$39 26 18.1 & A \\\\\\\\\\nMP J0605-5036 & 1040$\\\\pm$ 70 & $ 358\\\\pm 35$ & 43.0$\\\\pm$ 8.0 & $-0.85\\\\pm0.10$ & $-1.29\\\\pm$0.08 & D & 9.4 & 105 & 06 05 47.25 & $-$50 36 41.7 & A \\\\\\\\\\nMP J0618-7340 & 750$\\\\pm$ 50 & \\\\nodata & 25.0$\\\\pm$ 6.0 & \\\\nodata & $-1.37\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & 06 18 47.54 & $-$73 40 40.8 & M \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nMP J0648-7118 & 1000$\\\\pm$ 50 & $ 300\\\\pm 30$ & 42.0$\\\\pm$ 7.0 & $-0.96\\\\pm0.09$ & $-1.28\\\\pm$0.07 & S & 2.5 & 45 & 06 48 37.38 & $-$71 18 26.4 & A \\\\\\\\\\nMP J0731-6621 & 870$\\\\pm$ 40 & \\\\nodata & 40.0$\\\\pm$ 7.0 & \\\\nodata & $-1.24\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & 07 31 47.00 & $-$66 21 30.3 & M \\\\\\\\\\nMP J0839-7359 & 1450$\\\\pm$ 60 & \\\\nodata & 69.0$\\\\pm$ 7.0 & \\\\nodata & $-1.23\\\\pm$0.04 & DF & \\\\nodata & \\\\nodata & 08 39 33.28 & $-$73 59 37.4 & M \\\\\\\\\\nMP J1033-3418 & 5590$\\\\pm$250 & \\\\nodata & 268.0$\\\\pm$22.0 & \\\\nodata & $-1.23\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & 10 33 13.04 & $-$34 18 48.4 & M \\\\\\\\\\nMP J1119-3631 & 2440$\\\\pm$ 70 & $ 542\\\\pm 54$ & 113.0$\\\\pm$14.0 & $-1.21\\\\pm0.10$ & $-1.24\\\\pm$0.05 & S & 4.8 & 166 & 11 19 21.81 & $-$36 31 39.5 & A \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nMP J1208-3403 & 4650$\\\\pm$210 & \\\\nodata & 198.0$\\\\pm$18.0 & \\\\nodata & $-1.28\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & 12 08 39.17 & $-$34 03 10.7 & M \\\\\\\\\\nMP J1250-4026 & 6030$\\\\pm$180 & \\\\nodata & 299.0$\\\\pm$18.0 & \\\\nodata & $-1.21\\\\pm$0.03 & \\\\nodata & \\\\nodata & \\\\nodata & 12 50 05.68 & $-$40 26 28.7 & M \\\\\\\\\\nMP J1250-4119 & 1350$\\\\pm$ 60 & $ 167\\\\pm 16$ & 63.0$\\\\pm$ 9.0 & $-1.67\\\\pm0.09$ & $-1.24\\\\pm$0.06 & S & 7.4 & 123 & 12 50 46.49 & $-$41 19 35.7 & A \\\\\\\\\\nMP J1355-7806 & 1690$\\\\pm$ 90 & \\\\nodata & 44.0$\\\\pm$ 6.0 & \\\\nodata & $-1.47\\\\pm$0.06 & DF & \\\\nodata & \\\\nodata & 13 55 35.57 & $-$78 06 43.7 & M \\\\\\\\\\nMP J1657-7423 & 1080$\\\\pm$ 50 & \\\\nodata & 50.0$\\\\pm$ 7.0 & \\\\nodata & $-1.24\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & 16 57 44.73 & $-$74 23 09.3 & M \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nMP J1710-7343 & 910$\\\\pm$ 70 & $ 47\\\\pm 4$ & 26.0$\\\\pm$ 6.0 & $-2.37\\\\pm0.10$ & $-1.44\\\\pm$0.10 & S & \\\\nodata & 149 & 17 10 17.73 & $-$73 43 19.1 & A \\\\\\\\\\nMP J1733-8342 & 4630$\\\\pm$210 & \\\\nodata & 198.0$\\\\pm$12.0 & \\\\nodata & $-1.27\\\\pm$0.03 & \\\\nodata & \\\\nodata & \\\\nodata & 17 33 55.38 & $-$83 42 48.0 & M \\\\\\\\\\nMP J1755-6916 & 1580$\\\\pm$ 90 & $ 486\\\\pm 48$ & 71.0$\\\\pm$ 7.0 & $-0.94\\\\pm0.09$ & $-1.25\\\\pm$0.05 & D & 0.5 & 90 & 17 55 30.23 & $-$69 16 49.8 & A \\\\\\\\\\nMP J1758-6738 & 3000$\\\\pm$140 & $ 478\\\\pm 47$ & 112.0$\\\\pm$ 9.0 & $-1.47\\\\pm0.09$ & $-1.33\\\\pm$0.04 & D & 31.2 & 119 & 17 58 51.25 & $-$67 38 30.5 & A \\\\\\\\\\nMP J1821-7457 & 2190$\\\\pm$110 & \\\\nodata & 77.0$\\\\pm$ 7.0 & \\\\nodata & $-1.35\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & 18 21 59.83 & $-$74 57 47.5 & M \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nMP J1909-7755 & 900$\\\\pm$ 70 & $ 182\\\\pm 18$ & 41.0$\\\\pm$ 6.0 & $-1.28\\\\pm0.09$ & $-1.25\\\\pm$0.07 & D & 27.9 & 81 & 19 09 57.19 & $-$77 56 01.5 & A \\\\\\\\\\nMP J1912-5349 & 1110$\\\\pm$ 70 & $ 441\\\\pm 44$ & 56.0$\\\\pm$ 8.0 & $-0.74\\\\pm0.09$ & $-1.21\\\\pm$0.06 & D & 17.0 & 45 & 19 12 20.77 & $-$53 49 01.3 & A \\\\\\\\\\nMP J1921-6217 & 2110$\\\\pm$ 40 & $ 400\\\\pm 40$ & 79.0$\\\\pm$ 8.0 & $-1.33\\\\pm0.08$ & $-1.33\\\\pm$0.04 & S & 3.4 & 113 & 19 21 03.06 & $-$62 17 25.2 & A \\\\\\\\\\nMP J1921-5431 & 4590$\\\\pm$210 & \\\\nodata & 66.0$\\\\pm$ 8.0 & \\\\nodata & $-1.71\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & 19 21 52.92 & $-$54 31 51.8 & M \\\\\\\\\\nMP J1929-3732 & 3260$\\\\pm$110 & $ 806\\\\pm 80$ & 135.0$\\\\pm$12.0 & $-1.12\\\\pm0.09$ & $-1.29\\\\pm$0.04 & S & 3.7 & 14 & 19 29 08.51 & $-$37 32 48.8 & A \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nMP J1940-4236 & 1340$\\\\pm$ 70 & \\\\nodata & 64.0$\\\\pm$ 9.0 & \\\\nodata & $-1.23\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & 19 40 58.04 & $-$42 36 49.5 & M \\\\\\\\\\nMP J1942-5553 & 2120$\\\\pm$110 & $ 385\\\\pm 38$ & 74.0$\\\\pm$ 8.0 & $-1.37\\\\pm0.08$ & $-1.36\\\\pm$0.05 & S & 6.7 & 176 & 19 42 06.97 & $-$55 53 32.6 & A \\\\\\\\\\nMP J1943-4030 & 4400$\\\\pm$140 & \\\\nodata & 153.0$\\\\pm$12.0 & \\\\nodata & $-1.36\\\\pm$0.03 & DF & \\\\nodata & \\\\nodata & 19 43 52.33 & $-$40 30 10.9 & M \\\\\\\\\\nMP J1953-4852 & 860$\\\\pm$ 30 & $ 143\\\\pm 14$ & 42.0$\\\\pm$ 8.0 & $-1.44\\\\pm0.09$ & $-1.22\\\\pm$0.08 & S & 4.7 & 115 & 19 53 39.88 & $-$48 52 13.8 & A \\\\\\\\\\nMP J2002-5252 & 2730$\\\\pm$130 & $ 411\\\\pm 41$ & 76.0$\\\\pm$ 9.0 & $-1.52\\\\pm0.09$ & $-1.45\\\\pm$0.05 & S & 4.5 & 29 & 20 02 22.89 & $-$52 52 51.8 & A \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nMP J2003-8340 & 1600$\\\\pm$ 80 & $ 253\\\\pm 25$ & 67.0$\\\\pm$ 6.0 & $-1.48\\\\pm0.09$ & $-1.28\\\\pm$0.04 & S & 3.5 & 106 & 20 03 30.73 & $-$83 41 00.0 & A \\\\\\\\\\nMP J2017-5747 & 1860$\\\\pm$160 & $ 287\\\\pm 28$ & 79.0$\\\\pm$ 8.0 & $-1.50\\\\pm0.08$ & $-1.28\\\\pm$0.05 & S & 11.8 & 28 & 20 17 48.11 & $-$57 47 11.9 & A \\\\\\\\\\nMP J2045-6018 & 11160$\\\\pm$340 & $2105\\\\pm210$ & 447.0$\\\\pm$24.0 & $-1.34\\\\pm0.09$ & $-1.30\\\\pm$0.02 & D & 41.6 & 44 & 20 45 21.82 & $-$60 18 51.5 & A \\\\\\\\\\nMP J2048-5750 & 2810$\\\\pm$130 & $ 494\\\\pm 49$ & 137.0$\\\\pm$10.0 & $-1.39\\\\pm0.09$ & $-1.22\\\\pm$0.03 & S & 5.7 & 18 & 20 48 36.64 & $-$57 50 47.6 & A \\\\\\\\\\nMP J2126-5439 & 1180$\\\\pm$ 80 & $ 282\\\\pm 28$ & 57.0$\\\\pm$ 8.0 & $-1.15\\\\pm0.12$ & $-1.22\\\\pm$0.06 & D & 17.1 & 147 & 21 26 53.65 & $-$54 39 36.0 & A \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nMP J2204-5831 & 900$\\\\pm$ 70 & $ 148\\\\pm 14$ & 44.0$\\\\pm$ 8.0 & $-1.45\\\\pm0.08$ & $-1.22\\\\pm$0.08 & S & 10.5 & 11 & 22 04 05.48 & $-$58 31 38.3 & A \\\\\\\\\\nMP J2222-4723 & 910$\\\\pm$ 70 & $ 509\\\\pm 50$ & 45.0$\\\\pm$ 9.0 & $-0.47\\\\pm0.09$ & $-1.21\\\\pm$0.09 & D & 9.1 & 148 & 22 22 53.71 & $-$47 23 12.1 & A \\\\\\\\\\nMP J2226-7654 & 900$\\\\pm$ 60 & $ 203\\\\pm 20$ & 35.0$\\\\pm$ 6.0 & $-1.19\\\\pm0.09$ & $-1.31\\\\pm$0.07 & S & 4.1 & 107 & 22 26 56.90 & $-$76 54 48.0 & A \\\\\\\\\\nMP J2229-3824 & 8210$\\\\pm$210 & \\\\nodata & 412.0$\\\\pm$23.0 & \\\\nodata & $-1.21\\\\pm$0.02 & \\\\nodata & \\\\nodata & \\\\nodata & 22 29 46.94 & $-$38 24 02.9 & M \\\\\\\\\\nMP J2308-6423 & 1750$\\\\pm$ 90 & $ 301\\\\pm 30$ & 39.0$\\\\pm$ 7.0 & $-1.41\\\\pm0.09$ & $-1.54\\\\pm$0.08 & D & 14.3 & 7 & 23 08 45.21 & $-$64 23 33.3 & A \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nMP J2313-4243 & 1390$\\\\pm$ 60 & \\\\nodata & 58.0$\\\\pm$ 9.0 & \\\\nodata & $-1.28\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & 23 13 58.76 & $-$42 43 38.1 & M \\\\\\\\\\nMP J2352-6154 & 1450$\\\\pm$ 40 & $ 311\\\\pm 31$ & 69.0$\\\\pm$ 8.0 & $-1.23\\\\pm0.10$ & $-1.23\\\\pm$0.05 & D & 56.1 & 148 & 23 52 55.52 & $-$61 54 06.9 & A \\\\\\\\\\nMP J2357-3445 & 8700$\\\\pm$350 & \\\\nodata & 117.0$\\\\pm$14.0 & \\\\nodata & $-1.74\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & 23 57 01.09 & $-$34 45 38.9 & M \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\\\end{table*}\\n\"\n },\n {\n \"name\": \"wntable.tex\",\n \"string\": \"\\\\begin{table*}\\n\\\\centerline{\\\\bf Table A.1: WN sample}\\n\\\\tiny\\n \\\\begin{tabular}{lrrrrrrrrrrrr}\\nName & $S_{325}$ & $S_{1400}$ & S$_{4850}$ & $\\\\alpha_{325}^{1400}$ & $\\\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\\\alpha_{J2000}$ & $\\\\delta_{J2000}$ & Pos \\\\\\\\\\n & mJy & mJy & mJy & & & & \\\\arcsec & $\\\\arcdeg$ & $^h\\\\;\\\\;$$^m\\\\;\\\\;\\\\;\\\\;$$^s\\\\;\\\\;\\\\,$ & \\\\arcdeg$\\\\;\\\\;\\\\;$ \\\\arcmin$\\\\;\\\\;\\\\;$ \\\\arcsec$\\\\;$ & \\\\\\\\\\n\\\\hline\\nWN J0000+4654 & 204$\\\\pm$ 9 & 21.1$\\\\pm$ 1.4 & $ 2.97\\\\pm0.13$ & $-1.55\\\\pm$0.06 & $-1.58\\\\pm0.06$ & D & 3.6 & 173 & 00 00 28.88 & +46 54 40.7 & V \\\\\\\\\\nWN J0007+3641 & 447$\\\\pm$18 & 28.8$\\\\pm$ 1.7 & $ 2.51\\\\pm0.11$ & $-1.88\\\\pm$0.05 & $-1.96\\\\pm0.06$ & S & 1.7 & 67 & 00 07 02.92 & +36 41 55.9 & V \\\\\\\\\\nWN J0007+4615 & 144$\\\\pm$ 7 & 16.9$\\\\pm$ 0.5 & \\\\nodata & $-1.47\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 00 07 15.05 & +46 15 40.8 & N \\\\\\\\\\nWN J0016+4311 & 105$\\\\pm$ 6 & 15.7$\\\\pm$ 1.5 & \\\\nodata & $-1.30\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 00 16 40.63 & +43 11 03.5 & N \\\\\\\\\\nWN J0029+3439 & 288$\\\\pm$12 & 40.9$\\\\pm$ 2.0 & $ 44.76\\\\pm1.05$ & $-1.34\\\\pm$0.04 & $ 0.07\\\\pm0.04$ & DF & 12.8 & 80 & 00 29 01.61 & +34 39 34.7 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0034+4142 & 84$\\\\pm$ 6 & 11.0$\\\\pm$ 0.5 & $ 2.50\\\\pm0.12$ & $-1.39\\\\pm$0.05 & $-1.19\\\\pm0.05$ & D & 23.7 & 154 & 00 34 29.21 & +41 42 09.5 & V \\\\\\\\\\nWN J0034+3238 & 120$\\\\pm$ 9 & 16.4$\\\\pm$ 0.5 & \\\\nodata & $-1.36\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 00 34 56.36 & +32 38 36.4 & N \\\\\\\\\\nWN J0038+7859 & 109$\\\\pm$ 6 & 15.1$\\\\pm$ 0.5 & $ 1.30\\\\pm0.09$ & $-1.35\\\\pm$0.04 & $-1.97\\\\pm0.06$ & S & 2.5 & 159 & 00 38 01.96 & +78 59 51.5 & V \\\\\\\\\\nWN J0040+3857 & 127$\\\\pm$ 7 & 17.5$\\\\pm$ 0.5 & $ 3.13\\\\pm0.14$ & $-1.36\\\\pm$0.04 & $-1.38\\\\pm0.04$ & S & 1.4 & 31 & 00 40 56.23 & +38 57 30.0 & V \\\\\\\\\\nWN J0043+4719$^{\\\\dag}$ & 99$\\\\pm$ 6 & 14.2$\\\\pm$ 1.3 & $ 41.81\\\\pm1.01$ & $-1.33\\\\pm$0.08 & $ 0.87\\\\pm0.08$ & T & 18.5 & 157 & 00 43 53.13 & +47 19 48.3 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nWN J0048+4137$^*$ & 277$\\\\pm$11 & 34.5$\\\\pm$ 1.9 & $ 1.75\\\\pm0.10$ & $-1.43\\\\pm$0.05 & $-2.40\\\\pm0.06$ & S & 2.5 & 17 & 00 48 46.34 & +41 37 20.8 & V \\\\\\\\\\nWN J0059+3958 & 152$\\\\pm$ 7 & 11.4$\\\\pm$ 1.4 & \\\\nodata & $-1.77\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 00 59 51.07 & +39 58 46.5 & N \\\\\\\\\\nWN J0112+4039 & 111$\\\\pm$ 7 & 15.4$\\\\pm$ 0.5 & \\\\nodata & $-1.35\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 01 12 26.31 & +40 39 30.1 & N \\\\\\\\\\nWN J0117+3715 & 165$\\\\pm$ 8 & 22.5$\\\\pm$ 0.6 & $ 6.62\\\\pm0.21$ & $-1.36\\\\pm$0.04 & $-0.98\\\\pm0.03$ & S & 1.4 & 71 & 01 17 10.02 & +37 15 16.3 & V \\\\\\\\\\nWN J0121+4305 & 389$\\\\pm$16 & 50.8$\\\\pm$ 2.5 & \\\\nodata & $-1.39\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 01 21 10.71 & +43 05 18.3 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0135+3303 & 94$\\\\pm$ 6 & 12.1$\\\\pm$ 0.5 & $ 10.22\\\\pm0.28$ & $-1.40\\\\pm$0.06 & $-0.14\\\\pm0.04$ & T & 1.8 & 18 & 01 35 07.24 & +33 03 47.4 & V \\\\\\\\\\nWN J0137+3250 & 177$\\\\pm$ 9 & 23.8$\\\\pm$ 1.6 & $ 16.06\\\\pm0.40$ & $-1.37\\\\pm$0.06 & $-0.32\\\\pm0.06$ & T & 27.9 & 104 & 01 36 59.85 & +32 50 40.7 & V \\\\\\\\\\nWN J0155+8036 & 338$\\\\pm$14 & 38.0$\\\\pm$ 0.9 & $ 6.87\\\\pm0.21$ & $-1.50\\\\pm$0.03 & $-1.38\\\\pm0.03$ & D & 4.6 & 159 & 01 55 43.77 & +80 36 48.1 & V \\\\\\\\\\nWN J0207+3655 & 118$\\\\pm$ 6 & 17.5$\\\\pm$ 1.4 & \\\\nodata & $-1.31\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 02 07 22.59 & +36 55 16.0 & N \\\\\\\\\\nWN J0231+3600 & 303$\\\\pm$13 & 45.2$\\\\pm$ 2.2 & $ 7.66\\\\pm0.22$ & $-1.30\\\\pm$0.04 & $-1.43\\\\pm0.05$ & D & 14.8 & 59 & 02 31 11.48 & +36 00 26.6 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0240+3526 & 79$\\\\pm$ 5 & 10.2$\\\\pm$ 0.5 & \\\\nodata & $-1.40\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 02 40 31.10 & +35 26 55.1 & N \\\\\\\\\\nWN J0303+3733 & 1071$\\\\pm$43 & 127.9$\\\\pm$ 5.7 & $ 17.32\\\\pm0.43$ & $-1.46\\\\pm$0.04 & $-1.61\\\\pm0.04$ & D & 4.4 & 3 & 03 03 26.01 & +37 33 41.6 & V \\\\\\\\\\nWN J0303+3629 & 117$\\\\pm$ 6 & 17.1$\\\\pm$ 0.5 & \\\\nodata & $-1.32\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 03 03 29.87 & +36 29 56.1 & N \\\\\\\\\\nWN J0305+3525 & 110$\\\\pm$ 6 & 15.8$\\\\pm$ 1.3 & $ 3.74\\\\pm0.15$ & $-1.33\\\\pm$0.07 & $-1.16\\\\pm0.07$ & S & 1.9 & 64 & 03 05 47.42 & +35 25 13.4 & V \\\\\\\\\\nWN J0310+3644 & 289$\\\\pm$11 & 24.2$\\\\pm$ 0.6 & $ 2.45\\\\pm0.12$ & $-1.70\\\\pm$0.03 & $-1.84\\\\pm0.05$ & S & 2.0 & 118 & 03 10 54.80 & +36 44 02.5 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0315+3757 & 95$\\\\pm$ 5 & 13.3$\\\\pm$ 0.5 & $ 4.74\\\\pm0.17$ & $-1.35\\\\pm$0.05 & $-0.83\\\\pm0.04$ & S & 1.7 & 53 & 03 15 17.29 & +37 57 05.0 & V \\\\\\\\\\nWN J0323+3738 & 205$\\\\pm$ 9 & 22.6$\\\\pm$ 1.5 & $ 8.11\\\\pm0.25$ & $-1.51\\\\pm$0.06 & $-0.83\\\\pm0.06$ & DF & 9.7 & 100 & 03 23 38.24 & +37 38 39.3 & V \\\\\\\\\\nWN J0343+7540 & 118$\\\\pm$ 6 & 12.5$\\\\pm$ 1.6 & \\\\nodata & $-1.54\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 03 43 39.77 & +75 40 43.2 & N \\\\\\\\\\nWN J0346+3039 & 286$\\\\pm$12 & 35.6$\\\\pm$ 1.9 & $ 4.95\\\\pm0.18$ & $-1.43\\\\pm$0.05 & $-1.59\\\\pm0.05$ & D & 0.4 & 89 & 03 46 42.60 & +30 39 51.0 & V \\\\\\\\\\nWN J0352+3143 & 154$\\\\pm$ 7 & 21.8$\\\\pm$ 1.5 & \\\\nodata & $-1.34\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 03 52 24.49 & +31 43 03.1 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0359+3000 & 88$\\\\pm$ 6 & 12.1$\\\\pm$ 0.5 & \\\\nodata & $-1.36\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 03 59 12.86 & +30 00 51.7 & N \\\\\\\\\\nWN J0528+6549 & 96$\\\\pm$ 6 & 10.6$\\\\pm$ 2.4 & $ 1.08\\\\pm0.09$ & $-1.51\\\\pm$0.16 & $-1.84\\\\pm0.19$ & S & 1.9 & 108 & 05 28 46.07 & +65 49 57.3 & V \\\\\\\\\\nWN J0533+7205 & 117$\\\\pm$ 7 & 17.4$\\\\pm$ 1.6 & $ 2.42\\\\pm0.12$ & $-1.30\\\\pm$0.08 & $-1.59\\\\pm0.08$ & D & 2.9 & 140 & 05 33 38.64 & +72 05 52.7 & V \\\\\\\\\\nWN J0538+7348 & 132$\\\\pm$ 7 & 18.1$\\\\pm$ 0.5 & $ 3.20\\\\pm0.14$ & $-1.36\\\\pm$0.04 & $-1.39\\\\pm0.04$ & S & 2.1 & 113 & 05 38 25.59 & +73 48 39.6 & V \\\\\\\\\\nWN J0559+6926 & 87$\\\\pm$ 5 & 12.9$\\\\pm$ 0.5 & $ 1.88\\\\pm0.13$ & $-1.31\\\\pm$0.06 & $-1.55\\\\pm0.06$ & S & 0.3 & 85 & 05 59 06.04 & +69 26 37.8 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0610+6611 & 98$\\\\pm$ 6 & 12.5$\\\\pm$ 1.9 & $ 1.19\\\\pm0.09$ & $-1.41\\\\pm$0.11 & $-1.89\\\\pm0.14$ & S & 2.2 & 114 & 06 10 08.59 & +66 11 43.1 & V \\\\\\\\\\nWN J0617+5012 & 196$\\\\pm$ 9 & 26.5$\\\\pm$ 0.7 & $ 6.80\\\\pm0.23$ & $-1.37\\\\pm$0.04 & $-1.09\\\\pm0.03$ & D & 3.4 & 11 & 06 17 39.37 & +50 12 54.7 & V \\\\\\\\\\nWN J0625+5708 & 71$\\\\pm$ 4 & 10.3$\\\\pm$ 0.5 & $ 1.54\\\\pm0.10$ & $-1.32\\\\pm$0.07 & $-1.53\\\\pm0.06$ & D & 7.3 & 18 & 06 25 01.67 & +57 08 26.1 & V \\\\\\\\\\nWN J0627+7311 & 470$\\\\pm$19 & 61.9$\\\\pm$ 2.9 & $ 4.00\\\\pm0.17$ & $-1.39\\\\pm$0.04 & $-2.20\\\\pm0.05$ & S & $<0.3$ & 0 & 06 27 03.64 & +73 11 54.2 & V \\\\\\\\\\nWN J0633+6024 & 115$\\\\pm$ 6 & 13.4$\\\\pm$ 2.8 & $ 2.07\\\\pm0.11$ & $-1.47\\\\pm$0.15 & $-1.50\\\\pm0.17$ & S & 2.2 & 118 & 06 33 19.70 & +60 24 37.1 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0633+4653 & 3661$\\\\pm$146 & 520.1$\\\\pm$22.8 & $ 80.88\\\\pm1.74$ & $-1.34\\\\pm$0.04 & $-1.50\\\\pm0.04$ & T & 4.0 & 19 & 06 33 52.18 & +46 53 40.5 & V \\\\\\\\\\nWN J0641+4325 & 154$\\\\pm$ 7 & 15.6$\\\\pm$ 0.5 & \\\\nodata & $-1.57\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 06 41 08.23 & +43 25 00.3 & N \\\\\\\\\\nWN J0646+3912 & 166$\\\\pm$ 8 & 20.5$\\\\pm$ 2.4 & \\\\nodata & $-1.43\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 06 46 34.97 & +39 12 00.3 & N \\\\\\\\\\nWN J0648+4309 & 215$\\\\pm$ 9 & 30.4$\\\\pm$ 1.7 & $ 5.00\\\\pm0.19$ & $-1.34\\\\pm$0.05 & $-1.45\\\\pm0.05$ & DF & 1.5 & 151 & 06 48 01.10 & +43 09 47.8 & V \\\\\\\\\\nWN J0648+4137 & 91$\\\\pm$ 5 & 10.9$\\\\pm$ 1.5 & $ 1.69\\\\pm0.11$ & $-1.45\\\\pm$0.11 & $-1.50\\\\pm0.12$ & S & 13.2 & 94 & 06 48 14.58 & +41 37 18.8 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0650+4106 & 393$\\\\pm$16 & 53.5$\\\\pm$ 1.2 & $ 15.04\\\\pm0.41$ & $-1.37\\\\pm$0.03 & $-1.02\\\\pm0.03$ & DF & 3.0 & 26 & 06 50 41.66 & +41 06 39.1 & V \\\\\\\\\\nWN J0653+4434 & 115$\\\\pm$ 6 & 13.1$\\\\pm$ 0.5 & \\\\nodata & $-1.49\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 06 53 23.84 & +44 34 55.4 & N \\\\\\\\\\nWN J0656+5301 & 137$\\\\pm$ 7 & 18.7$\\\\pm$ 1.5 & \\\\nodata & $-1.36\\\\pm$0.07 & \\\\nodata & D & 56.1 & 88 & 06 56 38.40 & +53 01 18.1 & F \\\\\\\\\\nWN J0658+4444 & 407$\\\\pm$17 & 50.6$\\\\pm$ 2.4 & $ 13.91\\\\pm0.35$ & $-1.43\\\\pm$0.04 & $-1.04\\\\pm0.04$ & S & 1.7 & 73 & 06 58 27.43 & +44 44 16.4 & V \\\\\\\\\\nWN J0702+4448 & 147$\\\\pm$ 7 & 17.0$\\\\pm$ 0.5 & \\\\nodata & $-1.48\\\\pm$0.04 & \\\\nodata & S & 7.8 & 119 & 07 02 16.79 & +44 48 59.7 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0711+4242 & 140$\\\\pm$ 6 & 16.0$\\\\pm$ 0.5 & \\\\nodata & $-1.49\\\\pm$0.04 & \\\\nodata & S & 3.3 & 17 & 07 11 40.25 & +42 42 09.6 & F \\\\\\\\\\nWN J0715+4655 & 89$\\\\pm$ 6 & 10.4$\\\\pm$ 0.5 & $ 1.86\\\\pm0.13$ & $-1.47\\\\pm$0.06 & $-1.38\\\\pm0.07$ & S & 0.2 & 114 & 07 15 02.03 & +46 55 26.3 & V \\\\\\\\\\nWN J0716+5107 & 204$\\\\pm$ 9 & 28.4$\\\\pm$ 0.7 & $ 4.54\\\\pm0.18$ & $-1.35\\\\pm$0.04 & $-1.47\\\\pm0.04$ & D & 1.2 & 8 & 07 16 40.50 & +51 07 04.7 & V \\\\\\\\\\nWN J0717+4611$^*$ & 724$\\\\pm$29 & 107.8$\\\\pm$ 4.8 & $ 45.30\\\\pm1.00$ & $-1.30\\\\pm$0.04 & $-0.70\\\\pm0.04$ & T & 6.2 & 16 & 07 17 58.49 & +46 11 39.1 & V \\\\\\\\\\nWN J0720+5140 & 95$\\\\pm$ 6 & 11.6$\\\\pm$ 0.5 & \\\\nodata & $-1.44\\\\pm$0.05 & \\\\nodata & S & 3.2 & 101 & 07 20 00.20 & +51 40 28.5 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0720+5758 & 93$\\\\pm$ 7 & 13.9$\\\\pm$ 0.5 & $ 2.37\\\\pm0.12$ & $-1.30\\\\pm$0.05 & $-1.42\\\\pm0.05$ & S & 2.0 & 109 & 07 20 09.56 & +57 58 32.9 & V \\\\\\\\\\nWN J0721+3324 & 313$\\\\pm$13 & 36.8$\\\\pm$ 1.9 & $ 2.35\\\\pm0.13$ & $-1.47\\\\pm$0.05 & $-2.21\\\\pm0.06$ & DF & 2.0 & 143 & 07 21 56.85 & +33 24 53.8 & V \\\\\\\\\\nWN J0725+4123$^*$ & 272$\\\\pm$12 & 35.5$\\\\pm$ 1.9 & \\\\nodata & $-1.39\\\\pm$0.05 & \\\\nodata & S & 8.3 & 156 & 07 25 57.08 & +41 23 05.1 & F \\\\\\\\\\nWN J0727+3020$^*$ & 93$\\\\pm$ 6 & 12.8$\\\\pm$ 1.9 & \\\\nodata & $-1.36\\\\pm$0.11 & \\\\nodata & D & 34.8 & 103 & 07 27 48.50 & +30 21 00.7 & F \\\\\\\\\\nWN J0736+6845 & 84$\\\\pm$ 5 & 12.4$\\\\pm$ 0.5 & \\\\nodata & $-1.31\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 07 36 36.42 & +68 45 56.8 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0737+7146 & 79$\\\\pm$ 5 & 10.3$\\\\pm$ 0.5 & \\\\nodata & $-1.40\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 07 37 09.93 & +71 46 29.3 & N \\\\\\\\\\nWN J0740+6319 & 254$\\\\pm$11 & 26.1$\\\\pm$ 1.7 & \\\\nodata & $-1.56\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 07 40 27.01 & +63 19 55.2 & N \\\\\\\\\\nWN J0741+5611 & 313$\\\\pm$13 & 44.4$\\\\pm$ 1.0 & $ 7.08\\\\pm0.24$ & $-1.34\\\\pm$0.03 & $-1.48\\\\pm0.03$ & S & 0.5 & 20 & 07 41 15.38 & +56 11 35.9 & V \\\\\\\\\\nWN J0747+3654 & 289$\\\\pm$12 & 36.8$\\\\pm$ 0.8 & \\\\nodata & $-1.41\\\\pm$0.03 & \\\\nodata & S & 2.1 & 2 & 07 47 29.38 & +36 54 38.1 & F \\\\\\\\\\nWN J0747+4527 & 138$\\\\pm$ 7 & 19.1$\\\\pm$ 2.2 & \\\\nodata & $-1.35\\\\pm$0.09 & \\\\nodata & S & 3.5 & 109 & 07 47 29.56 & +45 27 16.3 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0751+3300 & 98$\\\\pm$ 7 & 11.5$\\\\pm$ 0.5 & $ 1.90\\\\pm0.12$ & $-1.47\\\\pm$0.05 & $-1.44\\\\pm0.06$ & S & 0.4 & 139 & 07 51 48.04 & +33 00 07.1 & V \\\\\\\\\\nWN J0756+5010 & 204$\\\\pm$ 9 & 29.9$\\\\pm$ 0.7 & \\\\nodata & $-1.31\\\\pm$0.04 & \\\\nodata & S & 1.7 & 93 & 07 56 24.63 & +50 10 12.5 & F \\\\\\\\\\nWN J0801+7134 & 120$\\\\pm$ 6 & 13.5$\\\\pm$ 2.3 & \\\\nodata & $-1.50\\\\pm$0.13 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 08 01 18.68 & +71 34 01.6 & N \\\\\\\\\\nWN J0809+6624 & 257$\\\\pm$11 & 32.2$\\\\pm$ 2.3 & \\\\nodata & $-1.42\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 08 09 19.28 & +66 24 09.5 & N \\\\\\\\\\nWN J0810+4948 & 146$\\\\pm$ 7 & 18.1$\\\\pm$ 1.4 & $ 2.16\\\\pm0.13$ & $-1.43\\\\pm$0.07 & $-1.74\\\\pm0.08$ & S & $<0.3$ & 0 & 08 10 34.92 & +49 48 37.5 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0812+3424 & 160$\\\\pm$ 8 & 19.9$\\\\pm$ 1.4 & \\\\nodata & $-1.43\\\\pm$0.06 & \\\\nodata & D & 6.6 & 58 & 08 12 14.43 & +34 24 09.3 & F \\\\\\\\\\nWN J0813+4828 & 184$\\\\pm$ 9 & 23.3$\\\\pm$ 1.7 & $ 15.20\\\\pm0.40$ & $-1.42\\\\pm$0.06 & $-0.32\\\\pm0.06$ & D & 0.9 & 173 & 08 13 38.10 & +48 28 41.5 & V \\\\\\\\\\nWN J0819+5628 & 95$\\\\pm$ 6 & 11.7$\\\\pm$ 0.5 & \\\\nodata & $-1.43\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 08 19 33.65 & +56 28 38.1 & N \\\\\\\\\\nWN J0829+3834$^*$ & 112$\\\\pm$ 6 & 12.7$\\\\pm$ 1.3 & \\\\nodata & $-1.49\\\\pm$0.08 & \\\\nodata & S & 1.6 & 0 & 08 29 17.35 & +38 34 52.6 & F \\\\\\\\\\nWN J0830+3018 & 109$\\\\pm$ 6 & 13.9$\\\\pm$ 1.2 & \\\\nodata & $-1.41\\\\pm$0.07 & \\\\nodata & S & 3.5 & 89 & 08 30 36.91 & +30 18 11.8 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0834+4820 & 128$\\\\pm$ 7 & 17.9$\\\\pm$ 0.5 & $ 3.65\\\\pm0.18$ & $-1.35\\\\pm$0.04 & $-1.27\\\\pm0.04$ & S & 0.4 & 99 & 08 34 25.85 & +48 20 00.8 & V \\\\\\\\\\nWN J0835+3439 & 143$\\\\pm$ 7 & 19.1$\\\\pm$ 1.3 & \\\\nodata & $-1.38\\\\pm$0.06 & \\\\nodata & D & 58.0 & 168 & 08 35 22.92 & +34 39 49.8 & F \\\\\\\\\\nWN J0842+3540 & 110$\\\\pm$ 6 & 15.0$\\\\pm$ 0.5 & \\\\nodata & $-1.36\\\\pm$0.04 & \\\\nodata & S & 1.1 & 0 & 08 42 10.82 & +35 40 42.2 & F \\\\\\\\\\nWN J0842+3101 & 76$\\\\pm$ 5 & 10.5$\\\\pm$ 3.6 & \\\\nodata & $-1.36\\\\pm$0.24 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 08 42 16.35 & +31 01 11.6 & N \\\\\\\\\\nWN J0843+3723 & 290$\\\\pm$13 & 35.8$\\\\pm$ 1.9 & \\\\nodata & $-1.43\\\\pm$0.05 & \\\\nodata & S & 1.1 & 5 & 08 43 02.09 & +37 23 18.1 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nWN J0850+4830$^*$ & 192$\\\\pm$ 9 & 18.9$\\\\pm$ 1.4 & $ 1.53\\\\pm0.13$ & $-1.59\\\\pm$0.06 & $-2.02\\\\pm0.09$ & S & 0.3 & 52 & 08 50 56.50 & +48 30 46.2 & V \\\\\\\\\\nWN J0852+3311 & 179$\\\\pm$ 8 & 24.6$\\\\pm$ 1.5 & \\\\nodata & $-1.36\\\\pm$0.05 & \\\\nodata & D & 6.1 & 13 & 08 52 50.55 & +33 11 41.0 & F \\\\\\\\\\nWN J0901+6547$^{\\\\dag}$ & 140$\\\\pm$ 7 & 19.0$\\\\pm$ 0.5 & $ 71.60\\\\pm1.57$ & $-1.37\\\\pm$0.04 & $ 1.07\\\\pm0.03$ & D & 37.6 & 117 & 09 01 27.69 & +65 47 25.8 & V \\\\\\\\\\nWN J0901+3151 & 135$\\\\pm$ 8 & 20.1$\\\\pm$ 1.4 & \\\\nodata & $-1.30\\\\pm$0.06 & \\\\nodata & D & 20.1 & 109 & 09 01 48.50 & +31 51 59.4 & F \\\\\\\\\\nWN J0903+8246 & 112$\\\\pm$ 6 & 15.5$\\\\pm$ 0.5 & \\\\nodata & $-1.35\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 09 03 44.81 & +82 46 02.0 & N \\\\\\\\\\n\\\\end{tabular}\\n\\\\end{table*}\\n\\n\\\\begin{table*}\\n\\\\tiny\\n\\\\begin{tabular}{lrrrrrrrrrrrr}\\nName & $S_{325}$ & $S_{1400}$ & S$_{4850}$ & $\\\\alpha_{325}^{1400}$ & $\\\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\\\alpha_{J2000}$ & $\\\\delta_{J2000}$ & Pos \\\\\\\\\\n & mJy & mJy & mJy & & & & \\\\arcsec & $\\\\arcdeg$ & $^h\\\\;\\\\;$$^m\\\\;\\\\;\\\\;\\\\;$$^s\\\\;\\\\;\\\\,$ & \\\\arcdeg$\\\\;\\\\;\\\\;$ \\\\arcmin$\\\\;\\\\;\\\\;$ \\\\arcsec$\\\\;$ & \\\\\\\\\\n\\\\hline\\nWN J0911+6306 & 118$\\\\pm$ 6 & 12.9$\\\\pm$ 1.3 & \\\\nodata & $-1.52\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 09 11 34.24 & +63 06 21.7 & N \\\\\\\\\\nWN J0913+6104 & 297$\\\\pm$12 & 33.8$\\\\pm$ 1.8 & \\\\nodata & $-1.49\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 09 13 05.21 & +61 04 11.7 & N \\\\\\\\\\nWN J0915+8133 & 127$\\\\pm$ 5 & 18.6$\\\\pm$ 0.6 & $ 2.99\\\\pm0.13$ & $-1.32\\\\pm$0.04 & $-1.47\\\\pm0.04$ & S & 2.3 & 127 & 09 15 09.29 & +81 33 34.1 & V \\\\\\\\\\nWN J0920+5544 & 142$\\\\pm$ 7 & 13.5$\\\\pm$ 1.2 & \\\\nodata & $-1.61\\\\pm$0.07 & \\\\nodata & D & 8.9 & 129 & 09 20 46.78 & +55 44 21.8 & F \\\\\\\\\\nWN J0923+4602 & 107$\\\\pm$ 5 & 12.1$\\\\pm$ 0.5 & \\\\nodata & $-1.49\\\\pm$0.06 & \\\\nodata & D & 21.6 & 172 & 09 23 10.44 & +46 02 59.0 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0928+6003 & 119$\\\\pm$ 6 & 11.0$\\\\pm$ 0.5 & $ 2.14\\\\pm0.11$ & $-1.63\\\\pm$0.05 & $-1.32\\\\pm0.06$ & S & 3.4 & 128 & 09 28 44.58 & +60 03 01.7 & V \\\\\\\\\\nWN J0930+4358 & 118$\\\\pm$ 7 & 12.0$\\\\pm$ 0.5 & \\\\nodata & $-1.57\\\\pm$0.05 & \\\\nodata & S & 3.1 & 88 & 09 30 12.14 & +43 58 27.2 & F \\\\\\\\\\nWN J0930+3207 & 218$\\\\pm$ 9 & 31.1$\\\\pm$ 1.7 & \\\\nodata & $-1.33\\\\pm$0.05 & \\\\nodata & S & 11.7 & 58 & 09 30 53.32 & +32 07 20.8 & F \\\\\\\\\\nWN J0939+6323 & 268$\\\\pm$11 & 39.7$\\\\pm$ 2.0 & $ 10.86\\\\pm0.29$ & $-1.31\\\\pm$0.05 & $-1.04\\\\pm0.05$ & T & 30.3 & 27 & 09 39 54.89 & +63 23 31.9 & V \\\\\\\\\\nWN J0940+3838 & 108$\\\\pm$ 6 & 11.8$\\\\pm$ 1.6 & \\\\nodata & $-1.52\\\\pm$0.10 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 09 40 26.15 & +38 38 35.0 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J0946+6726 & 632$\\\\pm$25 & 84.7$\\\\pm$ 3.7 & $ 40.19\\\\pm0.88$ & $-1.38\\\\pm$0.04 & $-0.60\\\\pm0.04$ & T & 44.8 & 114 & 09 46 44.25 & +67 26 41.8 & V \\\\\\\\\\nWN J0948+6305 & 731$\\\\pm$29 & 90.5$\\\\pm$ 1.9 & $ 14.46\\\\pm0.38$ & $-1.43\\\\pm$0.03 & $-1.48\\\\pm0.03$ & D & 3.1 & 134 & 09 48 40.83 & +63 05 42.0 & V \\\\\\\\\\nWN J0952+5153 & 211$\\\\pm$10 & 16.1$\\\\pm$ 1.3 & \\\\nodata & $-1.76\\\\pm$0.06 & \\\\nodata & S & 2.7 & 166 & 09 52 49.14 & +51 53 05.0 & F \\\\\\\\\\nWN J0955+6023 & 103$\\\\pm$ 6 & 10.9$\\\\pm$ 1.6 & $ 4.32\\\\pm0.15$ & $-1.54\\\\pm$0.11 & $-0.75\\\\pm0.12$ & DF & 3.1 & 129 & 09 55 30.01 & +60 23 17.1 & V \\\\\\\\\\nWN J1002+5512 & 119$\\\\pm$ 5 & 17.7$\\\\pm$ 0.5 & \\\\nodata & $-1.30\\\\pm$0.05 & \\\\nodata & S & 10.4 & 58 & 10 02 39.24 & +55 12 55.5 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1003+4448 & 94$\\\\pm$ 5 & 13.9$\\\\pm$ 2.0 & \\\\nodata & $-1.31\\\\pm$0.11 & \\\\nodata & DF & 17.2 & 93 & 10 03 30.22 & +44 48 16.2 & F \\\\\\\\\\nWN J1012+3334$^*$ & 168$\\\\pm$ 8 & 16.4$\\\\pm$ 1.6 & \\\\nodata & $-1.59\\\\pm$0.07 & \\\\nodata & D & 22.1 & 6 & 10 12 00.43 & +33 35 00.9 & F \\\\\\\\\\nWN J1013+3254 & 102$\\\\pm$ 7 & 14.2$\\\\pm$ 0.5 & \\\\nodata & $-1.35\\\\pm$0.05 & \\\\nodata & S & $<0.3$ & 89 & 10 13 06.54 & +32 54 33.2 & F \\\\\\\\\\nWN J1014+7407 & 170$\\\\pm$ 8 & 21.8$\\\\pm$ 0.6 & $ 3.76\\\\pm0.14$ & $-1.41\\\\pm$0.04 & $-1.41\\\\pm0.04$ & S & 2.2 & 150 & 10 14 15.75 & +74 07 56.2 & V \\\\\\\\\\nWN J1015+3038 & 285$\\\\pm$12 & 38.0$\\\\pm$ 1.9 & \\\\nodata & $-1.38\\\\pm$0.04 & \\\\nodata & D & 12.8 & 151 & 10 15 08.92 & +30 38 02.0 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1015+7432 & 146$\\\\pm$ 7 & 21.4$\\\\pm$ 0.6 & \\\\nodata & $-1.31\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 10 15 52.49 & +74 32 20.0 & N \\\\\\\\\\nWN J1018+3634 & 137$\\\\pm$ 7 & 20.0$\\\\pm$ 1.4 & \\\\nodata & $-1.32\\\\pm$0.06 & \\\\nodata & S & $<0.3$ & 180 & 10 18 03.13 & +36 34 43.2 & F \\\\\\\\\\nWN J1019+5244 & 85$\\\\pm$ 5 & 10.5$\\\\pm$ 0.4 & \\\\nodata & $-1.43\\\\pm$0.06 & \\\\nodata & D & 16.5 & 145 & 10 19 20.59 & +52 44 33.2 & F \\\\\\\\\\nWN J1022+3308 & 90$\\\\pm$ 5 & 10.1$\\\\pm$ 0.4 & \\\\nodata & $-1.50\\\\pm$0.05 & \\\\nodata & S & 7.8 & 136 & 10 22 37.44 & +33 08 43.6 & F \\\\\\\\\\nWN J1026+2943 & 81$\\\\pm$ 6 & 12.0$\\\\pm$ 1.2 & \\\\nodata & $-1.31\\\\pm$0.08 & \\\\nodata & S & 11.9 & 20 & 10 26 12.04 & +29 43 48.0 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1029+4838 & 118$\\\\pm$ 8 & 17.2$\\\\pm$ 1.4 & $ 2.80\\\\pm0.16$ & $-1.32\\\\pm$0.07 & $-1.46\\\\pm0.08$ & S & 2.0 & 131 & 10 29 32.99 & +48 38 09.0 & V \\\\\\\\\\nWN J1030+5415 & 223$\\\\pm$10 & 29.2$\\\\pm$ 1.6 & \\\\nodata & $-1.39\\\\pm$0.05 & \\\\nodata & S & 6.1 & 44 & 10 30 42.94 & +54 15 35.9 & F \\\\\\\\\\nWN J1036+3936 & 153$\\\\pm$ 7 & 16.7$\\\\pm$ 0.5 & \\\\nodata & $-1.52\\\\pm$0.04 & \\\\nodata & T & 17.5 & 107 & 10 36 21.29 & +39 36 59.4 & F \\\\\\\\\\nWN J1038+4229 & 816$\\\\pm$33 & 114.0$\\\\pm$ 5.1 & \\\\nodata & $-1.35\\\\pm$0.04 & \\\\nodata & S & 1.2 & 3 & 10 38 41.04 & +42 29 51.5 & F \\\\\\\\\\nWN J1041+5859 & 193$\\\\pm$ 9 & 25.2$\\\\pm$ 0.6 & $ 6.96\\\\pm0.22$ & $-1.39\\\\pm$0.04 & $-1.04\\\\pm0.03$ & D & 11.2 & 119 & 10 41 29.64 & +58 59 23.5 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1043+3953 & 95$\\\\pm$ 8 & 13.9$\\\\pm$ 0.5 & \\\\nodata & $-1.32\\\\pm$0.05 & \\\\nodata & S & $<0.3$ & 79 & 10 43 32.24 & +39 53 46.8 & F \\\\\\\\\\nWN J1052+4826 & 1039$\\\\pm$41 & 154.2$\\\\pm$ 6.8 & \\\\nodata & $-1.31\\\\pm$0.04 & \\\\nodata & D & 10.0 & 108 & 10 52 53.05 & +48 26 33.8 & F \\\\\\\\\\nWN J1053+5424 & 467$\\\\pm$20 & 66.4$\\\\pm$ 1.4 & $ 7.94\\\\pm0.25$ & $-1.34\\\\pm$0.03 & $-1.70\\\\pm0.03$ & D & 1.1 & 34 & 10 53 36.31 & +54 24 42.1 & V \\\\\\\\\\nWN J1055+3047 & 342$\\\\pm$14 & 39.0$\\\\pm$ 2.0 & \\\\nodata & $-1.49\\\\pm$0.05 & \\\\nodata & S & 7.1 & 147 & 10 55 18.52 & +30 47 23.2 & F \\\\\\\\\\nWN J1057+3156 & 221$\\\\pm$10 & 22.2$\\\\pm$ 1.5 & \\\\nodata & $-1.57\\\\pm$0.06 & \\\\nodata & T & 28.7 & 20 & 10 57 56.56 & +31 56 21.0 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1057+3007 & 276$\\\\pm$12 & 39.5$\\\\pm$ 2.0 & \\\\nodata & $-1.33\\\\pm$0.05 & \\\\nodata & D & 24.6 & 90 & 10 57 57.45 & +30 07 02.9 & F \\\\\\\\\\nWN J1058+3506 & 205$\\\\pm$10 & 24.0$\\\\pm$ 1.5 & \\\\nodata & $-1.47\\\\pm$0.05 & \\\\nodata & S & 1.3 & 126 & 10 58 14.74 & +35 06 40.9 & F \\\\\\\\\\nWN J1058+7003 & 82$\\\\pm$ 4 & 10.5$\\\\pm$ 0.5 & \\\\nodata & $-1.41\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 10 58 34.95 & +70 03 17.6 & N \\\\\\\\\\nWN J1059+4341 & 99$\\\\pm$ 8 & 12.3$\\\\pm$ 1.6 & \\\\nodata & $-1.43\\\\pm$0.10 & \\\\nodata & D & 29.1 & 66 & 10 59 43.88 & +43 41 05.2 & F \\\\\\\\\\nWN J1101+3520$^*$ & 120$\\\\pm$ 7 & 17.5$\\\\pm$ 2.1 & \\\\nodata & $-1.32\\\\pm$0.09 & \\\\nodata & S & 8.1 & 1 & 11 01 14.35 & +35 20 12.7 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nWN J1111+3311 & 92$\\\\pm$ 6 & 13.3$\\\\pm$ 0.5 & \\\\nodata & $-1.32\\\\pm$0.05 & \\\\nodata & S & 6.7 & 16 & 11 11 40.79 & +33 12 00.9 & F \\\\\\\\\\nWN J1115+5016 & 232$\\\\pm$10 & 33.9$\\\\pm$ 0.8 & $ 5.47\\\\pm0.22$ & $-1.32\\\\pm$0.03 & $-1.46\\\\pm0.04$ & D & 0.2 & 117 & 11 15 06.87 & +50 16 23.9 & V \\\\\\\\\\nWN J1117+5251 & 1439$\\\\pm$57 & 198.7$\\\\pm$ 8.7 & \\\\nodata & $-1.36\\\\pm$0.04 & \\\\nodata & D & 9.5 & 6 & 11 17 24.37 & +52 51 54.6 & F \\\\\\\\\\nWN J1122+3239 & 143$\\\\pm$ 7 & 19.5$\\\\pm$ 1.4 & \\\\nodata & $-1.36\\\\pm$0.06 & \\\\nodata & S & 4.2 & 89 & 11 22 33.53 & +32 39 40.9 & F \\\\\\\\\\nWN J1123+3141 & 623$\\\\pm$25 & 74.0$\\\\pm$ 3.3 & \\\\nodata & $-1.46\\\\pm$0.04 & \\\\nodata & T & 25.8 & 83 & 11 23 55.85 & +31 41 26.1 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1124+3228 & 263$\\\\pm$11 & 38.9$\\\\pm$ 0.9 & \\\\nodata & $-1.31\\\\pm$0.03 & \\\\nodata & S & 5.7 & 165 & 11 24 34.17 & +32 28 19.6 & F \\\\\\\\\\nWN J1126+8318 & 175$\\\\pm$ 8 & 25.8$\\\\pm$ 1.6 & \\\\nodata & $-1.31\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 11 26 26.48 & +83 18 23.8 & N \\\\\\\\\\nWN J1128+4822 & 280$\\\\pm$12 & 29.9$\\\\pm$ 0.7 & \\\\nodata & $-1.53\\\\pm$0.03 & \\\\nodata & S & 1.2 & 171 & 11 28 05.19 & +48 22 56.6 & F \\\\\\\\\\nWN J1128+6416 & 257$\\\\pm$11 & 31.0$\\\\pm$ 1.7 & $ 3.20\\\\pm0.17$ & $-1.45\\\\pm$0.05 & $-1.82\\\\pm0.06$ & S & 0.8 & 116 & 11 28 12.10 & +64 16 25.3 & V \\\\\\\\\\nWN J1130+4911 & 134$\\\\pm$ 6 & 18.9$\\\\pm$ 1.5 & \\\\nodata & $-1.34\\\\pm$0.07 & \\\\nodata & T & 37.0 & 145 & 11 30 17.53 & +49 11 17.7 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1139+3048 & 819$\\\\pm$33 & 119.6$\\\\pm$ 5.3 & \\\\nodata & $-1.32\\\\pm$0.04 & \\\\nodata & D & 9.0 & 40 & 11 39 14.34 & +30 48 50.7 & F \\\\\\\\\\nWN J1139+3706 & 139$\\\\pm$ 8 & 16.7$\\\\pm$ 1.4 & \\\\nodata & $-1.45\\\\pm$0.07 & \\\\nodata & S & 3.5 & 32 & 11 39 43.04 & +37 06 55.7 & F \\\\\\\\\\nWN J1141+6924 & 81$\\\\pm$ 5 & 11.8$\\\\pm$ 0.5 & \\\\nodata & $-1.32\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 11 41 09.71 & +69 24 16.3 & N \\\\\\\\\\nWN J1148+5116 & 148$\\\\pm$ 7 & 20.5$\\\\pm$ 1.7 & \\\\nodata & $-1.35\\\\pm$0.07 & \\\\nodata & D & 6.7 & 50 & 11 48 01.92 & +51 16 29.6 & F \\\\\\\\\\nWN J1148+6233 & 98$\\\\pm$ 5 & 14.1$\\\\pm$ 0.5 & $ 1.37\\\\pm0.09$ & $-1.33\\\\pm$0.05 & $-1.88\\\\pm0.06$ & S & 2.4 & 144 & 11 48 44.42 & +62 33 24.6 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1148+3519 & 114$\\\\pm$ 7 & 13.9$\\\\pm$ 1.7 & \\\\nodata & $-1.44\\\\pm$0.09 & \\\\nodata & D & 20.0 & 7 & 11 48 54.29 & +35 19 10.1 & F \\\\\\\\\\nWN J1151+4436 & 78$\\\\pm$ 5 & 11.1$\\\\pm$ 0.5 & \\\\nodata & $-1.34\\\\pm$0.06 & \\\\nodata & D & 15.1 & 20 & 11 51 16.80 & +44 36 10.0 & F \\\\\\\\\\nWN J1152+3732$^*$ & 414$\\\\pm$17 & 17.1$\\\\pm$ 1.4 & \\\\nodata & $-2.18\\\\pm$0.06 & \\\\nodata & S & 15.0 & 119 & 11 52 36.34 & +37 32 43.9 & F \\\\\\\\\\nWN J1154+5415 & 153$\\\\pm$ 7 & 19.1$\\\\pm$ 0.5 & $ 1.05\\\\pm0.10$ & $-1.42\\\\pm$0.04 & $-2.33\\\\pm0.08$ & S & $<0.3$ & 0 & 11 54 18.97 & +54 15 11.4 & V \\\\\\\\\\nWN J1203+8350 & 132$\\\\pm$ 6 & 18.5$\\\\pm$ 0.5 & \\\\nodata & $-1.35\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 12 03 30.63 & +83 50 37.1 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1204+5014 & 94$\\\\pm$ 5 & 11.3$\\\\pm$ 1.7 & \\\\nodata & $-1.45\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 12 04 31.11 & +50 14 49.8 & N \\\\\\\\\\nWN J1206+3136 & 167$\\\\pm$ 9 & 22.2$\\\\pm$ 1.5 & \\\\nodata & $-1.38\\\\pm$0.06 & \\\\nodata & D & 16.6 & 53 & 12 06 48.10 & +31 36 50.9 & F \\\\\\\\\\nWN J1208+4301 & 162$\\\\pm$ 8 & 13.9$\\\\pm$ 1.4 & \\\\nodata & $-1.68\\\\pm$0.08 & \\\\nodata & T & 8.0 & 27 & 12 08 42.77 & +43 01 42.3 & F \\\\\\\\\\nWN J1216+4446 & 191$\\\\pm$ 8 & 13.6$\\\\pm$ 0.5 & \\\\nodata & $-1.81\\\\pm$0.04 & \\\\nodata & S & 6.1 & 98 & 12 16 46.84 & +44 46 51.3 & F \\\\\\\\\\nWN J1218+3143 & 1906$\\\\pm$76 & 281.5$\\\\pm$12.4 & \\\\nodata & $-1.31\\\\pm$0.04 & \\\\nodata & S & 5.6 & 65 & 12 18 31.47 & +31 43 41.7 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1219+4644 & 140$\\\\pm$ 8 & 20.9$\\\\pm$ 0.6 & $ 2.84\\\\pm0.14$ & $-1.30\\\\pm$0.04 & $-1.59\\\\pm0.05$ & S & 0.2 & 157 & 12 19 31.79 & +46 44 49.6 & V \\\\\\\\\\nWN J1223+4256 & 116$\\\\pm$ 6 & 17.2$\\\\pm$ 0.5 & \\\\nodata & $-1.31\\\\pm$0.04 & \\\\nodata & S & 4.3 & 179 & 12 23 11.32 & +42 56 57.3 & F \\\\\\\\\\nWN J1224+4956 & 145$\\\\pm$ 7 & 21.4$\\\\pm$ 1.6 & \\\\nodata & $-1.31\\\\pm$0.06 & \\\\nodata & T & 39.6 & 66 & 12 24 21.03 & +49 56 49.2 & F \\\\\\\\\\nWN J1224+5436 & 790$\\\\pm$31 & 69.1$\\\\pm$ 1.5 & $ 6.30\\\\pm0.20$ & $-1.67\\\\pm$0.03 & $-1.92\\\\pm0.03$ & D & 0.9 & 16 & 12 24 52.35 & +54 36 39.9 & V \\\\\\\\\\nWN J1226+4836 & 155$\\\\pm$ 8 & 17.0$\\\\pm$ 0.5 & \\\\nodata & $-1.51\\\\pm$0.04 & \\\\nodata & S & 4.8 & 115 & 12 26 22.45 & +48 36 39.6 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nWN J1232+4621$^*$ & 133$\\\\pm$ 6 & 19.8$\\\\pm$ 1.8 & \\\\nodata & $-1.30\\\\pm$0.07 & \\\\nodata & DF & 12.5 & 156 & 12 32 39.79 & +46 21 48.1 & F \\\\\\\\\\nWN J1242+3915 & 549$\\\\pm$22 & 78.4$\\\\pm$ 1.7 & \\\\nodata & $-1.33\\\\pm$0.03 & \\\\nodata & D & 11.2 & 51 & 12 42 53.09 & +39 15 48.6 & F \\\\\\\\\\nWN J1247+6121 & 103$\\\\pm$ 5 & 15.4$\\\\pm$ 2.4 & \\\\nodata & $-1.30\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 12 47 45.31 & +61 21 23.3 & N \\\\\\\\\\nWN J1249+4043 & 160$\\\\pm$ 7 & 22.8$\\\\pm$ 1.4 & \\\\nodata & $-1.33\\\\pm$0.05 & \\\\nodata & D & 37.0 & 80 & 12 49 27.43 & +40 43 49.3 & F \\\\\\\\\\nWN J1258+3212 & 182$\\\\pm$12 & 19.9$\\\\pm$ 1.5 & \\\\nodata & $-1.52\\\\pm$0.06 & \\\\nodata & S & 6.7 & 131 & 12 58 23.62 & +32 12 42.4 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1258+5041 & 230$\\\\pm$11 & 28.8$\\\\pm$ 2.0 & \\\\nodata & $-1.42\\\\pm$0.06 & \\\\nodata & T & 44.9 & 58 & 12 58 50.96 & +50 41 42.3 & F \\\\\\\\\\nWN J1259+3121 & 268$\\\\pm$11 & 34.0$\\\\pm$ 1.8 & \\\\nodata & $-1.41\\\\pm$0.05 & \\\\nodata & DF & 20.6 & 1 & 12 59 51.96 & +31 21 05.6 & F \\\\\\\\\\nWN J1300+5311 & 157$\\\\pm$ 7 & 19.2$\\\\pm$ 0.5 & $ 2.70\\\\pm0.16$ & $-1.44\\\\pm$0.04 & $-1.58\\\\pm0.05$ & S & 0.3 & 7 & 13 00 36.25 & +53 11 52.4 & V \\\\\\\\\\nWN J1302+3206 & 383$\\\\pm$16 & 54.0$\\\\pm$ 1.2 & \\\\nodata & $-1.34\\\\pm$0.03 & \\\\nodata & S & 4.7 & 102 & 13 02 03.07 & +32 06 35.6 & F \\\\\\\\\\nWN J1303+8024 & 165$\\\\pm$ 7 & 22.2$\\\\pm$ 0.6 & $ 5.05\\\\pm0.18$ & $-1.37\\\\pm$0.03 & $-1.19\\\\pm0.04$ & D & 4.1 & 145 & 13 03 33.92 & +80 24 42.2 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1303+5437 & 145$\\\\pm$ 7 & 15.4$\\\\pm$ 1.4 & \\\\nodata & $-1.54\\\\pm$0.07 & \\\\nodata & D & 16.5 & 88 & 13 03 45.48 & +54 37 28.9 & F \\\\\\\\\\nWN J1306+4726 & 100$\\\\pm$ 7 & 13.1$\\\\pm$ 0.5 & \\\\nodata & $-1.39\\\\pm$0.05 & \\\\nodata & S & 10.2 & 40 & 13 06 35.99 & +47 26 10.1 & F \\\\\\\\\\nWN J1310+5706 & 112$\\\\pm$ 6 & 15.9$\\\\pm$ 0.5 & \\\\nodata & $-1.34\\\\pm$0.04 & \\\\nodata & S & 4.2 & 99 & 13 10 22.96 & +57 06 57.9 & F \\\\\\\\\\nWN J1310+3820 & 69$\\\\pm$ 4 & 10.3$\\\\pm$ 1.5 & \\\\nodata & $-1.30\\\\pm$0.12 & \\\\nodata & S & 4.4 & 18 & 13 10 24.08 & +38 20 44.1 & F \\\\\\\\\\nWN J1312+6646 & 291$\\\\pm$12 & 41.6$\\\\pm$ 0.9 & $ 8.56\\\\pm0.24$ & $-1.33\\\\pm$0.03 & $-1.27\\\\pm0.03$ & D & 6.3 & 118 & 13 12 45.59 & +66 46 36.1 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1314+3649 & 286$\\\\pm$11 & 36.4$\\\\pm$ 0.8 & \\\\nodata & $-1.41\\\\pm$0.03 & \\\\nodata & S & 1.3 & 90 & 13 14 17.86 & +36 49 14.6 & F \\\\\\\\\\nWN J1314+3515$^*$ & 169$\\\\pm$ 7 & 20.2$\\\\pm$ 1.7 & \\\\nodata & $-1.45\\\\pm$0.07 & \\\\nodata & DF & 34.2 & 47 & 13 14 25.00 & +35 15 53.9 & F \\\\\\\\\\nWN J1315+4337 & 149$\\\\pm$ 8 & 16.3$\\\\pm$ 0.5 & \\\\nodata & $-1.52\\\\pm$0.04 & \\\\nodata & S & 1.3 & 152 & 13 15 19.05 & +43 37 57.1 & F \\\\\\\\\\nWN J1321+3311 & 141$\\\\pm$ 8 & 19.0$\\\\pm$ 0.6 & \\\\nodata & $-1.37\\\\pm$0.04 & \\\\nodata & D & 14.7 & 63 & 13 21 13.55 & +33 11 31.2 & F \\\\\\\\\\nWN J1323+4713 & 106$\\\\pm$ 5 & 14.9$\\\\pm$ 0.5 & \\\\nodata & $-1.34\\\\pm$0.04 & \\\\nodata & S & 2.5 & 139 & 13 23 08.31 & +47 13 10.7 & F \\\\\\\\\\n\\\\end{tabular}\\n\\\\end{table*}\\n\\n\\\\begin{table*}\\n\\\\tiny\\n\\\\begin{tabular}{lrrrrrrrrrrrr}\\nName & $S_{325}$ & $S_{1400}$ & S$_{4850}$ & $\\\\alpha_{325}^{1400}$ & $\\\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\\\alpha_{J2000}$ & $\\\\delta_{J2000}$ & Pos \\\\\\\\\\n & mJy & mJy & mJy & & & & \\\\arcsec & $\\\\arcdeg$ & $^h\\\\;\\\\;$$^m\\\\;\\\\;\\\\;\\\\;$$^s\\\\;\\\\;\\\\,$ & \\\\arcdeg$\\\\;\\\\;\\\\;$ \\\\arcmin$\\\\;\\\\;\\\\;$ \\\\arcsec$\\\\;$ & \\\\\\\\\\n\\\\hline\\nWN J1327+5341 & 196$\\\\pm$ 9 & 27.4$\\\\pm$ 0.7 & \\\\nodata & $-1.35\\\\pm$0.04 & \\\\nodata & S & 0.6 & 162 & 13 27 12.77 & +53 41 20.6 & F \\\\\\\\\\nWN J1327+5332 & 163$\\\\pm$ 7 & 20.5$\\\\pm$ 0.6 & $ 2.70\\\\pm0.17$ & $-1.42\\\\pm$0.04 & $-1.61\\\\pm0.06$ & D & 0.3 & 89 & 13 27 37.86 & +53 32 10.8 & V \\\\\\\\\\nWN J1329+3046$^*$ & 86$\\\\pm$ 5 & 11.7$\\\\pm$ 1.7 & \\\\nodata & $-1.37\\\\pm$0.11 & \\\\nodata & S & 1.6 & 6 & 13 29 31.75 & +30 46 13.6 & F \\\\\\\\\\nWN J1329+3046$^*$ & 88$\\\\pm$ 5 & 12.1$\\\\pm$ 2.0 & \\\\nodata & $-1.36\\\\pm$0.13 & \\\\nodata & S & 3.6 & 129 & 13 29 55.12 & +30 46 51.2 & F \\\\\\\\\\nWN J1330+6505 & 74$\\\\pm$ 6 & 10.5$\\\\pm$ 0.5 & $ 2.34\\\\pm0.12$ & $-1.34\\\\pm$0.06 & $-1.21\\\\pm0.06$ & S & 1.8 & 5 & 13 30 02.77 & +65 04 59.3 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nWN J1330+3037$^*$ & 496$\\\\pm$20 & 64.5$\\\\pm$ 2.9 & \\\\nodata & $-1.40\\\\pm$0.04 & \\\\nodata & D & 25.5 & 140 & 13 30 53.67 & +30 37 59.1 & F \\\\\\\\\\nWN J1330+3604 & 103$\\\\pm$ 5 & 15.1$\\\\pm$ 0.5 & \\\\nodata & $-1.31\\\\pm$0.05 & \\\\nodata & D & 9.6 & 0 & 13 30 56.83 & +36 04 01.6 & F \\\\\\\\\\nWN J1330+5344$^*$ & 525$\\\\pm$21 & 71.0$\\\\pm$ 3.2 & $ 8.10\\\\pm0.29$ & $-1.37\\\\pm$0.04 & $-1.74\\\\pm0.05$ & DF & 2.5 & 173 & 13 30 58.90 & +53 44 07.8 & V \\\\\\\\\\nWN J1331+2937 & 93$\\\\pm$ 5 & 12.5$\\\\pm$ 1.3 & $ 3.44\\\\pm0.13$ & $-1.37\\\\pm$0.09 & $-1.04\\\\pm0.09$ & S & 2.7 & 40 & 13 31 21.58 & +29 37 12.6 & V \\\\\\\\\\nWN J1332+3009$^*$ & 239$\\\\pm$10 & 35.3$\\\\pm$ 2.0 & \\\\nodata & $-1.31\\\\pm$0.05 & \\\\nodata & D & 39.2 & 161 & 13 32 45.73 & +30 09 59.9 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nWN J1333+3037$^*$ & 423$\\\\pm$17 & 21.5$\\\\pm$ 0.6 & \\\\nodata & $-2.04\\\\pm$0.03 & \\\\nodata & S & 0.4 & 179 & 13 33 21.20 & +30 37 35.1 & F \\\\\\\\\\nWN J1333+4913 & 149$\\\\pm$ 7 & 22.2$\\\\pm$ 0.6 & $ 4.78\\\\pm0.23$ & $-1.30\\\\pm$0.04 & $-1.22\\\\pm0.04$ & T & 5.4 & 40 & 13 33 56.42 & +49 13 27.1 & V \\\\\\\\\\nWN J1335+3222$^*$ & 150$\\\\pm$ 7 & 18.3$\\\\pm$ 1.4 & \\\\nodata & $-1.44\\\\pm$0.06 & \\\\nodata & D & 8.8 & 85 & 13 35 35.44 & +32 22 48.7 & F \\\\\\\\\\nWN J1336+3820 & 116$\\\\pm$ 6 & 15.6$\\\\pm$ 0.5 & \\\\nodata & $-1.37\\\\pm$0.04 & \\\\nodata & S & 3.4 & 61 & 13 36 40.88 & +38 20 02.2 & F \\\\\\\\\\nWN J1337+3149 & 142$\\\\pm$ 7 & 19.6$\\\\pm$ 1.9 & \\\\nodata & $-1.36\\\\pm$0.08 & \\\\nodata & D & 35.2 & 21 & 13 37 02.46 & +31 49 49.2 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1337+3401 & 109$\\\\pm$ 8 & 14.3$\\\\pm$ 0.5 & \\\\nodata & $-1.39\\\\pm$0.04 & \\\\nodata & S & 3.5 & 56 & 13 37 10.50 & +34 01 26.8 & F \\\\\\\\\\nWN J1339+5320 & 104$\\\\pm$ 5 & 13.9$\\\\pm$ 0.5 & $ 1.80\\\\pm0.15$ & $-1.38\\\\pm$0.05 & $-1.63\\\\pm0.07$ & D & 0.1 & 138 & 13 39 59.25 & +53 20 07.8 & V \\\\\\\\\\nWN J1341+4953 & 153$\\\\pm$ 8 & 16.4$\\\\pm$ 1.4 & \\\\nodata & $-1.53\\\\pm$0.07 & \\\\nodata & D & 18.6 & 160 & 13 41 25.70 & +49 53 41.8 & F \\\\\\\\\\nWN J1346+6736 & 107$\\\\pm$ 6 & 14.5$\\\\pm$ 0.5 & $ 2.82\\\\pm0.16$ & $-1.37\\\\pm$0.04 & $-1.32\\\\pm0.05$ & S & $<0.3$ & 0 & 13 46 37.02 & +67 36 21.7 & V \\\\\\\\\\nWN J1347+3033 & 341$\\\\pm$14 & 42.4$\\\\pm$ 2.2 & \\\\nodata & $-1.43\\\\pm$0.05 & \\\\nodata & D & 37.3 & 151 & 13 47 16.09 & +30 33 07.6 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1352+4259 & 1213$\\\\pm$48 & 173.9$\\\\pm$ 7.7 & \\\\nodata & $-1.33\\\\pm$0.04 & \\\\nodata & D & 12.1 & 19 & 13 52 28.39 & +42 59 18.1 & F \\\\\\\\\\nWN J1353+3336 & 107$\\\\pm$ 6 & 15.9$\\\\pm$ 1.9 & \\\\nodata & $-1.31\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 13 53 07.46 & +33 36 24.6 & N \\\\\\\\\\nWN J1355+3848 & 204$\\\\pm$ 8 & 25.6$\\\\pm$ 0.6 & \\\\nodata & $-1.42\\\\pm$0.03 & \\\\nodata & S & 2.3 & 59 & 13 55 29.50 & +38 48 11.1 & F \\\\\\\\\\nWN J1359+7446$^*$ & 214$\\\\pm$ 9 & 12.9$\\\\pm$ 0.5 & $ 1.26\\\\pm0.10$ & $-1.92\\\\pm$0.05 & $-1.87\\\\pm0.07$ & S & 2.5 & 12 & 13 59 16.90 & +74 46 42.6 & V \\\\\\\\\\nWN J1400+4348 & 178$\\\\pm$ 7 & 20.2$\\\\pm$ 1.5 & \\\\nodata & $-1.49\\\\pm$0.06 & \\\\nodata & S & 6.4 & 93 & 14 00 51.84 & +43 48 07.2 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1403+3109 & 328$\\\\pm$13 & 45.7$\\\\pm$ 2.2 & \\\\nodata & $-1.35\\\\pm$0.04 & \\\\nodata & S & 11.0 & 25 & 14 03 39.47 & +31 09 11.4 & F \\\\\\\\\\nWN J1410+4615 & 103$\\\\pm$ 5 & 14.2$\\\\pm$ 1.4 & \\\\nodata & $-1.36\\\\pm$0.08 & \\\\nodata & S & 4.4 & 79 & 14 10 48.17 & +46 15 57.5 & F \\\\\\\\\\nWN J1416+3821 & 94$\\\\pm$ 6 & 13.1$\\\\pm$ 0.5 & \\\\nodata & $-1.35\\\\pm$0.05 & \\\\nodata & D & 7.6 & 14 & 14 16 13.21 & +38 21 56.7 & F \\\\\\\\\\nWN J1418+4546 & 186$\\\\pm$ 8 & 17.9$\\\\pm$ 0.5 & $ 2.70\\\\pm0.14$ & $-1.60\\\\pm$0.04 & $-1.52\\\\pm0.05$ & S & 0.5 & 18 & 14 18 38.40 & +45 46 38.4 & V \\\\\\\\\\nWN J1420+6735 & 382$\\\\pm$15 & 33.1$\\\\pm$ 1.7 & $ 1.22\\\\pm0.09$ & $-1.67\\\\pm$0.05 & $-2.65\\\\pm0.07$ & S & 2.0 & 173 & 14 20 03.34 & +67 35 07.5 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1420+4126 & 128$\\\\pm$ 6 & 18.7$\\\\pm$ 0.6 & \\\\nodata & $-1.32\\\\pm$0.04 & \\\\nodata & S & 5.3 & 65 & 14 20 50.23 & +41 26 26.1 & F \\\\\\\\\\nWN J1421+3103 & 110$\\\\pm$ 5 & 13.6$\\\\pm$ 0.5 & \\\\nodata & $-1.43\\\\pm$0.05 & \\\\nodata & S & 0.4 & 127 & 14 21 07.69 & +31 03 03.9 & F \\\\\\\\\\nWN J1422+3452 & 163$\\\\pm$ 7 & 10.7$\\\\pm$ 1.3 & \\\\nodata & $-1.86\\\\pm$0.09 & \\\\nodata & S & 13.3 & 151 & 14 22 05.17 & +34 52 14.4 & F \\\\\\\\\\nWN J1422+4212 & 258$\\\\pm$10 & 35.4$\\\\pm$ 1.8 & \\\\nodata & $-1.36\\\\pm$0.05 & \\\\nodata & S & 5.1 & 164 & 14 22 44.38 & +42 12 00.2 & F \\\\\\\\\\nWN J1426+3522 & 89$\\\\pm$ 5 & 11.5$\\\\pm$ 1.6 & \\\\nodata & $-1.40\\\\pm$0.11 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 14 26 56.32 & +35 22 34.7 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1431+3015 & 101$\\\\pm$ 5 & 14.3$\\\\pm$ 1.5 & \\\\nodata & $-1.34\\\\pm$0.09 & \\\\nodata & D & 28.9 & 158 & 14 31 17.77 & +30 15 00.2 & F \\\\\\\\\\nWN J1431+7317 & 129$\\\\pm$ 6 & 17.9$\\\\pm$ 1.3 & $ 4.65\\\\pm0.19$ & $-1.35\\\\pm$0.06 & $-1.08\\\\pm0.07$ & D & 11.2 & 47 & 14 31 28.01 & +73 17 29.7 & V \\\\\\\\\\nWN J1433+3044 & 144$\\\\pm$ 6 & 16.7$\\\\pm$ 1.3 & \\\\nodata & $-1.48\\\\pm$0.06 & \\\\nodata & D & 14.5 & 100 & 14 33 56.51 & +30 44 25.5 & F \\\\\\\\\\nWN J1435+3523 & 160$\\\\pm$ 7 & 22.3$\\\\pm$ 1.6 & \\\\nodata & $-1.35\\\\pm$0.06 & \\\\nodata & S & 8.0 & 64 & 14 35 53.99 & +35 24 06.8 & F \\\\\\\\\\nWN J1436+6319 & 3507$\\\\pm$140 & 514.0$\\\\pm$22.4 & $ 64.84\\\\pm1.39$ & $-1.31\\\\pm$0.04 & $-1.67\\\\pm0.04$ & D & 3.8 & 154 & 14 36 37.28 & +63 19 13.9 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1437+7409 & 111$\\\\pm$ 5 & 16.4$\\\\pm$ 0.5 & $ 1.32\\\\pm0.11$ & $-1.31\\\\pm$0.05 & $-2.02\\\\pm0.07$ & S & $<0.3$ & 0 & 14 37 35.89 & +74 09 22.2 & V \\\\\\\\\\nWN J1439+3729 & 142$\\\\pm$ 7 & 17.1$\\\\pm$ 0.5 & \\\\nodata & $-1.45\\\\pm$0.04 & \\\\nodata & D & 7.2 & 157 & 14 39 49.99 & +37 29 03.4 & F \\\\\\\\\\nWN J1440+3707$^*$ & 219$\\\\pm$ 9 & 16.7$\\\\pm$ 1.3 & \\\\nodata & $-1.76\\\\pm$0.06 & \\\\nodata & S & 7.4 & 61 & 14 40 03.63 & +37 07 27.4 & F \\\\\\\\\\nWN J1444+4114 & 97$\\\\pm$ 5 & 13.2$\\\\pm$ 1.4 & \\\\nodata & $-1.37\\\\pm$0.09 & \\\\nodata & D & 30.1 & 151 & 14 44 27.65 & +41 14 38.3 & F \\\\\\\\\\nWN J1444+4112 & 109$\\\\pm$ 6 & 13.1$\\\\pm$ 0.5 & \\\\nodata & $-1.45\\\\pm$0.05 & \\\\nodata & D & 12.6 & 96 & 14 44 48.82 & +41 12 25.5 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1447+5423 & 97$\\\\pm$ 6 & 13.3$\\\\pm$ 0.5 & \\\\nodata & $-1.36\\\\pm$0.05 & \\\\nodata & S & 11.0 & 174 & 14 47 54.36 & +54 23 25.2 & F \\\\\\\\\\nWN J1450+3534 & 95$\\\\pm$ 5 & 10.2$\\\\pm$ 0.4 & \\\\nodata & $-1.53\\\\pm$0.05 & \\\\nodata & S & 3.3 & 62 & 14 50 20.69 & +35 34 46.5 & F \\\\\\\\\\nWN J1451+3649 & 254$\\\\pm$10 & 29.8$\\\\pm$ 2.3 & \\\\nodata & $-1.47\\\\pm$0.06 & \\\\nodata & T & 50.7 & 101 & 14 51 11.62 & +36 49 34.4 & F \\\\\\\\\\nWN J1454+3210 & 264$\\\\pm$11 & 37.6$\\\\pm$ 0.9 & \\\\nodata & $-1.33\\\\pm$0.03 & \\\\nodata & S & 3.0 & 22 & 14 54 11.64 & +32 10 16.8 & F \\\\\\\\\\nWN J1459+6405 & 339$\\\\pm$14 & 40.0$\\\\pm$ 3.6 & \\\\nodata & $-1.46\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 14 59 33.34 & +64 05 58.0 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1459+4947 & 175$\\\\pm$ 8 & 18.7$\\\\pm$ 0.5 & \\\\nodata & $-1.53\\\\pm$0.04 & \\\\nodata & S & 3.0 & 109 & 14 59 43.19 & +49 47 15.9 & F \\\\\\\\\\nWN J1500+3613 & 390$\\\\pm$16 & 52.9$\\\\pm$ 2.5 & \\\\nodata & $-1.37\\\\pm$0.04 & \\\\nodata & S & 2.2 & 76 & 15 00 09.01 & +36 13 25.8 & F \\\\\\\\\\nWN J1502+4756 & 221$\\\\pm$ 9 & 19.1$\\\\pm$ 1.5 & \\\\nodata & $-1.68\\\\pm$0.06 & \\\\nodata & D & 12.3 & 37 & 15 02 03.58 & +47 56 34.7 & F \\\\\\\\\\nWN J1508+5839 & 122$\\\\pm$ 6 & 12.5$\\\\pm$ 0.5 & $ 1.37\\\\pm0.09$ & $-1.56\\\\pm$0.05 & $-1.78\\\\pm0.06$ & D & 35.2 & 128 & 15 08 08.17 & +58 39 13.3 & V \\\\\\\\\\nWN J1509+5905$^*$ & 752$\\\\pm$30 & 107.3$\\\\pm$ 4.6 & $ 8.60\\\\pm0.26$ & $-1.33\\\\pm$0.04 & $-2.03\\\\pm0.04$ & DF & 1.8 & 74 & 15 09 32.34 & +59 05 24.5 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\nWN J1525+3010 & 145$\\\\pm$ 7 & 17.2$\\\\pm$ 0.5 & \\\\nodata & $-1.46\\\\pm$0.04 & \\\\nodata & S & 1.2 & 123 & 15 25 01.21 & +30 10 30.2 & F \\\\\\\\\\nWN J1525+5130 & 94$\\\\pm$ 5 & 10.7$\\\\pm$ 0.5 & $ 2.02\\\\pm0.13$ & $-1.49\\\\pm$0.06 & $-1.34\\\\pm0.06$ & S & 0.8 & 7 & 15 25 12.93 & +51 30 06.1 & V \\\\\\\\\\nWN J1528+6317 & 332$\\\\pm$14 & 40.0$\\\\pm$ 2.0 & $ 20.80\\\\pm0.52$ & $-1.45\\\\pm$0.04 & $-0.53\\\\pm0.05$ & DF & 6.0 & 121 & 15 28 06.47 & +63 17 40.2 & V \\\\\\\\\\nWN J1529+3454 & 124$\\\\pm$ 6 & 13.0$\\\\pm$ 0.5 & \\\\nodata & $-1.54\\\\pm$0.05 & \\\\nodata & S & 2.3 & 35 & 15 29 41.52 & +34 54 31.3 & F \\\\\\\\\\nWN J1537+3402 & 83$\\\\pm$ 5 & 11.6$\\\\pm$ 0.5 & \\\\nodata & $-1.35\\\\pm$0.05 & \\\\nodata & S & 1.7 & 31 & 15 37 50.57 & +34 02 33.3 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1543+3512 & 231$\\\\pm$10 & 23.6$\\\\pm$ 1.5 & \\\\nodata & $-1.56\\\\pm$0.05 & \\\\nodata & D & 9.2 & 0 & 15 43 29.49 & +35 12 29.7 & F \\\\\\\\\\nWN J1546+3935 & 155$\\\\pm$ 7 & 13.7$\\\\pm$ 0.5 & \\\\nodata & $-1.66\\\\pm$0.04 & \\\\nodata & D & 8.5 & 102 & 15 46 41.95 & +39 35 52.7 & F \\\\\\\\\\nWN J1546+3005 & 92$\\\\pm$ 6 & 13.0$\\\\pm$ 0.5 & \\\\nodata & $-1.34\\\\pm$0.05 & \\\\nodata & S & 2.3 & 144 & 15 46 57.65 & +30 05 38.1 & F \\\\\\\\\\nWN J1550+3830 & 229$\\\\pm$10 & 32.9$\\\\pm$ 1.7 & \\\\nodata & $-1.33\\\\pm$0.05 & \\\\nodata & S & 4.2 & 178 & 15 50 19.42 & +38 30 14.8 & F \\\\\\\\\\nWN J1552+3715 & 546$\\\\pm$22 & 27.3$\\\\pm$ 1.6 & \\\\nodata & $-2.05\\\\pm$0.05 & \\\\nodata & D & 18.6 & 120 & 15 52 07.07 & +37 15 07.1 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1555+4011 & 359$\\\\pm$14 & 50.9$\\\\pm$ 2.4 & \\\\nodata & $-1.34\\\\pm$0.04 & \\\\nodata & S & 1.1 & 90 & 15 55 02.50 & +40 11 58.2 & F \\\\\\\\\\nWN J1558+7028 & 114$\\\\pm$ 6 & 15.7$\\\\pm$ 2.1 & $ 1.68\\\\pm0.11$ & $-1.36\\\\pm$0.11 & $-1.80\\\\pm0.12$ & S & 2.1 & 38 & 15 58 37.92 & +70 28 11.2 & V \\\\\\\\\\nWN J1559+6110 & 130$\\\\pm$ 6 & 18.3$\\\\pm$ 1.3 & $ 3.47\\\\pm0.14$ & $-1.34\\\\pm$0.06 & $-1.34\\\\pm0.07$ & S & 0.3 & 20 & 15 59 50.65 & +61 10 57.8 & V \\\\\\\\\\nWN J1559+5926 & 116$\\\\pm$ 6 & 15.3$\\\\pm$ 1.3 & $ 41.70\\\\pm0.92$ & $-1.39\\\\pm$0.07 & \\\\nodata & D & 31.0 & 60 & 15 59 54.42 & +59 26 35.3 & V \\\\\\\\\\nWN J1604+5505 & 142$\\\\pm$ 7 & 20.7$\\\\pm$ 0.6 & \\\\nodata & $-1.32\\\\pm$0.04 & \\\\nodata & S & 1.1 & 15 & 16 04 21.91 & +55 05 45.4 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1606+6346 & 130$\\\\pm$ 6 & 19.0$\\\\pm$ 0.6 & $ 5.60\\\\pm0.19$ & $-1.32\\\\pm$0.04 & $-0.98\\\\pm0.04$ & D & 5.6 & 14 & 16 06 12.44 & +63 47 06.1 & V \\\\\\\\\\nWN J1606+4142 & 83$\\\\pm$ 5 & 12.3$\\\\pm$ 0.5 & \\\\nodata & $-1.31\\\\pm$0.05 & \\\\nodata & S & 3.2 & 145 & 16 06 30.58 & +41 42 10.8 & F \\\\\\\\\\nWN J1609+5725 & 70$\\\\pm$ 5 & 10.2$\\\\pm$ 0.5 & $ 2.13\\\\pm0.11$ & $-1.32\\\\pm$0.07 & $-1.26\\\\pm0.06$ & S & 1.7 & 60 & 16 09 28.14 & +57 25 02.8 & V \\\\\\\\\\nWN J1618+5736 & 233$\\\\pm$10 & 33.5$\\\\pm$ 1.8 & $ 6.38\\\\pm0.20$ & $-1.33\\\\pm$0.05 & $-1.34\\\\pm0.05$ & S & 2.1 & 102 & 16 18 07.35 & +57 36 11.7 & V \\\\\\\\\\nWN J1622+3447 & 156$\\\\pm$ 7 & 21.1$\\\\pm$ 0.6 & \\\\nodata & $-1.37\\\\pm$0.04 & \\\\nodata & S & 1.6 & 0 & 16 22 10.93 & +34 47 44.6 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1623+8213 & 166$\\\\pm$ 7 & 19.8$\\\\pm$ 0.6 & \\\\nodata & $-1.46\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 16 23 01.71 & +82 13 17.4 & N \\\\\\\\\\nWN J1624+4202 & 75$\\\\pm$ 5 & 11.0$\\\\pm$ 1.7 & \\\\nodata & $-1.31\\\\pm$0.12 & \\\\nodata & D & 24.4 & 19 & 16 24 37.86 & +42 02 10.5 & F \\\\\\\\\\nWN J1627+5430 & 146$\\\\pm$ 7 & 20.9$\\\\pm$ 0.6 & \\\\nodata & $-1.33\\\\pm$0.04 & \\\\nodata & S & 1.6 & 176 & 16 27 24.09 & +54 30 55.2 & F \\\\\\\\\\nWN J1628+3932 & 26737$\\\\pm$1069 & 3680.7$\\\\pm$35.1 & \\\\nodata & $-1.36\\\\pm$0.03 & \\\\nodata & M & 48.8 & 77 & 16 28 38.56 & +39 33 00.1 & F \\\\\\\\\\nWN J1633+7351 & 75$\\\\pm$ 5 & 10.1$\\\\pm$ 1.3 & $ 23.88\\\\pm0.55$ & $-1.37\\\\pm$0.11 & $ 0.69\\\\pm0.11$ & DF & 21.8 & 90 & 16 33 07.45 & +73 51 38.1 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1645+4413 & 135$\\\\pm$ 6 & 18.9$\\\\pm$ 0.6 & \\\\nodata & $-1.35\\\\pm$0.04 & \\\\nodata & S & 1.1 & 56 & 16 45 35.69 & +44 13 42.1 & F \\\\\\\\\\nWN J1704+3839 & 335$\\\\pm$14 & 34.5$\\\\pm$ 1.8 & \\\\nodata & $-1.56\\\\pm$0.05 & \\\\nodata & D & 23.8 & 145 & 17 04 00.50 & +38 39 56.7 & F \\\\\\\\\\nWN J1713+3656 & 116$\\\\pm$ 6 & 14.8$\\\\pm$ 0.5 & \\\\nodata & $-1.41\\\\pm$0.04 & \\\\nodata & S & 1.1 & 169 & 17 13 55.63 & +36 56 34.5 & F \\\\\\\\\\nWN J1714+7031 & 132$\\\\pm$ 6 & 14.2$\\\\pm$ 1.4 & $ 0.95\\\\pm0.09$ & $-1.53\\\\pm$0.08 & $-2.18\\\\pm0.11$ & S & 2.4 & 46 & 17 14 35.18 & +70 31 30.7 & V \\\\\\\\\\nWN J1714+5251 & 262$\\\\pm$11 & 37.9$\\\\pm$ 2.0 & \\\\nodata & $-1.32\\\\pm$0.05 & \\\\nodata & D & 26.6 & 80 & 17 14 37.93 & +52 51 30.1 & F \\\\\\\\\\n\\\\end{tabular}\\n\\\\end{table*}\\n\\n\\\\begin{table*}\\n\\\\tiny\\n\\\\begin{tabular}{lrrrrrrrrrrrr}\\nName & $S_{325}$ & $S_{1400}$ & S$_{4850}$ & $\\\\alpha_{325}^{1400}$ & $\\\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\\\alpha_{J2000}$ & $\\\\delta_{J2000}$ & Pos \\\\\\\\\\n & mJy & mJy & mJy & & & & \\\\arcsec & $\\\\arcdeg$ & $^h\\\\;\\\\;$$^m\\\\;\\\\;\\\\;\\\\;$$^s\\\\;\\\\;\\\\,$ & \\\\arcdeg$\\\\;\\\\;\\\\;$ \\\\arcmin$\\\\;\\\\;\\\\;$ \\\\arcsec$\\\\;$ & \\\\\\\\\\n\\\\hline\\nWN J1717+3828 & 368$\\\\pm$15 & 35.8$\\\\pm$ 2.0 & \\\\nodata & $-1.60\\\\pm$0.05 & \\\\nodata & M & 33.6 & 156 & 17 17 16.22 & +38 28 16.5 & F \\\\\\\\\\nWN J1718+5823 & 1098$\\\\pm$44 & 133.2$\\\\pm$ 2.7 & $ 11.26\\\\pm0.32$ & $-1.44\\\\pm$0.03 & $-1.98\\\\pm0.03$ & S & 0.3 & 107 & 17 18 18.51 & +58 23 21.8 & V \\\\\\\\\\nWN J1723+5822 & 88$\\\\pm$ 6 & 10.4$\\\\pm$ 0.5 & $ 2.27\\\\pm0.11$ & $-1.46\\\\pm$0.06 & $-1.23\\\\pm0.06$ & S & 4.7 & 103 & 17 23 01.98 & +58 22 44.0 & V \\\\\\\\\\nWN J1723+6844 & 105$\\\\pm$ 6 & 15.7$\\\\pm$ 1.3 & \\\\nodata & $-1.30\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 17 23 05.64 & +68 44 17.7 & N \\\\\\\\\\nWN J1731+4640 & 200$\\\\pm$ 9 & 15.7$\\\\pm$ 0.5 & \\\\nodata & $-1.74\\\\pm$0.04 & \\\\nodata & D & 11.6 & 106 & 17 31 46.10 & +46 40 03.1 & F \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1731+4654 & 323$\\\\pm$13 & 42.0$\\\\pm$ 2.1 & \\\\nodata & $-1.40\\\\pm$0.05 & \\\\nodata & S & 1.9 & 176 & 17 31 59.63 & +46 54 00.2 & F \\\\\\\\\\nWN J1732+6757 & 85$\\\\pm$ 5 & 11.9$\\\\pm$ 0.5 & $ 2.31\\\\pm0.11$ & $-1.35\\\\pm$0.05 & $-1.32\\\\pm0.05$ & D & 1.5 & 178 & 17 32 30.61 & +67 57 02.5 & V \\\\\\\\\\nWN J1733+4037 & 80$\\\\pm$ 5 & 11.2$\\\\pm$ 2.0 & \\\\nodata & $-1.35\\\\pm$0.13 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 17 33 31.13 & +40 37 00.6 & N \\\\\\\\\\nWN J1734+4527 & 87$\\\\pm$ 5 & 11.0$\\\\pm$ 0.5 & \\\\nodata & $-1.42\\\\pm$0.06 & \\\\nodata & D & 10.4 & 174 & 17 34 07.58 & +45 27 25.6 & F \\\\\\\\\\nWN J1734+3606 & 69$\\\\pm$ 3 & 10.2$\\\\pm$ 3.2 & $ 3.12\\\\pm0.13$ & $-1.31\\\\pm$0.22 & $-0.95\\\\pm0.25$ & S & 2.1 & 137 & 17 34 24.13 & +36 06 38.8 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1736+6502 & 193$\\\\pm$ 8 & 27.4$\\\\pm$ 1.6 & $ 4.40\\\\pm0.16$ & $-1.34\\\\pm$0.05 & $-1.47\\\\pm0.06$ & D & 16.0 & 159 & 17 36 37.50 & +65 02 28.7 & V \\\\\\\\\\nWN J1739+5309 & 78$\\\\pm$ 5 & 11.3$\\\\pm$ 0.5 & \\\\nodata & $-1.32\\\\pm$0.06 & \\\\nodata & S & 7.3 & 114 & 17 39 28.39 & +53 09 41.8 & F \\\\\\\\\\nWN J1749+5659 & 124$\\\\pm$ 7 & 15.9$\\\\pm$ 1.6 & \\\\nodata & $-1.41\\\\pm$0.08 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 17 49 21.19 & +56 59 59.6 & N \\\\\\\\\\nWN J1749+6248 & 104$\\\\pm$ 6 & 13.3$\\\\pm$ 0.5 & $ 2.93\\\\pm0.12$ & $-1.41\\\\pm$0.05 & $-1.22\\\\pm0.05$ & S & 1.7 & 48 & 17 49 27.04 & +62 48 54.0 & V \\\\\\\\\\nWN J1752+2949 & 135$\\\\pm$ 6 & 16.9$\\\\pm$ 0.5 & $ 2.29\\\\pm0.14$ & $-1.42\\\\pm$0.04 & $-1.61\\\\pm0.05$ & S & 3.2 & 102 & 17 52 56.67 & +29 49 28.3 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1801+3336 & 136$\\\\pm$ 6 & 11.6$\\\\pm$ 0.5 & $ 1.26\\\\pm0.12$ & $-1.69\\\\pm$0.05 & $-1.78\\\\pm0.08$ & S & 2.5 & 34 & 18 01 07.26 & +33 36 40.4 & V \\\\\\\\\\nWN J1802+3948 & 1102$\\\\pm$44 & 157.3$\\\\pm$ 6.8 & $ 27.67\\\\pm0.62$ & $-1.33\\\\pm$0.04 & $-1.40\\\\pm0.04$ & T & 19.2 & 13 & 18 02 31.65 & +39 48 59.6 & V \\\\\\\\\\nWN J1804+5547 & 173$\\\\pm$ 8 & 22.9$\\\\pm$ 1.7 & \\\\nodata & $-1.38\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 18 04 15.35 & +55 47 16.3 & N \\\\\\\\\\nWN J1804+3048 & 192$\\\\pm$ 8 & 27.7$\\\\pm$ 0.7 & $ 5.88\\\\pm0.18$ & $-1.33\\\\pm$0.04 & $-1.25\\\\pm0.03$ & S & 2.0 & 84 & 18 04 42.01 & +30 48 45.0 & V \\\\\\\\\\nWN J1806+6332 & 138$\\\\pm$ 7 & 17.7$\\\\pm$ 0.5 & \\\\nodata & $-1.41\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 18 06 23.66 & +63 32 07.9 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1807+5027 & 483$\\\\pm$19 & 71.4$\\\\pm$ 3.3 & $ 11.67\\\\pm0.31$ & $-1.31\\\\pm$0.04 & $-1.46\\\\pm0.04$ & D & 3.7 & 173 & 18 07 07.39 & +50 27 25.8 & V \\\\\\\\\\nWN J1807+6628 & 76$\\\\pm$ 5 & 10.9$\\\\pm$ 1.4 & $ 1.20\\\\pm0.11$ & $-1.33\\\\pm$0.10 & $-1.78\\\\pm0.13$ & S & 0.3 & 103 & 18 07 29.75 & +66 28 33.4 & V \\\\\\\\\\nWN J1810+6635 & 115$\\\\pm$ 8 & 14.1$\\\\pm$ 0.5 & $ 2.62\\\\pm0.12$ & $-1.44\\\\pm$0.04 & $-1.36\\\\pm0.05$ & S & 1.6 & 15 & 18 10 28.41 & +66 35 15.1 & V \\\\\\\\\\nWN J1811+6008 & 160$\\\\pm$ 7 & 17.8$\\\\pm$ 0.5 & $ 7.87\\\\pm0.24$ & $-1.50\\\\pm$0.04 & $-0.66\\\\pm0.03$ & DF & 3.5 & 31 & 18 11 18.38 & +60 08 42.9 & V \\\\\\\\\\nWN J1813+4847 & 92$\\\\pm$ 5 & 12.1$\\\\pm$ 0.5 & \\\\nodata & $-1.39\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 18 13 16.68 & +48 47 50.1 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1814+5009 & 120$\\\\pm$ 7 & 16.7$\\\\pm$ 0.5 & \\\\nodata & $-1.35\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 18 14 01.40 & +50 09 58.0 & N \\\\\\\\\\nWN J1815+3656 & 124$\\\\pm$ 6 & 17.6$\\\\pm$ 0.6 & $ 2.96\\\\pm0.14$ & $-1.34\\\\pm$0.04 & $-1.43\\\\pm0.05$ & S & 1.6 & 48 & 18 15 23.11 & +36 56 00.9 & V \\\\\\\\\\nWN J1816+3840 & 186$\\\\pm$ 8 & 27.3$\\\\pm$ 1.6 & \\\\nodata & $-1.31\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 18 16 26.11 & +38 40 53.0 & N \\\\\\\\\\nWN J1818+7042 & 1624$\\\\pm$65 & 199.6$\\\\pm$ 8.8 & $ 30.50\\\\pm0.74$ & $-1.44\\\\pm$0.04 & $-1.51\\\\pm0.04$ & D & 1.4 & 10 & 18 18 04.24 & +70 42 59.5 & V \\\\\\\\\\nWN J1818+3852 & 105$\\\\pm$ 6 & 12.6$\\\\pm$ 0.5 & $ 1.29\\\\pm0.09$ & $-1.45\\\\pm$0.05 & $-1.84\\\\pm0.07$ & S & 2.6 & 64 & 18 18 42.17 & +38 52 20.4 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1818+3428 & 167$\\\\pm$ 7 & 23.7$\\\\pm$ 0.6 & $ 5.68\\\\pm0.19$ & $-1.34\\\\pm$0.04 & $-1.15\\\\pm0.03$ & T & 7.5 & 103 & 18 18 47.90 & +34 28 24.0 & V \\\\\\\\\\nWN J1818+6144 & 149$\\\\pm$ 6 & 21.9$\\\\pm$ 1.5 & $ 1.11\\\\pm0.10$ & $-1.31\\\\pm$0.06 & $-2.40\\\\pm0.09$ & S & 1.6 & 11 & 18 18 50.55 & +61 44 18.4 & V \\\\\\\\\\nWN J1819+3122 & 77$\\\\pm$ 5 & 10.5$\\\\pm$ 0.5 & \\\\nodata & $-1.36\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 18 19 28.60 & +31 22 19.3 & N \\\\\\\\\\nWN J1819+6213 & 106$\\\\pm$ 6 & 12.7$\\\\pm$ 0.5 & $ 0.47\\\\pm0.08$ & $-1.45\\\\pm$0.05 & $-2.66\\\\pm0.14$ & S & 1.6 & 41 & 18 19 52.26 & +62 13 58.0 & V \\\\\\\\\\nWN J1820+5711 & 136$\\\\pm$ 7 & 20.3$\\\\pm$ 1.5 & \\\\nodata & $-1.30\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 18 20 51.14 & +57 11 06.5 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1821+3602 & 3398$\\\\pm$136 & 99.0$\\\\pm$ 4.2 & $233.33\\\\pm4.90$ & $-2.42\\\\pm$0.04 & $ 0.69\\\\pm0.04$ & T & 35.0 & 55 & 18 21 02.20 & +36 02 15.7 & V \\\\\\\\\\nWN J1821+3601$^{\\\\dag}$ & 151$\\\\pm$ 6 & 10.2$\\\\pm$ 1.5 & $105.26\\\\pm2.53$ & $-1.85\\\\pm$0.11 & $ 1.88\\\\pm0.12$ & D & 34.9 & 55 & 18 21 22.59 & +36 01 03.3 & V \\\\\\\\\\nWN J1829+6914 & 207$\\\\pm$ 9 & 13.0$\\\\pm$ 1.3 & $ 2.25\\\\pm0.12$ & $-1.90\\\\pm$0.08 & $-1.41\\\\pm0.09$ & S & 1.8 & 22 & 18 29 05.68 & +69 14 06.1 & V \\\\\\\\\\nWN J1829+4919 & 98$\\\\pm$ 6 & 14.2$\\\\pm$ 0.5 & $ 7.95\\\\pm0.24$ & $-1.32\\\\pm$0.06 & $-0.47\\\\pm0.04$ & D & 12.5 & 173 & 18 29 33.74 & +49 19 55.6 & V \\\\\\\\\\nWN J1829+5945 & 346$\\\\pm$14 & 50.4$\\\\pm$ 2.4 & $ 8.82\\\\pm0.25$ & $-1.32\\\\pm$0.04 & $-1.40\\\\pm0.04$ & S & 1.7 & 26 & 18 29 57.26 & +59 45 03.2 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1830+6422 & 70$\\\\pm$ 3 & 10.3$\\\\pm$ 0.5 & \\\\nodata & $-1.31\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 18 30 45.82 & +64 22 26.3 & N \\\\\\\\\\nWN J1832+5354$^{\\\\dag}$ & 226$\\\\pm$10 & 28.7$\\\\pm$ 1.6 & $ 23.82\\\\pm0.59$ & $-1.41\\\\pm$0.05 & $-0.15\\\\pm0.05$ & D & 19.4 & 56 & 18 32 41.16 & +53 54 34.0 & V \\\\\\\\\\nWN J1836+5210 & 191$\\\\pm$ 9 & 24.2$\\\\pm$ 1.5 & $ 3.54\\\\pm0.15$ & $-1.41\\\\pm$0.05 & $-1.55\\\\pm0.06$ & S & 1.4 & 10 & 18 36 23.22 & +52 10 28.4 & V \\\\\\\\\\nWN J1839+4710 & 176$\\\\pm$ 8 & 22.8$\\\\pm$ 1.6 & \\\\nodata & $-1.40\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 18 39 14.54 & +47 10 59.4 & N \\\\\\\\\\nWN J1843+5932 & 998$\\\\pm$40 & 148.2$\\\\pm$ 6.6 & $ 30.87\\\\pm0.70$ & $-1.31\\\\pm$0.04 & $-1.26\\\\pm0.04$ & T & 7.7 & 64 & 18 43 31.70 & +59 32 59.3 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1847+5423 & 108$\\\\pm$ 6 & 15.8$\\\\pm$ 1.3 & $ 6.67\\\\pm0.23$ & $-1.32\\\\pm$0.07 & $-0.69\\\\pm0.07$ & DF & 2.9 & 67 & 18 47 04.03 & +54 23 06.6 & V \\\\\\\\\\nWN J1852+5711$^*$ & 387$\\\\pm$16 & 53.4$\\\\pm$ 2.5 & \\\\nodata & $-1.36\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 18 52 08.35 & +57 11 42.7 & N \\\\\\\\\\nWN J1857+7411 & 160$\\\\pm$ 7 & 19.9$\\\\pm$ 0.6 & \\\\nodata & $-1.43\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 18 57 03.60 & +74 11 31.2 & N \\\\\\\\\\nWN J1859+5900 & 98$\\\\pm$ 6 & 11.7$\\\\pm$ 0.5 & $ 1.64\\\\pm0.12$ & $-1.46\\\\pm$0.06 & $-1.56\\\\pm0.07$ & S & 0.5 & 171 & 18 59 40.34 & +59 00 36.8 & V \\\\\\\\\\nWN J1859+5416 & 81$\\\\pm$ 4 & 10.1$\\\\pm$ 1.6 & $ 2.70\\\\pm0.14$ & $-1.43\\\\pm$0.12 & $-1.06\\\\pm0.13$ & S & 1.7 & 17 & 18 59 57.65 & +54 16 21.8 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1907+8532 & 69$\\\\pm$ 4 & 10.2$\\\\pm$ 0.4 & \\\\nodata & $-1.31\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 19 07 26.54 & +85 32 35.2 & N \\\\\\\\\\nWN J1911+6342 & 185$\\\\pm$10 & 23.3$\\\\pm$ 1.5 & $ 3.37\\\\pm0.14$ & $-1.42\\\\pm$0.05 & $-1.56\\\\pm0.06$ & S & 1.8 & 7 & 19 11 49.54 & +63 42 09.6 & V \\\\\\\\\\nWN J1912+8627 & 126$\\\\pm$ 7 & 18.8$\\\\pm$ 1.2 & $ 2.55\\\\pm0.13$ & $-1.30\\\\pm$0.05 & $-1.61\\\\pm0.07$ & S & 2.4 & 178 & 19 12 06.26 & +86 27 10.1 & V \\\\\\\\\\nWN J1917+6635 & 75$\\\\pm$ 5 & 11.2$\\\\pm$ 0.5 & $ 2.37\\\\pm0.12$ & $-1.30\\\\pm$0.06 & $-1.25\\\\pm0.06$ & S & 1.9 & 152 & 19 17 35.50 & +66 35 38.5 & V \\\\\\\\\\nWN J1917+7149 & 280$\\\\pm$12 & 40.4$\\\\pm$ 2.1 & \\\\nodata & $-1.33\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 19 17 56.11 & +71 49 19.7 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1923+6047 & 83$\\\\pm$ 5 & 12.4$\\\\pm$ 0.5 & $ 2.56\\\\pm0.13$ & $-1.30\\\\pm$0.06 & $-1.27\\\\pm0.05$ & S & 2.4 & 91 & 19 23 33.18 & +60 47 56.8 & V \\\\\\\\\\nWN J1925+5203 & 199$\\\\pm$ 9 & 27.5$\\\\pm$ 1.7 & $ 4.30\\\\pm0.16$ & $-1.36\\\\pm$0.05 & $-1.49\\\\pm0.06$ & D & 8.6 & 52 & 19 25 16.97 & +52 03 34.4 & V \\\\\\\\\\nWN J1925+5742 & 100$\\\\pm$ 6 & 14.5$\\\\pm$ 0.5 & $ 1.58\\\\pm0.11$ & $-1.32\\\\pm$0.06 & $-1.78\\\\pm0.06$ & S & 2.0 & 9 & 19 25 22.22 & +57 42 27.3 & V \\\\\\\\\\nWN J1926+5710 & 136$\\\\pm$ 7 & 20.2$\\\\pm$ 0.6 & $ 4.55\\\\pm0.18$ & $-1.31\\\\pm$0.04 & $-1.20\\\\pm0.04$ & S & 1.8 & 161 & 19 26 43.85 & +57 10 00.5 & V \\\\\\\\\\nWN J1927+6436 & 661$\\\\pm$26 & 80.3$\\\\pm$ 3.5 & $ 6.62\\\\pm0.21$ & $-1.44\\\\pm$0.04 & $-2.01\\\\pm0.04$ & D & 20.1 & 120 & 19 27 22.83 & +64 36 02.6 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J1944+6552 & 1367$\\\\pm$55 & 147.2$\\\\pm$ 6.5 & $ 19.45\\\\pm0.47$ & $-1.53\\\\pm$0.04 & $-1.63\\\\pm0.04$ & S & 1.8 & 165 & 19 44 23.99 & +65 52 23.8 & V \\\\\\\\\\nWN J1953+7052 & 75$\\\\pm$ 7 & 10.3$\\\\pm$ 0.5 & $ 3.22\\\\pm0.15$ & $-1.36\\\\pm$0.07 & $-0.94\\\\pm0.05$ & D & 14.4 & 150 & 19 53 21.10 & +70 52 19.8 & V \\\\\\\\\\nWN J1954+7011 & 460$\\\\pm$19 & 63.4$\\\\pm$ 2.9 & \\\\nodata & $-1.36\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 19 54 30.53 & +70 11 33.5 & N \\\\\\\\\\nWN J2044+7044 & 311$\\\\pm$13 & 41.7$\\\\pm$ 0.9 & $ 7.18\\\\pm0.22$ & $-1.38\\\\pm$0.03 & $-1.42\\\\pm0.03$ & D & 1.3 & 83 & 20 44 57.80 & +70 44 03.8 & V \\\\\\\\\\nWN J2052+6925 & 113$\\\\pm$ 6 & 16.1$\\\\pm$ 1.3 & \\\\nodata & $-1.33\\\\pm$0.07 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 20 52 33.78 & +69 25 09.3 & N \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J2053+6849 & 109$\\\\pm$ 5 & 15.8$\\\\pm$ 0.5 & $ 2.59\\\\pm0.13$ & $-1.32\\\\pm$0.05 & $-1.45\\\\pm0.05$ & S & 2.8 & 13 & 20 53 38.68 & +68 48 54.7 & V \\\\\\\\\\nWN J2139+3125 & 249$\\\\pm$10 & 28.0$\\\\pm$ 0.7 & \\\\nodata & $-1.50\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 39 32.31 & +31 25 18.7 & N \\\\\\\\\\nWN J2146+3330 & 105$\\\\pm$ 6 & 10.8$\\\\pm$ 0.5 & \\\\nodata & $-1.56\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 46 55.47 & +33 30 01.7 & N \\\\\\\\\\nWN J2147+3137 & 215$\\\\pm$ 9 & 25.4$\\\\pm$ 1.6 & \\\\nodata & $-1.46\\\\pm$0.05 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 21 47 35.21 & +31 37 58.9 & N \\\\\\\\\\nWN J2158+3424 & 182$\\\\pm$ 8 & 25.3$\\\\pm$ 0.7 & $ 4.48\\\\pm0.17$ & $-1.35\\\\pm$0.04 & $-1.39\\\\pm0.04$ & T & 7.9 & 163 & 21 58 54.14 & +34 24 47.8 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J2213+3411 & 320$\\\\pm$13 & 29.8$\\\\pm$ 2.2 & \\\\nodata & $-1.63\\\\pm$0.06 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 13 12.48 & +34 11 42.8 & N \\\\\\\\\\nWN J2219+2951 & 151$\\\\pm$10 & 13.2$\\\\pm$ 0.5 & \\\\nodata & $-1.67\\\\pm$0.04 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 22 19 28.65 & +29 51 57.4 & N \\\\\\\\\\nWN J2221+3800 & 99$\\\\pm$ 6 & 14.4$\\\\pm$ 0.5 & $ 2.18\\\\pm0.11$ & $-1.32\\\\pm$0.05 & $-1.52\\\\pm0.05$ & S & 1.4 & 5 & 22 21 49.53 & +38 00 38.4 & V \\\\\\\\\\nWN J2222+3305 & 232$\\\\pm$10 & 30.4$\\\\pm$ 1.7 & $ 3.53\\\\pm0.14$ & $-1.39\\\\pm$0.05 & $-1.73\\\\pm0.05$ & S & 1.4 & 13 & 22 22 15.19 & +33 05 44.1 & V \\\\\\\\\\nWN J2245+3937 & 204$\\\\pm$ 8 & 15.5$\\\\pm$ 1.3 & $ 5.65\\\\pm0.21$ & $-1.76\\\\pm$0.07 & $-0.81\\\\pm0.07$ & DF & 4.0 & 168 & 22 45 02.74 & +39 37 27.9 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J2250+4131 & 128$\\\\pm$ 7 & 15.2$\\\\pm$ 1.4 & $ 2.03\\\\pm0.11$ & $-1.46\\\\pm$0.07 & $-1.62\\\\pm0.09$ & S & 1.5 & 25 & 22 50 51.16 & +41 31 16.4 & V \\\\\\\\\\nWN J2313+4053 & 101$\\\\pm$ 6 & 11.3$\\\\pm$ 1.4 & \\\\nodata & $-1.50\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 23 13 06.34 & +40 53 40.6 & N \\\\\\\\\\nWN J2313+4253 & 94$\\\\pm$ 7 & 13.4$\\\\pm$ 1.5 & $ 3.41\\\\pm0.14$ & $-1.33\\\\pm$0.09 & $-1.10\\\\pm0.10$ & S & 1.4 & 13 & 23 13 08.62 & +42 53 13.0 & V \\\\\\\\\\nWN J2313+3842$^*$ & 304$\\\\pm$13 & 13.2$\\\\pm$ 2.6 & \\\\nodata & $-2.15\\\\pm$0.14 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 23 13 47.75 & +38 42 26.2 & N \\\\\\\\\\nWN J2319+4251 & 321$\\\\pm$14 & 40.2$\\\\pm$ 2.9 & $ 3.88\\\\pm0.14$ & $-1.42\\\\pm$0.06 & $-1.88\\\\pm0.07$ & S & 1.5 & 20 & 23 19 47.25 & +42 51 09.2 & V \\\\\\\\\\n&&&&&&&&&&&\\\\\\\\\\t\\t \\nWN J2337+3421 & 84$\\\\pm$ 4 & 12.4$\\\\pm$ 1.3 & \\\\nodata & $-1.31\\\\pm$0.09 & \\\\nodata & \\\\nodata & \\\\nodata & \\\\nodata & 23 37 23.43 & +34 21 51.5 & N \\\\\\\\\\nWN J2338+4047 & 115$\\\\pm$ 6 & 16.9$\\\\pm$ 0.5 & $ 5.06\\\\pm0.18$ & $-1.31\\\\pm$0.04 & $-0.97\\\\pm0.04$ & D & 15.7 & 8 & 23 38 11.10 & +40 47 19.6 & V \\\\\\\\\\nWN J2350+3631 & 196$\\\\pm$ 8 & 22.8$\\\\pm$ 0.6 & $ 2.20\\\\pm0.11$ & $-1.47\\\\pm$0.04 & $-1.88\\\\pm0.04$ & DF & 2.7 & 165 & 23 50 25.69 & +36 31 27.6 & V \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\n$^{\\\\dag}$ Not a real USS source; see notes\\n\\n$^*$ See notes\\n\\n\\\\end{table*}\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002297.extracted_bib","string":"\\begin{thebibliography}{}\n\\bibitem[Abell \\etal\\ 1989]{abe89} Abell, G. 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We present here the results of two \\sax\\ observations in which the source has shown a variation of about 30\\% in flux with a corresponding spectral variability. We interpret the overall spectral energy distribution in terms of an homogeneous SSC model and, by using also the TeV upper limit from a short Mark 6 pointing, derive constraints on the physical parameters of the source, in particular on the magnetic field strength. The overall Spectral Energy Distribution makes 1ES~1101--232 a very promising candidate for TeV detection. \\keywords{(Galaxies:) BL Lacertae objects: general -- X--rays: galaxies -- BL Lacertae objects: individual: 1ES~1101--232 }"},"latex":{"kind":"list like","value":[{"name":"9325.tex","string":"\\documentclass{aa}\n%%\\documentclass[referee]{aa}\n\n\n\\include{psfig}\n\n\\def\\doublespace{\\baselineskip 24pt}\n\\def\\singlespace{\\baselineskip 15pt}\n\\def\\e20{\\times 10^{20} {\\rm cm}^{-2} }\n\\def\\sax{{\\it Beppo}SAX}\n\\def\\NH{N_{\\rm H}}\n\\def\\ecs{\\rm \\,erg~ cm^{-2}\\,s^{-1} }\n\\def\\mincir{\\ \\raise -2.truept\\hbox{\\rlap{\\hbox{$\\sim$}}\\raise5.truept \n\\hbox{$<$}\\ }} % minore o circa uguale\n\n\\begin{document}\n\n\\thesaurus{03(11.02.1; 13.25.3)}\t\n%A\\&A Section 03: (Extragalactic Astronomy)\n%%(11.02.1; % {\\it (Galaxies:)} BL Lacertae objects: general\n%%13.25.3 %X--rays: general)\n\n\n\n\\title{X--ray variability and prediction of TeV emission in the HBL 1ES~1101--232}\n\\author{A. Wolter,\n\\inst{1} \nF. Tavecchio, \\inst{1} A. Caccianiga,\\inst{2} G. Ghisellini,\\inst{1} G. Tagliaferri \\inst{1}\n}\n\n\\offprints{A. Wolter: anna@brera.mi.astro.it}\n\n\\institute{Osservatorio Astronomico di Brera,\n\t\tVia Brera, 28\n\t\t20121 MILANO, Italy\n\\and Observatorio Astronomico de Lisboa, Tapada da Ajuda, P-1300 Lisboa, Portugal\n}\n\n\\date{Received ....; accepted ....}\n\\maketitle\n\\markboth{A. Wolter et al.}{The HBL 1ES~1101--232}{}\n\n\\begin{abstract}\n\n1ES~1101--232 is a bright BL Lac of the High frequency peak class. \nWe present here the results of two \\sax\\ observations in which the\nsource has shown a variation of about 30\\% in flux with a corresponding\nspectral variability.\nWe interpret the overall spectral energy distribution in terms\nof an homogeneous SSC model and, by using also the TeV upper limit\nfrom a short Mark 6 pointing, derive constraints\non the physical parameters of the source, in particular on the magnetic \nfield strength.\nThe overall Spectral Energy Distribution makes\n1ES~1101--232 a very promising candidate for TeV detection. \n\n\\keywords{(Galaxies:) BL Lacertae objects: general --\n\t X--rays: galaxies -- BL Lacertae objects: individual: 1ES~1101--232\n }\n\\end{abstract}\n\n\\section{Introduction}\n\\noindent\n\nBL Lac objects form a minority class of active nuclei (see e.g. Urry \\& \nPadovani, 1995), but nevertheless their high luminosities and extreme \nvariability in all bands \nmake them an interesting subclass to study intrinsic properties of\nnuclear emission. Furthermore, it is matter of discussion the position of\nBL Lacs with respect to other active nuclei in the framework of Unification\nModels. The current picture claims that BL Lacs are the fraction of \nFanaroff-Riley I galaxies that point their jet towards us, but many\ndetails still need to be worked out. Often, BL Lacs are studied together\nwith other classes of flat radio spectrum sources, to form the class of blazars.\n\nRecently a sequence has been proposed for the subclass of gamma ray\nbright blazars, and possibly valid for all blazars, based on their \nbolometric luminosity\n(Ghisellini et al. 1998, Fossati et al. 1998). \nThe overall spectral energy distribution has two peaks \n(in $\\nu F_\\nu$ representation), \nthe one at lower energies due to synchrotron radiation and the higher energy \none to Inverse Compton scattering. \nIt is proposed that the value of the peak frequency is the result\nof the balance between radiative cooling and acceleration of the \ncorresponding electrons (see e.g. Ghisellini, 1999):\nin less luminous objects the radiative cooling is less efficient, allowing\nthe accelerated electrons to reach higher energies.\nAs a consequence, both the synchrotron and the inverse Compton peaks\nshift to higher frequencies as the bolometric intrinsic\nluminosity decreases.\nIn this view, the class of BL Lacertae objects known as HBL \n(High frequency peak BL Lacs)\nhas a smaller bolometric luminosity and a higher synchrotron peak frequency\nthan the class of LBL (Low frequency peak BL Lacs).\nHBL are mostly found in X--ray selected samples, since they are expected to \nproduce most of their synchrotron emission in the X--ray band. \nIf the emission peak (as in the LBL objects) is\nat frequencies smaller than the observed X--ray band, the X--ray spectrum is \nsteep (i.e. the steepening part above the peak), while HBL with a flat \nX--ray spectrum should have their peak in the observed X--ray band.\n\nAs part of a program aimed at a spectral survey of soft X--ray selected \nBL Lacs with \\sax\\ (Wolter et al. 1998), \nwe have studied also 1ES~1101--232 (z=0.186), \na bright BL Lac selected from the Slew Survey (Perlman et al. 1996) \nthat shows an extreme behavior with a very flat X--ray spectrum.\nThe object was detected, besides in the 0.1-10 keV energy band, also\nup to $\\sim$ 100 keV in only $\\sim 6000$ sec. \nThe best fit of the source in the 0.1-100 keV band is given by a broken \npower law, with Galactic low energy absorption, that has a break energy\nE$_0$=1.36 (1.11--1.65) keV.\nThe spectral slope (energy index) derived from the PDS is consistent\nwith the one derived from the MECS above the break energy E$_0$:\n$\\alpha_x$ = 1.03 (0.99--1.08) (Wolter et al. 1998).\n\nWe have constructed also the Spectral Energy Distribution (SED) for this\nobject, using flux measurements collected from the literature, from radio to\nX--rays.\nWe have fitted a cubic polynomial to the \ndistribution in order to find the peak of the SED, that indeed \nfalls in the \\sax\\ band (log $\\nu_{peak} \\sim$ 17.48, corresponding to \n$\\sim 1.3$ keV).\nFor this object, therefore, the break energy derived from\nthe spectral fit in the X--ray band is consistent, albeit within its\nlarge indetermination, with the position of the synchrotron \npeak as derived from the overall distribution (SED). \n\nThe SED of 1ES~1101--232 is similar to that of the flaring state\nof Mkn 501 (Pian et al. 1998) and 1ES~2344+514 (Catanese et al. 1998; \nGiommi et al. 2000), \nand therefore we could expect a strong TeV emission. \nA quasi--simultaneous X--ray and TeV observation has been\ntherefore scheduled, to confirm the X--ray spectrum of the source, and\nits overall shape,\nto detect possible variations in flux, that could constrain the physical\nparameters of the source, and to monitor the TeV emission to search\nfor possible detection. \n\n%__________________________________________________ Two col. table\n\\begin{table*}\n \\caption{Fit results for 1ES~1101--232 LECS+MECS data OBS. 19/06/98 {\\bf Low state}}\n\\begin{tabular}[h]{| l l c c c r r r|}\n \\hline\nModel & $N_{\\rm H}^a$ & $\\alpha_1$ & $\\alpha_2$ & $E_0$ & $F^{\\rm b}$ & $\\chi^2(dof)$ & Prob. \\\\\n & & & & keV & & & \\\\\n(1) & 5.76 & -- & 1.19(1.16-1.22) & -- & 2.60 & 267.1(195) & $<$ 0.5\\%\\\\\n(2) & 8.3(7.1-10.4) & -- & 1.25(1.22-1.29) & -- & 2.57 & 240.5(195) & 1.5\\%\\\\\n(3) & 5.76 &0.80(0.58-0.96)& 1.29(1.25-1.33) & 1.34(1.08-1.82) &2.55 & 216.2(194) & 13\\% \\\\\n\\hline\n\\end{tabular}\n\\begin{list}{}{}\n\\item (1) Single p.l., $N_{\\rm H}$=$N_{\\rm H}^{\\rm Gal}$, LECS/MECS ratio free; \n(2) Single p.l., $N_{\\rm H}$ free, LECS/MECS ratio=0.7 ; \n(3) Broken p.l., $N_{\\rm H}=N_{\\rm H}^{\\rm Gal}$, LECS/MECS ratio = 0.7. \nErrors quoted are 90\\% confidence intervals. \\\\\n$^{\\rm a}$ Column density in $\\e20$. \\\\\n$^{\\rm b}$ Unabsorbed [2--10 keV] flux in $10^{-11} \\ecs$. \\\\\n\\end{list}\n\\label{broken_n}\n\\end{table*}\n%__________________________________________________ Two col. table\n\\begin{table*}\n \\caption{Fit results for 1ES~1101--232 LECS+MECS data OBS. 04/01/97 {\\bf High state} } \n\\begin{tabular}[h]{| l l c c c r r r|}\n \\hline\nModel & $N_{\\rm H}^{\\rm a}$ & $\\alpha_1$ & $\\alpha_2$ & $E_0$ & $F^{\\rm b}$ & $\\chi^2(dof)$ & Prob. \\\\\n & & & & keV & & & \\\\\n(1) & 5.76 & -- & 0.97(0.95-1.00) & -- & 3.81 & 224.0 (182) & $<$ 2\\%\\\\\n(2) & 8.9(7.2-12.6) & -- & 1.03(0.99-1.08) & -- & 3.79 & 205.1 (182) & 11 \\%\\\\\n(3) & 5.76 &0.59(0.35-0.74) & 1.05(1.01-1.08) & 1.36(1.11-1.65) &3.76 & 191.6 (181) & 28 \\%\\\\\n\\hline\n\\end{tabular}\n\\begin{list}{}{}\n\\item \n(1) Single p.l., $N_{\\rm H}$=$N_{\\rm H}^{\\rm Gal}$, LECS/MECS ratio free; \n(2) Single p.l., $N_{\\rm H}$ free, LECS/MECS ratio=0.7; \n(3) Broken p.l., $N_{\\rm H}$=$N_{\\rm H}^{\\rm Gal}$, LECS/MECS ratio = 0.7.\nErrors quoted are 90\\% confidence intervals. \\\\\n$^{\\rm a}$ Column density in $\\e20$. \\\\\n$^{\\rm b}$ Unabsorbed [2-10 keV] flux in $10^{-11} \\ecs$. \\\\\n\\end{list}\n \\label{broken_o}\n\\end{table*}\n\n\nThe \\sax\\ data are presented here. The TeV observation, conducted in \nnon--optimal weather condition, did not yield a detection, but we will use\nthe upper limit (Chadwick et al. 1999a) to derive useful information on\nthe physical mechanisms at work in this source.\nThe plan of the paper is as follows: in Section 2 we describe the observational\ndata obtained with \\sax\\ in the two epochs, in Section 3 we summarize the TeV\npredictions and observations, that help constraining the parameters of the\nsource, by using the SED and theoretical models of emission as explained in\nSection 4. Section 5 presents our results and conclusions.\n\n\nThroughout the paper a Hubble constant H$_0$=50 $km\\, s^{-1}\\, Mpc^{-1}$ \nand a Friedman universe with a deceleration parameter $q_0$=0 are assumed.\n\n\n \n\\section{ \\sax\\ data}\n\nThe X--ray astronomy satellite \\sax\\ is a project of the Italian\nSpace Agency (ASI) with a participation of the Netherlands Agency for \nAerospace Programs (NIVR).\nThe scientific payload comprises four Narrow Field Instruments [NFI:\nLow Energy Concentrator Spectrometer (LECS), Medium Energy Concentrator\nSpectrometer (MECS), High Pressure Gas Scintillation Proportional Counter\n(HPGSPC), and Phoswich Detector System (PDS)], all pointing in the\nsame direction, and two Wide Field Cameras (WFC), pointing in\nopposite directions perpendicular to the NFI common axis. A detailed\ndescription of the entire \\sax\\ mission can be found in Butler \\& Scarsi (1990)\nand Boella et al. (1997a). \n\nThe MECS consists of three equal units, each composed of a grazing\nincidence mirror unit and of a position sensitive gas scintillation \nproportional counter, with a field of view of\n56 arcmin diameter, working range 1.3--10 keV, energy resolution $\\sim 8\\%$\nand angular resolution $\\sim 0.7$ arcmin (FWHM) at 6 keV.\nThe effective area at 6 keV is 155 cm$^2$ (Boella et al. 1997b)\n\nThe LECS is a unit similar to the MECS, with a thinner window that\ngrants a lower energy cut-off (sensitive in the energy range 0.1-10.0 keV)\nbut also reduces the FOV to 37 arcmin diameter (Parmar et al. 1997). \nThe LECS energy resolution is a factor $\\sim 2.4$ better\nthan that of the ROSAT PSPC ($\\sim 32\\%$ at 0.28 keV), while the \neffective area is smaller: 22 cm$^{2}$ at 0.28 and and 50 cm$^{2}$ at 6 keV.\n\nThe PDS is a system of four crystals, sensitive in the 13--200~keV band and\nmounted on a couple of rocking collimators, which points two units on the\ntargets and two units $3.5^{\\circ}$ aside respectively, to monitor the\nbackground.\nThe position of the collimators flips every 96 seconds.\nThanks to the stability of the instrumental background, the PDS has shown \nan unprecedented sensitivity in its energy range, allowing 3$\\sigma$ detection \nof $\\alpha \\sim 1$ sources as faint as 10 m Crab \nwith 10 ks of effective exposure time (Guainazzi \\& Matteuzzi, 1997).\n\nThe source is not detected by the HPGSPC, so we will not discuss this \ninstrument.\n\n\n\\subsection{Observation of June 1998}\n\n\\begin{figure}\n\\psfig{file=9325.f1,width=8truecm,height=6truecm,angle=-90}\n\\caption{X--ray spectrum (LECS+MECS+PDS) of June 1998, with broken power law fit\n(model 3 from Table~\\ref{broken_n})}\n\\label{fignew}\n\\end{figure}\n\nThe object has been observed in AO2 on 19 June 1998 for a total of \n8958 sec (LECS -- 3167 net counts); \n24895 sec (MECS(2+3) -- 10612 net counts) and \n10792 sec (PDS on source -- 1320 net counts).\nThe AO2 observation has been performed with only 2 MECS (MECS2 and MECS3)\nsince MECS1 was no longer active.\nThe source has been observed almost in the same period (May 1998) by the \nMark6 telescope (working in the GeV-TeV range). \n\nThe extraction of the \\sax\\ data has been performed with FTOOLS v4.0 and the\nspectral analysis with XSPEC v9.0, using the most recently available matrices\n(September 1997 release).\nThe data analysis has been performed on the same guidelines as outlined\nby the \\sax\\ Cookbook ({\\small\\verb+http://www.sdc.asi.it/software/cookbook/+})\nand described e.g. in Wolter et al. (1998).\nWe summarize here that counts are extracted in a circular region of 8.5'/4' \n(LECS/MECS) radius, and the background is taken from the blank \nsky images distributed by the \\sax\\ Data Center, in a region corresponding \nto the one used to extract\nsource counts. Counts are binned so as to have at least 30 total counts \nin each bin to ensure applicability of the $\\chi^2$ statistics.\nFit to LECS data are performed only up to 4 keV, as the\nresponse matrix of LECS is not well calibrated above this\nenergy (see Orr et al. 1998).\nAll confidence levels are computed using $\\Delta \\chi^2$ = 2.7 (corresponding\nto 90\\% for 1 interesting parameter), unless otherwise stated. \n\nFor the LECS+MECS combined data, \na single power law is not acceptable ($> 3 \\sigma$) with $N_{\\rm H}$\nfixed at the Galactic value.\nIf $N_{\\rm H}$ is left free, the fit with a single power law is acceptable only\nat about $3 \\sigma$ (Prob $\\sim 1.5\\%$). The residuals are however \nskewed, showing that the fit is not good.\nThe fit is significantly improved (F--test at $>$ 99.99 \\% probability) by\nusing a broken power law shape. \nResults for the three models for LECS and MECS data are listed in \nTable~\\ref{broken_n}.\n\nFor each observation, in the first fit \n(single power-law model with Galactic $N_{\\rm H}$) we left the \nLECS normalization free\nwith respect to the MECS normalization to account for the residual \nerrors in intensity cross-calibration (see Cusumano, Mineo, Guainazzi\net al. in preparation). The fitted value \nof 0.696 (1997) and 0.701 (1998) fall in the range\nexpected given the current knowledge of the cross-calibration\n(F. Fiore, private communication; see also \n{\\small\\verb+http://www.sdc.asi.it/software/cookbook/cross_cal.html+}).\nSince the ratio of the two normalizations depends\non the position of the source in the detector, and not on the model\nchosen, we fix the LECS/MECS normalization to 0.7 also for the\nother subsequent models. \n\n\nThe PDS exposure time is not even twice than in AO1 (10.8 ks vs. 6.4 ks). \nSince the spectrum is steeper and the source is \nfainter than in the AO1 observation, the PDS detection is \nnot more significant than the AO1 detection ($2.6 \\sigma$). \nIn order to fit the PDS data alone we rebin them to 6 data points. \nWe fix the absorbing column to the Galactic value (N$_H = 5.76 \\times \n10^{20}$ cm$^{-2}$) while the normalization with respect to the MECS\nand index are left free.\nThe best fit slope is\n$\\alpha_{PDS}$ = 1.02 [$<$ 2.65], and the PDS/MECS ratio is 0.90, consistent\nwith what expected on the basis of cross-calibration of the instruments,\nwith a $\\chi^2$ = 2.2(4 dof), for\na probability of 70\\%, therefore statistically acceptable.\nHowever, given the low statistical \nsignificance of the PDS data, the uncertainty on the slope is high. \nWe therefore fit the total spectrum, from 0.1 keV to $\\sim $50 keV, using \nLECS, MECS and PDS data together: the result of the broken power law fit\nis shown in Figure~\\ref{fignew}. \nIt yields an unabsorbed flux in the [2--10 keV] band of\n$F_X=2.54 \\times 10^{-11}$ erg cm$^{-2}$ s$^{-1}$, \nand a corresponding luminosity in the same band of\n$L_X = 4.7\\times 10^{45}$ erg s$^{-1}$.\nThe PDS data are consistent with the LECS+MECS extrapolation.\n\n\n\\subsection {Comparison of the 1997 and 1998 observations}\n\nFor ease of comparison, we report in Table~\\ref{broken_o} the AO1 observation \nresults of 1ES~1101--232, from Wolter et al. (1998).\nThe LECS exposure was 5195 sec (2484 net counts), the MECS exposure\nwas 13830 (9509 net counts) and the PDS on-source exposure was 6410 sec (1996 \nnet counts).\nThe best fit models of the LECS+MECS spectra for various spectral \nshapes are listed in Table~\\ref{broken_o}, while in Figure~\\ref{figold} \nthe LECS+MECS+PDS \nspectrum is plotted, with the best fit of model (3).\n\n\\begin{figure}\n\\psfig{file=9325.f2,width=8truecm,height=6truecm}\n\\caption{X--ray spectrum (LECS+MECS+PDS) of Jan 1997, with broken power law fit\n(model 3 from Table~\\ref{broken_o}).}\n\\label{figold}\n\\end{figure}\n\n\nIn order to compare the two observations, we first check directly the count\nrates in the two epochs. The best representation is the ratio of\nthe two observed spectra, that does not depend on the choice of models\nand parameters. We therefore bin the two spectra, the relative \nbackground and response matrices in 32 channels, in order to avoid having \nempty bins after background subtraction. We then divide the two \nbackground-subtracted count rates and plot the results (after having \nflagged out the energy ranges that are not well calibrated in the matrices) \nin Fig.~\\ref{figrap}. \nThe ratio is consistent with being flat up to $\\sim 2$ keV, and steepening \nafter it, showing that a change in the spectrum occurred above $\\sim 2$ keV. \nThe two instruments, LECS and MECS, give a consistent ratio\nin the overlapping energy range. A fit with a constant in the interval \n0.5--10 keV is not statistically acceptable.\n\n\n\\begin{figure}\n\\psfig{file=9325.f3,width=8truecm,height=6truecm,angle=-90}\n\\caption{Ratio of data point from the Jun 1998 and Jan 1997 observations. \nStars indicate data points from the LECS instrument, crosses data points\nfrom the MECS instrument.\nThe trend in the data, with a drop above $\\sim$2 keV, is evident.}\n\\label{figrap}\n\\end{figure}\n\nAlso comparing the fit results for the two observations of Jan 1997 and \nJun 1998, we see that the high energy slope\n($\\alpha_2$) is steeper in the second one. The flux, with all the\nthree best fit models reported in the tables, is a factor of $\\sim$ 32\\% \nlower in the second than in the first one. \nThe low energy slope ($\\alpha_1$) and the break energy ($E_0$) are\ninstead consistent within the errors between the two observations.\n\nWe can make therefore the hypothesis that the different fluxes and \nspectra between the two epochs are \nexplained by a change in the spectral slope above the peak of the synchrotron\nemission. Hence we fit all the data (1997+1998) simultaneously, keeping the low\nenergy slope and break energy tied (equal one to each other, but free to \nvary) between the two observations. \nOn the contrary, the high energy slopes in the two observations are left \nindependent.\nThe $N_{\\rm H}$ is fixed to the galactic value, that fits well both \nobservations. The PDS data are not used for the comparison, being of \nlow statistical significance; the LECS and MECS data are re-binned to\n100 total counts for each bin, to improve the significance of the individual\ndata points, since no small range feature is present. The LECS/MECS \nnormalization is again fixed to 0.7.\n\n\\begin{figure}\n\\psfig{file=9325.f4a,width=7truecm,height=5.5truecm,angle=-90}\n\\psfig{file=9325.f4b,width=7truecm,height=5.5truecm,angle=-90}\n\\caption{LECS+MECS spectrum and broken power law fit for Jan 1997 (Upper Panel)\nand Jun 1998 (Lower Panel) observations. The broken power law fit of the two\nobservations combined is given in the text.}\n\\label{figcom}\n\\end{figure}\n\n\n\\begin{table}\n\\caption{Unabsorbed Fluxes and Rest--Frame Luminosities for the two \nobservations in the (0.1--2) and (2--10) keV energy bands.}\n\\begin{tabular}[htb]{| l c c c c |}\n \\hline\nDate & $F$[0.1-2] & $F$[2-10] & $L$[0.1-2] & $L$[2-10] \\\\\n & \\multicolumn{2}{c}{$\\times 10^{-11} \\ecs$}&\\multicolumn{2}{c|}{$\\times 10^{45}$ erg s$^{-1}$} \\\\\n\\hline \n04/01/97 & 3.46 & 3.85 & 5.4 & 6.8 \\\\\n19/06/98 & 3.32 & 2.53 & 5.3 & 4.7 \\\\\n\\hline\n\\end{tabular}\n\\label{fluxes}\n\\end{table}\n\n\nThe resulting values of $\\alpha_1$ and $E_0$ are consistent with those of both\nsingle observations: $\\alpha_1$=0.72 [0.44, 0.88]; \n$E_0=1.17 [0.93, 1.43]$ keV.\nThe high energy slope is \n$\\alpha_2^{1998}$ = 1.26 [1.19, 1.32], vs. \n$\\alpha_2^{1997}$ = 1.01 [0.95, 1.07], confirming that the slope indeed\nsteepened significantly. The $\\chi^2$ of the fit is 184.4 with 178 dof, \ncorresponding to a probability of 36\\%.\nThe errors quoted here are 90\\% confidence for \n4 parameters of interest ($\\Delta\\chi^2 = 7.76$).\nThe combined spectra (LECS and MECS) for both \nobservations with the best fit model are shown in Figure~\\ref{figcom}.\nWe report in Table~\\ref{fluxes} the unabsorbed fluxes and rest-frame\nluminosities in the \n0.1--2 and 2--10 keV bands for the two observations using the combined \nfit results.\n\n\nThe fluxes derived using the combined model are consistent with the\nfluxes derived from the two independent fits to the observations. We can\ntherefore attribute the observed flux variation entirely to a steepening\nof the high energy ($>$2 keV) portion of the spectrum. There is no\nevidence, within the statistical uncertainties, of a change in $\\alpha_1$\nor $E_0$, although in other well known sources (Mkn501, Mkn421, PKS2155--304) \nan increase in flux seems to be linked to an increase in $E_0$ and/or the \nhigh energy slope.\n\n\n\\section{The TeV band }\n\nBlazars as a class have been shown to emit a large fraction of their power\nat high energies, in the MeV--TeV band.\nThe current models assume that the high energy emission is produced by\nInverse Compton scattering (e.g. the SSC model or the EC model, see Ghisellini\net al. (1998) for the relevance of the two mechanisms), and the location of \nthe peak of the Compton component depends mainly on the lower energy peak due \nto the Synchrotron component. \n\nIn particular, objects of the LBL kind, that have the synchrotron peak\nat soft energies,\nshow their second peak at energies in the MeV--GeV range, and are in fact \ndetected by EGRET on board CGRO (see Mukherjee et al. 1997).\nObjects of the HBL kind, that have their synchrotron peak at UV--X--ray frequencies,\ninstead, should show the Compton peak in an even higher energy band. In fact,\nup to now, the only sources of VHE gamma rays (in the TeV band, by using\n$\\check{\\rm C}$erenkov detectors) are HBL: \nMkn 421 (Punch et al. 1992), Mkn 501 (Quinn et al. 1996), \n1ES~2344+514 (Catanese et al. 1998), \nPKS 2155--304 (Chadwick et al. 1999b).\n\nThe new $\\check{\\rm C}$erenkov arrays allow the detection of bright sources \nin relatively short exposure times, and therefore it has been possible to \nmonitor their variability:\nsome of these objects have in fact shown periods of flaring activity on \ntime-scales as short as 15 minutes (Gaidos et al. 1996, Aharonian et al. 1999).\n\nAnother point of debate is the amount of absorption of VHE photons due to \nthe cosmic infra--red background. The aforementioned detected objects in fact\nare all nearby.\nDetection of sources that lie further away can therefore help in constraining\nthe amount of the IR background (e.g. Stecker and De Jager, 1998).\n\nThe simultaneous detection of X--ray and TeV emission allows us to estimate\na number of physical parameters of the source, such as the magnetic field and\nthe Doppler factor (see e.g. Tavecchio et al. 1998). \nWe will show in Section 4 that a number of interesting constraints can be \nderived also by using the upper limit derived in the TeV band, together \nwith the X--ray band information.\n\n\\subsection {Predictions of TeV emission in 1ES~1101--232 from phenomenological\nconstraints.}\n\nA very simple prediction of the TeV emission can be made by following \nthe scheme presented e.g. in Fossati et al. (1998).\nIn this model a) the ratio of the frequencies of the high (Compton) and low \n(synchrotron) energy peaks is constant and equal to $5\\times 10^{8}$ and\nb) the high energy peak and the radio luminosity have a fixed ratio, \n$\\nu_\\gamma L_{peak,\\gamma} \\over \\nu_{5GHz} L_{5GHz}$ =$3 \\times 10^{3}$. \nThis model represents the average SED observed for \nthe various classes, while single sources can deviate from\nthis average phenomenological parameterization.\nThis very simple relationship, however, allows us to make order of magnitude\nprediction even not knowing the physical conditions at the source. From \nthe two expressions above we can derive both the expected frequency\nof the second peak and its intensity.\nThe peak of the synchrotron emission is measured (this paper and Wolter \net al. 1998) at\n$\\nu_s = 3 \\times 10^{17}$ Hz: the Compton peak is therefore expected\nat $\\nu_C = 1.5 \\times 10^{26}$ Hz which corresponds to $\\sim$0.6 TeV.\nThe measured radio flux at 5 GHz is $5 \\times 10^{-15}$ erg \ncm$^{-2}$ s$^{-1}$ (see references in Table~\\ref{refere}).\nThe expected flux at the Compton peak (0.6 TeV) is therefore\n$\\sim 8. \\times 10^{-12}$ photon cm$^{-2}$ s$^{-1}$. \n\nAnother prediction can be made from the observed X--ray flux, by using the\nrecipe of Stecker, De Jager \\& Salamon (1996). Within an SSC scenario they\nuse simple scaling arguments to predict the TeV fluxes for HBL, based on the \nX--ray flux and the assumption that the properties of the emission are similar \nto those observed for Mkn 421. Their argument is partially\nsupported by the actual detection of (a few) other sources\nfor which they predicted possible detectability.\nThe factor of increase between the synchrotron and Compton \ncomponent is $10^9$, and, assuming $L_C/L_s \\sim 1$,\nthey derive $\\nu_{TeV} F_{TeV} \\sim \\nu_{X} F_{X}$.\nTherefore, from the observed X--ray properties for 1ES~1101--232 (peak around\n1 keV and flux of 2.5--3.8 $\\times 10^{-11} \\ecs$), we infer that the expected\nCompton peak is around 1 TeV with a flux of $1.5$--$2.5 \\times 10^{-11}$ \nphoton cm$^{-2}$ s$^{-1}$.\n\nThese estimates make 1ES 1101--232 a good TeV candidate, at the border\nof current sensitivities, and possibly well above it\nduring flaring activities.\n\n\n\\subsection{TeV Observations}\n\n1ES~1101--232 has been observed on the nights of 19--27 May 1998\nwith the Durham University Mark 6 atmospheric $\\check{\\rm C}$erenkov telescope.\nWe summarize here the data analysis and the results presented in \nChadwick et al. (1999a). \nThe telescope uses the imaging technique to separate VHE gamma rays from the \ncosmic ray background, together with a robust noise-free trigger (Armstrong\net al. 1999). Data are taken in 15 minutes segments, alternating \nON-source with an equal number of OFF-source observations. \nAfter removal of cloud--affected data, there are a total of\n10.5 hours ON-source data and the same amount of OFF-source data.\nData are screened for ``good\" events by the selection criteria listed in\nTable 2 of Chadwick et al. (1999a).\nThe source was not detected and an upper limit of \n$F_{TeV}$ [$> 300$ GeV] = 3.7$\\times 10^{-11}$ photons cm$^{-2}$ s$^{-1}$ \nhas been derived.\n\nThe data have been investigated for time variability on time-scales of days \n(at a flux limit of $\\sim 1 \\times 10^{-10}$ cm$^{-2}$ s$^{-1}$) \nand 15 min intervals. There is no evidence for any bursting behavior\n(Chadwick, private communication).\n\n\n\\section {SED construction and TeV predictions from theoretical models.}\n\n\nWe have constructed the overall Spectral Energy Distribution (SED), using\nboth data from literature and the \\sax\\ spectra from the two observations. \nWe construct two different SED, one for each \\sax\\ observation, that are\nclearly modeled by a different synchrotron state.\nThe two SED are presented in Fig.~\\ref{figsedb}.\n\n\\begin{table}\n\\caption{References for the data points of Fig~\\ref{figsedb}.}\n\\begin{tabular}[h]{|l l|}\n\\hline\nBand \t& Reference\t\\\\\n\\hline\nRadio 1.4GHz & NVSS: Condon et al. 1998 AJ 115, 1693 \\\\\nRadio 1.4GHz & Remillard et al. 1989 ApJ 345, 140 \\\\\nRadio 5 GHz & Perlman et al. 1996 ApJS 104, 251 \\\\\nRadio 5 GHz & Giommi et al. 1995 A\\&AS 109, 267 \\\\\nOptical V \t& Pesce et al. 1994 AJ 107, 494 \\\\\nOptical V & Lanzetta et al. 1995 ApJ 440, 435 \\\\\nOptical V & Giommi et al. 1995 A\\&AS 109, 267 \\\\\nOptical V & Jannuzi et al. 1994 ApJ 428, 130 \\\\\nOptical V & Falomo et al. 1994 ApJS 93, 125 \\\\\nIR J,H,K & Bersanelli et al. 1992 AJ 104, 28 \\\\\nIR K\t\t& Falomo et al. 1993 AJ 106, 11 \\\\\nUV 1400A \t& Pian \\& Treves 1993 ApJ 416, 130 \\\\\nUV 1400A \t& Edelson et al. 1992 ApJS 83, 1 \\\\\nX--ray 2 keV & Perlman et al. 1996 ApJS 104, 251 \\\\\nX--ray 2 keV & Giommi et al. 1995 A\\&AS 109, 267 \\\\\nEGRET \t\t& Fichtel et al. 1994 ApJS 94, 551 \\\\\n\\hline\n\\end{tabular}\n\\label{refere}\n\\end{table}\n\n\n\\begin{figure}\n\\psfig{file=9325.f5a,width=9.5truecm}\n\\psfig{file=9325.f5b,width=9.5truecm}\n\\caption{SED of the two \\sax\\ epoch observations {\\it Top:} 04/01/97 -- \nhigh state; {\\it Bottom:} 19/06/98 -- low state, plus models.\nLarge empty circles represent historical data from literature, while arrows\nindicate upper limits from EGRET (MeV) and Mark6 (GeV-TeV) experiments\nrespectively\n(see Table~\\ref{refere} for references). Small dots with error-bars are \nthe unfolded X--ray spectra discussed in this work.\nLines represent the spectra computed with the SSC model (see text for\ndetails) with different model parameters, reported in Table~\\ref{params}:\ndashed lines represent spectra calculated with $\\delta=10$ and two different \nvalues for the magnetic field $B$; similarly, solid lines represent spectra \ncalculated with $\\delta=20$ and two different values for the magnetic \nfield $B$. \n}\n\\label{figsedb}\n\\end{figure}\n\n\\begin{table}\n\\caption{Input parameters for the models of Fig.~\\ref{figsedb}}\n\n\\begin{tabular}[h]{| r r c c c c c c|}\n\\hline\n\\multicolumn{3}{|l}{High State} & & & & & \\\\\n\\hline\n \\# &$\\delta$ &$B$ &$\\gamma_b$ &$R$ &$K$ &$n_1$ &$n_2$ \\\\\n & &(G) &$\\times10^4$ &cm &cm$^{-3}$ & & \\\\\n\\hline\n1 & 10 & 0.3 & 15.8 &1$\\times10^{16}$ & 1.7$\\times10^4$ & 2 & 3.5\\\\\n2 & 10 & 0.6 & 11.2 &1$\\times10^{16}$ & 5.9$\\times10^4$ & 2 & 3.5\\\\\n3 & 20 & 0.1 & 19.3 &1$\\times10^{16}$ & 7.9$\\times10^3$ & 2 & 3.5\\\\\n4 & 20 & 0.2 & 13.5 &1$\\times10^{16}$ & 2.8$\\times10^4$ & 2 & 3.5\\\\\n\\hline\n\\hline\n\\multicolumn{3}{|l}{Low State} & & & & & \\\\\n\\hline\n \\# &$\\delta$ &$B$ &$\\gamma_b$ &$R$ &$K$ &$n_1$ &$n_2$ \\\\\n & &(G) &$\\times10^4$ &cm &cm$^{-3}$ & & \\\\\n\\hline\n1 & 10 & 0.5 & 8.45 & 1$\\times10^{16}$ & 2.5$\\times10^4$ & 2 & 3.9\\\\\n2 & 10 & 1.0 & 5.98 & 1$\\times10^{16}$ & 8.9$\\times10^3$ & 2 & 3.9\\\\\n3 & 20 & 0.1 & 13.3 & 1$\\times10^{16}$ & 6.3$\\times10^3$ & 2 & 3.9\\\\\n4 & 20 & 0.2 & 9.40 & 1$\\times10^{16}$ & 2.2$\\times10^3$ & 2 & 3.9\\\\\n\\hline\n\\end{tabular}\n\\label{params}\n\\end{table}\n\n\nWe have reproduced the SED in both X--ray states with a simple homogeneous SSC \nmodel.\nThe source is modeled as a spherical region with size $R$, uniform and\ntangled magnetic field $B$, in motion toward the observer with a bulk \nLorentz factor $\\Gamma$.\nThe region is filled by a population of relativistic electrons with a\ndistribution of Lorentz factors given by:\n$N(\\gamma )=K\\gamma^{-n_1}(1+\\gamma/\\gamma_{b})^{n_1-n_2}$, \nwhere the asymptotic slopes are $n_1$ and $n_2$, the break point\nis $\\gamma_{b}$ and $K$ is a normalization factor.\nThe self--Compton emission is derived taking into account the full \nKlein--Nishina (KN) cross section, computed using the relations reported in \nJones (1968; see also Blumenthal \\& Gould 1970). \nWe do not take into account absorption of IR photons by the infrared\nbackground, whose emission level is still uncertain. \nThis implies that in principle the derived curves are upper limits to the\ndetectable VHE emission, also because the redshift of 1ES~1101--232 is only\nslightly smaller\nthan the limit ($z=0.2$) chosen to monitor blazar emission in the TeV band\nby the HEGRA experiment (Rhode \\& Meyer, 1997).\nOn the other hand, a detection of the source in this band would provide also a\nmeasure of the density of IR background photons.\n\nAlthough the complete determination of the set of physical parameters for the\nSSC model requires the knowledge of the positions of both the synchrotron peak \nand the Inverse Compton peak (as discussed in Tavecchio et al. 1998), \nwe can put strong constraints to the parameters using the informations\nprovided by the X--ray spectrum and the TeV upper limit\nsuggesting that the condition $L_C/L_s\\leq 1$ applies.\n\nWe note here that the analytical relations discussed in Tavecchio et al. (1998)\nin the KN regime are obtained with a step approximation for the KN \ncross--section. \nIn the extreme KN regime the numerical values given by this \napproximation might differ from the results of the numerical model derived\nwith the full KN treatment, but we can use the analytical discussion as a \nguideline for the numerical model.\n\nTypical variability time-scales observed in HBLs \n($t_{var}\\sim\\,10^{3-4}$ s, see e.g\nZhang et al. 2000, Giommi et al. 1999, 2000) suggest Doppler factors \n$\\delta$ in the range 10--20 and sizes of $R \\leq 10^{16}$ cm. \nWe fixed the radius to $R=10^{16}$ cm. This choice directly puts a lower \nlimit to the value of the magnetic field:\n\n\\footnotesize\n\\begin{equation}\nB\\delta^{2+\\alpha _1} > A \\times\n (1+z)^{\\alpha _1} \\left[ \\frac{g} \n{\\nu_c\\nu_s} \\right] ^{(1-\\alpha _1)/2} \n\\left( \\frac {L_s}\n{ t_{var} L_C^{1/2}} \\right)\n\\label{ulower} \n\\end{equation} \n\\normalsize\n\n\\noindent\nwhere $g(\\alpha _1,\\alpha _2)$ is a constant related to\nthe spectral indices $\\alpha_1$ and $\\alpha _2$ and A is the\nappropriate constant\n(see Tavecchio et al. 1998 for details on (\\ref{ulower})).\nFrom this relation we can infer that an upper limit\non $L_C$ and an estimate of $t_{var}$ directly puts a lower \nlimit for $B$. The physical reason for this lower limit is related to the \nfact that the synchrotron peak Luminosity is proportional to the product\n$N_eB^2$ (where $N_e$ is the number of emitting electrons), while the ratio\nbetween the Compton peak Luminosity and the synchrotron peak Luminosity is \nproportional to $N_e$: therefore an upper limit to $L_C/L_s$ gives an upper \nlimit to $N_e$ and this, together with the synchrotron Luminosity, provides \nthe lower limit for the magnetic field $B$.\nAnother way of describing the effect, assuming that\nthe scattering is in the Thomson regime, is that in this case\nrequiring $L_C/L_s<1$ corresponds to require that the\nratio between the synchrotron and the magnetic energy densities \n$U_{syn}/U_B<1$.\nFor a given source size and Doppler factor the synchrotron radiation \nenergy density is fixed, and the above relation then corresponds to a \nlower limit on the value of the magnetic field.\n\n \nIn Fig.~\\ref{figsedb} we plot the spectrum of both states computed for \ntwo different values of $\\delta$ ($\\delta=10$ for the dashed lines,\n$\\delta=20$ for the solid lines), and for two different values of the magnetic\nfield $B$, as listed in Table~\\ref{params}.\nThe lowest value of $B$ has been determined by requiring\nnot to over-produce the high energy (TeV) emission, since, for a given\nsynchrotron luminosity, size and Doppler factor, the ratio\nbetween the self Compton and the synchrotron powers depends only on the\nmagnetic field.\n\nWe take this value, listed in Table~\\ref{params},\nfor the models 1 and 3 shown in Fig. 5.\nFor models 2 and 4 we have doubled the B value, and decreased the\nrelativistic electron density and $\\gamma_b$ accordingly, in order to produce\nthe same amount of synchrotron flux and about the same synchrotron peak\nfrequency.\nIn this case the self--Compton flux decreases, due to the decreased\nelectron density.\n\nThe transition from the high to the low state is consistent with a change\nof the second slope $n_2$ and with a decrease of $\\gamma_b$ by a factor\nof 1.5--2. This behavior is similar to what observed in the other well\nknown TeV BL Lac, such as PKS 2155--304 (see e.g. Chiappetti et al. 1999),\nMkn 501 (e.g. Pian et al 1998) and Mkn 421 (Maraschi et al. 1999), where\nhigh X-ray states are interpreted as states with either higher \n$\\gamma _b$ and/or higher magnetic field.\n\n\nIt is evident from Fig.~\\ref{figsedb} that a small change in the magnetic\nfield, while still consistent with the X--ray (\\sax) observations,\nproduces a dramatically different amount of TeV photons. Assuming that\nthe size of the source and the Doppler factor do not vary substantially\nwith time, variations of the synchrotron flux can be attributed to\nchanges of the density of electrons and/or the magnetic field. If this\nis the case, we expect that the TeV emission can be easily detected,\neither for X--ray fluxes slightly brighter than what observed up to now,\nor by longer TeV exposure times.\n\n\\section{Results and Conclusions}\n \nThe X--ray spectrum of 1ES~1101--232 as measured by \\sax\\ is fitted \nonly by a broken power law (a single power law or an absorbed \npower law are not statistically acceptable)\nwith a break at 1.3 - 1.9 keV. From the first to the second observation, \nthe spectrum varied at high energies, becoming softer (steeper). \nThe flux decrease, by about 32\\%, has occurred in the 2--10 keV band.\nThe PDS observation are not of statistical significance sufficient\nto put a real constraint on the spectrum.\n\nEven if the variation in the X--ray band is not dramatic, we can clearly\ndistinguish between the two states, that are modeled by different parameters\nof the synchrotron component.\n\nBy using the TeV upper limit and the two \\sax\\ observations we model also the\nhigher energy portion of the spectrum as a self--Compton component, by\nusing the model described e.g. in Tavecchio et al. (1998) that assumes a simple\nhomogeneous SSC model in the KN regime, in which the relativistic electrons\nhave a broken power law energy distribution. \n\nThe two X-ray states of the source are described by varying this\ndistribution, assuming that the other relevant parameters ($R$ and\n$\\delta$) are nearly constant.\n\n\nWe can compare these results with what found for the few TeV detected sources.\nThe choice of Doppler factor of 10 and 20 made here is in the interval of\nthe values of $\\delta$ found by other authors for Mkn 421, \nPKS2155--304 and Mkn501, that range\nfrom $\\delta \\sim 5$ (e.g. Takahashi, 1999; Mkn 421, Catanese et al. \n1998: Mkn 501) \nto $\\delta \\sim 30$ (e.g. Bednarek \\& Protheroe 1999: Mkn501; \nKataoka et al 2000: PKS2155--304;\nBednarek \\& Protheroe 1997: Mkn 421).\nAt the same time, values of $B$ in excess of 0.03 G and up to 1 G \n(Chiappetti et al. 1999) are found for the same sources.\n\nOf the three above mentioned objects, the most similar to 1ES~1101--232 \nis Mkn 501, for which different measures have been produced: e.g.\n$\\delta \\geq 15$ \\& $B=0.8 $G (Pian et al. 1998);\n$\\delta = 15$ \\& $B=0.2 $G (Kataoka et al. 1999);\n$\\delta = 30$ \\& $B=0.7 $G (Bednarek \\& Protheroe 1999),\nin good agreement with the values of Table~\\ref{params}.\n\n\nEven if based, besides the accurate X-ray spectral determination up \nto $\\sim 50$ keV, only on a TeV upper limit we can infer that\nthe physical conditions in 1ES~1101--232 are similar to the\nbrightest TeV sources, making it a very promising candidate for \nTeV observations, and a testbed for the SSC model.\nFurthermore, since the redshift of 1ES~1101--232 is intermediate,\na detection of this source in the VHE range would pose constraints\non the density of the IR background photons that is still at the moment\nvery uncertain.\n\n\\begin{acknowledgements}\nThis work has received partial financial support from the Italian \nSpace Agency. \nWe would like to thank Paula Chadwick and S.J. McQueen for informing us\nabout their VHE results in advance of publication, Paolo Giommi and Roberto\nDella Ceca for helpful discussion and comments, and an anonymous referee\nfor useful suggestions that improved the readability of the paper.\n\n\\end{acknowledgements}\n \n\\begin{thebibliography}{}\n\n\\bibitem{} Aharonian, F.A. et al., 1999, A\\&A, 341, 69\n\n\\bibitem{} Armstrong, P. et al., 1999, Experimental Astronomy, v. 9, 51\n\n\\bibitem{} Bednarek, W., \\& Protheroe, R.J., 1997, MNRAS, 290, 139 %(mkn421)\n\n\\bibitem{} Bednarek, W., \\& Protheroe, R.J., 1999, MNRAS, 310, 577\n%%astro-ph/9902050 %(mkn501)\n\n\\bibitem{} Blumenthal \\& Gould, 1970, Rev. of Modern Phys., 42, 237\n\n\\bibitem{} Boella G., Butler R.C., Perola G.C., et al., \n 1997a, A\\&AS 122, 299\n\n\\bibitem{} Boella G., Chiappetti L., Conti G., et al., \n 1997b, A\\&AS 122, 327\n\n\\bibitem{} Butler C., Scarsi L., 1990, SPIE 1344, 46\n\n\\bibitem{} Catanese M. et al., 1998, ApJ, 501, 616\n\n\\bibitem{} Chadwick, P.M., Lyons, K., McComb, T.J.L., Orford, K.J., Osborne, \nJ.L., Rayner, S.M., Shaw, S.E., and Turver, K.E., 1999a, ApJ, 521, 547\n\n\\bibitem{} Chadwick, P.M., Lyons, K., McComb, T.J.L., Orford, K.J., Osborne, \nJ.L., Rayner, S.M., Shaw, S.E., Turver, K.E., Wieczorek, G.J., 1999b, \nApJ, 513, 161\n\n\\bibitem{} Chiappetti, L., et al., 1999, ApJ, 521, 552\n\n\\bibitem{} Fossati, G., Maraschi, L., Celotti, A., Comastri, A., and\nGhisellini, G., 1998, MNRAS, 299, 433\n\n\\bibitem{} Gaidos, J.A., et al, 1996, Nature, 383, 319\n\n\\bibitem{} Ghisellini, G., 1999, in ``The BL Lac Phenomenon\",\nEd. 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M., \\& Padovani, P. 1995, PASP, 107, 803\n\n\\bibitem{} Wolter A., et al., 1998, A\\&A, 335, 899\n\n\\bibitem{} Zhang, Y.H., et al., 1999, ApJ, 527, 719\n%%astro-ph/9907325\n\\end{thebibliography}\n\n\n\\end{document}\n\n"}],"string":"[\n {\n \"name\": \"9325.tex\",\n \"string\": \"\\\\documentclass{aa}\\n%%\\\\documentclass[referee]{aa}\\n\\n\\n\\\\include{psfig}\\n\\n\\\\def\\\\doublespace{\\\\baselineskip 24pt}\\n\\\\def\\\\singlespace{\\\\baselineskip 15pt}\\n\\\\def\\\\e20{\\\\times 10^{20} {\\\\rm cm}^{-2} }\\n\\\\def\\\\sax{{\\\\it Beppo}SAX}\\n\\\\def\\\\NH{N_{\\\\rm H}}\\n\\\\def\\\\ecs{\\\\rm \\\\,erg~ cm^{-2}\\\\,s^{-1} }\\n\\\\def\\\\mincir{\\\\ \\\\raise -2.truept\\\\hbox{\\\\rlap{\\\\hbox{$\\\\sim$}}\\\\raise5.truept \\n\\\\hbox{$<$}\\\\ }} % minore o circa uguale\\n\\n\\\\begin{document}\\n\\n\\\\thesaurus{03(11.02.1; 13.25.3)}\\t\\n%A\\\\&A Section 03: (Extragalactic Astronomy)\\n%%(11.02.1; % {\\\\it (Galaxies:)} BL Lacertae objects: general\\n%%13.25.3 %X--rays: general)\\n\\n\\n\\n\\\\title{X--ray variability and prediction of TeV emission in the HBL 1ES~1101--232}\\n\\\\author{A. Wolter,\\n\\\\inst{1} \\nF. Tavecchio, \\\\inst{1} A. Caccianiga,\\\\inst{2} G. Ghisellini,\\\\inst{1} G. Tagliaferri \\\\inst{1}\\n}\\n\\n\\\\offprints{A. Wolter: anna@brera.mi.astro.it}\\n\\n\\\\institute{Osservatorio Astronomico di Brera,\\n\\t\\tVia Brera, 28\\n\\t\\t20121 MILANO, Italy\\n\\\\and Observatorio Astronomico de Lisboa, Tapada da Ajuda, P-1300 Lisboa, Portugal\\n}\\n\\n\\\\date{Received ....; accepted ....}\\n\\\\maketitle\\n\\\\markboth{A. Wolter et al.}{The HBL 1ES~1101--232}{}\\n\\n\\\\begin{abstract}\\n\\n1ES~1101--232 is a bright BL Lac of the High frequency peak class. \\nWe present here the results of two \\\\sax\\\\ observations in which the\\nsource has shown a variation of about 30\\\\% in flux with a corresponding\\nspectral variability.\\nWe interpret the overall spectral energy distribution in terms\\nof an homogeneous SSC model and, by using also the TeV upper limit\\nfrom a short Mark 6 pointing, derive constraints\\non the physical parameters of the source, in particular on the magnetic \\nfield strength.\\nThe overall Spectral Energy Distribution makes\\n1ES~1101--232 a very promising candidate for TeV detection. \\n\\n\\\\keywords{(Galaxies:) BL Lacertae objects: general --\\n\\t X--rays: galaxies -- BL Lacertae objects: individual: 1ES~1101--232\\n }\\n\\\\end{abstract}\\n\\n\\\\section{Introduction}\\n\\\\noindent\\n\\nBL Lac objects form a minority class of active nuclei (see e.g. Urry \\\\& \\nPadovani, 1995), but nevertheless their high luminosities and extreme \\nvariability in all bands \\nmake them an interesting subclass to study intrinsic properties of\\nnuclear emission. Furthermore, it is matter of discussion the position of\\nBL Lacs with respect to other active nuclei in the framework of Unification\\nModels. The current picture claims that BL Lacs are the fraction of \\nFanaroff-Riley I galaxies that point their jet towards us, but many\\ndetails still need to be worked out. Often, BL Lacs are studied together\\nwith other classes of flat radio spectrum sources, to form the class of blazars.\\n\\nRecently a sequence has been proposed for the subclass of gamma ray\\nbright blazars, and possibly valid for all blazars, based on their \\nbolometric luminosity\\n(Ghisellini et al. 1998, Fossati et al. 1998). \\nThe overall spectral energy distribution has two peaks \\n(in $\\\\nu F_\\\\nu$ representation), \\nthe one at lower energies due to synchrotron radiation and the higher energy \\none to Inverse Compton scattering. \\nIt is proposed that the value of the peak frequency is the result\\nof the balance between radiative cooling and acceleration of the \\ncorresponding electrons (see e.g. Ghisellini, 1999):\\nin less luminous objects the radiative cooling is less efficient, allowing\\nthe accelerated electrons to reach higher energies.\\nAs a consequence, both the synchrotron and the inverse Compton peaks\\nshift to higher frequencies as the bolometric intrinsic\\nluminosity decreases.\\nIn this view, the class of BL Lacertae objects known as HBL \\n(High frequency peak BL Lacs)\\nhas a smaller bolometric luminosity and a higher synchrotron peak frequency\\nthan the class of LBL (Low frequency peak BL Lacs).\\nHBL are mostly found in X--ray selected samples, since they are expected to \\nproduce most of their synchrotron emission in the X--ray band. \\nIf the emission peak (as in the LBL objects) is\\nat frequencies smaller than the observed X--ray band, the X--ray spectrum is \\nsteep (i.e. the steepening part above the peak), while HBL with a flat \\nX--ray spectrum should have their peak in the observed X--ray band.\\n\\nAs part of a program aimed at a spectral survey of soft X--ray selected \\nBL Lacs with \\\\sax\\\\ (Wolter et al. 1998), \\nwe have studied also 1ES~1101--232 (z=0.186), \\na bright BL Lac selected from the Slew Survey (Perlman et al. 1996) \\nthat shows an extreme behavior with a very flat X--ray spectrum.\\nThe object was detected, besides in the 0.1-10 keV energy band, also\\nup to $\\\\sim$ 100 keV in only $\\\\sim 6000$ sec. \\nThe best fit of the source in the 0.1-100 keV band is given by a broken \\npower law, with Galactic low energy absorption, that has a break energy\\nE$_0$=1.36 (1.11--1.65) keV.\\nThe spectral slope (energy index) derived from the PDS is consistent\\nwith the one derived from the MECS above the break energy E$_0$:\\n$\\\\alpha_x$ = 1.03 (0.99--1.08) (Wolter et al. 1998).\\n\\nWe have constructed also the Spectral Energy Distribution (SED) for this\\nobject, using flux measurements collected from the literature, from radio to\\nX--rays.\\nWe have fitted a cubic polynomial to the \\ndistribution in order to find the peak of the SED, that indeed \\nfalls in the \\\\sax\\\\ band (log $\\\\nu_{peak} \\\\sim$ 17.48, corresponding to \\n$\\\\sim 1.3$ keV).\\nFor this object, therefore, the break energy derived from\\nthe spectral fit in the X--ray band is consistent, albeit within its\\nlarge indetermination, with the position of the synchrotron \\npeak as derived from the overall distribution (SED). \\n\\nThe SED of 1ES~1101--232 is similar to that of the flaring state\\nof Mkn 501 (Pian et al. 1998) and 1ES~2344+514 (Catanese et al. 1998; \\nGiommi et al. 2000), \\nand therefore we could expect a strong TeV emission. \\nA quasi--simultaneous X--ray and TeV observation has been\\ntherefore scheduled, to confirm the X--ray spectrum of the source, and\\nits overall shape,\\nto detect possible variations in flux, that could constrain the physical\\nparameters of the source, and to monitor the TeV emission to search\\nfor possible detection. \\n\\n%__________________________________________________ Two col. table\\n\\\\begin{table*}\\n \\\\caption{Fit results for 1ES~1101--232 LECS+MECS data OBS. 19/06/98 {\\\\bf Low state}}\\n\\\\begin{tabular}[h]{| l l c c c r r r|}\\n \\\\hline\\nModel & $N_{\\\\rm H}^a$ & $\\\\alpha_1$ & $\\\\alpha_2$ & $E_0$ & $F^{\\\\rm b}$ & $\\\\chi^2(dof)$ & Prob. \\\\\\\\\\n & & & & keV & & & \\\\\\\\\\n(1) & 5.76 & -- & 1.19(1.16-1.22) & -- & 2.60 & 267.1(195) & $<$ 0.5\\\\%\\\\\\\\\\n(2) & 8.3(7.1-10.4) & -- & 1.25(1.22-1.29) & -- & 2.57 & 240.5(195) & 1.5\\\\%\\\\\\\\\\n(3) & 5.76 &0.80(0.58-0.96)& 1.29(1.25-1.33) & 1.34(1.08-1.82) &2.55 & 216.2(194) & 13\\\\% \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\\\begin{list}{}{}\\n\\\\item (1) Single p.l., $N_{\\\\rm H}$=$N_{\\\\rm H}^{\\\\rm Gal}$, LECS/MECS ratio free; \\n(2) Single p.l., $N_{\\\\rm H}$ free, LECS/MECS ratio=0.7 ; \\n(3) Broken p.l., $N_{\\\\rm H}=N_{\\\\rm H}^{\\\\rm Gal}$, LECS/MECS ratio = 0.7. \\nErrors quoted are 90\\\\% confidence intervals. \\\\\\\\\\n$^{\\\\rm a}$ Column density in $\\\\e20$. \\\\\\\\\\n$^{\\\\rm b}$ Unabsorbed [2--10 keV] flux in $10^{-11} \\\\ecs$. \\\\\\\\\\n\\\\end{list}\\n\\\\label{broken_n}\\n\\\\end{table*}\\n%__________________________________________________ Two col. table\\n\\\\begin{table*}\\n \\\\caption{Fit results for 1ES~1101--232 LECS+MECS data OBS. 04/01/97 {\\\\bf High state} } \\n\\\\begin{tabular}[h]{| l l c c c r r r|}\\n \\\\hline\\nModel & $N_{\\\\rm H}^{\\\\rm a}$ & $\\\\alpha_1$ & $\\\\alpha_2$ & $E_0$ & $F^{\\\\rm b}$ & $\\\\chi^2(dof)$ & Prob. \\\\\\\\\\n & & & & keV & & & \\\\\\\\\\n(1) & 5.76 & -- & 0.97(0.95-1.00) & -- & 3.81 & 224.0 (182) & $<$ 2\\\\%\\\\\\\\\\n(2) & 8.9(7.2-12.6) & -- & 1.03(0.99-1.08) & -- & 3.79 & 205.1 (182) & 11 \\\\%\\\\\\\\\\n(3) & 5.76 &0.59(0.35-0.74) & 1.05(1.01-1.08) & 1.36(1.11-1.65) &3.76 & 191.6 (181) & 28 \\\\%\\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\\\begin{list}{}{}\\n\\\\item \\n(1) Single p.l., $N_{\\\\rm H}$=$N_{\\\\rm H}^{\\\\rm Gal}$, LECS/MECS ratio free; \\n(2) Single p.l., $N_{\\\\rm H}$ free, LECS/MECS ratio=0.7; \\n(3) Broken p.l., $N_{\\\\rm H}$=$N_{\\\\rm H}^{\\\\rm Gal}$, LECS/MECS ratio = 0.7.\\nErrors quoted are 90\\\\% confidence intervals. \\\\\\\\\\n$^{\\\\rm a}$ Column density in $\\\\e20$. \\\\\\\\\\n$^{\\\\rm b}$ Unabsorbed [2-10 keV] flux in $10^{-11} \\\\ecs$. \\\\\\\\\\n\\\\end{list}\\n \\\\label{broken_o}\\n\\\\end{table*}\\n\\n\\nThe \\\\sax\\\\ data are presented here. The TeV observation, conducted in \\nnon--optimal weather condition, did not yield a detection, but we will use\\nthe upper limit (Chadwick et al. 1999a) to derive useful information on\\nthe physical mechanisms at work in this source.\\nThe plan of the paper is as follows: in Section 2 we describe the observational\\ndata obtained with \\\\sax\\\\ in the two epochs, in Section 3 we summarize the TeV\\npredictions and observations, that help constraining the parameters of the\\nsource, by using the SED and theoretical models of emission as explained in\\nSection 4. Section 5 presents our results and conclusions.\\n\\n\\nThroughout the paper a Hubble constant H$_0$=50 $km\\\\, s^{-1}\\\\, Mpc^{-1}$ \\nand a Friedman universe with a deceleration parameter $q_0$=0 are assumed.\\n\\n\\n \\n\\\\section{ \\\\sax\\\\ data}\\n\\nThe X--ray astronomy satellite \\\\sax\\\\ is a project of the Italian\\nSpace Agency (ASI) with a participation of the Netherlands Agency for \\nAerospace Programs (NIVR).\\nThe scientific payload comprises four Narrow Field Instruments [NFI:\\nLow Energy Concentrator Spectrometer (LECS), Medium Energy Concentrator\\nSpectrometer (MECS), High Pressure Gas Scintillation Proportional Counter\\n(HPGSPC), and Phoswich Detector System (PDS)], all pointing in the\\nsame direction, and two Wide Field Cameras (WFC), pointing in\\nopposite directions perpendicular to the NFI common axis. A detailed\\ndescription of the entire \\\\sax\\\\ mission can be found in Butler \\\\& Scarsi (1990)\\nand Boella et al. (1997a). \\n\\nThe MECS consists of three equal units, each composed of a grazing\\nincidence mirror unit and of a position sensitive gas scintillation \\nproportional counter, with a field of view of\\n56 arcmin diameter, working range 1.3--10 keV, energy resolution $\\\\sim 8\\\\%$\\nand angular resolution $\\\\sim 0.7$ arcmin (FWHM) at 6 keV.\\nThe effective area at 6 keV is 155 cm$^2$ (Boella et al. 1997b)\\n\\nThe LECS is a unit similar to the MECS, with a thinner window that\\ngrants a lower energy cut-off (sensitive in the energy range 0.1-10.0 keV)\\nbut also reduces the FOV to 37 arcmin diameter (Parmar et al. 1997). \\nThe LECS energy resolution is a factor $\\\\sim 2.4$ better\\nthan that of the ROSAT PSPC ($\\\\sim 32\\\\%$ at 0.28 keV), while the \\neffective area is smaller: 22 cm$^{2}$ at 0.28 and and 50 cm$^{2}$ at 6 keV.\\n\\nThe PDS is a system of four crystals, sensitive in the 13--200~keV band and\\nmounted on a couple of rocking collimators, which points two units on the\\ntargets and two units $3.5^{\\\\circ}$ aside respectively, to monitor the\\nbackground.\\nThe position of the collimators flips every 96 seconds.\\nThanks to the stability of the instrumental background, the PDS has shown \\nan unprecedented sensitivity in its energy range, allowing 3$\\\\sigma$ detection \\nof $\\\\alpha \\\\sim 1$ sources as faint as 10 m Crab \\nwith 10 ks of effective exposure time (Guainazzi \\\\& Matteuzzi, 1997).\\n\\nThe source is not detected by the HPGSPC, so we will not discuss this \\ninstrument.\\n\\n\\n\\\\subsection{Observation of June 1998}\\n\\n\\\\begin{figure}\\n\\\\psfig{file=9325.f1,width=8truecm,height=6truecm,angle=-90}\\n\\\\caption{X--ray spectrum (LECS+MECS+PDS) of June 1998, with broken power law fit\\n(model 3 from Table~\\\\ref{broken_n})}\\n\\\\label{fignew}\\n\\\\end{figure}\\n\\nThe object has been observed in AO2 on 19 June 1998 for a total of \\n8958 sec (LECS -- 3167 net counts); \\n24895 sec (MECS(2+3) -- 10612 net counts) and \\n10792 sec (PDS on source -- 1320 net counts).\\nThe AO2 observation has been performed with only 2 MECS (MECS2 and MECS3)\\nsince MECS1 was no longer active.\\nThe source has been observed almost in the same period (May 1998) by the \\nMark6 telescope (working in the GeV-TeV range). \\n\\nThe extraction of the \\\\sax\\\\ data has been performed with FTOOLS v4.0 and the\\nspectral analysis with XSPEC v9.0, using the most recently available matrices\\n(September 1997 release).\\nThe data analysis has been performed on the same guidelines as outlined\\nby the \\\\sax\\\\ Cookbook ({\\\\small\\\\verb+http://www.sdc.asi.it/software/cookbook/+})\\nand described e.g. in Wolter et al. (1998).\\nWe summarize here that counts are extracted in a circular region of 8.5'/4' \\n(LECS/MECS) radius, and the background is taken from the blank \\nsky images distributed by the \\\\sax\\\\ Data Center, in a region corresponding \\nto the one used to extract\\nsource counts. Counts are binned so as to have at least 30 total counts \\nin each bin to ensure applicability of the $\\\\chi^2$ statistics.\\nFit to LECS data are performed only up to 4 keV, as the\\nresponse matrix of LECS is not well calibrated above this\\nenergy (see Orr et al. 1998).\\nAll confidence levels are computed using $\\\\Delta \\\\chi^2$ = 2.7 (corresponding\\nto 90\\\\% for 1 interesting parameter), unless otherwise stated. \\n\\nFor the LECS+MECS combined data, \\na single power law is not acceptable ($> 3 \\\\sigma$) with $N_{\\\\rm H}$\\nfixed at the Galactic value.\\nIf $N_{\\\\rm H}$ is left free, the fit with a single power law is acceptable only\\nat about $3 \\\\sigma$ (Prob $\\\\sim 1.5\\\\%$). The residuals are however \\nskewed, showing that the fit is not good.\\nThe fit is significantly improved (F--test at $>$ 99.99 \\\\% probability) by\\nusing a broken power law shape. \\nResults for the three models for LECS and MECS data are listed in \\nTable~\\\\ref{broken_n}.\\n\\nFor each observation, in the first fit \\n(single power-law model with Galactic $N_{\\\\rm H}$) we left the \\nLECS normalization free\\nwith respect to the MECS normalization to account for the residual \\nerrors in intensity cross-calibration (see Cusumano, Mineo, Guainazzi\\net al. in preparation). The fitted value \\nof 0.696 (1997) and 0.701 (1998) fall in the range\\nexpected given the current knowledge of the cross-calibration\\n(F. Fiore, private communication; see also \\n{\\\\small\\\\verb+http://www.sdc.asi.it/software/cookbook/cross_cal.html+}).\\nSince the ratio of the two normalizations depends\\non the position of the source in the detector, and not on the model\\nchosen, we fix the LECS/MECS normalization to 0.7 also for the\\nother subsequent models. \\n\\n\\nThe PDS exposure time is not even twice than in AO1 (10.8 ks vs. 6.4 ks). \\nSince the spectrum is steeper and the source is \\nfainter than in the AO1 observation, the PDS detection is \\nnot more significant than the AO1 detection ($2.6 \\\\sigma$). \\nIn order to fit the PDS data alone we rebin them to 6 data points. \\nWe fix the absorbing column to the Galactic value (N$_H = 5.76 \\\\times \\n10^{20}$ cm$^{-2}$) while the normalization with respect to the MECS\\nand index are left free.\\nThe best fit slope is\\n$\\\\alpha_{PDS}$ = 1.02 [$<$ 2.65], and the PDS/MECS ratio is 0.90, consistent\\nwith what expected on the basis of cross-calibration of the instruments,\\nwith a $\\\\chi^2$ = 2.2(4 dof), for\\na probability of 70\\\\%, therefore statistically acceptable.\\nHowever, given the low statistical \\nsignificance of the PDS data, the uncertainty on the slope is high. \\nWe therefore fit the total spectrum, from 0.1 keV to $\\\\sim $50 keV, using \\nLECS, MECS and PDS data together: the result of the broken power law fit\\nis shown in Figure~\\\\ref{fignew}. \\nIt yields an unabsorbed flux in the [2--10 keV] band of\\n$F_X=2.54 \\\\times 10^{-11}$ erg cm$^{-2}$ s$^{-1}$, \\nand a corresponding luminosity in the same band of\\n$L_X = 4.7\\\\times 10^{45}$ erg s$^{-1}$.\\nThe PDS data are consistent with the LECS+MECS extrapolation.\\n\\n\\n\\\\subsection {Comparison of the 1997 and 1998 observations}\\n\\nFor ease of comparison, we report in Table~\\\\ref{broken_o} the AO1 observation \\nresults of 1ES~1101--232, from Wolter et al. (1998).\\nThe LECS exposure was 5195 sec (2484 net counts), the MECS exposure\\nwas 13830 (9509 net counts) and the PDS on-source exposure was 6410 sec (1996 \\nnet counts).\\nThe best fit models of the LECS+MECS spectra for various spectral \\nshapes are listed in Table~\\\\ref{broken_o}, while in Figure~\\\\ref{figold} \\nthe LECS+MECS+PDS \\nspectrum is plotted, with the best fit of model (3).\\n\\n\\\\begin{figure}\\n\\\\psfig{file=9325.f2,width=8truecm,height=6truecm}\\n\\\\caption{X--ray spectrum (LECS+MECS+PDS) of Jan 1997, with broken power law fit\\n(model 3 from Table~\\\\ref{broken_o}).}\\n\\\\label{figold}\\n\\\\end{figure}\\n\\n\\nIn order to compare the two observations, we first check directly the count\\nrates in the two epochs. The best representation is the ratio of\\nthe two observed spectra, that does not depend on the choice of models\\nand parameters. We therefore bin the two spectra, the relative \\nbackground and response matrices in 32 channels, in order to avoid having \\nempty bins after background subtraction. We then divide the two \\nbackground-subtracted count rates and plot the results (after having \\nflagged out the energy ranges that are not well calibrated in the matrices) \\nin Fig.~\\\\ref{figrap}. \\nThe ratio is consistent with being flat up to $\\\\sim 2$ keV, and steepening \\nafter it, showing that a change in the spectrum occurred above $\\\\sim 2$ keV. \\nThe two instruments, LECS and MECS, give a consistent ratio\\nin the overlapping energy range. A fit with a constant in the interval \\n0.5--10 keV is not statistically acceptable.\\n\\n\\n\\\\begin{figure}\\n\\\\psfig{file=9325.f3,width=8truecm,height=6truecm,angle=-90}\\n\\\\caption{Ratio of data point from the Jun 1998 and Jan 1997 observations. \\nStars indicate data points from the LECS instrument, crosses data points\\nfrom the MECS instrument.\\nThe trend in the data, with a drop above $\\\\sim$2 keV, is evident.}\\n\\\\label{figrap}\\n\\\\end{figure}\\n\\nAlso comparing the fit results for the two observations of Jan 1997 and \\nJun 1998, we see that the high energy slope\\n($\\\\alpha_2$) is steeper in the second one. The flux, with all the\\nthree best fit models reported in the tables, is a factor of $\\\\sim$ 32\\\\% \\nlower in the second than in the first one. \\nThe low energy slope ($\\\\alpha_1$) and the break energy ($E_0$) are\\ninstead consistent within the errors between the two observations.\\n\\nWe can make therefore the hypothesis that the different fluxes and \\nspectra between the two epochs are \\nexplained by a change in the spectral slope above the peak of the synchrotron\\nemission. Hence we fit all the data (1997+1998) simultaneously, keeping the low\\nenergy slope and break energy tied (equal one to each other, but free to \\nvary) between the two observations. \\nOn the contrary, the high energy slopes in the two observations are left \\nindependent.\\nThe $N_{\\\\rm H}$ is fixed to the galactic value, that fits well both \\nobservations. The PDS data are not used for the comparison, being of \\nlow statistical significance; the LECS and MECS data are re-binned to\\n100 total counts for each bin, to improve the significance of the individual\\ndata points, since no small range feature is present. The LECS/MECS \\nnormalization is again fixed to 0.7.\\n\\n\\\\begin{figure}\\n\\\\psfig{file=9325.f4a,width=7truecm,height=5.5truecm,angle=-90}\\n\\\\psfig{file=9325.f4b,width=7truecm,height=5.5truecm,angle=-90}\\n\\\\caption{LECS+MECS spectrum and broken power law fit for Jan 1997 (Upper Panel)\\nand Jun 1998 (Lower Panel) observations. The broken power law fit of the two\\nobservations combined is given in the text.}\\n\\\\label{figcom}\\n\\\\end{figure}\\n\\n\\n\\\\begin{table}\\n\\\\caption{Unabsorbed Fluxes and Rest--Frame Luminosities for the two \\nobservations in the (0.1--2) and (2--10) keV energy bands.}\\n\\\\begin{tabular}[htb]{| l c c c c |}\\n \\\\hline\\nDate & $F$[0.1-2] & $F$[2-10] & $L$[0.1-2] & $L$[2-10] \\\\\\\\\\n & \\\\multicolumn{2}{c}{$\\\\times 10^{-11} \\\\ecs$}&\\\\multicolumn{2}{c|}{$\\\\times 10^{45}$ erg s$^{-1}$} \\\\\\\\\\n\\\\hline \\n04/01/97 & 3.46 & 3.85 & 5.4 & 6.8 \\\\\\\\\\n19/06/98 & 3.32 & 2.53 & 5.3 & 4.7 \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\\\label{fluxes}\\n\\\\end{table}\\n\\n\\nThe resulting values of $\\\\alpha_1$ and $E_0$ are consistent with those of both\\nsingle observations: $\\\\alpha_1$=0.72 [0.44, 0.88]; \\n$E_0=1.17 [0.93, 1.43]$ keV.\\nThe high energy slope is \\n$\\\\alpha_2^{1998}$ = 1.26 [1.19, 1.32], vs. \\n$\\\\alpha_2^{1997}$ = 1.01 [0.95, 1.07], confirming that the slope indeed\\nsteepened significantly. The $\\\\chi^2$ of the fit is 184.4 with 178 dof, \\ncorresponding to a probability of 36\\\\%.\\nThe errors quoted here are 90\\\\% confidence for \\n4 parameters of interest ($\\\\Delta\\\\chi^2 = 7.76$).\\nThe combined spectra (LECS and MECS) for both \\nobservations with the best fit model are shown in Figure~\\\\ref{figcom}.\\nWe report in Table~\\\\ref{fluxes} the unabsorbed fluxes and rest-frame\\nluminosities in the \\n0.1--2 and 2--10 keV bands for the two observations using the combined \\nfit results.\\n\\n\\nThe fluxes derived using the combined model are consistent with the\\nfluxes derived from the two independent fits to the observations. We can\\ntherefore attribute the observed flux variation entirely to a steepening\\nof the high energy ($>$2 keV) portion of the spectrum. There is no\\nevidence, within the statistical uncertainties, of a change in $\\\\alpha_1$\\nor $E_0$, although in other well known sources (Mkn501, Mkn421, PKS2155--304) \\nan increase in flux seems to be linked to an increase in $E_0$ and/or the \\nhigh energy slope.\\n\\n\\n\\\\section{The TeV band }\\n\\nBlazars as a class have been shown to emit a large fraction of their power\\nat high energies, in the MeV--TeV band.\\nThe current models assume that the high energy emission is produced by\\nInverse Compton scattering (e.g. the SSC model or the EC model, see Ghisellini\\net al. (1998) for the relevance of the two mechanisms), and the location of \\nthe peak of the Compton component depends mainly on the lower energy peak due \\nto the Synchrotron component. \\n\\nIn particular, objects of the LBL kind, that have the synchrotron peak\\nat soft energies,\\nshow their second peak at energies in the MeV--GeV range, and are in fact \\ndetected by EGRET on board CGRO (see Mukherjee et al. 1997).\\nObjects of the HBL kind, that have their synchrotron peak at UV--X--ray frequencies,\\ninstead, should show the Compton peak in an even higher energy band. In fact,\\nup to now, the only sources of VHE gamma rays (in the TeV band, by using\\n$\\\\check{\\\\rm C}$erenkov detectors) are HBL: \\nMkn 421 (Punch et al. 1992), Mkn 501 (Quinn et al. 1996), \\n1ES~2344+514 (Catanese et al. 1998), \\nPKS 2155--304 (Chadwick et al. 1999b).\\n\\nThe new $\\\\check{\\\\rm C}$erenkov arrays allow the detection of bright sources \\nin relatively short exposure times, and therefore it has been possible to \\nmonitor their variability:\\nsome of these objects have in fact shown periods of flaring activity on \\ntime-scales as short as 15 minutes (Gaidos et al. 1996, Aharonian et al. 1999).\\n\\nAnother point of debate is the amount of absorption of VHE photons due to \\nthe cosmic infra--red background. The aforementioned detected objects in fact\\nare all nearby.\\nDetection of sources that lie further away can therefore help in constraining\\nthe amount of the IR background (e.g. Stecker and De Jager, 1998).\\n\\nThe simultaneous detection of X--ray and TeV emission allows us to estimate\\na number of physical parameters of the source, such as the magnetic field and\\nthe Doppler factor (see e.g. Tavecchio et al. 1998). \\nWe will show in Section 4 that a number of interesting constraints can be \\nderived also by using the upper limit derived in the TeV band, together \\nwith the X--ray band information.\\n\\n\\\\subsection {Predictions of TeV emission in 1ES~1101--232 from phenomenological\\nconstraints.}\\n\\nA very simple prediction of the TeV emission can be made by following \\nthe scheme presented e.g. in Fossati et al. (1998).\\nIn this model a) the ratio of the frequencies of the high (Compton) and low \\n(synchrotron) energy peaks is constant and equal to $5\\\\times 10^{8}$ and\\nb) the high energy peak and the radio luminosity have a fixed ratio, \\n$\\\\nu_\\\\gamma L_{peak,\\\\gamma} \\\\over \\\\nu_{5GHz} L_{5GHz}$ =$3 \\\\times 10^{3}$. \\nThis model represents the average SED observed for \\nthe various classes, while single sources can deviate from\\nthis average phenomenological parameterization.\\nThis very simple relationship, however, allows us to make order of magnitude\\nprediction even not knowing the physical conditions at the source. From \\nthe two expressions above we can derive both the expected frequency\\nof the second peak and its intensity.\\nThe peak of the synchrotron emission is measured (this paper and Wolter \\net al. 1998) at\\n$\\\\nu_s = 3 \\\\times 10^{17}$ Hz: the Compton peak is therefore expected\\nat $\\\\nu_C = 1.5 \\\\times 10^{26}$ Hz which corresponds to $\\\\sim$0.6 TeV.\\nThe measured radio flux at 5 GHz is $5 \\\\times 10^{-15}$ erg \\ncm$^{-2}$ s$^{-1}$ (see references in Table~\\\\ref{refere}).\\nThe expected flux at the Compton peak (0.6 TeV) is therefore\\n$\\\\sim 8. \\\\times 10^{-12}$ photon cm$^{-2}$ s$^{-1}$. \\n\\nAnother prediction can be made from the observed X--ray flux, by using the\\nrecipe of Stecker, De Jager \\\\& Salamon (1996). Within an SSC scenario they\\nuse simple scaling arguments to predict the TeV fluxes for HBL, based on the \\nX--ray flux and the assumption that the properties of the emission are similar \\nto those observed for Mkn 421. Their argument is partially\\nsupported by the actual detection of (a few) other sources\\nfor which they predicted possible detectability.\\nThe factor of increase between the synchrotron and Compton \\ncomponent is $10^9$, and, assuming $L_C/L_s \\\\sim 1$,\\nthey derive $\\\\nu_{TeV} F_{TeV} \\\\sim \\\\nu_{X} F_{X}$.\\nTherefore, from the observed X--ray properties for 1ES~1101--232 (peak around\\n1 keV and flux of 2.5--3.8 $\\\\times 10^{-11} \\\\ecs$), we infer that the expected\\nCompton peak is around 1 TeV with a flux of $1.5$--$2.5 \\\\times 10^{-11}$ \\nphoton cm$^{-2}$ s$^{-1}$.\\n\\nThese estimates make 1ES 1101--232 a good TeV candidate, at the border\\nof current sensitivities, and possibly well above it\\nduring flaring activities.\\n\\n\\n\\\\subsection{TeV Observations}\\n\\n1ES~1101--232 has been observed on the nights of 19--27 May 1998\\nwith the Durham University Mark 6 atmospheric $\\\\check{\\\\rm C}$erenkov telescope.\\nWe summarize here the data analysis and the results presented in \\nChadwick et al. (1999a). \\nThe telescope uses the imaging technique to separate VHE gamma rays from the \\ncosmic ray background, together with a robust noise-free trigger (Armstrong\\net al. 1999). Data are taken in 15 minutes segments, alternating \\nON-source with an equal number of OFF-source observations. \\nAfter removal of cloud--affected data, there are a total of\\n10.5 hours ON-source data and the same amount of OFF-source data.\\nData are screened for ``good\\\" events by the selection criteria listed in\\nTable 2 of Chadwick et al. (1999a).\\nThe source was not detected and an upper limit of \\n$F_{TeV}$ [$> 300$ GeV] = 3.7$\\\\times 10^{-11}$ photons cm$^{-2}$ s$^{-1}$ \\nhas been derived.\\n\\nThe data have been investigated for time variability on time-scales of days \\n(at a flux limit of $\\\\sim 1 \\\\times 10^{-10}$ cm$^{-2}$ s$^{-1}$) \\nand 15 min intervals. There is no evidence for any bursting behavior\\n(Chadwick, private communication).\\n\\n\\n\\\\section {SED construction and TeV predictions from theoretical models.}\\n\\n\\nWe have constructed the overall Spectral Energy Distribution (SED), using\\nboth data from literature and the \\\\sax\\\\ spectra from the two observations. \\nWe construct two different SED, one for each \\\\sax\\\\ observation, that are\\nclearly modeled by a different synchrotron state.\\nThe two SED are presented in Fig.~\\\\ref{figsedb}.\\n\\n\\\\begin{table}\\n\\\\caption{References for the data points of Fig~\\\\ref{figsedb}.}\\n\\\\begin{tabular}[h]{|l l|}\\n\\\\hline\\nBand \\t& Reference\\t\\\\\\\\\\n\\\\hline\\nRadio 1.4GHz & NVSS: Condon et al. 1998 AJ 115, 1693 \\\\\\\\\\nRadio 1.4GHz & Remillard et al. 1989 ApJ 345, 140 \\\\\\\\\\nRadio 5 GHz & Perlman et al. 1996 ApJS 104, 251 \\\\\\\\\\nRadio 5 GHz & Giommi et al. 1995 A\\\\&AS 109, 267 \\\\\\\\\\nOptical V \\t& Pesce et al. 1994 AJ 107, 494 \\\\\\\\\\nOptical V & Lanzetta et al. 1995 ApJ 440, 435 \\\\\\\\\\nOptical V & Giommi et al. 1995 A\\\\&AS 109, 267 \\\\\\\\\\nOptical V & Jannuzi et al. 1994 ApJ 428, 130 \\\\\\\\\\nOptical V & Falomo et al. 1994 ApJS 93, 125 \\\\\\\\\\nIR J,H,K & Bersanelli et al. 1992 AJ 104, 28 \\\\\\\\\\nIR K\\t\\t& Falomo et al. 1993 AJ 106, 11 \\\\\\\\\\nUV 1400A \\t& Pian \\\\& Treves 1993 ApJ 416, 130 \\\\\\\\\\nUV 1400A \\t& Edelson et al. 1992 ApJS 83, 1 \\\\\\\\\\nX--ray 2 keV & Perlman et al. 1996 ApJS 104, 251 \\\\\\\\\\nX--ray 2 keV & Giommi et al. 1995 A\\\\&AS 109, 267 \\\\\\\\\\nEGRET \\t\\t& Fichtel et al. 1994 ApJS 94, 551 \\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\\\label{refere}\\n\\\\end{table}\\n\\n\\n\\\\begin{figure}\\n\\\\psfig{file=9325.f5a,width=9.5truecm}\\n\\\\psfig{file=9325.f5b,width=9.5truecm}\\n\\\\caption{SED of the two \\\\sax\\\\ epoch observations {\\\\it Top:} 04/01/97 -- \\nhigh state; {\\\\it Bottom:} 19/06/98 -- low state, plus models.\\nLarge empty circles represent historical data from literature, while arrows\\nindicate upper limits from EGRET (MeV) and Mark6 (GeV-TeV) experiments\\nrespectively\\n(see Table~\\\\ref{refere} for references). Small dots with error-bars are \\nthe unfolded X--ray spectra discussed in this work.\\nLines represent the spectra computed with the SSC model (see text for\\ndetails) with different model parameters, reported in Table~\\\\ref{params}:\\ndashed lines represent spectra calculated with $\\\\delta=10$ and two different \\nvalues for the magnetic field $B$; similarly, solid lines represent spectra \\ncalculated with $\\\\delta=20$ and two different values for the magnetic \\nfield $B$. \\n}\\n\\\\label{figsedb}\\n\\\\end{figure}\\n\\n\\\\begin{table}\\n\\\\caption{Input parameters for the models of Fig.~\\\\ref{figsedb}}\\n\\n\\\\begin{tabular}[h]{| r r c c c c c c|}\\n\\\\hline\\n\\\\multicolumn{3}{|l}{High State} & & & & & \\\\\\\\\\n\\\\hline\\n \\\\# &$\\\\delta$ &$B$ &$\\\\gamma_b$ &$R$ &$K$ &$n_1$ &$n_2$ \\\\\\\\\\n & &(G) &$\\\\times10^4$ &cm &cm$^{-3}$ & & \\\\\\\\\\n\\\\hline\\n1 & 10 & 0.3 & 15.8 &1$\\\\times10^{16}$ & 1.7$\\\\times10^4$ & 2 & 3.5\\\\\\\\\\n2 & 10 & 0.6 & 11.2 &1$\\\\times10^{16}$ & 5.9$\\\\times10^4$ & 2 & 3.5\\\\\\\\\\n3 & 20 & 0.1 & 19.3 &1$\\\\times10^{16}$ & 7.9$\\\\times10^3$ & 2 & 3.5\\\\\\\\\\n4 & 20 & 0.2 & 13.5 &1$\\\\times10^{16}$ & 2.8$\\\\times10^4$ & 2 & 3.5\\\\\\\\\\n\\\\hline\\n\\\\hline\\n\\\\multicolumn{3}{|l}{Low State} & & & & & \\\\\\\\\\n\\\\hline\\n \\\\# &$\\\\delta$ &$B$ &$\\\\gamma_b$ &$R$ &$K$ &$n_1$ &$n_2$ \\\\\\\\\\n & &(G) &$\\\\times10^4$ &cm &cm$^{-3}$ & & \\\\\\\\\\n\\\\hline\\n1 & 10 & 0.5 & 8.45 & 1$\\\\times10^{16}$ & 2.5$\\\\times10^4$ & 2 & 3.9\\\\\\\\\\n2 & 10 & 1.0 & 5.98 & 1$\\\\times10^{16}$ & 8.9$\\\\times10^3$ & 2 & 3.9\\\\\\\\\\n3 & 20 & 0.1 & 13.3 & 1$\\\\times10^{16}$ & 6.3$\\\\times10^3$ & 2 & 3.9\\\\\\\\\\n4 & 20 & 0.2 & 9.40 & 1$\\\\times10^{16}$ & 2.2$\\\\times10^3$ & 2 & 3.9\\\\\\\\\\n\\\\hline\\n\\\\end{tabular}\\n\\\\label{params}\\n\\\\end{table}\\n\\n\\nWe have reproduced the SED in both X--ray states with a simple homogeneous SSC \\nmodel.\\nThe source is modeled as a spherical region with size $R$, uniform and\\ntangled magnetic field $B$, in motion toward the observer with a bulk \\nLorentz factor $\\\\Gamma$.\\nThe region is filled by a population of relativistic electrons with a\\ndistribution of Lorentz factors given by:\\n$N(\\\\gamma )=K\\\\gamma^{-n_1}(1+\\\\gamma/\\\\gamma_{b})^{n_1-n_2}$, \\nwhere the asymptotic slopes are $n_1$ and $n_2$, the break point\\nis $\\\\gamma_{b}$ and $K$ is a normalization factor.\\nThe self--Compton emission is derived taking into account the full \\nKlein--Nishina (KN) cross section, computed using the relations reported in \\nJones (1968; see also Blumenthal \\\\& Gould 1970). \\nWe do not take into account absorption of IR photons by the infrared\\nbackground, whose emission level is still uncertain. \\nThis implies that in principle the derived curves are upper limits to the\\ndetectable VHE emission, also because the redshift of 1ES~1101--232 is only\\nslightly smaller\\nthan the limit ($z=0.2$) chosen to monitor blazar emission in the TeV band\\nby the HEGRA experiment (Rhode \\\\& Meyer, 1997).\\nOn the other hand, a detection of the source in this band would provide also a\\nmeasure of the density of IR background photons.\\n\\nAlthough the complete determination of the set of physical parameters for the\\nSSC model requires the knowledge of the positions of both the synchrotron peak \\nand the Inverse Compton peak (as discussed in Tavecchio et al. 1998), \\nwe can put strong constraints to the parameters using the informations\\nprovided by the X--ray spectrum and the TeV upper limit\\nsuggesting that the condition $L_C/L_s\\\\leq 1$ applies.\\n\\nWe note here that the analytical relations discussed in Tavecchio et al. (1998)\\nin the KN regime are obtained with a step approximation for the KN \\ncross--section. \\nIn the extreme KN regime the numerical values given by this \\napproximation might differ from the results of the numerical model derived\\nwith the full KN treatment, but we can use the analytical discussion as a \\nguideline for the numerical model.\\n\\nTypical variability time-scales observed in HBLs \\n($t_{var}\\\\sim\\\\,10^{3-4}$ s, see e.g\\nZhang et al. 2000, Giommi et al. 1999, 2000) suggest Doppler factors \\n$\\\\delta$ in the range 10--20 and sizes of $R \\\\leq 10^{16}$ cm. \\nWe fixed the radius to $R=10^{16}$ cm. This choice directly puts a lower \\nlimit to the value of the magnetic field:\\n\\n\\\\footnotesize\\n\\\\begin{equation}\\nB\\\\delta^{2+\\\\alpha _1} > A \\\\times\\n (1+z)^{\\\\alpha _1} \\\\left[ \\\\frac{g} \\n{\\\\nu_c\\\\nu_s} \\\\right] ^{(1-\\\\alpha _1)/2} \\n\\\\left( \\\\frac {L_s}\\n{ t_{var} L_C^{1/2}} \\\\right)\\n\\\\label{ulower} \\n\\\\end{equation} \\n\\\\normalsize\\n\\n\\\\noindent\\nwhere $g(\\\\alpha _1,\\\\alpha _2)$ is a constant related to\\nthe spectral indices $\\\\alpha_1$ and $\\\\alpha _2$ and A is the\\nappropriate constant\\n(see Tavecchio et al. 1998 for details on (\\\\ref{ulower})).\\nFrom this relation we can infer that an upper limit\\non $L_C$ and an estimate of $t_{var}$ directly puts a lower \\nlimit for $B$. The physical reason for this lower limit is related to the \\nfact that the synchrotron peak Luminosity is proportional to the product\\n$N_eB^2$ (where $N_e$ is the number of emitting electrons), while the ratio\\nbetween the Compton peak Luminosity and the synchrotron peak Luminosity is \\nproportional to $N_e$: therefore an upper limit to $L_C/L_s$ gives an upper \\nlimit to $N_e$ and this, together with the synchrotron Luminosity, provides \\nthe lower limit for the magnetic field $B$.\\nAnother way of describing the effect, assuming that\\nthe scattering is in the Thomson regime, is that in this case\\nrequiring $L_C/L_s<1$ corresponds to require that the\\nratio between the synchrotron and the magnetic energy densities \\n$U_{syn}/U_B<1$.\\nFor a given source size and Doppler factor the synchrotron radiation \\nenergy density is fixed, and the above relation then corresponds to a \\nlower limit on the value of the magnetic field.\\n\\n \\nIn Fig.~\\\\ref{figsedb} we plot the spectrum of both states computed for \\ntwo different values of $\\\\delta$ ($\\\\delta=10$ for the dashed lines,\\n$\\\\delta=20$ for the solid lines), and for two different values of the magnetic\\nfield $B$, as listed in Table~\\\\ref{params}.\\nThe lowest value of $B$ has been determined by requiring\\nnot to over-produce the high energy (TeV) emission, since, for a given\\nsynchrotron luminosity, size and Doppler factor, the ratio\\nbetween the self Compton and the synchrotron powers depends only on the\\nmagnetic field.\\n\\nWe take this value, listed in Table~\\\\ref{params},\\nfor the models 1 and 3 shown in Fig. 5.\\nFor models 2 and 4 we have doubled the B value, and decreased the\\nrelativistic electron density and $\\\\gamma_b$ accordingly, in order to produce\\nthe same amount of synchrotron flux and about the same synchrotron peak\\nfrequency.\\nIn this case the self--Compton flux decreases, due to the decreased\\nelectron density.\\n\\nThe transition from the high to the low state is consistent with a change\\nof the second slope $n_2$ and with a decrease of $\\\\gamma_b$ by a factor\\nof 1.5--2. This behavior is similar to what observed in the other well\\nknown TeV BL Lac, such as PKS 2155--304 (see e.g. Chiappetti et al. 1999),\\nMkn 501 (e.g. Pian et al 1998) and Mkn 421 (Maraschi et al. 1999), where\\nhigh X-ray states are interpreted as states with either higher \\n$\\\\gamma _b$ and/or higher magnetic field.\\n\\n\\nIt is evident from Fig.~\\\\ref{figsedb} that a small change in the magnetic\\nfield, while still consistent with the X--ray (\\\\sax) observations,\\nproduces a dramatically different amount of TeV photons. Assuming that\\nthe size of the source and the Doppler factor do not vary substantially\\nwith time, variations of the synchrotron flux can be attributed to\\nchanges of the density of electrons and/or the magnetic field. If this\\nis the case, we expect that the TeV emission can be easily detected,\\neither for X--ray fluxes slightly brighter than what observed up to now,\\nor by longer TeV exposure times.\\n\\n\\\\section{Results and Conclusions}\\n \\nThe X--ray spectrum of 1ES~1101--232 as measured by \\\\sax\\\\ is fitted \\nonly by a broken power law (a single power law or an absorbed \\npower law are not statistically acceptable)\\nwith a break at 1.3 - 1.9 keV. From the first to the second observation, \\nthe spectrum varied at high energies, becoming softer (steeper). \\nThe flux decrease, by about 32\\\\%, has occurred in the 2--10 keV band.\\nThe PDS observation are not of statistical significance sufficient\\nto put a real constraint on the spectrum.\\n\\nEven if the variation in the X--ray band is not dramatic, we can clearly\\ndistinguish between the two states, that are modeled by different parameters\\nof the synchrotron component.\\n\\nBy using the TeV upper limit and the two \\\\sax\\\\ observations we model also the\\nhigher energy portion of the spectrum as a self--Compton component, by\\nusing the model described e.g. in Tavecchio et al. (1998) that assumes a simple\\nhomogeneous SSC model in the KN regime, in which the relativistic electrons\\nhave a broken power law energy distribution. \\n\\nThe two X-ray states of the source are described by varying this\\ndistribution, assuming that the other relevant parameters ($R$ and\\n$\\\\delta$) are nearly constant.\\n\\n\\nWe can compare these results with what found for the few TeV detected sources.\\nThe choice of Doppler factor of 10 and 20 made here is in the interval of\\nthe values of $\\\\delta$ found by other authors for Mkn 421, \\nPKS2155--304 and Mkn501, that range\\nfrom $\\\\delta \\\\sim 5$ (e.g. Takahashi, 1999; Mkn 421, Catanese et al. \\n1998: Mkn 501) \\nto $\\\\delta \\\\sim 30$ (e.g. Bednarek \\\\& Protheroe 1999: Mkn501; \\nKataoka et al 2000: PKS2155--304;\\nBednarek \\\\& Protheroe 1997: Mkn 421).\\nAt the same time, values of $B$ in excess of 0.03 G and up to 1 G \\n(Chiappetti et al. 1999) are found for the same sources.\\n\\nOf the three above mentioned objects, the most similar to 1ES~1101--232 \\nis Mkn 501, for which different measures have been produced: e.g.\\n$\\\\delta \\\\geq 15$ \\\\& $B=0.8 $G (Pian et al. 1998);\\n$\\\\delta = 15$ \\\\& $B=0.2 $G (Kataoka et al. 1999);\\n$\\\\delta = 30$ \\\\& $B=0.7 $G (Bednarek \\\\& Protheroe 1999),\\nin good agreement with the values of Table~\\\\ref{params}.\\n\\n\\nEven if based, besides the accurate X-ray spectral determination up \\nto $\\\\sim 50$ keV, only on a TeV upper limit we can infer that\\nthe physical conditions in 1ES~1101--232 are similar to the\\nbrightest TeV sources, making it a very promising candidate for \\nTeV observations, and a testbed for the SSC model.\\nFurthermore, since the redshift of 1ES~1101--232 is intermediate,\\na detection of this source in the VHE range would pose constraints\\non the density of the IR background photons that is still at the moment\\nvery uncertain.\\n\\n\\\\begin{acknowledgements}\\nThis work has received partial financial support from the Italian \\nSpace Agency. \\nWe would like to thank Paula Chadwick and S.J. McQueen for informing us\\nabout their VHE results in advance of publication, Paolo Giommi and Roberto\\nDella Ceca for helpful discussion and comments, and an anonymous referee\\nfor useful suggestions that improved the readability of the paper.\\n\\n\\\\end{acknowledgements}\\n \\n\\\\begin{thebibliography}{}\\n\\n\\\\bibitem{} Aharonian, F.A. et al., 1999, A\\\\&A, 341, 69\\n\\n\\\\bibitem{} Armstrong, P. et al., 1999, Experimental Astronomy, v. 9, 51\\n\\n\\\\bibitem{} Bednarek, W., \\\\& Protheroe, R.J., 1997, MNRAS, 290, 139 %(mkn421)\\n\\n\\\\bibitem{} Bednarek, W., \\\\& Protheroe, R.J., 1999, MNRAS, 310, 577\\n%%astro-ph/9902050 %(mkn501)\\n\\n\\\\bibitem{} Blumenthal \\\\& Gould, 1970, Rev. of Modern Phys., 42, 237\\n\\n\\\\bibitem{} Boella G., Butler R.C., Perola G.C., et al., \\n 1997a, A\\\\&AS 122, 299\\n\\n\\\\bibitem{} Boella G., Chiappetti L., Conti G., et al., \\n 1997b, A\\\\&AS 122, 327\\n\\n\\\\bibitem{} Butler C., Scarsi L., 1990, SPIE 1344, 46\\n\\n\\\\bibitem{} Catanese M. et al., 1998, ApJ, 501, 616\\n\\n\\\\bibitem{} Chadwick, P.M., Lyons, K., McComb, T.J.L., Orford, K.J., Osborne, \\nJ.L., Rayner, S.M., Shaw, S.E., and Turver, K.E., 1999a, ApJ, 521, 547\\n\\n\\\\bibitem{} Chadwick, P.M., Lyons, K., McComb, T.J.L., Orford, K.J., Osborne, \\nJ.L., Rayner, S.M., Shaw, S.E., Turver, K.E., Wieczorek, G.J., 1999b, \\nApJ, 513, 161\\n\\n\\\\bibitem{} Chiappetti, L., et al., 1999, ApJ, 521, 552\\n\\n\\\\bibitem{} Fossati, G., Maraschi, L., Celotti, A., Comastri, A., and\\nGhisellini, G., 1998, MNRAS, 299, 433\\n\\n\\\\bibitem{} Gaidos, J.A., et al, 1996, Nature, 383, 319\\n\\n\\\\bibitem{} Ghisellini, G., 1999, in ``The BL Lac Phenomenon\\\",\\nEd. L. Takalo, ASP conf. series, 159, 311. \\n\\n\\\\bibitem{} Ghisellini, G., Celotti, A., Fossati, G., Maraschi, L., and\\nComastri, A., 1998, MNRAS, 301, 451\\n\\n\\\\bibitem{} Giommi, P., Padovani, P., Perlman, E., 2000, MNRAS, in press,\\nastro-ph/9907377\\n\\n\\\\bibitem{} Giommi, P., et al., 1999, A\\\\&A, 51, 59\\n\\n\\\\bibitem{} Guainazzi M. \\\\& Matteuzzi A., 1997, SDC-TR 011\\n\\n\\\\bibitem{} Jones, 1968, Phys. Rev, 167, 1159\\n\\n\\\\bibitem{} Kataoka, J., et al. 2000, ApJ, 528, 243 %(2155)\\n\\n\\\\bibitem{} Kataoka, J., et al. 1999, ApJ, 514, 138 %(mkn 501)\\n\\n\\\\bibitem{} Maraschi, L., et al., 1999, ApJL, 526, L81\\n\\n\\\\bibitem{} Mukherjee, R., et al. 1997, ApJ, 490, 116\\n\\n\\\\bibitem{} Orr, A. et al. 1998, Nuclear Physics B Proceedings\\nSupplements, L. Scarsi, H. Bradt, P. Giommi and F. Fiore (eds.), Elsevier\\nScience B.V\\n\\n\\\\bibitem{} Parmar A.N., Martin D.D.E., Bavdaz M., et al., \\n 1997, A\\\\&AS 122, 309\\n\\n\\\\bibitem{} Perlman E.S., Stocke J.T., Schachter, J.F., Elvis, M.,\\nEllingson, E., Urry, C.M., Potter M., Impey C.D., Kolchinsky, P. 1996, \\nApJS, 104, 251 \\n\\n\\\\bibitem{} Pian, E., et al. 1998, ApJ, 492, L17\\n\\n\\\\bibitem{} Punch, M., et al., 1992, Nature, 358, 477\\n\\n\\\\bibitem{} Quinn J., et al., ApJ, 1996, 456, L83\\n\\n\\\\bibitem{} Rhode, W., Meyer, H., 1997, Proceedings of the International \\nConference on ``Relativistic Jets in AGNs\\\", p.223-227\\n\\n\\\\bibitem{} Stecker, F.W., De Jager, O.C. \\\\& Salamon, M.H.,\\n1996, Ap.J. 473, L75\\n\\n\\\\bibitem{} Stecker F.W., \\\\& De Jager, O.C. 1998, A\\\\&A, 334, L85\\n\\n\\\\bibitem{} Takahashi, T., et al. 1999, Astropart. Phys., 11, 173 \\n\\n\\\\bibitem{} Tavecchio, F., et al., 1998, ApJ, 509, 608\\n\\n\\\\bibitem{} Urry, C. M., \\\\& Padovani, P. 1995, PASP, 107, 803\\n\\n\\\\bibitem{} Wolter A., et al., 1998, A\\\\&A, 335, 899\\n\\n\\\\bibitem{} Zhang, Y.H., et al., 1999, ApJ, 527, 719\\n%%astro-ph/9907325\\n\\\\end{thebibliography}\\n\\n\\n\\\\end{document}\\n\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002298.extracted_bib","string":"\\begin{thebibliography}{}\n\n\\bibitem{} Aharonian, F.A. et al., 1999, A\\&A, 341, 69\n\n\\bibitem{} Armstrong, P. et al., 1999, Experimental Astronomy, v. 9, 51\n\n\\bibitem{} Bednarek, W., \\& Protheroe, R.J., 1997, MNRAS, 290, 139 %(mkn421)\n\n\\bibitem{} Bednarek, W., \\& Protheroe, R.J., 1999, MNRAS, 310, 577\n%%astro-ph/9902050 %(mkn501)\n\n\\bibitem{} Blumenthal \\& Gould, 1970, Rev. of Modern Phys., 42, 237\n\n\\bibitem{} Boella G., Butler R.C., Perola G.C., et al., \n 1997a, A\\&AS 122, 299\n\n\\bibitem{} Boella G., Chiappetti L., Conti G., et al., \n 1997b, A\\&AS 122, 327\n\n\\bibitem{} Butler C., Scarsi L., 1990, SPIE 1344, 46\n\n\\bibitem{} Catanese M. et al., 1998, ApJ, 501, 616\n\n\\bibitem{} Chadwick, P.M., Lyons, K., McComb, T.J.L., Orford, K.J., Osborne, \nJ.L., Rayner, S.M., Shaw, S.E., and Turver, K.E., 1999a, ApJ, 521, 547\n\n\\bibitem{} Chadwick, P.M., Lyons, K., McComb, T.J.L., Orford, K.J., Osborne, \nJ.L., Rayner, S.M., Shaw, S.E., Turver, K.E., Wieczorek, G.J., 1999b, \nApJ, 513, 161\n\n\\bibitem{} Chiappetti, L., et al., 1999, ApJ, 521, 552\n\n\\bibitem{} Fossati, G., Maraschi, L., Celotti, A., Comastri, A., and\nGhisellini, G., 1998, MNRAS, 299, 433\n\n\\bibitem{} Gaidos, J.A., et al, 1996, Nature, 383, 319\n\n\\bibitem{} Ghisellini, G., 1999, in ``The BL Lac Phenomenon\",\nEd. L. Takalo, ASP conf. series, 159, 311. \n\n\\bibitem{} Ghisellini, G., Celotti, A., Fossati, G., Maraschi, L., and\nComastri, A., 1998, MNRAS, 301, 451\n\n\\bibitem{} Giommi, P., Padovani, P., Perlman, E., 2000, MNRAS, in press,\nastro-ph/9907377\n\n\\bibitem{} Giommi, P., et al., 1999, A\\&A, 51, 59\n\n\\bibitem{} Guainazzi M. \\& Matteuzzi A., 1997, SDC-TR 011\n\n\\bibitem{} Jones, 1968, Phys. Rev, 167, 1159\n\n\\bibitem{} Kataoka, J., et al. 2000, ApJ, 528, 243 %(2155)\n\n\\bibitem{} Kataoka, J., et al. 1999, ApJ, 514, 138 %(mkn 501)\n\n\\bibitem{} Maraschi, L., et al., 1999, ApJL, 526, L81\n\n\\bibitem{} Mukherjee, R., et al. 1997, ApJ, 490, 116\n\n\\bibitem{} Orr, A. et al. 1998, Nuclear Physics B Proceedings\nSupplements, L. Scarsi, H. Bradt, P. Giommi and F. Fiore (eds.), Elsevier\nScience B.V\n\n\\bibitem{} Parmar A.N., Martin D.D.E., Bavdaz M., et al., \n 1997, A\\&AS 122, 309\n\n\\bibitem{} Perlman E.S., Stocke J.T., Schachter, J.F., Elvis, M.,\nEllingson, E., Urry, C.M., Potter M., Impey C.D., Kolchinsky, P. 1996, \nApJS, 104, 251 \n\n\\bibitem{} Pian, E., et al. 1998, ApJ, 492, L17\n\n\\bibitem{} Punch, M., et al., 1992, Nature, 358, 477\n\n\\bibitem{} Quinn J., et al., ApJ, 1996, 456, L83\n\n\\bibitem{} Rhode, W., Meyer, H., 1997, Proceedings of the International \nConference on ``Relativistic Jets in AGNs\", p.223-227\n\n\\bibitem{} Stecker, F.W., De Jager, O.C. \\& Salamon, M.H.,\n1996, Ap.J. 473, L75\n\n\\bibitem{} Stecker F.W., \\& De Jager, O.C. 1998, A\\&A, 334, L85\n\n\\bibitem{} Takahashi, T., et al. 1999, Astropart. Phys., 11, 173 \n\n\\bibitem{} Tavecchio, F., et al., 1998, ApJ, 509, 608\n\n\\bibitem{} Urry, C. M., \\& Padovani, P. 1995, PASP, 107, 803\n\n\\bibitem{} Wolter A., et al., 1998, A\\&A, 335, 899\n\n\\bibitem{} Zhang, Y.H., et al., 1999, ApJ, 527, 719\n%%astro-ph/9907325\n\\end{thebibliography}"}],"string":"[\n {\n \"name\": \"astro-ph0002298.extracted_bib\",\n \"string\": \"\\\\begin{thebibliography}{}\\n\\n\\\\bibitem{} Aharonian, F.A. et al., 1999, A\\\\&A, 341, 69\\n\\n\\\\bibitem{} Armstrong, P. et al., 1999, Experimental Astronomy, v. 9, 51\\n\\n\\\\bibitem{} Bednarek, W., \\\\& Protheroe, R.J., 1997, MNRAS, 290, 139 %(mkn421)\\n\\n\\\\bibitem{} Bednarek, W., \\\\& Protheroe, R.J., 1999, MNRAS, 310, 577\\n%%astro-ph/9902050 %(mkn501)\\n\\n\\\\bibitem{} Blumenthal \\\\& Gould, 1970, Rev. of Modern Phys., 42, 237\\n\\n\\\\bibitem{} Boella G., Butler R.C., Perola G.C., et al., \\n 1997a, A\\\\&AS 122, 299\\n\\n\\\\bibitem{} Boella G., Chiappetti L., Conti G., et al., \\n 1997b, A\\\\&AS 122, 327\\n\\n\\\\bibitem{} Butler C., Scarsi L., 1990, SPIE 1344, 46\\n\\n\\\\bibitem{} Catanese M. et al., 1998, ApJ, 501, 616\\n\\n\\\\bibitem{} Chadwick, P.M., Lyons, K., McComb, T.J.L., Orford, K.J., Osborne, \\nJ.L., Rayner, S.M., Shaw, S.E., and Turver, K.E., 1999a, ApJ, 521, 547\\n\\n\\\\bibitem{} Chadwick, P.M., Lyons, K., McComb, T.J.L., Orford, K.J., Osborne, \\nJ.L., Rayner, S.M., Shaw, S.E., Turver, K.E., Wieczorek, G.J., 1999b, \\nApJ, 513, 161\\n\\n\\\\bibitem{} Chiappetti, L., et al., 1999, ApJ, 521, 552\\n\\n\\\\bibitem{} Fossati, G., Maraschi, L., Celotti, A., Comastri, A., and\\nGhisellini, G., 1998, MNRAS, 299, 433\\n\\n\\\\bibitem{} Gaidos, J.A., et al, 1996, Nature, 383, 319\\n\\n\\\\bibitem{} Ghisellini, G., 1999, in ``The BL Lac Phenomenon\\\",\\nEd. 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M., \\\\& Padovani, P. 1995, PASP, 107, 803\\n\\n\\\\bibitem{} Wolter A., et al., 1998, A\\\\&A, 335, 899\\n\\n\\\\bibitem{} Zhang, Y.H., et al., 1999, ApJ, 527, 719\\n%%astro-ph/9907325\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":294,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002299"},"title":{"kind":"string","value":""},"authors":{"kind":"list like","value":[],"string":"[]"},"abstract":{"kind":"string","value":""},"latex":{"kind":"list like","value":[],"string":"[]"},"bibtex":{"kind":"list like","value":[],"string":"[]"}}},{"rowIdx":295,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002300"},"title":{"kind":"string","value":"Rotational modes of non-isentropic stars and the gravitational radiation driven instability"},"authors":{"kind":"list like","value":[{"author":"Shijun Yoshida and Umin Lee"}],"string":"[\n {\n \"author\": \"Shijun Yoshida and Umin Lee\"\n }\n]"},"abstract":{"kind":"string","value":"We investigate the properties of $r$-mode and inertial mode of slowly rotating, non-isentropic, Newtonian stars, by taking account of the effects of the Coriolis force and the centrifugal force. The Coriolis force is the dominant restoring force for both $r$-mode and inertial mode, which are also called rotational mode in this paper. For the velocity field produced by the oscillation modes the $r$-mode has the dominant toroidal component over the spheroidal component, while the inertial mode has the comparable toroidal and spheroidal components. In non-isentropic stars the specific entropy of the fluid depends on the radial distance from the center, and the interior structure is in general divided into two kinds of layers of fluid stratification that is stable or unstable against convection. Because of the non-isentropic structure, low frequency oscillations of the star are affected by the buoyant force, which has no effects on oscillations of isentropic stars. In this paper we employ simple polytropic models with the polytropic index $n=1$ as the background neutron star models for the modal analysis. For the non-isentropic models we consider only two cases, that is, the models with the stable fluid stratification in the whole interior and the models that are fully convective. For simplicity we call these two kinds of models ``radiative'' and ``convective'' models in this paper. For both cases, we assume the deviation of the models from isentropic structure is small. Examining the dissipation timescales due to the gravitational radiation and several viscous processes for the polytropic neutron star models, we find that the gravitational radiation driven instability of the nodeless $r$-modes associated with $l'=|m|$ remains strong even in the non-isentropic models, where $l'$ and $m$ are the indices of the spherical harmonic function representing the angular dependence of the eigenfunction. Calculating the rotational modes of the radiative models as functions of the angular rotation frequency $\\Omega$, we find that the inertial modes are strongly modified by the buoyant force at small $\\Omega$, where the buoyant force as a dominant restoring force becomes comparable with or stronger than the Coriolis force. Because of this property we obtain the mode sequences in which the inertial modes at large $\\Omega$ are identified as $g$-modes or the $r$-modes with $l'=|m|$ at small $\\Omega$. We also note that as $\\Omega$ increases from $\\Omega=0$ the retrograde $g$-modes become retrograde inertial modes, which are unstable against the gravitational radiation reaction."},"latex":{"kind":"list like","value":[{"name":"ms.tex","string":"%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% %\n% Rotational modes of non-isentropic stars and %\n% the gravitational radiation driven instability %\n% %\n% S. YOSHIDA and U. LEE %\n% %\n% Astronomical Institute, %\n% Graduate School of Science, Tohoku University, % \n% Sendai 980-8578, Japan %\n% %\n% yoshida@astr.tohoku.ac.jp %\n% %\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\documentstyle[aaspp4]{article}\n\n\\received{}\n\\accepted{}\n\\journalid{VOL}{JOURNAL DATE}\n\\articleid{START PAGE}{END PAGE}\n\\paperid{MANUSCRIPT ID}\n\n\\slugcomment{}\n\\lefthead{Yoshida, Lee}\n\\righthead{}\n\n\\begin{document}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% O. FRONT MATTER %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\title{Rotational modes of non-isentropic stars and the gravitational radiation \n driven instability }\n%\n\\author{Shijun Yoshida and Umin Lee}\n%\n\\affil{Astronomical Institute, Graduate School of Science, \nTohoku University, Sendai 980-8578, \nJapan \\\\ yoshida@astr.tohoku.ac.jp, lee@astr.tohoku.ac.jp}\n\n\n\\begin{abstract}\nWe investigate the properties of\n$r$-mode and inertial mode of slowly rotating, non-isentropic, \nNewtonian stars, by taking account of the effects of \nthe Coriolis force and the centrifugal force.\nThe Coriolis force is the dominant restoring force \nfor both $r$-mode and inertial mode, which are also called rotational mode \nin this paper. \nFor the velocity field produced by the oscillation modes\nthe $r$-mode has the dominant toroidal component over the \nspheroidal component, while the inertial mode has\nthe comparable toroidal and spheroidal components.\nIn non-isentropic stars the specific entropy of the fluid\ndepends on the radial distance from the center, and\nthe interior structure is in general divided into\ntwo kinds of layers of fluid stratification that is\nstable or unstable against convection.\nBecause of the non-isentropic structure, low frequency\noscillations of the star are affected by the buoyant force, which\nhas no effects on oscillations of isentropic stars.\nIn this paper we employ simple polytropic models with the polytropic index $n=1$\nas the background neutron star models for the modal analysis.\nFor the non-isentropic models we consider only two cases, that is,\nthe models with the stable fluid stratification in the whole interior\nand the models that are fully convective.\nFor simplicity we call these two kinds of models ``radiative'' and ``convective''\nmodels in this paper.\nFor both cases, we assume the deviation of the models from isentropic \nstructure is small.\nExamining the dissipation timescales due to \nthe gravitational radiation and \nseveral viscous processes for the polytropic neutron star models,\nwe find that the gravitational radiation driven instability of \nthe nodeless $r$-modes associated with $l'=|m|$ remains strong \neven in the non-isentropic models,\nwhere $l'$ and $m$ are the indices \nof the spherical harmonic function representing the angular dependence\nof the eigenfunction.\nCalculating the rotational modes of the radiative models \nas functions of the angular rotation frequency $\\Omega$, we find that\nthe inertial modes are strongly modified \nby the buoyant force at small $\\Omega$, where the buoyant force\nas a dominant restoring force becomes\ncomparable with or stronger than the Coriolis force.\nBecause of this property we obtain the mode sequences \nin which the inertial modes at large $\\Omega$\nare identified as $g$-modes or the $r$-modes with $l'=|m|$ at small $\\Omega$.\nWe also note that as $\\Omega$ increases from $\\Omega=0$\nthe retrograde $g$-modes become retrograde inertial modes,\nwhich are unstable against the gravitational radiation reaction.\n\\end{abstract}\n\n\n\\keywords{instabilities --- stars: neutron --- \nstars: oscillations --- stars: rotation}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% I. INTRODUCTION %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\section{Introduction}\n\n\nSince the recent discovery of the gravitational radiation driven instability of\nthe $r$-modes by Andersson (1998) and Friedman \\& Morsink (1998),\na large number of papers have been published on the properties of the \nrotational modes of rotating stars because of their possible importance \nin astrophysics\n(e.g., Kojima 1998, Andersson, Kokkotas \\& Schutz 1998, \nKokkotas \\& Stergioulas 1998, Lindblom \\& Isper 1998, Beyer \\& Kokkotas \n1999, Lindblom, Mendell \\& Owen 1999, Kojima \\& Hosonuma 1999, \nLockitch \\& Friedman 1999, Yoshida \\& Lee 2000, Lockitch 1999, Yoshida \net al 1999).\nHere, we have used the term of ``rotational mode'' to refer to both $r$-mode and \ninertial mode of rotating stars.\nAs an important consequence of the instability, for example, Lindblom, Owen \n\\& Morsink (1998) argued that due to the instability, \nthe maximum angular rotation velocity of hot neutron stars is \nstrongly restricted. \nOwen et al. (1998) also suggested that\nthe gravitational radiation emitted from hot young neutron stars due to\nthe $r$-mode instability would be one of the potential sources\nfor the gravitational wave detectors, e.g. LIGO.\n\n\n\nThe dominant restoring force for the rotational modes\nis the Coriolis force and the characteristic frequency \nis comparable to the angular rotation frequency $\\Omega$ of the star \n(e.g., Greenspan 1964, Pedlosky 1987). \nThe $r$-modes are characterized by the properties that\nthe toroidal motion dominates the spheroidal motion in the velocity field, and that \nthe oscillation frequency $\\omega$ observed in the corotating frame of the star \nis given by $\\omega=2m\\Omega/(l'(l'+1))$ \nin the limit of $\\Omega\\rightarrow0$, \nwhere $m$ and $l'$ are the indices of the spherical harmonic function $Y_{l'}^m$ \nrepresenting the toroidal component of the velocity field of the mode\n(e.g., Papaloizou \\& Pringle 1978 , Provost, Berthomieu \\& Rocca 1981, \nSaio 1982). \nOn the other hand, the inertial modes have the comparable toroidal and\nspheroidal components of the velocity field and therefore they are not necessarily\nrepresented by a single spherical harmonic function\n(e.g, Lee, Strohmayer \\& Van Horn 1992, Yoshida \\& Lee 2000). \nNote that the inertial mode of this kind is also called ``rotation mode'' or \n``generalized $r$-mode'' (Lindblom \\& Ipser 1998, Lockitch \\& Friedman 1999). \n\n\n\nMost of the recent studies on the $r$-mode instability\ndriven by the gravitational radiation reaction are restricted to \nthe case of neutron stars with isentropic structure, since the barotropic\n(one-parameter) equation of state, $p=p(\\rho)$ is usually assumed for\nboth the interior structure and the small amplitude oscillation.\nIn isentropic stars\nthe specific entropy of the fluid in the interior is constant and\nthe buoyant force has no effects on the oscillation.\nHowever, stars in general have non-isentropic interior structure, \nwhich may be divided into\ntwo kinds of layers with fluid stratification \nstable or unstable against convection.\nIt is well know that the property of the oscillation modes of\nnon-isentropic stars is substantially different from that of isentropic stars,\nsince the buoyant force comes into play as a restoring force for \nlow frequency oscillations like $g$-mode propagating in the layers with the stable \nstratification (see, e.g., Unno et al 1989).\nThis is also the case for rotational modes, which have low oscillation\nfrequencies comparable to the spin rate $\\Omega$ of the star.\nFor example, we note that\nthe $r$-mode associated with $l'=|m|$ having the nodeless eigenfunction in the\nradial direction is the only $r$-mode permitted in an isentropic star for a given $m$\n(e.g, Lockitch \\& Friedman 1999, Yoshida \\& Lee 2000), \nbut in non-isentropic stars with the stable fluid stratification all\nthe $r$-modes with $l'\\ge |m|$ are possible for a given $m$, and there are\nin principle an infinite number of $r$-modes for given $l'$ and $m$\n(e.g., Provost et al 1981, Saio 1982, Lee \\& Saio 1997). \nWe therefore consider it important to investigate the modal properties of \nthe rotational modes in non-isentropic stars, particularly in order to\nanswer the question whether the property of \nthe $r$-mode instability for neutron star models with non-isentropic structure\nremains the same as that for isentropic neutron star models.\n\n\n\n\nIn this paper, we study the $r$-mode and the inertial mode oscillations\nof slowly rotating, non-isentropic, Newtonian stars, where\nuniform rotation and adiabatic oscillation are assumed\nto simplify the mathematical treatments. \nThe effects of the rotational deformation of the equilibrium structure \non the eigenfunction and eigenfrequency are included in the analysis, \nusing the formulation by Yoshida \\& Lee (2000) \n(see also Lee \\& Saio 1986, Lee 1993).\nWe employ simple polytropic models \nwith the polytropic index $n=1$\nas the background neutron star models.\nFor the non-isentropic models we consider only two cases, that is,\nthe models that have stable fluid stratification in the whole interior\nand those that are in convective equilibrium.\nIn this paper, following the conventions used \nin the field of stellar evolution and pulsation, \nwe simply call these two kinds of models\n``radiative'' and ``convective'' models, respectively, although\nno energy transport in the interior is considered.\nThe plan of this paper is as follows. \nIn \\S 2, we briefly describe the basic equations employed in the linear modal analysis\nof slowly rotating stars.\nIn \\S 3, we show numerical results for the rotational modes of non-isentropic \nstars, and discuss the properties of the eigenfrequency and eigenfunction of the modes.\nIn \\S 4, we examine the stability of simple neutron star models\nagainst the $r$-modes, computing their growth or damping timescales due \nto the gravitational radiation reaction and some viscous damping processes.\n\\S 5 is for conclusions.\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% II. Method of Solutions %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\section{Method of Solutions}\n\n\nThe method of solutions used in this paper is exactly the same as that \napplied in Yoshida \\& Lee (2000). Here, therefore, we briefly describe \nthe basic equations and the method of calculation. \nThe details are given in Yoshida \\& Lee (2000). \n\n\\subsection{Equilibrium Configurations}\n\n\nWe consider oscillations of uniformly rotating Newtonian stars. \nThus the angular rotation frequency of the star, $\\Omega$ is constant.\nWe assume the polytropic relation for the equilibrium structure of the model, \nand the relation between the pressure $p$ and the mass density $\\rho$ is given by\n%\n\\begin{equation}\np = K \\, \\rho^{1 + \\frac{1}{n}} \\, ,\n\\end{equation}\n%\nwhere $n$ and $K$ are the polytropic index and the structure constant determined by\ngiving the mass and the radius of the model, \nrespectively. \nIn this investigation, assuming slow rotation, we employ \nthe Chandrasekhar-Milne expansion (see, e.g, Tassoul 1978) to obtain \nthe equilibrium structure of rotating stars. \nIn this technique the effects of the \ncentrifugal force and the equilibrium deformation are treated \nas small perturbations to the non-rotating spherical symmetric structure \nof the star. \nThe small expansion parameter due to rotation is chosen as \n$\\bar{\\Omega}=\\Omega (R^3/G M)^{1/2}$, where $R$ and $M$ are \nthe radius and the mass of the non-rotating star, respectively. \nThe equilibrium configurations are constructed with accuracy up to the order of \n${\\bar{\\Omega}}^2$. For simplicity, we consider a sequence of slowly \nrotating stars whose central density is the same as that of the \nnon-rotating star. \n\n\n\\subsection{Perturbation Equations}\n\n\n\nIn the perturbation analysis, we introduce a parameter $a$ that is \nconstant on the distorted effective potential surface of the star. In practice, \nthe parameter $a$ is defined such that\n%\n\\begin{equation}\n\\Psi (r,\\theta) = \\Psi_0 (a) \\, , \\label{ep-co}\n\\end{equation}\n%\nwhere $\\Psi_0$ and $\\Psi$ are the effective potentials for the non-rotating \nand slowly rotating models, respectively. Note that $\\Psi_0$ is equal to \nthe gravitational potential and $\\Psi$ is the sum of the gravitational \npotential and the centrifugal potential. With this parameter $a$, \nthe distorted equi-potential surface may be given by\n%\n\\begin{equation}\nr = a \\lbrace 1 + \\epsilon (a,\\theta,\\varphi) \\rbrace \\, ,\n\\label{def-a}\n\\end{equation}\n%\nwhere $\\epsilon$ is the function of the order of \n${\\bar{\\Omega}}^2$, and is obtained by giving the functional forms\nof $\\Psi$ and $\\Psi_0$ using the Chandrasekhar-Milne expansion (Yoshida \\& Lee 2000). \nHere we have used spherical polar coordinates $(r,\\theta,\\varphi)$. \nHowever, we employ hereafter the parameter $a$ as the radial coordinate, \nin stead of the polar radial coordinate $r$.\n\n\nThe governing equations of nonradial oscillations of a rotating star are \nobtained by linearizing the basic equations used in fluid mechanics\n(e.g., Unno et al 1989). \nIn the following, we use $\\delta$ and $\\Delta$ to denote the Eulerian and \nthe Lagrangian changes of physical quantities, respectively.\nSince the equilibrium state is assumed to be stationary and axisymmetric, \nthe perturbations may be\nrepresented by a Fourier component proportional to \n$e^{i(\\sigma t + m \\varphi)}$, where $\\sigma$ is the frequency observed in \nan inertial frame and $m$ is the azimuthal quantum number. \nThe continuity equation may be linearized to be\n%\n\\begin{equation}\n\\delta \\rho = - \\nabla_i (\\rho \\xi^i), \\label{del_rho} \\label{mass_con} \n\\end{equation}\n%\nwhere $\\xi^i$ is the Lagrangian displacement vector, and we have made use of\n$\\delta v^i = i(\\sigma + m \\Omega) \\xi^i \\equiv i \\omega \\xi^i$\nwith $\\omega$ being the oscillation frequency observed in the corotating \nframe of the star. \nHere $\\nabla_i$ denotes the covariant derivative derived from the metric\n$g_{ij}$. \n\nIn this study, we consider only adiabatic oscillations. \nThus, the perturbed equation of state is given by\n\\begin{equation}\n\\delta p = \\Gamma p \\left( \\frac{\\delta \\rho}{\\rho} +\n\\xi^i A_i \\right) \\, , \\label{del_p} \n\\end{equation}\n%\nwhere\n$\\Gamma$ is the adiabatic exponent defined as\n%\n\\begin{equation}\n\\Gamma = \\left( \\frac{ \\partial \\ln p}{\\partial \\ln \\rho} \\right)_{ad} \\, ,\n\\end{equation}\n%\nand $A_i$ is the generalized Schwarzschild discriminant\\footnote{Since \nthe Schwarzschild discriminant $A_i$ is proportional to $\\nabla_i s$ with $s$\nbeing the specific entropy, a model with $A_i=0$ \nthroughout the interior is called isentropic model in this paper.\nUsing the same barotropic \n(one-parameter) equation of state, $p=p(\\rho)$ for both\nthe equilibrium structure and the perturbation leads to isentropic models.} given by\n%\n\\begin{equation}\nA_i \\equiv \\frac{1}{\\rho} \\nabla_i \\rho - \\frac{1}{\\Gamma p} \\nabla_i p \\, ,\n\\label{def_A}\n\\end{equation}\n%\nand the positive and negative values of $A_i$ indicate the fluid stratification\nunstable and stable against convection, respectively.\n\n\nThe linearized Euler's equation is\n\\begin{equation}\n-\\omega^2 \\xi_i + \\nabla_i \n\\left( \\frac{\\delta p}{\\rho} + \\delta \\Phi \\right) + \n\\left(\\frac{\\delta p}{\\rho} \\, g_{ij}+\\xi_j \\frac{1}{\\rho} \\nabla_i p\n\\right) \\, A^j + \n2 i \\omega \\Omega \\xi^j \\nabla_j \\varphi_i \n= 0 \\, , \\label{pert_Euler}\n\\end{equation}\n%\nwhere $\\Phi$ denotes the gravitational potential, \nand $\\varphi^i$ is the rotational Killing vector, with which the 3-velocity\nof the equilibrium fluid of a rotating star is given as \n$v^i=\\Omega\\varphi^i$. The perturbed Poisson equation is\n%\n\\begin{equation}\n\\nabla_i \\nabla^i \\delta \\Phi = 4\\pi G\\delta \\rho \\, ,\n\\label{pert_Poisson}\n\\end{equation}\n%\nwhere $G$ is the gravitational constant. \n\n\n\n\nPhysically acceptable solutions of the linear differential equations are \nobtained by imposing boundary conditions at the inner and outer \nboundaries of the star. The inner boundary conditions are the regularity \ncondition of the perturbed quantities at the stellar center. \nThe outer boundary conditions at the surface of the star are \n$\\Delta p/\\rho=0$\nand the continuity of the perturbed gravitational potential at the surface to\nthe solution of $\\nabla_i\\nabla^i\\delta\\Phi=0$ that vanishes at the infinity.\n\n\nIn order to solve the system of partial differential equations given above, \nwe employ the series expansion in terms of spherical harmonics to\nrepresent the angular dependence of the perturbed quantities.\nThe Lagrangian displacement vector, $\\xi^i$ is expanded in terms of the \nvector spherical harmonics as\n%\n\\begin{equation} \n\\xi^a = \\sum_{l\\geq\\vert m \\vert}^{\\infty} a \\, S_l(a) \nY_l^m (\\theta,\\varphi) e^{i \\sigma t} \\, , \\label{v_a}\n\\end{equation}\n%\n\\begin{equation}\n\\xi^\\theta = \\sum_{l,l'\\geq\\vert m \\vert}^{\\infty} \n\\left\\{ H_l (a) {Y_l^m}_{,\\theta} + T_{l'} (a) \\frac{1}{\\sin \\theta} \\, \n{Y_{l'}^m}_{,\\varphi} \\right\\} e^{i \\sigma t} \\, , \\label{v_t}\n\\end{equation}\n%\n\\begin{equation}\n\\xi^\\varphi = \\frac{1}{\\sin^2 \\theta} \n\\sum_{l,l'\\geq\\vert m \\vert}^{\\infty} \\left\\{ H_l (a) {Y_l^m}_{,\\varphi}\n - T_{l'} (a) {\\sin \\theta} \\, {Y_{l'}^m}_{,\\theta}\n \\right\\} e^{i \\sigma t} \\, \\label{v_p} \n\\end{equation}\n%\n(Regge \\& Wheeler 1957, see also Thorne 1980). \nThe perturbed scalar quantity such as $\\delta \\Phi$ is expressed as\n%\n\\begin{equation} \n\\delta \\Phi = \\sum_{l\\geq\\vert m \\vert}^{\\infty} \\delta \\Phi_l (a) \\, \nY_l^m (\\theta,\\varphi) e^{i \\sigma t} \\, . \\label{d_phi}\n\\end{equation}\n%\nHere, the expansion coefficients $T_{l'}$ are called ``axial'' \n(or ``toroidal'') and the other coefficients are called \n``polar'' (or ``spheroidal''). It is known that\nthese two set of components are decoupled when $\\Omega=0$.\n\n\nSubstituting the perturbed quantities expanded in terms of the spherical \nharmonics into the linearized basic \nequations ($\\ref{del_rho}$), ($\\ref{del_p}$), ($\\ref{pert_Euler}$) \nand ($\\ref{pert_Poisson}$), we obtain an infinite system of coupled linear \nordinary differential equations for the expansion coefficients. \nNotice that the system of differential equations employed in this paper\nis arranged to give\neigenfunctions and eigenfrequencies consistent up to the order of $\\bar\\Omega^3$ \nfor slow rotation.\nThe explicit expressions for the governing equations are given in Appendix of \nYoshida \\& Lee (2000). \n\n\nSince the equilibrium state of a rotating star is invariant under \nthe parity transformation defined by $\\theta \\to \\pi - \\theta$, \nthe linear perturbations have definite parity for that transformation. \nIn this paper, a set of modes whose scalar perturbations such as \n$\\delta \\Phi$ are symmetric with respect to the equator is called ``even'' \nmodes, while the other set of modes whose scalar perturbations are antisymmetric \nwith respect to the equator is called ``odd'' modes \n(see, e.g., Berthomieu et al. 1978).\nFor positive integers $j=1,~2,~3,~\\cdots$, we have $l=|m|+2j-2$ and \n$l'=l+1$ for even modes, and $l=|m|+2j-1$ and $l'=l-1$ for odd modes, \nwhere the symbols $l$ and $l'$ have been used to denote the spheroidal \nand toroidal components of the displacement vector $\\xi^i$, \nrespectively (see equations (\\ref{v_a})--(\\ref{d_phi})). \nNote that we do not use the term of the even (the odd) parity mode to refer to\nthe polar (the axial) mode, although this terminology is used traditionally in \nrelativistic perturbation theory (e.g., Regge \\& Wheeler 1957). \n\n\nOscillations of rotating stars are also divided into prograde and retrograde modes.\nWhen observed in the corotating frame of the star,\nwave patterns of the prograde modes are propagating\nin the same direction as rotation of the star, \nwhereas those of the retrograde modes are\npropagating in the opposite direction to the rotation.\nFor positive values of $m$, the prograde and retrograde modes have negative and positive\n$\\omega$, respectively.\n\n\n\nFor numerical calculations, we truncate the infinite set of linear \nordinary differential equations to obtain a finite set by discarding all \nthe expansion coefficients associated with $l$ higher than $l_{max}$. \nThis truncation determines the number of the expansion coefficients \nkept in the spherical harmonic expansion of each perturbed quantity. \nWe denote this number as $k_{max}$. Our basic equation becomes a \nsystem of $4\\times k_{max}$-th order linear ordinary differential equations, which,\ntogether with the boundary conditions, are numerically solved as an \neigenvalue problem of $\\omega\\equiv \\sigma+m\\Omega$ by using a Henyey type \nrelaxation method (e.g., Unno et al . 1989, see also Press et al. 1992).\n\n\n\nWe cannot determine a priori $k_{max}$,\nthe number of the expansion coefficients kept in the eigenfunctions. \nIn this paper, we start with an appropriate trial \nvalue of $k_{\\mbox{\\tiny max}}$ to compute an oscillation mode \nat a given value of $\\bar\\Omega$. \nThen, we increase the \nvalue of $k_{\\mbox{\\tiny max}}$, until the eigenfrequency converges within \nan appropriate numerical error, where the mode identification is done\nby examining the form and the number of nodes of the dominant expansion coefficients.\nWe consider that the mode thus obtained\nwith the sufficient number of the expansion coefficients\nis the correct oscillation mode we want for the rotating model at $\\bar\\Omega$.\n\n\n\nIn order to check our numerical code, we calculate eigenfrequencies of \nthe $r$-modes of the $n=3$ and $\\Gamma=5/3$ polytropic model \nat $\\bar{\\Omega}=0.1$. In Table 1, our \nresults are tabulated together with those calculated by Saio (1982) \nby using a semi-analytical \nperturbative approach. As shown by Table 1, our results are in good \nagreement with Saio's results. \n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% III. Rotational Modes of Non-isentropic.... %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\section{Rotational Modes of Slowly Rotating Non-isentropic Stars}\n\n\nBecause it is believed that \nisentropic structure is a good approximation for young and hot neutron stars,\nin this study we concentrate our attention to the case that \nthe deviation of the non-isentropic models from isentropic structure \nis sufficiently small.\nIn this case, we may assume that the adiabatic exponent $\\Gamma$ is given by\n% \n\\begin{eqnarray} \n\\frac{1}{\\Gamma} = \\frac{n}{n+1} + \\gamma \\, ,\n\\label{def-gamma}\n\\end{eqnarray}\n%\nwhere $\\gamma$ is a constant giving the deviation from the isentropic structure.\nBy substituting equation (\\ref{def-gamma}) into equation (\\ref{def_A}), \nwe obtain an explicit form of $A_i$ as:\n%\n\\begin{eqnarray}\nA_i &=& - \\, \\gamma \\, \\nabla_i \\ln p \\, .\n\\end{eqnarray}\n%\nIn this study, we only consider oscillations of polytropic models with the index $n=1$.\nPositive and negative values of $\\gamma$ are respectively for convective and radiative\nmodels.\nIsentropic models are given by $\\gamma=0$.\nSince our formulation for stellar oscillations of rotating stars is \naccurate only up to the order of $\\bar{\\Omega}^3$, we shall apply our method \nto the oscillation modes in the range of $\\bar\\Omega\\le 0.1$.\n \n\nFor convenience of later discussions, it may be useful to review\nthe properties of $r$-modes and inertial modes\nof isentropic models with $\\gamma=0$ (see, e.g., Yoshida \\& Lee 2000). \nBecause of \nthe asymptotic behavior of the eigenfrequency of the rotational modes\nin the limit of $\\Omega\\rightarrow 0$, it is \nconvenient to introduce a non-dimensional frequency $\\kappa$ as follows:\n%\n\\begin{equation}\n\\frac{\\omega}{\\Omega} = \\kappa \\, . \\label{def-kappa}\n\\end{equation}\n%\nSince the rotational deformation is of the order of $\\bar\\Omega^2$,\nthe effects on the frequency of the rotational modes appear as the terms of \nthe order of $\\bar\\Omega^3$. \nTherefore, we may expand the dimensionless \neigenfrequency $\\kappa$ of the rotational modes in powers of $\\bar\\Omega$ as follows: \n%\n\\begin{equation}\n\\kappa = \\kappa_0 + \\kappa_2 \\, \\bar{\\Omega}^2 \n + O(\\bar{\\Omega}^4) \\, , \\label{def-kappa0}\n\\end{equation}\n%\nwhere\n%\n\\begin{equation}\n\\kappa_0 = \\frac{2 m}{l'(l'+1)} \\, \n\\label{r-fre}\n\\end{equation}\n%\nfor the $r$-modes associated with the indices \n$l'$ and $m$ of vector harmonics with the axial \nparity (see, e.g. Papaloizou \\& Pringle 1978).\nFor the inertial modes, there is no analytic expression for $\\kappa_0$ in general.\n\n\n\nAs suggested by Provost et al. (1981) and Saio (1982),\nthe $r$-mode associated with $l'=|m|$\nhaving the nodeless eigenfunction $T_{l'}(r)$ is the only $r$-mode permitted\nfor isentropic stars for a given $m$.\nIn the limit of $\\Omega\\rightarrow 0$, we have \n$\\kappa\\rightarrow\\kappa_0=2m/l'(l'+1)$.\nAmong the expansion coefficients of the eigenfunctions \nthe toroidal component $T_{l'=|m|}$ is dominating.\nFor the inertial modes,\nthe value of $\\kappa$ in the limit of $\\Omega\\rightarrow 0$\nis also finite but different from \n$\\kappa_0 = {2 m}/{l'(l'+1)}$. \n\nThe inertial modes are characterized by the two angular \nquantum numbers $l_0$ and $m$, where the value of $l_0$ is \nthe maximum index $l$ of spherical harmonics associated with \nthe dominant expansion coefficients \nof the eigenfunctions (see Lockitch \\& Friedman 1999, Yoshida \\& Lee 2000). \nNote that our definition of $l_0$ is not the same as that of Lockitch \\& \nFriedman (1999), but the same as that of Lindblom \\& Ipser (1998) and \nYoshida \\& Lee (2000).\nNote also that odd (even) parity modes have odd (even) values\nof $l_0-|m|$, and that\nthe odd parity mode having $l_0-|m|=1$ is the $r$-mode associated with $l'=|m|$.\nThe value of $\\kappa_0$ for the inertial modes depends not only on the\nindices $m$ and $l_0$, but also on the equilibrium structure \nof stars (e.g., Yoshida \\& Lee 2000). \nFor given values of $l_0$ and $m$, the number of different inertial modes is\nequal to $l_0 - \\vert m\\vert(\\ge 2)$. \nHowever, there seems to be no good quantum number to classify the different inertial\nmodes associated with the same $l_0$ and $m$.\nWe here introduce an ordering integer $n$ to use the labellings such as \n$i_n$ and $\\omega_n$ for these inertial modes.\nSince the frequencies of the inertial modes with the same $l_0$ and $m$\nare found in a sequence given by, in the case of $m>0$,\n%\n\\begin{equation}\n\\omega_{-(l_0 - \\vert m\\vert-1)/2} < \\cdots < \\omega_{-1} < 0 \\leq \n\\omega_{0} < \\omega_{1} < \\cdots < \n\\omega_{(l_0 - \\vert m\\vert-1)/2}\\, \n\\end{equation}\n% \nfor odd parity modes, and\n%\n\\begin{equation}\n\\omega_{-(l_0 - \\vert m\\vert)/2} < \\cdots < \\omega_{-1} < 0 < \n\\omega_{1} < \\cdots < \n\\omega_{(l_0 - \\vert m\\vert)/2}\\, \n\\end{equation}\n%\nfor even parity modes, we may define \nthe ordering number $n$ as an integer that satisfies\nthe inequality $|l_0-|m|-1|/2\\ge |n| \\ge 0$ for odd parity inertial modes, and\n$|l_0-|m||/2\\ge |n| >0$ for even parity inertial modes\n(see Lockitch \\& Friedman 1998, Yoshida \\& Lee 2000).\nWe apply this classification to the inertial modes of both isentropic and \nnon-isentropic stars in the following discussions.\n\n\n\n\\subsection{$r$-modes}\n\n\n\nFor the radiative models, all the\n$r$-modes associated with $l'\\ge |m|$ are possible for a given $m$, \nand there are in principle \na countable infinite number of $r$-modes for given $l'$ and $m$. \nThe $r$-modes with the same $l'$ and $m$ may be classified by counting\nthe number of nodes\nof the axial components $T_{l'}$ in the radial direction.\nFor them the values of $\\kappa_2$ are different, but the values of $\\kappa_0$\nare the same and equal to $2m/l'(l'+1)$.\nIt is important to note that this classification \nof the $r$-modes is applicable only in the limit of $\\bar\\Omega\\rightarrow 0$\nand $\\kappa\\rightarrow \\kappa_0=2m/l'(l'+1)$, \nsince \nthe components associated with the other values of $l'$ will come into play \nfor large $\\bar\\Omega$\n(see, e.g. Provost et al. 1981, Saio 1982).\nLet us introduce an integer $k$ to denote\nthe number of nodes of the toroidal eigenfunction $T_{l'}$,\nwhere the node at the center of the \nstar is excluded from the count.\nThen, the $r$-modes are \ncompletely specified by the three quantum numbers $m$, $l'$ and $k$. \nIn this paper, for given $l'$ and $m$,\nwe employ the notation of $r_k$ to denote the $r$-mode whose \ntoroidal eigenfunction $T_{l'}(r)$ has $k$ nodes in the radial direction.\n\n\nIn Figures 1 to 3, the dimensionless eigenvalues $\\kappa$ are given versus \n$\\bar{\\Omega}$ for several \nlow-radial-order $r$-modes with $m=1$, 2, and 3\nfor the $n=1$ polytropic model with $\\gamma=-10^{-4}$, where\nthe $r$-modes with $l'= |m|$, $l'= |m| + 1$ and \n$l'= |m| + 2$ are given in each figure.\nModes with $l'= |m| + 1$ \nare even parity modes, and those with $l'=|m|$ and $l'=|m|+2$ are odd parity modes. \nIn the figures, the eigenvalues $\\kappa$ of the $i_0$-modes with $l_0=|m|+2 k+1$,\ncalculated at $\\bar{\\Omega}=0.1$ \nfor the $n=1$ isentropic model, are designated by\nthe filled circles, where the integer $k$ corresponds to the number in the subscript \nof the notation $r_k$.\nFigures 1 to 3 clearly show that\nthe qualitative behavior of the eigenfrequencies as functions of $\\bar\\Omega$\nis not strongly dependent on the azimuthal quantum number $m$. \nFrom these figures we also understand that\nthe $r$-modes of the radiative model with $\\gamma < 0$\nare divided into three distinctive classes according to the asymptotic \nbehavior of the eigenvalues at large $\\bar\\Omega$.\n%\nThe first class of the $r$-modes consists of the nodeless $r_0$-modes \nassociated with $l'=|m|$. \nThe eigenvalue $\\kappa$ of the $r$-modes of this class is well approximated by \nequations (17) and (18) at any values of $\\bar\\Omega$ examined in this paper.\nNote that the $r_0$-mode with $m=l'=1$ is a \npeculiar mode in the sense that $\\kappa$ is almost constant since\n$\\kappa_2=0$ and $\\kappa=\\kappa_0+O(\\bar\\Omega^4)$ (see Saio 1982, Greenspan 1964). \n%\nThe second class consists of the $r_k$-modes with \n$l'=\\vert m \\vert$ and $k>0$. \nEquations (\\ref{def-kappa0}) and (\\ref{r-fre}) can give good values for \nthe eigenvalue $\\kappa$ of the $r$-modes of this class\nonly when $\\bar{\\Omega}$ is sufficiently small.\nAs $\\bar\\Omega$ increases, $\\kappa$ tends to\nthe $i_0$ inertial modes with $l_0=|m|+2 k+1$ of the isentropic model. \nNote that the $i_0$-modes are odd parity inertial modes \n(see equations (19) and (20)).\nWe therefore consider that at large $\\bar\\Omega$ \nthe $r_k$-modes of this class become\nidentical with the $i_0$-modes with $l_0=|m|+2 k+1$, for which $\\kappa$\nis almost constant.\n%\nThe third class of the $r$-modes consists of the $r_k$-modes with \n$l' > \\vert m \\vert$ and $k\\ge0$.\nThe eigenvalue $\\kappa$ of the $r$-modes of this class is well represented by\nequations (17) and (18) only when $\\bar\\Omega$ is sufficiently small, and\nit becomes small monotonically as $\\bar\\Omega$ increases.\nThe $r$-modes of this class may have no corresponding inertial modes\nof the isentropic model.\n\n\nAs proved by Friedman \\& Schutz (1978), oscillation modes whose frequency $\\sigma$\nobserved in an inertial frame\nsatisfies the condition $\\sigma(\\sigma+m\\Omega)=\\sigma\\omega<0$ \nare unstable to the gravitational radiation reaction. \nThe condition for the instability\nmay be rewritten as $0 < \\kappa < m$ for retrograde modes with $\\omega>0$ and $m>0$. \nFigures 1 to 3 show that the $r$-mode with $l'\\geq2$ \nsatisfies the inequality $0 < \\kappa < m$ for the range of $\\bar\\Omega$\nexamined in this paper.\nIt is also found that the $r_k$-modes with $l'=1$ \nand $k>0$ also satisfy the inequality $0 < \\kappa < m$ for $\\bar\\Omega>0$.\nThe reason for the instability of the $r_k$-modes with $l'=1$ and $k>0$ may be\nunderstood by noting that the \npolar components with the index $l=2$ can be responsible for the emission \nof gravitational radiation. \nWe may conclude that the $r_0$-mode with $l'=\\vert m\\vert=1$ is \nthe only $r$-mode that is stable against \nthe gravitational radiation reaction. \n \n\n \nIn Figure 4, the eigenfrequencies $\\kappa$ of three $r$-modes with $m=2$\nare plotted as functions of $|\\gamma|$, where\nwe have assumed $\\bar\\Omega=0.01$. \nThe three modes are respectively the $r_0$-mode with $l'=m=2$, \nthe $r_1$-mode with $l'=m=2$, and the $r_0$-mode with $l'=3$ and $m=2$.\nThese three $r$-modes belong to the first, second, and third classes of the $r$-modes\ndiscussed in the previous paragraph.\nThe solid lines and the dotted \nlines are used to denote the cases of negative and positive $\\gamma$, \nrespectively.\nNote that although we can obtain the three $r$-modes without any difficulty\nfor the radiative models with negative $\\gamma$, \nwe cannot always calculate the $r$-modes of the second and the third classes\nfor the convective models with positive $\\gamma$.\nLet us first discuss the case of the radiative models.\nAs shown by Figure 4, the eigenvalue $\\kappa$ of the $r_0$-mode with $l'=|m|=2$ \nis practically independent of $|\\gamma|$ and has values approximately equal to\n$\\kappa_0=2m/l'(l'+1)=2/3$.\nHowever, $\\kappa$ of the $r_1$-mode with $l'=|m|=2$ \nis dependent on $|\\gamma|$.\nAt small $|\\gamma|$, the $r_1$-mode has the eigenvalue close to $\\kappa_0=0.517$, \nwhich corresponds to \nthe inertial mode with $l_0-\\vert m \\vert = 3$ of the isentropic model, but \nit tends to $2m/l'(l'+1)=2/3$ as $|\\gamma|$ increases.\nThe $r_0$-mode with $l'=3$ and $m=2$ also has the eigenfrequency $\\kappa$\nwhich depends on $|\\gamma|$.\nAlthough the value of $\\kappa$ is close to $\\kappa_0=2m/l'(l'+1)=1/3$ \nat large $|\\gamma|$, it tends to zero as $|\\gamma|\\rightarrow 0$.\nThis behavior of $\\kappa\\rightarrow 0$ in the limit of $|\\gamma|\\rightarrow 0$\nis consistent with the fact that the $r$-modes associated with \n$l'> \\vert m\\vert$ do not exist in isentropic stars, for which $\\gamma=0$. \nLet us next discuss the case of the convective models with $\\gamma>0$.\nThe eigenvalue $\\kappa$ of the $r_0$-mode with $l'=|m|=2$ is only weakly dependent on\n$\\gamma$, as in the case of the radiative models.\nNote that the curves for the $r_0$-mode with $l'=|m|=2$ for negative and positive $\\gamma$\nare almost indistinguishable in Figure 4.\nThe $r_1$-mode with $l'=|m|=2$ for the convective models behaves differently than \nthat for the radiative models as $|\\gamma|$ increases.\nIn fact, the value of $\\kappa$ decreases\nrapidly with increasing $\\gamma$ and \nthe $r_1$-mode cannot be found at large values of $\\gamma>0$.\nNo $r_0$-mode with $l'=3$ and $m=2$ are found for the convective models.\n\n\n\nLet us discuss the properties of the eigenfunctions of the $r$-modes \nfor the radiative models.\nSince the amplitude of the displacement vector\nis much larger than that of the scalar perturbations, in the following discussions\nwe may show only the displacement vector of the modes.\nIn Figures 5 to 7, we show the expansion coefficients \n$S_l$, $H_l$ and ${\\it i} T_{l'}$ as functions of the fractional radius $a/R$\nfor the $r$-modes with $m=2$, where we have assumed $\\gamma=-10^{-4}$, and\nthe amplitude is normalized at the surface such that $iT_{l'}=1$. \nHere, $l=|m|$ and $l'=l+1$ for even modes, and $l=|m|+1$ and $l'=l-1$ for odd modes.\nThe modes given in Figures 5 to 7 are respectively\nthe $r_0$-mode with $l'=2$, the $r_1$-mode with $l'=2$, and the $r_0$-mode with $l'=3$. \nIn each figure, the eigenfunctions for the cases of \n$\\bar{\\Omega}= 10^{-3}$ and $\\bar{\\Omega}= 10^{-1}$ \nare shown in panels $(a)$ and $(b)$, respectively. \nThe panels $(a)$ of Figures 5 to 7 show that \nthe toroidal component $iT_{l'}$ of the $r$-modes is dominating the other expansion \ncoefficients when $\\bar\\Omega$ is small. \nHowever, as shown by the panels (b), although $iT_{l'}$\nof the $r_0$-mode with $l'=2$ remains dominant even at \n$\\bar{\\Omega}= 0.1$, the toroidal components $iT_{l'}$\nof the $r_1$-mode with $l'=2$ and the $r_0$-mode with $l'=3$\nare not necessarily dominating any more at $\\bar{\\Omega}= 0.1$.\nThe properties of the eigenfunctions of the $r_1$-mode with $l'=m=2$ \nat large $\\bar\\Omega$ may be regarded as those of the inertial modes. \n%\nIt is interesting to note that\nthe displacement vector of the $r_0$-mode with $l'=3$ has large amplitude \nin the deep interior and almost vanishing amplitude near the stellar \nsurface at large $\\bar\\Omega$. \nThis suggests that because of the low frequencies $\\omega$ in the corotating frame\nthe buoyant force is as important as the Coriolis force to determine the\nmode character at large $\\bar\\Omega$.\n \n\n\\subsection{Inertial modes}\n\n\nFor the radiative models with the polytropic index $n=1$ and $\\gamma = -10^{-4}$,\nthe eigenfrequencies $\\bar{\\omega}\\equiv\\omega/(GM/R^3)^{1/2}$ \nof low frequency oscillations\nare shown as functions of $\\bar\\Omega$\nfor $m=1$, 2, and 3 in Figures 8 to 10,\nwhere even and odd parity modes are displayed in panels (a) and (b), respectively.\nThe straight dashed lines drawn in the figures are given by\n$\\bar{\\omega}=0$ and $\\bar{\\omega}= m \\bar{\\Omega}$ (see below).\nIn the figures, the inertial modes of the $n=1$ isentropic model \ncomputed at $\\bar\\Omega=0.1$ are designated by the filled circles.\nWe note that the oscillation modes in a mode sequence\nare regarded as inertial modes when $\\bar\\Omega$ is large, and\nas internal gravity ($g$-) modes when $\\bar\\Omega$ is small.\nIf we follow one of the continuous mode sequences from large $\\bar\\Omega$ \nto small $\\bar\\Omega$,\nwe may physically understand the behavior of the low frequency oscillation \nin the radiative models as a function of $\\bar\\Omega$.\nAt large $\\bar\\Omega$, the Coriolis force is dominating as the restoring force\nand the oscillation mode is identified as an inertial mode.\nAs $\\bar\\Omega$ decreases, however, the buoyant force \nbecomes dominating the Coriolis force\nand the mode becomes identical with a $g$-mode \nin the limit of $\\bar\\Omega\\rightarrow 0$.\nBecause of the effects of the buoyant force in the radiative model,\nthe frequency $\\bar\\omega$ of the inertial modes deviates from that\nof the inertial modes of the isentropic model as $\\bar\\Omega$ decreases.\n\n\nThe modes within the two straight dashed lines depicted in Figures 8, 9 \nand 10 are\nunstable against the gravitational radiation driven instability \nin the sense that they satisfy the frequency condition\n$\\sigma(\\sigma+m\\Omega) < 0$ (Friedman \\& Schutz 1978).\nWe can see from Figure 8 that the $i_k$-modes with $k\\neq0$ and \n$m=1$ are stable against the instability for all $\\bar{\\Omega}$. \nFigures 9 and 10 show that as $\\bar\\Omega$ increases\nall the retrograde $g$-modes with $|m|\\geq 2$, which are stable \nagainst the instability when $\\bar\\Omega\\sim0$, \nbecome retrograde inertial modes, which are unstable against the instability \nat large $\\bar{\\Omega}$.\n\n\n\nThere are several cases where we find it practically impossible to\nobtain completely continuous mode sequences \nbetween the $g$-modes at small $\\bar\\Omega$ and\nthe inertial modes at large $\\bar\\Omega$.\nIn such sequences, there exist a domain of $\\bar\\Omega$, in which \nthere appear a lot of modes having a large number of nodes\nof the dominant expansion coefficients, and it is difficult to identify the\nsame oscillation modes as those computed in the previous steps in $\\bar\\Omega$.\nIn Figures 8 to 10, the domains of $\\bar\\Omega$ with this difficulty are indicated by\nthe dotted lines in the mode sequences.\nUnfortunately, we cannot remove the difficulty by increasing $k_{max}$.\nOne of the reasons for the difficulty may be attributed to the method of\ncalculation we employ in this paper.\nAs discussed in Unno et al (1989), since we have truncated \nthe infinite system of differential equations to obtain a finite system of equations,\nthe numerical procedure used here inevitably contains\na process of inverting matrices which are singular at some value of the ratio\n$2\\Omega/\\omega\\sim 1$, depending on the oscillation mode we are interested in.\nIn this paper, we assume that there always exist a continuous mode sequence\nbetween the $g$-mode and inertial mode as a function of $\\bar\\Omega$, \neven if the mode sequence contains\na domain of $\\bar\\Omega$ in which the modes we are interested in cannot be\nobtained numerically.\n\n\n\\subsection{Connection rules between the $g$-modes, $r$-modes and inertial modes}\n\n\n\nIn order to find \nthe connection rule between the $g$-modes at small $\\bar\\Omega$ and \nthe inertial modes at large $\\bar\\Omega$, we tabulate first the\nfrequencies of the $g$-modes at $\\bar\\Omega=0$ \nfor the radiative model with the index $n=1$ and $\\gamma=-10^{-4}$ in Table 2.\nTo obtain a clear understanding of the global correspondence between \nthe $g$-, $r$-, and inertial modes, with the help of Table 2 and Figures 8 to 10, \nwe give schematic diagrams\nfor the connection rules between the several low-radial-order modes as follows: \n\n\\noindent\nFor odd parity modes we have\n%\n\\begin{eqnarray}\n\\footnotesize\n&\\left[\n\\begin{array}{llll}\n & & &\\cdots\\\\\n & &\ni_{2\\phm{-}}(l_0=\\vert m\\vert+5)&\\cdots\\\\ \n &i_{1\\phm{-}}(l_0=\\vert m\\vert+3)&\ni_{1\\phm{-}}(l_0=\\vert m\\vert+5)&\\cdots\\\\\ni_{0\\phm{-}}(l_0=\\vert m\\vert +1)&i_{0\\phm{-}}(l_0=\\vert m\\vert+3)&\ni_{0\\phm{-}}(l_0=\\vert m\\vert+5)&\\cdots\\\\ \n &i_{-1}(l_0=\\vert m\\vert +3) &\ni_{-1}(l_0=\\vert m\\vert +5) &\\cdots\\\\\n & &\ni_{-2}(l_0=\\vert m\\vert +5) &\\cdots\\\\\n & & &\\cdots\\\\\n\\end{array} \n\\right]& \\label{ina-odd}\\\\\n& & \\nonumber\\\\\n&\\Updownarrow& \\nonumber\\\\\n& & \\nonumber\\\\\n&\\left[\n\\begin{array}{llll}\n & & &\\cdots\\\\\n & &g_{1\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert+3)&\\cdots\\\\ \n &g_{1\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert+1)&\ng_{2\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert+1)&\\cdots\\\\\nr_{0\\phm{-}}(l'_{\\phm{0}}=\\vert m\\vert)\\phm{+1}& \nr_{1\\phm{-}}(l'_{\\phm{0}}=\\vert m\\vert)\\phm{+3}&\nr_{2\\phm{-}}(l'_{\\phm{0}}=\\vert m\\vert)\\phm{+5}&\\cdots\\\\\n &g_{-1}(l_{\\phm{0}}=\\vert m\\vert+1)&\ng_{-2}(l_{\\phm{0}}=\\vert m\\vert+1)&\\cdots\\\\\n & &g_{-1}(l_{\\phm{0}}=\\vert m\\vert+3)&\\cdots\\\\\n & & &\\cdots\\\\\n\\end{array}\n\\right]& \\ , \\label{gra-odd}\n\\end{eqnarray}\n%\nand for even parity modes we have\n%\n\\begin{eqnarray}\n\\footnotesize\n&\\left[\n\\begin{array}{llll}\n & & &\\cdots\\\\\n & &i_{3\\phm{-}}(l_0=\\vert m\\vert+6)&\\cdots\\\\ \n &i_{2\\phm{-}}(l_0=\\vert m\\vert+4)&\ni_{2\\phm{-}}(l_0=\\vert m\\vert+6)&\\cdots\\\\\ni_{1\\phm{-}}(l_0=\\vert m\\vert+2)&i_{1\\phm{-}}(l_0=\\vert m\\vert+4)&\ni_{1\\phm{-}}(l_0=\\vert m\\vert+6)&\\cdots\\\\\ni_{-1}(l_0=\\vert m\\vert+2) &i_{-1}(l_0=\\vert m\\vert+4) &\ni_{-1}(l_0=\\vert m\\vert+6)&\\cdots\\\\\n &i_{-2}(l_0=\\vert m\\vert+4) &\ni_{-2}(l_0=\\vert m\\vert+6)&\\cdots\\\\\n & &i_{-3}(l_0=\\vert m\\vert+6)&\\cdots\\\\\n & & &\\cdots\\\\\n\\end{array} \n\\right]& \\label{ina}\\\\\n& & \\nonumber\\\\\n&\\Updownarrow& \\nonumber\\\\\n& & \\nonumber\\\\\n&\\left[\n\\begin{array}{llll}\n & & &\\cdots\\\\\n & &g_{1\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert+4) &\\cdots\\\\ \n &g_{1\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert+2)&\n g_{2\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert+2)&\\cdots\\\\\ng_{1\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert)\\phm{+2}& \ng_{2\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert)\\phm{+4}&\ng_{3\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert)\\phm{+6}&\\cdots\\\\\ng_{-1}(l_{\\phm{0}}=\\vert m\\vert)\\phm{+2} & \ng_{-2}(l_{\\phm{0}}=\\vert m\\vert)\\phm{+4} &\ng_{-3}(l_{\\phm{0}}=\\vert m\\vert)\\phm{+6} &\\cdots\\\\\n &g_{-1}(l_{\\phm{0}}=\\vert m\\vert+2) &\n g_{-2}(l_{\\phm{0}}=\\vert m\\vert+2) &\\cdots\\\\\n & &g_{-1}(l_{\\phm{0}}=\\vert m\\vert+4) &\\cdots\\\\\n & & &\\cdots\\\\\n\\end{array}\n\\right]& \\ , \\label{gra}\n\\end{eqnarray}\n%\nwhere the two corresponding modes occupy the same position \nin the two matrices connected with an arrow. \n\n\nFrom the diagrams,\nwe may find the connection rule between the $g_{\\pm k}$-modes with $l$ and $m$ and \nthe inertial modes $i_{\\pm j}$ with $l_0$ and $m$: \n\\begin{equation}\ng_{\\pm k}(l=l^j)\\longleftrightarrow i_{\\pm j}(l_0=l^j+2k), \\label{g-i}\n\\end{equation}\nwhere $l^j=|m|+2j-2$ for even modes and $l^j=|m|+2j-1$ for odd modes,\nand $j$ and $k$ are positive integers.\n%\nThe symbol $g_{\\pm k}$ denotes the $g$-mode\nwith $k$ radial nodes of the expansion coefficient $S_l$, \nhaving positive and negative frequencies $\\omega$\nobserved in the corotating frame of the star when $\\bar\\Omega\\not=0$.\n\n\nThe connection rule between the $r$-modes\nassociated with $l'=|m|$ and the inertial modes $i_0$ with $l_0$ and $m$ may be given by\n%\n\\begin{equation}\nr_{j-1} ( l' = \\vert m \\vert ) \\longleftrightarrow i_0 \n(l_0 = |m| + 2 j -1) \\, ,\n\\label{r-i-odd}\n\\end{equation}\n%\nwhere $j$ is a positive integer.\nNote that the \n$i_0$-mode with $l_0 = \\vert m \\vert +1$ is exactly the same as \nthe $r_0$-modes with $l'=\\vert m \\vert$. \nTo establish the connection rules given above, we have neglected the effects of\navoided crossings between the modes associated with different values of $l$ and/or $k$, since\nthe mode property is carried over at the crossings.\n\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% V. DISSIPATION TIMESCALES ..... %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\section{Dissipation Timescales for $r$-modes of Non-isentropic Stars}\n\n\nFor the rotational modes of non-isentropic models, we have found that\nall the $r$-modes except the $r_0$-mode with $l'=|m|=1$ \nare unstable to the gravitational radiation reaction \nin the sense that the frequency $\\sigma$ satisfies the condition \n$\\sigma(\\sigma+m\\Omega)<0$.\nLet us determine the stability of the $r$-modes of the non-isentropic models\nagainst the gravitational radiation driven instability, taking account of\nthe dissipative processes due to the shear and bulk viscosity, where\nwe will follow the method of calculation almost the same as that employed\nin the previous stability analyses of the $r_0$-mode with $l'=|m|$ and the\ninertial modes for isentropic models\n(Lindblom et al 1998, Owen et al 1998, Andersson et al 1998, \nKokkotas \\& Stergioulas 1998, Lindblom et al 1999, Lockitch \\& Friedman 1999,\nYoshida \\& Lee 2000).\n\n\n\n\n\nThe damping timescale of the $r_0$-mode associated with $l'=|m|$\nfor sufficiently small $\\bar{\\Omega}$ may be estimated by (Lindblom et al 1998)\n%\n\\begin{eqnarray}\n\\frac{1}{\\tau} &=& \\frac{1}{\\tilde \\tau_S} \\left( \\frac{10^9 K}{T} \\right)^2\n+ \\frac{1}{\\tilde \\tau_B} \\left( \\frac{T}{10^9 K} \\right)^6\n\\left( \\frac{\\Omega^2}{\\pi G \\bar{\\rho}} \\right) \\nonumber \\\\\n&+& \\sum_{l=2}^{\\infty} \\frac{1}{\\tilde \\tau_{J,l}} \n\\left( \\frac{\\Omega^2}{\\pi G \\bar{\\rho}} \\right)^{l+1}\n+ \\sum_{l=2}^{\\infty} \\frac{1}{\\tilde \\tau_{D,l}} \n\\left( \\frac{\\Omega^2}{\\pi G \\bar{\\rho}} \\right)^{l+2} \\, ,\n \\label{tau2}\n\\end{eqnarray}\n%\nwhere $\\bar{\\rho}$ is the average density of the star.\nThe dissipative timescales $\\tilde\\tau$ are calculated for each oscillation mode\nin the limit of $\\bar\\Omega\\rightarrow 0$ so that\nthey are independent of the rotation frequency $\\Omega$.\nHere, the first, second, third and fourth terms in the right-hand side of \nequation (\\ref{tau2}) are contributions from the shear viscosity, \nthe bulk viscosity, the current multipole radiation and the mass \nmultipole radiation, respectively. \nThe expression (\\ref{tau2}) of the damping timescales has been derived on the assumptions that\nthe frequency of the modes is well represented by a linear function of $\\Omega$ and the\ntoroidal component of the displacement vector is dominating.\nAlthough the assumptions are reasonable for the $r_0$-modes with $l'=|m|$ \n(see Yoshida and Lee 2000),\nthey are not necessarily correct for the $r_k$-modes with $l'=|m|$ and $k>0$, \nfor which we use\n%\n\\begin{eqnarray}\n\\frac{1}{\\tau} &=& \\frac{1}{\\tilde \\tau_S} \\left( \\frac{10^9 K}{T} \\right)^2\n+ \\frac{1}{\\tilde \\tau_B} \\left( \\frac{T}{10^9 K} \\right)^6\n\\left( \\frac{\\pi G \\bar{\\rho}}{\\Omega^2} \\right) \\nonumber \\\\\n&+& \\sum_{l=2}^{\\infty} \\frac{1}{\\tilde \\tau_{J,l}} \n\\left( \\frac{\\Omega^2}{\\pi G \\bar{\\rho}} \\right)^{l+1}\n+ \\sum_{l=2}^{\\infty} \\frac{1}{\\tilde \\tau_{D,l}} \n\\left( \\frac{\\Omega^2}{\\pi G \\bar{\\rho}} \\right)^{l+2} \\, ,\n \\label{tau2b}\n\\end{eqnarray}\n%\nbecause these $r$-modes become inertial modes at large $\\bar\\Omega$.\nThe difference between these two expressions is found\nin the second terms in the right-hand side of the two equations. \nWhen $\\bar\\Omega$ is small, equation (\\ref{tau2b}) gives the correct \nexpression of $\\tau^{-1}$ for inertial modes of isentropic stars\n(See, Lockitch \\& Friedman 1999, Yoshida \\& Lee 2000).\nTo determine the damping timescales $\\tilde\\tau$ in (\\ref{tau2b}) in the limit of \n$\\bar\\Omega\\rightarrow 0$,\nwe assume that the dissipative timescale $\\tilde\\tau^{-1}$ \ndepends on $\\bar\\Omega$ as $a\\bar\\Omega^2+b$ for each dissipative process, where\nthe two unknown constants $a$ and $b$ are\ndetermined by calculating $\\tilde\\tau^{-1}$ and $d\\tilde\\tau^{-1}/d\\bar\\Omega$\nat $\\bar\\Omega=0.1$.\nThe $\\tilde\\tau^{-1}$ in the limit of $\\bar\\Omega\\rightarrow0$ is given by\n$\\tilde\\tau^{-1}=b$.\nWe note that equation (\\ref{tau2b}) is not necessarily a correct approximation for \nnon-isentropic stars. \nWe use the expression (\\ref{tau2b}) simply \nbecause we want to give rough \nestimates of the dissipative timescales, in order to compare the timescales \nwith those of the isentropic case.\n\n \nIn Table 3, we tabulate the dissipation timescales $\\tilde\\tau$ in the unit of second for \nthe various dissipative processes for the $r_k$-modes with $l'=\\vert m \\vert$, \nwhere the radius and the mass of the $n=1$ polytropic neutron star model\nat $\\Omega=0$ are chosen to be $R=12.57\\mbox{km}$ and $M=1.4M_{\\sun}$, \nrespectively. \nNote that in Table 3 we have not included the $r_k$-modes with $l'>|m|$,\nsince the frequency $\\omega$ becomes vanishingly small at large $\\bar\\Omega$ \n(see Figures 1 to 3) \nand hence the magnitude of the gravitational radiation driven\ninstability, which is proportional to $\\omega$, becomes quite small.\nFor the $r_0$-modes with $l'=|m|$,\nin order to see the effects of the buoyancy force on \nthe stability, the results for the four different values of $\\gamma$ are tabulated. \nAs shown by Table 3, the gravitational radiation driven instability \nfor the $r_0$-modes with $l'=\\vert m \\vert$ \nis not affected by introducing the deviation from isentropic structure and remains\nstrong even for the non-isentropic models.\nAs for the $r_k$-modes with $l'=|m|$ and $k> 0$, it is found that \nthe dissipative timescales are comparable to those of the corresponding inertial \nmodes (compare Table 4 of Yoshida \\& Lee 2000). Thus, we may conclude that the $r$-mode \ninstability driven by the gravitational radiation reaction is dominated by \nthe $r_0$-mode with $l'=\\vert m \\vert = 2$ both in isentropic and in non-isentropic stars. \n\n\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% CONCLUSIONS %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\section{Conclusions}\n\n \nIn this paper, we have numerically investigated the properties of rotational \nmodes for slowly rotating, \nnon-isentropic, Newtonian stars, where the effects of \nthe centrifugal force are taken into consideration to calculate the modes\nwith accuracy up to the order of $\\bar\\Omega^3$.\nEstimating the dissipation timescales due to the \ngravitational radiation and the shear and bulk viscosity\nfor simple polytropic neutron star models with the index $n=1$,\nwe have shown that the gravitational radiation driven instability\nof the $r_0$-mode with $l'=|m|$ is hardly \naffected by introducing the deviation from the\nisentropic structure, and that the instability of the $r_0$-modes with $l'=|m|=2$\nremains strongest even for the non-isentropic models.\nNote that the $r_0$-modes with $l'=|m|$ are the only $r$-modes possible in\nisentropic stars and their modal property does not very much depend on $\\Omega$ and \nthe deviation from isentropic structure.\nWe thus conclude that \nthe result of the stability analysis of the $r_0$-modes with $l'=|m|$\nfor isentropic stars remains valid even for non-isentropic stars.\n\n\nWe have numerically found that for the radiative models\nthe inertial modes at large $\\bar\\Omega$ \nbecome identical with the $r_k$-modes with $l'=|m|$ and $k>0$ and $g$-modes\nin the limit of $\\bar\\Omega\\rightarrow 0$ because of the effect of the buoyant force, \nwhere the integer $k$ denotes the number of node of the \neigenfunction with dominant amplitude.\nThis behavior of the $g$-modes or the inertial modes as functions of $\\Omega$\nhas been suggested by, for example,\nSaio (1999) and Lockitch \\& Friedman (1999).\nWe find the connection rules between the $r_k$-modes with $l'=|m|$ and $k>0$ and\n$g$-modes at small $\\bar\\Omega$ and\nthe inertial modes at large $\\bar\\Omega$.\nWe also suggest that the $r_k$-modes with $l'>|m|$ and $k\\ge 0$, \nwhose frequency in the corotating frame\nbecomes vanishingly small as $\\bar\\Omega$ increases, \nhave at large $\\bar\\Omega$ no corresponding inertial\nmodes of the isentropic models.\n\n\nGood progress has been made in the understanding of\nthe properties of the $r$-mode instability \ndue to the gravitational radiation since its discovery.\nRecently, for example, Yoshida et al (1999) have shown that the results \nof the $r$-mode instability obtained by using the slow rotation approximation,\nas employed in this paper,\nare consistent with the results obtained \nby calculating directly the $r$-mode oscillations \nof rotating stars without the approximation. \nKojima (1998) and Kojima \\& Hosonuma (1999) have studied the time evolutional \nbehavior of $r$-modes by using the Laplace transformation technique\nfor slowly rotating relativistic models. \nLockitch (1999) also obtained $r$-modes and \nrotation modes for slowly rotating, incompressible, relativistic stars. \nHowever, we believe it necessary to show\nthat the gravitational radiation driven instability\nof $r$-modes remains sufficiently robust in more realistic and unrestricted situations,\ntaking account of the effects of differential rotation, magnetic field \nand general relativity, for example.\nTo investigate the $r$-mode instability in more general situations is one of\nour future studies.\n\n\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% END OF MAIN BODY OF PAPER %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\acknowledgements\n\n\nWe would like to thank Prof. H. Saio for useful comments and discussions. \nS.Y. was supported by Research Fellowship of the Japan Society for \nthe Promotion of Science for Young Scientists. \n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% BIBLIOGRAPHY %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{thebibliography}{}\n\n\\bibitem[Andersson 1998]{nils97}\n Andersson, N. 1998, \\apj, 502, 708\n%\n\\bibitem[Andersson et al.\\ 1998]{aks98}\n Andersson, N., Kokkotas, K., \\& Schutz B. F. 1998, \\apj, 510, 846\n%\n\\bibitem[Berthomieu et al. 1978]{be78}\nBerthomieu, G., Gonczi, G., Graff, Ph., Provost, J., \\& Rocca, A. 1978, \n\\aap, 70, 597 \n%\n\\bibitem[Beyer \\& Kokkotas 1999]{bk99}\n Beyer, H. R., \\& Kokkotas, K. D. 1999, \\mnras, 308, 745\n%\n\\bibitem[Friedman \\& Morsink 1998]{jfs97} \n Friedman, J. L., \\& Morsink, S. M. 1998, \\apj, 502, 714\n%\n\\bibitem[Friedman \\& Schutz 1978]{fs87} \n Friedman, J. L., \\& Schutz, B. F. 1978, \\apj, 222, 281\n%\n\\bibitem[Greenspan 1964]{g64}\n Greenspan, H. P. 1964, The Theory of Rotating Fluids (Cambridge: Cambridge \nUniv. Press)\n%\n\\bibitem[Kojima 1998]{k98}\n Kojima, Y. 1998, \\mnras, 293, 49\n%\n\\bibitem[Kojima \\& Hosonuma 1999]{kh99}\n Kojima, Y., \\& Hosonuma, M. 1999, \\apj, 520, 788\n%\n\\bibitem[Kokkotas \\& Stergioulas 1998]{ks98}\n Kokkotas, K., \\& Stergioulas, N. 1998, \\aap, 341, 110\n%\n\\bibitem[Lee 1993]{l93}\n Lee, U. 1993, \\apj, 405, 359\n%\n\\bibitem[Lee \\& Saio 1986]{ls86}\n Lee, U., \\& Saio, H. 1986, \\mnras, 221, 365\n%\n\\bibitem[Lee \\& Saio 1997]{ls97}\n Lee, U., \\& Saio, H. 1997, \\apj, 491, 839\n%\n\\bibitem[Lee et al.\\ 1992]{lsvh92}\n Lee, U., Strohmayer, T. D., \\& Van Horn, H. M. 1992, \\apj, 397, 647\n%\n\\bibitem[Lindblom \\& Ipser 1998]{li98}\n Lindblom, L., \\& Ipser, J. R. 1998, \\prd, 59, 044009\n%\n\\bibitem[Lindblom et al.\\ 1999]{lmo99}\n Lindblom, L., Mendell, G., \\& Owen, B. J. 1999, \\prd, 60, 064006\n%\n\\bibitem[Lindblom et al.\\ 1998]{lom98}\n Lindblom, L., Owen, B. J., \\& Morsink, S. M. 1998, \\prl, 80, 4843\n%\n\\bibitem[Lockitch \\ 1999]{lo99}\n Lockitch, K. H. 1999, Ph.D. Thesis (University of Wisconsin-Milwaukee), \n(gr-qc/9909029) \n%\n\\bibitem[Lockitch \\& Friedman\\ 1999]{lf99}\n Lockitch, K. H., \\& Friedman J. L. 1999, \\apj, 521, 764\n%\n\\bibitem[Owen et al.\\ 1998]{o98}\n Owen, B. J., Lindblom, L., Cutler, C., Schutz, B. F., Vecchio, A., \\&\n Andersson, N. 1998, \\prd, 58, 084020\n%\n\\bibitem[Papaloizou \\& Pringle 1978]{pp78}\n Papaloizou, J., \\& Pringle, J. E. 1978, \\mnras, 182, 423\n%\n\\bibitem[Pedlosky 1987]{pe87}\n Pedlosky, J. 1987, Geophysical Fluid Dynamics, Second Edition \n(Berlin: Springer-Verlag)\n%\n\\bibitem[Press et al. 1992]{pr92}\n Press, W. H., Teukolsky, S. A., Vetterling, W. T., \\& Flannery, B. P. \n1992, Numerical Recipes: The Art of Scientific Computing, Second Edition \n(Cambridge: Cambridge Univ. Press)\n%\n\\bibitem[Provost et al. 1981]{pea81}\n Provost, J., Berthomieu, G., \\& Rocca, A. 1981, \\aap, 94, 126\n%\n\\bibitem[Regge \\& Wheeler 1957]{rw57}\n Regge, T., \\& Wheeler, J. A. 1957, Phys. Rev., 108, 1063\n%\n\\bibitem[Saio 1982]{s82}\n Saio, H. 1982, \\apj, 256, 717\n%\n\\bibitem[Saio 1999]{s99}\n Saio, H. 1999, private communication. \n%\n\\bibitem[Tassoul 1978]{t78}\n Tassoul, J.-L. 1978, Theory of Rotating Stars (Princeton: Princeton Univ.\nPress)\n%\n\\bibitem[Thorne 1980]{th80}\n Thorne, K. S. 1980, Rev. Mod. Phys., 52, 299\n%\n\\bibitem[Unno et al. 1989]{u89}\n Unno, W., Osaki, Y., Ando, H., Saio, H., \\& Shibahashi, H. 1989, \n Nonradial Oscillations of Stars, Second Edition (Tokyo: Univ. Tokyo Press) \n%\n\\bibitem[Yoshida et al 1999]{ykye99}\n Yoshida, S'i., Karino, S., Yoshida, S., \\& Eriguchi, Y. 1999, \n Submitted to \\mnras (astro-ph/9910532)\n%\n\\bibitem[Yoshida \\& Lee 2000]{yl00}\n Yoshida, S., \\& Lee, U. 2000, \\apj, in press. (astro-ph/9908197)\n%\n\\end{thebibliography}\n%\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% FIGURES %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\begin{figure}\n\\epsscale{.6}\n\\plotone{fig1.eps}\n\\caption{Dimensionless frequencies $\\kappa=\\omega/\\Omega$ for the\nlow-radial-order $r$-modes with $m=1$ are plotted as functions of the dimensionless \nangular rotation frequency $\\bar{\\Omega}=\\Omega/(GM/R^3)^{1/2}$, \nfor the $n=1$ polytropic model with $\\gamma=-10^{-4}$. \nThe solid, the dotted and the dashed curves are\nfor the $r_0$, $r_1$, and $r_2$-modes, respectively. \nThe attached label $l'$ \ndenotes the angular quantum number $l'$ associated with the spherical harmonic function\nrepresenting the toroidal component of the displacement vector.\nNote that the eigenvalue of the \n$r$-modes is given by $\\kappa_0=2 m/(l'(l'+1))$ in the limit of $\\bar\\Omega\\rightarrow 0$. \nThe filled circles at $\\bar{\\Omega}=0.1$ denote the eigenvalues $\\kappa$ of \nthe inertial modes calculated for the isentropic model \nwith the index $n=1$ and $\\gamma=0$ at $\\bar{\\Omega}=0.1$. }\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.6}\n\\plotone{fig2.eps}\n\\caption{Same as Figure 1, but for $m=2$.}\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.6}\n\\plotone{fig3.eps}\n\\caption{Same as Figure 2, but for $m=3$.}\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.6}\n\\plotone{fig4.eps}\n\\caption{Dimensionless frequencies $\\kappa$ for the low-radial-order \n$r$-modes with $m=2$ are plotted as functions of $|\\gamma|$ for the $n=1$ polytropic model \nat $\\bar{\\Omega}=10^{-2}$. \nThe attached label $l'$ denotes the index of the spherical harmonic function for \nthe toroidal component of the displacement vector.\nThe number of nodes of $iT_{l'}$ in the radial direction \nis indicated by the subscript in the notation $r_k$ attached to the mode sequences. \nThe solid line and the dotted line are given for negative \nand positive values of $\\gamma$, respectively.} \n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.4}\n\\plottwo{fig5a.eps}{fig5b.eps}\n\\caption{The first expansion coefficients $S_l$, $H_l$, $iT_{l'}$ for \nthe $r_0$ mode with $l'=m=2$ are plotted against $a/R$ for \nthe polytropic model with the index $n=1$ and $\\gamma=-10^{-4}$. \nPanels $(a)$ and $(b)$ are for the cases of\n$\\bar{\\Omega}=10^{-3}$ and $\\bar{\\Omega}=10^{-1}$, respectively. \nThe eigenfunctions are normalized so that $T_{l'}(a=R)=1$. \nThe attached labels $S_l$, $H_l$, and $iT_{l'}$ denote the expansion coefficients \nof the displacement vector.}\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.4}\n\\plottwo{fig6a.eps}{fig6b.eps}\n\\caption{Same as Figure 5, but for the $r_1$-mode with $l'=2$.}\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.4}\n\\plottwo{fig7a.eps}{fig7b.eps}\n\\caption{Same as Figure 5, but for the $r_0$-mode with $l'=3$.}\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.4}\n\\plottwo{fig8a.eps}{fig8b.eps}\n\\caption{Dimensionless frequencies \n$\\bar{\\omega}=\\omega/(GM/R^3)^{1/2}$ for the low-radial-order \n$g$- and inertial modes with $m=1$ are plotted as functions of \n$\\bar{\\Omega}=\\Omega/(GM/R^3)^{1/2}$, \nfor the $n=1$ polytropic model with $\\gamma=-10^{-4}$. \nThe even and the odd parity modes are shown in panels $(a)$ and $(b)$, \nrespectively. \nThe attached labels \n$g_{\\pm k}(l)\\longleftrightarrow i_{\\pm j}(l_0-\\vert m\\vert)$ \nindicates the connection rule between the $g$-modes and inertial modes.\nThe filled circles at $\\bar{\\Omega}=0.1$ denote the eigenfrequencies $\\bar\\omega$\nof the inertial modes for the $n=1$ isentropic model at $\\bar{\\Omega}=0.1$.\nThe part indicated by the dotted line in the mode sequence is the domain\nof $\\bar\\Omega$, in which the modes belonging to the sequence cannot be \ncalculated. The two dashed lines are given by $\\bar{\\omega}=0$ \nand $\\bar{\\omega}= m \\bar{\\Omega}$.} \n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.4}\n\\plottwo{fig9a.eps}{fig9b.eps}\n\\caption{Same as Figure 8, but for $m=2$.}\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.4}\n\\plottwo{fig10a.eps}{fig10b.eps}\n\\caption{Same as Figure 9, but for $m=3$.}\n\\end{figure}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% TABLES %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\clearpage\n\n\\begin{deluxetable}{ccccc}\n\\footnotesize\n\\tablecaption{$(\\omega/\\Omega-\\kappa_0)/{\\bar{\\Omega}}^2\\ \n$\\tablenotemark{a} \\ \nfor $r$-modes of the $n=3$ polytrope with $\\Gamma=5/3$ \\label{code-check}}\n\\tablewidth{250pt}\n\\tablehead{\n\\colhead{$m$} & \\colhead{$l'$} & \\colhead{Mode} & \n\\colhead{Present} & \\colhead{Saio 1982} \n}\n\\startdata\n 1 & 1 & $r_0$ & \\phm{-}0.000 & \\phm{-}0.000 \\nl\n & & $r_1$ & -0.040 & -0.040 \\nl\n & & $r_2$ & -0.115 & -0.114 \\nl\n & 2 & $r_0$ & -0.100 & -0.099 \\nl\n & & $r_1$ & -0.191 & -0.190 \\nl\n & & $r_2$ & -0.315 & -0.312 \\nl\n & 3 & $r_0$ & -0.037 & -0.037 \\nl\n & & $r_1$ & -0.063 & -0.061 \\nl\n & & $r_2$ & -0.097 & -0.096 \\nl\n 2 & 2 & $r_0$ & \\phm{-}0.121 & \\phm{-}0.120 \\nl\n & & $r_1$ & \\phm{-}0.024 & \\phm{-}0.024 \\nl\n & & $r_2$ & -0.001 & -0.001 \\nl\n & 3 & $r_0$ & -0.037 & -0.037 \\nl\n & & $r_1$ & -0.071 & -0.070 \\nl\n & & $r_2$ & -0.115 & -0.114 \\nl\n 3 & 3 & $r_0$ & \\phm{-}0.174 & \\phm{-}0.173 \\nl\n & & $r_1$ & \\phm{-}0.064 & \\phm{-}0.063 \\nl\n & & $r_2$ & \\phm{-}0.028 & \\phm{-}0.027 \\nl\n\\enddata\n\\tablenotetext{a}{$\\kappa_0$ is defined as $\\kappa_0=2 m/(l' (l'+1))$. \nThe eigenfrequencies are calculated at $\\bar{\\Omega}=0.1$. }\n\\end{deluxetable}\n\n\\begin{deluxetable}{ccc}\n\\footnotesize\n\\tablecaption{The eigenfrequency $\\bar{\\omega}$ \nfor low-radial-order $g$-modes of the $n=1$ polytrope\nwith $\\gamma=-10^{-4}$ at $\\Omega=0$ \\label{g-mode}}\n\\tablewidth{250pt}\n\\tablehead{\n\\colhead{$l$} & \\colhead{$g_1$} & \\colhead{$g_2$} \n}\n\\startdata\n 1 & $1.20\\times 10^{-2}$ & $7.69\\times 10^{-3}$ \\nl\n 2 & $1.68\\times 10^{-2}$ & $1.15\\times 10^{-2}$ \\nl\n 3 & $2.01\\times 10^{-2}$ & $1.44\\times 10^{-2}$ \\nl\n 4 & $2.26\\times 10^{-2}$ & $1.68\\times 10^{-2}$ \\nl\n 5 & $2.47\\times 10^{-2}$ & $1.88\\times 10^{-2}$ \\nl\n 6 & $2.65\\times 10^{-2}$ & $2.05\\times 10^{-2}$ \\nl\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{cccccccccc}\n\\footnotesize\n\\tablecaption{Dissipative timescales $\\tilde\\tau$ of $r$-modes\\tablenotemark{a} \n\\ for the polytropic neutron star models with the index $n=1$. }\n\\tablewidth{0pt}\n\\tablehead{\n\\colhead{$m$} & \\colhead{mode} & \\colhead{$\\gamma$} \n & \\colhead{$\\kappa_0$}\n & \\colhead{$\\tilde \\tau_B$(s)} & \\colhead{$\\tilde \\tau_S$(s)} \n & \\colhead{$\\tilde \\tau_{J,\\vert m\\vert}$(s)\\tablenotemark{b}} \n & \\colhead{$\\tilde \\tau_{D,\\vert m\\vert+1}$(s)} \n & \\colhead{$\\tilde \\tau_{J,\\vert m\\vert+2}$(s)}\n} \n\\startdata\n1&$r_1$&\n$0$\n & 0.691 &$ 5.89\\times 10^{9} $&$ 9.23\\times 10^{7} $\n &$ \\cdots$&$ -2.46\\times 10^{5} $&$ -1.27\\times 10^{8} $\n\\nl\n & &\n$-10^{-4}$\n & 1.000 &$ 6.08\\times 10^{9} $&$ 9.04\\times 10^{7} $\n &$ \\cdots$&$ -2.31\\times 10^{5} $&$ -1.58\\times 10^{8} $\n\\nl\n & & & & & & & & \\nl\n2&$r_0$&\n$\\phm{-}10^{-4}$\n &0.667 &$ 2.03\\times 10^{11} $&$ 2.50\\times 10^{8} $\n &$ -3.31\\times 10^{0} $&$ -3.49\\times 10^{2}$&$ \\cdots$\n\\nl\n & &\n$0$\n &0.667 &$ 2.03\\times 10^{11} $&$ 2.50\\times 10^{8} $\n &$ -3.31\\times 10^{0} $&$ -3.49\\times 10^{2}$&$ \\cdots$\n\\nl\n & &\n$-10^{-4}$\n &0.667 &$ 2.03\\times 10^{11} $&$ 2.50\\times 10^{8} $\n &$ -3.31\\times 10^{0} $&$ -3.49\\times 10^{2}$&$ \\cdots$\n\\nl\n & &\n$-10^{-2}$\n &0.667 &$ 2.10\\times 10^{11} $&$ 2.54\\times 10^{8} $\n &$ -3.31\\times 10^{0} $&$ -3.49\\times 10^{2}$&$ \\cdots$\n\\nl\n & & & & & & & & \\nl\n &$r_1$& \n$0$\n &0.517 &$ 6.47\\times 10^{9} $&$ 6.18\\times 10^{7} $\n &$ -1.31\\times 10^{8} $&$ -8.39\\times 10^{4} $\n &$ -1.88\\times 10^{6} $\n\\nl\n & &\n$-10^{-4}$\n &0.667 &$ 6.79\\times 10^{9} $&$ 6.01\\times 10^{7} $\n &$\\phm{-}2.18\\times 10^{7}\\ \\tablenotemark{c} $\n &$ -7.05\\times 10^{4} $&$ -2.06\\times 10^{6} $\n\\nl\n & & & & & & & & \\nl\n3&$r_0$&\n$\\phm{-}10^{-4}$\n &0.500 &$ 6.64\\times 10^{10} $&$ 1.43\\times 10^{8} $\n &$ -3.17\\times 10^{1} $&$ -1.88\\times 10^{3}$&$\\dots$\n\\nl\n & &\n$0$\n &0.500 &$ 6.63\\times 10^{10} $&$ 1.43\\times 10^{8} $\n &$ -3.17\\times 10^{1} $&$ -1.88\\times 10^{3}$&$\\dots$\n\\nl\n & &\n$-10^{-4}$\n &0.500 &$ 6.64\\times 10^{10} $&$ 1.43\\times 10^{8} $\n &$ -3.17\\times 10^{1} $&$ -1.88\\times 10^{3}$&$\\dots$\n\\nl\n & &\n$-10^{-2}$\n &0.500 &$ 6.97\\times 10^{10} $&$ 1.46\\times 10^{8} $\n &$ -3.17\\times 10^{1} $&$ -1.87\\times 10^{3}$&$\\dots$\n\\nl\n & & & & & & & & \\nl\n &$r_1$& \n$0$\n &0.413 &$ 6.97\\times 10^{9} $&$ 4.78\\times 10^{7} $\n &$ -1.86\\times 10^{10} $&$ -5.30\\times 10^{5}$\n &$ -4.07\\times 10^{6} $\n\\nl\n & &\n$-10^{-4}$\n &0.500 &$ 7.42\\times 10^{9} $&$ 4.63\\times 10^{7} $\n &$\\phm{-}2.39\\times 10^{5}\\ \\tablenotemark{c} $\n &$ -4.37\\times 10^{5} $&$ -4.48\\times 10^{6} $ \n\\nl\n\\enddata\n\\tablenotetext{a}{We present dissipative timescales only for those \nthat are unstable to gravitational radiation reaction.}\n\\tablenotetext{b}{We present dissipative timescales $\\tilde{\\tau}_l$ due to \nthe gravitational radiation reaction only for\nthe dominant multipole moments.}\n\\tablenotetext{c}{For these dissipative timescales, we obtain positive\nvalues, which should be negative by definition. The reason for the\ninconsistent result may be because the extrapolation formula (\\ref{tau2b}) \nfor $\\tau^{-1}$, which is obtained at $\\bar\\Omega=0$, does not necessarily work well\nfor arbitrary values of $\\bar\\Omega$. \nFor instance, we find that\n$\\tilde{\\tau}_{J,\\vert m\\vert}/\\tilde{\\tau}_{D,\\vert m\\vert+1} \\sim 10^{3}$ \nfor $m=2$ and \n$\\tilde{\\tau}_{J,\\vert m\\vert}/\\tilde{\\tau}_{D,\\vert m\\vert+1} \\sim 10^{2}$ \nfor $m=3$, where the dissipative timescales are estimated at \n$\\bar{\\Omega}=0.1$. \nThis may suggest that \nthe mass multipole radiation dominates the current one \nfor the $r_1$-modes for large $\\bar\\Omega$. \nThus, our conclusions on the stability of the $r_1$-modes \nextrapolated for large $\\bar\\Omega$\nare not altered at all.}\n\\end{deluxetable}\n\n\n\\end{document}\n\n\n"}],"string":"[\n {\n \"name\": \"ms.tex\",\n \"string\": \"%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n% %\\n% Rotational modes of non-isentropic stars and %\\n% the gravitational radiation driven instability %\\n% %\\n% S. YOSHIDA and U. LEE %\\n% %\\n% Astronomical Institute, %\\n% Graduate School of Science, Tohoku University, % \\n% Sendai 980-8578, Japan %\\n% %\\n% yoshida@astr.tohoku.ac.jp %\\n% %\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\\\documentstyle[aaspp4]{article}\\n\\n\\\\received{}\\n\\\\accepted{}\\n\\\\journalid{VOL}{JOURNAL DATE}\\n\\\\articleid{START PAGE}{END PAGE}\\n\\\\paperid{MANUSCRIPT ID}\\n\\n\\\\slugcomment{}\\n\\\\lefthead{Yoshida, Lee}\\n\\\\righthead{}\\n\\n\\\\begin{document}\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%% O. FRONT MATTER %%\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\n\\\\title{Rotational modes of non-isentropic stars and the gravitational radiation \\n driven instability }\\n%\\n\\\\author{Shijun Yoshida and Umin Lee}\\n%\\n\\\\affil{Astronomical Institute, Graduate School of Science, \\nTohoku University, Sendai 980-8578, \\nJapan \\\\\\\\ yoshida@astr.tohoku.ac.jp, lee@astr.tohoku.ac.jp}\\n\\n\\n\\\\begin{abstract}\\nWe investigate the properties of\\n$r$-mode and inertial mode of slowly rotating, non-isentropic, \\nNewtonian stars, by taking account of the effects of \\nthe Coriolis force and the centrifugal force.\\nThe Coriolis force is the dominant restoring force \\nfor both $r$-mode and inertial mode, which are also called rotational mode \\nin this paper. \\nFor the velocity field produced by the oscillation modes\\nthe $r$-mode has the dominant toroidal component over the \\nspheroidal component, while the inertial mode has\\nthe comparable toroidal and spheroidal components.\\nIn non-isentropic stars the specific entropy of the fluid\\ndepends on the radial distance from the center, and\\nthe interior structure is in general divided into\\ntwo kinds of layers of fluid stratification that is\\nstable or unstable against convection.\\nBecause of the non-isentropic structure, low frequency\\noscillations of the star are affected by the buoyant force, which\\nhas no effects on oscillations of isentropic stars.\\nIn this paper we employ simple polytropic models with the polytropic index $n=1$\\nas the background neutron star models for the modal analysis.\\nFor the non-isentropic models we consider only two cases, that is,\\nthe models with the stable fluid stratification in the whole interior\\nand the models that are fully convective.\\nFor simplicity we call these two kinds of models ``radiative'' and ``convective''\\nmodels in this paper.\\nFor both cases, we assume the deviation of the models from isentropic \\nstructure is small.\\nExamining the dissipation timescales due to \\nthe gravitational radiation and \\nseveral viscous processes for the polytropic neutron star models,\\nwe find that the gravitational radiation driven instability of \\nthe nodeless $r$-modes associated with $l'=|m|$ remains strong \\neven in the non-isentropic models,\\nwhere $l'$ and $m$ are the indices \\nof the spherical harmonic function representing the angular dependence\\nof the eigenfunction.\\nCalculating the rotational modes of the radiative models \\nas functions of the angular rotation frequency $\\\\Omega$, we find that\\nthe inertial modes are strongly modified \\nby the buoyant force at small $\\\\Omega$, where the buoyant force\\nas a dominant restoring force becomes\\ncomparable with or stronger than the Coriolis force.\\nBecause of this property we obtain the mode sequences \\nin which the inertial modes at large $\\\\Omega$\\nare identified as $g$-modes or the $r$-modes with $l'=|m|$ at small $\\\\Omega$.\\nWe also note that as $\\\\Omega$ increases from $\\\\Omega=0$\\nthe retrograde $g$-modes become retrograde inertial modes,\\nwhich are unstable against the gravitational radiation reaction.\\n\\\\end{abstract}\\n\\n\\n\\\\keywords{instabilities --- stars: neutron --- \\nstars: oscillations --- stars: rotation}\\n\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%% I. INTRODUCTION %%\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\n\\\\section{Introduction}\\n\\n\\nSince the recent discovery of the gravitational radiation driven instability of\\nthe $r$-modes by Andersson (1998) and Friedman \\\\& Morsink (1998),\\na large number of papers have been published on the properties of the \\nrotational modes of rotating stars because of their possible importance \\nin astrophysics\\n(e.g., Kojima 1998, Andersson, Kokkotas \\\\& Schutz 1998, \\nKokkotas \\\\& Stergioulas 1998, Lindblom \\\\& Isper 1998, Beyer \\\\& Kokkotas \\n1999, Lindblom, Mendell \\\\& Owen 1999, Kojima \\\\& Hosonuma 1999, \\nLockitch \\\\& Friedman 1999, Yoshida \\\\& Lee 2000, Lockitch 1999, Yoshida \\net al 1999).\\nHere, we have used the term of ``rotational mode'' to refer to both $r$-mode and \\ninertial mode of rotating stars.\\nAs an important consequence of the instability, for example, Lindblom, Owen \\n\\\\& Morsink (1998) argued that due to the instability, \\nthe maximum angular rotation velocity of hot neutron stars is \\nstrongly restricted. \\nOwen et al. (1998) also suggested that\\nthe gravitational radiation emitted from hot young neutron stars due to\\nthe $r$-mode instability would be one of the potential sources\\nfor the gravitational wave detectors, e.g. LIGO.\\n\\n\\n\\nThe dominant restoring force for the rotational modes\\nis the Coriolis force and the characteristic frequency \\nis comparable to the angular rotation frequency $\\\\Omega$ of the star \\n(e.g., Greenspan 1964, Pedlosky 1987). \\nThe $r$-modes are characterized by the properties that\\nthe toroidal motion dominates the spheroidal motion in the velocity field, and that \\nthe oscillation frequency $\\\\omega$ observed in the corotating frame of the star \\nis given by $\\\\omega=2m\\\\Omega/(l'(l'+1))$ \\nin the limit of $\\\\Omega\\\\rightarrow0$, \\nwhere $m$ and $l'$ are the indices of the spherical harmonic function $Y_{l'}^m$ \\nrepresenting the toroidal component of the velocity field of the mode\\n(e.g., Papaloizou \\\\& Pringle 1978 , Provost, Berthomieu \\\\& Rocca 1981, \\nSaio 1982). \\nOn the other hand, the inertial modes have the comparable toroidal and\\nspheroidal components of the velocity field and therefore they are not necessarily\\nrepresented by a single spherical harmonic function\\n(e.g, Lee, Strohmayer \\\\& Van Horn 1992, Yoshida \\\\& Lee 2000). \\nNote that the inertial mode of this kind is also called ``rotation mode'' or \\n``generalized $r$-mode'' (Lindblom \\\\& Ipser 1998, Lockitch \\\\& Friedman 1999). \\n\\n\\n\\nMost of the recent studies on the $r$-mode instability\\ndriven by the gravitational radiation reaction are restricted to \\nthe case of neutron stars with isentropic structure, since the barotropic\\n(one-parameter) equation of state, $p=p(\\\\rho)$ is usually assumed for\\nboth the interior structure and the small amplitude oscillation.\\nIn isentropic stars\\nthe specific entropy of the fluid in the interior is constant and\\nthe buoyant force has no effects on the oscillation.\\nHowever, stars in general have non-isentropic interior structure, \\nwhich may be divided into\\ntwo kinds of layers with fluid stratification \\nstable or unstable against convection.\\nIt is well know that the property of the oscillation modes of\\nnon-isentropic stars is substantially different from that of isentropic stars,\\nsince the buoyant force comes into play as a restoring force for \\nlow frequency oscillations like $g$-mode propagating in the layers with the stable \\nstratification (see, e.g., Unno et al 1989).\\nThis is also the case for rotational modes, which have low oscillation\\nfrequencies comparable to the spin rate $\\\\Omega$ of the star.\\nFor example, we note that\\nthe $r$-mode associated with $l'=|m|$ having the nodeless eigenfunction in the\\nradial direction is the only $r$-mode permitted in an isentropic star for a given $m$\\n(e.g, Lockitch \\\\& Friedman 1999, Yoshida \\\\& Lee 2000), \\nbut in non-isentropic stars with the stable fluid stratification all\\nthe $r$-modes with $l'\\\\ge |m|$ are possible for a given $m$, and there are\\nin principle an infinite number of $r$-modes for given $l'$ and $m$\\n(e.g., Provost et al 1981, Saio 1982, Lee \\\\& Saio 1997). \\nWe therefore consider it important to investigate the modal properties of \\nthe rotational modes in non-isentropic stars, particularly in order to\\nanswer the question whether the property of \\nthe $r$-mode instability for neutron star models with non-isentropic structure\\nremains the same as that for isentropic neutron star models.\\n\\n\\n\\n\\nIn this paper, we study the $r$-mode and the inertial mode oscillations\\nof slowly rotating, non-isentropic, Newtonian stars, where\\nuniform rotation and adiabatic oscillation are assumed\\nto simplify the mathematical treatments. \\nThe effects of the rotational deformation of the equilibrium structure \\non the eigenfunction and eigenfrequency are included in the analysis, \\nusing the formulation by Yoshida \\\\& Lee (2000) \\n(see also Lee \\\\& Saio 1986, Lee 1993).\\nWe employ simple polytropic models \\nwith the polytropic index $n=1$\\nas the background neutron star models.\\nFor the non-isentropic models we consider only two cases, that is,\\nthe models that have stable fluid stratification in the whole interior\\nand those that are in convective equilibrium.\\nIn this paper, following the conventions used \\nin the field of stellar evolution and pulsation, \\nwe simply call these two kinds of models\\n``radiative'' and ``convective'' models, respectively, although\\nno energy transport in the interior is considered.\\nThe plan of this paper is as follows. \\nIn \\\\S 2, we briefly describe the basic equations employed in the linear modal analysis\\nof slowly rotating stars.\\nIn \\\\S 3, we show numerical results for the rotational modes of non-isentropic \\nstars, and discuss the properties of the eigenfrequency and eigenfunction of the modes.\\nIn \\\\S 4, we examine the stability of simple neutron star models\\nagainst the $r$-modes, computing their growth or damping timescales due \\nto the gravitational radiation reaction and some viscous damping processes.\\n\\\\S 5 is for conclusions.\\n\\n\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%% II. Method of Solutions %%\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\n\\\\section{Method of Solutions}\\n\\n\\nThe method of solutions used in this paper is exactly the same as that \\napplied in Yoshida \\\\& Lee (2000). Here, therefore, we briefly describe \\nthe basic equations and the method of calculation. \\nThe details are given in Yoshida \\\\& Lee (2000). \\n\\n\\\\subsection{Equilibrium Configurations}\\n\\n\\nWe consider oscillations of uniformly rotating Newtonian stars. \\nThus the angular rotation frequency of the star, $\\\\Omega$ is constant.\\nWe assume the polytropic relation for the equilibrium structure of the model, \\nand the relation between the pressure $p$ and the mass density $\\\\rho$ is given by\\n%\\n\\\\begin{equation}\\np = K \\\\, \\\\rho^{1 + \\\\frac{1}{n}} \\\\, ,\\n\\\\end{equation}\\n%\\nwhere $n$ and $K$ are the polytropic index and the structure constant determined by\\ngiving the mass and the radius of the model, \\nrespectively. \\nIn this investigation, assuming slow rotation, we employ \\nthe Chandrasekhar-Milne expansion (see, e.g, Tassoul 1978) to obtain \\nthe equilibrium structure of rotating stars. \\nIn this technique the effects of the \\ncentrifugal force and the equilibrium deformation are treated \\nas small perturbations to the non-rotating spherical symmetric structure \\nof the star. \\nThe small expansion parameter due to rotation is chosen as \\n$\\\\bar{\\\\Omega}=\\\\Omega (R^3/G M)^{1/2}$, where $R$ and $M$ are \\nthe radius and the mass of the non-rotating star, respectively. \\nThe equilibrium configurations are constructed with accuracy up to the order of \\n${\\\\bar{\\\\Omega}}^2$. For simplicity, we consider a sequence of slowly \\nrotating stars whose central density is the same as that of the \\nnon-rotating star. \\n\\n\\n\\\\subsection{Perturbation Equations}\\n\\n\\n\\nIn the perturbation analysis, we introduce a parameter $a$ that is \\nconstant on the distorted effective potential surface of the star. In practice, \\nthe parameter $a$ is defined such that\\n%\\n\\\\begin{equation}\\n\\\\Psi (r,\\\\theta) = \\\\Psi_0 (a) \\\\, , \\\\label{ep-co}\\n\\\\end{equation}\\n%\\nwhere $\\\\Psi_0$ and $\\\\Psi$ are the effective potentials for the non-rotating \\nand slowly rotating models, respectively. Note that $\\\\Psi_0$ is equal to \\nthe gravitational potential and $\\\\Psi$ is the sum of the gravitational \\npotential and the centrifugal potential. With this parameter $a$, \\nthe distorted equi-potential surface may be given by\\n%\\n\\\\begin{equation}\\nr = a \\\\lbrace 1 + \\\\epsilon (a,\\\\theta,\\\\varphi) \\\\rbrace \\\\, ,\\n\\\\label{def-a}\\n\\\\end{equation}\\n%\\nwhere $\\\\epsilon$ is the function of the order of \\n${\\\\bar{\\\\Omega}}^2$, and is obtained by giving the functional forms\\nof $\\\\Psi$ and $\\\\Psi_0$ using the Chandrasekhar-Milne expansion (Yoshida \\\\& Lee 2000). \\nHere we have used spherical polar coordinates $(r,\\\\theta,\\\\varphi)$. \\nHowever, we employ hereafter the parameter $a$ as the radial coordinate, \\nin stead of the polar radial coordinate $r$.\\n\\n\\nThe governing equations of nonradial oscillations of a rotating star are \\nobtained by linearizing the basic equations used in fluid mechanics\\n(e.g., Unno et al 1989). \\nIn the following, we use $\\\\delta$ and $\\\\Delta$ to denote the Eulerian and \\nthe Lagrangian changes of physical quantities, respectively.\\nSince the equilibrium state is assumed to be stationary and axisymmetric, \\nthe perturbations may be\\nrepresented by a Fourier component proportional to \\n$e^{i(\\\\sigma t + m \\\\varphi)}$, where $\\\\sigma$ is the frequency observed in \\nan inertial frame and $m$ is the azimuthal quantum number. \\nThe continuity equation may be linearized to be\\n%\\n\\\\begin{equation}\\n\\\\delta \\\\rho = - \\\\nabla_i (\\\\rho \\\\xi^i), \\\\label{del_rho} \\\\label{mass_con} \\n\\\\end{equation}\\n%\\nwhere $\\\\xi^i$ is the Lagrangian displacement vector, and we have made use of\\n$\\\\delta v^i = i(\\\\sigma + m \\\\Omega) \\\\xi^i \\\\equiv i \\\\omega \\\\xi^i$\\nwith $\\\\omega$ being the oscillation frequency observed in the corotating \\nframe of the star. \\nHere $\\\\nabla_i$ denotes the covariant derivative derived from the metric\\n$g_{ij}$. \\n\\nIn this study, we consider only adiabatic oscillations. \\nThus, the perturbed equation of state is given by\\n\\\\begin{equation}\\n\\\\delta p = \\\\Gamma p \\\\left( \\\\frac{\\\\delta \\\\rho}{\\\\rho} +\\n\\\\xi^i A_i \\\\right) \\\\, , \\\\label{del_p} \\n\\\\end{equation}\\n%\\nwhere\\n$\\\\Gamma$ is the adiabatic exponent defined as\\n%\\n\\\\begin{equation}\\n\\\\Gamma = \\\\left( \\\\frac{ \\\\partial \\\\ln p}{\\\\partial \\\\ln \\\\rho} \\\\right)_{ad} \\\\, ,\\n\\\\end{equation}\\n%\\nand $A_i$ is the generalized Schwarzschild discriminant\\\\footnote{Since \\nthe Schwarzschild discriminant $A_i$ is proportional to $\\\\nabla_i s$ with $s$\\nbeing the specific entropy, a model with $A_i=0$ \\nthroughout the interior is called isentropic model in this paper.\\nUsing the same barotropic \\n(one-parameter) equation of state, $p=p(\\\\rho)$ for both\\nthe equilibrium structure and the perturbation leads to isentropic models.} given by\\n%\\n\\\\begin{equation}\\nA_i \\\\equiv \\\\frac{1}{\\\\rho} \\\\nabla_i \\\\rho - \\\\frac{1}{\\\\Gamma p} \\\\nabla_i p \\\\, ,\\n\\\\label{def_A}\\n\\\\end{equation}\\n%\\nand the positive and negative values of $A_i$ indicate the fluid stratification\\nunstable and stable against convection, respectively.\\n\\n\\nThe linearized Euler's equation is\\n\\\\begin{equation}\\n-\\\\omega^2 \\\\xi_i + \\\\nabla_i \\n\\\\left( \\\\frac{\\\\delta p}{\\\\rho} + \\\\delta \\\\Phi \\\\right) + \\n\\\\left(\\\\frac{\\\\delta p}{\\\\rho} \\\\, g_{ij}+\\\\xi_j \\\\frac{1}{\\\\rho} \\\\nabla_i p\\n\\\\right) \\\\, A^j + \\n2 i \\\\omega \\\\Omega \\\\xi^j \\\\nabla_j \\\\varphi_i \\n= 0 \\\\, , \\\\label{pert_Euler}\\n\\\\end{equation}\\n%\\nwhere $\\\\Phi$ denotes the gravitational potential, \\nand $\\\\varphi^i$ is the rotational Killing vector, with which the 3-velocity\\nof the equilibrium fluid of a rotating star is given as \\n$v^i=\\\\Omega\\\\varphi^i$. The perturbed Poisson equation is\\n%\\n\\\\begin{equation}\\n\\\\nabla_i \\\\nabla^i \\\\delta \\\\Phi = 4\\\\pi G\\\\delta \\\\rho \\\\, ,\\n\\\\label{pert_Poisson}\\n\\\\end{equation}\\n%\\nwhere $G$ is the gravitational constant. \\n\\n\\n\\n\\nPhysically acceptable solutions of the linear differential equations are \\nobtained by imposing boundary conditions at the inner and outer \\nboundaries of the star. The inner boundary conditions are the regularity \\ncondition of the perturbed quantities at the stellar center. \\nThe outer boundary conditions at the surface of the star are \\n$\\\\Delta p/\\\\rho=0$\\nand the continuity of the perturbed gravitational potential at the surface to\\nthe solution of $\\\\nabla_i\\\\nabla^i\\\\delta\\\\Phi=0$ that vanishes at the infinity.\\n\\n\\nIn order to solve the system of partial differential equations given above, \\nwe employ the series expansion in terms of spherical harmonics to\\nrepresent the angular dependence of the perturbed quantities.\\nThe Lagrangian displacement vector, $\\\\xi^i$ is expanded in terms of the \\nvector spherical harmonics as\\n%\\n\\\\begin{equation} \\n\\\\xi^a = \\\\sum_{l\\\\geq\\\\vert m \\\\vert}^{\\\\infty} a \\\\, S_l(a) \\nY_l^m (\\\\theta,\\\\varphi) e^{i \\\\sigma t} \\\\, , \\\\label{v_a}\\n\\\\end{equation}\\n%\\n\\\\begin{equation}\\n\\\\xi^\\\\theta = \\\\sum_{l,l'\\\\geq\\\\vert m \\\\vert}^{\\\\infty} \\n\\\\left\\\\{ H_l (a) {Y_l^m}_{,\\\\theta} + T_{l'} (a) \\\\frac{1}{\\\\sin \\\\theta} \\\\, \\n{Y_{l'}^m}_{,\\\\varphi} \\\\right\\\\} e^{i \\\\sigma t} \\\\, , \\\\label{v_t}\\n\\\\end{equation}\\n%\\n\\\\begin{equation}\\n\\\\xi^\\\\varphi = \\\\frac{1}{\\\\sin^2 \\\\theta} \\n\\\\sum_{l,l'\\\\geq\\\\vert m \\\\vert}^{\\\\infty} \\\\left\\\\{ H_l (a) {Y_l^m}_{,\\\\varphi}\\n - T_{l'} (a) {\\\\sin \\\\theta} \\\\, {Y_{l'}^m}_{,\\\\theta}\\n \\\\right\\\\} e^{i \\\\sigma t} \\\\, \\\\label{v_p} \\n\\\\end{equation}\\n%\\n(Regge \\\\& Wheeler 1957, see also Thorne 1980). \\nThe perturbed scalar quantity such as $\\\\delta \\\\Phi$ is expressed as\\n%\\n\\\\begin{equation} \\n\\\\delta \\\\Phi = \\\\sum_{l\\\\geq\\\\vert m \\\\vert}^{\\\\infty} \\\\delta \\\\Phi_l (a) \\\\, \\nY_l^m (\\\\theta,\\\\varphi) e^{i \\\\sigma t} \\\\, . \\\\label{d_phi}\\n\\\\end{equation}\\n%\\nHere, the expansion coefficients $T_{l'}$ are called ``axial'' \\n(or ``toroidal'') and the other coefficients are called \\n``polar'' (or ``spheroidal''). It is known that\\nthese two set of components are decoupled when $\\\\Omega=0$.\\n\\n\\nSubstituting the perturbed quantities expanded in terms of the spherical \\nharmonics into the linearized basic \\nequations ($\\\\ref{del_rho}$), ($\\\\ref{del_p}$), ($\\\\ref{pert_Euler}$) \\nand ($\\\\ref{pert_Poisson}$), we obtain an infinite system of coupled linear \\nordinary differential equations for the expansion coefficients. \\nNotice that the system of differential equations employed in this paper\\nis arranged to give\\neigenfunctions and eigenfrequencies consistent up to the order of $\\\\bar\\\\Omega^3$ \\nfor slow rotation.\\nThe explicit expressions for the governing equations are given in Appendix of \\nYoshida \\\\& Lee (2000). \\n\\n\\nSince the equilibrium state of a rotating star is invariant under \\nthe parity transformation defined by $\\\\theta \\\\to \\\\pi - \\\\theta$, \\nthe linear perturbations have definite parity for that transformation. \\nIn this paper, a set of modes whose scalar perturbations such as \\n$\\\\delta \\\\Phi$ are symmetric with respect to the equator is called ``even'' \\nmodes, while the other set of modes whose scalar perturbations are antisymmetric \\nwith respect to the equator is called ``odd'' modes \\n(see, e.g., Berthomieu et al. 1978).\\nFor positive integers $j=1,~2,~3,~\\\\cdots$, we have $l=|m|+2j-2$ and \\n$l'=l+1$ for even modes, and $l=|m|+2j-1$ and $l'=l-1$ for odd modes, \\nwhere the symbols $l$ and $l'$ have been used to denote the spheroidal \\nand toroidal components of the displacement vector $\\\\xi^i$, \\nrespectively (see equations (\\\\ref{v_a})--(\\\\ref{d_phi})). \\nNote that we do not use the term of the even (the odd) parity mode to refer to\\nthe polar (the axial) mode, although this terminology is used traditionally in \\nrelativistic perturbation theory (e.g., Regge \\\\& Wheeler 1957). \\n\\n\\nOscillations of rotating stars are also divided into prograde and retrograde modes.\\nWhen observed in the corotating frame of the star,\\nwave patterns of the prograde modes are propagating\\nin the same direction as rotation of the star, \\nwhereas those of the retrograde modes are\\npropagating in the opposite direction to the rotation.\\nFor positive values of $m$, the prograde and retrograde modes have negative and positive\\n$\\\\omega$, respectively.\\n\\n\\n\\nFor numerical calculations, we truncate the infinite set of linear \\nordinary differential equations to obtain a finite set by discarding all \\nthe expansion coefficients associated with $l$ higher than $l_{max}$. \\nThis truncation determines the number of the expansion coefficients \\nkept in the spherical harmonic expansion of each perturbed quantity. \\nWe denote this number as $k_{max}$. Our basic equation becomes a \\nsystem of $4\\\\times k_{max}$-th order linear ordinary differential equations, which,\\ntogether with the boundary conditions, are numerically solved as an \\neigenvalue problem of $\\\\omega\\\\equiv \\\\sigma+m\\\\Omega$ by using a Henyey type \\nrelaxation method (e.g., Unno et al . 1989, see also Press et al. 1992).\\n\\n\\n\\nWe cannot determine a priori $k_{max}$,\\nthe number of the expansion coefficients kept in the eigenfunctions. \\nIn this paper, we start with an appropriate trial \\nvalue of $k_{\\\\mbox{\\\\tiny max}}$ to compute an oscillation mode \\nat a given value of $\\\\bar\\\\Omega$. \\nThen, we increase the \\nvalue of $k_{\\\\mbox{\\\\tiny max}}$, until the eigenfrequency converges within \\nan appropriate numerical error, where the mode identification is done\\nby examining the form and the number of nodes of the dominant expansion coefficients.\\nWe consider that the mode thus obtained\\nwith the sufficient number of the expansion coefficients\\nis the correct oscillation mode we want for the rotating model at $\\\\bar\\\\Omega$.\\n\\n\\n\\nIn order to check our numerical code, we calculate eigenfrequencies of \\nthe $r$-modes of the $n=3$ and $\\\\Gamma=5/3$ polytropic model \\nat $\\\\bar{\\\\Omega}=0.1$. In Table 1, our \\nresults are tabulated together with those calculated by Saio (1982) \\nby using a semi-analytical \\nperturbative approach. As shown by Table 1, our results are in good \\nagreement with Saio's results. \\n\\n\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%% III. Rotational Modes of Non-isentropic.... %%\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\n\\\\section{Rotational Modes of Slowly Rotating Non-isentropic Stars}\\n\\n\\nBecause it is believed that \\nisentropic structure is a good approximation for young and hot neutron stars,\\nin this study we concentrate our attention to the case that \\nthe deviation of the non-isentropic models from isentropic structure \\nis sufficiently small.\\nIn this case, we may assume that the adiabatic exponent $\\\\Gamma$ is given by\\n% \\n\\\\begin{eqnarray} \\n\\\\frac{1}{\\\\Gamma} = \\\\frac{n}{n+1} + \\\\gamma \\\\, ,\\n\\\\label{def-gamma}\\n\\\\end{eqnarray}\\n%\\nwhere $\\\\gamma$ is a constant giving the deviation from the isentropic structure.\\nBy substituting equation (\\\\ref{def-gamma}) into equation (\\\\ref{def_A}), \\nwe obtain an explicit form of $A_i$ as:\\n%\\n\\\\begin{eqnarray}\\nA_i &=& - \\\\, \\\\gamma \\\\, \\\\nabla_i \\\\ln p \\\\, .\\n\\\\end{eqnarray}\\n%\\nIn this study, we only consider oscillations of polytropic models with the index $n=1$.\\nPositive and negative values of $\\\\gamma$ are respectively for convective and radiative\\nmodels.\\nIsentropic models are given by $\\\\gamma=0$.\\nSince our formulation for stellar oscillations of rotating stars is \\naccurate only up to the order of $\\\\bar{\\\\Omega}^3$, we shall apply our method \\nto the oscillation modes in the range of $\\\\bar\\\\Omega\\\\le 0.1$.\\n \\n\\nFor convenience of later discussions, it may be useful to review\\nthe properties of $r$-modes and inertial modes\\nof isentropic models with $\\\\gamma=0$ (see, e.g., Yoshida \\\\& Lee 2000). \\nBecause of \\nthe asymptotic behavior of the eigenfrequency of the rotational modes\\nin the limit of $\\\\Omega\\\\rightarrow 0$, it is \\nconvenient to introduce a non-dimensional frequency $\\\\kappa$ as follows:\\n%\\n\\\\begin{equation}\\n\\\\frac{\\\\omega}{\\\\Omega} = \\\\kappa \\\\, . \\\\label{def-kappa}\\n\\\\end{equation}\\n%\\nSince the rotational deformation is of the order of $\\\\bar\\\\Omega^2$,\\nthe effects on the frequency of the rotational modes appear as the terms of \\nthe order of $\\\\bar\\\\Omega^3$. \\nTherefore, we may expand the dimensionless \\neigenfrequency $\\\\kappa$ of the rotational modes in powers of $\\\\bar\\\\Omega$ as follows: \\n%\\n\\\\begin{equation}\\n\\\\kappa = \\\\kappa_0 + \\\\kappa_2 \\\\, \\\\bar{\\\\Omega}^2 \\n + O(\\\\bar{\\\\Omega}^4) \\\\, , \\\\label{def-kappa0}\\n\\\\end{equation}\\n%\\nwhere\\n%\\n\\\\begin{equation}\\n\\\\kappa_0 = \\\\frac{2 m}{l'(l'+1)} \\\\, \\n\\\\label{r-fre}\\n\\\\end{equation}\\n%\\nfor the $r$-modes associated with the indices \\n$l'$ and $m$ of vector harmonics with the axial \\nparity (see, e.g. Papaloizou \\\\& Pringle 1978).\\nFor the inertial modes, there is no analytic expression for $\\\\kappa_0$ in general.\\n\\n\\n\\nAs suggested by Provost et al. (1981) and Saio (1982),\\nthe $r$-mode associated with $l'=|m|$\\nhaving the nodeless eigenfunction $T_{l'}(r)$ is the only $r$-mode permitted\\nfor isentropic stars for a given $m$.\\nIn the limit of $\\\\Omega\\\\rightarrow 0$, we have \\n$\\\\kappa\\\\rightarrow\\\\kappa_0=2m/l'(l'+1)$.\\nAmong the expansion coefficients of the eigenfunctions \\nthe toroidal component $T_{l'=|m|}$ is dominating.\\nFor the inertial modes,\\nthe value of $\\\\kappa$ in the limit of $\\\\Omega\\\\rightarrow 0$\\nis also finite but different from \\n$\\\\kappa_0 = {2 m}/{l'(l'+1)}$. \\n\\nThe inertial modes are characterized by the two angular \\nquantum numbers $l_0$ and $m$, where the value of $l_0$ is \\nthe maximum index $l$ of spherical harmonics associated with \\nthe dominant expansion coefficients \\nof the eigenfunctions (see Lockitch \\\\& Friedman 1999, Yoshida \\\\& Lee 2000). \\nNote that our definition of $l_0$ is not the same as that of Lockitch \\\\& \\nFriedman (1999), but the same as that of Lindblom \\\\& Ipser (1998) and \\nYoshida \\\\& Lee (2000).\\nNote also that odd (even) parity modes have odd (even) values\\nof $l_0-|m|$, and that\\nthe odd parity mode having $l_0-|m|=1$ is the $r$-mode associated with $l'=|m|$.\\nThe value of $\\\\kappa_0$ for the inertial modes depends not only on the\\nindices $m$ and $l_0$, but also on the equilibrium structure \\nof stars (e.g., Yoshida \\\\& Lee 2000). \\nFor given values of $l_0$ and $m$, the number of different inertial modes is\\nequal to $l_0 - \\\\vert m\\\\vert(\\\\ge 2)$. \\nHowever, there seems to be no good quantum number to classify the different inertial\\nmodes associated with the same $l_0$ and $m$.\\nWe here introduce an ordering integer $n$ to use the labellings such as \\n$i_n$ and $\\\\omega_n$ for these inertial modes.\\nSince the frequencies of the inertial modes with the same $l_0$ and $m$\\nare found in a sequence given by, in the case of $m>0$,\\n%\\n\\\\begin{equation}\\n\\\\omega_{-(l_0 - \\\\vert m\\\\vert-1)/2} < \\\\cdots < \\\\omega_{-1} < 0 \\\\leq \\n\\\\omega_{0} < \\\\omega_{1} < \\\\cdots < \\n\\\\omega_{(l_0 - \\\\vert m\\\\vert-1)/2}\\\\, \\n\\\\end{equation}\\n% \\nfor odd parity modes, and\\n%\\n\\\\begin{equation}\\n\\\\omega_{-(l_0 - \\\\vert m\\\\vert)/2} < \\\\cdots < \\\\omega_{-1} < 0 < \\n\\\\omega_{1} < \\\\cdots < \\n\\\\omega_{(l_0 - \\\\vert m\\\\vert)/2}\\\\, \\n\\\\end{equation}\\n%\\nfor even parity modes, we may define \\nthe ordering number $n$ as an integer that satisfies\\nthe inequality $|l_0-|m|-1|/2\\\\ge |n| \\\\ge 0$ for odd parity inertial modes, and\\n$|l_0-|m||/2\\\\ge |n| >0$ for even parity inertial modes\\n(see Lockitch \\\\& Friedman 1998, Yoshida \\\\& Lee 2000).\\nWe apply this classification to the inertial modes of both isentropic and \\nnon-isentropic stars in the following discussions.\\n\\n\\n\\n\\\\subsection{$r$-modes}\\n\\n\\n\\nFor the radiative models, all the\\n$r$-modes associated with $l'\\\\ge |m|$ are possible for a given $m$, \\nand there are in principle \\na countable infinite number of $r$-modes for given $l'$ and $m$. \\nThe $r$-modes with the same $l'$ and $m$ may be classified by counting\\nthe number of nodes\\nof the axial components $T_{l'}$ in the radial direction.\\nFor them the values of $\\\\kappa_2$ are different, but the values of $\\\\kappa_0$\\nare the same and equal to $2m/l'(l'+1)$.\\nIt is important to note that this classification \\nof the $r$-modes is applicable only in the limit of $\\\\bar\\\\Omega\\\\rightarrow 0$\\nand $\\\\kappa\\\\rightarrow \\\\kappa_0=2m/l'(l'+1)$, \\nsince \\nthe components associated with the other values of $l'$ will come into play \\nfor large $\\\\bar\\\\Omega$\\n(see, e.g. Provost et al. 1981, Saio 1982).\\nLet us introduce an integer $k$ to denote\\nthe number of nodes of the toroidal eigenfunction $T_{l'}$,\\nwhere the node at the center of the \\nstar is excluded from the count.\\nThen, the $r$-modes are \\ncompletely specified by the three quantum numbers $m$, $l'$ and $k$. \\nIn this paper, for given $l'$ and $m$,\\nwe employ the notation of $r_k$ to denote the $r$-mode whose \\ntoroidal eigenfunction $T_{l'}(r)$ has $k$ nodes in the radial direction.\\n\\n\\nIn Figures 1 to 3, the dimensionless eigenvalues $\\\\kappa$ are given versus \\n$\\\\bar{\\\\Omega}$ for several \\nlow-radial-order $r$-modes with $m=1$, 2, and 3\\nfor the $n=1$ polytropic model with $\\\\gamma=-10^{-4}$, where\\nthe $r$-modes with $l'= |m|$, $l'= |m| + 1$ and \\n$l'= |m| + 2$ are given in each figure.\\nModes with $l'= |m| + 1$ \\nare even parity modes, and those with $l'=|m|$ and $l'=|m|+2$ are odd parity modes. \\nIn the figures, the eigenvalues $\\\\kappa$ of the $i_0$-modes with $l_0=|m|+2 k+1$,\\ncalculated at $\\\\bar{\\\\Omega}=0.1$ \\nfor the $n=1$ isentropic model, are designated by\\nthe filled circles, where the integer $k$ corresponds to the number in the subscript \\nof the notation $r_k$.\\nFigures 1 to 3 clearly show that\\nthe qualitative behavior of the eigenfrequencies as functions of $\\\\bar\\\\Omega$\\nis not strongly dependent on the azimuthal quantum number $m$. \\nFrom these figures we also understand that\\nthe $r$-modes of the radiative model with $\\\\gamma < 0$\\nare divided into three distinctive classes according to the asymptotic \\nbehavior of the eigenvalues at large $\\\\bar\\\\Omega$.\\n%\\nThe first class of the $r$-modes consists of the nodeless $r_0$-modes \\nassociated with $l'=|m|$. \\nThe eigenvalue $\\\\kappa$ of the $r$-modes of this class is well approximated by \\nequations (17) and (18) at any values of $\\\\bar\\\\Omega$ examined in this paper.\\nNote that the $r_0$-mode with $m=l'=1$ is a \\npeculiar mode in the sense that $\\\\kappa$ is almost constant since\\n$\\\\kappa_2=0$ and $\\\\kappa=\\\\kappa_0+O(\\\\bar\\\\Omega^4)$ (see Saio 1982, Greenspan 1964). \\n%\\nThe second class consists of the $r_k$-modes with \\n$l'=\\\\vert m \\\\vert$ and $k>0$. \\nEquations (\\\\ref{def-kappa0}) and (\\\\ref{r-fre}) can give good values for \\nthe eigenvalue $\\\\kappa$ of the $r$-modes of this class\\nonly when $\\\\bar{\\\\Omega}$ is sufficiently small.\\nAs $\\\\bar\\\\Omega$ increases, $\\\\kappa$ tends to\\nthe $i_0$ inertial modes with $l_0=|m|+2 k+1$ of the isentropic model. \\nNote that the $i_0$-modes are odd parity inertial modes \\n(see equations (19) and (20)).\\nWe therefore consider that at large $\\\\bar\\\\Omega$ \\nthe $r_k$-modes of this class become\\nidentical with the $i_0$-modes with $l_0=|m|+2 k+1$, for which $\\\\kappa$\\nis almost constant.\\n%\\nThe third class of the $r$-modes consists of the $r_k$-modes with \\n$l' > \\\\vert m \\\\vert$ and $k\\\\ge0$.\\nThe eigenvalue $\\\\kappa$ of the $r$-modes of this class is well represented by\\nequations (17) and (18) only when $\\\\bar\\\\Omega$ is sufficiently small, and\\nit becomes small monotonically as $\\\\bar\\\\Omega$ increases.\\nThe $r$-modes of this class may have no corresponding inertial modes\\nof the isentropic model.\\n\\n\\nAs proved by Friedman \\\\& Schutz (1978), oscillation modes whose frequency $\\\\sigma$\\nobserved in an inertial frame\\nsatisfies the condition $\\\\sigma(\\\\sigma+m\\\\Omega)=\\\\sigma\\\\omega<0$ \\nare unstable to the gravitational radiation reaction. \\nThe condition for the instability\\nmay be rewritten as $0 < \\\\kappa < m$ for retrograde modes with $\\\\omega>0$ and $m>0$. \\nFigures 1 to 3 show that the $r$-mode with $l'\\\\geq2$ \\nsatisfies the inequality $0 < \\\\kappa < m$ for the range of $\\\\bar\\\\Omega$\\nexamined in this paper.\\nIt is also found that the $r_k$-modes with $l'=1$ \\nand $k>0$ also satisfy the inequality $0 < \\\\kappa < m$ for $\\\\bar\\\\Omega>0$.\\nThe reason for the instability of the $r_k$-modes with $l'=1$ and $k>0$ may be\\nunderstood by noting that the \\npolar components with the index $l=2$ can be responsible for the emission \\nof gravitational radiation. \\nWe may conclude that the $r_0$-mode with $l'=\\\\vert m\\\\vert=1$ is \\nthe only $r$-mode that is stable against \\nthe gravitational radiation reaction. \\n \\n\\n \\nIn Figure 4, the eigenfrequencies $\\\\kappa$ of three $r$-modes with $m=2$\\nare plotted as functions of $|\\\\gamma|$, where\\nwe have assumed $\\\\bar\\\\Omega=0.01$. \\nThe three modes are respectively the $r_0$-mode with $l'=m=2$, \\nthe $r_1$-mode with $l'=m=2$, and the $r_0$-mode with $l'=3$ and $m=2$.\\nThese three $r$-modes belong to the first, second, and third classes of the $r$-modes\\ndiscussed in the previous paragraph.\\nThe solid lines and the dotted \\nlines are used to denote the cases of negative and positive $\\\\gamma$, \\nrespectively.\\nNote that although we can obtain the three $r$-modes without any difficulty\\nfor the radiative models with negative $\\\\gamma$, \\nwe cannot always calculate the $r$-modes of the second and the third classes\\nfor the convective models with positive $\\\\gamma$.\\nLet us first discuss the case of the radiative models.\\nAs shown by Figure 4, the eigenvalue $\\\\kappa$ of the $r_0$-mode with $l'=|m|=2$ \\nis practically independent of $|\\\\gamma|$ and has values approximately equal to\\n$\\\\kappa_0=2m/l'(l'+1)=2/3$.\\nHowever, $\\\\kappa$ of the $r_1$-mode with $l'=|m|=2$ \\nis dependent on $|\\\\gamma|$.\\nAt small $|\\\\gamma|$, the $r_1$-mode has the eigenvalue close to $\\\\kappa_0=0.517$, \\nwhich corresponds to \\nthe inertial mode with $l_0-\\\\vert m \\\\vert = 3$ of the isentropic model, but \\nit tends to $2m/l'(l'+1)=2/3$ as $|\\\\gamma|$ increases.\\nThe $r_0$-mode with $l'=3$ and $m=2$ also has the eigenfrequency $\\\\kappa$\\nwhich depends on $|\\\\gamma|$.\\nAlthough the value of $\\\\kappa$ is close to $\\\\kappa_0=2m/l'(l'+1)=1/3$ \\nat large $|\\\\gamma|$, it tends to zero as $|\\\\gamma|\\\\rightarrow 0$.\\nThis behavior of $\\\\kappa\\\\rightarrow 0$ in the limit of $|\\\\gamma|\\\\rightarrow 0$\\nis consistent with the fact that the $r$-modes associated with \\n$l'> \\\\vert m\\\\vert$ do not exist in isentropic stars, for which $\\\\gamma=0$. \\nLet us next discuss the case of the convective models with $\\\\gamma>0$.\\nThe eigenvalue $\\\\kappa$ of the $r_0$-mode with $l'=|m|=2$ is only weakly dependent on\\n$\\\\gamma$, as in the case of the radiative models.\\nNote that the curves for the $r_0$-mode with $l'=|m|=2$ for negative and positive $\\\\gamma$\\nare almost indistinguishable in Figure 4.\\nThe $r_1$-mode with $l'=|m|=2$ for the convective models behaves differently than \\nthat for the radiative models as $|\\\\gamma|$ increases.\\nIn fact, the value of $\\\\kappa$ decreases\\nrapidly with increasing $\\\\gamma$ and \\nthe $r_1$-mode cannot be found at large values of $\\\\gamma>0$.\\nNo $r_0$-mode with $l'=3$ and $m=2$ are found for the convective models.\\n\\n\\n\\nLet us discuss the properties of the eigenfunctions of the $r$-modes \\nfor the radiative models.\\nSince the amplitude of the displacement vector\\nis much larger than that of the scalar perturbations, in the following discussions\\nwe may show only the displacement vector of the modes.\\nIn Figures 5 to 7, we show the expansion coefficients \\n$S_l$, $H_l$ and ${\\\\it i} T_{l'}$ as functions of the fractional radius $a/R$\\nfor the $r$-modes with $m=2$, where we have assumed $\\\\gamma=-10^{-4}$, and\\nthe amplitude is normalized at the surface such that $iT_{l'}=1$. \\nHere, $l=|m|$ and $l'=l+1$ for even modes, and $l=|m|+1$ and $l'=l-1$ for odd modes.\\nThe modes given in Figures 5 to 7 are respectively\\nthe $r_0$-mode with $l'=2$, the $r_1$-mode with $l'=2$, and the $r_0$-mode with $l'=3$. \\nIn each figure, the eigenfunctions for the cases of \\n$\\\\bar{\\\\Omega}= 10^{-3}$ and $\\\\bar{\\\\Omega}= 10^{-1}$ \\nare shown in panels $(a)$ and $(b)$, respectively. \\nThe panels $(a)$ of Figures 5 to 7 show that \\nthe toroidal component $iT_{l'}$ of the $r$-modes is dominating the other expansion \\ncoefficients when $\\\\bar\\\\Omega$ is small. \\nHowever, as shown by the panels (b), although $iT_{l'}$\\nof the $r_0$-mode with $l'=2$ remains dominant even at \\n$\\\\bar{\\\\Omega}= 0.1$, the toroidal components $iT_{l'}$\\nof the $r_1$-mode with $l'=2$ and the $r_0$-mode with $l'=3$\\nare not necessarily dominating any more at $\\\\bar{\\\\Omega}= 0.1$.\\nThe properties of the eigenfunctions of the $r_1$-mode with $l'=m=2$ \\nat large $\\\\bar\\\\Omega$ may be regarded as those of the inertial modes. \\n%\\nIt is interesting to note that\\nthe displacement vector of the $r_0$-mode with $l'=3$ has large amplitude \\nin the deep interior and almost vanishing amplitude near the stellar \\nsurface at large $\\\\bar\\\\Omega$. \\nThis suggests that because of the low frequencies $\\\\omega$ in the corotating frame\\nthe buoyant force is as important as the Coriolis force to determine the\\nmode character at large $\\\\bar\\\\Omega$.\\n \\n\\n\\\\subsection{Inertial modes}\\n\\n\\nFor the radiative models with the polytropic index $n=1$ and $\\\\gamma = -10^{-4}$,\\nthe eigenfrequencies $\\\\bar{\\\\omega}\\\\equiv\\\\omega/(GM/R^3)^{1/2}$ \\nof low frequency oscillations\\nare shown as functions of $\\\\bar\\\\Omega$\\nfor $m=1$, 2, and 3 in Figures 8 to 10,\\nwhere even and odd parity modes are displayed in panels (a) and (b), respectively.\\nThe straight dashed lines drawn in the figures are given by\\n$\\\\bar{\\\\omega}=0$ and $\\\\bar{\\\\omega}= m \\\\bar{\\\\Omega}$ (see below).\\nIn the figures, the inertial modes of the $n=1$ isentropic model \\ncomputed at $\\\\bar\\\\Omega=0.1$ are designated by the filled circles.\\nWe note that the oscillation modes in a mode sequence\\nare regarded as inertial modes when $\\\\bar\\\\Omega$ is large, and\\nas internal gravity ($g$-) modes when $\\\\bar\\\\Omega$ is small.\\nIf we follow one of the continuous mode sequences from large $\\\\bar\\\\Omega$ \\nto small $\\\\bar\\\\Omega$,\\nwe may physically understand the behavior of the low frequency oscillation \\nin the radiative models as a function of $\\\\bar\\\\Omega$.\\nAt large $\\\\bar\\\\Omega$, the Coriolis force is dominating as the restoring force\\nand the oscillation mode is identified as an inertial mode.\\nAs $\\\\bar\\\\Omega$ decreases, however, the buoyant force \\nbecomes dominating the Coriolis force\\nand the mode becomes identical with a $g$-mode \\nin the limit of $\\\\bar\\\\Omega\\\\rightarrow 0$.\\nBecause of the effects of the buoyant force in the radiative model,\\nthe frequency $\\\\bar\\\\omega$ of the inertial modes deviates from that\\nof the inertial modes of the isentropic model as $\\\\bar\\\\Omega$ decreases.\\n\\n\\nThe modes within the two straight dashed lines depicted in Figures 8, 9 \\nand 10 are\\nunstable against the gravitational radiation driven instability \\nin the sense that they satisfy the frequency condition\\n$\\\\sigma(\\\\sigma+m\\\\Omega) < 0$ (Friedman \\\\& Schutz 1978).\\nWe can see from Figure 8 that the $i_k$-modes with $k\\\\neq0$ and \\n$m=1$ are stable against the instability for all $\\\\bar{\\\\Omega}$. \\nFigures 9 and 10 show that as $\\\\bar\\\\Omega$ increases\\nall the retrograde $g$-modes with $|m|\\\\geq 2$, which are stable \\nagainst the instability when $\\\\bar\\\\Omega\\\\sim0$, \\nbecome retrograde inertial modes, which are unstable against the instability \\nat large $\\\\bar{\\\\Omega}$.\\n\\n\\n\\nThere are several cases where we find it practically impossible to\\nobtain completely continuous mode sequences \\nbetween the $g$-modes at small $\\\\bar\\\\Omega$ and\\nthe inertial modes at large $\\\\bar\\\\Omega$.\\nIn such sequences, there exist a domain of $\\\\bar\\\\Omega$, in which \\nthere appear a lot of modes having a large number of nodes\\nof the dominant expansion coefficients, and it is difficult to identify the\\nsame oscillation modes as those computed in the previous steps in $\\\\bar\\\\Omega$.\\nIn Figures 8 to 10, the domains of $\\\\bar\\\\Omega$ with this difficulty are indicated by\\nthe dotted lines in the mode sequences.\\nUnfortunately, we cannot remove the difficulty by increasing $k_{max}$.\\nOne of the reasons for the difficulty may be attributed to the method of\\ncalculation we employ in this paper.\\nAs discussed in Unno et al (1989), since we have truncated \\nthe infinite system of differential equations to obtain a finite system of equations,\\nthe numerical procedure used here inevitably contains\\na process of inverting matrices which are singular at some value of the ratio\\n$2\\\\Omega/\\\\omega\\\\sim 1$, depending on the oscillation mode we are interested in.\\nIn this paper, we assume that there always exist a continuous mode sequence\\nbetween the $g$-mode and inertial mode as a function of $\\\\bar\\\\Omega$, \\neven if the mode sequence contains\\na domain of $\\\\bar\\\\Omega$ in which the modes we are interested in cannot be\\nobtained numerically.\\n\\n\\n\\\\subsection{Connection rules between the $g$-modes, $r$-modes and inertial modes}\\n\\n\\n\\nIn order to find \\nthe connection rule between the $g$-modes at small $\\\\bar\\\\Omega$ and \\nthe inertial modes at large $\\\\bar\\\\Omega$, we tabulate first the\\nfrequencies of the $g$-modes at $\\\\bar\\\\Omega=0$ \\nfor the radiative model with the index $n=1$ and $\\\\gamma=-10^{-4}$ in Table 2.\\nTo obtain a clear understanding of the global correspondence between \\nthe $g$-, $r$-, and inertial modes, with the help of Table 2 and Figures 8 to 10, \\nwe give schematic diagrams\\nfor the connection rules between the several low-radial-order modes as follows: \\n\\n\\\\noindent\\nFor odd parity modes we have\\n%\\n\\\\begin{eqnarray}\\n\\\\footnotesize\\n&\\\\left[\\n\\\\begin{array}{llll}\\n & & &\\\\cdots\\\\\\\\\\n & &\\ni_{2\\\\phm{-}}(l_0=\\\\vert m\\\\vert+5)&\\\\cdots\\\\\\\\ \\n &i_{1\\\\phm{-}}(l_0=\\\\vert m\\\\vert+3)&\\ni_{1\\\\phm{-}}(l_0=\\\\vert m\\\\vert+5)&\\\\cdots\\\\\\\\\\ni_{0\\\\phm{-}}(l_0=\\\\vert m\\\\vert +1)&i_{0\\\\phm{-}}(l_0=\\\\vert m\\\\vert+3)&\\ni_{0\\\\phm{-}}(l_0=\\\\vert m\\\\vert+5)&\\\\cdots\\\\\\\\ \\n &i_{-1}(l_0=\\\\vert m\\\\vert +3) &\\ni_{-1}(l_0=\\\\vert m\\\\vert +5) &\\\\cdots\\\\\\\\\\n & &\\ni_{-2}(l_0=\\\\vert m\\\\vert +5) &\\\\cdots\\\\\\\\\\n & & &\\\\cdots\\\\\\\\\\n\\\\end{array} \\n\\\\right]& \\\\label{ina-odd}\\\\\\\\\\n& & \\\\nonumber\\\\\\\\\\n&\\\\Updownarrow& \\\\nonumber\\\\\\\\\\n& & \\\\nonumber\\\\\\\\\\n&\\\\left[\\n\\\\begin{array}{llll}\\n & & &\\\\cdots\\\\\\\\\\n & &g_{1\\\\phm{-}}(l_{\\\\phm{0}}=\\\\vert m\\\\vert+3)&\\\\cdots\\\\\\\\ \\n &g_{1\\\\phm{-}}(l_{\\\\phm{0}}=\\\\vert m\\\\vert+1)&\\ng_{2\\\\phm{-}}(l_{\\\\phm{0}}=\\\\vert m\\\\vert+1)&\\\\cdots\\\\\\\\\\nr_{0\\\\phm{-}}(l'_{\\\\phm{0}}=\\\\vert m\\\\vert)\\\\phm{+1}& \\nr_{1\\\\phm{-}}(l'_{\\\\phm{0}}=\\\\vert m\\\\vert)\\\\phm{+3}&\\nr_{2\\\\phm{-}}(l'_{\\\\phm{0}}=\\\\vert m\\\\vert)\\\\phm{+5}&\\\\cdots\\\\\\\\\\n &g_{-1}(l_{\\\\phm{0}}=\\\\vert m\\\\vert+1)&\\ng_{-2}(l_{\\\\phm{0}}=\\\\vert m\\\\vert+1)&\\\\cdots\\\\\\\\\\n & &g_{-1}(l_{\\\\phm{0}}=\\\\vert m\\\\vert+3)&\\\\cdots\\\\\\\\\\n & & &\\\\cdots\\\\\\\\\\n\\\\end{array}\\n\\\\right]& \\\\ , \\\\label{gra-odd}\\n\\\\end{eqnarray}\\n%\\nand for even parity modes we have\\n%\\n\\\\begin{eqnarray}\\n\\\\footnotesize\\n&\\\\left[\\n\\\\begin{array}{llll}\\n & & &\\\\cdots\\\\\\\\\\n & &i_{3\\\\phm{-}}(l_0=\\\\vert m\\\\vert+6)&\\\\cdots\\\\\\\\ \\n &i_{2\\\\phm{-}}(l_0=\\\\vert m\\\\vert+4)&\\ni_{2\\\\phm{-}}(l_0=\\\\vert m\\\\vert+6)&\\\\cdots\\\\\\\\\\ni_{1\\\\phm{-}}(l_0=\\\\vert m\\\\vert+2)&i_{1\\\\phm{-}}(l_0=\\\\vert m\\\\vert+4)&\\ni_{1\\\\phm{-}}(l_0=\\\\vert m\\\\vert+6)&\\\\cdots\\\\\\\\\\ni_{-1}(l_0=\\\\vert m\\\\vert+2) &i_{-1}(l_0=\\\\vert m\\\\vert+4) &\\ni_{-1}(l_0=\\\\vert m\\\\vert+6)&\\\\cdots\\\\\\\\\\n &i_{-2}(l_0=\\\\vert m\\\\vert+4) &\\ni_{-2}(l_0=\\\\vert m\\\\vert+6)&\\\\cdots\\\\\\\\\\n & &i_{-3}(l_0=\\\\vert m\\\\vert+6)&\\\\cdots\\\\\\\\\\n & & &\\\\cdots\\\\\\\\\\n\\\\end{array} \\n\\\\right]& \\\\label{ina}\\\\\\\\\\n& & \\\\nonumber\\\\\\\\\\n&\\\\Updownarrow& \\\\nonumber\\\\\\\\\\n& & \\\\nonumber\\\\\\\\\\n&\\\\left[\\n\\\\begin{array}{llll}\\n & & &\\\\cdots\\\\\\\\\\n & &g_{1\\\\phm{-}}(l_{\\\\phm{0}}=\\\\vert m\\\\vert+4) &\\\\cdots\\\\\\\\ \\n &g_{1\\\\phm{-}}(l_{\\\\phm{0}}=\\\\vert m\\\\vert+2)&\\n g_{2\\\\phm{-}}(l_{\\\\phm{0}}=\\\\vert m\\\\vert+2)&\\\\cdots\\\\\\\\\\ng_{1\\\\phm{-}}(l_{\\\\phm{0}}=\\\\vert m\\\\vert)\\\\phm{+2}& \\ng_{2\\\\phm{-}}(l_{\\\\phm{0}}=\\\\vert m\\\\vert)\\\\phm{+4}&\\ng_{3\\\\phm{-}}(l_{\\\\phm{0}}=\\\\vert m\\\\vert)\\\\phm{+6}&\\\\cdots\\\\\\\\\\ng_{-1}(l_{\\\\phm{0}}=\\\\vert m\\\\vert)\\\\phm{+2} & \\ng_{-2}(l_{\\\\phm{0}}=\\\\vert m\\\\vert)\\\\phm{+4} &\\ng_{-3}(l_{\\\\phm{0}}=\\\\vert m\\\\vert)\\\\phm{+6} &\\\\cdots\\\\\\\\\\n &g_{-1}(l_{\\\\phm{0}}=\\\\vert m\\\\vert+2) &\\n g_{-2}(l_{\\\\phm{0}}=\\\\vert m\\\\vert+2) &\\\\cdots\\\\\\\\\\n & &g_{-1}(l_{\\\\phm{0}}=\\\\vert m\\\\vert+4) &\\\\cdots\\\\\\\\\\n & & &\\\\cdots\\\\\\\\\\n\\\\end{array}\\n\\\\right]& \\\\ , \\\\label{gra}\\n\\\\end{eqnarray}\\n%\\nwhere the two corresponding modes occupy the same position \\nin the two matrices connected with an arrow. \\n\\n\\nFrom the diagrams,\\nwe may find the connection rule between the $g_{\\\\pm k}$-modes with $l$ and $m$ and \\nthe inertial modes $i_{\\\\pm j}$ with $l_0$ and $m$: \\n\\\\begin{equation}\\ng_{\\\\pm k}(l=l^j)\\\\longleftrightarrow i_{\\\\pm j}(l_0=l^j+2k), \\\\label{g-i}\\n\\\\end{equation}\\nwhere $l^j=|m|+2j-2$ for even modes and $l^j=|m|+2j-1$ for odd modes,\\nand $j$ and $k$ are positive integers.\\n%\\nThe symbol $g_{\\\\pm k}$ denotes the $g$-mode\\nwith $k$ radial nodes of the expansion coefficient $S_l$, \\nhaving positive and negative frequencies $\\\\omega$\\nobserved in the corotating frame of the star when $\\\\bar\\\\Omega\\\\not=0$.\\n\\n\\nThe connection rule between the $r$-modes\\nassociated with $l'=|m|$ and the inertial modes $i_0$ with $l_0$ and $m$ may be given by\\n%\\n\\\\begin{equation}\\nr_{j-1} ( l' = \\\\vert m \\\\vert ) \\\\longleftrightarrow i_0 \\n(l_0 = |m| + 2 j -1) \\\\, ,\\n\\\\label{r-i-odd}\\n\\\\end{equation}\\n%\\nwhere $j$ is a positive integer.\\nNote that the \\n$i_0$-mode with $l_0 = \\\\vert m \\\\vert +1$ is exactly the same as \\nthe $r_0$-modes with $l'=\\\\vert m \\\\vert$. \\nTo establish the connection rules given above, we have neglected the effects of\\navoided crossings between the modes associated with different values of $l$ and/or $k$, since\\nthe mode property is carried over at the crossings.\\n\\n\\n\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%% V. DISSIPATION TIMESCALES ..... %%\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\n\\\\section{Dissipation Timescales for $r$-modes of Non-isentropic Stars}\\n\\n\\nFor the rotational modes of non-isentropic models, we have found that\\nall the $r$-modes except the $r_0$-mode with $l'=|m|=1$ \\nare unstable to the gravitational radiation reaction \\nin the sense that the frequency $\\\\sigma$ satisfies the condition \\n$\\\\sigma(\\\\sigma+m\\\\Omega)<0$.\\nLet us determine the stability of the $r$-modes of the non-isentropic models\\nagainst the gravitational radiation driven instability, taking account of\\nthe dissipative processes due to the shear and bulk viscosity, where\\nwe will follow the method of calculation almost the same as that employed\\nin the previous stability analyses of the $r_0$-mode with $l'=|m|$ and the\\ninertial modes for isentropic models\\n(Lindblom et al 1998, Owen et al 1998, Andersson et al 1998, \\nKokkotas \\\\& Stergioulas 1998, Lindblom et al 1999, Lockitch \\\\& Friedman 1999,\\nYoshida \\\\& Lee 2000).\\n\\n\\n\\n\\n\\nThe damping timescale of the $r_0$-mode associated with $l'=|m|$\\nfor sufficiently small $\\\\bar{\\\\Omega}$ may be estimated by (Lindblom et al 1998)\\n%\\n\\\\begin{eqnarray}\\n\\\\frac{1}{\\\\tau} &=& \\\\frac{1}{\\\\tilde \\\\tau_S} \\\\left( \\\\frac{10^9 K}{T} \\\\right)^2\\n+ \\\\frac{1}{\\\\tilde \\\\tau_B} \\\\left( \\\\frac{T}{10^9 K} \\\\right)^6\\n\\\\left( \\\\frac{\\\\Omega^2}{\\\\pi G \\\\bar{\\\\rho}} \\\\right) \\\\nonumber \\\\\\\\\\n&+& \\\\sum_{l=2}^{\\\\infty} \\\\frac{1}{\\\\tilde \\\\tau_{J,l}} \\n\\\\left( \\\\frac{\\\\Omega^2}{\\\\pi G \\\\bar{\\\\rho}} \\\\right)^{l+1}\\n+ \\\\sum_{l=2}^{\\\\infty} \\\\frac{1}{\\\\tilde \\\\tau_{D,l}} \\n\\\\left( \\\\frac{\\\\Omega^2}{\\\\pi G \\\\bar{\\\\rho}} \\\\right)^{l+2} \\\\, ,\\n \\\\label{tau2}\\n\\\\end{eqnarray}\\n%\\nwhere $\\\\bar{\\\\rho}$ is the average density of the star.\\nThe dissipative timescales $\\\\tilde\\\\tau$ are calculated for each oscillation mode\\nin the limit of $\\\\bar\\\\Omega\\\\rightarrow 0$ so that\\nthey are independent of the rotation frequency $\\\\Omega$.\\nHere, the first, second, third and fourth terms in the right-hand side of \\nequation (\\\\ref{tau2}) are contributions from the shear viscosity, \\nthe bulk viscosity, the current multipole radiation and the mass \\nmultipole radiation, respectively. \\nThe expression (\\\\ref{tau2}) of the damping timescales has been derived on the assumptions that\\nthe frequency of the modes is well represented by a linear function of $\\\\Omega$ and the\\ntoroidal component of the displacement vector is dominating.\\nAlthough the assumptions are reasonable for the $r_0$-modes with $l'=|m|$ \\n(see Yoshida and Lee 2000),\\nthey are not necessarily correct for the $r_k$-modes with $l'=|m|$ and $k>0$, \\nfor which we use\\n%\\n\\\\begin{eqnarray}\\n\\\\frac{1}{\\\\tau} &=& \\\\frac{1}{\\\\tilde \\\\tau_S} \\\\left( \\\\frac{10^9 K}{T} \\\\right)^2\\n+ \\\\frac{1}{\\\\tilde \\\\tau_B} \\\\left( \\\\frac{T}{10^9 K} \\\\right)^6\\n\\\\left( \\\\frac{\\\\pi G \\\\bar{\\\\rho}}{\\\\Omega^2} \\\\right) \\\\nonumber \\\\\\\\\\n&+& \\\\sum_{l=2}^{\\\\infty} \\\\frac{1}{\\\\tilde \\\\tau_{J,l}} \\n\\\\left( \\\\frac{\\\\Omega^2}{\\\\pi G \\\\bar{\\\\rho}} \\\\right)^{l+1}\\n+ \\\\sum_{l=2}^{\\\\infty} \\\\frac{1}{\\\\tilde \\\\tau_{D,l}} \\n\\\\left( \\\\frac{\\\\Omega^2}{\\\\pi G \\\\bar{\\\\rho}} \\\\right)^{l+2} \\\\, ,\\n \\\\label{tau2b}\\n\\\\end{eqnarray}\\n%\\nbecause these $r$-modes become inertial modes at large $\\\\bar\\\\Omega$.\\nThe difference between these two expressions is found\\nin the second terms in the right-hand side of the two equations. \\nWhen $\\\\bar\\\\Omega$ is small, equation (\\\\ref{tau2b}) gives the correct \\nexpression of $\\\\tau^{-1}$ for inertial modes of isentropic stars\\n(See, Lockitch \\\\& Friedman 1999, Yoshida \\\\& Lee 2000).\\nTo determine the damping timescales $\\\\tilde\\\\tau$ in (\\\\ref{tau2b}) in the limit of \\n$\\\\bar\\\\Omega\\\\rightarrow 0$,\\nwe assume that the dissipative timescale $\\\\tilde\\\\tau^{-1}$ \\ndepends on $\\\\bar\\\\Omega$ as $a\\\\bar\\\\Omega^2+b$ for each dissipative process, where\\nthe two unknown constants $a$ and $b$ are\\ndetermined by calculating $\\\\tilde\\\\tau^{-1}$ and $d\\\\tilde\\\\tau^{-1}/d\\\\bar\\\\Omega$\\nat $\\\\bar\\\\Omega=0.1$.\\nThe $\\\\tilde\\\\tau^{-1}$ in the limit of $\\\\bar\\\\Omega\\\\rightarrow0$ is given by\\n$\\\\tilde\\\\tau^{-1}=b$.\\nWe note that equation (\\\\ref{tau2b}) is not necessarily a correct approximation for \\nnon-isentropic stars. \\nWe use the expression (\\\\ref{tau2b}) simply \\nbecause we want to give rough \\nestimates of the dissipative timescales, in order to compare the timescales \\nwith those of the isentropic case.\\n\\n \\nIn Table 3, we tabulate the dissipation timescales $\\\\tilde\\\\tau$ in the unit of second for \\nthe various dissipative processes for the $r_k$-modes with $l'=\\\\vert m \\\\vert$, \\nwhere the radius and the mass of the $n=1$ polytropic neutron star model\\nat $\\\\Omega=0$ are chosen to be $R=12.57\\\\mbox{km}$ and $M=1.4M_{\\\\sun}$, \\nrespectively. \\nNote that in Table 3 we have not included the $r_k$-modes with $l'>|m|$,\\nsince the frequency $\\\\omega$ becomes vanishingly small at large $\\\\bar\\\\Omega$ \\n(see Figures 1 to 3) \\nand hence the magnitude of the gravitational radiation driven\\ninstability, which is proportional to $\\\\omega$, becomes quite small.\\nFor the $r_0$-modes with $l'=|m|$,\\nin order to see the effects of the buoyancy force on \\nthe stability, the results for the four different values of $\\\\gamma$ are tabulated. \\nAs shown by Table 3, the gravitational radiation driven instability \\nfor the $r_0$-modes with $l'=\\\\vert m \\\\vert$ \\nis not affected by introducing the deviation from isentropic structure and remains\\nstrong even for the non-isentropic models.\\nAs for the $r_k$-modes with $l'=|m|$ and $k> 0$, it is found that \\nthe dissipative timescales are comparable to those of the corresponding inertial \\nmodes (compare Table 4 of Yoshida \\\\& Lee 2000). Thus, we may conclude that the $r$-mode \\ninstability driven by the gravitational radiation reaction is dominated by \\nthe $r_0$-mode with $l'=\\\\vert m \\\\vert = 2$ both in isentropic and in non-isentropic stars. \\n\\n\\n\\n\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%% CONCLUSIONS %%\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\n\\\\section{Conclusions}\\n\\n \\nIn this paper, we have numerically investigated the properties of rotational \\nmodes for slowly rotating, \\nnon-isentropic, Newtonian stars, where the effects of \\nthe centrifugal force are taken into consideration to calculate the modes\\nwith accuracy up to the order of $\\\\bar\\\\Omega^3$.\\nEstimating the dissipation timescales due to the \\ngravitational radiation and the shear and bulk viscosity\\nfor simple polytropic neutron star models with the index $n=1$,\\nwe have shown that the gravitational radiation driven instability\\nof the $r_0$-mode with $l'=|m|$ is hardly \\naffected by introducing the deviation from the\\nisentropic structure, and that the instability of the $r_0$-modes with $l'=|m|=2$\\nremains strongest even for the non-isentropic models.\\nNote that the $r_0$-modes with $l'=|m|$ are the only $r$-modes possible in\\nisentropic stars and their modal property does not very much depend on $\\\\Omega$ and \\nthe deviation from isentropic structure.\\nWe thus conclude that \\nthe result of the stability analysis of the $r_0$-modes with $l'=|m|$\\nfor isentropic stars remains valid even for non-isentropic stars.\\n\\n\\nWe have numerically found that for the radiative models\\nthe inertial modes at large $\\\\bar\\\\Omega$ \\nbecome identical with the $r_k$-modes with $l'=|m|$ and $k>0$ and $g$-modes\\nin the limit of $\\\\bar\\\\Omega\\\\rightarrow 0$ because of the effect of the buoyant force, \\nwhere the integer $k$ denotes the number of node of the \\neigenfunction with dominant amplitude.\\nThis behavior of the $g$-modes or the inertial modes as functions of $\\\\Omega$\\nhas been suggested by, for example,\\nSaio (1999) and Lockitch \\\\& Friedman (1999).\\nWe find the connection rules between the $r_k$-modes with $l'=|m|$ and $k>0$ and\\n$g$-modes at small $\\\\bar\\\\Omega$ and\\nthe inertial modes at large $\\\\bar\\\\Omega$.\\nWe also suggest that the $r_k$-modes with $l'>|m|$ and $k\\\\ge 0$, \\nwhose frequency in the corotating frame\\nbecomes vanishingly small as $\\\\bar\\\\Omega$ increases, \\nhave at large $\\\\bar\\\\Omega$ no corresponding inertial\\nmodes of the isentropic models.\\n\\n\\nGood progress has been made in the understanding of\\nthe properties of the $r$-mode instability \\ndue to the gravitational radiation since its discovery.\\nRecently, for example, Yoshida et al (1999) have shown that the results \\nof the $r$-mode instability obtained by using the slow rotation approximation,\\nas employed in this paper,\\nare consistent with the results obtained \\nby calculating directly the $r$-mode oscillations \\nof rotating stars without the approximation. \\nKojima (1998) and Kojima \\\\& Hosonuma (1999) have studied the time evolutional \\nbehavior of $r$-modes by using the Laplace transformation technique\\nfor slowly rotating relativistic models. \\nLockitch (1999) also obtained $r$-modes and \\nrotation modes for slowly rotating, incompressible, relativistic stars. \\nHowever, we believe it necessary to show\\nthat the gravitational radiation driven instability\\nof $r$-modes remains sufficiently robust in more realistic and unrestricted situations,\\ntaking account of the effects of differential rotation, magnetic field \\nand general relativity, for example.\\nTo investigate the $r$-mode instability in more general situations is one of\\nour future studies.\\n\\n\\n\\n\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%% END OF MAIN BODY OF PAPER %%\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\n\\\\acknowledgements\\n\\n\\nWe would like to thank Prof. H. Saio for useful comments and discussions. \\nS.Y. was supported by Research Fellowship of the Japan Society for \\nthe Promotion of Science for Young Scientists. \\n\\n\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%% BIBLIOGRAPHY %%\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\\\begin{thebibliography}{}\\n\\n\\\\bibitem[Andersson 1998]{nils97}\\n Andersson, N. 1998, \\\\apj, 502, 708\\n%\\n\\\\bibitem[Andersson et al.\\\\ 1998]{aks98}\\n Andersson, N., Kokkotas, K., \\\\& Schutz B. F. 1998, \\\\apj, 510, 846\\n%\\n\\\\bibitem[Berthomieu et al. 1978]{be78}\\nBerthomieu, G., Gonczi, G., Graff, Ph., Provost, J., \\\\& Rocca, A. 1978, \\n\\\\aap, 70, 597 \\n%\\n\\\\bibitem[Beyer \\\\& Kokkotas 1999]{bk99}\\n Beyer, H. R., \\\\& Kokkotas, K. D. 1999, \\\\mnras, 308, 745\\n%\\n\\\\bibitem[Friedman \\\\& Morsink 1998]{jfs97} \\n Friedman, J. L., \\\\& Morsink, S. M. 1998, \\\\apj, 502, 714\\n%\\n\\\\bibitem[Friedman \\\\& Schutz 1978]{fs87} \\n Friedman, J. L., \\\\& Schutz, B. F. 1978, \\\\apj, 222, 281\\n%\\n\\\\bibitem[Greenspan 1964]{g64}\\n Greenspan, H. P. 1964, The Theory of Rotating Fluids (Cambridge: Cambridge \\nUniv. Press)\\n%\\n\\\\bibitem[Kojima 1998]{k98}\\n Kojima, Y. 1998, \\\\mnras, 293, 49\\n%\\n\\\\bibitem[Kojima \\\\& Hosonuma 1999]{kh99}\\n Kojima, Y., \\\\& Hosonuma, M. 1999, \\\\apj, 520, 788\\n%\\n\\\\bibitem[Kokkotas \\\\& Stergioulas 1998]{ks98}\\n Kokkotas, K., \\\\& Stergioulas, N. 1998, \\\\aap, 341, 110\\n%\\n\\\\bibitem[Lee 1993]{l93}\\n Lee, U. 1993, \\\\apj, 405, 359\\n%\\n\\\\bibitem[Lee \\\\& Saio 1986]{ls86}\\n Lee, U., \\\\& Saio, H. 1986, \\\\mnras, 221, 365\\n%\\n\\\\bibitem[Lee \\\\& Saio 1997]{ls97}\\n Lee, U., \\\\& Saio, H. 1997, \\\\apj, 491, 839\\n%\\n\\\\bibitem[Lee et al.\\\\ 1992]{lsvh92}\\n Lee, U., Strohmayer, T. D., \\\\& Van Horn, H. M. 1992, \\\\apj, 397, 647\\n%\\n\\\\bibitem[Lindblom \\\\& Ipser 1998]{li98}\\n Lindblom, L., \\\\& Ipser, J. R. 1998, \\\\prd, 59, 044009\\n%\\n\\\\bibitem[Lindblom et al.\\\\ 1999]{lmo99}\\n Lindblom, L., Mendell, G., \\\\& Owen, B. J. 1999, \\\\prd, 60, 064006\\n%\\n\\\\bibitem[Lindblom et al.\\\\ 1998]{lom98}\\n Lindblom, L., Owen, B. J., \\\\& Morsink, S. M. 1998, \\\\prl, 80, 4843\\n%\\n\\\\bibitem[Lockitch \\\\ 1999]{lo99}\\n Lockitch, K. H. 1999, Ph.D. Thesis (University of Wisconsin-Milwaukee), \\n(gr-qc/9909029) \\n%\\n\\\\bibitem[Lockitch \\\\& Friedman\\\\ 1999]{lf99}\\n Lockitch, K. H., \\\\& Friedman J. L. 1999, \\\\apj, 521, 764\\n%\\n\\\\bibitem[Owen et al.\\\\ 1998]{o98}\\n Owen, B. J., Lindblom, L., Cutler, C., Schutz, B. F., Vecchio, A., \\\\&\\n Andersson, N. 1998, \\\\prd, 58, 084020\\n%\\n\\\\bibitem[Papaloizou \\\\& Pringle 1978]{pp78}\\n Papaloizou, J., \\\\& Pringle, J. E. 1978, \\\\mnras, 182, 423\\n%\\n\\\\bibitem[Pedlosky 1987]{pe87}\\n Pedlosky, J. 1987, Geophysical Fluid Dynamics, Second Edition \\n(Berlin: Springer-Verlag)\\n%\\n\\\\bibitem[Press et al. 1992]{pr92}\\n Press, W. H., Teukolsky, S. A., Vetterling, W. T., \\\\& Flannery, B. P. \\n1992, Numerical Recipes: The Art of Scientific Computing, Second Edition \\n(Cambridge: Cambridge Univ. Press)\\n%\\n\\\\bibitem[Provost et al. 1981]{pea81}\\n Provost, J., Berthomieu, G., \\\\& Rocca, A. 1981, \\\\aap, 94, 126\\n%\\n\\\\bibitem[Regge \\\\& Wheeler 1957]{rw57}\\n Regge, T., \\\\& Wheeler, J. A. 1957, Phys. Rev., 108, 1063\\n%\\n\\\\bibitem[Saio 1982]{s82}\\n Saio, H. 1982, \\\\apj, 256, 717\\n%\\n\\\\bibitem[Saio 1999]{s99}\\n Saio, H. 1999, private communication. \\n%\\n\\\\bibitem[Tassoul 1978]{t78}\\n Tassoul, J.-L. 1978, Theory of Rotating Stars (Princeton: Princeton Univ.\\nPress)\\n%\\n\\\\bibitem[Thorne 1980]{th80}\\n Thorne, K. S. 1980, Rev. Mod. Phys., 52, 299\\n%\\n\\\\bibitem[Unno et al. 1989]{u89}\\n Unno, W., Osaki, Y., Ando, H., Saio, H., \\\\& Shibahashi, H. 1989, \\n Nonradial Oscillations of Stars, Second Edition (Tokyo: Univ. Tokyo Press) \\n%\\n\\\\bibitem[Yoshida et al 1999]{ykye99}\\n Yoshida, S'i., Karino, S., Yoshida, S., \\\\& Eriguchi, Y. 1999, \\n Submitted to \\\\mnras (astro-ph/9910532)\\n%\\n\\\\bibitem[Yoshida \\\\& Lee 2000]{yl00}\\n Yoshida, S., \\\\& Lee, U. 2000, \\\\apj, in press. (astro-ph/9908197)\\n%\\n\\\\end{thebibliography}\\n%\\n\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%% FIGURES %%\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\n\\\\begin{figure}\\n\\\\epsscale{.6}\\n\\\\plotone{fig1.eps}\\n\\\\caption{Dimensionless frequencies $\\\\kappa=\\\\omega/\\\\Omega$ for the\\nlow-radial-order $r$-modes with $m=1$ are plotted as functions of the dimensionless \\nangular rotation frequency $\\\\bar{\\\\Omega}=\\\\Omega/(GM/R^3)^{1/2}$, \\nfor the $n=1$ polytropic model with $\\\\gamma=-10^{-4}$. \\nThe solid, the dotted and the dashed curves are\\nfor the $r_0$, $r_1$, and $r_2$-modes, respectively. \\nThe attached label $l'$ \\ndenotes the angular quantum number $l'$ associated with the spherical harmonic function\\nrepresenting the toroidal component of the displacement vector.\\nNote that the eigenvalue of the \\n$r$-modes is given by $\\\\kappa_0=2 m/(l'(l'+1))$ in the limit of $\\\\bar\\\\Omega\\\\rightarrow 0$. \\nThe filled circles at $\\\\bar{\\\\Omega}=0.1$ denote the eigenvalues $\\\\kappa$ of \\nthe inertial modes calculated for the isentropic model \\nwith the index $n=1$ and $\\\\gamma=0$ at $\\\\bar{\\\\Omega}=0.1$. }\\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n\\\\epsscale{.6}\\n\\\\plotone{fig2.eps}\\n\\\\caption{Same as Figure 1, but for $m=2$.}\\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n\\\\epsscale{.6}\\n\\\\plotone{fig3.eps}\\n\\\\caption{Same as Figure 2, but for $m=3$.}\\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n\\\\epsscale{.6}\\n\\\\plotone{fig4.eps}\\n\\\\caption{Dimensionless frequencies $\\\\kappa$ for the low-radial-order \\n$r$-modes with $m=2$ are plotted as functions of $|\\\\gamma|$ for the $n=1$ polytropic model \\nat $\\\\bar{\\\\Omega}=10^{-2}$. \\nThe attached label $l'$ denotes the index of the spherical harmonic function for \\nthe toroidal component of the displacement vector.\\nThe number of nodes of $iT_{l'}$ in the radial direction \\nis indicated by the subscript in the notation $r_k$ attached to the mode sequences. \\nThe solid line and the dotted line are given for negative \\nand positive values of $\\\\gamma$, respectively.} \\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n\\\\epsscale{.4}\\n\\\\plottwo{fig5a.eps}{fig5b.eps}\\n\\\\caption{The first expansion coefficients $S_l$, $H_l$, $iT_{l'}$ for \\nthe $r_0$ mode with $l'=m=2$ are plotted against $a/R$ for \\nthe polytropic model with the index $n=1$ and $\\\\gamma=-10^{-4}$. \\nPanels $(a)$ and $(b)$ are for the cases of\\n$\\\\bar{\\\\Omega}=10^{-3}$ and $\\\\bar{\\\\Omega}=10^{-1}$, respectively. \\nThe eigenfunctions are normalized so that $T_{l'}(a=R)=1$. \\nThe attached labels $S_l$, $H_l$, and $iT_{l'}$ denote the expansion coefficients \\nof the displacement vector.}\\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n\\\\epsscale{.4}\\n\\\\plottwo{fig6a.eps}{fig6b.eps}\\n\\\\caption{Same as Figure 5, but for the $r_1$-mode with $l'=2$.}\\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n\\\\epsscale{.4}\\n\\\\plottwo{fig7a.eps}{fig7b.eps}\\n\\\\caption{Same as Figure 5, but for the $r_0$-mode with $l'=3$.}\\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n\\\\epsscale{.4}\\n\\\\plottwo{fig8a.eps}{fig8b.eps}\\n\\\\caption{Dimensionless frequencies \\n$\\\\bar{\\\\omega}=\\\\omega/(GM/R^3)^{1/2}$ for the low-radial-order \\n$g$- and inertial modes with $m=1$ are plotted as functions of \\n$\\\\bar{\\\\Omega}=\\\\Omega/(GM/R^3)^{1/2}$, \\nfor the $n=1$ polytropic model with $\\\\gamma=-10^{-4}$. \\nThe even and the odd parity modes are shown in panels $(a)$ and $(b)$, \\nrespectively. \\nThe attached labels \\n$g_{\\\\pm k}(l)\\\\longleftrightarrow i_{\\\\pm j}(l_0-\\\\vert m\\\\vert)$ \\nindicates the connection rule between the $g$-modes and inertial modes.\\nThe filled circles at $\\\\bar{\\\\Omega}=0.1$ denote the eigenfrequencies $\\\\bar\\\\omega$\\nof the inertial modes for the $n=1$ isentropic model at $\\\\bar{\\\\Omega}=0.1$.\\nThe part indicated by the dotted line in the mode sequence is the domain\\nof $\\\\bar\\\\Omega$, in which the modes belonging to the sequence cannot be \\ncalculated. The two dashed lines are given by $\\\\bar{\\\\omega}=0$ \\nand $\\\\bar{\\\\omega}= m \\\\bar{\\\\Omega}$.} \\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n\\\\epsscale{.4}\\n\\\\plottwo{fig9a.eps}{fig9b.eps}\\n\\\\caption{Same as Figure 8, but for $m=2$.}\\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n\\\\epsscale{.4}\\n\\\\plottwo{fig10a.eps}{fig10b.eps}\\n\\\\caption{Same as Figure 9, but for $m=3$.}\\n\\\\end{figure}\\n\\n\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n%% TABLES %%\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\\n\\n\\\\clearpage\\n\\n\\\\begin{deluxetable}{ccccc}\\n\\\\footnotesize\\n\\\\tablecaption{$(\\\\omega/\\\\Omega-\\\\kappa_0)/{\\\\bar{\\\\Omega}}^2\\\\ \\n$\\\\tablenotemark{a} \\\\ \\nfor $r$-modes of the $n=3$ polytrope with $\\\\Gamma=5/3$ \\\\label{code-check}}\\n\\\\tablewidth{250pt}\\n\\\\tablehead{\\n\\\\colhead{$m$} & \\\\colhead{$l'$} & \\\\colhead{Mode} & \\n\\\\colhead{Present} & \\\\colhead{Saio 1982} \\n}\\n\\\\startdata\\n 1 & 1 & $r_0$ & \\\\phm{-}0.000 & \\\\phm{-}0.000 \\\\nl\\n & & $r_1$ & -0.040 & -0.040 \\\\nl\\n & & $r_2$ & -0.115 & -0.114 \\\\nl\\n & 2 & $r_0$ & -0.100 & -0.099 \\\\nl\\n & & $r_1$ & -0.191 & -0.190 \\\\nl\\n & & $r_2$ & -0.315 & -0.312 \\\\nl\\n & 3 & $r_0$ & -0.037 & -0.037 \\\\nl\\n & & $r_1$ & -0.063 & -0.061 \\\\nl\\n & & $r_2$ & -0.097 & -0.096 \\\\nl\\n 2 & 2 & $r_0$ & \\\\phm{-}0.121 & \\\\phm{-}0.120 \\\\nl\\n & & $r_1$ & \\\\phm{-}0.024 & \\\\phm{-}0.024 \\\\nl\\n & & $r_2$ & -0.001 & -0.001 \\\\nl\\n & 3 & $r_0$ & -0.037 & -0.037 \\\\nl\\n & & $r_1$ & -0.071 & -0.070 \\\\nl\\n & & $r_2$ & -0.115 & -0.114 \\\\nl\\n 3 & 3 & $r_0$ & \\\\phm{-}0.174 & \\\\phm{-}0.173 \\\\nl\\n & & $r_1$ & \\\\phm{-}0.064 & \\\\phm{-}0.063 \\\\nl\\n & & $r_2$ & \\\\phm{-}0.028 & \\\\phm{-}0.027 \\\\nl\\n\\\\enddata\\n\\\\tablenotetext{a}{$\\\\kappa_0$ is defined as $\\\\kappa_0=2 m/(l' (l'+1))$. \\nThe eigenfrequencies are calculated at $\\\\bar{\\\\Omega}=0.1$. }\\n\\\\end{deluxetable}\\n\\n\\\\begin{deluxetable}{ccc}\\n\\\\footnotesize\\n\\\\tablecaption{The eigenfrequency $\\\\bar{\\\\omega}$ \\nfor low-radial-order $g$-modes of the $n=1$ polytrope\\nwith $\\\\gamma=-10^{-4}$ at $\\\\Omega=0$ \\\\label{g-mode}}\\n\\\\tablewidth{250pt}\\n\\\\tablehead{\\n\\\\colhead{$l$} & \\\\colhead{$g_1$} & \\\\colhead{$g_2$} \\n}\\n\\\\startdata\\n 1 & $1.20\\\\times 10^{-2}$ & $7.69\\\\times 10^{-3}$ \\\\nl\\n 2 & $1.68\\\\times 10^{-2}$ & $1.15\\\\times 10^{-2}$ \\\\nl\\n 3 & $2.01\\\\times 10^{-2}$ & $1.44\\\\times 10^{-2}$ \\\\nl\\n 4 & $2.26\\\\times 10^{-2}$ & $1.68\\\\times 10^{-2}$ \\\\nl\\n 5 & $2.47\\\\times 10^{-2}$ & $1.88\\\\times 10^{-2}$ \\\\nl\\n 6 & $2.65\\\\times 10^{-2}$ & $2.05\\\\times 10^{-2}$ \\\\nl\\n\\\\enddata\\n\\\\end{deluxetable}\\n\\n\\\\clearpage\\n\\n\\\\begin{deluxetable}{cccccccccc}\\n\\\\footnotesize\\n\\\\tablecaption{Dissipative timescales $\\\\tilde\\\\tau$ of $r$-modes\\\\tablenotemark{a} \\n\\\\ for the polytropic neutron star models with the index $n=1$. }\\n\\\\tablewidth{0pt}\\n\\\\tablehead{\\n\\\\colhead{$m$} & \\\\colhead{mode} & \\\\colhead{$\\\\gamma$} \\n & \\\\colhead{$\\\\kappa_0$}\\n & \\\\colhead{$\\\\tilde \\\\tau_B$(s)} & \\\\colhead{$\\\\tilde \\\\tau_S$(s)} \\n & \\\\colhead{$\\\\tilde \\\\tau_{J,\\\\vert m\\\\vert}$(s)\\\\tablenotemark{b}} \\n & \\\\colhead{$\\\\tilde \\\\tau_{D,\\\\vert m\\\\vert+1}$(s)} \\n & \\\\colhead{$\\\\tilde \\\\tau_{J,\\\\vert m\\\\vert+2}$(s)}\\n} \\n\\\\startdata\\n1&$r_1$&\\n$0$\\n & 0.691 &$ 5.89\\\\times 10^{9} $&$ 9.23\\\\times 10^{7} $\\n &$ \\\\cdots$&$ -2.46\\\\times 10^{5} $&$ -1.27\\\\times 10^{8} $\\n\\\\nl\\n & &\\n$-10^{-4}$\\n & 1.000 &$ 6.08\\\\times 10^{9} $&$ 9.04\\\\times 10^{7} $\\n &$ \\\\cdots$&$ -2.31\\\\times 10^{5} $&$ -1.58\\\\times 10^{8} $\\n\\\\nl\\n & & & & & & & & \\\\nl\\n2&$r_0$&\\n$\\\\phm{-}10^{-4}$\\n &0.667 &$ 2.03\\\\times 10^{11} $&$ 2.50\\\\times 10^{8} $\\n &$ -3.31\\\\times 10^{0} $&$ -3.49\\\\times 10^{2}$&$ \\\\cdots$\\n\\\\nl\\n & &\\n$0$\\n &0.667 &$ 2.03\\\\times 10^{11} $&$ 2.50\\\\times 10^{8} $\\n &$ -3.31\\\\times 10^{0} $&$ -3.49\\\\times 10^{2}$&$ \\\\cdots$\\n\\\\nl\\n & &\\n$-10^{-4}$\\n &0.667 &$ 2.03\\\\times 10^{11} $&$ 2.50\\\\times 10^{8} $\\n &$ -3.31\\\\times 10^{0} $&$ -3.49\\\\times 10^{2}$&$ \\\\cdots$\\n\\\\nl\\n & &\\n$-10^{-2}$\\n &0.667 &$ 2.10\\\\times 10^{11} $&$ 2.54\\\\times 10^{8} $\\n &$ -3.31\\\\times 10^{0} $&$ -3.49\\\\times 10^{2}$&$ \\\\cdots$\\n\\\\nl\\n & & & & & & & & \\\\nl\\n &$r_1$& \\n$0$\\n &0.517 &$ 6.47\\\\times 10^{9} $&$ 6.18\\\\times 10^{7} $\\n &$ -1.31\\\\times 10^{8} $&$ -8.39\\\\times 10^{4} $\\n &$ -1.88\\\\times 10^{6} $\\n\\\\nl\\n & &\\n$-10^{-4}$\\n &0.667 &$ 6.79\\\\times 10^{9} $&$ 6.01\\\\times 10^{7} $\\n &$\\\\phm{-}2.18\\\\times 10^{7}\\\\ \\\\tablenotemark{c} $\\n &$ -7.05\\\\times 10^{4} $&$ -2.06\\\\times 10^{6} $\\n\\\\nl\\n & & & & & & & & \\\\nl\\n3&$r_0$&\\n$\\\\phm{-}10^{-4}$\\n &0.500 &$ 6.64\\\\times 10^{10} $&$ 1.43\\\\times 10^{8} $\\n &$ -3.17\\\\times 10^{1} $&$ -1.88\\\\times 10^{3}$&$\\\\dots$\\n\\\\nl\\n & &\\n$0$\\n &0.500 &$ 6.63\\\\times 10^{10} $&$ 1.43\\\\times 10^{8} $\\n &$ -3.17\\\\times 10^{1} $&$ -1.88\\\\times 10^{3}$&$\\\\dots$\\n\\\\nl\\n & &\\n$-10^{-4}$\\n &0.500 &$ 6.64\\\\times 10^{10} $&$ 1.43\\\\times 10^{8} $\\n &$ -3.17\\\\times 10^{1} $&$ -1.88\\\\times 10^{3}$&$\\\\dots$\\n\\\\nl\\n & &\\n$-10^{-2}$\\n &0.500 &$ 6.97\\\\times 10^{10} $&$ 1.46\\\\times 10^{8} $\\n &$ -3.17\\\\times 10^{1} $&$ -1.87\\\\times 10^{3}$&$\\\\dots$\\n\\\\nl\\n & & & & & & & & \\\\nl\\n &$r_1$& \\n$0$\\n &0.413 &$ 6.97\\\\times 10^{9} $&$ 4.78\\\\times 10^{7} $\\n &$ -1.86\\\\times 10^{10} $&$ -5.30\\\\times 10^{5}$\\n &$ -4.07\\\\times 10^{6} $\\n\\\\nl\\n & &\\n$-10^{-4}$\\n &0.500 &$ 7.42\\\\times 10^{9} $&$ 4.63\\\\times 10^{7} $\\n &$\\\\phm{-}2.39\\\\times 10^{5}\\\\ \\\\tablenotemark{c} $\\n &$ -4.37\\\\times 10^{5} $&$ -4.48\\\\times 10^{6} $ \\n\\\\nl\\n\\\\enddata\\n\\\\tablenotetext{a}{We present dissipative timescales only for those \\nthat are unstable to gravitational radiation reaction.}\\n\\\\tablenotetext{b}{We present dissipative timescales $\\\\tilde{\\\\tau}_l$ due to \\nthe gravitational radiation reaction only for\\nthe dominant multipole moments.}\\n\\\\tablenotetext{c}{For these dissipative timescales, we obtain positive\\nvalues, which should be negative by definition. The reason for the\\ninconsistent result may be because the extrapolation formula (\\\\ref{tau2b}) \\nfor $\\\\tau^{-1}$, which is obtained at $\\\\bar\\\\Omega=0$, does not necessarily work well\\nfor arbitrary values of $\\\\bar\\\\Omega$. \\nFor instance, we find that\\n$\\\\tilde{\\\\tau}_{J,\\\\vert m\\\\vert}/\\\\tilde{\\\\tau}_{D,\\\\vert m\\\\vert+1} \\\\sim 10^{3}$ \\nfor $m=2$ and \\n$\\\\tilde{\\\\tau}_{J,\\\\vert m\\\\vert}/\\\\tilde{\\\\tau}_{D,\\\\vert m\\\\vert+1} \\\\sim 10^{2}$ \\nfor $m=3$, where the dissipative timescales are estimated at \\n$\\\\bar{\\\\Omega}=0.1$. \\nThis may suggest that \\nthe mass multipole radiation dominates the current one \\nfor the $r_1$-modes for large $\\\\bar\\\\Omega$. \\nThus, our conclusions on the stability of the $r_1$-modes \\nextrapolated for large $\\\\bar\\\\Omega$\\nare not altered at all.}\\n\\\\end{deluxetable}\\n\\n\\n\\\\end{document}\\n\\n\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002300.extracted_bib","string":"\\begin{thebibliography}{}\n\n\\bibitem[Andersson 1998]{nils97}\n Andersson, N. 1998, \\apj, 502, 708\n%\n\\bibitem[Andersson et al.\\ 1998]{aks98}\n Andersson, N., Kokkotas, K., \\& Schutz B. F. 1998, \\apj, 510, 846\n%\n\\bibitem[Berthomieu et al. 1978]{be78}\nBerthomieu, G., Gonczi, G., Graff, Ph., Provost, J., \\& Rocca, A. 1978, \n\\aap, 70, 597 \n%\n\\bibitem[Beyer \\& Kokkotas 1999]{bk99}\n Beyer, H. R., \\& Kokkotas, K. D. 1999, \\mnras, 308, 745\n%\n\\bibitem[Friedman \\& Morsink 1998]{jfs97} \n Friedman, J. L., \\& Morsink, S. M. 1998, \\apj, 502, 714\n%\n\\bibitem[Friedman \\& Schutz 1978]{fs87} \n Friedman, J. L., \\& Schutz, B. F. 1978, \\apj, 222, 281\n%\n\\bibitem[Greenspan 1964]{g64}\n Greenspan, H. P. 1964, The Theory of Rotating Fluids (Cambridge: Cambridge \nUniv. Press)\n%\n\\bibitem[Kojima 1998]{k98}\n Kojima, Y. 1998, \\mnras, 293, 49\n%\n\\bibitem[Kojima \\& Hosonuma 1999]{kh99}\n Kojima, Y., \\& Hosonuma, M. 1999, \\apj, 520, 788\n%\n\\bibitem[Kokkotas \\& Stergioulas 1998]{ks98}\n Kokkotas, K., \\& Stergioulas, N. 1998, \\aap, 341, 110\n%\n\\bibitem[Lee 1993]{l93}\n Lee, U. 1993, \\apj, 405, 359\n%\n\\bibitem[Lee \\& Saio 1986]{ls86}\n Lee, U., \\& Saio, H. 1986, \\mnras, 221, 365\n%\n\\bibitem[Lee \\& Saio 1997]{ls97}\n Lee, U., \\& Saio, H. 1997, \\apj, 491, 839\n%\n\\bibitem[Lee et al.\\ 1992]{lsvh92}\n Lee, U., Strohmayer, T. D., \\& Van Horn, H. M. 1992, \\apj, 397, 647\n%\n\\bibitem[Lindblom \\& Ipser 1998]{li98}\n Lindblom, L., \\& Ipser, J. R. 1998, \\prd, 59, 044009\n%\n\\bibitem[Lindblom et al.\\ 1999]{lmo99}\n Lindblom, L., Mendell, G., \\& Owen, B. J. 1999, \\prd, 60, 064006\n%\n\\bibitem[Lindblom et al.\\ 1998]{lom98}\n Lindblom, L., Owen, B. J., \\& Morsink, S. M. 1998, \\prl, 80, 4843\n%\n\\bibitem[Lockitch \\ 1999]{lo99}\n Lockitch, K. H. 1999, Ph.D. Thesis (University of Wisconsin-Milwaukee), \n(gr-qc/9909029) \n%\n\\bibitem[Lockitch \\& Friedman\\ 1999]{lf99}\n Lockitch, K. H., \\& Friedman J. L. 1999, \\apj, 521, 764\n%\n\\bibitem[Owen et al.\\ 1998]{o98}\n Owen, B. J., Lindblom, L., Cutler, C., Schutz, B. F., Vecchio, A., \\&\n Andersson, N. 1998, \\prd, 58, 084020\n%\n\\bibitem[Papaloizou \\& Pringle 1978]{pp78}\n Papaloizou, J., \\& Pringle, J. E. 1978, \\mnras, 182, 423\n%\n\\bibitem[Pedlosky 1987]{pe87}\n Pedlosky, J. 1987, Geophysical Fluid Dynamics, Second Edition \n(Berlin: Springer-Verlag)\n%\n\\bibitem[Press et al. 1992]{pr92}\n Press, W. H., Teukolsky, S. A., Vetterling, W. T., \\& Flannery, B. P. \n1992, Numerical Recipes: The Art of Scientific Computing, Second Edition \n(Cambridge: Cambridge Univ. Press)\n%\n\\bibitem[Provost et al. 1981]{pea81}\n Provost, J., Berthomieu, G., \\& Rocca, A. 1981, \\aap, 94, 126\n%\n\\bibitem[Regge \\& Wheeler 1957]{rw57}\n Regge, T., \\& Wheeler, J. A. 1957, Phys. Rev., 108, 1063\n%\n\\bibitem[Saio 1982]{s82}\n Saio, H. 1982, \\apj, 256, 717\n%\n\\bibitem[Saio 1999]{s99}\n Saio, H. 1999, private communication. \n%\n\\bibitem[Tassoul 1978]{t78}\n Tassoul, J.-L. 1978, Theory of Rotating Stars (Princeton: Princeton Univ.\nPress)\n%\n\\bibitem[Thorne 1980]{th80}\n Thorne, K. S. 1980, Rev. Mod. Phys., 52, 299\n%\n\\bibitem[Unno et al. 1989]{u89}\n Unno, W., Osaki, Y., Ando, H., Saio, H., \\& Shibahashi, H. 1989, \n Nonradial Oscillations of Stars, Second Edition (Tokyo: Univ. Tokyo Press) \n%\n\\bibitem[Yoshida et al 1999]{ykye99}\n Yoshida, S'i., Karino, S., Yoshida, S., \\& Eriguchi, Y. 1999, \n Submitted to \\mnras (astro-ph/9910532)\n%\n\\bibitem[Yoshida \\& Lee 2000]{yl00}\n Yoshida, S., \\& Lee, U. 2000, \\apj, in press. (astro-ph/9908197)\n%\n\\end{thebibliography}"}],"string":"[\n {\n \"name\": \"astro-ph0002300.extracted_bib\",\n \"string\": \"\\\\begin{thebibliography}{}\\n\\n\\\\bibitem[Andersson 1998]{nils97}\\n Andersson, N. 1998, \\\\apj, 502, 708\\n%\\n\\\\bibitem[Andersson et al.\\\\ 1998]{aks98}\\n Andersson, N., Kokkotas, K., \\\\& Schutz B. F. 1998, \\\\apj, 510, 846\\n%\\n\\\\bibitem[Berthomieu et al. 1978]{be78}\\nBerthomieu, G., Gonczi, G., Graff, Ph., Provost, J., \\\\& Rocca, A. 1978, \\n\\\\aap, 70, 597 \\n%\\n\\\\bibitem[Beyer \\\\& Kokkotas 1999]{bk99}\\n Beyer, H. R., \\\\& Kokkotas, K. D. 1999, \\\\mnras, 308, 745\\n%\\n\\\\bibitem[Friedman \\\\& Morsink 1998]{jfs97} \\n Friedman, J. L., \\\\& Morsink, S. M. 1998, \\\\apj, 502, 714\\n%\\n\\\\bibitem[Friedman \\\\& Schutz 1978]{fs87} \\n Friedman, J. L., \\\\& Schutz, B. F. 1978, \\\\apj, 222, 281\\n%\\n\\\\bibitem[Greenspan 1964]{g64}\\n Greenspan, H. P. 1964, The Theory of Rotating Fluids (Cambridge: Cambridge \\nUniv. Press)\\n%\\n\\\\bibitem[Kojima 1998]{k98}\\n Kojima, Y. 1998, \\\\mnras, 293, 49\\n%\\n\\\\bibitem[Kojima \\\\& Hosonuma 1999]{kh99}\\n Kojima, Y., \\\\& Hosonuma, M. 1999, \\\\apj, 520, 788\\n%\\n\\\\bibitem[Kokkotas \\\\& Stergioulas 1998]{ks98}\\n Kokkotas, K., \\\\& Stergioulas, N. 1998, \\\\aap, 341, 110\\n%\\n\\\\bibitem[Lee 1993]{l93}\\n Lee, U. 1993, \\\\apj, 405, 359\\n%\\n\\\\bibitem[Lee \\\\& Saio 1986]{ls86}\\n Lee, U., \\\\& Saio, H. 1986, \\\\mnras, 221, 365\\n%\\n\\\\bibitem[Lee \\\\& Saio 1997]{ls97}\\n Lee, U., \\\\& Saio, H. 1997, \\\\apj, 491, 839\\n%\\n\\\\bibitem[Lee et al.\\\\ 1992]{lsvh92}\\n Lee, U., Strohmayer, T. D., \\\\& Van Horn, H. M. 1992, \\\\apj, 397, 647\\n%\\n\\\\bibitem[Lindblom \\\\& Ipser 1998]{li98}\\n Lindblom, L., \\\\& Ipser, J. R. 1998, \\\\prd, 59, 044009\\n%\\n\\\\bibitem[Lindblom et al.\\\\ 1999]{lmo99}\\n Lindblom, L., Mendell, G., \\\\& Owen, B. J. 1999, \\\\prd, 60, 064006\\n%\\n\\\\bibitem[Lindblom et al.\\\\ 1998]{lom98}\\n Lindblom, L., Owen, B. J., \\\\& Morsink, S. M. 1998, \\\\prl, 80, 4843\\n%\\n\\\\bibitem[Lockitch \\\\ 1999]{lo99}\\n Lockitch, K. H. 1999, Ph.D. Thesis (University of Wisconsin-Milwaukee), \\n(gr-qc/9909029) \\n%\\n\\\\bibitem[Lockitch \\\\& Friedman\\\\ 1999]{lf99}\\n Lockitch, K. H., \\\\& Friedman J. L. 1999, \\\\apj, 521, 764\\n%\\n\\\\bibitem[Owen et al.\\\\ 1998]{o98}\\n Owen, B. J., Lindblom, L., Cutler, C., Schutz, B. F., Vecchio, A., \\\\&\\n Andersson, N. 1998, \\\\prd, 58, 084020\\n%\\n\\\\bibitem[Papaloizou \\\\& Pringle 1978]{pp78}\\n Papaloizou, J., \\\\& Pringle, J. E. 1978, \\\\mnras, 182, 423\\n%\\n\\\\bibitem[Pedlosky 1987]{pe87}\\n Pedlosky, J. 1987, Geophysical Fluid Dynamics, Second Edition \\n(Berlin: Springer-Verlag)\\n%\\n\\\\bibitem[Press et al. 1992]{pr92}\\n Press, W. H., Teukolsky, S. A., Vetterling, W. T., \\\\& Flannery, B. P. \\n1992, Numerical Recipes: The Art of Scientific Computing, Second Edition \\n(Cambridge: Cambridge Univ. Press)\\n%\\n\\\\bibitem[Provost et al. 1981]{pea81}\\n Provost, J., Berthomieu, G., \\\\& Rocca, A. 1981, \\\\aap, 94, 126\\n%\\n\\\\bibitem[Regge \\\\& Wheeler 1957]{rw57}\\n Regge, T., \\\\& Wheeler, J. A. 1957, Phys. Rev., 108, 1063\\n%\\n\\\\bibitem[Saio 1982]{s82}\\n Saio, H. 1982, \\\\apj, 256, 717\\n%\\n\\\\bibitem[Saio 1999]{s99}\\n Saio, H. 1999, private communication. \\n%\\n\\\\bibitem[Tassoul 1978]{t78}\\n Tassoul, J.-L. 1978, Theory of Rotating Stars (Princeton: Princeton Univ.\\nPress)\\n%\\n\\\\bibitem[Thorne 1980]{th80}\\n Thorne, K. S. 1980, Rev. Mod. Phys., 52, 299\\n%\\n\\\\bibitem[Unno et al. 1989]{u89}\\n Unno, W., Osaki, Y., Ando, H., Saio, H., \\\\& Shibahashi, H. 1989, \\n Nonradial Oscillations of Stars, Second Edition (Tokyo: Univ. Tokyo Press) \\n%\\n\\\\bibitem[Yoshida et al 1999]{ykye99}\\n Yoshida, S'i., Karino, S., Yoshida, S., \\\\& Eriguchi, Y. 1999, \\n Submitted to \\\\mnras (astro-ph/9910532)\\n%\\n\\\\bibitem[Yoshida \\\\& Lee 2000]{yl00}\\n Yoshida, S., \\\\& Lee, U. 2000, \\\\apj, in press. (astro-ph/9908197)\\n%\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":296,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002301"},"title":{"kind":"string","value":""},"authors":{"kind":"list like","value":[],"string":"[]"},"abstract":{"kind":"string","value":"Cartan torsion contribution to Sachs-Wolfe effect in the inflationary phase of the Universe is discussed.From the COBE data of the microwave anisotropy is possible to compute the spin-density in the Universe as $10^{16}$ mks units.The spin-density fluctuations at the hadron era is shown to coincide with the anisotropy temperature fluctuations."},"latex":{"kind":"list like","value":[{"name":"astro-ph0002301.tex","string":"\\documentstyle[12pt]{article}\n\\begin{document}\n\\thispagestyle{empty}\n\n\\begin{center}\n\\LARGE \\tt \\bf{Sachs-Wolfe effect in Spacetimes with Torsion}\n\\end{center}\n\n\\vspace{2.5cm}\n\n\\begin{center} {\\large L.C. Garcia de Andrade\\footnote{Departamento de\nF\\'{\\i}sica Te\\'{o}rica - Instituto de F\\'{\\i}sica - UERJ\n\nRua S\\~{a}o Fco. Xavier 524, Rio de Janeiro, RJ\n\nMaracan\\~{a}, CEP:20550-003 , Brasil.\n\nE-mail : GARCIA@DFT.IF.UERJ.BR}}\n\\end{center}\n\n\\vspace{2.0cm}\n\n\\begin{abstract}\nCartan torsion contribution to Sachs-Wolfe effect in the inflationary phase of the Universe is discussed.From the COBE data of the microwave anisotropy is possible to compute the spin-density in the Universe as $10^{16}$ mks units.The spin-density fluctuations at the hadron era is shown to coincide with the anisotropy temperature fluctuations.\n\\end{abstract}\n\n\\vspace{1.0cm}\n\n\\begin{center}\n\\large{PACS number(s) : 0420,0450}\n\\end{center}\n\n\\newpage\nThe Sachs-Wolfe effect \\cite{1,2,3} is given by\n\\begin{equation}\n\\frac{{\\delta}T}{T}=-{\\Phi}\n\\label{1}\n\\end{equation}\nwhere ${\\Phi}$ is the Newtonian gravitational potential.Since there vis no restriction on the origin of the gravitational potential in this expression one may extend this expression to allow for alternative theories of gravity.Thus one is able to compute the anisotropy fluctuations in the CMB temperatures.In this letter we shall be concerned with the computation of the temperature fluctuations in the context of weak field limit approximation of the Einstein-Cartan gravity.In Newtonian approximation the Einstein-Cartan field equation may be expressed as\n\\begin{equation}\n\\frac{1}{c^{2}}{\\frac{{\\partial}^{2}{\\Phi}}{{{\\partial}t}^{2}}}-{{\\nabla}^{2}}{\\Phi}=-4{\\pi}G({\\rho}-G{\\sigma}^{2})\n\\label{2}\n\\end{equation}\nwhere ${\\sigma}^{2}$ is the spin-torsion energy density and ${\\rho}$ is the usual matter density.Since the cosmological spacetime used is of the form\n\\begin{equation}\nds^{2}=dt^{2}-(1-2{\\Phi})(dx^{2}+dy^{2}+dz^{2})\n\\label{3}\n\\end{equation}\nis homogeneous ${{\\nabla}^{2}}{\\Phi}=0$ equation (\\ref{2}) reduces to\n\\begin{equation}\n\\ddot{\\Phi}=-4{\\pi}Gc^{2}({\\rho}-G{\\sigma}^{2})\n\\label{4}\n\\end{equation}\nSolution of this expression can be easily obtained obtained by considering the RHS of (\\ref{4}) is constant in the average, thus\n\\begin{equation}\n{\\Phi}(t)=-4{\\pi}Gc^{2}({\\rho}-G{\\sigma}^{2})t^{2}+Bt+C\n\\label{5}\n\\end{equation}\nwhere $B$ and $C$ are integration constants.Therefore spin-torsion effects contribute to the temperature fluctuations through the term\n\\begin{equation}\n{\\frac{{\\delta}T}{T}}_{torsion}=4{\\pi}G^{2}c^{2}{\\sigma}^{2}t^{2}\n\\label{6}\n\\end{equation}\nSince at the inflation era $t=10^{-35}s$ and from COBE data $\\frac{{\\delta}T}{T}<10^{-5}$ one may obtain an expression for the spin-torsion density at the inflation era as\n\\begin{equation}\n{\\sigma}^{2}=\\frac{1}{4{\\pi}}(G^{-2}c^{-2}t^{-2}){\\frac{{\\delta}T}{T}}_{torsion}\n\\label{7}\n\\end{equation}\nwhich yields ${\\sigma}=10^{16}$ mks-units.Notice that this value is much weaker than the value obtained by de Sabbata and Sivaram \\cite{4} for the maximum spin-torsion density at the Planck era of the Universe which is ${\\sigma}_{Pl}=10^{71}$.In the hadron era \\cite{4} for example $G^{2}{\\sigma}^{2}=T^{2}$ and one may obtain the classical density fluctuation as \n\\begin{equation}\n\\frac{{\\delta}T}{T}=\\frac{{\\delta}{\\sigma}}{\\sigma}\n\\label{8}\n\\end{equation}\nThis amazing result shows that the spin-torsion density fluctuation coincides with the matter density fluctuation which allow us to obtain the spin-torsion density fluctuation from the COBE data.Similar results in the Relativistic Einstein-Cartan gravity with dilaton fields has been recently obtained by Palle \\cite{5} and myself \\cite{6}.\n\\section*{Acknowledgement}\nI am very much indebt to Prof.I.Shapiro and Prof.R.Ramos for helpful discussions on the subject of this paper. Financial support from CNPq. and FAPESP is gratefully acknowledged.\n\\begin{thebibliography}{6}\n\\bibitem{1} Sachs,R.K.and Wolfe,A.M.1967,ApJ,147,73\n\\bibitem{2} Peebles,J.Principles of Physical Cosmology,1993,Princeton University Press.\n\\bibitem{3} White,M.and Hu,W.Astronomy and Astrophysics,1999,astro-ph/9609105\n\\bibitem{4} de Sabbata,V. and Sivaram,C.Spin and Torsion and Gravitation,1995,World Scientific\n\\bibitem{5} Palle,D.,On Primordial density fluctuation in the Einstein-Cartan Gravity,1999,gr-qc Los Alamos archives.\n\\bibitem{6} Garcia de Andrade,L.C.,Phys.Lett.B468,1999,28.\n\\end{thebibliography}\n\\end{document}\n"}],"string":"[\n {\n \"name\": \"astro-ph0002301.tex\",\n \"string\": \"\\\\documentstyle[12pt]{article}\\n\\\\begin{document}\\n\\\\thispagestyle{empty}\\n\\n\\\\begin{center}\\n\\\\LARGE \\\\tt \\\\bf{Sachs-Wolfe effect in Spacetimes with Torsion}\\n\\\\end{center}\\n\\n\\\\vspace{2.5cm}\\n\\n\\\\begin{center} {\\\\large L.C. Garcia de Andrade\\\\footnote{Departamento de\\nF\\\\'{\\\\i}sica Te\\\\'{o}rica - Instituto de F\\\\'{\\\\i}sica - UERJ\\n\\nRua S\\\\~{a}o Fco. Xavier 524, Rio de Janeiro, RJ\\n\\nMaracan\\\\~{a}, CEP:20550-003 , Brasil.\\n\\nE-mail : GARCIA@DFT.IF.UERJ.BR}}\\n\\\\end{center}\\n\\n\\\\vspace{2.0cm}\\n\\n\\\\begin{abstract}\\nCartan torsion contribution to Sachs-Wolfe effect in the inflationary phase of the Universe is discussed.From the COBE data of the microwave anisotropy is possible to compute the spin-density in the Universe as $10^{16}$ mks units.The spin-density fluctuations at the hadron era is shown to coincide with the anisotropy temperature fluctuations.\\n\\\\end{abstract}\\n\\n\\\\vspace{1.0cm}\\n\\n\\\\begin{center}\\n\\\\large{PACS number(s) : 0420,0450}\\n\\\\end{center}\\n\\n\\\\newpage\\nThe Sachs-Wolfe effect \\\\cite{1,2,3} is given by\\n\\\\begin{equation}\\n\\\\frac{{\\\\delta}T}{T}=-{\\\\Phi}\\n\\\\label{1}\\n\\\\end{equation}\\nwhere ${\\\\Phi}$ is the Newtonian gravitational potential.Since there vis no restriction on the origin of the gravitational potential in this expression one may extend this expression to allow for alternative theories of gravity.Thus one is able to compute the anisotropy fluctuations in the CMB temperatures.In this letter we shall be concerned with the computation of the temperature fluctuations in the context of weak field limit approximation of the Einstein-Cartan gravity.In Newtonian approximation the Einstein-Cartan field equation may be expressed as\\n\\\\begin{equation}\\n\\\\frac{1}{c^{2}}{\\\\frac{{\\\\partial}^{2}{\\\\Phi}}{{{\\\\partial}t}^{2}}}-{{\\\\nabla}^{2}}{\\\\Phi}=-4{\\\\pi}G({\\\\rho}-G{\\\\sigma}^{2})\\n\\\\label{2}\\n\\\\end{equation}\\nwhere ${\\\\sigma}^{2}$ is the spin-torsion energy density and ${\\\\rho}$ is the usual matter density.Since the cosmological spacetime used is of the form\\n\\\\begin{equation}\\nds^{2}=dt^{2}-(1-2{\\\\Phi})(dx^{2}+dy^{2}+dz^{2})\\n\\\\label{3}\\n\\\\end{equation}\\nis homogeneous ${{\\\\nabla}^{2}}{\\\\Phi}=0$ equation (\\\\ref{2}) reduces to\\n\\\\begin{equation}\\n\\\\ddot{\\\\Phi}=-4{\\\\pi}Gc^{2}({\\\\rho}-G{\\\\sigma}^{2})\\n\\\\label{4}\\n\\\\end{equation}\\nSolution of this expression can be easily obtained obtained by considering the RHS of (\\\\ref{4}) is constant in the average, thus\\n\\\\begin{equation}\\n{\\\\Phi}(t)=-4{\\\\pi}Gc^{2}({\\\\rho}-G{\\\\sigma}^{2})t^{2}+Bt+C\\n\\\\label{5}\\n\\\\end{equation}\\nwhere $B$ and $C$ are integration constants.Therefore spin-torsion effects contribute to the temperature fluctuations through the term\\n\\\\begin{equation}\\n{\\\\frac{{\\\\delta}T}{T}}_{torsion}=4{\\\\pi}G^{2}c^{2}{\\\\sigma}^{2}t^{2}\\n\\\\label{6}\\n\\\\end{equation}\\nSince at the inflation era $t=10^{-35}s$ and from COBE data $\\\\frac{{\\\\delta}T}{T}<10^{-5}$ one may obtain an expression for the spin-torsion density at the inflation era as\\n\\\\begin{equation}\\n{\\\\sigma}^{2}=\\\\frac{1}{4{\\\\pi}}(G^{-2}c^{-2}t^{-2}){\\\\frac{{\\\\delta}T}{T}}_{torsion}\\n\\\\label{7}\\n\\\\end{equation}\\nwhich yields ${\\\\sigma}=10^{16}$ mks-units.Notice that this value is much weaker than the value obtained by de Sabbata and Sivaram \\\\cite{4} for the maximum spin-torsion density at the Planck era of the Universe which is ${\\\\sigma}_{Pl}=10^{71}$.In the hadron era \\\\cite{4} for example $G^{2}{\\\\sigma}^{2}=T^{2}$ and one may obtain the classical density fluctuation as \\n\\\\begin{equation}\\n\\\\frac{{\\\\delta}T}{T}=\\\\frac{{\\\\delta}{\\\\sigma}}{\\\\sigma}\\n\\\\label{8}\\n\\\\end{equation}\\nThis amazing result shows that the spin-torsion density fluctuation coincides with the matter density fluctuation which allow us to obtain the spin-torsion density fluctuation from the COBE data.Similar results in the Relativistic Einstein-Cartan gravity with dilaton fields has been recently obtained by Palle \\\\cite{5} and myself \\\\cite{6}.\\n\\\\section*{Acknowledgement}\\nI am very much indebt to Prof.I.Shapiro and Prof.R.Ramos for helpful discussions on the subject of this paper. Financial support from CNPq. and FAPESP is gratefully acknowledged.\\n\\\\begin{thebibliography}{6}\\n\\\\bibitem{1} Sachs,R.K.and Wolfe,A.M.1967,ApJ,147,73\\n\\\\bibitem{2} Peebles,J.Principles of Physical Cosmology,1993,Princeton University Press.\\n\\\\bibitem{3} White,M.and Hu,W.Astronomy and Astrophysics,1999,astro-ph/9609105\\n\\\\bibitem{4} de Sabbata,V. and Sivaram,C.Spin and Torsion and Gravitation,1995,World Scientific\\n\\\\bibitem{5} Palle,D.,On Primordial density fluctuation in the Einstein-Cartan Gravity,1999,gr-qc Los Alamos archives.\\n\\\\bibitem{6} Garcia de Andrade,L.C.,Phys.Lett.B468,1999,28.\\n\\\\end{thebibliography}\\n\\\\end{document}\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002301.extracted_bib","string":"\\begin{thebibliography}{6}\n\\bibitem{1} Sachs,R.K.and Wolfe,A.M.1967,ApJ,147,73\n\\bibitem{2} Peebles,J.Principles of Physical Cosmology,1993,Princeton University Press.\n\\bibitem{3} White,M.and Hu,W.Astronomy and Astrophysics,1999,astro-ph/9609105\n\\bibitem{4} de Sabbata,V. and Sivaram,C.Spin and Torsion and Gravitation,1995,World Scientific\n\\bibitem{5} Palle,D.,On Primordial density fluctuation in the Einstein-Cartan Gravity,1999,gr-qc Los Alamos archives.\n\\bibitem{6} Garcia de Andrade,L.C.,Phys.Lett.B468,1999,28.\n\\end{thebibliography}"}],"string":"[\n {\n \"name\": \"astro-ph0002301.extracted_bib\",\n \"string\": \"\\\\begin{thebibliography}{6}\\n\\\\bibitem{1} Sachs,R.K.and Wolfe,A.M.1967,ApJ,147,73\\n\\\\bibitem{2} Peebles,J.Principles of Physical Cosmology,1993,Princeton University Press.\\n\\\\bibitem{3} White,M.and Hu,W.Astronomy and Astrophysics,1999,astro-ph/9609105\\n\\\\bibitem{4} de Sabbata,V. and Sivaram,C.Spin and Torsion and Gravitation,1995,World Scientific\\n\\\\bibitem{5} Palle,D.,On Primordial density fluctuation in the Einstein-Cartan Gravity,1999,gr-qc Los Alamos archives.\\n\\\\bibitem{6} Garcia de Andrade,L.C.,Phys.Lett.B468,1999,28.\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":297,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002302"},"title":{"kind":"string","value":"Spirals and the size of the disk in EX\\,Dra"},"authors":{"kind":"list like","value":[{"author":"V. Joergens \\inst{1,2}"},{"author":"H.C. Spruit \\inst{1}"},{"author":"R.G.M. Rutten \\inst{3,4}"}],"string":"[\n {\n \"author\": \"V. Joergens \\\\inst{1,2}\"\n },\n {\n \"author\": \"H.C. Spruit \\\\inst{1}\"\n },\n {\n \"author\": \"R.G.M. Rutten \\\\inst{3,4}\"\n }\n]"},"abstract":{"kind":"string","value":"Observations at high spectral and temporal resolution are presented of the dwarf nova EX\\,Dra in outburst. The disk seen in the \\ion{He}{i} line reconstructed by Doppler tomography shows a clear two-armed spiral pattern pointing to spiral shocks in the disk. The Balmer and \\ion{He}{ii} maps also give evidence for the presence of spirals. The eclipse as seen in the red continuum indicates a disk radius of 0.31 times the orbital separation, which might be large enough to explain the observed spiral shocks through excitation by the tidal field of the secondary. The eclipse in the Balmer line profiles, well resolved in our observations, indicates a somewhat smaller disk size (0.25). We discuss the possibility that this is related to an optical depth effect in the lines. \\keywords{accretion disks -- hydrodynamics -- Cataclysmic Variables -- stars: EX\\,Dra}"},"latex":{"kind":"list like","value":[{"name":"bh033.tex","string":"\n%\\documentstyle[epsf]{l-aa}\n\\documentclass{aa}\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\bd}{\\begin{displaymath}}\n\\newcommand{\\ed}{\\end{displaymath}}\n\\newcommand{\\gapprox}{\\;\\rlap{\\lower 2.5pt \n \\hbox{$\\sim$}}\\raise 1.5pt\\hbox{$>$}\\;} \n\\newcommand{\\lapprox}{\\;\\rlap{\\lower 2.5pt \n \\hbox{$\\sim$}}\\raise 1.5pt\\hbox{$<$}\\;} \n\\newcommand{\\pr}{\\prime}\n\\newcommand{\\p}{\\partial}\n\\newcommand{\\rd}{{\\rm d}} \n\n%\\newcommand{\\mk}{\\bf} % temporary markup by boldface\n\\newcommand{\\mk}{} % udno temporary markup\n\n\\usepackage{graphicx}\n\\begin{document}\n \\thesaurus{06 % A&A Section 6: Form. struct. and evolut. of stars\n 02.01.2 %accretion\n 02.08.1 %hydro\n 08.02.2 %ecl binaries\n 08.09.2 EX\\,Dra\n }\n%\n \\title{Spirals and the size of the disk in EX\\,Dra}\n% \\subtitle{}\n\n% \n \\author{V. Joergens \\inst{1,2} \\and H.C. Spruit \\inst{1}\n \\and R.G.M. Rutten \\inst{3,4}}\n\n% \\offprints{}\n \n \\institute{Max-Planck-Institut f\\\"ur Astrophysik, Postfach 1523, \n D-85740 Garching bei M\\\"unchen, Germany \\and\n Max-Planck-Institut f\\\"ur Extraterrestrische Physik, \n Postfach 1603, D-85740 Garching bei M\\\"unchen, Germany \\and\n Netherlands Foundation for Research in Astronomy \\and\n Royal Greenwich Observatory, Apartado de Correos 321, \n 38780 Santa Cruz de La Palma, Canary Islands, Spain\n }\n\n \\date{Received }\n\n \\maketitle\n\n% \\maintitlerunninghead{}\n\n% \\authorrunninghead{}\n\n\\begin{abstract}\nObservations at high spectral and temporal resolution are presented of\nthe dwarf nova EX\\,Dra in outburst. \nThe disk seen in the \\ion{He}{i} line reconstructed by Doppler tomography\nshows a clear two-armed spiral pattern pointing to spiral shocks in the disk.\nThe Balmer and \\ion{He}{ii} maps also give evidence for \nthe presence of spirals. \nThe eclipse as seen in the red continuum indicates a disk radius of 0.31 times\nthe orbital separation, which might be\nlarge enough to explain the observed spiral shocks through\nexcitation by the tidal field of the secondary. \nThe eclipse in the Balmer line profiles, well \nresolved in our observations, indicates a somewhat smaller disk size (0.25).\nWe discuss the possibility that this is related to an optical depth effect \nin the lines.\n\\keywords{accretion disks -- hydrodynamics -- Cataclysmic Variables -- stars: \nEX\\,Dra}\n\\end{abstract}\n\n\\section{Introduction}\n\nSpiral shocks in accretion disks have been predicted from numerical \nsimulations (Sawada et al. 1986, 1987, R\\'o\\.zyczka \\& Spruit 1993, Yukawa et \nal. 1997), and analytic considerations (Spruit 1987, Spruit et al. 1987, \nLarson 1990). They are excited by the tidal field of the secondary if the \ndisk extends \nfar enough into the Roche lobe and can result in two prominent spiral arms.\nIf shock dissipation is the main mechanism damping the wave, it extends over \nthe entire disk and causes accretion at an effective $\\alpha$-value of \n$0.01(H/r)^{3/2}$ (Spruit 1987, Larson 1990, Godon 1997). \n\nThe first observational evidence for shock waves in accretion disks of \ncataclysmic variables (CVs) was the detection of a clear two-armed \nstructure in the disk of IP\\,Peg during rise to outburst (Steeghs et \nal. 1997). The spiral pattern, interpreted as evidence for shock waves,\nhas also been seen during outburst maximum (Harlaftis et al. 1999) and early \ndecline of outburst (Morales-Rueda et al. 2000).\n\nAt the temperatures expected from dwarf nova disks models, whether in outburst \nor in quiescence, the predicted spirals are tightly wound and would be hard to \ndetect observationally (Bunk et al. 1990), so that their presence in the \nobservations is somewhat unexpected.\nSpirals this strong are most naturally explained if the disk\ntemporarily extends rather far into the primary Roche lobe, so that\nthe tidal force of the secondary causes a strong disturbance. A strong\nnon-axisymmetric disturbance, however, would also cause the gas to\nloose angular momentum quickly (transfered to the secondary), so that\nthe disk would shrink to a smaller radius where the tidal force is\nweaker. Spirals in disks of CVs would then be understandable if they are a\ntemporary phenomenon, perhaps restricted to\noutbursts. To test this, more observations of different systems at\nsufficient spectral resolution and signal-to-noise are needed\n(Steeghs \\& Stehle 1999). \n\nWith high quality spectroscopic studies of different CVs it should also be \npossible to answer the question if spiral shocks in CV accretion disks are a \ncommon phenomenon. Systems suitable for this purpose would be bright and \nhave frequent outbursts, such as SS\\,Cyg and EX\\,Dra. \n\nEX\\,Dra is a double--eclipsing dwarf nova with a 5-hour orbit \n(Barwig et al. 1993, Billington et al. 1996, system parameters by \nFiedler et al. 1997).\nThere is suggestive evidence for asymmetric structures in the \\ion{He}{i}\nDoppler map reconstructed from outburst data taken in 1993 (Joergens et al. \n2000). From eclipse maps obtained at various stages in the outburst cycle Baptista \\& \nCatalan (1999) claim that spiral waves form at the early stages of an \noutburst. We report in this paper on observations at high spectral and temporal\nresolution during an outburst in 1996.\n\n\\section{Observations and reduction}\nEX\\,Dra was observed on the nights of July 27\nand 28 1996, with the ISIS spectrograph on the 4.2\\,m William\nHerschel Telescope. \nThe red ISIS arm was equipped with the TEK\\,5 CCD,\nthe blue arm with TEK\\,1 CCD, covering the \nwavelength ranges 6375-6778\\,{\\AA} and\n4585-4993\\,{\\AA} respectively, at a dispersion of\n0.4\\,{\\AA}/pixel. \nThe spectra were observed during seeing of 1.4 -- 1.7 arc sec, \nusing an exposure time of 60s.\n%, corresponding to 0.3\\% of the binary orbit. \nThe spectra were optimally-extracted, including the elimination of \ncosmic ray hits but not the correction of Pixel-to-pixel variations of the \ndetector sensitivity. \nSlit losses due to variable atmospheric conditions were \ncorrected using a faint comparison star on the slit.\nThe red spectra, but not the blue spectra, were flux calibrated. \n\nOur spectra were taken roughly in the middle of an outburst. Photometric \nobservation at the Wendelstein observatory showed that the system was already \nin outburst on 26 July, and in quiescence on 4 August (Barwig, private comm.). \nVSNET (1998) records show that the system was in quiescence on 24 July \nand in outburst one day later and in quiescence again on 1 August. The outburst \ntherefore started on 25 August, three days before our observations.\n\n\n\\section{Interpretation of the Doppler maps}\n\\label{interpret}\n\nDoppler maps were computed from the phase-folded spectra of 28 July, using the IDL-based \nfast-maximum entropy package described by Spruit (1998)\\footnote{available \nat http:www.mpa-garching.mpg.de/$\\sim$henk}. \nFor further details on Doppler tomography see Marsh \\& Horne (1988). \n{\\mk The eclipsed part of the data (phases -0.12 to 0.12) has been \nexcluded from the reconstruction process, and does not affect the maps produced.\nFor information, however, these parts of the data are included in the spectra\nshown in Fig.~1. \nThey were used separately to derive disk sizes in the lines and\nthe continuum.}\n\nFig. \\ref{colla} shows the results for the four strongest lines in the spectra,\nH$_\\alpha$, H$_\\beta$, \\ion{He}{i}\\,$\\lambda 6678$ and \\ion{He}{ii}\\,$\\lambda \n4686$. The phase-folded spectra are shown in the left column, the \ncorresponding Doppler maps in the right and in the middle the spectra \nreconstructed from the maps. The theoretical\ntrajectory of the mass transfering stream\nhas been plotted in the \\ion{He}{ii} image, together with the Keplerian \nvelocity along the stream path (cp. Marsh\\,\\&\\,Horne 1988). Bars\nconnecting the two arcs indicate correspondence in physical space, and are \nannotated with radius r/a and the azimuth $\\Phi$ relative to the primary.\nThe system parameters \n%($\\mbox{M}_1=0.75,\\mbox{q}=0.75,\\mbox{i}=84.2$) \nand the ephemeris are from Fiedler et al. (1997).\n\n\\begin{figure*}\n\\vbox{\n%row 1: H-alpha spectrum , reco, map.\n\\hbox{\\mbox{}\\hfill\n \\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f1}\n \\hfill\\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f2}\n \\hfill\\includegraphics[height=5.4cm]{bh033.f3}\\hfill\\mbox{}}\n%row 2: H-beta , reco, map.\n\\hbox{\\mbox{}\\hfill\\includegraphics[width=5.3cm,height=3.5cm,angle=90]\n{bh033.f4}\n \\hfill\\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f5}\n \\hfill\\includegraphics[height=5.4cm]{bh033.f6}\\hfill\\mbox{}}\n% row 3: He I 6678 , reco, map.\n\\hbox{\\mbox{}\\hfill\\includegraphics[width=5.3cm,height=3.5cm,angle=90]\n{bh033.f7}\n \\hfill\\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f8}\n \\hfill\\includegraphics[height=5.4cm]{bh033.f9}\\hfill\\mbox{}}\n% row 4: He II , reco, map.\n\\hbox{\\mbox{}\\hfill\\includegraphics[width=5.3cm,height=3.5cm,angle=90]\n{bh033.f10}\n \\hfill\\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f11}\n \\hfill\\includegraphics[height=5.4cm]{bh033.f12}\\hfill\\mbox{}}\n}\n\\caption{\\label{colla} Phase-folded spectra of EX\\,Dra in outburst on 28 July \n1996 \n(left column), corresponding Doppler maps (right column), and the spectra \nreconstructed from the maps (middle). Top to bottom: H$_\\alpha$, H$_\\beta$,\n\\ion{He}{i}, \\ion{He}{ii}. The mass transferring stream (see text) and\nthe Doppler \nimage of the Roche lobe of the secondary star are over plotted on the \n\\ion{He}{ii} \nimage. Upper and lower intensity cuts of the Doppler maps have been adjusted \nsuch that the disk emission has roughly the same contrast in each image.\n}\n\\end{figure*}\n\nThe \\ion{He}{i} image shows the spirals clearest:\nasymmetric disk emission is concentrated \nin two arms in the first and third quadrant. \nWe interpret this deviation from a Keplerian disk\nas indication of the presence of spiral shock waves in the accretion \ndisk. The image looks quite similar to\nthe \\ion{He}{i} map of IP\\,Peg published by Steeghs et al. (1997). \nAs in the case of IP\\,Peg, the arms do not follow a circle centered on the white \ndwarf, but are somewhat elongated along the V$_y$-axis. \nThis is the pattern expected from spiral shocks (Steeghs \n\\& Stehle 1999). The asymmetry of the spirals in the EX\\,Dra disk \nis smaller than in the IP\\,Peg observations\n(Steeghs et al. 1997, Harlaftis et al. 1999, Morales-Rueda et al. 2000), \nperhaps indicating that the shocks are weaker.\nThe spiral arm in the upper right is stronger in intensity as well as in\nasymmetry than that one in the lower left. This pattern is also seen in the \nDoppler maps of IP\\,Peg. \nAs in the case of IP\\,Peg, the Balmer lines show similar, \nbut less clearly defined structures.\n\nThe Doppler images, with the exception of \\ion{He}{ii}, \nshow strong emission from the secondary star, also visible during the \noutburst in 1993 (Joergens et al. 2000). This indicates \nheating of the secondary by radiation from the inner disk. \nThe temperatures are obviously \nnot high enough to excite the \\ion{He}{ii} line. \nThe \\ion{He}{ii} line also differs \nfrom the other lines by the presence of a prominent emission patch \nat the theoretical gas stream trajectory.\nThe center of this hot spot emission is somewhat below the trajectory,\nconsistent with quiescence observations of EX\\,Dra (Billington et al.\n1996, Joergens et al. 2000). \n\n\\section{The disk radius}\n\\label{disk}\nThe large width of the \\ion{He}{ii} line is as expected for a high\nexcitation line produced near the center of a disk in outburst. The\neclipse of the \\ion{He}{ii} line is visible in the spectrum up to a velocity\nof about 1500\\,km/s. The orbital velocity at the disk edge is about 4.3\ntimes lower than this. Assuming Keplerian rotation, the disk region\neclipsed at 1500\\,km/s \nis about 20 times smaller in radius than the outer radius \nof the disk. At our phase resolution, the 1500 km/s emission is thus \npoint-like, \nand can be used to measure the width of the secondary's shadow on the orbital \nplane, $\\Delta\\phi=0.08\\pm0.005$. From the position of the hot spot in the \\ion{He}{ii}\nmap, we can estimate a disk size of $r/a=0.32 \\pm 0.04$. \n\nThe eclipse of the Balmer and \\ion{He}{i} lines shows that the blue\ndisk emission reappears (at V$\\approx 350$km/s) at the same phase as\nthe last red emission disappears, within \nthe measurement uncertainty. The size of the disk as seen in these lines is thus,\nby a coincidence, nearly as wide as the occulting shadow of the secondary. \nHence the disk radius as seen in the Balmer lines is \n$r_{\\rm dB}/a\\approx 2\\pi\\Delta\\phi/2=0.25\\pm0.02$. \n\nWe can compare this with the disk size as measured from the eclipse in the\ncontinuum. The light curve in the continuum between 6400 and 6500{\\AA}, \nextracted from our spectra, is shown in Fig. 2. The width of the eclipse is \n$w=0.17\\pm 0.005$ orbits. With $\\Delta\\phi=0.08$, this implies a disk radius \n$r_{\\rm d}/a=0.31\\pm 0.01$.\n\nFiedler et al. (1997) find a value of 0.11 for the eclipse width of\nthe white dwarf, from analysis of a mean blue light curve in quiescence. The \ndisk as seen in the continuum thus appears to be larger in outburst than in \nquiescence, as expected. \nThe eclipse width values of 0.17 in outburst and 0.11 in \nquiescence are also compatible with the eclipse light curves of Baptista \\& \nCatalan (1999). These authors measured the eclipses of EX\\,Dra\nat various stages in the \noutburst cycle.\n\n\\begin{figure}\n \\includegraphics[height=0.49\\textwidth,angle=270]\n{bh033.f13}\n\\caption{Spectrophotometric light curve of the wavelength range \n6400--6500{\\AA}.}\n\\end{figure}\n\n\\section{Discussion and conclusions}\nWe find evidence for spiral structures in the outburst accretion disk\nof EX\\,Dra similar to those found in IP\\,Peg by Steeghs\\,et\\,al. (1997). \nThe pattern of intensity and velocity perturbations agrees with that predicted \nfrom numerical simulations of spiral shock waves (Steeghs\\,\\&\\,Stehle 1999). It\nis best seen in the \\ion{He}{i} line, somewhat less clearly in the Balmer and \n\\ion{He}{ii} lines. \nIn EX Dra the pattern appears somewhat less clearly and\nasymmetric than in IP\\,Peg.\n\nIn particular, it is less clear in the \n\\ion{He}{ii} line, suggesting lower temperatures and shock strengths\nof the spirals of EX\\,Dra. \nPossibly the observability of spirals in the \\ion{He}{ii} map \nis hampered by strong hot spot emission visible in this line.\n\nWe derive a disk radius \nof $r/a=0.31\\pm0.01$ from the red continuum eclipse light curve.\nFrom numerical simulations, Steeghs \\&\nStehle find that disk sizes \\mbox{$r_{\\rm d}/a\\,=\\,0.3-0.4$} \nare needed to excite \nspirals that are strong enough to generate an observable pattern in the \nspectra.\n(Transformation from $r_{\\rm d}/a$ to $r_{\\rm d}/R_{L_1}$ is given by\nR$_{L_1}=0.53\\,a$ for q=0.75, cp. Plavec \\& Kratochvil 1964.)\nSince the tidal force is a very steep function of $r/a$, the \nspirals rapidly become weak at smaller disk sizes. The {\\mk disk \nsize we find here in EX\\,Dra} is at the lower limit of the required size. \n\nFurther evidence for the size of the disk in EX\\,Dra in outburst was\nobtained by Baptista \\& Catalan (1999). \nRadial intensity distributions presented there\nshow disk radii of 0.30\\,$a$ in quiescence\nand 0.49\\,$a$ in outburst. The authors see hints of spirals in their \neclipse maps, during the early outburst stages.\nThis may be compared with the \nobservations presented here, which show spirals and a \ndisk size of 0.31\\,$a$ three days after the beginning of an outburst.\n \nThe eclipses of the Balmer lines in our spectra yield significantly {\\em smaller} \ndisks sizes than the continuum eclipse, $r_{\\rm dB}/a=0.25\\pm 0.02$.\nSince it is known that the line emission is produced primarily in the outer\nparts of the disk (e.g. Rutten et al. 1994), one might have expected the disk \nas seen in the lines to be larger, if anything, than in the continuum. \n\nA possible resolution of this conflict may lie in the optical depth effects \naffecting the emission lines in systems seen at high inclination. {\\mk The low central \nintensity of the Balmer lines in high-inclination CVs (often below the continuum)\nshows that such effects are strong. As shown by Horne \\& Marsh (1986),\nthe effects are strongest for lines of sight parallel and perpendicular\nto the orbital motion, leading to reduced line emission from these directions\ncompared to intermediate lines of sight (near $45^\\circ$ to the orbit).\nThe bias towards intermediate angles will give the appearance of a somewhat\nsmaller disk size. It is still to be determined if this suggestion also\nworks quantitatively.}\n\n%As shown by\n%Horne \\& Marsh (1986), the low central intensity of the Balmer lines\n%in dwarf nova disks at high orbital inclination are the result of\n%self-absorption in the lines. The self-absorption is strong along\n%lines of sight perpendicular and tangential to the orbits of the gas,\n%where the velocity gradient is small. The effect is weakest along\n%lines of sight at intermediate angles to the orbit, where the gradient\n%of the orbital velocity (projected along the line of sight) is\n%largest. At the very high inclination of EX\\,Dra, the effect could be\n%strong. The outer parts of the disk that determine the eclipse\n%width are seen with the line of sight nearly parallel to the orbital\n%motion. We may expect the emission in these regions to be weakened by \n%self-absorption, thus mimicking a somewhat smaller disk. \n%A more detailed comparison of the Horne \\& Marsh \n%optical depth effect with observations is needed to establish if this\n%explanation is quantitatively adequate.\n\n\\begin{acknowledgements}\nWe thank Dr.\\ Heinz Barwig for providing the photometric information on\nEX\\,Dra. We thank the anonymous referee \nfor the comments, which helped to improve the presentation of the data and to \ncorrect an error. This work was done in the context of the research network \n`Accretion onto black holes, compact objects and protostars' (TMR Grant \nERB-FMRX-CT98-0195). The Isaac Newton \nTelescope is operated on the island of La Palma by the Isaac Newton Group of \nTelescopes in the Spanish Observatorio del Roque de los Muchachos of the \nInstituto de Astrofisica de Canarias.\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\n\\bibitem{} Baptista R., Catalan M.S., 1999, astro-ph/9905096\n\n\\bibitem{} Barwig H., Fiedler H., Reimers D., Bade N., 1993, \n in: Compact Stars in Binary Systems,\n eds.\\ H. van Woerden, Abstracts of IAU Symp.\\ 165, p.\\ 89\n\n\\bibitem{} Billington I., Marsh T.R., Dhillon V.S., 1996, MNRAS 278, 673 \n\n\\bibitem{} Bunk, W., Verbunt, F.; Livio, M., 1990, A\\&A 232, 371\n\n\\bibitem{} Fiedler H., Barwig H., Mantel K.H., 1997 A\\&A, 327, 173\n\n\\bibitem{} Godon P., 1997, ApJ 480, 329\n\n\\bibitem{} Harlaftis E. T., Steeghs D., Horne K., Martin E., Magazzu A.,\n1999, MNRAS 306, 348\n\n\\bibitem{} Horne K., Marsh T., 1986, MNRAS 218, 761\n\n\\bibitem{} Joergens V., Mantel K.H., Barwig H., B\\\"arnbantner O., Fiedler H.,\n 2000 A\\&A, in press\n\n\\bibitem{} Larson R.B., 1990, MNRAS 243, 588\n\n\\bibitem{} Marsh T., Horne K., 1988, MNRAS 235, 269\n\n\\bibitem{} Morales-Rueda L., Marsh T. R., Billington I., 2000, MNRAS, in press \n\n\\bibitem{} Plavec M., Kratochvil P., 1964, Bulletin of the Astronomical \nInstitute of Czechoslovakia 15, 165\n\n\\bibitem{} R\\'o\\.zyczka M., Spruit H.C.,1993, ApJ 417, 677 \n\n\\bibitem{} Rutten R.G.M, Dhillon V.S., Horne K., Kuulkers E., 1994, A\\&A 283, 441\n\n\\bibitem{} Sawada, K., Matsuda, T., Hachisu, I., 1986, MNRAS 219, 75\n\n\\bibitem{} Sawada, K., Matsuda, T., Inoue M., Hachisu, I., 1987, MNRAS, 224, 307\n\n\\bibitem{} Spruit H.C., 1987, A\\&A 184, 173 \n\n\\bibitem{} Spruit H.C., 1998, astro-ph/9806141\n\n\\bibitem{} Spruit H.C., Matsuda T., Inoue M. and Sawada K., 1987, MNRAS 229, \n517 \n \n\\bibitem{} Steeghs D., Harlaftis E.T., Horne K., 1997 MNRAS 290, 28,\nerratum in 1998 MNRAS 296, 463\n\n\\bibitem{} Steeghs D., Horne K., Stehle R., Harlaftis E.T., 1998, AAS 193, 520\n\n\\bibitem{} Steeghs D., Stehle R., 1999, MNRAS 307, 99 \n\n\\bibitem{} Yukawa H., Boffin H. M. J., Matsuda T., 1997, MNRAS 292, 321\n\n\\bibitem{} VSNET, 1998, http://www.kusastro.kyoto-u.ac.jp/vsnet\n\n\\end{thebibliography}\n\n\\end{document}\n"}],"string":"[\n {\n \"name\": \"bh033.tex\",\n \"string\": \"\\n%\\\\documentstyle[epsf]{l-aa}\\n\\\\documentclass{aa}\\n\\\\newcommand{\\\\be}{\\\\begin{equation}}\\n\\\\newcommand{\\\\ee}{\\\\end{equation}}\\n\\\\newcommand{\\\\bd}{\\\\begin{displaymath}}\\n\\\\newcommand{\\\\ed}{\\\\end{displaymath}}\\n\\\\newcommand{\\\\gapprox}{\\\\;\\\\rlap{\\\\lower 2.5pt \\n \\\\hbox{$\\\\sim$}}\\\\raise 1.5pt\\\\hbox{$>$}\\\\;} \\n\\\\newcommand{\\\\lapprox}{\\\\;\\\\rlap{\\\\lower 2.5pt \\n \\\\hbox{$\\\\sim$}}\\\\raise 1.5pt\\\\hbox{$<$}\\\\;} \\n\\\\newcommand{\\\\pr}{\\\\prime}\\n\\\\newcommand{\\\\p}{\\\\partial}\\n\\\\newcommand{\\\\rd}{{\\\\rm d}} \\n\\n%\\\\newcommand{\\\\mk}{\\\\bf} % temporary markup by boldface\\n\\\\newcommand{\\\\mk}{} % udno temporary markup\\n\\n\\\\usepackage{graphicx}\\n\\\\begin{document}\\n \\\\thesaurus{06 % A&A Section 6: Form. struct. and evolut. of stars\\n 02.01.2 %accretion\\n 02.08.1 %hydro\\n 08.02.2 %ecl binaries\\n 08.09.2 EX\\\\,Dra\\n }\\n%\\n \\\\title{Spirals and the size of the disk in EX\\\\,Dra}\\n% \\\\subtitle{}\\n\\n% \\n \\\\author{V. Joergens \\\\inst{1,2} \\\\and H.C. Spruit \\\\inst{1}\\n \\\\and R.G.M. Rutten \\\\inst{3,4}}\\n\\n% \\\\offprints{}\\n \\n \\\\institute{Max-Planck-Institut f\\\\\\\"ur Astrophysik, Postfach 1523, \\n D-85740 Garching bei M\\\\\\\"unchen, Germany \\\\and\\n Max-Planck-Institut f\\\\\\\"ur Extraterrestrische Physik, \\n Postfach 1603, D-85740 Garching bei M\\\\\\\"unchen, Germany \\\\and\\n Netherlands Foundation for Research in Astronomy \\\\and\\n Royal Greenwich Observatory, Apartado de Correos 321, \\n 38780 Santa Cruz de La Palma, Canary Islands, Spain\\n }\\n\\n \\\\date{Received }\\n\\n \\\\maketitle\\n\\n% \\\\maintitlerunninghead{}\\n\\n% \\\\authorrunninghead{}\\n\\n\\\\begin{abstract}\\nObservations at high spectral and temporal resolution are presented of\\nthe dwarf nova EX\\\\,Dra in outburst. \\nThe disk seen in the \\\\ion{He}{i} line reconstructed by Doppler tomography\\nshows a clear two-armed spiral pattern pointing to spiral shocks in the disk.\\nThe Balmer and \\\\ion{He}{ii} maps also give evidence for \\nthe presence of spirals. \\nThe eclipse as seen in the red continuum indicates a disk radius of 0.31 times\\nthe orbital separation, which might be\\nlarge enough to explain the observed spiral shocks through\\nexcitation by the tidal field of the secondary. \\nThe eclipse in the Balmer line profiles, well \\nresolved in our observations, indicates a somewhat smaller disk size (0.25).\\nWe discuss the possibility that this is related to an optical depth effect \\nin the lines.\\n\\\\keywords{accretion disks -- hydrodynamics -- Cataclysmic Variables -- stars: \\nEX\\\\,Dra}\\n\\\\end{abstract}\\n\\n\\\\section{Introduction}\\n\\nSpiral shocks in accretion disks have been predicted from numerical \\nsimulations (Sawada et al. 1986, 1987, R\\\\'o\\\\.zyczka \\\\& Spruit 1993, Yukawa et \\nal. 1997), and analytic considerations (Spruit 1987, Spruit et al. 1987, \\nLarson 1990). They are excited by the tidal field of the secondary if the \\ndisk extends \\nfar enough into the Roche lobe and can result in two prominent spiral arms.\\nIf shock dissipation is the main mechanism damping the wave, it extends over \\nthe entire disk and causes accretion at an effective $\\\\alpha$-value of \\n$0.01(H/r)^{3/2}$ (Spruit 1987, Larson 1990, Godon 1997). \\n\\nThe first observational evidence for shock waves in accretion disks of \\ncataclysmic variables (CVs) was the detection of a clear two-armed \\nstructure in the disk of IP\\\\,Peg during rise to outburst (Steeghs et \\nal. 1997). The spiral pattern, interpreted as evidence for shock waves,\\nhas also been seen during outburst maximum (Harlaftis et al. 1999) and early \\ndecline of outburst (Morales-Rueda et al. 2000).\\n\\nAt the temperatures expected from dwarf nova disks models, whether in outburst \\nor in quiescence, the predicted spirals are tightly wound and would be hard to \\ndetect observationally (Bunk et al. 1990), so that their presence in the \\nobservations is somewhat unexpected.\\nSpirals this strong are most naturally explained if the disk\\ntemporarily extends rather far into the primary Roche lobe, so that\\nthe tidal force of the secondary causes a strong disturbance. A strong\\nnon-axisymmetric disturbance, however, would also cause the gas to\\nloose angular momentum quickly (transfered to the secondary), so that\\nthe disk would shrink to a smaller radius where the tidal force is\\nweaker. Spirals in disks of CVs would then be understandable if they are a\\ntemporary phenomenon, perhaps restricted to\\noutbursts. To test this, more observations of different systems at\\nsufficient spectral resolution and signal-to-noise are needed\\n(Steeghs \\\\& Stehle 1999). \\n\\nWith high quality spectroscopic studies of different CVs it should also be \\npossible to answer the question if spiral shocks in CV accretion disks are a \\ncommon phenomenon. Systems suitable for this purpose would be bright and \\nhave frequent outbursts, such as SS\\\\,Cyg and EX\\\\,Dra. \\n\\nEX\\\\,Dra is a double--eclipsing dwarf nova with a 5-hour orbit \\n(Barwig et al. 1993, Billington et al. 1996, system parameters by \\nFiedler et al. 1997).\\nThere is suggestive evidence for asymmetric structures in the \\\\ion{He}{i}\\nDoppler map reconstructed from outburst data taken in 1993 (Joergens et al. \\n2000). From eclipse maps obtained at various stages in the outburst cycle Baptista \\\\& \\nCatalan (1999) claim that spiral waves form at the early stages of an \\noutburst. We report in this paper on observations at high spectral and temporal\\nresolution during an outburst in 1996.\\n\\n\\\\section{Observations and reduction}\\nEX\\\\,Dra was observed on the nights of July 27\\nand 28 1996, with the ISIS spectrograph on the 4.2\\\\,m William\\nHerschel Telescope. \\nThe red ISIS arm was equipped with the TEK\\\\,5 CCD,\\nthe blue arm with TEK\\\\,1 CCD, covering the \\nwavelength ranges 6375-6778\\\\,{\\\\AA} and\\n4585-4993\\\\,{\\\\AA} respectively, at a dispersion of\\n0.4\\\\,{\\\\AA}/pixel. \\nThe spectra were observed during seeing of 1.4 -- 1.7 arc sec, \\nusing an exposure time of 60s.\\n%, corresponding to 0.3\\\\% of the binary orbit. \\nThe spectra were optimally-extracted, including the elimination of \\ncosmic ray hits but not the correction of Pixel-to-pixel variations of the \\ndetector sensitivity. \\nSlit losses due to variable atmospheric conditions were \\ncorrected using a faint comparison star on the slit.\\nThe red spectra, but not the blue spectra, were flux calibrated. \\n\\nOur spectra were taken roughly in the middle of an outburst. Photometric \\nobservation at the Wendelstein observatory showed that the system was already \\nin outburst on 26 July, and in quiescence on 4 August (Barwig, private comm.). \\nVSNET (1998) records show that the system was in quiescence on 24 July \\nand in outburst one day later and in quiescence again on 1 August. The outburst \\ntherefore started on 25 August, three days before our observations.\\n\\n\\n\\\\section{Interpretation of the Doppler maps}\\n\\\\label{interpret}\\n\\nDoppler maps were computed from the phase-folded spectra of 28 July, using the IDL-based \\nfast-maximum entropy package described by Spruit (1998)\\\\footnote{available \\nat http:www.mpa-garching.mpg.de/$\\\\sim$henk}. \\nFor further details on Doppler tomography see Marsh \\\\& Horne (1988). \\n{\\\\mk The eclipsed part of the data (phases -0.12 to 0.12) has been \\nexcluded from the reconstruction process, and does not affect the maps produced.\\nFor information, however, these parts of the data are included in the spectra\\nshown in Fig.~1. \\nThey were used separately to derive disk sizes in the lines and\\nthe continuum.}\\n\\nFig. \\\\ref{colla} shows the results for the four strongest lines in the spectra,\\nH$_\\\\alpha$, H$_\\\\beta$, \\\\ion{He}{i}\\\\,$\\\\lambda 6678$ and \\\\ion{He}{ii}\\\\,$\\\\lambda \\n4686$. The phase-folded spectra are shown in the left column, the \\ncorresponding Doppler maps in the right and in the middle the spectra \\nreconstructed from the maps. The theoretical\\ntrajectory of the mass transfering stream\\nhas been plotted in the \\\\ion{He}{ii} image, together with the Keplerian \\nvelocity along the stream path (cp. Marsh\\\\,\\\\&\\\\,Horne 1988). Bars\\nconnecting the two arcs indicate correspondence in physical space, and are \\nannotated with radius r/a and the azimuth $\\\\Phi$ relative to the primary.\\nThe system parameters \\n%($\\\\mbox{M}_1=0.75,\\\\mbox{q}=0.75,\\\\mbox{i}=84.2$) \\nand the ephemeris are from Fiedler et al. (1997).\\n\\n\\\\begin{figure*}\\n\\\\vbox{\\n%row 1: H-alpha spectrum , reco, map.\\n\\\\hbox{\\\\mbox{}\\\\hfill\\n \\\\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f1}\\n \\\\hfill\\\\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f2}\\n \\\\hfill\\\\includegraphics[height=5.4cm]{bh033.f3}\\\\hfill\\\\mbox{}}\\n%row 2: H-beta , reco, map.\\n\\\\hbox{\\\\mbox{}\\\\hfill\\\\includegraphics[width=5.3cm,height=3.5cm,angle=90]\\n{bh033.f4}\\n \\\\hfill\\\\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f5}\\n \\\\hfill\\\\includegraphics[height=5.4cm]{bh033.f6}\\\\hfill\\\\mbox{}}\\n% row 3: He I 6678 , reco, map.\\n\\\\hbox{\\\\mbox{}\\\\hfill\\\\includegraphics[width=5.3cm,height=3.5cm,angle=90]\\n{bh033.f7}\\n \\\\hfill\\\\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f8}\\n \\\\hfill\\\\includegraphics[height=5.4cm]{bh033.f9}\\\\hfill\\\\mbox{}}\\n% row 4: He II , reco, map.\\n\\\\hbox{\\\\mbox{}\\\\hfill\\\\includegraphics[width=5.3cm,height=3.5cm,angle=90]\\n{bh033.f10}\\n \\\\hfill\\\\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f11}\\n \\\\hfill\\\\includegraphics[height=5.4cm]{bh033.f12}\\\\hfill\\\\mbox{}}\\n}\\n\\\\caption{\\\\label{colla} Phase-folded spectra of EX\\\\,Dra in outburst on 28 July \\n1996 \\n(left column), corresponding Doppler maps (right column), and the spectra \\nreconstructed from the maps (middle). Top to bottom: H$_\\\\alpha$, H$_\\\\beta$,\\n\\\\ion{He}{i}, \\\\ion{He}{ii}. The mass transferring stream (see text) and\\nthe Doppler \\nimage of the Roche lobe of the secondary star are over plotted on the \\n\\\\ion{He}{ii} \\nimage. Upper and lower intensity cuts of the Doppler maps have been adjusted \\nsuch that the disk emission has roughly the same contrast in each image.\\n}\\n\\\\end{figure*}\\n\\nThe \\\\ion{He}{i} image shows the spirals clearest:\\nasymmetric disk emission is concentrated \\nin two arms in the first and third quadrant. \\nWe interpret this deviation from a Keplerian disk\\nas indication of the presence of spiral shock waves in the accretion \\ndisk. The image looks quite similar to\\nthe \\\\ion{He}{i} map of IP\\\\,Peg published by Steeghs et al. (1997). \\nAs in the case of IP\\\\,Peg, the arms do not follow a circle centered on the white \\ndwarf, but are somewhat elongated along the V$_y$-axis. \\nThis is the pattern expected from spiral shocks (Steeghs \\n\\\\& Stehle 1999). The asymmetry of the spirals in the EX\\\\,Dra disk \\nis smaller than in the IP\\\\,Peg observations\\n(Steeghs et al. 1997, Harlaftis et al. 1999, Morales-Rueda et al. 2000), \\nperhaps indicating that the shocks are weaker.\\nThe spiral arm in the upper right is stronger in intensity as well as in\\nasymmetry than that one in the lower left. This pattern is also seen in the \\nDoppler maps of IP\\\\,Peg. \\nAs in the case of IP\\\\,Peg, the Balmer lines show similar, \\nbut less clearly defined structures.\\n\\nThe Doppler images, with the exception of \\\\ion{He}{ii}, \\nshow strong emission from the secondary star, also visible during the \\noutburst in 1993 (Joergens et al. 2000). This indicates \\nheating of the secondary by radiation from the inner disk. \\nThe temperatures are obviously \\nnot high enough to excite the \\\\ion{He}{ii} line. \\nThe \\\\ion{He}{ii} line also differs \\nfrom the other lines by the presence of a prominent emission patch \\nat the theoretical gas stream trajectory.\\nThe center of this hot spot emission is somewhat below the trajectory,\\nconsistent with quiescence observations of EX\\\\,Dra (Billington et al.\\n1996, Joergens et al. 2000). \\n\\n\\\\section{The disk radius}\\n\\\\label{disk}\\nThe large width of the \\\\ion{He}{ii} line is as expected for a high\\nexcitation line produced near the center of a disk in outburst. The\\neclipse of the \\\\ion{He}{ii} line is visible in the spectrum up to a velocity\\nof about 1500\\\\,km/s. The orbital velocity at the disk edge is about 4.3\\ntimes lower than this. Assuming Keplerian rotation, the disk region\\neclipsed at 1500\\\\,km/s \\nis about 20 times smaller in radius than the outer radius \\nof the disk. At our phase resolution, the 1500 km/s emission is thus \\npoint-like, \\nand can be used to measure the width of the secondary's shadow on the orbital \\nplane, $\\\\Delta\\\\phi=0.08\\\\pm0.005$. From the position of the hot spot in the \\\\ion{He}{ii}\\nmap, we can estimate a disk size of $r/a=0.32 \\\\pm 0.04$. \\n\\nThe eclipse of the Balmer and \\\\ion{He}{i} lines shows that the blue\\ndisk emission reappears (at V$\\\\approx 350$km/s) at the same phase as\\nthe last red emission disappears, within \\nthe measurement uncertainty. The size of the disk as seen in these lines is thus,\\nby a coincidence, nearly as wide as the occulting shadow of the secondary. \\nHence the disk radius as seen in the Balmer lines is \\n$r_{\\\\rm dB}/a\\\\approx 2\\\\pi\\\\Delta\\\\phi/2=0.25\\\\pm0.02$. \\n\\nWe can compare this with the disk size as measured from the eclipse in the\\ncontinuum. The light curve in the continuum between 6400 and 6500{\\\\AA}, \\nextracted from our spectra, is shown in Fig. 2. The width of the eclipse is \\n$w=0.17\\\\pm 0.005$ orbits. With $\\\\Delta\\\\phi=0.08$, this implies a disk radius \\n$r_{\\\\rm d}/a=0.31\\\\pm 0.01$.\\n\\nFiedler et al. (1997) find a value of 0.11 for the eclipse width of\\nthe white dwarf, from analysis of a mean blue light curve in quiescence. The \\ndisk as seen in the continuum thus appears to be larger in outburst than in \\nquiescence, as expected. \\nThe eclipse width values of 0.17 in outburst and 0.11 in \\nquiescence are also compatible with the eclipse light curves of Baptista \\\\& \\nCatalan (1999). These authors measured the eclipses of EX\\\\,Dra\\nat various stages in the \\noutburst cycle.\\n\\n\\\\begin{figure}\\n \\\\includegraphics[height=0.49\\\\textwidth,angle=270]\\n{bh033.f13}\\n\\\\caption{Spectrophotometric light curve of the wavelength range \\n6400--6500{\\\\AA}.}\\n\\\\end{figure}\\n\\n\\\\section{Discussion and conclusions}\\nWe find evidence for spiral structures in the outburst accretion disk\\nof EX\\\\,Dra similar to those found in IP\\\\,Peg by Steeghs\\\\,et\\\\,al. (1997). \\nThe pattern of intensity and velocity perturbations agrees with that predicted \\nfrom numerical simulations of spiral shock waves (Steeghs\\\\,\\\\&\\\\,Stehle 1999). It\\nis best seen in the \\\\ion{He}{i} line, somewhat less clearly in the Balmer and \\n\\\\ion{He}{ii} lines. \\nIn EX Dra the pattern appears somewhat less clearly and\\nasymmetric than in IP\\\\,Peg.\\n\\nIn particular, it is less clear in the \\n\\\\ion{He}{ii} line, suggesting lower temperatures and shock strengths\\nof the spirals of EX\\\\,Dra. \\nPossibly the observability of spirals in the \\\\ion{He}{ii} map \\nis hampered by strong hot spot emission visible in this line.\\n\\nWe derive a disk radius \\nof $r/a=0.31\\\\pm0.01$ from the red continuum eclipse light curve.\\nFrom numerical simulations, Steeghs \\\\&\\nStehle find that disk sizes \\\\mbox{$r_{\\\\rm d}/a\\\\,=\\\\,0.3-0.4$} \\nare needed to excite \\nspirals that are strong enough to generate an observable pattern in the \\nspectra.\\n(Transformation from $r_{\\\\rm d}/a$ to $r_{\\\\rm d}/R_{L_1}$ is given by\\nR$_{L_1}=0.53\\\\,a$ for q=0.75, cp. Plavec \\\\& Kratochvil 1964.)\\nSince the tidal force is a very steep function of $r/a$, the \\nspirals rapidly become weak at smaller disk sizes. The {\\\\mk disk \\nsize we find here in EX\\\\,Dra} is at the lower limit of the required size. \\n\\nFurther evidence for the size of the disk in EX\\\\,Dra in outburst was\\nobtained by Baptista \\\\& Catalan (1999). \\nRadial intensity distributions presented there\\nshow disk radii of 0.30\\\\,$a$ in quiescence\\nand 0.49\\\\,$a$ in outburst. The authors see hints of spirals in their \\neclipse maps, during the early outburst stages.\\nThis may be compared with the \\nobservations presented here, which show spirals and a \\ndisk size of 0.31\\\\,$a$ three days after the beginning of an outburst.\\n \\nThe eclipses of the Balmer lines in our spectra yield significantly {\\\\em smaller} \\ndisks sizes than the continuum eclipse, $r_{\\\\rm dB}/a=0.25\\\\pm 0.02$.\\nSince it is known that the line emission is produced primarily in the outer\\nparts of the disk (e.g. Rutten et al. 1994), one might have expected the disk \\nas seen in the lines to be larger, if anything, than in the continuum. \\n\\nA possible resolution of this conflict may lie in the optical depth effects \\naffecting the emission lines in systems seen at high inclination. {\\\\mk The low central \\nintensity of the Balmer lines in high-inclination CVs (often below the continuum)\\nshows that such effects are strong. As shown by Horne \\\\& Marsh (1986),\\nthe effects are strongest for lines of sight parallel and perpendicular\\nto the orbital motion, leading to reduced line emission from these directions\\ncompared to intermediate lines of sight (near $45^\\\\circ$ to the orbit).\\nThe bias towards intermediate angles will give the appearance of a somewhat\\nsmaller disk size. It is still to be determined if this suggestion also\\nworks quantitatively.}\\n\\n%As shown by\\n%Horne \\\\& Marsh (1986), the low central intensity of the Balmer lines\\n%in dwarf nova disks at high orbital inclination are the result of\\n%self-absorption in the lines. The self-absorption is strong along\\n%lines of sight perpendicular and tangential to the orbits of the gas,\\n%where the velocity gradient is small. The effect is weakest along\\n%lines of sight at intermediate angles to the orbit, where the gradient\\n%of the orbital velocity (projected along the line of sight) is\\n%largest. At the very high inclination of EX\\\\,Dra, the effect could be\\n%strong. The outer parts of the disk that determine the eclipse\\n%width are seen with the line of sight nearly parallel to the orbital\\n%motion. We may expect the emission in these regions to be weakened by \\n%self-absorption, thus mimicking a somewhat smaller disk. \\n%A more detailed comparison of the Horne \\\\& Marsh \\n%optical depth effect with observations is needed to establish if this\\n%explanation is quantitatively adequate.\\n\\n\\\\begin{acknowledgements}\\nWe thank Dr.\\\\ Heinz Barwig for providing the photometric information on\\nEX\\\\,Dra. We thank the anonymous referee \\nfor the comments, which helped to improve the presentation of the data and to \\ncorrect an error. This work was done in the context of the research network \\n`Accretion onto black holes, compact objects and protostars' (TMR Grant \\nERB-FMRX-CT98-0195). The Isaac Newton \\nTelescope is operated on the island of La Palma by the Isaac Newton Group of \\nTelescopes in the Spanish Observatorio del Roque de los Muchachos of the \\nInstituto de Astrofisica de Canarias.\\n\\\\end{acknowledgements}\\n\\n\\\\begin{thebibliography}{}\\n\\n\\\\bibitem{} Baptista R., Catalan M.S., 1999, astro-ph/9905096\\n\\n\\\\bibitem{} Barwig H., Fiedler H., Reimers D., Bade N., 1993, \\n in: Compact Stars in Binary Systems,\\n eds.\\\\ H. van Woerden, Abstracts of IAU Symp.\\\\ 165, p.\\\\ 89\\n\\n\\\\bibitem{} Billington I., Marsh T.R., Dhillon V.S., 1996, MNRAS 278, 673 \\n\\n\\\\bibitem{} Bunk, W., Verbunt, F.; Livio, M., 1990, A\\\\&A 232, 371\\n\\n\\\\bibitem{} Fiedler H., Barwig H., Mantel K.H., 1997 A\\\\&A, 327, 173\\n\\n\\\\bibitem{} Godon P., 1997, ApJ 480, 329\\n\\n\\\\bibitem{} Harlaftis E. T., Steeghs D., Horne K., Martin E., Magazzu A.,\\n1999, MNRAS 306, 348\\n\\n\\\\bibitem{} Horne K., Marsh T., 1986, MNRAS 218, 761\\n\\n\\\\bibitem{} Joergens V., Mantel K.H., Barwig H., B\\\\\\\"arnbantner O., Fiedler H.,\\n 2000 A\\\\&A, in press\\n\\n\\\\bibitem{} Larson R.B., 1990, MNRAS 243, 588\\n\\n\\\\bibitem{} Marsh T., Horne K., 1988, MNRAS 235, 269\\n\\n\\\\bibitem{} Morales-Rueda L., Marsh T. R., Billington I., 2000, MNRAS, in press \\n\\n\\\\bibitem{} Plavec M., Kratochvil P., 1964, Bulletin of the Astronomical \\nInstitute of Czechoslovakia 15, 165\\n\\n\\\\bibitem{} R\\\\'o\\\\.zyczka M., Spruit H.C.,1993, ApJ 417, 677 \\n\\n\\\\bibitem{} Rutten R.G.M, Dhillon V.S., Horne K., Kuulkers E., 1994, A\\\\&A 283, 441\\n\\n\\\\bibitem{} Sawada, K., Matsuda, T., Hachisu, I., 1986, MNRAS 219, 75\\n\\n\\\\bibitem{} Sawada, K., Matsuda, T., Inoue M., Hachisu, I., 1987, MNRAS, 224, 307\\n\\n\\\\bibitem{} Spruit H.C., 1987, A\\\\&A 184, 173 \\n\\n\\\\bibitem{} Spruit H.C., 1998, astro-ph/9806141\\n\\n\\\\bibitem{} Spruit H.C., Matsuda T., Inoue M. and Sawada K., 1987, MNRAS 229, \\n517 \\n \\n\\\\bibitem{} Steeghs D., Harlaftis E.T., Horne K., 1997 MNRAS 290, 28,\\nerratum in 1998 MNRAS 296, 463\\n\\n\\\\bibitem{} Steeghs D., Horne K., Stehle R., Harlaftis E.T., 1998, AAS 193, 520\\n\\n\\\\bibitem{} Steeghs D., Stehle R., 1999, MNRAS 307, 99 \\n\\n\\\\bibitem{} Yukawa H., Boffin H. M. J., Matsuda T., 1997, MNRAS 292, 321\\n\\n\\\\bibitem{} VSNET, 1998, http://www.kusastro.kyoto-u.ac.jp/vsnet\\n\\n\\\\end{thebibliography}\\n\\n\\\\end{document}\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002302.extracted_bib","string":"\\begin{thebibliography}{}\n\n\\bibitem{} Baptista R., Catalan M.S., 1999, astro-ph/9905096\n\n\\bibitem{} Barwig H., Fiedler H., Reimers D., Bade N., 1993, \n in: Compact Stars in Binary Systems,\n eds.\\ H. van Woerden, Abstracts of IAU Symp.\\ 165, p.\\ 89\n\n\\bibitem{} Billington I., Marsh T.R., Dhillon V.S., 1996, MNRAS 278, 673 \n\n\\bibitem{} Bunk, W., Verbunt, F.; Livio, M., 1990, A\\&A 232, 371\n\n\\bibitem{} Fiedler H., Barwig H., Mantel K.H., 1997 A\\&A, 327, 173\n\n\\bibitem{} Godon P., 1997, ApJ 480, 329\n\n\\bibitem{} Harlaftis E. T., Steeghs D., Horne K., Martin E., Magazzu A.,\n1999, MNRAS 306, 348\n\n\\bibitem{} Horne K., Marsh T., 1986, MNRAS 218, 761\n\n\\bibitem{} Joergens V., Mantel K.H., Barwig H., B\\\"arnbantner O., Fiedler H.,\n 2000 A\\&A, in press\n\n\\bibitem{} Larson R.B., 1990, MNRAS 243, 588\n\n\\bibitem{} Marsh T., Horne K., 1988, MNRAS 235, 269\n\n\\bibitem{} Morales-Rueda L., Marsh T. R., Billington I., 2000, MNRAS, in press \n\n\\bibitem{} Plavec M., Kratochvil P., 1964, Bulletin of the Astronomical \nInstitute of Czechoslovakia 15, 165\n\n\\bibitem{} R\\'o\\.zyczka M., Spruit H.C.,1993, ApJ 417, 677 \n\n\\bibitem{} Rutten R.G.M, Dhillon V.S., Horne K., Kuulkers E., 1994, A\\&A 283, 441\n\n\\bibitem{} Sawada, K., Matsuda, T., Hachisu, I., 1986, MNRAS 219, 75\n\n\\bibitem{} Sawada, K., Matsuda, T., Inoue M., Hachisu, I., 1987, MNRAS, 224, 307\n\n\\bibitem{} Spruit H.C., 1987, A\\&A 184, 173 \n\n\\bibitem{} Spruit H.C., 1998, astro-ph/9806141\n\n\\bibitem{} Spruit H.C., Matsuda T., Inoue M. and Sawada K., 1987, MNRAS 229, \n517 \n \n\\bibitem{} Steeghs D., Harlaftis E.T., Horne K., 1997 MNRAS 290, 28,\nerratum in 1998 MNRAS 296, 463\n\n\\bibitem{} Steeghs D., Horne K., Stehle R., Harlaftis E.T., 1998, AAS 193, 520\n\n\\bibitem{} Steeghs D., Stehle R., 1999, MNRAS 307, 99 \n\n\\bibitem{} Yukawa H., Boffin H. M. J., Matsuda T., 1997, MNRAS 292, 321\n\n\\bibitem{} VSNET, 1998, http://www.kusastro.kyoto-u.ac.jp/vsnet\n\n\\end{thebibliography}"}],"string":"[\n {\n \"name\": \"astro-ph0002302.extracted_bib\",\n \"string\": \"\\\\begin{thebibliography}{}\\n\\n\\\\bibitem{} Baptista R., Catalan M.S., 1999, astro-ph/9905096\\n\\n\\\\bibitem{} Barwig H., Fiedler H., Reimers D., Bade N., 1993, \\n in: Compact Stars in Binary Systems,\\n eds.\\\\ H. van Woerden, Abstracts of IAU Symp.\\\\ 165, p.\\\\ 89\\n\\n\\\\bibitem{} Billington I., Marsh T.R., Dhillon V.S., 1996, MNRAS 278, 673 \\n\\n\\\\bibitem{} Bunk, W., Verbunt, F.; Livio, M., 1990, A\\\\&A 232, 371\\n\\n\\\\bibitem{} Fiedler H., Barwig H., Mantel K.H., 1997 A\\\\&A, 327, 173\\n\\n\\\\bibitem{} Godon P., 1997, ApJ 480, 329\\n\\n\\\\bibitem{} Harlaftis E. T., Steeghs D., Horne K., Martin E., Magazzu A.,\\n1999, MNRAS 306, 348\\n\\n\\\\bibitem{} Horne K., Marsh T., 1986, MNRAS 218, 761\\n\\n\\\\bibitem{} Joergens V., Mantel K.H., Barwig H., B\\\\\\\"arnbantner O., Fiedler H.,\\n 2000 A\\\\&A, in press\\n\\n\\\\bibitem{} Larson R.B., 1990, MNRAS 243, 588\\n\\n\\\\bibitem{} Marsh T., Horne K., 1988, MNRAS 235, 269\\n\\n\\\\bibitem{} Morales-Rueda L., Marsh T. R., Billington I., 2000, MNRAS, in press \\n\\n\\\\bibitem{} Plavec M., Kratochvil P., 1964, Bulletin of the Astronomical \\nInstitute of Czechoslovakia 15, 165\\n\\n\\\\bibitem{} R\\\\'o\\\\.zyczka M., Spruit H.C.,1993, ApJ 417, 677 \\n\\n\\\\bibitem{} Rutten R.G.M, Dhillon V.S., Horne K., Kuulkers E., 1994, A\\\\&A 283, 441\\n\\n\\\\bibitem{} Sawada, K., Matsuda, T., Hachisu, I., 1986, MNRAS 219, 75\\n\\n\\\\bibitem{} Sawada, K., Matsuda, T., Inoue M., Hachisu, I., 1987, MNRAS, 224, 307\\n\\n\\\\bibitem{} Spruit H.C., 1987, A\\\\&A 184, 173 \\n\\n\\\\bibitem{} Spruit H.C., 1998, astro-ph/9806141\\n\\n\\\\bibitem{} Spruit H.C., Matsuda T., Inoue M. and Sawada K., 1987, MNRAS 229, \\n517 \\n \\n\\\\bibitem{} Steeghs D., Harlaftis E.T., Horne K., 1997 MNRAS 290, 28,\\nerratum in 1998 MNRAS 296, 463\\n\\n\\\\bibitem{} Steeghs D., Horne K., Stehle R., Harlaftis E.T., 1998, AAS 193, 520\\n\\n\\\\bibitem{} Steeghs D., Stehle R., 1999, MNRAS 307, 99 \\n\\n\\\\bibitem{} Yukawa H., Boffin H. M. J., Matsuda T., 1997, MNRAS 292, 321\\n\\n\\\\bibitem{} VSNET, 1998, http://www.kusastro.kyoto-u.ac.jp/vsnet\\n\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":298,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002303"},"title":{"kind":"string","value":"Design optimization of MACHe3,\\\\ a project of superfuid \\hetrois detector for direct Dark Matter search."},"authors":{"kind":"list like","value":[{"author":"F. Mayet $^{a,}\\!$\\thanksref{corr}"}],"string":"[\n {\n \"author\": \"F. Mayet $^{a,}\\\\!$\\\\thanksref{corr}\"\n }\n]"},"abstract":{"kind":"string","value":"MACHe3 (MAtrix of Cells of superfluid \\hetro) is a project of a new detector for direct Dark Matter (DM) search. A cell of superfluid \\hetrois has been developed and the idea of using a large number of such cells in a high granularity detector is proposed. \\noindent This paper presents, after a brief description of the superfluid \\hetrois cell, the simulation of the response of different matrix configurations allowing to define an optimum design as a function of the number of cells and the volume of each cell. The background rejection, for several configurations, is presented both for neutrons and \\gams of various kinetic energies."},"latex":{"kind":"list like","value":[{"name":"mac3new.tex","string":"\\documentclass{elsart}\n\\usepackage{graphicx}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n%\n%\n%\n\\newcommand{\\GeVc} {\\mbox{$ {\\mathrm{GeV}}/c $}}\n\\newcommand{\\GeVcc} {\\mbox{$ {\\mathrm{GeV}}/c^2 $}}\n\\newcommand{\\MeVc} {\\mbox{$ {\\mathrm{MeV}}/c $}}\n\\newcommand{\\hetrois} {\\mbox{$ ^{3}{\\mathrm{He}} $}~}\n\\newcommand{\\hetro} {\\mbox{$ ^{3}{\\mathrm{He}} $}}\n\\newcommand{\\tritium} {\\mbox{$ ^{3}{\\mathrm{H}} $}~}\n\\newcommand{\\hequatre} {\\mbox{$ ^{4}{\\mathrm{He}}}}\n\\newcommand{\\citeup}{\\cite}\n\\newcommand{\\cher}{\\u{C}erenkov }\n\\newcommand{\\Cher}{\\u{C}ERENKOV }\n\\newcommand{\\neut}{$\\tilde{\\chi}$~}\n\\newcommand{\\neutt}{$\\tilde{\\chi}$}\n\\newcommand{\\mydeg} {\\mbox{$ ^\\circ $}}\n\\newcommand{\\DM} {Dark Matter}\n\\newcommand{\\gam} {{$\\gamma$-ray}~} \n\\newcommand{\\gams} {{$\\gamma$-rays}~} \n\n\n\n\n\n%\n%\n% A useful Journal macro\n\\def\\Journal#1#2#3#4{{#1} {\\bf #2}, #3 (#4)}\n%\n% Some useful journal names\n\\def\\NCA{\\em Nuovo Cimento}\n\\def\\NIM{\\em Nucl. Instrum. Methods}\n%\\def\\NIMA{{\\em Nucl. Instrum. Methods} A}\n\\def\\NIMA#1#2#3{{\\rm Nucl.~Instr.~and~Meth.} {\\bf#1} (19#2) #3}\n\\def\\NPB{{\\em Nucl. Phys.} B}\n\\def\\PLB{{\\em Phys. Lett.} B}\n%\\def\\PRL{\\em Phys. Rev. Lett.}\n\\def\\PRD{{\\em Phys. Rev.} D}\n\\def\\PRB#1#2#3{{\\rm Phys. Rev.} {\\bf{B#1}} (19#2) #3}\n\\def\\ZPC{{\\em Z. Phys.} C}\n\\def\\PRL#1#2#3{{\\rm Phys.~Rev.~Lett.} {\\bf{#1}} (19#2) #3}\n%\n%\n%\n\\begin{document}\n\\runauthor{ }\n\\begin{frontmatter}\n\\title{Design optimization of MACHe3,\\\\ a project of superfuid \\hetrois detector for direct Dark Matter search.}\n\\author{F. Mayet $^{a,}\\!$\\thanksref{corr}}\n\\author{, D. Santos $^{a,}\\!$\\thanksref{corr}}\n\\author{, G. Perrin $^{a}$,}\n\\author{ Yu. M. Bunkov $^{b}$, H. Godfrin $^{b}$}\n\\thanks[corr]{corresponding authors : Frederic.Mayet@isn.in2p3.fr, santos@isn.in2p3.fr, tel: +33 4-76-28-40-21, fax: +33\n4-76-28-40-04}\n\\address{$^{a}$ Institut des Sciences Nucl\\'eaires, \\\\\n CNRS/IN2P3 and Universit\\'e Joseph Fourier, \\\\\n 53, avenue des Martyrs, 38026 Grenoble cedex, France}\n\\address{$^{b}$ Centre de Recherche sur les Tr\\`es Basses Temp\\'eratures, \\\\\n CNRS, BP166, 38042 Grenoble cedex 9, France} \n\\begin{abstract}\nMACHe3 (MAtrix of Cells of superfluid \\hetro) is a project of a new detector for direct Dark Matter (DM) search. A cell of superfluid \\hetrois\nhas been developed and the idea of using a large number of such cells in a high granularity detector is proposed.\n\\noindent\nThis paper presents, after a brief description of the superfluid \\hetrois cell, the simulation of the response \n of different matrix configurations allowing to define an optimum design as a function of the number of cells and the volume\n of each cell. The background rejection, for several configurations, is presented both for neutrons and \\gams of various kinetic\n energies.\n\\end{abstract}\n\\begin{keyword}\nDark Matter, Supersymmetry, Superfluid Helium-3, Bolometer.\\\\ {\\it PACS : }95.35; 67.57; 07.57.K; 11.30.P\n\\end{keyword}\n\\end{frontmatter}\n\\newpage\n\\section{Introduction to MACHe3}\nAs previously suggested \\cite{vieux1,vieux2}, superfluid \\hetrois provides a suitable working medium for the detection of low energy \nrecoil interactions. Recent studies \\cite{prl95} have shown the possibility to use a superfluid \\hetrois cell at ultra low temperatures\n(T$\\simeq$100 $\\mu$K).\nThe primary device consisted of a small copper cubic box (V$\\simeq$ 0.125 cm$^{3}$) filled with \\hetro. It is immersed in a larger\nvolume containing liquid \\hetrois and thin plates of copper nuclear-cooling refrigerant, see fig. \\ref{fig:design}. \nTwo vibrating wires are placed inside the cell, forming a Lancaster type bolometer\\cite{prl95}. A small hole on one \nof the box walls connects the box to the main \\hetrois volume, thus allowing the diffusion of the thermal excitations of the \\hetrois generated \nby the energy deposited in the bolometer by the interacting particle.\\\\\nThis high sensitivity device is used as follows : the incoming particle deposits an amount of energy in the cell, which is converted into \n\\hetrois quasiparticles. These are detected by their damping effect on the vibrating wire. It must be pointed out that the size of the\nhole governs the relaxing time (quasiparticles escape time) and the Q factor of the resonator governs the rising time, see figure \n\\ref{fig:signal}. The present device has a rather high Q factor (Q $\\simeq 10^{4}$), giving a rising time of the order of one second.\nAlthough the primary experiment was still rudimentary, it has allowed to detect signals down to a threshold of 1 keV \\cite{prl95}.\nMany ideas are under study to improve the sensitivity of such a cell. Recently, the fabrication of \nmicromechanical silicon resonators has been reported \\cite{trique} and the possibility to use such wires at\nultra-low temperatures is under study.\\\\\nThe aim of the present article is to show that, by using a large number of these cells, a \nhigh granularity superfluid \\hetrois detector could be used for direct Dark Matter (DM) search\\footnote{It should be noticed that such a device need \nto be placed in an underground site to \nreduce cosmic rays (mainly muons) background. It should also be surrounded by neutron and \\gam shieldings.}. \nFor this purpose we have evaluated, by simulation of different kind of background events, the rejection coefficients that may be achieved with such a device.\n%\n\\section{Particle interactions in \\hetrois}\nAs other direct DM search detectors (Edelweiss\\cite{edel}, CRESST\\cite{cresst}, CUORE\\cite{cuore}), the identification of \nWIMPs (\\neutt)\\footnote{In particular, we shall suppose all through this work a neutralino (\\neutt), the lightest supersymmetric\nparticle, as the particle making up the bulk of galactic cold DM.} may be obtained by detecting \ntheir elastic scaterring on a nucleus of a sensitive medium. \nIn the case of \\hetro, the \\neut is expected to transfer \\cite{next} up to 6 keV. The maximum \\hetrois recoil energy is given by :\n\\begin{center}\n$\\mathrm{E}^{max}_{recoil}=2\\times \\frac{mM^{2}}{(m+M)^2}\\times v^2$\n\\end{center}\n\\noindent\nwhere $m$ is the mass of the \\hetrois nucleus, $M$ the mass of the \\neut and $v$ is the relative speed of the \\neut.\nAssuming that $M \\gg m$, as the accelerator experiments claim , this relation yields to $\\mathrm{E}^{max}_{recoil}=2mv^2$, which gives for $v \\simeq 300 km.s^{-1}$, \na maximum recoil energy of $\\sim$ 6 keV.\\\\\nHence, in order to evaluate the\nexpected background for such a detection, it is necessary to know the proportion of events releasing less than 6 keV in the \n\\hetrois cell.\nThe main background components for direct DM search are : thermal and fast neutrons, muons and gamma rays.\n%\n%\n%\n\\subsection{Neutron interaction in \\hetrois}\n\\label{sec:intera}\nThe total cross-section interaction for a neutron in \\hetrois ranges from $\\sigma_{tot} \\simeq 1000$ barns, \nfor low energy neutrons(E$_{n} \\simeq$ 1 eV), down to $\\sigma_{tot} \\simeq 1$ barn\nfor 1 MeV neutrons. The main processes are : elastic scattering which starts being predominant above 600 keV, and neutron \ncapture: \\hetro(n,p)\\tritium , which is largely predominant for low energy neutrons ($E_{n} \\leq 10$ keV) :\n\\begin{center}\nn+ $^{3}$He $\\rightarrow$ p+$^{3}$H +764 keV\n\\end{center}\n\\noindent\nThe energy released by the neutron capture is shared by the recoil ions : the tritium $^{3}$H with kinetic energy 191 keV \nand the proton with kinetic energy 573 keV. The range \\cite{ltemp} for these two particles\nis fairly short : typically 12 $\\mu$m for tritium and 67 $\\mu$m for proton; consequently neutrons undergoing capture in \\hetrois are expected \nto produce 764 keV within the cell, \nthus being clearly separated from the expected \\neut signal (E $\\leq $ 6keV). The tritium produced by neutron capture\nwill eventually decay with a half-life of 12 years by $\\beta$-decay with an end-point electron spectrum at 18 keV. It \nmeans that the number of neutrons capture per cell must be counted to estimate the contribution of this kind of events\non the false \\neut rate.\\\\\nThe capture cross-section decreases with increasing neutron kinetic energy, but on the other hand, the energy released in \nthe \\hetrois cell by the elastic scattering is getting larger, thus\ndiminishing the probability to leave less than 6 keV. From this, it is clear that the worst case will be 8 keV neutrons for which the capture \nprocess is\nless predominant, and the energy left by (n,n) interaction is always less or equal to 6 keV.\\\\\nIn order to reduce contamination from neutron background, the idea is either to have a correlation among the cells, which means a large number \nof \\hetrois cells, or to have a cell large enough for the neutron to be slowed down until it is captured.\n%\n%\n%\n\\subsection{$\\gamma$-ray interaction in \\hetrois}\nAs \\hetrois presents the property to have a low\nphotoelectric cross-section, Compton scaterring is largely predominant between 100 keV and 10 MeV (for 100 keV \\gams : \n$\\sigma_{comp}/\\sigma_{phot} \\simeq$ 10). Consequently, the strategy to\nseparate a \\neut event from a $\\gamma$-ray event is two fold : either the cell is large enough for the $\\gamma$-ray to undergo multi-Compton \nscattering within one cell \\footnote{This will of course be efficient for an energy greater than 10 keV.}, or the number of cells in the \nmatrix is large enough so that there could be an\ninteraction in more than one cell (this will be referred to as a correlated event or a multi-cell event). It will be shown, in the next\nsection, that having a relatively large cell in a large matrix presents the best rejection against $\\gamma$-ray events.\\\\\nThe copper used to build the cells must be produced by a controlled procedure with respect to the radioactive contaminations. Nevertheless, the interaction\nof \\gams with the copper will produce X-rays and scaterred electrons by Compton and photo-electric interactions. These kind of interactions have been\ntaken into account in our simulations and they enhance the correlation among the different cells fired by an incoming \\gam.\n%\n%\n% \n\\section{Simulation of the response of MACHe3 to background events.}\n\\label{simumatrix}\nThe aim of this simulation is to evaluate the capability of a superfluid \\hetrois matrix to reject background events, by taking advantage \nboth on correlation among the cells (multi-cell events) and energy loss measurement. The simulation has been done with a complete Monte-Carlo \nsimulation using GEANT3.21 \\cite{geant} package and in particular the GCALOR-MICAP(1.04/10) \\cite{micap} package for slow neutrons.\nThe simulated detector consists of a cube containing a variable number of cubic \\hetrois cells, as it can be seen on figure \\ref{fig:10kev}. It is immersed in a large volume containing \\hetrois\n($\\rho_{SF}$=0.08 $g.cm^{-3}$). Each\ncell is surrounded by a thin copper layer and it is separated from the others by a gap of 2 $mm$ (filled with \\hetro). The events are generated \nin a direction perpendicular\\footnote{It has been checked that this procedure does\nnot affect the values and general behaviour of the matrix parameters, keeping the calculation time short.} to one of the matrix faces. The number of\nevents per simulation is of the order of 200$\\times10^{3}$.\nThe idea is to find the best matrix design (number of cubic cells and the size of each cell) for which\n the rejection power, taking into account the correlation among the cells and the energy loss measurement, is the highest. \n\n\\noindent\nAs said previously, a typical \\neut is expected to release less than 6 keV in the \\hetrois cell. As the elastic \ncross-section between a \\neut and \\hetrois is fairly small ($\\sigma \\lesssim\n10^{-3} pb$), a\n\\neut event is expected to be characterized by a single-cell event, with equal probability among all the cells of the matrix.\\\\\nConsequently, the rejection against background events will be achieved by choosing only events having the following characteristics :\n\\begin{itemize}\n{\n\\item Only one cell fired (single-cell event). The quality parameter related to this selection will be defined below as C$_{geo}$.\n\\item Energy measurement in this cell below 6 keV and above a threshold of 0.5 keV (quality parameter : R$_{ener}$).\n\\item An additional constraint can be imposed : the fired cell is in the inner part of the matrix (quality parameter : C$_{veto}$). This condition, which considers the outermost cell layer\nas a veto, will allow to reject low energy neutrons interacting elastically, as shown below.\n}\n\\end{itemize}\nLet N be the number of events giving a signal in the matrix (any energy, any number of cells), N$_{1}$ the number of single-cell events \n(any energy) and N$_{6}$ the number of single-cell events with an energy measurement below 6 keV. M$_{1}$ and M$_{6}$ will be referred with\nthe same meaning as N$_{1}$ and N$_{6}$, but for events firing a cell in the inner part of the detector (out of the veto).\\\\\nThen, we may define the following parameters as :\n\\begin{itemize}\n{\n\\item C$_{geo}$$=\\frac{\\mathrm{N}_{1}}{\\mathrm{N}}$ ; the correlation coefficient (proportion of single-cell events).\n\\item R$_{ener}=\\frac{\\mathrm{N}_{1}}{\\mathrm{N}_{6}}$ ; the rejection by energy measurement.\n\\item C$_{veto}=\\frac{\\mathrm{N}_{1}}{\\mathrm{M}_{1}}$ ; the veto coefficient.\n\\item R$_{int}=\\frac{\\mathrm{N}}{\\mathrm{M}_{6}}$ ; the intrinsic rejection.}\n\\end{itemize}\n\n\\subsection{Design optimization.}\nIn order to define the optimimum matrix design (number of cubic cells and size of the cells), a complete simulation has been done.\nThe results concerning three types of background are presented : 10 keV\nneutrons, 1 MeV neutrons and 2.6 MeV $\\gamma$-rays. For each sample, the four parameters defined above are evaluated in various configurations : cell size\nof 0.5, 1.0, 2.5 and 5.0 $cm$ and matrix containing $3^{3}$, $5^{3}$, $7^{3}$, $10^{3}$ ($20^{3}$) cells. The best design will be the one for which C$_{geo}$\n is the lowest (thus minimizing the proportion of single-cell background events) and R$_{ener}$ is the highest (meaning a low proportion of background events\n with an energy measurement below 6 keV).\n%\n\\subsection{$\\gamma$-ray background.} \nDue to the fact that it is a simulation without any constraint on the detector volume, the correlation coefficient depends\nstrongly on the size of the matrix, with a small dependence on the cell size, as shown on figure \\ref{fig:cgeo26m}. \nThe best correlation is obtained for 8000 cells of size\n2.5 $cm$ (C$_{geo} \\simeq 45 \\%$). In order to keep a reasonable number of cells, it can be noticed that a matrix \nof same volume (1000 cells of 5.0 $cm$ side) presents also a good correlation \n(C$_{geo} \\simeq 55 \\%$). A multi-cell event can either be a multi-Compton event, or a single-Compton event for which the \nelectron is escaping the cell and firing a neighbouring cell. This last process depends mainly on the cell size and explains the fact that C$_{geo}$ \nremains constant for cell sides larger than 1 $cm$, see fig. \\ref{fig:cgeo26m}.\\\\\nIt has been found that the energy rejection (R$_{ener}$) depends mainly on the size of the cell.\nFor a large cell (5 $cm$ side), a rejection R$_{ener} \\simeq 90 $ is obtained, allowing to reject 98 \\%\nof the 2.6 MeV $\\gamma$-rays.\nThe total rejection (see fig. \\ref{fig:rejall}), which take into account the correlation and energy selection, together with \nveto selection and interaction probability, is R$\\simeq$700 for 1000 cells of size 5.0 $cm$ (for 2.6 MeV \\gams).\\\\\nConsequently, for \\gam background rejection purpose, a cell of 5.0 $cm$ side presents the best energy rejection and a matrix of 1000 cells \nof this size allows to obtain a good correlation coefficient. In section \\ref{gamrejsec}, the rejection of such a matrix as a function\nof the \\gam energy will be presented.\n% \n%\n\\subsection{Low energy neutron background.}\nFigures \\ref{fig:cgeon10} and \\ref{fig:cenern10} present the correlation coefficient (C$_{geo}$) and the energy rejection \n(R$_{ener}$) as a function of the cell size, for different matrix sizes and an incident neutron energy of 10 keV. \nThe correlation coefficient depends both on the size of the cell\nand of the matrix, since the neutron capture is the predominant process at this energy. \nThe best correlation is obtained for 8000 cells of size\n2.5 $cm$ (C$_{geo} \\simeq 85 \\%$), but a larger cell (5 $cm$ side), with only 1000 cells presents also a similar correlation \n(C$_{geo} \\simeq 86 \\%$). The energy rejection (R$_{ener}$) depends not only on the size of the cell, but also on the size \nof the matrix. \nThe best rejection (R$_{ener}\\simeq 22$) is achieved for a large cell (5 $cm$ side) and a large matrix (1000 cells). \nThe total rejection, shown on fig.\\ref{fig:rejall}, is R$\\simeq$80 for 1000 cells of 5 $cm$ side, meaning that only 1.25 \\% of the incoming\n10 keV neutrons may simulate a \\neut event. It must be pointed out that 10 keV represent the worst case for rejection purpose, as it can be\nseen on figure \\ref{fig:rejall}. \n\n\\subsection{Fast neutron background.}\nFigures \\ref{fig:cgeon1} and \\ref{fig:cenern1} show the correlation coefficient (C$_{geo}$) and the energy rejection \n(R$_{ener}$) as a function of the cell size, for different matrix sizes and an incident neutron energy of 1 MeV. As well as \nfor low energy neutrons, the\ncorrelation coefficient depends on the matrix and cell sizes. A correlation of $\\sim$ 65 \\% is achieved for a\nlarge \\hetrois volume (1000 cells of 5 $cm$ or 8000 cells of 2.5 $cm$). \nA large matrix of big cells (1000 cells of 5 $cm$) allows to obtain a rather large energy rejection (R$_{ener} \\simeq 500$),\nleading to a total rejection of the order of 1000 (see fig.\\ref{fig:rejall}), meaning that 99.9\\% of 1 MeV neutrons arriving on\nthe \\hetrois matrix may be discriminated from a \\neut event.\\\\\n\\noindent\nFor these three particle samples, the simulation has shown that a large cell (125 $cm^3$) allows to obtain \na large energy rejection, and a large matrix (1000 cells or more) allows to have a good correlation among cells, \nthus rejecting efficiently \\gams and neutrons of kinetic energy E$\\simeq$1 MeV. Hence, for background \nrejection consideration the optimum configuration is a matrix of 1000 cells of 5 $cm$ side.\n\n\\subsection{Rejection power of a superfluid \\hetrois matrix.}\nAs shown previously, a matrix of $10^{3}$ large cells (125 $cm^{3}$ each) presents the best rejection power, both for neutrons and\n$\\gamma$-rays. This section presents the various coefficients, as defined in section \\ref{sec:intera}, as a function of the energy of the \nincoming particle.\\\\\n\\subsubsection{Rejection against \\gam background.}\n\\label{gamrejsec}\nFigure \\ref{fig:coeffgam} shows the correlation coefficient, the veto coefficient, the energy rejection and the total rejection as a function of\nthe $\\gamma$-ray energy. A good correlation is achieved for high energy $\\gamma$-rays ($E_{\\gamma} \\geq $1 MeV), whereas low\nenergy $\\gamma$-rays are mainly rejected by the veto. In fact, 80 keV X-rays undergo photoelectric effect in\nthe copper layer ($\\sigma_{phot} \\simeq 10^{4}$barn)\nsurrounding the cell; the scaterred electrons may escape the copper layer and leave a few keV in the cell. This will mainly happen\nin the outermost cells.\\\\\nFigure \\ref{fig:rejall} presents the total rejection as a function of the $\\gamma$-ray energy. It can be concluded that an \\hetrois\nmatrix provides a rejection ranging between 10 and 1000, depending on the $\\gamma$-ray energy. It must be pointed out that this is\nthe rejection power of the matrix itself. For instance, 90\\% of X-rays will be rejected by the matrix, but the flux of\nsuch particles will be reduced substantially by an inner and outer copper shielding.\n\\subsubsection{Rejection against neutron background.}\nFigure \\ref{fig:coeffneut} presents the four matrix parameters as a function of the neutron energy. A correlation better than 70 \\% is \nachieved for neutrons\nof energy greater than 100 keV (fig. \\ref{fig:coeffneut}, upper left), while low energy neutrons are mainly rejected by the veto. Indeed, 60 \\% of 10 keV neutrons are captured in\nthe first layer (fig. \\ref{fig:coeffneut}, upper right). The energy measurement constitute an efficient selection for low energy \nneutron (R$_{ener}\\simeq$ 100 for 1 keV neutrons) and for\nfast neutrons (R$_{ener}\\simeq$ 1000 for 1 MeV neutrons). As expected 10 keV neutrons have the worst energy rejection (R$_{ener}\\simeq$ 15).\\\\\nThe total rejection\\footnote{This coefficient takes into account the interaction probability and will be used to evaluate the \nfalse event rate.} (ratio between number of incoming particles and number of false \\neut events), shown on figure \\ref{fig:rejall},\nindicates that only one 1 keV\nneutron out of 2000 may simulate a \\neut event. The rejection falls down to 75 for 10 keV neutrons (mainly rejected by the veto) and is of the\norder of 1000 for 1 MeV neutrons.\n\n\\noindent \nIt must be pointed out that the evaluated rejection is for a \"naked matrix\", i.e. without taking into account any lead or paraffin shielding\n or any separation between electron and ion recoils. It represents the capability of the \\hetrois matrix to reject background events by means of energy loss\nmeasurements and correlation considerations. As a conclusion, it can be said that the \\hetrois matrix presents a rejection power ranging between 75 and 2000 for\nneutrons, and between 10 and 800 for $\\gamma$-rays,depending on their kinetic energies.\n\n\\subsection{An evaluation of the neutron-induced false event rate.}\nAs neutrons recoiling off nuclei may easily simulate a \\neut event, it is crucial to evaluate the neutron-induced false event rate.\\\\\nIn contrast to most DM detectors, MACHe3 may be sensitive to rather low energy neutrons, and its response depends strongly on their kinetic\nenergies. For this purpose, a simulation \nof a paraffin neutron shielding has been done, in order to evaluate the expected neutron spectrum trough this shielding.\\\\\nThe simulated device is a large ($1m\\times 1m$) paraffin block ($\\rho$=0.95 g.cm$^{-3}$) with a width of 30 $cm$. \nIn order to be conservative, as well as keeping the calculation times short, we choose to generate the events in a direction perpendicular \nto the face of the paraffin block and considering that all neutrons crossing the block are supposed to enter the matrix volume.\\\\\nA benchmark study has been done, to compare MCNP calculation code\\cite{mcnp} and GEANT3.21. We found that these two codes give similar results, \nexcept for thermal neutrons (below 1 eV) for which GEANT underevaluate the flux. Again, to be conservative, we choose the one giving \nthe highest flux (MCNP)\\footnote{MCNP is much faster than GEANT, in this case, allowing shorter calculation times.}.\\\\\nWe have used the measured neutron spectrum \\cite{Chazal:1998qn} in Laboratoire Souterrain de Modane (LSM), between 2 and 6 MeV \\footnote{The thermal neutron flux, evaluated \nin \\cite{Chazal:1998qn} to be (1.6$\\pm0.1)\\times 10^{-6} cm^{-2}s^{-1}$, will be highly suppressed by the 30 $cm$ paraffin shielding}, with an\nintegrated flux of $\\Phi_{n}\\simeq 4\\times 10^{-6} cm^{-2}s^{-1}$. We found an overall neutron flux through the shielding of 5.1$\\times 10^{-8} cm^{-2}s^{-1}$, with the \nneutron kinetic energy ranging between\n$10^{-2}$ eV and 6 MeV (see the upper curve on fig. \\ref{fig:neutfalse}).\\\\\nUsing this flux and the expected rejection factor (fig. \\ref{fig:rejall}), we evaluated the false\n\\neut rate induced by neutron background, see fig. \\ref{fig:neutfalse}. We \nfound a rate of $\\sim$0.1 false event per day through the\n1.5$m^{2}$ surface detector (1000 cells of 125 $cm^{3}$). Even with such a conservative approach, this contamination is much lower than the expected \\neut rate (of the order of \n$\\sim$1 day$^{-1}$\nin a detector of this size \\cite{next}). \n\\subsection{An evaluation of the muon-induced false event rate.}\nThe muon background flux in an underground laboratory (Gran Sasso) has been measured by \\cite{muons}. They found a mean flux of \n$\\Phi_{\\mu}=2.3\\times 10^{-4} m^{-2}s^{-1}$\nfor an average kinetic energy $<\\!$$E$$>$=200 GeV.\\\\\nAn evaluation of the $\\mu$-induced event rate has been done. The same procedure as above (see section \\ref{simumatrix}) has been used, \nwithout paraffin shielding; i.e. the events are\ngenerated in a direction perpendicular to one of the matrix faces. This is a conservative approach because the worst case is in which muons are \npassing in between 2 cell layers. As expected, most of the $\\mu$-events interact in all the crossed cells (75\\%\ninteract in 10 cells, with an average energy left of $\\sim$ 1 MeV). The correlation coefficient is C$_{geo}\n\\simeq 2.1\\%$ (meaning 97.9$\\%$ of $\\mu$-events are rejected), with an energy rejection R$_{ener} \\simeq 40$, leading to an overall rejection \nof R$\\simeq 2100$. This lead to a\n$\\mu$-induced false \\neut rate of the order of 0.0095 day$^{-1}$m$^{-2}$, which is more than two orders of magnitude below the\nexpected \\neut rate. The layers may be shifted, thus allowing a much higher rejection against muon background\nevents.\n\\subsection{\\gam background.}\nAs shown in section \\ref{gamrejsec}, a high granularity superfluid \\hetrois detector provides an intrinsic rejection ranging \nbetween 10 and 800 for $\\gamma$-rays, depending on their kinetic energies. This selection, based on the correlation among the cells \nand energy loss measurement, may be improved by adding a discrimination between\nrecoils and electrons. Different experimental approaches should be tested. A complete study of an inner and outer cryostat shielding is also\nneeded, as well as an evaluation of natural radioactivity of materials. Nevertheless, this simulation indicates that an important intrinsic rejection can be achieved.\n\n\\section{Conclusion}\nIn this prospective paper, we have demonstrate that a large matrix ($\\sim$ 1000 cells) of large cells (125 $cm^{3}$) is the\npreferred design for a superfluid \\hetrois detector searching for DM, as far as background rejection is concerned. \nAn experimental work needs to be done to demonstrate the possibility to use such a large volume of superfluid $ ^{3}{\\mathrm{He}}$-B at ultra-low temperatures. This work has evaluated the background\nrejection of a high granularity superfluid \\hetrois detector for a large range of kinetic energies,\nboth for neutrons and $\\gamma$-rays. It has been shown that, by means of\ncorrelation among the cells and energy loss measurement, a high rejection may be obtained for $\\gamma$-ray, neutron and muon background. Using the\nmeasured muon and neutron flux in an underground laboratory, we have evaluated the contamination to be one order of \nmagnitude (two orders\nfor muons) less than the expected \\neut rate. For background rejection purpose, the main advantage of a superfluid \\hetrois detector is to present a high \nrejection against neutron background, mainly because of the\nhigh capture cross-section at low energy. As neutrons interact {\\it a priori} like \\neutt, they are the\nultimate background noise for DM detectors.\\\\\n\n\\textbf{Acknowledgements}\\\\\nThe authors are grateful to D. Kerdraon and L. Perrot for the help concerning the use of MCNP calculation code, and also\nF. Ohlsson-Malek for the fruitful discussions on the GEANT code. \n\n\\begin{thebibliography}{99}\n\\bibitem{vieux1}G. R. Pickett, in {\\em Proc. of the European Workshop on Low Temperature Devices for \nthe Detection of Low Energy Neutrinos and Dark Matter (1988 Annecy, France)}, edited by L. Gonzales-Mestres and D. Perret-Gallix (Ed.\nFrontieres).\n\n\\bibitem{vieux2}Yu. M. Bunkov \\textit{et al.}, in {\\em Proc. of the International Workshop on Superconductivity and Particle Detection (1994 Toledo,\nSpain) eds. T.A. Girard, A. Morales and G. Waysand, World Scientific, p.21 (1995)}\n\n\\bibitem{prl95}D. I. Bradley \\textit{et al.}, \\PRL{75}{95}{1887}.\\\\\nC. B\\\"{a}uerle \\textit{et al.}, \\PRB{57}{98}{22}.\n\\bibitem{trique}S. Triqueneaux \\textit{et al.}, in {\\em Proc. of the 22nd International Conf. on Low Temperature Physics},\nAugust 1999, Physica B (in print).\n\\bibitem{next}D. Santos, F. Mayet, G. Perrin \\textit{et al., to be submitted to Phys. Rev. D}.\n\\bibitem{edel}L. Berge \\textit{et al.}, astro-ph/9801199\n\\bibitem{cresst}M. Bravin \\textit{et al.}, hep-ex/9904005 \n\\bibitem{cuore}A. Alessandrello \\textit{et al.}, in {\\em Proc. Dark matter in astrophysics and particle physics 1998.}\n\\bibitem{ltemp}J. S. Meyer and T. Sloan, J. of Low Temp. Phys. (108) 1997.\n\\bibitem{geant}R. Brun, F. Carminati, {\\em GEANT Detector Description and Simulation Tool}, CERN \nProgam Library Long Writeup W5013, September 1993.\n\\bibitem{micap}J. O. Johnson, T. A. Gabriel, {\\em A user's guide to MICAP}, ORNL/TM-10340, January 1988\\\\\nC. Zeitniz and T. A. Gabriel, \\NIMA{349}{94}{106}.\n\\bibitem{mcnp}J. F. Briesmeister, {\\em MCNP $^{TM}$, A general Monte Carlo N-particle transport code}, LANL Report LA-12625-M(93)\n%\\cite{Chazal:1998qn}\n\\bibitem{Chazal:1998qn}\nV.~Chazal {\\it et al.},\n%``Neutron background measurements in the underground laboratory of Modane,''\nAstropart.\\ Phys.\\ {\\bf 9}, 163 (1998).\n\\bibitem{muons}\nC.~Arpesella,\n%``Background measurements at GRAN SASSO laboratory,''\nLNGS-92-28\n{\\it Contribution to TAUP '91 Workshop, Toledo, Spain, Sep 9-13, 1991}.\\\\\nH. V. Klapdor-Kleingrothaus {\\it et al.}, hep-ph/9910205.\n\\end{thebibliography}\n\\newpage\n\\listoffigures\n\n\n%******************************************************\n% \n\\newpage\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{Fig2BPRB.eps}\n{\\noindent\n\\caption{Ultra-low temperature nuclear stage and bolometer cell.\n\\label{fig:design}}}\n\\end{center}\n\\end{figure}\n%\n\\newpage\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{henri_background.eps}\n{\\noindent\n\\caption{Temperature recorded inside the bolometer as a function of time.\n\\label{fig:signal}}}\n\\end{center}\n\\end{figure}\n%\n\\newpage\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.40]{10kev.matrix.epsi}\n{\\noindent\n\\caption{2-dimensionnal view of a proposed matrix of 1000 cells (125 $cm^{3}$ each). The events generated in a direction \nperpendicular to the upper face, are 10 keV neutrons. It can be noticed that most of\nneutrons of this energy are captured in the first layer.\n\\label{fig:10kev}}}\n\\end{center}\n\\end{figure}\n%\n%\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{cgeo.g26.epsi}\n\\caption{Correlation coefficient (C$_{geo}$) as a function of the size of the \\hetrois cell for 2.6 MeV $\\gamma$-rays. \nThe different curves correspond to different matrix sizes as indicated by the labels. \n\\label{fig:cgeo26m}}\n\\end{center}\n\\end{figure}\n%\n%\n\\newpage\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{cgeo.n10k.epsi}\n\\caption{Correlation coefficient (C$_{geo}$) as a function of the size of the \\hetrois cell for 10 keV neutrons. The different curves\ncorrespond to different matrix sizes as indicated by the labels.\n\\label{fig:cgeon10}}\n\\end{center}\n\\end{figure}\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{cener.n10k.epsi}\n\\caption{Energy Rejection (R$_{ener}$) as a function of the size of the \\hetrois cell for 10 keV neutrons. The different curves\ncorrespond to different matrix sizes as indicated by the labels. \n\\label{fig:cenern10}}\n\\end{center}\n\\end{figure}\n\n\\newpage\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{cgeo.n1m.epsi}\n\\caption{Correlation coefficient (C$_{geo}$) as a function of the size of the \\hetrois cell for 1 MeV neutrons. The different curves\ncorrespond to different matrix sizes as indicated by the labels. \n\\label{fig:cgeon1}}\n\\end{center}\n\\end{figure}\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{cener.n1m.epsi}\n\\caption{Energy Rejection (R$_{ener}$) as a function of the size of the \\hetrois cell for 1 MeV neutrons. The different curves\ncorrespond to different matrix sizes as indicated by the labels. \n\\label{fig:cenern1}}\n\\end{center}\n\\end{figure}\n\n\\newpage\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{coeffneut.epsi}\n{\\noindent\n\\caption{Neutrons interacting in MACHe3 : The four matrix parameters, defined in sec. \\ref{simumatrix}, as a function of the neutron energy, for a matrix of 1000 cells (125 $cm^{3}$ each).\n\\label{fig:coeffneut}}}\n\\end{center}\n\\end{figure}\n%\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{coeffgam.epsi}\n{\\noindent\n\\caption{\\gams interacting in MACHe3 : The four matrix parameters, defined in sec. \\ref{simumatrix}, as a function of the $\\gamma$-ray energy, for a matrix of 1000 cells (125\n$cm^{3}$ each).\n\\label{fig:coeffgam}}}\n\\end{center}\n\\end{figure}\n%\n\\newpage\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.8]{rejall.epsi}\n{\\noindent\n\\caption{Total Rejection as a function of the incident particle energy, for a matrix of 1000 cells (125\n$cm^{3}$ each). The different set of points correspond to \\gams (squares) and neutrons (circles). The total rejection is defined as the ratio \nbetween the number of incoming particles and the number of false \\neut events (less than 6 keV in one non-peripheric cell).\n\\label{fig:rejall}}}\n\\end{center}\n\\end{figure}\n\\newpage\n%\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.60]{neutronfinal.epsi}\n{\\noindent\n\\caption{The upper curve is the simulated neutron spectrum through a 30 $cm$ wide paraffin \nshielding, the measured spectrum at LSM being the input. Comparing with the measured neutron flux, this shielding allows \nan overall reduction factor of $\\sim$ 50. The lowest curve represents the neutron induced false \\neut rate \nin MACHe3. This spectrum has been obtained by combining the upper curve with the total rejection \n(fig. \\ref{fig:rejall}), with a threshold of 500 eV. The overall counting rate, due to neutron background, is \nevaluated to be $\\sim$ 0.1 day$^{-1}$ in a 1000 cells detector.\n\\label{fig:neutfalse}}}\n\\end{center}\n\\end{figure}\n\n\n\n\n\n\\end{document}\n"}],"string":"[\n {\n \"name\": \"mac3new.tex\",\n \"string\": \"\\\\documentclass{elsart}\\n\\\\usepackage{graphicx}\\n\\\\usepackage{amsmath}\\n\\\\usepackage{amssymb}\\n%\\n%\\n%\\n\\\\newcommand{\\\\GeVc} {\\\\mbox{$ {\\\\mathrm{GeV}}/c $}}\\n\\\\newcommand{\\\\GeVcc} {\\\\mbox{$ {\\\\mathrm{GeV}}/c^2 $}}\\n\\\\newcommand{\\\\MeVc} {\\\\mbox{$ {\\\\mathrm{MeV}}/c $}}\\n\\\\newcommand{\\\\hetrois} {\\\\mbox{$ ^{3}{\\\\mathrm{He}} $}~}\\n\\\\newcommand{\\\\hetro} {\\\\mbox{$ ^{3}{\\\\mathrm{He}} $}}\\n\\\\newcommand{\\\\tritium} {\\\\mbox{$ ^{3}{\\\\mathrm{H}} $}~}\\n\\\\newcommand{\\\\hequatre} {\\\\mbox{$ ^{4}{\\\\mathrm{He}}}}\\n\\\\newcommand{\\\\citeup}{\\\\cite}\\n\\\\newcommand{\\\\cher}{\\\\u{C}erenkov }\\n\\\\newcommand{\\\\Cher}{\\\\u{C}ERENKOV }\\n\\\\newcommand{\\\\neut}{$\\\\tilde{\\\\chi}$~}\\n\\\\newcommand{\\\\neutt}{$\\\\tilde{\\\\chi}$}\\n\\\\newcommand{\\\\mydeg} {\\\\mbox{$ ^\\\\circ $}}\\n\\\\newcommand{\\\\DM} {Dark Matter}\\n\\\\newcommand{\\\\gam} {{$\\\\gamma$-ray}~} \\n\\\\newcommand{\\\\gams} {{$\\\\gamma$-rays}~} \\n\\n\\n\\n\\n\\n%\\n%\\n% A useful Journal macro\\n\\\\def\\\\Journal#1#2#3#4{{#1} {\\\\bf #2}, #3 (#4)}\\n%\\n% Some useful journal names\\n\\\\def\\\\NCA{\\\\em Nuovo Cimento}\\n\\\\def\\\\NIM{\\\\em Nucl. Instrum. Methods}\\n%\\\\def\\\\NIMA{{\\\\em Nucl. Instrum. Methods} A}\\n\\\\def\\\\NIMA#1#2#3{{\\\\rm Nucl.~Instr.~and~Meth.} {\\\\bf#1} (19#2) #3}\\n\\\\def\\\\NPB{{\\\\em Nucl. Phys.} B}\\n\\\\def\\\\PLB{{\\\\em Phys. Lett.} B}\\n%\\\\def\\\\PRL{\\\\em Phys. Rev. Lett.}\\n\\\\def\\\\PRD{{\\\\em Phys. Rev.} D}\\n\\\\def\\\\PRB#1#2#3{{\\\\rm Phys. Rev.} {\\\\bf{B#1}} (19#2) #3}\\n\\\\def\\\\ZPC{{\\\\em Z. Phys.} C}\\n\\\\def\\\\PRL#1#2#3{{\\\\rm Phys.~Rev.~Lett.} {\\\\bf{#1}} (19#2) #3}\\n%\\n%\\n%\\n\\\\begin{document}\\n\\\\runauthor{ }\\n\\\\begin{frontmatter}\\n\\\\title{Design optimization of MACHe3,\\\\\\\\ a project of superfuid \\\\hetrois detector for direct Dark Matter search.}\\n\\\\author{F. Mayet $^{a,}\\\\!$\\\\thanksref{corr}}\\n\\\\author{, D. Santos $^{a,}\\\\!$\\\\thanksref{corr}}\\n\\\\author{, G. Perrin $^{a}$,}\\n\\\\author{ Yu. M. Bunkov $^{b}$, H. Godfrin $^{b}$}\\n\\\\thanks[corr]{corresponding authors : Frederic.Mayet@isn.in2p3.fr, santos@isn.in2p3.fr, tel: +33 4-76-28-40-21, fax: +33\\n4-76-28-40-04}\\n\\\\address{$^{a}$ Institut des Sciences Nucl\\\\'eaires, \\\\\\\\\\n CNRS/IN2P3 and Universit\\\\'e Joseph Fourier, \\\\\\\\\\n 53, avenue des Martyrs, 38026 Grenoble cedex, France}\\n\\\\address{$^{b}$ Centre de Recherche sur les Tr\\\\`es Basses Temp\\\\'eratures, \\\\\\\\\\n CNRS, BP166, 38042 Grenoble cedex 9, France} \\n\\\\begin{abstract}\\nMACHe3 (MAtrix of Cells of superfluid \\\\hetro) is a project of a new detector for direct Dark Matter (DM) search. A cell of superfluid \\\\hetrois\\nhas been developed and the idea of using a large number of such cells in a high granularity detector is proposed.\\n\\\\noindent\\nThis paper presents, after a brief description of the superfluid \\\\hetrois cell, the simulation of the response \\n of different matrix configurations allowing to define an optimum design as a function of the number of cells and the volume\\n of each cell. The background rejection, for several configurations, is presented both for neutrons and \\\\gams of various kinetic\\n energies.\\n\\\\end{abstract}\\n\\\\begin{keyword}\\nDark Matter, Supersymmetry, Superfluid Helium-3, Bolometer.\\\\\\\\ {\\\\it PACS : }95.35; 67.57; 07.57.K; 11.30.P\\n\\\\end{keyword}\\n\\\\end{frontmatter}\\n\\\\newpage\\n\\\\section{Introduction to MACHe3}\\nAs previously suggested \\\\cite{vieux1,vieux2}, superfluid \\\\hetrois provides a suitable working medium for the detection of low energy \\nrecoil interactions. Recent studies \\\\cite{prl95} have shown the possibility to use a superfluid \\\\hetrois cell at ultra low temperatures\\n(T$\\\\simeq$100 $\\\\mu$K).\\nThe primary device consisted of a small copper cubic box (V$\\\\simeq$ 0.125 cm$^{3}$) filled with \\\\hetro. It is immersed in a larger\\nvolume containing liquid \\\\hetrois and thin plates of copper nuclear-cooling refrigerant, see fig. \\\\ref{fig:design}. \\nTwo vibrating wires are placed inside the cell, forming a Lancaster type bolometer\\\\cite{prl95}. A small hole on one \\nof the box walls connects the box to the main \\\\hetrois volume, thus allowing the diffusion of the thermal excitations of the \\\\hetrois generated \\nby the energy deposited in the bolometer by the interacting particle.\\\\\\\\\\nThis high sensitivity device is used as follows : the incoming particle deposits an amount of energy in the cell, which is converted into \\n\\\\hetrois quasiparticles. These are detected by their damping effect on the vibrating wire. It must be pointed out that the size of the\\nhole governs the relaxing time (quasiparticles escape time) and the Q factor of the resonator governs the rising time, see figure \\n\\\\ref{fig:signal}. The present device has a rather high Q factor (Q $\\\\simeq 10^{4}$), giving a rising time of the order of one second.\\nAlthough the primary experiment was still rudimentary, it has allowed to detect signals down to a threshold of 1 keV \\\\cite{prl95}.\\nMany ideas are under study to improve the sensitivity of such a cell. Recently, the fabrication of \\nmicromechanical silicon resonators has been reported \\\\cite{trique} and the possibility to use such wires at\\nultra-low temperatures is under study.\\\\\\\\\\nThe aim of the present article is to show that, by using a large number of these cells, a \\nhigh granularity superfluid \\\\hetrois detector could be used for direct Dark Matter (DM) search\\\\footnote{It should be noticed that such a device need \\nto be placed in an underground site to \\nreduce cosmic rays (mainly muons) background. It should also be surrounded by neutron and \\\\gam shieldings.}. \\nFor this purpose we have evaluated, by simulation of different kind of background events, the rejection coefficients that may be achieved with such a device.\\n%\\n\\\\section{Particle interactions in \\\\hetrois}\\nAs other direct DM search detectors (Edelweiss\\\\cite{edel}, CRESST\\\\cite{cresst}, CUORE\\\\cite{cuore}), the identification of \\nWIMPs (\\\\neutt)\\\\footnote{In particular, we shall suppose all through this work a neutralino (\\\\neutt), the lightest supersymmetric\\nparticle, as the particle making up the bulk of galactic cold DM.} may be obtained by detecting \\ntheir elastic scaterring on a nucleus of a sensitive medium. \\nIn the case of \\\\hetro, the \\\\neut is expected to transfer \\\\cite{next} up to 6 keV. The maximum \\\\hetrois recoil energy is given by :\\n\\\\begin{center}\\n$\\\\mathrm{E}^{max}_{recoil}=2\\\\times \\\\frac{mM^{2}}{(m+M)^2}\\\\times v^2$\\n\\\\end{center}\\n\\\\noindent\\nwhere $m$ is the mass of the \\\\hetrois nucleus, $M$ the mass of the \\\\neut and $v$ is the relative speed of the \\\\neut.\\nAssuming that $M \\\\gg m$, as the accelerator experiments claim , this relation yields to $\\\\mathrm{E}^{max}_{recoil}=2mv^2$, which gives for $v \\\\simeq 300 km.s^{-1}$, \\na maximum recoil energy of $\\\\sim$ 6 keV.\\\\\\\\\\nHence, in order to evaluate the\\nexpected background for such a detection, it is necessary to know the proportion of events releasing less than 6 keV in the \\n\\\\hetrois cell.\\nThe main background components for direct DM search are : thermal and fast neutrons, muons and gamma rays.\\n%\\n%\\n%\\n\\\\subsection{Neutron interaction in \\\\hetrois}\\n\\\\label{sec:intera}\\nThe total cross-section interaction for a neutron in \\\\hetrois ranges from $\\\\sigma_{tot} \\\\simeq 1000$ barns, \\nfor low energy neutrons(E$_{n} \\\\simeq$ 1 eV), down to $\\\\sigma_{tot} \\\\simeq 1$ barn\\nfor 1 MeV neutrons. The main processes are : elastic scattering which starts being predominant above 600 keV, and neutron \\ncapture: \\\\hetro(n,p)\\\\tritium , which is largely predominant for low energy neutrons ($E_{n} \\\\leq 10$ keV) :\\n\\\\begin{center}\\nn+ $^{3}$He $\\\\rightarrow$ p+$^{3}$H +764 keV\\n\\\\end{center}\\n\\\\noindent\\nThe energy released by the neutron capture is shared by the recoil ions : the tritium $^{3}$H with kinetic energy 191 keV \\nand the proton with kinetic energy 573 keV. The range \\\\cite{ltemp} for these two particles\\nis fairly short : typically 12 $\\\\mu$m for tritium and 67 $\\\\mu$m for proton; consequently neutrons undergoing capture in \\\\hetrois are expected \\nto produce 764 keV within the cell, \\nthus being clearly separated from the expected \\\\neut signal (E $\\\\leq $ 6keV). The tritium produced by neutron capture\\nwill eventually decay with a half-life of 12 years by $\\\\beta$-decay with an end-point electron spectrum at 18 keV. It \\nmeans that the number of neutrons capture per cell must be counted to estimate the contribution of this kind of events\\non the false \\\\neut rate.\\\\\\\\\\nThe capture cross-section decreases with increasing neutron kinetic energy, but on the other hand, the energy released in \\nthe \\\\hetrois cell by the elastic scattering is getting larger, thus\\ndiminishing the probability to leave less than 6 keV. From this, it is clear that the worst case will be 8 keV neutrons for which the capture \\nprocess is\\nless predominant, and the energy left by (n,n) interaction is always less or equal to 6 keV.\\\\\\\\\\nIn order to reduce contamination from neutron background, the idea is either to have a correlation among the cells, which means a large number \\nof \\\\hetrois cells, or to have a cell large enough for the neutron to be slowed down until it is captured.\\n%\\n%\\n%\\n\\\\subsection{$\\\\gamma$-ray interaction in \\\\hetrois}\\nAs \\\\hetrois presents the property to have a low\\nphotoelectric cross-section, Compton scaterring is largely predominant between 100 keV and 10 MeV (for 100 keV \\\\gams : \\n$\\\\sigma_{comp}/\\\\sigma_{phot} \\\\simeq$ 10). Consequently, the strategy to\\nseparate a \\\\neut event from a $\\\\gamma$-ray event is two fold : either the cell is large enough for the $\\\\gamma$-ray to undergo multi-Compton \\nscattering within one cell \\\\footnote{This will of course be efficient for an energy greater than 10 keV.}, or the number of cells in the \\nmatrix is large enough so that there could be an\\ninteraction in more than one cell (this will be referred to as a correlated event or a multi-cell event). It will be shown, in the next\\nsection, that having a relatively large cell in a large matrix presents the best rejection against $\\\\gamma$-ray events.\\\\\\\\\\nThe copper used to build the cells must be produced by a controlled procedure with respect to the radioactive contaminations. Nevertheless, the interaction\\nof \\\\gams with the copper will produce X-rays and scaterred electrons by Compton and photo-electric interactions. These kind of interactions have been\\ntaken into account in our simulations and they enhance the correlation among the different cells fired by an incoming \\\\gam.\\n%\\n%\\n% \\n\\\\section{Simulation of the response of MACHe3 to background events.}\\n\\\\label{simumatrix}\\nThe aim of this simulation is to evaluate the capability of a superfluid \\\\hetrois matrix to reject background events, by taking advantage \\nboth on correlation among the cells (multi-cell events) and energy loss measurement. The simulation has been done with a complete Monte-Carlo \\nsimulation using GEANT3.21 \\\\cite{geant} package and in particular the GCALOR-MICAP(1.04/10) \\\\cite{micap} package for slow neutrons.\\nThe simulated detector consists of a cube containing a variable number of cubic \\\\hetrois cells, as it can be seen on figure \\\\ref{fig:10kev}. It is immersed in a large volume containing \\\\hetrois\\n($\\\\rho_{SF}$=0.08 $g.cm^{-3}$). Each\\ncell is surrounded by a thin copper layer and it is separated from the others by a gap of 2 $mm$ (filled with \\\\hetro). The events are generated \\nin a direction perpendicular\\\\footnote{It has been checked that this procedure does\\nnot affect the values and general behaviour of the matrix parameters, keeping the calculation time short.} to one of the matrix faces. The number of\\nevents per simulation is of the order of 200$\\\\times10^{3}$.\\nThe idea is to find the best matrix design (number of cubic cells and the size of each cell) for which\\n the rejection power, taking into account the correlation among the cells and the energy loss measurement, is the highest. \\n\\n\\\\noindent\\nAs said previously, a typical \\\\neut is expected to release less than 6 keV in the \\\\hetrois cell. As the elastic \\ncross-section between a \\\\neut and \\\\hetrois is fairly small ($\\\\sigma \\\\lesssim\\n10^{-3} pb$), a\\n\\\\neut event is expected to be characterized by a single-cell event, with equal probability among all the cells of the matrix.\\\\\\\\\\nConsequently, the rejection against background events will be achieved by choosing only events having the following characteristics :\\n\\\\begin{itemize}\\n{\\n\\\\item Only one cell fired (single-cell event). The quality parameter related to this selection will be defined below as C$_{geo}$.\\n\\\\item Energy measurement in this cell below 6 keV and above a threshold of 0.5 keV (quality parameter : R$_{ener}$).\\n\\\\item An additional constraint can be imposed : the fired cell is in the inner part of the matrix (quality parameter : C$_{veto}$). This condition, which considers the outermost cell layer\\nas a veto, will allow to reject low energy neutrons interacting elastically, as shown below.\\n}\\n\\\\end{itemize}\\nLet N be the number of events giving a signal in the matrix (any energy, any number of cells), N$_{1}$ the number of single-cell events \\n(any energy) and N$_{6}$ the number of single-cell events with an energy measurement below 6 keV. M$_{1}$ and M$_{6}$ will be referred with\\nthe same meaning as N$_{1}$ and N$_{6}$, but for events firing a cell in the inner part of the detector (out of the veto).\\\\\\\\\\nThen, we may define the following parameters as :\\n\\\\begin{itemize}\\n{\\n\\\\item C$_{geo}$$=\\\\frac{\\\\mathrm{N}_{1}}{\\\\mathrm{N}}$ ; the correlation coefficient (proportion of single-cell events).\\n\\\\item R$_{ener}=\\\\frac{\\\\mathrm{N}_{1}}{\\\\mathrm{N}_{6}}$ ; the rejection by energy measurement.\\n\\\\item C$_{veto}=\\\\frac{\\\\mathrm{N}_{1}}{\\\\mathrm{M}_{1}}$ ; the veto coefficient.\\n\\\\item R$_{int}=\\\\frac{\\\\mathrm{N}}{\\\\mathrm{M}_{6}}$ ; the intrinsic rejection.}\\n\\\\end{itemize}\\n\\n\\\\subsection{Design optimization.}\\nIn order to define the optimimum matrix design (number of cubic cells and size of the cells), a complete simulation has been done.\\nThe results concerning three types of background are presented : 10 keV\\nneutrons, 1 MeV neutrons and 2.6 MeV $\\\\gamma$-rays. For each sample, the four parameters defined above are evaluated in various configurations : cell size\\nof 0.5, 1.0, 2.5 and 5.0 $cm$ and matrix containing $3^{3}$, $5^{3}$, $7^{3}$, $10^{3}$ ($20^{3}$) cells. The best design will be the one for which C$_{geo}$\\n is the lowest (thus minimizing the proportion of single-cell background events) and R$_{ener}$ is the highest (meaning a low proportion of background events\\n with an energy measurement below 6 keV).\\n%\\n\\\\subsection{$\\\\gamma$-ray background.} \\nDue to the fact that it is a simulation without any constraint on the detector volume, the correlation coefficient depends\\nstrongly on the size of the matrix, with a small dependence on the cell size, as shown on figure \\\\ref{fig:cgeo26m}. \\nThe best correlation is obtained for 8000 cells of size\\n2.5 $cm$ (C$_{geo} \\\\simeq 45 \\\\%$). In order to keep a reasonable number of cells, it can be noticed that a matrix \\nof same volume (1000 cells of 5.0 $cm$ side) presents also a good correlation \\n(C$_{geo} \\\\simeq 55 \\\\%$). A multi-cell event can either be a multi-Compton event, or a single-Compton event for which the \\nelectron is escaping the cell and firing a neighbouring cell. This last process depends mainly on the cell size and explains the fact that C$_{geo}$ \\nremains constant for cell sides larger than 1 $cm$, see fig. \\\\ref{fig:cgeo26m}.\\\\\\\\\\nIt has been found that the energy rejection (R$_{ener}$) depends mainly on the size of the cell.\\nFor a large cell (5 $cm$ side), a rejection R$_{ener} \\\\simeq 90 $ is obtained, allowing to reject 98 \\\\%\\nof the 2.6 MeV $\\\\gamma$-rays.\\nThe total rejection (see fig. \\\\ref{fig:rejall}), which take into account the correlation and energy selection, together with \\nveto selection and interaction probability, is R$\\\\simeq$700 for 1000 cells of size 5.0 $cm$ (for 2.6 MeV \\\\gams).\\\\\\\\\\nConsequently, for \\\\gam background rejection purpose, a cell of 5.0 $cm$ side presents the best energy rejection and a matrix of 1000 cells \\nof this size allows to obtain a good correlation coefficient. In section \\\\ref{gamrejsec}, the rejection of such a matrix as a function\\nof the \\\\gam energy will be presented.\\n% \\n%\\n\\\\subsection{Low energy neutron background.}\\nFigures \\\\ref{fig:cgeon10} and \\\\ref{fig:cenern10} present the correlation coefficient (C$_{geo}$) and the energy rejection \\n(R$_{ener}$) as a function of the cell size, for different matrix sizes and an incident neutron energy of 10 keV. \\nThe correlation coefficient depends both on the size of the cell\\nand of the matrix, since the neutron capture is the predominant process at this energy. \\nThe best correlation is obtained for 8000 cells of size\\n2.5 $cm$ (C$_{geo} \\\\simeq 85 \\\\%$), but a larger cell (5 $cm$ side), with only 1000 cells presents also a similar correlation \\n(C$_{geo} \\\\simeq 86 \\\\%$). The energy rejection (R$_{ener}$) depends not only on the size of the cell, but also on the size \\nof the matrix. \\nThe best rejection (R$_{ener}\\\\simeq 22$) is achieved for a large cell (5 $cm$ side) and a large matrix (1000 cells). \\nThe total rejection, shown on fig.\\\\ref{fig:rejall}, is R$\\\\simeq$80 for 1000 cells of 5 $cm$ side, meaning that only 1.25 \\\\% of the incoming\\n10 keV neutrons may simulate a \\\\neut event. It must be pointed out that 10 keV represent the worst case for rejection purpose, as it can be\\nseen on figure \\\\ref{fig:rejall}. \\n\\n\\\\subsection{Fast neutron background.}\\nFigures \\\\ref{fig:cgeon1} and \\\\ref{fig:cenern1} show the correlation coefficient (C$_{geo}$) and the energy rejection \\n(R$_{ener}$) as a function of the cell size, for different matrix sizes and an incident neutron energy of 1 MeV. As well as \\nfor low energy neutrons, the\\ncorrelation coefficient depends on the matrix and cell sizes. A correlation of $\\\\sim$ 65 \\\\% is achieved for a\\nlarge \\\\hetrois volume (1000 cells of 5 $cm$ or 8000 cells of 2.5 $cm$). \\nA large matrix of big cells (1000 cells of 5 $cm$) allows to obtain a rather large energy rejection (R$_{ener} \\\\simeq 500$),\\nleading to a total rejection of the order of 1000 (see fig.\\\\ref{fig:rejall}), meaning that 99.9\\\\% of 1 MeV neutrons arriving on\\nthe \\\\hetrois matrix may be discriminated from a \\\\neut event.\\\\\\\\\\n\\\\noindent\\nFor these three particle samples, the simulation has shown that a large cell (125 $cm^3$) allows to obtain \\na large energy rejection, and a large matrix (1000 cells or more) allows to have a good correlation among cells, \\nthus rejecting efficiently \\\\gams and neutrons of kinetic energy E$\\\\simeq$1 MeV. Hence, for background \\nrejection consideration the optimum configuration is a matrix of 1000 cells of 5 $cm$ side.\\n\\n\\\\subsection{Rejection power of a superfluid \\\\hetrois matrix.}\\nAs shown previously, a matrix of $10^{3}$ large cells (125 $cm^{3}$ each) presents the best rejection power, both for neutrons and\\n$\\\\gamma$-rays. This section presents the various coefficients, as defined in section \\\\ref{sec:intera}, as a function of the energy of the \\nincoming particle.\\\\\\\\\\n\\\\subsubsection{Rejection against \\\\gam background.}\\n\\\\label{gamrejsec}\\nFigure \\\\ref{fig:coeffgam} shows the correlation coefficient, the veto coefficient, the energy rejection and the total rejection as a function of\\nthe $\\\\gamma$-ray energy. A good correlation is achieved for high energy $\\\\gamma$-rays ($E_{\\\\gamma} \\\\geq $1 MeV), whereas low\\nenergy $\\\\gamma$-rays are mainly rejected by the veto. In fact, 80 keV X-rays undergo photoelectric effect in\\nthe copper layer ($\\\\sigma_{phot} \\\\simeq 10^{4}$barn)\\nsurrounding the cell; the scaterred electrons may escape the copper layer and leave a few keV in the cell. This will mainly happen\\nin the outermost cells.\\\\\\\\\\nFigure \\\\ref{fig:rejall} presents the total rejection as a function of the $\\\\gamma$-ray energy. It can be concluded that an \\\\hetrois\\nmatrix provides a rejection ranging between 10 and 1000, depending on the $\\\\gamma$-ray energy. It must be pointed out that this is\\nthe rejection power of the matrix itself. For instance, 90\\\\% of X-rays will be rejected by the matrix, but the flux of\\nsuch particles will be reduced substantially by an inner and outer copper shielding.\\n\\\\subsubsection{Rejection against neutron background.}\\nFigure \\\\ref{fig:coeffneut} presents the four matrix parameters as a function of the neutron energy. A correlation better than 70 \\\\% is \\nachieved for neutrons\\nof energy greater than 100 keV (fig. \\\\ref{fig:coeffneut}, upper left), while low energy neutrons are mainly rejected by the veto. Indeed, 60 \\\\% of 10 keV neutrons are captured in\\nthe first layer (fig. \\\\ref{fig:coeffneut}, upper right). The energy measurement constitute an efficient selection for low energy \\nneutron (R$_{ener}\\\\simeq$ 100 for 1 keV neutrons) and for\\nfast neutrons (R$_{ener}\\\\simeq$ 1000 for 1 MeV neutrons). As expected 10 keV neutrons have the worst energy rejection (R$_{ener}\\\\simeq$ 15).\\\\\\\\\\nThe total rejection\\\\footnote{This coefficient takes into account the interaction probability and will be used to evaluate the \\nfalse event rate.} (ratio between number of incoming particles and number of false \\\\neut events), shown on figure \\\\ref{fig:rejall},\\nindicates that only one 1 keV\\nneutron out of 2000 may simulate a \\\\neut event. The rejection falls down to 75 for 10 keV neutrons (mainly rejected by the veto) and is of the\\norder of 1000 for 1 MeV neutrons.\\n\\n\\\\noindent \\nIt must be pointed out that the evaluated rejection is for a \\\"naked matrix\\\", i.e. without taking into account any lead or paraffin shielding\\n or any separation between electron and ion recoils. It represents the capability of the \\\\hetrois matrix to reject background events by means of energy loss\\nmeasurements and correlation considerations. As a conclusion, it can be said that the \\\\hetrois matrix presents a rejection power ranging between 75 and 2000 for\\nneutrons, and between 10 and 800 for $\\\\gamma$-rays,depending on their kinetic energies.\\n\\n\\\\subsection{An evaluation of the neutron-induced false event rate.}\\nAs neutrons recoiling off nuclei may easily simulate a \\\\neut event, it is crucial to evaluate the neutron-induced false event rate.\\\\\\\\\\nIn contrast to most DM detectors, MACHe3 may be sensitive to rather low energy neutrons, and its response depends strongly on their kinetic\\nenergies. For this purpose, a simulation \\nof a paraffin neutron shielding has been done, in order to evaluate the expected neutron spectrum trough this shielding.\\\\\\\\\\nThe simulated device is a large ($1m\\\\times 1m$) paraffin block ($\\\\rho$=0.95 g.cm$^{-3}$) with a width of 30 $cm$. \\nIn order to be conservative, as well as keeping the calculation times short, we choose to generate the events in a direction perpendicular \\nto the face of the paraffin block and considering that all neutrons crossing the block are supposed to enter the matrix volume.\\\\\\\\\\nA benchmark study has been done, to compare MCNP calculation code\\\\cite{mcnp} and GEANT3.21. We found that these two codes give similar results, \\nexcept for thermal neutrons (below 1 eV) for which GEANT underevaluate the flux. Again, to be conservative, we choose the one giving \\nthe highest flux (MCNP)\\\\footnote{MCNP is much faster than GEANT, in this case, allowing shorter calculation times.}.\\\\\\\\\\nWe have used the measured neutron spectrum \\\\cite{Chazal:1998qn} in Laboratoire Souterrain de Modane (LSM), between 2 and 6 MeV \\\\footnote{The thermal neutron flux, evaluated \\nin \\\\cite{Chazal:1998qn} to be (1.6$\\\\pm0.1)\\\\times 10^{-6} cm^{-2}s^{-1}$, will be highly suppressed by the 30 $cm$ paraffin shielding}, with an\\nintegrated flux of $\\\\Phi_{n}\\\\simeq 4\\\\times 10^{-6} cm^{-2}s^{-1}$. We found an overall neutron flux through the shielding of 5.1$\\\\times 10^{-8} cm^{-2}s^{-1}$, with the \\nneutron kinetic energy ranging between\\n$10^{-2}$ eV and 6 MeV (see the upper curve on fig. \\\\ref{fig:neutfalse}).\\\\\\\\\\nUsing this flux and the expected rejection factor (fig. \\\\ref{fig:rejall}), we evaluated the false\\n\\\\neut rate induced by neutron background, see fig. \\\\ref{fig:neutfalse}. We \\nfound a rate of $\\\\sim$0.1 false event per day through the\\n1.5$m^{2}$ surface detector (1000 cells of 125 $cm^{3}$). Even with such a conservative approach, this contamination is much lower than the expected \\\\neut rate (of the order of \\n$\\\\sim$1 day$^{-1}$\\nin a detector of this size \\\\cite{next}). \\n\\\\subsection{An evaluation of the muon-induced false event rate.}\\nThe muon background flux in an underground laboratory (Gran Sasso) has been measured by \\\\cite{muons}. They found a mean flux of \\n$\\\\Phi_{\\\\mu}=2.3\\\\times 10^{-4} m^{-2}s^{-1}$\\nfor an average kinetic energy $<\\\\!$$E$$>$=200 GeV.\\\\\\\\\\nAn evaluation of the $\\\\mu$-induced event rate has been done. The same procedure as above (see section \\\\ref{simumatrix}) has been used, \\nwithout paraffin shielding; i.e. the events are\\ngenerated in a direction perpendicular to one of the matrix faces. This is a conservative approach because the worst case is in which muons are \\npassing in between 2 cell layers. As expected, most of the $\\\\mu$-events interact in all the crossed cells (75\\\\%\\ninteract in 10 cells, with an average energy left of $\\\\sim$ 1 MeV). The correlation coefficient is C$_{geo}\\n\\\\simeq 2.1\\\\%$ (meaning 97.9$\\\\%$ of $\\\\mu$-events are rejected), with an energy rejection R$_{ener} \\\\simeq 40$, leading to an overall rejection \\nof R$\\\\simeq 2100$. This lead to a\\n$\\\\mu$-induced false \\\\neut rate of the order of 0.0095 day$^{-1}$m$^{-2}$, which is more than two orders of magnitude below the\\nexpected \\\\neut rate. The layers may be shifted, thus allowing a much higher rejection against muon background\\nevents.\\n\\\\subsection{\\\\gam background.}\\nAs shown in section \\\\ref{gamrejsec}, a high granularity superfluid \\\\hetrois detector provides an intrinsic rejection ranging \\nbetween 10 and 800 for $\\\\gamma$-rays, depending on their kinetic energies. This selection, based on the correlation among the cells \\nand energy loss measurement, may be improved by adding a discrimination between\\nrecoils and electrons. Different experimental approaches should be tested. A complete study of an inner and outer cryostat shielding is also\\nneeded, as well as an evaluation of natural radioactivity of materials. Nevertheless, this simulation indicates that an important intrinsic rejection can be achieved.\\n\\n\\\\section{Conclusion}\\nIn this prospective paper, we have demonstrate that a large matrix ($\\\\sim$ 1000 cells) of large cells (125 $cm^{3}$) is the\\npreferred design for a superfluid \\\\hetrois detector searching for DM, as far as background rejection is concerned. \\nAn experimental work needs to be done to demonstrate the possibility to use such a large volume of superfluid $ ^{3}{\\\\mathrm{He}}$-B at ultra-low temperatures. This work has evaluated the background\\nrejection of a high granularity superfluid \\\\hetrois detector for a large range of kinetic energies,\\nboth for neutrons and $\\\\gamma$-rays. It has been shown that, by means of\\ncorrelation among the cells and energy loss measurement, a high rejection may be obtained for $\\\\gamma$-ray, neutron and muon background. Using the\\nmeasured muon and neutron flux in an underground laboratory, we have evaluated the contamination to be one order of \\nmagnitude (two orders\\nfor muons) less than the expected \\\\neut rate. For background rejection purpose, the main advantage of a superfluid \\\\hetrois detector is to present a high \\nrejection against neutron background, mainly because of the\\nhigh capture cross-section at low energy. As neutrons interact {\\\\it a priori} like \\\\neutt, they are the\\nultimate background noise for DM detectors.\\\\\\\\\\n\\n\\\\textbf{Acknowledgements}\\\\\\\\\\nThe authors are grateful to D. Kerdraon and L. Perrot for the help concerning the use of MCNP calculation code, and also\\nF. Ohlsson-Malek for the fruitful discussions on the GEANT code. \\n\\n\\\\begin{thebibliography}{99}\\n\\\\bibitem{vieux1}G. R. Pickett, in {\\\\em Proc. of the European Workshop on Low Temperature Devices for \\nthe Detection of Low Energy Neutrinos and Dark Matter (1988 Annecy, France)}, edited by L. Gonzales-Mestres and D. Perret-Gallix (Ed.\\nFrontieres).\\n\\n\\\\bibitem{vieux2}Yu. M. Bunkov \\\\textit{et al.}, in {\\\\em Proc. of the International Workshop on Superconductivity and Particle Detection (1994 Toledo,\\nSpain) eds. T.A. Girard, A. Morales and G. Waysand, World Scientific, p.21 (1995)}\\n\\n\\\\bibitem{prl95}D. I. Bradley \\\\textit{et al.}, \\\\PRL{75}{95}{1887}.\\\\\\\\\\nC. B\\\\\\\"{a}uerle \\\\textit{et al.}, \\\\PRB{57}{98}{22}.\\n\\\\bibitem{trique}S. Triqueneaux \\\\textit{et al.}, in {\\\\em Proc. of the 22nd International Conf. on Low Temperature Physics},\\nAugust 1999, Physica B (in print).\\n\\\\bibitem{next}D. Santos, F. Mayet, G. Perrin \\\\textit{et al., to be submitted to Phys. Rev. D}.\\n\\\\bibitem{edel}L. Berge \\\\textit{et al.}, astro-ph/9801199\\n\\\\bibitem{cresst}M. Bravin \\\\textit{et al.}, hep-ex/9904005 \\n\\\\bibitem{cuore}A. Alessandrello \\\\textit{et al.}, in {\\\\em Proc. Dark matter in astrophysics and particle physics 1998.}\\n\\\\bibitem{ltemp}J. S. Meyer and T. Sloan, J. of Low Temp. Phys. (108) 1997.\\n\\\\bibitem{geant}R. Brun, F. Carminati, {\\\\em GEANT Detector Description and Simulation Tool}, CERN \\nProgam Library Long Writeup W5013, September 1993.\\n\\\\bibitem{micap}J. O. Johnson, T. A. Gabriel, {\\\\em A user's guide to MICAP}, ORNL/TM-10340, January 1988\\\\\\\\\\nC. Zeitniz and T. A. Gabriel, \\\\NIMA{349}{94}{106}.\\n\\\\bibitem{mcnp}J. F. Briesmeister, {\\\\em MCNP $^{TM}$, A general Monte Carlo N-particle transport code}, LANL Report LA-12625-M(93)\\n%\\\\cite{Chazal:1998qn}\\n\\\\bibitem{Chazal:1998qn}\\nV.~Chazal {\\\\it et al.},\\n%``Neutron background measurements in the underground laboratory of Modane,''\\nAstropart.\\\\ Phys.\\\\ {\\\\bf 9}, 163 (1998).\\n\\\\bibitem{muons}\\nC.~Arpesella,\\n%``Background measurements at GRAN SASSO laboratory,''\\nLNGS-92-28\\n{\\\\it Contribution to TAUP '91 Workshop, Toledo, Spain, Sep 9-13, 1991}.\\\\\\\\\\nH. V. Klapdor-Kleingrothaus {\\\\it et al.}, hep-ph/9910205.\\n\\\\end{thebibliography}\\n\\\\newpage\\n\\\\listoffigures\\n\\n\\n%******************************************************\\n% \\n\\\\newpage\\n\\\\begin{figure}\\n\\\\begin{center}\\n\\\\includegraphics[scale=0.55]{Fig2BPRB.eps}\\n{\\\\noindent\\n\\\\caption{Ultra-low temperature nuclear stage and bolometer cell.\\n\\\\label{fig:design}}}\\n\\\\end{center}\\n\\\\end{figure}\\n%\\n\\\\newpage\\n\\\\begin{figure}\\n\\\\begin{center}\\n\\\\includegraphics[scale=0.55]{henri_background.eps}\\n{\\\\noindent\\n\\\\caption{Temperature recorded inside the bolometer as a function of time.\\n\\\\label{fig:signal}}}\\n\\\\end{center}\\n\\\\end{figure}\\n%\\n\\\\newpage\\n\\\\begin{figure}\\n\\\\begin{center}\\n\\\\includegraphics[scale=0.40]{10kev.matrix.epsi}\\n{\\\\noindent\\n\\\\caption{2-dimensionnal view of a proposed matrix of 1000 cells (125 $cm^{3}$ each). The events generated in a direction \\nperpendicular to the upper face, are 10 keV neutrons. It can be noticed that most of\\nneutrons of this energy are captured in the first layer.\\n\\\\label{fig:10kev}}}\\n\\\\end{center}\\n\\\\end{figure}\\n%\\n%\\n\\\\begin{figure}\\n\\\\begin{center}\\n\\\\includegraphics[scale=0.55]{cgeo.g26.epsi}\\n\\\\caption{Correlation coefficient (C$_{geo}$) as a function of the size of the \\\\hetrois cell for 2.6 MeV $\\\\gamma$-rays. \\nThe different curves correspond to different matrix sizes as indicated by the labels. \\n\\\\label{fig:cgeo26m}}\\n\\\\end{center}\\n\\\\end{figure}\\n%\\n%\\n\\\\newpage\\n\\\\begin{figure}\\n\\\\begin{center}\\n\\\\includegraphics[scale=0.55]{cgeo.n10k.epsi}\\n\\\\caption{Correlation coefficient (C$_{geo}$) as a function of the size of the \\\\hetrois cell for 10 keV neutrons. The different curves\\ncorrespond to different matrix sizes as indicated by the labels.\\n\\\\label{fig:cgeon10}}\\n\\\\end{center}\\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n\\\\begin{center}\\n\\\\includegraphics[scale=0.55]{cener.n10k.epsi}\\n\\\\caption{Energy Rejection (R$_{ener}$) as a function of the size of the \\\\hetrois cell for 10 keV neutrons. The different curves\\ncorrespond to different matrix sizes as indicated by the labels. \\n\\\\label{fig:cenern10}}\\n\\\\end{center}\\n\\\\end{figure}\\n\\n\\\\newpage\\n\\\\begin{figure}\\n\\\\begin{center}\\n\\\\includegraphics[scale=0.55]{cgeo.n1m.epsi}\\n\\\\caption{Correlation coefficient (C$_{geo}$) as a function of the size of the \\\\hetrois cell for 1 MeV neutrons. The different curves\\ncorrespond to different matrix sizes as indicated by the labels. \\n\\\\label{fig:cgeon1}}\\n\\\\end{center}\\n\\\\end{figure}\\n\\n\\\\begin{figure}\\n\\\\begin{center}\\n\\\\includegraphics[scale=0.55]{cener.n1m.epsi}\\n\\\\caption{Energy Rejection (R$_{ener}$) as a function of the size of the \\\\hetrois cell for 1 MeV neutrons. The different curves\\ncorrespond to different matrix sizes as indicated by the labels. \\n\\\\label{fig:cenern1}}\\n\\\\end{center}\\n\\\\end{figure}\\n\\n\\\\newpage\\n\\\\begin{figure}\\n\\\\begin{center}\\n\\\\includegraphics[scale=0.55]{coeffneut.epsi}\\n{\\\\noindent\\n\\\\caption{Neutrons interacting in MACHe3 : The four matrix parameters, defined in sec. \\\\ref{simumatrix}, as a function of the neutron energy, for a matrix of 1000 cells (125 $cm^{3}$ each).\\n\\\\label{fig:coeffneut}}}\\n\\\\end{center}\\n\\\\end{figure}\\n%\\n\\\\begin{figure}\\n\\\\begin{center}\\n\\\\includegraphics[scale=0.55]{coeffgam.epsi}\\n{\\\\noindent\\n\\\\caption{\\\\gams interacting in MACHe3 : The four matrix parameters, defined in sec. \\\\ref{simumatrix}, as a function of the $\\\\gamma$-ray energy, for a matrix of 1000 cells (125\\n$cm^{3}$ each).\\n\\\\label{fig:coeffgam}}}\\n\\\\end{center}\\n\\\\end{figure}\\n%\\n\\\\newpage\\n\\\\begin{figure}\\n\\\\begin{center}\\n\\\\includegraphics[scale=0.8]{rejall.epsi}\\n{\\\\noindent\\n\\\\caption{Total Rejection as a function of the incident particle energy, for a matrix of 1000 cells (125\\n$cm^{3}$ each). The different set of points correspond to \\\\gams (squares) and neutrons (circles). The total rejection is defined as the ratio \\nbetween the number of incoming particles and the number of false \\\\neut events (less than 6 keV in one non-peripheric cell).\\n\\\\label{fig:rejall}}}\\n\\\\end{center}\\n\\\\end{figure}\\n\\\\newpage\\n%\\n\\\\begin{figure}\\n\\\\begin{center}\\n\\\\includegraphics[scale=0.60]{neutronfinal.epsi}\\n{\\\\noindent\\n\\\\caption{The upper curve is the simulated neutron spectrum through a 30 $cm$ wide paraffin \\nshielding, the measured spectrum at LSM being the input. Comparing with the measured neutron flux, this shielding allows \\nan overall reduction factor of $\\\\sim$ 50. The lowest curve represents the neutron induced false \\\\neut rate \\nin MACHe3. This spectrum has been obtained by combining the upper curve with the total rejection \\n(fig. \\\\ref{fig:rejall}), with a threshold of 500 eV. The overall counting rate, due to neutron background, is \\nevaluated to be $\\\\sim$ 0.1 day$^{-1}$ in a 1000 cells detector.\\n\\\\label{fig:neutfalse}}}\\n\\\\end{center}\\n\\\\end{figure}\\n\\n\\n\\n\\n\\n\\\\end{document}\\n\"\n }\n]"},"bibtex":{"kind":"list like","value":[{"name":"astro-ph0002303.extracted_bib","string":"\\begin{thebibliography}{99}\n\\bibitem{vieux1}G. R. Pickett, in {\\em Proc. of the European Workshop on Low Temperature Devices for \nthe Detection of Low Energy Neutrinos and Dark Matter (1988 Annecy, France)}, edited by L. Gonzales-Mestres and D. Perret-Gallix (Ed.\nFrontieres).\n\n\\bibitem{vieux2}Yu. M. Bunkov \\textit{et al.}, in {\\em Proc. of the International Workshop on Superconductivity and Particle Detection (1994 Toledo,\nSpain) eds. T.A. Girard, A. Morales and G. Waysand, World Scientific, p.21 (1995)}\n\n\\bibitem{prl95}D. I. Bradley \\textit{et al.}, \\PRL{75}{95}{1887}.\\\\\nC. B\\\"{a}uerle \\textit{et al.}, \\PRB{57}{98}{22}.\n\\bibitem{trique}S. Triqueneaux \\textit{et al.}, in {\\em Proc. of the 22nd International Conf. on Low Temperature Physics},\nAugust 1999, Physica B (in print).\n\\bibitem{next}D. Santos, F. Mayet, G. Perrin \\textit{et al., to be submitted to Phys. Rev. D}.\n\\bibitem{edel}L. Berge \\textit{et al.}, astro-ph/9801199\n\\bibitem{cresst}M. Bravin \\textit{et al.}, hep-ex/9904005 \n\\bibitem{cuore}A. Alessandrello \\textit{et al.}, in {\\em Proc. Dark matter in astrophysics and particle physics 1998.}\n\\bibitem{ltemp}J. S. Meyer and T. Sloan, J. of Low Temp. Phys. (108) 1997.\n\\bibitem{geant}R. Brun, F. Carminati, {\\em GEANT Detector Description and Simulation Tool}, CERN \nProgam Library Long Writeup W5013, September 1993.\n\\bibitem{micap}J. O. Johnson, T. A. Gabriel, {\\em A user's guide to MICAP}, ORNL/TM-10340, January 1988\\\\\nC. Zeitniz and T. A. Gabriel, \\NIMA{349}{94}{106}.\n\\bibitem{mcnp}J. F. Briesmeister, {\\em MCNP $^{TM}$, A general Monte Carlo N-particle transport code}, LANL Report LA-12625-M(93)\n%\\cite{Chazal:1998qn}\n\\bibitem{Chazal:1998qn}\nV.~Chazal {\\it et al.},\n%``Neutron background measurements in the underground laboratory of Modane,''\nAstropart.\\ Phys.\\ {\\bf 9}, 163 (1998).\n\\bibitem{muons}\nC.~Arpesella,\n%``Background measurements at GRAN SASSO laboratory,''\nLNGS-92-28\n{\\it Contribution to TAUP '91 Workshop, Toledo, Spain, Sep 9-13, 1991}.\\\\\nH. V. Klapdor-Kleingrothaus {\\it et al.}, hep-ph/9910205.\n\\end{thebibliography}"}],"string":"[\n {\n \"name\": \"astro-ph0002303.extracted_bib\",\n \"string\": \"\\\\begin{thebibliography}{99}\\n\\\\bibitem{vieux1}G. R. Pickett, in {\\\\em Proc. of the European Workshop on Low Temperature Devices for \\nthe Detection of Low Energy Neutrinos and Dark Matter (1988 Annecy, France)}, edited by L. Gonzales-Mestres and D. Perret-Gallix (Ed.\\nFrontieres).\\n\\n\\\\bibitem{vieux2}Yu. M. Bunkov \\\\textit{et al.}, in {\\\\em Proc. of the International Workshop on Superconductivity and Particle Detection (1994 Toledo,\\nSpain) eds. T.A. Girard, A. Morales and G. Waysand, World Scientific, p.21 (1995)}\\n\\n\\\\bibitem{prl95}D. I. Bradley \\\\textit{et al.}, \\\\PRL{75}{95}{1887}.\\\\\\\\\\nC. B\\\\\\\"{a}uerle \\\\textit{et al.}, \\\\PRB{57}{98}{22}.\\n\\\\bibitem{trique}S. Triqueneaux \\\\textit{et al.}, in {\\\\em Proc. of the 22nd International Conf. on Low Temperature Physics},\\nAugust 1999, Physica B (in print).\\n\\\\bibitem{next}D. Santos, F. Mayet, G. Perrin \\\\textit{et al., to be submitted to Phys. Rev. D}.\\n\\\\bibitem{edel}L. Berge \\\\textit{et al.}, astro-ph/9801199\\n\\\\bibitem{cresst}M. Bravin \\\\textit{et al.}, hep-ex/9904005 \\n\\\\bibitem{cuore}A. Alessandrello \\\\textit{et al.}, in {\\\\em Proc. Dark matter in astrophysics and particle physics 1998.}\\n\\\\bibitem{ltemp}J. S. Meyer and T. Sloan, J. of Low Temp. Phys. (108) 1997.\\n\\\\bibitem{geant}R. Brun, F. Carminati, {\\\\em GEANT Detector Description and Simulation Tool}, CERN \\nProgam Library Long Writeup W5013, September 1993.\\n\\\\bibitem{micap}J. O. Johnson, T. A. Gabriel, {\\\\em A user's guide to MICAP}, ORNL/TM-10340, January 1988\\\\\\\\\\nC. Zeitniz and T. A. Gabriel, \\\\NIMA{349}{94}{106}.\\n\\\\bibitem{mcnp}J. F. Briesmeister, {\\\\em MCNP $^{TM}$, A general Monte Carlo N-particle transport code}, LANL Report LA-12625-M(93)\\n%\\\\cite{Chazal:1998qn}\\n\\\\bibitem{Chazal:1998qn}\\nV.~Chazal {\\\\it et al.},\\n%``Neutron background measurements in the underground laboratory of Modane,''\\nAstropart.\\\\ Phys.\\\\ {\\\\bf 9}, 163 (1998).\\n\\\\bibitem{muons}\\nC.~Arpesella,\\n%``Background measurements at GRAN SASSO laboratory,''\\nLNGS-92-28\\n{\\\\it Contribution to TAUP '91 Workshop, Toledo, Spain, Sep 9-13, 1991}.\\\\\\\\\\nH. V. Klapdor-Kleingrothaus {\\\\it et al.}, hep-ph/9910205.\\n\\\\end{thebibliography}\"\n }\n]"}}},{"rowIdx":299,"cells":{"paper_id":{"kind":"string","value":"astro-ph0002304"},"title":{"kind":"string","value":"The frequency content of $\\delta$ Sct stars as determined by photometry"},"authors":{"kind":"list like","value":[{"author":"Ennio Poretti"}],"string":"[\n {\n \"author\": \"Ennio Poretti\"\n }\n]"},"abstract":{"kind":"string","value":"--"},"latex":{"kind":"list like","value":[{"name":"eporetti.tex","string":"%\\documentstyle[11pt,paspconf,epsf]{article}\n\\documentstyle[11pt,newpasp,twoside,epsfig]{article}\n\\markboth{E. Poretti}{Photometry of $\\delta$ Sct stars}\n\\setcounter{page}{1}\n\n\n\\begin{document}\n\n\\title{The frequency content of $\\delta$ Sct stars as\ndetermined by photometry}\n\n\\author{Ennio Poretti}\n\\affil{Osservatorio Astronomico di Brera, Via E.~Bianchi 46, 23807 Merate, Italy}\n\n\n% The abstract is entered in a LaTeX \"environment\", designated with paired\n% \\begin{abstract} -- \\end{abstract} commands. Other environments are\n% identified by the name in the curly braces.\n\n\n\\begin{abstract}\nThe results obtained by means of the photometric approach to the study of\n$\\delta$ Sct stars are extensively discussed. The different frequency contents of\nthe three best candidates for asteroseismological studies (FG Vir, 4 CVn\nand XX Pyx) are presented and compared; the importance of the amplitude\nvariations and of the combination terms is emphasized. \nThe analysis of other multiperiodic variables shows how a large variety\nof nonradial modes are excited; in some cases, modifications of\nthe power spectrum can be\nobserved over a few years and new modes can be seen to grow. Among monoperiodic\npulsators, constant as well as variable amplitudes can be observed. \nThe difficulty of identifying an \noscillation yielding quantum numbers is emphasized; the possibilities offered by\n$\\delta$ Sct stars belonging to binary systems and open clusters are\ndiscussed. In this respect, combining the photometric and the spectroscopic\napproaches could lead to a solution. A comparison is also made between low- and\nhigh-amplitude pulsators, finding similarities.\n\nThe use of a reliable Period--Luminosity--Colour relationships toward\nthe shortest periods can greatly help \nmode identification in the galactic stars; moreover, it could provide an independent\nverification of extragalactic distances. \n\n\\end{abstract}\n\n% Keywords should be included, but they are not printed in the hardcopy.\n\n\\keywords{photometry, pulsating stars, $\\delta$ Sct stars, data analysis}\n\n\n\\section{Introduction}\n$\\delta$ Sct variables are now a well-defined class of stars.\nThey are located on or just above the zero-age main sequence,\nin the lowest part of the classical instability strip. $\\delta$\nSct stars have masses between 1.5 and 2.5 M$_{\\sun}$ and they are\nclose to the end of the core hydrogen burning phase (Breger \\&\nPamyatnykh 1998). The presence of convective\nzones and related phenomena such as convective overshooting, make them\nvery interesting objects for the understanding of stellar evolution. \nThe investigation of pulsational properties of pre-main sequence stars\nallowed their instability strip in the H-R diagram to be defined\n(Marconi \\& Palla 1998); some of these stars showing $\\delta$ Sct variability\nwere discovered (Kurtz \\& Muller 1999).\n\nPhotometric monitoring is the most practiced approach to study\nthe properties of $\\delta$ Sct stars and several stars have been\ndeeply investigated. However, the spectroscopic approach tells us that\nmany modes that are not photometrically detectable are actually excited.\nRotation acts as an important factor in the increase of the number of\nexcited modes.\n\nThe observed frequencies are between 5 and 35~cd$^{-1}$ and \nmultiperiodicity is very common; only a few stars show a monoperiodic\nbehaviour above the current limit of the detectable amplitude from\nground, i.e., $\\sim$1~mmag. The observed modes are in the domain\nof pressure ($p$) modes; there is no observational evidence that\ngravity ($g$) modes are excited in $\\delta$ Sct stars, even if some cases \nare suggested. At the moment, $g$-modes seem to be present only in\nthe $\\gamma$ Dor stars, which in turn do not show $p$-modes.\n\nThe great observational effort made by several teams allows us to\nhandle a well-defined phenomenological scenario of the $\\delta$\nSct variability. This contribution tries to summarize the results\nobtained in the past years by means of extended photometric time\nseries. The paper is structured as follows:\n\\begin{list} { } { }\n\\item 2.~The best candidates for asteroseismological studies\n\\begin{list} { } { }\n\\item 2.1~FG Vir: 24 independent modes\n\\item 2.2~XX Pyx: strong and rapid amplitude changes \n\\item 2.3~4 CVn: presence of combination terms and amplitude variations\n\\item 2.4~Comparison between FG Vir, XX Pyx and 4 CVn\n\\end{list}\n\\item 3.~Other stars studied by the Merate Group\n\\begin{list} { } { }\n\\item 3.1~44 Tau: variable amplitude and recurrent ratio 0.77\n\\item 3.2~BH Psc: variable amplitude and rich pulsational content\n\\item 3.3~V663 Cas: growth of new modes\n\\item 3.4~The help of the spectroscopic approach\n\\end{list}\n\\item 4.~Monoperiodic pulsators\n\\item 5.~$\\delta$ Sct stars in binary systems\n\\item 6.~$\\delta$ Sct stars in open clusters\n\\item 7.~The frequency content of high amplitude $\\delta$ Sct stars\n\\item 8.~Summing-up and Conclusions\n\\item 9.~The future: the exportation of the results on galactic stars\n to \\\\ \\hspace*{4truemm} extragalactic research\n\\end{list}\n In what manner\nthe photometric results can be used to identify modes (i.e., to\nclassify the oscillation in terms of quantum numbers $n$, $\\ell$ and $m$)\nis discussed by Garrido (2000). Some\nimprovements, both observational and theoretical, are probably\nnecessary to make new, substantial steps forward.\nA better connection between theory and observation will allow us\nto really progress in the asteroseismology of these stars.\n\n\n\\section{The best candidates for asteroseismological studies}\nThe studies and the related papers on $\\delta$ Sct stars\n follow a recurrent paradigm in the process of the\ndetermination of the frequency content. \nIn most cases a first solution, often wrongly considered a ``good'' solution, \nis obtained on the basis of a few, fragmented nights. At this stage, the\nobservations are hardly useful for a significant analysis.\nHowever, since the complicated light behaviour of our stars always\nleaves some unclear facts, the same authors or another team plan a second\nrun. As a consequence, it appears that the solution proposed in the first\npaper was indeed preliminary.\n A very interesting result often obtained while doing this refinement\nis the detection of variations in amplitude and/or in frequency for the excited\nmodes. Therefore, more observations are requested and, in general, they are\nnever sufficient \\ldots\\@ We can however obtain more and more satisfactory results from\nthe observational works on $\\delta$ Sct stars by delving deeper and deeper in this\nprocess, even if it involves stronger and stronger efforts.\nThe three cases reported below are probably the best examples that the \n$\\delta$ Sct community can offer.\n\n\n\\subsection{FG Vir: 24 independent modes} \\label{fg}\n\nFG Vir can be considered a cornerstone in the development of our knowledge\nof $\\delta$ Sct stars. After a few nights of observations by L\\'opez de Coca\net al. (1984), it was studied first by Mantegazza, Poretti, \\& Bossi (1994)\non the basis of a single-site campaign carried out at the European Southern\nObservatory, Chile. These authors proposed seven certain frequencies and a \npossible eighth one; they also claimed the presence of undetected terms,\nowing to the relatively high level of noise in some parts of the power\nspectrum. A successive multisite campaign (Breger et al. 1998)\nconfirmed the seven frequencies,\ndemonstrating how a single site observing run can be successful in the\ndetection of the main components of a multiperiodic pulsator. However, the eighth,\nsmall-amplitude frequency was an alias and the misidentification originated\nfrom the combination of the spectral window with the noise. A search for the\npresence of the hitherto previously undetectable terms was undertaken and the number of\nfrequencies increased to at least 24. However, new campaigns on this star\nare considered necessary to improve the frequency resolution\nand a time baseline of several months is requested.\n\n\n\\begin{figure}[ht]\n\\setlength{\\textwidth}{5.3in}\n\\plotone{eporetti1.eps}\n\\caption{Roughly a half of the $y$ (filled circles) and $v$ (open circles)\nmeasurements obtained during the 1995 multisite campaign on FG Vir are shown.\nThe fits of the 24 frequency solutions\nderived by Breger et al. (1998) are represented as solid curves}\n\\label{multi}\n\\end{figure}\n\nThe light curves obtained in a multisite campaign look quite fine and they\nbear witness to the efforts made by the $\\delta$ Sct researchers to\nimprove the quality and the quantity of the data; Fig.~\\ref{multi} shows the \nvery dense $v$ and $y$ light curves obtained on a baseline spanning 20 days, a subset\nof the 1995 campaign. \nConsidering all the frequencies now known in the light curve, it seems that\nthe pulsation of FG Vir is much more stable than that of XX Pyx and 4 CVn:\nthe amplitude variability is very limited and the frequency values \nseem to be stable over a baseline of decades. The frequencies are mainly \ndistributed in two subgroups: the first ranges from 9.2 to 11.1~cd$^{-1}$,\nthe second from 19.2 to 24.2~cd$^{-1}$. An isolated peak is found at\n 16.1~cd$^{-1}$ and a few between 28.1 to 34.1~cd$^{-1}$. Contrasting with\nthe 22 independent frequencies found, only 2 combination terms have been detected.\n It should be noted that\nthe identification was accepted at an amplitude S/N limit of 4.0 for an\nindependent term and 3.5 for a combination frequency. Kuschnig et al. (1997)\nsupply a theoretical basis for these assumptions. The combination terms are related\nto the $f_1$ term, which has an amplitude 5 times larger than the other ones.\nThis term also displays an asymmetric shape, since the 2$f_1$ harmonic \nis also observed ($R_{21}=A_{\\rm 2f}/A_{\\rm f}=0.04$).\n\nPhotometric measurements are adequate to perform mode identification by\nmeans of the phase shifts in different colours. Viskum et al. (1998) and\nBreger et al. (1999a) agree \nthat the dominant mode can be identified with $\\ell$=1 and the \n12.15~cd$^{-1}$ mode with the radial fundamental. \nConsidering the sophisticated pulsational modeling proposed by Breger et al.\n(1999a),\nFG Vir looks as a very good candidate to match theory and observations.\n\n\\subsection{XX Pyx: strong and rapid amplitude changes} \\label{xx}\n\nOur knowledge on XX Pyx has rapidly grown in the last years, following the\nparadigm described above.\nIts variability was discovered with the Whole\nEarth Telescope (Handler et al. 1996) and then\nthe first solution of the light curve (based on 116.7 hours of photometry)\nwas already very good: 7 frequencies between 27.01 and 38.11~cd$^{-1}$ were\nunambiguously found. However, a second campaign was planned \nto match the requirements of stellar seismology. Not\nonly was the number of frequencies increased to 13 (Handler et al. 1997), but,\nas noted above, the possibility\nof comparing different observing seasons immediately evidenced \nthe variability of the amplitudes. The three dominating modes change their\nphotometric amplitude within one month at certain times, while the amplitudes\ncan remain constant at other times (Handler et al. 1998): Fig.~\\ref{xxamp}\nshows the behaviour of these modes. The investigation about the nature of these\nvariations considered various hypotheses: oblique pulsator, precession of the pulsational\naxis, beating of closely spaced frequencies. However, none of them \n can explain satisfactorily the amplitude changes.\nIt is important to note that no change in the pulse shape of the $f_1$ mode seems\nto accompany the amplitude variations, \nwhile changes are expected in case of frequency beating. In the\nsame way, evolutionary effects, binarity, magnetic field cannot explain period changes.\n\n\\begin{figure}[t]\n\\setlength{\\textwidth}{4.3in}\n\\vspace*{1.5em}\n\\plotone{eporetti2.eps}\n\\caption{The three main pulsation modes of XX Pyx. The rapid variability of their\n amplitude is detected by subdividing the\nmeasurements in different subsets. White histograms indicate upper limit values\nfor the amplitude.}\n\\label{xxamp}\n\\end{figure}\nThe distribution of the frequencies is clearly shifted toward high values. \nA 2$f_1$ harmonic term is observed; Handler et al.\n(1996) suggested the presence of very small combination terms as a representation of \nnonlinearities originating in the outer part of the star's envelope, but \nthey are very close to the significance limit. \n\n\nAs a last step, a pulsational model of XX Pyx was undertaken, but a\nunique solution could not be proposed (Pamyatnykh et al. 1998).\nThe presence of a frequency spacing of $\\approx$$\\,26\\, \\mu$Hz was used\nto analyze different possibilities, but \n the seismic modeling\nwas unable to match the observed frequencies since the mean departures exceed the\nmean observational frequency by at least one order of magnitude.\nUnfortunately,\nthis star is very faint ($V$=11.5) and line-profile variations, which could help\nin the mode identifications, are very difficult to measure with the requested\naccuracy. An improvement is expected from the results of a new multisite\ncampaign (Arentoft et al. 2000), perpetuating the observational paradigm\nof $\\delta$ Sct stars.\n\\subsection{4 CVn: presence of combinations terms and amplitude variations} \\label{ai} \n\nSeveral campaigns were organized on this bright ($V$=6.1) star, allowing the\ndetermination of a set of reliable frequencies on nine occasions over 30\nyears. They are mostly free from the 1~cd$^{-1}$ alias problem and are \naccurate to 0.001 cd$^{-1}$. Breger et al. (1999b) propose a\nsolution of the light curve composed of 18 independent frequencies and 16\ncombination terms $f_i\\pm f_j$; the residual rms is decreased to the level\nexpected for the noise.\n\nThe frequency content of 4 CVn is characterized by the grouping of all\nthe 18 independent frequencies in the interval 4.749--8.595 cd$^{-1}$.\nIn the 1996 campaign, 5 have an amplitude larger than 9 mmag; 5 others \nhave an amplitude between 6.4 and 3.2 mmag. After a single peak at 1.6\nmmag, the other terms (also including the combination terms) have an\namplitude smaller than 1 mmag. However, the main result of the survey\nof 4 CVn is the large variability of the amplitude. This is surely not\nan effect of the noise distribution, since the most relevant changes\nalso occur in the largest amplitude terms. Fig.~\\ref{figcvn} shows 6 cases\nof such variations: note\nthe decrease in the amplitude of the 5.05~cd$^{-1}$ term and the \ncorresponding increase in that of the 8.59~cd$^{-1}$ term. Other terms,\nsuch as the 6.98~cd$^{-1}$ term, show a more stable value for the amplitude.\nIt is quite impossible to discern a rule in the behaviour of the \namplitudes. A complete discussion of the amplitude changes in the light\ncurves of 4 CVn is given by Breger (2000a).\n\nThe presence of a large number of combination terms is another important\naspect; they flank the set of the independent frequencies. The sums\n$f_i+f_j$ are more numerous than the differences $f_i-f_j$: this should be\na selection effect since the signal at low frequencies is more difficult\nto detect owing to the presence of a higher level of noise.\n\nThe pulsational modes of 4 CVn have also been investigated for the variability\nof the period: some results have been obtained (Breger \\& Pamyatnykh 1998), but\nthe matter has to be investigated further, probably considering also the \nhigh-amplitude $\\delta$ Sct stars (Szeidl 2000). The lack of a\nwell-defined trend in the observed changes is the main difficulty to face\nwhen proposing an explanation. \n\n\\begin{figure}[ht]\n\\setlength{\\textwidth}{4.3in}\n\\plotone{eporetti3.eps}\n\\caption{4 CVn: the variability of the amplitude is evident for several modes.\nAll the available datasets are shown here}\n\\label{figcvn}\n\\end{figure}\n%\\smallskip\n%\\smallskip\n\nFrom a methodological point of view, it is important to notice the relevant\ncontribution of the measurements performed by the 0.75 m Automatic Photometric\nTelescope ``Wolfgang'' located at Washington Camp in Arizona, USA\n(Breger \\& Hiesberger 1999). As a matter of\nfact, the data are of excellent quality (standard deviation 3 mmag in\n$B$ and $V$ light), even if a variation in the brightness differences \nbetween the two comparison stars (about 2 mmag) was observed. It\ncoincides with the two subsets (each lasting 4 weeks) in which the\nmeasurements are separated by a gap of two weeks. According to the\nauthors, the sudden variation is probably a consequence of instrumental\nproblems of the APT and it is not due to the variation of the comparison stars. \nThe solution of this kind of problem can in the future ensure the\ncollection of a large quantity of good-quality data by means of robotic\ntelescopes, a new frontier for the study of $\\delta$ Sct stars.\n\n\\newpage\n\n\\subsection{Comparison between FG Vir, XX Pyx and 4 CVn}\nFigure~\\ref{figfre} shows the frequency content of the well-studied pulsators\ndescribed in this section; the combination terms are omitted. At first glance,\nit also appears that their content is completely different: high frequencies only\nfor XX Pyx, low frequencies only for 4 CVn, two groups of intermediate \nfrequency values for FG Vir. The obvious conclusion is that $\\delta$ Sct stars are\nvery complicated pulsators and that a general recipe cannot be used to predict\ntheir mode excitation.\n\n\nAs regards the similarities between $\\delta$ Sct stars it should be noted\nthat the frequency content of 4 CVn matches very closely that of HD~2724\n(Mantegazza \\& Poretti 1999): at least 7 frequencies have almost the same\nvalue. Among the high-amplitude terms in 4 CVn, only the 5.05~cd$^{-1}$\nterm has no correspondence in HD 2724. The combination frequencies, very\nnumerous in 4 CVn, are not seen in the light curve of HD 2724. This\ncan be due both to the smaller amplitude of the modes excited in HD\n2724 and to the lack of a powerful tool such as a multisite campaign, not yet\nexploited on HD 2724. The physical parameters of the two stars are very similar,\ntoo.\nSo, it seems that we can have the possibility to group stars and not\nonly to observe a different behaviour for every star.\n\n\\begin{figure}[ht]\n\\setlength{\\textwidth}{4.3in}\n\\plotone{eporetti4.eps}\n\\caption{The different distribution of the frequencies is evident in\nthe cases of XX Pyx, 4 CVn and FG Vir. Amplitudes are in mmag; combination\nterms and harmonics are not shown.}\n\\label{figfre}\n\\end{figure}\n\nThe variations of the amplitudes are a further complication, even if we can\nargue that the disappearance or the damping of some terms can enhance or\nmake discernible other modes, increasing the number of known frequencies. The\ncause of the amplitude variability is not clear: it can either be intrinsic or\noriginate from the beating of two close frequencies. Both in the case of\nXX Pyx and 4 CVn the intrinsic damping is considered by the respective authors\nas a more satisfactory explanation since the other hypothesis could not match\nsome observations.\n\n\\section{Other stars studied by the Merate Group}\nIn our effort to reveal the pulsational behaviour of\n$\\delta$ Sct stars the Merate group regularly performed some campaigns on selected objects.\nAt the beginning (second half of the eighties) there was no well-studied\nobject and the main goal of our studies was to monitor different variables\nand try to solve the light curves as satisfactorily as possible. As a matter\nof fact, the history of the worldwide observations of FG Vir started with\nour campaign in 1992 (Mantegazza et al. 1994). \n\nOur contribution to the field was guaranteed by the extensive campaigns carried\nout in Merate (as a rule one target was observed for several weeks) and at\nESO, in both cases using a 0.5-m telescope. Breger (2000b) reports on\nthe list of our campaigns.\nHere we would like to discuss some interesting cases.\n\n\\subsection{44 Tau: variable amplitude and recurrent ratio 0.77} \\label{ff}\n\nThis star has an important place in the development of the studies\nperformed by the Merate group. The intensive survey carried out in 1989\nallowed us to verify for the first time the variability of the amplitude\nof some modes; this fact drove a change in our approach\nto the study of $\\delta$ Sct stars. It was realized that a few nights on an\nobject cannot constitute a significant improvement on the knowledge of the\npulsational behaviour and therefore the planning of an observational \ncampaign must satisfy critical parameters such as frequency resolution (i.e.,\na long baseline), alias damping (long nights or, better, multisite \nobservations), evaluation of observational errors and spectral window\neffects, \\ldots\n\nSeveral datasets were available on 44 Tau and a comparison among them\nled to the detection of amplitude variations (Poretti, Mantegazza, \\&\nRiboni 1992). \nHowever, this bright star ($V$=5.5) was considered a good target \nfor other teams also; Akan (1993) and Park \\& Lee (1995) provided other intensive\ndatasets and the verification of the amplitude variations was an important\ngoal of their studies. Figure~\\ref{fff} summarizes the results: the\nthree papers quoted above supply the three values around 1990.\nThe 6.90~cd$^{-1}$ term is always the dominant one even if a slight decrease\nhas been observed in the last years, in correspondence with an increase in\nthe amplitude of the 7.01~cd$^{-1}$ term. Note also the similar behaviour of\nthe 9.12 and 9.56~cd$^{-1}$ terms and the stability of the other ones.\nThe general look of Fig.~\\ref{fff} suggests a real variation in the\namplitudes rather than the effect of uncertainties in the amplitude \ndetermination.\n\nThe frequency detected in the light curve of 44 Tau also emphasizes\nhow complicated it is to type the modes. In several old papers the\n0.77 ratio between two modes was considered as a clear fingerprint of\nthe pulsation in the fundamental and first overtone radial modes, as\nhappens in high-amplitude $\\delta$ Sct stars. However, \nseveral examples of ratios in the range 0.76-0.78 can be found among the seven\nterms: 6.90/8.96, 7.01/8.96, 6.90/9.12, 7.01/9.12, 7.30/9.56, 8.96/11.52 \n\\ldots \\@ As a consequence, it is quite evident that nonradial modes can also\nshow the same ratio even in a small bunch of terms (only seven here) \nand that trying to find two frequencies showing\na 0.77 ratio to type them as radial modes is naive and misleading.\n\nAs a final remark, it should be noted that 44 Tau is probably \na unique case in the $\\delta$ Sct scenario owing to the very\nsmall $v\\sin i$ value, i.e., 4 km~s$^{-1}$. In a certain sense,\nit proves that a multimode pulsation can be found in a slow \nrotator or in a pole-on star.\n\n\\begin{figure}[ht]\n\\setlength{\\textwidth}{4.3in}\n\\plotone{eporetti5.eps}\n\\caption{44 Tau: the values of the amplitudes are reported for all\nthe available datasets and for all the 7 detected modes. Note the\nopposite trend of the 7.01 and 9.56~cd$^{-1}$ terms. Amplitudes\nare in mag.} \n\\label{fff}\n\\end{figure}\n\n\\subsection{BH Psc: variable amplitude and rich pulsational content}\n\nBH Psc was observed by our group in 1989, 1991, 1994 and 1995 at the\nEuropean Southern Observatory, Chile. The analysis of the first two\ncampaigns showed a very complex light variability resulting from\nthe superposition of more than 10 pulsation modes with frequencies\nbetween 5 and 12~cd$^{-1}$ and semi-amplitudes between 17 and 3 mmag\n(Mantegazza, Poretti, \\& Zerbi 1995).\nThe fit left a high r.m.s.\\ residual 2.3 times greater than that\nmeasured between the two comparison stars. A second photometric campaign\nwas carried out in October and November 1994; we hoped to reveal more\nterms and to check the stability of their amplitudes. The analysis of \nthe new data allowed us to single out 13 frequencies (Mantegazza, Poretti,\n\\& Bossi 1996). They are concentrated\nin the region 5--11.5~cd$^{-1}$: this distribution is slightly larger than that\nobserved for 4 CVn, but they can be considered very similar. However, more\nterms should be present, with an amplitude below 3 mmag, since a good 15\\%\nof the variance could not be explained with the detected terms and the noise.\nMoreover, the standard deviation around the mean value was considerably\nhigher in 1991 than in 1994 (26 mmag against 18 mmag); considerations about\nthe amplitudes of the modes confirmed that the pulsation energy in 1994\nwas lower than in 1991. BH Psc constitutes another example of a $\\delta$\nSct star showing strong amplitude variations.\n\nFigure~\\ref{bhpsc} shows the fit of the 13-term solution to the $B$\nmeasurements in some nights: undetected terms are the more\nprobable explanations for the systematic deviations which\nappear on some occasions. According to the paradigm discussed in Sect.~2 and\nlooking at Fig.~\\ref{bhpsc}, we were at the point where deeper observations\nare needed and we organized \na multisite campaign in September and October 1995.\n The analysis of the 1174 $B$ and 1251 $V$ measurements \nstrengthens the hypothesis of a strong amplitude variation, probably\nas rapid as in the case of XX Pyx (Mantegazza et al., in preparation).\n\n\n\\begin{figure}[t]\n\\setlength{\\textwidth}{4.8in}\n\\plotone{eporetti6.eps}\n\\caption{BH Psc: $\\Delta B$ differential magnitudes obtained in\n1994 (dots) and their least-squares fit with the 13-sinusoid\nmodel (solid lines): note in some parts the deviations of the points from the\ncalculated light curve, which suggest the presence of undetected terms.} \n\\label{bhpsc}\n\\end{figure}\n\n\\subsection{V663 Cas: growth of new modes} \nThe solution of the light curve of V663 Cas$\\equiv$HD~16439$\\equiv$SAO~4710\nwas not an\neasy task. At the beginning it was considered as a monoperiodic pulsator with\n$f_1$=17.13~cd$^{-1}$ \n(Sedano, Rodr\\'{\\i}guez, \\& L\\'opez de Coca 1987), but an observing \ncampaign in the winter of 1988--89 \nevidenced a second peak at 10.13~cd$^{-1}$ (Mantegazza \\& Poretti\n1990). The\namplitude of this second peak is only 3 mmag, so we considered that this\nterm was not detected by Sedano et al. owing to their limited dataset.\nThe panels in the left column of Fig.~\\ref{sao} show the detection of \nthese terms in the 1988--89 dataset. The analysis of the original data\nallowed us to identify the $f_1$ term (top panel). Then the frequency\nof this term (but neither its amplitude or its phase) was introduced\nas a known constituent (k.c.) in the subsequent iteration, in which the\n$f_2$ term was detected (middle panel). Once more, these two terms were\nintroduced as k.c.'s: in this case no significant third term was revealed\n(bottom panel).\n\nStill following the paradigm of the study of the $\\delta$ Sct stars,\na second intensive campaign was performed in the winter of 1994--95 \n(Poretti, Mantegazza, \\& Bossi 1996). The\nresults of the frequency analysis are shown in the panels of the right\ncolumn of Fig.~\\ref{sao}. After the easy detection of the $f_1$ term \n(top panel), the second spectrum looks different: the structure\nat about 10~cd$^{-1}$ is more complex than the one observed in the\n1988--89 dataset (to compare the two middle panels). Indeed, after\nconsidering the $f_2$ term, a new $f_3$ term was revealed at\n10.48~cd$^{-1}$ and the noise around 18~cd$^{-1}$ was higher than\nin the 1988--89 dataset (bottom panel).\n\nSince the time\nbaseline, the number, and the standard deviation of the measurements are the\nsame for the two observing seasons, this fact cannot be related to a sampling\nproblem. Moreover, the amplitude of the $f_1$ term has slightly decreased \nfrom 15.9 to 14.0 mmag in $B$ light. By comparing the two observing\nseasons we can discern the growth of new modes in the light curve\nof V663 Cas.\n\n\\begin{figure}[t]\n\\setlength{\\textwidth}{4.3in}\n\\plotone{eporetti7.eps}\n\\caption{V663 Cas: comparison between the power spectra obtained\nin the analysis of the 1988--89 data (left column) and of the 1994--95\nones (right column). Each spectrum is obtained by considering the\nterms detected in the previous ones as known constituents (k.c.).\nThe appearance of a new term is clearly visible\ncomparing the two bottom panels.}\n\\label{sao}\n\\end{figure}\n\n\\subsection{The help of the spectroscopic approach} \\label {syn}\n\nIt is quite evident that every star carries a brick with which to\nbuild our castle of knowledge about $\\delta$ Sct pulsations, and\nresults on one star have consequences for the analysis of the next\none. However, mode identification from photometric data always leaves\nsome uncertainties. For this reason we turned toward spectroscopy:\nindependent constraints on mode typing and detection of low and high\ndegree $\\ell$ modes can be obtained from the analysis of the time\nseries of the individual pixels defining the line profiles. Moreover,\ntrying to fill the gap between the output of the observations and\nthe inputs for a reliable pulsational model, we tried to discriminate\nbetween different modes through a direct fit of pulsational model to\nspectroscopic and photometric data. Such a {\\it synergic} approach is\ndescribed by Mantegazza (2000).\n\n\n\\section{Monoperiodic pulsators}\n\nIt is a quite accepted concept that detecting as many frequencies as\npossible in the light curves is mandatory in order to make progress\nin the field of asteroseismology. Only in this way is it possible to\ncompare the values predicted by the theoretical models with the observed\nones. Consequently, the observation of monoperiodic stars has been put\naside in the last decade. However, even these variables display a wide\nvariety of intriguing behaviour. \n\n\\subsubsection{Beta Cas:} It is probably the best known monoperiodic\npulsator, also included in the secondary target list of the MONS\nsatellite. Riboni, Poretti, \\& Galli (1994) proved that a constant value\nof the frequency cannot fit the times of maximum brightness collected\nsince 1965; on the other hand, a constant value (9.897396~cd$^{-1}$)\ncan fit all the datasets since 1983. Hence, a probable variation of the\nperiod occurred between 1965 and 1983. On the other hand, the amplitude\nhas remained stable ($\\Delta V$~=~0.03 mag) over a 25-year baseline since\nno significant variation could be inferred. Considering the value of\nthe period (0.101 d), this behaviour is typical for a high-amplitude\n$\\delta$ Sct star rather than for a small amplitude one.\n\n\\subsubsection{\\it AZ CMi:} The light curve of AZ CMi is asymmetrical\n($R_{21}$=0.13 in $V$ light; Poretti 2000) and very stable in shape and\namplitude ($\\Delta V$=0.055 mag); hints of a possible decreasing value\nof the amplitude need more observations to be confirmed. $B$ and $V$\nphotometry is available: the measured phase shift is $\\phi_{B-V}-\\phi_V$=\n--9$\\pm$9 degrees. Since it is negative, such a value slightly suggests\na nonradial mode, but the error bar hampers a definite identification\n(Poretti et al. 1996).\n\n\\smallskip\n\nThe examples reported above seem to suggest that monoperiodic stars are\nsimple and stable pulsators even if the ambiguity\nbetween radial or nonradial modes cannot be solved. However, the analysis of \nother cases complicates the scenario a little:\n\\smallskip\n\n\\subsubsection{\\it BF Phe:} All the measurements available on this star\nare well satisfied by the single term $f$=16.0166 ~cd$^{-1}$ (Poretti et\nal. 1996). The reality of a secondary peak was discussed and, at the end,\nrejected. The amplitude observed in 1991 in $V$ light is very similar to\nthat observed in 1993 in $y$ light. However, in $b$ light the amplitude\nobserved in 1989 (25 mmag) is larger than that observed in 1993 (16 mmag)\nand this discrepancy cannot be explained by errors in the measurements;\nunfortunately BF Phe was measured in 1989 in the $b$-light only. Hence,\nthis monoperiodic pulsator shows an amplitude that has changed by a\nfactor of 1.7 in two years, if we consider the amplitude was the same\nin 1991 and 1993.\n\n\\subsubsection{\\it 28 And:} Rodr\\'\\i guez et al. (1993) demonstrated\nthat 28 And$\\equiv$GN And is a monoperiodic pulsator. They carried out\na frequency analysis on the datasets available in the literature and when\nthe main frequency is prewhitened the resulting periodograms do not show\nany trace of another significant peak. New $uvby$ photometric data were\nacquired in 1996 (Rodr\\'\\i guez et al. 1998); the observed amplitude\nof the light curves is very small compared with any other previous\ndataset. More precisely, the amplitude was about 19 times smaller than\nthat observed five years before. In this new dataset a second term was\ndetected; however, the reality of this term is not well-established,\nsince it is marginally significant (S/N=4.1 and other smaller peaks are\nvisible in the power spectrum). Further observations are requested to\nverify if 28 And will display a pulsational behaviour similar to that\nof V663 Cas, with new frequencies slowly growing to a detectable level.\n\nThe cases of genuine monoperiodic $\\delta$ Sct stars as BF Phe and\n(probably) 28~And yield the observational evidence that in\nthese pulsators also the amplitudes of the excited modes are affected\nby variations. Moreover, a multiperiodic pulsator as V663 Cas can show \na different pulsational content in different seasons, greatly complicating\nobservational investigation. \nAs a matter of fact we proved that the changing amplitude is not\na prerogative of pulsators with a large number of excited modes (as observed\nin XX Pyx, 4 CVn and 44 Tau). It is also possible to find a $\\delta$ Sct\npulsator displaying a single period with a very small amplitude:\nthe light curve of HD~19279 has a full amplitude of only 4.2 mmag\n(Mantegazza \\& Poretti 1993).\n\nMoreover, the detection of a single frequency in the light curve is not\nan indication of radial pulsation for $\\delta$ Sct stars of low amplitude.\nTable \\ref{tabmono} lists the physical parameters as determined\n by means of Hipparcos parallaxes and Str\\\"omgren\nphotometry: as can be noticed, these stars display a large variety of \npulsational constants $Q$'s and, hence, different excited modes.\n\\vspace*{-1.0em}\n\n\n\\begin{table}[b!]\n\\caption{Determination of the pulsational constant $Q$ for the monoperiodic\n$\\delta$ Sct stars discussed here. M$_{\\rm bol}$ values were determined by\nusing the Hipparcos parallaxes} \\label {tabmono}\n\\begin{center}\n%\\scriptsize\n\\small\n\\begin{tabular}{llr c r r r r}\n\\tableline\n \\multicolumn{2}{c}{Star} & HIP & & \\multicolumn{1}{c}{T$_{\\rm eff}$} &\n \\multicolumn{1}{c}{$\\log$ g} & \\multicolumn{1}{c}{M$_{\\rm bol}$} &\n \\multicolumn{1}{c}{$Q$} \\\\\n \\multicolumn{2}{c}{ } & & & \\multicolumn{1}{c}{[K]} &\n \\multicolumn{1}{c}{} & \\multicolumn{1}{c}{} &\n \\multicolumn{1}{c}{[d$^{-1}$]} \\\\\n%\\hline\n\\tableline \n\\noalign{\\smallskip}\nAZ & CMi & 37705 & & 7800 & 3.6 & 0.8 & 0.020 \\\\\nBF & Phe & 117515& & 7500 & 4.1 & 2.5 & 0.034 \\\\\n28 & And & 2355 & & 7500 & 3.7 & 1.4 & 0.018 \\\\\n$\\beta$ & Cas & 746 & & 7000 & 3.6 & 1.2 & 0.020 \\\\\n%$\\tau$ & Peg & & 8180 & 3.8 & 1.0 & 0.016 \\\\\n\\noalign{\\smallskip}\n\\tableline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\section{$\\delta$ Sct stars in binary systems}\nIn principle, the study of $\\delta$ Sct stars belonging to binary\nsystems can supply useful suggestions to understand the physics\nof the pulsation driving. The complications introduced by the \ncompanion are much less important than the measurable parameters we can\nattain. Lampens \\& Boffin (2000) provide a review on\n$\\delta$ Sct stars in stellar systems. Here we would like \nto draw attention to a few binary systems:\n\\smallskip\n\n\\subsubsection{$\\theta^2$ {\\it Tau}:} It is the component of a wide binary\n($P$=140.728~d) and there is no interaction between the two\nstars. However, it is a well-studied pulsator. Breger et al. (1989)\ndetermined five frequencies, very close to each other (from 13.23 to\n14.62~cd$^{-1}$), without regular spacing among them. Such a very close\n(much closer than in the case of 4 CVn), isolated multiplet is not usual\nin the solution of light curves. The amplitudes of the modes seem to be\nvery stable, even if recently Zhiping, Aiying, \\& Dawei (1997) claimed\nto have evidence of amplitude variations; further campaigns could be useful\nto clarify the matter.\n\n\\subsubsection{$\\theta$ {\\it Tuc:}} This double line spectroscopic\nbinary is located near the South Celestial Pole, which makes it very\nsuitable for long-term monitoring. The orbital period is 7.1036 d;\na regular spacing is observed among the 10 detected frequencies, which\ntake place in the interval 15.8--20.3~cd$^{-1}$ (Papar\\'o et al. 1996).\nLow-frequency terms have been observed and they are ascribed to the\norbital period. The mode identification was performed by Sterken (1997)\nusing the Str\\\"omgren photometry: the results are not conclusive for\nmost of the frequencies, but the $f$=20.28~cd$^{-1}$ is reconcilable with\na radial mode. De Mey, Daems, \\& Sterken (1998) confirmed this result\nand they also found that the system has a very low mass ratio, $q$=0.09.\nThe possibility that the regular spacing is related to the slow rotation\nof the $\\delta$ Sct star deserves further attention. De Mey et al. (1998)\nalso found 1.7$\\,$$
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astro-ph0002203
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Nuclear Matter and its Role in Supernovae, Neutron Stars and Compact Object Binary Mergers\thanksref{X}
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"author": "James M. Lattimer"
}
] |
The equation of state (EOS) of dense matter plays an important role in the supernova phenomenon, the structure of neutron stars, and in the mergers of compact objects (neutron stars and black holes). During the collapse phase of a supernova, the EOS at subnuclear densities controls the collapse rate, the amount of deleptonization and thus the size of the collapsing core and the bounce density. Properties of nuclear matter that are especially crucial are the symmetry energy and the nuclear specific heat. The nuclear incompressibility, and the supernuclear EOS, play supporting roles. In a similar way, although the maximum masses of neutron stars are entirely dependent upon the supernuclear EOS, other important structural aspects are more sensitive to the equation of state at nuclear densities. The radii, moments of inertia, and the relative binding energies of neutron stars are, in particular, sensitive to the behavior of the nuclear symmetry energy. The dependence of the radius of a neutron star on its mass is shown to critically influence the outcome of the compact merger of two neutron stars or a neutron star with a small mass black hole. This latter topic is especially relevant to this volume, since it stems from research prompted by the tutoring of David Schramm a quarter century ago.
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[
{
"name": "paper_lp.tex",
"string": "\\documentclass{elsart}\n\\usepackage{natbib}\n\\begin{document}\n\\runauthor{Lattimer, James M}\n\\begin{frontmatter}\n\\title{Nuclear Matter and its Role in Supernovae, Neutron Stars\nand Compact Object Binary Mergers\\thanksref{X}}\n\\author[SUNYSB]{James M. Lattimer} and\n\\author[SUNYSB]{Madappa Prakash}\n\\thanks[X]{Partially supported by USDOE Grants DE-AC02-87ER40317 and\nDE-FG02-88ER-40388,\nand by NASA ATP Grant \\# NAG 52863.}\n\\address[SUNYSB]{Dept. of Physics \\& Astronomy, State University of New York at\nStony Brook,\nStony Brook, NY 11794-3800}\n\\begin{abstract}\nThe equation of state (EOS) of dense matter plays an important role in the\nsupernova phenomenon, the structure of neutron stars, and in the\nmergers of compact objects (neutron stars and black holes). During\nthe collapse phase of a supernova, the EOS at subnuclear\ndensities controls the collapse rate, the amount of deleptonization\nand thus the size of the collapsing core and the bounce density.\nProperties of nuclear matter that are especially crucial are the\nsymmetry energy and the nuclear specific heat. The nuclear\nincompressibility, and the supernuclear EOS, play\nsupporting roles. In a similar way, although the maximum masses of\nneutron stars are entirely dependent upon the supernuclear EOS,\nother important structural aspects are more sensitive to the\nequation of state at nuclear densities. The radii, moments of\ninertia, and the relative binding energies of neutron stars are, in\nparticular, sensitive to the behavior of the nuclear symmetry energy.\nThe dependence of the radius of a neutron star on its mass is shown to\ncritically influence the outcome of the compact merger of two neutron\nstars or a neutron star with a small mass black hole. This latter\ntopic is especially relevant to this volume, since it stems from\nresearch prompted by the tutoring of David Schramm a quarter century\nago.\\end{abstract}\n\\begin{keyword}Nuclear Matter; Supernovae; Neutron Stars; Binary Mergers\n\\PACS 26.50.+x \\sep 26.60.+c \\sep 97.60.Bw \\sep 97.60.Jd \\sep 97.80.-d\n\\end{keyword}\\end{frontmatter}\n\\section{Introduction}\nThe equation of state (EOS) of dense matter plays an important role in\nthe supernova phenomenon and in the structure and evolution of neutron\nstars. Matter in the collapsing core of a massive star at the end of\nits life is compressed from white dwarf-like densities of about $10^6$\ng cm$^{-3}$ to two or three times the nuclear saturation density,\nabout $3\\cdot10^{14}$ g cm$^{-3}$ or $n_s=0.16$ baryons fm$^{-3}$. The\ncentral densities of neutron stars may range up to 5--10 $n_s$. At\ndensities around $n_s$ and below matter may be regarded as a mixture\nof neutrons, protons, electrons and positrons, neutrinos and\nantineutrinos, and photons. At higher densities, additional\nconstituents, such as hyperons, kaons, pions and quarks may be\npresent, and there is no general consensus regarding the properties of\nsuch ultradense matter. Fortunately for astrophysics, however, the\nsupernova phenomenon and many aspects of neutron star structure may\nnot depend upon ultradense matter, and this article will focus on the\nproperties of matter at lower densities.\n\nThe main problem is to establish the state of the nucleons, which may\nbe either bound in nuclei or be essentially free in continuum states.\nNeither temperatures nor densities are large enough to excite\ndegrees of freedom, such as hyperons, mesons or quarks.\nElectrons are rather weakly interacting and may be treated as an ideal\nFermi gas: at densities above $10^7$ g cm$^{-3}$, they are\nrelativisitic. Because of their even weaker interactions, photons and\nneutrinos (when they are confined in matter) may also be treated as\nideal gases.\n\nAt low enough densities and temperatures, and provided the matter does\nnot have too large a neutron excess, the relevant nuclei are stable in\nthe laboratory, and experimental information may be used directly.\nThe so-called Saha equation may be used to determine their relative\nabundances. Under more extreme conditions, there are a number of\nimportant physical effects which must be taken into account. At\nhigher densities, or at moderate temperatures, the neutron chemical\npotential increases to the extent that the density of nucleons outside\nnuclei can become large. It is then important to treat matter outside\nnuclei in a consistent fashion with that inside. These nucleons will\nmodify the nuclear surface, decreasing the surface tension. At finite\ntemperatures, nuclear excited states become populated, and these\nstates can be included by treating nuclei as warm drops of nuclear\nmatter. At low temperatures, nucleons in nuclei are degenerate and\nFermi-liquid theory is probably adequate for their description.\nHowever, near the critical temperature above which the dense phase of\nmatter inside nuclei can no longer coexist with the lighter phase of\nmatter outside nuclei, the equilibrium of the two phases of matter is\ncrucial.\n\nThe fact that at subnuclear densities the spacing between nuclei may\nbe of the same order of magnitude as the nuclear size itself will lead\nto substantial reductions in the nuclear Coulomb energy. Although\nfinite temperature ``plasma'' effects will modify this, the\nzero-temperature Wigner-Seitz approximation employed by Baym, Bethe\n\\& Pethick~\\cite{BBP} is usually adequate. Near the nuclear\nsaturation density, nuclear deformations must be dealt with, including\nthe possibilities of ``pasta-like'' phases and matter turning\n``inside-out'' ({\\it i.e.}, the dense nuclear matter envelopes a\nlighter, more neutron-rich, liquid). Finally, the translational\nenergy of the nuclei may be important under some conditions. This\nenergy is important in that it may substantially reduce the average\nsize of the nuclear clusters.\n\nAn acceptable way of bridging the regions of low density and\ntemperature, in which the nuclei can be described in terms of a simple\nmass formula, and high densities and/or high temperatures in which the\nmatter is a uniform bulk fluid, is to use a compressible liquid\ndroplet model for nuclei in which the drop maintains thermal,\nmechanical, and chemical equilibrium with its surroundings. This\nallows us to address both the phase equilibrium of nuclear matter,\nwhich ultimately determines the densities and temperatures in which\nnuclei are permitted, and the effects of an external nucleon fluid on\nthe properties of nuclei. Such a model was originally developed by\nLattimer {\\it et al.\\/} \\cite{LPRL} and modified by Lattimer \\&\nSwesty~\\cite{LS}. This work was a direct result of David Schramm's\nlegendary ability to mesh research activities of various groups, in\nthis case to pursue the problem of neutron star decompression. After\nthe fact, the importance of this topic for supernovae became apparent.\n\n\\section{Nucleon Matter Properties}\n\nThe compressible liquid droplet model rests upon\nthe important fact that in a many-body system\nthe nucleon-nucleon interaction exhibits saturation.\nEmpirically, the energy per particle of bulk nuclear matter\nreaches a minimum, about --16 MeV, at a density\n$n_s\\cong 0.16~{\\rm fm}^{-3}$.\nThus, close to $n_s$, its\ndensity dependence is approximately parabolic. The nucleon-nucleon\ninteraction is optimized for equal numbers of neutrons and protons\n(symmetric matter), so a parabolic dependence on the neutron\nexcess or proton fraction, $x$, can be assumed. About a third to a\nhalf of the energy\nchange made by going to asymmetric matter is due to the nucleon\nkinetic energies, and to a good approximation, this varies as\n$(1-2x)^2$ all the way to pure neutron matter ($x=0$). The $x$\ndependence of the potential terms in most theoretical models can also\nbe well approximated by a quadratic dependence.\nFinally, since at low temperatures the\nnucleons remain degenerate, their temperature dependence to\nleading order is also quadratic. Therefore, for analytical purposes,\nthe nucleon free energy per baryon can be approximated as\n$f_{bulk}(n,x)$, in MeV, as\n\\begin{eqnarray}\nf_{bulk}(n,x)\\simeq-16+S_v(n)(1-2x)^2+{K_s\\over18}\\Biggl({n\\over\nn_s}-1\\Biggr)^2\\cr\n-{K^\\prime_s\\over27}\\Biggl({n\\over\nn_s}-1\\Biggr)^3-a_v(n,x)T^2 \\,,\\label{bulk}\n\\end{eqnarray}\nwhere $a_v(n)=(2m^*/\\hbar^2)(\\pi/12n)^{2/3}$. The expansion\nparameters, whose values are uncertain to varying degrees, are the\nincompressibility, $K_s=190-250$ MeV, the skewness parameter\n$K_s^\\prime=1780-2380$ MeV, the symmetry energy coefficient $S_v\\equiv\nS_v(n_s)=25-36$ MeV, and the bulk level density parameter,\n$a_v(n_s,x=1/2)\\simeq(1/15)(m^*(n_s,x=1/2)/m)$ MeV$^{-1}$, where $m^*$\nis the effective mass of the nucleon. Values for $m^*(n_s,x=1/2)/m$\nare in the range $0.7-0.9$. The general definition of the\nincompressibility is $K=9dP/dn=9d(n^2df_{bulk}/dn)/dn$, where $P$ is\nthe pressure, and $K_s\\equiv K(n_s,1/2)$. It is worthwhile noting\nthat the symmetry energy and nucleon effective mass (which directly\naffects the matter's specific heat) are density dependent, but these\ndependencies are difficult to determine from experiments. The\nparameters, and their density dependences, characterize the nuclear\nforce model and are essential to our understanding of astrophysical\nphenomena.\n\nThe experimental determination of these parameters has come from\ncomparison of the total masses and energies of giant resonances of laboratory\nnuclei with theoretical predictions. Some of these comparisons are\neasily illustrated with the compressible liquid droplet model. In\nthis model, the nucleus is treated as uniform drop of nuclear matter\nwith temperature $T$, density $n_i$ and proton fraction $x_i$. The\nnucleus will, in general, be surrounded by and be in equilibrium with\na vapor of matter with density $n_o$ and proton fraction $x_o$. At\nlow ambient densities $n$ and vanishing temperature, the outside vapor\nvanishes. Even at zero temperature, if $n$ is large enough, greater\nthan the so-called neutron drip density $n_d\\simeq1.6\\cdot10^{-3}$\nfm$^{-3}$, the neutron chemical potential of the nucleus is positive\nand ``free'' neutrons exist outside the nucleus. At finite\ntemperature, the external vapor consists of both neutrons and protons.\nIn addition, because of their high binding energy, $\\alpha-$particles\nwill also be present. The total free energy density is the sum of the\nvarious components:\n\\begin{equation}\nF=F_H+F_o+F_\\alpha+F_e+F_\\gamma\\,.\n\\end{equation}\nHere, $F_H$ and $F_o$ represent the free energy densities of the heavy\nnuclei and the outside vapor, respectively. The energy densities of\nthe electrons and photons, $F_e$ and $F_\\gamma$, are independent of\nthe baryons and play no role in the equilibrium. For simplicity, we\nneglect the role of $\\alpha$-particles in the following discussion\n(although it is straightforward to include their effect~\\cite{LPRL}).\n\nIn the compressible liquid drop model, it is assumed that the nuclear\nenergy can be written as an expansion in $A^{1/3}$ and $(1-2x_i)^2$:\n\\begin{equation}\nF_H=un_i[f_{bulk}+f_{surf}+f_{Coul}+f_{trans}]\\,,\\label{ftot}\n\\end{equation}\nwhere the $f$'s represent free energies per baryon due to the bulk,\nsurface, Coulomb, and translation, respectively. The bulk energy, for\nexample, is given by Eq.~(\\ref{bulk}). The surface energy can be\nparametrized as\n\\begin{equation}f_{surf}=4\\pi R^2\\sigma(x_i,T)\\equiv4\\pi R^2h(T)[\\sigma_o-\\sigma_s(1-2x_i)^2]\\,,\\label{fsurf}\n\\end{equation}\nwhere $R$ is the nuclear charge radius,\n$h(T)$ is a calculable function of temperature,\n$\\sigma_o$ is the surface tension of symmetric matter, \nand $\\sigma_s=(n_i^2/36\\pi)^{1/3}S_s$ where $S_s$ is the\nsurface symmetry energy coefficient from the traditional mass formula. In\nthis simplified discussion, the influence of the neutron\nskin~\\cite{LPRL}, which distinguishes the ``drop model'' from the ``droplet\nmodel'', is omitted. The Coulomb energy, in the Wigner-Seitz\napproximation~\\cite{BBP}, is\n\\begin{equation}\nf_{Coul}=0.6x_i^2A^2e^2D(u)/R\\,,\\label{fcoul}\n\\end{equation}\nwhere $D(u)=1-1.5u^{1/3}+0.5u$ and $u$ is the fraction of the\nvolume occupied by nuclei. If the fractional mass of matter outside\nthe nuclei is small, $u\\simeq n/n_i$.\n\nIt is clear that additional parameters, $S_s$ and another involving\nthe temperature dependence of $h$, exist in conjunction with those\ndefining the expansions of the bulk energy. The temperature\ndependence is related to the matter's critical temperature $T_c$ at\nwhich the surface disappears. It is straightforward to demonstrate\nfrom the thermodynamic relations defining $T_c$, namely $\\partial\nP_{bulk}/\\partial n=0$ and $\\partial^2 P_{bulk}/\\partial n^2=0$, that\n$T_c\\propto \\sqrt{K_s}$. Therefore, the specific heat to be\nassociated with the surface energy will in general be proportional to\n$T_c^{-2}\\propto K_s^{-1}$. About half the total specific\nheat originates in the surface, so $K_s$ influences the temperature\nfor a given matter entropy, important during stellar collapse.\n\nThe equilibrium between nuclei and their surroundings is determined by\nminimizing $F$ with respect to its internal variables, at fixed\n$n,Y_e$, and $T$. This is described in more detail in Refs.~\\cite{LPRL,\nLS}, and leads to equilibrium conditions involving the pressure and the\nbaryon chemical potentials, as well\nas a condition determining the nuclear size $R$. The latter is analogous\nto the one found by Baym, Bethe \\& Pethick~\\cite{BBP} who equated\nthe nuclear surface energy with twice the Coulomb energy. The\nrelations in Eqs.~(\\ref{fsurf}) and (\\ref{fcoul}) lead to\n\\begin{equation}\nR=\\Biggl[{15\\sigma(x_i)\\over8\\pi e^2 x_i^2\nn_i^2}\\Biggr]^{1/3}\\,.\n\\end{equation}\nExperimental limits to $K_s$, most importantly from RPA analyses of\nthe breathing mode of the giant monopole resonance~\\cite{Blaizot}, give\n$K_s\\cong230$ MeV. It is also possible to obtain values from the\nso-called scaling model developed from the compressibile liquid drop\nmodel. The finite-nucleus incompressibility is\n\\begin{equation}\nK(A,Z)=(M/\\hbar^2)R^2E^2_{br}\\,,\\end{equation} where $M$ is the\nmass of the nucleus and $E_{br}$ is the breathing-mode\nenergy. $K(A,Z)$ is commonly expanded as\n\\begin{equation}\nK(A,Z)=K_s+K_{surf}A^{-1/3}+K_{vI}I^2+K_{surfI}I^2A^{-1/3}\n+K_CZ^2A^{-4/3}\\,,\\label{compaz}\\end{equation} and then fit by\nleast squares to the data for $E_{br}$. Here the asymmetry\n$I=1-2Z/A$. For a given assumed value of $K_s$, and taking\n$K_{surfI}=0$, Pearson~\\cite{P}\nshowed that experimental data gave\n\\begin{eqnarray}K_C\\simeq15.4-0.065 K_s\\pm2 {\\rm~MeV}\\,,\\quad\nK_{surf}\\simeq230-3.2 K_s\\pm50 {\\rm~MeV}\\,.\\label{constr}\\end{eqnarray}\nWith minimal assumptions regarding the form of the nuclear force,\nPearson~\\cite{P} demonstrated that values of $K_s$ ranging from\n200 MeV to more than 350 MeV could be consistent with experimental\ndata.\n\nBut the liquid drop model predicts other relations between the parameters:\n\\begin{eqnarray}K(A,Z)&=&R^2{\\partial^2 E(Z,A)/A\\over\\partial\nR^2}\\Biggr|_A=9n^2{\\partial^2E(Z,A)/A\\over\\partial n^2}\\Biggr|_A\\,,\\cr\n0=P(A,Z)&=&R{\\partial^2 E(Z,A)/A\\over\\partial R}\\Biggr|_A=3n{\\partial\nE(Z,A)/A\\over\\partial n}\\Biggr|_A\\,.\n\\end{eqnarray}\nHere $E(Z,A)$ is the total energy of the nucleus, and is equivalent to\nEq.~(\\ref{ftot}). The second of these equations simply expresses the\nequilibrium between the nucleus and the surrounding vacuum, which\nimplies that the pressure of the bulk matter inside the nucleus is\nbalanced by the pressure due to the curvature of the surface and the\nCoulomb energy. It can then be shown that\n\\begin{eqnarray}\nK_C&=&-(3e^2/5r_o)[8+27n_s^3f_{bulk}^{\\prime\\prime\\prime}(n_s)/K_s]\\,,\\cr\nK_{surf}&=&4\\pi r_o^2\\sigma_o[9n_s^2\\sigma_o^{\\prime\\prime}/\\sigma_o+22+\n54n_s^3f_{bulk}^{\\prime\\prime\\prime}(n_s)/K_s]\\,,\\cr\nK_{surfI}&=&4\\pi r_o^2\\sigma_s[9n_s^2\\sigma_s^{\\prime\\prime}/\\sigma_s+22+\n54n_s^3f_{bulk}^{\\prime\\prime\\prime}(n_s)/K_s]\\,,\\cr\nK_I&=&9[n_s^2S_v^{\\prime\\prime}(n_s)-2n_oS_v^\\prime(n_s)-9n_s^4S_v^\\prime(n_s)\nf_{bulk}^{\\prime\\prime\\prime}(n_s)/K_s]\\,.\\label{dropcomp}\n\\end{eqnarray}\nPrimes denote derivatives with respect to the density. From these\nrelations, and again assuming $K_{surfI}=0$, Pearson demonstrated that\nan interesting correlation between $K_s$ and $K^\\prime_s$, where\n$K^\\prime_s\\equiv-27n_s^3f_{bulk}^{\\prime\\prime\\prime}(n_s)$, could be\nobtained:\n\\begin{equation}\nK^\\prime_s=-0.0860K_s^2+(28.37\\pm2.65)K_s\\,.\\label{comp}\\end{equation}\nAssuming $K_s\\simeq190-250$ MeV, this suggests that\n$K_s^\\prime=1780-2380$ MeV, a potential constraint.\nAlternatively, eliminating $K_s^\\prime$, one finds\n\\begin{equation}\nK_s=137.4-26.36n_s^2\\sigma_o^{\\prime\\prime}/\\sigma_o\\pm23.2\n{\\rm~MeV}\\,.\\end{equation} The second derivative of the surface\ntension can be deduced from Hartree-Fock or Thomas-Fermi semi-infinite\nsurface calculations. For example, if a parabolic form of $f_{bulk}$\nis used, one finds\n\\begin{equation}\nn_s^2\\sigma_o^{\\prime\\prime}/\\sigma_o=-6\\end{equation} leading to\n$K_s=295.5\\pm23.2$ MeV. In general, the density dependence of $S_v$\nwill decrease the magnitudes of $K_s$ and $\\sigma_o^{\\prime\\prime}$\nfrom the above values.\n\nIt is hoped current experimental work will tighten these constraints.\nA shortcoming of the scaling model is that, to date, the surface\nsymmetry energy term was neglected. This is not required, however,\nand further work is necessary to resolve this matter.\n\nBecause the surface energy represents the energy difference between uniformly\nand realistically distributed nuclear material in a nucleus, the\nparameter $S_s$ can be related to the density dependence of $S_v(n)$ and\nto $K_s$. If $f_{bulk}$ is assumed to behave quadratically with\ndensity around $n_s$, this relation can be particularly simply\nexpressed~\\cite{L}:\n\\begin{equation}\n{S_s\\over S_v}={3\\over\\sqrt{2}}{a_{1/2}\\over r_o}\\int_0^1\n{\\sqrt{x}\\over1-x}\\Biggl[{S_v\\over S_v(xn_s)}-1\\Biggr]dx. \\end{equation}\nHere, $S_v\\equiv S_v(n_s)$, $a_{1/2}=(dr/d\\ln n)_{n_s/2}$ is a measure\nof the thickness of the nuclear surface and $r_o=(4\\pi\nn_s/3)^{-1/3}=R/A^{1/3}$. If $S_v(n)$ is linear, then the integral is\n2; if $S_v(n)\\propto n^{2/3}$, then the integral is 0.927. Since\n$a_{1/2}$ will be sensitive to the value of $K_s$, we expect the value\nof $S_s/S_v$ to be also.\n\nExperimentally, there are two major sources of information regarding\nthe symmetry energy parameters: nuclear masses and giant resonance energies.\nHowever, because of the small excursions in $A^{1/3}$ afforded by\nlaboratory nuclei, each source provides only a correlation between\n$S_s$ and $S_v$. For example, the total symmetry energy in\nthe liquid droplet model (now explicitly including the presence of the\nneutron skin, see Ref.~\\cite{LPRL}) is\n\\begin{equation}\nE_{sym}=(1-2x_i)^2S_v/[1+(S_s/S_v)A^{-1/3}].\n\\end{equation}\nEvaluating $\\alpha=d \\ln S_s/d \\ln S_v$ near the ``best-fit''\nvalues $S_{s0}$ and $S_{v0}$, one finds\n\\begin{equation}\n\\alpha\\simeq2+S_{v0}<A>^{1/3}/S_{s0}\\simeq6\\,,\\label{ssfit}\n\\end{equation}\nwhere $<A>^{1/3}$ for the fitted nuclei is about 5. Thus, as the\nvalue of $S_v$ is changed in the mass formula, the value of $S_s$ must\nvary rapidly to compensate.\n\nAn additional correlation between these parameters can be obtained\nfrom the fitting of isovector giant resonances, and this has the\npotential of breaking the degeneracy of $S_v$ and $S_s$, because it\nhas a different slope~\\cite{L}. Lipparini \\& Stringari~\\cite{Lip}\nused a hydrodynamical model of the nucleus to derive the isovector\nresonance energy:\n\\begin{eqnarray}\nE_d&=&\\sqrt{{24\\hbar^2\\over m^*}{NZ\\over A} \\Bigl[\\int\n{nr^2S_v\\over S_v(n)} d^3r\\Bigr]^{-1}}\\cr&\\simeq&96.5\\sqrt{{m\\over\nm^*}\n{S_v\\over30{\\rm~MeV}}\\Biggl[1+{5S_s\\over3S_vA^{1/3}}\\Biggr]^{-1}}A^{-1/3}\n{\\rm~MeV},\n\\label{lsdip}\n\\end{eqnarray}\nwhere $m^*$ is an effective nucleon mass. This relation results in a\nslightly less-steep correlation between $S_s$ and $S_v$,\n\\begin{equation}\n\\alpha=2/m^*+(3/5)S_{v0}<A>^{1/3}/S_{s0}\\simeq4-5\\,.\n\\end{equation}\nUnfortunately the value\nof $m^*$ is an undetermined parameter and this slope is not very\ndifferent from that obtained from fitting masses. Therefore,\nuncertainties in the model make a large difference to the crossing\npoint of these two correlations. A strong theoretical attack,\nperhaps using further RPA analysis,\ntogether with more experiments to supplement\nthe relatively meager amount of existing data, would be very useful.\n\n\\section{The Equation of State and the Collapse of Massive Stars}\n\nMassive stars at the end of their lives are believed to consist of a\nwhite dwarf-like iron core of 1.2--1.6 M$_\\odot$ having low entropy\n($s\\le1$), surrounded by layers of less processed material from shell\nnuclear burning. The effective Chandrasekhar mass, the maximum mass\nthe degenerate electron gas can support, is dictated by the entropy\nand the average lepton content, $Y_L$, believed to be around\n0.41--0.43. As mass is added to the core by shell Si-burning, the\ncore eventually becomes unstable and collapses.\n\nDuring the collapse, the lepton content decreases due to net electron\ncapture on nuclei and free protons. But when the core density\napproaches $10^{12}$ g cm$^{-3}$, the neutrinos can no longer escape\nfrom the core on the dynamical collapse time~\\cite{Sato}. After\nneutrinos become trapped, $Y_L$ is frozen at a value of about\n0.38--0.40, and the entropy is also thereafter fixed. The core\ncontinues to collapse until the rapidly increasing pressure reverses\nthe collapse at a bounce density of a few times nuclear density.\n\nThe immediate outcome of the shock generated by the bounce is also\ndependent upon $Y_L$. First, the shock energy is determined by the\nnet binding energy of the post-bounce core, and is proportional to\n$Y_e^{10/3}$~\\cite{LBY}. Second, the shock is largely dissipated by\nthe energy required to dissociate massive nuclei in the\nstill-infalling matter of the original iron core outside the\npost-bounce core. The larger the $Y_L$ of the core, the larger its\nmass and the smaller this shell. Therefore, the progress of the shock\nis very sensitive to the value of $Y_L$.\n\nThe final value of $Y_L$ is controlled by weak interaction rates, and\nis strongly dependent upon the fraction of free protons, $X_p$, which\nis proportional to $\\exp (\\mu_p/T)$, and the phase space available for\nproton capture on nuclei, which is proportional to $\\mu_e-\\hat\\mu$, where\n$\\hat\\mu=\\mu_n-\\mu_p$. Both are sensitive to the proton fraction in\nnuclei ($x_i$) and are largely controlled by $Y_L$. In addition, the\nspecific heat controls the temperature which has a direct\ninfluence upon the free proton abundance and the net electron capture\nrate. In spite of the intricate feedback, nuclear parameters\nrelating chemical potentials to composition, especially $S_v$ and\n$S_s$, are obviously important.\n\n\\begin{figure}[h]\n\\vspace{24pc}\n\\special{psfile=muhat.ps hoffset=430 voffset=-20 hscale=58 vscale=58\nangle=90}\n\\caption{Comparison of $\\hat\\mu=\\mu_n-\\mu_p$ as a function of $x_i$\nfor various assumed values of $S_v$, both including and excluding the\neffects of the surface symmetry energy.}\n\\label{muhat}\n\\end{figure}\n\nAs an example, consider\n$\\hat\\mu=\\mu_n-\\mu_p=-{n_i}^{-1}\\partial F_H/\\partial x_i$.\nWith the model of Eqs.~(\\ref{ftot})-(\\ref{fcoul}), one has\n\\begin{equation}\\hat\\mu=4S_v(1-2x_i)-\\Biggl({72\\pi e^2D\\over5x_in_i}\\Biggr)^{1/3}\n{\\sigma_o-\\sigma_s(1-2x_i)(1-6x_i)\\over(\\sigma_o-\\sigma_s(1-2x_i)^2)^{1/3}}\\,.\n\\label{muhate}\\end{equation}\nRecall that $\\sigma_s\\propto S_s$. Although the bulk and Coulomb terms alone\n(Eq.~\\ref{muhate} with $\\sigma_s=0$) imply that $\\hat\\mu$ for a given\n$x_i$ rises with increasing $S_v$, the proper inclusion of the surface\nsymmetry energy gives rise to the opposite behavior. This is\nillustrated in Fig.~\\ref{muhat}.\n\n\\begin{figure}[h]\n\\vspace{25pc}\n\\special{psfile=nulum.plt hoffset=-40 voffset=310 hscale=58 vscale=55\nangle=270}\n\\caption{The neutrino luminosities during infall as a function of the\nbulk symmetry energy parameter.}\n\\label{nulum}\n\\end{figure}\n\nUncertainties in nuclear parameters can thus be expected to have an\ninfluence upon the collapse of massive stars, for example, in the\ncollapse rate, the final trapped lepton fraction, and the radius at\nwhich the bounce-generated shock initially stalls. Swesty, Lattimer\n\\& Myra~\\cite{SLM} investigated the effects upon stellar collapse of\naltering parameters in a fashion constrained by nuclear systematics.\nThey found that as long as the parameters permitted a neutron star\nmaximum mass above the PSR1913+16 mass limit (1.44 M$_\\odot$), the\nshock generated by core bounce consistently stalls near 100 km,\nindependently of the assumed $K_s$ in the range 180--375 MeV and $S_v$\nin the range 27--35 MeV. Ref.~\\cite{SLM} also found that the final\ntrapped lepton fraction is also apparently independent of variations\nin both $K_s$ and $S_v$. These results are in contrast to earlier\nsimulations which had used EOSs that could not support\ncold, catalyzed 1.4 M$_\\odot$ stars, or in which $S_s$ was not varied\nconsistently with $S_v$. The strong feedback between the EOS,\nweak interactions, neutrino transport, and hydrodynamics is\nan example of {\\em Mazurek's Law}.\n\nIn fact, the only significant consequence of varying $S_v$ involved the\npre-bounce neutrino luminosities. Increasing\n$S_v$ increases the electron capture rate (proportional to\n$\\mu_e-\\hat\\mu$ and therefore increases the $\\nu_e$ luminosity during\ncollapse, as shown in Fig.~\\ref{nulum}. Nevertheless, the collapse\nrate also increases, so that neutrino trapping occurs sooner and the\nfinal trapped lepton fraction does not change. It is possible that\nlarge neutrino detectors such as Super-Kamiokande or SNO may be able\nto observe an enhanced early rise in neutrino luminosity from nearby\ngalactic supernovae.\n\n\\section{The Structure of Neutron Stars}\n\nThe theoretical study of the structure of neutron stars is crucial if\nnew observations of masses and radii are to lead to effective\nconstraints on the EOS of dense matter. This study becomes ever more\nimportant as laboratory studies may be on the verge of yielding\nevidence about the composition and stiffness of matter beyond $n_s$.\nTo date, several accurate mass determinations of neutron stars are\navailable, and they all lie in a narrow range ($1.25-1.44$ M$_\\odot$).\nThere is some speculation that the absence of neutron stars with\nmasses above 1.5 M$_\\odot$ implies that $M_{max}$ for neutron stars\nhas approximately this value. However, since fewer than 10 neutron\nstars have been weighed, and all these are in binaries, this\nconjecture is premature. Theoretical studies of dense matter\nindicate that considerable uncertainties exist in\nthe high-density behavior of the EOS largely because of the poorly\nconstrained many-body interactions.\nThese uncertainties are reflected in a significant\nuncertainty in the maximum mass of a beta-stable neutron star, which\nranges from 1.5--2.5 M$_\\odot$.\n\nThere is some theoretical support for a\nlower mass limit for neutron stars in the range $1.1-1.2$ M$_\\odot$.\nThis follows from the facts that the collapsing core of a massive star\nis always greater than 1 M$_\\odot$ and the minimum mass of a\nprotoneutron star with a low-entropy inner core of $\\sim0.6$ M$_\\odot$\nand a high-entropy envelope is at least 1.1 M$_\\odot$.\nObservations from the Earth of thermal radiation from neutron star\nsurfaces could yield values of the quantity\n$R_\\infty=R/\\sqrt{1-2GM/Rc^2}$, which results from redshifting the\nstars luminosity and temperature. \n$M-R$ trajectories for representative EOSs (discussed below) \nare shown in\nFigure \\ref{fig:M-R}. \nIt appears difficult to simultaneously have $M>1$M$_\\odot$ and $R_\\infty < \n12$ km. \nThose pulsars with at least some suspected thermal\nradiation generically yield effective values of $R_\\infty$ so small\nthat it is believed that the radiation originates from polar hot spots\nrather than from the surface as a whole. Other attempts to deduce a\nradius include analyses~\\cite{Tit} of X-ray bursts from sources 4U\n1705-44 and 4U 1820-30 which implied rather small values,\n$9.5<R_\\infty<14$ km. However, the modeling of the photospheric\nexpansion and touchdown on the neutron star surface requires a model\ndependent relationship between the color and effective temperatures,\nrendering these estimates uncertain. Absorption lines in X-ray\nspectra have also been investigated with a view to deducing the\nneutron star radius. Candidates for the matter producing the\nabsorption lines are either the accreted matter from the companion\nstar or the products of nuclear burning in the bursts. In the former\ncase, the most plausible element is thought to be Fe, in which case\nthe relation $R\\approx3.2GM/c^2$, only slightly larger than the\nminimum possible value based upon causality,~\\cite{LPMY,glen} is\ninferred. In the latter case, plausible candidates are Ti and Cr, and\nlarger values of the radius would be obtained. In both cases, serious\ndifficulties remain in interpreting the large line widths, of order\n100--500 eV, in the $4.1 \\pm 0.1$ keV line observed from many sources.\nA first attempt at using light curves and pulse fractions from pulsars\nto explore the $M-R$ relation suggested relatively large radii, of\norder 15 km~\\cite{Page}. However, this method, which assumed dipolar\nmagnetic fields, was unable to satisfactorily reconcile the calculated\nmagnitudes of the pulse fractions and the shapes of the light curves\nwith observations.\n\n\n\\begin{figure}[h]\n\\vspace{23pc}\n\\special{psfile=figure3.ps hoffset=445 voffset=-10 hscale=65 vscale=60\nangle=90}\n\\caption{$M-R$ curves for the EOSs listed in Table 1. The diagonal\nlines represent two theoretical estimates (LP=Ref.~\\cite{LP};\nRP=Ref.~\\cite{RP}) of the locus of points for $\\Delta I/I=1.4\\%$ for\nextremal limits of $P_t$, 0.25 and 0.65 MeV fm$^{-3}$. The large dots\non the $M-R$ curves are the exact results. The region to the left of\nthe contours labeled 0.65 is not allowed if current glitch models are\ncorrect~\\cite{Link}.}\n\\label{fig:M-R}\n\\end{figure}\n\nProspects for a radius determination have improved in recent years,\nhowever, with the detection of a nearby neutron star, RX J185635-3754,\nin X-rays and optical radiation~\\cite{Walter}. The observed X-rays,\nfrom the ROSAT satellite, are consistent with blackbody emission with\nan effective temperature of about 57 eV and very little extinction.\nIn addition, the fortuitous location of the star in the foreground of\nthe R CrA molecular cloud limits the distance to $D<120$ pc. The fact\nthat the source is not observable in radio and its lack of variability\nin X-rays implies that it is not a pulsar unlike other identified\nradio-silent isolated neutron stars. This gives the hope that the\nobserved radiation is not contaminated with non-thermal emission as is\nthe case for pulsars. The X-ray observations of RXJ185635-3754 alone\nyield $R_\\infty\\approx 7.3 (D/120 {\\rm~pc}){\\rm~ km}$ for a best-fit\nblackbody. Such a value is too small to be consistent with any\nneutron star with more than 1 M$_\\odot$. But the optical flux is\nabout a factor of 2.5 brighter than what is predicted for the X-ray\nblackbody, which is consistent with there being a heavy-element\natmosphere~\\cite{Romani}. With such an atmosphere, it is\nfound~\\cite{ALPW} that the effective temperature is reduced to\napproximately 50 eV and $R_\\infty$ is also increased, to a value of\napproximately $21.6 (D/120 {\\rm~pc}){\\rm~ km}$. Upcoming parallax\nmeasurements with the Hubble Space Telescope should permit a distance\ndetermination to about 10-15\\% accuracy. If X-ray spectral features\nare discovered with the planned Chandra and XMM space observatories,\nthe composition of the neutron star atmosphere can be inferred, and\nthe observed redshifts will yield independent mass and radius\ninformation. In this case, {\\em both} the mass and radius of this\nstar will be found.\n\nFurthermore, a proper motion of 0.34 $^{\\prime\\prime}$ yr$^{-1}$ has\nbeen detected, in a direction that is carrying the star away from the\nUpper Scorpius (USco) association~\\cite{ALPW}. With an assumed\ndistance of about 80 pc, the positions of RX J185635-3754 and this\nassociation overlap about 800,000 years ago. The runaway\nOB star $\\zeta$ Oph is also moving away from USco, appearing to have\nbeen ejected on the order of a million years ago. The superposition\nof these three objects is interesting, and one can speculate that this is\nnot coincidental. If upcoming parallax measurements are consistent\nwith a distance to RX J185635-3754 of about 80 pc, the evidence for\nthis scenario will be strong, and a good age estimate will result.\n\nIn this section, a striking empirical relationship is noted which\nconnects the radii of neutron stars and the pressure of matter in the\nvicinity of $n_s$. In addition, a number of analytic, exact,\nsolutions to the general relativistic TOV equation of hydrostatic\nequilibrium are explored that lead to several useful approximations\nfor neutron star structure which directly correlate observables such as\nmasses, radii, binding energies, and moments of inertia. The binding\nenergy, of which more than 99\\% is carried off in neutrinos, will be\nrevealed from future neutrino observations of supernovae. Moments of\ninertia are connected with glitches observed in the spin down of\npulsars, and their observations yield some interesting conclusions\nabout the distribution of the moment of inertia within the rotating\nneutron star. From such comparisons, it may become easier to draw\nconclusions about the dense matter EOS when firm observations of\nneutron star radii or moments of inertia become available to accompany\nthe several known accurate mass determinations.\n\n\\subsection{Neutron Star Radii}\n\n\\begin{table*}\n%\\caption{EOS symbols}\n\\caption{Equations of state used in this work. Approach refers to the\nbasic theoretical paradigm. Composition refers to strongly\ninteracting components (n=neutron, p=proton, H=hyperon, K=kaon,\nQ=quark); all approaches include leptonic contributions.}\n\\vspace*{0.1in}\n\\begin{center}\n\\begin{tabular}{l|l|l|l} \\hline\\hline\nSymbol & Reference & Approach & Composition \\\\ \\hline\nFP & \\cite{FP} & Variational & np \\\\\nPS & \\cite{PS} & Potential & n$\\pi^0$ \\\\\nWFF(1-3) & \\cite{WFF} & Variational & np \\\\\nAP(1-4) & \\cite{Akmal} & Variational & np \\\\\nMS(1-3) & \\cite{MS} & Field Theoretical & np \\\\ \nMPA(1-2) & \\cite{MPA} & Dirac-Brueckner HF & np \\\\\nENG & \\cite{Engvik} & Dirac-Brueckner HF & np \\\\\nPAL(1-6) & \\cite{PAL} & Schematic Potential & np \\\\\nGM(1-3) & \\cite{GM} & Field Theoretical & npH \\\\\nGS(1-2) & \\cite{GS} & Field Theoretical & npK\\\\\nPCL(1-2) & \\cite{PCL} & Field Theoretical & npHQ\n\\\\ \nSQM(1-3) & \\cite{PCL} & Quark Matter & Q $(u,d,s)$\\\\\n\\hline\n\\end{tabular}\n\\label{eosname}\n%\\end{table}\n\\end{center}\n\\end{table*}\n\nThe composition of a neutron star chiefly depends on the nature of\nstrong interactions, which are not well understood in dense matter.\nThe several possible models investigated~\\cite{LPMY,physrep}\ncan be conveniently grouped into three broad categories:\nnonrelativistic potential models, field-theoretical models, and\nrelativistic Dirac-Brueckner-Hartree-Fock models. In each of these\napproaches, the presence of additional softening components such as\nhyperons, Bose condensates or quark matter, can be incorporated.\n\nFigure \\ref{fig:M-R} displays the mass-radius relation for several\nrecent EOSs (the abbreviations are explained in Table~\\ref{eosname}).\nEven a cursory glance indicates that in the mass range from $1-1.5$\nM$_\\odot$ it is usually the case that the radius has little dependence\nupon the mass. The lone exception is the model GS1, in which a kaon\ncondensate, leading to considerable softening, appears. While it is\ngenerally assumed that a stiff EOS leads to both a large maximum mass\nand a large radius, many counter examples exist. For example, MS3 has\na relatively small maximum mass but has large radii compared to most other\nEOSs with larger maximum masses. Also, not\nall EOSs with extreme softening have small radii (viz., GS2).\nNonetheless, for stars with mass greater than 1 M$_\\odot$, only models\nwith a large degree of softening can have $R_\\infty<12$ km. Should\nthe radius of a neutron star ever be accurately determined to satisfy\n$R_\\infty<12$ km, a strong case can be made for the existence of\nextreme softening.\n\n\n\\begin{figure}[h]\n\\vspace{25pc}\n\\special{psfile=p-r.ps hoffset=430 voffset=-22 hscale=65 vscale=60\nangle=90}\n\\caption{Empirical relation between $P$ and $R$ for various EOSs (see\nTable~\\ref{eosname} for details). The upper and lower panels show\nresults for gravitational masses of 1 M$_\\odot$ and 1.4 M$_\\odot$,\nrespectively. Symbols show $PR^{-1/4}$ in units of MeV fm$^{-3}$\nkm$^{-1/4}$ at the three indicated fiducial densities.}\n\\label {fig:P-R}\n\\end{figure}\n\nIt is relevant that a Newtonian polytrope with $n=1$ has the property\nthat the stellar radius is independent of both the mass and central\ndensity. In fact, numerical relativists have often approximated\nequations of state with $n=1$ polytropes.\nAn $n=1$ polytrope has the property that the radius is proportional to the\nsquare root of the constant $K$ in the polytropic pressure law\n$P=K\\rho^{1+1/n}$. This suggests that there might be a quantitative\nrelation between the radius and the pressure that does not depend upon\nthe equation of state at the highest densities, which determines the\noverall softness or stiffness (and hence, the maximum mass).\n\nTo make the relation between matter properties and the nominal neutron star\nradius definite, Fig.~\\ref{fig:P-R} shows the remarkable empirical\ncorrelation which exists between the radii of 1 and 1.4 M$_\\odot$ stars and the\nmatter's pressure evaluated at densities of 1, 1.5 and 2 $n_s$.\nTable~\\ref{eosname} explains the EOS symbols used in Fig.~\\ref{fig:P-R}.\nDespite the relative insensitivity of radius to mass for a particular\n``normal'' equation of state, the nominal radius $R_M$, which is defined as the\nradius at a particular mass $M$ in solar units, still varies widely with the\nEOS employed. Up to $\\sim 5$ km differences are seen in $R_{1.4}$, for\nexample, in Fig.~\\ref{fig:P-R}. This plot is restricted to EOSs which\nhave maximum masses larger than about 1.55 M$_\\odot$ and to those which do not\nhave strong phase transitions (such as those due to a Bose condensate or quark\nmatter). Such EOSs violate these correlations, especially for the case of 1.4\nM$_\\odot$ stars. We emphasize that this correlation is valid only for cold,\ncatalyzed neutron stars, i.e., it will not be valid for protoneutron stars\nwhich have finite entropies and might contain trapped neutrinos. The\ncorrelation has the form\n\\begin{equation}\nR \\simeq {\\rm constant}~\\cdot[P(n)]^{0.23-0.26}\\,,\n\\label{correl}\n\\end{equation}\nwhere $P$ is the total pressure inclusive of leptonic contributions\nevaluated at the density $n$. An exponent of 1/4 was chosen for\ndisplay in Fig.~\\ref{fig:P-R}, but the correlation holds for a small\nrange of exponents about this value. The correlation is marginally\ntighter for the baryon density $n=1.5 n_s$ and $2 n_s$ cases. Thus,\ninstead of the power 1/2 that the Newtonian polytrope relations would\npredict, a power of approximately 1/4 is suggested when the effects of\nrelativity are included. The value of the\nconstant in Eq.~(\\ref{correl}) depends upon the chosen density, and\ncan be obtained from Fig.~\\ref{fig:P-R}.\n\nThe exponent of 1/4 can be quantitatively understood by using a\nrelativistic generalization of the $n=1$ polytrope, due to\nBuchdahl~\\cite{Buchdahl}. For the EOS\n\\begin{equation}\n\\rho=12\\sqrt{p_*P}-5P\\,,\\label{buch}\n\\end{equation}\nwhere $p_*$ is a constant, there is an analytic solution to Einstein's\nequations:\n\\begin{eqnarray}\ne^\\nu &\\equiv& g_{tt}=(1-2\\beta)(1-\\beta-u)(1-\\beta+u)^{-1}\\,;\\cr\ne^\\lambda &\\equiv&\ng_{rr}=(1-2\\beta)(1-\\beta+u)(1-\\beta-u)^{-1}(1-\\beta+\\beta\\cos Ar^\\prime)^{-2}\\,;\\cr\n8\\pi PG/c^4 &=& A^2u^2(1-2\\beta)(1-\\beta+u)^{-2}\\,;\\cr\n8\\pi\\rho G/c^2&=& 2A^2u(1-2\\beta)(1-\\beta-3u/2)(1-\\beta+u)^{-2}\\,;\\cr\nu&=&\\beta(Ar^\\prime)^{-1}\\sin Ar^\\prime\\,;\\qquad\nr = r^\\prime(1-\\beta+u)(1-2\\beta)^{-1}\\,;\\cr\nA^2 &=& 288\\pi p_*Gc^{-4}(1-2\\beta)^{-1};\\qquad R=\\pi(1-\\beta)(1-2\\beta)^{-1}A^{-1}.\n\\label{buch1}\n\\end{eqnarray}\n\nThe free parameters of this solution are $\\beta\\equiv GM/Rc^2$ and the\nscale $p_*$. Note that $R\\propto p_*^{-1/2}(1+\\beta^2/2+\\dots)$, so\nfor a given value of $p_*$, the radius increases only very slowly\nwith mass, exactly as expected from an $n=1$\nNewtonian polytrope. It is instructive to analyze the response of $R$\nto a change of pressure at some fiducial density $\\rho$, for a fixed\nmass $M$. One finds\n\\begin{equation}\n{d\\ln R\\over d\\ln P}\\Biggr|_{\\rho,M} = {{d\\ln R\\over d\\ln\np_*}\\Bigr|_\\beta {d\\ln p_*\\over d\\ln P}\\Bigr|_{\\rho}\\over1+{d\\ln\nR\\over d\\ln\\beta}\\Bigr|_{p_*}}=\n\\Biggl(1-{5\\over6}\\sqrt{P\\over p_*}\\Biggr){(1-\\beta)(1-2\\beta)\\over2(1-3\\beta+3\\beta^2)}.\n\\end{equation}\nIn the limit $\\beta\\rightarrow0, P\\rightarrow0$ and $d\\ln\nR/d\\ln P\\rightarrow1/2$, the value characteristic of an $n=1$ Newtonian\npolytrope. Finite values of $\\beta$ and $P$ render the\nexponent smaller than 1/2. If the stellar radius is about 15 km,\n$p_*=\\pi/(288 R^2)\\approx4.85\\cdot10^{-5}$ km$^{-2}$. If the fiducial\ndensity is $\\rho\\approx 1.5m_bn_s\\approx2.02\\cdot10^{-4}$ km$^{-2}$\n(with $m_b$ the baryon mass), Eq.~(\\ref{buch}) implies that\n$P\\approx8.5\\cdot10^{-6}$ km$^{-2}$. For $M=1.4$ M$_\\odot$, the value\nof $\\beta$ is 0.14, and $d\\ln R/d\\ln P\\simeq0.31$. This result is\nmildly sensitive to the choices for $\\rho$ and $R$, and the Buchdahl\nsolution is not a perfect representation of realistic EOSs;\nnevertheless, it provides a reasonable explanation of the\ncorrelation in Eq.~(\\ref{correl}).\n\nThe existence of this correlation is significant because, in large\npart, the pressure of degenerate matter near the nuclear saturation\ndensity $n_s$ is determined by the symmetry properties of the EOS.\nThus, the measurement of a neutron star radius, if not so small as to\nindicate extreme softening, could provide an important clue to the\nsymmetry properties of matter. In either case, valuable information\nis obtained.\n\n\\begin{figure}[h]\n\\vspace{23pc}\n\\special{psfile=alp9.ps hoffset=15 voffset=-70 hscale=65 vscale=50}\n\\caption{Left panel: $M-R$ curves for selected PAL parametrizations~\\cite{PAL}\n showing the\nsensitivity to symmetry energy. The left panel shows variations\narising from different choices of the symmetry energy at the nuclear\nsaturation density $S_v=S_v(n_s)$; the right panel shows variations\narising from different choices of the density dependence of the\npotential part of the symmetry energy $F(u)=S_v(n)/S_v(n_s)$ where $u=n/n_s$.}\n\\label{fig:alp9}\n\\end{figure}\n\nThe specific energy of nuclear matter near the saturation density may\nbe expressed as an expansion in the asymmetry $(1-2x)$, as\ndisplayed in Eq.~(\\ref{bulk}), that can be terminated after the quadratic\nterm~\\cite{PAL}. Leptonic contributions must be added to\nEq.~(\\ref{bulk}) to obtain the total energy and pressure; the electron\nenergy per baryon is $f_e=(3/4)\\hbar cx(3\\pi^2nx)^{1/3}$. Matter in\nneutron stars is in beta equilibrium, i.e., $\\mu_e - \\mu_n + \\mu_p =\n\\partial (f_{bulk}+f_e)/\\partial x=0$, so the electronic contributions\nmay be eliminated to recast the pressure as~\\cite{Ppuri}\n\\begin{eqnarray}\nP=n^2\\Biggl[S_v^\\prime(n)(1-2x)^2+{xS_v(n)\\over n}(1-2x)+\\cr\n{K_s\\over9n_s}\\Bigl({n\\over\nn_s}-1\\Bigr)-{K_s^\\prime\\over54n_s}\\Bigl({n\\over n_s}-1\\Bigr)^2\\Biggr]\\,,\n\\end{eqnarray}\nwhere $x$ is now the beta equilibrium value. At the saturation density,\n\\begin{eqnarray}\nP_s=n_s(1-2x_s)[n_sS_v^\\prime(n_s)(1-2x_s)+S_v x_s]\\,,\n\\end{eqnarray}\nwhere the equilibrium proton fraction at $n_s$ is\n\\begin{eqnarray}\nx_s\\simeq(3\\pi^2 n_s)^{-1}(4S_v/\\hbar c)^3 \\simeq 0.04\n\\end{eqnarray}\nfor $S_v=30$ MeV. Due to the small value of $x_s$, one finds that\n$P_s\\simeq n_s^2 S_v^\\prime(n_s)$. If the pressure is evaluated at a\nlarger density, other nuclear parameters besides $S_v$ and\n$S_v^\\prime(n_s)$, become significant. For $n=2n_s$, one thus has\n\\begin{eqnarray}\nP(2n_s)\\simeq 4n_s [n_sS_v^\\prime(2n_s)+(K_s - K_s^\\prime/6)/9] \\,.\n\\end{eqnarray}\nIf it is assumed that $S_v(n)$ is linear in density, $K_s\\sim220$ MeV and\n$K_s^\\prime\\sim2000$ MeV (as indicated in Eq.~\\ref{comp}), the symmetry\ncontribution is still about 70\\% of the total.\n\nThe sensitivity of the radius to the symmetry energy is graphically\nshown by the parametrized EOS of PAL~\\cite{PAL} in\nFig.~\\ref{fig:alp9}. The symmetry energy function $S_v(n)$ is a\ndirect input in this parametrization. The figure shows the dependence\nof mass-radius trajectories as the quantities $S_v$ and $S_v(n)$ are\nalternately varied. Clearly, the density dependence of $S_v(n)$ is\nmore important in determining the neutron star radius. Note also the\nweak sensitivity of the maximum neutron star mass to $S_v$.\n\nAt present, experimental guidance concerning the density dependence of the\nsymmetry energy is limited and mostly based upon the division of the nuclear\nsymmetry energy between volume and surface contributions, as discussed in the\nprevious section. Upcoming experiments involving heavy-ion collisions (at GSI,\nDarmstadt), which might sample densities up to $\\sim (3-4)n_s$, will be limited\nto analyzing properties of the symmetric nuclear matter EOS through a study of\nmatter, momentum, and energy flow of nucleons. Thus, studies of heavy nuclei\nfar off the neutron drip lines will be necessary in order to pin down the\nproperties of the neutron-rich regimes encountered in neutron stars.\n\n\\subsection{Neutron Star Moments of Inertia and Binding Energies}\n\nBesides the stellar radius, other global attributes of\nneutron stars are potentially observable, including the moment of inertia\nand the binding energy. These quantities depend\nprimarily upon the ratio $M/R$ as opposed to details of the EOS,\nas can be readily seen by evaluating them using analytic\nsolutions to Einstein's equations. Although over 100 analytic\nsolutions to Einstein's equations are known~\\cite{Delgaty}, nearly all of\nthem are physically unrealistic. However, three analytic solutions are\nof particular interest in neutron star structure.\n\nThe first is the well-known Schwarzschild interior solution for an\nincompressible fluid, $\\rho=\\rho_c$, where $\\rho$ is the mass-energy\ndensity. This is mostly of interest because it determines the maximum\ncompression $\\beta=GM/Rc^2$ for a neutron star, namely 4/9, based upon\nthe pressure being finite. Two aspects of the incompressible fluid\nthat are physically unrealistic, however, include the fact that the\nsound speed is everywhere infinite, and that the density does not\nvanish on the star's surface.\n\nThe second analytic solution, B1, due to Buchdahl~\\cite{Buchdahl}, is\ndescribed in Eq.~(\\ref{buch1}).\n\nThe third analytic solution (TolVII) was discovered by Tolman~\\cite{Tolman} in\n1939, and is the case when the mass-energy density\n$\\rho$ varies quadratically, that is,\n\\begin{equation}\n\\rho=\\rho_c[1-(r/R)^2].\n\\end{equation}\nIn fact, this is an adequate representation, as displayed in\nFig.~\\ref{fig:prof} for neutron stars more massive than 1.2 M$_\\odot$. The\nequations of state used are listed in Table~\\ref{eosname}. The largest\ndeviations from this general relation exist for models with extreme softening\n(GS1, GS2, PCL2) and which have relatively low maximum masses (see\nFig.~\\ref{fig:M-R}). It is significant that all models must, of course,\napproach this behavior at both extremes $r\\rightarrow0$ and $r\\rightarrow R$.\n\n\\begin{figure}[h]\n\\vspace{28pc}\n\\special{psfile=rhorad.ps hoffset=430 voffset=5 hscale=58 vscale=65\nangle=90}\n\\caption{Each panel shows mass-energy density profiles in the\ninteriors of selected stars (masses indicated) ranging from about 1.2\nM$_\\odot$ to the maximum mass (solid line) for\nthe given equation of state (see\nTable~\\ref{eosname}). The thick black lines show the simple quadratic\napproximation $1-(r/R)^2$.}\n\\label{fig:prof}\n\\end{figure}\n\nBecause the Tolman solution is often overlooked in the\nliterature (for exceptions, see, for example, Refs.~\\cite{Delgaty,Indians})\nit is\nsummarized here. It is useful in establishing interesting and simple relations\nthat are insensitive to the equation of state. In terms of the variable\n$x=r^2/R^2$ and the parameter $\\beta$, the assumption\n$\\rho=\\rho_c(1-x)$ results in $\\rho_c=15\\beta c^2/(8\\pi GR^2)$. The\nsolution of Einstein's equations for this density distribution is:\n\\begin{eqnarray}\ne^{-\\lambda} &=& 1-\\beta x(5-3x)\\,,\\qquad e^\\nu = (1-5\\beta/3)\\cos^2\\phi\\,,\n\\cr\nP &=& {c^4\\over4\\pi R^2 G}[\\sqrt{3\\beta e^{-\\lambda}}\\tan\\phi-{\\beta\\over2}(5-3x)\\,,\n\\qquad n= {\\rho c^2+P\\over m_bc^2}{\\cos\\phi\\over\\cos\\zeta}\\,, \\cr\n\\phi &=& (w_1-w)/2+\\zeta\\,, \\quad \\phi_c = \\phi(x=0)\\,, \\quad \\zeta = \\tan^{-1}\\sqrt{\\beta/[3(1-2\\beta)]}\\,,\\cr\nw &=& \\log[x-5/6+\\sqrt{e^{-\\lambda}/(3\\beta)}]\\,, \\qquad w_1 = w(x=1)\\,.\n\\end{eqnarray}\nThe central values of $P/\\rho c^2$ and $c_s^2$ are\n\\begin{equation}\n{P\\over\\rho c^2}\\Biggr|_c={2\\over15}\\sqrt{3\\over\\beta}\\Bigr({c_{sc}\\over\nc}\\Bigr)^2\\,,\\quad \\Bigr({c_{sc}\\over c}\\Bigr)^2=\\tan\\phi_c\\Bigr(\\tan\\phi_c+\\sqrt{\\beta\\over3}\\Bigr)\\,.\n\\end{equation}\nThis solution, like that of Buchdahl's, is scale-free, with the\nparameters $\\beta$ and $\\rho_c$ (or $M$ or $R$). Here, $n$ is the baryon\ndensity, $m_b$ is the nucleon mass, and $c_{sc}$ is the sound speed at\nthe star's center. When $\\phi_0=\\pi/2$, or $\\beta\\approx0.3862$,\n$P_c$ becomes infinite, and when $\\beta\\approx0.2698$, $c_{sc}$\nbecomes causal ({i.e., $c$). Recall that for an incompressible fluid,\n$P_c$ becomes infinite when $\\beta=4/9$. For the Buchdahl solution,\n$P_c$ becomes infinite when $\\beta=2/5$ and the causal limit is\nreached when $\\beta=1/6$. For comparison, if causality is enforced at\nhigh densities, it has been empirically determined that\n$\\beta<0.34$~\\cite{LPMY,glen}.\n\nThe general applicability of these exact solutions can be gauged by analyzing\nthe moment of inertia, which, for a star uniformly\nrotating with angular velocity $\\Omega$, is\n\\begin{equation}I=(8\\pi/3)\\int_0^R r^4(\\rho+P/c^2)e^{(\\lambda-\\nu)/2}\n(\\omega/\\Omega) dr\\,.\\label{inertia}\\end{equation}\nThe metric function $\\omega$ is a solution of the equation\n\\begin{equation}\nd[r^4e^{-(\\lambda+\\nu)/2}\\omega^\\prime]/dr+4r^3\\omega\nde^{-(\\lambda+\\nu)/2}/dr=0\n\\label{diffomeg}\n\\end{equation}\nwith the surface boundary condition\n\\begin{equation}\\omega_R=\\Omega-{R\\over3}\\omega^\\prime_R\n=\\Omega\\left[1-{2GI\\over R^3c^2}\\right].\n\\label{boundary}\n\\end{equation}\nThe second equality in the above follows from the definition of $I$ and the TOV\nequation. Writing $j=\\exp[-(\\nu+\\lambda)/2]$, the\nTOV equation becomes\n\\begin{equation}\nj^\\prime=-4\\pi Gr(P/c^2+\\rho)je^\\lambda/c^2\\,.\n\\end{equation}\nThen, one has\n\\begin{equation}\nI=-{2c^2\\over3G}\\int {\\omega\\over\\Omega}r^3dj =\n{c^2R^4\\omega^\\prime_R\\over6G\\Omega} \\,. \\end{equation}\n\n\\begin{figure}[h]\n\\vspace{23pc}\n\\special{psfile=mominert.ps hoffset=430 voffset=-10 hscale=60 vscale=60\nangle=90}\n\\caption{The moment of inertia $I$ in units of $MR^2$ for the equations of\nstate listed in Table~\\ref{eosname}. $I_{Inc}, I_{B 1}, I_{VII}$ and $I_{RP}$\nare approximations described in the text.}\n\\label{mominert}\n\\end{figure}\n\nUnfortunately, an\nanalytic representation of $\\omega$ or the moment of inertia for any of the\nthree exact solutions is not available. However, approximations which are\nvalid to within 0.5\\% are\n\\begin{eqnarray}\nI_{Inc}/MR^2 &\\simeq& 2(1-0.87\\beta-0.3\\beta^2)^{-1}/5\\,, \\\\\nI_{B1}/MR^2 &\\simeq& (2/3-4/\\pi^2)(1-1.81\\beta+0.47\\beta^2)^{-1}\\,, \\\\\nI_{T VII}/MR^2 &\\simeq& 2(1-1.1\\beta-0.6\\beta^2)^{-1}/7\\,.\n\\end{eqnarray}\nIn each case, the small $\\beta$ limit reduces to the corresponding Newtonian\nresults. Fig.~\\ref{mominert} indicates\nthat the Tolman approximation is rather good. Ravenhall\n\\& Pethick~\\cite{RP} suggested that the expression\n\\begin{equation}\nI_{RP}/MR^2\\simeq0.21/(1-2u)\n\\end{equation}\nwas a good approximation for the moment of inertia; however, we find\nthat this expression is not a good overall fit, as shown in\nFig.~\\ref{mominert}. For low-mass stars ($\\beta<0.12$), none of these\napproximations is suitable, but it is unlikely that any neutron stars\nare this rarefied. It should be noted that the Tolman approximation\ndoes not adequately approximate some EOSs, especially ones that are\nrelatively soft, such as GM3, GS1, GS2, PAL6 and PCL2.\n\nThe binding energy formally represents the energy gained by assembling\n$N$ baryons. If the baryon mass is $m_b$, the binding energy is\nsimply $BE=Nm_b-M$ in mass units. However, the quantity $m_b$ has various\ninterpretations in the literature. Some authors assume it is about\n940 MeV/$c^2$, the same as the neutron or proton mass. Others assume\nit is about 930 MeV/$c^2$, corresponding to the mass of C$^{12}$/12 or\nFe$^{56}$/56. The latter would yield the energy released in a\nsupernova explosion, which consists of the energy released by the\ncollapse of a white-dwarf-like iron core, which itself is considerably\nbound. The difference, 10 MeV per baryon, corresponds to a shift of\n$10/940\\simeq0.01$ in the value of $BE/M$. In any case, the binding\nenergy is directly observable from the detection of neutrinos from a\nsupernova event; indeed, it would be the most precisely determined\naspect.\n\n\\begin{figure}[h]\n\\vspace{25pc}\n\\special{psfile=bind.ps hoffset=435 voffset=-0 hscale=58 vscale=60\nangle=90}\n\\caption{The binding energy of neutron stars as a function of stellar mass for\nthe equations of state listed in Table~\\ref{eosname}. The predictions of\nEq.~(\\ref{lybind}) are shown by the shaded region.}\n\\label{bind}\n\\end{figure}\n\nLattimer \\& Yahil~\\cite{LY} suggested that the binding energy could be\napproximated as\n\\begin{equation}\nBE\\approx 1.5\\cdot10^{51} (M/{\\rm M}_\\odot)^2 {\\rm~ergs} = 0.084\n(M/{\\rm M}_\\odot)^2 {\\rm~M}_\\odot\\,.\n\\label{lybind}\n\\end{equation}\nThis formula, in general, is accurate to about $\\pm20$\\%. The largest\ndeviations are for extremely soft EOSs, as shown in\nFig.~\\ref{bind}.\n\n\\begin{figure}[h]\n\\vspace{25pc}\n\\special{psfile=bind1.ps hoffset=432 voffset=-0 hscale=58 vscale=60\nangle=90}\n\\caption{The binding energy per unit gravitational mass as a function of\ncompactness for the equations of state listed in Table~\\ref{eosname}. The\nshaded region shows the prediction of Eq.~(\\ref{newbind})\nwith $\\pm5$\\% errors.}\n\\label{bind1}\n\\end{figure}\n\nHowever, a more accurate representation of the binding energy is given by\n\\begin{equation}\nBE/M \\simeq 0.6\\beta/(1-0.5\\beta)\\,, \\label{newbind}\n\\end{equation}\nwhich incorporates some radius dependence. Thus, the observation of supernova\nneutrinos, and the estimate of the total radiated neutrino energy, will yield\nmore accurate information about $M/R$ than about $M$ alone.\n\nIn the cases of the incompressible fluid and the Buchdahl solution, analytic\nresults for the binding energy can be found:\n\\begin{eqnarray}\nBE_{Inc}/M &=& {3\\over4\\beta}\\Bigl({\\sin^{-1}\\sqrt{2\\beta}\\over\n\\sqrt{2\\beta}}-\\sqrt{1-2\\beta}\\Bigr)-1\\,, \\\\\nBE_{B1}/M &=& (1-1.5\\beta)\\sqrt{1-2\\beta}(1-\\beta)^{-1}-1\\,.\\label{analbind}\n\\end{eqnarray}\nThe analytic results, the Tolman VII solution, and the fit of\nEq.~(\\ref{newbind}) are compared to some recent equations of state in\nFig.~\\ref{bind1}. It can be seen that, except for very soft cases\nlike PS, PCL2, PAL6, GS1 and GS2, both the Tolman VII and Buchdahl\nsolutions are rather realistic.\n\n\\subsection{Crustal Fraction of the Moment of Inertia}\n\nIn the investigation of pulsar glitches, many models associate the\nglitch size with the fraction of the moment of inertia which resides\nin the star's crust, usually defined to be the region in which dripped\nneutrons coexist with nuclei. The high-density crust boundary is set\nby the phase boundary between nuclei and uniform matter, where the\npressure is $P_t$ and the density $n_t$. The low-density boundary is\nthe neutron drip density, or for all practical purposes, simply the\nstar's surface since the amount of mass between the neutron drip point\nand the surface is negligible. We define $\\Delta R$ to be the\ndistance between the points where the density is $n_t$ and zero. One\ncan apply Eq.~(\\ref{inertia}) to determine the moment of inertia of the\ncrust alone with the assumptions that $P/c^2<<\\rho$, $m(r)\\simeq M$,\nand $\\omega j\\simeq\\omega_R$ in the crust. One finds\n\\begin{equation}\n\\Delta I\\simeq{8\\pi\\over3}{\\omega_R\\over\\Omega}\\int_{R-\\Delta\nR}^R \\rho r^4e^\\lambda dr\\simeq\n{8\\pi\\over3GM}{\\omega_R\\over\\Omega}\\int_0^{P_t}r^6dP\\,,\n\\label{deltai}\n\\end{equation}\nwhere $M$ is the star's total mass and the TOV equation was used in\nthe last step. In the crust, the fact that the EOS is\nof the approximate polytropic form $P\\simeq K\\rho^{4/3}$ can be used\nto find an approximation for the integral $\\int r^6dP$, {\\em viz.}\n\\begin{equation}\n\\int_0^{P_t}r^6dP\\simeq P_tR^6\\left[1+\n%{8P_t\\over n_t m_nc^2}{4.5+(\\Lambda-1)^{-1}\\over\\Lambda-1}\n{2P_t\\over n_t m_nc^2}{(1+7\\beta)(1-2\\beta)\\over\\beta^2}\\right]^{-1}\\,.\n\\end{equation}\nSince the approximation Eq.~(\\ref{newbind}) gives $I$ in terms of $M$ and $R$,\nand $\\omega_R/\\Omega$ is given in terms of $I$ and $R$ in Eq.~(\\ref{boundary}),\nthe quantity $\\Delta I/I$ can thus be expressed as a function of $M$ and $R$\nwith the only dependence upon the equation of state (EOS) arising from the\nvalues of $P_t$ and $n_t$; there is no explicit dependence upon the\nhigher-density EOS. However, the major dependence is upon the value of $P_t$,\nsince $n_t$ enters only as a correction. We then find\n\\begin{equation}{\\Delta I\\over I}\\simeq{28\\pi P_t\nR^3\\over3 Mc^2}{(1-1.67\\beta-0.6\\beta^2)\\over\\beta}\\left[1+{2P_t\\over n_t\nm_bc^2}{(1+7\\beta)(1-2\\beta)\\over\\beta^2}\\right]^{-1}.\n\\label{dii}\n\\end{equation}\n\nIn general, the EOS parameter $P_t$, in the units of MeV fm$^{-3}$, varies over\nthe range $0.25<P_t<0.65$ for realistic EOSs. The determination\nof this parameter requires a calculation of the structure of matter containing\nnuclei just below nuclear matter density that is consistent with the assumed\nnuclear matter EOS. Unfortunately, few such calculations have been\nperformed.\nLike the fiducial pressure at and above nuclear density which appears in the\nrelation Eq.~(\\ref{correl}), $P_t$ should depend sensitively\n upon the behavior of the\nsymmetry energy near nuclear density.\n\nChoosing $n_t=0.07$ fm$^{-3}$, we compare Eq.~(\\ref{dii}) in Fig.~\\ref{fig:M-R}\nwith full structural calculations. The agreement is good. We also note that\nRavenhall \\& Pethick~\\cite{RP} developed a different, but nearly equivalent,\nformula for the quantity $\\Delta I/I$ as a function of $M, R, P_t$ and $\\mu_t$,\nwhere $\\mu_t$ is the neutron chemical potential at the core-crust phase\nboundary. This prediction is also displayed in Fig.~\\ref{fig:M-R}.\n\nLink, Epstein \\& Lattimer~\\cite{Link} established a lower limit to the radii of\nneutron stars by using a constraint derived from pulsar glitches. They showed\nthat glitches represent a self-regulating instability for which the star\nprepares over a waiting time. The angular momentum requirements of glitches in\nthe Vela pulsar indicate that more than\n$0.014$ of the star's moment of inertia drives\nthese events. If glitches originate in the liquid of the inner crust, this\nmeans that $\\Delta I/I>0.014$. A minimum radius can be found by combining this\nconstraint with the largest realistic value of $P_t$ from any equation of\nstate. Stellar models that are compatible with this constraint must fall to\nthe right of the $P_t=0.65$ MeV fm$^{-3}$ contour in Fig.~\\ref{fig:M-R}. This\nimposes a constraint upon the radius, namely that\n$R>3.6+3.9 M/{\\rm M}_\\odot$ km.\n\n\\section{The Merger of a Neutron Star with a Low-Mass Black Hole}\nThe general problem of the origin and evolution of systems containing a neutron\nstar and a black hole was first detailed by Lattimer \\& Schramm~\\cite{LSch},\nalthough the original motivation was due to Schramm. Although speculative\nat the time,\nSchramm insisted that this would prove to be an interesting topic from the\npoints of view of nucleosynthesis and gamma-ray emission. The contemporaneous\ndiscovery~\\cite{HT} of the first-known binary system containing twin compact\nobjects, PSR 1913+16, which was also found to have an orbit which would decay\nbecause of gravitational radiation within $10^{10}$ yr, bolstered his argument.\nEventually, this topic formed the core of Lattimer's thesis~\\cite{thesisL},\nand the\nrecent spate of activity, a quarter century later, in the investigation of the\nevolution and mergers of such compact systems has wonderfully demonstrated\nSchramm's prescience.\n\nCompact binaries form naturally as the result of evolution of massive\nstellar binaries. The estimated lower mass limit for supernovae (and\nneutron star or black hole production) is approximately 8 M$_\\odot$.\nObservationally, the number of binaries formed within a given\nlogarithmic separation is approximately constant, but the relative\nmass distributions are uncertain. There is some indication that the\ndistribution in binary mass ratios might be flat. The number of\npossible progenitor systems can then be estimated. Most progenitor systems\ndo not survive the more massive star becoming a supernova. In the\nabsence of a kick velocity it is easily found that the loss of more\nthan half of the mass from the system will unbind it. However, the\nfact that pulsars are observed to have mean velocites in excess of a\nfew hundred km/s implies that neutron stars are usually produced with\nlarge ``kick'' velocities originating in the supernova explosion. In\nthe case that the kick velocity, which is thought to be randomly\ndirected, opposes the star's orbital velocity, the chances\nof the post-supernova binary remaining intact increases. In\naddition, the separation in a surviving binary will be reduced\nsignificantly. Subsequent evolution then progresses to the supernova\nexplosion of the companion. More of these systems survive because in\nmany cases the more massive component explodes. But the surviving\nsystems should both have greatly reduced separations and orbits with\nhigh eccentricity.\n\n\\begin{figure}[h]\n\\vspace{24pc}\n\\special{psfile=reduc.ps hoffset=435 voffset=-20 hscale=60 vscale=55 angle=90}\n\\caption{The reduction of the gravitational radiation orbital decay time as a\nfunction of initial orbital eccentricity. The dashed line is the inverse of\nthe Peters~\\cite{Peters} $f$ function; the dotted line shows $f^{-3/4}$,\nwhich reasonably reproduces the exact result.}\n\\label{reduc}\n\\end{figure}\n\nGravitational radiation then causes the binary's\norbit to decay, such that circular orbits of two masses $M_1$ and\n$M_2$ with initial semimajor axes $a$\nsatisfying\n\\begin{equation}\na<2.8[M_1M_2(M_1+M_2)/{\\rm M}_\\odot^3]^{1/4} {\\rm R}_\\odot\\,,\n\\label{decay}\n\\end{equation}\nwill fully decay within\nthe age of the Universe ($\\sim10^{10}$ yr). Highly\neccentric orbits will decay much faster, as shown in Fig.~\\ref{reduc}.\nThe dashed curve shows the inverse of the factor~\\cite{Peters} by which\nthe gravitational wave luminosity of an eccentric system exceeds that\nof a circular system:\n\\begin{equation}\nf=(1+73e^2/24+37e^4/96)(1-e^2)^{-7/2}.\n\\label{peters}\n\\end{equation}\nBecause the eccentricity also decays, the exact reduction factor is\nnot as strong as $1/f$. A\nreasonable approximation to the exact result is $f^{-3/4}$, shown by the\ndotted line in Fig.~\\ref{reduc}. The coefficient 2.8 in\nEq.~(\\ref{decay}) is increased by a factor of $f^{-3/16}$ or about 2 for\nmoderate eccentricities.\n\nRef.~\\cite{LSch} argued that mergers of neutron stars and black holes, and the\nsubsequent ejection of a few percent of the neutron star's mass, could easily\naccount for all the {\\em r}-process nuclei in the cosmos. Ref.~\\cite{LSch} is\nalso the earliest reference to the idea that compact object binary mergers are\nassociated with gamma-ray bursts. A later seminal contribution by Eichler,\nLivio, Piran \\& Schramm~\\cite{eichler} argued that mergers of neutron stars\noccur frequently enough to explain the origin of gamma-ray bursters.\n\nSince the timescale of gamma-ray bursts, being of order seconds to several\nminutes, is much longer than the coalescence timescale of a binary merger\n(which is of order the orbital frequency at the last stable orbit, a few\nmilliseconds), it is believed that a coalescence involves the formation of an\naccretion disc. Although neutrino emission from accreting material, resulting\nin neutrino-antineutrino annihilation along the rotational axis, has been\nproposed as a source of gamma rays, it seems more likely that amplification of\nmagnetic fields within the disc might trigger observed bursts. In either case,\nthe lifetime of the accretion disc is still problematic, if it is formed by the\nbreakup of the neutron star near the Roche limit. Its lifetime would probably\nbe only about a hundred times greater than the orbital frequency, or less than\na second. However, this timescale would be considerably enhanced if the\naccretion disc could be formed at larger radii than the Roche limit.\nA possible mechanism is stable mass transfer from the neutron star to\nthe black hole that would cause the neutron star to spiral away as it\nloses mass~\\cite{Kochanek,PZ}.\n\nThe classical Roche limit is based upon an incompressible fluid of density\n$\\rho$ and mass $M_2$ in orbit about a mass $M_1$. In Newtonian gravity, this\nlimit is\n\\begin{equation}\nR_{Roche, Newt}=(M_1/0.0901\\pi\\rho)^{1/3}= 19.2\n(M_1/{\\rm M}_\\odot\n\\rho_{15})^{1/3}{\\rm~km}\\,,\\label{roche}\n\\end{equation}\nwhere $\\rho_{15}=\\rho/10^{15}$ g cm$^{-3}$. Using general relativity,\nFishbone~\\cite{Fishbone} found that at the last stable circular orbit\n(including the case when the black hole is rotating) the number 0.0901\nin Eq.~(\\ref{roche}) becomes 0.0664. In geometrized units,\n$R_{Roche}/M_1=13(14.4)(M_1^2\\rho_{15}/{\\rm M}_\\odot^2)^{-1/3}$, where\nthe numerical coefficient refers to the Newtonian (last stable orbit\nin GR) case. In other words, if the neutron star's mean density is\n$\\rho_{15}=1$, the Roche limit is encountered beyond the last stable\norbit if the black hole mass is less than about 5.9 M$_\\odot$. Thus,\nfor small enough black holes, mass overflow and transfer from the\nneutron star to the black hole could begin outside the last stable\ncircular orbit. And, as now discussed, the mass transfer\nmay proceed stably for some\nconsiderable time. In fact, the neutron star might move to 2--3 times\nthe orbital radius where mass transfer began. This would provide a\nnatural way to lengthen the lifetime of an accretion disc, by simply\nincreasing its size.\n\nThe final evolution of a compact binary is now discussed. Define\n$q=m_{ns}/M_{BH}$, $\\mu=m_{ns}M_{BH}/M$, and $M=M_{BH}+m_{ns}$, where\n$m_{ns}$ and $M_{BH}$ are the neutron star and black hole masses,\nrespectively. The orbital angular momentum is\n\\begin{equation}\nJ^2=G\\mu^2 Ma=GM^3aq^2/(1+q)^4\\,.\n\\label{j2}\n\\end{equation}\nWe can employ Paczy\\'nski's~\\cite{pacz} formula for the Roche radius of the\nsecondary:\n\\begin{equation}\nR_\\ell/a=0.46[q/(1+q)]^{1/3}\\,,\n\\label{rl}\n\\end{equation}\nor a better fit by Eggleton~\\cite{eggleton}:\n\\begin{equation}\nR_\\ell/a=0.49[.6+q^{-2/3}\\ln(1+q^{1/3})]^{-1}\\,.\n\\label{eggleton}\n\\end{equation}\n\n\\begin{figure}[h]\n\\vspace{22pc}\n\\special{psfile=alpha.ps hoffset=410 voffset=-20 hscale=55 vscale=50 angle=90}\n\\caption{$d\\ln R/d\\ln m_{ns}\\equiv\\alpha$ (solid curve) and neutron star radius\n$R$ (dashed curve) as functions of neutron star mass $m_{ns}$ for a typical\ndense matter equation of state.}\n\\label{alpha}\n\\end{figure}\nThe orbital separation $a$ at the moment of mass transfer is obtained by\nsetting $R_\\ell=R$, the neutron star radius. For stable mass transfer, the\nstar's radius has to increase more quickly than the Roche radius as mass is\ntransferred. Thus, we must have, using Paczy\\'nski's formula,\n\\begin{equation}\n{d\\ln R\\over d\\ln m_{ns}}\\equiv\\alpha\\ge{d\\ln R_\\ell\\over d\\ln m_{ns}}= {d\\ln\na\\over d\\ln m_{ns}}+{1\\over3}\\label{dlnrdlnm2}\\end{equation}\nfor stable mass transfer.\n$\\alpha$ is defined in this expression, and is shown\nin Fig.~\\ref{alpha} for a typical EOS.\nIf the mass\ntransfer is conservative, than $\\dot J=\\dot J_{GW}$, where\n\\begin{equation}\n\\dot J_{GW}=-{32\\over5}{G^{7/2}\\over c^5}{\\mu^2 M^{5/2}\\over a^{7/2}}=\n-{32\\over5}{G^{7/2}\\over c^5}{q^2 M^{9/2}\\over(1+q)^4a^{7/2}}\\label{dotgw}\n\\end{equation}\nand\n\\begin{equation}\n{\\dot J\\over J}={\\dot a\\over2a}+{\\dot q(1-q)\\over\nq(1+q)}\\,.\\label{dotj}\n\\end{equation}\nThis leads to\n\\begin{equation}\n\\dot q\\left({\\alpha\\over2}+{5\\over6}-q\\right)\\ge -{32\\over5}{G^3\\over c^5}{q^2\nM^3\\over(1+q)a^4}\\,.\\label{dotq}\\end{equation} Since $m_{ns}<M_{BH}$,\n$\\dot q\\le0$, and the condition for stable\nmass transfer is simply $q\\le5/6+\\alpha/2$. For moderate\nmass neutron stars, $\\alpha\\approx0$, so in this case the condition is simply\n$q\\le5/6$, which might even be achievable in a binary neutron star system.\nHad we used the more exact formula of Eggleton, Eq. (\\ref{eggleton}), we would\nhave found $q\\le0.78$. Note that it has often been assumed that\n$R\\propto m_{ns}^{-1/3}$ in such discussions~\\cite{PZ}, which is equivalent to\n$\\alpha=-1/3$. This is unjustified, and results in the upper limit\n$q=2/3$ which might inappropriately rule out stable mass transfer in the case\nof two neutron stars.\n\nA number of other conditions must hold for stable mass transfer to occur.\nFirst, the orbital separation $a$ at the onset\nmust exceed the last stable orbit around the black hole, so that $a>6GM_{BH}/c^2$,\nor\n%$$[q^2(1+q)]^{1/3}\\ge2.76{GM_2\\over Rc^2}\\,.\\EQN{agt6m}$$\n\\begin{equation}\nq\\ge6{R_\\ell\\over a}{GM_{BH}\\over Rc^2}\\,.\n\\label{agt6m}\\end{equation}\nSecond, the tidal bulge raised on the neutron star must stay outside of the\nblack hole's Schwarzschild radius. Kochanek~\\cite{Kochanek} gives an estimate\nof the height of the tidal bulge needed to achieve the required mass loss rate:\n\\begin{equation}\n{\\Delta r\\over R}=\\Biggl[{-\\dot q\\over\\beta_t(1+q)\\Omega}\\Biggr]^{1/3}\\,,\\label{tidal}\n\\end{equation}\nwhere $\\beta_t$ is a dimensionless parameter of order 1 and\n$\\Omega=G^{1/2}M^{1/2}/a^{3/2}$ is the orbital frequency. For $\\dot q$ we\nuse the equality in Eq.~(\\ref{dotq}), which is equivalent to\n\\begin{equation}\nR_{sh}=2GM_{BH}/c^2\\le a-R-\\Delta r\\,.\\label{r-dr}\\end{equation} Finally, so\nthat the assumption of a Roche geometry is valid, it should be possible for\ntidal synchronization of the neutron star to be maintained. Bildstein \\&\nCutler~\\cite{BC} considered this, and derived an upper limit for the separation\n$a_{syn}$ at which tidal synchronization could occur by integrating the maximum\ntorque on the neutron star as it spirals in from infinity and finding where the\nneutron star spin frequency could first equal the orbital frequency. They find\n\\begin{equation}\na_{syn}\\le{M_{BH}^2m_{ns}^2\\over400M^3}\\Bigl({R\\over m_{ns}}\\Bigr)^6\\,,\\label{synch}\\end{equation}\nwhich translates to\n\\begin{equation}\n400\\Bigl({GM_{BH}\\over Rc^2}\\Bigr)^5{a\\over R_\\ell}{(1+q)^3\\over q}\\le1\\,.\\label{tidsyn}\n\\end{equation}\n\nNext we consider the effect of putting some of the angular momentum into an\naccretion disc. Following the discussion of Ref.~\\cite{BC}, we\nassume an accretion disc contains an amount of angular momentum that grows at\nthe rate\n\\begin{equation}\n\\dot J_d=-(1-f)M^{3/2}a^{1/2}(1+q)^{-4}\\dot q\\,,\\label{dotjd}\\end{equation}\nwhere $f$ is a parameter, taken to be a fit to the numerical results of Hut \\&\nPaczy\\'nski~\\cite{HP}:\n\\begin{equation}\nf=5q^{1/3}/3-3q^{2/3}/2\\,.\\label{hut}\\end{equation}\nWe then find the new condition for angular momentum conservation to be\n\\begin{equation}\n\\dot J+\\dot J_d=\\dot J_{GW}\\,,\\label{jdot}\\end{equation}\nwhich yields\n\\begin{equation}\n\\dot q\\Biggl[{\\alpha\\over2}-{1\\over6}+{f-q^2\\over1+q}\\Biggr]\\ge\n-{32\\over5}{G^3\\over c^5}{q^2 M^3\\over(1+q)a^4}\\,.\\label{dotqd}\\end{equation}\nTherefore, the new condition for stable mass transfer is\n\\begin{equation}\n(q^2-f)/(1+q)\\le \\alpha/2-1/6\\,.\\label{smtf}\\end{equation}\nThe case $f=1$ corresponds to neglecting the existance of an accretion disc.\n\nIt remains to determine when an accretion disc is likely to form. Initially,\nmatter flowing from the neutron star to the black hole through the inner\nLagrangian point passes close to the black hole and falls in. However, as the\nneutron star spirals away, the accretion stream trajectory moves outside the\nSchwarzschild radius. When the trajectory doesn't even penetrate the\nmarginally stable orbit, an accretion disc will begin to form. Particle\ntrajectory computations of the Roche geometry by Shore, Livio \\& van den\nHuevel~\\cite{SLv} suggest that its closest approach to the black hole is\n\\begin{equation}\nR_c=a(1+q)(0.5-0.227\\ln q)^4\\,.\n\\label{shore}\n\\end{equation}\nEquating $R_c$ to $6GM_{BH}/c^2$ yields\n\\begin{equation}\n(0.5-0.227\\ln q)^4(1+q)\\ge6{GM_{BH}\\over Rc^2}{R_\\ell\\over a}\\,.\n\\label{disc}\n\\end{equation}\n\n\\begin{figure}[h]\n\\vspace{24pc}\n\\special{psfile=smt.plt hoffset=435 voffset=-20 hscale=60 vscale=55 angle=90}\n\\caption{The dark and light shaded regions show the binary masses for which\nmass transfer in a black hole--neutron star binary will be stable in the\nabsence of, and the presence of, an accretion disc. The constraints\nEq.~(\\ref{agt6m}) ($a>6M_{BH}$), Eq.~(\\ref{r-dr}) (Tidal bulge OK),\nEq.~(\\ref{tidsyn}) (Tidal synchronization), and Eq.~(\\ref{disc})\n(Accretion disc\nforms) are shown by the appropriately labelled curves. The parallel, diagonal,\ndashed lines show evolutionary tracks for the labelled total BH+NS masses,\nbeginning in each case with $m_{ns}=1.5$ M$_\\odot$.}\n\\label{smt}\n\\end{figure}\n\nThese constraints and allowed regions for stable mass transfer are shown in\nFig.~\\ref{smt}. Apparently, stable mass transfer ceases when\n$m_{ns}\\approx0.14$ M$_\\odot$ if the formation of an accretion disc is ignored.\nIf the effects of disc formation are included, the stable mass transfer ceases\nwhen $m_{ns}\\approx0.22$ M$_\\odot$. In both cases, the neutron star mass\nremains above its minimum mass (about 0.09 M$_\\odot$ for the equation of state\nused here). Thus, the neutron star does not ``explode'' by reaching its\nminimum mass.\n\n\\begin{figure}[orbit]\n\\vspace{22pc}\n\\special{psfile=orbit.plt hoffset=400 voffset=-25 hscale=58 vscale=55 angle=90}\n\\caption{The separation of a 1.5 M$_\\odot$ neutron star with a 3 M$_\\odot$\nblack hole during a merger is indicated by the dot-dashed line during inspiral\nand by a solid line in the outspiral during stable mass transfer. Other curves\nshow the neutron star mass and radius during the stable mass transfer\n(outspiral) phase. Solid (dashed) lines are computed by ignoring (including)\nthe effects of an accretion disc.}\n\\label{orbit}\n\\end{figure}\n\nFig.~\\ref{orbit} shows the time development of the orbital separation\n$a$ and the neutron star's mass and radius during the inspiral and\nstable mass transfer phases. Solid lines are calculated assuming\nthere is no accretion disc formed, while dashed lines show the effects\nof accretion disc formation. The time evolutions during stable mass\ntransfer are obtained from Eq.~(\\ref{dotq}) and Eq.~(\\ref{dotqd}),\nusing $\\dot m_{ns}=\\dot q M/(1+q)^2$. With disc\nformation, the mass transfer is accelerated and the duration of the\nstable mass transfer phase is shortened considerably. Also, the\nneutron star spirals out to a smaller radius, and does not\nlose as much mass, as in the case when the accretion disc is\nignored.\n\nTherefore, if stable mass transfer can take place, the\ntimescale over which mass transfer occurs will be much longer than an orbital\nperiod, and lasts perhaps a few tenths of a second. This is not long enough to\nexplain gamma-ray bursts. However, we have also seen the likelihood that an\naccretion disc forms is quite large. Furthermore, the accretion disc extends\nto about 100 km. Even though this is considerably less than Ref.~\\cite{PZ}\nestimated, the lifetime of such an extended disc is considerable. To order of\nmagnitude, it is given by the viscous dissipation time, or\n\\begin{equation}\n\\tau_{visc}\\sim{D^2\\over\\alpha c_s H}.\n\\label{visc}\n\\end{equation}\nHere $D$ is the radial size of the disc, $\\alpha$ is the disc's\nviscosity parameter,\n$c_s$ is the sound speed and $H$ is the disc's thickness. Note that\n$c_s\\approx\\Omega H$ where $\\Omega=2\\pi/P=\\sqrt{GM_{BH}/D^3}$ is the Kepler\nfrequency. Thus,\n\\begin{equation}\n\\tau_{visc}\\sim {P\\over2\\pi\\alpha} \\Biggl({D\\over H}\\Biggr)^2\\,.\n\\end{equation}\nSince the magnitude of $\\alpha$ is still undetermined,\nand usually quoted~\\cite{Bran} to be about 0.01,\nand $H$ is likely to be of order $R$, we find $\\tau_{visc}\\sim 230$ s for our\ncase. This alleviates the timescale problem for these models. Numerical\nsimulations of such events are in progress, and it remains to be seen if a\nviable gamma-ray burst\nmodel from neutron star--black hole coalescence is possible.\nIf it is, a great deal of the credit should rest with Dave.\n\nWe thank Ralph Wijers for discussions\nconcerning accretion disks.\n\n\\begin{thebibliography}{999}\n\\bibitem{BBP} G. Baym, H.A. Bethe, and C.J. Pethick, {\\em\nNucl. Phys.} {\\bf A175} (1971) 225. \\\\\n\\bibitem{LPRL} J.M. Lattimer, C.J. Pethick, D.G. Ravenhall, and D.Q. Lamb,\n{\\em Nucl. Phys.} {\\bf A432} (1985) 646. \\\\\n\\bibitem{LS} J.M. Lattimer and F.D. Swesty, {\\em Nucl. Phys.} {\\bf A535}\n(1991) 331. \\\\\n\\bibitem{Blaizot} J.P. Blaizot, J.F. Berger, J. Decharg\\'e, and\nM. Girod, {\\em Nucl. Phys.} {\\bf A591} (1995) 431;\nD.H. Youngblood, H.L. Clark, and Y.-W. Lui, {\\em Phys. Rev. Lett.}\n{\\bf 82} (199) 691. \\\\\n\\bibitem{P}J.M. Pearson, {\\em Phys. Lett.} {\\bf B271} (1991) 12. \\\\\n\\bibitem{L} J.M. Lattimer, in {\\em Nuclear Equation of State\\/},\nA. Ansari and L. Satpathy, eds., World Scientific, Singapore, 1996, p. 83. \\\\\n\\bibitem{Lip} E. Lipparini and S. Stringari, {\\em Phys. Lett.} {\\bf B112}\n(1982) 421. \\\\\n\\bibitem{Sato} K. Sato, {\\em Prog. Theor. Phys.} {\\bf 53} (1975) 595;\n{\\bf 54} (1975) 1325. \\\\\n\\bibitem{LBY} J.M. Lattimer, A. Burrows, and A. Yahil, {\\em Astrophys. J.}\n{\\bf 288} (1985) 644. \\\\\n\\bibitem{SLM} F.D. Swesty, J.M. Lattimer, and E. Myra, {\\em Astrophys. J.}\n{\\bf 425} (1994) 195. \\\\\n\\bibitem{LP} J.M. Lattimer and M. Prakash, in preparation (2000). \\\\\n\\bibitem{RP} D.G. Ravenhall and C.J. Pethick, {\\em Astrophys. J.} {\\bf\n424} (1994) 846. \\\\\n\\bibitem{Link} B. Link, R.I. Epstein, and J.M. Lattimer, {\\em\nPhys. Rev. Lett.} {\\bf 83} (1999) 3362.\\\\\n\\bibitem{Tit}L. Titarchuk, {\\em Astrophys. J.} {\\bf 429} (1994) 340;\nF. Haberl and L. Titarchuk,\n{\\em Astron. Astrophys.} {\\bf 299} (1995) 414. \\\\\n\\bibitem{LPMY} J.M. Lattimer, M. Prakash, D. Masak, and A. Yahil, {\\em\nAstrophys. J.} {\\bf 355} (1990) 241. \\\\\n\\bibitem{glen} N.K. Glendenning, {\\em Phys. Rev. D} {\\bf 46} (1992) 4161. \\\\\n\\bibitem{Page}D. Page, {\\em Astrophys. J.} {\\bf 442} (1995) 273. \\\\\n\\bibitem{Walter}F.M. Walter, S.J. Wolk and R. Neuh\\\"auser,\n{\\em Nature} {\\bf 379} (1996) 233; F.M. Walter, {\\em et al}.,\n{\\em Nature} {\\bf 389} (1997) 358. \\\\\n\\bibitem{Romani} R.W. Romani, {\\em Astrophys. J.} {\\bf 313} (1987) 718. \\\\\n\\bibitem{ALPW} P. An, J.M. Lattimer, M. Prakash and F.M. Walter, in\npreparation (2000). \\\\\n\\bibitem{FP} B. Friedman and V.R. Pandharipande, {\\em Nucl. Phys.} {\\bf\nA361} (1981) 502. \\\\\n\\bibitem{PS} V. R. Pandharipande and R. A. Smith, {\\em Nucl. Phys.} {\\bf A237} (1975) 507. \\\\\n\\bibitem{WFF} R.B. Wiringa, V. Fiks, and A. Fabrocine, {\\em Phys. Rev.}\n{\\bf C38} (1988)1010. \\\\\n\\bibitem{Akmal} A. Akmal and V.R. Pandharipande, {\\em Phys. Rev.} {\\bf\nC56} (1997) 2261. \\\\\n\\bibitem{MS} H. M\\\"uller and B.D. Serot, {\\em Nucl. Phys.} {\\bf 606}\n(1996) 508. \\\\\n\\bibitem{MPA} H. M\\\"uther, M. Prakash, and T.L. Ainsworth, {\\em Phys. Lett.}\n{\\bf 199} (1987) 469. \\\\\n\\bibitem{Engvik} L. Engvik, M. Hjorth-Jensen, E. Osnes, G. Bao, and\nE. \\O stgaard, {\\em Phys. Rev. Lett.} {\\bf 73} (1994) 2650. \\\\\n\\bibitem{PAL} M. Prakash, T.L. Ainsworth, and J.M. Lattimer, {\\em\nPhys. Rev. Lett.} {\\bf 61} (1988) 2518. \\\\\n\\bibitem{GM} N.K. Glendenning and S.A. Moszkowski, {\\em Phys. Rev. Lett.}\n{\\bf 67} (1991) 2414. \\\\\n\\bibitem{GS} N.K. Glendenning and J\\\"uergen Schaffner-Bielich,\n{\\em Phys. Rev.} {\\bf C60} (1999) 025803. \\\\\n\\bibitem{PCL} M. Prakash, J. R. Cooke and J. M. Lattimer, {\\em Phys. Rev.} {\\bf 52} (1995) 661. \\\\\n\\bibitem{physrep} M. Prakash, I. Bombaci, M. Prakash, J.M. Lattimer,\nP. Ellis, and R. Knorren, {\\em Phys. Rep.} {\\bf 280} (1997) 1. \\\\\n\\bibitem{Buchdahl} H.A. Buchdahl, {\\em Astrophys. J.} {\\bf 147} (1967) 310. \\\\\n\\bibitem{Ppuri} M. Prakash, in {\\em Nuclear Equation of State\\/},\nA. Ansari and L. Satpathy, eds., World Scientific, Singapore, 1996, p. 229. \\\\\n\\bibitem{Delgaty} M.S.R. Delgaty and\nK. Lake, {\\em Computer Physics Communications}\n{\\bf 115} (1998) 395. \\\\\n\\bibitem{Tolman} R.C. Tolman, {\\em Phys. Rev.} {\\bf 55} (1939) 364. \\\\\n\\bibitem{Indians} M.C. Durgapal and A. K. Pande,\n{\\em J. Pure \\& Applied Phys.} {\\bf 18} (1980) 171. \\\\\n\\bibitem{LY} J.M. Lattimer and A. Yahil, {\\em Astrophys. J.} {\\bf 340} (1989)\n 426.\\\\\n\\bibitem{LSch} J.M. Lattimer and D.N. Schramm, {\\em Astrophys. J. (Letters)\\/},\n{\\bf 192} (1974) L145; {\\em Astrophys. J.\\/} {\\bf 210} (1976) 549. \\\\\n\\bibitem{HT} R.A. Hulse and J.H. Taylor, {\\em Astrophys. J. (Letters)\\/}, {\\bf\n195} (1975) L51.\\\\\n\\bibitem{thesisL} J.M. Lattimer, Ph.D thesis, University of Texas at\nAustin, unpublished (1976). \\\\\n\\bibitem{Peters} P.C. Peters, {\\em Phys. Rev.} {\\bf 136} (1964) 1224. \\\\\n\\bibitem{eichler} D. Eichler, M. Livio, T. Piran, and\nD.N. Schramm, {\\em Nature}\n{\\bf 340} (1989) 126. \\\\\n\\bibitem{Kochanek} C.S. Kochanek, {\\em Astrophys. J.} {\\bf 398} (1992)\n234. \\\\\n\\bibitem{PZ}S.F. Portegies Zwart, {\\em Astrophys. J. (Letters)}, {\\bf 503}\n(1998) L53. \\\\\n\\bibitem{Fishbone} L. Fishbone, {\\em Astrophys. J. (Letters)}, {\\bf 175} (1972)\nL155. \\\\\n\\bibitem{pacz} B. Paczy\\'nski, {\\em Ann. Rev. Astron. Astrophys.} {\\bf\n9} (1971) 183. \\\\\n\\bibitem{eggleton} P.P. Eggleton, {\\em Astrophys. J.} {\\bf 368} (1978) 369. \\\\\n\\bibitem{BC} L. Bildstein and C. Cutler, {\\em Astrophys. J.\\/} {\\bf 400} (1992)\n175. \\\\\n\\bibitem{HP} P. Hut and B. Paczy\\'nski, {\\em Astrophys. J.\\/} {\\bf 284}\n(1984) 675. \\\\\n\\bibitem{SLv} S. Shore, M. Livio, and E.P.J. van den Huevel, in {\\em\nInteracting Binaries}, Saas-Fee Advanced Course 22 for Astronomy and\nAstrophysics, 1992, 145. \\\\\n\\bibitem{Bran} A. Brandenburg, A. Nordlund, R.F. Stein, and U. Torkelsson,\n{\\em Astrophys. J. (Letters)} {\\bf 458} (1996) L45.\n\n\n\\end{thebibliography}\n\\end{document}\n\\end\n\n\\begin{table*}\n\\caption{EOS symbols}\n\\label{eosname}\n\\begin{center}\n\\begin{tabular}{l|c|c} \\hline\nSymbol & Reference & Notes \\\\ \\hline\nAV1, AV2, AV3, A\\&P, A\\&P2 & \\cite{Akmal} & Variational calculation \\\\\nFP & \\cite{FP} & Variational calculation \\\\\nWFF1, WFF2, WFF3 & \\cite{WFF} & Variational calculation \\\\\nMPA1, MPA2 & \\cite{MPA} & Dirac-Brueckner Hartree Fock \\\\\nEngvik & \\cite{Engvik} & Dirac-Brueckner Hartree Fock \\\\\nPAL1, PAL2, PAL3, PAL4, PAL5 & \\cite{PAL} & Schematic potential \\\\\nGMH1, GMH2, GMH3 & \\cite{GM} & Field-theoretical \\\\\nMS1, MS2, MS3 & \\cite{MS} & Field-theoretical \\\\\nkaon & \\cite{LP} & Schematic potential with kaons \\\\\nGS1, GS2 & \\cite{SG} & Field-theoretical with kaons \\\\ \\hline\n\\end{tabular}\n%\\end{table}\n\\end{center}\n\\end{table*}\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002203.extracted_bib",
"string": "\\begin{thebibliography}{999}\n\\bibitem{BBP} G. Baym, H.A. Bethe, and C.J. Pethick, {\\em\nNucl. Phys.} {\\bf A175} (1971) 225. \\\\\n\\bibitem{LPRL} J.M. Lattimer, C.J. Pethick, D.G. Ravenhall, and D.Q. Lamb,\n{\\em Nucl. Phys.} {\\bf A432} (1985) 646. \\\\\n\\bibitem{LS} J.M. Lattimer and F.D. Swesty, {\\em Nucl. Phys.} {\\bf A535}\n(1991) 331. \\\\\n\\bibitem{Blaizot} J.P. Blaizot, J.F. Berger, J. Decharg\\'e, and\nM. Girod, {\\em Nucl. Phys.} {\\bf A591} (1995) 431;\nD.H. Youngblood, H.L. Clark, and Y.-W. Lui, {\\em Phys. Rev. Lett.}\n{\\bf 82} (199) 691. \\\\\n\\bibitem{P}J.M. Pearson, {\\em Phys. Lett.} {\\bf B271} (1991) 12. \\\\\n\\bibitem{L} J.M. Lattimer, in {\\em Nuclear Equation of State\\/},\nA. Ansari and L. Satpathy, eds., World Scientific, Singapore, 1996, p. 83. \\\\\n\\bibitem{Lip} E. Lipparini and S. Stringari, {\\em Phys. Lett.} {\\bf B112}\n(1982) 421. \\\\\n\\bibitem{Sato} K. Sato, {\\em Prog. Theor. Phys.} {\\bf 53} (1975) 595;\n{\\bf 54} (1975) 1325. \\\\\n\\bibitem{LBY} J.M. Lattimer, A. Burrows, and A. Yahil, {\\em Astrophys. J.}\n{\\bf 288} (1985) 644. \\\\\n\\bibitem{SLM} F.D. Swesty, J.M. Lattimer, and E. Myra, {\\em Astrophys. J.}\n{\\bf 425} (1994) 195. \\\\\n\\bibitem{LP} J.M. Lattimer and M. Prakash, in preparation (2000). \\\\\n\\bibitem{RP} D.G. Ravenhall and C.J. Pethick, {\\em Astrophys. J.} {\\bf\n424} (1994) 846. \\\\\n\\bibitem{Link} B. Link, R.I. Epstein, and J.M. Lattimer, {\\em\nPhys. Rev. Lett.} {\\bf 83} (1999) 3362.\\\\\n\\bibitem{Tit}L. Titarchuk, {\\em Astrophys. J.} {\\bf 429} (1994) 340;\nF. Haberl and L. Titarchuk,\n{\\em Astron. Astrophys.} {\\bf 299} (1995) 414. \\\\\n\\bibitem{LPMY} J.M. Lattimer, M. Prakash, D. Masak, and A. Yahil, {\\em\nAstrophys. J.} {\\bf 355} (1990) 241. \\\\\n\\bibitem{glen} N.K. Glendenning, {\\em Phys. Rev. D} {\\bf 46} (1992) 4161. \\\\\n\\bibitem{Page}D. Page, {\\em Astrophys. J.} {\\bf 442} (1995) 273. \\\\\n\\bibitem{Walter}F.M. Walter, S.J. Wolk and R. Neuh\\\"auser,\n{\\em Nature} {\\bf 379} (1996) 233; F.M. Walter, {\\em et al}.,\n{\\em Nature} {\\bf 389} (1997) 358. \\\\\n\\bibitem{Romani} R.W. Romani, {\\em Astrophys. J.} {\\bf 313} (1987) 718. \\\\\n\\bibitem{ALPW} P. An, J.M. Lattimer, M. Prakash and F.M. Walter, in\npreparation (2000). \\\\\n\\bibitem{FP} B. Friedman and V.R. Pandharipande, {\\em Nucl. Phys.} {\\bf\nA361} (1981) 502. \\\\\n\\bibitem{PS} V. R. Pandharipande and R. A. Smith, {\\em Nucl. Phys.} {\\bf A237} (1975) 507. \\\\\n\\bibitem{WFF} R.B. Wiringa, V. Fiks, and A. Fabrocine, {\\em Phys. Rev.}\n{\\bf C38} (1988)1010. \\\\\n\\bibitem{Akmal} A. Akmal and V.R. Pandharipande, {\\em Phys. Rev.} {\\bf\nC56} (1997) 2261. \\\\\n\\bibitem{MS} H. M\\\"uller and B.D. Serot, {\\em Nucl. Phys.} {\\bf 606}\n(1996) 508. \\\\\n\\bibitem{MPA} H. M\\\"uther, M. Prakash, and T.L. Ainsworth, {\\em Phys. Lett.}\n{\\bf 199} (1987) 469. \\\\\n\\bibitem{Engvik} L. Engvik, M. Hjorth-Jensen, E. Osnes, G. Bao, and\nE. \\O stgaard, {\\em Phys. Rev. Lett.} {\\bf 73} (1994) 2650. \\\\\n\\bibitem{PAL} M. Prakash, T.L. Ainsworth, and J.M. Lattimer, {\\em\nPhys. Rev. Lett.} {\\bf 61} (1988) 2518. \\\\\n\\bibitem{GM} N.K. Glendenning and S.A. Moszkowski, {\\em Phys. Rev. Lett.}\n{\\bf 67} (1991) 2414. \\\\\n\\bibitem{GS} N.K. Glendenning and J\\\"uergen Schaffner-Bielich,\n{\\em Phys. Rev.} {\\bf C60} (1999) 025803. \\\\\n\\bibitem{PCL} M. Prakash, J. R. Cooke and J. M. Lattimer, {\\em Phys. Rev.} {\\bf 52} (1995) 661. \\\\\n\\bibitem{physrep} M. Prakash, I. Bombaci, M. Prakash, J.M. Lattimer,\nP. Ellis, and R. Knorren, {\\em Phys. Rep.} {\\bf 280} (1997) 1. \\\\\n\\bibitem{Buchdahl} H.A. Buchdahl, {\\em Astrophys. J.} {\\bf 147} (1967) 310. \\\\\n\\bibitem{Ppuri} M. Prakash, in {\\em Nuclear Equation of State\\/},\nA. Ansari and L. Satpathy, eds., World Scientific, Singapore, 1996, p. 229. \\\\\n\\bibitem{Delgaty} M.S.R. Delgaty and\nK. Lake, {\\em Computer Physics Communications}\n{\\bf 115} (1998) 395. \\\\\n\\bibitem{Tolman} R.C. Tolman, {\\em Phys. Rev.} {\\bf 55} (1939) 364. \\\\\n\\bibitem{Indians} M.C. Durgapal and A. K. Pande,\n{\\em J. Pure \\& Applied Phys.} {\\bf 18} (1980) 171. \\\\\n\\bibitem{LY} J.M. Lattimer and A. Yahil, {\\em Astrophys. J.} {\\bf 340} (1989)\n 426.\\\\\n\\bibitem{LSch} J.M. Lattimer and D.N. Schramm, {\\em Astrophys. J. (Letters)\\/},\n{\\bf 192} (1974) L145; {\\em Astrophys. J.\\/} {\\bf 210} (1976) 549. \\\\\n\\bibitem{HT} R.A. Hulse and J.H. Taylor, {\\em Astrophys. J. (Letters)\\/}, {\\bf\n195} (1975) L51.\\\\\n\\bibitem{thesisL} J.M. Lattimer, Ph.D thesis, University of Texas at\nAustin, unpublished (1976). \\\\\n\\bibitem{Peters} P.C. Peters, {\\em Phys. Rev.} {\\bf 136} (1964) 1224. \\\\\n\\bibitem{eichler} D. Eichler, M. Livio, T. Piran, and\nD.N. Schramm, {\\em Nature}\n{\\bf 340} (1989) 126. \\\\\n\\bibitem{Kochanek} C.S. Kochanek, {\\em Astrophys. J.} {\\bf 398} (1992)\n234. \\\\\n\\bibitem{PZ}S.F. Portegies Zwart, {\\em Astrophys. J. (Letters)}, {\\bf 503}\n(1998) L53. \\\\\n\\bibitem{Fishbone} L. Fishbone, {\\em Astrophys. J. (Letters)}, {\\bf 175} (1972)\nL155. \\\\\n\\bibitem{pacz} B. Paczy\\'nski, {\\em Ann. Rev. Astron. Astrophys.} {\\bf\n9} (1971) 183. \\\\\n\\bibitem{eggleton} P.P. Eggleton, {\\em Astrophys. J.} {\\bf 368} (1978) 369. \\\\\n\\bibitem{BC} L. Bildstein and C. Cutler, {\\em Astrophys. J.\\/} {\\bf 400} (1992)\n175. \\\\\n\\bibitem{HP} P. Hut and B. Paczy\\'nski, {\\em Astrophys. J.\\/} {\\bf 284}\n(1984) 675. \\\\\n\\bibitem{SLv} S. Shore, M. Livio, and E.P.J. van den Huevel, in {\\em\nInteracting Binaries}, Saas-Fee Advanced Course 22 for Astronomy and\nAstrophysics, 1992, 145. \\\\\n\\bibitem{Bran} A. Brandenburg, A. Nordlund, R.F. Stein, and U. Torkelsson,\n{\\em Astrophys. J. (Letters)} {\\bf 458} (1996) L45.\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002204
|
OBSERVED SMOOTH ENERGY IS ANTHROPICALLY EVEN MORE LIKELY AS QUINTESSENCE THAN AS COSMOLOGICAL CONSTANT
|
[
{
"author": "Sidney Bludman"
},
{
"author": "Deutsches Elektronen-Synchrotron DESY"
},
{
"author": "Hamburg"
},
{
"author": "Philadelphia \\thanks{Supported in part by Department of Energy grant DE-FGO2-95ER40893}"
}
] |
For a universe presently dominated by static or dynamic vacuum energy, cosmological constant (LCDM) or quintessence (QCDM), we calculate the asymptotic collapsed mass fraction as function of the present ratio of vacuum energy to clustered mass, $\omq/\omm$. Identifying these collapsed fractions as anthropic probabilities, we find the present ratio $\omq/\omm \sim 2$ to be reasonably likely in LCDM, and very likely in QCDM.
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[
{
"name": "Cosmo99WS.tex",
"string": "\\documentclass{article} %2.8.00 f\n\\usepackage[dvips]{graphicx,color} \\usepackage{epsfig}\n\\DeclareGraphicsExtensions{.ep.gz,.eps,.ps,lps.gz}\n\\setlength{\\textheight}{22.5cm} \\setlength{\\textwidth}{15.6cm}\n\\setlength{\\oddsidemargin}{0.4cm} \\setlength{\\topmargin}{-5mm}\n\\newcommand{\\ombe}{\\Omega_B}\n\\newcommand{\\omm}{\\Omega_{m0}}\n\\newcommand{\\omlam}{\\Omega_{\\Lambda}}\n\\newcommand{\\omq}{\\Omega_{Q0}}\n\\newcommand{\\omx}{\\Omega_{X0}}\n\\newcommand{\\bc}{\\begin{center}}\n\\newcommand{\\ec}{\\end{center}}\n\\begin{document} %follows before \\title\n\\title{\\bf OBSERVED SMOOTH ENERGY IS ANTHROPICALLY EVEN MORE LIKELY AS\n QUINTESSENCE THAN AS COSMOLOGICAL CONSTANT}\n\n\\author{Sidney Bludman\\\\Deutsches Elektronen-Synchrotron DESY, Hamburg\\\\\n University of Pennsylvania, Philadelphia \\thanks{Supported in\n part by Department of Energy grant DE-FGO2-95ER40893}}\n\n\\maketitle\n\n\\abstract{For a universe presently dominated by static or dynamic\n vacuum energy, cosmological constant (LCDM) or quintessence (QCDM),\n we calculate the asymptotic collapsed mass fraction as function of\n the present ratio of vacuum energy to clustered mass, $\\omq/\\omm$.\n Identifying these collapsed fractions as anthropic probabilities, we\n find the present ratio $\\omq/\\omm \\sim 2$ to be reasonably likely in LCDM,\n and very likely in QCDM.}\n\\section {A Cosmological Constant or Quintessence?}\n\nAbsent a symmetry principle protecting its value, no theoretical\nreason for making the cosmological constant zero or small has been\nfound. Inflation makes the universe flat, so that, at present, the\nvacuum or smooth energy density $\\Omega_{Q0}=1-\\omm < 1$, is $10^{120}$\ntimes smaller than would be expected on current particle theories. To\nexplain this small but non-vanishing present value, a dynamic vacuum energy,\nquintessence, has been invoked, which obeys the equation\nof state $w_Q \\equiv P/\\rho <0$. (The limiting case, $w_Q=-1$, a static\nvacuum energy or Cosmological Constant, is homogeneous on all scales.)\n\nAccepting this small but non-vanishing value for static or dynamic\nvacuum energy, the {\\em Cosmic Coincidence} problem now becomes\npressing: Why do we live when the clustered matter density\n$\\Omega(a)$, which is diluting as $a^{-3}$ with cosmic scale $a$, is\njust now\ncomparable to the static vacuum energy or present value of the smooth\nenergy:\n $$u_0^3 \\equiv \\Omega_{Q0}/\\omm \\sim 2 . $$\n\nThe observational evidence\\cite{WCOS}\nis for a flat, low-density universe:\\\\\n \n(1) $\\Omega_m+\\Omega_Q=1 \\pm 0.2$ \\\\\n(Location of first Doppler peak in the CBR anisotroy at $l \\sim 200$);\\\\\n(2) $\\omm=0.3 \\pm 0.05$. (Slow evolution\nof rich clusters, mass power spectrum, CBR anisotropy, cosmic flows);\\\\\n(3) $\\omq=1-\\omm \\sim 2/3$ (curvature in SNIa Hubble diagram, dynamic\nage,height of first Doppler peak, cluster evolution).\\\\\nOf these, the SNIa evidence is most subject to systematic errors due\nto precursor intrinsic evolution and the possibilty of grey dust extinction.\n\nThe combined data implies a flat, low-density universe with $\\omm \\sim\n1/3$, with negative pressure $ -1 \\leq w_Q \\leq -1/2 $. In this\npaper, we use the evolution of large-scale structure to distinguish\nthe two limiting cases:\\\\ \\\\\nLCDM: Cosmological constant: $w_Q=-1, \\quad n_Q\\equiv 3(1+w_Q)=0 \\quad \\omlam =2/3 $ \\\\\nQCDM: Quintessence: $ w_Q =-1/2, n_Q=3/2,\\quad \\Omega_{Q0}=1/3$ .\n\n\\section {Evolution of a Low Density Flat Universe}\n\nThe Friedmann equation in a flat universe with clustered matter and\nsmooth energy density is\n$$\nH^2(x) \\equiv (\\dot{a}/a)^2=(8 \\pi G/3)(\\rho_m+\\rho_Q), $$\nor, in units of $\\rho_{cr}(x)=3H^2(x)/8\\pi G$,\n$1=\\Omega_m(x)+\\Omega_Q(x),$ where the reciprocal scale factor $x \\equiv\na_0/a \\equiv 1+z \\rightarrow \\infty$ in the far past, $\\rightarrow 0$\nin the far future.\n\nWith the EOS $w \\equiv P/\\rho$, different kinds of energy density dilute at\ndifferent rates $\\rho \\sim a^{-n},~n \\equiv 3(1+w)$, and contribute to\nthe deceleration at different rates $(1+3w)/2$ shown in the table:\\\\ \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n \\begin{table}[h]{\\bfseries Energy Dilution for Various Equations of\n State}\\\\[1ex]\n \\centering\n \\begin{tabular*}{115mm}{@{\\extracolsep{\\fill}}l|ccc@{}} \\hline\n \n {\\em substance} &{\\em w} &{\\em n} &{\\em (1+3w)/2} \\\\ \\hline\n radiation & 1/3 & 4 &1 \\\\\n NR matter & 0 & 3 &1/2 \\\\\n quintessence & -1/2 & 3/2 &-1/4 \\\\\n cosmolconst & -1 & 0 &-1 \\\\\n \\hline \n \\end{tabular*}\\\\[0.5ex]\n \\end{table}\\\\\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nThe expansion rate in present Hubble units is \n$$ E(x) \\equiv H(x)/H_0=(\\omm x^3+ (1-\\omm) x^n_Q)^{1/2}. $$\nThe Friedmann equation has an unstable fixed point\nin the far past and a stable attractor in the far future. (Note the\ntacit application of the anthropic principle: Why does our universe\nexpand, rather than contract?)\n\nThe second Friedmann equation is $-\\ddot{a} a/{\\dot{a}^2}=(1+3w_Q\n\\Omega_Q)/2 $. The ratio of smooth energy to matter energy,\n$\\Omega_Q/\\Omega_m \\equiv u^3=u_0^3x^{3w_Q}$, where $ \\Omega_{Q0} /\n\\omm \\equiv u_0^3 \\sim 2$ is the present ratio. \nAs shown by the inflection points in the middle curves of the figure,\nfor fixed $\\Omega_{Q0}/\\Omega_{m0}$, QCDM (upper middle curve) expands\nfaster than LCDM (lower middle curve), but begins accelerating only\nat the present epoch. The top and bottom curves refer respectively to\na De Sitter universe ($\\Omega_m=0$), which is always accelerating, and\nan SCDM universe ($\\Omega_m=1$), which is always decelerating.\n\\nopagebreak\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{figure}[b]\n\\begin{center} \n\\epsfig{file=RecPresplot.eps,width=12cm,height=6.5cm} \n\\end{center} \\end{figure}\n%\\epsfig{} could include adding bounding box to .ps file, but I have already\n%written bounding box onto top of .eps. \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n \n\\pagebreak\nAs summarized in the table below, quintessence dominance begins 3.6\n Gyr earlier and more gradually than cosmological constant dominance.\n (In this table, the deceleration $q(x) \\equiv -\\ddot{a}/aH_0^2$ is\n measured in {\\em present} Hubble units.) The recent lookback time\n$$H_0t_L(z)=z-(1+q_0)z^2+...,\\quad z<1 ,$$\nwhere $q_0=0$ for QCDM and $=- 1/2$ for LCDM. \n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n \\begin{table}[h]{\\bfseries Comparative Evolution of LCDM and QCDM}\\\\[1ex] \n \\centering\n \\noindent\n \\begin{tabular*}{125mm}{@{\\extracolsep{\\fill}}l|cc@{}} \\hline\n {\\em event} & {\\em LCDM} & {\\em QCDM} \\\\\n \\hline \\hline\n {\\bf Onset of Vacuum Dominance}& & \\\\\n reciprocal scale x*=$a_0/a=1+z$ &$u_0$=1.260 &$u_0^2$=1.587 \\\\\n age t(x*) ($H_0^{-1}$) &0.720 &0.478 \\\\\n $h_{65}^{-1}$Gyr &10.8 &7.2 \\\\ \\hline\n horizon(x*) ($cH_0^{-1})$ &2.39 &1.58 \\\\\n $h_{65}^{-1}$Gpc &11.0 &7.24 \\\\ \\hline\n deceleration q(x*) at freeze-out &-0.333 &0.333\n \\\\ \\hline \\hline\n {\\bf Present Epoch} & & \\\\\n age t0 ($H_0^{-1}$) &0.936 &0.845 \\\\\n $h_{65}^{-1}$Gyr &14.0 &12.7 \\\\ \\hline\n horizon &3.26 &2.96 \\\\\n $h_{65}^{-1}$Gpc &15.0 &13.6 \\\\ \\hline\n present deceleration $q_0$ &-0.500 &0 \\\\ \\hline \n \n \n \\end{tabular*}\n \\end{table}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n \n The density ratio $u^3(a)\\equiv \\Omega_Q/\\Omega_m=u_0^3 x^{3 w_Q}$,\n increases as the matter density decreases. The\n matter-smooth energy transition $\\Omega_Q/\\Omega_m=1$ took place only\n recently at $x*^{-w_Q}=u_0$ or at $x*=1+z*=u_0^2=1.5874$ for QCDM\n and, even later, at $x*=1+z*=u_0=1.260$ for LCDM. Because, for the\n same value of $u_0$, a matter-QCDM freeze-out would take place\n earlier and more slowly than a matter-LCDM freeze-out, it imposes a\n stronger constraint on structure evolution. To permit evolution to the same\n present structure, QCDM would require a smaller value of $\\omq/\\omm$ than\n does LCDM.\n\n\\section{Growth of Large Scale Structure}\n\nThe background density for large-scale structure formation\n is overwhelmingly Cold Dark Matter (CDM), consisting of clustered\n matter $\\Omega_m$ and smooth energy or quintessence $\\Omega_Q$.\n Baryons, contributing only a fraction to $\\Omega_m$, collapse after\n the CDM and, particularly in small systems, produce the large\n overdensities that we see. \n \n Structure formation begins and ends with matter dominance, and is\n characterized by two scales: The horizon scale at the first\n cross-over, from radiation to matter dominance, determines the power\n spectrum $P(k,a)$, which is presently characterized by a scale\n factor $\\Gamma=\\omm h =0.25 \\pm 0.05$. The horizon scale at the\n second cross-over, from matter to smooth energy, determines a second\n scale factor, which for quintessence, is $\\Gamma_Q$ at $\\sim\n 130~Mpc$, the scale of voids, superclusters. A cosmological\n constant is smooth at all scales.\n \n \n Quasars formed as far back as $z \\sim 5$, galaxies at $z \\geq 6.7$,\n ionizing sources at $z=(10-30)$. The formation of {\\em any} such\n structures, already sets an upper bound $x*<30$ or $(\\omlam /\n \\omm)<1000, \\omq<30$, for {\\em any} structure to have formed. A\n much stronger upper bound, $u_0<5$, is set by when {\\em typical}\n galaxies form i.e. by using the observed LSS, not to fix $\\omlam$ or\n $u_0^3$, but to estimate the probability of our observing this ratio\n $\\omq/\\omm$ at the present epoch.\n \n For LCDM, Martel {\\it et al} \\cite{MSW} and Garriga {\\it et\n al} \\cite{MS} calculate the asymptotic mass fraction that\n ultimately collapses into galaxies to be\n$$f_{c,\\infty}=\\mbox{erfc}(\\beta^{1/2}),$$\nremarkably a broad function of only $\\beta\n\\equiv \\delta_{i,c}^2/2(\\sigma_i)^2$, where\n$\\sigma_i^2=(1.7-2.3)/(1+z_i)$ is the variance of the mass power\nspectrum and $\\delta_{i,c}$\nis the minimum density contrast which will\nmake an ultimately bound perturbation. This minimum density contrast\ngrows with scale factor $a$, and is approximately unity at\nrecombination. Thus, except for a numerical\nfactor of order unity \\cite{MS}, $\\delta_{i,c} \\sim x*/(1+z_i)$, \nthe freeze-out projected back to recombination.\nBoth numerator and denominator\nin $\\beta$ refer to the time of recombination, but this initial time\nor red-shift cancels out in the quotient. \n \n\n\\section{$\\Omega_Q \\sim \\Omega_m$ is \nQuite Likely for Our Universe}\n\n\nFor a cosmological constant, an anthropic argument has\nalready been given \\cite{E,V,MSW,GLV}, assuming a universe of subuniverses\nwith all possible values for the vacuum energy $\\rho_V$ or $\\omlam$.\nIn each of these subuniverses, the probability\nfor habitable galaxies to have emerged before the present epoch, is a\nfunction of $\\omlam$ or the present ratio $\\omlam/\\omm$ \n$$\\mathcal{P}(\\rho_V) \\propto (\\mbox{prior distribution in} ~\\rho_V)\n\\times(\\mbox{asymptotic mass fraction} ~f_{c,\\infty}). $$\nMSW,\nassuming nothing about initial conditions, assume a prior flat in\n$\\omlam$. GLV argue that the prior should be determined by a theory\nof initial conditions and is {\\em not} flat for most theories.\n \nFollowing MSW, we assume a flat prior, so that the differential\nprobability $\\mathcal{P}$ for our being here to observe a value\n$\\rho_V$ in our universe is simply proportional to the asymptotic\ncollapsed mass fraction for this $\\rho_V$. For LCDM,\n$$\\delta_{i,c}=1.1337 u_0/(1+z_i) , \\quad \\quad 1.1337=(27/2)^{2/3}/5.\n$$\nAs function of the ratio $\\omlam/\\omm=u_0^3$, the LCDM probability\ndistribution has a broad peak about $u_0^3 \\approx 12-30$. The value\nobserved in our universe $u_0^3 \\approx 2$ has reasonable probability\n$4-10\\%$.\n\nThis argument \\cite{MSW,GLV} for LCDM ($w_Q=-1$) is easily extended to\nQCDM ($w_Q=-1/2$). The variance of the power spectrum, $\\sigma^2$, is\ninsensitive to $w_Q$ for $w_Q<-1/3$ \\cite{WS}. For $w_Q=-1/2$, the numerical\nfactor in $\\delta_{i,c}$ is the same as for $w_Q=-1$, but $x*=u_0^2$ in\nplace of $u_0$, \nso that $\\delta_{i,c}=1.1337\nu_0^2/(1+z_i)$. Thus $\\beta_{QCDM}(u_0)=\\beta_{LCDM}(\\sqrt{u_0})$, so\nthat the QCDM probability distribution now peaks at $u_0^3 \\approx\n3.5-5.5$. With QCDM, the probability for observing $u_0^3 \\approx 2$\nis now increased to about 50\\%.\n\n\\begin{thebibliography}{99}\n\n\\bibitem{WCOS} L. Wang, R.R. Caldwell, J.P. Ostriker and\n P.J. Steinhardt, astro-ph/9901388.\n\n\\bibitem{E} G. Efstathiou, M.N.R.A.S. {\\bf 274}, L73 (1995).\n\n\\bibitem{V} A. Vilenkin, Phys. Rev. Lett. {\\bf 74}, 846 (1995).\n\n\\bibitem{MSW} H. Martel, P.R. Shapiro and S. Weinberg, Ap. J. {\\bf\n 492},29 (1998) (MSW).\n\n\\bibitem{GLV} J. Garriga, M. Livio and A. Vilenkin, astro-ph/9906210 (GLV).\n\n\\bibitem{WS} L. Wang and P.J. Steinhardt, Ap. J {\\bf 508}, 483 (1998).\n\n\\bibitem{MS} H. Martel and P.R. Shapiro, astro-ph/9903425 (MS).\n\\end{thebibliography}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002204.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{WCOS} L. Wang, R.R. Caldwell, J.P. Ostriker and\n P.J. Steinhardt, astro-ph/9901388.\n\n\\bibitem{E} G. Efstathiou, M.N.R.A.S. {\\bf 274}, L73 (1995).\n\n\\bibitem{V} A. Vilenkin, Phys. Rev. Lett. {\\bf 74}, 846 (1995).\n\n\\bibitem{MSW} H. Martel, P.R. Shapiro and S. Weinberg, Ap. J. {\\bf\n 492},29 (1998) (MSW).\n\n\\bibitem{GLV} J. Garriga, M. Livio and A. Vilenkin, astro-ph/9906210 (GLV).\n\n\\bibitem{WS} L. Wang and P.J. Steinhardt, Ap. J {\\bf 508}, 483 (1998).\n\n\\bibitem{MS} H. Martel and P.R. Shapiro, astro-ph/9903425 (MS).\n\\end{thebibliography}"
}
] |
astro-ph0002205
|
Photometric catalog of nearby globular clusters (I) \thanks { Based on data collected at the European Southern Observatory, La Silla, Chile.}
|
[
{
"author": "A. Rosenberg \\inst{1}"
},
{
"author": "G. Piotto \\inst{2}"
},
{
"author": "I. Saviane \\inst{2}"
},
{
"author": "A. Aparicio \\inst{3}"
}
] |
We present the first part of the first large and homogeneous CCD color-magnitude diagram (CMD) data base, comprising 52 nearby Galactic globular clusters (GGC) imaged in the $V$ and $I$ bands using only two telescopes (one for each hemisphere). The observed clusters represent $75\%$ of the known Galactic globulars with $(m-M)_V\leq 16.15$~mag, cover most of the globular cluster metallicity range ($-2.2 \leq {[Fe/H]}\leq -0.4$), and span Galactocentric distances from $\sim1.2$ to $\sim18.5$ kpc. In this paper, the CMDs for the 39 GGCs observed in the southern hemisphere are presented. The remaining 13 northern hemisphere clusters of the catalog are presented in a companion paper. For four clusters (NGC~4833, NGC~5986, NGC~6543, and NGC~6638) we present for the first time a CMD from CCD data. The typical CMD span from the $22^{nd}$ $V$ magnitude to the tip of the red giant branch. Based on a large number of standard stars, the absolute photometric calibration is reliable to the $\sim0.02$~mag level in both filters. This catalog, because of its homogeneity, is expected to represent a useful data base for the measurement of the main absolute and relative parameters characterizing the CMD of GGCs. \keywords{Astronomical data base: miscellaneous - Catalogs - Stars: Hertzsprung-Russel (HR) - Stars: population II - Globular clusters: general } %% %\keywords{Astronomical data bases: catalogs -- stars: Hertzsprung-Russell (HR) %and C-M diagrams -- Stars: population II -- Globular clusters: general}
|
[
{
"name": "h1679.tex",
"string": "\n\\documentclass{aa}\n\\usepackage{psfig}\n\\usepackage[T1]{fontenc}\n\\usepackage{times}\n\n\n\\def\\donothing{} %% Cf. nota.\n\n\\begin{document}\n\\thesaurus{\t\n20(04.01.1; 04.03.1; 08.08.1; 08.16.3; 10.07.2)\n}\n%\\thesaurus{\t20(04.03.1;\t% Astronomical Databases (Catalogs)\n%\t\t08.08.1; % (stars): Hertzsprung-Russell diagram \n%\t\t08.16.3; % (stars): Population II \n%\t\t10.07.2) % Globular clusters:\t\tGeneral \n%\t\t}\n\\title { Photometric catalog of nearby globular clusters (I)\n\\thanks\t{\tBased on data collected at the European Southern Observatory, \n\t\tLa Silla, Chile.}\n\t}\n\\subtitle {A large homogeneous $(V,I)$ color-magnitude diagram data-base}\n\\author {\tA. Rosenberg \\inst{1}, \n\t\tG. Piotto \\inst{2},\n\t\tI. Saviane \\inst{2} \\and \n\t\tA. Aparicio \\inst{3} }\n\\offprints {\tAlfred Rosenberg: alf@iac.es}\n\\institute{\t\n\t\tTelescopio Nazionale Galileo, \n\t\tvicolo dell'Osservatorio 5, I--35122 Padova, Italy\n\\and\n\t\tDipartimento di Astronomia, Univ. di Padova, \n\t\tvicolo dell'Osservatorio 5, I--35122 Padova, Italy\n\\and\n\t\tInstituto de Astrofisica de Canarias, \n\t\tVia Lactea, E-38200 La Laguna, Tenerife, Spain\n\t}\n\\date{}\n\\titlerunning {{\\it VI} photometric catalog of nearby GGC's (I)}\n\\authorrunning {Rosenberg A., et al.}\n\\maketitle\n\n\n\\begin{abstract}\n\nWe present the first part of the first large and homogeneous CCD\ncolor-magnitude diagram (CMD) data base, comprising 52 nearby Galactic\nglobular clusters (GGC) imaged in the $V$ and $I$ bands using only two\ntelescopes (one for each hemisphere). The observed clusters represent\n$75\\%$ of the known Galactic globulars with $(m-M)_V\\leq 16.15$~mag,\ncover most of the globular cluster metallicity range \n($-2.2 \\leq {\\rm [Fe/H]}\\leq -0.4$), and span Galactocentric distances\nfrom $\\sim1.2$ to $\\sim18.5$ kpc.\n\nIn this paper, the CMDs for the 39 GGCs observed in the southern\nhemisphere are presented. The remaining 13 northern hemisphere\nclusters of the catalog are presented in a companion paper. For\nfour clusters (NGC~4833, NGC~5986, NGC~6543, and NGC~6638) we present\nfor the first time a CMD from CCD data. The typical CMD span from the\n$22^{\\rm nd}$ $V$ magnitude to the tip of the red giant branch. Based on a\nlarge number of standard stars, the absolute photometric calibration\nis reliable to the $\\sim0.02$~mag level in both filters.\n\nThis catalog, because of its homogeneity, is expected to represent a\nuseful data base for the measurement of the main absolute and relative\nparameters characterizing the CMD of GGCs.\n\n\\keywords{Astronomical data base: miscellaneous - Catalogs - \nStars: Hertzsprung-Russel (HR) - Stars: population II - Globular clusters:\ngeneral }\n%%\n%\\keywords{Astronomical data bases: catalogs -- stars: Hertzsprung-Russell (HR) \n%and C-M diagrams -- Stars: population II -- Globular clusters: general}\n\\end{abstract}\n\n\\section{Introduction} \n\\label{intro}\n\nThere are two main properties which make the study of the Galactic\nglobular clusters (GGC) particularly interesting: 1) each cluster\n(with possible rare exceptions) is made up by a single population of\nstars, all born at the same time, in the same place, and out of the\nsame material; 2) GGC stars have the oldest measurable age in the\nUniverse, and therefore we believe they are the oldest fossil records\nof the formation history of our Galaxy.\n\nAmong the many tools we have to investigate the properties of a\nstellar population, the color-magnitude diagrams (CMD) are the most\npowerful ones, as they allow to recover for each individual star\nits evolutionary phase, giving precious information on the age of the\nentire stellar system, its chemical content, and its distance. This\ninformation allows us to locate the system in the space, giving a base\nfor the distance scale, study the formation histories of the Galaxy, \nand test our knowledge of stellar evolution models.\n\nIn particular, the study of a large sample of simple stellar systems,\nas the GGCs, provides important clues to the Milky Way formation\nhistory. Recently, many studies on the relative ages of the GGCs have\nbeen presented with results at least controversial: while some authors\nfind a notable age spread ($\\sim5$ Gyrs) among the clusters,\nothers find that the bulk of GGCs is coeval. This controversy is\nsurely mainly due to the heterogeneity of the data used in each study,\nwhere the combination of photographic and/or CCD data from the early\nepochs of solid state detectors has been frequently used. For this\nreason, a survey of both southern and northern GGCs has been started\ntwo years ago by means of 1-m class telescopes, i.e. the 91cm European\nSouthern Observatory (ESO) / Dutch telescope and the 1m Isaac Newton\nGroup (ING) / Jacobus Kapteyn telescope (JKT). We were able to collect\nthe data for 52 of the 69 known GGCs with $(m-M)_V\\leq16.15$.\nThirty-nine have been observed with the Dutch telescope (data that are\npresented in this paper, hereafter Paper I), and the remaining ones\nwith the JKT (the corresponding CMDs will be presented in a companion\npaper, Rosenberg et al. \\cite{rosenberg00}, hereafter Paper II).\n\nAs a first exploitation of this new data base, we have conducted a GGC\nrelative age investigation based on the best 34 CMDs of our catalog\n(Rosenberg et al. \\cite{rosenberg99}, hereafter Paper III), showing\nthat most of the GGCs have the same age. We have also used our data\nbase to obtain a photometric metallicity ranking scale (Saviane et\nal. \\cite{saviane00}, hereafter Paper IV), based on the red giant\nbranch (RGB) morphology. We measured a complete set of metallicity\nindices, based on the morphology and position of the RGB. Using a\ngrid of selected RGB fiducial points, we defined a function in the\n$(V-I)_0$, $M_{\\rm I}$, [Fe/H] space which is able to reproduce the\nwhole set of GGC RGBs in terms of a single parameter (the\nmetallicity). The use of this function will improve the current\ndeterminations of metallicity and distances within the Local Group.\n\nThere are many other parameters that can be measured from a\nhomogeneous, well calibrated CMD data base: the horizontal branch (HB)\nlevel, homogeneous reddening and distances, etc. We are presently\nworking on these problems. However, we believe it is now the time to\npresent to the community this data base to give to anyone interested\nthe opportunity to take advantage of it.\n\nIn the next section, we will describe the observations collected at\nthe ESO/Dutch telescope during two runs in 1997. The data reduction\nand calibration is presented in Sect.~\\ref{dat}, while in\nSect.~\\ref{comparison} a cross check of the calibration between the two\nruns is given. In order to facilitate the reader's work, we have\nincluded the main parameters characterizing our clusters in\nSect.~\\ref{parameter}. Finally, the observed fields for each\ncluster, and the obtained CMDs are presented and briefly discussed in\nSect.~\\ref{cmds}.\n\n\\begin{figure}\n\\psfig{figure=h1679f1.ps,width=8cm}\n\\label{dist}\n\\caption{ Heliocentric distribution of all GGCs with\n$(m-M)_V\\leq16.15$~mag. In the {\\it upper panel}, the GGCs projection\nover the Galactic plane is presented. The {\\it open circles} represent\nthe clusters studied in the present paper (Paper I); the {\\it open\nsquares}, the GGCs of Paper II; and {\\it the asterisk}, the GGC Pal~1\n(Rosenberg et al. \\cite{rosenberg98}). The clusters which are not\nincluded in our catalog are marked by {\\it open triangles}. In the\n{\\it lower panel}, the XZ projection is shown. The Milky Way is\nschematically represented.}\n\\end{figure}\n\n\\begin{table}\n\\caption[]{Observed clusters at the DUTCH in 1997}\n\\label{list}\n\\begin{tabular}{rcccccc}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nID & Cluster & Other & Obs. & Obs. & Seeing & Long.\\\\\n & (NGC) & Name & date & fields & $V/I(\\arcsec$) & Exp.(s)\\\\\n\\noalign{\\smallskip}\n\\hline \n\\noalign{\\smallskip}\n 1 & 104 & 47 Tuc \t\t& 23/Dec & 2 & 1.4/1.3 & 1800 \\\\\n 2 & 288 & - \t \t& 24/Dec & 3 & 1.4/1.4 & 1800 \\\\\n 3 & 362 & - \t \t& 26/Dec & 3 & 1.6/1.5 & 1200 \\\\\n 4 & 1261 & - \t\t& 24/Dec & 3 & 1.3/1.3 & 1800 \\\\\n\\hline\n 5 & 1851 & - \t \t& 23/Dec & 2 & 1.3/1.2 & 1800 \\\\\n 6 & 1904 & M 79 \t \t& 24/Dec & 3 & 1.3/1.2 & 1800 \\\\\n 7 & 2298 & - \t\t& 23/Dec & 2 & 1.3/1.2 & 1800 \\\\\n 8 & 2808 & - \t \t& 11/Apr & 2 & 1.3/1.2 & 1500 \\\\\n\\hline\n 8 & 2808 & - \t \t& 26/Dec & 2 & 1.5/1.4 & 1500 \\\\\n 9 & - & E3 \t \t& 23/Dec & 2 & 1.5/1.4 & 1800 \\\\\n10 & 3201 & - \t \t& 12/Apr & 2 & 1.5/1.4 & 900 \\\\\n10 & 3201 & - \t \t& 24/Dec & 3 & 1.3/1.2 & 900 \\\\\n\\hline\n11 & 4372 & - \t \t& 13/Apr & 2 & 1.3/1.2 & 1500 \\\\\n12 & 4590 & M 68 \t& 14/Apr & 2 & 1.2/1.2 & 1500 \\\\\n13 & 4833 & - \t& 15/Apr & 2 & 1.3/1.2 & 1500 \\\\\n14 & 5139 & $\\omega$ Cen\t& 11/Apr & 2 & 1.2/1.2 & 900 \\\\\n\\hline\n15 & 5897 & -\t\t\t& 12/Apr & 1 & 1.4/1.4 & 1500 \\\\\n16 & 5927 & -\t\t\t& 13/Apr & 1 & 1.3/1.2 & 1500 \\\\\n17 & 5986 & -\t\t\t& 14/Apr & 1 & 1.3/1.3 & 1500 \\\\\n18 & 6093 & M 80\t \t& 12/Apr & 2 & 1.3/1.2 & 1500 \\\\\n\\hline\n19 & 6101 & -\t\t\t& 15/Apr & 1 & 1.8/1.7 & 1500 \\\\\n20 & 6121 & M 4 \t \t& 13/Apr & 2 & 1.3/1.2 & 900 \\\\\n21 & 6171 & M 107\t \t& 14/Apr & 2 & 1.4/1.3 & 1500 \\\\\n22 & 6266 & M 62\t \t& 14/Apr & 1 & 1.7/1.6 & 1500 \\\\\n\\hline\n23 & 6304 & -\t\t\t& 15/Apr & 1 & 1.5/1.3 & 1500 \\\\\n24 & 6352 & -\t\t\t& 11/Apr & 1 & 1.4/1.3 & 1500 \\\\\n25 & 6362 & -\t\t\t& 12/Apr & 1 & 1.4/1.3 & 1200 \\\\\n26 & 6397 & -\t\t\t& 13/Apr & 2 & 1.3/1.2 & 900 \\\\\n\\hline\n27 & 6496 & -\t\t\t& 14/Apr & 1 & 1.4 1.2 & 1200 \\\\\n28 & 6541 & -\t\t\t& 11/Apr & 2 & 1.3/1.2 & 1200 \\\\\n29 & 6544 & -\t\t\t& 15/Apr & 1 & 1.4/1.4 & 1500 \\\\\n30 & 6624 & -\t\t\t& 12/Apr & 1 & 1.3/1.2 & 1500 \\\\\n\\hline\n31 & 6626 & M 28\t \t& 13/Apr & 1 & 1.2/1.1 & 1500 \\\\\n32 & 6637 & M 69\t \t& 14/Apr & 1 & 1.2/1.1 & 1200 \\\\\n33 & 6638 & -\t\t\t& 13/Apr & 1 & 1.2/1.2 & 900 \\\\\n34 & 6656 & M 22\t \t& 15/Apr & 2 & 1.2/1.2 & 1500 \\\\\n\\hline\n35 & 6681 & M 70 \t \t& 11/Apr & 1 & 1.3/1.2 & 1500 \\\\\n36 & 6717 & Pal 9\t \t& 12/Apr & 1 & 1.3/1.2 & 1500 \\\\\n37 & 6723 & -\t\t\t& 13/Apr & 1 & 1.2/1.1 & 1200 \\\\\n38 & 6752 & -\t\t\t& 14/Apr & 1 & 1.3/1.2 & 1200 \\\\\n\\hline\n39 & 6809 & M 55 \t \t& 15/Apr & 1 & 1.3/1.1 & 900 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n\\section{Observations} \n\\label{obs}\n\nThe data were collected during two runs in 1997: the first in April\n($\\rm 11^{th}-15^{th}$) and the second in December ($\\rm 23^{rd},\n24^{th}$ and\n$\\rm 26^{th}$). All nights of the first run and the first two of the\nsecond run were photometric and had a stable seeing.\n\nObservations were done with the ESO 91cm DUTCH telescope, at La Silla\n(Chile). The same same CCD$\\#33$ was used in both runs, a thinned CCD\nwith $512\\times512$ pixels, each projecting $0.\\arcsec442$ on the sky, with\na total field of view of $3.77\\times3.77 (\\arcmin)^2$, and the same\nset of $V$ Johnson and $i$ Gunn filters.\n\nTwo short ($10-45$s), one medium ($90-120$s) and one long\n($600-1800$s) exposures were taken in each band (depending on the\ncluster distance modulus) for one to three fields (in order to ensure\na statistically significant sample of stars) for each of the proposed\nobjects. Also a large number of Landolt (\\cite{landolt92}) standard\nstars were\nmeasured during each night.\n\nIn Table~\\ref{list} the 39 observed GGCs are presented. Column 1 gives\nan identification number adopted in this paper; cluster NGC numbers\nand alternative names are given in columns 2 and 3. The observing\ndates are in column 4, the number of covered fields in column 5, the\nmean seeing for each filter in column 6, and the integration time for\nthe long exposures in column 7. In Fig.~\\ref{dist} we show the\nheliocentric distribution of the clusters of our entire catalog.\n\n\\section{Data reduction and calibration}\n\\label{dat}\n\nThe images were corrected for a constant bias, dark current, and for\nspatial sensitivity variations using the respective master flats,\ncomputed as the median of all available sky flats of the specific\nrun. Afterwards, photometry was performed using the\nDAOPHOT/ALLSTAR/ALLFRAME software, made available to us by Dr. Stetson\n(see Stetson \\cite{stetson87}, \\cite{stetson94}). A preliminary\nphotometry was carried out in order to construct a short list of stars\nfor each single frame. This list was used to accurately match the\ndifferent frames. With the correct coordinate transformations among the\nframes, we obtained a single image, median of all the frames,\nregardless of the filter. In this way we could eliminate all the\ncosmic rays and obtain the highest signal/noise image for star\nfinding. We ran the DAOPHOT/FIND routine on the median image and\nperformed PSF fitting photometry in order to obtain the deepest list\nof stellar objects free from spurious detections. Finally, this list\nwas given as input to ALLFRAME, for the simultaneous profile fitting\nphotometry of all the individual frames. We constructed the model PSF\nfor each image using typically from 60 to 120 stars.\n\nThe absolute calibration of the observations to the V-Johnson and\nI-Cousins systems is based on a set of standard stars from the catalog\nof Landolt (\\cite{landolt92}). Specifically, the observed standard\nstars were in the fields: PG0231, SA95 (41, 43, 96, 97, 98, 100, 101,\n102, 112, 115), SA98 (556, 557, 563, 580, 581, L1, 614, 618, 626, 627,\n634, 642), RUBIN 149, RUBIN 152, PG0918, PG0942, PG1047, PG1323,\nPG1525, PG1530, PG1633, and Mark A. At least 3 exposures were taken\nfor each standard field, with a total of $\\sim100$ standard star\nmeasurements per night and per filter.\n\nThe reduction and aperture photometry of standard star fields were\nperformed in the same way as for the cluster images. The aperture\nmagnitudes were corrected for atmospheric extinction, assuming\n$A_V=0.14$ and $A_I=0.08$ as extinction coefficients for the $V$ and\n$i$ filters, respectively.\n\n\\begin{figure}\n\\centerline{\\psfig{figure=h1679f2.ps,width=8.8cm}} \n\\caption[]{Calibration equation for each observing night. The {\\it\nupper panels} refer to the run of April, while the {\\it lower panels}\nrefer to the December run. In all cases, the $V$ filter curves are on\nthe {\\it left side}, while the $I$ filter curves on the right.}\n\\label{calib} \n\\end{figure} \n\n\\begin{table}\n\\begin{center}\n\\caption[]{Calibration parameters for each observing night.}\n\\label{calib_par}\n\\begin{tabular}{ccccc}\n& Filter V & & & \\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nDate & $a_{\\rm m}$ & error & Cons. & error\\\\\n\\noalign{\\smallskip}\n\\hline \n\\noalign{\\smallskip}\n11/Apr & +0.024 & $\\pm0.001$ & -3.034 & $\\pm0.002$ \\\\\n12/Apr & +0.024 & $\\pm0.002$ & -3.025 & $\\pm0.004$ \\\\\n13/Apr & +0.024 & $\\pm0.002$ & -3.059 & $\\pm0.003$ \\\\\n14/Apr & +0.024 & $\\pm0.001$ & -3.034 & $\\pm0.002$ \\\\\n15/Apr & +0.024 & $\\pm0.003$ & -3.057 & $\\pm0.004$ \\\\\n23/Dec & +0.022 & $\\pm0.001$ & -2.777 & $\\pm0.001$ \\\\\n24/Dec & +0.022 & $\\pm0.001$ & -2.790 & $\\pm0.001$ \\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n& Filter I & & & \\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nDate & $a_{\\rm m}$ & error & Cons. & error\\\\\n\\noalign{\\smallskip}\n\\hline \n\\noalign{\\smallskip}\n11/Apr & -0.012 & $\\pm0.003$ & -4.081 & $\\pm0.004$ \\\\\n12/Apr & -0.012 & $\\pm0.002$ & -4.069 & $\\pm0.003$ \\\\\n13/Apr & -0.012 & $\\pm0.003$ & -4.086 & $\\pm0.004$ \\\\\n14/Apr & -0.012 & $\\pm0.001$ & -4.072 & $\\pm0.002$ \\\\\n15/Apr & -0.012 & $\\pm0.001$ & -4.076 & $\\pm0.004$ \\\\\n23/Dec & -0.017 & $\\pm0.002$ & -3.805 & $\\pm0.002$ \\\\\n24/Dec & -0.017 & $\\pm0.002$ & -3.829 & $\\pm0.002$ \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\nAs shown in Fig.~\\ref{calib}, a straight line well reproduces the\ncalibration equations. As the seeing and the overall observing\nconditions were stable during the run, the slopes of the calibration\nequations for each observing run and for each filter have been\ncomputed using the data from all the nights. As it can be seen in\nTable~\\ref{calib_par}, the standard deviations of the calibration\nconstants for each run and filter is $0.015$mag, corroborating our\nassumption that all nights were photometric, and that we can assume a\nconstant slope for each filter and run.\n\nStandard stars for which previous problems were reported (PG 1047C,\nRU149A, RU149G, PG1323A; see Johnson \\& Bolte \\cite{johnsonbolte98})\nwere excluded, as well as saturated stars, those close to a cosmic ray,\netc... After this cleaning, the mean slope was computed, and finally\nthe different night constants were found using this slope to fit the\nindividual data, night by night. The adopted values are presented in\nTable~\\ref{calib_par}. The typical errors ($rms$) are also given.\n\nThe calibration curves are shown in Fig.~\\ref{calib} for both runs. In\nthis figure, the {\\it dotted line} represents the best fitting\nequation, while the {\\it continuous line} is obtained by best fitting\nthe data imposing the adopted mean slope. The two lines are almost\noverlapping. The mean number of standard star measures used for\ncomputing the curve per night and filter is $\\sim75$. Notice the wide\ncolor coverage for the standard stars.\n\nThe last step on the calibration is the aperture correction. As no\navailable bright and isolated stars exist on the cluster images, we\nused DAOPHOT to subtract from the image the stars in the neighborhood\nof the brightest ones, in order to compute the difference between the\naperture and the PSF-fitting magnitudes. In view of the stable seeing\nconditions, we used the same aperture for calculating the aperture\nphotometry of the standard and cluster stars.\n\n\n\\section{Photometric homogeneity of the two runs}\n\\label{comparison}\n\n\\begin{figure} \n\\centerline{\\psfig{figure=h1679f3.ps,width=8.8cm}} \n\\caption[]{Comparison of the magnitudes and colors of 456 stars in\ncommon between the April and December runs, for the GGC\nNGC~3201. Stars with photometric internal errors smaller than 0.02 mag\nhave been selected. The mean differences are given in each panel. {\\it\nNote:} a few NGC~3201 RR~Lyrae stars can be identified in the interval\n$14.2 < V < 15.2$ (lower two panels), and between $0.4 < (V-I) <\n0.9$.}\n\\label{compare}\n\\end{figure}\n\nIn order to check the photometric homogeneity of the data and of the\ncalibration to the standard photometric system, one cluster (NGC~3201)\nwas observed in both runs. Having one common field, it is possible to\nanalyze the individual star photometry, and test if any additional\nzero point difference and/or color term exist. The latter check is\ncrucial when measures of the relative position of CMD features are\ngoing to be done. The comparison between the two runs is presented in\nFig.~\\ref{compare}, where 456 common stars with internal photometric\nerrors (as given by ALLFRAME) smaller than 0.02 mag are\nused. Fig.~\\ref{compare} shows that there are no systematic differences\nbetween the two runs.\n\nThe slope of the straight lines best fitting all the points in both\nthe (V,$\\Delta V^{\\rm apr}_{\\rm dec}$) plane and the (V,$\\Delta I^{\\rm\napr}_{\\rm dec}$) plane is $\\leq 0.001\\pm0.002$, and $\\leq\n0.002\\pm0.003$ in the (V-I,$\\Delta (V-I)^{\\rm apr}_{\\rm dec}$)\nplane. The zero point differences are always $\\le 0.01$ mag. This\nensures the homogeneity of our database, particularly for relative\nmeasurements within the CMDs.\n\n\n\n\\section{Parameters for the GGC sample}\n\\label{parameter}\n\n\\begin{table*}\n\\label{param01}\n\\caption[]{Identifications, positional data and metallicity estimates\nfor the observed clusters.}\n\\begin{center}\n\\begin{tabular}{rlccccccccccc}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n\\multicolumn{1}{c}{ID} & \n\\multicolumn{1}{c}{Cluster} & \n\\multicolumn{1}{c}{$RA^{ \\mathrm{a}}$} & \n\\multicolumn{1}{c}{$DEC^{ \\mathrm{b}}$} &\n\\multicolumn{1}{c}{${\\it l}^{ \\mathrm{c}}$} & \n\\multicolumn{1}{c}{${\\it b}^{ \\mathrm{d}}$} &\n\\multicolumn{1}{c}{$R_{\\odot}^{ \\mathrm{e}}$} &\n\\multicolumn{1}{c}{$R_{\\rm GC}^{ \\mathrm{f}}$} &\n\\multicolumn{1}{c}{$X^{ \\mathrm{g}}$} &\n\\multicolumn{1}{c}{$Y^{ \\mathrm{h}}$} &\n\\multicolumn{1}{c}{$Z^{ \\mathrm{i}}$} & \n\\multicolumn{2}{c}{[Fe/H]} \\\\\n\\multicolumn{1}{c}{} & \n\\multicolumn{1}{c}{} & \n\\multicolumn{1}{c}{($^{h \\; m \\; s}$)} & \n\\multicolumn{1}{c}{($^{\\rm o} \\;$ \\arcmin $\\;$ \\arcsec)} &\n\\multicolumn{1}{c}{$(^{\\rm o})$} & \n\\multicolumn{1}{c}{$(^{\\rm o})$} &\n\\multicolumn{1}{c}{(kpc)} &\n\\multicolumn{1}{c}{(kpc)} &\n\\multicolumn{1}{c}{(kpc)} &\n\\multicolumn{1}{c}{(kpc)} &\n\\multicolumn{1}{c}{(kpc)} &\n\\multicolumn{1}{c}{$ZW84^{ \\mathrm{j}}$} &\n\\multicolumn{1}{c}{$CG97^{ \\mathrm{k}}$} \\\\\n\n\\noalign{\\smallskip}\n\\hline \n\\noalign{\\smallskip}\n\n 1 & NGC~104 & 00 24 05.2 & -72 04 51 & 305.90 & -44.89 & 4.3 & 7.3 &\n+1.8 & -2.5 & -3.0 & -0.71 & -0.78\\\\\n 2 & NGC~288 & 00 52 47.5 & -26 35 24 & 152.28 & -89.38 & 8.1 & 11.4 &\n-0.1 & +0.0 & -8.1 & -1.40 & -1.14\\\\\n 3 & NGC~362 & 01 03 14.3 & -70 50 54 & 301.53 & -46.25 & 8.3 & 9.2 &\n+3.0 & -4.9 & -6.0 & -1.33 & -1.09\\\\\n 4 & NGC~1261 & 03 12 15.3 & -55 13 01 & 270.54 & -52.13 &16.0 & 17.9 &\n+0.1 & -9.8 &-12.6 & -1.32 & -1.08\\\\\n\\hline\t\t\t\t\t\t\t\t\t\t \n 5 & NGC~1851 & 05 14 06.3 & -40 02 50 & 244.51 & -35.04 &12.2 & 16.8 &\n-4.3 & -9.0 & -7.0 & -1.23 & -1.03\\\\\n 6 & NGC~1904 & 05 24 10.6 & -24 31 27 & 227.23 & -29.35 &12.6 & 18.5 &\n-7.5 & -8.1 & -6.2 & -1.67 & -1.37\\\\\n 7 & NGC~2298 & 06 48 59.2 & -36 00 19 & 245.63 & -16.01 &10.6 & 15.6 &\n-4.2 & -9.3 & -2.9 & -1.91 & -1.71\\\\\n 8 & NGC~2808 & 09 12 02.6 & -64 51 47 & 282.19 & -11.25 & 9.3 & 10.9 &\n+1.9 & -8.9 & -1.8 & -1.36 & -1.11\\\\\n\\hline\t\t\t\t\t\t\t\t\t\t \n 9 & E3 & 09 20 59.3 & -77 16 57 & 292.27 & -19.02 & 4.2 & 7.6 &\n+1.5 & -3.7 & -1.4 & - & - \\\\\n10 & NGC~3201 & 10 17 36.8 & -46 24 40 & 277.23 & +08.64 & 5.1 & 8.9 &\n+0.6 & -5.0 & +0.8 & -1.53 & -1.24\\\\\n11 & NGC~4372 & 12 25 45.4 & -72 39 33 & 300.99 & -09.88 & 4.9 & 6.9 &\n+2.5 & -4.2 & -0.8 & -2.03 & -1.88\\\\\n12 & NGC~4590 & 12 39 28.0 & -26 44 34 & 299.63 & +36.05 &10.1 & 10.0 &\n+4.0 & -7.1 & +5.9 & -2.11 & -2.00\\\\\n\\hline\t\t\t\t\t\t\t\t\t\t \n13 & NGC~4833 & 12 59 35.0 & -70 52 29 & 303.61 & -08.01 & 5.9 & 6.9 &\n+3.2 & -4.8 & -0.8 & -1.92 & -1.71\\\\\n14 & NGC~5139 & 13 26 45.9 & -47 28 37 & 309.10 & +14.97 & 5.1 & 6.3 &\n+3.1 & -3.8 & +1.3 &\\phantom{-}-$1.62^{1}$& -\\\\\n15 & NGC~5897 & 15 17 24.5 & -21 00 37 & 342.95 & +30.29 &12.7 & 7.6\n&+10.5 & -3.2 & +6.4 & -1.93 & -1.73\\\\\n16 & NGC~5927 & 15 28 00.5 & -50 40 22 & 326.60 & +04.86 & 7.4 & 4.5 &\n+6.2 & -4.1 & +0.6 & -0.33 & -0.64\\\\\n\\hline\t\t\t\t\t\t\t\t\t\t \n17 & NGC~5986 & 15 46 03.5 & -37 47 10 & 337.02 & +13.27 &10.3 & 4.7 &\n+9.2 & -3.9 & +2.4 & -1.65 & -1.35\\\\\n18 & NGC~6093 & 16 17 02.5 & -22 58 30 & 352.67 & +19.46 & 8.7 & 3.1 &\n+8.1 & -1.0 & +2.9 & -1.75 & -1.47\\\\\n19 & NGC~6121 & 16 23 35.5 & -26 31 31 & 350.97 & +15.97 & 2.2 & 6.0 &\n+2.0 & -0.3 & +0.6 & -1.27 & -1.05\\\\\n20 & NGC~6101 & 16 25 48.6 & -72 12 06 & 317.75 & -15.82 &15.1 & 11.0\n&+10.8 & -9.8 & -4.1 & -1.95 & -1.76\\\\\n\\hline\t\t\t\t\t\t\t\t\t\t \n21 & NGC~6171 & 16 32 31.9 & -13 03 13 & 003.37 & +23.01 & 6.3 & 3.3 &\n+5.8 & +0.3 & +2.4 & -1.09 & -0.95\\\\\n22 & NGC~6266 & 17 01 12.6 & -30 06 44 & 353.58 & +07.32 & 6.7 & 1.8 &\n+6.6 & -0.7 & +0.9 & -1.23 & -1.02\\\\\n23 & NGC~6304 & 17 14 32.5 & -29 27 44 & 355.83 & +05.38 & 6.0 & 2.2 &\n+5.9 & -0.4 & +0.6 & -0.38 & -0.66\\\\\n24 & NGC~6352 & 17 25 29.2 & -48 25 22 & 341.42 & -07.17 & 5.6 & 3.3 &\n+5.2 & -1.8 & -0.7 & -0.50 & -0.70\\\\\n\\hline\t\t\t\t\t\t\t\t\t\t \n25 & NGC~6362 & 17 31 54.8 & -67 02 53 & 325.55 & -17.57 & 7.5 & 5.1 &\n+5.9 & -4.0 & -2.3 & -1.18 & -0.99\\\\\n26 & NGC~6397 & 17 40 41.3 & -53 40 25 & 338.17 & -11.96 & 2.2 & 6.0 &\n+2.0 & -0.8 & -0.5 & -1.94 & -1.76\\\\\n27 & NGC~6496 & 17 59 02.0 & -44 15 54 & 348.02 & -10.01 &11.6 & 4.4\n&+11.1 & -2.4 & -2.0 & -0.50 & -0.70\\\\\n28 & NGC~6544 & 18 07 20.6 & -24 59 51 & 005.84 & -02.20 & 2.5 & 5.5 &\n+2.5 & +0.3 & -0.1 & -1.48 & -1.20\\\\\n\\hline\t\t\t\t\t\t\t\t\t\t \n29 & NGC~6541 & 18 08 02.2 & -43 42 20 & 349.29 & -11.18 & 7.4 & 2.1 &\n+7.2 & -1.4 & -1.4 & -1.79 & -1.53\\\\\n30 & NGC~6624 & 18 23 40.5 & -30 21 40 & 002.79 & -07.91 & 7.9 & 1.2 &\n+7.8 & +0.4 & -1.1 & -0.50 & -0.70\\\\\n31 & NGC~6626 & 18 24 32.9 & -24 52 12 & 007.80 & -05.58 & 5.7 & 2.5 &\n+5.7 & +0.8 & -0.6 & -1.23 & -1.03\\\\\n32 & NGC~6638 & 18 30 56.2 & -25 29 47 & 007.90 & -07.15 & 8.2 & 1.5 &\n+8.0 & +1.1 & -1.0 & -1.00 & -0.90\\\\\n\\hline\t\t\t\t\t\t\t\t\t\t \n33 & NGC~6637 & 18 31 23.2 & -32 20 53 & 001.72 & -10.27 & 8.2 & 1.5 &\n+8.1 & +0.2 & -1.5 & -0.72 & -0.78\\\\\n34 & NGC~6656 & 18 36 24.2 & -23 54 12 & 009.89 & -07.55 & 3.2 & 5.0 &\n+3.1 & +0.5 & -0.4 &\\phantom{-}-$1.64^{1}$& -\\\\\n35 & NGC~6681 & 18 43 12.7 & -32 17 31 & 002.85 & -12.51 & 8.7 & 2.0 &\n+8.5 & +0.4 & -1.9 & -1.64 & -1.35\\\\\n36 & NGC~6717 & 18 55 06.2 & -22 42 03 & 012.88 & -10.90 & 7.1 & 2.4 &\n+6.8 & +1.6 & -1.3 & -1.33 & -1.09\\\\\n\\hline\t\t\t\t\t\t\t\t\t\t \n37 & NGC~6723 & 18 59 33.2 & -36 37 54 & 000.07 & -17.30 & 8.6 & 2.6 &\n+8.2 & +0.0 & -2.5 & -1.12 & -0.96\\\\\n38 & NGC~6752 & 19 10 51.8 & -59 58 55 & 336.50 & -25.63 & 3.9 & 5.3 &\n+3.2 & -1.4 & -1.7 & -1.54 & -1.24\\\\\n39 & NGC~6809 & 19 39 59.4 & -30 57 44 & 008.80 & -23.27 & 5.3 & 3.9 &\n+4.8 & +0.7 & -2.1 & -1.80 & -1.54\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\\\\\nIn the following cases, the [Fe/H] values were taken directly from\n($^1$) ZW84.\n\\end{center}\n\n\\begin{tabular}{lrl}\n$^{\\mathrm{a}}$ Right Ascension (2000)&\nSun-Centered coordinates: & \n$^{\\mathrm{g}}$ X: Toward the Galactic Center\\\\\n$^{\\mathrm{b}}$ Declination (2000) &\n &\n$^{\\mathrm{h}}$ Y: in direction of Galactic rotation \\\\\n$^{\\mathrm{c}}$ Galactic Longitude &\n &\n$^{\\mathrm{i}}$ Z: Towards North Galactic Plane \\\\\n$^{\\mathrm{d}}$ Galactic Latitude &\n & \n \\\\\n$^{\\mathrm{e}}$ Heliocentric Distance &\n[Fe/H] (From Rutledge et al. 1997):&\n$^{\\mathrm{j}}$ in the ZW84 scale\\\\\n$^{\\mathrm{f}}$ Galactocentric Distance &\n & \n$^{\\mathrm{k}}$ in the CG97 scale\\\\\n\\end{tabular}\n\n\\end{table*}\n\n\\begin{table*}\n\\begin{center}\n\\caption[]{Photometric Parameters.}\n\\label{param2}\n\\begin{tabular}{rlclcrrccccrrc}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n\n\\multicolumn{1}{r}{ID} & \n\\multicolumn{1}{c}{Cluster} & \n\\multicolumn{1}{c}{${\\rm E(B-V)^{ \\mathrm{a}}}$} & \n\\multicolumn{1}{c}{$V_{\\rm HB} ^{ \\mathrm{b}}$} & \n\\multicolumn{1}{c}{${\\rm (m-M)_V^{ \\mathrm{c}}}$} & \n\\multicolumn{1}{r}{${\\rm V_t}^{ \\mathrm{d}}$} & \n\\multicolumn{1}{r}{${\\rm Mv_t}^{ \\mathrm{e}}$} &\n\\multicolumn{1}{c}{\\rm $U-B^{ \\mathrm{f}}$} & \n\\multicolumn{1}{c}{\\rm $B-V^{ \\mathrm{f}}$} & \n\\multicolumn{1}{c}{\\rm $V-R^{ \\mathrm{f}}$} & \n\\multicolumn{1}{c}{\\rm $V-I^{ \\mathrm{f}}$} & \n\\multicolumn{1}{r}{$S_{\\rm RR} ^{ \\mathrm{g}}$} & \n\\multicolumn{1}{r}{$HBR^{ \\mathrm{h}}$} \\\\\n\n\\noalign{\\smallskip}\n\\hline \n\\noalign{\\smallskip}\n 1 & NGC~104 & 0.05 & 14.05* & 13.32 & 3.95 & -9.37 & 0.37 & 0.88 &\n0.53 & 1.14 & 0.4 & -0.99\\\\\n 2 & NGC~288 & 0.03 & 15.40* & 14.64 & 8.09 & -6.55 & 0.08 & 0.65 &\n0.45 & 0.94 & 4.8 & 0.98\\\\\n 3 & NGC~362 & 0.05 & 15.43 & 14.75 & 6.40 & -8.35 & 0.16 & 0.77 &\n0.49 & 1.01 & 5.9 & -0.87\\\\\n 4 & NGC~1261 & 0.01 & 16.68* & 16.05 & 8.29 & -7.76 & 0.13 & 0.72 &\n0.45 & 0.93 & 14.9 & -0.71\\\\\n\\hline\t\t\t \t\t\t\t\t\t\t\t \n 5 & NGC~1851 & 0.02 & 16.18* & 15.49 & 7.14 & -8.35 & 0.17 & 0.76 &\n0.49 & 1.01 & 10.1 & -0.36\\\\\n 6 & NGC~1904 & 0.01 & 16.15* & 15.53 & 7.73 & -7.80 & 0.06 & 0.65 &\n0.44 & 0.91 & 5.3 & 0.89\\\\\n 7 & NGC~2298 & 0.13 & 16.11 & 15.54 & 9.29 & -6.25 & 0.17 & 0.75 &\n0.54 & 1.11 & 9.5 & 0.93\\\\\n 8 & NGC~2808 & 0.23 & 16.30* & 15.55 & 6.20 & -9.35 & 0.28 & 0.92 &\n0.57 & 1.18 & 0.4 & -0.49\\\\\n\\hline\t\t\t \t\t\t\t\t\t\t\t \n 9 & E 3 & 0.30 & 14.80 & 14.07 & 11.35 & -2.72 & - & - &\n- & - & 0.0 & -\\\\\n10 & NGC~3201 & 0.21 & 14.75* & 14.17 & 6.75 & -7.42 & 0.38 & 0.96 &\n0.62 & 1.23 & 91.3 & 0.08\\\\\n11 & NGC~4372 & 0.42 & 15.30 & 14.76 & 7.24 & -7.52 & 0.31 & 1.10 &\n0.72 & 1.50 & 0.0 & 1.00\\\\\n12 & NGC~4590 & 0.04 & 15.75* & 15.14 & 7.84 & -7.30 & 0.04 & 0.63 &\n0.46 & 0.94 & 49.3 & 0.17\\\\\n\\hline\t\t\t \t\t\t\t\t\t\t\t \n13 & NGC~4833 & 0.33 & 15.45 & 14.87 & 6.91 & -7.96 & 0.29 & 0.93 &\n0.63 & 1.33 & 11.8 & 0.93\\\\\n14 & NGC~5139 & 0.12 & 14.53 & 13.92 & 3.68 &-10.24 & 0.19 & 0.78 &\n0.51 & 1.05 & 12.2 & - \\\\\n15 & NGC~5897 & 0.08 & 16.35 & 15.77 & 8.53 & -7.24 & 0.08 & 0.74 &\n0.50 & 1.04 & 8.9 & 0.86\\\\\n16 & NGC~5927 & 0.47 & 16.60 & 15.81 & 8.01 & -7.80 & 0.85 & 1.31 &\n0.79 & 1.63 & 0.0 & -1.00\\\\\n\\hline\t\t\t \t\t\t\t\t\t\t\t \n17 & NGC~5986 & 0.27 & 16.50 & 15.90 & 7.52 & -8.38 & 0.30 & 0.90 &\n0.58 & 1.22 & 4.4 & 0.97\\\\\n18 & NGC~6093 & 0.18 & 16.25* & 15.25 & 7.33 & -7.92 & 0.21 & 0.84 &\n0.56 & 1.11 & 4.1 & 0.93\\\\\n19 & NGC~6121 & 0.36 & 13.36* & 12.78 & 5.63 & -7.15 & 0.43 & 1.03 &\n0.69 & 1.42 & 70.4 & -0.06\\\\\n20 & NGC~6101 & 0.04 & 16.60 & 16.02 & 9.16 & -6.86 & 0.06 & 0.68 &\n0.50 & - & 19.8 & 0.84\\\\\n\\hline\t\t\t \t\t\t\t\t\t\t\t \n21 & NGC~6171 & 0.33 & 15.65* & 15.01 & 7.93 & -7.08 & 0.69 & 1.10 &\n0.72 & 1.45 & 32.5 & -0.73\\\\\n22 & NGC~6266 & 0.47 & 16.25 & 15.59 & 6.45 & -9.14 & 0.52 & 1.19 &\n0.74 & 1.58 & 19.1 & 0.32\\\\\n23 & NGC~6304 & 0.52 & 16.25 & 15.49 & 8.22 & -7.27 & 0.82 & 1.31 &\n0.77 & 1.70 & 0.0 & -1.00\\\\\n24 & NGC~6352 & 0.21 & 15.25* & 14.39 & 7.96 & -6.43 & 0.64 & 1.06 &\n0.66 & 1.50 & 0.0 & -1.00\\\\\n\\hline\t\t\t \t\t\t\t\t\t\t\t \n25 & NGC~6362 & 0.09 & 15.35* & 14.65 & 7.73 & -6.92 & 0.29 & 0.85 &\n0.56 & 1.14 & 56.4 & -0.58\\\\\n26 & NGC~6397 & 0.18 & 12.95* & 12.31 & 5.73 & -6.58 & 0.12 & 0.73 &\n0.49 & 1.03 & 0.0 & 0.98\\\\\n27 & NGC~6496 & 0.13 & 16.47 & 15.72 & 8.54 & -7.18 & 0.45 & 0.98 & \n- & - & 0.0 & -1.00\\\\\n28 & NGC~6544 & 0.74 & 14.90 & 14.28 & 7.77 & -6.51 & 0.73 & 1.46 &\n0.98 & 1.92 & - & 1.00\\\\\n\\hline\t\t\t \t\t\t\t\t\t\t\t \n29 & NGC~6541 & 0.12 & 15.30 & 14.72 & 6.30 & -8.42 & 0.13 & 0.76 &\n0.49 & 1.01 & 0.0 & 1.00\\\\\n30 & NGC~6624 & 0.27 & 16.11 & 15.32 & 7.87 & -7.45 & 0.60 & 1.11 &\n0.67 & 1.42 & 1.0 & -1.00\\\\\n31 & NGC~6626 & 0.41 & 15.70 & 15.07 & 6.79 & -8.28 & 0.46 & 1.08 &\n0.69 & 1.41 & 6.4 & 0.90\\\\\n32 & NGC~6638 & 0.40 & 16.50 & 15.80 & 9.02 & -6.78 & 0.56 & 1.15 &\n0.72 & 1.50 & 38.9 & -0.30\\\\\n\\hline\t\t\t \t\t\t\t\t\t\t\t \n33 & NGC~6637 & 0.17 & 15.85 & 15.11 & 7.64 & -7.47 & 0.48 & 1.01 &\n0.62 & 1.28 & 0.0 & -1.00\\\\\n34 & NGC~6656 & 0.34 & 14.25* & 13.55 & 5.10 & -8.45 & 0.28 & 0.98 &\n0.68 & 1.42 & 7.5 & 0.91\\\\\n35 & NGC~6681 & 0.07 & 15.70* & 14.93 & 7.87 & -7.06 & 0.12 & 0.72 &\n0.47 & 0.99 & 3.0 & 0.96\\\\\n36 & NGC~6717 & 0.21 & 15.56 & 14.90 & 9.28 & -5.62 & 0.35 & 1.00 &\n0.65 & 1.37 & 5.6 & 0.98\\\\\n\\hline\t\t\t \t\t\t\t\t\t\t\t \n37 & NGC~6723 & 0.05 & 15.45* & 14.82 & 7.01 & -7.81 & 0.21 & 0.75 &\n0.50 & 1.05 & 21.8 & -0.08\\\\\n38 & NGC~6752 & 0.04 & 13.80* & 13.08 & 5.40 & -7.68 & 0.07 & 0.66 &\n0.43 & 0.93 & 0.0 & 1.00\\\\\n39 & NGC~6809 & 0.07 & 14.45* & 13.82 & 6.32 & -7.50 & 0.11 & 0.72 &\n0.48 & 1.00 & 10.0 & 0.87\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\nThe HB levels (column 4) with an asterisk have been measured directly on\nour CMDs.\n\\end{center}\n\n\\begin{tabular}{llll}\n$^{\\mathrm{a}}$ Foreground reddening &\n$^{\\mathrm{e}}$ Absolute visual magnitude \\\\\n$^{\\mathrm{b}}$ HB Level &\n$^{\\mathrm{f}}$ Integrated color indices \\\\\n$^{\\mathrm{c}}$ Apparent visual distance modulus &\n$^{\\mathrm{g}}$ Specific frequency of RR Lyrae variables \\\\\n$^{\\mathrm{d}}$ Integrated $V$ mag. of clusters &\n$^{\\mathrm{h}}$ HB ratio: $HBR=(B-R)/(B+V+R)$ \\\\\n\\end{tabular}\n\\end{table*}\n\n\\begin{table*}\n\\begin{center}\n\\caption[]{Kinematics, and Structural Parameters}\n\\label{param3}\n\\begin{tabular}{rlrrccccccc}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nID & \nCluster & \n$V_{\\rm r}^{ \\mathrm{a}}$ & \n$V_{\\rm LSR}^{ \\mathrm{b}}$ & \n$c^{ \\mathrm{c}}$ & \n$r_{\\rm c}^{ \\mathrm{d}}$ & \n$r_{\\rm h}^{ \\mathrm{e}}$ & \n$lg(t_{\\rm c})^{ \\mathrm{f}}$ & \n$lg(t_{\\rm h})^{ \\mathrm{g}}$ & \n$\\mu_{\\rm V}^{ \\mathrm{h}}$ & \n$\\rho_{\\rm 0}^{ \\mathrm{i}}$ \\\\\n\\noalign{\\smallskip}\n\\hline \n\\noalign{\\smallskip}\n01 & NGC~104 & $-18.7\\pm0.2$ & $-28.0$ & 2.04 & 0.37 & 2.79 & 7.99\n& 9.24 & 14.43 & 4.87 \\\\\n02 & NGC~288 & $-46.6\\pm0.4$ & $-53.9$ & 0.96 & 1.42 & 2.22 & 9.09\n& 8.99 & 19.95 & 1.84 \\\\\n03 & NGC~362 & $+223.5\\pm0.5$ & $+213.3$ & 1.94c& 0.17 & 0.81 & 7.79\n& 8.43 & 14.88 & 4.74 \\\\\n04 & NGC~1261 & $+68.2\\pm4.6$ & $+53.4$ & 1.27 & 0.39 & 0.75 & 8.79\n& 8.81 & 17.65 & 2.97 \\\\\n\\hline\t\t \n05 & NGC~1851 & $+320.9\\pm1.0$ & $+302.1$ & 2.24 & 0.08 & 0.52 & 7.41\n& 8.50 & 14.15 & 5.17 \\\\\n06 & NGC~1904 & $+207.5\\pm0.5$ & $+188.3$ & 1.72 & 0.16 & 0.80 & 7.87\n& 8.66 & 16.23 & 4.01 \\\\\n07 & NGC~2298 & $+148.9\\pm1.2$ & $+129.8$ & 1.28 & 0.34 & 0.78 & 8.02\n& 8.36 & 18.79 & 2.90 \\\\\n08 & NGC~2808 & $ +93.6\\pm2.4$ & $+80.1$ & 1.77 & 0.26 & 0.76 & 8.35\n& 8.77 & 15.17 & 4.62 \\\\\n\\hline\t\t \n09 & E3 & - & - & - & 0.75 & 1.87 & 2.06\n& - & 23.10 & 1.12 \\\\\n10 & NGC~3201 & $+494.0\\pm0.2$ & $+481.9$ & 1.31 & 1.45 & 2.68 & 8.82\n& 8.79 & 18.77 & 2.69 \\\\\n11 & NGC~4372 & $ +72.3\\pm1.3$ & $+63.8$ & 1.30 & 1.75 & 3.90 & 8.88\n& 9.23 & 20.51 & 2.19 \\\\\n12 & NGC~4590 & $ -95.2\\pm0.4$ & $-97.1$ & 1.64 & 0.69 & 1.55 & 8.60\n& 8.90 & 18.67 & 2.53 \\\\\n\\hline\t\t \n13 & NGC~4833 & $+200.2\\pm1.2$ & $+192.7$ & 1.25 & 1.00 & 2.41 & 8.79\n& 8.77 & 18.45 & 3.07 \\\\\n14 & NGC~5139 & $+232.3\\pm0.5$ & $+229.4$ & 1.24 & 2.58 & 4.18 & 9.76\n& 9.72 & 16.77 & 3.13 \\\\\n15 & NGC~5897 & $+101.5\\pm1.0$ & $+110.0$ & 0.79 & 1.96 & 2.11 & 9.78\n& 9.31 & 20.49 & 1.38 \\\\\n16 & NGC~5927 & $-115.7\\pm3.1$ & $-114.5$ & 1.60 & 0.42 & 1.15 & 8.53\n& 8.71 & 17.45 & 3.90 \\\\\n\\hline\t\t \n17 & NGC~5986 & $ +88.9\\pm3.7$ & $+94.3$ & 1.22 & 0.63 & 1.05 & 8.97\n& 8.78 & 17.56 & 3.31 \\\\\n18 & NGC~6093 & $ +9.3\\pm3.1$ & $+19.7$ & 1.95 & 0.15 & 0.65 & 7.60\n& 8.32 & 15.19 & 4.82 \\\\\n19 & NGC~6121 & $ +70.2\\pm0.3$ & $+79.8$ & 1.59 & 0.83 & 3.65 & 7.57\n& 8.64 & 17.88 & 3.83 \\\\\n20 & NGC~6101 & $+361.4\\pm1.7$ & $+357.2$ & 0.80 & 1.15 & 1.71 & 9.44\n& 9.22 & 20.12 & 1.63 \\\\\n\\hline\t\t \n21 & NGC~6171 & $ -33.8\\pm0.3$ & $-20.6$ & 1.51 & 0.54 & 2.70 & 8.10\n& 8.75 & 18.84 & 3.14 \\\\\n22 & NGC~6266 & $ -65.8\\pm2.5$ & $-56.3$ & 1.70c& 0.18 & 1.23 & 7.54\n& 8.55 & 15.35 & 5.15 \\\\\n23 & NGC~6304 & $-107.3\\pm3.6$ & $-97.4$ & 1.80 & 0.21 & 1.41 & 7.45\n& 8.56 & 17.34 & 4.40 \\\\\n24 & NGC~6352 & $-120.9\\pm3.0$ & $-116.7$ & 1.10 & 0.83 & 2.00 & 8.64\n& 8.71 & 18.42 & 3.05 \\\\\n\\hline\t\t \n25 & NGC~6362 & $ -13.1\\pm0.6$ & $-15.1$ & 1.10 & 1.32 & 2.18 & 9.09\n& 8.83 & 19.19 & 2.27 \\\\\n26 & NGC~6397 & $ +18.9\\pm0.1$ & $+21.4$ & 2.50c& 0.05 & 2.33 & 4.93\n& 8.35 & 15.65 & 5.69 \\\\\n27 & NGC~6496 & $-112.7\\pm5.7$ & $-107.0$ & 0.70 & 1.05 & 1.87 & 8.46\n& 8.46 & 20.10 & 1.94 \\\\\n28 & NGC~6544 & $ -27.3\\pm3.9$ & $-15.7$ & 1.63c& 0.05 & 1.77 & 5.23\n& 7.82 & 17.13 & 5.78 \\\\\n\\hline\t\t \n29 & NGC~6541 & $-156.2\\pm2.7$ & $-150.3$ & 2.00c& 0.30 & 1.19 & 8.04\n& 8.58 & 15.58 & 4.36 \\\\\n30 & NGC~6624 & $ +53.9\\pm0.6$ & $+63.9$ & 2.50c& 0.06 & 0.82 & 6.71\n& 8.50 & 15.42 & 5.24 \\\\\n31 & NGC~6626 & $ +17.0\\pm1.0$ & $+28.5$ & 1.67 & 0.24 & 1.56 & 7.73\n& 8.78 & 16.08 & 4.73 \\\\\n32 & NGC~6638 & $ +18.1\\pm3.9$ & $+29.4$ & 1.40 & 0.26 & 0.66 & 8.00\n& 8.02 & 17.27 & 4.06 \\\\\n\\hline\t\t \n33 & NGC~6637 & $ +39.9\\pm2.8$ & $+49.3$ & 1.39 & 0.34 & 0.83 & 8.40\n& 8.69 & 16.83 & 3.83 \\\\\n34 & NGC~6656 & $-148.9\\pm0.4$ & $-137.2$ & 1.31 & 1.42 & 3.26 & 8.62\n& 8.86 & 17.32 & 3.65 \\\\\n35 & NGC~6681 & $+218.6\\pm1.2$ & $+227.9$ & 2.50c& 0.03 & 0.93 & 5.82\n& 8.40 & 15.28 & 5.42 \\\\\n36 & NGC~6717 & $ +22.8\\pm3.4$ & $+34.6$ & 2.07c& 0.08 & 0.68 & 6.61\n& 8.14 & 16.48 & 4.68 \\\\\n\\hline\t\t \n37 & NGC~6723 & $ -94.5\\pm3.6$ & $-86.7$ & 1.05 & 0.94 & 1.61 & 9.02\n& 8.94 & 17.92 & 2.82 \\\\\n38 & NGC~6752 & $ -24.5\\pm1.9$ & $-24.4$ & 2.50c& 0.17 & 2.34 & 6.95\n& 8.65 & 15.20 & 4.92 \\\\\n39 & NGC~6809 & $+174.8\\pm0.4$ & $+183.4$ & 0.76 & 2.83 & 2.89 & 9.40\n& 8.89 & 19.13 & 2.15 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\smallskip\n\n\\begin{tabular}{lll}\n\n$^{\\mathrm{a}}$Heliocentric radial velocity &\n$^{\\mathrm{d}}$The core radii &\n$^{\\mathrm{g}}$Log. of core relaxation time at $r_{\\rm h}$ \\\\\n$^{\\mathrm{b}}$Radial velocity relative to the(LSR) &\n$^{\\mathrm{e}}$The core median radii &\n$^{\\mathrm{h}}$Central surface brightness \\\\\n$^{\\mathrm{c}}$Concentration parameter $[c=log(r_{\\rm t}/r_{\\rm c})]$ &\n$^{\\mathrm{f}}$Log. of relaxation time in years &\n$^{\\mathrm{i}}$Log. of central luminosity density \\\\\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\nIn order to facilitate the readers work, we present in Tables\n3\\donothing{}, \\ref{param2} and \\ref{param3} the basic parameters\navailable for our GGCs sample\\footnote {Unless otherwise stated, the\ndata presented in these tables are taken from the McMaster catalog\ndescribed by Harris (\\cite{harris96}).}.\n\nIn Table~3\\donothing{} we give the coordinates, the position, and the\nmetallicity of the clusters: right ascension and declination (epoch\nJ2000, columns 3 and 4); Galactic longitude and latitude (columns 5\nand 6); Heliocentric (column 7) and Galactocentric (column 8)\ndistances (assuming $R_{\\sun}$=8.0 kpc); spatial components (X,Y,Z)\n(columns 9, 10 and 11) in the Sun-centered coordinate system (X\npointing toward the Galactic center, Y in direction of Galactic\nrotation, Z toward North Galactic Pole) and, finally, the metallicity\ngiven in Rutledge et al. (\\cite{rutledge97}), on both the Zinn \\& West\n(\\cite{zinnwest84}) and Carretta \\& Gratton (\\cite{carretagratton97})\nscales.\n\nIn Table~\\ref{param2}, the photometric parameters are given. Column 3\nlists the foreground reddening; column 4, the $V$ magnitude level of\nthe horizontal branch; column 5, the apparent visual distance modulus;\nintegrated $V$ magnitudes of the clusters are given in column 6;\ncolumn 7 gives the absolute visual magnitude. Columns 8 to 11 give the\nintegrated color indices (uncorrected for reddening). Column 12 gives\nthe specific frequency of RR Lyrae variables, while column 13 list the\nhorizontal-branch morphological parameter (Lee \\cite{lee90}).\n\nIn Table~\\ref{param3}, we present the kinematical and structural\nparameters for the observed clusters. Column 3 gives the heliocentric\nradial velocity (km/s) with the observational (internal) uncertainty;\ncolumn 4, the radial velocity relative to the local standard of rest;\ncolumn 5, the concentration parameter ($c = \\log (r_{\\rm t}/r_{\\rm\nc})$); a 'c' denotes a core-collapsed cluster; columns 6 and 7, the\ncore and the half mass radii in arcmin; column 8, the logarithm of the\ncore relaxation time, in years; and column 9 the logarithm of the\nrelaxation time at the half mass radius. Column 10, the central\nsurface brightness in $V$; and column 11, the logarithm of central\nluminosity density (Solar luminosities per cubic parsec).\n \n\n\\section{The Color-Magnitude Diagrams}\n\\label{cmds}\n\nIn this section the $V$ vs. $(V-I)$ CMDs for the 39 GGCs and the\ncovered fields are presented.\n\nThe same color and magnitude scale has been used in plotting the CMDs,\nso that differential measures can be done directly using the plots.\nTwo dot sizes have been used, with the bigger ones corresponding to\nthe better measured stars, normally selected on the basis of error\n($\\leq0.1$) and sharpness parameter (Stetson 1987). In some\nexceptional cases, a selection on radius is also done in order to make\nevident the cluster stars over the field stars, or to show\ndifferential reddening effects. The smaller size dots show all the\nmeasured stars with errors (as calculated by DAOPHOT) smaller than\n0.15 mag.\n\nThe images of the fields are oriented with the North at the top and\nEast on the left side. As explained in Sect.~\\ref{obs}, each field\ncovers $3.77\\times3.77(\\arcmin)^2$, and the overlaps between fields of\nthe same object are about $20-25\\%$ of the area. For some clusters,\nonly short exposures were obtained for the central fields.\n\nIn the next subsections, we present the single CMDs and clusters, and\ngive some references to the best existing CMDs. This is by no means a\ncomplete bibliographical catalog: a large number of CMDs are available\nin the literature for many of the clusters of this survey, but we will\nconcentrate just on the best CCD photometric works. The tables with\nthe position and photometry of the measured stars will be available\nvia a web interface at IAC and Padova in the near future.\n\n\\paragraph {\\bf NGC 104 (47 Tucanae).}(Fig.~\\ref{ngc104})\n\nThe cluster 47 Tucanae is (after $\\omega$ Centauri) the second\nbrightest globular cluster in the sky, and consequently a lot of work\nhas been done on this object. 47 Tucanae has been often indicated as\nthe prototype of the metal-rich GGCs, characterized by a well\npopulated red HB (RHB) clump and an extended RGB that also in our CMD\nspans $\\sim$2~mag in color from the RHB to the reddest stars at the\ntip.\n\nA classical CMD of 47~Tucanae is that presented by Hesser et\nal. (\\cite{hesser87}) where a composite CMD was obtained from the\nsuperposition of $B$ and $V$ CCD photometry for the main sequence (MS)\nand photographic data for the evolved part of the diagram. The same\nyear, Alcaino \\& Liller (\\cite{alcainoliller87a}) published a BVI CCD\nphotometry. One year later, Armandroff (\\cite{armandroff88}) presented\nthe RGB $V$ and $I$ bands photometry for this cluster (together with\nother five). In 1994, Sarajedini \\& Norris (\\cite{sarajedininorris94})\npresented a study of the RGB and HB stars in the $B$ and $I$ bands.\nSosin et al. (\\cite{sosin97a}) and Rich et al. (\\cite{rich97}) have\npublished a $B$,$V$ photometry based on HST data.\n\nA recent work in the $V$ and $I$ bands has been presented by Kaluzny\net al. (\\cite{kaluzny98}), who focussed their study on the variable\nstars. They do not find any RR-Lyrae, but many other variables (mostly\nlocated in the BSS region), identified as binary stars. As already\nstated by these authors, a small difference is found between their and\nour photometry. Indeed, their magnitudes coincide with ours at\n$\\sim 12.5$~mag in both bands, but there is a small deviation from\nlinearity of $\\sim -0.015$ magnitudes per magnitude (with the Kaluzny\net al. stars brighter than ours), in both bands (computed from 90\ncommon stars with small photometric errors) within a magnitude range\nof $\\sim 3$ mag. We are confident that our calibration, within the\nquoted errors, is correct, as further confirmed by the comparison\nwith other authors for other objects, as discussed below. Although\nsmall, these differences could be important in relative measures, if\nthey appear randomly in different CMDs. For example, in this case, the\n$\\Delta V_{\\rm TO}^{\\rm HB}$ parameter is $\\sim0.05$ mag smaller in\nKaluzny et al. (\\cite{kaluzny98}) CMD than in our one, implying, for\nthe 47 Tuc metallicity, an age difference of $\\sim0.8$ \\rm Gyrs. We\nwant to stress the importance of a homogeneous database for a\nreliable measurement of differential parameters on the CMDs.\n\n\\paragraph {\\bf NGC~288 and NGC~362.} \n(Figs.~\\ref{ngc288} and \\ref{ngc362})\n\nThe diagram of NGC~288 is well defined and presents an extended blue\nhorizontal branch (EBHB) which extends from the blue side of the\nRR-Lyrae region, to just above the TO. Conversely,\nNGC~362 has a populated RHB with just a few blue HB stars.\n\nThese two clusters define one of the most studied second parameter\ncouple: despite their similar metallicities, their HB morphologies are\ndifferent. Much work have been done on both clusters in order to try\nto understand the origin of such differences: Bolte (\\cite{bolte89})\nand Sarajedini \\& Demarque (\\cite{sarajedinidemarque90}) in the $B$\nand $V$ bands, and Green \\& Norris (\\cite{greennorris90}) in the $B$\nand $R$ bands, based on homogeneous CCD photometry, obtain an age\ndifference of $\\sim3$ \\rm Gyrs, NGC~288 being older than NGC~362. A\nsimilar conclusion is obtained in our study (Paper III), where NGC~362\nis found $\\sim20\\%$ younger than NGC~288. It has also been proposed\n(e.g. Green \\& Norris \\cite{greennorris90}) that these age differences\nmight be responsible of the HB differences between the two clusters.\nOn the other side, Buonanno et al. (\\cite{buonanno98}) and Salaris \\&\nWeiss (\\cite{salarisweiss98}) do not find significant age\ndifferences. Another $B$,$V$ photometry of NGC~362 based on HST data\nis in Sosin et al. (\\cite{sosin97a}).\n\nIt might be worth to remark here that, as it will be discussed in\nPaper II, there are clusters with different HB morphologies, though\nwith the same metallicities and ages (within errors). This means that\nthe analysis of a single couple of GGCs can not be considered\nconclusive for understanding the second parameter problem, while a\nlarge scale study (as that feasible with this catalog) can be of more\nhelp.\n\n\\paragraph {\\bf NGC 1261.} (Fig.~\\ref{ngc1261})\n\nThis cluster is the object with the largest distance in our southern\nhemisphere sample. It is located at $\\sim 16$~kpc from the Sun.\n\nThree major CCD CMDs have been published for NGC~1261: Bolte \\&\nMarleau (\\cite{boltemarleau89}) in $B,V$, Alcaino et\nal. (\\cite{alcaino92}) in $B,V,R,I$, and Ferraro et\nal. (\\cite{ferraro93b}) in the $B$ and $V$ bands.\n\nThe CMD is characterized by an HB which is similar to the HB of\nNGC~1851. From here on, clusters with an HB well populated both on the\nred and blue side of the RR-Lyrae gap will be named bimodal HB\nclusters, though a more objective classification would require taking\ninto account the color distribution of stars along the HB including\nthe RR Lyrae (Catelan et al. \\cite{catelan98}). NGC 1261 has a\nmetallicity very close to that of the previous couple; Chaboyer et\nal. (\\cite{chaboyer96}), Richer et al. (\\cite{richer96}) and Rosenberg\net al. (Paper III) find that it is younger (similar in age to NGC~362)\nthan the bulk of GGCs. A blue straggler (BS) is clearly visible in\nFig.~\\ref{ngc1261}.\n\n\\paragraph {\\bf NGC 1851.} (Fig.~\\ref{ngc1851})\n\nThis cluster has a bimodal HB, with very well defined RHB and blue HB\n(BHB). Also in this case, a BS sequence is visible in\nFig.~\\ref{ngc1851}. It is curious that, again, a bimodal cluster\nresults to be younger than the GGCs bulk. From the 34 clusters in the\npresent catalog, only 4 result to be surely younger, i.e. the already\ndescribed NGC~362 and NGC~1261, this cluster, and NGC~2808: three of\nthem have a bimodal HB (cf. Rosenberg et al. \\cite{rosenberg99} for a\ndetailed discussion). There exist other two recent $(V,I)$ CCD\nphotometries of NGC~1851 by Walker (\\cite{walker98}) and Saviane et\nal. (\\cite{saviane98}). The three photometries are all in agreement\nwithin the errors, confirming our calibration to the standard\nsystem. A CMD of NGC~1851 in the $B$,$V$ bands from HST is in Sosin et\nal. (\\cite{sosin97a}). Older CCD photometries are found in Alcaino et\nal (\\cite{alcaino90a}) ($B,V,I$ bands) and Walker (\\cite{walker92})\n($B,V$ bands)\n\n\\paragraph {\\bf NGC 1904 (M~79).} (Fig.~\\ref{ngc1904})\n\nM~79 is the farthest cluster ($R_{\\rm GC}=18.5$ kpc) from the Galactic\ncenter in our sample. The main feature in the CMD of\nFig.~\\ref{ngc1904} is the EBHB. Previous CMDs from CCD photometry are\nin Heasley et al. (\\cite{heasley83}) ($U,B,V$ bands), Gratton \\&\nOrtolani (\\cite{grattonortolani86}) ($B,V$ bands), Ferraro et\nal. (\\cite{ferraro93a}) ($B,V$ bands), Alcaino et\nal. (\\cite{alcaino94}) ($B,V,R,I$ bands), and Kravtsov et\nal. (\\cite{kravstov97}) ($U,B,V$ bands),\nand the $B$,$V$ photometry from HST in Sosin et al. (\\cite{sosin97a}). \n\n\\paragraph {\\bf NGC 2298.} (Fig.~\\ref{ngc2298})\n\nThis cluster is poorly sampled, particularly for the bright part of\nthe diagram (due to problems with a short exposure). Only four BHB\nstars are present in the HB region. Recent photometric works on this\nobject are in Gratton \\& Ortolani (\\cite{grattonortolani86}) ($B,V$\nbands), Alcaino \\& Liller (\\cite{alcainoliller86a}) ($B,V,R,I$ bands),\nJanes \\& Heasley (\\cite{janesheasley88}) ($U,B,V$ bands), and Alcaino\net al. (\\cite{alcaino90b}) ($B,V,R,I$ bands).\n\n\\paragraph {\\bf NGC 2808.} (Fig.~\\ref{ngc2808})\n\nThis cluster has some differential reddening (Walker 1999), as it\ncan be inferred also from the broadening of the sequences in the CMD\nof Fig.~\\ref{ngc2808}, and a moderate field contamination. The most\ninteresting features of the CMD are the bimodal HB and the EBHB tail\nwith other two gaps, as extensively discussed in Sosin et al.\n(\\cite{sosin97b}). As previously discussed, NGC~2808 is another bimodal\nHB cluster at intermediate metallicity with a younger age (Rosenberg\net al. \\cite{rosenberg99}). Apart from the already quoted $B$, and\n$V$ band photometry from HST data by Sosin et al. (\\cite{sosin97b}),\nthere are many other CCD photometries: \nGratton \\& Ortolani (\\cite{grattonortolani86}) ($B,V$ bands), \nBuonanno et al. (\\cite{buonanno89}) ($B,V$ bands),\nFerraro et al. (\\cite{ferraro90}) ($B,V$ bands), \nAlcaino et al. (\\cite{alcaino90c}) ($B,V,R,I$ bands),\nByun \\& Lee (\\cite{byunlee93}),\nFerraro et al. (\\cite{ferraro97}) ($V,I$ bands), and\nmore recently Walker (\\cite{walker99}) ($B,V$ bands).\n\n\\paragraph {\\bf E3.} (Fig.~\\ref{e3})\n\nThis cluster is one of the less populated clusters in our Galaxy,\nresembling some Palomar-like globular as Pal~1 (Rosenberg et\nal. \\cite{rosenberg98}). As in Pal~1, there are no HB stars in the CMD, and\nthe entire population of observed stars is smaller than 1000 objects. E3 is\nsuspected to have a metallicity close to that of Pal~1. From the $\\delta\n(V-I)_{\\rm @2.5}$ (Paper III) measured on Fig.~\\ref{e3}, E3 is coeval with\nthe other GGCs of similar metallicity, though the result is necessarily\nvery uncertain, due to the high contamination and the small number of RGB\nstars. E3 is the cluster with the better defined MS binary sequence\n(Veronesi et al. \\cite{veronesi96}), which can be also seen in\nFig.~\\ref{e3}. Previous CCD CMDs are in McClure et al. (\\cite{mcclure85})\n($B,V$ bands), Gratton \\& Ortolani (\\cite{grattonortolani87}) ($B,V$\nbands), and Veronesi et al. (\\cite{veronesi96}) ($B,V,R,I$ bands).\n\n\\paragraph {\\bf NGC 3201.} (Fig.~\\ref{ngc3201})\n\nThe two lateral fields presented in Fig.~\\ref{ngc3201} were observed\nin both runs, in order to test the homogeneity of the data and\ninstrumentation (see Sect.~\\ref{comparison}). The HB of NGC~3201 has\na bimodal appearance, though it is not younger than the bulk of GGCs\nof the same metallicity group, at variance with the previously\ndiscussed cases. It has a small differential reddening. A blue\nstraggler (BS) sequence is visible in Fig.~\\ref{ngc3201}. Previous\nCCD studies of this cluster include Penny (\\cite{penny84}) ($B,V,I$\nbands), Alcaino et al. (\\cite{alcaino89}) ($B,V,R,I$ bands), Brewer et\nal. (\\cite{brewer93}) ($U,B,V,I$ bands) and Covino \\& Ortolani\n(\\cite{covinoortolani97}) ($B,V$ bands).\n\n\\paragraph {\\bf NGC 4372.} (Fig.~\\ref{ngc4372})\n\nThe principal characteristic of the CMD of this cluster is the\nbroadening of all the sequences, consequence of the high differential\nreddening, probably due to the Coal-sack Nebulae. In the CMD of\nFig.~\\ref{ngc4372} the darker dots are from the stars in the lowest\nreddening region (south east) of the observed fields. We have computed\nthe reddening field for this cluster from the shift of the CMDs\nobtained in different positions, finding that it is homogeneously\ndistributed in space and quite easy to correct by a second order\npolynomial surface. Two previous CCD photometries can be found in\nAlcaino et al. (\\cite{alcaino91}) ($B,V,R,I$ bands) and Brocato et\nal. (\\cite{brocato96}) ($B,V$ bands).\n\n\\paragraph {\\bf NGC 4590 (M~68).} (Fig.~\\ref{ngc4590})\n\nThis cluster is probably the lowest metallicity cluster of the present\nsample. It has a well defined CMD, with an HB populated on both sides\nof the instability strip, and including some RR-Lyrae stars. It has\nsometimes been classified as one of the oldest GGCs (Salaris et al\n\\cite{salaris97}), and, in fact, we find that M68 is old, though\ncoeval with the rest of the metal poor clusters (Paper III). Other\nCCD CMDs for this cluster are in McClure et al. (\\cite{mcclure87})\n($B,V$ bands), Alcaino et al. (\\cite{alcaino90d}) ($B,V,R,I$ bands)\nand Walker (\\cite{walker94}) ($B,V,I$ bands).\n\n\\paragraph {\\bf NGC 4833.} (Fig.~\\ref{ngc4833})\n\nNGC~4833 is another metal-poor cluster, with an extended BHB, likely\nwith gaps, for which we have not found any previous CCD photometry.\n\n\\paragraph {\\bf NGC 5139 ($\\omega$ Centauri).} (Fig.~\\ref{ngc5139}) \n\nNGC~5139 is the intrinsically brightest cluster in our Galaxy. Apart\nfrom this, there are many other properties of $\\omega$ Centauri which\nmake it a very particular object. Its stellar population shows\nmetallicity variations as large as $\\sim1.5$~dex from star to star\n(Norris et al. \\cite{norris96}). Its overall properties suggest that\nthis clusters could have a different origin from the bulk of GGCs. It\nhas an extended BHB and probably numerous BSS. The broad sequences in\nthe CMD are mainly due to the metallicity variations though likely\nthere is some differential reddening in the field of $\\omega$\nCentauri. Due to its peculiarities, $\\omega$ Centauri has been (and\nis!) extensively studied; there is a large number of photometries,\nand we cannot cite all of them. The most recent and interesting CCD\nCMDs are in: Alcaino \\& Liller (\\cite{alcainoliller87b}), who present\na multi-band ($B,V,R,I$) photometry, but poorly sampled, specially\nfor the evolved part of the diagram; Noble et al. (\\cite{noble91})\npresent a deep $B,V$ diagram, where the MS is well sampled, but the RGB\nis not so clear and only 3-5 stars are present in the HB; Elson et al.\n(\\cite{elson95}) present a HST $V,I$ photometry of the MS; Lynga\n(\\cite{lynga96}) presents a $BVRI$ study of the evolved part of the\ndiagram ($\\sim 2$ mag below the HB); Kaluzny et al. (\\cite{kaluzny96},\n\\cite{kaluzny97a}) present a $V, I$ CMD covering more than $10^5$ stars.\n\n\\paragraph {\\bf NGC 5897.} (Fig.~\\ref{ngc5897}) \n\nNGC~5897 is a metal poor cluster with a blue, not extended HB, typical\nfor its metallicity. All the sequences of Fig.~\\ref{ngc5897} are well\ndefined and populated, including a BS sequence. Two CCD photometric\nstudies exist for this cluster: Sarajedini (\\cite{sarajedini92})\n($B,V$ bands) and Ferraro et al. (\\cite{ferraro92}) ($U,B,V,I$ bands).\n\n\\paragraph {\\bf NGC 5927.} (Fig.~\\ref{ngc5927})\n\nNGC~5927 has the highest metallicity among the objects of our\ncatalog. It has, as most of the GGCs with [Fe/H]$>-0.8$, a well\npopulated red horizontal branch (RHB), and an extended RGB, which, in\nour CMD, covers more than $\\sim$2.5~mag in ($V-I$), from the RHB\n(partially overlapped with the RGB) to the reddest stars of the RGB\ntip. It has a high reddening, possibly differential, judging from the\nbroadening of the RGB, and, due to its location (projected towards the\nGalactic center), the field object contamination (disk and bulge\nstars) is very high. Previous CCD photometries are in \nFriel \\& Geisler (\\cite{frielgeisler91}) (Washington photometry), \nSarajedini \\& Norris (\\cite{sarajedininorris94}) ($B,V$ bands), \nSamus et al. (\\cite{samus96}) ($B,V,I$ bands), Sosin et al.\n(\\cite{sosin97a}), and Rich et al. (\\cite{rich97}) (HST $B,V$ bands).\n\n\\paragraph {\\bf NGC 5986.} (Fig.~\\ref{ngc5986})\n\nTo our knowledge, this is the first CCD photometry for this\ncluster. NGC~5986 is an intermediate metallicity cluster, but with a\nmetal-poor like HB. The broadening of the CMD suggests some\ndifferential reddening. Contamination by field stars is clearly\nvisible, as expected on the basis of the position within the Galaxy of\nthis cluster.\n\n\\paragraph {\\bf NGC 6093 (M~80).} (Fig.~\\ref{ngc6093})\n\nNGC~6093 is a bright and moderately metal poor cluster, and one of the\ndensest globular clusters in the Galaxy. It has an EBHB, which extends\nwell below the TO as clearly visible also in the CMD of\nFig.~\\ref{ngc6093}, with gaps (Ferraro et al. 1998). Three recent CCD\nphotometries that cover the entire object, with CMD from the brightest\nstars to above the TO exist for this cluster: Brocato et\nal. (\\cite{brocato98}) ($B,V$ bands) and Ferraro et al.\n(\\cite{ferraro98}) (HST $U,V$, and far-UV (F160BW) bands). A\nground-based multicolor $U,B,V,I$ CCD CMD has been published also by\nAlcaino et al. (\\cite{alcaino98}).\n\n\\paragraph {\\bf NGC 6101.} (Fig.~\\ref{ngc6101})\n\nNGC~6101 was observed under not very good seeing conditions, and this\nis the reason for the brighter limiting magnitude. Its CMD has the\nmorphology expected for a metal-poor cluster: the HB is predominantly\nblue, and the giant branch is steep. In Fig.~\\ref{ngc6101} we note\nthat, starting from the BSS sequence, there is a sequence of stars\nparallel to the RGB on its blue side. In view of the position of the\ncluster ($l,b$)=(318,$-16$) these can unlikely be bulge stars; it is\npossible that on the same line of sight there is an open cluster,\nthough the slope of the two RGBs are quite similar, implying an\nunlikely similar metallicity. A larger field coverage of NGC~6101 is\ndesirable. \nThe only previous CCD photometry that exists for\nthis cluster is the $B$ and $V$ study by Sarajedini \\& Da Costa\n(\\cite{sarajedinidacosta91}), which shows these stars in the same CMD\nlocation. However, being the background-foreground stellar contamination\nheavier, the sequences we discussed can hardly be seen.\n\n\\paragraph {\\bf NGC 6121 (M~4).} (Fig.~\\ref{ngc6121})\n\nThis cluster is the closest GGC, located approximately at\n$\\sim2.2$~kpc from the Sun, though, due to the large reddening caused\nby the nebulosity in Scorpio-Ophiuchus, it has an apparent visual\ndistance modulus larger than NGC~6397. The reddening is differential,\nthough (as in the case of NGC~4372) it is homogeneously distributed in\nspace. The mean regions of the CMD can be improved using an\nappropriate second order polynomial fit to the reddening distribution,\nat least on the two fields shown in Fig.~\\ref{ngc6121}. The stars from\nthe southern field have been plotted as darker dots; they are located\non the redder (more reddened) part of the CMD. The two most recent CMD\nof M4 are in Ibata et al. (\\cite{ibata99}) ($V,I,U$ filters) and Pulone et\nal. (\\cite{pulone99}), who present (near IR) HST studies of the faint part of\nthe MS and of the WD sequence. Other recent CMDs from the RGB tip to\nbelow the MSTO are in Alcaino et al. (\\cite{alcaino97a}), who\npresented an $UBVI$ CCD photometry, and Kanatas et\nal. (\\cite{kanatas95}), who obtained a composite ($B,V$) CMD from\n$V\\sim12$ to $V\\sim25$.\n\n\\paragraph {\\bf NGC 6171 (M~107).} (Fig.~\\ref{ngc6171})\n\nPrevious CCD studies of NGC~6171 are the $(J,K)$ and $(B,V)$\nphotometry by Ferraro et al. (\\cite{ferraro95} and \\cite{ferraro91},\nrespectively). This cluster is affected by a moderate reddening, which\ncould be slightly differential. It has a RHB, with a few stars bluer\nthan the instability strip blue edge.\n\n\\paragraph {\\bf NGC 6266 (M~62).} (Fig.~\\ref{ngc6266})\n\nThis cluster is located very close to the Galactic center, and it has\na high differential reddening. It seems to have both a RHB and a BHB\nresembling the HB of NGC~1851. Previous $B,V$ bands CCD works are in\nCaloi et al. (\\cite{caloi87}), and Brocato et\nal. (\\cite{brocato96}). A de-reddened CMD and RR-Lyrae stars are also\nstudied in Malakhova et al. (\\cite{malakhova97}).\n\n\\paragraph {\\bf NGC 6304.} (Fig.~\\ref{ngc6304})\n\nNGC~6304 is a high metallicity cluster very close to the Galactic\ncenter, and has one of the highest reddenings in our sample. It has\nsome disk and bulge star contamination. There is a second RGB fainter\nand redder than the main RGB (bulge star contamination or a more\nabsorbing patch?), but the most noticeable feature is the extremely\nlong RGB. The reddest star of its RGB is located $\\sim$3.7~mag redward\nfrom the RHB! To our knowledge, this is the most extended RGB known\nfor a GGC. The most recent CCD CMD for this cluster comes from the $V$\nand $K$ photometry by Davidge et al. (\\cite{davidge92}) which covers\nthe hottest RGB stars and the HB.\n\n\\paragraph {\\bf NGC 6352.} (Fig.~\\ref{ngc6352})\n\nNGC~6352 is another high metallicity bulge GGC, with a CMD typical of\na cluster with this metal content. The most recent CCD study on this\ncluster is in Fullton et al. (\\cite{fullton95}), where a $VI_{\\rm c}$ CMD\nfrom HST data combined with ground-based observations is\npresented. Another study of the RGB and HB regions of this cluster is\npresented by Sarajedini \\& Norris (\\cite{sarajedininorris94}) in the\n$B,V$ bands.\n\n\\paragraph {\\bf NGC 6362.} (Fig.~\\ref{ngc6362})\n\nNGC~6362 presents a well defined CMD with a bimodal HB. The most\nrecent CMD on this cluster is given by Piotto et al.\n(\\cite{piotto99}), who present observations of the center of the\ncluster obtained with the HST/WFPC2 camera in the $B$ and $V$\nbands. The only previous ground-based CCD photometry is in Alcaino \\&\nLiller (\\cite{alcainoliller86b}). Our field has been also observed in\nthe same filters by Walker (priv. comm.), who made available to us his\ndata for a cross-check of the photometric calibration. We find that\nthe two photometries agree within the errors. In particular, we found\na zero point difference of 0.02~mag for the $V$ band and 0.01~mag for\nthe $I$ band, with a negligible -0.001 color term difference between\nWalker and our data. These discrepancies are well within the\nuncertainties, and allow to further confirm our calibration to the\nstandard (Landolt \\cite{landolt92}) system.\n\n\\paragraph {\\bf NGC 6397.} (Fig.~\\ref{ngc6397})\n\nThis cluster is the GGC with the smallest apparent distance\nmodulus. Cool et al. (\\cite{cool96}) and King et al.\n(\\cite{king98}) present an extremely well defined \nCMD of the main sequence of this cluster, from HST\ndata, from just below the TO down to $I=24.5$, which correspond to a\nmass of less than $0.1 M_\\odot$. Other HST studies on this cluster have\nbeen presented by Burgarella et al. (\\cite{burgarella94}), De Marchi\n\\& Paresce (\\cite{demarchiparesce94}), Cool et al. (\\cite{cool95}) and\nKing et al. (\\cite{king95}). Many ground-based CCD data have also\nbeen published: Auriere et al. (\\cite{auriere90}), Anthony-Twarog et\nal. (\\cite{anthonytwarog92}) (Stromgren photometry), Lauzeral et\nal. (\\cite{lauzeral92}, \\cite{lauzeral93}), Kaluzny (\\cite{kaluzny97b})\n($B,V$ bands) and Alcaino et al. (\\cite{alcaino87}: $B,V$ bands;\n\\cite{alcaino97b}: $U,B,V,I$ bands).\n\n\\paragraph {\\bf NGC 6496.} (Fig.~\\ref{ngc6496})\n\nNGC~6496 is another metal rich GGC which presents an extended RGB. In\nthis case, the reddest stars are $\\sim$ 2~mag redder than the RHB. It\nhas also a remarkably tilted RHB, already noted by Richtler et al.\n(\\cite{richtler94}), who present a CCD $(B,V)$ photometry of this\ncluster; Armandroff (\\cite{armandroff88}) gives $(V,I)$ CCD\nphotometry. A tilted RHB can be noted not only in this CMD, but also\nin the CMDs of most of the very metal-rich clusters of our\nsample. Such a feature is usually not present in the canonical models.\nThe RHB is well populated, and there are two stars located on the BHB\nregion. This is quite unusual considering the metallicity of NGC~6496,\nand it would be interesting to study the membership and to obtain a\nCMD on a larger field. Another CCD photometry of this cluster is in\nFriel \\& Geisler (\\cite{frielgeisler91}) in the Washington\nsystem. Sarajedini \\& Norris (\\cite{sarajedininorris94}) present a $B$\nand $V$ photometry for the RGB and HB region.\n\n\\paragraph {\\bf NGC 6541.} (Fig.~\\ref{ngc6541})\n\nNGC 6541 is located rather close to the Galactic center, and this\nexplains the high field star contamination of the CMD. It has a BHB, as\nexpected from its metal content. The only previous CCD study of this\ncluster is the multicolor photometry by Alcaino et\nal. (\\cite{alcaino97c}).\n\n\\paragraph {\\bf NGC 6544.} (Fig.~\\ref{ngc6544})\n\nThis is an example of a terrible ``spotty'' field with a high (the\nhighest in our sample) and highly differential reddening, due to the\nlocation of NGC~6544, which is very close to the Galactic plane and\nprojected towards the Galactic center. Interestingly enough, despite\nits intermediate metallicity, there are only BHB stars. Probably, the\nuse of the HST in this case is almost inevitable if we want to\nestimate the age of this kind of clusters. We have not found any\nprevious CCD photometry of this cluster.\n\n\\paragraph {\\bf NGC 6624.} (Fig.~\\ref{ngc6624})\n\nAnother member of the metal-rich group is presented in\nFig.~\\ref{ngc6624}. Despite of being the cluster closest to the Galactic\ncenter, NGC~6624 has a moderate field star contamination, and a very\nwell\ndefined RGB and RHB. The reddest stars of the RGB are in this case\n$\\sim2.2$~mag redder than the RHB. \n\nRichtler et al. (\\cite{richtler94}) present a $B$ and $V$ CCD CMD of\nthis cluster extending well below the TO, while Sarajedini \\& Norris\n(\\cite{sarajedininorris94}) present a photometric study of the RGB\nand HB in the same bands. A $B,V$ CMD from HST data is in Sosin \\& King\n(\\cite{sosinking95}) and Sosin et al. (\\cite{sosin97a}).\n\n\\paragraph {\\bf NGC 6626 (M~28).} (Fig.~\\ref{ngc6626})\n\nAgain a high differential reddening is present in the field of NGC\n6626, which is located close to the Galactic center. NGC 6626 seems to\nhave an extended BHB, and maybe a few RHB stars, though the field star\ncontamination makes it rather difficult to see them. Previous CCD photometry\nis given by Davidge et al. (\\cite{davidge96}), who present a deep\nnear infrared photometry.\n\n\\paragraph {\\bf NGC 6637 (M~69).} (Fig.~\\ref{ngc6637})\n\nThe CMD of NGC 6637 presents the typical distribution in color for the\nRGB stars discussed for other metal rich clusters, with the reddest\nstars $\\sim2.4$~mag redder than the RHB. Previous $B$ and $V$ CCD\nphotometry is presented by Richtler et al. (\\cite{richtler94}), and\nthe RGB-HB region is also studied by Sarajedini \\& Norris\n(\\cite{sarajedininorris94}) in the same bands.\n\n\\paragraph {\\bf NGC 6638.} Fig.~\\ref{ngc6638}\n\nAffected by high differential reddening, the CMD this cluster is not\nvery well defined. However, the HB is clearly populated on both sides\nof the instability strip, and probably there are many RR-Lyrae. We\nhave not found any previous CCD photometries of this cluster.\n\n\\paragraph {\\bf NGC 6656 (M~22).} (Fig.~\\ref{ngc6656})\n\nA possible internal dispersion in metallicity has been proposed for\nM22. It presents an EBHB with some HB stars as faint as the\nTO, and several possible RR-Lyrae stars. It is close to the\nGalactic center and to the Galactic plane, with a high\nreddening.\n\nPiotto \\& Zoccali (\\cite{piottozoccali99}) published the most recent\nstudy of this cluster. From a combination of HST data and ground based\nCCD photometry, they produced a CMD extending from the tip of the RGB\nto below $0.2 M_\\odot$. Anthony-Twarog et al. (\\cite{anthonytwarog95})\npresent $uvbyCa$ data for over 300 giant and HB stars, while in\nDavidge \\& Harris (\\cite{davidgeharris96}) there is a deep near\ninfrared study.\n\n\\paragraph {\\bf NGC 6681 (M~70).} (Fig.~\\ref{ngc6681})\n\nNGC 6681 has a predominantly blue HB with a few HB stars on the red side\nof the instability strip. Brocato et al. (\\cite{brocato96}) present\nthe only other available CCD photometry for this cluster in the $B$\nand $V$ bands.\n\n\\paragraph {\\bf NGC 6717 (Palomar~9).} (Fig.~\\ref{ngc6717})\n\nNGC~6717 is a poorly populated cluster (as most of the\n``Palomar-like'' objects), and the CMD is contaminated by bulge\nstars. The RGB is difficult to identify, and its HB is blue,\nresembling that of NGC 288. Notice that there is a very bright field\nstar close to the cluster, located at the north side of it. Brocato\net al. (\\cite{brocato96}) present the first CCD photometry for this\ncluster; their $B$ and $V$ CMD resembles that of\nFig.~\\ref{ngc6717}. Recently, Ortolani et al. (\\cite{ortolani99})\npresented a new CMD, in the same bands, but the CMD branches are more\npoorly defined.\n\n\\paragraph {\\bf NGC 6723.} (Fig.~\\ref{ngc6723})\n\nNGC 6723 has both a red and blue HB, and the overall morphology is\ntypical of a cluster of intermediate metallicity. Alcaino et\nal. (\\cite{alcaino99}) present the most recent CCD study (multicolor\nphotometry), with a CMD extending down to $V\\sim21$. \nFullton \\& Carney (\\cite{fulltoncarney96}) have obtained a\ndeep $B$ and $V$ photometry, extending to $V\\sim24$, though the\nresults of this study have not been completely published, yet.\n\n\\paragraph {\\bf NGC 6752.} (Fig.~\\ref{ngc6752})\n\nNGC~6752 has been largely studied in the past. It has a very well\ndefined EBHB. Penny \\& Dickens (\\cite{pennydickens86}) presented a\n$B$ and $V$ CCD study from a combination of data from two telescopes,\nand published a CMD from the RGB tip to $V\\sim24$ mag, though with a\nsmall number of measured stars. In the same year, Buonanno et\nal. (\\cite{buonanno86}) present a CMD in the same bands for stars from\n$\\sim1$ mag above the TO to $\\sim5$ mag below it. More recently,\nRenzini et al. 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Rood and Renzini, p. 92\n\\bibitem[1987]{stetson87}\t\tStetson P.B.,\n1987, PASP 99, 191\n\\bibitem[1994]{stetson94}\t\tStetson P.B., \n1994, PASP 106, 250\n\\bibitem[1996]{veronesi96} \t\tVeronesi C., Zaggia S., Piotto G., Ferraro F.R., Bellazzini M., \n1996, ASP Conf. Ser. 92, 301\n\\bibitem[1992]{walker92} \t\tWalker A.R., \n1992, PASP 104, 1063\n\\bibitem[1994]{walker94} \t\tWalker A.R., \n1994, AJ 108, 555\n\\bibitem[1998]{walker98} \t\tWalker A.R., \n1998, AJ 116, 220\n\\bibitem[1999]{walker99} \t\tWalker A.R., \n1999, AJ 118, 432\n\\bibitem[1997]{zaggia97} \t\tZaggia S., Piotto G., Capaccioli M., \n1997, A\\&A 327, 1004\n\\bibitem[1984]{zinnwest84}\t\tZinn R., West M.J., \n1984, ApJS 55, 45\n\\end{thebibliography}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-4cm}{\n\\psfig{figure=h1679f4.ps,width=10.9cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\hspace{-2cm}\n\\fbox{\\psfig{figure=h1679f4a.ps,width=4cm}} &\n\\fbox{\\psfig{figure=h1679f4b.ps,width=4cm}} \n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~104 (47 Tucanae)}\n\\label{ngc104}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f5.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f5a.ps,width=4cm}} &\n\\fbox{\\psfig{figure=h1679f5b.ps,width=4cm}} \\\\\n\\fbox{\\psfig{figure=h1679f5c.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~288}\n\\label{ngc288}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f6.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f6a.ps,width=4cm}} &\n\\fbox{\\psfig{figure=h1679f6b.ps,width=4cm}} \\\\\n\\fbox{\\psfig{figure=h1679f6c.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~362}\n\\label{ngc362}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f7.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f7a.ps,width=4cm}} &\n\\fbox{\\psfig{figure=h1679f7b.ps,width=4cm}} \\\\\n\\fbox{\\psfig{figure=h1679f7c.ps,width=4cm}} \n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~1261}\n\\label{ngc1261}\n\\end{figure*}\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f8.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f8a.ps,width=4cm}} &\n\\fbox{\\psfig{figure=h1679f8b.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~1851}\n\\label{ngc1851}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f9.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f9a.ps,width=4cm}} &\n\\fbox{\\psfig{figure=h1679f9b.ps,width=4cm}} \\\\ \n&\n\\fbox{\\psfig{figure=h1679f9c.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~1904 (M~79)}\n\\label{ngc1904}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f10.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f10a.ps,width=4cm}} &\n\\fbox{\\psfig{figure=h1679f10b.ps,width=4cm}} \n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~2298}\n\\label{ngc2298}\n\n\\vspace {-1.5cm}\n\n\\begin{tabular}{c@{}c}\n\\raisebox{-6.5cm}{\n\\psfig{figure=h1679f11.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n&\n\\fbox{\\psfig{figure=h1679f11a.ps,width=4cm}} \\\\\n\\fbox{\\psfig{figure=h1679f11c.ps,width=4cm}} &\n\\fbox{\\psfig{figure=h1679f11b.ps,width=4cm}} \\\\\n&\n\\fbox{\\psfig{figure=h1679f11d.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~2808}\n\\label{ngc2808}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f12.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f12a.ps,width=4cm}} &\n\\fbox{\\psfig{figure=h1679f12b.ps,width=4cm}} \n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for E3}\n\\label{e3}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f13.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f13b.ps,width=4cm}} &\n\\fbox{\\psfig{figure=h1679f13a.ps,width=4cm}} \\\\\n&\n\\fbox{\\psfig{figure=h1679f13c.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~3201}\n\\label{ngc3201}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f14.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n&\n\\fbox{\\psfig{figure=h1679f14a.ps,width=4cm}}\n\\\\\n\\fbox{\\psfig{figure=h1679f14b.ps,width=4cm}} \n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~4372}\n\\label{ngc4372}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f15.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f15a.ps,width=4cm}} &\n\\\\\n\\fbox{\\psfig{figure=h1679f15b.ps,width=4cm}} \n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~4590 (M~68)}\n\\label{ngc4590}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f16.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f16a.ps,width=4cm}} &\n\\fbox{\\psfig{figure=h1679f16b.ps,width=4cm}} \n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~4833}\n\\label{ngc4833}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f17.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f17a.ps,width=4cm}} &\n\\fbox{\\psfig{figure=h1679f17b.ps,width=4cm}} \n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~5139 ($\\omega$ Centauri)}\n\\label{ngc5139}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f18.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f18a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~5897}\n\\label{ngc5897}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f19.ps,width=10.9cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f19a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~5927}\n\\label{ngc5927}\n\\end{figure*}\n\n\n\\clearpage\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f20.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f20a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~5986}\n\\label{ngc5986}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f21.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f21a.ps,width=4cm}}\\\\\n&\n\\fbox{\\psfig{figure=h1679f21b.ps,width=4cm}} \n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~6093 (M~80)}\n\\label{ngc6093}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f22.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f22a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6101}\n\\label{ngc6101}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f23.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f23a.ps,width=4cm}} \\\\\n\\fbox{\\psfig{figure=h1679f23b.ps,width=4cm}} \n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~6121 (M~4)}\n\\label{ngc6121}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f24.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f24a.ps,width=4cm}} &\n\\fbox{\\psfig{figure=h1679f24b.ps,width=4cm}} \n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~6171 (M~107)}\n\\label{ngc6171}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f25.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f25a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6266}\n\\label{ngc6266}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-8cm}{\n\\psfig{figure=h1679f26.ps,width=16.5cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\hspace{-4cm}\n\\fbox{\\psfig{figure=h1679f26a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6304 (M~62)}\n\\label{ngc6304}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f27.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f27a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6352}\n\\label{ngc6352}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f28.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f28a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6362}\n\\label{ngc6362}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f29.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f29a.ps,width=4cm}} \\\\\n\\fbox{\\psfig{figure=h1679f29b.ps,width=4cm}} \n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~6397}\n\\label{ngc6397}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f30.ps,width=10.9cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f30a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6496}\n\\label{ngc6496}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f31.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f31a.ps,width=4cm}} &\n\\fbox{\\psfig{figure=h1679f31b.ps,width=4cm}} \n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~6541}\n\\label{ngc6541}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f32.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f32a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6544}\n\\label{ngc6544}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f33.ps,width=10.9cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f33a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6624}\n\\label{ngc6624}\n\\end{figure*}\n\n\n\\clearpage\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f34.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f34a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6626 (M~28)}\n\\label{ngc6626}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f35.ps,width=10.9cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f35a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6637 (M~69)}\n\\label{ngc6637}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f36.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f36a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6638}\n\\label{ngc6638}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f37.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f37a.ps,width=4cm}} \\\\\n\\fbox{\\psfig{figure=h1679f37b.ps,width=4cm}} \n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered fields for NGC~6656 (M~22)}\n\\label{ngc6656}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f38.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f38a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6681 (M~70)}\n\\label{ngc6681}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f39.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f39a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6717 (Palomar~9)}\n\\label{ngc6717}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f40.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f40a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6723}\n\\label{ngc6723}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f41.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f41a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6752}\n\\label{ngc6752}\n\\end{figure*}\n\n\n\\begin{figure*}\n\\begin{tabular}{c@{}c}\n\\raisebox{-6cm}{\n\\psfig{figure=h1679f42.ps,width=8.8cm}\n} &\n\\begin{minipage}[t]{8.8cm}\n\\begin{tabular}{c@{}c}\n\\fbox{\\psfig{figure=h1679f42a.ps,width=4cm}}\n\\end{tabular}\n\\end{minipage}\n\\end{tabular}\n\\caption[]{CMD and covered field for NGC~6809 (M~55)}\n\\label{ngc6809}\n\\end{figure*}\n\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002205.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[1986a]{alcainoliller86a} \tAlcaino G., Liller W., \n1986a, A\\&A 161, 61\n\\bibitem[1986b]{alcainoliller86b} \tAlcaino G., Liller W., \n1986b, AJ 91, 303\n\\bibitem[1987a]{alcainoliller87a} \tAlcaino G., Liller W., \n1987a, ApJ 319, 304\n\\bibitem[1987b]{alcainoliller87b} \tAlcaino G., Liller W., \n1987b, AJ 94, 1585\n\\bibitem[1987]{alcaino87} \t\tAlcaino G., Buonanno R., Caloi V., et al., \n1987, AJ 94, 917\n\\bibitem[1989]{alcaino89} \t\tAlcaino G., Liller W., Alvarado F., \n1989, A\\&A 216, 68\n\\bibitem[1990a]{alcaino90a} \t\tAlcaino G., Liller W., Alvarado F., Wenderoth E., \n1990a, AJ 99, 817\n\\bibitem[1990b]{alcaino90b} \t\tAlcaino G., Liller W., Alvarado F., Wenderoth E., \n1990b, A\\&AS 83, 269\n\\bibitem[1990c]{alcaino90c} \t\tAlcaino G., Liller W., Alvarado F., Wenderoth E., \n1990c, ApJS 72, 693\n\\bibitem[1990d]{alcaino90d} \t\tAlcaino G., Liller W., Alvarado F., Wenderoth E., \n1990d, AJ 99, 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}
] |
astro-ph0002206
|
On The Reddening in X-ray Absorbed Seyfert 1 Galaxies
|
[
{
"author": "S. B. Kraemer\\altaffilmark{1}"
},
{
"author": "I. M. George\\altaffilmark{2}"
},
{
"author": "T. J. Turner\\altaffilmark{3}"
},
{
"author": "\\& D. M. Crenshaw\\altaffilmark{1}"
}
] |
There are several Seyfert galaxies for which there is a discrepancy between the small column of neutral hydrogen deduced from X-ray observations and the much greater column derived from the reddening of the optical/UV emission lines and continuum. The standard paradigm has the dust within the highly ionized gas which produces O~VII and O~VIII absorption edges (i.e., a ``dusty warm absorber''). We present an alternative model in which the dust exists in a component of gas in which hydrogen has been stripped, but which is at too low an ionization state to possess significant columns of O~VII and O~VIII (i.e, a ``lukewarm absorber''). The lukewarm absorber is at sufficient radial distance to encompass much of the narrow emission-line region, and thus accounts for the narrow-line reddening, unlike the dusty warm absorber. We test the model by using a combination of photoionization models and absorption edge fits to analyze the combined {ROSAT}/{ASCA} dataset for the Seyfert 1.5 galaxy, NGC 3227. We show that the data are well fit by a combination of the lukewarm absorber and a more highly ionized component similar to that suggested in earlier studies. We predict that the lukewarm absorber will produce strong UV absorption lines of N~V, C~IV, Si~IV and Mg~II. Finally, these results illustrate that singly ionized helium is an important, and often overlooked, source of opacity in the soft X-ray band (100 - 500 eV).
|
[
{
"name": "reddening.tex",
"string": "\\documentstyle[12pt,aasms4]{article}\n\n\\def\\arcsecpoint{$''\\!.$}\n\\received{1999-NOV-30}\n\\accepted{2000-Jan-7}\n%\\journalid{}{}\n%\\articleid{}{}\n\n\\slugcomment{to appear in {\\it The Astrophysical Journal}}\n\n\\lefthead{Kraemer, George, Turner, \\& Crenshaw}\n\\righthead{On The Reddening in X-ray Absorbed Seyfert 1 Galaxies}\n\n\\begin{document}\n\n\\title{On The Reddening in X-ray Absorbed Seyfert 1 Galaxies}\n\n\\author{S. B. Kraemer\\altaffilmark{1},\nI. M. George\\altaffilmark{2},\nT. J. Turner\\altaffilmark{3},\n\\& D. M. Crenshaw\\altaffilmark{1}}\n\n \n\n\\altaffiltext{1}{Catholic University of America,\nNASA's Goddard Space Flight Center, Code 681,\nGreenbelt, MD 20771; stiskraemer@yancey.gsfc.nasa.gov, \ncrenshaw@buckeye.gsfc.nasa.gov.}\n\n\\altaffiltext{2}{Universities Space Research Association,\nNASA's Goddard Space Flight Center, Code 660,\nGreenbelt, MD 20771; ian.george@gsfc.nasa.gov.}\n\n\\altaffiltext{3}{University of Maryland, Baltimore County,\nNASA's Goddard Space Flight Center, Code 660,\nGreenbelt, MD 20771; turner@lucretia.gsfc.nasa.gov.}\n\n\n\\begin{abstract}\n\n\nThere are several Seyfert galaxies for which there is a discrepancy\nbetween the small column of neutral hydrogen deduced from X-ray\nobservations and the much greater column derived from the reddening of the\noptical/UV emission lines and continuum. The standard paradigm\nhas the dust within the highly ionized gas which produces\nO~VII and O~VIII absorption edges (i.e., a ``dusty warm absorber''). \nWe present an alternative model in which the dust exists in\na component of gas in which hydrogen has been stripped,\nbut which is at too low an ionization state to possess significant\ncolumns of O~VII and O~VIII (i.e, a ``lukewarm absorber''). The lukewarm\nabsorber is at sufficient radial\ndistance to encompass much of the narrow emission-line region, and thus\naccounts for the narrow-line reddening, unlike the dusty warm \nabsorber. We test the model by using a combination of photoionization \nmodels and absorption edge fits to analyze the combined\n{\\it ROSAT}/{\\it ASCA} dataset for the Seyfert 1.5 galaxy, NGC 3227. \nWe show that the data are well fit by a combination of \nthe lukewarm absorber and a more highly ionized component similar\nto that suggested in earlier studies. We predict that the lukewarm\nabsorber will produce strong \nUV absorption lines of N~V, C~IV, Si~IV and Mg~II.\nFinally, these results illustrate that singly \nionized helium is an important, and often overlooked, source of opacity in the\nsoft X-ray band (100 - 500 eV). \n\n\n\\end{abstract}\n\n\\keywords{galaxies: Seyfert - X-rays: galaxies}\n\n\n\\section{Introduction}\n\n\nThe presence of absorption edges of O~VII and O~VIII in\nthe X-ray (Reynolds 1997; George et al. 1998a) indicates that there\nis a significant amount of intrinsic ionized material along our line-of-sight \nto \nthe nucleus in\na large fraction ($\\sim$ 0.5) of Seyfert 1 galaxies.\nIn addition to highly ionized gas (referred to as an X-ray or ``warm'' absorber), \nX-ray spectra often show evidence for a less-ionized\nabsorber. This component has been modeled using neutral gas \n(cf. George et al. 1998b), and its relationship to the \n``warm'' absorber is unclear.\nInterestingly, there are several instances in which this additional neutral \ncolumn is too small by as much as an order of magnitude to explain\nthe reddening of the continuum and emission lines, assuming \ntypical Galactic dust/gas ratios (cf. Shull \\& van Steenburg 1985). \nThis inconsistency was first noted\nin regard to the absence of\nhigh ionization emission lines in the {\\it IUE} spectra of MCG -6-30-15 (Reynolds\n\\& Fabian 1995). \nThe first quantitative comparison of the neutral\ncolumns inferred from the X-ray data to that derived from the reddening was \nfor the QSO IRAS 13349+2438 by Brandt, Fabian, \\& Pounds (1996), who\nsuggested that the dust exists within the highly ionized\nX-ray absorber (ergo, a dusty warm absorber). \nIt has been suggested\n that dusty warm absorbers are present in several other Seyferts \n(NGC 3227: Komossa \\& Fink 1997a;\nNGC 3786: Komossa \\& Fink 1997b; IRAS 17020+4544: Leighly et al. 1997,\nKomossa \\& Bade 1998; MCG -6-30-15: Reynolds et al. 1997). \nSince it is unlikely that dust could form\nwithin the highly ionized gas responsible for the O~VII and O~VIII\nabsorption, it has been suggested that\nthe dust is evaporated off the putative molecular torus (at $\\sim$ 1 pc) and, \nsubsequently, swept up in an radially outflowing wind (cf. Reynolds 1997). \n\n \nIn this paper, we present an alternative explanation.\nIt is possible that there is a component \nof dusty gas (which we will refer to as the ``lukewarm'' absorber), with an \nionization state such that hydrogen is nearly completely ionized but\nthe O~VII and O~VIII columns are negligible, which has\na sufficient total column to\naccount for the reddening. Such a possibility has been mentioned by\nBrandt et al. (1996), while Reynolds et al. (1997) have suggested that\nthe dusty warm absorber in MCG -6-30-15 may have multiple zones. \nHere we suggest that the lukewarm absorber lies far into the \nnarrow-line region (NLR).\nSuch a component has been detected \nin the Seyfert galaxy NGC 4151 (Kraemer et al. 1999), and it\nlies at sufficient radial distance to cover much of the NLR.\nWe will demonstrate that the combination of a \ndusty lukewarm absorber and a more highly ionized (O~VII and O~VIII)\nabsorber is consistent with the observed X-ray data\nand with the \nreddening of the narrow emission lines in the Seyfert 1 galaxy NGC 3227.\n\n\\section{Absorption and Reddening in NGC 3227}\n\n NGC 3227 ($z$ $=$ 0.003) is a well studied Sb galaxy with an active nucleus,\n usually classified as a Seyfert 1.5 (Osterbrock \\& Martel 1993). \n X-ray observations of NGC 3227 with {\\it ROSAT}\n and {\\it ASCA} reveal the presence of ionized\n gas along the line-of-sight to the nucleus (Ptak et al. 1994; \n Reynolds 1997; George et al. 1998b). \n Using the combined {\\it ASCA} and {\\it ROSAT} dataset\n obtained in 1993, \n George et al. \n characterized the absorber with an ionization\n parameter (number of photons with energies $\\geq$ 1 Ryd\n per hydrogen atom at the ionized\n face of the cloud) U $\\approx$ 2.4, and a column density \n N$_{\\rm H}$ $\\approx$ 3 x 10$^{21}$ cm$^{-2}$.\n\n The UV and optical emission lines and continuum in NGC 3227 are heavily \n reddened. \n Cohen (1983) measured a narrow H$\\alpha$/H$\\beta$ ratio $\\approx$ 4.68,\n and derived \n a reddening of E$_{B-V}$ $=$ 0.51 $\\pm$ 0.04, assuming the intrinsic\n decrement to be equal to the Case B value (Osterbrock 1989).\n Cohen derived a somewhat larger reddening from the [S~II] lines, E$_{B-V}$ \n $=$ 0.94 $\\pm$0.23, which may be less reliable due to the weakness of \n [S~II] $\\lambda$4072 \n(see Wampler 1968).\n The ratio of \n broad H$\\alpha$/H$\\beta$ $\\approx$ 5.1, indicating that the broad and narrow \n lines are similarly reddened. Winge et al. (1995) used the\n total (narrow $+$ broad) H$\\alpha$/H$\\beta$ ratio to derive a somewhat \n smaller reddening, E$_{B-V}$ $\\approx$ 0.28.\n {\\it IUE} spectra show the UV \n continuum of NGC 3227\n is also heavily reddened (Komossa \\& Fink 1997a). Based on the Balmer lines, \n assuming Galactic dust properties \n and dust/gas ratio, the derived reddening requires a hydrogen \n (H~I and H~II combined)\n column density $\\geq$ 2 x 10$^{21}$ cm$^{-2}$\n (cf. Shull \\& Van Steenberg 1985), which\n is much greater than the estimated neutral column,\n but similar to that of the ionized gas \n detected in X-rays in 1993 \n ($N_{\\rm H}$ $\\approx$ 3 x 10$^{21}$ cm$^{-2}$; \n George et al. 1998b).\n \nSeveral workers have suggested that NGC~3227 contains a screen of \nneutral material (in addition to that in the Galaxy)\nalong the line-of-sight to the nucleus.\nBesides the ionized absorber, \nboth Komossa \\& Fink (1997a) and George et al. (1998b) \nfound a column density of $\\lesssim$ 3 x 10$^{20}$ cm$^{-2}$\nof neutral material, in addition to\nthe Galactic column ($\\sim$ 2.1 x 10$^{20}$ cm$^{-2}$, cf. Murphy et al.\n1996), is required to model the X-ray spectrum \nbelow $\\sim$500~eV.\nA higher column density ($\\sim$ 6 x 10$^{20}$ cm$^{-2}$)\nhas been suggested based on 21-cm VLA observations \n(Mundell et al. 1997).\nHowever the angular resolution of the VLA data is poor \n(12$''$, or $\\sim$ 850 pc) and Mundell et al. did not make a direct detection \nof H~I absorption against the radio continuum source in the inner nucleus.\nIn this paper we argue that based on the current data, there is\nno reason to include a significant column of completely neutral material. \nWe show that a dusty lukewarm absorber lying outside the NLR\nis consistent with both the reddening of the optical continuum and \nnarrow lines, and with the attenuation of the X-ray spectrum \nbelow $\\sim$500~eV.\n\n\n\n\n\n\\section{Modeling The Absorber}\n\n\\subsection{The Lukewarm Component}\n\n The photoionization code we use has been described in previous publications\n (cf. Kraemer et al. 1994). For the sake of simplicity, we assume that the\n lukewarm absorber can be represented as a single zone, described by\n one set of initial conditions (i.e., density, ionization parameter, \n elemental abundances, and dust fraction). The gas is ionized by\n the continuum radiation emitted by the central source in the active\n nucleus of NGC 3227. \n \n\n In order to fit the SED, we first determined the intrinsic luminosity at\n the Lyman limit. Since NGC 3227 is heavily reddened, we fit the\n value at the Lyman limit based on the optical continuum flux.\n From the average fluxes measured by Winge et al. (1995), after correcting for \n a reddening of E$_{B-V}$ $=$ 0.4 (the average of the reddening\n quoted by Cohen (1983) and Winge et al.), assuming\n the reddening curve of Savage \\& Mathis (1979), we find that\n the intrinsic flux at 5525 \\AA~ is \n F$_{\\lambda}$ $\\approx$ 2.5 x 10$^{-14}$\n ergs s$^{-1}$ cm$^{-2}$ \\AA$^{-1}$.\n Interestingly, the optical luminosities of NGC 3227 and NGC 4151\n are roughly equal and, therefore, we have made the assumption that the\n two galaxies have similar optical-UV SEDs. Using the same ratio of\n optical to UV flux for NGC 3227 as in NGC 4151 (Nelson et al. 1999), we \n determine\n F$_{\\nu}$ at the Lyman limit to be \n $\\sim$ 6.2 x 10$^{-26}$ ergs s$^{-1}$ cm$^{-2}$ Hz$^{-1}$. The\n X-ray continuum from 2 -- 10 keV can be fit with an index,\n $\\alpha$ $\\approx$ 0.6 (George et al. 1998b), from which\n we derive a flux at 2 keV of $\\sim$ 2.20 x 10$^{-29}$ ergs s$^{-1}$ cm$^{-2}$ \n Hz$^{-1}$. Since an extrapolation \n of the X-ray continuum\n underpredicts the\n flux at the Lyman limit by more than two orders of magnitude, the continuum\n must steepen below 2 keV. \nHence, we have modeled the \n EUV to X-ray SED \nas a series of power-laws of the form\n F$_{\\nu}$ $\\propto$ $\\nu^{-\\alpha}$, \nwith\n$\\alpha = 1$ below 13.6~eV, \n$\\alpha = 2$ over the range 13.6~eV $\\leq h\\nu <$ 500~eV, \nand $\\alpha = 0.6$ above 500~eV.\n\nGiven this simple parameterization, the \nsteepening of the continuum cannot occur at a much lower energy, otherwise\nthe EUV continuum would be too soft\\footnote[2]{It is possible to have a lower break energy and a \nsufficient number of He~II ionizing photons if the EUV continuum has\na significant ``Big Blue Bump'', as suggested by Mathews \\& Ferland (1987).\nAlthough assuming such a continuum does not appreciably affect our predictions,\na full exploration of parameter space is beyond the scope of this paper.}\n to produce the observed He~II $\\lambda$4686/H$\\beta$ ratio\n($\\approx$ 0.23), specifically since the strong [O~I] $\\lambda$6300\nline indicates that much of the NLR gas is optically thick (for the\nrelative narrow emission-line strengths, see Cohen 1983).\nThe luminosity in ionizing photons, from 13.6 -- 10,000 eV, is\n$\\sim$ 1.5 x 10$^{53}$ photons s$^{-1}$. \n\nWe have assumed roughly solar element abundances (cf. Grevesse \\& Anders 1989),\nwhich are, by number relative to H, as follows: He $=$ 0.1, \nC $=$ 3.4 x 10$^{-4}$, N $=$ 1.2 x 10$^{-4}$, O $=$ 6.8 x 10$^{-4}$,\nNe $=$ 1.1 x 10$^{-4}$, Mg $=$ 3.3 x 10$^{-5}$, Si $=$ 3.1 x 10$^{-5}$,\nS $=$ 1.5 x 10$^{-5}$, and Fe $=$ 4.0 x 10$^{-5}$.\n We assume that both\nsilicate and carbon dust grains are present in the gas, with a power-law\ndistribution in sizes (see Mathis, Rumpl, \\& Nordsieck 1977). Thus, we\nhave modified the abundances listed above by depletion\nof elements from gas-phase onto dust grains, as follows (cf. Snow \\& Witt\n1996): C, 20\\%; O, 15\\%; Si, Mg and Fe, 50\\%. \n\nFor our model, we require that 1) the absorber lies outside the\nmajority of the NLR emission, and 2) the column of gas is fixed\nto obtain the observed reddening.\nBased on the WFPC2 narrow-band [O~III] $\\lambda$5007 imaging\n(Schmitt \\& Kinney 1996), we have\nplaced the lukewarm absorber at least 100 pc from the central source, \nand truncated the model at a hydrogen column density N$_{H}$ \n$=$ 2 x 10$^{21}$ cm$^{-2}$. We\nadjusted the ionization\nparameter such that the model \nproduced a reasonable match to the absorption in the \nobserved soft X-ray continuum (see below). \n\n\n\\subsection{Comparison to the X-ray data}\n\n\nTo compare our model predictions to the X-ray\ndata,\nwe used the 1993 \n{\\it ASCA} (0.6--10~keV) and {\\it ROSAT} PSPC (0.1--2.5~keV)\ndata described in George et al (1998b), excluding the flare \n(``t3'' in Fig 4 of George et al). Following standard \npractice, the normalizations of each of the 4 {\\it ASCA} instruments \nand of the {\\it ROSAT} dataset were allowed to vary independently.\nThe 5-7~keV band was also excluded from the analysis due to the \npresence of the strong, broad Fe emission line.\nWe assumed the continuum described above, except that the \nspectral index above 500~eV was allowed to vary during the analysis.\nIn addition to the lukewarm absorber (and Galactic absorption),\nany highly-ionized gas was modeled by a series of \nedges of fixed energy.\nThis is somewhat problematic since neither the {\\it ASCA} nor \n{\\it ROSAT} instruments have sufficient \nspectral resolution and/or sensitivity to resolve all the possible \nedges. We have therefore \ntested for the edges most likely to be visible in highly ionized gas\n(e.g., O~VII and O~VIII).\n\nAn acceptable fit to the data was obtained \n($\\chi^2 = 1195$ for 1176 degrees of freedom; $\\chi^2_{\\nu} = 1.02$) \nwith the following parameters for the lukewarm absorber:\nU $=$ 0.13, n$_{H}$ $=$ 20 cm$^{-3}$, and the distance of the cloud from the\nionizing source is $\\approx$ 120 pc. The predicted electron temperature\nat the ionized face of this component is $\\approx$ 18,000K and, therefore, it is thermally stable\n(cf. Krolik, McKee, \\& Tarter 1981).\nThe best-fitting value for the spectral index above 500~eV \nwas $0.58\\pm0.03$, consistent with \nour initial assumptions. We find evidence of absorption by several ions,\nwith the following column densities: C~V, 6.5 x 10$^{17}$ cm$^{-2}$; O~VI,\n2.9 x 10$^{17}$ cm$^{-2}$; O~VII, 7.8 x 10$^{17}$ cm$^{-2}$;\nO~VIII, 1.0 x 10$^{18}$ cm$^{-2}$; and, Ne~IX, 4.9 x 10$^{17}$ cm$^{-2}$. The \nO~VII and O~VIII edges translate to an effective \nhydrogen column density of highly-ionized gas of\n$\\gtrsim$2 x 10$^{21}$ cm$^{-2}$. \nThe data/model ratios from this fit are shown in Fig. 1. The slight\nunderprediction of the absorption below 300 eV in the {\\it ROSAT} band\nis easily rectified by a small ($\\sim$ 20\\%) increase in the column density of the\nlukewarm absorber.\n\nThe ionic column densities \nfor the lukewarm absorber are listed in Table~1\nand, as expected, the column densities of O~VII and\nare too small to make detectable \ncontributions to the X-ray absorption edges ($\\tau_{\\rm OVII}$ $<$ 0.01,\nas opposed to $\\approx$ 0.19 for the highly-ionized gas). Therefore, this \ncomponent does not resemble \nthe X-ray absorbers most frequently discussed to date\n(eg Reynolds 1997; George et al 1998a).\nOn the other hand, the model\npredicts substantial columns for H~I, N~V, Si~IV, C~IV, and Mg~II, which\nwould result in strong and, for the most part, saturated, UV resonance \nabsorption lines.\n\n{\\it ASCA} observed NGC~3227 again in 1995. \nGeorge et al (1998b) have shown that \nduring this epoch the observed spectrum was significantly different, \nconsistent with a thick, highly-ionized cloud moving into and \nattenuating $\\sim$85\\% of the line-of-sight to X-ray source.\nUnder our hypothesis that the lukewarm absorber is located \n$\\gtrsim$100~pc from the nucleus, hence, we do not expect \nit to have varied between these two epochs. \nWe have therefore checked and found that indeed the 1995 {\\it ASCA} \ndataset are consistent with \nthe soft X-ray attenuation from our lukewarm absorber. \n(Although the lack of simultaneous {\\it ROSAT} PSPC data \nduring 1995 prevents a stringent test.)\n\n\n\\section{Discussion}\n\nWe have shown that the X-ray spectrum of NGC~3227 is \nconsistent with attenuation by the sum of a highly-ionized absorber \nand a lukewarm absorber.\nWe suggest that these are physically different components of the \ncircumnuclear material surrounding NGC~3227. \nThe characteristics of the highly-ionized absorber\nare similar to those previously suggested for NGC 3227\n(George et al. 1998b); \nthis is in the range of \nand generally similar to those in other Seyfert 1s (Reynolds\n1997; George et al. 1998a). \nSuch absorbers have been observed to vary on timescales \n$\\lesssim$3~yr (and much faster in some cases), and are probably \ndue to gas well within the NLR.\n\nThe main result of this paper is that the second component, \nour ``lukewarm absorber'', has the appropriate physical conditions \nto simultaneously explain the absorption seen \nbelow 0.5 keV in the X-ray band (previously modeled as \ncompletely neutral gas) {\\it and} the \nreddening seen in the optical/UV.\nAgreement with the soft X-ray data is the result of \nthe lukewarm gas containing significant opacity due to\nHe~II. \nAgreement with the reddening of the narrow emission lines \nplaces the component outside the NLR.\n\n\nAlthough the lukewarm absorber has the appropriate physical conditions and \nradial distance to redden the NLR, it must also have a sufficiently\nhigh covering fraction to be detected.\nFor example, Reynolds (1997) found that 4/20 of radio-quiet active galaxies show both\nintrinsic X-ray absorption and reddening. Thus,\nthe global covering factor of the dusty ionized absorber must be\n20\\%, within the solid angle that we see these objects (cf., Antonucci\n1993). Kraemer et al. (1999) have shown that the covering factor \nfor optically thin gas in NGC 4151, similar to our lukewarm model, can be quite\nlarge ($\\sim$ 30\\%). In addition, Crenshaw et al. (1999) find\nthat $\\sim$ 60\\% of Seyfert 1 galaxies have UV absorbers with a \nglobal covering factor $\\geq$ 50\\%, and an ionization parameter\nsimilar to the lukewarm absorber, but with lower columns on average\n(cf. Crenshaw \\& Kraemer 1999). Therefore, it is entirely plausible that there would be \noptically thin NLR gas along our line-of-sight to the nucleus in a fraction\nof Seyfert 1s. \n\nThe lukewarm model predicts a column of Mg~II of 3.3 x 10$^{14}$ cm$^{-2}$,\nwhich would produce strong Mg~II $\\lambda$2800 absorption.\nIt is interesting that NGC 3227 is one of the few Seyfert 1s to show\nevidence of Mg~II $\\lambda$2800 in absorption (Ulrich 1988). While\nKriss (1998) has shown that Mg~II absorption can arise in clouds \ncharacterized by small\ncolumn density and low ionization parameter (N$_{H}$ $\\sim$ 10$^{19.5}$ \ncm$^{-2}$, U $\\sim$ 10$^{-2.5}$), our results predict that it may also\narise in a large column of highly ionized NLR gas, even if a substantial\nfraction of Mg is depleted onto dust grains. \n\nThe lukewarm model predicts average grain temperatures of 30K -- 60K,\nfor grains with radii from 0.25 $\\mu$m -- 0.005 $\\mu$m, respectively. The\nreradiated IR continuum, which is produced primarily by the silicate\ngrains (cf. Mezger, Mathis, \\& Panagia 1982), peaks near 60 $\\mu$m. \nAssuming a covering factor of unity, this component only accounts for\n$\\sim$ 1\\% of the observed IR flux from NGC 3227, (which is $\\approx$ 7.98 Jy\nat 60 $\\mu$m; {\\it The IRAS Point Source Catalog} [1985]). It is likely that\nmost of the thermal IR emission in NGC 3227 arises in the dense\n(n$_{H}$ $\\geq$ 10$^{3}$ cm$^{-3}$) NLR gas in which the narrow emission\nlines are formed, as is the case for the Seyfert 2 galaxy, Mrk 3\n(Kraemer \\& Harrington 1986).\n\n\\section{Summary}\n\n\n\n Using the combined 1993 {\\it ROSAT}/{\\it ASCA} dataset for NGC 3227, \n and photoionization model predictions, we have demonstrated that the observed\n reddening may occur in dusty, photoionized gas which is in a much lower\n ionization state than X-ray absorbers detected\n (by their O~VII and O~VIII edges)\n in Seyfert 1 galaxies (cf. Reynolds 1997; George et al. 1998a) and the\n dusty warm absorbers that have been proposed (cf. Komossa \\& Fink 1997a). This \n component (the lukewarm absorber) is $\\sim$ 120 pc from the\n central ionizing source and its physical conditions are\n similar to those in optically thin gas present in the NLR of the Seyfert 1 \n galaxy NGC 4151. If this model is correct, we predict that strong UV \nresonance absorption lines with high column densities\n from the lukewarm absorber will be observed in NGC 3227.\n\n We have confirmed earlier results regarding the presence of an X-ray absorber\n within NGC 3227 with O~VII and O~VIII optical depths similar to those\n determined by Reynolds (1997). This component lies closer to the\n central source than the lukewarm absorber, but is essentially transparent\n to EUV and soft X-ray radiation and, hence, does not effectively screen\n the lukewarm gas. We find no requirement\n for neutral gas in addition\n to the Galactic column.\n\n These results illustrate that a moderately large ($\\sim$ 10$^{21}$ cm$^{-2}$)\n column of ionized gas can produce significant soft X-ray absorption if\n much of the helium is in the singly ionized state. \n Since\nclouds with large He~II columns may be a common feature of \nthe NLR of Seyfert galaxies, such a component should be \nincluded in modeling the X-ray absorption.\nIf such a component\n is present along our line-of-sight in an active galaxy, it is\n likely that the intrinsic neutral column has been overestimated. \n\n\\acknowledgments\n\n S.B.K. and D.M.C. acknowledge support from NASA grant NAG5-4103. 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This is attenuated by a highly-ionized absorber\n(giving rise to the O VII \\& O VIII edges), and a dusty \nlukewarm absorber (giving rise to the H I \\& He II edges, as well as\nadditional opacity throughout the spectrum below $\\sim$1~keV). \nFinally the spectrum is attenuated by Galactic absorption leading to the \nobserved spectrum (bold line).\n{\\it Lower panel}: The data/model ratios for the {\\it ROSAT}\\ PSPC data\n(open circles) and {\\it ASCA}\\ SIS data (filled triangles). \nThe SIS data are weighted means of the 2 instruments.\nBoth the PSPC and SIS datasets have been rebinned in energy-space \nfor clarity.\nThe 5--7~keV band was excluded from the analysis due to the \nintense Fe K-shell emission (open triangles).}\n\\label{fig1} \n\n%\\figcaption[bbb_low.eps]{\n%}\\label{fig2} \n\n%\\figcaption[sed1.eps]{\n%}\\label{fig3} \n\n%\\figcaption[sed2.eps]{\n%}\\label{fig4} \n\n%\\figcaption[fig5.eps]{\n%}\\label{fig5} \n\n\t\t\t\t \t\t\t\t \n\\clearpage\n\\plotfiddle{fig1a.ps}{11cm}{270}{70}{70}{-280}{380}\n\n%\\clearpage\n%\\plotone{fig2.eps}\n\n%\\clearpage\n%\\plotone{fig3.eps}\n\n%\\clearpage\n%\\plotone{fig4.eps}\n\n%\\clearpage\n%\\plotone{fig5.eps}\n\n%\\clearpage\n%\\plotone{fig4.eps}\n\n%\\clearpage\n%\\plotone{fig5.eps}\n\\end{document}\n\n\n\n\n\n\n\n\n"
},
{
"name": "table.tex",
"string": "\\documentstyle[apjpt4]{article}\n\\begin{document}\n\\ptlandscape\n\\begin{deluxetable}{lcccccccccc}\n\\tablenum{1}\n\\tablecolumns{11}\n\\tablecaption{Lukewarm Model: Ionic Column Densities$^{a}$ (in units of \ncm$^{-2}$)}\n\\tablewidth{0pt}\n\\tablehead{\n\\colhead{Element} & \\colhead{I} &\n\\colhead{II} & \n\\colhead{III} &\n\\colhead{IV} &\n\\colhead{V} &\n\\colhead{VI} &\n\\colhead{VII} &\n\\colhead{VIII} &\n\\colhead{IX} &\n\\colhead{X} \n}\n\\startdata\nH & 2.8 x 10$^{18}$ & 2.0 x 10$^{21}$ & & & & & & & & \\\\\nHe & 6.9 x 10$^{16}$ & 8.4 x 10$^{19}$ & 1.2 x 10$^{20}$ & & & & & & & \\\\\nC & -- & 4.8 x 10$^{15}$ & 1.1 x 10$^{17}$ & 1.7 x 10$^{17}$ & 2.3 x 10$^{17}$ \n& 1.8 x 10$^{16}$ & 2.1 x 10$^{14}$ & & & \\\\\nN & -- & 1.6 x 10$^{15}$ & 5.9 x 10$^{16}$ & 9.4 x 10$^{16}$ & 4.5 x 10$^{16}$ \n& 3.9 x 10$^{16}$ & 9.1 x 10$^{14}$ & -- & & \\\\\nO & 6.0 x 10$^{13}$ & 7.9 x 10$^{15}$ & 5.1 x 10$^{17}$ & 3.1 x 10$^{17}$ \n& 1.9 x 10$^{17}$ & 1.1 x 10$^{17}$ & 2.9 x 10$^{16}$ & 3.1 x 10$^{14}$ & -- & \\\\\nNe & -- & 4.8 x 10$^{14}$ & 8.6 x 10$^{16}$ & 3.2 x 10$^{16}$ & 7.3 x 10$^{16}$\n& 2.8 x 10$^{16}$ & 9.5 x 10$^{14}$ & 5.7 x 10$^{14}$ & -- & -- \\\\\nSi & -- & 1.2 x 10$^{15}$ & 1.6 x 10$^{15}$ & 2.9 x 10$^{15}$ & 5.8 x 10$^{15}$\n& 1.0 x 10$^{16}$ & 8.0 x 10$^{15}$ & 1.8 x 10$^{15}$ & 1.8 x 10$^{14}$ & -- \\\\\nMg & -- & 3.3 x 10$^{14}$ & 9.5 x 10$^{15}$ & 1.9 x 10$^{15}$ & 4.5 x 10$^{15}$\n& 9.6 x 10$^{15}$ & 6.7 x 10$^{15}$ & 1.3 x 10$^{15}$ & 9.4 x 10$^{13}$ & -- \\\\\n\\enddata\n\\tablenotetext{a}{Columns $<$ 10$^{13}$ cm$^{-2}$ are not listed.}\n\\end{deluxetable}\n\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002207
|
Time Resolved GRB Spectroscopy\footnote{Paper presented at the 5th Huntsville Symposium, Huntsville (Alabama), 19 - 22 October 1999.}
|
[
{
"author": "Marco Tavani$^*$"
},
{
"author": "David Band$^{\\dagger}$"
},
{
"author": "Giancarlo Ghirlanda$^*$"
}
] |
We present the main results of a study of time-resolved spectra of 43 intense GRBs detected by BATSE. We considered the 4-parameter Band model and the Optically Thin Synchrotron Shock model (OTSSM). We find that the large majority of time-resolved spectra of GRBs are in remarkable agreement with the OTSSM. However, about 15 \% of {initial GRB pulses} show an apparent low-energy photon suppression. This phenomenon indicates that complex radiative conditions modifying optically thin emission may occur during the initial phases of some GRBs.
|
[
{
"name": "GP-20.tex",
"string": "\\documentstyle[epsfig,longtable]{aipproc}\n\n\\begin{document}\n\\title{Time Resolved GRB Spectroscopy\\footnote{Paper presented at the 5th \nHuntsville Symposium, Huntsville (Alabama), 19 - 22 October 1999.}} \n\\author{Marco Tavani$^*$,\n David Band$^{\\dagger}$,\n Giancarlo Ghirlanda$^*$ }\n% Marco Feroci$^{\\ddagger}$}\n\\address{\n$^*$Istituto Fisica Cosmica -- CNR, Milan (Italy)\\\\\n$^{\\dagger}$X-2, Los Alamos National Laboratory, Los Alamos, NM 87545}\n\n\\maketitle\n\n\n\\begin{abstract}\nWe present the main results of a study of\ntime-resolved spectra of 43 intense GRBs detected by BATSE. \nWe considered the 4-parameter Band model and the \nOptically Thin Synchrotron Shock model (OTSSM). \nWe find that the large majority of time-resolved spectra of GRBs\nare in remarkable agreement with the OTSSM. \nHowever, about 15 \\% of {\\it initial GRB pulses} \nshow an apparent low-energy photon suppression. \nThis phenomenon indicates that complex radiative\n conditions modifying optically thin emission \n may occur during the initial phases of some GRBs.\n\n\\end{abstract}\n\n\\section*{Introduction}\n\nWe study a sample of 43 GRBs selected for the high-quality \nof their time-resolved spectra obtained\nwith the BATSE Spectroscopy Detectors \n(sensitive in the energy range $25 - 1800$~keV).\nThe time over which each spectrum\nwas accumulated was varied so that the signal-to-noise ratio was greater\nthan 15 (in the hard X-ray energy band). \nThese data provide excellent temporal resolution: in many cases\nwe obtain more than 10 spectra per burst with accumulation times as short\nas 256 ms.\n\n\n\\section*{Spectral Models}\n\nWe fitted each GRB time-resolved spectrum \n with two models: (1) the Band model [1], and \n(2) the Optically Thin Synchrotron Shock Model (OTSSM) \n\\cite{A:mtav:3,A:mtav:4}.\nThe (purely phenomenological) \n4-parameter Band model \\cite{A:mtav:1} \nconsists of two power-law components \n(of spectral indexes $\\alpha$ and $\\beta$) \njoined smoothly by an exponential roll-over near a break \nenergy $E_{0}$.\n\n\n\\begin{eqnarray}\nN(E) & = & A {\\left( \\frac{E}{{\\rm 100 \\, keV}} \n\\right)^\\alpha} \\exp \\left( - \\frac{E}{E_{0}} \\right) \n\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\n\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\; \\; \\; \\; {\\rm for} \\;\\;\n E \\leq \\left( \\alpha - \\beta \\right) E_{0} \\\\\n% \\nonumber \\\\\nN(E) & = & \\left[A {\\left( \\frac{ \\left( \\alpha - \\beta \\right) \nE_{0}}{{\\rm 100 \\, keV}} \\right)^{\\alpha - \\beta}} \n\\exp \\left( \\beta - \\alpha \\right)\\right] \\left(\\frac{E}{{\\rm 100 \\, keV}} \n\\right)^\\beta \n \\; \\; \\; {\\rm for} \\;\\;\n E \\geq \\left( \\alpha - \\beta \\right) E_{0} \n\\end{eqnarray}\n\n\nWe used the (three-parameter) OTSSM of Refs.\n\\cite{A:mtav:3,A:mtav:4}. \nWe performed an independent spectral fitting for the Band \nand OTSSM models for each of the time-resolved spectra of all \nGRBs of our sample.\nFor each GRB we obtain 4 (3) best fit parameters\nas a function of time\n %(actually it is the integration time of every time-resolved spectrum) \nrepresenting the complete spectral evolution.\n \n\n\n\\section*{Results}\n\nWe find GRB spectral evolutions of two types:\n(1) a ``tracking behaviour\", with spectral parameters in approximate\none-to-one correspondence with the changing energy flux,\nand (2) a ``hard-to-soft evolution\", with spectral parameters evolving \nindependently of the energy flux (see, e.g., ref. \\cite{A:mtav:2}).\n \nFig.\\ref{GP-20-fig01} shows the distribution for \\textit{all} \ncollected time-resolved spectra of the \n%3-$\\sigma$ values of the \nlow-energy spectral index $\\alpha$. A \nfew bursts show values $\\alpha \\ge$ --2/3 typically during the \ninitial-rising part of their most intense pulses.\nThe high energy spectral index $\\beta$ is less constrained, \nand in some cases varies substantially over consecutive spectra within \nthe same burst. The $\\beta$ distribution (Fig.\\ref{GP-20-fig02} -- left\npanel) \nis peaked near --2 for the Band model representation, and is\nbroader for the OTSSM fits.\nBreak energies $E_{0}$ are typically well below 500 keV. \nInterestingly, we find that the OTSSM provides a very good representation\nof time-resolved spectral data. \nFig.\\ref{GP-20-fig02} (right panel) show the cumulative distribution\n of the reduced $\\chi^2$ for the Band and OTSSM models.\n\n\\section*{Discussion}\n\nWe studied 43 GRBs from the BATSE spectral archive \nselected by their large signal-to-noise ratios. \nWe collected information for a total of 1046 spectra. \n\nOur results indicate that the OTSSM is quite successful \nin describing the majority of GRB spectra.\nFig.\\ref{GP-20-fig03} shows the spectral evolution of the remarkable\nGRB~990123 demonstrating the validity of the OTSSM for\n very intense bursts. \nHowever, violations of the simple OTSSM are apparent in about \n$15\\%$ (at $3\\sigma$ level) of our time resolved spectra. \nThese violations (typically with a low-energy index $\\alpha > -2/3$) \nalways occur at the beginning of major GRB pulses (as in\nFig.\\ref{GP-20-fig04}). \n\nThe OTSSM was derived \\cite{A:mtav:3} for idealized plasma \nand hydrodynamic conditions that are most likely\nvalid far from the central source. \nSeveral plasma and dynamic conditions (probably \ninvolving emission sites close to a central object) may produce \nthe apparent suppression of soft photons at the beginning of\nsome GRB pulses.\n\n\n\\begin{references}\n\\bibitem{A:mtav:1} Band, D., Matteson, J., Ford, L., \\textit{et. al}; \\textit{ApJ} {\\bf413}, 281-292 (1993).\n\\bibitem{A:mtav:2} Ford, L.A., et al.; ApJ {\\bf 439}, 307 (1995).\n\\bibitem{A:mtav:3} Tavani, M.; \\textit{ApJ} {\\bf466}, 768-778 (1996).\n\\bibitem{A:mtav:4} Tavani, M., Ghirlanda G., Band D.; in preparation\n(2000).\n\\end{references}\n\n\\begin{figure}[b!] % fig 1\n\\centerline{\\epsfig{file=GP-20-fig01.eps,height=9cm,width=12cm}}\n%\\vspace*{9cm}\n%\\vspace{0.01pt}\n\\caption{Low-energy\n($\\alpha$) spectral index distribution from all the time-resolved spectra}\n\\label{GP-20-fig01}\n\\end{figure}\n\n\\begin{figure}[b!] % fig 2\n\\centerline{\\epsfig{file=GP-20-fig02.eps,height=7cm,width=14cm}}\n%\\vspace*{7cm}\n%\\vspace{1pt}\n\\caption{\\textit{Left panel:} High energy spectral index \n$\\beta$ distributions for the Band model (\\textit{solid line})\n and the OTSSM (\\textit{dotted line}). \n\\textit{Right panel:} Reduced $\\chi^2$ distributions.}\n\\label{GP-20-fig02}\n\\end{figure}\n\n\n\\begin{figure}[b!] % fig 4\n\\centerline{\\epsfig{file=GP-20-fig03.eps,height=18cm, width=14cm}}\n%\\vspace*{18cm}\n%\\vspace{2pt}\n\\caption{GRB~990123 spectral evolution of the 4-parameter \nBand model (\\textit{left column}) and the 3-parameter\n OTSSM (\\textit{right column}). The $\\alpha$ parameter is \nfixed in the OTSSM.}\n\\label{GP-20-fig03}\n\\end{figure}\n\n\n\n\\begin{figure}[b!] % fig 3\n\\centerline{\\epsfig{file=GP-20-fig04.eps,height=18cm, width=14cm}}\n%\\vspace*{18cm}\n%\\vspace{2pt}\n\\caption{GRB~910814 spectral evolution \nof the 4-parameter Band model (\\textit{left column}) and the 3-parameter\n OTSSM (\\textit{right column}). The $\\alpha$ parameter is fixed in the\nOTSSM.}\n\\label{GP-20-fig04}\n\\end{figure}\n\n\n \n\\end{document}\n\n \n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002207.extracted_bib",
"string": "\\bibitem{A:mtav:1} Band, D., Matteson, J., Ford, L., \\textit{et. al}; \\textit{ApJ} {\\bf413}, 281-292 (1993).\n\n\\bibitem{A:mtav:2} Ford, L.A., et al.; ApJ {\\bf 439}, 307 (1995).\n\n\\bibitem{A:mtav:3} Tavani, M.; \\textit{ApJ} {\\bf466}, 768-778 (1996).\n\n\\bibitem{A:mtav:4} Tavani, M., Ghirlanda G., Band D.; in preparation\n(2000).\n"
}
] |
astro-ph0002208
|
The superbubble model for LiBeB production and Galactic evolution
|
[
{
"author": "Etienne Parizot and Luke Drury"
}
] |
We show that the available constraints relating to $^{6}$LiBeB Galactic evolution can be accounted for by the so-called superbubble model, according to which particles are efficiently accelerated inside superbubbles out of a mixture of supernova ejecta and ambient interstellar medium. The corresponding energy spectrum is required to be flat at low energy (in $E^{-1}$ below 500~MeV/n, say), as expected from Bykov's acceleration mechanism. The only free parameter is also found to have the value expected from standard SB dynamical evolution models. Our model predicts a slope 1 (primary) and a slope 2 (secondary) behaviour at respectively low and high metallicity, with all intermediate slopes achieved in the transition region, between $10^{-2}$ and $10^{-1}Z_{\odot}$.
|
[
{
"name": "parizot.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{E. Parizot \\& L. Drury}{The superbubble model for LiBeB\nproduction and Galactic evolution}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{The superbubble model for LiBeB production and Galactic\nevolution}\n\\author{Etienne Parizot and Luke Drury}\n\\affil{Dublin Institute for Advanced Studies, 5 Merrion Square, Dublin\n2, Ireland}\n\n\\begin{abstract}\nWe show that the available constraints relating to $^{6}$LiBeB\nGalactic evolution can be accounted for by the so-called superbubble\nmodel, according to which particles are efficiently accelerated inside\nsuperbubbles out of a mixture of supernova ejecta and ambient\ninterstellar medium. The corresponding energy spectrum is required to\nbe flat at low energy (in $E^{-1}$ below 500~MeV/n, say), as expected\nfrom Bykov's acceleration mechanism. The only free parameter is also\nfound to have the value expected from standard SB dynamical evolution\nmodels. Our model predicts a slope 1 (primary) and a slope 2\n(secondary) behaviour at respectively low and high metallicity, with\nall intermediate slopes achieved in the transition region, between\n$10^{-2}$ and $10^{-1}Z_{\\odot}$.\n\\end{abstract}\n\n\\section{Introduction}\n\nGalactic nucleosynthesis and chemical evolution are about how a given\nelement is produced in the universe and how its abundance evolved from\nthe primordial universe on. In the case of the light elements, it is\nwidely agreed that the nucleosynthesis occurs through spallation\nreactions induced by energetic particles (EPs) interacting with the\ninterstellar medium (ISM). In these reactions, an heavier nucleus\n(most significantly C, N or O) is `broken into pieces' and transmuted\ninto one of the lighter $^{6}$Li, $^{7}$Li, $^{9}$Be, $^{10}$B or\n$^{11}$B nuclei. Except for $^{7}$Li, this spallative nucleosynthesis\nis thought to be the main (if not the only) light element production\nmechanism. The case of $^{11}$B is slightly more complicated, as\nneutrino-induced spallation in supernovae (the so-called\n$\\nu$-process) is sometimes invoked to increase the B/Be and\n$^{11}\\mathrm{B}/^{10}\\mathrm{B}$ ratios which one would expect should\nthe light elements be produced by nucleo-spallation alone.\n\nConcerning the Galactic evolution of light element abundances, Fields\net al. (2000) have recently re-analyzed the available data as a\nfunction of O/H, discussing the uncertainties associated with the\nmethods used to derive the O abundance, the stellar parameters and the\nincompleteness of the samples. According to their results, Be and B\nevolution can be described in terms of two distinct production\nprocesses: i) a primary process dominating at low metallicity and\nleading to a linear increase of the Be and B abundances with respect\nto O -- `slope 1' -- followed by ii) a secondary process compatible\nwith the standard expectations of the Galactic cosmic ray\nnucleosynthesis scenario (GCRN) -- `slope 2'. This behaviour is\ncharacterized by a transition metallicity,\n$Z_{\\mathrm{t}}\\equiv(\\mathrm{O/H})_{\\mathrm{t}}$, below which the\nBe/O and B/O ratios are constant and above which they are proportional\nto O/H. Although the value of $Z_{\\mathrm{t}}$ is rather uncertain\nbecause very few data points have yet been reported at $Z <\nZ_{\\mathrm{t}}$, energetics arguments show that a primary process\n\\emph{is} indeed required below, say, $10^{-2}Z_{\\odot}$ (Parizot \\&\nDrury 1999a,b,2000b, Ramaty et al. 2000), and therefore the very\nexistence of a transition metallicity separating a primary from a\nsecondary evolution scheme seems reasonably well established. In\nspite of the current large uncertainties on the exact value of\n$Z_{\\mathrm{t}}$, Fields et al. find a range of possible values\nbetween $10^{-1.9}$ and $10^{-1.4}(\\mathrm{O/H})_{\\odot}$ (see also\nOlive, this conference).\n\nThis two-slope picture seems to reconcile the two competing theories\nfor light element nucleosynthesis, namely GCRN which predicts a\nsecondary behaviour for Be and B evolution (e.g. Vangioni-Flam et al. \n1990, Fields \\& Olive 1999), and the superbubble model which predicts\na primary behaviour at low metallicity (Parizot \\& Drury 1999b,2000b,\nRamaty et al. 2000). However, we show here that when applied to the\nwhole lifetime of the Galaxy (not only to the early Galaxy), the\nsuperbubble model \\emph{alone} actually predicts the entire two-slope\nbehaviour inferred from observations, and accounts for all the\nqualitative and quantitative constraints currently available. \nImplications for particle acceleration inside a superbubble (SB) are\nalso analyzed.\n\n\n\\section{Description of the SB model}\n\nThe superbubble model is based on the observation that most massive\nstars are born in associations, and evolve quickly enough to explode\nas SNe in the vicinity of their parent molecular cloud. The dynamical\neffect of repeated SN explosions in a small region of the Galaxy is to\nblow large bubbles -- superbubbles -- of hot, rarefied material,\nsurrounded by shells of swept-up and compressed ISM. The interior of\nsuperbubbles consists of the ejecta and stellar winds of evolved\nmassive stars \\emph{plus} a given amount of ambient ISM evaporated off\nthe shell and dense clumps passing through the bubble. The exact\nfraction of the ejecta material inside the SB is not well known, and\ncan be expected to vary with time and from one SB to another. \nHowever, this fraction, which we note $x$, is all we need to know in\norder to fully determine the mean composition of the matter inside\nSBs. Noting $\\alpha_{\\mathrm{ej}}(\\mathrm{X})$ and\n$\\alpha_{\\mathrm{ISM}}(\\mathrm{X})$ the abundances of element X among\nthe SN ejecta and in the ISM, respectively, we can indeed write the\nabundance of X inside the SB as:\n\\begin{equation}\n\t\\alpha_{\\mathrm{SB}}(\\mathrm{X}) =\n\tx\\alpha_{\\mathrm{ej}}(\\mathrm{X})\n\t+ (1 - x)\\alpha_{\\mathrm{ISM}}(\\mathrm{X}).\n\t\\label{SBAbundances}\n\\end{equation}\n\nThe second assumption of the SB model is that the material inside\nsuperbubbles is efficiently accelerated by a combination of shocks\nproduced by SN explosions and supersonic stellar winds, secondary\nshocks reflected by other shocks or clumps of denser material, and a\nstrong magnetic turbulence created by the global activity of all the\nmassive stars. Two different SB models have been proposed so far,\nassuming different EP compositions and energy spectra. In our model\n(Parizot \\& Drury 1999b,2000b), we follow Bykov \\& Fleishman (1992) and\nBykov (1995,1999) and argue that the SB acceleration process produces\na rather flat spectrum at low energy, namely in $E^{-1}$, as expected\nfrom multiple shock acceleration theory (Markowith \\& Kirk 1999), up\nto a few hundreds of MeV/n, say. Above this value, the spectrum of\nthe superbubble EPs (SBEPs) is either cut off through a steep\npower-law or turned into the standard cosmic ray source spectrum\n(CRS), in $E^{-2}$. The exact behaviour of this so-called `SB\nspectrum' at high energy is important in itself and should be derived\nfrom a detailed calculation of the particle acceleration, but we do no\nconsider it here, as it is not relevant to our problem (most of the\nLiBeB production arises from the most numerous low-energy particles\nanyway). The other SB model proposed so far (Ramaty \\& Lingenfelter\n1999, Ramaty et al. 2000) assumes that the SBEPs \\emph{are} actually\nthe cosmic rays and thus their energy spectrum is the standard CRS\nspectrum ($Q(p)\\propto p^{-2}$).\n\nTo summarize, the essence of the SB model is that repeated SN\nexplosions occurring in OB associations lead to the acceleration of EPs\nhaving either the CRS spectrum or the SB spectrum, and a composition\ngiven by Eq.~(1), where the only free parameter is the proportion of\nthe ejecta inside the SB: $x$. In principle, $x$ can be derived from\nthe study of SB evolution dynamics, coupled with a gas evaporation\nmodel. But we shall first study LiBeB evolution for itself with no\nexternal prejudice about the value of $x$, and therefore consider it\nas a free parameter which we vary from 0 (i.e. SBEPs have the ambient\nISM composition) to 1 (i.e. SBEPs are made of pure SN ejecta). Later,\nwe compare the value derived from the LiBeB constraints with the value\nexpected from standard SB dynamical models.\n\n\n\\section{Be and B Galactic evolution}\n\n\\subsection{Qualitative features}\n\nHaving parameterized our problem as above, we can easily calculate the\nBe/O production ratio in the Galaxy as a function of\n$Z_{\\mathrm{ISM}}\\equiv (\\mathrm{O/H})_{\\mathrm{ISM}}$. We consider\nSBs blown by 100 SNe exploding continuously over a lifetime of 30~Myr. \nWe then integrate the Be production rates induced by the SBEPs and\ndivide the result by the total O yield (added up assuming a Salpeter\nIMF and SN yields from Woosley \\& Weaver 1995). The result is plotted\nin Fig.~1 for various values of $x$ and the two investigated spectra. \nThe main difference between the latter is the Be production\nefficiency, i.e. the number of Be produced per erg of SBEP. Apart from\nthe SB spectrum being more efficient, both figures show distinctively\nthe sought-for two-slope behaviour, with a transition metallicity\n$Z_{\\mathrm{t}}$ depending on the actual value of $x$. This behaviour\nderives directly from Eq.~(1). Replacing X by O there, we see that\nthe abundance of O among the SBEPs is essentially\n$x\\alpha_{\\mathrm{ej}}(\\mathrm{O})$ at low metallicity, and\n$(1-x)\\alpha_{\\mathrm{ISM}}(\\mathrm{O})$ above a transition\nmetallicity $Z_{\\mathrm{t}} \\sim \\frac{x}{1-x}Z_{\\mathrm{ej}}$ (where\n$Z_{\\mathrm{ej}}\\sim 10 Z_{\\odot}$). Therefore, remembering that O is\nthe main progenitor of Be, we find that the SB model predicts a\nprimary behaviour below $Z_{\\mathrm{t}}$ (production efficiency\nindependent of $Z_{\\mathrm{ISM}}$), and a secondary behaviour above\n$Z_{\\mathrm{t}}$, since the SB model is then essentially identical to\nthe GCRN model (except maybe for the assumed energy spectrum).\n\nIncidentally, it is interesting to note that the SB model can be\nconsidered as a correction of the GCRN scenario, taking into account\nthe chemical inhomogeneity of the early Galaxy. Indeed, since\nparticle acceleration occurs precisely in those places where metals\nare released (i.e. superbubbles), the SBEP composition is considerably\nricher in O than the average ISM, as long as the SN ejecta dominate\nthe O content of the SBs. Afterwards, it makes little difference, as\nfar as composition is concerned, whether the EPs producing LiBeB are\naccelerated inside SBs or in the regular ISM.\n\n%%%%%%%%%%%%%%\n\\begin{figure}\n\\plottwo{parizotfig1a.eps}{parizotfig1b.eps}\n\\caption{Be/O yield ratios obtained with the CRS spectrum (left) and\nthe SB spectrum (right), as a function of the ambient metallicity, for\nvarious values of the mixing parameter, $x$. The Be yield is\ncalculated for a SBEP total energy of $10^{50}$ erg per SN.}\n\\end{figure}\n%%%%%%%%%%%%%%\n\nFinally, we see from Fig.~1 that the predicted slope 1 and slope 2\ncorrelations between Be and O are limit behaviours for very low and\nvery high metallicity respectively. Depending on the value of $x$,\nany intermediate value for the Be-O slope is reached over a given\nrange of stellar metallicity. This is in contrast with what would\narise if the two-slope behaviour were to be explained in terms of two\ndifferent mechanisms (e.g. the SB model at low $Z$ and GCRN at high\n$Z$). In that case, indeed, one would have a sharp change of slope at\nthe precise metallicity where the secondary process becomes dominant,\nwith no intermediate values. Of course, expected physical\nfluctuations of the parameters would weaken this effect, and current\nobservational error bars prevent us from distinguishing conclusively\nbetween the two pictures. But we argue that the observed `slope 1.45'\nbehaviour reported by Boesgaard \\& Ryan (this conference) can be\nexplained (in principle) only if there is a continuous\n\\emph{transition} from slope 1 to slope 2 within a \\emph{unique} model\n(as in the SB model above ), rather than two unrelated models with a\nslope 2 eventually superseding a slope 1.\n\n\n\\subsection{Quantitative features}\n\nQuantitatively, the Be/O ratio at low metallicity derived from the\nobservations is about $4\\,10^{-9}$ (Parizot \\& Drury 2000b). This can\nbe achieve either by the CRS spectrum model, provided $x \\sim 50\\%$,\nor by the SB spectrum model, provided $x \\sim 2 or 3\\%$ (see Fig.~1). \nSo far, both models are equally acceptable since we chose not to\naccept any prejudice about the value of $x$ from outside the\nrestricted field of LiBeB evolution. But when considering the\ntransition metallicity associated with the two possible models, we see\nthat the CRS spectrum implies $Z_{\\mathrm{t}}\\ga 10^{-1}Z_{\\odot}$,\nwell outside the range derived by Fields et al. On the other hand,\nthe value of $Z_{\\mathrm{t}}$ predicted by SB spectrum model falls\nexactly in the required range. As a conclusion, the SB model is fully\nconsistent with the observations provided that i) the SBEP spectrum is\nflattened at low energy (in $E^{-1}$), and ii) the SN ejecta amount to\na few percent of all the matter present inside SBs.\n\nNow let us extend the scope of our study. Quite remarkably, the first\ncondition above is exactly what is expected from the SB acceleration\nmodel developed by Bykov et al. As for the second condition, it is in\nperfect agreement with the dynamical model for SB evolution worked out\nby Mac Low \\& Mc Cray (1988). In other words, had we looked\nbeforehand for a theoretically preferred value of $x$, we would have\nchosen just the particular value which turns out to account for the\nvarious constraints of Be Galactic evolution. Therefore, our results\nactually bring support not only to the SB model as the natural\nframework for Be and B evolution studies, but also to the SB\nacceleration model and standard SB dynamics.\n\n%%%%%%%%%%%%%%\n\\begin{figure}\n\\plottwo{parizotfig2a.eps}{parizotfig2b.eps}\n\\caption{Li/Be (left) and $^{6}$Li/$^{9}$Be (right) production ratios\nobtained with the SB spectrum model, as a function of the ambient\nmetallicity, for various values of the mixing parameter, $x$.}\n\\end{figure}\n%%%%%%%%%%%%%%\n\nConcerning B, unfortunately, only qualitative constraints can be\nchecked against the SB model (successfully in this instance), since\neither a significant $\\nu$-process or a LECR component is required\nanyway to account for the observed B/Be and\n$^{11}\\mathrm{B}/^{10}\\mathrm{B}$ ratios. However, Li does provide\nadditional quantitative constraints. First, in order not to break the\nSpite plateau, the Li/Be production ratio must be lower than $\\sim\n100$. This is shown to be satisfied for any value of $x$ greater than\nabout 1\\% in Fig.~(2a). Second, the measurement of the $^{6}$Li\nabundance in two halo stars of metallicity $Z \\simeq\n10^{-2.3}Z_{\\odot}$ indicates that the $^{6}$Li/$^{9}$Be ratio in\nthese stars should be in the range 20--80 (see Vangioni-Flam, Cass\\'e,\n\\& Audouze 2000 and references therein), in contrast with the solar\nvalue of $\\sim 6$. This could not be explained if the proportion of\nSN ejecta inside SBs were of the order of 50\\% (CRS spectrum model). \nHowever, it is quite remarkable again that the value of a few percent\nderived from the SB spectrum model is totally consistent with the\nobserved value of the $^{6}$Li/$^{9}$Be ratio, both a low metallicity\nand at solar metallicity.\n\n\n\\section{Conclusion}\n\nThe SB model described above has been shown to be fully consistent\nwith the qualitative and quantitative constraints of LiBeB Galactic\nevolution: 1) it explains the inferred two-slope behaviour in the\nframework of one sole model; 2) it provides the correct value of Be/O\nat low metallicity; 3) it predicts the correct value of the transition\nmetallicity; 4) it does not break the Spite plateau; 5) it is\nconsistent with the $^{6}$Li/$^{9}$Be ratio at any metallicity. Most\nimportantly, these successes rely on the value of only one free\nparameter, namely the proportion of SN ejecta inside a SB. The value\nwhich we find is of the order of a few percent, i.e. exactly in the\nrange derived from standard SB dynamical evolution. Likewise, the SB\nmodel is found to be successful only if the SBEPs have the SB\nspectrum, i.e a flattened shape at low energy (in $E^{-1}$). But this\nis exactly what is predicted by the SB acceleration model of Bykov et\nal. As a conclusion, the SB model appears to account for all the\navailable constraints about LiBeB evolution by making only the most\nstandard assumptions about the involved models relating to other\nfields of astrophysics. This may be considered as lending support to\nthese models as well.\n\n% Finally, we wish to mention that the SB model has important\n% implications for Galactic chemical evolution in general. Let us\n% consider a SB formed in the very early Galaxy, when the ambient\n% metallicity were below, say, $10^{-2}Z_{\\odot}$. At the end of its\n% lifetime, the interior of such a SB amounts to about\n% $10^{5}\\,\\mathrm{M}_{\\odot}$ of material with a mean metallicity of\n% $Z_{\\mathrm{SB}} \\simeq xZ_{\\mathrm{ej}} \\sim 3\\,10^{-1}Z_{\\odot}$\n% (assuming $x\\sim 3\\%$ and $Z_{\\mathrm{ej}}\\sim 10 Z_{\\odot}$). This\n% gas is then mixes with the ambient medium and collapses into a new\n% generation of stars. Now what will be the metallicity of these new\n% stars? One should actually expect to find stars with very different\n% metallicities, ranging from $Z_{\\mathrm{ISM}}$ (uncontaminated ISM at\n% that time) to $Z_{\\mathrm{SB}}$, depending on the fraction of pure SB\n% gas which composes them. All these stars, however, will have formed\n% at the same time, and show the same elemental abundance ratios, namely\n% those of the parent SB. The resulting Be-O correlation, for instance,\n% can thus be interpreted as a \\emph{dilution line}. On the Galactic\n% scale, we then observe a superposition of dilution lines from many\n% different SBs at different ages of the Galaxy. And since each SB has\n% its own set of parameters, the different lines cannot be perfectly\n% superimposed and we should expect some scatter in the data. We argue\n% that this phenomenon is responsible for the observed scatter in the Be\n% and B data (Primas, this conference; see also Parizot \\& Drury,\n% 2000a). But presumably the same applies to any element in the\n% periodic table.\n\n\n\n\\acknowledgments This work were supported by the TMR programme of the European\nUnion under contract FMRX-CT98-0168.\n\n\\begin{references}\n\n\\reference Bykov A. M. 1995, Space Sci. Rev., 74, 397\n\n\\reference Bykov A. M. 1999, in ``LiBeB, cosmic rays and gamma-ray\nline astronomy'', ASP Conference Series, eds. R. Ramaty, E.\nVangioni-Flam, M. Casse, K. Olive\n\n\\reference Bykov A. M., \\& Fleishman G. D. 1992, MNRAS, 255, 269\n\n\\reference Fields B. D., \\& Olive K. A., 1999, ApJ, 516, 797\n\n\\reference Fields B. D., Olive K. A., Vangioni-Flam E., \\& Cass\\'e M.\n2000, submitted to ApJ (astro-ph/9911320)\n\n\\reference Mac Low M. M., \\& McCray R., 1988, ApJ, 324, 776\n\n\\reference Markowith A., \\& Kirk J. G. 1999, A\\&A, 347, 391\n\n\\reference Parizot E., \\& Drury L. 1999a, A\\&A, 346, 686\n\n\\reference Parizot E., \\& Drury L. 1999b, A\\&A, 349, 673\n\n\\reference Parizot E., \\& Drury L. 2000a, A\\&A, submitted\n\n\\reference Parizot E., \\& Drury L. 2000b, A\\&A, submitted\n\n\\reference Ramaty R., \\& Lingenfelter R. E. 1999, in ``LiBeB, cosmic\nrays and gamma-ray line astronomy'', ASP Conference Series, eds. R.\nRamaty, E. Vangioni-Flam, M. Casse, K. Olive\n\n\\reference Ramaty R., Scully S. T., Lingenfelter R. E., \\& Kozlovsky\nB. 2000, ApJ, in press (astro-ph/9909021)\n\n\\reference Vangioni-Flam, E., Cass\\'e, M., Audouze, J., \\& Oberto, Y.\n1990, ApJ 364, 586\n\n\\reference Vangioni-Flam, E., Cass\\'e, M., \\& Audouze, J. 2000,\nsubmitted to Physics Reports\n\n\\reference Woosley S. E., \\& Weaver T. A. 1995, ApJSS, 101, 181\n\n\\end{references}\n\n\n\\end{document}\n"
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astro-ph0002209
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ISO observations of the reflection nebula Ced\,201: evolution of carbonaceous dust \thanks{Based on observations at the Cal Tech submillimeter observatory (CSO) and with ISO, an ESA project with instruments funded by ESA member states (especially the PI countries: France, Germany, the Netherlands and the United Kingdom) and with the participation of ISAS and NASA.}
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[
{
"author": "D. Cesarsky\\inst{1,2}"
},
{
"author": "J. Lequeux\\inst{3}"
},
{
"author": "C. Ryter\\inst{4}"
},
{
"author": "M. G\\'erin\\inst{5}"
}
] |
We present spectrophotometric imaging mid--IR observations of the reflection nebula Ced\,201. Ced\,201 is a part of a molecular cloud illuminated by a B9.5V star moving through it at more than 12 km s$^{-1}$. The spectra of Ced\,201 give evidence for transformation of very small carbonaceous grains into the carriers of the Aromatic Infrared Bands (AIBs), due to the radiation field of the illuminating star and/or to shock waves created by its motion. These very small grains emit mainly very broad bands and a continuum. We suggest that they are present everywhere in the interstellar medium but can only be detected in the mid--IR under special circumstances such as those prevailing in this reflection nebula. The efficiency of energy conversion of stellar light into mid--infrared emission is 7.5\%~ for both the very small grains and the AIB carriers, and the fraction of interstellar carbon locked in these emitters is approximately 15\%. % \keywords {ISM: Ced\,201 - dust, extinction - Infrared: ISM: lines and bands} %
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"name": "ced201-9feb.tex",
"string": "\\documentclass{aa}\n\\usepackage{psfig}\n%\\usepackage{graphics}\n%\n\\newcommand{\\Msun}{\\mbox{M$_{\\scriptsize \\odot}$}}\n\\newcommand{\\Usun}{\\mbox{U$_{\\scriptsize \\odot}$}}\n\\newcommand{\\degrees}{$^{\\circ}$}\n\\newcommand{\\etal}{et al.}\n\\newcommand{\\HI}{\\mbox{H\\,{\\sc i}}}\n\\newcommand{\\HII}{\\mbox{H\\,{\\sc ii}}}\n\\newcommand{\\NeII}{\\mbox{Ne\\,{\\sc ii}}}\n\\newcommand{\\NeIII}{\\mbox{Ne\\,{\\sc iii}}}\n\\newcommand{\\ArII}{\\mbox{Ar\\,{\\sc ii}}}\n\\newcommand{\\ArIII}{\\mbox{Ar\\,{\\sc iii}}}\n\\newcommand{\\OIII}{\\mbox{O\\,{\\sc iii}}}\n\\newcommand{\\SII}{\\mbox{S\\,{\\sc ii}}}\n\\newcommand{\\SIII}{\\mbox{S\\,{\\sc iii}}}\n\\newcommand{\\SIV}{\\mbox{S\\,{\\sc iv}}}\n\\newcommand{\\CII}{\\mbox{C\\,{\\sc ii}}}\n\\newcommand{\\NII}{\\mbox{N\\,{\\sc ii}}}\n\\newcommand{\\mum}{\\mbox{$\\mu$m}}\n\\newcommand{\\flux}{{\\hbox{\\,erg\\,\\,s$^{-1}$\\,cm$^{-2}$\\,sr$^{-1}$}}}\n%\n\\begin{document}\n\\thesaurus{08\t% Interstellar medium\n\t(09.09.1 Ced\\,201; 09.04.1; 13.09.4)}\n\\title {ISO observations of the reflection nebula Ced\\,201:\nevolution of carbonaceous dust\n\\thanks{Based on observations at the Cal Tech submillimeter observatory (CSO)\nand with ISO, an ESA project with instruments funded by ESA\nmember states (especially the PI countries: France, Germany, the\nNetherlands and the United Kingdom) and with the participation of ISAS\nand NASA.}}\n\n\\author{D. Cesarsky\\inst{1,2}\\and\n J. Lequeux\\inst{3}\\and\n\tC. Ryter\\inst{4}\\and\n\tM. G\\'erin\\inst{5}\n}\n\\offprints{james.lequeux@obspm.fr}\n\\institute{\t\nInstitut d'Astrophysique Spatiale, Bat. 121, Universit\\'e Paris\nXI, F-91450 Orsay CEDEX, France\n\\and\nMax Plank Institut f\\\"ur extraterrestrische Physik, Postfach 1603, \nD-85740 Garching, Germany\n\\and\nDEMIRM,Observatoire de Paris, 61 Avenue de l'Observatoire, F-75014\nParis, France\n\\and\nSAp/DAPNIA/DSM, CEA-Saclay, F-91191 Gif sur Yvette CEDEX, France\n\\and\nEcole Normale Sup\\'erieure, 24 Rue Lhomond, F-75238 Paris CEDEX 05, France\n}\n%\n\\date{Received 16 November 1999; accepted 28 January 2000}\n%\n\\maketitle \n \n\\markboth{Cesarsky D., Lequeux J., Ryter C. et al.}\n {Ced\\,201 and evolution of carbonaceous dust}\n\n%\n\\begin{abstract}\nWe present spectrophotometric imaging mid--IR observations of the reflection\nnebula Ced\\,201. Ced\\,201 is a part of a molecular cloud illuminated by a B9.5V\nstar moving through it at more than 12 km s$^{-1}$. The spectra of \nCed\\,201 give evidence for transformation of very small carbonaceous \ngrains into the carriers of the Aromatic Infrared Bands (AIBs), \ndue to the radiation field of the illuminating star and/or to shock \nwaves created by its motion. These very small grains emit mainly very \nbroad bands and a continuum. We suggest that they are present\neverywhere in the interstellar medium but can only be detected in the\nmid--IR under special circumstances such as those prevailing in this\nreflection nebula. The efficiency of energy conversion of stellar light into\nmid--infrared emission is 7.5\\%~ for both the very small grains and\nthe AIB carriers, and the fraction of interstellar \ncarbon locked in these emitters is approximately 15\\%. \n%\n\\keywords\t{ISM: Ced\\,201\t\t\t-\n\t\tdust, extinction\t\t-\n\t\tInfrared: ISM: lines and bands}\n%\n\\end{abstract}\n\\section{Introduction}\nThe mid--infrared emission bands at 3.3, 6.2, 7.7, 8.6, 11.3 and 12.7\\,\\mum~\nare ubiquitous in the interstellar medium (ISM). The coincidence of these bands\nwith characteristic wavelengths of aromatic molecules and attached functional\ngroups (see e.g. Allamandola et al. \\cite{Allamandola89}) is sufficiently \nconvincing to call them Aromatic Infrared Bands (AIBs). Other, more neutral\ndesignations are Unidentified Infrared Bands (UIBs) or Infrared Emission\nFeatures (IEFs). The designation should stabilize in the future. Their\ncarriers are very small grains (or big molecules) heated transiently by the\nabsorption of a single UV (Sellgren et al. \\cite{Sellgren83}) or visible\n(Uchida et al. \\cite{Uchida98}; Pagani et al. \\cite{Pagani99}) photon. They\nare often identified with Polycyclic Aromatic Hydrocarbons (PAHs) (L\\'eger \\&\nPuget \\cite{Leger}, Allamandola et al. \\cite{Allamandola85}). Duley \\& Williams\n(\\cite{Duley88}) and Duley et al. (\\cite{Duley93}) have proposed an alternative\ninterpretation in which the carriers of the AIBs are not free particles but\n``graphitic islands'' (i.e. akin to PAHs) loosely attached to each other so\nthat the heat conductivity is small. Then their thermal behaviour is\ncomparable to that of free particles. Similar models have been also proposed\nby others. The carriers could also be \\mbox{3--D} very small particles. In this\nLetter, we will not enter into this debate and will simply call them the {\\it \nAIB carriers}.\n\nThe origin of the AIB carriers is still unclear. The idea that they are formed \nin the envelopes of carbon stars is not supported by observation and meets \nwith theoretical difficulties (e.g. Cherchneff et al. \\cite{Cherchneff}). They\nmight be formed outside carbon star envelopes from carbonaceous particles\ncondensed previously in these envelopes. Schnaiter et al. (\\cite{Schnaiter99})\nand others have proposed such an evolutionary scheme from carbon stars to \nplanetary nebulae. However the AIB carriers formed in this way might not \nsurvive the strong UV field of planetary nebulae. For example, Cox et al. \n(\\cite{Cox}) find no AIB in the Helix nebula, an old carbon--rich planetary \nnebula. Another possibility is that they are formed in the ISM from \ncarbonaceous grains or carbonaceous mantles covering silicate nuclei. Boulanger\net al. (\\cite{Boulanger}) and Gry et al. (\\cite{Gry}) have suggested that \nthe strong variations in the IRAS 12\\,\\mum/100\\,\\mum~ interstellar flux ratio\nare due to the release of transiently heated particles (emitting at 12\\,\\mum)\nby bigger particles, respectively due to UV irradiation or to shattering by\nshocks. Thanks to the Infrared Space Observatory (ISO), we know now that in the\ngeneral ISM the emission in the IRAS 12\\,\\mum~ band is dominated by AIBs.\nVariations in the ratio of AIB carriers to big grains are thus confirmed.\nLaboratory experiments shed some light on this process. Scott et al.\n(\\cite{Scott97}) have observed the release of aromatic carbon clusters\ncontaining in excess of 30 carbon atoms by solid hydrogenated amorphous carbon\n(HAC) irradiated by a strong UV laser pulse. The energy deposited by the laser\npulse per unit target area is similar to the energy of a central collision\nbetween two grains of 10 nm radius at a velocity of 10 km s$^{-1}$. This is an\nindication for a possible release of AIB carriers in interstellar shocks. \n\nISO has also shown the existence of variations of AIB spectra that may be\nrelated to a transformation of carbonaceous grains. Recently, Uchida et al.\n(\\cite{Uchida00}) have observed a broadening of the 6.2, 7.7 and 8.6\\,\\mum~\nAIBs when going from strong to weak radiation field in the reflection nebula\nvdB\\,17 = NGC\\,1333. They also notice an increase of the flux ratio\n$I$(5.50--9.75\\,\\mum)/$I$(10.25--14.0\\,\\mum) with increasing radiation field in\nseveral reflection nebulae. \n\nWe present mid--IR spectrophotometric and CO(2--1) line observations of \nanother reflection nebula, Ced\\,201, that shed light into this transformation.\nSection 2 describes briefly the observations and reductions. Sect. 3 describes\nthe results, and Sect. 4 contains a discussion and the conclusions. \n\n\\section{ISO observations and data reduction}\n\nThe observations have been made with the 32$\\times$32 element mid-infrared\ncamera (ISOCAM) on board of ISO, with the Circular Variable Filters (CVFs) (see\nCesarsky et al. \\cite{CCesarsky} for a complete description). The observations\nemployed a 6\\arcsec/pixel magnification, yielding a field of view of about\n3\\arcmin$\\times$3\\arcmin. Full scans of the two CVFs in the long-wave channel\nof the camera have been performed, covering a wavelength range from 5.15 to\n17\\,\\mum. 10 exposures of 2.1s each were added for each step of the CVF, and 20\nextra exposures were added at the beginning of each scan in order to limit the\neffect of the transient response of the detectors. The total observing time\nwas about 1 hour. The raw data were processed as described in Cesarsky\n\\etal~(\\cite{M17}) using the CIA software\\footnote{CIA is a joint development\nby the ESA Astrophysics Division and the ISOCAM Consortium led by the ISOCAM\nPI, C. Cesarsky.} (Starck et al. \\cite{Starck}). However, the new transient\ncorrection described by Coulais \\& Abergel (\\cite{Coulais}) has been applied,\nyielding considerable improvements with respect to previous methods.\n\n%\n\\section{Results}\n%Figure 1\n\\begin{figure}[t!]\n%\\picplace{8cm}\n\\vspace{-0.8cm}\n%\\hspace*{-0.5cm}\n\\psfig{file=cedtotal.ps,width=8.8cm,angle=0.0}\n%\\resizebox{\\hsize}{!}{\\includegraphics{cedtotal.ps}}\n\n\\caption{Contours of the total mid-IR emission (5--17\\mum) of Ced\\,201\nsuperimposed over the Digital Sky Survey image. Note the absence of stars in \nthe NE half of the image, due to extinction by the molecular cloud.}\n\\end{figure}\n\n\n%Figure 2\n\\begin{figure}[t!]\n%\\picplace{14cm}\n%\\vspace{-0.9cm}\n%\\hspace*{-0.5cm}\n\\psfig{file=ced201spectres.ps,width=8.8cm,angle=270.0}\n%\\rotatebox{270}{\\resizebox{\\hsize}{!}{\\includegraphics{ced201spectres.ps}}}\n%\\vspace{-0.4cm}\n\\caption{Spectra of Ced\\,201 in the CO(2--1) line, obtained with the Caltech\nSubmillimeter Telescope (HPBW 30\\arcsec) on a 30\\arcsec$\\times$30\\arcsec \ngrid. For each spectrum, abscissae give the LSR velocities from -8 to -2\nkm s$^{-1}$ and ordinates give the antenna temperatures $T_A^*$ from -1 to\n20 K. The main--beam efficiency of the telescope is 0.76. The coordinates\nare in arcsec relative to the reference \nposition $\\alpha$(J2000) = 22h 13m 24.4s, $\\delta$(J2000) = 70\\degrees~ \n15\\arcmin~ 24\\arcsec. The exciting star is 19\\arcsec~ to the south. The CO \nline emission peaks in the direction of the star.\n}\n\\end{figure}\n\nThe reflection nebula Ced\\,201 is a rather compact object at a distance of 420\npc (Casey \\cite{Casey}), on the edge of a molecular cloud. It is excited by\nthe B9.5\\,V star BD +69\\degrees1231. Witt et al. (\\cite{Witt}) notice that\nthe radial velocity of this star differs from that of the molecular cloud by\n11.7 $\\pm$ 3.0 km s$^{-1}$ so that Ced\\,201 is probably the result of an\naccidental encounter of the star with the molecular cloud, while for most other\nreflection nebulae the exciting star was born {\\it in situ}. An arc-like\nstructure located between the star and the denser parts of the cloud to the\nnorth and the north-east at about 18\\arcsec~ from the star might represent a\nshock due to the supersonic motion of the star. It is not very clearly visible\non Fig. 1 but is well visible on the red POSS1 image delivered by ALADIN \n(http://aladin.u-strasbg.fr). \n\nOur CVF observation shows a small source surrounded by a faint extended\nemission (Fig. 1). The absolute positioning of the ISOCAM images is uncertain\ndue to the lens wheel not always returning to its nominal position (the maximum\nerror is 2 times the Pixel Field of View, viz. 12 arcsec here) and the images\nhave to be recentered on known objects when possible. Since we see on the\nspectra of the pixels corresponding to the strong source a continuum between\n5.15 and 5.5\\,\\mum~ that we attribute to the photospheric emission of the\nexciting star (see Fig. 3), we have recentered the CVF image at these\nwavelengths on the nominal SIMBAD position of BD +69\\degrees1231\n($\\alpha$(J2000) = 22h 13m 27s, $\\delta$(J2000) =\n70\\degrees~15\\arcmin~18\\arcsec). This resulted in Fig. 1. Unfortunately the \nastrometry of BD +69\\degrees1231 is itself somewhat problematic due to the\nsurrounding bright nebulosity and the location of the CVF image on the optical\nimage is correspondingly uncertain. Also, the proper motion of the star from\nthe original BD position is unknown.\n\nFig. 2 presents a set of CO(2--1) spectra of the molecular cloud obtained by us\nat the Caltech Submillimeter \nObservatory with 30\\arcsec~ HPBW and 30\\arcsec~ sampling. These observations\nare better sampled than the CO(2--1) map of Kemper et al. (\\cite{Kemper};\n21\\arcsec~ HPBW, 60\\arcsec~ sampling) but are in good agreement. The line\nintensity peaks in the direction of the star, probably due to local\nexcitation of CO. The higher--resolution $^{13}$CO(2--1) map of Kemper et al. \n(\\cite{Kemper}; 21\\arcsec~ HPBW, 20\\arcsec~ sampling) shows that this is not \nthe position of maximum column density which peaks well to the NE of the \nstar, confirming this conclusion. The $^{12}$CO profiles are double peaked in \nthis area,\nin particular towards the arc, and this makes difficult the search for line \nwings which would be a signature of a shock. There is however some suggestion\nof a negative--velocity wing near the star, in the same sense as the radial \nvelocity of this star.\n\n%Figure 3\n\\begin{figure*}[t!]\n%\\begin{figure}[t!]\n%\\picplace{6cm}\n\\vspace{-0.6cm}\n%\\hspace*{-0.5cm}\n{\\psfig{file=cedspectra.ps,width=18.0cm,height=18.0cm,angle=0.0}}\n%\\psfig{file=cedspectra.ps,width=8.8cm,height=8.8cm,angle=0.0} \n%\\resizebox{\\hsize}{!}{\\includegraphics{cedspectra.ps}}\n\n\\vspace{-0.4cm}\n\\caption{ISOCAM CVF spectra of the central 7$\\times$7 CVF spectra of\nCed\\,201 on a grid with 6\\arcsec$\\times$6\\arcsec~ spacing. The zodiacal \nlight has been subtracted. North is to the top and east is to the left. For\neach plot, the spectral range is from 5\\,\\mum~ to 17\\,\\mum~ and the flux scale\nspans from 0.0 to 11.0 mJy/arcsec$^2$. The offsets are expressed with respect\nto the centroid of the total mid-infrared emission, see Fig. 1.}\n\\end{figure*}\n%\\end{figure}\n\nFig. 3 displays a set of 7$\\times$7 CVF spectra on a grid with \n6\\arcsec$\\times$6\\arcsec~ spacing centered on the exciting star. One sees\ntypical AIB spectra near the emission peak evolving towards fainter, different\nspectra 12--18 arcseconds away. The spectra near the peak show not only the\nclassical AIBs, but also the S(3) rotation line of H$_2$ at 9.6\\,\\mum~ and the\nS(5) line at 6.91\\,\\mum~ or the line of [\\ArII] at 6.98\\,\\mum, which cannot be\nseparated at our resolution. The 12.7\\,\\mum~ AIB might be contaminated by the\n[\\NeII] 12.8 \\mum~ line. These spectra are typical for a low--excitation\nphotodissociation region (PDR). The AIBs are superimposed on a continuum rising\ntowards long wavelengths. This could be the continuum emission of \\mbox{3--D}\nvery small grains (VSGs). The AIBs are broader and much fainter relative to\nthe continuum. The 11.3\\,\\mum~ AIB is now the strongest one at this location.\nThe 7.7 and 8.6\\,\\mum~ AIBs are merged into a single broad band. The most\nstriking feature is the strong emission plateau extending from 11 to 14\\,\\mum.\nThese spectra resemble Class B spectra (Tokunaga \\cite{Tokunaga97}) \n(Class A spectra are the usual AIB spectra). \n\n\n\n\n%\n\\section{Discussion and conclusions}\n\nFig. 3 shows a behaviour of the spectrum with radiation field similar\nto that observed by Uchida et al. (\\cite{Uchida00}) in some other\nreflection nebulae. We find a trend for the 7.7\\,\\mum~AIBs to become\nbroader at {\\it fainter} radiation\nfields away from the exciting star, Fig. 4. The trend is not clear for the \nother bands, but we should not forget that there is contamination by the\nAIBs from foreground and background material. We suggests that some\ncarbonaceous material that emits the continuum and broad bands far from the\nstar is processed through the effect of the star \nthat moves through the molecular cloud, producing AIB carriers: the \ncontinuum is only 2 times fainter 12\\arcsec~ from\nthe star than close to the star, demonstrating the partial disappearance\nof its carriers near the star while the AIBs become very strong. The very\nappearance at relatively large distances from the star (at least 18\\arcsec) \nof a continuum rising towards long wavelengths is surprising. \n\n\nThis continuum must be emitted by VSGs \nheated by single (visible) photons. These grains must be quite smaller than\nthe ``classical'' VSGs which require a strong radiation field to emit\nin the wavelength range of ISOCAM (Contursi et al. \\cite{Contursi}).\nThe spectra seen far from the star remind strongly of Class B spectra\nseen in carbon--rich \nproto--planetary nebulae (Guillois et al. \\cite{Guillois96}). In the \nlaboratory, such spectra are produced (in absorption) by natural coals\nrich in aromatic cycles (Guillois et al. \\cite{Guillois96}) or by a-C:H\nmaterials produced by laser pyrolysis of hydrocarbons (Herlin et al. \n\\cite{Herlin98}; Schnaiter et al. \\cite{Schnaiter99}). In Ced\\,201,\nthese carbonaceous grains must be very small (radius of the order of 1 nm)\nsince they are heated transiently by visible photons to the temperatures\nof $\\simeq$ 250 K necessary to emit the observed mid--IR features. \nSince this is also the approximate size of the classical AIB carriers\nit would not be appropriate to say that these particles release these carriers.\nOne should invoke instead chemi--physical transformations like aromatization\n(Ryter \\cite{Ryter}). In any case, these\nsmall grains were already present before the star penetrated the molecular \ncloud. They are expected to be present elsewhere in the ISM.\n\n\n%Figure 4\n\\begin{figure}[t!]\n\\vspace{-0.6cm}\n\\psfig{file=ced_width.ps,width=8.8cm,height=8.8cm,angle=0.0} \n\\caption{Lorentzian widths of four AIB features from Fig. 3 plotted as a\nfunction of the angular distance to the exciting star, normalized to the width\nof the Lorentzian at zero distance. The error bars show the internal\ndispersion, i.e. the dispersion of values obtained at the same distance from\nthe central star (i.e. 1 value at distance 0 -- hence null dispersion, 4 values\nat distance 6 arcsec, etc.)}\n\\end{figure}\n\nWe find that assuming spherical symmetry the total emissivity per unit volume\nin the CVF spectral range (5.15 to 17\\,\\mum) decreases approximately as the\ninverse square root of the distance to the star, independently of the shape of\nthe spectrum. We base the following calculation on the light diffusion model of\nWitt et al. (\\cite{Witt}), who postulate a uniform density that we find equal\nto n(H) = 2n(H$_2$) = 1800 cm$^{-3}$. This density corresponds to a visual \nextinction of only 0.02 mag. per 6\\arcsec~ angular distance. Since the \nintegrated mid--IR emission is proportional to the stellar radiation density,\nwe can derive an energy conversion efficiency, $\\eta$ = 7.5 \\%~ (emitted in\n4$\\pi$ steradians). Knowing\nthe density, the radiation field of the B9.5\\,V star, and adopting an\nabsorption cross--section per carbon atom of $3\\times 10^{-18}$ cm$^{-2}$\n(Allamandola et al. \\cite{Allamandola89}) and an interstellar carbon abundance\nC/H=$2.3\\times 10^{-4}$ (Snow \\& Witt \\cite{Snow95}; see also Andrievsky et al.\n\\cite{Andrievsky} for carbon abundance in B stars), we find that the fraction\nof carbon locked in the very small particles emitting in the mid--IR is 15\\% .\n This is in agreement with the independent analysis of Kemper et al.\n(\\cite{Kemper}) who find that 10\\% of the gas--phase carbon is locked in\nparticles smaller than 1.5 nm. The {\\it absorption} by these particles\ncontributes to 1/4 of the {\\it extinction} in the visible, a considerable\nfraction. \n\nWe have examined the ratio of the strength of the 6.2\\mum~ (a vibration of\nthe aromatic skeleton) and of the\n11.3\\mum~AIB features (a C--H bending mode) as a function of distance to the \nexciting star. No variation has been seen in this ratio within our rather \nlarge (30 \\%) errors.\n\nIt is interesting to note that Witt et al. (\\cite{Witt}) find from UV--visible\nscattering studies of Ced\\,201 that the grains responsible for the visible\nscattering have a narrow size distribution skewed towards big, \nwavelength--sized grains. This is mostly seen within about 20\\arcsec~ from \nthe star. On the other hand the very strong 2175 \\AA~ extinction band suggests\nthe presence of many smaller carbon grains. All this is evidence for\ngrain processing by the radiation of the star, or/and by\nshattering of grains by a shock wave associated with its motion. The very\nsmall carbonaceous grains we see in Ced\\,201 through their mid--IR emission\nmight be responsible for the 2175 \\AA~ band.\n \nIn summary, we have shown the existence of transformations near a star of very\nsmall, \\mbox{3--D} hydrogenated carbonaceous grains which are probably present\neverywhere in the ISM. This transformation of carbonaceous grains into AIB\ncarriers might be due either to the radiation of a B9.5V star, or to a shock\ninduced by the supersonic motion of the star through the molecular cloud.\nAlthough the existence of a shock is indicated by an optical arc visible\n18\\arcsec~ from the star (and also suspected from our CO observations), there\nis no obvious sign of it in the spectra shown in Fig. 3 and it may\nnot be the cause of the transformation. The very small grains as well as the\nAIB carriers formed from them are excited by the light of the star. The\nconversion efficiency between received excitation energy and mid--IR emitted \nenergy is\nof the order of 7.5\\% for both kinds of particles, and the fraction of carbon\nlocked in these particles is approximately 15\\%.\n%\n\\begin{acknowledgements} We thank Cecile Reynaud and Olivier Guillois for \ninteresting discussions, Kris Sellgren for suggesting Fig. 4 and the referee\nAdolf N. Witt for his useful remarks. The CSO is funded by NSF contract AST\n96-15025.\n\\end{acknowledgements}\n%\n%\n\\begin{thebibliography}{}\n\n%\\bibitem[1996a]{Allain1}\n%Allain T., Leach S., Sedlmayr E. 1996, A\\&A 305, 602\n\n%\\bibitem[1996]{Allain2}\n%Allain T., Leach S., Sedlmayr E. 1996, A\\&A 305, 616\n\n%\\bibitem[1979]{Aitken}\n%Aitken D.K., Roche P.F., Spencer P.M., Jones B. 1979, ApJ 223, 925\n\n\\bibitem[1985]{Allamandola85}\nAllamandola L.J., Tielens A.G.G.M., Barker J.R. 1985, ApJ 290, L25\n\n\\bibitem[1989]{Allamandola89}\nAllamandola L.J., Tielens A.G.G.M., Barker J.R. 1989, ApJS 71, 733\n\n\\bibitem[1999]{Andrievsky}\nAndrievsky S.M., Korotin S.A., Luck R.E., Kostynchuk L. Yu. 1999, A\\&A 350, 598\n\n%\\bibitem[1997]{Biviano}\n%Biviano A. et al. 1997, {\\it Proc. First ISO Workshop on Analytical\n%Spectroscopy}, ESA SP-419 \n\n%\\bibitem[1997]{Blouin}\n%Blouin D., McCutcheon W.H., Dewdney P.E., Roger R.S., Purton C.R.,\n%Kester D., Bontekoe Tj.R. 1997, MNRAS 287, 455\n\n\\bibitem[1990]{Boulanger}\nBoulanger F., Falgarone, E., Puget J.L., Helou G. 1990, ApJ 364, 136\n\n\\bibitem[1991]{Casey}\nCasey S.C. 1991, ApJ 371, 183\n\n\\bibitem[1996a]{CCesarsky}\nCesarsky C.J., Abergel A, Agn\\`ese P. \\etal ~1996a, A\\&A 315, L32\n\n%\\bibitem[1996c]{NGC7023}\n%Cesarsky D., Lequeux J., Abergel A., P\\'erault M., Palazzi E., Madden\n%S., Tran D. 1996c, A\\&A 315, L305\n\n\\bibitem[1996b]{M17}\nCesarsky D., Lequeux J., Abergel A. et al., 1996b, A\\&A 315, L309\n\n%\\bibitem[1998]{M31}\n%Cesarsky D., Lequeux J., Pagani L., Ryter C., Loinard L., Sauvage M.\n%1998, A\\&A 337, L35 \n\n\\bibitem[1992]{Cherchneff}\nCherchneff I., Barker J.R., Tielens A.G.G.M. 1992, ApJ 401, 269\n\n%\\bibitem[1989]{Cohen89}\n%Cohen M., Tielens A.G.G.M., Bregman J., Witteborn F.C., Rank D.M., \n%Allamandola L.J., Wooden D.H., de Muizon M. 1989, ApJ 341, 246\n\n\\bibitem[1998]{Contursi}\nContursi A., Lequeux J., Hanus M., et al. 1998, A\\&A 336, 662\n\n\\bibitem[1999]{Coulais}\nCoulais A., Abergel A. 1999, in {\\it The Universe as seen\nby ISO}, ed. P. Cox \\& M.F. 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Roellig, San Francisco (ASP), 149 \n\n\\bibitem[1998]{Uchida98}\nUchida K.I., Sellgren K., Werner M. 1998, ApJ 493, L109\n\n\\bibitem[2000]{Uchida00}\nUchida K.I., Sellgren K., Werner M.W., Houdashelt M.L. 2000, ApJ in press\n(astro-ph/9910123)\n\n%\\bibitem[1996]{Verstraete}\n%Verstraete L., Puget J.-L., Falgarone E., Drapatz S., Wright C.M.,\n%Timmermann R. 1996, A\\&A 315, L337\n\n%\\bibitem[1986]{Witt86}\n%Witt, A.N., Schild, R.E. 1986, ApJS 62, 839\n\n\\bibitem[1987]{Witt}\nWitt, A.N., Bohlin, R.C., Stecher, T.P., Graff, S.M. 1987, ApJ 321, 912\n\n\\end{thebibliography}\n%\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002209.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n%\\bibitem[1996a]{Allain1}\n%Allain T., Leach S., Sedlmayr E. 1996, A\\&A 305, 602\n\n%\\bibitem[1996]{Allain2}\n%Allain T., Leach S., Sedlmayr E. 1996, A\\&A 305, 616\n\n%\\bibitem[1979]{Aitken}\n%Aitken D.K., Roche P.F., Spencer P.M., Jones B. 1979, ApJ 223, 925\n\n\\bibitem[1985]{Allamandola85}\nAllamandola L.J., Tielens A.G.G.M., Barker J.R. 1985, ApJ 290, L25\n\n\\bibitem[1989]{Allamandola89}\nAllamandola L.J., Tielens A.G.G.M., Barker J.R. 1989, ApJS 71, 733\n\n\\bibitem[1999]{Andrievsky}\nAndrievsky S.M., Korotin S.A., Luck R.E., Kostynchuk L. Yu. 1999, A\\&A 350, 598\n\n%\\bibitem[1997]{Biviano}\n%Biviano A. et al. 1997, {\\it Proc. First ISO Workshop on Analytical\n%Spectroscopy}, ESA SP-419 \n\n%\\bibitem[1997]{Blouin}\n%Blouin D., McCutcheon W.H., Dewdney P.E., Roger R.S., Purton C.R.,\n%Kester D., Bontekoe Tj.R. 1997, MNRAS 287, 455\n\n\\bibitem[1990]{Boulanger}\nBoulanger F., Falgarone, E., Puget J.L., Helou G. 1990, ApJ 364, 136\n\n\\bibitem[1991]{Casey}\nCasey S.C. 1991, ApJ 371, 183\n\n\\bibitem[1996a]{CCesarsky}\nCesarsky C.J., Abergel A, Agn\\`ese P. \\etal ~1996a, A\\&A 315, L32\n\n%\\bibitem[1996c]{NGC7023}\n%Cesarsky D., Lequeux J., Abergel A., P\\'erault M., Palazzi E., Madden\n%S., Tran D. 1996c, A\\&A 315, L305\n\n\\bibitem[1996b]{M17}\nCesarsky D., Lequeux J., Abergel A. et al., 1996b, A\\&A 315, L309\n\n%\\bibitem[1998]{M31}\n%Cesarsky D., Lequeux J., Pagani L., Ryter C., Loinard L., Sauvage M.\n%1998, A\\&A 337, L35 \n\n\\bibitem[1992]{Cherchneff}\nCherchneff I., Barker J.R., Tielens A.G.G.M. 1992, ApJ 401, 269\n\n%\\bibitem[1989]{Cohen89}\n%Cohen M., Tielens A.G.G.M., Bregman J., Witteborn F.C., Rank D.M., \n%Allamandola L.J., Wooden D.H., de Muizon M. 1989, ApJ 341, 246\n\n\\bibitem[1998]{Contursi}\nContursi A., Lequeux J., Hanus M., et al. 1998, A\\&A 336, 662\n\n\\bibitem[1999]{Coulais}\nCoulais A., Abergel A. 1999, in {\\it The Universe as seen\nby ISO}, ed. P. Cox \\& M.F. Kessler, ESA SP-427, 61\n\n\\bibitem[1998]{Cox}\nCox P., Boulanger F., Huggins P.J., et al. 1998, ApJ 495, L23\n\n\\bibitem[1993]{Duley93}\nDuley W.W., Jones A.P., Taylor S.D., Williams D.A. 1993, MNRAS 260, 415\n\n\\bibitem[1988]{Duley88}\nDuley W.W., Williams D.A. 1988, MNRAS 231, 969\n\n%\\bibitem[1981]{Duley}\n%Duley W.W., Williams D.A. 1981, MNRAS 196, 269\n\n%\\bibitem[1998]{Groenewegen}\n%Groenewegen M.A.T., Whitelock P.A., Smith C.H., Kerschbaum F. 1998,\n%MNRAS 293, 18\n\n\\bibitem[1998]{Gry}\nGry C., Boulanger F., Falgarone E. et al., 1998, A\\&A 331, 1070\n\n\\bibitem[1996]{Guillois96}\nGuillois O., Nenner I., Papoulard C., Reynaud C. 1996, ApJ 464, 810\n\n\\bibitem[1998]{Herlin98}\nHerlin N., Bohn I., Reynaud C. et al., 1998, A\\&A 30, 1127\n\n%\\bibitem[1994]{Jansen}\n%Jansen D.L., van Dishoeck E.F., Black J.H. 1994, A\\&A 282, 605\n\n%\\bibitem[1996]{Justtanont}\n%Justtanont K., Barlow M.J., Skinner C.J., Roche P.F., Aitken D.K., Smith C.H.\n%1996, A\\&A 309, 612\n\n\\bibitem[1999]{Kemper}\nKemper C., Spaans M., Jansen D.J. et al., 1999, ApJ 515, 649\n\n%\\bibitem[1980]{Kutner}\n%Kutner M.L., Machnik D.E., Tucker K.D., Dickman R.L. 1980, ApJ 237, 734\n\n\\bibitem[1984]{Leger}\nL\\'eger A., Puget J.-L. 1984, A\\&A 137, L5\n\n%\\bibitem[1999]{Mutschke99}\n%Mutschke H., Andersen A.C., Cl\\'ement D., Henning Th., Peiter G. 1999,\n%A\\&A 345, 187\n\n\\bibitem[1999]{Pagani99}\nPagani L., Lequeux J., Cesarsky D. et al., 1999, A\\&A 351, 447\n\n%\\bibitem[1971]{Racine}\n%Racine R. 1971, AJ 76, 321\n\n%\\bibitem[1996]{Roefselma}\n%Roefselma P.R., Cox P., Tielens A.G.G.M., et al. 1996. A\\&A 315, L289\n\n%\\bibitem[1996]{Reach}\n%Reach W.T., Abergel A., Boulanger F. \\etal ~1996, A\\&A 315, L381\n\n\\bibitem[1991]{Ryter}\nRyter C. 1991, Annales de Physique 16, 507\n\n%\\bibitem[1998]{Schnaiter98}\n%Schnaiter M., Mutschke H., Dorschner J., Henning Th., Salama F. 1998,\n%ApJ 498. 486\n\n\\bibitem[1999]{Schnaiter99}\nSchnaiter M., Henning, Th., Mutschke H. et al., 1999, ApJ 519, 687 \n\n%\\bibitem[1997]{Scott}\n%Scott A.D., Duley W.W., Jahani H.R. 1997, ApJ 490, L175\n\n\\bibitem[1997]{Scott97}\nScott A.D., Duley W.W., Pinho G.P. 1997, ApJ 489, L193\n\n\\bibitem[1983]{Sellgren83}\nSellgren K, Werner M.W., Dinerstein H.L. 1983, ApJ 271, L13\n\n\\bibitem[1989]{Snow95}\nSnow T.P., Witt A.N. 1995, Science 270, 1455\n\n\\bibitem[1999]{Starck}\nStarck J.L., Abergel A., Aussel H. et al., 1999, A\\&AS 134, 135\n\n\\bibitem[1997]{Tokunaga97}\nTokunaga A. 1997, in ASP Conf. Ser. 124, Diffuse Infrared Radiation and the\nIRTS, ed. H. Okuda, T. Matsumoto, T.L. Roellig, San Francisco (ASP), 149 \n\n\\bibitem[1998]{Uchida98}\nUchida K.I., Sellgren K., Werner M. 1998, ApJ 493, L109\n\n\\bibitem[2000]{Uchida00}\nUchida K.I., Sellgren K., Werner M.W., Houdashelt M.L. 2000, ApJ in press\n(astro-ph/9910123)\n\n%\\bibitem[1996]{Verstraete}\n%Verstraete L., Puget J.-L., Falgarone E., Drapatz S., Wright C.M.,\n%Timmermann R. 1996, A\\&A 315, L337\n\n%\\bibitem[1986]{Witt86}\n%Witt, A.N., Schild, R.E. 1986, ApJS 62, 839\n\n\\bibitem[1987]{Witt}\nWitt, A.N., Bohlin, R.C., Stecher, T.P., Graff, S.M. 1987, ApJ 321, 912\n\n\\end{thebibliography}"
}
] |
astro-ph0002210
|
A vestige low metallicity gas shell surrounding the radio galaxy 0943--242 at $z=2.92$
|
[
{
"author": "L. Binette\\inst{1}"
},
{
"author": "J. D. Kurk\\inst{2}"
},
{
"author": "M. Villar-Mart\\'\\i n\\inst{3}"
},
{
"author": "H. J. A. R\\\"ottgering\\inst{2} %and R. W. Hunstead\\inst{4} %and E. V\\'azquez-Semadeni\\inst{1}"
}
] |
Observations are presented showing the doublet \civww\ absorption lines superimposed on the \civ\ emission in the radio galaxy 0943--242. Within the errors, the redshift of the absorption system that has a column density of $\nciv = 10^{14.5 \pm 0.1} \,\cms$ coincides with that of the deep \lya\ absorption trough observed by R\"ottgering et~al. (1995). The gas seen in absorption has a resolved spatial extent of at least 13\,kpc (the size of the extended emission line region). We first model the absorption and emission gas as co-spatial components with the same metallicity and degree of excitation. Using the information provided by the emission and absorption line ratios of \civ\ and \lya, we find that the observed quantities are incompatible with photoionization or collisional ionization of cloudlets with uniform properties. We therefore reject the possibility that the absorption and emission phases are co-spatial and favour the explanation that the absorption gas has low metallicity and is located further away from the host galaxy (than the emission line gas). The larger size considered for the outer halo makes plausible the proposed metallicity drop relative to the inner emission gas. In absence of confining pressure comparable to that of the emission gas, the outer halo of 0943--242 is considered to have a very low density allowing the metagalactic ionizing radiation to keep it higly ionized. In other radio galaxies where the jet has pressurized the outer halo, the same gas would be seen in emission (since the emissivity scales as $n_H^2$) and not in absorption as a result of the lower filling factor of the denser condensations. This would explain the anticorrelation found by Ojik et~al. (1997) between \lya\ emission sizes (or radio jet sizes) and the observation (or not) of \hi\ in absorption. The estimated low metallicity for the absorption gas in 0943--242 ($Z \sim 0.01 \zsol$) and its proposed location --outer halo outside the radio cocoon-- suggest that its existence preceeds the observed AGN phase and is a vestige of the initial starburst at the onset of formation of the parent galaxy. \keywords{Galaxies: individual: 0943--242 -- Cosmology: early Universe -- Galaxies: active -- Galaxies: formation -- Galaxies: ISM -- Line: formation }
|
[
{
"name": "luc.tex",
"string": "\\documentclass[printer]{aa}\n\n%%%%%%%%%%% Essential Variable abbreviations\n\\newcommand{\\etal}{\\hbox{et~al.}}\n\\newcommand{\\msol}{\\hbox{\\,${\\rm M_{\\sun}}$}}\n\\newcommand{\\eg}{\\hbox{e.g.}}\n\\newcommand{\\cf}{\\hbox{cf.}}\n\\newcommand{\\ie}{\\hbox{i.e.}}\n\\newcommand{\\dex}{\\hbox\\,{dex}}\n\\newcommand{\\cms}{\\hbox{\\,${\\rm cm^{-2}}$}}\n\\newcommand{\\cmsq}{\\hbox{\\,${\\rm cm}\\,{\\rm s}^{-2}$}}\n\\newcommand{\\gcc}{\\hbox{\\,${\\rm g\\,cm^{-3}}$}}\n\\newcommand{\\cmc}{\\hbox{\\,${\\rm cm^{-3}}$}}\n\\newcommand{\\kms}{\\hbox{\\,${\\rm km\\,s^{-1}}$}}\n\\newcommand{\\lu}{\\hbox{${\\rm erg\\, cm^{-2}\\, s^{-1}}$}}\n\\newcommand{\\kcmc}{\\hbox{\\,${\\rm K\\, cm^{-3}}$}}\n\\newcommand{\\up}{\\hbox{$U$}}\n\\newcommand{\\nh}{\\hbox{$N_{H}$}}\n\\newcommand{\\nhi}{\\hbox{$N_{HI}$}}\n\\newcommand{\\nhii}{\\hbox{$N_{HII}$}}\n\\newcommand{\\nciv}{\\hbox{$N_{CIV}$}}\n\\newcommand{\\map}{\\hbox{{\\sc mappings i}c}}\n\\newcommand{\\gam}{\\hbox{$\\Gamma$}}\n\\newcommand{\\gamb}{\\hbox{$\\Gamma$}}\n\\newcommand{\\gamo}{\\hbox{$\\Gamma$}}\n\\newcommand{\\gamc}{\\hbox{$\\Gamma$}}\n\\newcommand{\\vs}{\\hbox{$V_{shock}$}}\n\\newcommand{\\zce}{\\hbox{$Z_{C}^{emi}$}}\n\\newcommand{\\zca}{\\hbox{$Z_{C}^{abs}$}}\n\\newcommand{\\zsol}{\\hbox{$Z_{\\sun}$}}\n\n%%%%% Essential Atomic spectral notation\n\\newcommand{\\mgiiw}{\\hbox{Mg\\,{\\sc ii}\\,$\\lambda\\lambda $2798}}\n\\newcommand{\\mgii}{\\hbox{Mg\\,{\\sc ii}}}\n\\newcommand{\\mgv}{\\hbox{[Mg\\,{\\sc v}]}}\n\\newcommand{\\ciii}{\\hbox{C\\,{\\sc iii}]}}\n\\newcommand{\\ciiiw}{\\hbox{C\\,{\\sc iii}]$\\lambda $1909}}\n\\newcommand{\\civ}{\\hbox{C\\,{\\sc iv}}}\n\\newcommand{\\civw}{\\hbox{C\\,{\\sc iv}\\,$\\lambda\\lambda $1549}}\n\\newcommand{\\civww}{\\hbox{C\\,{\\sc iv}\\,$\\lambda\\lambda $1548, 1551}}\n\\newcommand{\\nv}{\\hbox{N\\,{\\sc v}}}\n\\newcommand{\\nvw}{\\hbox{N\\,{\\sc v}$\\lambda $1240}}\n\\newcommand{\\ovi}{\\hbox{O\\,{\\sc vi}}}\n\\newcommand{\\oviw}{\\hbox{O\\,{\\sc vi}$\\lambda $1035}}\n\\newcommand{\\ov}{\\hbox{O\\,{\\sc v}]}}\n\\newcommand{\\ovw}{\\hbox{O\\,{\\sc v}]$\\lambda $1218}}\n\\newcommand{\\oiii}{\\hbox{[O\\,{\\sc iii}]}}\n\\newcommand{\\oiiiw}{\\hbox{[O\\,{\\sc iii}]$\\lambda $5007}}\n\\newcommand{\\oiiiuvw}{\\hbox{O\\,{\\sc iii}]$\\lambda $1663}}\n\\newcommand{\\oiiiuv}{\\hbox{O\\,{\\sc iii}]}}\n\\newcommand{\\oiiitw}{\\hbox{[O\\,{\\sc iii}]$\\lambda $4363}}\n\\newcommand{\\oii}{\\hbox{[O\\,{\\sc ii}]}}\n\\newcommand{\\oiiw}{\\hbox{[O\\,{\\sc ii}]$\\lambda\\lambda $3727}}\n\\newcommand{\\oiibw}{\\hbox{[O\\,{\\sc ii}]$\\lambda\\lambda $7325}}\n\\newcommand{\\lya}{\\hbox{Ly$\\alpha$}}\n\\newcommand{\\lyaw}{\\hbox{Ly$\\alpha$\\,$\\lambda $1216}}\n\\newcommand{\\ha}{\\hbox{H$\\alpha$}}\n\\newcommand{\\haw}{\\hbox{H$\\alpha$\\,$\\lambda $6563}}\n\\newcommand{\\hb}{\\hbox{H$\\beta$}}\n\\newcommand{\\hbw}{\\hbox{H$\\beta$\\,$\\lambda $4861}}\n\\newcommand{\\hi}{\\hbox{H\\,{\\sc i}}}\n\\newcommand{\\hii}{\\hbox{H\\,{\\sc ii}}}\n\\newcommand{\\hg}{\\hbox{H$\\gamma$}}\n\\newcommand{\\hgw}{\\hbox{H$\\gamma$\\,$\\lambda $4340}}\n\\newcommand{\\heii}{\\hbox{He\\,{\\sc ii}}}\n\\newcommand{\\heiii}{\\hbox{He\\,{\\sc iii}}}\n\\newcommand{\\heiiw}{\\hbox{He\\,{\\sc ii}\\,$\\lambda $4686}}\n\\newcommand{\\heiiuw}{\\hbox{He\\,{\\sc ii}\\,$\\lambda $1640}}\n\\newcommand{\\hei}{\\hbox{He\\,{\\sc i}}}\n\\newcommand{\\heiw}{\\hbox{He\\,{\\sc i}\\,$\\lambda $5876}}\n\\newcommand{\\lw}[1]{\\hbox{$\\lambda$\\,#1\\AA}}\n\\newcommand{\\lww}[2]{\\hbox{$\\lambda \\lambda$#1/#2 \\AA}}\n\\newcommand{\\lwww}[3]{\\hbox{$\\lambda \\lambda$#1/#2/#3 \\AA}}\n\n\\usepackage{graphics}\n%%%%%%%%%%\n\n\\begin{document}\n\n\\thesaurus{11(11.09.1;12.05.1;11.01.2;11.06.1;11.09.4;02.12.1) }\n\n\\title{A vestige low metallicity gas shell surrounding the radio\ngalaxy 0943--242 at $z=2.92$}\n\n%\\subtitle{Low metallicity shell in 0943--242}\n\n\\author{L. Binette\\inst{1}, J. D. Kurk\\inst{2}, \nM. Villar-Mart\\'\\i n\\inst{3}, H. J. A. R\\\"ottgering\\inst{2}\n%and R. W. Hunstead\\inst{4} \n%and E. V\\'azquez-Semadeni\\inst{1} \n }\n\n\\authorrunning{Binette et~al.}\n\n\\offprints{Luc Binette}\n\n\\institute{Instituto de Astronom\\'\\i a, UNAM, \n\tAp. 70-264, 04510 M\\'exico, DF, M\\'exico ~(e-mail: binette@astroscu.unam.mx) \n\\and Leiden Observatory, P. O. Box 9513, 2300 RA, Leiden, The Netherlands\n\\and Department of Physical Sicences, University of Hertfordshire,\nCollege Lane, Hatfield Herts, AL10 9AB, England \n%Institut d'Astrophysique de Paris (IAP),\n%98 bis Bd Arago, F75014 Paris, France \n%Division of Physics and Astronomy, \n%University of Hertfordshire, College Lane, Hatfield, HERTS AL109AB,UK \n%\\and School of Physics, University of Sydney, NSW 2006, Australia \n}\n\\date{Received / Accepted}\n\n\\maketitle\n\n\\begin{abstract}\n\nObservations are presented showing the doublet \\civww\\ absorption\nlines superimposed on the \\civ\\ emission in the radio galaxy\n0943--242. Within the errors, the redshift of the absorption system\nthat has a column density of $\\nciv = 10^{14.5 \\pm 0.1} \\,\\cms$\ncoincides with that of the deep \\lya\\ absorption trough observed by\nR\\\"ottgering et~al. (1995). The gas seen in absorption has a resolved\nspatial extent of at least 13\\,kpc (the size of the extended emission\nline region). We first model the absorption and emission gas as\nco-spatial components with the same metallicity and degree of\nexcitation. Using the information provided by the emission and\nabsorption line ratios of \\civ\\ and \\lya, we find that the observed\nquantities are incompatible with photoionization or collisional\nionization of cloudlets with uniform properties. We therefore reject\nthe possibility that the absorption and emission phases are co-spatial\nand favour the explanation that the absorption gas has low metallicity\nand is located further away from the host galaxy (than the emission\nline gas). The larger size considered for the outer halo makes\nplausible the proposed metallicity drop relative to the inner emission\ngas. In absence of confining pressure comparable to that of the\nemission gas, the outer halo of 0943--242 is considered to have a very\nlow density allowing the metagalactic ionizing radiation to keep it\nhigly ionized. In other radio galaxies where the jet has pressurized\nthe outer halo, the same gas would be seen in emission (since the\nemissivity scales as $n_H^2$) and not in absorption as a result of the \nlower filling factor of the denser condensations. This would\nexplain the anticorrelation found by Ojik et~al. (1997) between \\lya\\\nemission sizes (or radio jet sizes) and the observation (or not) of\n\\hi\\ in absorption. The estimated low metallicity for the absorption\ngas in 0943--242 ($Z \\sim 0.01 \\zsol$) and its proposed location\n--outer halo outside the radio cocoon-- suggest that its existence\npreceeds the observed AGN phase and is a vestige of the initial\nstarburst at the onset of formation of the parent galaxy.\n\n\\keywords{Galaxies: individual: 0943--242 -- Cosmology: early\nUniverse -- Galaxies: active -- Galaxies: formation -- Galaxies: ISM\n-- Line: formation }\n\\end{abstract}\n\n\\section{Introduction}\n\nVery high redshift ($z>2$) radio galaxies (hereafter HZRG) show\nemission lines of varying degree of excitation. In virtually all\nobjects, the \\lya\\ line is the strongest and is usually accompanied by\nhigh excitation lines of \\civw, \\ciiiw, \\heiiuw\\ and, at times, \\nvw\\\n(R\\\"ottgering et~al. 1997 and references therein). An important\ncharacteristic of the emision gas is its spatial scale. The sizes of\nthe \\lya\\ emission region range from $15$ to 120\\,kpc (van~Ojik \\etal\\\n1997).\n\nMost ground work on HZRG is performed at rather low resolution ($\\sim\n20$\\AA) to maximize the probability of line detection and the S/N.\nHowever a very potent discovery was made by van~Ojik \\etal\\ (1997,\nhereafter vO97) at much higher resolution, that of extended \\hi\\ {\\it\nabsorption} gas. In effect, out of 18 HZRG spectra taken at the\nunusually high resolution of $\\simeq 1.5$--3\\AA, vO97 found --in 60\\% of\nthe objects-- deep absorption troughs superimposed on the Ly$\\alpha$\nemission profiles. Furthermore, out of the 10 radio galaxies smaller\nthan 50\\,kpc, strong \\hi\\ absorption is found in 9 of them. The\nabsorption gas appears to have a covering factor near unity over very\nlarge scales, namely as large as the underlying emission gas.\n\nThe current paper addresses the problem of the ionization state of\nboth the absorption and the emission gas as well as the\ninterconnection between the two. The main justifications behind this\nwork are the following: HZRG are probably the progenitors of the\nmassive central cluster galaxies (Pentericci et~al. 1999) and as such\nare an important means by which we can study large ellipticals and\ntheir environment at such high redshift, a time not so long after, or\neven during their formation. Furthermore, the extended gas as detected\nin \\civ\\ (see below) is chemically enriched and therefore represents\ndebris of past intense stellar formation periods and is interesting to\nstudy in their own right. What is the fate of such gas? How quickly\nhas the enrichment of this large scale gas proceeded? Will this gas be\nheated up into a hot wind and enrich the intergalactic X-ray gas in\ncluster of galaxies? Will it on the contrary condense into sheets or\ncondensations? A better understanding of the various gaseous phases\nwhich co-exist in high redshift objects would help anwering these\nquestions.\n\nTo determine the physical conditions of the absorption gas, new\nobservations were carried out at the wavelength of \\civ\\ and \\heii\\ in\n0943--242, the first radio galaxy reported to show large scale absorption\ntroughs (R\\\"ottgering et~al. 1995, hereafter RO95). The new spectrum\n shows the \\civ\\ absorption doublet at the same redshift\\footnote{We will\ndistinguish between absorption and emission redshifts using\nsubscripts, as in $z_a$ and $z_e$, respectively.} $z_{a}$ as the \\lya\\\nabsorption trough (RO95). Clearly and surprisingly the gas in absorption is\nhighly ionized and probably of comparable excitation to the gas seen\nin emission. \n\n\nThis paper is structured as follows. We first present observations\nwhich show \\civ\\ in absorption in 0943--242 (Sect.\\,~\\ref{observ}). In\nSect.\\,~\\ref{hypo} we derive a ratio (\\gamo) relating the observed\nemission and absorption quantities which depends somewhat on the\nionization fraction of H but not explicitely on the C/H metallicity\nratio. At first, we postulate that the emission and absorption gas\ncomponents are co-spatial and share the same excitation mechanism and\nphysical conditions and proceed to model \\gamo\\ with a one-zone\nequilibrium photoionization model. We improve on the model using a\nstratified photoionized slab. As the observed ratio cannot be\nreproduced even in the case of collisional ionization, we discuss in\nSect.~\\ref{intergam} two alternative interpretations of this\nsignificant discrepancy. We demonstrate the many advantages of the\nwinning scenario in which the absorption gas is further out and of\nmuch lower density, pressure and metallicity than the emission gas.\n\n%Our conclusions (Sect.~\\ref{conclusions}) is that\n\n\\section{Observations of \\civ\\ (and \\lya) in absorption in 0943--242} \\label{observ}\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{luc1000.f4}}\n\\caption{An expanded plot of the \\lya\\ spectral region obtained by\nRO95. The \\hii\\ emission gas redshift is $z_e=2.9233 \\pm 0.0003$\nand the main absorber of column $\\nhi = 10^{19.0\\pm 0.2}$\\,\\cms\\ lies\nat $z_a=2.9200\\pm 0.0002$.}\n\\label{fig:lya}\n\\end{figure}\n\n\\subsection{Earlier observations of 0943--242 at $z_e = 2.92$ } \\label{oldobs}\n\nThe low resolution spectrum of 0943--242 shown in RO95 and \ndiscussed also in van~Ojik et~al. (1996) displays the characteristic\nemission lines of a distant radio galaxy: strong \\lya, weaker \\civ,\n\\heii\\ and possibly \\ciii. This object was also observed at intermediate \nresolution (1.5\\AA) by RO95 in the region of \\lya\\ with the slit\npositioned along the radio axis. The initial discovery of extended\nabsorption troughs was based on this latter spectrum which we\nreproduce in Fig.~\\ref{fig:lya}.\n\n\n\\subsection{New observations of $C\\,{IV}$ and $He\\,{II}$ at intermediate resolution}\n\nWith the objective of providing constraints on the abundances and\nkinematics of the gas in 0943--242, sensitive high-resolution spectroscopic\nobservations centered at the \\civ\\ and \\heii\\ lines were performed\n%were carried out by some of us (RH) and later reduced (JK). \n%The observations were done\nat the Anglo Australian Telescope (AAT) on 1995 March 31 and April 1\nunder photometric conditions and with a seeing which varied from 1\\arcsec\\\nto 2\\arcsec. The RGO spectrograph was used with a 1200 grooves\nmm$^{-1}$ grating and a Tektronix 1024$^2$ thinned CCD, yielding\nprojected pixel sizes of $0.79\\arcsec\\ \\times 0.6$\\AA. The projected\nslit width was 1.3\\arcsec, resulting in a resolution as measured from\nthe copper-argon calibration spectrum of 1.5\\AA\\ FWHM; the slit was\noriented at a position angle of 74$^\\circ$, i.e. along the radio axis\n(as in RO95).\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{luc1000.f1}}\n\\caption{The full-resolution AAT spectrum showing the \\civww\\ and\n\\heiiuw\\ lines.}\n\\label{fig:full}\n\\end{figure}\n\n\nThe total integration time of 25000s was split into 2$\\times$2000s and\n7$\\times$3000s exposures in order to facilitate removal of cosmic\nrays. Exposure times were chosen to ensure that the background was\ndominated by shot noise from the sky rather than CCD readout noise.\nBetween observations the telescope was moved, shifting the object slit\nby about 3 spatial pixels, so that for each exposure the spectrum was\nrecorded on a different region of the detector. The individual spectra\nwere flat-fielded and sky-subtracted in a standard way using the\nlong-slit package in the NOAO reduction system IRAF. The precise\noffsets along the slit were determined using the position of the peak\nof the spatial profile of the \\civ\\ and \\heii\\ lines. Using these offsets, the\nimages were registered using linear interpolation and summed to obtain\nthe two-dimensional spectrum. The resultant seeing in the final\ntwo-dimensional spectrum, measured from two stars on the slit, was\n1.5\\arcsec\\ FWHM. The corresponding FWHM of \\civ\\ emission along the\nslit was 2.2\\arcsec, giving a deconvolved (Gaussian) width of\n1.6\\arcsec\\ or 12\\,kpc. Within the errors, this is the same as that\nfound for \\lya\\ emission by RO95.\n\nThe two-dimensional spectrum was weighted summed over a 7 pixel\n(5\\arcsec) aperture to obtain a one-dimensional spectrum. In\nFig.~\\ref{fig:full} we show the AAT data in the form of a\nfull-resolution spectrum.\n\n\n\\subsection{Profile fitting of the emission and absorption\n\\lya\\ and $C\\,{IV}$ lines}\n\nOne deep trough is observed in the \\lya\\ emission line\n(Fig.~\\ref{fig:lya}) which was interpreted as a large scale \\hi\\\nabsorber by RO95. In addition there are a number of weaker\ntroughs, presumably due to weak \\hi\\ absorption. Fitting the emission\nline by a Gaussian and the \\hi\\ absorption by Voigt profiles, RO95\ninfer a column density \\nhi\\ of $ 10^{19.0\\pm 0.2}$\\,\\cms\\ for the deep\ntrough, a redshift $z_a=2.9200\\pm 0.0002$ and a Doppler parameter $b$ of\n$55\\pm5$\\,\\kms. For the three shallow troughs, they find \\nhi\\ ranging\nfrom $10^{13.8}$ to $10^{14.1}$ \\cms\\ and $b$ ranging from 7 to 100\n\\kms. The redshift difference of the absorbers relative to systemic\nvelocity when converted into inflow/outflow velocities indicate values\nnot exceeding 800\\,\\kms. Because at the bottom of the main trough no\nemission is observed, the covering factor of the absorbing gas must be\nequal or larger than unity over the complete area subtended by the\n\\lya\\ emission, indicating that the spatial scale of the absorber\nexceeds 13\\,kpc. This work will concern only the deep absorption\ntrough.\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{luc1000.f2}}\n\\caption{An expanded plot of the full-resolution spectrum \nwith the fit superimposed (solid line).}\n\\label{fig:CIVfit}\n\\end{figure}\n\nTo parameterize the \\civ\\ profile we have assumed that the underlying\nemission line is Gaussian, with Voigt profiles due to the\n\\civ\\ doublet absorption superimposed. We used an iterative\nscheme that minimizes the sum of the squares of the difference between\nthe model and the observed spectrum, thereby solving for the\nparameters of the model (e.g.\\ Webb 1987, vO97). Initial values were assumed\nfor the shape of the Gaussian profile and the redshift of the\nabsorber.\n\n\\begin{table}\n\\caption{\\label{ta:parameters}Parameters for the Gaussian and Voigt\nprofile fits}\n\\label{ewciv}\n\\begin{flushleft}\n\\begin{tabular}{l@{}rr} \\hline\n{\\bf Emission} & {\\bf \\civ} & {\\bf \\heii} \\\\ \\hline\nOffset ($10^{-17}$ erg cm$^{-2}$ s$^{-1}$) &\n0.29 $\\pm$ 0.01 & 0.32 $\\pm$ 0.07 \\\\\nPeak ($10^{-17}$ erg cm$^{-2}$ s$^{-1}$) &\n1.90 $\\pm$ 0.1 & 1.75 $\\pm$ 0.2 \\\\\nPosition of peak (\\AA) &\n6078.2 $\\pm$ 0.5 & 6434.5 $\\pm$ 0.5 \\\\\n$z_e$ & 2.9247 $\\pm$ 0.0003 & 2.925 $\\pm$ 0.001 \\\\\nFWHM (\\kms) &\n1430 $\\pm$ 50 & 1025 $\\pm$ 45 \\\\ \\hline\n{\\bf Absorption} & {\\bf \\civ} & \\\\ \\hline\n$z_a$ & 2.9202 $\\pm$ .0002 & \\\\\n$b$ (\\kms) & 45 $\\pm$ 15 & \\\\\n\\nciv\\ (cm $^{-2}$)& 10$^{14.5 \\pm 0.1}$ & \\\\\nPosition of $1^{\\rm st}$ trough (\\AA)& 6068.2 & \\\\\nPosition of $2^{\\rm nd}$ trough (\\AA)& 6078.3 & \\\\ \\hline\n\\end{tabular}\n\\end{flushleft}\n\\end{table}\n\n\nIn Fig.\\,\\ref{fig:CIVfit} we show a portion of the spectrum with the\nmodel fits superimposed. The Gaussian fitted to the \\civ\\ emission\nline peaks at $z_e = 2.9247 \\pm 0.0003$ and has a FWHM of\n$29\\pm2$\\AA. We have corrected all wavelengths to the vacuum\nheliocentric system ($\\simeq $+1.13\\,\\AA) before computing the redshifts.\nThe two troughs in this figure correspond to the\n\\civww\\ doublet produced by the same absorption\nsystem. Therefore, within the fitting procedure, the wavelength\nseparation and the ratio of the two profiles' depths are fixed by\natomic physics while the two values for $b$ are set to be equal. The\nfit gives for the location of the bottoms of the two troughs\n$\\lambda=$ 6068.2 and 6078.3\\AA\\ resulting in a redshift of 2.9202\n$\\pm$ 0.0002. Within the errors this redshift is equivalent to that of\nthe main \\hi\\ absorber and in the subsequent analysis we will assume\nthat the \\lya\\ and \\civ\\ {\\it absorption} gas belongs to the same\nabsorber. We derive a Doppler parameter $b$ for the doublet of $45\n\\pm 15 \\kms$ and a column density \\nciv\\ of 10$^{14.5 \\pm 0.1}\\,\\cms$\nas summarized in Table~\\ref{ewciv}.\n\nAs expected, \\heii\\ appears only in emission without any\nabsorption since it is not a resonance line. Parameters for the\n\\heii\\ emission profile were obtained by fitting a Gaussian\nusing the same iterative scheme (see Fig.~1 in R\\\"ottgering \\& Miley\n1997). The peak is positioned at $z_e = 2.925 \\pm 0.001$ and has a FWHM\nof $22 \\pm2$\\AA. The fitted parameters of the emission and\nabsorption profiles are presented in Table~\\ref{ewciv}. We recall that\nthe FWHM of the \\lya\\ emission profile is $1575 \\pm 75 \\,\n\\kms$ (vO97), significantly larger than that of \\heii\\ \n(see Table~\\ref{ewciv}). Inspection of the various profiles in\nFig.~\\ref{fig:lya} and Fig.~\\ref{fig:full} (or Fig.~\\ref{fig:CIVfit})\nsuggests the presence of an excess flux on the blue wings of all the\nemission profiles. Combining information from all the emission lines,\nour best estimate of the emission gas redshift is $z_e=2.924\\pm\n0.002$.\n\n\n\\subsection{Velocity shear and subcomponents} \\label{shear}\n\nTo investigate whether there is any velocity shear in the \\civ\\\nemission profile we fitted spatial Gaussian profiles to the emission\nline as a function of wavelength. In Fig.\\ \\ref{fig:relloc} we show\nthe wavelength maxima of these spatial profiles and a line fitted\nthrough these points. The spatial profile of the \\civ\\ emission\nspectrum is displaced by 0.2\\arcsec, corresponding to a displacement\nof 1.5 kpc, over a wavelength range of 50\\AA. RO95 measured a\ncomparable shift for \\lya\\ of 1.8 kpc\\footnote{This new value of $0.33\n\\pm 0.06 \\, {\\rm pixels} \\times 0.74 \\, {\\rm arcsec/pixel} = \n0.2442 \\, {\\rm arcsec} \\times 7.36 \\, {\\rm kpc/arcsec} = 1.80 \\pm 0.33$\\,kpc\nis to be preferred to that quoted by RO95 of 2.5\\,kpc.} although it\nappears that the latter displacement is due to a far more pronounced\nand abrupt difference in locations of the \\lya\\ peak on both sides of\nthe absorption trough. As Fig.\\,\\ref{fig:relloc} shows, the peaks of\n\\civ\\ emission form a wavy line. We believe the velocity shear in the\nC{\\sc iv} profile to be less significant than the shear in the\n\\lya\\ profile. We cannot rule out that the small velocity shear might\nbe masking a possible break up of the absorption regions into a few\nsaturated absorption components of smaller $b$.\n\n\n\n\\begin{figure}\n\\resizebox{\\hsize}{!}{\\includegraphics{luc1000.f3}}\n\\caption{The relative location of the peak of the \\civ\\ \nemission at constant wavelength as a function of wavelength. The line\nis a weighted fit to these peaks. The zero offset is arbitrary.}\n\\label{fig:relloc}\n\\end{figure}\n\n\n%The velocity dispersion measured from an absorption line reflects both\n%the thermal motions of the atoms (i.e. temperature) and the large\n%scale motions within the clouds, such as turbulence, rotation,\n%expansion or contraction. Assuming that to a first approximation the\n%large scale motions also give rise to a Gaussian distribution of\n%velocities, with dispersion parameter $b_{ls}$, the two contributions\n%to the line width add in quadrature (Pettini et~al.\\ 1990)\n%\\begin{equation} b_{fit}^2 = b_{ls}^2 + \\frac{2kT}{m_C} = b_{ls}^2 + 1.65 \n%\\times 10^{-2} T \n%\\end{equation} \n%\n%\\noindent where $b_{fit}$ is the measured Doppler parameter in km s$^{-1}$,\n%$b_{ls}$ the Doppler parameter due to large scale motion, $T$ the\n%average temperature in Kelvin, $k$ the Boltzmann's constant and $m_H$\n%the mass of an hydrogen atom. Assuming the cloud has a temperature of\n%$T \\sim 10^4$\\,K, which is typical for a two-phase medium, the\n%velocity of the large scale motion is 43 km/s.\n\n\nA concern about the determination of \\nciv\\ is the possibility that\nthat there exist subcomponents in the absorption systems that have\nhigh column densities but low $b$ values and are, therefore, not\nacounted for whenever individual velocity subcomponents are not\nresolved. Although we cannot strictly exclude this possibility, we\nadopt the stand of Jenkins (1986) and Steidel (1990a) who, using\nextensive absorption line studies, argue that this is unlikely to be\nthe case, at least for \\civ, and that a single-component\ncurve-of-growth analysis can be used to infer total columns\nalthough the inferred {\\it effective} $b$ value has no physival meaning in\nterms of temperature. It is interesting to note that the\nphysical conditions inferred from the \\civ\\ fit are fully consistent with\nthe observed ratio of the doublet (since both troughs are equally well\nfitted). If the underlying continuum was flat, the \\nciv\\ column and\nthe $b$ value we infer would imply a theoretical ratio of\nequivalent widths of $W_0(1548)/W_0(1551) = 1.4$, which is where the\ncurve of growth just begins to leave the linear part (Steidel 1990a).\nClearly the \\nhi\\ column might be susceptible to a larger error since\n\\lya\\ is saturated. With these caveats in mind, we will assume in the\nfollowing analysis that the adopted columns do not lie far off from\nreality.\n\n\n\\section{A simple model for the ionized gas in emission and absorption} \\label{hypo}\n\nOur initial hypothesis is that the absorption gas is a subcomponent of\nthe emission gas, sharing the same excitation mechanism and\nmetallicity. We discuss the physical conditions of such gas and\nproceed to calculate an observable quantity, \\gam, against which to\ncompare the information provided by the \\lya\\ and \\civ\\ lines in\n0943--242.\n\n\\subsection{Relation between the ionized absorption \nand emission components}\n\nThe \\civ\\ and \\lya\\ lines are both resonant lines and therefore prone\nto be seen in absorption against a strong underlying source. This\nproperty has consequences for the emission gas as well. In\neffect, for a geometry consisting of many condensations for which the\ncumulative covering factor approaches unity, the resonant line photons\nmust scatter many times in between the condensations before they can\nescape. In this case, the emerging flux of any resonant line from a\nnon uniform distribution of gas will not in general be an isotropic\nquantity but will depend on geometrical factors and on the relative\norientation of the observer, a point which we now develop further.\n\nWe propose that some kind of asymmetry within the emission gas\ndistribution can explain how a fraction of the ionized gas can be\nseen in absorption against other nearby components in emission. Let us\nsuppose that the emission region is composed of low filling factor\nionized gas condensations which are denser (therefore brighter)\ntowards the nuclear ionizing source. In this picture, the \\lya\\ or\n\\civ\\ photons are generated within and escape from such condensations,\nafter which they start scattering on the surface of neighboring\ncondensations until final escape from the galaxy (we assume that the\ncumulative covering factor is unity). Let us now suppose an\nasymmetry\\footnote{The asymmetry would take place either in space or\nin velocity domain or both.} in the global distribution of the outer\ncondensations respective to the plane of the sky. In this case, the\ntotal number of scatterings on neighboring condensations before final\nescape will differ depending on the perspective of the absorber.\nSince for an observer situated on the side with an excess of\ncondensations many of the resonant photons would have been\n`reflected' away, we expect that the reduced flux would appear as an\nabsorption line at the same velocity as that of the condensations\nresponsible for reflecting away the resonant photons. The outer\ncondensations (responsible for the absorption) must necessarily be of lower\ndensity in order to be of negligible emissivity respective\nto the inner (denser and therefore brighter) emission gas, otherwise\nthe outer gas would out-shine in emission!\n\nWe should point out that for a density of the absorption gas as high\nas 100\\cmc\\ as argued for in vO97, such a gas cannot be photoionized\nby the metagalactic background radiation which would be much too\nfeeble to produce \\civ. The ionization to such a degree of the\nabsorption gas is in itself puzzling. We adopt as working hypothesis\nthat it is --similarly to the emission gas-- photoionized by the AGN\nor by the hard radiation from photoionizing shocks.\n\nFinally, the fact that both the absorption and emission gas contain a\nsignificant amount of C$^{+3}$ argues in favor of a common geometry\nand excitation mechanism for the gas, the underlying hypothesis behind\nthe calculations developed below.\n\n%\\section{Calculations and results for 0943--242} \n\n\\subsection{The observable quantity \\gam\\ }\n\nThe quantities determined from observation of 0943--242 are the\nfollowing: the emission line ratio measured by R\\\"ottgering\net~al. (1997) is ${I_{CIV}\\over I_{Ly\\alpha}} = 0.194$. We adopt the\nvalue of 0.17 following estimation of the missing flux due to the\nabsorption troughs. As for the absorption gas, the \\hi\\ and \\civ\\\ncolumn densities are $10^{19}\\,\\cms$ and $10^{14.5}\\, \\cms$, respectively, as\ndiscussed in Sect.~\\ref{observ}. These four quantities carry\ninformation on the three ionization species H$^{0}$, H$^{+}$ and C$^{+3}$. We\ndefine the ratio \\gamo\\ as the following product of the emission and\nabsorption ratios:\n\n\\begin{equation}\n\\gamo = {I_{CIV}\\over I_{Ly\\alpha}} {N_{HI} \\over N_{CIV}} = 0.17\n{10^{19.0}\\over10^{14.5}} \\simeq 5400\n\\end{equation}\n\n\\noindent where $\\nhi/\\nciv$ is the ratio of the\nmeasured absorption columns. If, as postulated above, the gas\nresponsible for absorption is simply a subset of the line emitting\ngas, the ratio \\gam\\ does not explicitly depend on the abundance of\ncarbon as shown below.\n\n\\subsection{The simplest case of an homogeneous one-zone slab}\n\nTo compute \\gamc, in a first stage let us consider an homogeneous slab\nof thickness $L$ of uniform gas density, temperature and ionization\nstate to represent both the gas in emission and in\nabsorption. Ignoring any peculiar scattering effects, the emission\nline ratio ${I_{CIV}\\over I_{Ly\\alpha}} $ is given by the ratio of the\nlocal emissivities $j_{CIV}/j_{Ly\\alpha}$ since the slab is\nhomogeneous. For the emissivity of the \\civ\\ line, we have\n\n\\begin{eqnarray}\n4 \\pi j_{CIV} = 8.63\\, 10^{-6} \\, h\\nu_{C_{\\sc iv}} \\, n_e n_{CIV}\n \\nonumber \\\\ \\times {\\Omega_{C_{\\sc IV}} \\over \\omega_1} \n\\exp{(-h\\nu_{CIV}/kT)}/\\sqrt{T}\n\\end{eqnarray}\n\n\\noindent (Osterbrock 1989) \nwhere $T$ is the temperature, $\\Omega_{C_{\\sc IV}}$ the collision\nstrength of the combined doublet, $ \\omega_1$ the statistical weight\nof the ground state and $h\\nu_{CIV}$ the mean energy of the \\civ\\\nexcited level. For the \\lya\\ emissivity, we have\n\n\\begin{equation}\n4 \\pi j_{Ly\\alpha} = h\\nu_{Ly\\alpha } \\, n_e n_{HII} \\, \\alpha_{2p}^{eff}(T) \n\\end{equation}\n\n\\noindent where $\\alpha_{2p}^{eff}$ is the effective recombination\ncoefficient rate to level $2p$ of H (Osterbrock 1989). By putting the\ntemperature dependence and all the atomic constants in the function\n$f(T)$, the emission line ratio becomes:\n\n\\begin{equation}\n{I_{CIV}\\over I_{Ly\\alpha}} = { \\zce n_H \\eta_{CIV} \\over n_H y_{HII}} f(T) \\label{eqemi}\n\\end{equation}\n\n\\noindent where $n_H$ is the total hydrogen density, \\zce\\ the carbon\nabundance relative to H of the emission gas, $\\eta_{CIV}$ the\nfraction of triply ionized C and $y_{HII}$ the ionization fraction of\nH. \n\nThe ratio of column densities \\nhi/\\nciv\\ can be written as:\n\n\\begin{equation}\n {N_{HI} \\over N_{CIV}} = { n_H\nx_{HI} \\over \\zca n_H \\eta_{CIV} } \\label{eqabs}\n\\end{equation}\n\n\\noindent where $x_{HI}$ is the neutral fraction of H inside our\nhomogeneous slab and \\zca\\ the carbon abundance of the {\\em absorption}\ngas. As we are testing the case which equates the absorption gas with the\nemission gas, then $\\zca=\\zce$. We denote as \\gamc\\ the product of\nthe two calculated ratios:\n\n\\begin{equation}\n\\gamc = {I_{CIV}\\over I_{Ly\\alpha}} {N_{HI} \\over N_{CIV}} =\n{ x_{HI} \\over y_{HII} } f(T) \\label{eqstd}\n\\end{equation}\n\n\\noindent We note that \\gamc\\ is not directly dependent on either \nthe abundance of C or on its ionization state. It is, however,\ndependent on the temperature and on the ionization state of H through\nthe ratio\\footnote{For all practical purposes, the high ionization\nregime under consideration implies that $y_{HII} = 1$.} ${ x_{HI}\n\\over y_{HII} }$. To compute\nthis ratio, it is necessary to postulate an excitation mechanism. For\nthis purpose, we have used the code \\map\\ (Binette, Dopita \\& Tuohy\n1985; Ferruit et~al 1997) to compute ${ x_{HI} \\over y_{HII} }$ under\nthe assumption of either collisional ionization or\nphotoionization. Here are the results.\n\n\\begin{enumerate}\n\n\\item{\\it Photoionization.}\nPutting in the atomic constants and calculating the equilibrium\ntemperature and ${ x_{HI} \\over y_{HII} }$ in the case of\nphotoionization by a power law of index $\\alpha$ ($F_{\\nu} \\propto\n\\nu^{\\alpha}$) of either $-0.5$ or $-1$, we find that the calculated \n\\gamc\\ always lies within the range 0.8--12. The explored range in\nionization parameter\\footnote{We use the customary definition of the\nionization parameter $\\up\\ = \\varphi_H/n_H$ as the ratio between the\ndensity of ionizing photons (impinging on the slab) and the total H\ndensity at the face of the slab.} \\up\\ covered all the values which\nproduce significant \\civ\\ in emission (${\\civ}/C > 8$\\%), that is\n$10^{-3.5} < \\up\\ < 10^{-1}$.\n\n\\item{\\it Collisional ionization.}\nIn this sequence of models, we calculated the ionization equilibrium\nof a plasma whose temperature varied from 30\\,000\\,K to 50\\,000\\,K.\nWe find that \\gamc\\ remains in the similar low range of 6--13. At the\nlower temperature end, \\lya\\ emission is enhanced considerably by \ncollisional excitation, which contributes in reducing \\gamc.\n\n\\item{\\it Additional heating sources.} To cover the case of\nphotoionization at a higher temperature than the equilibrium value\n(due to additional heating sources such as shocks), we artificially\nincreased the photoionized plasma temperature to 40\\,000\\,K or\n50\\,000\\,K for calculations with the same values of \\up\\ as\nabove. This did not extend the range of \\gamc\\ obtained.\n\n\\end{enumerate}\n\nWe conclude that for the simple one-zone case, \\gamc\\ consistently remains\nbelow the observed value by more than two orders of magnitude.\n\n \n\n\\begin{figure} %macro col in ico.sm \n\\resizebox{\\hsize}{!}{\\includegraphics{luc1000.f5}}\n\\caption[]{{\\bf a:} Calculated and observed \\gamb\\ as a function\nof the column density \\nciv. The filled circle represents the observed\nvalue for 0943--242. {\\bf b:} The same models as a function of the\ncolumn ratio \\nhi/\\nhii. In both panels, the solid line represents a\nsequence of photoionized slabs with \\up\\ increasing from left to\nright, starting at $10^{-2.5}$. The gas total metallicity is either\nsolar ($Z=1$) or 1/50th solar. The separation between tick marks\ncorresponds to an increment of 0.25\\,dex in \\up. All slab\ncalculations were truncated at a depth corresponding to the observed\n$\\nhi = 10^{19}\\,\\cms$. The slab total column or $\\nhii$ can be\ninferred from panel~b. [If we were to reduce by 100 the abundance of\nthe absorption gas while keeping solar the emission gas ($\\zca/\\zce =\n0.01$, see Eqs~\\ref{eqemi} and \\ref{eqabs}), this would be equivalent\nto translating by 2\\,dex both up and to the left the $Z=1$ sequence of\npanel~a.] The dotted line represents a sequence of slabs of arbitrary\nuniform temperatures (all with $\\up = 10^{-2}$ and $Z=1$) covering the\nrange 10\\,000\\,K to 40\\,000\\,K (from left to right) by increments of\n0.1\\,dex in $T$. The open triangle represents a slab photoionized by\na high velocity shock of \\vs\\ = 500\\,\\kms\\ from Dopita \\& Sutherland\n1996. }\n\\label{omeg}\n\\end{figure} \n\t\n\n\\subsection{The ionization stratified slab} \\label{upseq}\n\nTo verify whether a stratified slab geometry might alter the above\ndiscrepancy in \\gam, we have calculated in a similar fashion to\nBergeron \\& Stasi\\'nska (1986) and Steidel (1990b) the internal\nionization and temperature structure of a slab photoionized by\nradiation impinging on one-side (i.e. one-dimensional ``outward only''\nradiation transfer) using the code \\map. We adopted a power law of\nindex $\\alpha =-1$ as energy distribution. Since the column densities\nof H and C are useful diagnostics on their own right, we present in\nFig.~\\ref{omeg} the value of \\gamb\\ for a slab as a function of \\nciv\\\n(left panel) and \\nhi/\\nhii\\ (right panel). (One can interpret\n\\nhi/\\nhii\\ of Panel~b as the mean neutral fraction of the slab:\n$\\left<{x_{HI} / y_{HII}}\\right>$.)\n\nThe solid line in Fig.~\\ref{omeg} represents a sequence of different\nslab models with increasing ionization parameter from left to right\ncovering the range $10^{-2.5} \\le \\up \\le 10^{-1}$ for a gas of either\nsolar metallicity ($Z=1$) or with a significantly reduced metallicity of\n${1}/{50}$th solar. The practical constraint that \\civ\\ be a strong\nemission line implies that $\\up \\ge 10^{-2.5}$. In all calculations,\nthe thickness of the slab is set by the observable condition that\n$\\nhi = 10^{19}\\,\\cms$.\n%(The abscissa of panel $b$ can be used to derive the \n% corresponding \\nhii\\ of the slab.) \nInterestingly, such parameters result in a slab which in all cases is\n``marginally'' ionization-bounded with less than 10\\% of the ionizing\nphotons {\\it not} absorbed.\n\nThe monotonic increase of the \\nciv\\ column with \\up\\ is in part due\nto the increasing fraction of \\civ\\ but mostly it is the result of the\nslab getting thicker (larger \\nhii\\ at constant \\nhi) since $x_{HI}$\ndecreases monotonically throughout the slab with increasing \\up. The\nslope or curvature of the two solid lines reflect changes in the\ninternal temperature stratification of the slab with increasing \\up.\nBecause of the dependence of \\gamc\\ on $T$ (see Eq.~\\ref{eqstd}),\nthere exists an indirect dependence of \\gamc\\ on the {\\it total}\nmetallicity given that the equilibrium temperature is governed by\ncollisional excitation of metal lines (when $Z \\gg 0.005$).\n\nThe striking result from the slab calculations in Fig.~\\ref{omeg} is\nthat the models with solar metallicity are still two order of\nmagnitudes below the observed \\gamo. Another way of looking at this\ndiscrepancy is to consider separately the ${I_{CIV}\\over\nI_{Ly\\alpha}}$ emission ratio or the ${N_{HI} \\over N_{CIV}}$\ncolumn ratio. Forgetting \\gam, just to achieve the observed column of\n\\nciv\\ ($10^{14.5}$ \\cms), one would have to use a gas metallicity\nbelow solar by a factor $\\ga 50$ (see sequence with $Z=0.02 \\zsol$),\nwhich cannot be done without irremediably weakening the \\civ\\ {\\it\nemission} line to oblivion. Alternatively, reducing \\up\\ much below\n$10^{-2.5}$ in the solar case can reproduce the \\nciv\\ column but again the\n\\civ\\ {\\it emission} line would be totally negligible.\n\nMight the observed ${I_{CIV}\\over I_{Ly\\alpha}} = 0.17$ emission line\nratio be anomalous? This is not the case as the observed value in\n0943--242 is typical of the value observed in others HZRG without, for\ninstance, any evidence of dust attenuation of \\lya. This ratio is also\nthat expected from photoionization models if a sufficiently high value\nof \\up\\ is used (Villar-Mart\\'\\i n et~al. 1996).\n\nAnother possibility to consider is the presence of other heating\nsources such as shocks which would increase the temperature above the\nequilibrium temperature given by photoionization alone.\nAlternatively, small condensations in rapid expansion would result in\nstrong adiabatic cooling and the temperature would be less than given\nby cooling from line emission alone. To explore such cases, we have calculated\nvarious isothermal photoionized slabs of different (but uniform)\ntemperatures (all with $\\up = 10^{-2}$). They cover the range\n10\\,000--40\\,000\\,K and are represented by the dotted line in\nFig.~\\ref{omeg}. These models are in no better agreement with respect\nto \\gamo. (Varying \\up\\ for any of these isothermal temperature slabs\nwould result in an horizontal line). We also computed \\gamc\\ for a\nsolar metallicity (precursor) slab submitted to the ionizing flux of a\n$500\\,\\kms$ photoionizing shock (Dopita \\& Sutherland 1996). This\nmodel which is represented by an open triangle in Fig.~\\ref{omeg} does\nnot fare better than the power law photoionization models.\n\n\\section{Discussion} \\label{discussion}\n\n\\subsection{Interpretation of the large \\gamo\\ } \\label{intergam}\n\nWhat is the significance of the obvious discrepancy between models and\nthe observed \\gam? Clearly, the working hypothesis that the emitting\nand absorption gas phases are physically the same, is now ruled out\nand an alternative explanation must be sought for, based on our result\nthat the two gas phases (absorption vs. emission) are physically\ndistinct. We consider the two following explanations in\nSect.~\\ref{large} and \\ref{twophase}.\n\n\\subsubsection{The absorption gas is metal-poor and further out.} \\label{large}\nSince the absorption gas in this picture is not spatially associated\nwith the emission gas, its metallicity is unconstrained. It turns out\nthat the value of $\\gamc\\ \\simeq 5400$ is easily reproduced by simply\nusing $\\zca/\\zce\\ \\sim 0.005$ in the one-zone case (see\nEqs~\\ref{eqemi} and \\ref{eqabs}). The more rigorous stratified slab\ngeometry would favor a value of $\\zca/\\zce\\ \\sim 0.01$ to reproduce\nthe same \\gam, assuming both gas phases to have equal excitation.\nCan we disentangle the absolute abundance values? We cannot rely on\nthe emission spectra alone to derive a precise and independent value\nfor \\zca\\ as the emission lines are very model-dependent, with fluxes\nfrom lines like \\civ\\ depending critically on the temperature. It can\nrealistically be argued, however, that a\n\\zce\\ less than half solar could {\\it not} reproduce the observed metal line\nratios. On the other hand, a \\zce\\ much higher than solar cannot be\nruled out in absence of direct knowledge of the ionizing continuum\ndistribution. We consider more plausible a near solar value for \\zce\\\non the ground that the extended emission lines extend over 13\\,kpc and\ntherefore sample a huge galactic region very distinct from that of the\nnucelar BLR (hidden here) which has been shown to be ultra-solar in\nhigh $z$ QSOs (Hamann \\& Ferland 1999 and references therein). An\nattempt, on the other hand, to model separately the absorption columns\nobserved in 0943--242 as described below in Sect.~\\ref{metal} is more\ndependable since temperature is much less of an issue. The value\ninferred below of $\\zca \\sim 0.01 \\zsol$ is consistent with those observed\nin absorbers of comparable redshift along the line of sight of more\ndistant QSOs (Steidel 1990a). Since measured galactic metallicity gradients\nare always negative and a function of the distance to\nthe nucleus, such a contrast in metallicity between absorption and\nemission gas makes more sense if the absorption gas is located much\nfurther out than the emission gas which extends to at least 13\\,kpc in\n0943--242.\n\nWe emphasize that this scenario does not entail that the absorption\ngas does not belong to the environment of the parent\nradio galaxy. As argued by vO97, the high frequency of\ndetection of \\hi\\ aborbers in 9 out of 10 radio galaxies {\\it smaller}\nthan 50\\,kpc, much in excess of the density of absorbers along any\nline of sight to distant QSOs, is a compelling argument for concluding\nthat the absorption gas is spatially related to the parent galaxy. Our\npostulate is that the large scale \\hi\\ {\\it absorption} gas\nis the same gas which is seen instead in {\\it emission} in those radio\ngalaxies with \\lya\\ sizes {\\it larger} than 50\\,kpc. In effect,\nabsorption troughs are not seen when the emission gas extends beyond\n50\\,kpc. Such objects in general also have much larger radio sizes \nas shown by vO97. Kinematically, the gas which is seen in emission at the\nlargest spatial scales shows narrow FWHM. For instance a reresentative case is\nthe radio galaxy 1243+036 ($z_e=3.57$) which was studied in great\ndetail by van Ojik et~al. (1996) and which reveals the presence of\nvery faint \\lya\\ emission extending up to 136\\,kpc, a region labelled\n``outer halo''. This emission gas has a FWHM of 250\\,\\kms\\ and shows\nclear evidence for rotational support.\n\nA straightforward explanation of why the same gas is seen in emission\nin some objects while in absorption in others might simply be the\nenvironmental pressure. A larger pressure, like the one adopted by\nvO97 can cause the warm gas to condense and hence reduce his filling\nfactor as compared to similar gas components in a low pressure\nenvironment. Due to this process, high pressures and consequently\nhigh densities lead to detectable \\lya\\ since emissivities scale\nproportionally to $n_H^2$, but also to an overall smaller covering\nfactor (hence no detectable absorption) while low pressures lead to\nlarge covering factors (hence absorption) as well as negligible\nemissivities. Differences in pressure in the outer halo would therefore\nnaturally account for the reported dichotomy of detecting\n\\hi\\ troughs exclusively in those emission \\lya\\ objects devoid of\nvery large scale emission ($\\la 50$\\,kpc)\n\nSince absorption troughs tend to be absent in radio galaxies showing\nthe largest radio scales, we propose that the gas which is seen in\nabsorption must lie {\\it outside} the zone of influence of the radio\njet cocoon, a region with pressure of order\n$10^{6}\\,\\kcmc$ (vO97). An unpressurized outer halo responsible for\nthe absorption troughs ought to precede the regime in which the radio\nmaterial has expanded sufficiently outward to pressurize the outer\nhalo. The eventual increase in environmental pressure would either\ndisrupt the gas or compresses it into small clumps (making it\nunobservable in absorption when the covering factor dwindles),\nwhich becomes visible in emission if it lies within the ionizing\ncone. vO97 assumed that the absorption and emission gas were\nboth immersed in zones of comparable surrounding pressure ($n_{\\rm H}\nT \\sim 10^6$ \\kcmc) and were therefore of comparable density ($\\sim\n100$\\,\\cmc\\ for a photoionized gas). We propose instead that whenever\naborption troughs are observed, the absorption gas must lie outside the\nradio jet cocoon, allowing for a lower density and high covering\nfactor.\n\n\nThe clear-cut advantages of locating the \\hi\\ absorber \nin an unpressurized outer halo are threefold:\n\\begin{enumerate}\n\n\\item We can now get the high excitation of the low density absorption\ngas for free. In effect, if the density of the absorption gas is as\nlow as $10^{-3}$--$10^{-2}$\\,\\cmc, the metagalactic background\nradiation suffices to photoionize the absorption gas to the high\ndegree observed in 0943--242, whether it does or does not lie within\nthe ionizing cone of the nucleus. Conversely, for the objects devoid\nof absorption, when a higher pressure has set in in the outer halo (as\nwe presume to be the case in 1243+036), the gas is much denser and can\nbe seen in emission only if it lies whithin the ionizing cone (since a\nhigh density gas of $\\sim 100$\\,\\cmc\\ cannot be kept highly ionized by\nthe background metagalactic radiation). This picture would be in\naccord with the findings of van Ojik et~al. (1996) who detect \\lya\\\nin emission in 1243+036 only along the radio axis (presumably the same\naxis as that of the ionizing radiation cone) and {\\it not} in the\ndirection perpendicular to it.\n\n\\item The much smaller velocity dispersion ($b \\simeq 45\\,\\kms$) of the\nabsorption gas as compared to the emission gas (FWHM$/2.35 \\simeq\n600\\,\\kms$, cf. Table~\\ref{ewciv}) is more readily explained if the\nabsorption gas lies undisturbed at relatively large distances from the\nparent galaxy.\n\n\\item It explains why the absorption (yet ionized) \ngas in 0943--242 is not seen in emission while being more massive than\nthe inner emission \\lya\\ gas observed within 13\\,kpc. In effect, the\nmass of ionized gas either in emission or absorption around 0943--242\ninferred by vO97 are $1.4 \\, 10^8 \\, \\msol$ and $ 10^7 ({ x_{HI} /\ny_{HII} })^{-1}$ \\msol, respectively. Adopting the conservative value\nof $\\left<{x_{HI} / y_{HII}}\\right> \\simeq 0.03$ (cf. panel~b in\nFig.~\\ref{omeg}), the total ionized mass of the absorption ionized gas\ntherefore exceed that of the inner emission gas by at least a factor\ntwo and yet it is not seen in emission! This huge pool of ionized gas\ncan remain undetectable in emission only if it has a very low\ndensity, as argued above. It is customary to assume a volume filling\nfactor of $10^{-5}$ for the gas detected in emission in radio galaxies\nand that this gas is immersed in a region characterized by a pressure\nof order $10^{6}\\,\\kcmc$ (vO97; van Ojik 1996). If we suppose\ninstances where the outer halo has much lower pressure than this, it\ncan be shown that for the same outer halo mass, the luminosity in\n\\lya\\ would scale inversely to the volume filling factor. Hence, the gas\nwould be weaker in emission by a factor of $10^{-5}$ if its filling\nfactor approached unity (with the mean density being lower by the same\namount). This scheme would easily explain why the outer halo of\n0943--242 is not seen in emission despite its huge mass (comparable\nincidentally to the outer halo mass measured in emission in 1243+036 of\n$2.8 \\, 10^8 \\, \\msol$ by Ojik et~al. 1996).\n\n\\end{enumerate}\n\n\n%%%%%%% other hypothesis\n\\subsubsection{A two-phase gas medium} \\label{twophase}\nDue to radiative cooling (which goes as $n_H^2$ and rise steeply with\n$T$), density enhancements can condense out of the emitting gas and\nform a population of about 100 times denser and 100 times cooler\nclouds in pressure equilibrium with the ambient medium. If we\nmaintain that the pressure characterizing the absorption and the\nemission gas is comparable ($\\sim 10^6\\,\\kcmc$) and that either gas\nphase has a temperature typical of photoionization, $T\\sim 10^4 \\,$K,\nwe obtain (adopting a similar notation to vO97 but adapted to the case\nof 0943--242) that the size and the number of small {\\em homogeneous}\nabsorbing condensations required to cover the emission region would be\n$0.85 r_{03} \\,$pc and $2.4 \\, 10^8 r_{03}^{-2} $ clouds,\nrespectively, where $r_{03} = 0.03~~~$ $\\times \\left<{x_{HI} /\ny_{HII}}\\right>^{-1}$ [as above we adopt 0.03 as the reference neutral H\nfraction]. Can we find an alternative interpretation to (1) above for\nexplaining the large \\gamo\\ that does not require low metallicities\nfor the absorption gas? Such a possibility would arise if the \\nhi\\\ncolumn was not directly related to the \\nciv\\ column. For instance, in\nthe auto-gravitating absorber model of Petitjean et~al. (1992), which\nconsists of a self-gravitating gas condensation with a dense neutral\ncore surrounded by photoionized outer layers, could in principle give\nratios between columns of \\hi\\ and \\civ\\ which do not reflect the\nabundance ratio but represents rather the average impact parameter for\nour line of sight. Of course, these models have to be rescaled to a\npressure of $n_{\\rm H} T = 10^6\\,\\kcmc$ implying much smaller sizes\nbut requiring much higher ionizing fluxes (both by a factor $\\sim 10^4$). \nThis rescaling poses no conceptual problems if we\nassume that the photoionization is by the central AGN. \nUsing their Figures and Table~4 (Petitjean\net~al. 1992), we infer that the number of auto-gravitating\ncondensations needed to achieve a covering factor of unity and a mean\n\\hi\\ column of $10^{19}\\,\\cms$ would have to be large, in excess\nof $10^{9.5}$, for instance, for the model C$^{10}_{7000}$. However,\nafter inspection of the various \\nciv\\ columns derived from their\nextensive grid of models, we did not find any model which would\nreproduce the observed \\civ\\ column without having a metallicity $\\le\n0.1 \\zsol$. The gain in $Z$ is therefore insufficient to get $\\zca\\\n\\simeq \\zce\\ > 0.5$ and we conclude that this explanation for a high\n\\gamo\\ is unworkable.\n\n\\subsection{Metallicity determination of the absorption gas} \\label{metal}\n\nOur favoured interpretation of the large \\gamo\\ is that the absorption\ngas is of very low metallicity compared to the (inner/denser) emission\ngas. Furthermore, a close parallel in the physical conditions of the\nabsorption gas could be made with those adopted for the study of QSO\nabsorbers (e.g. Steidel 1990a,b; Bergeron \\& Stasi\\'nska 1986),\nnamely the densities, the metallicities and the excitation mechanism\n(photoionization by a hard metagalactic background radiation). The\nobserved \\nhi\\ column of $10^{19}\\,\\cms$ would position the 0943--242\nabsorber in the category of ``Lyman limit system'' according to\nSteidel (1992). The coincidence in physical conditions might be\nfortuitous and it does not imply per\\,se a common origin or\ncorrespondance between QSO absorbers and outer halos of radio\ngalaxies. Under the sole assumption of similar physical conditions,\nwhat estimate of the metallicity can we derive for C? From the\n\\nciv/\\nhi\\ ratio, we cannot determine the ionization parameter and\ntherefore directly apply the results and models of Steidel (1990b) who\ndetermined for each Lyman limit system a probable range of \\up\\ from\nupper limits or from measurements of other species than \\civ. It is\nnevertheless reasonable to assume that the excitation degree in\n0943--242 is comparable to that encountered in high excitation QSO\nabsorbers. To determine an appropriate value for \\up, we adopted the\nset of data provided by the three Lyman limit systems observed in the\nspectrum of the QSO HS1700+6416 by Vogel \\& Reimers (1993) who\nsuccessfully measured the columns of up to 3--4 ionization species of\neach of the three elements C, N and O. Amongst our $\\alpha =-1 $\nmodel sequence (Sect.\\,\\ref{upseq}), we selected the model which had\nthe same \\up\\ ($\\simeq 0.007$) as Vogel \\& Reimers (1993) and inferred\nthat the observed columns in 0943--242 implied that the Carbon\nmetallicity of the absorption gas was 1\\% \nsolar (that is C/H $\\sim 4 \\, 10^{-6}$), which is broadly \nconsistent with the range of \\zca\\ values favored in\nSect.\\,\\ref{large}.\n\n\\subsection{Mean density and cloud sizes}\n\nWhat would be the minimum density assuming the absorption gas to be\nuniformly distributed? If our proposed picture was correct, a\nrepresentative size for the absorption gas volume is that given by the\nouter halo as seen in emission in other HZRG. Let us adopt the value\nmeasured for 1243+036 by van~Ojik et~al. (1996) of 136\\,kpc. Assuming\nthe same mean ionization parameter as used above (0.007), we derive a\ntotal gas column of $\\nh = \\nhii \\simeq 10^{21}\\,\\cms$. Hence\nthe mean density for a volume filling factor unity on a scale of the\n1243+036 outer halo would be $\\simeq 2 \\, 10^{-3} \\,\\cmc$ which is a value\nsufficiently low to allow photoionization by the feeble ionizing\nmetagalactic background radiation.\n\n\\subsection{Comparison with the metallicity of BAL QSOs}\n\nOur estimate of the metallicity for the outer halo of 0943--242 is at\nodds with the super-solar metallicities (e.g. Hamann 1997, Papovich\net~al. 2000) of the ``associated'' absorbers seen in high redshift\nQSOs. The QSO emission gas itself (the BLR) is similarly characterized\nby super-solar metallicities (cf. Hamann \\& Ferland 1999 and\nreferences therein). If we consider QSOs and HZRG as equivalent\nphenomena observed at different angles, it may appear at first\nsurprizing that the metallicities of the absorption components are so\ndifferent. However, we show below that this contradiction is only\napparent as we are probably dealing with totally different gas\ncomponents.\n\n\\begin{enumerate}\n\\item {\\it Kinematics.} The HZRG large scale absorbers \nare kinematically very quiescent. In effect, the modulus of the\nvelocity offset between the absorbers and the parent galaxy is usually\nless than 400\\,\\kms\\ for the dominant absorber (vO97)\\footnote{Highly\nblueshifted P-cygni profiles are now known to exist in\nradio galaxies with $z \\ge 3.5$ (Dey 1999).}. A substantial\nfraction of HZRG absorbers are actually infalling (Binette\net~al. 1998). This is far from being the case for QSO ``associated''\nabsorbers whose ejection velocities can extend up to many thousands\n\\kms\\ (Hamann \\& Ferland 1999). For instance, the two associated\nsystems (with detected metal lines) recently studied by Papovich\net~al. (2000) are blueshifted by 680 and 4900\\,\\kms, respectively.\n\n\\item {\\it Selection effect.} \nQSOs are spatially unresolved with a size of the source light beam\nless than a few light-weeks across. In the case of HZRG absorbers, the\nbackgound source is the emission gas which extends over a scale $\\sim\n35$\\,kpc. This huge difference in scale results in a totally different\nbias on what is preferentially observed. In effect, the extended\nabsorbers of HZRG are weighted towards the largest volumes and hence\ntowards the most massive gas components (the total mass of the\nabsorption component exceeds $10^8 \\, \\msol$ in 0943--242). By\ncontrast, in the case of QSO associated absorbers, the mass of gas\ndirectly seen in absorption is tiny (e.g. $\\sim 4 \\, 10^{-6} \\,\\msol$\nif one considers a background light beam one light-month diameter and\na total gas absorption column of $10^{18}\\,\\cms$).\n%Interestingly, for {\\it both} the HZRG and the QSOs, such masses\n%represent lower limits since the absorber in either case is likely to\n%extend beyond the size of the background source.\n\n\\item {\\it Coexistence with the BLR.} \nTo the extent that QSO associated absorbers represent gas components\nexpelled from the BLR, we should not be surprized that their\nmetallicity turn out comparable to the BLR. Given that in HZRG we do\nnot directly see the pointlike AGN, we cannot expect to see any BLR\ncomponent in absorption. As for the extended gas detected in HZRG,\nthere exists no evidence in favour of super-solar metallicities on\nlarge scales $> 10$\\,kpc\\ (\\nv\\ when detected is strong only in\nthe nucleus)\n%If we take the example of 0943--242, there is no evidence of over-solar \n%abundances since \\nvw\\ is less than 10\\% of \\lya\\ (cf. Fig.~2 in RO95). \nIf a fraction of associated absorbers correspond to\nintervening galaxies close to the QSO, we might expect to see amongst\ncounterpart HZRGs one or more \\civ\\ or\n\\lya\\ absorbers of small spatial extent relative to the size of the extended\nemission gas. The weak \\hi\\ absorption found by Chambers\net~al. (1990) in 4C41.17 might be such occurrence given its partial\ncoverage of the \\lya\\ background.\n\\end{enumerate}\n\nWe conclude that HZRG absorbers, when their size is comparable to\ngalactic halos (as those found by vO97), have probably little to do\nwith QSO associated absorbers. A more suitable analogy to the\nabsorption gas of HZRG is that of the Francis cluster of galaxies at\n$z=2.38$ which is characterized by large scale absorption gas on a\nscale of $\\ga 4$\\,Mpc (Francis et~al. 2000).\n\n\n\\subsection{Constraints on radio galaxy evolution}\n\nThe size of the radio source can be used as a clock that measures the\ntime elapsed since the start of the radio activity. A number of\nobserved characteristics of distant radio galaxies change as a\nfunction of radio size, -- ie. as function of time elapsed\n(cf. R\\\"ottgering et~al. 2000). For $z\\sim 1$ 3CR radio\nsources, these include optical morphology (Best et~al. 1996),\ndegree of ionisation, velocity dispersion and gas kinematics (Best\net~al. 2000). At higher redshifts ($z>2$), only the smaller radio\ngalaxies are affected by \\hi\\ absorption (vO97). \nAll these observations seem to dictate an evolutionary scenario in\nwhich the radio jet has a dramatic impact on its environment while\nadvancing on its way out of the host galaxy (Rottgering et~al. 2000,\nBest et~al. 2000). \n\n\\section{Conclusions} \\label{conclusions}\n\nThe detection of \\civ\\ absorption in radio galaxy 0943--242 at the\nsame redshift as the deep \\lya\\ trough observed by RO95 demonstrates\nthat the detected absorption gas is highly ionized. Having assumed\nthat the \\hi\\ and \\civ\\ columns measured from the Voigt profile\nfitting were representative of the dominant gas phase (by mass) in the\nouter halo, we have effectively ruled out that the absorption and\nemission gas occupy the same position in 0943--242. We subsequently\nreassessed the picture proposed by vO97 in which both the large scale\nemission gas and the absorption gas were of comparable density ($n_H\n\\sim 100\\,\\cmc$). In the former picture, the absorption gas was\nbelieved to lie outside the AGN ionization bicone (see their Fig.~11\nin vO97). To ionize the gas to such a degree without using the AGN\nflux is problematic. We have proposed an alternative picture in\nwhich the absorption gas is of very low metallicity and lies far away\n(in the outer halo) from the inner pressurized radio jet cocoon.\nSince in this new scheme the density of the absorption gas is expected\nto be very low, the metagalactic background radiation now suffices to\nphotoionize it. Furthermore, the structure of the absorption gas is\nnow drastically simplified since we do not need over $\\sim 10^{10}$\ncondensations of size $\\sim 1$pc and density $\\sim 10^2\\,\\cmc$ to\nreach a covering factor close to unity. We can now reach similarly\nhigh covering factor using a single or few shells of very low density\nwhich have a volume filling factor close to unity (assuming a density\nof $\\sim 10^{-2.5}\\,\\cmc$).\n\nIt appears to us that the low metallicity inferred ($Z \\simeq 0.01\n\\zsol$) and the proposed location of the absorption gas in 0943--242\n--outside the radio cocoon, in an outer halo which is seen in\nemission in other radio galaxies (as in 1243+036)-- strongly suggest\nthat the absorbers' existence precedes the observed AGN phase. Unless\nthis non-primordial gas has been enriched by still undetected pop III\nstars, we consider that it more likely corresponds to a vestige gas\nphase expelled from the parent galaxy during the initial starburst at\nthe onset of its formation.\n\nIf the \\civ\\ doublet was detected in absorption in other radio\ngalaxies with deep \\lya\\ absorption troughs, there are many aspects\nwhich would be worth studying. For instance, how uniform is the\nexcitation of the absorption gas across the region over which it is\ndetected? Is a single phase sufficient? This could be tested by an\nattempt to detect absorption troughs of \\mgiiw\\ or imaging the troughs\nin \\civ\\ with an integral field spectrograph on an 8-m class\ntelescope. How different is the metallicity of the absorption gas in\nthe other radio galaxies? The information gathered could then be used\nto infer the enrichment history of the outer halo gas which surrounds\nHZRG.\n\n\n\\begin{acknowledgements}\nWe are grateful for the referee's comments which raised many\ninteresting issues we had overlooked. We thank Richard Hunstead and\nJoanne Baker for taking part in the observations. 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E. 1999, A\\&A in press\n\n\n\\bibitem[\\protect\\citename{Vogel \\& Reimers} 1993]{vore93} \nVogel, S., Reimers, D. 1993, A\\&A 274, L5\n\n\\bibitem[\\protect\\citename{Vogel \\& Reimers} 1995]{vore95} \nVogel, S., Reimers, D. 1995, A\\&A 294, 377\n\n\\bibitem[\\protect\\citename{Webb} 1987]{webb} \nWebb, J. 1987, PhD thesis, University of Cambridge (UK)\n\n\n\\end{thebibliography} \n\\end{document}\n\n\\end{document}\n\n\n%%%%%%%%%%%%%%%%%%%%% cut out but usefull text to keep %%%%%%%%%%%%%%%%%%%\n\n%on the hi gas in general\nThe absorbers are intrinsic to the HZRG and the \\hi\\ masses are\nestimated by vO97 to lie in the range $\\sim 10^7 - 10^8 \\msol$. For\nthe main absorbers with \\hi\\ columns $> 10^{17}$\\,\\cms, the velocity\noffset between the absorption troughs and the emission gas is $\\la\n400\\,$\\kms\\ as shown in Fig.~\\ref{figoffset}.\n\n\\begin{figure} %macro col in ico.sm \n\\resizebox{\\hsize}{!}{\\includegraphics{luc1000.f5}}\n\\caption[]{Ejection velocity \\hi\\ gas according to its \\hi\\ column\n(data from van~Ojik \\etal\\ 1997). Different parent radio galaxies are\nrepresented by different symbols.}\n\\label{figoffset}\n\\end{figure} \n\n\n%on bicones\nIn the later case, the orientation of the putative ionizing cones\n(lying suposedly near the plane of the sky) would explain the weakness\nor absence of a strong nuclear underlying UV continuum. \n\n%other way to talk about equivalence of abs and emis.\nvan~Ojik \\etal\\ has argued that the gas responsible of the \\hi\\ absorption\nthroughs in 18 HZRG of their sample was ionized rather than neutral, with an\n\\hi/\\hii\\ ratio $\\le .25$. Obviously, the observation in 0943--242 of\n\\civ\\ in absorption not only confirms their interpretation but also suggests\nthat the absorption gas is rather highly ionized, possibly to a similar\ndegree as the emission gas.\n\n%on the velocity field\nIf we consider that the velocity field increases towards the nucleus\nfor the gas as for the stars, this difference in kinematics might be\npartly the result of a geometrical selection effect in the sense that\nthe {\\it emission} gas tends to be biased towards the brightest\nemission region towards the nucleus (with large FWHM) while the {\\it\nabsorption} gas is more likely to be contrasted against emission when\nit is situated in our direction further out from the nucleus (at the\nperiphery of the emission region) where the velocity field is on\naverage more quiescent.\n\n%on column of ionized gas\n\\footnote{The electron column density of an ionization bounded slab is \n$N_e \\sim 10{23}\\,$\\cms.}\n\n%on what the HZRG gas is NOT\n\\subsection{The velocity field of the emission gas} \\label{velo}\n\nIt is important at this point to clarify what the absorption gas {\\it\nis not} and point out in which way the phenomenon referred to here\ndistinguishes itself from the realm of lower redshift galaxies. First,\nthe absorption troughs in the vO97 sample of HZRG {\\it cannot} be\nstellar in origin as the underlying continuum is comparatively very\nweak. The absorption troughs clearly occur at the expense of the\nbroader emission lines. Second, the absorption gas belongs to the\nenvironment of the parent radio galaxies and is therefore not just a\nchance interloper absorber at a random redshift between us and the\nHZRG (see vO97). To the extent that the absorption gas {\\it density}\nindirectly inferred by vO97 is correct, the metagalactic background\nradiation is much too weak to be responsible for its ionization. As\nfor the kinematics of the gas, vO97 generally found a rather smooth\ngaussian-like kinematic for the emission gas after correcting for the\nabsorption troughs when present. This is in contrast with McCarthy\net~al. (1996) who reported complex motions and significant amplitudes\nin velocity differences (across the extended ionized region) in his\nsample of 50 3CR radio galaxies. These differences can be reconciled\nif we consider the following: firstly, the extended ionized regions\nare much larger in the vo97 HZRG sample compared to the intermediate\nredshift 3CR sample of McCarthy et~al. (1996), therefore the HZRG\nbeing bigger might simply contain a much larger numbers of velocity\nkinks which statistically smooth out, secondly, McCarthy et~al. (1996)\nstudied the extended ionized gas with few exceptions through the light\nof non-resonant lines (\\ha, \\oii\\ and \\oiii) while vO97 looked only\nat \\lya. In the case of \\lya, a much smoother and diffuse distribution\nof line photons can be explained by the scattering of \\lya\\ between\nfloating ``debris'' of gas surrounding the bright emission line\nspots. In this case, the emergent spectrum and brightness distribution\nof \\lya\\ would simply reflect the distribution of gas of low\nemissivity surrounding the few regions of strong emission.\n \n%on the multiphase implications on metallicity\nAlternatively, could the homogeneous slab geometry adopted in\nmetallicity studies of QSO absorbers be seriously flawed, in which\ncase the very low metallicities inferred of the absorbers might be\nsignificantly underestimated. For instance, the twophase absorber\nmodel of Petitjean et~al. (1992) which consists of a dense core with\nphotoionized outer layers, a geometry which solves the problem of\nexcess \\hei\\ observed in the $z_a=2.14$ absorber seen in the QSO\nHS~1700$+$6416 spectrum (Petitjean et~al. 1992), leads to a\nmetallicity which is an order of magnitude higher to that originally\ninferred from Vogel \\& Reimers (1995) who used a simple slab geometry.\nIn this respect, the absorption and emission measurements in 0943--242\narguably puts us (as shown below) in an advantageous position for\ntesting whether the standard hypothesis of homogeneity used in the\ndetermination of metallicity from various absorption/emission lines is\ngenerally valid.\n\n%about the HeI problem and the twophase solution\n\\subsection{Two-phase medium and the \\hei\\ problem in HS\\,1700+6416}\n\nThe ratio of absorption columns of \\hi/\\hei\\ from three high-redshift\nabsorbers measured by Reimers \\& Vogel (1993) in the spectrum of the\nQSO HS\\,1700+6416 indicated a value 5--7 times lower than predicted by\nphotoionization (once \\up\\ has been set from fitting the various\nmetallic line columns of C and O). Many interpretations has been\nproposed for this descrepancy (e.g. Viegas \\& Fria\\c ca 1995 and\nreferences therein). Interestingly, a two-phase medium is also one of\nthe solution proposed which reconcile photoionization with the\nobservations as showed Petitjean et~al. (1996). \n\n%section about shocks and their problems\n\\subsection{About shocks vs. photoionization} \\label{shocks}\n\nThe conclusions reached from models of \\gam\\ do not depend on whether\nthe clouds are photoionized by a nuclear source or by a diffuse hot\nhalo or by the radiative cooling of hot coronal gas from very high\nvelocity photoionizing shocks (\\vs $> 200 \\,\\kms$). The common ground\nin all these cases is that the region producing the following strong\nlines of \\civ\\ or \\lya\\ is at (both) ionization and temperature\nequilibrium as this is invariably the case in large scale photoionized\ngas. We have not considered the case of intermediate velocity shocks\n(i.e. not photon dominated) in the range 110-170\\,\\kms\\ where the gas\nis not only collisionally ionized but also out of equilibrium as it\nrecombines and cool. However, the steady flow shock models calculated\nso far do not match well the observations. In effect, while the\nobserved strength of \\heiiuw\\ in HZRG is typically in the range of\nhalf to twice the strength of \\civ\\ (see van~Ojik 1995 or R\\\"ottgering\net~al. 1997), shocks with $\\vs < 200 \\,$\\kms\\ although emitting a\nrelatively strong \\civ\\ result in an \\heii\\ flux weaker by a factor 4\n(e.g. Raymond et~al. 1997). Furthermore, intermediate shock velocities\npredict an \\oiiiuvw\\ line twice stronger than \\heii\\ while the\nopposite is observed: \\oiiiuv\\ is either not observed or is weaker by\na factor 4 (McCarthy 1993). In the case of the absorption gas,\nproblems are encountered as well. The column densities of \\civ\\ in a\nsolar metallicity shock with $\\vs < 200$\\,\\kms\\ is $ \\le 3 \\, 10^{13}$\n\\,\\cms\\ (from our own calculations using \\map\\ or from Raymond\net~al. 1991). It would require a minimum of 8--10 such shocks covering\nuniformly a region in excess of 30\\,kpc to attain the observed value,\nthis appears unrealistic. On the other hand, intermediate velocity\nshocks may be playing an important role in the gas distribution and\nmorphology by pressurizing gas shells and condensations. An\ninteresting possibility is the hybrid shock model with an externally\nimposed nuclear photoionizing field as proposed by Viegas-Aldrovandi\n\\& Contini (1989) and Contini \\& Viegas (1992 and references therein)\nfor the NLR of Seyfert although the shock structure would have to be\nmatter-bounded in order to match the observed small absorption columns.\n\nSteady flow shocks of high velocity as calculated by Dopita \\&\nSutherland (1996 hereafter DS96) can reproduce the observed emission\nlines. The \\lya, \\civ, \\heii\\ lines in this case are generated in the\nphotoionized precursor (by the EUV irradiated by the shock) as well as\ndownstream where a photoionized nebula is generated. To apply such\nmodels to the absorption gas and derive a column $\\nhi =\n10^{19}\\,\\cms$ would require computing a matter-bounded precursor and\nan incomplete shock structure in which only part of the ioinizing\nradiation has been absorbed. In any event, \\gamc\\ would correspond to\nthe slab photoionized case and occupy a similar region as that of such\nmodels in Fig.~\\ref{omeg} as shown by the open triangle in\nFig.~\\ref{omeg}. Using the shock spectral energy distributions of\nTable.~4 in DS96, we have calculated a {\\it rest frame} \\civ\\\nequivalent widths of $\\sim 10^{4.5}$\\AA\\ for their steady flow model\nwith \\vs\\ = 500\\,\\kms. The observed range by van~Ojik et~al. (1997) is\n30--60\\AA. However, such small values do not put a strong constraint on\nany model since the excess continuum observed --unless proven\notherwise-- might be stellar in origin or the result of scattered\nnuclear continuum by dust. Moreover, even for the competing idea of\nanysotropic nuclear photoionization, we expect to see very little\nintrinsic continuum as the beamed radiation is presumed (conveniently)\nto lie on the plane of the sky. One significant objection to\nphotoionizing shocks is the \\oviw\\ catastrophe. In effect, this line\nis a major coolant in any gas freely recombining from temperatures as\nhigh as those foreseen in the DS96 models ($>10^{5.7}$) and is\nexpected to be amongst the strongest lines, comparable even to \\lya!\nIn the models caluclated by DS96, it is predicted to be at least 5--8\ntimes stronger than \\civ, which is never observed. A mean ratio of\nonly $\\simeq 0.5$ is reported for radio galaxies by McCarthy (1993).\n\n%on the excitation mechanism of the emission/absorption gas\n\\subsection{Thermal and ionization equilibrium}\n\nFor the majority of HZRG in which the high excitation emission lines of\n\\civ\\ or \\nv\\ are strong lines, it is generally believed that the excitation\nmechanism is photoionization by a hard ionizing continuum either\ngenerated by high velocity shocks with $\\vs > 200\\, \\kms$ [the\nso-called ``photoionizing shocks'' (see Dopita \\& Sutherland 1996 and\nBinette, Dopita \\& Tuohy 1985)] or from the active nucleus which is\nobscured at optical wavelengths (in our line of sight). In either\ncase, because photoionization is the process ultimately responsible\nfor the emission of the above lines (including \\lya), the emitting\nplasma lies in the regime of thermal and ionization equilibrium which\nprovides an important and useful simplification to the calculations\npresented below. Intermediate velocity shocks (which are therefore not\nphoton-dominated) are by contrast out of equilibrium, a possibility\nnot covered here. For reasons given in Sect.~\\ref{shocks}, such shocks\nare unsuitable for fitting the emission line ratios and, furthermore,\nbecause the plasma in shocks recombine at such a fast rate, they\nalways result in much smaller columns of \\civ\\ than has been observed\nin 0943--242 ($\\nciv = 10^{14.5}\\,\\cms$), for instance. In our\ncalculations, we will consider both the case of equilibrium\ncollisional ionization and of equilibrium photoionization.\n\n \n%on the velocity field of the absorbers\n\\subsubsection{The velocity field}\nIf one considers only the largest absorbers in the vO97 sample which\nhave \\hi\\ columns $> 10^{17}$\\,\\cms, the velocity offset between the\nabsorption troughs and the emission gas is $\\la 400\\,$\\kms, much less\nthan the FWHM of the {\\it emission} \\lya\\ profile of the parent galaxy\nwhich lie in the range 800--1600\\,\\kms. The internal velocity\ndispersion of the absorption gas derived from the \\hi\\ profiles\n(i.e. the Doppler parameter) are quite small, within the range $\\simeq\n9$--80\\,\\kms\\ (with only 3 out of 22 absorbers exceeding this range).\nClearly, a very strong gradient in velocity dispersion of the gas\nwould be required to exist between the denser inner regions and the\nexternal more quiescent gas.\n\n%on the mass of the absorption gas comapred to the emission gas\nInterestingly, a comparable mass of ionized gas is inferred by vO97\nfor both the ionized absorption gas and the emission gas, that is a\nfew $10^8 \\msol$. If \\civ\\ was seen in absorption in all cases, it\nwould imply that the degree of ionization must be very high and,\ntherefore, that the ionized mass of the absorption gas should more\nrealistically approach a few $10^{10} \\msol$. On the other hand, the\nfact that the absorption troughs are deep and reach near zero flux\nimplies that it is not bright in emission. Yet if the absorption gas is\nso massive in ionized gas it implies that it must be of considerably\nmuch smaller density (as we have postulated above) than the emission\ngas otherwise the {\\it absorption} gas would be brighter in emission than\nthe emission gas it is masking. The fact that both components appear\nin 0943--242 to be of comparable excitation and that the absorption gas \nis at least of comparable mass argue to the emission gas argues in\nfavour of a common geometry and excitation mechanism, the underlying\nhypothesis behind the calculations developed below.\n\n%on the effect of a stratified temperature\nThe slab temprature structure determines at each position\nthe ratio ${ x_{HI} \\over y_{HII} } f(T)$ which we have shown in\nEq.~\\ref{eqstd} locally determine \\gamc. \n \n\n%on the multiphase discussion\nIf for instance we suppose that the \\hi\\ gas\nlies within dense cores of gas condensations which are highly ionized\nonly at the surface, then our inference about the metallicity of such\ngas would be systematically wrong since our line of sight would be\nsampling two unrelated gas phases. In this picture, the condensations\nmust have a covering factor approaching unity, not unlike what vO97\nproposed. As for \\civ, the depth of the observed troughs indicates\nthat the covering factor cannot be less than $\\sim 0.3$ while that of\n\\hi\\ is at or near unity.\n\n\n%justification: absorption gas always metal poor while emission gas is \n%enriched\n\nIn principle, being able to see in absorption the same ionization\nspecies as those seen in emission can be used to ascertain not only\nthe ionization state of the gas but also its metallicity. In HZRG in\ngeneral, the strength of the emission lines consistently points\ntowards at least near solar or possibly higher metallicity (Robinson\net~al. 1987, McCarthy 1993, Villar-Mart\\'\\i n et~al. 1996, 1997) although\nunavoidable uncertainties in the model parameters still preclude more\nprecise determination. The picture derived from high $z_a$ intervening\nabsorbers in QSO spectra, however, consistently point towards very low\nmetallicities with C/H a factor of ten or more smaller than solar\n(e.g. Vogel \\& Reimers 1995, Petitjean et~al. 1996). Does this\nsystematic metallicity difference between the emission and absorption\ngas components (which are spatially unrelated in the case of QSO\nabsorbers) repeat itself when comparing gas components belonging to\nthe environment of the same parent radio galaxy? This is one aspect\nguiding the present work.\n\n\n%on the number of dense condensations needed to cover the extended gas\nAs clearly demonstrated by vO97, if both the absorption and emission\ngas phases (both being ionized) are confined by the same pressure\n(from a putative hot phase with $\\sim 10^6\\,\\kcmc$), the combined\nrequirement of $\\nhi \\simeq 10^{17.5-19}$\\,\\cms\\ and of a covering factor\nnear unity for the absorpion gas implies the existence of a an\nextremely large number of condensations (in excess of $10^{10}$ for\n0943--242 and up to $10^{12}$ for the other HZRG). \n\n%introduction: procedure\nAgainst this background we have analyse the \\hi\\ and \\civ\\ absorption\ncolumns observed in 0943--242. In the first part of this paper, we\nwill consider the emission and the absorption gas components are both\nsharing the same excitation mechanism and physical conditions. Having\ncomplementary information about the emission and absorption gas will\nallow us to check whether this assumption is confirmed and if not what\nunderlying assumption in our simple model is most likely to be false.\n\n\n\n% NEW text suggested by Huub\nConstraints on evolution: \nThe size of the radio source can be used as a clock that\nmeasures the time elapsed since the start of the radio activity. A\nnumber of observed characteristics of distant radio galaxies change as\na function of radio size, -- ie. time elapsed.\nFor $z\\sim 1$ 3CR radio these include the optical morphologies (Best\net al. 1996) degree of ionisation, velocity dispersion and gas\nkinematics (Best et al 2000). \\nocite{bes99b}\nAt higher z (z>2) only the smaller rg are afffected by \nHI absorption (van Ojik et al. ) \n\nAll these observations seem to dictate an evolutionary scenario in\nwhich the radio jet has a dramatic impact on its environment while\nadvancing on its way out of the host galaxy (R\\\"ottgering et~al. 1999)\n(this proceedings I send you) Best et al 2000 (First page first issue\nof MN in 2000 !) During its trip through the ISM of the radio galaxy,\nthe radio jets interact violently with the emission line gas, and the\nresulting shocks ionise the gas and stir up the kinematics. As the\nradio source further increases in size, the radio jet clears its path\nand the bow shock at the edge of the cocoon has left most of the ISM\nof the galaxy behind. The shockfront at the outer edge of the cocoon\nionises the neutral gas that was responsible for the HI absorption\nseen in the Ly$\\alpha$ profiles of the smaller sources. As a result,\nthe larger radio sources do not show this absorption.\nThe finding of this paper that there has to exist \na large reservoir of gas outside the emission line region \nis fully consistent with this scenario. \n\n"
}
] |
[
{
"name": "astro-ph0002210.extracted_bib",
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M. 1992, ApJ 401, 481\n\n\n\\bibitem[\\protect\\citename{Best et~al. }1996]{best1996}\nBest, P. N., Longair, M. S., R\\\"ottgering, H. J. A., MNRAS 280, L9\n\n\\bibitem[\\protect\\citename{Best et~al. }2000]{best2000}\nBest, P. N., R\\\"ottgering, H. J. A., Longair, M. S. 2000, MNRAS 311, 23\n\n\\bibitem[\\protect\\citename{Dey }1999]{dey1999}\nDey, A. 1999, in proc. of the KNAW colloquium ``The Most Distant Radio\nGalaxies'' held in Amsterdam on 15-17 October 1997, eds \nP.N. Best and M.D. Lehnert, Amsterdam\n\n\\bibitem[\\protect\\citename{Dopita \\& Sutherland }1996]{ds96} Dopita, M. A.,\nSutherland, R. S. 1996, ApJS 102, 161 (DS96)\n\n\\bibitem[\\protect\\citename{Ferruit \\etal\\ }1997]{febi97} Ferruit P.,\nBinette, L., Sutherland, R. S., P\\'econtal, E. 1997, A\\&A 322, 73\n\n\\bibitem[\\protect\\citename{Francis et~al. }2000]{fran2000} Francis,\nP. J., Wilson, G. M., Woodgate, B. E. 2000, ApJ submitted\n\n\\bibitem[\\protect\\citename{Hamann}1997]{ham97} Hamann, F. 1997, \nApJS 109, 279\n\n\\bibitem[\\protect\\citename{Hamann}1999]{ham99} Hamann, F., Ferland, G. 1999, \nARA\\&A 37, 487\n\n\\bibitem[\\protect\\citename{Jenkins} 1986]{jen86} \nJenkins, E. B. 1986, ApJ 304, 739\n\n\\bibitem[\\protect\\citename{McCarthy}1993]{mc:mc} McCarthy, P. 1993,\nARA\\&A 31, 639\n\n%\\bibitem[\\protect\\citename{McCarthy et~al. }1996]{mls96}\n%McCarthy P. J., Baum S., Spinrad H. 1996, ApJS 106, 281\n\n\\bibitem[\\protect\\citename{Osterbrock}1989]{os:agn} Osterbrock, D.,\n1989, in Astrophysics of gaseous nebulae and active galactic nuclei,\nUniversity Science Books: Mill Valley\n\n\\bibitem[\\protect\\citename{Papovich et~al. } 2000]{papo2000} \nPapovich, C., Norman, C. A., Bowen, D. V., Heckman, T., Savaglio, S.,\nKoekemoer, A. M., Blades, J. 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N., de Breuck, C., Kurk, J.,\nPentericci, L. 2000, in proc. of ``Perspectives in Radio Astronomy:\nscientific imperatives at cm and mm wavelengths'', eds: M. P. van\nHaarlem and J. M. van der Hulst, in press\n\n%\\bibitem[\\protect\\citename{van Ojik}1995]{vO95} van Ojik R. 1995,\n%PhD thesis, Leiden University (The Netherlands)\n\n\\bibitem[\\protect\\citename{van Ojik \\etal\\ }1996]{vO96} van Ojik, R.,\nR\\\"ottgering, H. J. A., Carilli, C. L., Miley, G. K., Bremer, M. N.,\nMacchetto, F. 1996, A\\&A 313, 25 (vO96)\n\n\\bibitem[\\protect\\citename{van Ojik \\etal\\ }1997]{vO97} van Ojik R., \nR\\\"ottgering, H. J. A., Miley, G. K., Hunstead, R. W. 1997, A\\&A\n317, 358 (vO97)\n\n\\bibitem[\\protect\\citename{Steidel} 1990a]{steidela} \nSteidel, C. C. 1990, ApJS 72, 1\n\n\\bibitem[\\protect\\citename{Steidel} 1990b]{steidelb} \nSteidel, C. C. 1990, ApJS 74, 37\n\n\\bibitem[\\protect\\citename{Steidel} 1992]{steidel92} \nSteidel, C. C. 1992, PASP 104, 843\n\n%\\bibitem[\\protect\\citename{Viegas-Aldrovandi \\& Contini }1989]{vi:co} \n%Viegas-Aldrovandi, S. M., Contini, M. 1989, ApJ 339, 689\n\n%\\bibitem[\\protect\\citename{Viegas \\& Fria\\c ca }1995]{vi:fr} \n%Viegas, S. M., Fria\\c ca 1995, MNRAS 272, L35\n\n\\bibitem[\\protect\\citename{Villar-Mart\\'\\i n \\etal\\ }1996]{vi96} \nVillar-Mart\\'\\i n, M., Binette, L., Fosbury, R. A. E. 1996, A\\&A 312, 751\n\n%\\bibitem[\\protect\\citename{Villar-Mart\\'\\i n \\etal\\ }1997]{vi97} \n%Villar-Mart\\'\\i n, M., Tadhunter, C., Clark, N. 1997, A\\&A 323, 21\n\n%\\bibitem[\\protect\\citename{Villar-Mart\\'\\i n \\etal\\ }1999]{vi99} \n%Villar-Mart\\'\\i n, M., Binette, L., Fosbury, R. A. E. 1999, A\\&A in press\n\n\n\\bibitem[\\protect\\citename{Vogel \\& Reimers} 1993]{vore93} \nVogel, S., Reimers, D. 1993, A\\&A 274, L5\n\n\\bibitem[\\protect\\citename{Vogel \\& Reimers} 1995]{vore95} \nVogel, S., Reimers, D. 1995, A\\&A 294, 377\n\n\\bibitem[\\protect\\citename{Webb} 1987]{webb} \nWebb, J. 1987, PhD thesis, University of Cambridge (UK)\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002211
|
Energy implications of temperature fluctuations in photoionized plasma
|
[
{
"author": "Luc Binette and Valentina Luridiana \\affil{Instituto de Astronom\\ii a"
},
{
"author": "Universidad Nacional Aut\\'onoma de M\\'exico}"
}
] |
We quantify the energy radiated through all the collisionally excited lines in a photoionized nebula which is permeated by temperature fluctuations. We assume that these correspond to hot spots which are the results of an unknown heating process distinct from the photoelectric heating. We consider all the effects of using a higher mean temperature (as compared to the equilibrium temperature) due to the fluctuations not only on each emission line but also on the ionization state of the gas. If this yet unknown process was to radiate a fixed amount of energy, we find that the fluctuations should correlate with metallicity $Z$ when it exceeds 0.7 solar. The excess energy radiated in the lines as a result of the fluctuations is found to scale proportionally to their amplitude \tsq. When referred to the total energy absorbed through photoionization, the excess energy is comparable in magnitude to \tsq.
|
[
{
"name": "valentina.tex",
"string": "%%%\n%%% Sample proceedings article for rmaa.cls\n%%%\n%%% Converted to RMAA(SC) style and annotated by Will Henney \n%%% (04 Oct1999) \n\n%% This file contains examples of many of the commands in the LaTeX\n%% document class rmaa.cls, such as the commands for specifying data\n%% for the title page and the commands for including postscript\n%% figures. For more details, you should consult the accompanying\n%% Author Guide (`rmuser.tex'). A further sample document\n%% (`rmtest.tex') contains examples of some commands not used in this\n%% file, eg. for marking up tables. You may also want to use this file\n%% as a template for your own article. \n\n%% Note: This article was originally published in `IAU Symposium 182:\n%% Herbig-Haro Objects and the Birth of Low-mass Stars',\n%% ed. B. Reipurth & C. Bertout (Dordrecht: Kluwer). Hopefully, I've\n%% changed it enough to avoid copyright violation!\n\n%% All proceedings articles must begin with the following line\n\\documentclass[]{rmaa}\n%%\n%% The file `rmaa.cls' should be somewhere in your TeX search path\n%% (e.g, in the current directory, or in a personal or system-wide\n%% directory of LaTeX packages. \n%%\n%% This will not work with old versions of LaTeX: any version\n%% of LaTeX2e should be OK, but LaTeX209 is too old. If LaTeX\n%% complains that it doesn't recognise the command `\\documentclass'\n%% then your LaTeX installation needs updating!\n\n%% The following package allows one to do the citations\n%% semi-automatically. It defines the commands \\cite{KEY},\n%% \\scite{KEY}, and \\pcite{KEY} which respectively produce citations\n%% in the following styles: \n%% (AUTHOR YEAR)\n%% AUTHOR (YEAR)\n%% AUTHOR YEAR\n%% For this to work, you need to pay attention to the formatting of\n%% the `\\bibitem's in your `thebibliography ' environment, qv.\n%\\usepackage{rmaacite}\n%% If you would rather do your citations by hand, then comment out the \n%% above line\n\n%% Here, you can put the definitions of your own personal macros.\n%% All the special commands defined in AASTEX 4.0 (e.g. \\ion{}{},\n%% \\gtrsim, \\arcsec, \\apj, etc) are already defined. I haven't checked \n%% if there are any new ones in AASTEX 5.0 yet.\n\n%AUTHORS NEW COMMANDS \n\\newcommand{\\map}{\\hbox{{\\sc mappings i}c}}\n\\newcommand{\\ii}{\\'{\\i}}\n\\def\\ion#1#2{#1$\\;${\\small\\rm\\@Roman{#2}}\\relax}\n\\newcommand{\\up}{\\hbox{$U$}}\n\\newcommand{\\cms}{\\hbox{\\,${\\rm cm^{-2}}$}}\n\\newcommand{\\cmc}{\\hbox{\\,${\\rm cm^{-3}}$}}\n\\newcommand{\\etal}{\\hbox{et~al.}}\n\\newcommand{\\msol}{\\hbox{\\,${\\rm M_{\\sun}}$}}\n\\newcommand{\\eg}{\\hbox{e.g.}}\n\\newcommand{\\cf}{\\hbox{cf.}}\n\\newcommand{\\ie}{\\hbox{i.e.}}\n\\newcommand{\\dex}{\\hbox\\,{dex}}\n\n\\newcommand{\\gama}{\\hbox{$\\Gamma_{abs.}$}}\n\\newcommand{\\gamh}{\\hbox{$\\Gamma_{heat.}$}}\n\\newcommand{\\teff}{\\hbox{$T_{eff}$}}\n\\newcommand{\\tsq}{\\hbox{$t^2$}}\n\\newcommand{\\teq}{\\hbox{$T_{eq}$}}\n\\newcommand{\\tmean}{\\hbox{$\\bar T_0$}}\n\\newcommand{\\trec}{\\hbox{$\\bar T_{rec}$}}\n\\newcommand{\\tcolij}{\\hbox{$\\bar T_{col.}^{ij}$}}\n\n\\newcommand{\\ha}{\\hbox{H$\\alpha$}}\n\\newcommand{\\haw}{\\hbox{H$\\alpha$\\,$\\lambda $6563}}\n\\newcommand{\\hb}{\\hbox{H$\\beta$}}\n\\newcommand{\\hbw}{\\hbox{H$\\beta$\\,$\\lambda $4861}}\n\\newcommand{\\hi}{\\hbox{H\\,{\\sc i}}}\n\\newcommand{\\hii}{\\hbox{H\\,{\\sc ii}}}\n\\newcommand{\\nii}{\\hbox{[N\\,{\\sc ii}]}}\n\\newcommand{\\niiw}{\\hbox{[N\\,{\\sc ii}]$\\lambda $6583}}\n\\newcommand{\\niitw}{\\hbox{[N\\,{\\sc ii}]$\\lambda $5755}}\n\\newcommand{\\oiii}{\\hbox{[O\\,{\\sc iii}]}}\n\\newcommand{\\oiiiw}{\\hbox{[O\\,{\\sc iii}]$\\lambda $5007}}\n\\newcommand{\\oiiitw}{\\hbox{[O\\,{\\sc iii}]$\\lambda $4363}}\n\\newcommand{\\ciii}{\\hbox{C\\,{\\sc iii}]}}\n\\newcommand{\\ciiiw}{\\hbox{C\\,{\\sc iii}]$\\lambda\\lambda $1909}}\n\n%%\n%% The following commands specify the title, authors etc\n%%\n\\title{Energy implications of temperature fluctuations in\nphotoionized plasma}\n\\author{Luc Binette and Valentina Luridiana\n\\affil{Instituto de Astronom\\ii a \\\\\nUniversidad Nacional Aut\\'onoma de M\\'exico}\n}\n%\\altaffiltext{1}{Just to see that the affiliation subscripts work OK}\n%% Note that the \\affil{} command is inside the argument of the\n%% \\author{} command and that a short version of the address should go \n%% here. More complicated author/address examples are discussed in the \n%% Author Guide (`rmuser.tex') and illustrated in the example document\n%% `rmtest.tex' \n\n%% The full postal addresses are specified here - they will be typeset \n%% at the end of the article. Here is also the place to put email\n%% addresses. \n\\fulladdresses{\n\n\\item L. Binette: Instituto de Astronom\\ii a, UNAM, Ap. 70-264, 04510 D.F.,\nM\\'exico (binette@astroscu.unam.mx)\n\n\\item V. Luridiana: Instituto de Astronom\\ii a, UNAM, Ap. 70-264, 04510 D.F.,\nM\\'exico (vale@astroscu.unam.mx)\n}\n\n\n%% Note that the `\\fulladdresses' command defines a list-like\n%% environment, so each separate address must be preceded by the\n%% `\\item' command (here there is only one, since the authors share the \n%% same address). \n\n%% Title/author for running headers\n\\shortauthor{Binette \\& Luridiana}\n\\shorttitle{Energy requirements of fluctuations}\n%% These will automatically be converted to upper case in the current\n%% style. \n\n%% No more than 5 keywords, chosen from the standard list\n\\keywords{ISM -- abundances -- planetary nebulae -- HII regions}\n\n%% The abstract:\n\\abstract{We quantify the energy radiated through all the collisionally excited\nlines in a photoionized nebula which is permeated by temperature\nfluctuations. We assume that these correspond to hot spots which are\nthe results of an unknown heating process distinct from the\nphotoelectric heating. We consider all the effects of using a higher\nmean temperature (as compared to the equilibrium temperature) due to\nthe fluctuations not only on each emission line but also on the\nionization state of the gas. If this yet unknown process was to\nradiate a fixed amount of energy, we find that the fluctuations should\ncorrelate with metallicity $Z$ when it exceeds 0.7 solar. The\nexcess energy radiated in the lines as a result of the fluctuations is\nfound to scale proportionally to their amplitude \\tsq. When referred\nto the total energy absorbed through photoionization, the excess\nenergy is comparable in magnitude to \\tsq.}\n%% If your spanish is up to it, you may want to supply the resumen by\n%% uncommenting the following line:\n%\\resumen{ }\n%% Alternatively, you can leave the translation to the editors. \n\n\n%% This command is so LaTeX won't stop on errors. I've put it in so\n%% you will still be able to compile the file even if you have lost\n%% the associated PS files of the figures. \n\\nonstopmode\n\n%% The following command is necessary before beginning the text of\n%% your article. There should be a matching \\end{document} at the end\n%% of the file. \n\\begin{document}\n\n%% This command is necessary to typeset the title, abstract, etc. \n\\maketitle\n\n%%\n%% And here starts the text....\n%%\n\\section{Introduction}\n\\label{sec:intro}\n \nThe temperatures of photoionized nebulae are observed to be significantly lower\nwhen derived using recombination lines rather than from forbidden line ratios\n(e.g. Peimbert et~al. 1995). This phenomenon has been ascribed to the\nexistence of temperature fluctuations permeating the nebulae. Assuming\nthat the fluctuations inferred by various authors\n(e.g. Peimbert et~al. 1995, Esteban et~al. 1998, Rola \\& Stasi\\'nska 1994) are\ncaused by an additional albeit {\\it unknown} heating agent (beside\nphotoionization), we proceed to quantify the energy contribution which\nthis unknown heating process must contribute to the total energy\nbudget of the nebula in order to account for the much higher\ntemperatures characterizing the collisionally excited lines as\ncompared to those inferred from recombination lines (or nebular Balmer\ncontinuum). In order to study the effects of arbitrary temperature\nfluctuations, we first describe the modifications made to the\nmultipurpose photoionization-shock code \\map\\ (Ferruit\net~al. 1997). In Section\\,\\ref{sec:cal}, we present photoionization\ncalculations in which we consider different levels of fluctuation\namplitudes and quantify how they alter the global energy budget\nof the nebula. A brief discussion is presented in Section\\,\\ref{sec:con}.\n\n\\section{The energy expense caused by nebular hot spots}\n\\label{sec:expen}\n\nWe present a few definitions followed by the procedure we adopt to\nimplement the effect of temperature fluctuations in the code \\map.\n\n\\subsection{Definitions of \\tsq\\ and mean temperature \\tmean\\ }\n\\label{sec:def}\n\nFollowing Peimbert (1967), we define the mean nebular temperature,\n\\tmean, as follows\n\n\\begin{equation}\n\\bar T_0=\\frac {\\int_V n_e^2 T dV}{\\int_V n_e^2 dV} \\; , \\label{eq:to}\n\\end{equation}\n\n\\noindent in the case of an homogeneous \nmetallicity nebula characterized by small temperature fluctuations;\n$n_e$ is the electronic density, $T$ the electronic temperature and\n$V$ the the volume over which the integration is carried out. The rms\namplitude $t$ of the temperature fluctuations is given by\n\n\\begin{equation}\nt^2 = \\frac {\\int_V n_e^2 (T - \\bar T_0)^2 dV} \n{\\bar T_0^2\\int_V n_e^2 dV} \\; . \\label{eq:tsq}\n\\end{equation}\n\n\\noindent Note that we simplified the expression presented by\nPeimbert (1967) whose definition of \\tsq\\ differs in principle with\neach ionic species density $n_i$ while in the above equations we\nimplicitely consider only ionized H (by setting $n_{H^+} = n_e$).\nSince \\tsq\\ in this paper is not an observed datum but an {\\it\na~priori} global property of the nebular model, such differences are\nnot important.\n\nThe intensity of a recombination line is in general proportional to \n$T^{\\alpha}$ while for a collisionally excited line it is proportional\nto $T^{\\beta} {\\rm exp}(-\\Delta E/kT)$ where $\\Delta E$ is the energy\nseparation of the two levels involved in the transition. In either\ncase, $\\beta$ and $\\alpha$ typically lie in the range $-0.5$ to $-1$.\n\n\n\n\\subsection{Approximating fluctuations as hot spots above \\teq} \\label{sec:hot}\n\nSince the fluctuations' amplitudes \\tsq\\ derived from observations are\nmuch larger that that predicted by photoionization models (cf.\nP\\'erez 1997), the solution to this inconsistency resides not in\nadding an additional uniform heating/cooling term to the thermal\nbalance equations (like heating by dust grain photoionization) since\nthis would simly result in a uniform raise of $T$ and not in larger\nfluctuations. What is required to increase \\tsq\\ in models is that\nsuch process be operating in a {\\it non-uniform} manner across the\nnebula and the picture which we propose is that of many hot spots\ncreated by this heating process.\n\n\n\\begin{figure}\n\\begin{center} \\leavevmode\n\\includegraphics[width=0.45\\textwidth]{valentinafig1.eps}\n\\caption{ \nA numerical simulation of temperature fluctuations consisting of hot\nspots characterized by an amplitude $\\tsq=0.005$ (from\nEq.~\\ref{eq:tsq}). The mean temperature \\tmean\\ obtained from\napplying Eq.~\\ref{eq:to} is 9800\\,K (horizontal solid line). Also\nshown the relative position of \\trec\\ and $T_{[OIII]4363}$. The\nfluctuations' lower bound temperature (to be associated to \\teq) is\n9500\\,K.\n%trec and t4363 are 9753 9954\n}\n\\label{fig:tsq} \n\\end{center}\n\\end{figure}\n\n\nIt is beyond the scope of this paper to consider any particular\nphysical process to account for the fluctuations nor to model them in\ndetails. Our aim is limited to study the effect of {\\it ad hoc}\ntemperature fluctuations {\\it a la} Peimbert on the energy budget\nunder the assumption that these arise from this unknown extra heating\nmechanism acting non-uniformly across the nebula.\n\nIn photoionization calculations, it is customary to define and use at\nevery point in the nebula a local equilibrium temperature, \\teq, which\nsatisfies the condition that the cooling by radiative processes equals\nthe heating due to the photoelectric effect. In our hot spots scheme,\nby construction, \\teq\\ corresponds to the temperature floor above which\ntake place all the fluctuations. For illustrative purposes, we show in\nFig.\\,\\ref{fig:tsq} a possible rendition of fluctuations (the solid\nwavy line) characterized by an amplitude $\\tsq=0.005$ (from\nEq.~\\ref{eq:to}) and consisting of hot spots. Because \\teq\\ is a\nminimum in the distribution of $T$ fluctuations, it defines the null\nenergy expense when calculating the extra energy emitted as result of\nthe hot spots.\n\n\\subsection{The determination of \\tmean\\ } \\label{sec:mean}\n\nThe fluctuations are taken into account by \\map\\ only in the\nstatistical sense, that is by defining and using temperatures which\nare derived from \\tmean. Given a certain amplitude of fluctuations\n\\tsq, we use everywhere a value for the mean temperature which is\nderived from the computed local equilibrium temperature (\\teq) and\nwhich takes into account that \\teq\\ is a lower extremum in the\ndistribution of $T$ fluctuations (consisting of hot spots). To define\n\\tmean, we found adequate using the following\nexpression (based on the inverse of Eq.\\,\\ref{eq:trec})\n\n\\begin{equation}\n\\bar T_0 \\simeq \\teq [1+\\gamma(\\gamma-1)t^2/2]^{-1/\\gamma} \\; . \\label{eq:tmean}\n\\end{equation}\n\n\\noindent but where the optimum value of $\\gamma$ \nhas been inferred using numerical simulations of the hot spots. One\nsimulation shown in Fig.\\,\\ref{fig:tsq} is characterized by\n$\\teq=9500$\\,K and $\\tsq =0.005$. By fitting $\\gamma$ so that the value\nof \\tmean\\ matches the numerically computed value of 9800\\,K, we\nobtain that $\\gamma \\approx -15$. Within the deduced regime in which\n$\\gamma \\ll -1$, the above equation varies slowly with $\\gamma$.\nThe purpose of this expresion is that it defines consistently \\tmean\\\nwhatever the value of the equilibrium temperature calculated by\n\\map. Interestingly, $\\gamma$ (or \\tmean) is invariant to\nsimultaneously scaling up and down of all the hot spot amplitudes\n(which is equivalent to increasing or decreasing \\tsq). On the other\nhand $\\gamma = -15$ strickly characterizes a specific distribution of\nhot spot frequencies and widths. It is the correct value for\nfluctuations resembling those depicted in Fig.\\,\\ref{fig:tsq} but for\nother radically different distributions of hot spot widths and\nfrequencies, $\\gamma = -15$ would only provide a first order albeit\nacceptable estimate of \\tmean. Despite this caveat, we estimate the\nuncertainties affecting the final determination of\n\\gamh\\ to be $< 20$\\%.\n\n\n\\subsection{Recombination processes} \\label{sec:recom}\n\nFor small fluctuations, the temperature can be expanded in a Taylor\nseries about the mean \\tmean. In the case of recombination lines\nthe intensity, $I_{rec}$, of a given line is affected by a factor\n\n\\begin{equation}\nI_{rec} \\propto \n\\bar T_0^\\alpha [1+\\alpha(\\alpha-1)t^2/2] \\; . \\label{eq:irec}\n\\end{equation}\n\n\\noindent This expression which can be used to compute individual\nrecombination line intensities in the presence of small fluctuations, is\nequivalent to calculating the intensity (which is proportional to\n$T^{\\alpha}$) using instead the effective temperature \\trec\\\n\n\\begin{equation}\n\\trec = \\langle T^\\alpha\\rangle^{1/\\alpha}\\simeq\nT_0 [1+\\alpha(\\alpha-1)t^2/2]^{1/\\alpha} \\; . \\label{eq:trec}\n\\end{equation}\n\nAs shown by Peimbert (1995 and references therein), the temperature\nfluctuations have in general much {\\it less} impact on recombination\nthan on collisional processes which are usually governed by the\nexponential factor. For this reason, we adopt the simplification of\nconsidering a single value of $\\alpha = -0.83$ for all recombination\nprocesses (such $\\alpha$ is the appropriate value for the \\hb\\ line at\n10000\\,K). This approximation will allow us to use a single\ntemperature \\trec\\ when solving for the ionization balance of H, He\nand all ions of metals (equations in which enter recombination rates).\n\nIf we consider the fluctuations drawn in Fig.~\\ref{fig:tsq} as\nexample, we see that the mean recombination temperature \\trec\\ derived\nusing Eq.~\\ref{eq:trec} lies slightly below \\tmean.\n\nInterestingly, in the case of the ionization-bounded dustfree models\nconsidered in this work, the adoption of one temperature or another\nwhen calculating recombination processes does not affect the global\nenergy budget of the recombination lines. In effect,\nthe total number of recombinations taking place across the whole\nnebula must equal the number of ionizing photons produced by the UV\nsource, whatever the value and behaviour of the temperature. It is a\nself-regulating process: a hotter nebula [which results in slower\nrecombinations rates and hence in a plasma containing less neutral H]\nof the type discussed below will simply turn out more massive in\nionized gas in order that the number of recombinations remains equal\nto the same number of ionizing photons. The sum of all hydrogen\nrecombination lines intensities will remain unchanged. Also constant\nis the total amount of heat deposited in the nebula through photoionization.\n\n\n\\subsection{Collisional processes} \\label{sec:coll}\n\nTo compute the forbidden line intensities, we solve for the population\nof each excited state of all ions of interest assuming a system of 5\nor more levels according to the ion. (In the case of intercombination,\nfine structure and resonance lines, we treat those as simple 2 level\nsystems.) More specifically, when evaluating the excitation ($\\propto\nT^{\\beta_{ij}} {\\rm exp}[-\\Delta E_{ij}/kT] $) and deexcitation\n($\\propto T^{\\beta_{ji}}$) rates of a given multi-level ion, each rate\n$ij$ (population) or $ji$ (depopulation) is calculated using\n\\tmean\\ (instead of \\teq) and then multiplied by the appropriate \ncorrection factor, either\n\n\\begin{eqnarray}\n{\\rm cf}^{exc.}_{ij} = \n1+ \\frac{t^2}{2} \\Bigl[ (\\beta_{ij} - 1 ) \n\\Bigl(\\beta_{ij} + 2 \\frac{\\Delta E_{ij}}{k \\tmean} \\Bigr) +\n\\Bigl(\\frac{\\Delta E_{ij}}{k \\tmean}\\Bigr)^2\n\\Bigr] \\label{eq:exc}\n\\end{eqnarray}\n\\noindent in the case of excitation, or\n\\begin{eqnarray}\n{\\rm cf}^{deexc.}_{ji} = \n 1 + \\beta_{ji} (\\beta_{ji} - 1 ) \n\\frac{t^2}{2} \\; , \\label{eq:deexc}\n\\end{eqnarray}\n\\noindent in the case of deexcitation.\nThese factors result in general in an enhancement of the collisional\nrates in the presence of temperature inhomogeneities. They are adapted\nfrom the work of Peimbert et~al. (1995) and were applied to all\ncollisionally excited transitions.\n\nFor the case of the particular rendition of the fluctuations depicted\nin Fig.\\,\\ref{fig:tsq}, the mean {\\it collisional} temperature\ncharacterizing the \\oiiitw\\ line (Peimbert et~al. 1995) is shown by the \nhorizontal dash line. Despite the large $\\Delta E_{ij}$ involved in\nthe emission of the line, the distance between this temperature and\n\\tmean\\ is nevertheless smaller than that separating \\tmean\\ from\n\\teq. Therefore, in some instances the extra energy radiated through\nhot spots might depend as much on the distance separating \\tmean\\ from\n\\teq\\ than on the above correction factors.\n\nInspection of the line ratios calculated with \\map\\ using \\tmean\\ and\nthe above correction factors confirms (as expected) that the higher is\n$\\Delta E_{ij}$ the higher the line intensity enhancement (at constant\n\\tsq). It can be shown on the other hand that the far infrared lines\n(or any transition for which ${\\rm exp}[-\\Delta E_{ij}/kT] \\approx 1$)\nare less affected by the fluctuations (similarly to the recombination\nlines) and can even become weaker as a result of the fluctuations, in\ncontrast to most collisionally excited lines.\n\n\n\\subsection{The energy radiated through hot spots} \\label{sec:ener}\n\nOur aim is to quantify the excess energy generated by temperature\nfluctuations under the assumption that these are caused by a putative\nheating mechanism which operates within small regions randomly\ndistributed across the nebula. To calculate this energy we simply\nintegrate over the nebular volume $V$ the luminosity of each line (or\ntransition) $ij$ using the statistically determined local \\tmean\\ and\nthe multiplicative correction factors of Eqs~\\ref{eq:exc} and\n\\ref{eq:deexc}, and then subtract the corresponding luminosity\nobtained by using the equilibrium temperature \\teq\\ instead. This\nexcess energy radiated in the form of collisionally excited lines can\nbe normalized respective to the total photoheating energy\navailable. This defines the quantity \\gamh\\\n\n\\begin{eqnarray}\n\\gamh\\ & = &\n { \\sum_{ij} \\int_{V} [4\\pi j_{ij}^{fluc} - 4\\pi\nj_{ij}^{eq}] \\; dV} \\over\n{\\sum_{ij} \\int_{V} 4\\pi j_{ij}^{eq} \\; dV + \\sum_{k} \\int_{V} q_k^{eq} \\; dV } \\nonumber \\\\ & & \\\\\n & = & {{L_{fluc} - L_{eq}}\\over{L_{eq} + Q_{eq}}} \\;, \\label{eq:gam}\n\\end{eqnarray}\n\n\\noindent where $j_{ij}^{fluc}$ corresponds to\nthe local nebular emissivity of line $ij$ calculated using \\tmean\\ and\ntaking into account the above correction factors while $j_{ij}^{eq}$\nis the corresponding emissivity assuming equilibrium temperature\neverywhere. The term with $q_k^{eq}$ corresponds to various cooling\nrates from processes {\\it not} involving line emission such as\nfreefree emission, while $Q_{eq}$ represents the total volume integrated\nvalue of this term. $L_{fluc}$ and $L_{eq}$ correspond to the\nintegrated energy loss across the whole nebula due to collisionally\nexcited lines with fluctuations and without, respectively. Since\n\\teq\\ must satisfy the condition that the cooling rate equals\neverywhere the heating rate, we obtain that $L_{eq} + Q_{eq}$ is also\nequal to the total energy deposited into the electronic gas by the\nphotoelectric effect. \n\nA larger fraction of the ionizing radiation simply keeps the\nnebula ionized (resulting in recombination lines) but does not affect\nthe nebular temperature. An alternative way therefore of expressing the\nimportance of the excess cooling due to the fluctuations is to use as\nreference the {\\it total} energy absorbed by the nebula {\\it\nincluding} the energy emitted as recombination lines and nebular\nrecombination continuum. We define \\gama\\ as follows\n\n\\begin{equation}\n\\gama\\ = {{L_{fluc} - L_{eq}}\\over{L_{total}^H}} \\; , \\label{eq:heat}\n\\end{equation}\n\n\\noindent with $L_{total}^H$ the ionizing luminosity of the exciting star\n\n\\begin{equation}\nL_{total}^H = \\int_{\\nu_0}^\\infty {{L_\\nu}} \\,d\\nu \\; , \\label{eq:ener}\n\\end{equation}\n\\noindent where $L_{\\nu}$ is the energy luminosity distribution of\nthe ionizing star and $\\nu_0$ the frequency corresponding to the\nionization treshold of H. To be consistent with this definition, we\nmust consider only nebular models which are ionization-bounded and\nfully covering the ionizing source (over 4$\\pi$ sterad). Depending on\nthe hardness of the ionizing radiation, \\gama\\ turns out to be 2--3\ntimes smaller than \\gamh\\ because of the larger fraction of the absorbed\nenergy which goes into photoionizing rather than into heating the gas.\n\nIn summary, the modifications made to \\map\\ to consider the effects of\n$T$ fluctuations not only include the calculation of the line\nintensities using the formalism described in Peimbert et~al (1995) but\nalso considers their impact on the ionization balance across the\nnebula through the use of \\trec\\ (instead of \\teq) to derive the\nrecombination rates. Since the nebula\nis substantially hotter {\\it on average} when $\\tsq > 0$, it will be more\nionized since the recombination rates are slower at higher\ntemperature. This in turn results in a lower photoionization and\nheating rates given that there is less neutral H in the nebula,\ntherefore the equilibrium temperature \\teq\\ computed by \\map\\ will be\nlower than without fluctuations. All these effects have been taken\ninto account self consistently and do {\\it not} affect the energy\nconservation principle in the case of ionization-bounded nebulae as\ndiscussed above and in in Sect.~\\ref{sec:recom}.\n\n\n\\section{Model calculations} \\label{sec:cal}\n\nWe have explored the behaviour of \\gamh\\ in photoionization models of\ndifferent metallicity ($Z$), excitation (\\up) and different spectral\nenergy distributions (hereafter SED). We will express the nebular\nmetallicity with respect to the solar abundances (from Anders \\&\nGrevesse 1989) for which we take that $Z=1$. To define other\nmetallicities, we simply scale the abundances of all the metals\nrespective to H by a constant multiplicative factor equal to $Z$. We\nsummarize below our results under various model conditions.\n\nFor the photoionized \\hii\\ regions, we have selected unblanketed LTE\natmosphere models from Hummer \\& Mihalas (1970) of temperatures \\teff\\\nof 40000\\,K, 45000\\,K and 50000\\,K [see Evans (1991) for a comparative\nstudy of nebular models using different model atmospheres]. To\nrepresent planetary nebulae, we simply employed black bodies of\n$10^5\\,$K and $10^{5.3}\\,$K truncated at 54.4\\,eV. The geometry\nadopted in the calculation is plane-parallel with a gas\ndensity of $n_H = 10\\,\\cmc$ in all cases. The excitation of the nebula\nis defined by the excitation parameter \\up\\ as follows\n\n \\begin{equation}\nU = {{1}\\over{cn_H}} \\int_{\\nu_0}^\\infty {{L_\\nu}\\over {4 \\pi r^2 \\, h\\nu}}\n\\,d\\nu = {{\\varphi_H}\\over {c n_H}} \\; , \\label{eq:upar}\n\\end{equation}\n\\noindent where $c$ is the speed of light, $h$ the Planck constant\nand $r$ the distance of the slab from the ionizing star. \\up\\ is the\nratio between the density of ionizing photons impinging on the slab \n($\\varphi_H/c$) and the total H density. All the calculations carried out\nwere ionization-bounded.\n\n\n\\begin{figure}\n\\begin{center} \\leavevmode\n\\includegraphics[width=0.95\\columnwidth]{valentinafig2.eps}\n\\caption{ \nBehaviour of \\gamh\\ in a sequence of photoionization models which have\ndifferent nebular metallicities (relative to solar $Z=1$). Two SED\nused in the calculations consisted of a 45000\\,K and a 100000\\,K star,\nrespectively. In all models $\\tsq = 0.04$ .}\n\\label{fig:zseq} \n\\end{center}\n\\end{figure}\n\nSince hotter SEDs result on the other hand in much higher\nphotoelectron energies and hence hotter nebulae at all metallicities,\nthe maximum of the long-dashed curve corresponding to the $10^5$\\,K\nblackbody in Fig.\\,\\ref{fig:zseq} is shifted towards higher $Z$\nrelative to the 45000\\,K SED.\n\n\n\n\\subsection{Dependence of excess heating on metallicity}\n\nWe have calculated nebular models of different metallicities covering\nthe range 1\\% solar ($Z=0.01$) to 4.7 times solar. In the models\npresented in Fig.\\,\\ref{fig:zseq} all other parameters are identical,\nnamely, \\up\\ = 0.01, \\tsq\\ = 0.04 and a spectral energy distribution\n(SED) having either \\teff\\ = 45000\\,K or 100000\\,K. It can be seen\nthat a maximum in \\gamh\\ occurs within the range $Z \\sim $ 0.2--0.4.\nFor the \\hii\\ region models, the average values for \\teq\\ across the\nnebulae are $\\sim 15000$\\,K, 9000\\,K, 5000\\,K and 1500\\,K for the\n$Z=0.01$, 0.7, 2.5 and 4.7 models, respectively. Given that the\nnebular temperatures decrease monotonically with increasing $Z$, the\ncurves' behaviour can be understood as follows: at very low\nmetallicities $Z \\ll 0.2$, the forbidden lines of metals are not the\nmain cooling agent and the fluctuations have therefore a negligible\nimpact on the total cooling. At higher $Z$ values around solar,\nhowever, the cooling due to metals is very large and the nebula turns\nout much cooler, to the extent that many optical lines become now less\nintense despite the increase of the metal abundances. At even higher\n$Z$, the optical lines are progressively `switched off' and cannot\ncontribute to the cooling of the nebula. In this regime, these lines\nhave $\\Delta E \\ll k\\tmean$ and become somewhat brighter as the\ntemperature is further lowered, explaining why the fluctuations now\ncause \\gamh\\ to become negative. The final rise at the upper $Z$ end\nin the \\hii\\ region model sequence (solid line) reflects the fact that\nat such low temperature the cooling can only be carried out by the low\nenergy transitions (far infrared lines) where again $\\Delta E > k\\tmean$.\n\n\n\\begin{figure}\n\\begin{center} \\leavevmode\n\\includegraphics[width=0.95\\columnwidth]{valentinafig3.eps}\n\\caption{ \nBehaviour of \\gamh\\ with increasing \\tsq. Two metallicities were used:\nsolar (labelled S) and 0.2 solar (labelled L) and 4 SED:\n40000\\,K,45000\\,K, 50000\\,K, 100000\\,K and 200000\\,K labelled 40, 45,\n50, 100 and 200, respectively (the L sequences are too close to allow\nlabelling of each SED). \\gamh\\ becomes approximately\nlinear at larger \\tsq. For comparison we show a thick line\nrepresenting $\\gamh = 2.5 \\tsq$.}\n\\label{fig:tsqh} \n\\end{center}\n%\\end{figure}\n\n\n%\\begin{figure}\n\\begin{center} \\leavevmode\n\\includegraphics[width=0.95\\columnwidth]{valentinafig4.eps}\n\\caption{ \nBehaviour of \\gama\\ with increasing \\tsq. Same notation as in\nFig.~\\ref{fig:tsqh}. For comparison we show thick lines representing\n$\\gama = \\tsq$ and $2.5 \\tsq$, respectively.}\n\\label{fig:tsqa} \n\\end{center}\n\\end{figure}\n\nThe abrupt decrease of \\gamh\\ above solar metallicity has interesting\nconsequences if the unknown heating process responsible for the\nfluctuations needed to radiate a comparable amount of energy in\ndifferent objects. This could arguably be the case for instance if\nthis process was reconnection of magnetic field lines. All other\nfactors being equal, nebulae three times solar would require much\nlarger amplitude turbulences (larger \\tsq) to radiate the same amount\nof energy than a solar metallicity nebula. In this case we might\nexpect to observe a correlation between \\tsq\\ and metallicity (beyond\n$Z \\ge 0.7$).\n\n\n\\subsection{Dependence of excess heating on \\tsq\\ }\n\nIn the following calculations, we adopt two representative metallicities\nof $Z=0.2$ and $Z=1$ (solar). We found no clear trends across\ndifferent SEDs of how \\gamh\\ varied with \\up\\ and therefore we only report\nresults concerning a single ionization parameter of value $10^{-2}$.\nCampbell (1988) has shown that the range of \\up\\ for most \\hii\\\ngalaxies lies in the range $10^{-2.6}$ to $10^{-1.8}$.\n\n \nIn Figs.\\,\\ref{fig:tsqh} and \\ref{fig:tsqa}, we show the behavior of both\n\\gamh\\ and \\gama\\ as a function of increasing \\tsq\\ of the models. Each \nline corresponds to a given SED and $Z$. The increase in \\gamh\\ is\nsteeper at small values of $\\tsq \\la 0.1$ followed by a more linear\nregime with a slope $\\le 2.5$ at large \\tsq. The radiated energy\ncontribution from the fluctuations (compared to photoelectric heating)\nis of order $2.5 \\tsq$ (Fig.~\\ref{fig:tsqh}) but with a wide\ndispersion when $Z=1$ (curves labelled S). For $Z=0.2$ there is no dependence\non the SED and the curves almost superimpose each other.\n\nIf we consider the total energy budget (photoheating plus\nrecombination energy, see Eq.~\\ref{eq:heat}) and not just the\nphotoelectric heating part, we find that \\gama\\ is comparable in\nmagnitude to \\tsq\\ (Fig.~\\ref{fig:tsqa}) but again with a wide\ndispersion which result from differences in either $Z$ or the SED.\n\n\\section{Discussion} \\label{sec:con}\n\nIf the turbulences are the result of heating by a yet undiscovered\nprocess, we infer from Fig.~\\ref{fig:tsqh} and \\ref{fig:tsqa} that the\nextra energy radiated via {\\it all} the collisionally excited lines\ndue to the turbulences is a substantial fraction ($\\gama >10$\\%) of\nthe total photoionization energy whenever $\\tsq\\ \\ga 0.02$ for\nplanetary nebulae and $\\tsq\\ \\ga 0.08$ for \\hii\\ regions,\nrespectively. Taking instead as reference only the heating by\nphotoionization (\\gama), these limits are reduced by two. In this case\nalmost all nebulae would radiate more than 10\\% (\\gama) of their\nenergy as a result of $T$ fluctuations. In effect, typical empirically\ndetermined \\tsq\\ values for galactic \\hii\\ regions lie in the range\n0.02--0.06 (Luridiana 1999). For extragalactic \\hii\\ regions\n(Luridiana et~al. 1999, Gonz\\'alez-Delgado et~al. 1994) and planetary\nnebulae (Peimbert et~al. 1995), even larger values have been\nencountered, of order 0.1 or more\\footnote{Measured values of\n\\tsq\\ in excess of 0.1 should be considered only as rough estimates\nsince the assumed regime of small fluctuations does not apply\nanymore.}. In those cases, the energy envolved can be a large\nfraction of the energy budget especially if the exciting stellar\ntemperature exceeds $10^5\\,$K.\n\nThe underlying assumption behind our calculations is that an external\nheating agent is at work to generate $T$ fluctuations. We should point\nout that there exist alternative explanations to the fluctuations\nwhich rest on photoionization alone and have not been completely ruled\nout. Possible mechanisms which we plan to study in some details:\n\n\\begin{enumerate}\n\\item{\\it Metallicity inhomogeneities}\nTemperature fluctuations would result naturally from nebulae\nconsisting of a multitude of condensations of greatly varying\nmetallicities (see Torres-Peimbert, Peimbert \\& Pe\\~na 1990)\n\\item{\\it Gas expansion}\nFluctuations could arise from an outflowing wind generated at the\nsurface of dense condensations (problyds) as a result of the champagne\neffect. Rapid adiabatic expansion would result in overcooled emission\nregions in the wake of the wind (resulting in negative $T$ fluctuations\nwith respect to \\teq).\n\\item{\\it Ionizing source variability}\nA rapidly varying ionizing field will generate a sequence of outwardly\npropagating ionization and recombination fronts. The basic asymmetry\nexisting between ionization fronts (propagating at a speed limited by\nchanges in opacity) and recombination fronts (non-propagating), would\nlead to temperature fluctuations.\n\\end{enumerate}\n\nTo our knowledge, none of these mechanisms have yet been incorporated\nexplicitly in any nebular model and we therefore cannot assess their\nparticular merits. Mechanisms which are good candidates to explain the\nextra heating assumed in this work (see also discussion by Stasi\\'nska\n1998) and which are not directly related to photoionization, have been\nproposed and include the following processes:\n\\begin{enumerate}\n\\item{\\it Shock heating} \nEither as a result of stellar wind or from supernovae. In the case of\ngiant \\hii\\ regions, this later mechanism was favored by\nLuridiana et~al. (1999).\n\\item{\\it Magnetic heating} Turbulent dissipation from Alf\\'en waves\nand magnetic line reconnection has been proposed to explain the\nvariations of the \\nii/\\ha\\ ratio emitted by the warm diffuse ionized\ngas in the Galaxy (Reynolds et~al. 2000). In the case of planetaries,\nthe large values of \\tsq\\ found would then make sense in the light of the\nsuccess of the magnetically accelerated wind models of Garc\\'\\i\na-Segura (2000). Furthermore, Peimbert et~al. (1995) has shown that\nthe nebulae with the highest gas velocity dispersion show the highest\nvalues of \\tsq, which would be consistent with an increasing\nrole played by magnetic acceleration of the gas in the objects with\nthe largest velocity dispersion.\n\\end{enumerate}\n\nIn summary, the current work shows how \\gama\\ and \\gamh\\ vary with\nmetallicity and \\tsq\\ as well as how these quantities are affected by\nthe ionizing energy distribution. Our results can be translated into\nenergy requirements (function of \\tsq) which competing\nexplanations of the temperature fluctuations must satisfy and, hence,\ncan be used to probe their respective viability.\n\n\\acknowledgements The work of LB was supported by the CONACyT grant 32139-E.\n\n%\\adjustlastcols\n\n%% When using the rmaacite package, the \\bibitem command should be of\n%% the format: \n%%\n%% \\bibitem[AUTHOR<YEAR>]{KEY} \n%%\n%% so that the \\cite{KEY}, etc. commands will work properly. \n%% \n%% If you are doing the citations manually, then you can just use\n%% `\\bibitem{}' instead. This will give you a warning about\n%% `multiply-defined labels' which you can safely ignore.\n%% \n\\begin{thebibliography}\n\n\\bibitem{u} Anders, E., \nGrevesse, N. 1989, Geochim. Cosmochim. Acta 53, 197 \n\n\\bibitem{a} Campbell, A. W. 1988, ApJ, 335, 644 \n\n\\bibitem{b} Evans, I. 1991, ApJS, 76, 985\n\n\\bibitem{c} Ferruit, P., Binette, L., Sutherland, R. S. and P\\'econtal,\nE. 1997, A\\&A, 322, 73 \n\n\\bibitem{d} Gonz\\'alez-Delgado, R. et~al. 1994, ApJ, 437, 239\n\n%\\bibitem{e} Gazol, A., Passot, T. \\& Sulem, P. L., \n%2000, in proc. of Astrophysical plasmas: Codes, Models and\n%Observations, RevMexAA conf. series, Eds. J. Franco and J. Arthur, in press\n\n\\bibitem{f} Hummer, D. G., \\& Mihalas, D. M. 1970, MNRAS, 147, 339\n\n\\bibitem{g} Luridiana, V., 1999, PhD thesis: Condiciones f\\'\\i sicas en\nnebulosas gaseosas, (UNAM: Mexico city)\n\n\\bibitem{h} Luridiana, V., Peimbert, M. \\& Leitherer, C. 1999, ApJ,\n527, 110\n\n\\bibitem{j} Peimbert, M. 1967, ApJ, 150, 825\n\n\\bibitem{k} Peimbert, M. 1995, in proc. of The Analysis of\nEmission Lines, ed. R. E. Williams and M. Livio (Cambridge: Cambridge\nUniversity Press), 165\n\n\\bibitem{l} Peimbert, M., Luridiana, V., \\& Torres-Peimbert, S. 1995, \nRevMexAA, 31, 131\n\n\\bibitem{n} P\\'erez, E. 1997, MNRAS, 290, 465\n\n\\bibitem{o} Reynolds, R. J., Haffner, L. M., \\& Tufte, S. L., 2000,\n in proc. of Astrophysical plasmas: Codes, Models and Observations,\n RevMexAA conf. series, Eds. J. Franco and J. Arthur, in press\n\n\\bibitem{p} Stasi\\'nska, G., 1998, in proc. of Abundance Profiles:\nDiagnostic Tools for Galaxy History, eds. D. Friedli, M. Edmunds,\nC. Robert, and L. Drissen, ASP Conf. Ser., 147, 142.\n\n\\bibitem{q} Torres-Peimbert, S., Peimbert, M., Pe\\~na, M., 1990, A\\&A,\n233, 540r\n\n%\\bibitem {} Vishniac, E. \\& Lazarian, A., 2000, in proc. of\n%Astrophysical plasmas: Codes, Models and Observations, RevMexAA\n%conf. series, Eds. J. Franco and J. Arthur, in press\n\n\\end{thebibliography}\n\n\\end{document}\n\n\n\n%%%%%%%%%%%%% bits of text kept for later \n\nIn order to calculate the energy expense implied by the larger\ntemperatures characterizing each collisionally excited line, we first\ndescribe below the modifications made to the multipurpose\nphotoionization-shock code \\map\\ (Ferruit et~al. 1997).\n\n\nWe do not attempt to model individually the fluctuations nor their\nphysical origin but simply consider their effect on the collisionally\nexcited lines following the statistical approach of Peimbert who\nquantifies the increase in brightness of each line in terms of\ndeparture of the temperature from \\tmean\\ using an expansion in Taylor\nseries of the appropriate temperature for each transition taking into\naccount the functional dependence with temperature of each line\nemissivity.\n"
}
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[
{
"name": "astro-ph0002211.extracted_bib",
"string": "\\begin{thebibliography}\n\n\\bibitem{u} Anders, E., \nGrevesse, N. 1989, Geochim. Cosmochim. Acta 53, 197 \n\n\\bibitem{a} Campbell, A. W. 1988, ApJ, 335, 644 \n\n\\bibitem{b} Evans, I. 1991, ApJS, 76, 985\n\n\\bibitem{c} Ferruit, P., Binette, L., Sutherland, R. S. and P\\'econtal,\nE. 1997, A\\&A, 322, 73 \n\n\\bibitem{d} Gonz\\'alez-Delgado, R. et~al. 1994, ApJ, 437, 239\n\n%\\bibitem{e} Gazol, A., Passot, T. \\& Sulem, P. L., \n%2000, in proc. of Astrophysical plasmas: Codes, Models and\n%Observations, RevMexAA conf. series, Eds. J. Franco and J. Arthur, in press\n\n\\bibitem{f} Hummer, D. G., \\& Mihalas, D. M. 1970, MNRAS, 147, 339\n\n\\bibitem{g} Luridiana, V., 1999, PhD thesis: Condiciones f\\'\\i sicas en\nnebulosas gaseosas, (UNAM: Mexico city)\n\n\\bibitem{h} Luridiana, V., Peimbert, M. \\& Leitherer, C. 1999, ApJ,\n527, 110\n\n\\bibitem{j} Peimbert, M. 1967, ApJ, 150, 825\n\n\\bibitem{k} Peimbert, M. 1995, in proc. of The Analysis of\nEmission Lines, ed. R. E. Williams and M. Livio (Cambridge: Cambridge\nUniversity Press), 165\n\n\\bibitem{l} Peimbert, M., Luridiana, V., \\& Torres-Peimbert, S. 1995, \nRevMexAA, 31, 131\n\n\\bibitem{n} P\\'erez, E. 1997, MNRAS, 290, 465\n\n\\bibitem{o} Reynolds, R. J., Haffner, L. M., \\& Tufte, S. L., 2000,\n in proc. of Astrophysical plasmas: Codes, Models and Observations,\n RevMexAA conf. series, Eds. J. Franco and J. Arthur, in press\n\n\\bibitem{p} Stasi\\'nska, G., 1998, in proc. of Abundance Profiles:\nDiagnostic Tools for Galaxy History, eds. D. Friedli, M. Edmunds,\nC. Robert, and L. Drissen, ASP Conf. Ser., 147, 142.\n\n\\bibitem{q} Torres-Peimbert, S., Peimbert, M., Pe\\~na, M., 1990, A\\&A,\n233, 540r\n\n%\\bibitem {} Vishniac, E. \\& Lazarian, A., 2000, in proc. of\n%Astrophysical plasmas: Codes, Models and Observations, RevMexAA\n%conf. series, Eds. J. Franco and J. Arthur, in press\n\n\\end{thebibliography}"
}
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astro-ph0002212
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The porous atmosphere of $\eta$-Carinae
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[
{
"author": "Nir J. Shaviv"
}
] |
We analyze the wind generated by the great 20 year long super-Eddington outburst of $\eta$-Carinae. We show that using classical stellar atmospheres and winds theory, it is impossible to construct a consistent wind model in which a sufficiently {\em small} amount of mass, like the one observed, is shed. One expects the super-Eddington luminosity to drive a thick wind with a mass loss rate substantially higher than the observed one. The easiest way to resolve the inconsistency is if we alleviate the implicit notion that atmospheres are homogeneous. An inhomogeneous atmosphere, or ``porous", allows more radiation to escape while exerting a smaller average force. Consequently, such an atmosphere yields a considerably lower mass loss rate for the same total luminosity. Moreover, all the applications of the Eddington Luminosity as a strict luminosity limit should be revised, or at least reanalyzed carefully. \vskip 0.5cm \centerline{\em To appear in the Astrophysical Journal Letters} \vskip 0.5cm
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"name": "ms.tex",
"string": "%Uses AASTeX v5.0\n%\n% The porous atmosphere of eta-Carinae / Nir Shaviv\n%\n\n\n\\documentclass[preprint,11pt]{aastex}\n\\usepackage{epsfig}\n\n%----------------------------- My definitions\n\n%\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\bt}{\\begin{table} \\begin{center}}\n\\newcommand{\\et}{\\end{center} \\end{table}}\n\\newcommand{\\ba}{\\begin{eqnarray}}\n\\newcommand{\\ea}{\\end{eqnarray}}\n\\newcommand{\\ie}{{\\it i.e.~}}\n\\newcommand{\\eg}{{\\it e.g.~}}\n%\n\\newcommand{\\citenp}[1]{\\citeauthor{#1}~\\citeyear{#1}}\n\\newcommand{\\sch}{Schwarzchild~}\n\\newcommand{\\BV}{Brunt-V\\\"ais\\\"al\\\"a~}\n\\newcommand{\\mt}{\\mathit}\n%\n\\newcommand{\\ms}{{\\cal M}_\\odot}\n\\newcommand{\\ls}{{\\cal L}_\\odot}\n\n\n% ---- For some reason the AAS definitions for <~ and >~ do\n% not work properly, so they are defined.\n\n\\def\\lesssim{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr<\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\n<\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\n<\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n<\\cr\\sim\\cr}}}}}\n\\def\\gtrsim{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr>\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr\n>\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr\n>\\cr\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\\cr\n>\\cr\\sim\\cr}}}}}\n\n\n%---------------------------- End of definitions\n\n\\begin{document}\n\n%\\def\\temp{\n\\title{The porous atmosphere of $\\eta$-Carinae}\n\\author{Nir J. Shaviv}\n\\affil{Canadian Institute for Theoretical\n Astrophysics, University of Toronto \\\\ 60 St. George St.,\n Toronto, ON M5S 3H8, Canada}\n%}\n\n\\begin{abstract}\n \n We analyze the wind generated by the great 20 year long\n super-Eddington outburst of $\\eta$-Carinae. We show that using\n classical stellar atmospheres and winds theory, it is impossible to\n construct a consistent wind model in which a sufficiently {\\em\n small} amount of mass, like the one observed, is shed. One expects\n the super-Eddington luminosity to drive a thick wind with a mass\n loss rate substantially higher than the observed one. The easiest\n way to resolve the inconsistency is if we alleviate the implicit\n notion that atmospheres are homogeneous. An inhomogeneous\n atmosphere, or ``porous\", allows more radiation to escape while\n exerting a smaller average force. Consequently, such an atmosphere\n yields a considerably lower mass loss rate for the same total\n luminosity. Moreover, all the applications of the Eddington\n Luminosity as a strict luminosity limit should be revised, or at\n least reanalyzed carefully.\n\n\\vskip 0.5cm\n\\centerline{\\em To appear in the Astrophysical Journal Letters}\n\\vskip 0.5cm\n\n\\end{abstract}\n\n\\keywords{\n Radiative transfer --- hydrodynamics --- instabilities --- stars:\n atmospheres --- stars: individual ($\\eta$ Carinae) }\n% to find at:http://www.noao.edu/apj/keywords96.html\n\n%------------------------------------------------------\n\n\n\\section{Introduction}\n\n $\\eta$-Carinae is probably one of the most remarkable stellar object\n to have ever been documented. About 150 years ago, the star began a\n 20 year long giant eruption during which it radiated a\n supernova-like energy of roughly $3 \\times 10^{49}~ergs$~\n (\\citenp{DH97}). Throughout the eruption it also shed some\n $1-2~\\ms$ of material carrying approximately $6\\times 10^{48}~ergs$\n as kinetic energy (\\citenp{DH97}), while expanding at a velocity of\n $650~km/sec$ (\\citenp{HA92}, \\citenp{C96}). $\\eta$-Carinae can\n therefore serve as a good laboratory for the study of atmospheres\n at extreme luminosity conditions.\n\n At first glance, it appears that the star shed a large amount of\n material. Indeed, the inferred mass loss rate during the great\n eruption of $\\sim 0.1~\\ms/yr$ is significantly larger than the mass\n loss rate inferred for the star today ($\\lesssim 10^{-3}~\\ms/yr$,\n \\citenp{DH97} and references therein). However, considering that the\n luminosity during the great eruption is estimated to be\n significantly above the Eddington limit, we shall show that the star\n should have had a much higher mass loss rate. In fact, it should\n have lost during the 20 year eruption more mass than its total mass,\n giving rise to an obvious discrepancy.\n\n A review of our current knowledge of $\\eta$ Car can be found in\n \\cite{DH97}. In section \\ref{sec:wind} we summarize how a wind\n solution for the star $\\eta$ Car should be constructed. Since the\n luminosity is very high, the effects of convection must be taken\n into account. In section \\ref{sec:discrepancy} we integrate the wind\n equations to show that no consistent solution for $\\eta$ Car exists\n within the possible range of observed parameters. Section\n \\ref{sec:bad} is devoted to possible classical solutions to the\n discrepancy, showing that no such possibility exists. In section\n \\ref{sec:good}, we show that a porous atmosphere is a simple and\n viable solution to the wind discrepancy.\n\n\\section{Solving for the Wind}\n\\label{sec:wind}\n\n Since the mass of $\\eta$-Car is estimated to be of order\n $100-120~\\ms$ (\\citenp{DH97}), the average luminosity in the great\n eruption was clearly super-Eddington (of the order of 5 times the\n Eddington limit). That is to say, the radiative force upwards,\n assuming the smallest possible opacity (for ionized matter) given by\n Thomson scattering, was significantly larger than the gravitational\n pull downwards. Optically thin winds formally diverge at the\n Eddington limit (e.g., \\citenp{Puls} and references therein).\n Consequently, a consistent wind solution requires an optically thick\n wind. We thus look for a wind in which the sonic point (which is the\n point at which the local speed of the outflow equals the speed of\n sound) is below the photosphere. Moreover, since the duration of\n the eruption is longer than the sound crossing time of the star by\n about a factor of 50, a stationary wind appears to be a good\n approximation.\n\n In practically all super-sonic wind theories which describe\n super-sonic outflows from an object at rest, a consistent stationary\n solution is obtained only when the net driving force of the wind\n (excluding the pressure gradient) vanishes at the sonic\n point\\footnote{ The exception is line driven winds in which the\n force is explicitly a function of $dv/dr$ which is actually an\n approximation to the line transfer equations. If we had written the\n proper radiation transfer equations for this case which only {\\em\n implicitly} depend on $dv/dr$, we would have recovered that the\n sonic point coincides with the point at which the total force\n vanishes (cf \\citenp{MWM84} \\S107). Moreover, line driven winds are\n important only under optically thin conditions while we describe the\n optically thick part of the wind. }. Thus, material experiencing a\n super-Eddington flux necessarily has to be above the sonic point.\n If most of the envelope carries a super Eddington flux, then no\n consistent stationary wind solution can be obtained and in fact, the\n object will evaporate on a dynamical time scale. In most systems\n however, this need not be the case. For example, in very hot systems\n (e.g., hot neutron stars during strong X-ray bursts, \\citenp{QP85}),\n the opacity in the deep layers is reduced due the reduced\n Klein-Nishina opacity for Compton scattering at high\n temperatures. Thus, the sonic point in these objects is found where\n the temperature is high enough to reduce the opacity to the point\n where the flux corresponds to the local Eddington limit.\n\n Another important effect, which should be taken into account, is\n convection. Deep inside the atmosphere, convection can carry a\n significant part (or almost all) of the energy flux, thus reducing\n the radiative pressure to a sub-Eddington value. In fact, as the\n radiative flux approaches the Eddington limit, convection generally\n arises and carries the lion share of the total energy flux (if it\n can) to keep the system at a sub-Eddington level\n (\\citenp{JSO73}). Although the total flux in the entire envelope (or\n almost all of it) can be equivalent to a super-Eddington flux, up to\n some depth below the photosphere, convection carries most of the\n flux so as to reduce the radiative flux alone into a sub-Eddington\n value. A consistent wind solution should therefore, have its sonic\n point at the location where the most efficient convection cannot\n carry enough flux any more. As we shall soon see, the problem in\n $\\eta$-Car is that this point is relatively deep within the\n atmosphere, where the density is so high that the expected mass loss\n is significantly {\\it higher} than the observed one.\n\n To see this in a robust way we integrated numerically the wind\n equations starting from the photosphere inwards. The equations are\n those that describe optically thick spherically symmetric winds\n (\\citenp{QP85}; \\citenp{Z73}; \\citenp{KH94}). The equations of mass\n conservation, momentum conservation and temperature gradient are\n\\begin{equation}\n 4 \\pi r^2 \\rho v = \\dot{M} = {\\rm const}\n\\end{equation}\n\\begin{equation}\n v {d v\\over dr} + {GM\\over r^2} +{1\\over \\rho}{dP_{g} \\over dr} -\n {\\chi {\\cal L}_r \\over 4 \\pi r^2 c} = 0\n\\end{equation}\n\\begin{equation}\n {d T \\over dr} = - {3 \\chi \\rho {\\cal L}_r \\over 16 \\pi r^2 c a T^3} (1 +\n {2 \\over 3 \\chi \\rho r}),\n\\end{equation}\nwith standard notation. The parenthesized term in the last equation\nis a simple approximate interpolation that has the correct asymptotic\nlimits for optical depths much larger and much smaller than unity\n(\\citenp{QP85}). The last equation is the integrated form of the\nenergy conservation equation. Unlike the aforementioned references, we\nspecifically include advection by a maximally efficient convection.\nThus, the integrated form of the energy conservation equation becomes\n\\begin{eqnarray}\n {\\cal L}_r + \\dot{M}\\left({v^2 \\over 2} + w - {GM\\over\n r}\\right) + {\\cal L}_{conv} &\\equiv& \\\\ {\\cal L}_r -{GM \\dot{M} \\over r} +\n {\\cal L}_{adv}+{\\cal L}_{conv} &=& \\Lambda_{tot} = {\\cal L}_{obs}+\n {\\cal L}_{kin,\\infty},\n\\label{eq:fluxes}\n\\end{eqnarray}\n were $\\Lambda_{tot}$, $\\dot{M}$, ${\\cal L}_{obs}$ and ${\\cal\n L}_{kin,\\infty}$ are the total energy output of the star, the wind\n mass loss rate, the observed luminosity at infinity and the kinetic\n energy flux at infinity. On the other hand, ${\\cal L}_r, v, w, {\\cal\n L}_{conv}, {\\cal L}_{adv}$ are respectively, the local radiative\n luminosity, velocity, enthalpy, convective flux and advected flux\n (as internal and kinetic energies). The expression adopted for\n ${\\cal L}_{conv}$ is $4 \\pi r^2 u v_{s}$ where $u$ is the internal\n energy per unit volume and $v_s$ is the speed of sound. By no means\n can convection be more efficient than this expression since highly\n dissipative shocks are unavoidable at higher speeds. It is likely\n that the maximally efficient convection is somewhat less efficient\n than this expression, but this will only aggravate the problem that\n we shall soon expose. Detailed calculations of the wind were\n carried out. The calculations include the latest version of the\n OPAL opacities (\\citenp{IR96}). It is found that the total opacity\n below the photosphere has comparable contributions from Thomson\n scattering and absorption processes. This implies that the {\\em\n modified} Eddington limit, in which the Thomson opacity is replaced\n by the local total opacity, is somewhat lower than the classical\n Eddington limit.\n\n\n Since $T_{\\mathit{eff}} \\sim 9000^{\\circ}$K\\footnote{This is the\n typical observed effective temperature for LBV's during outbursts\n (\\citenp{HD94}). If the temperature is higher than this value, the\n inferred bolometric magnitude of $\\eta$ Car during the eruption\n would be more negative, increasing the Eddington factor. If the\n temperature is lower than $\\sim 7000^\\circ$K, the opacity at the\n photosphere and outwards rises abruptly (\\citenp{D87}), thus\n reducing the modified Eddington limit. In both cases, the\n discrepancy will be aggravated.}, the average luminosity implies a\n photospheric radius of $10^{14}~cm$. Note that since it is a thick\n wind, the exact definition of the photosphere is ambiguous.\n Nevertheless, different definitions do not change the results by\n more than $10-20\\%$. Knowing that the observed mass loss rate is\n roughly $0.1~\\ms/yr$ (which gives the observed $2~\\ms$ of shed\n material in 20 years, \\citenp{DH97}), a specified flow speed at the\n photosphere can be translated to a required density. We can\n therefore integrate the wind equations inwards. If a consistent\n wind solution can be obtained for some value of the imposed velocity\n in the photosphere (which has to be between $v_s$ and $v_{\\infty}$),\n then the integration inwards should reach a sonic point at which the\n total force on the gas vanishes. This will be attained if the\n convective and advective fluxes can carry a significant amount of\n the total flux so as to reduce the residual radiative flux to a\n sub-Eddington one.\n\n\\section{The Discrepancy}\n\\label{sec:discrepancy}\n\n We define the luminosity needed to be carried by convection and\n advection in order to bring about the vanishing of the total local\n force as ${\\cal L}_{crit}$. If enough energy is advected and\n convected then ${\\cal L}_r$ will be reduced to the local modified\n Eddington flux:\n\\begin{equation}\n{\\cal L}_{Edd,mod}={4 \\pi c G M\\over \\chi}\n\\end{equation}\n with $\\chi$ the local opacity which can be larger than the Thomson\n opacity. Thus, from eq.~(\\ref{eq:fluxes}), the critical\n advective+convective flux can be written as\n\\begin{equation}\n{\\cal L}_{crit} = \\Lambda_{tot} + {G M {\\dot M}\\over r}-{\\cal L}_{Edd,mod}.\n\\end{equation}\n\n Figure \\ref{fig_1} shows the fraction $\\eta\\equiv({\\cal\n L}_{adv}+{\\cal L}_{conv})/{\\cal L}_{crit}$ at the sonic point. A\n consistent solution can be found only if $\\eta=1$ at the sonic\n point.\n\n Inspection of the figure clearly shows that the space of possible\n observed values does not contain a viable and consistent solution.\n This is of course irrespective of whether a solution from the\n photosphere outward can or cannot be obtained. The discrepancy\n arises because a wind corresponding to the observed low mass loss\n rate necessarily has a sonic point that is not deep enough to have\n either convection or advection as an efficient mean of transporting\n energy. This can be seen from the optical depth at which the sonic\n point is obtained. In all cases, $1 \\lesssim \\tau < 300$. However,\n convection is efficient only up to an optical depth of $\\tau \\sim c/\n v_s \\gg 300$ for $p_{rad} \\sim p_{gas}$ (\\citenp{S00b}), or even\n deeper for larger radiation pressures (i.e., when close to the\n Eddington limit).\n\n\\section{Unfeasible Solutions to the Discrepancy}\n\\label{sec:bad}\n\n Can the discrepancy be resolve with a classical assumption? Since\n the discrepancy is rather large, assuming the wind to emerge from an\n angular fraction $f$ from the star does not relax the problem (it\n actually aggravates the problem because more material will be blown\n away from the higher luminosity regions). Another possibility that\n fails is having a higher velocity in the photosphere than the one\n observed today for the shed material. This might be the case if the\n wind collides with previously ejected slow moving material. Even if\n such material did exist, the necessarily reduced mass loss rate\n inferred from the present day observed momentum aggravates the\n problem.\n\n The problem is not mitigated if we relax the assumption that the mass\n loss rate and the luminosity are assumed to be constant in time\n throughout the eruption.\n\n If one wishes to solve the problem using magnetic fields, then a\n solution can be found only if the magnetic energy density at the\n photosphere is significantly larger (by several orders of magnitude)\n then the equipartition value with the gas pressure. This of course\n seems unlikely.\n\n Another option is to have the distance estimate to $\\eta$-Car be\n three times smaller than $2300~pc$. A shorter distance will remove\n $\\eta$-Car out of the cluster Tr16 of massive stars inside which it\n is observed and leave it instead roaming the inter galactic arm\n space. Considering the short lifetime of the star, just a few\n million years, this possibility appears as very unlikely.\n\n The problem can be solved if the mass of the star corresponds to a\n sub-Eddington luminosity. This proposed solution requires $\\eta$-Car\n to be at least a $\\sim 1000~\\ms$ star. However, this suggestion is\n at variance with much lower estimates (see for instance\n \\citenp{DH97} and references therein). Nevertheless, having such a\n massive star is in fact not completely unrealistic and would have\n far reaching consequences if found to be true.\n\n\\section{A Viable Solution to the Discrepancy}\n\\label{sec:good}\n\n As the title suggests, there is a clear solution to the\n discrepancy. As the results show, the sonic point appears to be\n between the optical depths of $\\sim 1$ and $\\sim 300$. The exact\n value cannot be obtained since it requires the integration outward\n from the photosphere, which owing to the relatively inaccurate\n effective temperature and therefore opacity, yields a wide range of\n results. If the {\\it mean} radiative force between the point $\\eta=1$\n and the above found optical depth, is smaller than classically\n estimated, then a solution to the discrepancy can be found. Such a\n reduction in the mean radiative force is a natural result if the\n atmosphere is inhomogeneous.\n\n \\cite{S98} has shown that in an inhomogeneous atmosphere, the\n effective opacity used to calculate the average force is reduced\n relative to the effective opacity used for the radiation transfer in\n a homogeneous medium. The effective opacity used for the average\n force should be a volume {\\em flux weighted} average of the opacity\n per unit volume\\footnote{When the flux is frequency dependant, a\n similar average should be taken in order to find the radiative\n force. However, one then takes a flux weighted mean over {\\em\n frequency space}.} $\\chi_v \\equiv \\chi \\rho$. Namely,\n\\begin{equation}\n \\chi_{\\mt{eff}} = {\\left< \\chi \\rho F\\right> \\over \\left< F \\right>\n \\left<\\rho\\right>}.\n\\end{equation}\n\n The effect is universal and arises in inhomogeneous systems that\n conduct heat or electricity. Extensive discussions exist in the\n literature under a different terminology (\\citenp{I92}). The only\n requirement is therefore, that close to the Eddington limit the star\n develop inhomogeneities. The transformation from an homogeneous to\n an inhomogeneous atmosphere at luminosities close to but below\n Eddington luminosities, was recently found to take place generically\n even in Thomson scattering atmospheres (\\citenp{S99}; \\citenp{ST99};\n \\citenp{S00}).\n\n It was found that two different types of instabilities arise\n naturally when the luminosity approaches the Eddington limit\n (\\citenp{S00}). One instability is of a phase transition into a {\\em\n stationary} nonlinear pattern of ``fingers\" that facilitate the\n escape of the radiation. The second type of instability allows the\n growth of a propagating wave, from which one expects a {\\em\n propagating} nonlinear pattern to form. The two possibilities are\n summarized in figure \\ref{fig_2}. Both instabilities bring about a\n reduction of the average radiative force on the matter and a\n significant reduction of the mass loss rate since the sonic surface\n can sit near (or not much below) the photosphere. In both cases, the\n nonlinear pattern is necessarily expected to form in the region\n between the radius $r_{conv}$ at which $\\eta=1$, or in other words,\n that ${\\cal L}_{conv} + {\\cal L}_{adv}$ is large enough to have\n ${\\cal L}_r \\lesssim {\\cal L}_{Edd,mod}$, and the photosphere. When\n the pattern is stationary, the rarefied regions have a larger than\n Eddington flux and the sonic surface in these regions is near\n $r_{conv}$. On the other hand, if the pattern is propagating, the\n flux may be larger locally than the Eddington limit but the time\n average of the force on a mass element is less than Eddington. Since\n the instability does not occur above the photosphere, it should be\n homogeneous and hence super-Eddington with a super-sonic flow.\n\n Further analysis of the instabilities is needed to know which\n instability will dominate though it is more likely to be the phase\n transition since it is dynamically more important.\n\n\\section{Summary}\n\\label{sec:summary}\n\n To summarize, the super-Eddington luminosity emitted by $\\eta$-Car\n should have generated a much thicker wind with a sonic point placed\n significantly deeper than what can be directly inferred from the\n observations. A solution which lives in harmony with observations\n and theoretical modeling is a porous atmosphere, which allows more\n radiation to escape while exerting a smaller average force. It also\n means that the Eddington limit is not as destructive as one would a\n priori think it must be, even in a globally spherically symmetric\n case. Namely, all astrophysical analyses that employ the Eddington\n limit as a strict limit should be reconsidered carefully, even if\n they involve only unmagnetized Thomson scattering material. If\n $\\eta$-Carinae could have been super-Eddington for such a long\n duration without ``evaporating'', other systems can display a\n similar behavior.\n\n\n\\begin{thebibliography}{ll}\n\n \\bibitem[Currie et al.(1996)]{C96} Currie, D. G., Dowling, D. M.,\n Shaya, E. J., Hester, J., Scowen, P., Groth, E. J., Lynds, R. O., \\&\n Earl, J. Jr Wide Field/Planetary Camera Instrument Definition Team,\n 1996, \\apj, 112, 1115\n\n \\bibitem[Davidson(1987)]{D87} Davidson, K. 1987, \\apj, 317, 760\n\n \\bibitem[Davidson \\& Humphreys(1997)]{DH97} Davidson, K. \\&\n Humphreys, R. M., 1997, \\araa, 35, 1\n\n \\bibitem[Hiller \\& Allen(1992)]{HA92} Hillier, D. J. \\& Allen,\n D. A. 1992, \\aap, 262, 153\n\n \\bibitem[Humphreys \\& Davidson(1994)]{HD94} Humphreys,\n R. M. \\& Davidson, K. 1994, \\pasp, 106, 1025\n\n \\bibitem[Iglesias \\& Rogers(1996)]{IR96} Iglesias, C. A. \\& Rogers,\n F. J. 1996, \\apj, 464, 943\n\n \\bibitem[Isichenko(1992)]{I92} Isichenko, M. B. 1992,\n {Rev. Mod. Phys.}, 64, 961.\n\n \\bibitem[Joss et al.(1973)]{JSO73} Joss, P. C., Salpeter, E. E. \\& Ostriker,\n J. P. 1973, 181, 429\n\n \\bibitem[Kato \\& Hachisu(1994)]{KH94} Kato, M., \\& Hachisu, I. 1994,\n \\apj, 437, 802\n\n \\bibitem[Kudritzki et al.(1989)]{Puls} Kudritzki, R. P., Pauldrach,\n A., Puls, J. \\& Abbott, D. C. 1989 \\aap, 219, 205\n\n \\bibitem[Mihalas \\& Weibel Mihalas(1984)]{MWM84} Mihalas D., \\& Weibel\n Mihalas B. 1984, Foundations of radiation hydrodynamics, Oxford univ.\n press, Oxford\n\n \\bibitem[Quinn \\& Paczynski(1985)]{QP85} Quinn, T. \\& Paczynski, B.\n 1985, \\apj, 289, 634\n\n \\bibitem[Shaviv(1998)]{S98} Shaviv, N. J. 1998, \\apj, 494, L193\n\n \\bibitem[Shaviv(1999)]{S99} Shaviv, N. J. 1999, in {\\it Variable and\n Non-spherical Stellar Winds in Luminous Hot Stars, IAU Colloquium\n 169}, ed.~B.~Wolf, O.~Stahl,~A.~W.~Fullerton, Springer, p. 155\n\n \\bibitem[Shaviv(2000a)]{S00} Shaviv, N. J. 2000a, {submitted to\n \\apj}\n \\bibitem[Shaviv(2000b)]{S00b} Shaviv, N. J. 2000b, {submitted to\n \\apj}\n\n \\bibitem[Spiegel \\& Tao(1999)]{ST99} Spiegel, E. A., \\& Tao L. 1999,\n {Physics Reports}, 311, 163\n\n \\bibitem[\\.{Z}ytkow(1972)]{Z73} \\.{Z}ytkow, A. 1972, {Acta\n Astronomica}, 22, 103\n\n\\end{thebibliography}\n\n\\begin{figure}[p]\n\\centerline{\\epsfig{file=fig1.eps,width=4in,angle=-90}}\n\\caption{\n The fraction $\\eta = ({\\cal L}_{adv}+ {\\cal L}_{conv})/{\\cal\n L}_{crit}$ as a function of the photospheric velocity $v_{ph}$. A\n consistent wind solution requires (a) that the velocity at the\n photosphere $v_{ph}$ satisfy: $v_s \\le v_{ph}\n \\le v_\\infty$, and\n (b) , $\\eta(v=v_{s})=1$. The thick line corresponds to the nominal\n observed and inferred values ($M_\\star=100~\\ms$,\n $T_{\\mathit{eff}}=9000^\\circ$K, $\\dot{M}=0.1~\\ms/yr$, $\\int{\\cal\n L}_{obs}dt = 3\\times 10^{49}~erg$) while the additional lines depict\n the result when the values are changed to their reasonable limits\n (and even beyond). Clearly, no reasonable choice of parameters can\n result with a sonic point that is consistent with a wind solution\n (namely, we always find $\\eta(v=v_s)\\ll 1$). Basically, the\n discrepancy arises because the mass loss rate observed is too small\n to have the sonic point deep enough in the atmosphere where\n convection can be an efficient mean of energy transport. }\n\\label{fig_1}\n\\end{figure}\n\n\\begin{figure}[p]\n\\centerline{\\epsfig{file=fig2a.eps,width=3.5in}}\n\\centerline{\\epsfig{file=fig2b.eps,width=3.5in}}\n\\caption{\n The proposed atmospheric structure of $\\eta$ Carinae during its great\n eruption. A homogeneous atmosphere is unstable as a result of two\n generic instabilities that take place even in Thomson atmospheres\n when close to the Eddington limit (\\citenp{S00}). The effective\n opacity is therefore reduced (\\citenp{S98}) and with it the average\n radiative force. The two panels describe the two types of\n possibilities for having a `porous' atmosphere according to the\n characteristics of the instability that arises. An instability could\n produce a stationary pattern (first panel) if it originates from the\n phase transition instability and a moving pattern if it originates\n from the finite speed of light instability (second panel). See\n details in the text.}\n\\label{fig_2}\n\\end{figure}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002212.extracted_bib",
"string": "\\begin{thebibliography}{ll}\n\n \\bibitem[Currie et al.(1996)]{C96} Currie, D. G., Dowling, D. M.,\n Shaya, E. J., Hester, J., Scowen, P., Groth, E. J., Lynds, R. O., \\&\n Earl, J. Jr Wide Field/Planetary Camera Instrument Definition Team,\n 1996, \\apj, 112, 1115\n\n \\bibitem[Davidson(1987)]{D87} Davidson, K. 1987, \\apj, 317, 760\n\n \\bibitem[Davidson \\& Humphreys(1997)]{DH97} Davidson, K. \\&\n Humphreys, R. M., 1997, \\araa, 35, 1\n\n \\bibitem[Hiller \\& Allen(1992)]{HA92} Hillier, D. J. \\& Allen,\n D. A. 1992, \\aap, 262, 153\n\n \\bibitem[Humphreys \\& Davidson(1994)]{HD94} Humphreys,\n R. M. \\& Davidson, K. 1994, \\pasp, 106, 1025\n\n \\bibitem[Iglesias \\& Rogers(1996)]{IR96} Iglesias, C. A. \\& Rogers,\n F. J. 1996, \\apj, 464, 943\n\n \\bibitem[Isichenko(1992)]{I92} Isichenko, M. B. 1992,\n {Rev. Mod. Phys.}, 64, 961.\n\n \\bibitem[Joss et al.(1973)]{JSO73} Joss, P. C., Salpeter, E. E. \\& Ostriker,\n J. P. 1973, 181, 429\n\n \\bibitem[Kato \\& Hachisu(1994)]{KH94} Kato, M., \\& Hachisu, I. 1994,\n \\apj, 437, 802\n\n \\bibitem[Kudritzki et al.(1989)]{Puls} Kudritzki, R. P., Pauldrach,\n A., Puls, J. \\& Abbott, D. C. 1989 \\aap, 219, 205\n\n \\bibitem[Mihalas \\& Weibel Mihalas(1984)]{MWM84} Mihalas D., \\& Weibel\n Mihalas B. 1984, Foundations of radiation hydrodynamics, Oxford univ.\n press, Oxford\n\n \\bibitem[Quinn \\& Paczynski(1985)]{QP85} Quinn, T. \\& Paczynski, B.\n 1985, \\apj, 289, 634\n\n \\bibitem[Shaviv(1998)]{S98} Shaviv, N. J. 1998, \\apj, 494, L193\n\n \\bibitem[Shaviv(1999)]{S99} Shaviv, N. J. 1999, in {\\it Variable and\n Non-spherical Stellar Winds in Luminous Hot Stars, IAU Colloquium\n 169}, ed.~B.~Wolf, O.~Stahl,~A.~W.~Fullerton, Springer, p. 155\n\n \\bibitem[Shaviv(2000a)]{S00} Shaviv, N. J. 2000a, {submitted to\n \\apj}\n \\bibitem[Shaviv(2000b)]{S00b} Shaviv, N. J. 2000b, {submitted to\n \\apj}\n\n \\bibitem[Spiegel \\& Tao(1999)]{ST99} Spiegel, E. A., \\& Tao L. 1999,\n {Physics Reports}, 311, 163\n\n \\bibitem[\\.{Z}ytkow(1972)]{Z73} \\.{Z}ytkow, A. 1972, {Acta\n Astronomica}, 22, 103\n\n\\end{thebibliography}"
}
] |
astro-ph0002213
|
The Formation of the Hubble Sequence of Disk Galaxies: The Effects of Early Viscous Evolution
|
[
{
"author": "Department of Physics and Astronomy"
},
{
"author": "3400 N.Charles Street"
},
{
"author": "Baltimore"
},
{
"author": "MD 21218"
},
{
"author": "USA"
}
] |
We investigate a model of disk galaxies whereby viscous evolution of the gaseous disk drives material inwards to form a proto-bulge. We start from the standard picture of disk formation through the settling of gas into a dark halo potential well, with the disk initially coming into centrifugal equilibrium with detailed conservation of angular momentum. We derive generic analytic solutions for the disk-halo system after adiabatic compression of the dark halo, with free choice of the input virialized dark halo density profile and of the specific angular momentum distribution. We derive limits on the final density profile of the halo in the central regions. Subsequent viscous evolution of the disk is modelled by a variation of the specific angular momentum distribution of the disk, providing analytic solutions to the final disk structure. The assumption that the viscous evolution timescale and star formation timescale are similar leads to predictions of the properties of the stellar components. Focusing on small `exponential' bulges, ones that may be formed through a disk instability, we investigate the relationship between the assumed initial conditions, such as halo `formation', or assembly, redshift $z_f$, spin parameter $\lambda$, baryonic fraction $F$, and final disk properties such as global star formation timescale, gas fraction, and bulge-to-disk ratio. We find that the present properties of disks, such as the scale length, are compatible with a higher initial formation redshift if the re-distribution by viscous evolution is included than if it is ignored. We also quantify the dependence of final disk properties on the ratio $F/\lambda$, thus including the possibility that the baryonic fraction varies from galaxy to galaxy, as perhaps may be inferred from the observations.
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[
{
"name": "disk.tex",
"string": "\\documentstyle[epsfig]{mn1}\n\n\\font\\cap=cmcsc10\n\\def\\beq{\\begin{equation}}\n\\def\\eeq{\\end{equation}}\n\\def\\bey{\\begin{eqnarray}}\n\\def\\eey{\\end{eqnarray}}\n\\def\\RM{\\rm}\n\\def\\cm{\\,{\\rm {cm}}}\n\\def\\mpc{\\,{\\rm {Mpc}}}\n\\def\\kpc{\\,{\\rm {kpc}}}\n\\def\\kpch{\\,{h^{-1}{\\rm kpc}}}\n\\def\\mpch{\\,h^{-1}{\\rm {Mpc}}}\n\\def\\kms{\\,{\\rm {km\\, s^{-1}}}}\n\\def\\msun{M_\\odot}\n\\def\\vcir{V_c}\n\\def\\v200{V_{200}}\n\\def\\neff{n_{\\rm eff}}\n\\def\\rh{r_{200}}\n\\def\\Rd{R_d}\n\\def\\Mh{M}\n\\def\\Md{M_d}\n\\def\\Mb{M_b}\n\\def\\md{m_d}\n\\def\\mb{m_b}\n\\def\\mag{\\,\\rm mag}\n\\def\\Magd{{\\cal M}_d}\n\\def\\Ld{L_d}\n\\def\\mH{m_{\\rm H}}\n\\def\\mtold{\\Upsilon _d}\n\\def\\lsun{L_\\odot}\n\\def\\Eh{E}\n\\def\\Jh{J}\n\\def\\Jd{J_d}\n\\def\\fd{m_d}\n\\def\\fg{f_B}\n\\def\\fB{f_B}\n\\def\\Jg{J_g}\n\\def\\jd{j_d}\n\\def\\fv{f_V}\n\\def\\fr{f_R}\n\\def\\tCDM{\\rm \\tau CDM}\n\\def\\LCDM{\\rm \\Lambda CDM}\n\\def\\nhi{N_{\\rm HI}}\n\\def\\omnow{\\Omega_0}\n\\def\\obnow{\\Omega_{b,0}}\n\\def\\deltac{\\delta_c}\n\\def\\delch{\\delta_{0}}\n\\def\\rhoch{\\rho_{0}}\n\\def\\ovnow{\\Omega_{\\rm \\Lambda,0}}\n\\def\\rhoc{\\rho_{\\rm crit}}\n\n\\def\\erfc{{\\rm\\,erfc}}\n\\def\\ni{\\noindent} %No Indent%\n\\def\\ub{\\underbar}\n\\def\\hi{\\noindent \\hangindent=2.5em}\n\\def\\et{{\\it et\\thinspace al.}} %et al.%\n\\def\\pc{{\\rm\\,pc}}\n\\def\\cm{{\\rm\\,cm}}\n\\def\\kpc{{\\rm\\,kpc}}\n\\def\\Mpc{{\\rm\\,Mpc}}\n\\def\\mpc{{\\rm\\,Mpc}}\n\\def\\Gyr{{\\rm\\,Gyr}}\n\\def\\kmsec{{\\rm\\,km/s}}\n\\def\\kms{\\kmsec}\n\\def\\hnot{{\\rm\\,km/s/Mpc}}\n\\def\\msun{{\\rm\\,M_\\odot}}\n \\def\\lsun{{\\rm\\,L_\\odot}}\n\\def\\mdot{{\\rm\\,M_\\odot}}\n\\def\\surfb{{\\rm\\,mag/arcsec^2}}\n\\def\\surfden{{\\rm\\,M_\\odot/pc^2}}\n\\def\\numden{{\\rm\\,\\#/Mpc^3}}\n\\def\\araa{{\\rm ARA\\&A}, }\n\\def\\aj{{\\rm AJ}, } %Astronomical Journal%\n\\def\\apj{{\\rm ApJ}, } %Astrophysical Journal%\n\\def\\apjs{{\\rm ApJS}, } %Astrophysical Journal Supplements%\n\\def\\fcp{{\\rm Fund.~Cos.~Phys.}, } %Fundamentals of Cosmic Physics%\n\\def\\pasp{{\\rm PASP}, } %Publications of the Astronomical%\n %Society of the Pacific%\n\\def\\mn{{\\rm MNRAS}, } %Monthly Notices of the Royal%\n %Astronomical Society%\n\\def\\nat{{\\rm Nat}, } %Nature%\n\\def\\aa{{\\rm A\\&A}, } %Astronomy & Astrophysics%\n\\def\\aasup{{\\rm A\\&AS}, } %A & A Supplements%\n\\def\\baas{{\\rm BAAS}, } % Bulletin of the American A.S.%\n\n\n\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\def\\lta{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}}\n\\def\\gta{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}}\n\n\\def\\clock{\\count0=\\time \\divide\\count0 by 60\n \\count1=\\count0 \\multiply\\count1 by -60 \\advance\\count1 by \\time\n \\number\\count0:\\ifnum\\count1<10{0\\number\\count1}\\else\\number\\count1\\fi}\n\\def\\draft{\n \\rightline{DRAFT: \\today \\quad\\quad \\clock -- PLEASE DO NOT CIRCULATE!!}} \n \n\\title[Formation of Hubble Sequence]{The Formation of the Hubble Sequence of Disk Galaxies: The Effects of Early Viscous Evolution}\n\n\\author[B. Zhang and R.F.G. Wyse]{Bing Zhang and Rosemary F.G. Wyse\n\\thanks{E-mail: bingz@pha.jhu.edu (BZ); wyse@pha.jhu.edu (RFGW)} \\\\\nDepartment of Physics and Astronomy, Johns Hopkins University, 3400 N.Charles Street, Baltimore, MD 21218, USA }\n\n\n\\date{\\today}\n\\begin{document}\n\\maketitle\n \n \n\\begin{abstract}\n\nWe investigate a model of disk galaxies whereby viscous evolution of \nthe gaseous disk drives material inwards to form a proto-bulge. \nWe start from the standard picture of disk formation through the \nsettling of gas into a dark halo potential well, with the disk initially \ncoming into \ncentrifugal equilibrium with detailed conservation of angular momentum. \nWe derive generic analytic solutions for the disk-halo system \nafter adiabatic compression of the dark halo, with \nfree choice of the input virialized dark halo density profile and of the \nspecific angular momentum distribution.\nWe derive limits on the final density profile of the halo in the central \nregions. Subsequent viscous evolution of the disk is modelled by a \nvariation of the specific angular momentum distribution of the disk, \nproviding analytic solutions to the final disk structure. The assumption \nthat the viscous evolution timescale and star formation timescale are \nsimilar leads to predictions of the properties of the stellar components. \nFocusing on small `exponential' bulges, ones that may be formed through \na disk instability, we investigate the relationship \nbetween the assumed initial conditions, such as halo `formation', or \nassembly, redshift $z_f$, \nspin parameter $\\lambda$, baryonic fraction $F$, and final disk properties \nsuch as global star formation timescale, gas fraction, and bulge-to-disk \nratio. We find that the present properties of disks, such as the scale \nlength, are compatible with a higher \ninitial formation redshift if the re-distribution by \nviscous evolution is included than if it is ignored. We also quantify the \ndependence of final disk properties on \nthe ratio $F/\\lambda$, thus including the possibility that the baryonic \nfraction varies from galaxy to galaxy, as perhaps may be inferred from the \nobservations. \n\n\n\\end{abstract}\n\n\n\\begin{keywords}\ngalaxies: formation --- galaxies: structure --- galaxies: spiral\n--- cosmology: theory --- dark matter\n\\end{keywords}\n\n\\section{Introduction}\n\n The current picture of disk galaxy formation and evolution has as its \nbasis the dissipative infall of baryons within a dominant dark halo \npotential well (White \\& Rees 1978). \nThe collapse and spin-up of the baryons, with angular momentum \nconservation, can provide an explanation for many of the observed \nproperties of disks, with the standard initial conditions of baryonic \nmass fraction $F \\sim 0.1$ and dark halo angular momentum parameter \n$\\lambda \\sim 0.07$ (Fall \\& Efstathiou \n1980; Gunn 1982; Jones \\& Wyse 1983; Dalcanton, Spergel \\& Summers 1997; \nHernandez \\& Gilmore 1998; Mo, Mao \\& White 1998; van den Bosch 1998). \nGalaxies such \nas the Milky Way which have an old stellar population in the disk, must, \nwithin the context of a hierarchical-clustering scenario, \nevolve through only quiescent merging/accretion, so as to avoid excessive \nheating and disruption of the disk (Ostriker 1990). Further, the \nmerging processes with significant substructure cause \nangular momentum transport to the outer regions, \nwhich must somehow be suppressed to allow the formation of \nextended disks as observed (e.g. Zurek, Quinn \\& Salmon 1988; Silk \\& Wyse \n1993; Navarro \\& Steinmetz 1997). \n\nThus here we adopt the simplified picture \nthat disk galaxies form from \nsmooth gaseous collapse to centrifugal equilibrium, \nwithin a steady dark halo potential. We discuss \nwhere appropriate below how this may be modified to take account of \nsubsequent infall, or earlier star formation. \nOur model incorporates the adiabatic response of the dark halo to the disk \ninfall, and we provide new, more general, analytic solutions for the \ndensity profile, given a wide range of initial density profiles and \nangular momentum distributions. We provide new insight \ninto the `disk-halo' conspiracy within the \ncontext of this model, demonstrating how an imperfect conspiracy is \nimproved by the disk-halo interaction. We explicitly include \nsubsequent viscous evolution of the gas disk to provide the exponential \nprofile of the stellar disk, and develop \nanalytic expressions that illustrate the process. The resulting radial \ninflow builds up the central regions of \nthe disk and we investigate the properties of `bulges' that may form as a \nconsequence of instabilities of the central disk. We derive new \nconstraints on the characteristic redshift of disk star formation. \nWe obtain a simple relation connecting the initial\nconditions, such as spin parameter and baryonic mass fraction, to the \nefficiency of viscous evolution and star formation. \n\n\n\\section{The Disk Galaxy Formation Model} \n\nIn this section we shall derive the mass profiles of disk and halo after the collapse of the baryons. We shall follow earlier treatments of disk galaxy formation (e.g. \nMo, Mao \\& White 1998) by assuming that the \nvirialized dark halo, mixed with baryonic gas, is `formed' -- or at least \nassembled -- at redshift $z_f$. \nThis virialized halo has a limiting radius $r_{200}$ within which\nthe mean density is $200 \\rho_{crit} (z_f)$, and contains a baryonic \nmass fraction $F$. Then \n\\beq \\label{rh_h}\n\\rh ={V_{200} \\over 10 H(z_f)};\\,\\,\\,\\,\\,\\,\\,\nM_{tot}={V_{200} ^2\\rh \\over G}={V_{200} ^3 \\over 10 G H(z_f)} ,\n%\\eqno(2)\n\\eeq \nwhere $H(z_f)$ is the value of the Hubble parameter \nat redshift $z_f$, $M_{tot} (z_f)$ is \nthe total mass within virialized radius $r_{200}$, and \n$V_{200}$ is the circular velocity at $r_{200}$. \n\nThe baryonic gas cools and settles into a disk, causing the dark halo to\ncontract adiabatically (Blumenthal {\\it et al.} 1986). The specific \nangular momentum distribution of the gas is assumed to be \nconserved during these stages. We shall include below the subsequent \nre-arrangement of the disk due to angular momentum transport. This we \ninvestigate by variation of the disk angular momentum \ndistribution function, choosing an appropriate analytic functional form. \nLet \n$m_d (r)$ and $m_h(r)$ respectively \ndenote \nthe fraction of the total baryonic mass, and total dark mass, that is \ncontained within radius $r$, and denote the \nbaryonic mass angular momentum distribution \nfunction by \n\\beq\nm_d \\left( <j \\right)= f \\left( j/j_{max} \\right) ,\n\\eeq\nwhere $j_{max}$ is the maximum specific angular momentum of the disk.\n\nWe will be requiring that the functional form, $f(j/j_{max})$, vary as the \ndisk evolves, and it is convenient to introduce the notation \n$\\ell \\equiv j/j_{max}$ and define \n\\beq\nc_f \\equiv 1-\\int_0^1 f \\left( \\ell \\right) d \\ell ,\n\\eeq\nwhich represents the area above the angular momentum distribution function \ncurve $f(\\ell)$ for $0 \\leq \\ell \\leq 1$. We will mimic the effects of \nviscous evolution by decreasing the value of $c_f$ in our evolving disk \nmodels in section 4 below. \n\nIn terms of this parameter the total disk angular momentum is:\n\\begin{eqnarray}\nJ_d &=& F J_{tot}\\,\\,\\, =\\,\\,\\, M_d \\int_0^{j_{max}} j \\frac{dm_d}{dj} dj \\nonumber\\\\\n&=& M_d j_{max} \n\\left( 1-\\int_0^1 f \\left( \\ell \\right) d \\ell \\right ) \n\\,\\,\\, =\\,\\,\\, F M_{tot} j_{max} c_f ,\n\\end{eqnarray}\nwith $M_d = FM_{tot}$. \nThus $j_{max} c_f$ is the average specific angular momentum of the disk \nmaterial.\n\nThe specific angular momentum of the disk material is assumed to \nfollow that of the dark halo, but in general will not be a simple analytic \nfunction (e.g. Quinn \\& Binney 1992). For illustration, \nwe adopt an analytic monotonic increasing function $f(b,\\ell)$ containing \na free parameter $b$, with $ 0 \\leq b \\leq 1$. \nWe require the initial angular momentum distribution to be scale free, \nrepresenting the angular momentum distribution of the virialized halo, and will adopt $f(b=0,\\ell) = \\ell^n$. \nWe shall vary the value of the parameter $b$ to mimic \nthe effects of viscous evolution on the angular momentum distribution.\n\n\nThe total energy is:\n\\beq\nE_{tot} = - \\frac{\\epsilon_0 G M_{tot}^2}{2 r_{200}}= - \\frac{\\epsilon_0 M_{tot} V_{200}^2}{2} ,\n\\eeq\nwhere $\\epsilon_0$ is a constant of order unity, depending on the dark halo density \nprofile, and since it is constant for any specific halo model, we can \ntake $\\epsilon_0=1$ without loss of \ngenerality. The spin parameter $\\lambda$ is by definition\n\\beq\n\\lambda \\equiv J_{tot} | E_{tot} |^{1/2} G^{-1} M_{tot}^{-5/2}.\n\\eeq\nThus the mean specific angular momentum of the disk material \nmay be expressed as \n\\beq\nc_f j_{max} =\\sqrt{2} \\lambda V_{200} r_{200}. \n\\eeq\nAssuming spherical symmetry, the rotationally-supported disk has mass \nprofile given by \n\\beq\nm_d = f \\left( j/j_{max} \\right) = \nf \\left( \\frac{\\sqrt {G M_{tot} \\left( m_d \\right) r \\left( m_d\\right)}}{j_{max}} \\right) = f \\left( \\ell \\right) ,\n\\eeq\nwhile the initial virialized halo mass profile is \n\\beq\ng(R_{ini}) = m_h(R_{ini}) = M_{ini}(R_{ini}) /M_{tot} , \n\\eeq\nwith $R \\equiv r/r_{200}$.\n\n\\subsection{Constraints on the Final Dark Halo Profile and Mass Angular \nMomentum Distribution Function}\n\nThe above equations describe the disk and halo just upon the settling of the \ngas disk to the mid-plane, prior to the \nsubsequent adiabatic compression of the halo. \nA self-consistent calculation of the modified disk and halo density profiles \nmay be made by consideration of \nthe adiabatic \ninvariance of the angular action, \n$I_\\theta \\equiv \\int v_\\theta \\cdot r d \\theta = \\sqrt{G M_{tot}(r) r}$, \ntogether with the \nassumption of no shell crossing (cf. Blumenthal {\\it et al.} 1986). \n\nSuppose a dark matter particle initially at $r_{ini}$ \nfinally settles at $r(m_d)$, \nthe radius within which the \ndark halo mass fraction is $m_h$. Then under adiabatic invariance the disk \nmass profile, $m_d$, and the halo mass profile, $m_h$, are related by: \n\\begin{eqnarray}\nG M_{tot} \\left( m_d \\right) r \\left( m_d \\right) \n& =& G M_{tot} \\left( m_h \\right) r \\left( m_h \\right) \\\\\n& =& G M_{ini} \\left( m_h \\right) r_{ini} \\left( m_h \\right) \\\\\n& =& G M_{tot} m_h r_{200} g^{-1} \\left( m_h \\right) ,\n\\end{eqnarray}\nwhere $g^{-1} ( m_h) $ is the inverse function of $g(R)$, the initial \nvirialized \nhalo mass profile. \n\n\n\nFurther manipulation of these relations is simplified by introduction of the \nparameter $\\xi$, given by \n\\beq\n\\xi \\equiv \\frac{\\sqrt{G M_{tot} r_{200}}}{j_{max}} = \\frac{c_f}{\\sqrt{2} \n\\lambda}. \n\\eeq\nGenerally $\\xi$ is a quantity that is closely related to the overall disk \ncollapse factor.\n\nFrom equations (8) and (12), we have \n\\begin{eqnarray}\nm_d &=& f(\\ell) ,\\\\\n\\ell &=& \\xi \\left( m_h g^{-1} ( m_h ) \\right)^{1/2}, \n\\end{eqnarray}\nwhere $\\ell$ is the normalized specific angular momentum. Again, $ 0\n\\leq \\ell \\leq 1$, and $\\ell=1$ corresponds to the maximum specific\nangular momentum of the disk, which occurs at the edge of the disk,\nequivalently at the disk cutoff radius. The fraction of the dark\nmatter contained within the disk thus has a maximum value, $m_{hc}$,\ngiven by $\\ell = 1$ in the above equation, and for radii with $m_h \\geq\nm_{hc}$, $m_d =1$.\n\nTo illustrate the physical meaning of these parameters, consider the \nrigid singular isothermal halo, for which $g(m_{hc}) = m_{hc} = R_c$. Then \nfrom equation (15), $ R_c = R(\\ell=1) = 1/\\xi$ which \ncorresponds to the disk cutoff radius. \nThus in this case, remembering that $R$ is the normalized radius, \n$\\xi =1/R_c$ is the disk collapse factor.\n\nUp to now we know the mass profile of disk and halo after collapse, in\nterms of the normalized specific angular momentum $\\ell$, as given in\nequations (14) and (15), for given forms of the angular momentum\ndistribution function, $f$, and initial virialized dark halo mass profile,\n$g$. Next we shall obtain the relation between $\\ell$\nand radius $R$, to complete the derivation of the mass profiles of disk and\nhalo after collapse.\n\nReturning to a general halo density profile, \nthe total mass contained within the radius corresponding to $m_h$ is\n\\beq\nM (m_h) = M_{tot} \\left( (1-F) m_h + F m_d \\right). \n\\eeq\nFrom equations (9) - (12) and (16), we have\n\\begin{eqnarray}\nR & = & \\frac{G M_{ini} (m_h) r_{ini} (m_h)}{G M(m_h) r_{200}} \\\\\n & = & \\frac{m_h g^{-1} (m_h)}{(1-F) m_h + F m_d}.\n\\end{eqnarray}\nIntroducing the radius variable $x$ and coefficient $c_0$ as\n\\begin{eqnarray}\nx & \\equiv & \\xi (1-F) R, \\\\\nc_0 & \\equiv &\\xi F/(1-F),\n\\end{eqnarray}\nwe may finally derive the \nfunctional dependences on $\\ell$ of the disk mass $m_d$, of \nthe \nhalo mass $m_h$, and of the \nradius $x$:\n\\begin{eqnarray}\nm_d &=& f(\\ell), \\\\\nm_h g^{-1}(m_h) &=& \\frac{\\ell^2}{\\xi^2}, \\\\ \nx &=& \\frac{\\ell^2}{\\xi m_h (\\ell) + c_0 f(\\ell)}.\n\\end{eqnarray}\nThus $\\ell$ can be thought of as a normalized radius. \nAs we shall see later, $c_0$ is a measure of the compactness of the \nfinal collapsed disk \ndue to the competition between the spin parameter $\\lambda$ and \nthe baryonic mass fraction $F$. \n\n\n\nThese equations (21) - (23) can be used to derive disk and halo properties \nfor a free choice of virialized halo profile $g(R)$ and \nangular momentum distribution function $f(\\ell)$.\nWithin the disk cutoff radius, with $ 0 \\leq \\ell \\leq 1$, \nthe disk surface density, circular velocity and the disk-to-dark mass \nratio as function of radius $\\ell$ or $R$ have the generic forms:\n\\begin{eqnarray}\n\\Sigma_d &=& \\frac{10 H(z)F V_{200}}{2 \\pi G} \n\\frac{1}{R} \\frac{df}{d\\ell} \\frac{d \\ell}{dR}, \\\\\nV_c &=& \\frac{V_{200} \\ell} {\\xi R}, \\\\\n\\frac{M_d(\\ell)}{M_h(\\ell)} &=& \\frac{c_0 f(\\ell)} {\\xi m_h(\\ell)},\n\\end{eqnarray}\nwhere $M_d(\\ell) = M_d(\\ell=1)m_d(\\ell) = M_d m_d(\\ell)$ and $M_h(\\ell)$ is \ndefined similarly. \n\nThe circular velocity at radii beyond the disk cutoff, but within the halo, is given by:\n\\begin{eqnarray}\nV_c &=& \\frac{V_{200} \\sqrt{m_h g^{-1}(m_h)}}{R}, \\\\\nR &=& \\frac{m_h g^{-1}(m_h)}{(1-F) m_h + F}.\n\\end{eqnarray}\n\n\n\n\\begin{figure}\n\\centerline{\\psfig{file=fig1.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\\caption{The power-law approximations for the initial virialized \nhalo mass profile and angular momentum distributions are\n$m_h(\\ell) \\sim \\ell^m$ and $f(\\ell) \\sim \\ell^n$\nfor small $\\ell$. \nThe shaded region is the allowed parameter space for these models, \nconstrained by the surface-density profile, rotation curve and disk-to-halo \ncentral mass ratio. The line ABC is the maximum angular-momentum index \nconsistent with a disk surface density profile in the central regions \nthat declines with increasing radius, while the line DEF is the \nminimum angular-momentum index consistent with a finite value of the \ncentral circular velocity. The line BF denotes the maximum values of $n$ \nconsistent with a non-zero central disk-to-halo mass ratio. \nThe value $m=1$ corresponds to the singular isothermal sphere, the value $m=4/3$ \ncorresponds to the Hernquist (1990) and to the Navarro, Frenk \\& White \n(1997) profiles, while the value $m=3/2$ corresponds to the \nnon-singular isothermal sphere with a constant-density core.}\n\\end{figure}\n\n\n\nArmed with these relations, one may now look at various \ninitial virialized halo density profiles and angular momentum distributions, \nand determine the allowed parameter space from observed properties of disk \ngalaxies. It is convenient to adopt power-law approximations for \nthe initial virialized \nhalo mass profile and angular momentum distributions, such that \n$m_h(\\ell) \\sim \\ell^m$ and $f(\\ell) \\sim \\ell^n$\nfor \nsmall $\\ell$. Figure 1 shows the location of various fiducial models in the \nplane of these power law indices $m$ and $n$; the value $m=1$ corresponds \nto the singular isothermal sphere, the value $m=4/3$ \ncorresponds to the Hernquist (1990) and to the Navarro, Frenk \\& White \n(1997) \nprofiles, while the value $m=3/2$ corresponds to the \nnon-singular isothermal sphere with a constant-density core. These \nprofiles span the range of dark-halo profiles suggested by theory, and \nplausibly consistent with observations. \nThe shaded region is the allowed parameter space for these models, \nconstrained by the surface-density profile, rotation curve and disk-to-halo \ncentral mass ratio. \nThe line ABC is the maximum angular-momentum index consistent with a disk \nsurface density profile in the central regions \nthat declines with increasing radius, \nwhile the line DEF is the \nminimum angular-momentum index consistent with a finite value of the central \ncircular velocity. The line BF denotes the maximum values of $n$ consistent \nwith a non-zero central \ndisk-to-halo mass ratio. \n\nThis power-law approximation has an initial \nvirialized halo density profile at small radius as \n$\\rho_{h,ini}(R) \\sim R^{\\frac{m}{2-m}-3}$ (seen by solution of (22) for the form \nof $g$). Solving equations (21) - (23) \nabove gives the corresponding profile after adiabatic infall.\n In the central region, where the disk dominates the gravitational potential \n(i.e. $c_0 f(\\ell) \\gg \\xi m_h(\\ell)$), \nthe halo density profile is $\\rho_h(R) \\sim R^{\\frac{m}{2-n}-3}$. \nNote that in the region where the dark halo dominates the gravitational \npotential (i.e. $c_0 f(\\ell) \\ll \\xi m_h(\\ell)$), \nthe halo density profile is essentially unaffected by the disk, as expected. \n\nFor the case $n=m$, the central halo density profile is unaffected \nsince the disk mass density \nprofile and the initial virialized \nhalo density profile have the same dependence on $\\ell$. \nThe viable models within the shaded region have $n \\leq m$, so that \nthe final halo density profile in the central, disk-dominated region \nshould be steeper than its initial virialized profile \nin this region, not surprisingly. \nThus the final halo profile for \nthese models ranges from $\\rho_h \\sim R^{-0.75} $ \nto $\\rho_h \\sim R^{-2}$. It is interesting to note \nthat $\\rho_h \\sim R^{-0.75} $, the outcome of an initial\nvirialized halo with a constant density core responding \nto the settling of a disk with angular momentum index $n = 4/3$, \ncorresponds to the de-projected \nde~Vaucouleurs central density profile. Thus provided the virialized halo \ndoes not have a declining density profile with decreasing radius, which is \nunphysical, the final dark halo \ncannot have a constant density core, at least in the very central region \nwhere the disk dominates, but should be cuspy. \n\n\\subsection{The Singular Isothermal Sphere}\n\nThe singular isothermal sphere provides a virialized halo density profile \nthat is the most tractable analytically, and we can obtain some important \nscaling relations without having to specify the angular momentum \ndistribution $f(\\ell)$; aspects of the analysis of \nthis profile should hold in general, and provide insight. \n\nThe final disk and halo mass profiles are given by solution of:\n\\begin{eqnarray}\nx &=& \\frac{\\ell}{1 + c_0 \\frac{f(\\ell)}{\\ell}}, \\\\\nm_h &=& \\ell/\\xi, \\\\\nm_d &=& f(\\ell),\n\\end{eqnarray}\nwhere $ 0 \\leq \\ell \\leq 1$ and $c_0$ and $\\xi$, the parameters describing the compactness of the collapsed disk and its collapse factor, are defined above in \nequations (20) and (13). \n\nThe collapse factor, defined as the ratio of the pre-collapse radius\n$r_{200}$ to the cutoff disk radius $r_c$ at $\\ell =1$ (to be\ndistinguished from the final disk scale length) is \\beq\n\\frac{r_{200}}{r_{c}} = \\xi (1-F)(1+c_0)= \\frac {c_f}{\\sqrt{2}\n\\lambda} \\left( 1-F + \\frac{c_f}{\\sqrt{2}} \\frac{F}{\\lambda} \\right),\n\\eeq where $c_f$, defined in equation (3), is a measure of the shape\nof the angular momentum distribution, and small values of $c_f$ mean\nsteeply-rising angular momentum distributions.\n\n\\begin{figure}\n\\centerline{\\psfig{file=fig2-a.ps,width=2.6in,angle=0}}\n\\vspace{0.5cm}\n\n\n\\centerline{\\psfig{file=fig2-b.ps,width=2.6in,angle=0}}\n\\vspace{0.5cm}\n\\caption{The angular momentum distribution function for the Mestel profile, \n$f(\\ell)=1-(1-\\ell)^{3/2}$, is shown by the dashed line. \n(a) The angular momentum distribution function is\n$f(b,\\ell)= (1+b) \\ell -b \\ell^2 $ for models on line FED in Figure 1. \nThe different curves correspond to $b= 0, 1/4, 1/2, 3/4, 1$.\n(b) The angular momentum distribution function is\n$f(b,\\ell)=(1+10b)\\ell^{4/3}-10b\\ell^{22/15}$ \nfor models on line BC in Figure 1. The different curves correspond to $b= 0, 0.1, 0.3, 0.6, 1$.}\n\\end{figure}\n\n\nTypical angular momentum distributions for disks are shown in Figure 2 (a,b) \nand discussed below. Here one should just note that a value $c_f \\sim 0.5$ \nis reasonable. With this, and \n$\\lambda = 0.06$ and $F = 0.1$, we obtain $\\xi = 5.9 $ \nand \n$c_0 = 0.66$. The collapse factor as defined here is then about a factor of \n9. For fixed angular momentum distribution $c_f$, the collapse\nfactor depends not only on $1/\\lambda$ but also on \ncompactness \n$c_0 \\propto F/\\lambda$. This is consistent with the results of \nprevious studies\nof the collapse factor in two extreme cases (Jones \\& Wyse 1983; Peebles 1993): \nif the final \ndisk is so self-gravitating that the value of $F/\\lambda$ corresponds to \n$c_0 \\gg 1$, then \nthe collapse factor is $\\propto F/\\lambda^2$; on the other hand \nif the final disk is sufficiently far from self-gravitating, with small \n$F/\\lambda$ and $c_0 \\ll 1$, the collapse factor is $\\propto 1/\\lambda$. \nThe above collapse factor relationship is valid over the entire range of \nvalues for the parameters $\\lambda$ and $F$ (and is the most general \nrelation derived to date). \n\nIt should be noted that varying the normalized angular momentum distribution \nby varying $c_f $ changes the derived collapse factor; this is investigated \nfurther below. \n\nComparison between the sizes of observed disks and those predicted from such \ncollapse calculations provides a constraint on the redshift at which the \ncollapse happened (e.g. Mo, Mao \\& White 1998). Our \ndisk cutoff radius for non-trivial $f(\\ell)$ may be expressed in terms of \nthe initial conditions as :\n\\beq\nr_c= \\frac{\\sqrt{2} \\lambda V_{200}}\n{10 H(z_f) c_f (1-F + \\frac{c_f}{\\sqrt{2}} \\frac{F}{\\lambda})},\n\\eeq\nwhere $z_f$ is the `formation' or assembly redshift, at which \nthe halo is identified to \nhave given mass and circular velocity, with no mass infall after this epoch. \nOne can see from this relation that \nboth $\\lambda$ and $F/\\lambda$ are equally important; previous \ndeterminations considered the baryonic mass fraction fixed (Dalcanton, \nSpergel \\& Summers 1997; Mo, Mao \\& White \n1998). \n\nThe \nexplicit inclusion of the parameter $c_f$ allows us to take account of disk evolution, as gas is transformed to stars. \n Adopting a\ndisk cutoff radius at three disk scale-lengths (e.g. van der Kruit\n1987), and choosing specific values of the present-day \nstellar disk scale-length $r_d =\n3.5$kpc, $\\lambda =0.06$, $V_{200}=200$ kms$^{-1}$ and an\nEinstein-de-Sitter Universe with Hubble constant $ 0.5< h <1$, the\nabove relation gives the formation redshift $1.6 < z_f < 3.1$ for\n$F=0.05$ and $c_f=1/3$; $1.4 < z_f < 2.8$ for $F=0.1$ and $c_f =1/3$;\n$0.9 < z_f < 2.0$ for $F=0.05$ and $c_f =1/2$; $0.7 < z_f < 1.7$ for\n$F=0.1$ and $c_f=1/2$.\n\nConsistent with previous calculations, for fixed formation redshift\nsmaller values of $\\lambda$ can lead to smaller disk size; we have\nhere explicitly demonstrated that larger $F/\\lambda$ can also lead to\nthis result. Lower values of $c_f$ also lead to higher redshift of\nformation. Thus for no viscous evolution i.e. there is no angular\nmomentum redistribution during the evolution of the galactic disk and\n$c_f$ has a time-independent value, the formation redshift $z_f$\ndetermined by assuming fixed initial $\\lambda$ and $F$ and fixed disk\nsize $r_c$ is smaller than would be determined if $c_f$ could be\ndecreased (to mimic say viscous evolution). Lower values of $c_f$ for\ngiven total angular momentum content imply a larger disk scale-length;\nthe effect of viscous evolution is to re-arrange the disk material so\nas to increase the disk scale-length. Typical values of viscosity\nparameters lead to a factor of 1.5 increase in disk scale-length in a\nHubble time. As we demonstrate below, a smaller value for $c_f$\ncorresponds to larger bulge-to-disk ratio. This result is consistent\nwith the results of Mo, Mao \\& White (1998): halo and disk formation\nredshift can be pushed to higher value when a bulge is included.\nThese trends are general, and not tied to the specific model of the\nhalo density profile.\n\nOne should bear in mind that the old stars in the local thin disk of the \nMilky Way have ages of at least 10~Gyr, and may be as old as the oldest \nstars in the Galaxy (Edvardsson {\\it et al.} 1993); the age distribution of \nstars at other locations of the Galactic disk is very poorly-determined, but \nit is clear that a non-trivial component of the thin disk was in place at \nearly times (at redshift $z > 2$ for the cosmologies considered above). \nA common assumption in previous work is that the \nmass angular momentum distribution of the disk is that of \na solid-body, rotating \nuniform density sphere, $f(\\ell) = 1-(1-\\ell)^{3/2}$ (Mestel 1963). \nFor this distribution, $c_f = 0.4$, and one derives a low redshift of \nformation for a galaxy like the Milky Way (Mo, Mao \\& White 1998), which has \ndifficulties with the observations. \n\n\n\\subsubsection{The Singular Isothermal Halo with Simple $f(\\ell)$}\n\nAnalytic solutions to equations (29) - (31) can be obtained by assuming\na simple monotonic increasing function $f(b,\\ell)$ containing one parameter $b$ \nwith $ 0 \\leq b \\leq 1$. In order to avoid the situation where one obtains \na trivial \ncollapse factor due to a very small amount of disk material \nat very large radius, we \nrestrict the shape of the mass angular momentum distribution function $f(\\ell)$ \nto avoid too shallow an asymptotic slope as $f$ approaching 1 when $\\ell$ \nincreases (see Figure 2). \n From Figure 1, the singular isothermal halo at point F requires $f(\\ell) \\sim \n\\ell$ for \n$\\ell \\ll 1$. A simple form consistent with this is $f(\\ell) = (1+b) \n\\ell -b \\ell^2 $ with \n$0 \\leq \\ell \\leq 1$ and $0 \\leq b \\leq 1$. The angular momentum parameter \n$c_f = (3-b)/6$. Figure 2a \nshows this angular momentum distribution function with\ndifferent values of the parameter $b$, compared with the \nmass angular momentum distribution of a solid-body, rotating \nuniform density sphere, $f(\\ell) = 1-(1-\\ell)^{3/2}$ (Mestel 1963). \n The normalized total angular momentum $c_f$ \ncorresponds to the area above each curve. \n\nWithin the disk, where \n$ 0 \\leq \\ell \\leq 1$, \nthe galactic disk surface density, circular velocity and the disk-to-dark mass \nratio as a function of radius are:\n\\begin{eqnarray}\n\\Sigma_d(\\ell) = \\frac{10 V_{200} H(z) F(1-F)^2\\xi^2}{\\pi G} \\nonumber\\\\\n\\times \\frac{(1+b-2b\\ell)(1+c_0+c_0b-c_0b\\ell)^3}{2\\ell(1+c_0+c_0b)} , \n\\end{eqnarray}\n\\beq\nV_c(\\ell) = V_{200}(1-F)[1+c_0(1+b-b\\ell)] ,\n\\eeq\n\\beq\n\\frac{M_d(\\ell)}{M_h(\\ell)} = \\frac{(1+b-b\\ell)(3-b)F}{6\\sqrt{2}\\lambda(1-F)}, \\,\\\\\n\\eeq\nwhere\n\\beq\n\\ell = \\frac{[1+c_0(1+b)]\\xi (1-F) R}{1+bc_0 \\xi (1-F) R}.\n\\eeq\nFrom equation (27)-(28), the circular velocity at radii beyond the disk cutoff, but within the halo, is:\n\\beq\nV_c(R) = \\frac{V_{200} (1-F)}{2} \n\\left[ 1+ \\sqrt{1 + \\frac{4 F}{(1-F)^2 R}} \\right].\n\\eeq\n\nThese results are plotted in Figure 3 (a,b,c) for $\\lambda =0.06$, \n$F=0.1$, $ 0 \\leq \\ell \\leq 1$. \nThe different curves correspond to $b= 0, 1/4, 1/2, 3/4, 1$. Larger values \nof $b$ yield larger disk cut-off radii; note that the circular velocities \nfor points beyond the cut-off radius of a given model may be obtained by \nforming the envelope of the values for the cut-off radius for larger values \nof $b$. \nVarying the value of the parameter $b$ changes the angular momentum \ndistribution \nfunction similar to the effects of viscous evolution; \nthe ratio of disk mass to dark halo mass increases at small radius \nwith increasing $b$, which can be interpreted as due to radial inflow of \ndisk material. \n\n\n\n\\subsubsection{ Halo Density Profile and Angular Momentum Combinations}\n\nFor initial virialized halo profiles other than the singular isothermal \nsphere, the collapse factor has a more general \nform: \n\\beq\n\\frac{r_{200}}{r_{c}} = \\xi (1-F)(\\xi m_{hc} + c_0),\n\\eeq\nwhere $m_{hc}$ is the solution of $1= \\xi^2 m_{hc} g^{-1}(m_{hc})$ and is \nthe mass fraction of the dark halo that is contained within the cut-off \nradius of the disk. \nThe trend of the dependence of the collapse factor on the values of \n$\\lambda$ and $F$ remains the same as found above for the \nsingular isothermal halo. \n\n\n\n\n\\begin{figure}\n\\centerline{\\psfig{file=fig3-a.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\n\n\\centerline{\\psfig{file=fig3-b.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\n\n\\centerline{\\psfig{file=fig3-c.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\\caption{The model corresponding to point F in Figure 1. (a) the surface density, (b) circular velocity \nand (c) disk-to-halo mass ratio with $\\lambda =0.06$ and $F=0.1$. \nThe virialized halo is a singular isothermal sphere. \nThe angular momentum distribution function is $f(b,\\ell)= (1+b) \\ell -b \\ell^2 $.\nThe different curves correspond to $b= 0, 1/4, 1/2, 3/4, 1$. Larger values \nof $b$ yield larger disk cut-off radii. The disk-to-halo mass ratio increases slightly when approaching the centre.}\n\\end{figure}\n\n\n\n\\begin{figure}\n\\centerline{\\psfig{file=fig4-a.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\n\n\\centerline{\\psfig{file=fig4-b.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\n\n\\centerline{\\psfig{file=fig4-c.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\\caption{The model corresponding to point E in Figure 1. (a) the surface \ndensity, (b) circular \nvelocity and (c) disk-to-halo mass ratio with $\\lambda =0.06$ and $F=0.1$. \nThe virialized halo is Hernquist halo with core size $c=4$. \nThe angular momentum distribution function is \n$f(b,\\ell)= (1+b) \\ell -b \\ell^2 $. \nThe different curves correspond to $b= 0, 1/4, 1/2, 3/4, 1$. \nThe disk-to-halo mass ratio increases significantly when approaching \nthe centre.}\n\\end{figure}\n\n\n\\begin{figure}\n\\centerline{\\psfig{file=fig5-a.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\n\n\\centerline{\\psfig{file=fig5-b.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\n\n\\centerline{\\psfig{file=fig5-c.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\\caption{The model corresponding to point B in Figure 1. \n(a) the surface density, (b) circular velocity and \n(c) disk-to-halo mass ratio with $\\lambda =0.06$ and $F=0.1$. \nThe virialized halo is Hernquist halo with core size $c=4$. \nThe angular momentum distribution function is \n$f(b,\\ell)=(1+10b)\\ell^{4/3}-10b\\ell^{22/15}$. \nThe different curves correspond to $b= 0, 0.1, 0.3, 0.6, 1$.\nThe disk-to-halo mass ratio increases but not significantly when \napproaching the centre.}\n\\end{figure}\n\n\n\\begin{figure}\n\\centerline{\\psfig{file=fig6-a.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\n\n\\centerline{\\psfig{file=fig6-b.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\n\n\\centerline{\\psfig{file=fig6-c.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\\caption{The model corresponding to point D in Figure 1. (a) the surface \ndensity, (b) circular velocity and \n(c) disk-to-halo mass ratio with $\\lambda =0.06$ and $F=0.1$. \nThe virialized halo is non-singular isothermal halo with constant \ndensity core size $c=4$. \nThe angular momentum distribution function is \n$f(b,\\ell)= (1+b) \\ell -b \\ell^2 $. \nThe different curves correspond to $b= 0, 1/4, 1/2, 3/4, 1$. \nThe disk-to-halo mass ratio increases significantly when approaching \nthe centre.}\n\\end{figure}\n\n\n\\begin{figure}\n\\centerline{\\psfig{file=fig7-a.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\n\n\\centerline{\\psfig{file=fig7-b.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\n\n\\centerline{\\psfig{file=fig7-c.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\\caption{The model corresponding to point C in Figure 1. (a) the surface \ndensity, (b) circular velocity and \n(c) disk-to-halo mass ratio with $\\lambda =0.06$ and $F=0.1$. \nThe virialized halo is non-singular isothermal halo halo with \ncore size $c=4$. \nThe angular momentum distribution function is \n$f(b,\\ell)=(1+10b)\\ell^{4/3}-10b\\ell^{22/15}$. \nThe different curves correspond to $b= 0, 0.1, 0.3, 0.6, 1$.\nThe disk-to-halo mass ratio increases significantly when approaching \nthe centre.}\n\\end{figure}\n\n\n\nThe range of viable models represented by the shaded region in Figure 1 can \nbe investigated by the appropriate virialized halo profile \n$g(R)$ and angular momentum \ndistribution function $f(b,\\ell)$ corresponding to the points E,B,D and C. \nThe distribution of surface density, circular velocity and disk-to-halo mass \nratio for these models, varying parameter $b$, are shown in Figures 4--7, \nby choosing fixed $\\lambda =0.06$, $F=0.1$ (and \nhalo core size $c=4$ if the halo has a core radius). \n\n\nModel E: The results of a model corresponding to point E in Figure 1 \nare shown in Figure 4; this has \na Hernquist halo profile $g(R) = \\frac{(1+c)^2 R^2}{(1+cR)^2}$ and \n$f(b,\\ell)= (1+b) \\ell -b \\ell^2 $. The different curves correspond \nto $b= 0, 1/4, 1/2, 3/4, 1$.\n\nModel B: The results of a model corresponding to point B in Figure 1 \nare shown in Figure 5; this has a \nHernquist halo profile $g(R) = \\frac{(1+c)^2 R^2}{(1+cR)^2}$ and \n$f(b,\\ell)=(1+10b)\\ell^{4/3}-10b\\ell^{22/15}$. This $f(b,\\ell)$ is shown in \nFigure 2b.\nFor $ \\ell \\ll 1$, $f(b=0,\\ell) \\sim \\ell^{4/3}$; the \n$22/15$ index in the second term is determined by the requirement\nthat $f(b,\\ell)$ should be a monotonic increasing function of $\\ell$ \nfor all values of \n$0 \\leq b \\leq 1$. The different curves correspond to $b= 0, 0.1, 0.3, 0.6, 1$.\n\nModel D: The results of a model corresponding to point D in Figure 1 \nare shown in Figure 6; this has a \nnon-singular isothermal halo with a constant density core, \n$g(R) = \\frac{cR-arctan(cR)}{c-arctan(c)} $, and \n$f(b,\\ell)= (1+b) \\ell -b \\ell^2 $. Again the different curves correspond \nto $b= 0, 1/4, 1/2, 3/4, 1$.\n\nModel C: The results of a model corresponding to point C in Figure 1 \nare shown in Figure 7; this has a \nnon-singular isothermal halo with constant density core, \n$g(R) = \\frac{cR-arctan(cR)}{c-arctan(c)} $, and \n$f(b,\\ell)=(1+10b)\\ell^{4/3}-10b\\ell^{22/15}$. \nAgain the different curves correspond to $b= 0, 0.1, 0.3, 0.6, 1$.\n\n\nAs can be seen from the figures, the different halo profiles and angular \nmomentum distributions produce disks with a variety of surface density \nprofiles and rotation curves. \nAs in Figure 3b, the circular velocities \nfor points beyond the cut-off radius of a given model may be obtained by \nforming the envelope of the values for the cut-off radius for larger values \nof $b$. \nThus if the disk is very compact, from equations (27)-(28) or\nequation (38), we find that the circular velocity beyond the edge of the disk \ntends to decreases \nwith radius. The location of the edge of the disk depends on both \n$\\lambda$ and $F$ (in addition to $b$). Thus we have shown that \nrotation curves should show an imperfect disk--halo `conspiracy' if the disk \nis too compact or \ntoo massive. This is consistent with observations \n(Casertano \\& van Gorkom 1991).\n\nFurther, these figures demonstrate that with increasing $b$, the \ninner rotation curves become flat, and the \ntransition between disk-dominated and halo-dominated sections of the \nrotation curve becomes more and more smooth with increasing \n$b$. As discussed above, and illustrated in Figure 2, a higher value of\n$b$ corresponds to a flatter specific angular momentum distribution \nfunction, and increasing $b$ mimics the effects of viscous evolution\nin transporting angular momentum. This indicates that viscous evolution \ncan help the creation of an apparent disk-halo `conspiracy'.\n\nAs can be seen from equations (21) - (26), for given $c_0$ (the \ncompactness parameter defined in equation (20)), or \n$F/\\lambda$ ratio, within a given model of $f(\\ell,b)$ \nand virialized dark halo profile \n$g(R)$, the normalized properties of the disks formed for \n$b=0$ are very similar. In particular the disk \nsurface density profile, rotation curve and disk-to-halo mass \nratio profile scale similarly with $\\ell$. \nFor example, in the case of the singular isothermal sphere (model F), \nequations (34) - (37) show that for $b=0$ the \nnormalized disks \nare identical for given $F/\\lambda$ ratio. Thus $F/\\lambda$ \nmust be an important factor in distinguishing one disk from another. \nThe overall normalization of the surface density is $\\propto F/\\lambda^2$, \nso that \nagain $F/\\lambda$ and $\\lambda$ enter separately and are both \nimportant. \n\n\n\n\nNote that here we are not insisting that the surface density profile \nof the gas disk \nso formed be exponential, unlike previous work (Mo, Mao \\& White 1998). \nWe shall however appeal to viscous \nevolution tied to star formation to provide a stellar exponential disk. We \nnow turn to this. \n\n\\section{The Viscous Evolution and Star Formation}\n\nIn this paper we aim to link viscous evolution within \ndisks and the Hubble sequence of disk galaxies. One of the motivations for \ninvoking viscous disks is that if the timescale of angular momentum \ntransport via viscosity is similar to that of star formation, a stellar \nexponential disk is naturally produced independent of the initial gaseous disk \nsurface density profile (Silk \\& Norman 1981; \nLin \\& Pringle 1987; Saio \\& Yoshii 1990; Firmani, Hernandez \\& Gallagher 1996). \nAngular momentum transport and associated radial gas flows (both inwards and \noutwards) can also, as shown above, provide a tight `conspiracy' between \ndisk and halo rotation curves, and, as demonstrated below, provide a higher \nphase space density in bulges as compared to disks. \n\n\nThe star formation rate per unit area in a disk \ncan be represented by a modified \nSchmidt law involving the dynamical time and the gas density (Wyse 1986; \nWyse \\& Silk 1989). We shall use the form of the global star formation rate \nper unit area, $\\Sigma_{\\psi}$, of Kennicutt (1998), based on his \nobservations of the inner regions of nearby large disk galaxies: \n\\beq\n\\Sigma_{\\psi} =\\alpha \\Sigma_{gas}\\Omega_{gas},\n\\eeq\nwhere $\\Sigma_{gas}$ is total gas surface density, $\\Omega_{gas}$ is \nthe dynamical time at the edge of the gas disk, and the normalization \nconstant, related to the efficiency of star formation, has the value \n$\\alpha=0.017$ (Kennicutt 1998). Note that observations of the star-formation \nrates in the outer regions of disk galaxies suggest that it is actually \n{\\it volume\\/} density that should enter the Schmidt law, rather than \nsurface density, and since many (if not all) gas disks flare in their \nouter regions, equation (40) will over estimate the star formation rate \n(Ferguson {\\it et al.} 1998). This is beyond the scope of the present model, \nbut should be borne in mind and will be incorporated in our future work.\n\n\nFor our models here, the edge of the initial gas disk is where $\\ell=1$, \n$R=R_c$ and thus $\\Omega_{gas} = \\Omega_c$. \nFor halo formation redshift $z_f$, \nwe can obtain the relationship between global star formation timescale \nand the galaxy initial conditions \nin the general form using equation (1), (25) and (39):\n\\begin{eqnarray}\nt_*^{-1}&=&\\alpha \\Omega_c \n= \\alpha V_c(r_c)/r_c \\nonumber\\\\\n&=& 10 \\alpha H(z_f) \\xi (1-F)^2(\\xi m_{hc}+c_0)^2,\n\\end{eqnarray}\nwhere again $m_{hc}$ is the solution of $1= \\xi^2 m_{hc} g^{-1}(m_{hc})$, \nand is the fraction of the dark halo mass that is contained within the \ncut-off radius of the disk. The parameters $\\xi$ and $c_0$ are defined in \nequations (13) and (20); $F$ is the baryonic mass fraction in the initial density \nperturbation. \n\nIn the case of the singular isothermal halo, this relation has a simple \nform: \n\\beq\nt_*^{-1}= 10 \\alpha H(z_f) \\xi (1-F)^2(1+c_0)^2.\n\\eeq\nThe gas consumption timescale will be longer than the characteristic \nstar formation timescale due to the gas returned by stars during their \nevolution and death. For a standard stellar Initial Mass Function, \n$t_g \\sim 2.5t_*$ (e.g. Kennicutt {\\it et al.} 1994).\n\nThis modified Schmidt law is based on observations of the inner regions of\nnearby large disk galaxies, and simple theoretical principles.\nAssuming it holds at all epochs allows one to estimate the properties \nof present-day disks from \nthe initial conditions of earlier sections in this paper. \nLet us assume that the dark halo is fully virialized at redshift $z_f$. \nIn keeping with the spirit of hierarchical clustering, let us allow for \nsome star formation that could have taken place in the disk, from an earlier \nredshift $z_i$, and that the total mass of the system could increase until \n$z_f$ (although to maintain the thin disk, this accretion and merging must \nbe only of low mass, low density systems). \nSo for any time $t$ or redshift $z$ between $z_i$ and $z_f$,\n\\begin{eqnarray}\n\\frac{d M_g}{d t} &=& F \\frac{d M_{tot}}{d t} - \\frac{d M_*}{d t}, \\\\\n\\frac{d M_*}{d t} &=& \\frac{M_g}{t_g(z)},\n\\end{eqnarray}\nwhere $M_{tot}$ is defined in equation (1) and $M_*$ is mass locked up into \nstars.\nIn an Einstein-de-Sitter Universe, $H(z)= H_0 (1+z)^{3/2}$ and\n$H(z)t= 2/3$.\nWe have\n\\beq\n\\frac{d M_g}{dt} = A -\\frac{B M_g}{ t},\n\\eeq\nwhere $A=\\frac{3F V^3_{200}}{20 G} $ and \n$B=\\frac{8}{3} \\alpha \\xi(1-F)^2(1+c_0)^2 $, and $\\xi$ and $c_0$ are \nexpressed in terms of $c_f$, $\\lambda$ and $F$ through equations (13) and \n(20) in section 2.1. Hence, from equation (1), \n$M_{tot} \\propto \\frac{A}{F H(z)}$. \n\nIdentifying the dark halo to have fixed $V_{200}$, independent of redshift, \nleads to $A$ also being a constant, and thus the total mass grows as \n$M_{tot} \\propto t$. This differs from the standard solution of infall onto \na point, $M_{tot} \\propto t^{2/3}$ (Gunn \\& Gott 1972). \n\n\nThe solution to the above equation is then \n\\beq\nM_g = \\frac{A}{1+B} t \\left[ 1+ B\\left( \\frac{t}{t_i} \\right)^{-(1+B)} \\right], \n\\eeq\nwhere $t_i$ corresponds to the redshift $z_i$ of the onset of star \nformation. Thus at the halo formation redshift $z_f$, the disk gas fraction is \n\\beq\nf_g(z_f) = \\frac{1+B \\left( \\frac{1+z_f}{1+z_i} \\right)^{3(1+B)/2}}{1+B},\n\\eeq\nSince $B$ depends on $c_f$, $\\lambda$ and $F$, i.e. \n$B \\propto \\frac{c_f}{\\lambda} (1-F +\\frac{c_f}{\\sqrt{2}} \\frac{F}{\\lambda})^2$, \nthe value of the constant $B$ may be evaluated \nfor $\\lambda =0.06$ and various reasonable values of $F$ and $c_f$ as: \nfor $F=0.1$, $c_f= 1/3$, $B=0.30$;\nfor $F=0.05$, $c_f= 1/3$, $B=0.23$;\nfor $F=0.1$, $c_f= 0.5$, $B=0.59$;\nand for $F=0.05$, $c_f= 0.5$, $B=0.41$.\nFor fixed $\\lambda$ and $F$, small values of $B$ correspond to small values \nof $c_f$, and hence flatter specific angular momentum distributions.\n\nThus for $1+z_f \\lta 2(1+ z_i)$, $f_g(z_f) \\approx 1/(1+B)$, typically $\\gta 2/3$.\n\nWe assume that after $z_f$, there is no further infall, and that \nthe gas in the disk will be consumed with characteristic timescale $t_g(z_f)$.\nThus the gas fraction of a typical disk galaxy at the \npresent time is \n\\beq\nf_g=f_g(z_f) \\exp \\left[ -\\delta t(z_f)/t_g(z_f)\\right],\n\\eeq \nwhere $\\delta t(z_f)$ is the time interval between the halo formation redshift $z_f$ \nand present time $z=0$. \n\nAssuming an Einstein-de-Sitter universe, \nwe have $\\delta t(z_f)= t_0(1-H_0/H(z_f))$ and $t_0 H_0 = 2/3$. \nThus a typical value for the present gas fraction of disk galaxies is:\n\\beq\n\\ln \\left( \\frac{f_g(z_f)}{f_g} \\right) = B \\left[ (1+z_f)^{3/2}-1 \\right]. \n\\eeq\nWith the approximation $f_g(z_f) = 1/(1+B)$, we have\n\\beq\n(1+z_f)^{3/2} = 1+ \\frac{-\\ln f_g- \\ln (1+B)}{B}.\n\\eeq\n\n\nFor the Milky Way Galaxy, if we adopt $5 \\times 10^9 M_{\\odot}$ for the atomic \n$HI$ gas, and $1.3 \\times 10^9 M_{\\odot}$ for the molecular $H_2$ gas \n(Blitz 1996; Dame 1993), then with an estimate of \n$4 - 6 \\times 10^{10} M_{\\odot}$ for the total baryonic mass of the Milky Way \ndepending on stellar exponential scale length (Dehnen \\& Binney 1998), \nwe obtain gas fraction, the total gas mass includes $24 \\%$ helium mass, \n$f_g \\sim 15\\%$ or even higher depending on the mass model of \nthe Galaxy. As mentioned earlier, for fixed $\\lambda$ and $F$, \nsmall values of $B$ correspond to small values \nof $c_f$, and hence flatter specific angular momentum distributions.\nFor small values of the parameter $B$, say $B \\sim 0.3$, we obtain \n$z_f \\sim 2.4$, while for large values of $B$, $B \\sim 0.6$, \nwe obtain $z_f \\sim 1.2$. \nThe larger value of $z_f$ is preferred, given what we know of the \nage distribution of stars in the local thin disk (e.g. Edvardsson \\et \n1993). The effect of viscous evolution is equivalent to choosing \nsmall $c_f$, i.e. \nsmall values of $B$. So the inclusion of viscous evolution can give relatively \nhigher halo formation redshift, which is consistent with the results from the \nconstraint on the redshift of formation that we obtained from considerations \nof the size of the disk. \n\n\nIt should be noted that for fixed halo `formation' redshift $z_f$,\nthe star formation timescale $t_*^{-1} \\sim \\frac{1}{\\lambda} \n(1-F+\\frac{1}{2 \\sqrt{2}} \\frac{F}{\\lambda})^2$. \nAgain, both \n$\\lambda$ and $F/\\lambda$ are important. \nAs we discussed in the previous section, the structure of the normalized \ndisk \ndepends strongly on $F/\\lambda$ while the overall normalization depends strongly\non $\\lambda$ for fixed $F/\\lambda$. \nAs we show later, \nthe bulge-to-disk ratio also \ndepends on the importance of $\\lambda$ and $F/\\lambda$.\nThus many aspects of the Hubble sequence of disk galaxies -- \nstar formation timescale, \ndisk gas fraction, bulge-to-disk ratio -- depend on both $\\lambda$ and \n$F/\\lambda$. \n \n \nThe star formation timescale derived above is independent of $V_{200}$, \nwhich at first sight is surprising, given that the \nHubble sequence of disk galaxies has been interpreted as a sequence of \nstar formation timescales, relative to collapse times (Sandage 1986), and \nobservations show that the Hubble type of a disk galaxies is broadly \ncorrelated with the disk luminosity (Lake \\& Carlberg 1988; de Jong 1995).\nHowever, $V_{200}$ is not an easily-observed quantity. \n\nThe present-day luminosity of a disk in our model can be written as\n\\beq L = \\frac{F M_{tot}(1-f_g)}{\\gamma_*}=\\frac{F[1-f_g(B,z_f)]\nV_{200}^3}{10GH(z_f) \\gamma_*}, \\eeq with $\\gamma_*$ the current value\nof the mass-to-light ratio. Estimation of the predicted Tully-Fisher relation\ndepends on what model parameter we use for the width of the\nHI line. Obviously if we identify this with $V_{200}$ we have a\nreasonable relationship provided that the coefficient $\\gamma_{tf}$ is constant,\ni.e. $F[1-f_g(B,z_f)]/H(z_f) = \\gamma_{TF}$. This then requires that there\nshould be a correlation between $F$ and $z_f$, in the sense that for\nlarge $F$, $z_f$ is large. Then we can see from equation (42) that\nthis leads to the star formation timescale being small, \nimplying more efficient viscous\nevolution, and leading to larger B/T ratio. Large $z_f$ may be\ncorrelated with small $V_{200}$ in the context of\nhierarchical-clustering cosmologies, and in that case, a short \nstar formation time and large B/T\nratio should be correlated with low luminosity, which is not\nconsistent with observation. However, an interpretation that is compatible with observations is that high n-sigma fluctuations for\nfixed $V_{200}$ can form high luminosity disks with large B/T ratio. \n\n\n\nThe Tully-Fisher relationship is not\na simple relation between luminosity and $V_{200}$, but depends on\nwhere the circular velocity $V_c(R)$ is measured (Courteau 1997). The\nrelationship between $V_{200}$ and $V_c(R)$ obviously depends on the\ndetails of the halo density profile and the angular momentum\ndistribution. From the rotation curves in fig. 3 to fig. 7, we can see\nthat it is appropriate to choose for our estimate of $V_c$ the\ncircular velocity at the cutoff radius of disk, adopted as 3 three\nscale lengths. From equation (35), we have $V_c=V_{200}(1-F)(1+c_0)$,\nwhere $c_0=c_f F/\\sqrt{2}\\lambda (1-F)$, as defined in equation (20),\nis the compactness of disk. Now the predicted Tully-Fisher relation is\n\\beq L = \\frac{F[1-f_g(B,z_f)] V_c^3}{10GH(z_f)\n\\gamma_*(1+c_0)^3(1-F)^3}. \\eeq Requiring that the coefficient $\\gamma_{TF}$ \nin the Tully-Fisher relation be constant, i.e. $\\gamma_{TF} \\equiv F[1-f_g(B,z_f)]/H(z_f)(1+c_0)^3(1-F)^3$, then gives, from\nequation (42), $t_*^{-1} \\propto c_0/(1+c_0)$. So for small $c_0$, the\nstar formation timescale is large, which can cause less efficient\nviscous evolution. So less efficient viscous evolution and small\n$F/\\lambda$ will lead to small B/T ratio. Also small $c_0$ is\ncorrelated with large $z_f$ from the constancy of the coefficient in\nthe Tully-Fisher relation. Similarly large $z_f$ may be correlated\nwith small $V_{200}$ in the context of hierarchical clustering\ncosmology. So small $c_0$ and small $V_{200}$ will lead to small $V_c$\nand lower disk luminosity. Thus this version of the predicted Tully-Fisher relation appears fully compatible with the observations. \nHowever, one should bear in mind that we have adopted a fixed constant of\nproportionality $\\alpha$ in the star formation law, and this may well\nvary with global potential well depth (White \\& Frenk 1991) or local\npotential well depth (Silk \\& Wyse 1993).\n\nA further test of the model is the relation between disk scale and\ncircular velocity, and its variation with redshift; observations\nindicate that $R_d/V_c$ is smaller at high redshift, $z \\sim 1$ (Vogt\n{\\it et al.} 1996; Simard {\\it et al.} 1999). In our model there is\nlittle change in total mass between redshifts of unity and the\npresent, and so this evolution of disk size cannot be due to the halo\nmass growth, as had been proposed by Mao, Mo \\& White (1998). Instead\nin our model this is due to the different and changing scale lengths of\ngas and stars. In our model, due to early star formation, the gas\nfraction at $z_f$ is about $f_g(z_f) \\sim 1/(1+B)$, typically\n$2/3$. It is natural that the gas component of the disk will \nhave a larger scale length than the stellar component. The scale\nlength of the gas component can increase with time due to viscous\nevolution while the scale length of stellar component can also\nincrease with time due to the non-linear local star formation law\n(Saio \\& Yoshi 1990). So the stellar scale length at high redshift,\nwhen the gas fraction is large, should be much smaller than the\nstellar scale length at present time, when gas fraction is lower. \nThe study of detailed evolution of gas and stellar component is \nbeyond the scope of this paper; but the prediction of stellar size \nevolution of our model is qualitatively consistent with the observations.\n \nThe measured distribution of $R_d/V_c$ for the local disk galaxy sample is approximately peaked at $R_d/V_c \\sim -1.5$ ($R_d$ in kpc, $V_c$ in kms$^{-1}$) with a spread from -2 to -1 (Mao, Mo \\& White 1998; Courteau 1996). \nOur estimation of the disk size or scale length in Section 2 is valid for\ngalaxies at the present time, when the gas fraction is small. Then\nassuming the disk cut off radius is three scale lengths, \nfrom equation (41), $R_d/V_c =R_c/3V_c=\\alpha t_*/3$, \nand the present $R_d/V_c $ is an indication\nof the galactic global star formation timescale; \nfurther, from the constancy of $\\gamma_{TF}$, the coefficient of the Tully-Fisher relation in equation (52), we have \n\\beq R_d/V_c =\\alpha t_*/3=\\frac{G}{3} \\gamma_{TF} \\gamma_*\\frac{1+c_0}{c_0(1-f_g)}. \\eeq \nThus this ratio is also an indication of the disk compactness. \nAdopting the B-band mass-to-light ratio of our local disk $\\gamma_* \\sim 2.5 M_{\\odot}/L_{\\odot}$, and using the luminosity of our galaxy \n$L_B \\sim 3 \\times 10^{10} L_{\\odot}$ and $V_c \\sim 220$ kms$^{-1}$ to estimate \n$\\gamma_{TF}=L_B/V_c^3$, we can obtain that $\\log(R_d/V_c) \\simeq -2.0+\\log(\\frac{1+c_0}{c_0(1-f_g)})$. Obviously $\\log(R_d/V_c) \\sim -2$ roughly corresponds to the predicted lower limit of the local sample, which is consistent with observations. \nThe distribution of $F$ from 0.05 to 0.2 and the distribution of $\\lambda$ from 0.03 to 0.12 will cause the value of the compactness parameter $c_0$ to spread from 0.1 to 2 approximately. Adopting typical values $F=0.1$, $\\lambda=0.06$, $c_f=1/3$, the peak will be located at $\\log(R_d/V_c) = -1.5$ with $c_0=0.44$, which is again consistent with observations. The spread of $R_d/V_c$ is simply caused by the spread in the value of compactness parameter $c_0$.\n\n\n\n\n\\section{The Formation of Bulges and the Hubble Sequence}\n\nGalaxies classification schemes based on morphology are the basic first step \nin understanding how \ngalaxies form and evolve (van den Bergh 1998). \nThe bulge-to-disk luminosity ratio is \none of the three basic classification criterion for the \nHubble sequence (Sandage 1961). \nHowever, the relation between bulge-to-disk ratio and Hubble type \nhas a fair amount of scatter, some of which must be related to the \ndifficulty of a decomposition of the light profile into bulge and disk, \nand the bulge-to-disk \nratio is dependent on the band-pass used to define the luminosity \n(de Jong 1996). \nThe current observational data show that bulges can be \ndiverse and heterogeneous (Wyse, Gilmore \\& Franx 1997). \nSome share properties of disks and some are more similar to ellipticals. \nModels of bulge formation can be classified into \nseveral categories: the bulge is formed from early collapse of low angular \nmomentum gas, with short cooling time and efficient star formation \n(Eggen {\\it et al.} 1962; Larson 1976 -- who invoked viscosity to\ntransport angular momentum away from the proto-bulge; van den Bosch 1998); \nthe bulge is formed from merging of disk galaxies (Toomre \\& Toomre 1972; \nKauffmann, White \\& Guiderdoni 1993); the bulge is formed \nfrom the disk by secular evolution process \nafter bar instability (Combes {\\it et al.} 1990; \nNorman, Sellwood \\& Hasan 1996; Sellwood \\& Moore 1999; \nAvila-Reese \\& Firmani 1999); the bulge is formed from early dynamical \nevolution of massive clumps formed in disk (Noguchi 1999).\nHowever it is speculated that large bulges, \nwhich tend to have de Vaucouleur's law \nsurface brightness profiles, share formation mechanisms with ellipticals, \nwhile smaller bulges, which tend to be better fit by an exponential profile, \nare formed from their disks through bar dissolution. \nIt should be noted that the significantly \nhigher phase space density of bulges when compared to disks suggests that \ngaseous inflow should play a part in the instability (Wyse 1998), \njust as invoked in \nearlier sections of this paper, for other reasons.\n\n\nHere we only consider this latter case, the formation of small bulges from\nthe disk. Early studies of disk instabilities showed that Toomre's local\nstability criterion $Q > 1$ is also sufficient for global stability to\naxisymmetric modes (Hohl 1971; Binney \\& Tremaine 1987). It is known that\nthe bar instability requires a similar condition (Hockney \\& Hohl 1969; Ostriker\n\\& Peebles 1973). Efstathiou, Lake \\& Negroponte (1982) used N-body\ntechniques to study the global bar instability of a pure exponential disk\nembedded in a dark halo and proposed a simple\ninstability criterion for the stellar disk, based on the \ndisk-to-halo mass ratio.\nHowever, it has been argued recently that there is no such simple \ncriterion for bar instability (Christodoulou, Shlosman \\& Tohline 1995; \nSellwood \\& Moore 1999). Further, recent N-body simulations \n(Sellwood \\& Moore 1999; Norman, Sellwood \\& Hasan 1996) \nshow that every massive disk form a bar during the early stages of \nevolution, but later the bar is \ndestroyed by the formation of a dense central object, once the mass of that \ncentral concentration reaches several percent of the total disk mass. \nThis can be understood in terms of \nthe linear mode analysis work and \nnonlinear processes of swing amplifier and feed back loops\n(Goldreich \\& Lynden-Bell 1965; Julian \\& Toomre 1966). Toomre (1981)\nargued that the bar-instability can be inhibited in two ways: one is that a \nlarge \ndark halo mass fraction can reduce the gain of the swing amplifier, while \nthe other is that \nfeedback through the centre can be shut off by a inner Lindblad \nresonance (ILR). The dense central object can destroy the bar via the second \nof these mechanisms. \nHowever, most of these studies assume that \nthe dark halo has a constant density core. On the contrary, \nwe have shown that dark halo profile cannot have a constant density core after \nadiabatic infall, if one starts from physical initial conditions. \nIt will be interesting to study bar formation under \ndifferent disk-halo profiles in addition to the well-studied harmonic core.\n \nWe will for simplicity adopt the simple criterion of Efstathiou, Lake \\& \nNegroponte (1982), interpreted to determine the size of a bar-unstable \nregion, with the radial extent of the bar, $r_b$ defined by \n\\beq\nM_d(r_b)/M_h(r_b) \\geq \\beta,\n\\eeq\nwith the value of the parameter $\\beta$ chosen to fit observations. \nAs we have argued in section 2, \n$F/\\lambda$ is the important quantity determining the overall normalization \nof the disk surface density. \nFrom N-body simulations (Warren {\\it et al.} 1992; Barnes \\& Efstathiou 1987; \nCole \\& Lacey 1996; \nSteinmetz \\& Bartelmann 1995),\nthe distribution of $\\lambda$ can be fit by a log-normal distribution:\n\\beq\nP(\\lambda)d\\lambda= \\frac{1}{\\sqrt{2\\pi}\\sigma_{\\lambda}} \nexp \\left[ {-\\frac{\\ln^2(\\lambda/\\lambda_0)}\n{2\\sigma_{\\lambda}}}\\frac{d\\lambda}{\\lambda} \\right],\n\\eeq\nwhere $\\lambda_0=0.06$ and $\\sigma_{\\lambda}=0.5$ (this result is fairly \nindependent of the slope of the power spectrum of density fluctuations). \n\nWhat of the possible range of the baryonic fraction $F$? \nSome \nprevious studies suggested that $F \\sim \\lambda$ as an explanation of the \ndisk-halo `conspiracy' \n(Fall \\& Efstathiou 1980; Jones \\& Wyse 1983; \nRyden \\& Gunn 1987; Hernandez \\& Gilmore 1998).\nSome interpretations of the observed Tully-Fisher relationship \nsuggest that indeed $F$ is not invariant (McGaugh \\& de Blok 1998). \nHere we shall assume that the distribution of $F$, similar to $\\lambda$,\n is log-normal, \ncentreed at $F_0=0.1$ with\n$\\sigma_{F}=0.05$. So $F$ is mainly within the range $0.05 \\sim 0.2$. \n\nWe generated a Monte Carlo sample of disks, with fixed \nhalo $V_{200}$ and halo formation\nredshift $z_f$, but with values \nof $F$ and $\\lambda$ following the above distributions. \nThen for given virialized dark halo profiles $g(R)$ and \nangular momentum distribution $f(b,\\ell)$ in Figure 1,\nwe can calculate the star formation timescale from equation (41).\nThe parameter $b$ represents the efficiency of viscous evolution; on the \nassumption that \nthe viscous timescale is equal to the star formation timescale, we can \nuse a simple linear correlation between the value of $b$ and the \nstar formation timescale. Then the value of parameter $b$ can be obtained. \nFrom equations (21), (22), (23), (26), (50) and (54), one can calculate \nthe bulge-to-disk ratio and final disk gas fraction.\n\n\nThus we can plot B/T ratio versus disk gas fraction, for the whole Monte \nCarlo \nsample, confining the parameter space of $\\lambda$ and $F$ to give \nsmall bulges with $B/T < 0.5$. \nLarger values of B/T would correspond to such an unstable disk that the\nexercise is invalid. Disks that are too stable, having low $F/\\lambda$ or\nlarge $\\lambda$, will evolve little and probably end up as low surface\nbrightness systems. \n\n\n\n\n\\begin{figure}\n\\centerline{\\psfig{file=fig8-a.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\n\n\\centerline{\\psfig{file=fig8-b.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\n\n\\caption{The model corresponding to point F in Figure 1. \n(a) The sample of disk galaxies \nwith different $\\lambda$ and $F$.\n(b) The relation between B/T ratio and gas fraction for these sample\ngalaxies at current age. The different curves in this plot correspond to\ndifferent values of $(1-F)\\lambda/F \\approx \\lambda/F$, which sets the overall trend.}\n\\end{figure}\n\n\n\n\\begin{figure}\n\\centerline{\\psfig{file=fig9-a.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\n\n\\centerline{\\psfig{file=fig9-b.ps,width=2.6in,angle=0}}\n\\hspace{0.5cm}\n\n\n\\caption{The model corresponding to point E in Figure 1. \n(a) The sample of disk galaxies \nwith different $\\lambda$ and $F$. Overly-unstable disks are denoted by asterisk symbols. Bulgeless disks or low surface-brightness disks are denoted by cross symbols.\n(b) The relation between B/T ratio and gas fraction for these sample\ngalaxies at current age. The different curves in this plot correspond to\ndifferent values of $(1-F)\\lambda/F \\approx \\lambda/F$, which sets the overall trend.}\n\\end{figure}\n\n\n\n\nFigure 8a shows model F, representing the singular isothermal halo. \nAssuming the typical values $\\lambda=0.06$ and $F=0.1$, then \nthe choice of $\\beta \\sim 0.8$ is required to allow the existence of \nbulges.\nThis is just the value of $\\beta$ used in the \nglobal bar instability criterion (Efstathiou, Lake \\& Negroponte 1982). \nFor this model the disk-to-halo mass ratio varies little with radius (as \nshown in Figure 3a), so the B/T ratio is strongly \ndependent on $\\lambda/F$. Only a small range of values of $\\lambda/F$ is \nallowed, so as to \nnot over-produce either bulge-less disks or completely unstable disks. \n\n\nThe relation between B/T ratio and gas fraction for this model is given in \nFigure 8b; there a general trend in the observed sense, \nwith large scatter. The different curves in this plot correspond to\ndifferent values of $\\lambda/F$, which sets the overall trend. \n\nFigure 9 (a,b) shows the equivalent plots of model E, \nrepresenting a Hernquist profile halo model, which is probably a \nmore realistic case. Here the \nthe disk-to-halo mass ratio varies strongly with radius when approaching the \ncentre, and the allowed parameter space for values of \n$\\lambda$ and of $F$ that allowing the formation of\nbulges can be large. Overly-unstable disks are denoted by asterisk symbols \nin Figure 9a, and \nlow surface-brightness disks are denoted by cross symbols. \nThe relation between B/T ratio and\ngas fraction is similar to that for the isothermal halo. \n\n\\subsection{Constraints from the Milky Way}\n\nThe Milky Way bulge is reasonably well-fit by an exponential profile, with a \nscale-length approximately one-tenth that of the disk (Kent {\\it et al.} 1991). The morphology \nof the bulge is consistent with some triaxiality (Blitz \\& Spergel 1991; Binney {\\it et al.} 1997). Perhaps the Milky \nWay is a system in which the bulge has formed from the disk, through a bar \ninstability? \nObservations show no evidence for a significant young or even \nintermediate-age stellar population in \nthe field population of the \nGalactic Bulge (Feltzing \\& Gilmore 1999), despite their being ongoing star \nformation in the inner disk. This implies that \nif the bulge were formed from the disk through bar dissolution, \nonly one \nsuch episode is allowed, and this should have happened at high redshift. \nIn the context of the present model, the lower star formation rates and \nlonger viscosity timescales of later times act to stabilize the system. \nHowever, it remains to be seen if the observed relative \nfrequencies of bars, bulges and central mass concentration is consistent \nwith the models of bar dissolution. \n\n\n\\section{Summary}\n\nIn the context of hierarchical clustering cosmology, the \ndark halo of a disk galaxy can be formed by quiescently merging small \nsub-halos into the primary dark halo, or by smoothly accreting matter \ninto the \ndark halo. We derive the generic solution to the adiabatic infall model of\ndisk galaxy formation pioneered by many authors \n(Mestel 1963; Fall \\& Efstathiou 1980; \nGunn 1982; Faber 1982; Jones \\& Wyse 1983; Ryden \\& Gunn 1987; \nDalcanton, Summer \\& Spergel 1997; Mo, Mao \\& White 1998; \nHernandez \\& Gilmore 1998). \nThrough exploring the allowed parameter space of dark halo profile and angular \nmomentum distribution function, we show that the central halo\ndensity profile should be cuspy, with the power law index ranging \nfrom $-0.75 $ to $-2$, in the central regions where the disk mass dominates. \n\n\nUsing a modified Schmidt law of \nglobal star formation rate, we derive a simple scaling relationship between\nthe disk gas fraction and the assembly redshift. \nWe explicitly allow a distribution in the values of the baryonic mass \nfraction, $F$, in addition of the \ndistribution in values of the spin parameter $\\lambda$.\nThese two are found to play different role in determining the structural \nproperties of the final disk, the star formation properties and \nbulge-to-disk ratio. \n\nWe mimic viscous evolution of disks by varying the specific angular momentum \ndistribution of the disk, to redistribute angular momentum as a function of \ntime. We derive a consistent picture of the formation of galaxies like the \nMilky Way, with old stars in the disk. \nUnder the assumption that the viscous evolution timescale is equal to the star \nformation timescale, we can further combine the $\\lambda$ and $F$ with \nthe efficiency of angular momentum redistribution caused by viscosity. \nAssuming that small bulges are formed from their disks \nthrough bar dissolution,\nwe can use the global bar instability condition to obtain bulge-to-total \nratio, and explore the dependence on $F$, $\\lambda$ and the viscous \nevolution efficiency. \n\n\nThe inclusion of viscous evolution has the merits of addressing several \nimportant \nissues: the conspiracy between disk and halo, the formation of the \nexponential profile \nof stellar disk, the high phase space density of bulges. \nWe have presented an analytic treatment, to illustrate these points and \nidentify areas of particular need for more work. \n \n\n\n\n\\section*{Acknowledgments}\nWe acknowledge support from NASA, ATP Grant NAG5-3928.\nBZ thanks Colin Norman, Jay Gallagher for helpful comments.\nRFGW thanks all at the Center for Particle Astrophysics, UC Berkeley, for \ntheir hospitality during the early stages of this work.\n\n\n\n\n\\begin{thebibliography}{}\n\n\\bibitem[]{} Avila-Reese, V. \\& Firmani, C., 1999, in Carral, P. \\& Cepa, J., eds, ASP Conf. Ser. Vol. 163; Star Formation in Early-Type Galaxies.\nAstron Soc. Pac., San Francisco, p.243.\n\n\\bibitem[]{} Barnes, J. \\& Efstathiou, G., 1987, \\apj 319, 575.\n\n\\bibitem[]{} Binney J., Gerhard, O. \\& Spergel, D., 1997, \\mn 288, 365.\n\n\\bibitem[]{} Binney J. \\& Tremain, S., 1987, Galactic Dynamics, Princeton University Press \n\n\\bibitem[]{} Blitz, L., 1996, in Latter, W.B., Radford, S.J.E., Jewell, P.R., Mangum, J.G. \\& Bally, J.,eds, Proc IAU Symp. vol. 170, CO: Twenty-Five Years of Millimeter-Wave Spectroscopy. Kluwer Academic Publishers, p11.\n \n\\bibitem[]{} Blitz, L. \\& Spergel, D., 1991, \\apj 370, 205.\n\n\\bibitem[]{} Blumenthal, G.R., Faber, S.M., Flores, R. \\& Primack, J.R., 1986, \\apj 301, 27.\n\n\\bibitem[]{} Casertano, S. \\& van Gorkom, J.H., 1991, \\apj 101, 1231.\n\n\\bibitem[]{} Christodoulou, D.M., Shlosman, I. \\& Tohline, J.E., 1995, \\apj 443, 563. \n\n\\bibitem[]{} Cole, S. \\& Lacey, C., 1996, \\mn 281, 716. \n\n\\bibitem[]{} Combes, F., Debbasch, F., Friedli, D., \\& Pfenniger, D., 1990, \\aa 233, 82. \n\n\\bibitem[]{} Courteau, S., 1996, \\apjs 103, 363. \n\n\\bibitem[]{} Courteau, S., 1997, \\aj 114, 2402. \n\n\\bibitem[]{} Dalcanton, J.J., Spergel, D.N., \\& Summers, F.J., 1997, \\apj 482, 659. \n\n\\bibitem[]{} Dame, T., 1993, in ``Back to the Galaxy'', eds. 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Fall, S.M. \\& Lynden-Bell, D., Cambridge University Press, p111. \n\n\\bibitem[]{} Toomre, A. \\& Toomre, J., 1972, \\apj 178, 623. \n\n\\bibitem[]{} van den Bergh, S., 1998, Galaxy Morphology and Classification, \nCambridge University Pess. \n\n\\bibitem[]{} van den Bosch, F.C., 1998, \\apj 507, 601. \n\n\\bibitem[]{} van der Kruit, 1987, \\aa 173, 59.\n\n\\bibitem[]{} Vogt, N.P., Forbes, D.A., Phillips, A.C., Gronwall, C., Faber, S.M., Illingworth, G.D. \\& Koo, D.C., 1996, \\apj 465, L15. \n\n\\bibitem[]{} Warren, M.S., Quinn, P.J., Salmon, J.K. \\& Zurek, W.H., 1992, \\apj 399, 405. \n\n\\bibitem[]{} White, S.D.M. \\& Frenk, C.S., 1991, \\apj 379, 52. \n\n\\bibitem[]{} White, S.D.M. \\& Rees, M.J., 1978, \\mn 183, 341. \n\n\\bibitem[]{} Wyse, R.F.G., 1986, \\apj 311, L41. \n\n\\bibitem[]{} Wyse, R.F.G., 1998, \\mn 293, 429. \n\n\\bibitem[]{} Wyse, R.F.G., Gilmore, G. \\& Franx, M., 1997, \\araa 35, 637. \n\n\\bibitem[]{} Wyse, R.F.G. \\& Silk, J., 1989, \\apj 339, 700. \n\n\\bibitem[]{} Zurek, W.H., Quinn, P.J. \\& Salmon, J.K., 1988, \\apj 330, 519.\n\n\n\\end{thebibliography}\n\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"
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"name": "astro-ph0002213.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[]{} Avila-Reese, V. \\& Firmani, C., 1999, in Carral, P. \\& Cepa, J., eds, ASP Conf. Ser. Vol. 163; Star Formation in Early-Type Galaxies.\nAstron Soc. Pac., San Francisco, p.243.\n\n\\bibitem[]{} Barnes, J. \\& Efstathiou, G., 1987, \\apj 319, 575.\n\n\\bibitem[]{} Binney J., Gerhard, O. \\& Spergel, D., 1997, \\mn 288, 365.\n\n\\bibitem[]{} Binney J. \\& Tremain, S., 1987, Galactic Dynamics, Princeton University Press \n\n\\bibitem[]{} Blitz, L., 1996, in Latter, W.B., Radford, S.J.E., Jewell, P.R., Mangum, J.G. \\& Bally, J.,eds, Proc IAU Symp. vol. 170, CO: Twenty-Five Years of Millimeter-Wave Spectroscopy. Kluwer Academic Publishers, p11.\n \n\\bibitem[]{} Blitz, L. \\& Spergel, D., 1991, \\apj 370, 205.\n\n\\bibitem[]{} Blumenthal, G.R., Faber, S.M., Flores, R. \\& Primack, J.R., 1986, \\apj 301, 27.\n\n\\bibitem[]{} Casertano, S. \\& van Gorkom, J.H., 1991, \\apj 101, 1231.\n\n\\bibitem[]{} Christodoulou, D.M., Shlosman, I. \\& Tohline, J.E., 1995, \\apj 443, 563. \n\n\\bibitem[]{} Cole, S. \\& Lacey, C., 1996, \\mn 281, 716. \n\n\\bibitem[]{} Combes, F., Debbasch, F., Friedli, D., \\& Pfenniger, D., 1990, \\aa 233, 82. \n\n\\bibitem[]{} Courteau, S., 1996, \\apjs 103, 363. \n\n\\bibitem[]{} Courteau, S., 1997, \\aj 114, 2402. \n\n\\bibitem[]{} Dalcanton, J.J., Spergel, D.N., \\& Summers, F.J., 1997, \\apj 482, 659. \n\n\\bibitem[]{} Dame, T., 1993, in ``Back to the Galaxy'', eds. Holt, S.S \\& Verter, F., AIP Press: New York, p267.\n\n\\bibitem[]{} de Jong, R.S., 1995, Ph.D.\\ Thesis, University of Groningen. \n\n\\bibitem[]{} de Jong, R.S., 1996, \\aa 313, 45. \n\n\\bibitem[]{} Dehnen, W. \\& Binney, J., 1998, \\mn 294, 429.\n\n\\bibitem[]{} Edvardsson, B., Andersen, J., Gustafsson, B., Lambert, D.L., Nissen, P.E. \\& Tomkin, J., 1993, \\aa 275, 101.\n\n\\bibitem[]{} Efstathiou, G., Lake, G. \\& Negroponte, J., 1982, \\mn 199, 1069. \n\n\\bibitem[]{} Eggen, O., Lynden-Bell, D. \\& Sandage, A., 1962, \\apj 136, 748. \n\n\\bibitem[]{} Faber, S.M., 1982, in Bruck, H.A., Coyne, G.V. \\& Longair, M.S., eds, Astrophysical Cosmology, Pontificia Academia Scientiarvm, p191.\n\n\\bibitem[]{} Fall, S.M. \\& Efstathiou, G., 1980, \\mn 193, 189. \n \n\\bibitem[]{} Feltzing, S. \\& Gilmore, G., 1999, in Spite, M., eds, Galaxy Evolution: Connecting the Distant Universe with the Local Fossil Record, Kluwer Academic Publishers, p71.\n\n\\bibitem[]{} Ferguson, A.M.N., Wyse, R.F.G., Gallagher, J. \\& Hunter, D.A., 1998, \\apj 506, L19.\n\n\\bibitem[]{} Firmani, C., Hernandez, X. \\& Gallagher, J., 1996, \\aa 308, 403.\n\n\\bibitem[]{} Goldreich, P. \\& Lynden-Bell, D., 1965, \\mn 130, 125. \n\n\\bibitem[]{} Gunn, J.E., 1982, in Bruck, H.A., Coyne, G.V. \\& Longair, M.S., eds, Astrophysical Cosmology, Pontificia Academia Scientiarvm, p233.\n\n\\bibitem[]{} Gunn J.E. \\& Gott R., 1972, \\apj 176,1.\n\n\\bibitem[]{} Hernandez, X. \\& Gilmore, G., 1998, \\mn 294, 595. \n\n\\bibitem[]{} Hernquist, L., 1990, \\apj 356, 359. \n\n\\bibitem[]{} Hockney, R.W. \\& Hohl, F., 1969, \\aj 74, 1102. \n\n\\bibitem[]{} Hohl, F., 1971, \\aj 76, 202. \n\n\\bibitem[]{} Jones, B.J.T. \\& Wyse, R.F.G., 1983, \\aa 120, 165.\n\n\\bibitem[]{} Julian, W.H. \\& Toomre, A., 1966, \\apj 146, 810. \n\n\\bibitem[]{} Kauffmann, G., White, S.D.M. \\& Guiderdoni, B., 1993, \\mn 264, 201. \n\n\\bibitem[]{} Kennicutt, R.C., 1998, \\apj 498, 541. \n\n\\bibitem[]{} Kennicutt, R.C., Tamblyn, P. \\& Congdon, C.W., 1994, \\apj 435, 22. \n\n\\bibitem[]{} Kent, S.M., Dame, T.M. \\& Fazio, G., 1991, \\apj 378, 131.\n\n\\bibitem[]{} Lake, G. \\& Carlberg, R.G., 1988, \\aj 96, 1587. \n\n\\bibitem[]{} Larson, R.B., 1976, \\mn 176, 31. \n\n\\bibitem[]{} Lin, D.N.C. \\& Pringle, J.E., 1987, \\apj 168, 603. \n\n\\bibitem[]{} McGaugh, S.S. \\& de Blok, E., 1998, in ``Galactic Halos'', eds. \nZaritsky, D., APS Conference Series vol. 136, p210.\n\n\\bibitem[]{} Mestel, L., 1963, \\mn 126, 553. \n\n\\bibitem[]{} Mao, S., Mo, H.J., \\& White, S.D.M., 1998, \\mn 297, L71. \n\n\\bibitem[]{} Mo, H.J., Mao, S. \\& White, S.D.M., 1998, \\mn 295, 319. \n\n\\bibitem[]{} Navarro, J.F., Frenk, C.S. \\& White, S.D.M., 1997, \\apj 490, 493. \n\n\\bibitem[]{} Navarro, J.F. \\& Steinmetz, M., 1997, \\apj 478, 13.\n\n\\bibitem[]{} Noguchi, M., 1999, \\apj 514, 27.\n \n\\bibitem[]{} Norman, C.A., Sellwood, J. \\& Hasan, H., 1996, \\apj 462, 114. \n\n\\bibitem[]{} Ostriker, J.P. \\& Peebles, P.J.E., 1973, \\apj 186, 487. \n\n\\bibitem[]{} Ostriker, J.P., 1990, in ``Evolution of the Universe of Galaxies'', ASP Conference Proceedings Vol. 10, eds. Kron, R.G., p25.\n\n\\bibitem[]{} Peebles, P.J.E., 1993, Principle of Physical Cosmology, Chap. 22.\n\n\\bibitem[]{} Quinn, T. \\& Binney, J., 1992, \\mn 255, 729. \n\n\\bibitem[]{} Ryden, B.S. \\& Gunn, J.E., 1987, \\apj 318, 15.\n\n\\bibitem[]{} Saio, H. \\& Yoshii, Y., 1990, \\apj 363, 40. \n\n\\bibitem[]{} Sandage, A., 1961, The Atlas of Galaxies (Washington, D.C., Carnegie Institution of Washington) \n\n\\bibitem[]{} Sandage, A., 1986, \\aa 161, 89.\n\n\\bibitem[]{} Sellwood, J.A. \\& Moore, E.M., 1999, \\apj 510, 125. \n\n\\bibitem[]{} Silk, J. \\& Norman, C.A., 1981, \\apj 247, 59. \n\n\\bibitem[]{} Silk, J. \\& Wyse, R.F.G., 1993, Phys.\\ Rep.\\ 231, 295. \n\n\\bibitem[]{} Simard, L., Koo, D.C., Faber, S.M., Sarajedini, V.L., Vogt, N.P., Phillips, A.C., Gebhardt, K., Illingwortg, G.D. \\& Wu, K.L., 1999, \\apj 519, 563.\n\n\\bibitem[]{} Steinmetz M. \\& Bartelmann M., 1995, \\mn 272, 570. \n\n\\bibitem[]{} Toomre, A., 1981, In ``Structure and Evolution of Normal Galaxies'', eds. Fall, S.M. \\& Lynden-Bell, D., Cambridge University Press, p111. \n\n\\bibitem[]{} Toomre, A. \\& Toomre, J., 1972, \\apj 178, 623. \n\n\\bibitem[]{} van den Bergh, S., 1998, Galaxy Morphology and Classification, \nCambridge University Pess. \n\n\\bibitem[]{} van den Bosch, F.C., 1998, \\apj 507, 601. \n\n\\bibitem[]{} van der Kruit, 1987, \\aa 173, 59.\n\n\\bibitem[]{} Vogt, N.P., Forbes, D.A., Phillips, A.C., Gronwall, C., Faber, S.M., Illingworth, G.D. \\& Koo, D.C., 1996, \\apj 465, L15. \n\n\\bibitem[]{} Warren, M.S., Quinn, P.J., Salmon, J.K. \\& Zurek, W.H., 1992, \\apj 399, 405. \n\n\\bibitem[]{} White, S.D.M. \\& Frenk, C.S., 1991, \\apj 379, 52. \n\n\\bibitem[]{} White, S.D.M. \\& Rees, M.J., 1978, \\mn 183, 341. \n\n\\bibitem[]{} Wyse, R.F.G., 1986, \\apj 311, L41. \n\n\\bibitem[]{} Wyse, R.F.G., 1998, \\mn 293, 429. \n\n\\bibitem[]{} Wyse, R.F.G., Gilmore, G. \\& Franx, M., 1997, \\araa 35, 637. \n\n\\bibitem[]{} Wyse, R.F.G. \\& Silk, J., 1989, \\apj 339, 700. \n\n\\bibitem[]{} Zurek, W.H., Quinn, P.J. \\& Salmon, J.K., 1988, \\apj 330, 519.\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002214
|
REIONIZATION AND THE ABUNDANCE OF GALACTIC SATELLITES
|
[
{
"author": "James S. Bullock\\altaffilmark{1}"
},
{
"author": "Andrey V. Kravtsov\\altaffilmark{2} and David H. Weinberg"
}
] |
One of the main challenges facing standard hierarchical structure formation models is that the predicted abundance of galactic subhalos with circular velocities $v_c \sim 10-30\ks$ is an order of magnitude higher than the number of satellites actually observed within the Local Group. Using a simple model for the formation and evolution of dark halos, based on the extended Press-Schechter formalism and tested against N-body results, we show that the theoretical predictions can be reconciled with observations if gas accretion in low-mass halos is suppressed after the epoch of reionization. In this picture, the observed dwarf satellites correspond to the small fraction of halos that accreted substantial amounts of gas before reionization. The photoionization mechanism naturally explains why the discrepancy between predicted halos and observed satellites sets in at $v_c \sim 30\ks$, and for reasonable choices of the reionization redshift ($\zre \sim 5-12$) the model can reproduce both the amplitude and shape of the observed velocity function of galactic satellites. If this explanation is correct, then typical bright galaxy halos contain many low-mass dark matter subhalos. These might be detectable through their gravitational lensing effects, through their influence on stellar disks, or as dwarf satellites with very high mass-to-light ratios. This model also predicts a diffuse stellar component produced by large numbers of tidally disrupted dwarfs, perhaps sufficient to account for most of the Milky Way's stellar halo.
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[
{
"name": "bullock.2.00.tex",
"string": "\\documentstyle[emulateapj,pstricks,psfig]{article}\n\n% start definitions\n\\newcommand{\\beqa}{\\begin{eqnarray}}\n\\newcommand{\\eeqa}{\\end{eqnarray}}\n\n\\newcommand{\\lp}{\\left}\n\\newcommand{\\rp}{\\right}\n\n\\newcommand{\\hkpc}{\\ h^{-1}{\\rm kpc}}\n\\newcommand{\\hMsun}{\\ h^{-1}M_{\\odot}}\n\\newcommand{\\hMpc}{\\ h^{-1}{\\rm Mpc}}\n\\newcommand{\\gsim}{\\lower .1ex\\hbox{\\rlap{\\raise .6ex\\hbox{\\hskip .3ex\n {\\ifmmode{\\scriptscriptstyle >}\\else\n {$\\scriptscriptstyle >$}\\fi}}}\n \\kern -.4ex{\\ifmmode{\\scriptscriptstyle \\sim}\\else\n {$\\scriptscriptstyle\\sim$}\\fi}}}\n\\newcommand{\\lsim}{\\lower .1ex\\hbox{\\rlap{\\raise .6ex\\hbox{\\hskip .3ex\n {\\ifmmode{\\scriptscriptstyle <}\\else\n {$\\scriptscriptstyle <$}\\fi}}}\n \\kern -.4ex{\\ifmmode{\\scriptscriptstyle \\sim}\\else\n {$\\scriptscriptstyle\\sim$}\\fi}}}\n\\newcommand{\\beq}{\\begin{equation}}\n\\newcommand{\\eeq}{\\end{equation}}\n\\newcommand{\\ks}{\\rm ~km~s^{-1}}\n\\newcommand{\\cvir}{c_{\\rm {\\tiny{vir}}}}\n\\newcommand{\\Rvir}{R_{\\rm vir}}\n\\newcommand{\\Mvir}{M_{\\rm vir}}\n\\newcommand{\\Vvir}{V_{\\rm vir}}\n\\newcommand{\\rvir}{R_{\\rm vir}}\n\\newcommand{\\Dvir}{\\Delta_{\\rm vir}}\n\\newcommand{\\zre}{z_{\\rm re}}\n\n% end definitions\n\n\n\\begin{document}\n\\slugcomment{{\\em Astrophysical Journal, submitted}}\n\\lefthead{REIONIZATION AND THE ABUNDANCE OF GALACTIC SATELLITES}\n\\righthead{BULLOCK, KRAVTSOV, \\& WEINBERG}\n\n\n\\title{REIONIZATION AND THE ABUNDANCE OF GALACTIC SATELLITES}\\vspace{3mm}\n\n\\author{James S. Bullock\\altaffilmark{1}, Andrey V. Kravtsov\\altaffilmark{2} \nand David H. Weinberg}\n\\affil{Department of Astronomy, The Ohio State University,\n 140 W. 18th Ave, Columbus, OH 43210-1173}\n\n\n\\altaffiltext{1}{james,andrey,dhw@astronomy.ohio-state.edu}\n\\altaffiltext{2}{Hubble Fellow}\n\n\\begin{abstract}\nOne of the main challenges facing standard hierarchical structure\nformation models is that the predicted abundance of galactic subhalos\nwith circular velocities $v_c \\sim 10-30\\ks$ is an order of magnitude\nhigher than the number of satellites actually observed within the\nLocal Group. Using a simple model for the formation and evolution of\ndark halos, based on the extended Press-Schechter formalism and tested\nagainst N-body results, we show that the theoretical predictions can\nbe reconciled with observations if gas accretion in low-mass halos is\nsuppressed after the epoch of reionization. In this picture, the\nobserved dwarf satellites correspond to the small fraction of halos\nthat accreted substantial amounts of gas before reionization. The\nphotoionization mechanism naturally explains why the discrepancy\nbetween predicted halos and observed satellites sets in at $v_c \\sim\n30\\ks$, and for reasonable choices of the reionization redshift ($\\zre\n\\sim 5-12$) the model can reproduce both the amplitude and shape of\nthe observed velocity function of galactic satellites. If this\nexplanation is correct, then typical bright galaxy halos contain many\nlow-mass dark matter subhalos. These might be detectable through\ntheir gravitational lensing effects, through their influence on\nstellar disks, or as dwarf satellites with very high mass-to-light\nratios. This model also predicts a diffuse stellar component produced\nby large numbers of tidally disrupted dwarfs, perhaps sufficient to\naccount for most of the Milky Way's stellar halo.\n\\end{abstract}\n\\keywords{cosmology: theory -- galaxies:formation}\n\n\n%=====================\n\n\\section{Introduction}\n\n%=====================\n\n\nCold Dark Matter (CDM) models with scale-invariant initial fluctuation\nspectra define an elegant and well-motivated class of theories with\nmarked success at explaining most properties of the local and\nhigh-redshift universe. One of the few perceived problems of such\nmodels is the apparent overprediction of the number of satellites with\ncircular velocities $v_c \\sim 10-30 \\ks$ within the virialized dark\nhalos of the Milky Way and M31 (Klypin et al. 1999a, hereafter KKVP99;\nMoore et al. 1999; see also Kauffmann et al. 1993 and Gonzales et al.\n1998). The most recent of these investigations are based on\ndissipationless simulations, so the problem may be rephrased as a\nmismatch between the expected number of {\\em dark matter\\/} subhalos\norbiting within the Local Group and the observed number of satellite\ngalaxies. In order to overcome this difficulty, several authors have\nsuggested modifications to the standard CDM scenario. These include\n(1) reducing the small-scale power by either appealing to a\nspecialized model of inflation with broken scale invariance (e.g.,\nKamionkowski \\& Liddle 1999) or substituting Warm Dark Matter for CDM\n(e.g., Hogan 1999), and (2) allowing for strong self-interaction among\ndark matter particles, thereby enhancing satellite destruction within\ngalactic halos (e.g., Spergel and Steinhardt 1999; but see the\ncounter-argument by Miralda-Escud\\'e 2000). In this paper, we explore\na more conservative solution.\n\nMany authors have pointed out that accretion of gas onto low-mass\nhalos and subsequent star formation are inefficient in the presence of\na strong photoionizing background (Ikeuchi 1986; Rees 1986, Babul \\&\nRees 1992; Efstathiou 1992; Shapiro, Giroux, \\& Babul 1994; Thoul \\&\nWeinberg 1996; Quinn, Katz, \\& Efstathiou 1996). Motivated by these\nresults, we investigate whether the abundance of satellite galaxies\ncan be explained in hierarchical models if low-mass galaxy formation\nis suppressed after reionization, and we propose that the observable\nsatellites correspond to those halos that accreted a substantial\namount of gas before reionization. This solution is similar in some\nways to the idea that supernova feedback ejects gas from low-mass\nhalos (Dekel \\& Silk 1986), but it offers a natural explanation for\nwhy some satellite galaxies at each circular velocity\n survive, while most are too dim to be\nseen. In addition, the reionization solution seems physically\ninevitable, while the feedback mechanism may be inadequate in all but\nthe smallest halos (Mac Low \\& Ferrara 1998).\n\n\nOur approach to calculating the satellite abundance uses an extension\nof the Press-Schecter (1974) formalism to predict the mass accretion\nhistory of galactic halos and a simple model for orbital evolution of\nthe accreted substructure. For our analysis, we adopt a flat CDM\nmodel with a non-zero vacuum energy and the following parameters:\n$\\Omega_m = 0.3,\n\\Omega_{\\Lambda} = 0.7, h=0.7, \\sigma_8=1.0$, where $\\sigma_8$ is the\nrms fluctuation on the scale of $8h^{-1}$ Mpc, $h$ is the Hubble\nconstant in units of $100 \\ks {\\rm Mpc}^{-1}$, and $\\Omega_m$ and\n$\\Omega_{\\Lambda}$ are the density contributions of matter and the\nvacuum respectively, in units of the critical density. \n\n\n{\\pspicture(0.5,4.9)(12.0,18.) \n\\rput[tl]{0}(0.2,18.4){\\epsfxsize=9.cm \n\\epsffile{fig1.ps}} \n\\rput[tl]{0}(.1,9){ \n\\begin{minipage}{8.7cm} \n \\small\\parindent=4.5mm {\\sc Fig.}~1.--- Average cumulative velocity\n function of dark matter halos accreted by halos of mass $1.1\\times\n 10^{12}h^{-1}{\\ }{\\rm M_{\\odot}}$ ($z=0$). The average is over 300\n merger histories. The {\\em thin dashed line}\n represents velocity function of all accreted halos; the {\\em thick \n dashed line} corresponds to halos that survive effects of dynamical\n friction; the {\\em thin solid line} corresponds to halos that survive\n both the dynamical friction and tidal disruption. The {\\em thick\n solid line} is a fit to results of cosmological simulations\n presented in KKVP99. The figure shows that a substantial fraction\n of accreted substructures can be destroyed by $z=0$; most of the\n destruction occurs relatively early ($z\\gsim 0.5$).\n\\end{minipage} \n}\n\\endpspicture} \n\n\n\n\n\n\n\\section{Method}\n\n\\subsection{Modeling the Subhalo Distribution}\n\nBecause N-body simulations that resolve low-mass subhalos are\ncomputationally expensive, we develop an approximate analytic model\nfor the accretion history and orbital evolution of satellite halos\nwithin a typical Milky Way-size dark halo. Our general procedure is to\nuse the extended Press-Schechter method (Bond et al. 1991; Lacey \\&\nCole 1993, hereafter LC93) to construct the subhalo accretion history\nfor each galactic halo and then to determine which accreted subhalos\nare dragged to the center due to dynamical friction and which are\ntidally destroyed. The subhalos that survive at $z=0$ are used to\nconstruct the final velocity function of satellite halos.\n\nWe assume that the density profile of each halo is described by the\nNFW form (Navarro, Frenk, \\& White 1997): $\\rho_{\\rm NFW}(x) \\propto\nx^{-1}(1+x)^{-2}$, where $x=r/r_s$, and $r_{s}$ is a characteristic\ninner radius. Given a halo of mass $\\Mvir$ at redshift $z$, the model\nof Bullock et al. (1999) supplies the typical $r_s$ value and\nspecifies the profile completely. The circular velocity curve,\n$v^2(r) \\equiv GM(r)/r$, peaks at the radius $r_{\\rm max} \\simeq 2.16\nr_{\\rm s}$. Throughout this paper, we use $v_c$ to refer to the \ncircular velocity at $r_{\\rm max}$.\n\nWe begin by constructing mass growth and halo accretion histories for\nan ensemble of galaxy-sized dark matter halos. This is done using the\nmerger tree method of Somerville \\& Kolatt (1999, hereafter SK99). We\nmodified the method slightly to require that at each time step the\nnumber of progenitors in the mass range of interest be close to the\nexpected average. This modification significantly improves the\nagreement between the generated progenitor mass function and the\nanalytic prediction. We start with halos of mass $M_{\\rm vir}=1.1\n\\times 10^{12} \\hMsun$, at $z=0$, corresponding to $v_c = 220 \\ks$,\nand trace satellite accretion histories back to $z=10$ using time\nsteps chosen as described in SK98. We track only accreted halos that\nare more massive than $M_m = 7 \\times 10^6 h^{-1} M_{\\odot}$, which\ncorresponds to $v_c\\simeq 10\n\\ks$ at $z=10$ and $v_c \\simeq 4 \\ks$ at $z=0$, and treat the\naccretion of halos smaller than $M_m$ as diffuse mass growth.\n\n\nFor each step back in time, the merger tree provides a list of\nprogenitors. The most massive progenitor is identified with the\ngalactic halo and the rest of the progenitors (with $M > M_m$) are\nrecorded as accreted substructure. We are left with a record of the\nmass growth for the galactic halo, $M_{\\rm vir}(z)$, as well as the\nmass of each accreted subhalo, $M_a$, and the redshift of its\naccretion, $z_a$. For the results presented below, we use 300\nensembles of formation histories for galactic host halos. Our results\ndo not change if the number of ensembles is increased.\n\nEach subhalo is assigned an initial orbital\ncircularity, $\\epsilon$, defined as the ratio of the angular momentum\nof the subhalo to that of a circular orbit with the same energy\n$\\epsilon \\equiv J/J_{c}$. We choose $\\epsilon$ by drawing a random\nnumber uniformly distributed from 0.1 to 1.0, an approximation to the\ndistribution found in cosmological simulations (Ghigna et al. 1998).\nOur results are not sensitive to the choice of the above range. \nTo determine whether the accreted halo's orbit will decay,\nwe use Chandrasekhar's formula to calculate the decay time,\n$\\tau_{DF}^c$, of the orbit's circular radius $R_c$, as outlined in\nKlypin et al. (1999b). The circular radius is defined as the radius of\na circular orbit with the same energy as the actual orbit. Each\nsubhalo is assumed to start at $R_c = 0.5 \\Rvir(z_a)$, where\n$\\Rvir(z_a)$ is the virial radius of the host halo at the time of\naccretion. This choice approximately represents typical binding\nenergies of subhalos in simulations. \nThe amplitude of the resulting velocity function\nis somewhat sensitive to this choice. If we adopt $R_c = 0.75\n\\Rvir(z_a)$ (less bound orbits), the amplitude increases by $\\sim\n50\\%$. A change of this magnitude will not affect our conclusions,\ndiscussed in \\S 4. Once $\\tau_{\\small DF}^{\\rm c}$ is known, the\nfitting formula of Colpi et al. (1999) provides the appropriate decay\ntime for the given circularity\n\\beq \n\\tau_{\\small DF} = \\tau_{\\small DF}^{\\rm c} \\epsilon^{0.4}. \n\\eeq\nIf $\\tau_{DF}$ is smaller than the time left between $z_a$ and $z=0$,\n$\\tau_{DF} \\le t_0 - t_a$, then the subhalo will not survive until the\npresent, and it is therefore removed from the list of galactic\nsubhalos.\n\n\n\n\n\nIf $\\tau_{DF}$ is too long for the orbit to have decayed completely\n($\\tau_{DF} > t_0 - t_a$), we check whether the subhalo would have\nbeen tidally disrupted. We assume that the halo is disrupted if the\ntidal radius becomes smaller than $r_{\\rm max}$. Such a situation\nmeans either a drastic reduction in the measured $v_c$ (quickly\npushing $v_c$ below our range of interest) or that the halo (and any\ncentral baryonic component) should become unstable and rapidly\ndissolve (Moore, Katz \\& Lake 1996).\n\nThe tidal radius, $r_t$, is determined at the pericenter of the orbit\nat $z=0$, where the tides are the strongest. \nFor an orbit that has decayed to a final circular radius $R_c^0$, the\npericenter at this time, $R_{p}$, is given by the smaller of the roots\nof the bound orbit equation (e.g., van den Bosch et al. 1999) \n\\beq\n\\left(\\frac{R_c^0}{r}\\right)^2 - \\frac{1}{\\epsilon^2} = \\frac{2\n [\\Phi(R_c^0) - \\Phi(r)]}{\\epsilon^2 v^2(R_c^0)}. \n\\eeq \nHere,\n$\\Phi(r) = - 4.6 v_c^2 \\ln(1+x)/x$ is the potential of the host halo. \nOnce $R_p$ is known, we determine $r_t$ as outlined in Klypin et al. \n(1999b). If $r_t \\le r_{\\rm max}$ we declare the subhalo to be tidally\ndestroyed and remove it from the list of galactic subhalos.\nAccreted halos that survive ($\\tau_{DF} > t_0 - t_a$ and \n$r_t > r_{\\rm max}$) are assumed to preserve the $v_c$ \nthey had when they were accreted.\n\nThe resulting velocity function of surviving subhalos within the\nvirial radius of the host ($\\sim 200 \\hkpc$ at $z=0$), averaged over\nall merger histories, is shown by the thin solid line in Figure 1.\nThe error bars reflect the measured dispersion among different merger\nhistories. The thick straight line is the best fit to the\ncorresponding velocity function measured in the cosmological N-body\nsimulation of KKVP99. The upper dashed lines show the velocity\nfunction if the effects of dynamical friction and/or tidal disruption\nare ignored. The analytic model reproduces the N-body results\nremarkably well. We have not tuned any parameters to obtain this\nagreement, although we noted above that plausible changes in the\nassumed initial circular radius $R_c$ could change the analytic\nprediction by $\\sim 50\\%$. The good agreement suggests that our\nanalytic model captures the essential physics underlying the N-body\nresults. An interesting feature of the model is that the subhalos\nsurviving at $z=0$ are only a small fraction of the halos actually\naccreted, most of which are destroyed by tidal disruption. We discuss\nimplications of this satellite destruction in \\S4.\n\n\n\\subsection{Modeling Observable Satellites}\n\nThe second step in our model is to determine which of the surviving\nhalos at $z=0$ will host observable satellite galaxies.\nThe key assumption is that after the reionization redshift $\\zre$, \ngas accretion is suppressed\nin halos with $v_c < v_{T}$.\n We adopt a threshold of $v_{T} = 30 \\ks$,\nbased on the results of Thoul \\& Weinberg (1996), who showed that\ngalaxy formation is suppressed in the presence of a photoionizing\nbackground for objects smaller than $\\sim 30 \\ks$. This threshold was\nshown to be insensitive to the assumed spectral index and amplitude of\nthe ionizing background (a similar result was found by Quinn et al. 1996).\nShapiro et al.\\ (1997; see also Shapiro \\& Raga 2000) and\nBarkana \\& Loeb (2000) have suggested that very low mass \nsystems ($v_c \\la 10\\ks$)\ncould lose the gas they have already accreted after\nreionization occurs, but we do not consider this possibility here.\n\nThe calculation of the halo velocity function in \\S 2.1 is approximate\nbut straightforward, and we have checked its validity by comparing to \nN-body simulations. Determining which of these halos are luminous\nenough to represent known dwarf satellites requires more uncertain\nassumptions about gas cooling and star formation. We adopt a simple\nmodel that has two free parameters: the reionization redshift $\\zre$\nand the fraction $f=M(\\zre)/M_a$ of a subhalo's mass that must\nbe in place by $\\zre$ in order for the halo to host an observable galaxy.\n\nThe value of $\\zre$ is constrained to $\\zre \\ga 5$ \nby observations of high-$z$ quasars (e.g., Songaila et al. 1999)\nand to $\\zre \\la 50$ by measurements of small-angle CMB \nanisotropies, assuming typical ranges for the cosmological parameters\n(e.g., Griffiths, Barbosa, \\& Liddle 1999).\nThe value of $f$ is constrained by the requirement that observable\nhalos have mass-to-light ratios in the range of observed dwarf satellites.\nFor the subset of (dwarf irregular) satellite galaxies with well-determined\nmasses, the mass-to-light ratios span the range \n$M/L_V \\simeq 5 - 30$ (Mateo 1998); dwarf spheroidals have\nsimilar $M/L_V$, but with a broader range and larger observational\nuncertainties. We can estimate $M/L_V$ for model galaxies by\nassuming that they accrete a baryon mass $fM_a(\\Omega_b/\\Omega_m)$\nbefore $\\zre$ and convert that accreted gas with efficiency\n$\\epsilon_*$ into a stellar population with mass-to-light\nratio $M_*/L_V$, obtaining\n\\beq\n \\left(\\frac{M}{L_V}\\right) = f^{-1} \\left(\\frac{\\Omega_m}{\\Omega_b}\\right)\n \\left(\\frac{M_*}{L_V}\\right) \\epsilon_*^{-1} F_o.\n\\eeq\nThe factor $F_o$ is the fraction of the halo's virial mass $M_a$\nthat lies within its final optical radius (which may itself be\naffected by tidal truncation).\nFor the $M/L_V$ values quoted above, the optical radius\nis typically $\\sim 2 \\rm{kpc}$ (Mateo 1998), and\nrepresentative mass profiles of surviving halos imply $F_o(2 \\rm{kpc})\n\\simeq 0.5$; however, this factor must be considered uncertain\nat the factor of two level. The value of $\\epsilon_*$ is also\nuncertain because of the uncertain influence of supernova feedback,\nbut by definition $\\epsilon_* \\leq 1$.\nAdopting a value $M_*/L_V \\simeq 0.7$ typical for galactic\ndisk stars (Binney \\& Merrifield 1998), \n$\\Omega_m/\\Omega_b \\simeq 7$ (based on $\\Omega_m=0.3,$ $h=0.7$,\nand $\\Omega_b h^2 \\simeq 0.02$ from Burles \\& Tytler [1998]),\n$\\epsilon_* = 0.5$, and $F_o=0.5$, we obtain $(M/L_V) \\simeq 5 f^{-1}$.\nMatching the mass-to-light ratios of typical dwarf satellite\ngalaxies then implies $f \\sim 0.3$. With the uncertainties\ndescribed above, a range $f \\sim 0.1-0.8$ is plausible, and\nthe range in observed $(M/L_V)$ could reflect in large part\nthe variations in $f$ from galaxy to galaxy.\nValues of $f \\la 0.1$ would imply excessive mass-to-light ratios, \nunless the factor $F_o$ can be much smaller than we have assumed.\n\nIn sum, the two parameters that determine the fraction of\nsurviving halos that are observable are $\\zre$ and $f$,\nwith plausible values in the range $\\zre \\sim 5-50$ and $f \\sim 0.1-0.8$.\nFor a given subhalo of \nmass $M_a$ and accretion redshift $z_a$, we use equation (2.26) \nof LC93 to\nprobabilistically determine the redshift $z_f$ when the main\nprogenitor of the subhalo was first more massive than $M_f = f M_a$.\nWe associate the subhalo with an observable galactic satellite only if\n$z_f \\ge \\zre$.\n\n\\section{Results}\n\nFigure 2 shows results of our model for the specific choices of $\\zre\n= 8$ and $f=0.3$. The thin solid line is the velocity function of all\nsurviving subhalos at $z=0$, reproduced from Figure 1. The thick line\nand shaded region shows the average and scatter in the expected number\nof observable satellites ($z_f > \\zre$). The solid triangles show the\nobserved satellite galaxies of the Milky Way and M31 within radii of\n$200 \\hkpc$ from the centers of each galaxy (note that all results are\nscaled to a fiducial volume $1 h^{-3} \\rm{Mpc}^{3}$). We see that the\ntheoretical velocity function for visible satellites is consistent\nwith that observed, and that the total number of observable systems is\n$\\sim 10\\%$ of the total dark halo abundance. The reason for this\ndifference is that most of the halos form after reionization. The\nobservable satellites are within halos that formed early,\ncorresponding to rare, high peaks in the initial density field.\n\n\nOther combinations of $\\zre$ and $f$ can provide similar results\n because the fraction of mass in place by\nthe epoch of reionization is larger if reionization occurs later. We\nfind that the following pairs of choices also reproduce the observed\ngalactic satellite velocity function: \n$(f,\\zre)=(0.1,12)$;$(0.2,10)$;$(0.4,7)$;$(0.5,5)$.\n It is encouraging that successful\nparameter choices fall in the range of naturally expected values.\nHowever, our model fails if reionization occurs too early ($\\zre \\gsim\n12$), since the value of $f$ required to reproduce the observed\nvelocity function would imply excessively large $M/L_V$ ratios. We\nconclude that the observed abundance of satellite galaxies may be\nexplained in the CDM scenario if galaxy formation in low-mass halos is\nsuppressed after the epoch of reionization, provided that $\\zre \\lsim 12$.\n\n\n\\section{Discussion}\n\nThe suppression of gas accretion by the photoionizing background\noffers an attractive solution to the dwarf satellite problem.\nThe physical mechanism seems natural, almost inevitable, and requires\nno fine tuning of the primordial fluctuation spectrum or properties\nof the dark matter. Although, in principle, a similar explanation\ncould be obtained with supernova feedback, reionization\nnaturally explains why most subhalos are dark, \nwhile the fraction $\\sim 10\\%$ that accreted a substantial fraction of \ntheir mass before $\\zre$ remain visible today.\nWith feedback, it is not obvious why any dwarf satellites would\nsurvive, and certainly not the specific number observed.\nPhotoionization also naturally explains why the discrepancy with CDM \npredictions appears at $v_c \\sim 30 \\ks$, rather than at a higher or\nlower $v_c$. In contrast, studies of the feedback mechanism\nsuggest that it is difficult to achieve the required suppression of star\nformation in halos with $v_c \\gsim 15 \\ks$ (Mac Low \\& Ferrara 1998). \n\n\nIn order to obtain a reasonable $M/L$ ratio for satellite galaxies in\nthis scenario, the reionization redshift must be relatively low, $\\zre\n\\lsim 12$. For higher $\\zre$, it is hard to understand how dwarf\ngalaxies with $v_c < 30 \\ks$ could have formed at all, though a blue\npower spectrum or non-Gaussian primordial fluctuations could help, or\nperhaps dwarfs could form by fragmentation within larger\nproto-galaxies. Currently, the reionization redshift is constrained\nonly within the rather broad range $\\zre \\sim 5-50$, but it might be\ndetermined in the future by CMB experiments or by spectroscopic\nstudies of luminous high-$z$ objects.\n\n\n\nA clear prediction that distinguishes this model from models with\nsuppressed small-scale power or self-interacting dark matter is that\nthere should be a large number of low-mass subhalos associated with\nthe Milky Way and similar galaxies. If we assume that the model\npresented in \\S 2.2 applies in all cases, then the observed dwarf\nsatellites should be just the low $M/L$ tail of the underlying\npopulation. For example, in our fiducial case (Figure 2, $\\zre=8$,\n$f=0.3$), reducing $f$ by a factor of 3 --- corresponding to an\n\\textit{increase} in the average $M/L$ by a \n{\\pspicture(0,0)(2,13.) \n\\rput[tl]{0}(0,13.){\\epsfxsize=9.cm \n\\epsffile{fig2.ps}} \n\\rput[tl]{0}(0,4.){ \n\\begin{minipage}{8.9cm} \n \\small\\parindent=4.5mm {\\sc Fig.}~2.--- Cumulative velocity function\n of all dark matter subhalos surviving at $z=0$ ({\\em thin solid\n line}) and ``observable'' halos ($z_{\\rm f} > z_{\\rm re}$) ({\\em\n thick solid line with shading}), for the specific choice of $z_{\\rm\n re}=8$ and $f=0.3$. The velocity function represents the average\n over 300 merger histories for halos of mass $M_{\\rm\n vir}(z=0)=1.1\\times 10^{12}h^{-1}{\\ }{\\rm M_{\\odot}}$. The errorbars\n and shading show the dispersion measured from different merger\n histories. The observed velocity function of satellite galaxies\n around the Milky Way and M31 is shown by triangles.\n\n\\end{minipage} \n } \n\\endpspicture} \n\n\\noindent factor of 3 --- raises\nthe predicted number of galaxies by a factor of 6. Reducing $f$\n(increasing $M/L$) by a factor of 7 raises the predicted number of\nsatellites by a factor of 10, and accounts for $\\sim 98 \\%$ of the\ndark subhalos. Large area, deep imaging surveys may soon be able to\nreveal faint dwarf satellites that lie below current detection limits.\n\n\n\n\nDark halo satellites may also be detectable by their gravitational\ninfluence. For example, it may be possible to detect halo\nsubstructure via gravitational lensing. Mao \\& Schneider (1998) point\nout that at least in the case of the quadruply imaged QSO B 1422 +\n231, substructure may be needed in order to account for the observed\nflux ratios. It is also plausible that a large number of dark\nsatellites could have destructive effects on disk galaxies (Toth \\&\nOstriker 1992; Ibata \\& Razoumov 1998; Weinberg 1998). Moore et al.\n(1999) used a simple calculation based on the impulse approximation to\nestimate the amount of heating that the subclumps in their simulations\nwould produce on a stellar disk embedded at the halo center. They\nconcluded that this type of heating is not problematic for galaxies\nlike the Milky Way, but that the presence of galaxies with no thick\ndisk, such as NGC 4244, may be problematic. Our results indicate that\nthe variation in halo formation histories is substantial, suggesting\nthat thin disks could occur in recently formed systems with little\ntime for significant heating to have occurred, but a detailed\ninvestigation of this subject is certainly warranted.\n\nIt is tempting to identify some of these subhalos with the High\nVelocity Clouds (HVCs) (Braun \\& Burton 1999; Blitz et al. 1998). In\nour scenario, it would be possible to account for some of these\nobjects provided we modify the model of \\S2.2. We currently assume\nthat there is no accretion after reionization, and that most of the\ngas that accretes before $\\zre$ is converted into stars. However, it\nmay be that accretion starts again at low redshift, after the level of\nthe UV background drops (e.g., Babul \\& Rees 1992; Kepner, Babul \\&\nSpergel 1997), and these late-accreting systems might form stars\ninefficiently and retain their gas as HI. If this is the case, HVCs\nmay be associated with subhalos that are accreted at late times. We\nfind that, on average, $\\sim 60\\%$ of surviving subhalos fall into the\nhost halo after $z=1$, and $\\sim 40 \\%$ fall in after $z=0.5$.\n\n\nAnother prediction is that there should be a diffuse stellar\ndistribution in the Milky Way halo associated with the disruption of\nmany galactic satellites (see Figure 1). If we assume that the\ndestroyed subhalos had the same stellar content as the surviving\nhalos, then we can estimate the radial density profile of this\ncomponent by placing the stars from each disrupted halo at the\napocenter of its orbit, where they would spend most of their time.\nThis calculation yields a density profile $\\rho_*(r) \\propto\nr^{-\\alpha}$, with $\\alpha = 2.5 \\pm 0.3$, extending from $r \\simeq 10\n- 100 \\hkpc$, which is roughly consistent with the distribution of\nknown stellar halo populations such as RR Lyrae variables (e.g.,\nWetterer \\& McGraw 1996). The normalization of the profile is more\nuncertain, but for the parameters $\\zre = 8$ and $f = 0.3$, and with\nthe assumption that each halo with $z_f > \\zre$ has a mass in stars of\n$M_{*} = f (\\Omega_b/\\Omega_0) \\epsilon_* M_{a}$, we find that the\nstellar mass of the disrupted component is $M_*\n\\sim 5 \\times 10^{8} \\hMsun$. This diffuse distribution could make up\na large fraction of the stellar halo, perhaps all of it.\nObservationally, it may be difficult to distinguish a disrupted\npopulation from a stellar halo formed by other means, but perhaps\nphase space substructure may provide a useful diagnostic (e.g.,\nJohnston 1998; Helmi et al. 1999).\n\n\nThis disrupted population would not be present in models with\nsuppressed small scale power or warm dark matter. However, it would\nbe expected in the self-interacting dark matter scenario. In this\ncase, the distribution would probably extend to a larger radius\nbecause dark matter interactions would disrupt the satellite halos\nfurther out.\n\nThere are other problems facing the CDM hypothesis, such as the\npossible disagreement between the predicted inner slopes of halo\nprofiles and the rotation curves of dwarf and LSB galaxies (Moore et\nal. 1999; Kravtsov et al. 1998; Flores \\& Primack 1994; Moore 1994).\nThe mechanism proposed here does not solve this problem, though more\ncomplicated effects of gas dynamics and star formation might do so.\nWe have shown that one of the problems facing CDM can be resolved by a\nsimple gas dynamical mechanism. If this solution is the right one,\nthen the dark matter structure of the Milky Way halo resembles a\nscaled-down version of a typical galaxy cluster, but most of the\nlow-mass Milky Way subhalos formed too late to accrete gas and become\nobservable dwarf galaxies.\n\n\n\\acknowledgements \nWe thank Andrew Gould and Jordi Miralda-Escud\\'e for useful\ndiscussions. This work was supported in part by NASA LTSA grant\nNAG5-3525 and NSF grant AST-9802568. Support for A.V.K. was provided\nby NASA through Hubble Fellowship grant HF-01121.01-99A from the Space\nTelescope Science Institute, which is operated by the Association of\nUniversities for Research in Astronomy, Inc., under NASA contract\nNAS5-26555.\n\n\n\\vspace{-10pt}\n\n\\begin{thebibliography}{}\n\\bibitem{} Babul, A., \\& Rees, M.J. 1992, MNRAS, 255, 346\n\\bibitem{} Barkana, R., \\& Loeb, A. 1999, ApJ, 523, 54\n\\bibitem{} Binney, J., \\& Merrifield, M. 1998, Galactic Astronomy\n(Princeton: Princeton University Press)\n\\bibitem{} Bullock, J.S., Kolatt, T.S., Sigad, Y., Somerville, R.S., \n Kravtsov, A.V., Klypin, A., Primack, J.R., \\& Dekel, A. 1999, MNRAS, \n submitted (astro-ph/9908159)\n\\bibitem{} Burles, S., \\& Tytler, D. 1998, ApJ, 507, 732\n\n\\bibitem{} Colpi, M., Mayer, L., \\& Governato, F. 1999, ApJ, 525, 720\n\\bibitem{} Dekel, A., \\& Silk, J. 1986, ApJ, 303, 39\n\\bibitem{} Efstathiou, G. 1992, MNRAS, 256, 43\n\\bibitem{} Flores, R.A., \\& Primack, J.R. 1994, ApJ, 475, L5\n\\bibitem{} Ghigna, S., Moore, B., Governato, F., Lake, G., Quinn, T.,\n \\& Stadel, J. 1998, MNRAS, 300, 146\n\n\\bibitem{} Gilmore, G., King, I. R., \\& van der Kruit, P.C. 1989, \nThe Milky Way as a Galaxy (Mill Valley: University Science)\n\n\\bibitem{} Gonzalez, A.H., Williams, K.A., Bullock, J.S., Kolatt, T.S.,\n\\& Primack J.R. 1999, ApJ, in press (astro-ph/9908075)\n\n\\bibitem{} Griffiths, L.M., Barbosa, D., \\& Liddle, A. R., 1999,\nMNRAS, 308, 854\n\n\\bibitem{} Helmi, A., White, S.D.M., de Zeeuw, P.T., \\& Zhao, H.-S.\n 1999, Nature, 402, 53\n\n\\bibitem{} Ibata, R.A., \\& Razoumov A.O. 1998, A\\&A, 336, 130\n\n\\bibitem{} Ikeuchi, S. 1986, Ap \\& SS, 118, 509\n\n\\bibitem{} Johnston, K.V., 1998, ApJ, 495, 297\n\n\\bibitem{} Kamionkowski, M., \\& Liddle, A.R. 1999, Phys. Rev. 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Charlot (Gif-sur-Yvette: Editions Fronti\\'eres), 41\n\\bibitem{} Shapiro, P.R. \\& Raga, A.C. 2000, in\nAstrophysical Plasmas: Codes, Models, and Observations,\ned. S. J. Arthur, N. Brickhouse, and J. Franco, in press (astro-ph/0002100)\n\\bibitem{} Somerville, R.S., \\& Kolatt, T.S. 1999, MNRAS, 305, 1 (SK99)\n\\bibitem{} Songaila, A., Hu, E.M., Cowie, L.L., \\& McMahon, R.G. 1999, \nApJ, 525 L5\n\\bibitem{} Spergel, D.N., \\& Steinhardt, P.J. 1999, preprint \n (astro-ph/9909386)\n\\bibitem{} Thoul, A.A., \\& Weinberg D.H. 1996, ApJ, 465, 608 \n\\bibitem{} Toth, G., \\& Ostriker, J.P. 1992, ApJ, 389, 5\n\\bibitem{} Weinberg, M. 1998, MNRAS, 299, 499.\n\\bibitem{} Wetterer, C.J., \\& McGraw, J.T. 1996, AJ, 112, 1046\n\\end{thebibliography} \n\\end{document} \n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002214.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem{} Babul, A., \\& Rees, M.J. 1992, MNRAS, 255, 346\n\\bibitem{} Barkana, R., \\& Loeb, A. 1999, ApJ, 523, 54\n\\bibitem{} Binney, J., \\& Merrifield, M. 1998, Galactic Astronomy\n(Princeton: Princeton University Press)\n\\bibitem{} Bullock, J.S., Kolatt, T.S., Sigad, Y., Somerville, R.S., \n Kravtsov, A.V., Klypin, A., Primack, J.R., \\& Dekel, A. 1999, MNRAS, \n submitted (astro-ph/9908159)\n\\bibitem{} Burles, S., \\& Tytler, D. 1998, ApJ, 507, 732\n\n\\bibitem{} Colpi, M., Mayer, L., \\& Governato, F. 1999, ApJ, 525, 720\n\\bibitem{} Dekel, A., \\& Silk, J. 1986, ApJ, 303, 39\n\\bibitem{} Efstathiou, G. 1992, MNRAS, 256, 43\n\\bibitem{} Flores, R.A., \\& Primack, J.R. 1994, ApJ, 475, L5\n\\bibitem{} Ghigna, S., Moore, B., Governato, F., Lake, G., Quinn, T.,\n \\& Stadel, J. 1998, MNRAS, 300, 146\n\n\\bibitem{} Gilmore, G., King, I. R., \\& van der Kruit, P.C. 1989, \nThe Milky Way as a Galaxy (Mill Valley: University Science)\n\n\\bibitem{} Gonzalez, A.H., Williams, K.A., Bullock, J.S., Kolatt, T.S.,\n\\& Primack J.R. 1999, ApJ, in press (astro-ph/9908075)\n\n\\bibitem{} Griffiths, L.M., Barbosa, D., \\& Liddle, A. R., 1999,\nMNRAS, 308, 854\n\n\\bibitem{} Helmi, A., White, S.D.M., de Zeeuw, P.T., \\& Zhao, H.-S.\n 1999, Nature, 402, 53\n\n\\bibitem{} Ibata, R.A., \\& Razoumov A.O. 1998, A\\&A, 336, 130\n\n\\bibitem{} Ikeuchi, S. 1986, Ap \\& SS, 118, 509\n\n\\bibitem{} Johnston, K.V., 1998, ApJ, 495, 297\n\n\\bibitem{} Kamionkowski, M., \\& Liddle, A.R. 1999, Phys. Rev. Lett., submitted\n(astro-ph/9911103)\n\n\\bibitem{} Kauffmann, G., White, S.D.M., \\& Guiderdoni, B. 19993, MNRAS, 264,\n 201\n\\bibitem{} Kepner, J.V., Babul, A., \\& Spergel, D.N. 1997, ApJ 487, 61\n\\bibitem{} Klypin, A.A., Kravtsov, A.V., Valenzuela, O., \\& Prada, F.\n1999a, ApJ, 522, 82 (KKVP99)\n\n\\bibitem{} Klypin, A.A., Gottl�ber, S., Kravtsov, A.V., \\& Khokhlov, A.M.\n1999b, ApJ, 516, 530\n\n\\bibitem{} Kravtsov, A.V., Klypin, A.K., Bullock, J.S. \\& Primack J.R.\n 1998, ApJ, 502, 48\n\n\\bibitem{} Mac Low, M.-M., \\& Ferrara, A. 1998, ApJ, 513, 142\n\\bibitem{} Mao, S., \\& Schneider, P. 1998, MNRAS, 295, 587. ApJ, 465, 608\n\\bibitem{} Mateo, M.L. 1998, ARA\\&A, 36, 435\n\\bibitem{} Miralda-Escud\\'e, J. 2000, ApJ, submitted (astro-ph/0002050)\n\\bibitem{} Moore, B. 1994, Nature, 370, 620\n\\bibitem{} Moore, B., Katz, N. \\& Lake, G. 1996, ApJ 457, 455\n\\bibitem{} Moore, B., Ghigna, F., Governato, F., Lake, G., Stadel, J., \\& \nTozzi, P. 1999, ApJ, 524, L19\n\\bibitem{} Navarro, J.F., Frenk, C.S., White, S.D.M. 1997, ApJ, 490, 493 \n\\bibitem{} Press, W.H., \\& Schechter, P. 1974, ApJ, 187, 425\n\\bibitem{} Quinn, T., Katz, N., \\& Efstathiou, G. 1996, MNRAS, 278, L49\n\\bibitem{} Rees, M.J. 1986, MNRAS, 218, 25\n\\bibitem{} Shapiro, P.R., Giroux, M.L., \\& Babul, A. 1994, ApJ, 427, 25\n\\bibitem{} Shapiro, P.R., Raga, A.C., \\& Mellena, G.\n 1997, in Structure and Evolution of the Intergalactic\nMedium From QSO Absorption Line Systems, ed. P. Petitjean \\& S. Charlot (Gif-sur-Yvette: Editions Fronti\\'eres), 41\n\\bibitem{} Shapiro, P.R. \\& Raga, A.C. 2000, in\nAstrophysical Plasmas: Codes, Models, and Observations,\ned. S. J. Arthur, N. Brickhouse, and J. Franco, in press (astro-ph/0002100)\n\\bibitem{} Somerville, R.S., \\& Kolatt, T.S. 1999, MNRAS, 305, 1 (SK99)\n\\bibitem{} Songaila, A., Hu, E.M., Cowie, L.L., \\& McMahon, R.G. 1999, \nApJ, 525 L5\n\\bibitem{} Spergel, D.N., \\& Steinhardt, P.J. 1999, preprint \n (astro-ph/9909386)\n\\bibitem{} Thoul, A.A., \\& Weinberg D.H. 1996, ApJ, 465, 608 \n\\bibitem{} Toth, G., \\& Ostriker, J.P. 1992, ApJ, 389, 5\n\\bibitem{} Weinberg, M. 1998, MNRAS, 299, 499.\n\\bibitem{} Wetterer, C.J., \\& McGraw, J.T. 1996, AJ, 112, 1046\n\\end{thebibliography}"
}
] |
astro-ph0002215
|
Correlated intense X-ray and TeV activity \\ of Mrk~501 in 1998 June
|
[
{
"author": "R.M.~Sambruna\\altaffilmark{1}"
},
{
"author": "F.A.~ Aharonian\\altaffilmark{2}"
},
{
"author": "H.~Krawczynski\\altaffilmark{2}"
},
{
"author": "[3ex]"
}
] |
We present exactly simultaneous X-ray and TeV monitoring with {RXTE} and HEGRA of the TeV blazar Mrk 501 during 15 days in 1998 June. After an initial period of very low flux at both wavelengths, the source underwent a remarkable flare in the TeV and X-ray energy bands, lasting for about six days and with a larger amplitude at TeV energies than in the X-ray band. At the peak of the TeV flare, rapid TeV flux variability on sub-hour timescales is found. %The TeV flux changed by a factor $\sim$ 20, while %lower amplitudes were observed in the X-rays. Large spectral variations are observed at X-rays, with the 3--20~keV photon index of a pure power law continuum flattening from $\Gamma=2.3$ to $\Gamma=1.8$ on a timescale of 2--3 days. This implies that during the maximum of the TeV activity, the synchrotron peak shifted to energies $\gtrsim 50$ keV, a behavior similar to that observed during the longer-lasting, more intense flare in 1997 April. The TeV spectrum during the flare is described by a power law with photon index $\Gamma=1.9$ and an exponential cutoff at $\sim$ 4~TeV; an indication for spectral softening during the flare decay is observed in the TeV hardness ratios. Our results generally support a scenario where the TeV photons are emitted via inverse Compton scattering of ambient seed photons by the same electron population responsible for the synchrotron X-rays. The simultaneous spectral energy distributions (SEDs) can be fit with a one-zone synchrotron-self Compton model assuming a substantial increase of the magnetic field and the electron energy by a factor of 3 and 10, respectively.
|
[
{
"name": "m501.tex",
"string": "%\\documentstyle[12pt,aasms4]{article}\n%\\documentstyle[12pt,aasms4,flushrt]{article}\n\\documentstyle[11pt,aaspp4,flushrt]{article}\n% \\received{} \\accepted{~~}\n\n% REVISED: FEB 3, 2000 \n\n%\\journalid{}{} \\articleid{}{}\n\n\\def\\cl{\\centerline}\n%\\input{psfig.tex}\n% in aasms4 use $\\gtrsim$ and $\\lesssim$\n\n\\begin{document}\n\n\\title{Correlated intense X-ray and TeV activity \\\\\nof Mrk~501 in 1998 June} \n\n\\author{R.M.~Sambruna\\altaffilmark{1}, \nF.A.~ Aharonian\\altaffilmark{2}, \nH.~Krawczynski\\altaffilmark{2},\n\\\\[3ex]} \n\\author{\nA.G.~Akhperjanian\\altaffilmark{8},\n% M.~Andronache\\altaffilmark{5},\nJ.A.~Barrio\\altaffilmark{3,4},\nK.~Bernl\\\"ohr\\altaffilmark{2,5},\nH.~Bojahr\\altaffilmark{7},\nI.~Calle\\altaffilmark{4},\nJ.L.~Contreras\\altaffilmark{4},\nJ.~Cortina\\altaffilmark{4},\n% A.~Daum\\altaffilmark{2},\n% T.~Deckers\\altaffilmark{6},\nS.~Denninghoff\\altaffilmark{3},\nV.~Fonseca\\altaffilmark{4},\nJ.C.~Gonzalez\\altaffilmark{4},\nN.~G\\\"otting\\altaffilmark{5},\nG.~Heinzelmann\\altaffilmark{5},\nM.~Hemberger\\altaffilmark{2},\nG.~Hermann\\altaffilmark{2},\n% M.~He{\\ss}\\altaffilmark{2},\nA.~Heusler\\altaffilmark{2},\nW.~Hofmann\\altaffilmark{2},\n% H.~Hohl\\altaffilmark{7},\nD.~Horns\\altaffilmark{5},\nA.~Ibarra\\altaffilmark{4},\nR.~Kankanyan\\altaffilmark{2,8},\nM.~Kestel\\altaffilmark{3},\nJ.~Kettler\\altaffilmark{2},\nC.~K\\\"ohler\\altaffilmark{2},\nA.~Kohnle\\altaffilmark{2},\nA.~Konopelko\\altaffilmark{2},\nH.~Kornmeyer\\altaffilmark{3},\nD.~Kranich\\altaffilmark{3},\nH.~Lampeitl\\altaffilmark{2},\nA.~Lindner\\altaffilmark{5},\nE.~Lorenz\\altaffilmark{3},\nN.~Magnussen\\altaffilmark{7},\nO.~Mang\\altaffilmark{6},\nH.~Meyer\\altaffilmark{7},\nR.~Mirzoyan\\altaffilmark{3},\nA.~Moralejo\\altaffilmark{4},\nL.~Padilla\\altaffilmark{4},\nM.~Panter\\altaffilmark{2},\n% D.~Petry\\altaffilmark{3,}$^\\dag$,\nR.~Plaga\\altaffilmark{3},\nA.~Plyasheshnikov\\altaffilmark{2},\nJ.~Prahl\\altaffilmark{5},\nG.~P\\\"uhlhofer\\altaffilmark{2},\nG.~Rauterberg\\altaffilmark{6},\n% C.~Renault\\altaffilmark{2,}$^\\#$,\n% W.~Rhode\\altaffilmark{7},\nA.~R\\\"ohring\\altaffilmark{5},\nV.~Sahakian\\altaffilmark{8},\nM.~Samorski\\altaffilmark{6},\nM.~Schilling\\altaffilmark{6},\nD.~Schmele\\altaffilmark{5},\nF.~Schr\\\"oder\\altaffilmark{7},\nW.~Stamm\\altaffilmark{6},\nM.~Tluczykont\\altaffilmark{5},\nH.J.~V\\\"olk\\altaffilmark{2},\nB.~Wiebel-Sooth\\altaffilmark{7},\nC.~Wiedner\\altaffilmark{2},\nM.~Willmer\\altaffilmark{6},\nW.~Wittek\\altaffilmark{3}, The HEGRA collaboration,\\\\[3ex]}\n\\author{L.~Chou\\altaffilmark{1}, P.S.~Coppi\\altaffilmark{9}, \nR.~Rothschild\\altaffilmark{10}, C.M.~Urry\\altaffilmark{11}}\n\\altaffiltext{1}{Pennsylvania State University,\nDepartment of Astronomy and Astrophysics, \n525 Davey Lab, University Park, PA 16802}\n\\altaffiltext{2}{Max Planck Institut f\\\"ur Kernphysik,\nPostfach 103980, D-69029 Heidelberg, Germany}\n\\altaffiltext{3}{Max Planck Institut f\\\"ur Physik, F\\\"ohringer Ring\n6, D-80805 M\\\"unchen, Germany}\n\\altaffiltext{4}{Universidad Complutense, Facultad de Ciencias\nF\\'{\\i}sicas, Ciudad Universitaria, E-28040 Madrid, Spain }\n\\altaffiltext{5}{Universit\\\"at Hamburg, II. Institut f\\\"ur\nExperimentalphysik, Luruper Chaussee 149,\nD-22761 Hamburg, Germany}\n\\altaffiltext{6}{Universit\\\"at Kiel, Institut f\\\"ur Experimentelle und \nAngewandte Physik,\nLeibnizstra{\\ss}e 15-19, D-24118 Kiel, Germany}\n\\altaffiltext{7}{Universit\\\"at Wuppertal, Fachbereich Physik,\nGau{\\ss}str.20, D-42097 Wuppertal, Germany}\n\\altaffiltext{8}{Yerevan Physics Institute, Alikhanian Br. 2, 375036 Yerevan, \nArmenia}\n\\altaffiltext{9}{Yale University, New Haven, CT 06520-8101}\n\\altaffiltext{10}{Center for Astrophysics and Space Sciences, \nUniversity of California at San Diego, La Jolla, CA 92093}\n\\altaffiltext{11}{STScI, 3700 San Martin Dr., Baltimore, MD 21218}\n% \\hspace*{-4.04mm} $^\\dag\\,$ Now at Universidad Aut\\'{o}noma de \n% Barcelona,\n% Instituto de F \\'{\\i}sica d'Altes Energies, E-08193 Bellaterra, Spain\\\\\n% On leave from \n% Altai State University, Dimitrov Street 66, 656099 Barnaul, Russia\\\\\n% \\hspace*{-4.04mm} $^\\#\\,$ Now at LPNHE, Universit\\'es Paris VI-VII, 4\n% place Jussieu, F-75252 Paris Cedex 05, France\n\n\\begin{abstract}\nWe present exactly simultaneous X-ray and TeV monitoring with {\\it\nRXTE} and HEGRA of the TeV blazar Mrk 501 during 15 days in 1998 June.\nAfter an initial period of very low flux at both wavelengths, the\nsource underwent a remarkable flare in the TeV and X-ray energy bands, \nlasting for about six days and with a larger amplitude at \nTeV energies than in the X-ray band.\nAt the peak of the TeV flare, rapid TeV flux variability on sub-hour\ntimescales is found. \n%The TeV flux changed by a factor $\\sim$ 20, while\n%lower amplitudes were observed in the X-rays. \nLarge spectral variations are observed at X-rays, with the 3--20~keV\nphoton index of a pure power law continuum flattening from\n$\\Gamma=2.3$ to $\\Gamma=1.8$ on a timescale of 2--3 days. This implies\nthat during the maximum of the TeV activity, the synchrotron peak\nshifted to energies $\\gtrsim 50$ keV, a behavior similar to that\nobserved during the longer-lasting, more intense flare in 1997\nApril. The TeV spectrum during the flare is described by a \npower law with photon index $\\Gamma=1.9$ and an exponential cutoff at\n$\\sim$ 4~TeV; an indication for spectral softening during the flare\ndecay is observed in the TeV hardness ratios. Our results generally\nsupport a scenario where the TeV photons are emitted via inverse\nCompton scattering of ambient seed photons by the same electron\npopulation responsible for the synchrotron X-rays. The simultaneous\nspectral energy distributions (SEDs) can be fit with a one-zone\nsynchrotron-self Compton model assuming a substantial increase of the\nmagnetic field and the electron energy by a factor of 3 and 10,\nrespectively.\n\\end{abstract}\n\n\\noindent {\\underline{\\em Subject Headings:}} Galaxies:jets --\nX-rays:galaxies -- Radiation mechanisms:non-thermal -- BL Lacertae\nobjects:Mrk 501 --- Gamma rays:observations.\n\n\\section{Introduction} \n\nBL Lacertae objects (BL Lacs) are radio-loud AGN dominated by\nnon-thermal continuum emission from radio up to $\\gamma$-rays (MeV to\nTeV energies) from a relativistic jet oriented at small angles to the\nobserver (e.g., Urry \\& Padovani 1995). While the radio through\nUV/X-ray continuum is almost certainly due to synchrotron emission\nfrom relativistic electrons in the jet (Ulrich, Maraschi, \\& Urry 1997\nand references therein), the origin of the luminous $\\gamma$-ray\nradiation from BL Lacs is still uncertain. Possibilities include\ninverse Compton scattering of ambient photons off the jet electrons\n(Maraschi et al. 1992; Sikora, Begelman, \\& Rees 1994; Dermer et\nal. 1996), or hadronic processes (e.g.\\ Dar \\& Laor 1997; Mannheim\n1993). \n\nA breakthrough was provided by the discovery of TeV emission from a\nhandful of such sources, all characterized by a synchrotron peak at\nhigher energies (High-energy peaked BL Lacs, or HBLs). One of these is\nMrk 501 ($z$=0.034). This source came into much attention after it\nexhibited a prolonged period of intense TeV activity in 1997 (Catanese\net al. 1997; Hayashida et al.\\ 1998; Quinn et al.\\ 1999; Aharonian et\nal. 1997,1999a-c; Djannati-Atai et al. 1999), accompanied by\ncorrelated X-ray emission on timescales of days. Interestingly, this\nexceptional TeV activity was accompanied by unusually hard X-ray\nemission up to $\\gtrsim$ 100 keV (Pian et al. 1998a; Catanese et\nal. 1997; Lamer \\& Wagner 1999; Krawczynski et al.\\ 1999),\nunprecedented in this or any other BL Lac. The hard X-ray spectrum\nimplied a shift toward higher energies of the synchrotron peak,\nusually located at UV/soft X-rays (e.g., Sambruna, Maraschi, \\& Urry\n1996; Kataoka et al. 1999), by more than three decades, persistent\nover a timescale of $\\sim$ 10 days (Pian et al. 1998a). Further\nobservations with {\\it BeppoSAX} in April-May 1998 and in May 1999\nduring periods of TeV lower flux showed that the synchrotron peak had\ndecreased to $\\sim$ 20 and 0.5 keV, respectively (Pian et al. 1998b,\n1999). These secular variations of the synchrotron peak suggest a\npowerful mechanism of particle energization, operating over timescales\nof years.\n \nBecause of its bright TeV emission and unusual X-ray spectral\nproperties, we selected Mrk 501 for an intensive monitoring in 1998\nJune using HEGRA and the {\\it Rossi X-ray Timing Explorer} ({\\it\nRXTE}), with a sampling designed to probe correlated variability at\nthe two wavelengths on timescales of one day or shorter. Here we\nreport the first results of the campaign, which is characterized by\nthe detection of a strong flare at both TeV and X-ray energies after a\nperiod of very low activity. The structure of this paper is as\nfollows. We describe the sampling and the observations in \\S~2, the\nX-ray and TeV light curves in \\S~3.1, and the TeV and X-ray spectra in\n\\S\\S~3.2--3.3. Implications of the data are discussed in \\S~4.\n\n\\section{Sampling and Data Analysis} \n\nThe {\\it RXTE} observations of Mrk 501 started June 14 and ended June\n28, with a sampling of once per day. The exposure time, typically 2--7\nks during the first week of observations (as allowed by visibility),\ndecreased to 0.5--1 ks during the latest period of the campaign, due\nto reduced visibility constraints. The total exposure in 1998 June was\n45,184 s. The remaining 134 ks of the total allocated exposure were \nre-scheduled in 1998 July and August; these data will be presented in\na future publication, together with simultaneous observations at\nlonger wavelengths (Sambruna et al. 2000). The HEGRA observations\nstarted one day earlier and ended three days later than {\\it RXTE},\nwith typical integration times of 1.5--2 hours per night, covering\n100\\% of the {\\it RXTE} exposure.\n\n\\subsection{X-ray observations}\n\nThe {\\it RXTE} data were collected in the 2--60 keV band with the\nProportional Counter Array (PCA; Jahoda et al. 1996) and in the\n15--250 keV band with the High-Energy X-ray Timing Experiment (HEXTE;\nRothschild et al. 1998). For the best signal-to-noise ratio,\nStandard-2 mode PCA data gathered with the top layer of the operating\nPCUs 0, 1, and 2 were analyzed. The data were extracted using the\nscript \\verb+REX+ which adopts standard screening criteria; the net\nexposure after screening in each Good Time Interval ranges from 0.2 to\n6 ks (Table 2; see below). The background was evaluated using models\nand calibration files provided by the {\\it RXTE} GOF for a ``faint''\nsource (less than 40 c/s/PCU), using \\verb+pcabackest+ v.2.1b. Light\ncurves were extracted in various energy ranges to study the\nenergy-dependence of the flux variability; for simplicity, only the\nlight curves in 2--4 keV and 10--20 keV (at the two extrema of the\ntotal energy range of the PCA) will be shown here.\n\nThe HEXTE data were extracted from both clusters for the same time\nperiods as the PCA. Due to the weak nature of the hard X-ray flux, the\ndata were combined into pre-flare (MJD 50980--988) and flare (MJD\n50989--993) time intervals. In addition, the flare interval was\nfurther subdivided into the rising portion (MJD 50989--990) and the\nrest of the flare containing the peak intensity. The source signal is\ndetected to about 50 keV, and we present results from these average\nspectra only.\n\n%HEXTE light curve and spectrum were extracted only from detector A of\n%clusters 0 and 1, since a transient source appears to be contaminating\n%part of detector B. The source signal was detected up to 50 keV only\n%during the two days of maximum activity of the source (MJD 50991-992;\n%Figure 1), with large error bars. We will thus present here only the\n%results from the average HEXTE spectrum obtained during those two\n%days.\n\nResponse matrices for the PCA data were created with \\verb+PCARMF+\nv.3.5. Spectral analysis of the PCA and HEXTE data was performed\nwithin \\verb+XSPEC+ v.10.0, using the latest released versions of the\nspectral response files. The fits were performed in the energy ranges\n3--20 keV and 20--250 keV, where the calibrations are best known. The\nquoted uncertainties on the spectral parameters are 90\\% confidence\nfor one parameter of interest ($\\Delta\\chi^2$=2.7).\n\n\\subsection{TeV observations}\n\nThe HEGRA Cherenkov telescope system (Daum et al. 1997; Konopelko et\nal. 1999) is located on the Roque de los Muchachos on the Canary\nIsland of La Palma (lat.\\ 28.8$^\\circ$ N, long.\\ 17.9$^\\circ$ W, 2200\nm a.s.l.). The Mrk~501 observations described in this paper were\ntaken from June 14th, 1998 to July 3rd, 1998 and comprise 49~hours of\nbest quality data. The analysis tools, the procedure of data cleaning\nand fine tuning of the Monte Carlo simulations, as well as the\nestimate of the systematic errors on the differential $\\gamma$-ray\nenergy spectra, were discussed in detail by Aharonian et al. (1999a,b).\n\nThe analysis uses the standard ``loose'' $\\gamma$/hadron separation\ncuts which minimize systematic errors on flux and spectral estimates\nrather than yielding the optimal signal-to-noise ratio. A software\nrequirement of two IACTs within 200~m from the shower axis, each with\nmore than 40 photoelectrons per image and a ``distance'' parameter of\nsmaller than 1.7$^\\circ$ was used. Additionally, only events with a\nminimal stereo angle larger than 20$^\\circ$ were admitted to the\nanalysis. Integral fluxes above a certain energy threshold were\nobtained by integrating the differential energy spectra above the\nthreshold energy, rather than by simply scaling detection rates. By\nthis means integral fluxes were computed without assuming a certain\nsource energy spectrum. For data runs during which the weather or the\ndetector performance caused a Cosmic Ray detection rate deviating only\nslightly, i.e.\\ less than 15\\% from the expectation value, the\n$\\gamma$-ray detection rates and spectra were corrected accordingly.\nSpectral results above an energy threshold of 500~GeV were derived\nfrom the data of zenith angles smaller than 30$^\\circ$ (39~hours of\ndata). The determination of the diurnal integral flux estimates and\nthe search for variability within individual nights use all data.\n\n\\section{Results}\n\n\\subsection{Light curves}\n\nFigure 1 shows the HEGRA and energy-dependent {\\it RXTE} light curves\nre-binned on 1 day and 5408 s ($\\sim$ one orbit), respectively. The\nPCA light curves were accumulated in the energy ranges 2--4~keV and\n10--20~keV; for an assumed spectrum with a typical\n$\\Gamma_{3-20~keV}=2.3$ (see below), their effective energies are\n3~keV and 16 keV, respectively (not significantly dependent on the\nslope).\n\nAfter a period of very low activity at both TeV and X-rays, a strong\nflare is apparent at all energies starting on day MJD 50989 and ending\non day MJD 50994. At TeV energies, the flare has a broad base, lasting\napproximately six days, with a narrow ``core'' superposed, lasting two\ndays (MJD 50991--992), and a total max/min amplitude of a factor\n$\\sim$ 20. The X-rays track well the structure of the TeV flare,\nalthough with lower amplitudes (factor 4 and 2 at hard and soft\nX-rays, respectively). A correlation analysis using both the Discrete\nCorrelation Function and Modified Mean Deviation methods (Edelson \\&\nKrolik 1989; Hufnagel \\& Bregman 1992) confirm that there are no lags\nbetween the TeV and X-ray light curves, or between the soft and hard\nX-rays, larger than one day.\n\nTo explore correlations on short timescales, we examined light curves\nbinned at 900 s in TeV and 300 s at X-rays (the best compromise\nbetween time resolution and adequate signal-to-noise ratio in both\ncases). Figure 2 shows the TeV and X-ray light curves for the day of\nthe peak activity, i.e., MJD 50991, when intra-hour variability at TeV\nenergies was detected. The TeV flux varied by a factor $\\sim$ 2, with\nthe hypothesis of constant flux rejected at 99.4\\% confidence level\naccording to the $\\chi^2$ test. The doubling timescale of the TeV\nflux is well below 1~hour (approximately 20~min); to our knowledge,\nthis is the shortest flux variability timescale found for Mrk~501 so\nfar (e.g., Quinn et al. 1999), and comparable to Mrk 421 (Gaidos et\nal. 1996). Unfortunately, as Figure 2 shows, gaps in the {\\it RXTE}\nsampling prevent us from commenting on sub-hour correlated variability\nat X-rays. \n\nA very rapid X-ray flare, with an increase of the 2--10 keV flux by\n60\\% in $<$ 600 s, was recently detected from Mrk 501 with {\\it RXTE}\nin 1998 May (Catanese \\& Sambruna 2000). This result, together with\nour evidence for fast TeV variability, shows that Mrk 501 can vary on\nthe fastest timescales at both X-ray and TeV wavelengths as other TeV\nsources (Mrk 421; Maraschi et al. 1999), and calls for future dense\nX-ray/TeV monitorings, aimed at probing correlated variability on the\nshortest accessible timescales. \n\n\\subsection{Simultaneous TeV and X-ray spectra} \n\nBecause of the sampling, we are able to derive truly simultaneous\nX-ray and TeV spectra during the pre-flare and the flare states. The\nhigh-state spectra were accumulated during the days of maximum TeV\nactivity, MJD 50991--992, while the pre-flare spectra were accumulated\nin the time interval MJD 50979--990. Table 1 reports the results of\nthe spectral fitting of the simultaneous TeV and X-ray spectra, while\nthe data are shown in Figure 3.\n\nThe HEGRA spectrum during the flare state was fitted over the energy\nrange from 500~GeV to 20~TeV (above 10~TeV the evidence for emission\nis only marginal) with a power law plus an exponential cutoff,\ndN/dE=N$_0 \\times$ (E/TeV)$^{-\\Gamma} \\times e^{(-E/E_0)}$, with\nspectral parameters reported in Table 1 (with statistical\nuncertainties). \n%$N_0=(7.9 ~\\pm 1.0_{\\rm stat})\\times 10^{-11}$, cm$^{-2}$ s$^{-1}$\n%TeV$^{-1}$, $\\Gamma=1.92 ~\\pm 0.3_{\\rm stat}$, and\n%$E_0=4.0~(-0.9~+1.45)_{\\rm stat}$~TeV. \nThe parameters $E_0$ and $\\Gamma$ are strongly correlated: within\nsystematic errors the pairs of parameters ($\\Gamma=1.7$;\n$E_0=2.8$~TeV) and ($\\Gamma=2.2$; $E_0=6.6$~TeV) are also consistent\nwith the data. Note that the spectral parameters we measure for the\n1998 June outburst, i.e., a slope $\\Gamma=1.9$ and cutoff energy\n$E_0=4$ TeV, are very similar to those measured during the 1997\nflaring phase (Aharonian et al.\\ 1999a). For the pre-flare phase, the\nTeV-flux was too low to allow us to fit a power law model with an\nexponential cutoff (Table 1). A fit of a power law model to the ratio\nof the flare and the pre-flare spectra gives $(d$N/$d$E)$_{\\rm\nflare}/(d$N/$d$E$)_{\\rm pre-flare} \\propto $E$^\\beta$ with $\\beta =\n-0.17 \\pm 0.19$, consistent within statistics with no spectral\nevolution.\n%but indicating even a slightly harder TeV-spectrum before the flare.\n\nThe PCA spectra were fitted with a single power law with Galactic\nabsorption, 1.73 $\\times 10^{20}$ cm$^{-2}$ (Elvis, Lockman, \\& Wilkes\n1989). As can be seen from Table 1, this model provides an excellent\nfit to the X-ray spectra up to 20 keV, with the photon index\nflattening from $\\Gamma_{3-20~keV}=2.21$ during the pre-flare state to\n$\\Gamma_{3-20~keV}=1.89$ during the flare. No spectral breaks are\nrequired, i.e., there is no statistical improvement when a second\npower law is added to the fit. However, we can not exclude the\npresence of a spectral break at energies softer than sampled with the\nPCA, $\\sim$ 1--2 keV, as indeed detected with {\\it BeppoSAX} (Pian et\nal. 1998a).\n\nThe HEXTE data are fitted by a power law with a photon index\nconsistent with the extrapolation of the PCA slope in both high and\nlow states (Table 1). Indeed, fitting the PCA and HEXTE datasets\ntogether, we find that a single power law with a slope similar to the\nPCA slope describes well the 3--50 keV continuum during both the\npre-flare and flare epochs. Given the large uncertainties of the HEXTE\ndata, however, we can not rule out the presence of spectral breaks at\nenergies $\\gtrsim 10-20$ keV, as indeed detected by {\\it BeppoSAX}\n(Pian et al. 1998a,b).\n\n\\subsection{X-ray and TeV spectral variability} \n\nWe accumulated time-resolved PCA spectra for each data point of the\nX-ray light curves in Figure 1, and fitted them over the energy range\n3--20 keV with a single power law plus Galactic absorption. The\nresults of the fitting are reported in Table 2 (columns 3--5),\ntogether with the date of the spectrum (column 1) and its net exposure\n(column 2). The time progression of the PCA slope is plotted in Figure\n1, intermediate panel. Large variability is readily apparent, with\nthe photon index flattening from $\\Gamma_{3-20~keV} \\sim 2.3$ to\n$\\Gamma_{3-20~keV} \\sim 1.8$ with increasing flux. There is an\nindication that the X-ray continuum steepens during the decay stage of\nthe flare.\n\nThe X-ray spectral variations follow a well-defined pattern with the\nintensity. This is illustrated in Figure 4, where the 3--20 keV photon\nindex is plotted versus the 2--10 keV flux. The dotted lines mark the\ntime progression of the slope during the flaring activity, and clearly\nshow a ``clock-wise'' loop. This is similar to what was observed in\nother HBLs (PKS 2005--489, Perlman et al. 1999; PKS 2155--304, Sembay\net al. 1992, Sambruna 1999; Mrk 421, Takahashi et al. 1996) and can be\ninterpreted in terms of cooling of the synchrotron-emitting electrons\nin the jet (Kirk, Riegler, \\& Mastichiadis 1998).\n\nThe HEXTE spectrum accumulated at the beginning of the flare (see\n\\S~2) is fitted by a power law with slope $\\Gamma_{20-50~keV}=2.19 \\pm\n0.59$ and 20--50 keV flux F$_{20-50~keV}=(5.3 \\pm 1.6) \\times\n10^{-11}$ erg cm$^{-2}$ s$^{-1}$. During the peak and decreasing\nflare, $\\Gamma_{20-50~keV}=1.86 \\pm 0.28$ and F$_{20-50~keV}=(1.1 \\pm\n0.2) \\times 10^{-10}$ erg cm$^{-2}$ s$^{-1}$. Comparing to the\npre-flare flux from Table 1, the source brightened by a factor $\\sim$\n6 during the TeV flare in the HEXTE band, with an indication of a\nhardening of the 20--50 keV continuum.\n\nAt TeV energies, given the limited signal-to-noise ratio in the\npre-flare state, we investigated spectral variations by constructing\nhardness ratios. These are defined as the ratios of the flux in\n2--9.7~TeV to the flux in 0.8--2~TeV (the lower bound is chosen to\nassure negligible systematic errors due to threshold effects and 2~TeV\napproximately equals the median energy of photons with energies above\n0.8~TeV). The TeV hardness ratios are plotted versus the observation\ndate in Figure 1, bottom panel, together with 1$\\sigma$ uncertainties.\nIt is apparent that, within statistical uncertainties, the hardness\nratios in the pre-flare state (MJD 50979--990) and flare state (MJD\n50991--992) are very similar, despite that the absolute fluxes differ\nby one order of magnitude. Intriguingly, the spectrum seems to soften\nsubstantially during the decay stage, although the limited statistical\nsignificance of about 2$\\sigma$ prevents us from drawing firmer\nconclusions.\n\n\\section{Discussion}\n\nSince the typical flux variability timescale of Mrk 501 in TeV\n$\\gamma$-rays and X-rays can be much less than one day, it is\nimportant to have truly simultaneous observations in both bands. It is\nalso important to have reasonably continuous sampling on timescales of\nat least one day in order to have an accurate picture of the dynamics\nof the source. For this reason, we conducted a 15-day TeV/X-ray\nmonitoring with diurnal {\\it RXTE} observations exactly in the HEGRA\nvisibility windows. After 10 days of quiescence, the source exhibited\na strong flare at both TeV and X-rays lasting six days, with a flux\nexceeding the pre-flare level by a factor of $\\sim $~20 at TeV\nenergies during a 2-day maximum, and with lower amplitudes (factor\n2--4) at X-rays. We also report the first detection of TeV flux\nvariability on sub-hour timescales in Mrk 501 (\\S~3.1).\n\nBy chance, our multiwavelength campaign in 1998 June coincided with\nthe only high TeV activity of the source during that year. Luckily, we\nwere able to follow the evolution of the TeV flare not only during the\npre-flare and flare stage but also during the decay stage. \n%Comparison\n%with the TeV hardness ratios obtained with HEGRA for the rest of the\n%1998 observations shows that the June flare coincides with a period of\n%flatter-than-average continuum, probably corresponding to a\n%qualitatively different state of the source. \nThe TeV spectrum during the flare is similar to the spectra observed\nin 1997, suggesting that the flaring episode we witnessed in 1998 June\nwas a scaled-down version of the longer-lasting 1997 flare. This\nconclusion is bolstered by the strong spectral variations we observe\nin the X-rays. Our {\\it RXTE} observations show that the X-ray\ncontinuum in 3--20 keV flattened by $\\Delta\\Gamma_{3-20~keV} \\sim 0.5$\nfrom the beginning of the campaign ($\\Gamma_{3-20~keV}=2.3$) to the\nflare maximum ($\\Gamma_{3-20~keV}=1.8$). Interestingly, at the peak\nof the TeV flare the X-ray slope was similar to the 2--10 keV slope\nmeasured in 1997 April, May, and July with {\\it BeppoSAX} and {\\it\nRXTE} (Pian et al. 1998a; Lamer \\& Wagner 1999; Krawczynski et\nal. 1999). This implies a similar shift of the synchrotron peak\nfrequency at higher energies, $\\gtrsim 50$ keV (Figure 3). While in\nApril 1997 the X-ray continuum flattened by 0.4 within approximately\ntwo weeks, we see here a comparable flattening within only $\\sim$ 2--3\ndays. Note that large changes of the position of the synchrotron peak\nare relatively rare. Besides Mrk 501, they were observed to-date only\nin two HBLs, 1ES 2344+514 (Giommi, Padovani, \\& Perlman 1999) and 1ES\n1426+428 (Ghisellini, Tagliaferri, \\& Giommi 1999), but not in Mrk\n421, PKS 2155--304, or any other BL Lac. Our observations provide the\nfirst evidence that in Mrk 501 the synchrotron peak may change on\nrelatively short timescales ($\\sim$ a few days). \n\nSeveral models have been suggested to explain the TeV radiation from\nblazars. A popular scenario are the leptonic models, where TeV\n$\\gamma$-rays are produced via inverse Compton scattering of directly\naccelerated electrons on external and/or internal photons (e.g.,\nSikora 1997). For Mrk 501, an object without strong broad line\nemission, the synchrotron self-Compton (SSC) model is almost commonly\naccepted as the most probable explanation for the observed\nX-ray/TeV-$\\gamma$-ray emission (e.g., Tavecchio et al. 1998; Kataoka\net al. 1999). Presently, the SSC model is the only model (at least in\nits simplified, ``one-zone'' version) which has been developed to a\nlevel which allows conclusive predictions which can be compared with\nexperimental results. In particular, the SSC scenario is able to give\nsatisfactory fits to both the X-ray and the TeV spectra (Pian et\nal. 1998a; Hillas 1999; Krawczynski et al. 1999). We used the code\ndeveloped by Coppi (1992) to fit our simultaneous SEDs in Figure 3,\nassuming emission from a one-zone, homogeneous region and\nincorporating Klein-Nishina effects. The key parameters used in this\nmodel are the Doppler factor $\\delta_{\\rm j}$ of the relativistic\nplasma, the radius $R$ of the emission region, the magnetic field $B$,\nand the electrons' maximum energy $E_{max}$.\n\nThe results of the fits are shown in Figure 3 as solid lines, and the\nparameters' values are reported in the caption. As discussed further\nbelow, the models were computed without correcting for the\nextragalactic extinction of TeV photons due to $\\gamma$/$\\gamma$ pair\nproduction with the photons of the Diffuse Extragalactic Background\nRadiation (e.g.\\ Gould \\& Schr\\'{e}der 1966). In the lower panel, we\nplot the ratio of the data and best-fit model between the high-state\nand pre-flare. The latter plot emphasizes that, while the TeV spectra\nof both states are quite similar, the X-ray spectra of the pre-flare\nand the flare state are significantly different. In SSC models the\nhardening of the X-ray spectrum during the flare can be attributed to\na shift of the peak frequency $\\nu_{\\rm s}$ of the synchrotron\nradiation, $\\nu_{\\rm s}\\propto~B \\times E^2_{\\rm max}$. Assuming an\nincrease of both the magnetic field and the maximum energy during the\nflare, the dramatic changes of the X-ray spectrum are readily\nexplained (see Figure 3). While the increase of magnetic field does\nnot affect the $\\gamma$-ray spectrum, the increase of $E_{\\rm max}$\ndoes make the inverse Compton (IC) spectrum harder. However, since\nthe $\\gamma$-rays are produced in the Klein-Nishina regime, this\neffect is less pronounced in IC than in the synchrotron radiation\ncomponent. The fits shown in Figure 3 correspond to the following\nmodel parameters: $B$=0.03~G, $E_{\\rm max}=2$~TeV (exponential cutoff\nenergy), $R=4 \\times 10^{16}$\\,cm for pre-flare state, and $B$=0.1~G,\n$E_{\\rm max}=20$~TeV, $R=2.7 \\times 10^{15}$\\,cm for the flare state.\nFor both cases a Doppler factor of $\\delta_{\\rm j}=25$ is assumed.\nNote that the latter value of the Doppler factor implies that internal\nabsorption of the TeV $\\gamma$-rays by lower frequency photons can be\ncompletely neglected (e.g.\\ Celotti, Fabian, \\& Rees 1998).\nFurthermore, the chosen Doppler factor and radius of the emitting\nvolume in the flaring state imply time variability down to\n$t=R/(c~\\delta_{\\rm j}) =$1~hour which agrees with the observed flux\nvariability following from Figure 2. For the flare state with good\nstatistics up to $\\sim$ 10~TeV, the model over-predicts the TeV flux\nabove $\\sim$ 5~TeV, in particular by a factor of $\\sim$ 2.5 at 10~TeV.\nThis discrepancy should not be overemphasized, but could well be the\nresult of intergalactic extinction due to $\\gamma$/$\\gamma$ pair\nproduction.\n\nIn summary, we have performed a 2-week monitoring campaign of the HBL\nMrk 501 in 1998 June with HEGRA and {\\it RXTE}, with a sampling\ndesigned to probe TeV/X-ray correlation on timescales of several\nhours. We detected a strong flare at both wavelengths, rising from a\nperiod of very low activity, well correlated at TeV and X-rays on time\nscales of $\\lesssim$ 1 day, accompanied by large\n($\\Delta\\Gamma_{3-20~keV} \\sim 0.5$) spectral variability at\nX-rays. Our results support an interpretation in terms of a canonical\nsynchrotron-self Compton scenario. Future campaigns with a more\nintensive sampling designed to probe correlation on shorter time\nscales at both X-ray and TeV energies are needed to set more stringent\nconstraints on the radiative processes which play an important role in\nthe evolution of the flare.\n\n\\acknowledgements \n\nRMS acknowledges support from NASA contract NAS--38252 and NASA grant\nNAG--7121. RR acknowledges support by NASA contract NAS5-30720. We are\ngrateful to the {\\it RXTE} team, especially Evan Smith, for making\nthese observations possible, to the {\\it RXTE} GOF for constant\nsupport with the data analysis, and to Joe Pesce for a careful reading\nof the manuscript. HEGRA is supported by the German ministry for\nResearch and technology BMBF and the Spanish Research Council CICYT.\nWe thank the Instituto de Astrophys\\`{i}ca de Canarias for supplying\nexcellent working conditions at La Palma. 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Noble, p. 391; \n\n%{\\bf Urry et al. 1996}, ApJ, 463, 424\n\n\\reference {} Urry, C.M. \\& Padovani, P. 1995, PASP, 107, 803 \n\n%\\reference {} von Montigny, C. et al. 1995, ApJ, 440, 525 \n\n%\\reference {} Wehrle, A.E. et al. 1998, ApJ, 497, 178\n\n\\end{references} \n\n\\newpage\n\n\\noindent{\\bf Figure Captions}\n\n\\begin{itemize}\n \n\\item\\noindent Figure 1: Multiwavelength light curves of Mrk 501 in\n1998 June, as measured with HEGRA and {\\it RXTE}, binned at 1 day and\n5408 s (one orbit), respectively (top panel). The HEGRA flux units are\n$10^{-12}$ ph cm$^{-2}$ s$^{-1}$, the {\\it RXTE} data are in c\ns$^{-1}$. The HEGRA light curve was arbitrarily shifted by +1.5 in\nlogarithmic units for clarity of presentation. A strong flare is\ndetected at both TeV and X-rays, with increasing amplitude for\nincreasing energy. The flare was accompanied by large spectral\nvariations at X-rays (middle panel), with flatter slope with\nincreasing flux. Within the statistical errors, the TeV spectrum was\nrather hard during the whole pre-flare and flare phases, as shown by\nthe TeV hardness ratios in the bottom panel (upper limits are on\n1$\\sigma$ confidence limit to facilitate the comparison with the error\nbars of the flux estimates). There is an indication of spectral\nsoftening during the decay stage of the flare.\n\n\\item\\noindent Figure 2: TeV and X-ray light curves (binned at 900 s \nand 300 s, respectively) of Mrk 501 during the day of maximum TeV\nactivity in 1998 June. Significant variability of a factor $\\sim$2 on\n$\\sim$ 20 min timescale is detected at TeV energies. Unfortunately,\ngaps are present in the {\\it RXTE} monitoring and we can not comment\non correlated X-ray variability on these short timescales.\n\n\\item\\noindent Figure 3: Spectral energy distributions of Mrk 501 in\n1998 June during the peak of the TeV/X-ray flare (filled dots) and\nduring the pre-flare state (open dots). Only the PCA data are plotted\nfor clarity (Table 1). The solid lines are fits to the spectra with an\nhomogeneous SSC model (Coppi 1992), with the following fitted\nparameters: $B$=0.03~G, $E_{\\rm max}=2$~TeV, $R=4 \\times 10^{16}$ cm\nfor the pre-flare state; $B$=0.1~G, $E_{\\rm max}=20$~TeV, $R=2.7\n\\times 10^{15}$ cm for the high state. The bottom panel shows the\nratios of the model spectra and data for the flare and pre-flare\nstates.\n\n\\item\\noindent Figure 4: Plot of the X-ray 3--20 keV slope versus the\nobserved 2--10 keV flux, from fits to the time-resolved PCA spectra\n(Table 2). The trend of flattening slope with increasing flux is\napparent. The dotted lines mark the time progression of the slope,\nwhich appears to follow a ``clock-wise'' pattern during the\nflare. This behavior is consistent with the X-ray flare being due to\nelectron cooling (Kirk et al. 1998). \n\n\\end{itemize}\n\n\n\\newpage \n\n\\scriptsize\n\n\\oddsidemargin-0.85in\n\\textheight10.2in\n\\textwidth7.7in\n\\topmargin-0.8in\n\\footheight0in \n\\footskip0in \n~~~~ \\\\\n\n\\begin{center}\n\\begin{tabular}{lcccccc}\n\\multicolumn{7}{l}{{\\bf Table 1: Simultaneous average TeV and X-ray spectra}} \\\\\n\\multicolumn{7}{l}{ } \\\\ \\hline\n& & & & & & \\\\\nState$^{~a}$ && N$_0^{~b}$ & $\\Gamma$ & E$_0$ & F$^{~c}$ & $\\chi^2_r$/dofs \\\\\n & & & & (TeV) & (10$^{-11}$ erg cm$^{-2}$ s$^{-1}$) & \\\\\n& & & & & & \\\\ \\hline\n& & & & & & \\\\\n\\multicolumn{7}{l}{{\\bf A) TeV$^{~d}$ }} \\\\\n& & & & & & \\\\\nFlare && 7.9 $\\pm$ 1.0 & 1.92 $\\pm$ 0.3 & 4.0$^{+1.45}_{-0.90}$ &$\\cdots$ & 0.54/13 \\\\\nPre-flare && 0.5 $\\pm$ 0.1 & 2.31 $\\pm$ 0.20 & $\\cdots$ &$\\cdots$ & 1.4/9 \\\\ \n& & & & & & \\\\\n\\multicolumn{7}{l}{{\\bf B) X-ray$^{~e}$ }} \\\\\n& & & & & & \\\\\nFlare PCA && $\\cdots$ & 1.89 $\\pm 0.02$ &$\\cdots$ & 18.5 $\\pm$ 0.9 & 0.75/42 \\\\\nFlare HEXTE && $\\cdots$ & 2.19 $\\pm$ 0.29 & $\\cdots$ & 7.5 $\\pm$ 1.1 & 1.04/69 \\\\\nPre-flare PCA && $\\cdots$ & 2.21 $\\pm$ 0.02 &$\\cdots$ & 0.7 $\\pm$ 0.1 & 0.85/41 \\\\ \nPre-flare HEXTE && $\\cdots$ & 2.30 $\\pm$ 0.45 & $\\cdots$ & 1.8 $\\pm$ 0.4 & 0.87/69 \\\\\n& & & & & & \\\\ \\hline \n\n\n\\end{tabular}\n\\end{center}\n\n\\indent\\indent\\indent{\\bf Notes:} \\\\\n\\indent\\indent\\indent a=High state corresponds to the time interval MJD 50991--992. Low state corresponds to MJD 50979--987; \\\\\n\\indent\\indent\\indent b=Normalization of the power law, in 10$^{-11}$ ph cm$^{-2}$s$^{-1}$TeV$^{-1}$ for the HEGRA data; \\\\\n\\indent\\indent\\indent c=Observed flux in 2--10 keV (PCA) and 20--50 keV (HEXTE); \\\\\n\\indent\\indent\\indent d=Fits with a power law plus\nexponentional cutoff: dN/dE=N$_0 \\times$ (E/TeV)$^{-\\Gamma} \\times\ne^{(-E/E_0)}$. Errors on \\\\\n\\indent\\indent\\indent\\indent parameters are statistical; \\\\\n\\indent\\indent\\indent e=Fits with a single power law plus Galactic\nabsorption, N$_H=1.73 \\times 10^{20}$ cm$^{-2}$ (Elvis et al. 1989). \\\\\n\n\\newpage \n\n\\oddsidemargin-0.85in\n\\textheight10.2in\n\\textwidth7.7in\n\\topmargin-0.8in\n\\footheight0in \n\\footskip0in \n~~~~ \\\\\n\n\\begin{center}\n\\begin{tabular}{lrccc}\n\\multicolumn{5}{l}{{\\bf Table 2: X-ray spectral variability$^{~a}$}} \\\\\n\\multicolumn{5}{l}{ } \\\\ \\hline\n& & & & \\\\\nStart Date & Net Exp. & $\\Gamma_{3-20~keV}$ & $\\chi^2_r$ & F$_{2-10~keV}$ \\\\\n(MJD-50000) & (s) & & (for 42 dofs) & (10$^{-11}$ erg cm$^{-2}$ s$^{-1}$) \\\\& & & & \\\\ \\hline \n& & & & \\\\\n978.9 & 3168 & 2.29 $\\pm$ 0.04 & 0.55 & 5.91 \\\\\n979.9 & 3312 & 2.27 $\\pm$ 0.04 & 0.72 & 6.05 \\\\\n980.9 & 6304 & 2.31 $\\pm$ 0.03 & 0.57 & 6.04 \\\\\n981.9 & 6320 & 2.17 $\\pm$ 0.03 & 0.84 & 7.13 \\\\\n982.9 & 3488 & 2.22 $\\pm$ 0.04 & 0.66 & 6.29 \\\\\n983.0 & 4144 & 2.23 $\\pm$ 0.04 & 0.46 & 6.41 \\\\\n983.9 & 6192 & 2.21 $\\pm$ 0.03 & 0.73 & 8.41 \\\\\n984.0 & 1328 & 2.19 $\\pm$ 0.06 & 0.70 & 6.58 \\\\\n984.9 & 5040 & 2.16 $\\pm$ 0.03 & 0.70 & 6.08 \\\\\n985.1 & 464 & 2.26 $\\pm$ 0.10 & 0.68 & 6.02 \\\\\n985.9 & 3024 & 2.19 $\\pm$ 0.04 & 0.71 & 6.47 \\\\\n986.0 & 352 & 2.07 $\\pm$ 0.11 & 0.77 & 6.43 \\\\\n986.1 & 528 & 2.25 $\\pm$ 0.09 & 0.78 & 6.45 \\\\\n986.9 & 384 & 2.21 $\\pm$ 0.10 & 0.68 & 6.71 \\\\\n987.1 & 480 & 2.36 $\\pm$ 0.10 & 0.78 & 6.76 \\\\\n987.9 & 1536 & 2.28 $\\pm$ 0.06 & 1.04 & 7.05 \\\\\n988.0 & 592 & 2.20 $\\pm$ 0.08 & 0.71 & 7.29 \\\\\n988.9 & 1152 & 2.06 $\\pm$ 0.04 & 0.71 & 10.8 \\\\\n989.0 & 912 & 2.06 $\\pm$ 0.04 & 0.60 & 11.4 \\\\\n989.9 & 1296 & 1.96 $\\pm$ 0.03 & 0.65 & 12.1 \\\\\n990.0 & 208 & 2.03 $\\pm$ 0.08 & 0.52 & 11.3 \\\\\n990.0 & 512 & 2.06 $\\pm$ 0.06 & 0.74 & 11.3 \\\\\n990.9 & 1392 & 1.89 $\\pm$ 0.02 & 1.46$^{~b}$ & 16.9 \\\\\n991.0 & 656 & 1.86 $\\pm$ 0.03 & 0.99 & 18.1 \\\\\n991.9 & 432 & 1.91 $\\pm$ 0.03 & 0.52 & 20.5 \\\\\n992.0 & 512 & 1.93 $\\pm$ 0.04 & 0.65 & 20.0 \\\\\n992.9 & 528 & 2.01 $\\pm$ 0.04 & 0.47 & 15.4 \\\\\n993.0 & 736 & 2.08 $\\pm$ 0.04 & 0.82 & 15.4 \\\\\n& & & & \\\\ \\hline \n\n\\end{tabular}\n\\end{center}\n\n\\indent\\indent\\indent{\\bf Notes:} \\\\\n\\indent\\indent\\indent a=Fits to the PCA data in 3--20 keV with a single\npower law plus Galactic N$_H$ (1.73 $\\times 10^{20}$ cm$^{-2}$). \\\\\n\\indent\\indent\\indent\\indent Errors are \n90\\% confidence for one parameter of interest\n($\\Delta\\chi^2$=2.7). \\\\\n\\indent\\indent\\indent b=High $\\chi^2$ is due to instrumental absorption \nfeatures in the residuals around 4.8 keV (Xenon edge) \\\\\n\\indent\\indent\\indent\\indent and 8.5 keV (unknown origin). \n\n\\end{document} \n\n"
}
] |
[] |
astro-ph0002216
|
Space VLBI Observations of 3C 279 at 1.6 and 5 GHz
|
[
{
"author": "B. G. Piner\\altaffilmark{1}"
},
{
"author": "P. G. Edwards\\altaffilmark{2}"
},
{
"author": "A. E. Wehrle\\altaffilmark{1}"
},
{
"author": "H. Hirabayashi\\altaffilmark{2}"
},
{
"author": "J. E. J. Lovell\\altaffilmark{3}"
},
{
"author": "\\& S. C. Unwin\\altaffilmark{1}"
}
] |
We present VLBI Space Observatory Programme (VSOP) observations of the gamma-ray blazar 3C~279 at 1.6 and 5~GHz made on 1998 January 9-10 with the HALCA satellite and ground arrays including the Very Long Baseline Array (VLBA). The combination of the VSOP and VLBA-only images at these two frequencies maps the jet structure on scales from 1 to 100~mas. On small angular scales the structure is dominated by the quasar core and the bright secondary component `C4' located 3 milliarcseconds from the core (at this epoch) at a position angle of $-$115$^\circ$. On larger angular scales the structure is dominated by a jet extending to the southwest, which at the largest scale seen in these images connects with the smallest scale structure seen in VLA images. We have exploited two of the main strengths of VSOP: the ability to obtain matched-resolution images to ground-based images at higher frequencies and the ability to measure high brightness temperatures. A spectral index map was made by combining the VSOP 1.6~GHz image with a matched-resolution VLBA-only image at 5~GHz from our VSOP observation on the following day. The spectral index map shows the core to have a highly inverted spectrum, with some areas having a spectral index approaching the limiting value for synchrotron self-absorbed radiation of $\alpha = +2.5$ (where $S \propto \nu^{+\alpha}$). Gaussian model fits to the VSOP visibilities revealed high brightness temperatures ($>10^{12}$~K) that are difficult to measure with ground-only arrays. An extensive error analysis was performed on the brightness temperature measurements. Most components did not have measurable brightness temperature upper limits, but lower limits were measured as high as $5~\times~10^{12}$~K. This lower limit is significantly above both the nominal inverse Compton and equipartition brightness temperature limits. The derived Doppler factor, Lorentz factor, and angle to the line-of-sight in the case of the equipartition limit are at the upper end of the range of expected values for EGRET blazars.
|
[
{
"name": "ms.tex",
"string": "\\documentclass{article}\n\\usepackage{piner}\n\\usepackage[figuresright]{rotating}\n\\begin{document}\n\n\\submitted{To be published in The Astrophysical Journal, v537, Jul 1, 2000}\n\\title{Space VLBI Observations of 3C 279 at 1.6 and 5 GHz}\n\n\\author{B. G. Piner\\altaffilmark{1}, P. G. Edwards\\altaffilmark{2},\nA. E. Wehrle\\altaffilmark{1}, H. Hirabayashi\\altaffilmark{2},\nJ. E. J. Lovell\\altaffilmark{3}, \\\\ \\& S. C. Unwin\\altaffilmark{1}}\n\n\\altaffiltext{1}{Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak\nGrove Dr., Pasadena, CA 91109; B.G.Piner@jpl.nasa.gov, Ann.E.Wehrle@jpl.nasa.gov,\nStephen.C.Unwin@jpl.nasa.gov}\n\n\\altaffiltext{2}{Institute of Space and Astronautical Science, Sagamihara, Kanagawa 229-8510, Japan;\npge@vsop.isas.ac.jp, hirax@vsop.isas.ac.jp}\n\n\\altaffiltext{3}{Australia Telescope National Facility, PO Box 76, Epping NSW 1710, Australia;\nJim.Lovell@atnf.csiro.au}\n\n\\begin{abstract}\nWe present VLBI Space Observatory Programme (VSOP) observations of the gamma-ray blazar\n3C~279 at 1.6 and 5~GHz made on 1998 January 9-10 with the HALCA satellite and ground\narrays including the Very Long Baseline Array (VLBA).\nThe combination of the VSOP and VLBA-only images at these two frequencies maps the jet structure\non scales from 1 to 100~mas. On small angular scales the structure is dominated by\nthe quasar core and the bright secondary component `C4' located 3 milliarcseconds \nfrom the core (at this epoch) at a position angle of $-$115$^\\circ$.\nOn larger angular scales the structure is dominated by a jet extending to the southwest,\nwhich at the largest scale seen in these \nimages connects with the smallest scale structure seen in VLA images.\nWe have exploited two of the main strengths of VSOP: the ability to obtain matched-resolution\nimages to ground-based images at higher frequencies and the ability to measure\nhigh brightness temperatures. A spectral index map was made\nby combining the VSOP 1.6~GHz image with a matched-resolution VLBA-only\nimage at 5~GHz from our VSOP observation on the following day.\nThe spectral index map shows the core to have a highly inverted spectrum, with some areas\nhaving a spectral index approaching the limiting value for synchrotron self-absorbed radiation of \n$\\alpha = +2.5$ (where $S \\propto \\nu^{+\\alpha}$).\nGaussian model fits to the VSOP visibilities revealed high brightness temperatures ($>10^{12}$~K) that \nare difficult to measure with ground-only arrays. An extensive error analysis was performed\non the brightness temperature measurements. Most components did not have measurable\nbrightness temperature upper limits, but lower limits were measured as high as $5~\\times~10^{12}$~K.\nThis lower limit is significantly above both the nominal inverse\nCompton and equipartition brightness temperature limits. The derived Doppler factor, Lorentz factor, and\nangle to the line-of-sight in the case of the equipartition limit\nare at the upper end of the range of expected values for EGRET blazars. \n\\end{abstract}\n\n\\keywords{quasars: individual (3C~279) --- galaxies: active ---\ngalaxies: jets --- techniques: interferometric --- radio continuum: galaxies ---\nradiation mechanisms: non-thermal}\n\n\\section{Introduction}\n\\label{intro}\nThe quasar 3C~279 ($z$=0.536) is one of the most intensively studied quasars for several reasons.\nIt was the first radio source \n%for which the milliarcsecond scale structure was \nobserved to exhibit\nsuperluminal motion (Knight et al.\\ 1971; Whitney et al.\\ 1971; Cohen et al.\\ 1971). It was\nthe first blazar --- and remains one of the brightest --- detected in high-energy \n$\\gamma$-rays by the EGRET instrument on the {\\em Compton Gamma Ray Observatory}\n(Hartman et al.\\ 1992). The EGRET detection prompted several large multiwavelength studies\nof this source. Results of these studies are presented by Maraschi et al.\\ (1994),\nGrandi et al.\\ (1996), Hartman et al.\\ (1996), and Wehrle et al.\\ (1998). \nThe radio flux density of 3C~279 has been monitored by the Michigan group since 1965\nat frequencies of 4.8, 8.0, and 14.5 GHz (Aller et al.\\ 1985).\nThe observations presented in this paper occurred at the beginning of a total flux density flare\nthat would later reach the highest flux densities yet recorded in this program for 3C~279.\n\\footnote{http://www.astro.lsa.umich.edu/obs/radiotel/gif/1253-055.gif}\n\nFollowing the discovery of superluminal motion,\nthe parsec scale structure of 3C~279 has been monitored \nusing the VLBI technique.\nCotton et al.\\ (1979)\nmeasured a speed of 15~$c$ for the original superluminal jet component. \n(Throughout the paper we assume $H_{0}$=70 km s$^{-1}$ Mpc$^{-1}$ and $q_{0}$=0.1,\nand component speeds measured by others have been expressed in these terms.)\nUnwin et al.\\ (1989) and Carrara et al.\\ (1993) \ndescribe VLBI monitoring of 3C~279 at 5, 11, and 22~GHz throughout the 1980s.\nThese authors observed the motions of several new superluminal components, and\nfound that the speeds of these components were only one-quarter to one-third (3-5~$c$)\nof that measured for the original superluminal component during the 1970s. \nVLBI monitoring of 3C~279 has\nbeen undertaken at 22 and 43~GHz during the 1990s. Initial results of this high-frequency\nmonitoring are reported by Wehrle, Unwin, \\& Zook (1994) and Wehrle et al.\\ (1996), and\nfinal results will be reported by Wehrle et al.\\ (2000). \nHigh-resolution VLBI polarimetric images of 3C~279 have been made by\nLepp\\\"{a}nen, Zensus, \\& Diamond (1995), Lister, Marscher, \\& Gear (1998)\nand Wardle et al.\\ (1998). \nThe detection of circularly polarized radio emission by Wardle et al.\\ provides\nsome of the first direct evidence that electron-positron pairs are an\nimportant component of the jet plasma.\nOne notable feature of the VLBI \nobservations of this source has been the differing speeds and position angles of the\nVLBI components. Carrara et al.\\ (1993) and Abraham \\& Carrara (1998) claim that these\ncan be explained by ejection of components by a precessing jet. \n\n3C~279 was observed during the TDRSS space VLBI experiments\nat 2.3\\,GHz (Linfield et al.\\ 1989) and 15 GHz (Linfield et al.\\ 1990), \nwith source frame brightness temperatures between\n1.6 and 2.0~$\\times$~10$^{12}$~K being measured for this source.\nA brightness temperature of 1.9~$\\times$~10$^{12}$~K \n(translated from observed frame to source frame) was also measured for 3C~279 in the \n22~GHz VSOP Pre-Launch Survey (Moellenbrock et al.\\ 1996).\nThis source has been detected in VLBI observations up to frequencies of 215~GHz (Krichbaum et al.\\ 1997).\n%As one of the brightest, most intriguing, and best observed VLBI sources, 3C~279 was chosen\n%for a VSOP Key Science Project. \nThis paper reports on the VSOP observations of 3C~279 made\nduring the first Announcement of Opportunity period (AO1).\nHirabayashi et al.\\ (1999) and Edwards et al.\\ (1999) presented preliminary analyses of these\n5 and 1.6 GHz VSOP observations respectively. Here we present higher dynamic range images\n%made possible by our additional experience with VSOP data analysis, \ntogether with analysis and interpretation of model fits and a spectral index map.\n\n\\section{Observations}\n\\label{obs}\n\nThe quasar 3C~279 was observed on two consecutive days during the AO1 phase of the VSOP\nmission: on 1998 January 9 at 1.6~GHz, and on 1998 January 10 at 5~GHz. The VSOP mission \nuses the Japanese HALCA satellite as an element in a \nchangeable VLBI array in order to obtain visibility measurements\non baselines larger than the Earth's diameter. HALCA was launched on 1997 February 12 and\ncarries an 8 meter antenna through an elliptical orbit\nwith an apogee height of 21,400~km (yielding baselines up to 2.6 Earth diameters),\na perigee height of 560~km, and an orbital\nperiod of 6.3 hours. HALCA has operational observing bands at 1.6 and 5~GHz (18 and 6 cm).\nThe data from the satellite are recorded by a network of ground tracking\nstations and subsequently correlated with the data from the participating ground telescopes.\nThe VSOP system and initial science results are discussed by Hirabayashi et al.\\ (1998).\n\nThe observations of 1998 January 9--10 were conducted using the standard VSOP observing mode:\ntwo 16 MHz intermediate frequency bands, each 2-bit sampled at the \nNyquist rate in left circular polarization, for a total\ndata rate of 128 Mbps. The ground telescope arrays were made up of nine elements of the \nNRAO Very Long Baseline Array\\footnote{The National Radio Astronomy Observatory\nis a facility of the National Science Foundation operated\nunder cooperative agreement by Associated Universities, Inc.} (VLBA) --- Hancock did not observe\nbecause of a power failure --- with the addition of the 70 m telescopes at Goldstone, California, U.S.A.\nand Tidbinbilla, Australia on January 9, and the 64 m telescope at Usuda, Japan on January 10.\nThe total observing time on January 9\nwas 6 hours, including 3.5 hours of HALCA data from the tracking station at Green Bank, West Virginia,\ncovering the portion of HALCA's orbit from near perigee to near apogee. \nThe data from Goldstone were not used in the final image as it observed for only\na short time and there were significant calibration uncertainties with this data.\nThe total \nobserving time on January 10 was 10 hours, although for the final 1.5 hours only Mauna Kea, Usuda and\nHALCA observed and this data was also excluded from the final image (as four telescopes are\nrequired for amplitude self-calibration).\nThis observation included two HALCA tracking passes\nof 3 hours each (separated by 4 hours) by the tracking stations at Robledo, Spain and\nGoldstone, California, U.S.A. \nEach tracking pass covered the portion of HALCA's orbit from near perigee to near apogee.\nThe data from both observations were correlated at the VLBA correlator in Socorro.\nThrough the remainder of this paper, we use ``VSOP'' to refer to the HALCA+ground-array combination.\n\nCalibration and fringe-fitting were done with\nthe AIPS software package. 3C~279 is a strong source, and good fringes\nwere found to HALCA during all tracking passes. The antenna gain\nfor Saint Croix had to be adjusted upward by a factor of $\\sim$~2 from its nominal value at \n5~GHz since the VSOP observations were conducted at 4800--4832\\,MHz because HALCA's performance\nis better at these frequencies.\nFigure~1 shows the $(u,v)$ plane coverages\nof the two observations. These $(u,v)$ plane coverages result in highly elliptical beams:\nthe major to minor axis ratio of the 5~GHz beam is 8:1. The addition of Tidbinbilla to the \n1.6~GHz observation improves the north-south coverage and reduces this ratio to 4:1.\nPlots of correlated flux density vs. $(u,v)$ distance projected along a position angle of $-115\\arcdeg$\n(the position angle of the brightest structure) are shown in Figure~2. The addition of HALCA\nextends the projected $(u,v)$ distances compared to the ground-only baselines\nfrom 120 to 340 M$\\lambda$ at 5~GHz, and from\n65 to 120 M$\\lambda$ at 1.6~GHz. The beating evident in the correlated flux densities\nindicates that on milliarcsecond scales the morphology is dominated by two components\nof similar flux density.\n\n\\begin{figure*}[!t]\n\\plotfiddle{f1.eps}{3.5 in}{-90}{70}{70}{-263}{350}\n\\caption{$(u,v)$ plane coverages for the VSOP observations of 3C~279. The left\npanel shows the 1.6~GHz coverage, the right panel the 5~GHz coverage.}\n\\end{figure*}\n\n\\begin{figure*}[!t]\n\\plotfiddle{f2.eps}{5.0 in}{0}{50}{50}{-140}{-9}\n\\caption{Correlated flux density in Janskys vs. projected $(u,v)$ distance along position\nangle $-115\\arcdeg$. The top panel shows the 1.6~GHz observation, the bottom the\n5~GHz observation.}\n\\end{figure*}\n\n\\section{Results}\n\\label{results}\n\\subsection{Images}\n\\label{images}\nImages from these datasets were produced using standard CLEAN and\nself-calibration procedures from the Difmap software package (Shepherd, Pearson, \\& Taylor 1994).\nFigure~3 shows two images from the 5~GHz observation on 1998 January 10: the \nfull-resolution space VLBI image and the VLBA-only image made from the same\ndataset with the space baselines removed. Figure~4 shows the full-resolution space VLBI and\nthe VLBA-only images from the 1.6~GHz observation on the previous day\n(Tidbinbilla baselines were also removed from this ground-only image to reduce\nthe size of the $(u,v)$ holes). \n%Preliminary versions of these 5 and 1.6~GHz VSOP images have appeared in Hirabayashi et al.\\ (1999)\n%and Edwards et al.\\ (1999), respectively.\nThe VSOP images are displayed using uniform weighting (although cleaning was done with both\nuniform and natural weighting to model the extended structure), while the VLBA images are\ndisplayed with natural weighting. We stress the importance of using uniform weighting\nwith VSOP datasets. A naturally weighted\nVSOP image degrades the resolution of the ground-space array because of the\nhigher weighting of the larger ground antennas and the much denser sampling of the $(u,v)$ plane\non the ground baselines.\n\n\\begin{figure*}[!t]\n\\plotfiddle{f3.eps}{3.125 in}{-90}{65}{65}{-263}{305}\n\\caption{Images of 3C~279 from the 5~GHz VSOP observation on 1998 January 10. The image on\nthe left is the full-resolution space VLBI image, the image on the right is the VLBA-only image\nmade from the same dataset with the space baselines removed. The lowest contour in each image has\nbeen set equal to 3 times the rms noise level in that image. The peak flux densities are 3.98 and 6.67\nJy beam$^{-1}$, the contour levels are 6.0 mJy beam$^{-1}$\n$\\times$ 1,2,4,...512 and 1.4 mJy beam$^{-1}$ $\\times$ 1,2,4,...4096,\nand the beam sizes are 1.83~$\\times$~0.24~mas at 28$\\arcdeg$ and 3.52~$\\times$~1.51~mas\nat 4$\\arcdeg$ for the space and ground images respectively.\nModel-fit component positions are marked with asterisks.}\n\\end{figure*}\n\n\\begin{figure*}\n\\plotfiddle{f4.eps}{3.125 in}{-90}{65}{65}{-263}{305}\n\\caption{Images of 3C~279 from the 1.6~GHz VSOP observation on 1998 January 9. The image on\nthe left is the full-resolution space VLBI image, the image on the right is the VLBA-only image\nmade from the same dataset with the space\nand Tidbinbilla baselines removed. The lowest contour in each image has\nbeen set equal to 3 times the rms noise level in that image. The peak flux densities are 2.29 and 4.73\nJy beam$^{-1}$, the contour levels are 4.7\nmJy beam$^{-1}$ $\\times$ 1,2,4,...256 and 2.9 mJy beam$^{-1}$ $\\times$ 1,2,4,...1024,\nand the beam sizes are 2.71~$\\times$~0.77~mas at 28$\\arcdeg$ and 10.7~$\\times$~4.77~mas\nat $-2\\arcdeg$ for the space and ground images respectively.\nModel-fit component positions are marked with asterisks.}\n\\end{figure*}\n\nThe VSOP and VLBA-only images differ in scale by about a factor of four,\nshowing the greatly increased resolution provided by the space baselines. \nThe VSOP images presented in Figures~3 and 4 are the highest resolution images yet produced\nof 3C~279 at these frequencies. The 1.6 and 5~GHz VSOP images have formal dynamic ranges (peak:rms) of\n1,500:1 and 2,000:1 respectively, demonstrating that high dynamic range images can be made \ndespite the small size of the HALCA orbiting antenna. For comparison, the VLBA-only images have dynamic\nranges of 5,000:1 and 15,000:1 respectively. The 5~GHz VSOP image\nshows that on small angular scales 3C~279 is dominated\nby a double structure. This structure consists of the compact\ncore and inner jet region (the feature to the east) and a bright jet component about 3~mas from\nthe core along a position angle of $-115\\arcdeg$ (the feature to the west). \nThis bright jet component, `C4', is a well known feature first observed\nin 1985. This component will be discussed further in $\\S$~\\ref{comps}.\n\nThe structure on slightly larger angular scales is quite different.\nThe 5~GHz VLBA image and the 1.6~GHz VSOP image both show the double structure mentioned above\n(although in the 1.6~GHz image the jet component is brighter than the core which results in the jet component\nbeing placed at the phase center),\nas well as a more extended jet to the southwest along a position angle of approximately \n$-140\\arcdeg$. This position angle is similar to that seen in older VLBI images (see $\\S$~\\ref{comps}) as well as \nVLA and MERLIN images (de Pater \\& Perley 1983; Pilbratt, Booth, \\& Porcas 1987; Akujor et al.\\ 1994). \nThe resolutions of the 5~GHz VLBA image\nand the 1.6~GHz VSOP image are roughly equal, a fact that allows a spectral index map to be made from\nthese images ($\\S$~\\ref{index}). The jet emission in the 1.6~GHz VSOP image is quite complex,\nand it appears in Figure~4 that the jet may be limb brightened. \nHowever, we caution against over-interpreting these\ncomplex jet features because the CLEAN striping produced by the holes in the $(u,v)$ plane coverage\nruns parallel to the jet, and because simulations indicate that,\ndue to the lack of complete $(u,v)$ plane coverage,\nspace VLBI images may show such knotty structure\nwhen the actual brightness distribution is smoother (D. Murphy 1999, private communication).\nThe 1.6~GHz VLBA image shows structure extending out to $\\sim$~100~mas from the core, all the way\nout to the smallest size scales sampled by the 22\\,GHz VLA images of de Pater \\& Perley (1983).\n\n\\subsection{Model Fits}\n\\label{mfit}\nThe Difmap model-fitting routine was used to fit elliptical Gaussian components to the visibility data\nfor each image in Figures~3 and 4. When model fitting VSOP data, it is important to increase the weight\nof HALCA over the default weighting used by Difmap in order for the space baseline data to\nhave any effect on the model.\nWe increased the weight of HALCA during model fitting by a factor\nequal to the product of the ratios of the average ground baseline sensitivity to the average space baseline\nsensitivity ($\\sim$~50 for these observations)\nand the number of ground visibilities to the number of space visibilities \n($\\sim$~10 for these observations). This effectively achieves a ``uniform'' weighting during\nmodel fitting, and causes the space visibilities to have an effect on the model fitting\nequal to that of the ground visibilities.\n\nThe results of the model fitting are given in Table~\\ref{mfittab}. Component numbers are given\nonly for ease of later reference, and are not meant to identify the same component between images.\nTentative component identifications obtained from the discussion in $\\S$~\\ref{comps} are\ngiven in the third column. Note that the lower resolution images (e.g. the 1.6 GHz VLBA image)\nmay not properly split the flux between the core and the closest component.\nIn each case we have taken the far northeastern component to be the core, and have defined the other\ncomponent positions relative to the position of the core. In the 1.6~GHz VSOP image,\nthe southwestern jet is too complex to be fit with simple Gaussian components, and we left\nthe CLEAN components in this region during model fitting. When fitting elliptical components,\nthe model fitting chi-squared statistic\nis frequently minimized by an ellipse of zero axial ratio. This is unphysical in\nthe sense that these components have formally infinite brightness temperatures. In these cases\nan upper limit to the size of the component can be used instead of the best-fit value to find a \nlower limit to the brightness temperature. Since we use an error analysis method to find these\nlimits in $\\S$~\\ref{tb}, we have left these zero axial ratio components in the models if\nthey minimize the chi-squared for that model. Table~\\ref{mfittab} also gives the source frame\nbrightness temperatures for the VSOP models, where the maximum brightness temperature of\na Gaussian component is given by\n\\begin{equation}\n\\label{tbeq}\nT_{B}=1.22\\times10^{12}\\;\\frac{S(1+z)}{ab\\nu^{2}}\\;\\rm{K},\n\\end{equation}\nwhere $S$ is the flux density of the component in Janskys,\n$a$ and $b$ are the FWHMs of the major and minor axes respectively in mas,\n$\\nu$ is the observation frequency in GHz, and $z$ is the redshift.\n\n\\begin{table*}[!t]\n\\caption{Gaussian Models}\n\\label{mfittab}\n\\begin{center}\n\\begin{tabular}{l c l r r r r r r r} \\tableline \\tableline\n& & \\multicolumn{1}{c}{Tentative\\tablenotemark{a}} \n& \\multicolumn{1}{c}{$S$\\tablenotemark{b}} & \\multicolumn{1}{c}{$r$\\tablenotemark{c}}\n& \\multicolumn{1}{c}{PA\\tablenotemark{c}}\n& \\multicolumn{1}{c}{$a$\\tablenotemark{d}}\n& & \\multicolumn{1}{c}{$\\Phi$\\tablenotemark{e}} & \\multicolumn{1}{c}{$T_{B}$\\tablenotemark{f}} \\\\ \nImage & Comp. \\# & \\multicolumn{1}{c}{ID} \n& \\multicolumn{1}{c}{(Jy)} & \\multicolumn{1}{c}{(mas)}\n& \\multicolumn{1}{c}{(deg)}\n& \\multicolumn{1}{c}{(mas)} & \\multicolumn{1}{c}{$b/a$} & \\multicolumn{1}{c}{(deg)} &\n\\multicolumn{1}{c}{($10^{12}$ K)} \\\\ \\tableline\n5 GHz VSOP & 1 & Core & 1.71 & 0.00 & ... & 0.28 & 0.00 & 29.8 & ... \\\\ \n & 2 & & 3.91 & 0.23 & --107.1 & 0.56 & 0.35 & 38.6 & 2.90 \\\\ \n\t & 3 & & 1.36 & 0.55 & --118.4 & 0.83 & 0.35 & 44.4 & 0.46 \\\\ \n\t & 4 & C3? & 0.83 & 2.64 & --133.2 & 2.53 & 0.52 & 36.4 & 0.02 \\\\ \n\t & 5 & C4 & 3.39 & 3.26 & --112.1 & 0.46 & 0.50 & --12.7 & 2.63 \\\\ \n\t & 6 & C4 & 0.79 & 3.29 & --118.1 & 0.97 & 0.25 & 34.3 & 0.28 \\\\ \n5 GHz VLBA & 1 & Core & 4.17 & 0.00 & ... & 0.29 & 0.00 & 41.5 & \\\\ \n\t & 2 & & 2.87 & 0.53 & --130.9 & 0.38 & 0.00 & --81.7 & \\\\ \n\t & 3 & C3? & 0.64 & 2.47 & --133.1 & 1.50 & 0.71 & 2.0 & \\\\ \n\t & 4 & C4 & 4.23 & 3.25 & --115.0 & 0.63 & 0.51 & --2.3 & \\\\ \n\t & 5 & C2? & 0.06 & 6.50 & --154.4 & 2.78 & 0.33 & --12.1 & \\\\ \n\t & 6 & C2? & 0.05 & 11.00 & --149.4 & 3.47 & 0.56 & 34.0 & \\\\ \n\t & 7 & C1? & 0.14 & 17.45 & --141.8 & 4.58 & 0.85 & --7.1 & \\\\ \n\t & 8 & & 0.01 & 22.18 & --134.9 & 3.15 & 0.29 & 6.4 & \\\\\n1.6 GHz VSOP\n\\tablenotemark{g} & 1 & Core & 0.76 & 0.00 & ... & 1.95 & 0.00 & 34.4 & ... \\\\ \n\t & 2 & & 0.92 & 1.33 & --146.4 & 2.29 & 0.35 & 20.5 & 0.35 \\\\ \n\t & 3 & C3? & 1.57 & 2.59 & --125.9 & 1.93 & 0.16 & 55.4 & 1.92 \\\\ \n\t & 4 & C4 & 2.21 & 2.77 & --110.6 & 0.95 & 0.00 & 43.1 & ... \\\\\n1.6 GHz VLBA & 1 & Core & 0.23 & 0.00 & ... & 10.64 & 0.00 & 5.9 & \\\\ \n\t & 2 & C4 & 5.09 & 3.55 & --117.9 & 2.71 & 0.51 & 55.8 & \\\\ \n\t & 3 & C2? & 0.35 & 8.20 & --145.3 & 7.69 & 0.00 & 25.0 & \\\\ \n\t & 4 & C1? & 0.61 & 18.45 & --140.0 & 7.44 & 0.45 & 64.6 & \\\\ \n\t & 5 & & 0.13 & 48.58 & --144.2 & 27.19 & 0.46 & 33.2 & \\\\ \n\t & 6 & `C' & 0.14 & 88.35 & --140.8 & 60.26 & 0.28 & 65.1 & \\\\ \\tableline\n\\end{tabular}\n\\end{center}\n\\tablenotetext{a}{Tentative component identifications from the discussion in $\\S$~\\ref{comps}.\nA question mark indicates a more speculative identification.}\n\\tablenotetext{b}{Flux density in Janskys. Note that the lower resolution images (e.g. the 1.6 GHz VLBA image)\nmay not properly split the flux between the core and the closest component.}\n\\tablenotetext{c}{$r$ and PA are the polar coordinates of the\ncenter of the component relative to the presumed core.\nPosition angle is measured from north through east.}\n\\tablenotetext{d}{$a$ and $b$ are the FWHM of the major and minor axes of the Gaussian\ncomponent.}\n\\tablenotetext{e}{Position angle of the major axis measured from north through east.}\n\\tablenotetext{f}{Maximum source frame Gaussian brightness temperatures are given\nfor the VSOP models.}\n\\tablenotetext{g}{The southwestern jet is fit by clean components in this model.}\n\\end{table*}\n\n\\section{Discussion}\n\\label{discussion}\n\\subsection{Identification of Historical Components}\n\\label{comps}\nIn this section we consider the identification of components seen in these images\nwith previously published VLBI components, using these components' published positions and\nvelocities. We work from the innermost components outward, starting with the components\nfit to the 5~GHz VSOP image. We caution that any such identifications are highly\nspeculative, particularly for the older components where much time has elapsed since the\nlast published image. Note that prior to completion of the NRAO VLBA (1995), global VLBI\nnetwork sessions at 22 GHz occurred only twice per year and used less than half a dozen antennas.\n\nA total of six elliptical Gaussian components are required to fit the 5~GHz VSOP data. The first three of these\ncomponents are interior to 1~mas, and represent the core and two components of the inner jet.\nThe region interior to 1~mas has been studied by Wehrle et al.\\ (2000) at 22 and 43 GHz\nand Rantakyr\\\"{o} et al.\\ (1998) at 86 GHz, and\nthey find it to be a complex region with multiple components. \nAttempts to name components in this region have resulted in some confusion. The component named\n`C5' in three 11 GHz maps from 1989.3-1991.1 by Carrara et al.\\ (1993) and Abraham \\& Carrara (1998) \nis not the same component referred to\nas either `C5' by Wehrle et al.\\ (1994) at 22 GHz, \nLepp\\\"{a}nen et al.\\ (1995) at 22 GHz, and Lister et al.\\ (1998) at 43 GHz or\n`the stationary 1~mas feature' by Wehrle et al.\\ (1996) at 22 GHz. \nWehrle et al.\\ (1994) and Wehrle et al.\\ (1996)\nidentify a component between C5 and the core, and Lepp\\\"{a}nen et al.\\ (1995) identify two components\nin this region which they name `C6' and `C7'. Lister et al.\\ (1998) do not detect these components\nbut record another new component named `C8'. Clarification of the components in this region \nmust await completion of the Wehrle et al.\\ (2000) analysis.\n\nThe situation beyond $\\sim$~1~mas is easier to interpret. The bright feature at\n$\\sim$~3~mas is the component C4 that has been seen by many other authors (Unwin et al.\\ 1989; \nCarrara et al.\\ 1993; Wehrle et al.\\ 1994; Lepp\\\"{a}nen et al.\\ 1995; Wehrle et al.\\ 1996; Lister et al.\\ 1998;\nWardle et al.\\ 1998; Kellermann et al.\\ 1998).\nThis component has been moving along a position angle of $-115\\arcdeg$ for over 10 years.\nThe brightness distribution of C4 is asymmetric, with the leading edge being sharper than the trailing\nedge, and two model components are required to represent it (components~5 and 6 in the 5~GHz VSOP model).\nThe 43~GHz data of Wehrle et al.\\ (2000) also require two components to represent the structure of C4.\nThe sharp leading edge of this component is suggestive of a working surface or shock front. The \npolarization observations of Lepp\\\"{a}nen et al.\\ (1995), Lister et al.\\ (1998), and Wardle et al.\\ (1998)\nshow that C4 has\na magnetic field transverse to the jet, also indicative of a shock front. \nCarrara et al.\\ (1993) determined a motion of\n0.15$\\pm$0.01~mas/yr (4~$c$) for C4, however the position of C4 in our 5\\,GHz image\nis inconsistent with a simple extrapolation at this speed.\nHowever, we note that at the time of the observations of Carrara et al.\\\nC4 was $\\sim$1\\,mas from the core and in the region noted above as being\ndifficult to interpret.\nMore recent data from Wehrle et al. (2000) and Kellermann (1999, private communication)\nindicate a speed of $\\sim$7~$c$ for C4 between 1991 and 1999, which is consistent with\nthe position seen in the VSOP images in this paper.\nAlthough the larger scale structure\nhas a much different position angle than C4, C4 shows no signs of altering its path\nto follow the larger scale structure, and appears to be continuing along a position angle of $-115\\arcdeg$.\nComponent C4 \ndominates the emission in the 1.6~GHz VSOP image and\nit is represented by component~4 in the 1.6~GHz VSOP model.\n\nOlder VLBI measurements (Cotton et al.\\ 1979; Unwin et al.\\ 1989; Carrara et al.\\ 1993) followed a series of\ncomponents (C1--C3) moving along position angles of $-130$ to $-140\\arcdeg$. Since this is also the position\nangle of the larger scale structure seen in our images, it is reasonable that this string of components\nmay form the southwestern jet in our images. \nThe 5\\,GHz VSOP image shows \na fainter, more diffuse\ncomponent at a position angle of $-133\\arcdeg$ located $\\sim$2.6\\,mas from the core\n(component~4 in the 5\\,GHz model, component~3 in the 1.6~GHz model).\nEmission is also seen at this position in the images of \nKellermann et al.\\ (1998) and Wehrle et al.\\ (2000).\nAn attempt to identify this component with the most recent component \nejected along this position angle (C3) would\nimply a drastic deceleration for C3; a straightforward extrapolation of the motion of C3 given by \nCarrara et al.\\ (1993)\nwould place it at a separation of 4~mas in 1998 and so we consider such an identification unlikely. \nAn extrapolation of the motion of C2 estimated\nfrom the positions given by Unwin et al.\\ (1989) would place C2 between 6 and 10~mas from the core at the\nepoch of our VSOP observations, and conceivably identify it with either component~5 or 6 \nin the 5~GHz VLBA model\n(component~3 in the 1.6~GHz VLBA model). Cotton et al.\\ (1979) reported a large proper motion of\n0.5~mas/yr during the early 1970s; their data was re-examined and their interpretation judged to be correct\nby Unwin et al.\\ (1989). An extrapolation the motion of the Cotton et al.\\ (1979) component (which could also\nbe the component C1 of Unwin et al.\\ [1989] located $\\sim$8\\,mas from the core at 1984.25) \nwould place it about 15~mas from the core in 1998, and mean that\nit could be identified with the relatively bright component~7 of the 5~GHz VLBA model (component~4\nin the 1.6~GHz VLBA model). The uncertainties of extrapolating component motions \nmakes this analysis highly speculative; the validity of the assumption of\nconstant projected speed with time is unclear, and enough time has elapsed \nthat the fate of these older components will probably never be certain.\n\nA series of VLA maps of 3C~279 at varying resolution has been published by de Pater \\& Perley (1983).\nTheir highest resolution map shows a component (component `C') 95~mas from the core\nin position angle $-145\\arcdeg$. (This map has a higher resolution than the MERLIN maps of\nPilbratt et al.\\ [1987] and Akujor et al.\\ [1994] because it is at a higher frequency).\nOur 1.6~GHz VLBA image extends out to this distance from the core,\nand we see a 140 mJy component at 88~mas in position angle $-141\\arcdeg$ \n(component~6 in the 1.6~GHz VLBA model). We can tentatively identify this\nwith component C of de Pater \\& Perley (1983), given the large errors implied by their VLA beam \n(60~mas resolution) and the similar size of our model-fit component. These errors\nmake it impossible to infer anything about the motion of this component between 1982 and 1998.\nWe have, however, matched the largest scale VLBI structures with the smallest scale VLA structures, \nand established a continuous connection between the parsec and kiloparsec scales in this source.\n\n\\subsection{Spectral Index Map}\n\\label{index}\nConstruction of spectral index maps is often hindered by the differing resolutions of the images\nat different frequencies; however, a unique capability of the VSOP mission is that it can provide matched\nresolution images to ground-based images at higher frequencies, enabling\nthe construction of a spectral index map from two images of approximately equal resolution.\nWe have used this capability to produce a spectral index map from the 1.6~GHz VSOP image and the\n5~GHz VLBA-only image; this spectral index map is shown in Figure~5. \nThese two datasets were taken only 1 day apart, so the errors\ndue to component motions are negligible. To produce the spectral index map\nthe two images were restored with their average beam of \n3.12~$\\times$~1.14~mas with a major axis position angle of 15.9$\\arcdeg$, \neach image was restored from the clean components without residuals (the flux left over after\nthe clean components convolved by the dirty beam have been subtracted from the data),\nand no spectral index was calculated for pixels where the flux densities were less than 3 times the rms noise level\nin the images at both frequencies. \n(A spectral index map using images restored from clean components {\\em with\\/} residuals\nwas also produced and gave essentially the same results. We prefer to use the images\nwithout residuals as the residuals can then be used to assess the possible errors \nin the spectral index map.)\nIn the following discussion we use $S\\propto\\nu^{+\\alpha}$.\n\n\\begin{figure*}[!t]\n\\plotfiddle{f5.eps}{4.0 in}{0}{60}{60}{-162}{-72}\n\\caption{Spectral index map of 3C~279 made from the 1.6~GHz VSOP image and the 5~GHz VLBA image.\nThe gray-scale color bar along the bottom of the image\nindicates the value of the spectral index ($S\\propto\\nu^{+\\alpha}$), with lighter colors\nindicating an inverted spectrum and darker colors a steep spectrum. Spectral index contours are also\nplotted at intervals of 0.5, from $-2.5$ to 2.5. The beam used was the average of the\n1.6~GHz VSOP beam and the 5~GHz VLBA beam, or 3.12~$\\times$~1.14~mas at 15.9$\\arcdeg$.\nThe white pixels near the center of the jet represent an area where the flux was below the clipping\nlevel applied for calculation of the spectral index.}\n\\end{figure*}\n\nA major difficulty in making spectral index maps lies in correctly registering the two images.\nWe investigated several alignments of these two images, including aligning the peak core pixels\nand aligning the peak pixels in the bright jet component (C4). We doubled the number of pixels\nacross each image in order to measure the required shifts as accurately as possible.\nAligning the peak core pixels produced unphysical results, including a highly inverted spectral index\nalong the right edge of component C4. Of the different alignments tried, aligning the peak pixels in the \njet component C4 produced the most physically reasonable results. \nThe reason for this can be seen {\\em a posteriori\\/} from\nFigure~5. The spectral index is constant across component C4, meaning that the brightest pixels in C4 at\n1.6 and 5~GHz will represent the same physical location. On the other hand, there are steep spectral\nindex gradients across the core region, so the peak pixel in the core region will be at different\nlocations at 1.6 and 5~GHz. \n\nWe also constructed a map of the error in the spectral index; this error map is shown in Figure~6.\nThe error was calculated by standard propagation of errors, using the fluxes at each pixel\nin each residual map as the flux errors. This method actually gives a lower limit to the\nerror at each pixel, because it does not take into account calibration errors or errors in imaging the\nsource structure caused by the holes in the $(u,v)$ plane coverage. In the region comprising the southwestern\njet the errors in the spectral index $\\alpha$\nrange from $\\pm 0.05$ in the brighter parts of the jet (the knot at $\\sim$~18~mas)\nto $\\pm 0.3$ in the fainter parts. The formal errors in the core and C4 regions are quite low\nand so the errors in these regions will be dominated by the other effects mentioned above.\n\n\\begin{figure*}[!t]\n\\plotfiddle{f6.eps}{4.0 in}{0}{60}{60}{-162}{-72}\n\\caption{Error map for the spectral index map presented in Figure~5.\nThe error was calculated by standard propagation of errors, using the fluxes at each pixel\nin each residual map as the flux errors. The gray-scale color bar along the bottom of the image\nindicates the value of the logarithm of the error in the spectral index, with lighter colors\nindicating a larger error. Contours of the logarithm of the error are plotted at intervals\nof 0.5, from $-3.0$ to 0.0.}\n\\end{figure*}\n\nThe core of 3C~279 has an inverted spectrum with steep spectral index gradients. \nSuch inverted spectra are commonly interpreted as being due to self-absorption of the radio\nsynchrotron emission. The calculated spectral index in the core region\nranges from $\\sim$~1.0 at the western edge to the theoretical limiting value \nfor synchrotron self-absorption of 2.5 \n(assuming a constant magnetic field)\nover a small region at the eastern edge.\nSpectral indices approaching this theoretical value are almost never seen; the flatter\nspectra usually observed \nare commonly interpreted as being due to an inhomogeneous source made up of a number of\nsynchrotron components with differing turnover frequencies (e.g. Cotton et al.\\ 1980).\nThe highly inverted spectrum at the eastern edge may imply the detection of a homogeneous\ncompact component in this region, which should be an efficient producer of inverse Compton \ngamma-rays.\nThe spectral index gradients in the core imply\nthat components will have different measured separations at different frequencies.\nWe do indeed observe this frequency-dependent separation, the measured separation between the core and C4\nmodel components is 3.3~mas at 5~GHz and only 2.8~mas at 1.6~GHz. \nThe fact that the apparent position of the core is a function of wavelength is an important verification\nof the twin exhaust model, which argues that the observed core is that position in the throat\nof a nozzle where the opacity is of the order of unity.\n\nThe jet component C4 has a flat spectrum\nwith $\\alpha$ approximately 0.25. This is unusual, as jet components\nusually have steeper spectra ($\\alpha<0$). The southwestern jet also has structure\nin its spectral index distribution, with the edges of the jet appearing to have a steeper\nspectrum than the center. This spectral index structure is related to the apparent limb brightening\nat 1.6~GHz which, as noted above, should be interpreted with care.\n% due to the orientation of the CLEAN stripes in the 1.6~GHz VSOP image. \nAO2 VSOP observations of 3C~279 at 1.6~GHz \nin which the baselines to the orbiting antenna have a different orientation in the $(u,v)$ plane\nwill allow a consistency check on the brightness and spectral index structures transverse to the jet.\n\n\\subsection{High Brightness Temperatures}\n\\label{tb}\nSpace VLBI observations have a major advantage over \n%matched resolution\nground-based observations\n%at higher frequencies \nbecause they are able to measure higher brightness temperatures. This is\nbecause the smallest measurable major and minor axes in equation~[\\ref{tbeq}]\nare proportional to the resolution of the interferometer, which is proportional to \n1/(baseline $\\times$ frequency), so the denominator in equation~[\\ref{tbeq}]\ndepends only on baseline length.\n%because the maximum observable brightness temperature (see equation~[\\ref{tbeq}]) is proportional to \n%$A^{-1}\\nu^{-2}$, where $A$ is the smallest measurable area, and since $A\\propto\\nu^{-2}$, the\n%maximum observable brightness temperature is independent of frequency and depends only on baseline length.\nThe brightness temperature limit for ground-based VLBI is $\\sim 10^{11} S(1+z)/f^{2}$\nand that for space VLBI with HALCA is $\\sim 10^{12} S(1+z)/f^{2}$, where $S$ is the\nflux density in Janskys, $z$ is the redshift, and $f$ is the smallest size that can be measured expressed\nas a percentage of the beam size.\nThe improvement gained by space VLBI thus covers the interesting transition region around $10^{12}$~K,\nthe nominal inverse Compton brightness temperature limit (Kellermann \\& Pauliny-Toth 1969).\n\nObserved brightness temperatures are often used to calculate Doppler beaming factors by assuming an\nintrinsic brightness temperature and using the fact that $T_{B,obs} = \\delta T_{B,int}$, where\n$T_{B,obs}$ is the observed source frame brightness temperature, $T_{B,int}$ is the intrinsic brightness temperature,\nand $\\delta$ is the Doppler factor. The intrinsic brightness temperature depends on the physical\nmechanism imposing the limitation. Kellermann \\& Pauliny-Toth (1969) showed that inverse Compton losses\nlimit the intrinsic brightness temperatures to $\\sim~5~\\times~10^{11} - 1~\\times~10^{12}$~K, otherwise\nthe source can radiate away most of its energy on a timescale of days. Readhead (1994) proposed that\nthe limiting mechanism is equipartition of energy between the particles and magnetic field, and that\nintrinsic brightness temperatures are limited to $\\sim~5\\times~10^{10} - 1\\times~10^{11}$~K. \n\nTo be complete, brightness temperature measurements must be presented with associated errors.\nSince the brightness temperature depends on the product of the major and minor axes\nof the model-fit component, and these \naxis sizes can have large errors, the measured brightness temperature can also have large errors.\nError analysis of VLBI model-fit parameters has historically been problematic. In this paper we use\nthe ``Difwrap'' program\\footnote{http://halca.vsop.isas.ac.jp./survey/difwrap/} \n(Lovell 2000) to analyze the upper and lower limits on our\nbrightness temperature measurements. This program uses the method described by Tzioumis et al.\\ (1989)\nin which the parameter of interest is varied in steps around the best-fit value, allowing the other\nparameters to relax at each step, and the resultant model is then visually compared with the data to\ndetermine whether or not the fit remains acceptable. The brightness temperature of a component depends\non the flux density and size of the component, and the size depends on three of the Difmap model-fit parameters:\nthe major axis length, the axial ratio, and indirectly on the position angle of the major axis (since\ndifferent major axis lengths and axial ratios may be allowed at different position angles). The size\nerror analysis therefore searches a three-dimensional cube in parameter space, varying the major axis\nlength and position angle and the axial ratio over all possible combinations given input search ranges\nand step sizes. A visual inspection is done to determine the goodness of the fit\ninstead of using a numerical cutoff in the chi-squared because the true number of degrees of freedom is not\nwell known. Using the actual number of measured visibilities \n($\\sim 10^{5}$ for these observations) to determine the degrees of freedom gives\nerrors that are unrealistically small, and methods used by other authors did not have a clear\nphysical motivation (e.g. one degree of freedom per antenna per hour [Biretta, Moore, \\& Cohen 1986]).\n\nIn Table~\\ref{tbtab} we show our brightness temperature error analysis for the six components in\nTable~\\ref{mfittab} that have best-fit brightness temperatures over $10^{12}$~K. For each of these components\nwe searched a $7\\times7\\times7$ cube in major axis length, axial ratio, and major axis position angle.\nInitially we searched major axis lengths from zero to twice the best-fit length, axial ratios from zero to\none, and a range of $\\pm90\\arcdeg$ in position angle; and then refined the search to a smaller grid if\nnecessary. The parameter values yielding the maximum and minimum area that still gave an acceptable fit to\nthe data were recorded. A similar error analysis was done for the flux density, and the extreme allowed\nvalues of area and flux density were used to determine the maximum and minimum brightness temperatures.\nSince errors in flux density and size are searched for separately, the flux density was held constant during\nthe size error analysis and vice-versa. The position of the component was also held constant to avoid it\n`trading identities' with another model component. All other model components were allowed to vary.\n\n\\begin{table*}[!t]\n\\caption{Brightness Temperature Limits for Components with\nBest-fit Brightness Temperatures $> 10^{12}$ K}\n\\label{tbtab}\n\\begin{center}\n\\begin{tabular}{c c r r r r r r r r r} \\tableline \\tableline\n& & & \\multicolumn{1}{c}{Min.} & \\multicolumn{1}{c}{Max.\\tablenotemark{b}} & & \\multicolumn{1}{c}{Min.} \n& \\multicolumn{1}{c}{Max.} & & \\multicolumn{1}{c}{Min.} & \\multicolumn{1}{c}{Max.} \\\\ \nFreq. & & \\multicolumn{1}{c}{Flux} & \\multicolumn{1}{c}{Flux} & \\multicolumn{1}{c}{Flux} \n& \\multicolumn{1}{c}{Area} & \\multicolumn{1}{c}{Area} & \\multicolumn{1}{c}{Area} \n& \\multicolumn{1}{c}{$T_{B}$} & \\multicolumn{1}{c}{$T_{B}$} & \\multicolumn{1}{c}{$T_{B}$} \\\\ \n(GHz) & Comp.\\tablenotemark{a} & \\multicolumn{1}{c}{(Jy)} & \\multicolumn{1}{c}{(Jy)} & \\multicolumn{1}{c}{(Jy)} \n& \\multicolumn{1}{c}{(mas$^{2}$)} & \\multicolumn{1}{c}{(mas$^{2}$)} & \\multicolumn{1}{c}{(mas$^{2}$)} \n& \\multicolumn{1}{c}{($10^{12}$ K)} & \\multicolumn{1}{c}{($10^{12}$ K)} & \\multicolumn{1}{c}{($10^{12}$ K)} \\\\ \\tableline\n4.8 & 1 & 1.71 & 1.61 & ... & 0.0 & 0.0 & 0.114 & ... & 1.15 & ... \\\\ \n & 2 & 3.91 & 3.61 & ... & 0.110 & 0.0 & 0.146 & 2.90 & 2.01 & ... \\\\ \n & 5 & 3.39 & 3.06 & 3.60 & 0.105 & 0.070 & 0.274 & 2.63 & 0.91 & 4.19 \\\\ \n1.6 & 1 & 0.76 & 0.63 & ... & 0.0 & 0.0 & 0.636 & ... & 0.70 & ... \\\\ \n & 3 & 1.57 & 1.05 & ... & 0.578 & 0.0 & 2.905 & 1.92 & 0.25 & ... \\\\ \n & 4 & 2.21 & 2.09 & ... & 0.0 & 0.0 & 0.299 & ... & 4.91 & ... \\\\ \\tableline\n\\end{tabular}\n\\end{center}\n\\tablenotetext{a}{Component numbers from the VSOP model fits in Table~\\ref{mfittab}.}\n\\tablenotetext{b}{Upper limits to the component flux were not calculated for cases where\nthe component had a minimum area of zero.}\n\\end{table*}\n\nInspection of Table~\\ref{tbtab} shows that\nin all but one of the cases investigated the component shrinking to zero area and infinite\nbrightness temperature (in all cases caused by a valid fit with zero axial ratio at some position angle)\nproduced acceptable results,\nand therefore it appears that many measured brightness temperatures, \neven those measured by space VLBI, may have error bars that extend to infinity in the positive direction. \nThe measured lower limits also indicate a\nconsiderable error in the best-fit brightness temperature values: three of the six components with best-fit\nbrightness temperatures over $10^{12}$~K have minimum brightness temperatures under this value. \nThe other three\ncomponents have minimum brightness temperatures over $10^{12}$~K, with minimum brightness temperatures of\n1.2, 2.0, and 4.9~$\\times~10^{12}$~K being measured for components~1 and 2 of the 5~GHz VSOP model fit (the \ncore and first jet component) and component~4 of the 1.6~GHz VSOP model fit (C4) respectively.\nBower \\& Backer (1998) and Shen et al.\\ (1999) report brightness temperatures of $\\sim 3~\\times~10^{12}$~K\nfrom VSOP observations of NRAO~530 and PKS\\,1921$-$293 respectively, but without accompanying error analyses.\n\nIf a brightness distribution other than a Gaussian is used in the model fitting,\nthe derived values of the brightness temperature will be different. For example, the brightness\ntemperature of a homogeneous optically thick component is given by\n\\[T_{B}=1.77\\times10^{12}\\;\\frac{S(1+z)}{ab\\nu^{2}}\\;\\rm{K},\\]\nwhere the constant in front is different from that in equation~(\\ref{tbeq}), and $a$ and $b$\nare the lengths of the major and minor axes respectively rather than the FWHMs.\nThe visibility of a homogeneous optically thick component drops to 50\\% at the same baseline\nlength as a Gaussian when its diameter equals 1.6 times the Gaussian's FWHM\n(Pearson 1995), so we expect the homogeneous optically thick brightness temperature to\nbe about 0.6 of the Gaussian brightness temperature\n(see also Hirabayashi et al.\\ 1998 and in particular the correction in the erratum to this paper).\nWe have fit homogeneous optically thick components to the data,\nand for the two components in Table~\\ref{tbtab} where neither component type goes to zero size\n(components~2 and 5 of the 5~GHz model fit) we measure brightness temperatures of\n1.9 and 1.5~$\\times~10^{12}$~K respectively for homogeneous optically thick components\nrather than 2.9 and 2.6~$\\times~10^{12}$~K for Gaussian components,\nso we see about the expected decrease. Since the true brightness distribution is not known,\nand Gaussian components are the standard for VLBI model fitting and provide a somewhat better fit\nfor these observations, we remained with Gaussian components.\n\nOur highest brightness temperature lower limit of $\\sim~5~\\times~10^{12}$~K for component\nC4 at 1.6~GHz implies Doppler factor lower limits of 5 and 50 for the inverse Compton and\nequipartition brightness temperature limits respectively.\nA Doppler factor of 50 is at\nthe upper end of the Doppler factor distributions expected for flux-limited samples of flat-spectrum radio sources\n(Lister \\& Marscher 1997) and gamma-ray sources (Lister 1998).\nBower \\& Backer (1998) found similar values for the Doppler factor\nof NRAO~530 under these same two limiting conditions. \nIf VSOP observations reveal a brightness temperature much higher than $5~\\times~10^{12}$~K, or \nmany brightness temperatures around $5~\\times~10^{12}$~K, it may\nbe difficult to reconcile the high Doppler factors implied by the equipartition brightness temperature\nlimit with beaming statistics and with the relatively slow speeds\nmeasured in studies of apparent velocity distributions (e.g. Vermeulen 1995).\n\nUsing an estimated speed for C4\nof 7~$c$ (see $\\S$~\\ref{comps}), and assuming the pattern speed observed with VLBI\nequals the bulk fluid speed in the jet,\nbulk Lorentz factors and angles to the line-of-sight can be calculated for the jet.\nFor $\\delta=5$, $\\Gamma$=7.5 and $\\theta$=11$\\arcdeg$; for $\\delta=50$, $\\Gamma$=25.5 and $\\theta$=0.3$\\arcdeg$.\nAgain, the equipartition brightness temperature limit implies values for 3C~279 near\nthe extremes of expected EGRET source properties (Lister 1998).\n3C~279 and NRAO~530 have both been detected by EGRET, and Bower \\& Backer (1998) speculate that\nblazars detected by EGRET may be those where the equipartition brightness temperature\nlimit is briefly (on a timescale of years) superseded by the inverse Compton catastrophe limit.\n%Wehrle et al.\\ (1999) are fitting inverse Compton models\n%to 3C~279, as has been done previously for 3C~345 (Unwin et al.\\ 1994, 1997). Knowledge of the\n%inverse Compton Doppler factors will allow calculation of the intrinsic brightness temperatures in 3C~279.\n%Spectral parameters should be well enough determined to calculate the equipartition brightness\n%temperatures, which can then be compared to the intrinsic brightness temperatures to measure\n%any departures from equipartition in this source.\nThe observations presented in this paper occurred at the beginning of a total flux density flare at 5 GHz\nrecorded by the Michigan monitoring program that would later reach the highest flux density yet recorded \nin this program for 3C~279 at 5 GHz.\nMeasurements of the variability brightness temperature of this flare (L\\\"{a}hteenm\\\"{a}ki, Valtaoja, \\& Wiik 1999)\ntogether with VSOP brightness temperatures measured during AO2 should allow calculation of the intrinsic\nbrightness temperature and Doppler factor and allow us to estimate any departures from equipartition in this\nsource.\n\n\\section{Conclusions}\nWe have presented the first space VLBI images of 3C 279, which are the highest resolution images yet\nobtained of this source at 5 and 1.6 GHz. The parsec-scale emission is dominated by the core\nand the jet component C4 which has been visible in VLBI images since 1985.\nThe 1.6 GHz VSOP image and the 5 and 1.6 GHz VLBA-only images\nshow emission from a jet extending to the southwest. The 1.6 GHz VLBA-only image has structure that\nmatches that seen in the highest resolution VLA images, connecting the parsec and kiloparsec scale\nstructures in this source. \n\nWe have exploited two of the main strengths of VSOP: the ability to obtain matched-resolution\nimages to ground-based images at higher frequencies and the ability to measure\nhigh brightness temperatures. The spectral index map constructed from the 1.6 GHz VSOP image and\nthe 5 GHz VLBA-only image has an unusually inverted spectral index in the core region, approaching\nthe limiting value for synchrotron self-absorption of $+2.5$. \nAn extensive error analysis conducted on\nthe model-fit brightness temperatures reveals brightness temperature \nlower limits as high as $5~\\times~10^{12}$~K.\nThis lower limit is significantly above both the nominal inverse\nCompton and equipartition brightness temperature limits. The derived Doppler factor, Lorentz factor, and\nangle to the line-of-sight in the case of the equipartition limit\nare at the upper end of the range of expected values for EGRET blazars.\n\n\\acknowledgements\nPart of the work described in this paper has been carried out at the Jet\nPropulsion Laboratory, California Institute of Technology, under\ncontract with the National Aeronautics and Space Administration.\nA.E.W. acknowledges support from the NASA Long Term Space Astrophysics Program.\nWe gratefully acknowledge the VSOP Project, which is led by the Japanese Institute of Space and\nAstronautical Science in cooperation with many organizations and radio telescopes around the world.\nThe National Radio Astronomy Observatory is a facility of the National Science Foundation operated\nunder cooperative agreement by Associated Universities, Inc.\nThis research has made use of \ndata from the University of Michigan Radio Astronomy Observatory which is supported by\nthe National Science Foundation and by funds from the University of Michigan,\nand the NASA/IPAC extragalactic database (NED)\nwhich is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract\nwith the National Aeronautics and Space Administration.\n\n\\begin{references}\n\nAbraham, Z. \\& Carrara, E.A. 1998, ApJ, 496, 172\n\nAkujor, C.E., L\\\"{u}dke, E., Browne, I.W.A., Leahy, J.P., Garrington, S.T., Jackson, N., \\&\nThomasson, P. 1994, A\\&AS, 105, 247\n\nAller, H.D., Aller, M.F., Latimer, G.E., \\& Hodge, P.E. 1985, ApJS, 59, 513\n\nBiretta, J.A., Moore, R.L., \\& Cohen, M.H. 1986, ApJ, 308, 93\n\nBower, G.C. \\& Backer, D.C. 1998, ApJ, 507, L117\n\nCarrara, E.A., Abraham, Z., Unwin, S.C., \\& Zensus, J.A. 1993, A\\&A, 279, 83 \n\nCohen, M.H., Cannon, W., Purcell, G.H., Shaffer, D.B., Broderick, J.J.,\nKellermann, K.I., \\& Jauncey, D.L. 1971, ApJ, 170, 207\n\nCotton, W.D., et al.\\ 1979, ApJ, 229, L115\n\nCotton, W.D., et al.\\ 1980, ApJ, 238, L123\n\nde Pater, I. \\& Perley, R.A. 1983, ApJ, 273, 64\n\nEdwards, P.G., Hirabayashi, H., Lovell, J.E.J., Piner,B.G., Unwin, S.C., \\&\nWehrle, A.E. 1999, Astronomische Nachrichten, in press \n\nGrandi, P., et al.\\ 1996, ApJ, 459, 73\n\nHartman, R.C., et al.\\ 1992, ApJ, 385, L1\n\nHartman, R.C., et al.\\ 1996, ApJ, 461, 698\n\nHirabayashi, H., et al.\\ 1999, Adv. 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astro-ph0002217
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Properties of Gamma-Ray Burst Time Profiles Using Pulse Decomposition Analysis
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"author": "Andrew Lee and Elliott D. Bloom"
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The time profiles of many gamma-ray bursts consist of distinct pulses, which offers the possibility of characterizing the temporal structure of these bursts using a relatively small set of pulse shape parameters. This pulse decomposition analysis has previously been performed on a small sample of bright long bursts using binned data from BATSE, which comes in several data types, and on a sample of short bursts using the BATSE Time-Tagged Event (TTE) data type. We have developed an interactive pulse-fitting program using the phenomenological pulse model of Norris, et al. and a maximum-likelihood fitting routine. We have used this program to analyze the Time-to-Spill (TTS) data for all bursts observed by BATSE up through trigger number 2000, in all energy channels for which TTS data is available. We present statistical information on the attributes of pulses comprising these bursts, including relations between pulse characteristics in different energy channels and the evolution of pulse characteristics through the course of a burst. We carry out simulations to determine the biases that our procedures may introduce. We find that pulses tend to have shorter rise times than decay times, and tend to be narrower and peak earlier at higher energies. We also find that pulse brightness, pulse width, and pulse hardness ratios do not evolve monotonically within bursts, but that the ratios of pulse rise times to decay times tend to decrease with time within bursts.
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"name": "ms.tex",
"string": "\\documentclass[preprint]{aastex}\n%\\usepackage{epsfig}\n\\usepackage{amstex,amssymb}\n%\\usepackage{natbib}\n%\\citestyle{aa}\n\n\\newcommand{\\e}[2]{\\mbox{$#1 \\times 10^{#2}$}}\t% Scientific notation\n\\newcommand{\\?}{\\discretionary{/}{}{/}}\t\t% Break URLs without hyphens\n\n\\begin{document}\n\n\\title{Properties of Gamma-Ray Burst Time Profiles Using Pulse\nDecomposition Analysis}\n\n\\author{Andrew Lee and Elliott D. Bloom}\n\\affil{Stanford Linear Accelerator Center, Stanford University,\nStanford, California 94309}\n\\makeatletter\n\\email{alee@slac.stanford.edu and elliott@slac.stanford.edu}\n\\makeatother\n\n%\\and\n\n\\author{Vah\\'{e} Petrosian}\n\\affil{Center for Space Science and Astrophysics, Varian 302c,\nStanford University, Stanford, CA 94305-4060 \\altaffilmark{1}}\n\\makeatletter\n\\email{vahe@astronomy.stanford.edu}\n\\makeatother\n\n\\altaffiltext{1}{Also Astronomy Program and Department of Physics.}\n\n\\begin{abstract}\nThe time profiles of many gamma-ray bursts consist of distinct pulses,\nwhich offers the possibility of characterizing the temporal structure\nof these bursts using a relatively small set of pulse shape\nparameters. This pulse decomposition analysis has previously been\nperformed on a small sample of bright long bursts using binned data\nfrom BATSE, which comes in several data types, and on a sample of\nshort bursts using the BATSE Time-Tagged Event (TTE) data type. We\nhave developed an interactive pulse-fitting program using the\nphenomenological pulse model of Norris, \\emph{et al.} and a\nmaximum-likelihood fitting routine. We have used this program to\nanalyze the Time-to-Spill (TTS) data for all bursts observed by BATSE\nup through trigger number 2000, in all energy channels for which TTS\ndata is available. We present statistical information on the\nattributes of pulses comprising these bursts, including relations\nbetween pulse characteristics in different energy channels and the\nevolution of pulse characteristics through the course of a burst. We\ncarry out simulations to determine the biases that our procedures may\nintroduce. We find that pulses tend to have shorter rise times than\ndecay times, and tend to be narrower and peak earlier at higher\nenergies. We also find that pulse brightness, pulse width, and pulse\nhardness ratios do not evolve monotonically within bursts, but that\nthe ratios of pulse rise times to decay times tend to decrease with\ntime within bursts.\n\\end{abstract}\n\n\\keywords{gamma rays: bursts---methods: data analysis}\n\n\\section{Introduction}\n\nThere has been considerable recent progress in the study of gamma-ray\nbursts. Much of this results from the detection of bursts by BeppoSAX\nwith good locations that have allowed the detection of counterparts at\nother wavelengths. This has allowed measurements of redshifts that\nhave firmly established that these bursts are at cosmological\ndistances. However, only a few redshifts are known, so there is still\nmuch work to be done in determining the mechanisms that produce\ngamma-ray bursts. Investigation of time profiles and spectra can shed\nnew light on this subject.\n\nThe vast majority of gamma-ray bursts that have been observed have\nbeen observed \\emph{only} by BATSE. This data can be classified into\nthree major types: burst locations with relatively large\nuncertainties, temporal characteristics, and spectral characteristics.\nHere, we shall examine temporal characteristics of bursts, along with\nsome spectral characteristics.\n\nThe temporal structure of gamma-ray bursts exhibit very diverse\nmorphologies, from single simple spikes to extremely complex\nstructures. So far, the only clear division of bursts based on\ntemporal characteristics that has been found is the bimodal\ndistribution of the $T_{90}$ and $T_{50}$ intervals, which are\nmeasures of burst durations~\\citep{kouveliotou:1993,meegan:1996}. In\norder to characterize burst time profiles, it is useful to be able to\ndescribe them using a small number of parameters.\n\nMany burst time profiles appear to be composed of a series of\ndiscrete, often overlapping, pulses, often with a \\emph{fast rise,\nexponential decay} (FRED) shape~\\citep{norris:1996}. These pulses\nhave durations ranging from a few milliseconds to several seconds.\nThe different pulses might, for example, come from different spatial\nvolumes in or near the burst source. Therefore, it may be useful to\ndecompose burst time profiles in terms of individual pulses, each of\nwhich rises from background to a maximum and then decays back to\nbackground levels. Here, we have analyzed gamma-ray burst time\nprofiles by representing them in terms of a finite number of pulses,\neach of which is described by a small number of parameters. The BATSE\ndata used for this purpose is described in Section~\\ref{sec:tts}. The\nbasic characteristics of the time profiles based on the above model\nare described in Section~\\ref{sec:results} and some of the\ncorrelations between these characteristics are described in\nSection~\\ref{sec:correlate}. (Further analysis of these and other\ncorrelations and their significance are discussed in an accompanying\npaper, \\cite{lee:2000b}.) Finally, a brief discussion is presented in\nSection~\\ref{sec:discuss}.\n\n\\section{The BATSE Time-to-Spill Data}\n\\label{sec:tts}\n\nThe BATSE Time-to-Spill (TTS) burst data type records the times\nrequired to accumulate a fixed number of counts, usually 64, in each\nof four energy channels~\\citep{batse:flight}. These time intervals\ngive fixed multiples of the reciprocals of the average count rates\nduring the spill intervals. There has been almost no analysis done\nusing the TTS data because it is less convenient to use with standard\nalgorithms than the BATSE Time-Tagged Event (TTE) data or the various\nforms of binned BATSE data. The TTS data use the limited memory on\nboard the CGRO more efficiently than do the binned data types because\nat lower count rates, it stores spills less frequently, with each\nspill having the same constant fractional statistical error. On the\nother hand, the binned data types always store binned counts at the\nsame intervals, so that at low count rates the binned counts have a\nlarge fractional statistical error. The variable time resolution of\nthe TTS data ranges from under 50~ms at low background rates to under\n0.1~ms in the peaks of the brightest bursts. In contrast, the finest\ntime resolution available for binned data is 16~ms for the medium\nenergy resolution (MER) data, and then only for the first 33~seconds\nafter the burst trigger. The TTS data can store up to 16,384 spill\nevents (over $10^{6}$ counts) for each energy channel, and this is\nalmost always sufficient to record the complete time profiles of\nbright, long bursts. This is unlike the TTE data, which are limited\nto 32,768 counts in all four energy channels combined. For short\nbursts, the TTE data have finer time resolution than the TTS data,\nbecause it records the arrival times of individual counts with\n2~$\\mu$s resolution. Furthermore, the TTE data also contain data from\nbefore the burst trigger time. One reason why this is useful is that\nsome of the shortest bursts are nearly over by the time burst trigger\nconditions have been met, so the TTS and MER data aren't very useful\nfor these bursts.\n\nFigure~\\ref{b01577} shows a portion of the time profile of BATSE\ntrigger number 1577 (GRB 4B 920502B) that contains a spike with\nduration shorter than 1~ms. The data with the finest time resolution,\nthe time-tagged event (TTE) data, end long before the spike occurs, so\nthe TTS data give the best representation of the spike. The binned\ndata with the finest time resolution, the MER data with 16~ms bins,\nare unavailable for this burst, as are the PREB and DISCSC data with\n64~ms bins.\n\n\\begin{figure}\\plotone{f1.eps}\\caption{A portion of the TTS data for BATSE Trigger Number 1577 (4B 920502B). Note the fine time resolution of the TTS data for the spike more than 36 seconds after the burst trigger. \\label{b01577}}\n\\end{figure}\n\nFor a Poisson process, the individual event times in the TTE data and\nthe binned counts in the various binned data types follow the familiar\nexponential and the Poisson distributions, respectively. The spill\ntimes recorded in the TTS data follow the \\emph{gamma distribution},\nwhich is the distribution of times needed to accumulate a fixed number\nof independent (Poisson) events occurring at a given rate. The\nprobability of observing a spill time $t_{s}$ is\n\\begin{equation}\nP(t_{s})\\ =\\ \\frac{t_{s}^{N - 1} R^{N} e^{-Rt_{s}}}{\\Gamma(N)}\\ ,\n\\label{eq:gamma}\n\\end{equation}\nwhere $N$ is the number of events per spill and $R$ is the rate of\nindividual events. This probability distribution is closely related\nto the Poisson distribution, which gives the number of events\noccurring within fixed time intervals for the same process of\nindependent individual events, such as photon arrivals.\n\n\\subsection{The Pulse Model and the Pulse Fitting Procedure}\n\nWe now describe the pulse model used to fit GRB time profiles, and the\npulse-fitting procedure. The pulse model we use is the phenomological\npulse model of \\cite{norris:1996} In this model, each pulse is\ndescribed by five parameters with the functional form\n\\begin{equation}\nI(t)\\ =\\ A \\exp{\\left(-\\left\\vert\\frac{t\n - t_{\\text{max}}}{\\sigma_{r,d}}\\right\\vert^{\\nu}\\right)}\\ ,\n\\label{eq:pulse}\n\\end{equation}\nwhere $t_{\\text{max}}$ is the time at which the pulse attains its\nmaximum, $\\sigma_{r}$ and $\\sigma_{d}$ are the rise and decay times,\nrespectively, $A$ is the pulse amplitude, and $\\nu$\n(the~``peakedness'') gives the sharpness or smoothness of the pulse at\nits peak. Pulses can, and frequently do, overlap. \\cite{stern:1997b}\nhave used the same functional form to fit averaged time profiles\n(ATPs) of entire bursts.\n\nWe have developed an interactive pulse-fitting program that can\nautomatically find initial background level and pulse parameters using\na Haar wavelet denoised time profile~\\citep{donoho:denoise}, and\nallows the user to add or delete pulses graphically. The program then\nfinds the parameters of the pulses and a background with a constant\nslope by using a maximum-likelihood fit for the gamma distribution\n(equation~\\ref{eq:gamma}) that the TTS spill times\nfollow~\\citep{lee:1996,lee:1998,lee:thesis}.\n\nThe data that we use in this paper are the TTS data for all gamma-ray\nbursts in the BATSE 3B catalog~\\citep{batse:3b} up to trigger number\n2000, covering the period from 1991 April 21 through 1992 October 22,\nin all channels that are available and show time variation beyond the\nnormal Poisson noise of the background. We fit each channel of each\nburst separately and obtained 574 fits for 211 bursts, with a total of\n2465 pulses. In many cases, the data for a burst showed no activity\nin a particular energy channel, only the normal background counts, so\nthere were no pulses to fit. This occurred most frequently in energy\nchannel~4. In other cases, the data for a burst contained telemetry\ngaps or were completely missing in one or more channels, making it\nimpossible to fit those channels.\n\nThis procedure is likely to introduce selection biases, which can be\nquantified through simulation. To determine these biases, we\nsimulated a set of bursts with varying numbers of pulses with\ndistributions of pulse and background parameters based on the observed\ndistributions in actual bursts. We generated independent counts\naccording to the simulated time profiles to create simulated TTS data,\nwhich we subjected to the same pulse-fitting procedure used for the\nactual BATSE data. The detailed results of this simulation are\ndiscussed in the Appendix. We will contrast the results from the\nactual data with those from the simulations where necessary and\nrelevant.\n\n\\subsection{Count Rates and Time Resolution}\n\nThe time resolution of the TTS data can be determined from the fitted\nbackground rates and the amplitudes of the individual pulses\n(discussed later in Subsection~\\ref{sec:amp}), at both the background\nlevels and at the peaks of the pulses. Table~\\ref{tab:res},\ncolumns~(a) show the percentage of bursts in our fitted sample where\nthe time resolution at background levels and at the peak of the\nhighest amplitude pulse are finer than 64~ms and 16~ms, the time\nresolutions of the more commonly used DISCSC and MER data,\nrespectively. The background rates are taken at the time of the burst\ntrigger, and ignore the fitted constant slope of the background. The\nrates at the peaks of the highest amplitude pulses include the\nbackground rates at the peak times of the pulses calculated with the\nbackground slopes. However, these rates ignore overlapping pulses, so\nthe actual time resolution will be finer since the actual count rates\nwill be higher. Note that even at background levels, the TTS data\nalways have finer time resolution than the DISCSC data, except in\nenergy channel~4 where the DISCSC data have finer time resolution for\n32\\% of the bursts in our sample.\n\n\\begin{deluxetable}{crrrrrr}\n\\tablecaption{Percentage of (a) Bursts and (b) Individual Pulses with\nTime Resolution $<64$~ms, $<16$~ms. \\label{tab:res}} \\tablehead{\n\\colhead{} & \\multicolumn{4}{c}{(a) Bursts} & \\multicolumn{2}{c}{(b)\nIndividual} \\\\ \\cline{2-5} \\\\ \\colhead{Energy} &\n\\multicolumn{2}{c}{Background} & \\multicolumn{2}{c}{Highest Amplitude\nPulse} & \\multicolumn{2}{c}{Pulses} \\\\ \\colhead{Channel} & \\colhead{\\%\n$<64$~ms} & \\colhead{\\% $<16$~ms} & \\colhead{\\% $<64$~ms} &\n\\colhead{\\% $<16$~ms} & \\colhead{\\% $<64$~ms} & \\colhead{\\% $<16$~ms}}\n\\startdata 1 & 100\\% & 16\\% & 100\\% & 80\\% & 100\\% & 80\\% \\\\ 2 & 100\\%\n& 8\\% & 100\\% & 75\\% & 100\\% & 68\\% \\\\ 3 & 100\\% & 3\\% & 100\\% & 67\\%\n& 100\\% & 62\\% \\\\ 4 & 68\\% & 1\\% & 100\\% & 30\\% & 100\\% & 42\\% \\\\ All\n& 96\\% & 8\\% & 100\\% & 69\\% & 100\\% & 65\\% \\\\ \\enddata\n\\end{deluxetable}\n\nTable~\\ref{tab:res}, columns~(b) show the percentage of individual\npulses where the TTS data have time resolution finer than 16~ms and\n64~ms at the pulse peaks. Again, the count rates include the fitted\nbackground rates at the peak times of the pulses but ignore\noverlapping pulses. For all individual pulses, the TTS data have\nfiner time resolution at their peaks than the DISCSC data.\n\n\\section{General Characteristics of Pulses in Bursts}\n\\label{sec:results}\n\nIn this section we describe characteristics of pulses in individual\nbursts and in the sample as a whole.\n\n\\subsection{Numbers of Pulses}\n\nThe number of pulses in a fit range from 1 to 43, with a median of 2\npulses per fit in energy channels~1, 2, and 4, and a median of 3\npulses per fit in energy channel~3. (See Figure~\\ref{npulsech}.) The\nnumbers of pulses per fit follows the trend of pulse amplitudes, which\nwe shall see tend to be highest in energy channel~3, followed in order\nby channels~2, 1, and 4, respectively. This appears to occur because\nhigher amplitude pulses are easier to identify above the background,\nand is consistent with the simulation results shown in the Appendix.\n\n\\begin{figure}\\plotone{f2.eps}\\caption{Distribution of number of pulses per burst, by energy channel. Compare with Figure~\\ref{sim_npulse} from simulations. \\label{npulsech}}\n\\end{figure}\n\n\\cite{norris:1996} have used the pulse model of\nequation~\\ref{eq:pulse} to fit the time profiles of 45 bright, long\nbursts. They analyzed the BATSE PREB and DISCSC data types, which\ncontain four-channel discriminator data with 64~ms resolution\nbeginning 2 seconds before the burst trigger. For their selected\nsample of bursts, they fitted an average of 10 pulses per burst, with\nno time profiles consisting of only a single pulse. This number is\nconsiderably higher than the mean number of pulses per fit for our\nsample of bursts, probably because their sample was selected for high\npeak flux and long duration, which makes it easier to resolve more\npulses.\n\n\\subsection{Matching Pulses Between Energy Channels}\n\nTo see how attributes of pulses within a burst vary with energy, it is\nnecessary to match pulses in different energy channels. Although\nburst time profiles generally have similar features in different\nenergy channels, this matching is not straightforward, since the\nnumber of pulses fitted to a burst time profile is very often\ndifferent between energy channels. We have used a simple automatic\nalgorithm for matching pulses between adjacent energy channels. This\nalgorithm begins by taking all pulses from the channel with fewer\npulses. It then takes the same number of pulses of highest amplitude\nfrom the other channel, and matches them in time order with the pulses\nfrom the channel with fewer pulses. For example, the time profiles of\nBATSE trigger number 1577 were fitted with nine pulses in energy\nchannel~3, and only four pulses in channel~4. This algorithm simply\nmatches all four pulses in channel~4 in time order with the four\nhighest amplitude pulses in channel~3. While this method will not\nalways correctly match individual pulses between energy channels and\nwill result in broad statistical distributions, it should still\npreserve central tendencies and yield useful statistical information.\n\n\\subsection{Brightness Measures of Pulses: Amplitudes and Count Fluences}\n%\\subsection{Pulse Amplitudes}\n\\label{sec:amp}\n\nThe amplitude of a pulse, parameter $A$ in equation~\\ref{eq:pulse}, is\nthe maximum count rate within the pulse, and measures the observed\nintensity of the pulse, which depends on the absolute intensity of the\npulse at the burst source and the distance to the burst source. The\namplitudes of the fitted pulses ranged from 40 counts/second to over\n500,000 counts/second. (See Table~\\ref{tab:amp} and\nFigure~\\ref{amp}.) Pulses tend to have the highest amplitudes in\nenergy channel~3, followed in order by channels~2, 1, and~4, in\nagreement with \\cite{norris:1996}. The central 68\\% of the pulse\namplitude distributions span a range of about one order of magnitude\nin each of the four energy channels, with a somewhat greater range in\nchannel~3. We will see in the Appendix that the fitting procedure\ntends to miss pulses with low amplitudes, so that the distributions\nshown may be strongly affected by selection effects in the fitting\nprocedure.\n\n\\begin{deluxetable}{crrrr}\n\\tablecaption{Characteristics of Distribution of Pulse Amplitudes for All Pulses in All Bursts Combined. \\label{tab:amp}}\n\\tablehead{\n\\colhead{Energy} & \\colhead{Min. Amp.} & \\colhead{Median Amp.} & \\colhead{Max. Amp.} & \\colhead{Ratio} \\\\\n\\colhead{Channel} & \\colhead{(Counts / Sec.)} & \\colhead{(Counts / Sec.)} & \\colhead{(Counts / Sec.)} & \\colhead{84\\%ile / 16\\%ile}}\n\\startdata\n1 & 47 & 2200 & 136,000 & 10.8 \\\\\n2 & 85 & 2700 & 543,000 & 12.9 \\\\\n3 & 93 & 3000 & 250,000 & 16.2 \\\\\n4 & 43 & 1900 & 63,000 & 11.8 \\\\\n\\enddata\n\\end{deluxetable}\n\n\\begin{figure}\\plotone{f3.eps}\\caption{Distribution of pulse amplitudes for all pulses from all bursts, by energy channel. Note that the rapid decline at\nlow amplitudes is partly due to the BATSE triggering procedure and\npartly due to the fitting procedure. See Figure~\\ref{sim_amp}.\n\\label{amp}}\n\\end{figure}\n\nThe amplitude of the highest amplitude pulse in a burst is an\napproximation to the instantaneous peak flux above background of that\nburst in that energy channel. The peak flux is often used as an\nindicator of the distance to the burst source. Since pulses can\noverlap, the highest pulse amplitude can be less than the actual\nbackground-subtracted peak flux. The BATSE burst catalogs give\nbackground-subtracted peak fluxes for 64, 256, and 1024~ms time bins\nin units of photons/cm$^2$/second, for which effects such as the\nenergy acceptances of the detectors and the orientation of the\nspacecraft and hence the detectors relative to the source have been\naccounted for and removed. The BATSE burst catalog also lists raw\npeak count rates that are not background-subtracted or corrected for\nany of the effects described, averaged over 64, 256, and 1024~ms time\nbins in the second most brightly illuminated detector for each burst.\nThese peak count rates are primarily useful for comparison with the\nBATSE event trigger criteria. In some bursts, the highest pulses are\nconsiderably narrower than the shortest time bins used to measure peak\nflux in the BATSE burst catalog. For these bursts, these peak fluxes\nwill be lower than the true peak flux, and the fitted pulse amplitudes\nare likely to be a better measure of the true peak flux. The\ndistributions of the highest pulse amplitudes are shown in\nTable~\\ref{tab:peak_amp} and Figure~\\ref{peak_amp}. Since BATSE\nselectively triggers on events with high peak flux, the distributions\nmust be strongly affected by the trigger criteria.\n\n\\begin{deluxetable}{crrrr}\n\\tablecaption{Characteristics of Distribution of Pulse Amplitudes for Highest Amplitude Pulse in Each Burst. \\label{tab:peak_amp}}\n\\tablehead{\n\\colhead{Energy} & \\colhead{Min. Amp.} & \\colhead{Median Amp.} & \\colhead{Max. Amp.} & \\colhead{Ratio} \\\\\n\\colhead{Channel} & \\colhead{(Counts / Sec.)} & \\colhead{(Counts / Sec.)} & \\colhead{(Counts / Sec.)} & \\colhead{84\\%ile / 16\\%ile}}\n\\startdata\n1 & 241 & 2200 & 136,000 & 11.1 \\\\\n2 & 148 & 2800 & 543,000 & 9.9 \\\\\n3 & 116 & 3500 & 250,000 & 12.4 \\\\\n4 & 82 & 1500 & 63,000 & 18.8 \\\\\n\\enddata\n\\end{deluxetable}\n\n\\begin{figure}\\plotone{f4.eps}\\caption{Distribution of pulse amplitudes, highest amplitude pulse in each burst, by energy channel. Dashed lines are bursts containing only a single pulse. The more rapid decline at low\namplitudes as compared with that in Figure~\\ref{amp} is due to the\nstronger influence of the BATSE triggering procedure. The fitting\nprocedure has a weaker influence here. \\label{peak_amp}}\n\\end{figure}\n\nFigure~\\ref{npvsamp} shows the number of pulses in each fit plotted\nagainst the amplitudes of all of the pulses comprising each fit. It\nshows that in fits with more pulses, the minimum pulse amplitude,\nwhich can be seen from the left boundary of the distribution, tends to\nbe higher. This could result in part from intrinsic properties of the\nburst sources, but may also result at least in part from a selection\neffect: In a complex time profile with many overlapping pulses, low\namplitude pulses, which have poor signal-to-noise ratios, will be more\ndifficult to resolve, while in a less complex time profile, they will\nbe easier to resolve. This hypothesis appears to be confirmed by the\nsimulation results shown in the Appendix. Table~\\ref{tab:npvsafw},\ncolumns~(a) give the Spearman rank-order correlation coefficients,\ncommonly denoted as $r_{s}$, for the joint distribution of pulse\namplitudes and numbers of pulses in the corresponding bursts shown in\nFigure~\\ref{npvsamp}, as well as the probability that a random data\nset of the same size with no correlation between the two variables\nwould produce the observed value of $r_{s}$. It shows strong positive\ncorrelations between pulse amplitudes and the number of pulses in the\nfit for all energy channels. These correlations appear to be stronger\nthan those arising in the fits to simulations shown in\nTable~\\ref{tab:sim_npvsafw}, columns~(a).\n\n\\begin{figure}\\plotone{f5.eps}\\caption{Number of pulses per burst versus pulse amplitudes of all pulses, by energy channel. Compare with Figure~\\ref{sim_npvsamp} for simulated data. Note that there exists a positive\ncorrelation between the two quantities. \\label{npvsamp}}\n\\end{figure}\n\n\\begin{deluxetable}{crlrlrl}\n\\tablecaption{Correlation Between Number of Pulses per Burst and (a) Amplitudes, (b) Count Fluences, and (c) Widths of All Pulses. \\label{tab:npvsafw}}\n\\tablehead{\n\\colhead{Energy} & \\multicolumn{2}{c}{(a) Amplitude} & \\multicolumn{2}{c}{(b) Count Fluence} & \\multicolumn{2}{c}{(c) Width} \\\\\n\\colhead{Channel} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$r_{s}$} & \\colhead{Prob.}}\n\\startdata\n1 & 0.37 & \\e{3.9}{-18} & -0.17 & \\e{9.2}{-5} & -0.36 & \\e{1.8}{-17} \\\\\n2 & 0.36 & \\e{1.8}{-24} & -0.20 & \\e{3.4}{-8} & -0.35 & \\e{8.0}{-24} \\\\\n3 & 0.30 & \\e{4.2}{-20} & -0.04 & 0.21 & -0.23 & \\e{9.4}{-12} \\\\\n4 & 0.45 & \\e{2.2}{-15} & -0.13 & 0.027 & -0.28 & \\e{1.3}{-6} \\\\\n\\enddata\n\\end{deluxetable}\n\n%\\subsection{Count Fluences}\n\nThe area under the light curve of a pulse gives the total number of\ncounts contained in the pulse, which is its count fluence. It is\ngiven in terms of the pulse parameters and the gamma function by\n\\begin{equation}\n\\mathcal{F} = A \\int_{-\\infty}^{\\infty}{I(t)dt} = A \\frac{\\sigma_{r} + \\sigma_{d}}{\\nu}\\Gamma\\left(\\frac{1}{\\nu}\\right) .\n\\label{eq:area}\n\\end{equation}\nThe count fluence is a measure of the observed integrated luminosity\nof the pulse, which depends on the total number of photons emitted by\nthe source within the pulse and the distance to the burst source. We\nwill see in the Appendix that the fitting procedure tends to miss\npulses with low count fluences.\n\nFigure~\\ref{npvsarea} shows the number of pulses in each fit versus\nthe count fluences of the individual pulses. It shows that in bursts\ncontaining more pulses, the individual pulses tend to contain fewer\ncounts. We shall see in the next section that pulses tend to be\nnarrower in more complex bursts. This result for count fluences\nimplies that the tendency for pulses to be narrower is stronger than\nthe tendency for pulses to have higher amplitudes in more complex\nbursts. Table~\\ref{tab:npvsafw}, columns~(b) show that the\ncorresponding negative correlations between pulse count fluences and\nnumbers of pulses per fit are statistically significant in energy\nchannels~1 and 2, but not in channels~3 and 4. The fits to\nsimulations (Figure~\\ref{sim_npvsarea} and\nTable~\\ref{tab:sim_npvsafw}, columns~(b)) do not show the same\ntendency, so this most likely is not caused by selection effects in\nthe pulse-fitting procedure.\n\n\\begin{figure}\\plotone{f6.eps}\\caption{Number of pulses per burst versus count fluences of all pulses from all bursts, by energy channel. Compare with Figure~\\ref{sim_npvsarea} for simulated data. Note that there exists a negative correlation between the two quantities. \\label{npvsarea}}\n\\end{figure}\n\n%\\subsection{Timescales in Bursts}\n\\subsection{Pulse Widths and Time Delays}\n\nTimescales in gamma-ray bursts are likely to be characteristic of the\nphysical processes that produce them. However, since some, and\npossibly all, bursts are produced at cosmological distances, all\nobserved timescales will be affected by cosmological time dilation,\nand won't represent the physical timescales at the sources.\n\n\\subsubsection{Pulse Widths}\n\nThe most obvious timescale that appears in the pulse decomposition of\ngamma-ray burst time profiles is the pulse width, or duration. We\nshall measure the duration, or width, of a pulse using its full width\nat half maximum (FWHM), which is given by\n\\begin{equation}\nT_{\\text{FWHM}} = (\\sigma_{r} + \\sigma_{d}) (\\ln 2)^{\\frac{1}{\\nu}} .\n\\label{eq:fwhm}\n\\end{equation}\nThe distributions of the pulse widths, which are shown in\nFigure~\\ref{fwhmch} and columns~(a) of Table~\\ref{tab:fwhmnu}, peak\nnear one second in all energy channels, with no sign of the bimodality\nseen in total burst durations mentioned above. Pulses tend to be\nnarrower (shorter) at higher energies.\n\n\\begin{figure}\\plotone{f7.eps}\\caption{Distribution of pulse widths (FWHM) for all pulses from all bursts, by energy channel. Note that there is no indication that pulse widths have the bimodality observed in the distributions of the $T_{50}$ and $T_{90}$ measures of burst durations in the BATSE catalogs. Compare with the distribution for simulated\nbursts in Figure~\\ref{sim_fwhm}. \\label{fwhmch}}\n\\end{figure}\n\n\\begin{deluxetable}{crrrr}\n\\tablecaption{Characteristics of Distribution of (a) Pulse Widths and of (b) Peakedness $\\nu$ for All Pulses in All Bursts Combined. \\label{tab:fwhmnu}}\n\\tablehead{\n\\colhead{} & \\multicolumn{2}{c}{(a) FWHM} & \\multicolumn{2}{c}{(b) Peakedness $\\nu$} \\\\\n\\colhead{Energy} & \\colhead{Median} & \\colhead{Ratio} & \\colhead{Median} & \\colhead{Ratio} \\\\\n\\colhead{Channel} & \\colhead{(Seconds)} & \\colhead{84\\%ile / 16\\%ile} & \\colhead{$\\nu$} & \\colhead{84\\%ile / 16\\%ile}}\n\\startdata\n1 & 1.86 & 19.9 & 1.22 & 5.3 \\\\\n2 & 1.05 & 23.0 & 1.26 & 5.6 \\\\\n3 & 0.68 & 22.9 & 1.26 & 5.7 \\\\\n4 & 0.41 & 21.4 & 1.17 & 5.8 \\\\\nAll & 0.90 & 27.0 & 1.25 & 5.6 \\\\\n\\enddata\n\\end{deluxetable}\n\nThe narrowing of pulses in higher energy channels can also be measured\nfrom the ratios of pulse widths of matched pulses in adjacent energy\nchannels, as shown in Table~\\ref{tab:rfwhm}. We can test the\nhypothesis that pulses tend to be narrower at higher energies by\ncomputing the probability that the observed numbers of pulses width\nratios less than 1 will occur by chance if pulse width ratios less\nthan 1 and greater than 1 are equally probable. This probability can\nbe computed from the binomial distribution, and is shown in the last\ncolumn of Table~\\ref{tab:rfwhm}. The table shows less narrowing than\na simple comparison of median pulse widths from Table~\\ref{tab:fwhmnu}\nwould suggest, though it also shows that the hypothesis that pulses\n\\emph{do not} become narrower at higher energies is strongly excluded\nbetween channels~1 and 2 and between channels~2 and 3. Qualitatively\nsimilar kinds of trends have been shown to be present in individual\npulses~\\citep{norris:1996} and composite pulse shapes of many\nbursts~\\citep{link:1993,fenimore:1995b}. There are, however, some\nquantitative differences. For example, we find that there seems to be\nless narrowing at higher energies; the pulse width ratios tend to be\ncloser to 1 between energy channels~3 and 4 than for the lower energy\nchannels (although the statistics are poorer, as with anything\ninvolving channel~4), which is the opposite of the tendency found by\n\\cite{norris:1996}. We can use the Kolmogorov-Smirnov test to\ndetermine if the distributions of pulse width ratios are the same\nbetween adjacent energy channels. These results are shown in the last\ncolumn of Table~\\ref{tab:rfwhm}. This test shows significant\ndifferences in the distribution of pulse widths of matched pulses\nbetween adjacent energy channels.\n\n\\begin{deluxetable}{crrll}\n\\tablecaption{Ratios of Pulse Widths of Pulses Matched Between Adjacent Energy Channels. \\label{tab:rfwhm}}\n\\tablehead{\n\\colhead{Energy} & \\colhead{Median} & \\colhead{} & \\colhead{Binom.} & \\colhead{K-S} \\\\\n\\colhead{Channels} & \\colhead{Width Ratio} & \\colhead{\\% $<1$} & \\colhead{Prob.} & \\colhead{Prob.}}\n\\startdata\n2 / 1 & 0.73 & 304/446 = 68\\% & \\e{1.7}{-14} & \\e{1.1}{-5} \\\\\n3 / 2 & 0.68 & 436/625 = 70\\% & $<10^{-16}$ & \\e{8.7}{-7} \\\\\n4 / 3 & 0.83 & 153/258 = 59\\% & 0.0028 & 0.62 \\\\\n\\enddata\n\\end{deluxetable}\n\nThe fact that pulse widths decrease monotonically with energy, and the\nsignal-to-noise ratios of the different energy channels increase in\norder of the energy channels 3, 2, 1, 4, imply that the narrowing is\ncaused by the burst production mechanism itself.\n\n\\subsubsection{Pulse Widths and Numbers of Pulses}\n\nFigure~\\ref{npvsfwhm} and Table~\\ref{tab:npvsafw}, columns~(c) show\nthe relation between the number of pulses per burst and the widths of\nthe pulses. These show that pulses tend to be narrower in bursts with\nmore pulses. This may be an intrinsic property of GRBs, or it may be\na selection effect arising because narrower pulses have less overlap\nwith adjacent pulses, hence they are easier to resolve, so more pulses\ntend to be identified in bursts with narrower pulses. This may also\nbe a side effect of correlations between other burst and pulse\ncharacteristics with the number of pulses per burst and the pulse\nwidths. Table~\\ref{tab:npvsafw} shows strong negative correlations\nbetween the numbers of pulses per fit and the pulse widths. The fits\nto simulations shown in Figure~\\ref{sim_npvsfwhm} and\nTable~\\ref{tab:sim_npvsafw}, columns~(c) do not have the same\ntendency. This suggests that the negative correlation between the\nnumber of pulses in each fit and the pulse widths seen in the fits to\nactual bursts do not result from selection effects in the\npulse-fitting procedure, but are intrinsic to the burst production\nmechanism, or may arise from other effects.\n\n\\begin{figure}\\plotone{f8.eps}\\caption{Number of pulses per burst versus widths of all pulses from all bursts, by energy channel. Compare with Figure~\\ref{sim_npvsfwhm} for simulated data. Note that there exists a negative correlation\nbetween the two quantities. \\label{npvsfwhm}}\n\\end{figure}\n\n\\subsubsection{Time Delays Between Energy Channels}\n\\label{sec:delay}\n\nTable~\\ref{tab:timelag}, columns~(a) show the differences, or time\ndelays, between the peak times $t_{\\text{max}}$ of all pulses matched\nbetween adjacent energy channels. It shows a significant tendency for\nindividual pulses to peak earlier at higher energies. This has been\npreviously observed, and described as a hard-to-soft spectral\nevolution of the individual pulses~\\citep{norris:1986,norris:1996}.\nThe time delays found here are greater than those found by\n\\cite{norris:1996}, who found an average pulse peak time delay between\nadjacent energy channels of $\\sim 20$ ms. Comparing the peak times of\nthe highest amplitude pulses in each fit between adjacent energy\nchannels also shows a significant tendency for bursts to peak earlier\nat higher energies. (See Table~\\ref{tab:timelag}, columns~(b).) The\ntime delays between energy channels observed here and elsewhere are\nlikely to result from intrinsic properties of the burst sources.\n\n\\begin{deluxetable}{crrlrrl}\n\\tablecaption{Characteristics of Distribution of Time Delays Between Adjacent Energy Channels. \\label{tab:timelag}}\n\\tablehead{\n\\colhead{} & \\multicolumn{3}{c}{(a) All Matched Pulses} & \\multicolumn{3}{c}{(b) Highest Amplitude Pulse} \\\\\n\\colhead{Energy} & \\colhead{Med. Lag} & \\colhead{} & \\colhead{Binom.} & \\colhead{Med. Lag} & \\colhead{} & \\colhead{Binom.} \\\\\n\\colhead{Channels} & \\colhead{(Sec.)} & \\colhead{\\% $>0$} & \\colhead{Prob.} & \\colhead{(Sec.)} & \\colhead{\\% $>0$} & \\colhead{Prob.}}\n\\startdata\n1 - 2 & 0.11 & 290/446 = 65\\% & \\e{2.2}{-10} & 0.08 & 95/141 = 67\\% & \\e{3.7}{-5} \\\\\n2 - 3 & 0.27 & 459/625 = 73\\% & $<10^{-16}$ & 0.05 & 97/151 = 64\\% & 0.00047 \\\\\n3 - 4 & 0.01 & 140/258 = 54\\% & 0.17 & 0.14 & 47/67 = 70\\% & 0.00097 \\\\\n\\enddata\n\\end{deluxetable}\n\n\\subsection{Pulse Shapes: Asymmetries and the Peakedness $\\nu$}\n%\\subsection{Pulse Asymmetries}\n\nAlthough the pulse model uses separate rise and decay times as its\nbasic parameters, it is often more natural to consider the widths and\nasymmetries of pulses, which give equivalent information to the rise\nand decay times. The ratios of pulse rise times to decay times\n$\\sigma_{r}/\\sigma_{d}$ are a convenient way to measure the asymmetry\nof pulses, and depends only on the shapes of pulses. The asymmetry\nratios cover a very wide range of values, but there is a clear\ntendency for pulses to have slightly shorter rise times than decay\ntimes. (See Figure~\\ref{rdch}.)\n\nTable~\\ref{tab:rd} shows that the hypothesis that pulses are symmetric\nis strongly excluded in energy channels~2 and 3. The binomial\nprobability isn't computed for all pulses in all energy channels\ncombined, because pulses cannot be considered to be independent\nbetween energy channels. We also see that the degree of the asymmetry\nisn't significantly different for the different energy channels.\n\\cite{norris:1996} found far greater asymmetry, with average values of\n$\\sigma_{d}/\\sigma_{r}$ (the inverse of the ratio used here) ranging\nfrom 2 to 3 for their selected sample of bursts, and with about 90\\%\nof pulses having shorter rise times than decay times.\n\n\\begin{figure}\\plotone{f9.eps}\\caption{Distribution of pulse asymmetry ratios for all pulses from all bursts, by energy channel. See analysis in Table~\\ref{tab:rd}. \\label{rdch}}\n\\end{figure}\n\n\\begin{deluxetable}{crrrl}\n\\tablecaption{Characteristics of Distribution of Pulse Asymmetries for All Pulses in All Bursts Combined. \\label{tab:rd}}\n\\tablehead{\n\\colhead{Energy} & \\colhead{Median} & \\colhead{Ratio} & \\colhead{} & \\colhead{Binom.} \\\\\n\\colhead{Channel} & \\colhead{$\\sigma_{r} / \\sigma_{d}$} & \\colhead{84\\%ile / 16\\%ile} & \\colhead{\\% $\\sigma_{r} < \\sigma_{d}$} & \\colhead{Prob.}}\n\\startdata\n1 & 0.76 & 16.8 & 297/526 = 56\\% & 0.0030 \\\\\n2 & 0.76 & 16.1 & 457/776 = 59\\% & \\e{7.2}{-7} \\\\\n3 & 0.71 & 14.0 & 528/883 = 60\\% & \\e{5.8}{-9} \\\\\n4 & 0.80 & 15.9 & 158/280 = 56\\% & 0.031 \\\\\nAll & 0.75 & 15.4 & 1440/2465 = 58\\% & \\nodata \\\\\n\\enddata\n\\end{deluxetable}\n\n%\\subsection{The Peakedness Parameter $\\nu$}\n\nThe relation of the peakedness parameter $\\nu$ to physical\ncharacteristics of gamma-ray burst sources is far less clear than for\nother pulse attributes. Nevertheless, it does give information that\ncan be used to compare the shapes of different pulses. The peakedness\n$\\nu$ has a median value near 1.2 in all energy channels, so that\npulses tend to have shapes between an exponential, for which $\\nu =\n1$, and a Gaussian, for which $\\nu = 2$. (See Figure~\\ref{nuch} and\ncolumns~(b) of Table~\\ref{tab:fwhmnu}.) \\cite{stern:1997b} use the\nfunctional form of equation~\\ref{eq:pulse} to fit averaged time\nprofiles of many bursts rather than individual constituent pulses, and\nfind that $\\nu \\approx 1/3$ for the \\emph{averaged time profiles}.\n\n\\begin{figure}\\plotone{f10.eps}\\caption{Distribution of the peakedness parameter $\\nu$ for all pulses from all bursts, by energy channel. See analysis in Table~\\ref{tab:fwhmnu}, columns~(b). \\label{nuch}}\n\\end{figure}\n\n\\section{Correlations Between Pulse Characteristics}\n\\label{sec:correlate}\n\nCorrelations between different characteristics of pulses, or the lack\nthereof, may reveal much about gamma-ray bursts that the distributions\nof the individual characteristics cannot. Some correlations may arise\nfrom intrinsic properties of the burst sources, while others may\nresult from the differing distances to the sources. The first kind of\ncorrelation may be present among pulses of individual bursts or among\nthe whole population of bursts, while the second kind will not be\npresent among pulses of individual bursts. In order to distinguish\nbetween these two kinds of effects, it is useful to examine\ncorrelations of pulse characteristics both between different bursts,\nand between pulses within individual bursts.\n\nIt is simplest to find correlations between characteristics of all\npulses, but such correlations would combine both kinds of effects, and\nthe statistics would be weighted in favor of bursts containing more\npulses. It is also possible to select a single pulse from each burst,\nand find correlations between the characteristics of these pulses from\nburst to burst in order to look for effects arising from the distances\nto burst sources. However, if the correlations are taken using the\nsingle highest amplitude or highest fluence pulse from each burst,\nthen they could still be affected by correlations of pulse\ncharacteristics within individual bursts. For example, consider a\nsituation where amplitudes and durations of pulses within individual\nbursts are correlated, and where pulse amplitudes and durations follow\na common distribution for all bursts. In such a case, if we select\nthe single highest amplitude pulse from each burst, we would find a\nspurious correlation between highest pulse amplitude and duration\nbetween different bursts.\n\nCorrelation results which compare and contrast the cosmological and\nintrinsic effects will be discussed in greater detail in the\naccompanying paper \\cite{lee:2000b}. Here, we describe our method and\nsome other correlation results.\n\nOne way to find correlations of pulse characteristics within\nindividual bursts is to calculate a correlation coefficient for each\nburst and examine the distribution of the degrees of correlation, for\nexample to see if the correlation coefficients were positive for a\nlarge majority of bursts. The Spearman rank-order correlation\ncoefficient is used for this purpose here. When using the Spearman\nrank-order correlation coefficient, the coefficients for the\nindividual bursts are often not statistically significant because the\nnumber of pulses in each burst is not large, even though the\ncoefficents for the different bursts may be mostly positive or mostly\nnegative. We can test the hypothesis that there is no correlation\nbecause in the absence of any correlation, we would expect an equal\nnumber of bursts with positive correlations as with negative\ncorrelations, so the probability that the observed numbers of bursts\nwith positive and negative correlations could occur by chance if there\nwas no correlation is given by the binomial distribution. This is the\nmethod used here. This method ignores the strengths of the individual\ncorrelations, so it is more sensitive to a weak correlation that\naffects large numbers of bursts than it is to a strong correlation\nthat affects only a small number of bursts.\n\n\\subsection{Spectral Characteristics}\n\nThe data that we are using only has very limited spectral information,\nonly four energy channels. We can investigate spectral\ncharacteristics by using the \\emph{hardness ratios} of individual\npulses. The hardness ratio of a pulse between two specified energy\nchannels is the ratio of the fluxes or fluences of the pulse between\nthe two energy channels. Although the actual numerical values of the\nhardness ratios depend on the somewhat arbitrary boundaries of the\nenergy channels, the values can be compared between different pulses,\nand between different bursts.\n\nThere have been several claims of correlation between peak or average\nhardness ratios and durations among bursts, with shorter bursts being\nharder, and there has been some analysis of the cosmological\nsignificance of this. Here we investigate similar correlations for\nbursts, and for pulses in individual bursts.\n\n\\subsubsection{Pulse Widths}\n\nTable~\\ref{tab:hrampvswdta}, columns~(a) show the correlations between\nthe pulse amplitude hardness ratios and the pulse widths for the\nhighest amplitude pulse in each burst. The pulse widths used are\narithmetic means of the widths in the two adjacent energy channels\nthat the hardness ratios are taken between, \\emph{e.g.} hardness\nratios between channels~2 and 3 are compared with pulse widths\naveraged over channels~2 and 3. In all pairs of adjacent energy\nchannels, the highest amplitude pulse has a slight tendency to be\nnarrower when the burst is harder, as measured using peak flux, but\nthis does not appear to be statistically significant, except possibly\nbetween channels~3 and 4. This may be a signature of weak redshift\neffects; whereby the higher the redshift, the softer the spectrum and\nthe longer the duration.\n\n\\begin{deluxetable}{crlrlrl}\n\\tablecaption{Correlations Between Pulse Amplitude Hardness Ratio and (a) Pulse Widths, (b) Intervals Between Two Highest Amplitude Pulses, and (c) Amplitudes for Highest Amplitude Pulse(s) in Each Burst. \\label{tab:hrampvswdta}}\n\\tablehead{\n\\colhead{Energy} & \\multicolumn{2}{c}{(a) Width} & \\multicolumn{2}{c}{(b) Interval} & \\multicolumn{2}{c}{(c) Amplitude} \\\\\n\\colhead{Channels} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$r_{s}$} & \\colhead{Prob.}}\n\\startdata\n2 / 1 & -0.11 & 0.18 & -0.26 & 0.019 & 0.01 & 0.89 \\\\\n3 / 2 & -0.21 & 0.010 & -0.06 & 0.57 & 0.28 & 0.00059 \\\\\n4 / 3 & -0.41 & 0.00061 & -0.17 & 0.34 & 0.31 & 0.012 \\\\\n\\enddata\n\\end{deluxetable}\n\nTable~\\ref{tab:hrampfwhmamp}, columns~(a) shows the correlations\nbetween pulse amplitude hardness ratios and pulse widths within\nbursts. As evident, there is almost equal probability for positive\nand negative correlations. We conclude, therefore, that there is no\nsignificant tendency for longer or shorter duration pulses to have\nharder or softer spectra, measured using peak flux.\n\n\\begin{deluxetable}{crlrl}\n\\tablecaption{Correlations Between Pulse Amplitude Hardness Ratio and (a) Pulse Width and (b) Amplitude Within Bursts. \\label{tab:hrampfwhmamp}}\n\\tablehead{\n\\colhead{Energy} & \\multicolumn{2}{c}{(a) Width} & \\multicolumn{2}{c}{(b) Amplitude} \\\\\n\\colhead{Channels} & \\colhead{\\% Pos. Corr.} & \\colhead{Binom. Prob.} & \\colhead{\\% Pos. Corr.} & \\colhead{Binom. Prob.}}\n\\startdata\n2 / 1 & 45/83 = 54\\% & 0.44 & 44.5/83 = 54\\% & 0.51 \\\\\n3 / 2 & 50/95 = 53\\% & 0.61 & 49/95 = 52\\% & 0.76 \\\\\n4 / 3 & 14/33 = 42\\% & 0.38 & 20.5/33 = 62\\% & 0.16 \\\\\nAll & 109/211 = 52\\% & \\nodata & 114/211 = 54\\% & \\nodata \\\\\n\\enddata\n\\end{deluxetable}\n\n\\subsubsection{Intervals Between Pulses}\n\nTable~\\ref{tab:hrampvswdta}, columns~(b) show the correlations between\nthe pulse amplitude hardness ratios and the intervals between the two\nhighest amplitude pulses in each fit. The time intervals used are\nalso averaged over the two adjacent energy channels. In all pairs of\nadjacent energy channels, the two highest amplitude pulses have a\nslight tendency to be closer together when the burst is harder (as\nexpected from cosmological redshift effects), as measured using peak\nflux, but this is not statistically significant, except possibly\nbetween channels~1 and 2.\n\n\\subsubsection{Pulse Amplitudes}\n\nTable~\\ref{tab:hrampvswdta}, columns~(c) show the correlations between\nthe pulse amplitude hardness ratio and the pulse amplitudes for the\nhighest amplitude pulse in each burst. If the peak luminosity of the\nhighest amplitude pulse is a standard candle or has a narrow\ndistribution, the effects of cosmological redshift would introduce a\ncorrelation between hardness ratio and amplitude. In all pairs of\nadjacent energy channels, the highest amplitude pulse has a slight\ntendency to be stronger when the burst is harder, as measured using\npeak flux, but this is not statistically significant (except possibly\nbetween channels~2 and 3,) indicating that the distribution of the\nabove-mentioned luminosity is broad.\n\nTable~\\ref{tab:hrampfwhmamp}, columns~(b) shows the correlations\nbetween pulse amplitude hardness ratios and pulse amplitudes within\nbursts. The pulse amplitudes are summed over the two adjacent energy\nchannels that the hardness ratios are taken between. There appears to\nbe no statistically significant tendency for higher amplitude pulses\nto have harder or softer spectra, although slightly more bursts show a\npositive correlation (higher amplitude pulses are harder) than a\nnegative correlation (higher amplitude pulses are softer.) This\npoints to a weak or negligible intrinsic correlation between these\nquantities.\n\n\\subsubsection{Count Fluence Hardness Ratios}\n\nIn what follows, we carry out the same tests using the hardness ratio\nmeasured by count fluence instead of amplitude, for bursts and pulses\nwithin bursts.\n\nTable~\\ref{tab:hrtareavswdttarea}, columns~(a) shows the correlations\nbetween the total burst count fluence hardness ratios and the pulse\nwidths for the highest amplitude pulses of the bursts. A positive\ncorrelation (harder bursts having shorter durations) would be expected\nif pulse total energy had a narrow intrinsic distribution. There is\nno consistent or statistically significant tendency for the highest\namplitude pulse in each burst to be wider or narrower when the burst\nis harder or softer, as measured using fluence.\n\n\\begin{deluxetable}{crlrlrl}\n\\tablecaption{Correlations Between Total Burst Count Fluence Hardness Ratio and (a) Pulse Widths, (b) Intervals Between Two Highest Amplitude Pulses, and (c) Total Burst Count Fluences for Highest Amplitude Pulse(s) in Each Burst. \\label{tab:hrtareavswdttarea}}\n\\tablehead{\n\\colhead{Energy} & \\multicolumn{2}{c}{(a) Width} & \\multicolumn{2}{c}{(b) Interval} & \\multicolumn{2}{c}{(c) Count Fluence} \\\\\n\\colhead{Channels} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$r_{s}$} & \\colhead{Prob.}}\n\\startdata\n2 / 1 & 0.02 & 0.84 & -0.10 & 0.36 & -0.01 & 0.88 \\\\\n3 / 2 & -0.22 & 0.0078 & -0.07 & 0.52 & 0.00 & 0.98 \\\\\n4 / 3 & 0.10 & 0.42 & -0.23 & 0.19 & 0.21 & 0.084 \\\\\n\\enddata\n\\end{deluxetable}\n\nTable~\\ref{tab:hrareafwhmarea}, columns~(a) show the correlations\nbetween pulse count fluence hardness ratios and pulse widths within\nbursts. In channels~1 and 2, more bursts show negative correlations\nbetween the two quantities, \\emph{i.e.} longer duration pulses tend to\nhave softer spectra, as measured using count fluence, and this effect,\nwhich may be statistically significant, indicates the presence of an\nintrinsic correlation. There are no statistically significant effects\nbetween channels~2 and 3 or between channels~3 and 4.\n\n\\begin{deluxetable}{crlrl}\n\\tablecaption{Correlations Between Pulse Count Fluence Hardness Ratio and (a) Pulse Width and (b) Count Fluence Within Bursts. \\label{tab:hrareafwhmarea}}\n\\tablehead{\n\\colhead{Energy} & \\multicolumn{2}{c}{(a) Width} & \\multicolumn{2}{c}{(b) Count Fluence} \\\\\n\\colhead{Channels} & \\colhead{\\% Pos. Corr.} & \\colhead{Binom. Prob.} & \\colhead{\\% Pos. Corr.} & \\colhead{Binom. Prob.}}\n\\startdata\n2 / 1 & 52.5/83 = 63\\% & 0.016 & 51.5/83 = 62\\% & 0.028 \\\\\n3 / 2 & 47.5/95 = 50\\% & 1.0 & 47/95 = 49\\% & 0.49 \\\\\n4 / 3 & 18.5/33 = 56\\% & 0.49 & 20/33 = 66\\% & 0.61 \\\\\nAll & 118.5/211 = 56\\% & \\nodata & 118.5/211 = 56\\% & \\nodata \\\\\n\\enddata\n\\end{deluxetable}\n\nTable~\\ref{tab:hrtareavswdttarea}, columns~(b) shows the correlations\nbetween the total burst count fluence hardness ratios and the\nintervals between the two highest amplitude pulse in each fit. In all\npairs of adjacent energy channels, the two highest amplitude pulses\nhave a slight tendency to be closer together when the burst is harder\n(as expected from cosmological effects,) but this is not statistically\nsignificant.\n\nTable~\\ref{tab:hrtareavswdttarea}, columns~(c) shows the correlations\nbetween the total burst count fluence hardness ratios and the total\nburst count fluence in each fit. There is no consistent or\nstatistically significant tendency for harder or softer bursts to\ncontain fewer or more counts.\n\nTable~\\ref{tab:hrareafwhmarea}, columns~(b) shows the correlations\nbetween pulse count fluence hardness ratios and pulse count fluences\nwithin bursts. The pulse count fluences are summed over the two\nadjacent energy channels that the hardness ratios are taken between.\nIn channels~1 and 2, more bursts show negative correlations,\n\\emph{i.e.} higher fluence pulses tend to have softer spectra, but\nagain, this intrinsic effect appears weak, and there is no significant\neffect in the other pairs of energy channels.\n\n\\emph{In summary, there seems to be little intrinsic correlation\nbetween the spectra, as measured by hardness ratio, and other pulse\ncharacteristics between bursts and among pulses. There may be weak\n(statistically not very significant) evidence for trends expected from\ncosmological redshift effects.}\n\n\\subsection{Time Evolution of Pulse Characteristics Within Bursts}\n\nOne class of correlations between pulse characteristics within bursts\nare those between the pulse peak time and other pulse characteristics.\nThese indicate whether certain pulse characteristics tend to evolve in\na particular way during the course of a burst. Again, we have used\nthe method described in the previous section, calculating the Spearman\nrank-order correlation coefficients for the individual bursts, and\ntesting the observed numbers of bursts with positive and negative\ncorrelations using the binomial distribution.\n\n\\subsubsection{Pulse Asymmetry Ratios}\n\nTable~\\ref{tab:rdfwhmtmax}, columns~(a) show the number and fraction\nof bursts (in each channel) where there is a negative correlation\nbetween the pulse asymmetry ratio $\\sigma_{r}/\\sigma_{d}$ and peak\ntime, \\emph{i.e.}, the pulse asymmetry decreases with time. Fits for\nwhich the calculated Spearman rank-order correlation coefficient was\n0, indicating no correlation, were counted as half for decreasing and\nhalf for increasing in order to calculate, using the binomial\ndistribution, the probability of this occurring randomly if pulse\namplitudes within bursts are equally likely to increase as to decrease\nwith time. The probability was not calculated for all energy channels\ncombined, because fits to the same burst in different energy channels\ncannot be considered independent, so the binomial distribution cannot\nbe used.\n\nPulse asymmetry ratios more often decrease than increase with time\nduring bursts, except in energy channel~4, which has the fewest\npulses. This effect appears to be statistically significant in\nchannel~3, and possibly channels~1 and 2. The fits to simulations\n(See Table~\\ref{tab:sim_rdtmax}) show no tendency for pulse\nasymmetries to increase or decrease within bursts. This indicates\nthat the observed tendency for pulse asymmetry ratios to decrease with\ntime within actual bursts does not arise from selection effects in the\npulse-fitting procedure, so that any tendency would be intrinsic to\ngamma-ray bursts.\n\n\\begin{deluxetable}{crlrl}\n\\tablecaption{Correlations Between (a) Pulse Asymmetry Ratio and (b) Width and Pulse Peak Time Within Bursts. \\label{tab:rdfwhmtmax}}\n\\tablehead{\n\\colhead{Energy} & \\multicolumn{2}{c}{(a) $\\sigma_{r} / \\sigma_{d}$} & \\multicolumn{2}{c}{(b) Width} \\\\\n\\colhead{Channel} & \\colhead{\\% Decreasing} & \\colhead{Binom. Prob.} & \\colhead{\\% Decreasing} & \\colhead{Binom. Prob.}}\n\\startdata\n1 & 61.5/94 = 66\\% & 0.0028 & 47.5/94 = 51\\% & 0.92 \\\\\n2 & 66.5/109 = 61\\% & 0.022 & 60/109 = 55\\% & 0.29 \\\\\n3 & 81/116 = 70\\% & \\e{1.9}{-5} & 64/116 = 55\\% & 0.27 \\\\\n4 & 16/35 = 45\\% & 0.61 & 23.5/35 = 67\\% & 0.043 \\\\\nAll & 225/354 = 64\\% & \\nodata & 195/354 = 55\\% & \\nodata \\\\\n\\enddata\n\\end{deluxetable}\n\n\\subsubsection{Pulse Rise and Decay Times and Pulse Widths}\n\nWhen we examine the evolution of the rise and decay times separately,\ninstead of their ratios, and the evolution of the pulse widths, we\nfind that there is a nearly equal and opposite trend of decreasing\nrise times $\\sigma_{r}$ and increasing decay times $\\sigma_{d}$ as the\nburst progresses. This gives rise to the evolution of pulse asymmetry\nratios described above, although the statistical significance of the\nevolution of rise times and decay time are weaker than for the pulse\nasymmetry ratios. The decrease in rise times is possibly a slightly\nstronger effect than the increase in decay times. However, the\ncombined effect of these two trends is that there appears to be no\nstatistically significant evolution of pulse widths. (See\nTable~\\ref{tab:rdfwhmtmax}, columns~(b).) This is in agreement with\nthe results of \\cite{ramirez-ruiz:1999,ramirez-ruiz:1999b}, who found\nno evidence that pulse widths increase or decrease with time when\nfitting a power-law time dependence, using a small sample of complex\nbursts selected from the bright, long bursts fitted by\n\\cite{norris:1996}.\n\n\\subsubsection{Spectra}\n\nIt has been previously reported that bursts tend to show a\nhard-to-soft spectral evolution, which we can test by seeing how the\nhardness ratios of individual pulses vary with time.\nTable~\\ref{tab:hramphrareatmax}, columns~(a) show that the pulse\namplitude hardness ratios have a slight tendency to decrease with time\nduring bursts between all three pairs of adjacent energy channels.\nHowever, with the numbers of available bursts that are composed of\nmultiple pulses in adjacent energy channels, this tendency is\nstatistically insignificant.\n\n\\begin{deluxetable}{crlrl}\n\\tablecaption{Correlations Between (a) Pulse Amplitude and (b) Count Fluence Hardness Ratios and Pulse Peak Time Within Bursts. \\label{tab:hramphrareatmax}}\n\\tablehead{\n\\colhead{Energy} & \\multicolumn{2}{c}{(a) Amplitude HR} & \\multicolumn{2}{c}{(b) Count Fluence HR} \\\\\n\\colhead{Channels} & \\colhead{\\% Decreasing} & \\colhead{Binom. Prob.} & \\colhead{\\% Decreasing} & \\colhead{Binom. Prob.}}\n\\startdata\n2 / 1 & 46.5/83 = 56\\% & 0.27 & 42.5/83 = 51\\% & 0.83 \\\\\n3 / 2 & 54.5/95 = 57\\% & 0.15 & 61/95 = 64\\% & 0.0056 \\\\\n4 / 3 & 18.5/33 = 56\\% & 0.48 & 13/33 = 39\\% & 0.22 \\\\\nAll & 119.5/211 = 57\\% & \\nodata & 116.5/211 = 55\\% & \\nodata \\\\\n\\enddata\n\\end{deluxetable}\n\n\\subsubsection{Pulse Count Fluences}\n\nWhen we consider the time evolution of the pulse count fluence\nhardness ratios within bursts, we find no tendency for the hardness\nratio of energy channel~2 to channel~1 to increase or decrease, a\npossibly significant tendency for the hardness ratio of energy\nchannel~3 to 2 to decrease with time, and a statistically\ninsignificant tendency for the hardness ratio of channel~4 to 3 to\nincrease with time. (See Table~\\ref{tab:hramphrareatmax},\ncolumns~(b).)\n\n\\subsubsection{Other Pulse Characteristics}\n\nWe have conducted similar tests for other pulse characteristics and\nfound that none show any tendencies to increase or decrease with time\nwithin bursts that are clearly statistically significant\n\\citep{lee:thesis}. These pulse characteristics are the pulse\namplitude, the peakedness parameter $\\nu$, and the pulse count\nfluence; \\emph{e.g.}, we find no tendency for later pulses within a\nburst to be stronger or weaker, than earlier pulses.\n\n\\emph{In summary, we find no significant correlations between the peak\ntimes of pulses in bursts and any other pulse characteristics except\npossibly the pulse asymmetry ratio, so that the pulses appear to\nresult from random and independent emission episodes.}\n\n\\section{Discussion}\n\\label{sec:discuss}\n\nDecomposing burst time profiles into a superposition of discrete\npulses gives a compact representation that appears to contain their\nimportant features, so this seems to be a useful approach for\nanalyzing their characteristics. Our pulse decomposition analysis\nconfirms a number of previously reported properties of gamma-ray burst\ntime profiles using a larger sample of bursts with generally finer\ntime resolution than in prior studies. These properties include\ntendencies for the individual pulses comprising bursts to have shorter\nrise times than decay times; for the pulses to have shorter durations\nat higher energies; and for the pulses to peak earlier at higher\nenergies, which is sometimes described as a hard-to-soft spectral\nevolution of individual pulses.\n\nPulse rise times tend to decrease during the course of a burst, while\npulse decay times tend to increase. When examining pulse widths, or\ndurations, these two effects nearly balance each other; the apparent\ntendency for pulse widths to decrease during the course of a burst\nappears to be statistically insignificant. The ratios of pulse rise\ntimes to decay times tend to decrease during the course of a burst.\nThe evolution of pulse asymmetry ratios does not arise from selection\neffects in the pulse-fitting procedure, so it is most likely intrinsic\nto the bursters.\n\nNo other pulse characteristics show any time evolution within bursts,\nalthough it is possible that there is non-monotonic evolution; for\nexample, a pulse characteristic may tend to be greater at the\nbeginning and end of a burst and smaller in the middle, and the tests\nused here wouldn't be sensitive to this. In particular, it doesn't\nappear that either pulse amplitudes or pulse count fluences have any\ntendency to increase or decrease during the course of a burst. Also,\nlater pulses in a burst don't tend to be spectrally harder or softer\nthan earlier pulses, although there is spectral softening\n\\emph{within} most pulses. The spectra of pulses within a burst also\ndon't appear to be harder or softer for stronger or weaker pulses, or\nfor longer or shorter duration pulses.\n\nOne may therefore conclude that the pulses in a burst arise from\nrandom and independent emission episodes such as those expected in the\ninternal episodic shock model rather than the external shock models\nwhere the presence of distinguishable pulses must be attributed to\ninhomogeneities in the interaction of the blast wave shock and the\nclumpy interstellar medium.\n\nWhen examining similar correlations between the attributes of some\ncharacteristic pulses from burst to burst, we find some weak and\ntantalizing evidence which may be due to cosmological redshift\neffects. In the accompanying paper \\cite{lee:2000b} we describe the\ncorrelation studies which can distinguish between trends due to\ncosmological redshifts and intrinsic trends.\n\n\\acknowledgments\n\nWe thank Jeffrey Scargle and Jay Norris for many useful discussions.\nThis work was supported in part by Department of Energy contract\nDE--AC03--76SF00515.\n\n\\appendix\n\n\\section{Appendix: Testing for Selection Effects}\n\nThere are a number of ways in which the pulse-fitting procedure may\nintroduce selection effects into correlations between pulse\ncharacteristics. One is that the errors in the different fitted pulse\nparameters may be correlated. Another is that the pulse-fitting\nprocedure may miss some pulses by not identifying them above the\nbackground noise. Still another cause of selection effects is that\noverlapping pulses may be identified as a single broader pulse.\n\nIn order to determine the degree of importance of these selection\neffects, we have generated a sample of artificial burst time profiles\nusing the pulse model with randomly generated but known pulse\nparameters, fitted the simulated bursts using the same procedure used\nfor actual burst data, and compared the simulated and fitted pulse\ncharacteristics~\\citep{lee:thesis}.\n\n\\subsection{Numbers of Bursts and Pulses}\n\nA total of 286 bursts were generated, with only one energy channel for\neach burst. For many of these, the limit of $2^{20}$ counts was\nreached before the 240 second limit, which almost never occurred in\nthe actual BATSE TTS data. These simulated bursts contained a total\nof 2671 pulses that had peak times before the limits of $2^{20}$\ncounts and 240 seconds, while the fits to the simulated bursts\ncontained a total of only 1029 pulses. Of these, 223 of the simulated\nbursts and 198 of the fits to the simulations contained more than one\npulse. (See Figure~\\ref{sim_npulse} and Table~\\ref{tab:sim_npulse}.)\nNote that in the fits to actual BATSE data, the largest number of fits\ncontaining more than one pulse was 116 for energy channel~3, so that\nthe simulated data set is larger. Figure~\\ref{fitvssim} shows the\nnumber of pulses fitted versus the number of pulses originally\ngenerated for each simulated bursts. It shows that the greatest\ndifferences between the the fitted and the simulated numbers of pulses\ntend to occur in the most complex bursts. Figure~\\ref{sim_rdnp}\ncompares the numbers of pulses per fit between the simulations and the\nfits to simulations. Most (54\\%) of the fits to simulated bursts\ncontain fewer pulses than the initial simulations, and for nearly all\nof the remaining simulated bursts, the number of pulses are the same\nfor the initial simulations and the fits to simulations. The fits to\nsimulations have a mean of 15 fewer pulses than the initial\nsimulations, and a median of 1 fewer pulse. The fits to simulations\nhave a geometric mean of 0.63 times as many pulses as the initial\nsimulations, and a mean of 0.80 times as many pulses.\n\n\\begin{deluxetable}{crrrr}\n\\tablecaption{Characteristics of Distribution of Number of Pulses in Simulations. \\label{tab:sim_npulse}}\n\\tablehead{\n\\colhead{} & \\colhead{Median No.} & \\colhead{Mean No.} & \\colhead{Max. No.} & \\colhead{\\% Single} \\\\\n\\colhead{} & \\colhead{of Pulses} & \\colhead{of Pulses} & \\colhead{of Pulses} & \\colhead{Pulse}}\n\\startdata\nSimulation & 3 & 9.3 & 126 & 62/286 = 22\\% \\\\\nFit to Sim. & 2 & 3.6 & 19 & 88/286 = 31\\% \\\\\n\\enddata\n\\end{deluxetable}\n\n\\begin{figure}\\plotone{f11.eps}\\caption{Distribution of number of pulses in initial simulations (solid histogram) and in the results of the fits to the simulated data (dashed histogram). \\label{sim_npulse}}\n\\end{figure}\n\n\\begin{figure}\\plotone{f12.eps}\\caption{Number of pulses obtained from fits to the simulations versus number in the initial simulations. Note that the\nselection effect of the fitting procedure is more pronounced in bursts\nwith larger numbers of pulses. \\label{fitvssim}}\n\\end{figure}\n\n\\begin{figure}\\plotone{f13.eps}\\caption{(Left) Distribution of differences between\nnumbers of pulses from initial simulated bursts to fits to simulated\nbursts. A small number of bursts have many fewer pulses in the fits\nto simulations than in the initial simulations. (Right) Distribution\nof ratios of numbers of pulses from initial simulated bursts to fits\nto simulated bursts. \\label{sim_rdnp}}\n\\end{figure}\n\n\\subsection{Brightness Measures of Simulated Pulses}\n%\\subsection{Pulse Amplitudes}\n\nFigure~\\ref{sim_amp} shows the distribution of pulse amplitudes in the\noriginal simulations and in the fits to simulations. It shows that\nthe fitting procedure has a strong tendency to miss low amplitude\npulses. However, if we compare this with Figure~\\ref{amp}, we see\nthat in the fits to actual BATSE bursts, the fitting procedure found\npulses with considerably lower amplitudes than it found in the fits to\nsimulated bursts.\n\n\\begin{figure}\\plotone{f14.eps}\\caption{Distribution of pulse amplitudes for all pulses from all bursts in initial simulations (solid histogram) and in the results of the fits to the simulated data (dashed histogram). \\label{sim_amp}}\n\\end{figure}\n\nFigure~\\ref{sim_npvsamp} shows the number of pulses in each burst\nplotted against the amplitudes of all of the pulses comprising each\nfit. In the simulations, there are no correlations between pulse\namplitudes and the number of pulses in the time profile, because the\npulse amplitudes were generated independently of the number of pulses\nin each burst. In the fits to the simulations, pulse amplitudes tend\nto be higher in bursts containing more pulses. This must result from\nthe selection effect discussed in Section~\\ref{sec:amp}; it is easier\nto identify more pulses when they are stronger.\nTable~\\ref{tab:sim_npvsafw}, columns~(a) shows that even though there\nis no correlation between pulse amplitudes and the number of pulses\nfor the initial simulated data, the fitting procedure introduces a\nstrong positive correlation between these quantities; the tendency to\nmiss low amplitude pulses is greater in more complex bursts.\n\n\\begin{figure}\\plotone{f15.eps}\\caption{Number of pulses per fit versus pulse amplitudes of all pulses. \\label{sim_npvsamp}}\n\\end{figure}\n\n\\begin{deluxetable}{crlrlrl}\n\\tablecaption{Correlation Between Number of Pulses per Burst and (a) Amplitudes, (b) Count Fluences, and (c) Widths of All Pulses in Simulated Bursts. \\label{tab:sim_npvsafw}}\n\\tablehead{\n\\colhead{} & \\multicolumn{2}{c}{(a) Amplitude} & \\multicolumn{2}{c}{(b) Count Fluence} & \\multicolumn{2}{c}{(c) Width} \\\\\n\\colhead{} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$r_{s}$} & \\colhead{Prob.}}\n\\startdata\nSimulation & -0.04 & 0.042 & -0.02 & 0.31 & 0.01 & 0.76 \\\\\nFit to Sims. & 0.22 & \\e{7.1}{-13} & 0.11 & 0.00068 & -0.03 & 0.36 \\\\\n\\enddata\n\\end{deluxetable}\n\n%\\subsection{Count Fluences}\n\nFigure~\\ref{sim_area} shows the distribution of pulse count fluences\nin the original simulations and in the fits to simulations. It shows\nthat the fitting procedure has a strong tendency to miss pulses with\nlow count fluences, similar to what we have seen for low amplitude\npulses.\n\n\\begin{figure}\\plotone{f16.eps}\\caption{Distribution of pulse count fluences for all pulses from all bursts in initial simulations (solid histogram) and in the results of the fits to the simulated data (dashed histogram). \\label{sim_area}}\n\\end{figure}\n\nFigure~\\ref{sim_npvsarea} and Table~\\ref{tab:sim_npvsafw}, columns~(b)\ncompare the number of pulses in each time profile with the count\nfluences of the individual pulses. They show no tendency for pulses\nto contain fewer or more counts in bursts with more pulses, in either\nthe initial simulations (by design) or in the fits to simulations.\nUnlike pulse amplitudes, the tendency to miss low count fluence pulses\nappears to be independent of burst complexity. This differs from the\nresults seen in the fits to actual bursts, where bursts containing\nmore pulses tended to have pulses with lower count fluences. (See\nFigure~\\ref{npvsarea} and Table~\\ref{tab:npvsafw}, columns~(b).) This\nmay explain why the $2^{20}$ count limit for the TTS data was\nfrequently reached before the 240 second time limit in the simulated\nbursts, but rarely in the actual bursts; the total count fluence\nincreases linearly with the number of pulses in the simulated bursts,\nbut less rapidly in the actual BATSE bursts.\n\n\\begin{figure}\\plotone{f17.eps}\\caption{Number of pulses per burst versus count fluences of all pulses. \\label{sim_npvsarea}}\n\\end{figure}\n\n\\subsection{Pulse Widths}\n\nFigure~\\ref{sim_fwhm} shows the distribution of pulse widths in the\noriginal simulations and in the fits to simulations. The pulses in\nthe fits to simulations tend to be slightly longer in duration than in\nthe original simulations, but applying the Kolmogorov-Smirnov test to\nthe two distributions show that they are not significantly different;\nthe probability that they are the same distribution is 0.39. This\nagrees with what we have seen in Figures~\\ref{sim_amp} and\n\\ref{sim_area}, that the selection effects of the fitting procedure\nfor pulse amplitudes and for pulse count fluences are similar.\n\n\\begin{figure}\\plotone{f18.eps}\\caption{Distribution of pulse widths for all pulses from all bursts in initial simulations (solid histogram) and in the results of the fits to the simulated data (dashed histogram). \\label{sim_fwhm}}\n\\end{figure}\n\nFigure~\\ref{sim_npvsfwhm} and Table~\\ref{tab:sim_npvsafw}, columns~(c)\ncompare the number of pulses in each time profile with the widths of\nthe individual pulses. They show no tendency for pulses to be wider\nor narrower in bursts with more pulses, in either the simulations or\nthe fits to the simulations.\n\n\\begin{figure}\\plotone{f19.eps}\\caption{Number of pulses per burst versus widths of all pulses. \\label{sim_npvsfwhm}}\n\\end{figure}\n\n\\subsection{Time Evolution of Pulse Characteristics Within Bursts}\n\nIn the fits to actual BATSE data, it was found that pulse asymmetry\nratios tended to decrease over the course of a burst. (See\nTable~\\ref{tab:rdfwhmtmax}.) Table~\\ref{tab:sim_rdtmax} shows the\ncorrelations between pulse asymmetry ratio and peak times within\nbursts for the simulations and the fits to simulations. It shows no\ntendency for positive or negative correlations in either the\nsimulations or the fits to simulations.\n\n\\begin{deluxetable}{crl}\n\\tablecaption{Correlations Between Pulse Asymmetry Ratio and Pulse Peak Time Within Simulated Bursts. \\label{tab:sim_rdtmax}}\n\\tablehead{\n\\colhead{} & \\colhead{\\% Decreasing} & \\colhead{Binom. Prob.}}\n\\startdata\nSimulation & 92.5/223 = 41\\% & 0.016 \\\\\nFit to Sim. & 103/198 = 52\\% & 0.57 \\\\\n\\enddata\n\\end{deluxetable}\n\n{\n%\\bibliographystyle{abbrvnat}\n%\\bibstyle@aa\n%\\bibliographystyle{apj}\n%\\bibliography{apj-jour,alee}\n\\begin{thebibliography}{17}\n\\expandafter\\ifx\\csname natexlab\\endcsname\\relax\\def\\natexlab#1{#1}\\fi\n\n\\bibitem[{Donoho(1992)}]{donoho:denoise}\nDonoho, D.~L. 1992, De-Noising via Soft Thresholding, Department of Statistics\n Technical Report 409, Stanford University, Stanford, CA\n\n\\bibitem[{Fenimore \\& Bloom(1995)}]{fenimore:1995b}\nFenimore, E. \\& Bloom, J. 1995, \\apj, 453, 25\n\n\\bibitem[{Kouveliotou {et~al.}(1996)Kouveliotou, Briggs, \\&\n Fishman}]{huntsville:3}\nKouveliotou, C., Briggs, M.~F., \\& Fishman, G.~J., eds. 1996, Gamma-Ray Bursts:\n 3rd Huntsville Symposium, AIP Conf. Proc. No. 384 (Woodbury, NY: AIP)\n\n\\bibitem[{Kouveliotou {et~al.}(1993)}]{kouveliotou:1993}\nKouveliotou, C. {et~al.} 1993, \\apjl, 413, L101\n\n\\bibitem[{Lee(2000)}]{lee:thesis}\nLee, A. 2000, PhD thesis, Stanford University, Stanford, CA, (SLAC--R--553)\n\n\\bibitem[{Lee {et~al.}(2000)Lee, Bloom, \\& Petrosian}]{lee:2000b}\nLee, A., Bloom, E.~D., \\& Petrosian, V. 2000, \\apj, submitted,\n (SLAC--PUB--8365)\n\n\\bibitem[{Lee {et~al.}(1996)Lee, Bloom, \\& Scargle}]{lee:1996}\nLee, A., Bloom, E.~D., \\& Scargle, J.~D. 1996, in Gamma-Ray Bursts: 3rd\n Huntsville Symposium, ed. C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP\n Conf. Proc. No. 384 (Woodbury, NY: AIP), 47--51\n\n\\bibitem[{Lee {et~al.}(1998)Lee, Bloom, \\& Scargle}]{lee:1998}\nLee, A., Bloom, E.~D., \\& Scargle, J.~D. 1998, in Gamma-Ray Bursts: 4th\n Huntsville Symposium, ed. C.~A. Meegan, R.~D. Preece, \\& T.~M. Koshut, AIP\n Conf. Proc. No. 428 (Woodbury, NY: AIP), 261--265\n\n\\bibitem[{Link {et~al.}(1993)Link, Epstein, \\& Priedhorsky}]{link:1993}\nLink, B., Epstein, R.~I., \\& Priedhorsky, W.~C. 1993, \\apjl, 408, L81\n\n\\bibitem[{Meegan(1991)}]{batse:flight}\nMeegan, C.~A. 1991, {BATSE} Flight Software User's Manual, NASA/MSFC,\n Huntsville, AL\n\n\\bibitem[{Meegan {et~al.}(1996{\\natexlab{a}})}]{meegan:1996}\nMeegan, C.~A. {et~al.} 1996{\\natexlab{a}}, in Gamma-Ray Bursts: 3rd Huntsville\n Symposium, ed. C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP Conf.\n Proc. No. 384 (Woodbury, NY: AIP), 291--300\n\n\\bibitem[{Meegan {et~al.}(1996{\\natexlab{b}})}]{batse:3b}\nMeegan, C.~A. {et~al.} 1996{\\natexlab{b}}, \\apjs, 106, 65\n\n\\bibitem[{Norris {et~al.}(1986)}]{norris:1986}\nNorris, J.~P. {et~al.} 1986, \\apj, 301, 213\n\n\\bibitem[{Norris {et~al.}(1996)}]{norris:1996}\n---. 1996, \\apj, 459, 393\n\n\\bibitem[{Ramirez-Ruiz \\& Fenimore(1999{\\natexlab{a}})}]{ramirez-ruiz:1999b}\nRamirez-Ruiz, E. \\& Fenimore, E. 1999{\\natexlab{a}}, \\apj, submitted,\n (astro-ph/9910273)\n\n\\bibitem[{Ramirez-Ruiz \\& Fenimore(1999{\\natexlab{b}})}]{ramirez-ruiz:1999}\n---. 1999{\\natexlab{b}}, \\aaps, 138, 521\n\n\\bibitem[{Stern {et~al.}(1997)Stern, Poutanen, \\& Svensson}]{stern:1997b}\nStern, B., Poutanen, J., \\& Svensson, R. 1997, \\apjl, 489, L41\n\n\\end{thebibliography}\n}\n\n\\end{document}\n"
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{
"name": "astro-ph0002217.extracted_bib",
"string": "\\begin{thebibliography}{17}\n\\expandafter\\ifx\\csname natexlab\\endcsname\\relax\\def\\natexlab#1{#1}\\fi\n\n\\bibitem[{Donoho(1992)}]{donoho:denoise}\nDonoho, D.~L. 1992, De-Noising via Soft Thresholding, Department of Statistics\n Technical Report 409, Stanford University, Stanford, CA\n\n\\bibitem[{Fenimore \\& Bloom(1995)}]{fenimore:1995b}\nFenimore, E. \\& Bloom, J. 1995, \\apj, 453, 25\n\n\\bibitem[{Kouveliotou {et~al.}(1996)Kouveliotou, Briggs, \\&\n Fishman}]{huntsville:3}\nKouveliotou, C., Briggs, M.~F., \\& Fishman, G.~J., eds. 1996, Gamma-Ray Bursts:\n 3rd Huntsville Symposium, AIP Conf. Proc. No. 384 (Woodbury, NY: AIP)\n\n\\bibitem[{Kouveliotou {et~al.}(1993)}]{kouveliotou:1993}\nKouveliotou, C. {et~al.} 1993, \\apjl, 413, L101\n\n\\bibitem[{Lee(2000)}]{lee:thesis}\nLee, A. 2000, PhD thesis, Stanford University, Stanford, CA, (SLAC--R--553)\n\n\\bibitem[{Lee {et~al.}(2000)Lee, Bloom, \\& Petrosian}]{lee:2000b}\nLee, A., Bloom, E.~D., \\& Petrosian, V. 2000, \\apj, submitted,\n (SLAC--PUB--8365)\n\n\\bibitem[{Lee {et~al.}(1996)Lee, Bloom, \\& Scargle}]{lee:1996}\nLee, A., Bloom, E.~D., \\& Scargle, J.~D. 1996, in Gamma-Ray Bursts: 3rd\n Huntsville Symposium, ed. C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP\n Conf. Proc. No. 384 (Woodbury, NY: AIP), 47--51\n\n\\bibitem[{Lee {et~al.}(1998)Lee, Bloom, \\& Scargle}]{lee:1998}\nLee, A., Bloom, E.~D., \\& Scargle, J.~D. 1998, in Gamma-Ray Bursts: 4th\n Huntsville Symposium, ed. C.~A. Meegan, R.~D. Preece, \\& T.~M. Koshut, AIP\n Conf. Proc. No. 428 (Woodbury, NY: AIP), 261--265\n\n\\bibitem[{Link {et~al.}(1993)Link, Epstein, \\& Priedhorsky}]{link:1993}\nLink, B., Epstein, R.~I., \\& Priedhorsky, W.~C. 1993, \\apjl, 408, L81\n\n\\bibitem[{Meegan(1991)}]{batse:flight}\nMeegan, C.~A. 1991, {BATSE} Flight Software User's Manual, NASA/MSFC,\n Huntsville, AL\n\n\\bibitem[{Meegan {et~al.}(1996{\\natexlab{a}})}]{meegan:1996}\nMeegan, C.~A. {et~al.} 1996{\\natexlab{a}}, in Gamma-Ray Bursts: 3rd Huntsville\n Symposium, ed. C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP Conf.\n Proc. No. 384 (Woodbury, NY: AIP), 291--300\n\n\\bibitem[{Meegan {et~al.}(1996{\\natexlab{b}})}]{batse:3b}\nMeegan, C.~A. {et~al.} 1996{\\natexlab{b}}, \\apjs, 106, 65\n\n\\bibitem[{Norris {et~al.}(1986)}]{norris:1986}\nNorris, J.~P. {et~al.} 1986, \\apj, 301, 213\n\n\\bibitem[{Norris {et~al.}(1996)}]{norris:1996}\n---. 1996, \\apj, 459, 393\n\n\\bibitem[{Ramirez-Ruiz \\& Fenimore(1999{\\natexlab{a}})}]{ramirez-ruiz:1999b}\nRamirez-Ruiz, E. \\& Fenimore, E. 1999{\\natexlab{a}}, \\apj, submitted,\n (astro-ph/9910273)\n\n\\bibitem[{Ramirez-Ruiz \\& Fenimore(1999{\\natexlab{b}})}]{ramirez-ruiz:1999}\n---. 1999{\\natexlab{b}}, \\aaps, 138, 521\n\n\\bibitem[{Stern {et~al.}(1997)Stern, Poutanen, \\& Svensson}]{stern:1997b}\nStern, B., Poutanen, J., \\& Svensson, R. 1997, \\apjl, 489, L41\n\n\\end{thebibliography}"
}
] |
astro-ph0002218
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Intrinsic and Cosmological Signatures in Gamma-Ray Burst Time Profiles: Time Dilation
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[
{
"author": "Andrew Lee and Elliott D. Bloom"
}
] |
The time profiles of many gamma-ray bursts consist of distinct pulses, which offers the possibility of characterizing the temporal structure of these bursts using a relatively small set of pulse shape parameters. We have used a pulse decomposition procedure to analyze the Time-to-Spill (TTS) data for all bursts observed by BATSE up through trigger number 2000, in all energy channels for which TTS data is available. We obtain amplitude, rise and decay timescales, a pulse shape parameter, and the fluences of individual pulses in all of the bursts. We investigate the correlations between brightness measures (amplitude and fluence) and timescale measures (pulse width and separation) which may result from cosmological time dilation of bursts, or from intrinsic properties of burst sources or from selection effects. The effects of selection biases are evaluated through simulations. The correlations between these parameters among pulses within individual bursts give a measure of the intrinsic effects while the correlations among bursts could result both from intrinsic and cosmological effects. We find that timescales tend to be shorter in bursts with higher peak fluxes, as expected from cosmological time dilation effects, but also find that there are non-cosmological effects contributing to this inverse correlation. We find that timescales tend to be longer in bursts with higher total fluences, contrary to what is expected from cosmological effects. We also find that peak fluxes and total fluences of bursts are uncorrelated, indicating that they cannot both be good distance indicators for bursts.
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[
{
"name": "ms.tex",
"string": "\\documentclass[preprint]{aastex}\n\\usepackage{epsfig}\n\\usepackage{amstex,amssymb}\n%\\usepackage{natbib}\n%\\citestyle{aa}\n\n\\newcommand{\\e}[2]{\\mbox{$#1 \\times 10^{#2}$}}\t% Scientific notation\n\\newcommand{\\?}{\\discretionary{/}{}{/}}\t\t% Break URLs without hyphens\n\n\\begin{document}\n\n\\title{Intrinsic and Cosmological Signatures in Gamma-Ray Burst Time\nProfiles: Time Dilation}\n\n\\author{Andrew Lee and Elliott D. Bloom}\n\\affil{Stanford Linear Accelerator Center, Stanford University,\nStanford, California 94309}\n\\makeatletter\n\\email{alee@slac.stanford.edu and elliott@slac.stanford.edu}\n\\makeatother\n\n%\\and\n\n\\author{Vah\\'{e} Petrosian}\n\\affil{Center for Space Science and Astrophysics, Varian 302c,\nStanford University, Stanford, CA 94305-4060 \\altaffilmark{1}}\n\\makeatletter\n\\email{vahe@astronomy.stanford.edu}\n\\makeatother\n\n\\altaffiltext{1}{Also Astronomy Program and Department of Physics.}\n\n\\begin{abstract}\nThe time profiles of many gamma-ray bursts consist of distinct pulses,\nwhich offers the possibility of characterizing the temporal structure\nof these bursts using a relatively small set of pulse shape\nparameters. We have used a pulse decomposition procedure to analyze\nthe Time-to-Spill (TTS) data for all bursts observed by BATSE up\nthrough trigger number 2000, in all energy channels for which TTS data\nis available. We obtain amplitude, rise and decay timescales, a pulse\nshape parameter, and the fluences of individual pulses in all of the\nbursts. We investigate the correlations between brightness measures\n(amplitude and fluence) and timescale measures (pulse width and\nseparation) which may result from cosmological time dilation of\nbursts, or from intrinsic properties of burst sources or from\nselection effects. The effects of selection biases are evaluated\nthrough simulations. The correlations between these parameters among\npulses within individual bursts give a measure of the intrinsic\neffects while the correlations among bursts could result both from\nintrinsic and cosmological effects. We find that timescales tend to\nbe shorter in bursts with higher peak fluxes, as expected from\ncosmological time dilation effects, but also find that there are\nnon-cosmological effects contributing to this inverse correlation. We\nfind that timescales tend to be longer in bursts with higher total\nfluences, contrary to what is expected from cosmological effects. We\nalso find that peak fluxes and total fluences of bursts are\nuncorrelated, indicating that they cannot both be good distance\nindicators for bursts.\n\\end{abstract}\n\n\\keywords{gamma rays: bursts---cosmology: theory}\n\n\\section{Introduction}\n\nMany of the signatures of the cosmological time dilation and the\nradiation mechanisms of gamma-ray bursts (GRBs) are hidden in the\ntemporal and spectral characteristics of GRBs. The subject of this\npaper is the analysis of the temporal properties of the bursts, and\nthe correlations between intensities and timescales. We use the BATSE\nTime-to-Spill (TTS) data, which can give much higher time resolution\nthan other forms of BATSE data for most bursts. The advantages and\nshortcomings of this data, our decomposition of the time profiles into\npulses, and the evolution of burst characteristics are described in\ngreater detail in the accompanying paper \\cite{lee:2000}. What\nfollows is a brief summary. (See also\n\\cite{lee:1996,lee:1998,lee:thesis}.)\n\nMany burst time profiles appear to be composed of a series of\ndiscrete, often overlapping, pulses, often with a \\emph{fast rise,\nexponential decay} (FRED) shape~\\citep{norris:1996}. The different\npulses may represent emission from distinct subevents within the\ngamma-ray burst source. Therefore, it may be useful to decompose\nburst time profiles in terms of individual pulses, each of which rises\nfrom background to a maximum and then decays back to background\nlevels. We have analyzed gamma-ray burst time profiles by\nrepresenting them in terms of a finite number of pulses, each of which\nis described by a small number of parameters.\n\nWe have used the phenomological pulse model of \\cite{norris:1996} to\ndecompose gamma-ray burst time profiles into distinct pulses. In this\nmodel, each pulse is described by five parameters with the functional\nform\n\\begin{equation}\nI(t)\\ =\\ A \\exp{\\left(-\\left\\vert\\frac{t\n - t_{\\text{max}}}{\\sigma_{r,d}}\\right\\vert^{\\nu}\\right)}\\ ,\n\\label{eq:pulse}\n\\end{equation}\nwhere $t_{\\text{max}}$ is the time at which the pulse attains its\nmaximum, $\\sigma_{r}$ and $\\sigma_{d}$ are the rise and decay times,\nrespectively, $A$ is the pulse amplitude, and $\\nu$\n(the~``peakedness'') gives the sharpness or smoothness of the pulse at\nits peak.\n\nWe have developed an interactive pulse-fitting program to perform this\npulse decomposition on the BATSE TTS data. and used this program to\nfit pulses to all gamma-ray bursts in the BATSE 3B\ncatalog~\\citep{batse:3b} up to trigger number 2000 in all of the four\nBATSE LAD energy channels for which TTS data is available and shows\ntime variation beyond the normal Poisson noise for the background. We\nfit each channel of each burst separately. We have obtained 574 fits\nfor 211 bursts, with a total of 2465 pulses.\n\nIn this paper, we focus on the possibility of distinguishing between\nintrinsic signatures in the temporal characteristics and those which\narise from their cosmological distribution. A prominent example of\nthis is the cosmological time dilation effect, which we expect to see\nsince some, and possibly all, gamma-ray bursts originate at\ncosmological distances.\n\nAll timescales in GRBs will be lengthened by a factor of $1 + z$ where\n$z$ is the redshift of the burst, as a result of cosmological time\ndilation~\\citep{paczynski:1992,piran:1992}. However, this seemingly\nstraightforward test is not simple. First of all, given the great\ndiversity in burst time profiles, it is difficult to decide which\ntimescale is most appropriate for this test. It seems unlikely that\nany particular timescale is approximately the same in all bursts, so\nwe expect to find time dilation as a statistical effect, rather than\nfor individual bursts.\n\nSecondly, redshifts are known only for a few bursts, so that for the\nvast majority of bursts we need to use another measure of distance or\nredshift. Most past analyses have used some measure of apparent GRB\nbrightness for this purpose with the tacit assumption that the\ncorresponding intrinsic brightness is a standard candle or has a very\nnarrow distribution.\n\nThe observed apparent brightnesses of bursts are generally measured\nusing either peak fluxes, which give the instantaneous intensity of\nbursts when they peak, or fluences, which measure the total output of\nbursts integrated over their entire durations. The brightness\nmeasures can also be divided another way, into photon measures and\nenergy measures. Thus, there are several different measures of the\napparent brightnesses of bursts. The BATSE burst catalogs give peak\nphoton fluxes and total energy fluences for bursts. The pulse-fitting\ndata presented here can be used to determine count fluxes and count\nfluences. Most previous work on the evidence for time dilation in\nburst time profiles has binned the bursts into two or three brightness\nclasses using the peak flux as a measure of brightness, and compared a\nmeasure of total burst duration these classes. Use of fluence as a\nbrightness measure has been promoted by \\cite{petrosian:1996} and\n\\cite{lloyd:1999}.\n\nIn this paper, we use a number of different timescale and brightness\nmeasures. We will describe their correlations using power laws.\nAlthough cosmological models generally predict more complex\nrelationships than a simple power law, it would be fruitless to\nattempt to fit anything more complex than a power law using the\npulse-fitting data, which appears to have a large intrinsic scatter.\nTo contrast the cosmological versus the intrinsic signatures, we\ncompare the relations or correlations between strengths and timescales\namong bursts, which should contain the signatures of cosmological time\ndilations, with the same correlations among pulses of individual\nbursts, which can only contain the intrinsic effects. It is likely\nthat some of these correlations are affected by selection effects in\nour fitting procedures. To investigate the importance of these, we\nhave carried out extensive simulations which are described in the\naccompanying paper \\cite{lee:2000}. We use the results of these\nsimulations to test whether or not the correlations we find are\nproperties of the bursts or are products of our procedures. In the\nnext section, we define the various timescales and burst strengths\nused in this analysis. The correlations relevant to the ``time\ndilation'' tests are discussed in Section~\\ref{sec:timedilation} and\nthe correlations between other quantities within bursts and among\nbursts are described in Section~\\ref{sec:othercorr}. In\nSection~\\ref{sec:discuss} we discuss the significance of these\ncorrelations.\n\nIt should be noted that many of the simulated bursts were affected by\na truncation that almost never occurred in the actual BATSE TTS data.\nThe TTS data is truncated at $2^{20}$ counts or 240 seconds, whichever\noccurs first. In nearly all of the actual bursts, the 240 second\nlimit is reached first, while in many of the the simulated bursts, the\n$2^{20}$ count limit is reached first. This truncation can shorten\nthe observed time intervals between the first and last pulses in a\nburst, and between the two highest amplitude pulses in a burst, but\nnot the observed pulse widths or the observed time intervals between\nconsecutive pulses. \\emph{Therefore, all discussions of the first two\nkinds of time intervals in simulated bursts will only consider\nsimulated bursts where no pulses were truncated by the $2^{20}$ count\nlimit.}\n\n\\section{Timescales and Intensities}\n\nWe now describe the characteristics used in our correlation studies\nand the selection and procedural biases associated with each of them.\n\n\\subsection{Intensities}\n\nWe use peak count rates and count fluences as measures of burst\nintensity or strength. For individual pulses, the peak count rate is\ngiven by the amplitude $A$ and the count fluence by\n\\begin{equation}\n\\mathcal{F} = A \\int_{-\\infty}^{\\infty}{I(t)dt} = A \\frac{\\sigma_{r} + \\sigma_{d}}{\\nu}\\Gamma\\left(\\frac{1}{\\nu}\\right) .\n\\label{eq:area}\n\\end{equation}\nwhere $\\Gamma$ is the gamma function. For a burst, on the other hand,\nthe peak count rate is $A_{\\text{max}}$, the largest amplitude of the\npulses in the burst, and the total count fluence is $\\mathcal{F} =\n\\sum{\\mathcal{F}_{i}}$, summed over all pulses.\n\n\\subsection{Time Intervals Between Pulses}\n\nThe most obvious timescale for individual pulses is the \\emph{pulse width},\nwhich is given by\n\\begin{equation}\nT_{f} = A (\\sigma_{r} + \\sigma_{d}) (-\\ln f)^{\\frac{1}{\\nu}} .\n\\label{eq:fwfm}\n\\end{equation}\nwhere $f$ is the fraction of the peak height at which the width is\nmeasured. and $\\nu$ is the ``peakedness'' parameter. In this paper,\nwe use the case $f = 1/2$, for which the width is the full width at\nhalf maximum (FWHM). We will discuss the correlations between pulse\nwidth and intensity measures in the next section. Here we consider\nsome other timescales, namely the \\emph{time intervals between\npulses}, which may also be characteristic of the gamma-ray production\nmechanisms. There are several possible choices of time intervals.\nWe'll examine the \\emph{intervals between consecutive pulses} first,\nwhich may have the following selection effect: Two pulses with short\nseparations between their peaks may have a large overlap, and thus be\nidentified as only one pulse. This will limit the shortest interval\nbetween pulses, introducing a selection bias. On the other hand, when\ntwo pulses have a long separation between them, additional smaller\npulses may be resolved between them that wouldn't be resolved if the\nseparation were smaller. This will limit the the longest intervals\nbetween consecutive pulses, introducing another selection bias.\n\nFigure~\\ref{sim_interval} shows the distributions of the intervals\nbetween the peak times $t_{\\text{max}}$ of adjacent pulses for the\nsimulations and the fits to simulations. It shows that the fitting\nprocedure identifies pulses with longer separations correctly, but\nmisses most pulses with shorter separations.\n\n\\begin{figure}\\plotone{f1.eps}\\caption{Distribution of intervals between peak times of adjacent pulses in initial simulations (solid histogram) and in the results of the fits to the simulated data (dashed histogram). Note that a large number of bursts with small separations are combined\nwith nearby stronger pulses. \\label{sim_interval}}\n\\end{figure}\n\nFigure~\\ref{npvsdt} shows the time intervals between consecutive\npulses for bursts with different numbers of pulses, as derived from\nour fits to the BATSE data and from the simulations. Note that here\nand in similar figures to follow, we show only data from channels~2\nand 3. In general, channels 1 and 4 show similar behavior, but\nresults from these channels have lower significance because these\nchannels contain fewer pulses. Table~\\ref{tab:npvsint}, columns~(a)\ngives the Spearman rank-order correlation coefficients $r_{s}$ between\nthese two quantities, and the probabilities that the observed\ncorrelations have occured by chance. These show that pulses tend to\nbe closer together in bursts with more pulses, in both the actual\nbursts, and in the simulated bursts and in the fits to simulated\nbursts. One selection effect that may contribute to this result in\nactual bursts is that more complex bursts may simply be bursts with\nstronger signal-to-noise ratios, which allows more pulses to be\nresolved within any given time interval. Our analysis of the\nsimulated bursts and the fits to the simulations show similar\nresults. this result is as expected, since pulse peak times were\ngenerated independently of each other and of the number of pulses per\nburst, so more complex bursts will tend to have more pulses in any\ngiven time interval. The correlation is weaker for the fits to\nsimulated bursts than for the original simulated bursts because the\nfitting procedure tends to miss pulses with shorter separations.\n\n\\begin{figure}\n\\epsfig{file=f2a.eps}\n\\epsfig{file=f2b.eps}\\caption{Number of pulses per burst versus intervals between adjacent pulses for BATSE energy channels~2\nand 3 (upper panels) and for initial simulated bursts and fits to\nthese bursts (lower panels). Similar results were obtained for\nchannels~1 and 4, which have much fewer pulses. \\label{npvsdt}}\n\\end{figure}\n\n\\begin{deluxetable}{crlrlrl}\n\\tablecaption{Correlation Between Number of Pulses per Burst and Intervals Between (a) Adjacent, (b) First and Last, and (c) Two Highest Amplitude Pulses. \\label{tab:npvsint}}\n\\tablehead{\n\\colhead{Energy} & \\multicolumn{2}{c}{(a) Adjacent} & \\multicolumn{2}{c}{(b) First to Last} & \\multicolumn{2}{c}{(c) Two Highest} \\\\\n\\colhead{Channel} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$r_{s}$} & \\colhead{Prob.}}\n\\startdata\n1 & -0.39 & \\e{1.8}{-14} & 0.53 & \\e{3.6}{-8} & -0.07 & 0.50 \\\\\n2 & -0.47 & \\e{3.0}{-33} & 0.50 & \\e{2.7}{-8} & -0.12 & 0.23 \\\\\n3 & -0.24 & \\e{1.6}{-10} & 0.56 & \\e{4.4}{-11} & 0.14 & 0.13 \\\\\n4 & -0.27 & \\e{8.0}{-5} & 0.52 & 0.0013 & -0.16 & 0.35 \\\\\nSim. & -0.80 & 0 & 0.55 & \\e{1.1}{-14} & 0.01 & 0.86 \\\\\nFits to Sim. & -0.35 & \\e{6.5}{-23} & 0.49 & \\e{6.2}{-10} & -0.10 & 0.22 \\\\\n\\enddata\n\\end{deluxetable}\n\nAnother time interval, \\emph{the interval between the peak times of\nthe first and last pulses} in a burst, might be expected to give a\ngood measure of the \\emph{total duration} of the burst. However, the\ndetermination of this interval can be greatly affected by whether or\nnot low amplitude pulses can be identified above background. This is\nessentially the same effect as the sensitivity of the $T_{90}$\ninterval to the signal-to-noise ratios of\nbursts~\\citep{norris:1996c,lee:1997}.\n\nFigure~\\ref{npvsdur} and columns~(b) of Table~\\ref{tab:npvsint}\ncompare the number of pulses in each burst with the time interval\nbetween the first and last pulses in each burst. They show that the\ntime intervals between the first and last pulse are greater in bursts\nwith more pulses, both in actual bursts, and in simulated bursts and\nfits to simulated bursts. In actual bursts, this may result from the\nselection effect described above; more complex bursts may simply have\nstronger signal-to-noise ratios, making it easier to identify earlier\nand later pulses. In the simulated bursts and the fits to simulated\nbursts, this is also as expected since the peak times of pulses were\ngenerated independently of the number of pulses in each burst.\n\n\\begin{figure}\n\\epsfig{file=f3a.eps}\n\\epsfig{file=f3b.eps}\\caption{Same as\nFigure~\\ref{npvsdt}, except number of pulses per burst versus interval\nbetween first and last pulse in each burst. \\label{npvsdur}}\n\\end{figure}\n\nA third time interval, the interval \\emph{between the peak times of\nthe two highest amplitude pulses} in a burst, may also represent a\ncharacteristic time scale for the entire burst. Determination of this\ninterval should be less affected by the selection effects that we have\nseen with the intervals between consecutive pulses. However, the\nidentification of the two highest pulses may be affected by whether a\nparticular structure in a burst is identified as a single pulse with\nlarge amplitude or as multiple overlapping pulses with smaller\namplitudes. The interval between the two highest amplitude pulses\nshould be less influenced by the selection effects in the fitting\nprocedure that affect the interval between the first and last pulses\nin a burst.\n\nFigure~\\ref{npvsint} and Table~\\ref{tab:npvsint}, columns~(c) show the\ncorrelations between the number of pulses in each burst and the time\nintervals between the two highest amplitude pulses in each burst, both\nfor actual bursts, and for simulated bursts and fits to simulated\nbursts. It appears that unlike the first two time intervals described\nabove, there is no tendency for the third time interval to be shorter\nor longer in bursts with more pulses. This suggests that the interval\nbetween the two highest pulses in each fit isn't subject to the\nsignal-to-noise selection effects that affect both the intervals\nbetween adjacent pulses and the interval between the first and last\npulse in each burst.\n\n\\begin{figure}\n\\epsfig{file=f4a.eps}\n\\epsfig{file=f4b.eps}\\caption{Same as\nFigure~\\ref{npvsdt}, except number of pulses per burst versus\nintervals between two highest amplitude pulses in each\nburst. \\label{npvsint}}\n\\end{figure}\n\nThe upshot of the above analysis is that the correlations between time\nintervals and numbers of pulses per burst (or complexity) in the\nsimulated bursts is similar to that of the actual BATSE data,\nindicating that the simulated data provides a good representation of\nthese aspects of the actual data, and can be used to determine the\nbiases in the data and in the fitting procedure.\n\n\\section{Time Dilation}\n\\label{sec:timedilation}\n\nWe now consider the correlations between timescales and intensities\namong pulses within bursts and among the bursts to determine the\npresence of time dilation or time stretching and to test if this is\ndue to cosmological redshift of the sources.\n\n\\subsection{Peak Luminosity as a Standard Candle}\n\nIf we assume that the peak luminosities of bursts are approximately a\nstandard candle, then the correlations between pulse amplitudes and\ntimescales can be used to test time dilation. This corresponds to the\namplitudes of the constituent pulses in bursts. It has previously\nbeen found that higher amplitude pulses have shorter durations (are\nnarrower),~\\citep{davis:1994,norris:1994b,davis:thesis}, but it has\nbeen noted that this could be in part or entirely an intrinsic\nproperty of bursters.~\\citep{norris:1998}. A potential problem with\nusing peak flux as a distance measure for bursts observed by BATSE is\nthat data binned to 64~ms have been typically used, so that the peak\nfluxes of bursts with sharp spikes may be underestimated.\n(See~\\cite{lee:1997}.) This should be less of a problem with the\nvariable time resolution TTS data, where the time resolution is\ninversely proportional to the count rate and every spill represents\nthe same number of counts. The pulse-fitting data from actual BATSE\nbursts shown in the upper panels of Figure~\\ref{ampvsw} clearly shows\nthat higher amplitude pulses tend to be narrower, or have shorter\ndurations. Table~\\ref{tab:ampvsw} gives the Spearman rank-order\ncorrelation coefficients, which show that pulse amplitudes and pulse\nwidths are inversely correlated in all energy channels. The table\nalso gives fitted power laws for pulse amplitude as a function of\npulse width. These were obtained by applying the ordinary least\nsquares (OLS) bisector linear regression\nalgorithm~\\citep{isobe:1990,lee:thesis}.\n\n\\begin{figure}\n\\epsfig{file=f5a.eps}\n\\epsfig{file=f5b.eps}\\caption{Pulse amplitude versus pulse width (FWHM) for all pulses in all bursts combined. The solid lines are obtained from least-squares fits using the OLS bisector method to the logarithms. In the initial simulations and the fits to the simulations (bottom panels), the correlations were insignificant, so no fits were made. \\label{ampvsw}}\n\\end{figure}\n\n\\begin{deluxetable}{crlr}\n\\tablecaption{Correlation Between Pulse Amplitude and Pulse Width (FWHM) for All Pulses in All Bursts Combined, and the Fitted Power Law Index $\\alpha$. \\label{tab:ampvsw}}\n\\tablehead{\n\\colhead{Energy Channel} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$\\alpha$}}\n\\startdata\n1 & -0.53 & \\e{9.9}{-39} & $-0.73 \\pm 0.03$ \\\\\n2 & -0.49 & 0 & $-0.79 \\pm 0.02$ \\\\\n3 & -0.44 & \\e{1.3}{-42} & $-0.83 \\pm 0.02$ \\\\\n4 & -0.52 & \\e{2.4}{-20} & $-0.75 \\pm 0.03$ \\\\\nSimulation & 0.0068 & 0.73 & \\nodata \\\\\nFit to Sim. & -0.14 & \\e{2.1}{-6} & \\nodata \\\\\n\\enddata\n\\end{deluxetable}\n\nThe lower panels of Figure~\\ref{ampvsw} shows the pulse amplitudes\nversus pulse width for all pulses in all simulated bursts combined,\nfor the initial simulations and for the fits to the simulations. The\nfitting procedure tends to miss lower amplitude pulses, but doesn't\nappear to have strong selection effects in pulse width. However, the\nfitting procedure introduces an anticorrelation between pulse\namplitudes and pulse widths, as shown in the last two rows of\nTable~\\ref{tab:ampvsw}. By design, there is no correlation between\npulse width and pulse amplitude in the initial simulation, but there\nis a negative correlation between pulse width and pulse amplitude in\nthe fits to the simulations. However this correlation appear to be\nweaker and have far less statistical significance than in the fits to\nactual BATSE bursts.\n\nIt is difficult to draw concrete conclusions from the correlations in\nthe combined set of pulses. To distinguish cosmological from\nintrinsic correlations, we should compare the correlations among\nbursts and among pulses within individual bursts.\n\n\\subsection{Cosmological Effects}\n\nFor testing the first type of correlation, we use the peak fluxes of\neach of the bursts, \\emph{i.e.}, the amplitudes of the highest\namplitude pulses, and the widths of the same pulses. These data and\ntheir analysis (shown in Figure~\\ref{peak_ampvsw} and columns~(a) of\nTable~\\ref{tab:peak_ampvswint}) shows a strong inverse correlation\nbetween peak pulse amplitude and pulse width in the actual BATSE\nbursts, but not in the simulated bursts or the fits to the simulated\nbursts. This suggests that the correlations observed in the fits to\nactual bursts observed by BATSE are not caused by selection effects in\nthe fitting procedure, so they may arise from cosmological time\ndilation, intrinsic properties of the bursters, or selection effects\narising from the BATSE triggering criteria.\n\n\\begin{figure}\n\\epsfig{file=f6a.eps}\n\\epsfig{file=f6b.eps}\\caption{Same as Figure~\\ref{ampvsw}, except for the highest amplitude pulse in each burst. \\label{peak_ampvsw}}\n\\end{figure}\n\n\\begin{deluxetable}{crlrrlr}\n\\tablecaption{Correlation Between Highest Pulse Amplitude and (a) Width of Highest Amplitude Pulse and (b) Interval Between Two Highest Pulses in Each Burst, and the Fitted Power Law Index $\\alpha$. \\label{tab:peak_ampvswint}}\n\\tablehead{\n\\colhead{Energy} & \\multicolumn{3}{c}{(a) Pulse Width} & \\multicolumn{3}{c}{(b) Interval} \\\\\n\\colhead{Channel} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$\\alpha$} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$\\alpha$}}\n\\startdata\n1 & -0.57 & \\e{9.1}{-15} & $-0.60 \\pm 0.05$ & -0.42 & \\e{2.7}{-5} & $-0.86 \\pm 0.06$ \\\\\n2 & -0.52 & \\e{5.8}{-14} & $-0.61 \\pm 0.04$ & -0.42 & \\e{7.2}{-6} & $-0.91 \\pm 0.06$ \\\\\n3 & -0.51 & \\e{1.1}{-12} & $-0.67 \\pm 0.05$ & -0.34 & \\e{1.8}{-4} & $-0.83 \\pm 0.06$ \\\\\n4 & -0.71 & \\e{7.1}{-12} & $-0.64 \\pm 0.05$ & -0.40 & 0.017 & $-0.82 \\pm 0.11$ \\\\\nSim. & 0.0059 & 0.92 & \\nodata & 0.03 & 0.74 & \\nodata \\\\\nFit to Sim. & -0.075 & 0.20 & \\nodata & -0.01 & 0.93 & \\nodata \\\\\n\\enddata\n\\end{deluxetable}\n\n\\subsection{Intrinsic Effects}\n\nA more unambiguous test of the second type of correlation, intrinsic\ncorrelations, can come from analysis of pulse widths and amplitudes of\npulses within bursts, because correlations between pulse\ncharacteristics within bursts cannot be affected by the distances to\nthe sources, and are less likely to be affected by selection effects\ndue to the triggering process. To this end, we have carried out\nlinear least squares fits to the logarithms of the pulse amplitudes\nand widths in all actual BATSE bursts, and simulated bursts (before\nand after fitting) which contain more than one pulse. The results are\nshown in Table~\\ref{tab:ampfwhm}, which gives the numbers and\nfractions of fits that show inverse correlations as determined from\nthe Spearman coefficients, and the probabilities that this would occur\nby chance if there was no actual correlation, using the binomial\ndistribution. It also gives the distributions of power-law indices\n(slopes), which we denote as $\\alpha$, in four bins: $\\alpha < -1$,\n$-1 < \\alpha < 0$, $0 < \\alpha < 1$, and $\\alpha > 1$. (For these\nbins, the results are identical for three different linear regression\nmethods that are symmetric in the two variables being compared. See\n\\cite{isobe:1990,lee:thesis}.) The last column of\nTable~\\ref{tab:ampfwhm} gives the median power law index from the OLS\nbisector method. For all energy channels, a significant majority of\nfits show inverse correlations between pulse widths and pulse\namplitudes \\emph{within} bursts. When we examine the actual BATSE\nbursts for which the rank correlations have the greatest statistical\nsignificance, shown in the upper panels of Figure~\\ref{ampfwhm}, we\nfind that the vast majority of these show inverse correlations between\npulse widths and pulse amplitudes; in the bursts where the\ncorrelations are positive, the correlations also tend to be less\nstatistically significant. The pulse amplitudes most often vary as a\nsmall negative power of the pulse width. The power law indices are\nsignificantly different from those relating pulse amplitude to pulse\nwidth for the highest amplitude pulses in each\nburst~\\citep{petrosian:1999}. \\cite{ramirez-ruiz:1999b} found similar\nresults for the sample of 28 complex bursts fitted by\n\\cite{norris:1996}. As noted by those authors, this anticorrelation\ncould be consistent with internal shock models of GRBs.\n\n\\begin{figure}\n\\epsfig{file=f7a.eps}\n\\epsfig{file=f7b.eps}\\caption{Pulse amplitudes versus pulse widths within bursts for bursts with strongest\ncorrelations. The lines show the fitted power law indices to pulses\nin individual bursts with strong correlations. Note that in the BATSE bursts (upper\npanels), a large majority of the bursts show negative correlations (or\nslopes) while in the simulations (lower panels), the numbers with\npositive and negative correlations or slopes are much closer to equal.\n\\label{ampfwhm}}\n\\end{figure}\n\n\\begin{deluxetable}{crlrrrrr}\n\\tablecaption{Correlations Between Pulse Amplitude and Pulse Width Within Bursts, and the Distributions and Medians of the Fitted Power Law Index $\\alpha$. \\label{tab:ampfwhm}}\n\\tablehead{\n\\colhead{Energy} & \\colhead{\\% Neg.} & \\colhead{Binom.} & \\colhead{} & \\colhead{} & \\colhead{} & \\colhead{} & \\colhead{Med.} \\\\\n\\colhead{Channel} & \\colhead{Corr.} & \\colhead{Prob.} & \\colhead{$\\alpha < -1$} & \\colhead{$-1 < \\alpha < 0$} & \\colhead{$0 < \\alpha < 1$} & \\colhead{$\\alpha > 1$} & \\colhead{$\\alpha$}}\n\\startdata\n1 & 65/94 = 69\\% & 0.00020 & 21 & 42 & 22 & 9 & -0.37 \\\\\n2 & 74/109 = 68\\% & 0.00019 & 21 & 58 & 21 & 9 & -0.43 \\\\\n3 & 82.5/116 = 71\\% & \\e{5.4}{-6} & 17 & 63 & 21 & 15 & -0.46 \\\\\n4 & 26.5/35 = 76\\% & 0.0023 & 3 & 26 & 5 & 1 & -0.55 \\\\\nSim. & 104.5/223 = 47\\% & 0.35 & 39 & 55 & 65 & 64 & 0.55 \\\\\nFit to Sim. & 126.5/198 = 64\\% & \\e{9.3}{-5} & 32 & 86 & 53 & 24 & -0.39 \\\\\n\\enddata\n\\end{deluxetable}\n\nBecause of the possible far-reaching effects of this result, it is\nimportant to ensure that this is not due to a selection or analysis\nbias. Our simulations can to some degree answer this question.\nTable~\\ref{tab:ampfwhm} also shows that there are no correlations\namplitude and pulse width within the simulated bursts. In the fits to\nthe simulations, however, more bursts show a negative correlation\nbetween pulse amplitude and pulse width than show a positive\ncorrelation. This asymmetry appears to be as large as it is for the\nfits to actual BATSE data, which would suggest that the observed\ntendency for higher amplitude pulses within bursts to be narrower\narises largely from a selection effect in the pulse-fitting procedure.\nHowever, when we compare the fits to actual and simulated bursts for\nwhich the rank correlations have the greatest statistical\nsignificance, shown in the lower panels of Figure~\\ref{ampfwhm}, we\nfind a different result. In the simulated data, in the bursts with\ncorrelations between pulse widths and pulse amplitudes with higher\nstatistical significance, the fraction that have positive correlations\nbetween pulse widths and pulse amplitudes is similar to that in bursts\nwhere the rank correlations have weaker statistical significance; the\nasymmetry doesn't depend on the statistical significance of the\ncorrelations. This is unlike the fits to actual bursts, where almost\nall of the bursts with the most statistically significant correlations\nshow a negative slope~\\citep{petrosian:1999}. Therefore, the observed\ninverse correlations between pulse widths and pulse amplitudes within\nactual bursts appear to arise in part from intrinsic properties of the\nsources.\n\nHowever, some caution is necessary in the interpretation of these\nresults. This is because we find correlations between the errors in\nthe fitted pulse parameters by comparing the parameters used in the\nsimulations with those obtained from the fits to the simulations. For\nsimulated bursts consisting of a single pulse in both the original\nsimulation and in the fit, the identification of pulses between the\nsimulation and the fit is unambiguous and unaffected by the effects of\nmissing pulses. Figure~\\ref{sim_rampvsrw} shows that the errors in\nthe fitted pulse amplitudes and the fitted pulse widths tend to have\nan inverse correlation; when the fitted amplitude is larger than the\noriginal amplitude, the fitted width tends to be smaller than the\noriginal width, and vice versa. The same effect also appears when we\ncompare the highest amplitude pulses from all bursts, or all pulses\nmatched between the simulations and the fits to the simulations. This\nselection effect may cause weak inverse correlations between pulse\namplitude and pulse width within fits to actual or simulated bursts,\nso it may be another reason why a large majority of both actual BATSE\nbursts and fits to simulated bursts show an inverse correlation\nbetween pulse amplitude and pulse width within the bursts, as found\nhere and by \\cite{ramirez-ruiz:1999b}. \\emph{However, we conclude\nthat the evidence for intrinsic correlation between pulse amplitude\nand width is weak and requires further study. Therefore, caution\nshould be exercised in the interpretation of this result, in\nparticular in using it as evidence against the external shock model.}\n\n\\begin{figure}\\plotone{f8.eps}\\caption{Ratios of fitted to simulated pulse amplitudes versus ratios of fitted to simulated pulse widths, with line of constant count fluence, for single-pulse simulated bursts. Note that the errors arising from the fitting procedure for these\nquantities are anticorrelated, which would cause a bias in the fitting\nprocedure favoring anticorrelated pulse amplitudes and pulse widths. \\label{sim_rampvsrw}}\n\\end{figure}\n\n\\subsection{Other Timescales}\n\nCosmological time dilation must affect all timescales within bursts,\nnot only pulse widths. Some of these timescales may provide a more\nrobust test of cosmological time dilation. This is because use of a\npulse width as a burst duration is subject to the following\nuncertainty. Because of the spectral shift due to cosmological\nredshift, for the dimmer, hence more distant, bursts, BATSE will be\ndetecting higher energy rest frame photons. gamma-rays were\noriginally produced at higher energies but had redshifted to lower\nenergies when they were detected. Since both burst durations\n\\citep{fenimore:1995} and pulses \\citep{lee:2000} tend to be shorter\nat higher energies, this would weaken the correlations between\namplitude and width due to time dilation.\n\nWe have seen earlier that the \\emph{intervals between the peak times} of the\ntwo highest amplitude pulses in each burst do not appear to increase\nor decrease with energy, so that cosmological redshift of photon energies\nshould not affect these intervals. As shown in\nthe upper panels of Figure~\\ref{peakampvsint} and columns~(b) of\nTable~\\ref{tab:peak_ampvswint}, these intervals also show a\nsignificant inverse correlation with the amplitudes of the highest\namplitude pulses in the actual bursts, so they are shorter for\nbrighter bursts.\n\n\\begin{figure}\n\\epsfig{file=f9a.eps}\n\\epsfig{file=f9b.eps}\\caption{Highest pulse amplitude versus interval between two highest amplitude pulses in each burst. In the initial simulations and the fits to the simulations (bottom panels), the correlations were insignificant, so no fits were made. \\label{peakampvsint}}\n\\end{figure}\n\nSuch a trend does not seem to be present in the fits to the simulated\ndata, and is not present in the initial simulated data by design (See\nFigure~\\ref{peakampvsint}, lower panels, and bottom two rows of\nTable~\\ref{tab:peak_ampvswint}, columns~(b).) The distributions are\nvery similar for the simulated bursts and for the fits to the\nsimulations, although the fits to simulations tend to miss points when\nboth the peak amplitudes and the intervals between the two highest\namplitude pulses are small. Therefore, it appears that the\ncorrelations observed in the fits to actual bursts observed by BATSE\nare not caused by selection effects in the fitting procedure, but may\narise from cosmological time dilation or from intrinsic properties of\nthe bursts. An early study of time dilation using the intervals\nbetween pulses found inconsistent results~\\citep{neubauer:1996}, but a\nnumber for later studies have found evidence of time\ndilation~\\citep{norris:1996b,deng:1998,deng:1998b} consistent with our\nresults.\n\nTo see if some kind of correlation is present among pulses within\nbursts, we compare pulse amplitudes with time intervals between pulses\nwithin bursts as follows: For each burst time profile consisting of\nthree or more pulses, we order the individual pulses by decreasing\npulse amplitude. Then we look for correlations between the amplitude\nof each pulse and the absolute value of the intervals between it and\nthe pulse with the next lower amplitude. The results are shown in\nTable~\\ref{tab:ampint}. There appears to be a more frequent\noccurrence of inverse correlations than positive correlations between\npulse amplitudes and intervals between pulses within bursts in the\nBATSE data, but this is statistically insignificant in all energy\nchannels except possibly channel~1. This table also shows that the\nfitting procedure does not introduce any significant bias.\n\n\\begin{deluxetable}{crlrrrrr}\n\\tablecaption{Correlations Between Pulse Amplitude and Intervals Between Pulses Within Bursts, and Distributions and Medians of the Fitted Power Law Index $\\alpha$. \\label{tab:ampint}}\n\\tablehead{\n\\colhead{Energy} & \\colhead{\\% Neg.} & \\colhead{Binom.} & \\colhead{} & \\colhead{} & \\colhead{} & \\colhead{} & \\colhead{Med.} \\\\\n\\colhead{Channel} & \\colhead{Corr.} & \\colhead{Prob.} & \\colhead{$\\alpha < -1$} & \\colhead{$-1 < \\alpha < 0$} & \\colhead{$0 < \\alpha < 1$} & \\colhead{$\\alpha > 1$} & \\colhead{$\\alpha$}}\n\\startdata\n1 & 42/62 = 68\\% & 0.0052 & 5 & 38 & 14 & 5 & -0.47 \\\\\n2 & 54/89 = 61\\% & 0.044 & 9 & 49 & 26 & 5 & -0.44 \\\\\n3 & 55/95 = 58\\% & 0.12 & 4 & 51 & 34 & 6 & -0.32 \\\\\n4 & 17.5/24 = 73\\% & 0.064 & 2 & 15 & 5 & 2 & -0.48 \\\\\nSim. & 44/156 = 51\\% & 0.11 & 23 & 43 & 52 & 38 & 0.67 \\\\\nFit to Sim. & 74/132 = 56\\% & 0.16 & 17 & 60 & 34 & 21 & -0.29 \\\\\n\\enddata\n\\end{deluxetable}\n\nFinally, it should also be noted that the fitted power law indices for\nhighest pulse amplitude versus width of the highest amplitude pulse\nare smaller than -1, which is inconsistent with purely cosmological\neffects. For a given variation in the highest pulse amplitude, the\ncorresponding variation in pulse width is too great to be accounted\nfor by only cosmological time dilation. We have also seen that within\nindividual bursts, higher amplitude pulses have a strong tendency to\nbe narrower, which must result from intrinsic properties of the GRB\nsources themselves. It seems likely that the observed correlation\nbetween the highest pulse amplitude and the width of the highest\npulses in each burst could result from a combination of cosmological\nand non-cosmological effects.\n\nOne of the possible intrinsic effects that could contribute to the\ninverse correlations of pulse widths with pulse amplitudes is that the\ntotal energy in a burst, or within individual pulses, might tend to\nfall within a limited range, or might have an upper limit. This would\nbe the case if, for example, the fluence of a burst were a better\nmeasure of distance than the peak flux. In the next section, we\nrepeat the above tests using the fluence instead of peak flux as a\nmeasure of the strengths of bursts and pulses.\n\nOn the other hand, the power law indices for highest pulse amplitude\nversus the time interval between the peaks of the two highest pulses\nin each burst may be consistent with the expected results of\ncosmological time dilation alone. Furthermore, it seems likely that\nthis correlation is less affected by intrinsic properties of bursters\nor by selection effects than the correlation between the highest pulse\namplitude and the width of the same pulse in each burst. For example,\nif the range of radiated energy in entire bursts or in individual\npulses, were limited by the production mechanism, or by selection\neffects, this would be far less likely to affect intervals between\npulses than to affect pulse widths.\n\n\\subsection{Integrated Luminosity as a Standard Candle}\n\n\\cite{petrosian:1996} have suggested that the integrated luminosities\nof bursts, measured using either energies or photons, are likely to be\nbetter standard candles than their peak luminosities. This would be\nthe case if the total energy output of bursters fall in a narrow range\nof values, and much of the variation in flux results from the broad\nrange of burst durations. \\cite{petrosian:1996b,lee:1997} have also\nfound that the energy fluences of bursts and their durations show a\npositive correlation, which is the opposite of what cosmological time\ndilation should cause. In what follows we carry out similar tests for\nbursts and for pulses within individual bursts. We shall see that the\ncount fluences of bursts and pulse widths show a positive correlation,\nwhile the count fluences of bursts and time intervals between pulses\nshow no correlation, and neither of these effects can arise from\ncosmological effects. However, determining the significance of some\nof these correlations is difficult because the simulated bursts were\ngenerated with no correlations between pulse width and pulse\namplitude, and therefore have a positive correlation between pulse\nwidth and pulse count fluence.\n\nIn Figure~\\ref{tareavsw}, we show that the pulse widths of the highest\namplitude pulses have positive correlations with the total count\nfluences of each fit that appear to be significant in all energy\nchannels except perhaps in channel~3. (See also\nTable~\\ref{tab:tareavswint}, columns~(a).) The positive correlation\nappears somewhat stronger in the fits to simulations than in the\nsimulations. As mentioned above, this makes the interpretation of\nthis result difficult.\n\n\n\\begin{figure}\n\\epsfig{file=f10a.eps}\n\\epsfig{file=f10b.eps}\\caption{Total count fluence versus pulse width (FWHM) of highest amplitude pulse in each burst. \\label{tareavsw}}\n\\end{figure}\n\n\\begin{deluxetable}{crlrrlr}\n\\tablecaption{Correlation Between Total Count Fluence and (a) Pulse Width (FWHM) of Highest Amplitude Pulse in Each Burst and (b) Interval Between Two Highest Pulses in Each Burst, and the Fitted Power Law Index $\\beta$. \\label{tab:tareavswint}}\n\\tablehead{\n\\colhead{Energy} & \\multicolumn{3}{c}{(a) Pulse Width} & \\multicolumn{3}{c}{(b) Interval} \\\\\n\\colhead{Channel} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$\\alpha$} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$\\alpha$}}\n\\startdata\n1 & 0.29 & \\e{2.4}{-4} & $0.89 \\pm 0.06$ & 0.096 & 0.36 & $0.99 \\pm 0.03$ \\\\\n2 & 0.27 & \\e{2.7}{-4} & $0.91 \\pm 0.05$ & 0.15 & 0.11 & $1.03 \\pm 0.06$ \\\\\n3 & 0.17 & 0.023 & $0.93 \\pm 0.04$ & 0.26 & \\e{4.5}{-3} & $0.98 \\pm 0.06$ \\\\\n4 & 0.33 & \\e{5.8}{-3} & $0.95 \\pm 0.05$ & 0.25 & 0.15 & $1.09 \\pm 0.10$ \\\\\nSimulation & 0.23 & \\e{8.9}{-5} & $1.42 \\pm 0.18$ & -0.04 & 0.59 & \\nodata \\\\\nFit to Sim. & 0.33 & \\e{1.3}{-8} & $1.30 \\pm 0.17$ & -0.06 & 0.51 & \\nodata \\\\\n\\enddata\n\\end{deluxetable}\n\nCorrelations between pulse width and pulse count fluence \\emph{within}\nbursts do not appear to have been studied before. In\nTable~\\ref{tab:areafwhm}, we show the distribution and some moments of\nthe power law index $\\beta$, which is obtained from linear fits to the\nlogarithms of the fluence and widths of pulses in individual bursts.\nAs evident, a significant majority of fits in all energy channels and\nin the simulations show strong positive correlations between pulse\nwidth and pulse count fluence within individual bursts. (See\nTable~\\ref{tab:areafwhm} and the upper panels of\nFigure~\\ref{areafwhm}.) Pulse count fluences most often vary as a\nlarge positive power of the pulse width. (Because more bursts have\n$|\\beta| > 1$ than $|\\beta| < 1$, taking the median of the reciprocal\nof $\\beta$ is more appropriate.)\n\n\\begin{figure}\n\\epsfig{file=f11a.eps}\n\\epsfig{file=f11b.eps}\\caption{Pulse count fluences versus pulse widths within bursts for bursts with strongest correlations. The lines show the fitted power law indices to pulses in individual bursts with strong correlations. In the BATSE bursts\n(upper panels), nearly all bursts show positive correlations (or\nslopes), indicating that the distributions of pulse amplitudes within\nthe individual bursts are narrow. In the simulated bursts (lower\npanels), all bursts show positive correlations between pulse amplitude\nand pulse width because of the design of the\nsimulation. \\label{areafwhm}}\n\\end{figure}\n\n\\begin{deluxetable}{crlrrrrr}\n\\tablecaption{Correlations Between Pulse Count Fluence and Pulse Width Within Bursts, and Distributions and Medians of the Fitted Power Law Index $\\beta$. \\label{tab:areafwhm}}\n\\tablehead{\n\\colhead{Energy} & \\colhead{\\% Pos.} & \\colhead{Binom.} & \\colhead{} & \\colhead{} & \\colhead{} & \\colhead{} & \\colhead{} \\\\\n\\colhead{Channel} & \\colhead{Corr.} & \\colhead{Prob.} & \\colhead{$\\beta < -1$} & \\colhead{$-1 < \\beta < 0$} & \\colhead{$0 < \\beta < 1$} & \\colhead{$\\beta > 1$} & \\colhead{$\\displaystyle\\frac{1}{{\\text{Med.}}(1 / \\beta)}$}}\n\\startdata\n1 & 66/94 = 70\\% & \\e{8.9}{-5} & 14 & 15 & 23 & 42 & 1.88 \\\\\n2 & 77.5/109 = 71\\% & \\e{1.0}{-5} & 20 & 13 & 25 & 51 & 1.46 \\\\\n3 & 90.5/116 = 78\\% & $<10^{-16}$ & 16 & 12 & 38 & 50 & 1.29 \\\\\n4 & 27/35 = 77\\% & 0.0013 & 3 & 5 & 17 & 10 & 1.03 \\\\\nSim. & 198/223 = 89\\% & $<10^{-16}$ & 14 & 7 & 37 & 165 & 1.59 \\\\\nFit to Sim. & 167/198 = 84\\% & $<10^{-16}$ & 25 & 12 & 54 & 103 & 1.41 \\\\\n\\enddata\n\\end{deluxetable}\n\nThe last two rows of Table~\\ref{tab:areafwhm} and the lower panels of\nFigure~\\ref{areafwhm} show that the correlations in the fits to\nsimulations are similar, though somewhat weaker in the original\nsimulations, so that the observed correlation for the BATSE bursts is\nprobably not a result of the fitting procedure.\n\nFigure~\\ref{sim_rareavsrw} shows that there are no significant\ncorrelations between the errors in the fitted count fluences and the\nfitted pulse widths for simulated bursts consisting of a single pulse\nin both the simulation and the fit. Therefore, the uncorrelated\nerrors in the pulse count fluences and pulse widths would tend to\nsmear out any existing correlations rather than to create\ncorrelations, which is what we have seen above.\n\n\\begin{figure}\\plotone{f12.eps}\\caption{Ratios of fitted to simulated pulse count fluences versus ratios of fitted to simulated pulse widths for single-pulse simulated bursts. Note that unlike\nFigure~\\ref{sim_rampvsrw}, the errors here do not show any significant\ncorrelation. \\label{sim_rareavsrw}}\n\\end{figure}\n\nThe relation between the total count fluence and time interval between\nthe two highest amplitude pulses in the actual and simulated bursts\nare shown in Figure~\\ref{tareavsint} and columns~(b) of\nTable~\\ref{tab:tareavswint}.) The two quantities have positive\ncorrelations in all energy channels in the actual BATSE bursts, as\ndetermined from the Spearman rank-order correlation coefficients.\nHowever, the correlation is statistically insignificant in all\nchannels, except perhaps in channel~3.\n\n\\begin{figure}\n\\epsfig{file=f13a.eps}\n\\epsfig{file=f13b.eps}\\caption{Total count fluence versus interval between two highest pulses in each burst. In the initial simulations and the fits to the simulations (bottom panels), the correlations were insignificant, so no fits were made. \\label{tareavsint}}\n\\end{figure}\n\nThe distributions of the total burst count fluence versus \\emph{the\nintervals between the peak times} of the two highest amplitude pulses\nin each burst are very similar for the simulated bursts and for the\nfits to the simulations, although the fits to simulations tend to miss\npoints when the intervals between the two highest amplitude pulses are\nsmall. However, columns~(b) of Table~\\ref{tab:tareavswint} show no\nsignificant correlation for either the simulations or the fits to the\nsimulations. This indicates that any correlation that may be present\nin the BATSE bursts is intrinsic to the radiative process.\n\nWe can also compare the count fluences of individual pulses with the\ntime intervals between pulses within bursts. The results, shown in\nTable~\\ref{tab:areaint}, show no statistically significant\ncorrelations between these two quantities. The simulations and fits\nto simulations also show no statistically significant correlations.\n\n\\begin{deluxetable}{crlrrrrr}\n\\tablecaption{Correlations Between Pulse Count Fluence and Intervals Between Pulses Within Bursts, and Distributions and Medians of the Fitted Power Law Index $\\beta$. \\label{tab:areaint}}\n\\tablehead{\n\\colhead{Energy} & \\colhead{\\% Pos.} & \\colhead{Binom.} & \\colhead{} & \\colhead{} & \\colhead{} & \\colhead{} & \\colhead{} \\\\\n\\colhead{Channel} & \\colhead{Corr.} & \\colhead{Prob.} & \\colhead{$\\beta < -1$} & \\colhead{$-1 < \\beta < 0$} & \\colhead{$0 < \\beta < 1$} & \\colhead{$\\beta > 1$} & \\colhead{$\\displaystyle\\frac{1}{{\\text{Med.}}(1 / \\beta)}$}}\n\\startdata\n1 & 33/62 = 53\\% & 0.61 & 21 & 8.5 & 14.5 & 18 & 13.5 \\\\\n2 & 49.5/89 = 56\\% & 0.29 & 19 & 18 & 18 & 34 & 6.5 \\\\\n3 & 54.5/95 = 57\\% & 0.15 & 17 & 20 & 24 & 34 & 3.1 \\\\\n4 & 12/24 = 50\\% & 1.0 & 4 & 9 & 7 & 4 & -4.6 \\\\\nSim. & 71.5/156 = 46\\% & 0.30 & 57 & 13 & 18 & 68 & 4.1 \\\\\nFit to Sim. & 63/132 = 48\\% & 0.60 & 45 & 18 & 17 & 52 & 34 \\\\\n\\enddata\n\\end{deluxetable}\n\nIn summary, all correlations between \\emph{pulse} count fluences and\npulse widths are positive, and probably result from the simple fact\nthat pulses of longer duration tend to contain more counts. The\ncorrelation between total \\emph{burst} count fluence and the width of\nthe highest amplitude pulse in each burst is probably a result of this\ncorrelation and the fact that the majority of the total count fluence\nof a burst is often contained in a single pulse. The cosmological\neffects have been overwhelmed by other effects.\n\nIt is not clear why there appears to be no correlation between total\nburst count fluence and the interval between the two highest pulses in\neach burst. One possibility is that most of the observed bursts are\nsufficiently far away that the count fluence varies very little with\nluminosity distance. However, this would place many bursts at\nredshifts of $z > 10$, which seems unlikely given current evidence.\n\n\\section{Other Correlations}\n\\label{sec:othercorr}\n\n\\subsection{Correlations Between Flux and Fluence}\n\nSince the count fluence of a pulse scales as the product of its\namplitude and its width, and a factor involving the peakedness $\\nu$,\nor equivalently, since the amplitude of a pulse scales as its count\nfluence divided by its width, again with a factor involving $\\nu$,\nvarious selection effects could cause observed pulse amplitudes and\nwidths to have an inverse correlation or cause observed pulse count\nfluences and widths to have a positive correlation.\n\nFigure~\\ref{peak_ampvstarea} and Table~\\ref{tab:peak_ampvstarea} show\nthat there are no strong correlations between the amplitudes of the\nhighest amplitudes pulses and the total count fluences of the BATSE\nbursts, in any energy channel. This result is somewhat unexpected,\nbecause even in the absence of cosmological effects, we would expect\nboth peak flux and total fluence to scale approximately as the inverse\nsquare of the luminosity distance to the sources (the effects of the\ntime dilation factor $1 + z$ are much smaller), and hence to have a\npositive correlation with each other. The results from our\nsimulations are not helpful because the simulated bursts were also\ngenerated with a strong positive correlation between pulse amplitude\nand pulse count fluence. It appears that selection effects in the\npulse-fitting procedure tend to weaken these positive correlations,\nshown in the last two rows of Table~\\ref{tab:peak_ampvstarea}, when we\ncompare the simulations with the fits to the simulations. The absence\nof correlation in the actual bursts may indicate that the intrinsic\nrange of the \\emph{effective durations}, \\emph{i.e.} the total\nfluences divided by the peak fluxes \\citep{lee:1997}, is large enough\nto smear out distance effects expected in the distribution of fluences\nand peak fluxes. It also suggests that if one of the two brightness\nmeasures is a good indicator of distance, then the other cannot be,\nprobably due to selection effects, or due to cosmological evolution of\nthe sources.\n\n\\begin{figure}\n\\epsfig{file=f14a.eps}\n\\epsfig{file=f14b.eps}\\caption{Amplitude of highest amplitude pulse versus total count fluence in each burst. \\label{peak_ampvstarea}}\n\\end{figure}\n\n\\clearpage\n\n\\begin{deluxetable}{crlr}\n\\tablecaption{Correlation Between Amplitude of Highest Amplitude Pulse\nand Total Count Fluence in Each Burst, and the Fitted Power Law Index\n$\\gamma$. \\label{tab:peak_ampvstarea}}\n\\tablehead{\n\\colhead{Energy\nChannel} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$\\gamma$}}\n\\startdata\n1 & 0.13 & 0.096 & $0.92 \\pm 0.07$ \\\\\n2 & 0.043 & 0.57 & $0.93 \\pm 0.05$ \\\\\n3 & 0.15 & 0.053 & $0.87 \\pm 0.04$ \\\\\n4 & -0.036 & 0.77 & $0.96 \\pm 0.12$ \\\\\nSimulation & 0.65 & \\e{4.4}{-36} & $0.39 \\pm 0.03$ \\\\\nFit to Sim. & 0.61 & \\e{8.9}{-31} & $0.28 \\pm 0.06$ \\\\\n\\enddata\n\\end{deluxetable}\n\nHowever, when we consider the relation for pulses within individual\nbursts, we find that a significant majority of bursts in all energy\nchannels show a positive correlation between pulse count fluence and\namplitude within bursts. (See Table~\\ref{tab:amparea}.) In every\nenergy channel, the majority of bursts have pulse amplitudes varying\nas a small positive power $\\gamma$ of the pulse count fluence within\nbursts. Most simulated bursts, as expected, show a positive\ncorrelation between pulse amplitude and pulse count fluence, but in\nthe fits to the simulations, fewer bursts show a positive correlation.\nTherefore, the actual correlation in the BATSE bursts may have been\nweakened by selection effects in the pulse-fitting procedure.\n\n\\begin{deluxetable}{crlrrrrr}\n\\tablecaption{Correlations Between Pulse Amplitude and Pulse Count Fluence Within Bursts, and the Distributions and Medians of the Fitted Power Law Index $\\gamma$. \\label{tab:amparea}}\n\\tablehead{\n\\colhead{Energy} & \\colhead{\\% Pos.} & \\colhead{Binom.} & \\colhead{} & \\colhead{} & \\colhead{} & \\colhead{} & \\colhead{Med.} \\\\\n\\colhead{Channel} & \\colhead{Corr.} & \\colhead{Prob.} & \\colhead{$\\gamma < -1$} & \\colhead{$-1 < \\gamma < 0$} & \\colhead{$0 < \\gamma < 1$} & \\colhead{$\\gamma > 1$} & \\colhead{$\\gamma$}}\n\\startdata\n1 & 71/94 = 76\\% & \\e{7.2}{-7} & 8 & 18 & 54 & 14 & 0.48 \\\\\n2 & 86.5/109 = 79\\% & $<10^{-16}$ & 3 & 23 & 62 & 21 & 0.61 \\\\\n3 & 85/116 = 73\\% & \\e{4.8}{-7} & 6 & 22 & 75 & 13 & 0.63 \\\\\n4 & 24/35 = 69\\% & 0.028 & 3 & 8 & 19 & 5 & 0.61 \\\\\nSim. & 185/223 = 83\\% & $<10^{-16}$ & 11 & 24 & 172 & 16 & 0.34 \\\\\nFit to Sim. & 142.5/198 = 72\\% & $<10^{-16}$ & 15 & 40 & 121 & 18 & 0.20 \\\\\n\\enddata\n\\end{deluxetable}\n\nFigure~\\ref{sim_rampvsrarea} shows an apparent positive correlation\nbetween the errors in the fitted pulse amplitudes and fitted count\nfluences for simulated bursts consisting of a single pulse in both the\nsimulation and the fit. However, the Spearman rank-correlation\ncoefficient shows no significant correlation between the two sets of\nerrors. Therefore, the uncorrelated errors in the pulse amplitudes\nand pulse count fluences would tend to smear out any existing\ncorrelations rather than to create correlations, which is what we have\nseen above.\n\n\\begin{figure}\\plotone{f15.eps}\\caption{Ratios of fitted to simulated pulse amplitudes versus ratios of fitted to simulated pulse count fluences, with line of constant pulse width, for single-pulse simulated bursts. There appears to be a positive correlations between the errors in the\nfitted pulse amplitudes and count fluences, but the Spearman\nrank-correlation coefficient shows that they are actually\nuncorrelated. \\label{sim_rampvsrarea}}\n\\end{figure}\n\n\\subsection{Correlations Between Pulse Amplitude and Pulse Asymmetry}\n\nIt has been reported that when considering the averaged time profiles\nof bursts, the decay times from the peaks of bursts show an inverse\ncorrelation with peak flux, while the rise times to the peaks of\nbursts show a smaller inverse correlation or no variation at all with\npeak flux~\\citep{stern:1997,stern:1997b,litvak:1998,stern:1999}. Such\na result could not come from cosmological time dilation, but would\nhave to be caused by the burst production mechanism itself, or by some\nselection effect, perhaps resulting from the BATSE trigger criteria,\nwhich selects for fast-rising bursts~\\citep{higdon:1996}, but is\nindependent of burst decay times. It is possible that a similar\neffect could appear in the individual pulses comprising a burst, as a\n\\emph{positive} correlation between pulse amplitudes and pulse\nasymmetries as measured by the rise time to decay time ratios.\nAlthough there may be selection effects in the pulse-fitting\nprocedure, most of these should affect both rise and decay times\nsimilarly, and therefore shouldn't affect pulse asymmetry ratios.\n\nFor bursts consisting of a single pulse, the pulse rise and decay\ntimes are of course the rise and decay times for the entire burst.\nFigure~\\ref{sampvsrd} shows pulse asymmetries versus pulse amplitudes\nfor these bursts. There does not seem to be any clear correlations in\nthe actual BATSE bursts, but the range of pulse asymmetry ratios\nappear to be broader for lower amplitude bursts than for higher\namplitude bursts. The latter effect could result from the lower\nsignal-to-noise of lower amplitude pulses. The Spearman rank-order\ncorrelation coefficients shown in Table~\\ref{tab:ampvsrd},\ncolumns~(a), comparing pulse amplitudes and pulse asymmetries of\nsingle-pulse bursts essentially confirm this impression; the\ncorrelations for the actual BATSE bursts are very weak, and have\ndifferent signs in the different energy channels. In the simulated\nbursts, there are clearly no correlations in either the initial\nsimulations or in the fits to the simulations.\n\n\\begin{figure}\n\\epsfig{file=f16a.eps}\n\\epsfig{file=f16b.eps}\\caption{Pulse amplitude versus pulse asymmetry for single-pulse fits. In the initial simulations and the fits to the simulations (bottom panels), the correlations were insignificant, so no fits were made. \\label{sampvsrd}}\n\\end{figure}\n\n\\begin{deluxetable}{crlrrlr}\n\\tablecaption{Correlation Between Pulse Amplitude and Asymmetry for (a) Single Pulse Bursts and (b) Highest Amplitude Pulse in Each Burst, and the Fitted Power Law Index $\\delta$. \\label{tab:ampvsrd}}\n\\tablehead{\n\\colhead{Energy} & \\multicolumn{3}{c}{(a) Single Pulse Bursts} & \\multicolumn{3}{c}{(b) Highest, All Bursts} \\\\\n\\colhead{Channel} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$\\delta$} & \\colhead{$r_{s}$} & \\colhead{Prob.} & \\colhead{$\\delta$}}\n\\startdata\n1 & -0.25 & 0.049 & $-0.91 \\pm 0.10$ & -0.24 & 0.0020 & $-0.89 \\pm 0.06$ \\\\\n2 & -0.27 & 0.022 & $-0.89 \\pm 0.20$ & -0.32 & \\e{1.7}{-5} & $-0.84 \\pm 0.06$ \\\\\n3 & 0.01 & 0.93 & $0.87 \\pm 0.11$ & -0.15 & 0.051 & $-0.99 \\pm 0.04$ \\\\\n4 & -0.27 & 0.12 & $-0.86 \\pm 0.20$ & -0.13 & 0.30 & $-0.26 \\pm 0.09$ \\\\\nSim. & 0.11 & 0.42 & \\nodata & 0.081 & 0.17 & \\nodata \\\\\nFit to Sim. & -0.0059 & 0.96 & \\nodata & 0.066 & 0.27 & \\nodata \\\\\n\\enddata\n\\end{deluxetable}\n\nAlthough the properties of individual pulses in multiple-pulse bursts\nmay be different from those of the entire bursts, it may still be\nuseful to look for correlations between pulse amplitude and asymmetry\nfor individual pulses in multiple-pulse bursts. For the highest\namplitude pulses from each burst, plots of pulse asymmetry versus\npulse amplitude are shown in Figure~\\ref{peak_ampvsrd}, which again\nshow that pulse asymmetries span a larger range of values at lower\namplitudes in the actual BATSE bursts. The Spearman rank-order\ncorrelation coefficients given in Table~\\ref{tab:ampvsrd},\ncolumns~(b), show a marginally significant inverse correlations in\nenergy channels~1 and 3, a strong inverse correlation in channel~2,\nand no correlation in channel~4. Again, the simulated bursts show no\ncorrelation at all.\n\n\\begin{figure}\n\\epsfig{file=f17a.eps}\n\\epsfig{file=f17b.eps}\\caption{Pulse amplitude versus pulse asymmetry for highest amplitude pulse in each burst. In the initial simulations and the fits to the simulations (bottom panels), the correlations were insignificant, so no fits were made. \\label{peak_ampvsrd}}\n\\end{figure}\n\nFinally, we consider correlations between the amplitudes and\nasymmetries of pulses within bursts. Table~\\ref{tab:amprd} shows\ncharacteristics of the distributions of the power law indices $\\delta$\nobtained from fits to these quantities. There do not appear to be\nstatistically significant correlations, except possibly in channel 3.\n\n\\begin{deluxetable}{crlrrrrr}\n\\tablecaption{Correlations Between Pulse Asymmetry and Amplitude Within Bursts, and the Distributions and Medians of the Fitted Power Law Index $\\delta$. \\label{tab:amprd}}\n\\tablehead{\n\\colhead{Energy} & \\colhead{\\% Pos.} & \\colhead{Binom.} & \\colhead{} & \\colhead{} & \\colhead{} & \\colhead{} & \\colhead{Med.} \\\\\n\\colhead{Channel} & \\colhead{Corr.} & \\colhead{Prob.} & \\colhead{$\\delta < -1$} & \\colhead{$-1 < \\delta < 0$} & \\colhead{$0 < \\delta < 1$} & \\colhead{$\\delta > 1$} & \\colhead{$\\delta$}}\n\\startdata\n1 & 47/94 = 50\\% & 1 & 7 & 42 & 36 & 9 & -0.029 \\\\\n2 & 60/109 = 55\\% & 0.29 & 6 & 48 & 44 & 11 & -0.066 \\\\\n3 & 70.5/116 = 61\\% & 0.020 & 5 & 52 & 50 & 9 & 0.077 \\\\\n4 & 17/35 = 49\\% & 0.87 & 2 & 16 & 14 & 3 & -0.090 \\\\\nSim. & 109/223 = 49\\% & 0.74 & 5 & 106 & 103 & 9 & 0.0068 \\\\\nFit to Sim. & 100/198 = 51\\% & 0.89 & 13 & 81 & 94 & 10 & 0.063 \\\\\n\\enddata\n\\end{deluxetable}\n\nIn summary, there is no clear evidence of any correlations between\npulse amplitudes and pulse asymmetry, so that the variations of pulse\nrise and decay time with pulse amplitude don't appear to be\nsignificantly different.\n\n\\section{Summary and Discussion}\n\\label{sec:discuss}\n\nIn this paper, we use a pulse-fitting procedure to the TTS data from\nBATSE and determine the amplitudes, rise and decay times, and\nfluences. We investigate the correlations between all of these\nparameters of pulses in individual bursts and among different bursts.\nThe former gives a measure of correlations intrinsic to the energy and\nradiation generation in burst sources, while the latter are also\naffected by cosmological effects. Simulations are used to determine\nthe biases of the pulse-fitting procedure.\n\nIf the peak luminosities of pulses or bursts are approximate standard\ncandles, so that the peak fluxes would be good measures of distance,\nthen we expect to find negative correlations between fluxes and\ntimescales. We do find inverse correlations between the highest pulse\namplitude within a burst and two different timescales, the width of\nthe highest amplitude pulse and the time interval between the two\nhighest amplitude pulses. The former correlation, between pulse\namplitude and pulse width, which is expected from cosmological time\ndilation effects, is nevertheless not consistent with purely\ncosmological effects, but must be at least partially influenced by\nnon-cosmological effects. These non-cosmological effects may include\nintrinsic properties of the burst sources, or selection effects due to\nthe BATSE triggering procedure, but do not appear to be affected by\nthe pulse-fitting procedure. Our study indicates that the latter\ncorrelation, between pulse amplitude and time intervals between\npulses, may be less influenced by non-cosmological effects. The\ninverse correlation observed between pulse amplitude and pulse width\nwithin bursts results in part from selection effects in the\npulse-fitting procedure, but also appears to result in part from\nintrinsic properties of the burst sources.\n\nIf the total radiated energies of bursts are approximate standard\ncandles, so that the burst fluences would be good measures of\ndistance, then we expect to find negative correlations between\nfluences and timescales. We find instead a \\emph{positive}\ncorrelation between the total burst count fluence and the width of the\nhighest amplitude pulse, but no correlation with the time interval\nbetween the two highest amplitude pulses. The former correlation\nindicates that non-cosmological effects are stronger than any\ncosmological effects. This is supported by the positive correlation\nbetween pulse amplitude and pulse count fluence within bursts.\nHowever, it is not clear why total burst count fluence and time\nintervals between pulses show no correlation.\n\nIt is natural to expect that the peak flux of bursts and the total\ncount fluence of bursts should both decrease essentially the same way\n(except for a factor of $1 + z$) as the distance to the burst sources\nincrease. This would suggest that there should be positive\ncorrelations between the peak flux of bursts and the total count\nfluence of bursts. Strangely, the highest pulse amplitude and the\ntotal count fluence of bursts appear to have no statistically\nsignificant correlation with each other, implying that the two\nmeasures of brightness cannot both be good standard candles; at least\none, or more probably both, are poor measures of distance.\n\nThere do not appear to be any statistically significant correlations\nbetween pulse amplitude and pulse asymmetry, whether the comparison is\ni) of all pulses in all bursts combined, ii) of only the highest pulse\nin each burst, iii) of only the single-pulse bursts, or iv) of\ndifferent pulses within multiple-pulse bursts. This implies that the\ndifferences between the variations of pulse rise and decay time with\npulse amplitude are statistically insignificant, and both rise times\nand decay times tend to decrease as pulse amplitude increases.\n\n\\acknowledgments\n\nWe thank Jeffrey Scargle and Jay Norris for many useful discussions.\nThis work was supported in part by Department of Energy contract\nDE--AC03--76SF00515.\n\n{\n%\\bibliographystyle{abbrvnat}\n%\\bibstyle@aa\n%\\bibliographystyle{apj}\n%\\bibliography{apj-jour,alee}\n\\begin{thebibliography}{32}\n\\expandafter\\ifx\\csname natexlab\\endcsname\\relax\\def\\natexlab#1{#1}\\fi\n\n\\bibitem[{Davis(1995)}]{davis:thesis}\nDavis, S.~P. 1995, PhD thesis, The Catholic University of America, Washington,\n D.C.\n\n\\bibitem[{Davis {et~al.}(1994)}]{davis:1994}\nDavis, S.~P. {et~al.} 1994, in Gamma-Ray Bursts - Second Workshop, ed. G.~J.\n Fishman, J.~J. Brainerd, \\& K.~C. Hurley, AIP Conf. Proc. No. 307 (New York:\n AIP), 182--186\n\n\\bibitem[{Deng \\& Schaefer(1998{\\natexlab{a}})}]{deng:1998}\nDeng, M. \\& Schaefer, B.~E. 1998{\\natexlab{a}}, in Gamma-Ray Bursts: 4th\n Huntsville Symposium, ed. C.~A. Meegan, R.~D. Preece, \\& T.~M. Koshut, AIP\n Conf. Proc. No. 428 (Woodbury, NY: AIP), 251--255\n\n\\bibitem[{Deng \\& Schaefer(1998{\\natexlab{b}})}]{deng:1998b}\nDeng, M. \\& Schaefer, B.~E. 1998{\\natexlab{b}}, \\apjl, 502, L109\n\n\\bibitem[{Fenimore {et~al.}(1995)}]{fenimore:1995}\nFenimore, E. {et~al.} 1995, \\apjl, 448, L101\n\n\\bibitem[{Higdon \\& Lingenfelter(1996)}]{higdon:1996}\nHigdon, J. \\& Lingenfelter, R. 1996, in Gamma-Ray Bursts: 3rd Huntsville\n Symposium, ed. C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP Conf.\n Proc. No. 384 (Woodbury, NY: AIP), 402--406\n\n\\bibitem[{Isobe {et~al.}(1990)Isobe, Feigelson, Akritas, \\& Babu}]{isobe:1990}\nIsobe, T., Feigelson, E.~D., Akritas, M.~G., \\& Babu, G.~J. 1990, \\apj, 364,\n 104\n\n\\bibitem[{Kouveliotou {et~al.}(1996)Kouveliotou, Briggs, \\&\n Fishman}]{huntsville:3}\nKouveliotou, C., Briggs, M.~F., \\& Fishman, G.~J., eds. 1996, Gamma-Ray Bursts:\n 3rd Huntsville Symposium, AIP Conf. Proc. No. 384 (Woodbury, NY: AIP)\n\n\\bibitem[{Lee(2000)}]{lee:thesis}\nLee, A. 2000, PhD thesis, Stanford University, Stanford, CA, (SLAC--R--553)\n\n\\bibitem[{Lee {et~al.}(2000)Lee, Bloom, \\& Petrosian}]{lee:2000}\nLee, A., Bloom, E.~D., \\& Petrosian, V. 2000, \\apj, submitted,\n (astro-ph/0002217, SLAC--PUB--8364)\n\n\\bibitem[{Lee {et~al.}(1996)Lee, Bloom, \\& Scargle}]{lee:1996}\nLee, A., Bloom, E.~D., \\& Scargle, J.~D. 1996, in Gamma-Ray Bursts: 3rd\n Huntsville Symposium, ed. C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP\n Conf. Proc. No. 384 (Woodbury, NY: AIP), 47--51\n\n\\bibitem[{Lee {et~al.}(1998)Lee, Bloom, \\& Scargle}]{lee:1998}\nLee, A., Bloom, E.~D., \\& Scargle, J.~D. 1998, in Gamma-Ray Bursts: 4th\n Huntsville Symposium, ed. C.~A. Meegan, R.~D. Preece, \\& T.~M. Koshut, AIP\n Conf. Proc. No. 428 (Woodbury, NY: AIP), 261--265\n\n\\bibitem[{Lee \\& Petrosian(1997)}]{lee:1997}\nLee, T.~T. \\& Petrosian, V. 1997, \\apjl, 474, L37\n\n\\bibitem[{Litvak {et~al.}(1998)}]{litvak:1998}\nLitvak, M.~L. {et~al.} 1998, in Gamma-Ray Bursts: 4th Huntsville Symposium, ed.\n C.~A. Meegan, R.~D. Preece, \\& T.~M. Koshut, AIP Conf. Proc. No. 428\n (Woodbury, NY: AIP), 176--180\n\n\\bibitem[{Lloyd \\& Petrosian(1999)}]{lloyd:1999}\nLloyd, N.~M. \\& Petrosian, V. 1999, \\apj, 511, 550\n\n\\bibitem[{Meegan {et~al.}(1998)Meegan, Preece, \\& Koshut}]{huntsville:4}\nMeegan, C.~A., Preece, R.~D., \\& Koshut, T.~M., eds. 1998, Gamma-Ray Bursts:\n 4th Huntsville Symposium, AIP Conf. Proc. No. 428 (Woodbury, NY: AIP)\n\n\\bibitem[{Meegan {et~al.}(1996)}]{batse:3b}\nMeegan, C.~A. {et~al.} 1996, \\apjs, 106, 65\n\n\\bibitem[{Neubauer \\& Schaefer(1996)}]{neubauer:1996}\nNeubauer, J. \\& Schaefer, B.~E. 1996, in Gamma-Ray Bursts: 3rd Huntsville\n Symposium, ed. C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP Conf.\n Proc. No. 384 (Woodbury, NY: AIP), 67--71\n\n\\bibitem[{Norris(1996)}]{norris:1996c}\nNorris, J.~P. 1996, in Gamma-Ray Bursts: 3rd Huntsville Symposium, ed.\n C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP Conf. Proc. No. 384\n (Woodbury, NY: AIP), 13--22\n\n\\bibitem[{Norris {et~al.}(1996{\\natexlab{a}})Norris, Bonnell, Nemiroff, \\&\n Scargle}]{norris:1996b}\nNorris, J.~P., Bonnell, J.~T., Nemiroff, R.~J., \\& Scargle, J.~D.\n 1996{\\natexlab{a}}, in Gamma-Ray Bursts: 3rd Huntsville Symposium, ed.\n C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP Conf. Proc. No. 384\n (Woodbury, NY: AIP), 77--81\n\n\\bibitem[{Norris {et~al.}(1998)Norris, Scargle, Bonnell, \\&\n Nemiroff}]{norris:1998}\nNorris, J.~P., Scargle, J.~D., Bonnell, J.~T., \\& Nemiroff, R.~J. 1998, in\n Gamma-Ray Bursts: 4th Huntsville Symposium, ed. C.~A. Meegan, R.~D. Preece,\n \\& T.~M. Koshut, AIP Conf. Proc. No. 428 (Woodbury, NY: AIP), 171--175\n\n\\bibitem[{Norris {et~al.}(1994)}]{norris:1994b}\nNorris, J.~P. {et~al.} 1994, \\apj, 424, 540\n\n\\bibitem[{Norris {et~al.}(1996{\\natexlab{b}})}]{norris:1996}\n---. 1996{\\natexlab{b}}, \\apj, 459, 393\n\n\\bibitem[{Paczy\\'{n}ski(1992)}]{paczynski:1992}\nPaczy\\'{n}ski, B. 1992, \\nat, 355, 521\n\n\\bibitem[{Petrosian \\& Lee(1996{\\natexlab{a}})}]{petrosian:1996}\nPetrosian, V. \\& Lee, T.~T. 1996{\\natexlab{a}}, \\apjl, 467, L29\n\n\\bibitem[{Petrosian \\& Lee(1996{\\natexlab{b}})}]{petrosian:1996b}\nPetrosian, V. \\& Lee, T.~T. 1996{\\natexlab{b}}, in Gamma-Ray Bursts: 3rd\n Huntsville Symposium, ed. C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP\n Conf. Proc. No. 384 (Woodbury, NY: AIP), 82--86\n\n\\bibitem[{Petrosian {et~al.}(1999)Petrosian, Lloyd, \\& Lee}]{petrosian:1999}\nPetrosian, V., Lloyd, N., \\& Lee, A. 1999, in ASP Conf. Ser., Vol. 190, Gamma\n Ray Bursts: The First Three Minutes, ed. J.~Poutanen \\& R.~Svensson (San\n Francisco: ASP)\n\n\\bibitem[{Piran(1992)}]{piran:1992}\nPiran, T. 1992, \\apjl, 389, L45\n\n\\bibitem[{Ramirez-Ruiz \\& Fenimore(1999)}]{ramirez-ruiz:1999b}\nRamirez-Ruiz, E. \\& Fenimore, E. 1999, \\apj, submitted, (astro-ph/9910273)\n\n\\bibitem[{Stern {et~al.}(1997{\\natexlab{a}})Stern, Poutanen, \\&\n Svensson}]{stern:1997b}\nStern, B., Poutanen, J., \\& Svensson, R. 1997{\\natexlab{a}}, \\apjl, 489, L41\n\n\\bibitem[{Stern {et~al.}(1999)Stern, Poutanen, \\& Svensson}]{stern:1999}\n---. 1999, \\apj, 510, 312\n\n\\bibitem[{Stern {et~al.}(1997{\\natexlab{b}})Stern, Svensson, \\&\n Poutanen}]{stern:1997}\nStern, B., Svensson, R., \\& Poutanen, J. 1997{\\natexlab{b}}, in Proceedings of\n the 2nd INTEGRAL Workshop; St. Malo, France, September 1996\n\n\\end{thebibliography}\n}\n\n\\end{document}\n"
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[
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"name": "astro-ph0002218.extracted_bib",
"string": "\\begin{thebibliography}{32}\n\\expandafter\\ifx\\csname natexlab\\endcsname\\relax\\def\\natexlab#1{#1}\\fi\n\n\\bibitem[{Davis(1995)}]{davis:thesis}\nDavis, S.~P. 1995, PhD thesis, The Catholic University of America, Washington,\n D.C.\n\n\\bibitem[{Davis {et~al.}(1994)}]{davis:1994}\nDavis, S.~P. {et~al.} 1994, in Gamma-Ray Bursts - Second Workshop, ed. G.~J.\n Fishman, J.~J. Brainerd, \\& K.~C. Hurley, AIP Conf. Proc. No. 307 (New York:\n AIP), 182--186\n\n\\bibitem[{Deng \\& Schaefer(1998{\\natexlab{a}})}]{deng:1998}\nDeng, M. \\& Schaefer, B.~E. 1998{\\natexlab{a}}, in Gamma-Ray Bursts: 4th\n Huntsville Symposium, ed. C.~A. Meegan, R.~D. Preece, \\& T.~M. Koshut, AIP\n Conf. Proc. No. 428 (Woodbury, NY: AIP), 251--255\n\n\\bibitem[{Deng \\& Schaefer(1998{\\natexlab{b}})}]{deng:1998b}\nDeng, M. \\& Schaefer, B.~E. 1998{\\natexlab{b}}, \\apjl, 502, L109\n\n\\bibitem[{Fenimore {et~al.}(1995)}]{fenimore:1995}\nFenimore, E. {et~al.} 1995, \\apjl, 448, L101\n\n\\bibitem[{Higdon \\& Lingenfelter(1996)}]{higdon:1996}\nHigdon, J. \\& Lingenfelter, R. 1996, in Gamma-Ray Bursts: 3rd Huntsville\n Symposium, ed. C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP Conf.\n Proc. No. 384 (Woodbury, NY: AIP), 402--406\n\n\\bibitem[{Isobe {et~al.}(1990)Isobe, Feigelson, Akritas, \\& Babu}]{isobe:1990}\nIsobe, T., Feigelson, E.~D., Akritas, M.~G., \\& Babu, G.~J. 1990, \\apj, 364,\n 104\n\n\\bibitem[{Kouveliotou {et~al.}(1996)Kouveliotou, Briggs, \\&\n Fishman}]{huntsville:3}\nKouveliotou, C., Briggs, M.~F., \\& Fishman, G.~J., eds. 1996, Gamma-Ray Bursts:\n 3rd Huntsville Symposium, AIP Conf. Proc. No. 384 (Woodbury, NY: AIP)\n\n\\bibitem[{Lee(2000)}]{lee:thesis}\nLee, A. 2000, PhD thesis, Stanford University, Stanford, CA, (SLAC--R--553)\n\n\\bibitem[{Lee {et~al.}(2000)Lee, Bloom, \\& Petrosian}]{lee:2000}\nLee, A., Bloom, E.~D., \\& Petrosian, V. 2000, \\apj, submitted,\n (astro-ph/0002217, SLAC--PUB--8364)\n\n\\bibitem[{Lee {et~al.}(1996)Lee, Bloom, \\& Scargle}]{lee:1996}\nLee, A., Bloom, E.~D., \\& Scargle, J.~D. 1996, in Gamma-Ray Bursts: 3rd\n Huntsville Symposium, ed. C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP\n Conf. Proc. No. 384 (Woodbury, NY: AIP), 47--51\n\n\\bibitem[{Lee {et~al.}(1998)Lee, Bloom, \\& Scargle}]{lee:1998}\nLee, A., Bloom, E.~D., \\& Scargle, J.~D. 1998, in Gamma-Ray Bursts: 4th\n Huntsville Symposium, ed. C.~A. Meegan, R.~D. Preece, \\& T.~M. Koshut, AIP\n Conf. Proc. No. 428 (Woodbury, NY: AIP), 261--265\n\n\\bibitem[{Lee \\& Petrosian(1997)}]{lee:1997}\nLee, T.~T. \\& Petrosian, V. 1997, \\apjl, 474, L37\n\n\\bibitem[{Litvak {et~al.}(1998)}]{litvak:1998}\nLitvak, M.~L. {et~al.} 1998, in Gamma-Ray Bursts: 4th Huntsville Symposium, ed.\n C.~A. Meegan, R.~D. Preece, \\& T.~M. Koshut, AIP Conf. Proc. No. 428\n (Woodbury, NY: AIP), 176--180\n\n\\bibitem[{Lloyd \\& Petrosian(1999)}]{lloyd:1999}\nLloyd, N.~M. \\& Petrosian, V. 1999, \\apj, 511, 550\n\n\\bibitem[{Meegan {et~al.}(1998)Meegan, Preece, \\& Koshut}]{huntsville:4}\nMeegan, C.~A., Preece, R.~D., \\& Koshut, T.~M., eds. 1998, Gamma-Ray Bursts:\n 4th Huntsville Symposium, AIP Conf. Proc. No. 428 (Woodbury, NY: AIP)\n\n\\bibitem[{Meegan {et~al.}(1996)}]{batse:3b}\nMeegan, C.~A. {et~al.} 1996, \\apjs, 106, 65\n\n\\bibitem[{Neubauer \\& Schaefer(1996)}]{neubauer:1996}\nNeubauer, J. \\& Schaefer, B.~E. 1996, in Gamma-Ray Bursts: 3rd Huntsville\n Symposium, ed. C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP Conf.\n Proc. No. 384 (Woodbury, NY: AIP), 67--71\n\n\\bibitem[{Norris(1996)}]{norris:1996c}\nNorris, J.~P. 1996, in Gamma-Ray Bursts: 3rd Huntsville Symposium, ed.\n C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP Conf. Proc. No. 384\n (Woodbury, NY: AIP), 13--22\n\n\\bibitem[{Norris {et~al.}(1996{\\natexlab{a}})Norris, Bonnell, Nemiroff, \\&\n Scargle}]{norris:1996b}\nNorris, J.~P., Bonnell, J.~T., Nemiroff, R.~J., \\& Scargle, J.~D.\n 1996{\\natexlab{a}}, in Gamma-Ray Bursts: 3rd Huntsville Symposium, ed.\n C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP Conf. Proc. No. 384\n (Woodbury, NY: AIP), 77--81\n\n\\bibitem[{Norris {et~al.}(1998)Norris, Scargle, Bonnell, \\&\n Nemiroff}]{norris:1998}\nNorris, J.~P., Scargle, J.~D., Bonnell, J.~T., \\& Nemiroff, R.~J. 1998, in\n Gamma-Ray Bursts: 4th Huntsville Symposium, ed. C.~A. Meegan, R.~D. Preece,\n \\& T.~M. Koshut, AIP Conf. Proc. No. 428 (Woodbury, NY: AIP), 171--175\n\n\\bibitem[{Norris {et~al.}(1994)}]{norris:1994b}\nNorris, J.~P. {et~al.} 1994, \\apj, 424, 540\n\n\\bibitem[{Norris {et~al.}(1996{\\natexlab{b}})}]{norris:1996}\n---. 1996{\\natexlab{b}}, \\apj, 459, 393\n\n\\bibitem[{Paczy\\'{n}ski(1992)}]{paczynski:1992}\nPaczy\\'{n}ski, B. 1992, \\nat, 355, 521\n\n\\bibitem[{Petrosian \\& Lee(1996{\\natexlab{a}})}]{petrosian:1996}\nPetrosian, V. \\& Lee, T.~T. 1996{\\natexlab{a}}, \\apjl, 467, L29\n\n\\bibitem[{Petrosian \\& Lee(1996{\\natexlab{b}})}]{petrosian:1996b}\nPetrosian, V. \\& Lee, T.~T. 1996{\\natexlab{b}}, in Gamma-Ray Bursts: 3rd\n Huntsville Symposium, ed. C.~Kouveliotou, M.~F. Briggs, \\& G.~J. Fishman, AIP\n Conf. Proc. No. 384 (Woodbury, NY: AIP), 82--86\n\n\\bibitem[{Petrosian {et~al.}(1999)Petrosian, Lloyd, \\& Lee}]{petrosian:1999}\nPetrosian, V., Lloyd, N., \\& Lee, A. 1999, in ASP Conf. Ser., Vol. 190, Gamma\n Ray Bursts: The First Three Minutes, ed. J.~Poutanen \\& R.~Svensson (San\n Francisco: ASP)\n\n\\bibitem[{Piran(1992)}]{piran:1992}\nPiran, T. 1992, \\apjl, 389, L45\n\n\\bibitem[{Ramirez-Ruiz \\& Fenimore(1999)}]{ramirez-ruiz:1999b}\nRamirez-Ruiz, E. \\& Fenimore, E. 1999, \\apj, submitted, (astro-ph/9910273)\n\n\\bibitem[{Stern {et~al.}(1997{\\natexlab{a}})Stern, Poutanen, \\&\n Svensson}]{stern:1997b}\nStern, B., Poutanen, J., \\& Svensson, R. 1997{\\natexlab{a}}, \\apjl, 489, L41\n\n\\bibitem[{Stern {et~al.}(1999)Stern, Poutanen, \\& Svensson}]{stern:1999}\n---. 1999, \\apj, 510, 312\n\n\\bibitem[{Stern {et~al.}(1997{\\natexlab{b}})Stern, Svensson, \\&\n Poutanen}]{stern:1997}\nStern, B., Svensson, R., \\& Poutanen, J. 1997{\\natexlab{b}}, in Proceedings of\n the 2nd INTEGRAL Workshop; St. Malo, France, September 1996\n\n\\end{thebibliography}"
}
] |
astro-ph0002219
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Changes in the long term intensity variations in Cyg~X-2~and~LMC~X-3
|
[
{
"author": "B. Paul$^{1,}\\footnotemark[3]$"
},
{
"author": "S. Kitamoto$^2$ and F. Makino$^1$"
}
] |
We report the detection of changes in the long term intensity variations in two X-ray binaries Cyg X-2 and LMC X-3. In this work, we have used the long term light curves obtained with the All Sky Monitors (ASM) of the Rossi {X-ray Timing Explorer (RXTE), GINGA, ARIEL 5} and {VELA 5B} and scanning modulation collimator of {HEAO~1}. It is found that in the light curves of both the sources, obtained with these instruments at various times over the last 30 years, more than one periodic or quasi-periodic components are always present. The multiple prominent peaks in the periodograms have frequencies unrelated to each other. In Cyg X-2, {RXTE-ASM} data show strong peaks at 40.4 and 68.8 days, {GINGA-ASM} data show strong peaks at 53.7 and 61.3 days. Multiple peaks are also observed in LMC X-3. The various strong peaks in the periodograms of LMC X-3 appear at 104, 169 and 216 days with {RXTE-ASM}, and 105, 214 and 328 days with {GINGA-ASM}. The present results, when compared with the earlier observations of periodicities in these two systems, demonstrate the absence of any stable long period. The 78 day periodicity detected earlier in Cyg X-2 was probably due to the short time base in the {RXTE} data that were used and the periodicity of 198 days in LMC X-3 was due to a relatively short duration of observation with {HEAO~1}.
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[
{
"name": "ms.tex",
"string": "\\documentstyle[epsfig,aas2pp4]{article}\n\n\\begin{document}\n\n\\title{Changes in the long term intensity variations in Cyg~X-2~and~LMC~X-3}\n\n\\author{B. Paul$^{1,}\\footnotemark[3]$, S. Kitamoto$^2$ and F. Makino$^1$ }\n\\affil{$^1$Institute of Space and Astronautical Science,\n3-1-1 Yoshinodai, Sagamihara, Kanagawa 229-8510, Japan}\n\\affil{$^2$Department of Earth and Space Science, Faculty of Science,\nOsaka University 1-1, Machikaneyama, Toyonaka, Osaka, 560, Japan}\n\\affil{e-mail:~~bpaul@astro.isas.ac.jp, kitamoto@ess.sci.osaka-u.ac.jp,\nmakino@astro.isas.ac.jp}\n\\footnotetext[3]{On leave from the Tata Institute of Fundamental\nResearch, Homi Bhaba Road, Mumbai, 400005, India}\n\n\\begin{abstract}\n\nWe report the detection of changes in the long term intensity\nvariations in two X-ray binaries Cyg X-2 and LMC X-3. In this work, we have\nused the long term light curves obtained with the All Sky Monitors (ASM) of\nthe Rossi {\\it X-ray Timing Explorer (RXTE), GINGA, ARIEL 5} and {\\it VELA 5B}\nand scanning modulation collimator of {\\it HEAO~1}. It is found that in the\nlight curves of both the sources, obtained with these instruments at various\ntimes over the last 30 years, more than one periodic or quasi-periodic\ncomponents are always present. The multiple prominent peaks in the\nperiodograms have frequencies unrelated to each other. In Cyg X-2, {\\it\nRXTE-ASM} data show\nstrong peaks at 40.4 and 68.8 days, {\\it GINGA-ASM} data show strong peaks at\n53.7 and 61.3 days. Multiple peaks are also observed in LMC X-3. The various\nstrong peaks in the periodograms of LMC X-3 appear at 104, 169 and 216\ndays with {\\it RXTE-ASM}, and 105, 214 and 328 days with {\\it GINGA-ASM}. The\npresent results, when compared with the earlier observations of periodicities\nin these two systems, demonstrate the absence of any stable long period. The\n78 day periodicity detected earlier in Cyg X-2 was probably due to the\nshort time base in the {\\it RXTE} data that were used and the periodicity of\n198 days in LMC X-3 was due to a relatively short duration of observation with\n{\\it HEAO~1}.\n\n\\end{abstract}\n\n\\keywords{accretion, accretion disks -- stars: individual (Cyg X-2, LMC X-3)\n-- stars: neutron -- X-rays: binaries}\n\n\\section{Introduction}\n\nMany X-ray binaries are highly variable\nin their X-ray intensity over long time scales. But in most of the sources,\neither the intensity variations are aperiodic or their periodic nature has not\nyet been discovered because of long-period, low modulation or a lack of\nsensitive uninterrupted monitoring. The All Sky Monitor (ASM) onboard the Rossi\n{\\it X-ray Timing Explorer (RXTE)} has produced light curves of many bright\nX-ray binaries for about 1,000 days with large signal to noise ratio. The\n{\\it RXTE-ASM} data along with the {\\it GINGA-ASM, VELA 5B, ARIEL 5} and\n{\\it HEAO~1} data have a large time base and it is possible not only to\nsearch for any periodic or quasi periodic intensity variations of a few days\nto a few months time scale, but also to investigate changes in\nthe timing behaviour. Changes in the long term periodicity have been observed\nin SMC X-1 (Wojdowski et al. 1998) and GX 354-0 (Kong et al. 1998). We\nselected Cyg X-2 and LMC X-3 to study any possible changes in the long\nterm periodicity because in these two sources long term periodicity is\nknown to exist in data bases covering a very long time and also for the\nfact that light curves for the intervening period 1987--1991 were available\nfrom the {\\it GINGA-ASM}.\n\nCyg X-2, a bright X-ray source, was discovered by Byram et al. (1966)\nwith a sounding rocket experiment. A binary period of 9.8 days, other\norbital parameters and mass limits of the two components of this binary\nsystem were measured by Cowley et al. (1979). This is a low mass X-ray\nbinary and a typical Z source that shows Type-I X-ray bursts (Kahn \\&\nGrindlay 1984; Smale 1998), 18$-$50 Hz QPOs in the horizontal branch\nand 5.6 Hz QPOs in the nominal branch (Hasinger et al. 1986; Elsner et\nal. 1986; Wijnands et al. 1997; Kuulkers, Wijnands and van der Klis 1999).\nRecently, with the {\\it RXTE}, kHz\nQPOs with two peaks have also been detected from this source (Wijnands\net al. 1998). Vrtilek et al. (1988) discovered X-ray dips of different\ntypes and some were found to occur in one particular phase of the binary\nperiod. A 77 day periodicity was discovered from the {\\it VELA 5B }\nobservations (Smale \\& Lochner 1992). Wijnands, Kuulkers \\& Smale (1996)\nreported detection of a periodicity of 78 days from the first 160 days\nof ASM data, and showed that their result was supported by the archival\ndata of {\\it ARIEL 5} and {\\it VELA 5B}.\n\nLMC X-3, a high mass X-ray binary, was discovered with the {\\it UHURU}\nsatellite (Leong et al. 1971) and its position was measured accurately with\nthe {\\it HEAO~1} scanning modulation collimator (Johnston et al. 1978). From\nspectroscopic observations Cowley et al. (1983) discovered an orbital\nperiod of 1.7 days and a mass function of 2.3 M$_\\odot$. LMC X-3 is\nconsidered to be a very strong black hole candidate (BHC) due to the fact that\nthe mass of the compact object has a lower limit of 9 M$_\\odot$. But, {\\it\nHEAO~A2} observations revealed that unlike other known black hole candidates,\nLMC X-3 lacks rapid X-ray variability (Weisskopf et al. 1983). The lowest\ntime scale for 1\\% rms amplitude variation was derived from the {\\it EXOSAT}\nobservations to be 600~s (Treves et al. 1988). One possible\nexplanation for the lack of rapid X-ray variability is that most of the\ntime LMC X-3 is found to be in a high state with an unusually soft X-ray\nspectrum (White \\& Marshal 1984), and the rapid X-ray variations are\ngenerally subdued in Cyg X-1 like BHCs in their high state. {\\it GINGA}\nobservations showed that the energy spectrum consists of a soft, thermal\ncomponent and a hard, power-law component. In spite of large changes in\nmass accretion rate and disk temperature, the inner radius of the\naccretion disk was found to be remarkably constant and was suggested to\nbe related to the mass of the compact object (Ebisawa et al. 1993).\nLong term intensity variation is well known in LMC X-3 and Cowley et\nal. (1991) discovered a periodicity of 198 (or 99) days from\nthe {\\it HEAO~A1} and {\\it GINGA} large area counter data.\n\nThe light curves of Cyg X-2 and LMC X-3 obtained with the ASMs onboard the\n{\\it RXTE, GINGA, VELA 5B} (only for Cyg X-2), {\\it ARIEL 5} and the scanning\nmodulation collimator of the {\\it HEAO~1} (only for LMC X-3) have been used\nto investigate the long term intensity variations in these two sources and\nwe have found presence of multiple components of flux variations in both the\nsources. The data used here together covers a time base of 30 years for\nCyg X-2 and 26 years for LMC X-3.\n\n\\section{Data and analysis}\n\nThe ASM on board {\\it RXTE} scans the sky in a series of dwells of about 90 s\neach, \nand any given X-ray source is observed in about 5$-$10 such dwells every day.\nThe details about the ASM detectors and observations with the ASM are\ngiven in Levine et al. (1996). We have used the quick look ASM data\nobtained in the period 1996 February 20 to 1999 February 4, provided by the\n{\\it RXTE-ASM} team. The ASM data are available in two different forms, per\ndwell and one day average. The periodograms obtained from the\ntwo sets of data are identical except for a normalization. Hence the\nresults obtained from the one day average data are presented here. The {\\it\nGINGA-ASM} was operational during 1987 to 1991 and details of the detectors,\noperations, and the detection techniques have been described by Tsunemi et\nal. (1989). The all sky observations were performed about once every day when\nthe satellite was given one full rotation with about 70\\% sky coverage by\nthe ASM. The detection limit in one such rotation was of the order of 50\nmCrab and was dependent on the position of the source with respect to the\nsatellite equator. Archival data of {\\it VELA 5B} and {\\it ARIEL 5} were\nobtained from the HEASARC data base and {\\it HEAO~1} data for LMC X-3 were\ntaken from previously published work (Cowley et al. 1991). For details about\nthe {\\it ARIEL 5} ASM and the {\\it VELA 5} instrument please refer to\nHolt (1976) and Priedhorsky, Terrel \\& Holt (1983) respectively.\n\nTo search for periodicities in the unevenly sampled data, we have used the\nmethod suggested by Lomb (1976) \\& Scargle (1982). For Cyg X-2, we generated\nperiodograms in the period range of 10$-$160 days from the {\\it RXTE-ASM,\nGINGA-ASM, ARIEL 5} and {\\it VELA 5B} data. The {\\it ARIEL 5, VELA 5B} and\ninitial part of the {\\it RXTE-ASM} light curves were analyzed earlier and\nlong periods of 78 and 69 days were reported (Smale \\& Lochner 1992;\nWijnands et al. 1996, Kong et al. 1998). For LMC X-3, light curves from\n{\\it RXTE-ASM, GINGA-ASM, ARIEL 5} and {\\it HEAO~1} were used to generate\nperiodogram in the range of 20$-$500 days. {\\it VELA 5B} data for LMC X-3\nhas low signal to noise ratio and is not used here. The discovery of a 198\n(or 99) day periodicity from the {\\it HEAO 1} light curve was made by Cowley\net al. (1991), and the initial part of the {\\it RXTE-ASM} data also showed\nsimilar variation (Wilms et al. 1998). The period ranges chosen for the\nperiodogram analysis are such that a sub-harmonic or first harmonic of the\nearlier known periods can be identified for the respective sources. For\nCyg X-2, we also verified that in the 160-500 days range the periodograms\ngenerated from data sets are featureless except for {\\it ARIEL 5} which\nshows peaks around 180 and 360 days due to known yearly effect (Priedhorsky\net al. 1983).\n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=fig1.ps,width=2.2in,angle=-90}}\n\\caption{The {\\it RXTE-ASM} (1.5--12 keV) and {\\it GINGA-ASM}\n(1--20 keV) light curves of Cyg X-2. The days of the observations are given\nin truncated Julian days in the figure.}\n\\end{figure}\n\nThe significance of the various peaks detected in the periodograms is given\nin Table 1 in terms of the false alarm probability (FAP) calculated following\nthe\nmethod suggested by Horne \\& Baliunas (1986). The window functions, which\ncan induce artificial periodicities were calculated for the different time\nseries used here. The {\\it GINGA-ASM} time series, which is very susceptible\nto artificial periodicities because of its scarce sampling, does not show\nany alarming feature in the period\nrange used in this paper and the effect of the window function is less for\nthe other instruments. However, we wish to point out that the use of\nwindow function to find spectral leakage can sometimes be misleading for this\nkind of light curves. As an example, in the {\\it HEAO 1} light curve of LMC X-3,\nthe density of data points available is larger when the source is brighter,\nand this is likely to be true for other sources and instruments also. This\nresults in some features in the window function at periods near 80 and 160 days,\nwhereas a glance at the light curve (Figure 4) leaves no doubt about the\npresence of a periodic variation. We have verified the significance of the\npeaks in the periodograms independently using two more methods. Following\nKong et al. (1998), we have generated light curves using random numbers, with\nthe time series, average, and variance similar to the real light curves and\ncalculated the periodograms for 10,000 such light curves. The highest points\nin these periodograms were identified and a power which is larger than the\nhighest points of 99\\% of the periodograms is considered to correspond to a\nfalse alarm probability of 10$^{-2}$. The same process was carried out also\nfor 10,000 light curves with the same time series as the real light curves,\nbut the count rates redistributed randomly. The results from these two\nanalysis are found to be identical and the 10$^{-2}$ false alarm levels are\nindicated by dashed lines in all the periodograms. Absence\nof strong peaks in the periodograms calculated from the simulated and\nredistributed light curves confirms that the peaks observed in the periodograms\nof the real light curves are not artifact of observation windows.\n\n\\subsection{Cyg X-2}\n\nPresence of strong intensity variations by a factor of $\\sim$2--4 on time\nscale of weeks is well known in this source (Kuulkers, van der Klis, \\&\nVaughan 1996; Wijnands et al. 1996) and can be clearly seen in the light\ncurves of {\\it RXTE-ASM} and {\\it GINGA-ASM} (Figure 1). A periodic nature of\nthis intensity variation with period of less than 100 days is also apparent\nin the light curves.\n\nThe periodograms obtained from the {\\it RXTE-ASM, GINGA-ASM, ARIEL 5} and\n{\\it VELA 5B} data are shown in Figure 2. In the RXTE-ASM data, there are\nseveral significant peaks and the two most prominent ones are at 40.4 and\n68.8 days indicating the presence of multiple periodicities in this system.\nIn the {\\it GINGA-ASM} periodogram there are two prominent peaks at\n53.7 and 61.3 days and there are several smaller peaks. The periodogram of\nthe {\\it ARIEL 5} data is a very complicated one and has many prominent\npeaks at frequencies ranging between 30 and 80 days. In addition to\nthe 78 days peak noticed by Wijnands et al. (1996), there are other peaks at\n41, 46 and 54 days. The {\\it VELA 5B} data has low signal to noise\nratio and the power in the periodogram is much smaller, but two peaks at 33.9\nand 77.4 days can be clearly seen in Figure 2. The significance of the peaks\ndetected in various periodograms are given in Table 1.\n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=fig2.ps,width=4.2in,angle=-90}}\n\\caption[fig2.ps]{The Lomb-Scargle periodograms obtained from the\n{\\it RXTE-ASM, GINGA-ASM, ARIEL 5} and {\\it VELA 5B} light curves of\nCyg X-2. The horizontal dashed line represent the 99\\% confidence limits\n(see text for details).}\n\\end{figure}\n\nTo investigate whether these multiple peaks in the periodograms originate\nin different parts of the light curves or whether multiple peaks are present\nthroughout the entire light curve of each satellite, we have divided the\nlight curves\nof {\\it RXTE} and {\\it ARIEL 5} into three equal segments and generated\nperiodograms from each of them. There are several prominent peaks in each of\nthe periodograms, and the periods of these peaks are noted in Table 1 along\nwith the significance of their detection. Periodograms obtained from the three\n358 day segments of the {\\it RXTE} light curve are shown in Figure 3\nalong with the respective light curves. It is evident from Figure 3 and Table\n1 that there are multiple periodicities in this system that are uncorrelated\nand have varying amplitude and period. The higher frequency variation at\naround 40 days time scale appears to be more stable in frequency than the\nlower frequency variations around 70 days during these observations.\n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=fig3.ps,width=2.4in,angle=-90}}\n\\caption[fig3.ps]{Three segments of the {\\it RXTE-ASM} light curve of\nlength 358 days each and the corresponding Lomb-Scargle periodograms are\nshown on the left and right hand sides respectively. The 99\\% confidence\nlimits are shown with the dashed horizontal lines.}\n\\end{figure}\n\n\\subsection{LMC X-3}\n\nLong term light curves of LMC X-3, obtained with the {\\it RXTE-ASM, GINGA-ASM}\nand {HEAO~1} are shown in Figure 4. The {HEAO~1} data, plotted in the lower\npanel of the figure, very clearly shows almost periodic intensity variations\nat about 100 days. However, as Cowley et al. (1991) pointed out, the intensity\nmodulation is missing during the first 100 days. They concluded from this data\nthat the intensity variations in LMC X-3 is periodic at $\\sim$ 198 (or\npossibly $\\sim$ 99) days. The {\\it GINGA-ASM} light curve shown in the middle\npanel of the figure also indicates intensity modulations, but at a larger time\nscale of about 200 days. Two such modulations can be clearly identified at the\nend of the light curve and one more in the middle. There are also some episodes\nof about 100 days periodic variations in some parts of the {\\it GINGA-ASM} light\ncurve. The {\\it RXTE-ASM} light curve of LMC X-3, as shown in the top panel\nof Figure 4, shows a varying nature of the approximately 100 or 200 days\nintensity variations. At the beginning, there are three strong modulations at\nabout 100 days, similar to what was seen with {\\it HEAO~1}, but in the later\npart of the light curve, the modulations are much less prominent and have\nlarger time scale. Intensity variations in LMC X-3 are not clearly visible in\nthe {\\it ARIEL 5} light curve (not shown here) because of sparse sampling.\n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=fig4.ps,width=2.2in,angle=-90}}\n\\caption[fig4.ps]{The long term light curves of LMC X-3 obtained with\nthe {\\it RXTE-ASM, GINGA-ASM} and {\\it HEAO~1} satellites. The energy ranges\nare 1.5--12 keV, 1--20 keV and 1--13 keV respectively.}\n\\end{figure}\n\nIn Figure 5 we have shown the periodograms generated from the light curves of\nLMC X-3 obtained with all the four satellites mentioned above. There are three\nprominent peaks at 104.4, 168.8 and 215.6 days in the periodogram obtained\nfrom the {\\it RXTE-ASM} light curve. The peak at 104.4 days is narrow while\nthe other two are broad. In the periodogram of the {\\it GINGA-ASM}, however,\nthere are two prominent peaks at 214 and 328 days. There is also a less\nsignificant indication of some periodic component at 105 days. The {\\it HEAO~1}\ndata which have been extensively discussed by Cowley et al. (1991), predictably\nshows two peaks at 99 and 203 days with the former being narrower. Results\nfrom the {\\it RXTE} and {\\it HEAO~1} are similar in nature except for the fact\nthat the broad peak near 200 days is resolved into two components in the {\\it\nRXTE-ASM} data. This also shows that the two peaks near 100 and 200 days as\nseen in the periodogram of the {\\it HEAO~1} data are not related. The\nperiodogram of the {\\it GINGA-ASM} light curve also has a shape similar to the\nother two but the time scale is a factor of two larger. The {\\it ARIEL 5}\nlight curve has low signal to noise ratio and infrequent sampling and the\nperiodogram obtained from this data shows three less significant peaks at 90,\n96 and 130 days. At periods below 50 days, this periodogram is very noisy.\nFrom the four periodograms shown in Figure 5 it appears that there is a quasi\nperiodic component at around 100 days in LMC X-3 whose strength is time\ndependent. There is at least one more component at longer period of about\n200 days. The period excursion of the $\\sim$100 days component is significant,\nbut relatively smaller than the other periodicities.\n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=fig5.ps,width=4.2in,angle=-90}}\n\\caption[fig5.ps]{The Lomb-Scargle periodograms generated from the light\ncurves of LMC X-3 obtained with the {\\it RXTE-ASM, GINGA-ASM, HEAO~1} and\n{\\it ARIEL 5} detectors. The dashed horizontal lines indicate the 99\\%\nconfidence limits.}\n\\end{figure}\n\nTo investigate the nature of the multiple components of intensity variations\nin more detail, we have done further analysis of the {\\it RXTE-ASM} data of\nLMC X-3 in a manner similar to what was done with the Cyg X-2 data. We divided\nthe light curve into two segments, each 540 days long, and have generated the\nperiodograms from both of the segments that are shown in Figure 6.\nTwo large peaks at 104.3 and 177.8 days are clearly seen in the first\nperiodogram whereas the periodogram generated from the second part of the\nlight curve shows two peaks at 101.9 and 221.6 days with much less strength.\nIt appears that the $\\sim$104 day periodicity is suppressed in the second\npart of the {\\it RXTE} data and the second component of intensity variation\nhas moved to a longer time scale. The significance of the peaks in the\nperiodograms are given in Table 1.\n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=fig6.ps,width=2.0in,angle=-90}}\n\\caption[fig6.ps]{The Lomb-Scargle periodograms obtained from two segments\nof the {\\it RXTE-ASM} light curve of LMC X-3. Each segment of the light curve\nis of 540 days duration. The dashed horizontal lines indicate the 99\\%\nconfidence limits.}\n\\end{figure}\n\n\\subsection{Spectral variations}\n\nIn Cyg X-2, the hardness ratio and intensity that define its position in\nthe Z track and also the position of the Z track itself, changes significantly\nat short time scales. But at longer time scales, in between different\nobservations, a negative correlation was found between the hardness ratio and\ntotal intensity with {\\it EXOSAT} (Kuulkers et al. 1996), {\\it GINGA}\n(Wijnands et al. 1997) and also with the {\\it RXTE-ASM} during its first few\nmonths observations (Wijnands et al. 1996). The hardness ratio in LMC X-3, on\nthe other hand was found to have positive correlation with intensity (Cowley\net al. 1991). We have calculated the two hardness ratios HR1 (3.0-5.0\nkeV/1.5-3.0 keV) and HR2 (5.0-12 keV/3.0-5.0 keV) from the {\\it RXTE-ASM}\ndata as a function of the total intensity for the two sources (Figure 7)\nusing all the available data. In Cyg X-2, HR2 is negatively correlated\nwith luminosity (correlation coefficient -0.6 and probability of no correlation\n10$^{-30}$) but HR1 does not show any correlation (coefficient -0.04,\nprobability 0.5). If the data points are connected by lines, the HR2 plot\nappears like a loop indicating that HR2 follows two different tracks during\nthe rising and decaying phases of the intensity variations. Large deviation\nin the hardness plot of Cyg X-2 is due to movement of the source along the Z\ntrack (Wijnands et al. 1996) and changing position of the Z track in the\ncolor-color diagram. In LMC X-3, a weak positive correlation is\nfound for HR1 (0.5, 10$^{-5}$) but no correlation for HR2 (-0.07, 0.5). The\ncorrelation coefficients and probabilities were calculated using two different\nmethods: the linear and rank correlation, both gave identical results.\n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=fig7.ps,width=3.2in,angle=00}}\n\\caption[fig7.ps]{Hardness ratios HR1 (3-5 keV / 1.5-5 keV) and HR2\n(5-12 keV/ 3-5 keV) of Cyg X-2 and LMC X-3 obtained from the {\\it RXTE-ASM}\ndata are plotted against the total intensity. Cyg X-2 data points are averaged\nfor 3 days and LMC X-3 data points are averaged for 10 days.}\n\\end{figure}\n\n\n\\section{Discussion}\n\nApart from the binary period, long term periodic variations are known to be\npresent in many X-ray binaries. There are four sources in which the presence\nof long periods is very well established, (1) Her X-1, a 1.7 day binary with a\n35 day period (Giacconi et al. 1973), (2) LMC X-4, a 1.4 day binary with a\n30.5 day period (Lang et al. 1981), (3) SMC X-1, a 3.9 day binary with a\nlong period of 60 days (Wojdowski et al. 1998) and (4) SS 433, a 13.1 day\nbinary with a long period of 164 days (Margon et al. 1979).\nIncidentally, the first three of these sources are also X-ray pulsars. In\nSS 433, the periodicities are detected photometrically and spectroscopically\nin the optical band only. There is also evidence of periodic component in\nseveral other sources. Among the high mass X-ray binaries, periodicity has been\nobserved in Cyg X-1 at 300 days (Priedhorsky et al. 1983, also see Kitamoto\net al. (1999) for the {\\it GINGA-ASM} observations of a $\\sim$150 day period),\n4U 1907+09 at 42 days (Priedhorsky \\& Terrell 1984)\nand LMC X-3 at 198 (or 99) days (Cowley et al. 1991). Among the low\nmass X-ray binaries, Smale \\& Lochner (1992) found periodicity in three\nsources, Cyg X-2 (78 days), 4U 1820-303 (175 days) and 4U 1916-053 (199 days).\nA 106 day periodicity was discovered from an extragalactic point source in\nthe spiral galaxy M33 (Dubus et al. 1997). The {\\it RXTE-ASM} observations of\na large number of sources, for the past three years, detected intensity\nvariations in many sources (see Levine 1998 for a summary and the light\ncurves). Some of these sources are of periodic nature and there has also been\ndiscovery of new periodic sources using the {\\it RXTE-ASM} data (Sco X-1,\nPeele \\& White 1996; X2127+119, Corbet, Peele \\& Smith 1996). Unstable\nlong-term periodicity that is attributed to activity of the companion star\nor instability of the accretion disk has been observed in Aql X-1 \n(Kitamoto et al. 1993). The ratio of the long and orbital periods in\nthese sources has a wide range between 5 (in 4U 1907+09) and 22,000 in (4U\n1820-303). In the two binaries Cyg X-2 and LMC X-3, the reported long term\nperiodicity is larger by a factor of 8 and 116 than the respective orbital\nperiods.\n\nThe long periods in Her X-1, LMC X-4 and SS 433 are believed to be produced\nby the precession of the accretion disks. The mechanisms proposed to cause the\nprecession of the disks are, (1) forced precession of a tilted disk by the\ngravitational field of the companion star (Katz 1973) and (2) precession of a\ndisk that is slaved to a misaligned companion star (Roberts 1974). But, the\ntime scale of precession expected in the sources in which binary parameters\nare well known is in disagreement with the observed long periods (Priedhorsky\n\\& Holt 1987). One additional problem is that a large excursion is observed\nin the long period of Her X-1 (\\\"Ogelman 1985) and SS 433 (Margon 1984), and it\nmay also be present in LMC X-4. This is not explained in the above two models\nof disk precession (see Priedhorsky \\& Holt 1987, for a detailed discussion).\nHowever, in a realistic case, when various factors like magnetic pressure,\nradiation pressure, tidal force, relativistic frame dragging etc. are\nconsidered, it is possible to have significant deviation in the precession\nperiod from its time averaged value. Recent developments in the models,\nincluding tilted\nand twisted disks due to coronal winds (Schandl \\& Meyer 1994; Schandl 1996)\nand warped precessing disks due to radiation pressure (Maloney, Begelman \\&\nPringle 1996; Wijers \\& Pringle 1998) have a provision for variations in\nthe precession period. Other models have also been considered to explain\nthe long periods. These are 1) precession of the compact object (Tr\\\"umper et\nal. 1986), 2) influence of a third body (Fabian et al. 1986) and 3) periodic\nmodulation of the mass accretion rate (Priedhorsky \\& Holt 1987). Among\nthese models, the first one is not applicable for black hole sources,\nand the second one appears to be not true for the two pulsars Her X-1\n(Tananbaum et al. 1972) and LMC X-4 (Pietsch et al. 1985). In Her X-1 and LMC\nX-4, the presence of a third body required to produce the long period, would\nhave resulted in additional detectable variations in the pulsation property\n(Priedhorsky \\& Holt 1987). Periodic and asymmetric mass transfer, which is\ninduced by the disk's shadowing of the Roche-lobe overflow region, also\ncontributes to the slaved nature of the accretion disk and is a possible\nmechanism. Mass transfer feedback induced by X-ray irradiation may also\ngenerate the observed long term periodicities (Osaki 1985).\n\nNo clear understanding of the reason behind the observed\nlong-term periodicities stands out among all these possibilities.\nNone of the possibilities mentioned above can explain the long-term\nperiodicity in all the sources. In the high mass X-ray binaries, the\nperiodicity is\ngenerally believed to be related to disk precession and in the low mass\nX-ray binaries another possibility is some type of disk instability or\nmodulation in the mass accretion rate related to or induced by the\nX-ray radiation (Meyer 1986).\n\nVarying obscuration by the disk (caused by precession), which provides a good\nexplanation for the long term periodicity, should have the following\nobservational consequence. With increased absorption in the low intensity\nphase, a hardening in the spectrum is expected which is known to be present\nin Her X-1 and LMC X-4. The spectral hardening is likely to be more pronounced\nbetween the two lower energy bands. Contrary to this expectation, we find that\nin Cyg X-2, HR1 is uncorrelated to the total intensity whereas HR2 is \nanti-correlated, and in LMC X-3, HR1 has a weak positive correlation (Figure\n7). Therefore, the spectral variations do not provide very good support to\nthe disk obscuration scenario.\n\nThe present work involving light curves of these two sources with very\nlarge time base suggests that there is no stable periodicity in either of\nthese systems. There are indications that the oscillatory components seen\nin the light curves have varying amplitude and period. Forced or slaved\nprecession of the accretion disk is unlikely to be the mechanism behind\nthe quasi periodic intensity variations observed here. Scenarios including\ndisk precession induced by radiation pressure or tilted and twisted disk\nstructure induced by wind also require spectral variations different from\nthe observed pattern. The presence of a third body is also likely to produce\nmore regular patterns in the intensity variations. Another plausible\nexplanation for the observed behaviour is instability in the disk or in the\nmass accretion rate. But Kuulkers et al. (1996) have pointed out that changes\nin the mass accretion rate is unlikely to produce the long term behaviour\nobserved in Cyg X-2, because changes in the mass accretion rate on a time\nscale of less than a day and associated spectral changes are in fact known\nto produce the Z pattern (Hasinger \\& van der Klis 1989).\n\nHowever,\nif we look only at the {\\it RXTE} ASM data of Cyg X-2 (Figure 3), it appears\nthat there are two unrelated components of intensity variations at periods of\n$\\sim$40 and $>$60 days, with the first component more stable in period than \nthe second one. The results obtained from LMC X-3 (Figures 5 and 6) is somewhat\nsimilar with a relatively stable component at $\\sim$100 days and a highly\nvarying component at $>$130 days. It is possible that in both objects\nthere are two sources of intensity variation, the first one relatively\nstable with a smaller period caused by precession of the accretion disk or by\na third body and the second one unstable in time and having a longer time\nscale caused by disk instability or changes in the mass accretion rate.\nCoupling between the two components may result in incorrect measurement\nof the period of the first component.\n\n\\begin{acknowledgements}\n\nWe thank an anonymous referee for many suggestions which helped to improve\na previous version of the manuscript.\nThis research has made use of data obtained through the High Energy\nAstrophysics Science Archive Research Center Online Service, provided by the\nNASA/Goddard Space Flight Center. We also thank the {\\it RXTE-ASM} and {\\it\nGINGA-ASM} teams for providing the valuable data. B. 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N.\n1998, ApJ, 502, 253\n\n\\end{thebibliography}\n%\\end{references}\n\n%\\placetable{tbl-1}\n\\begin{deluxetable}{lccc}\n\\footnotesize\n\\tablenum{1}\n\\tablecaption{Different periods and their significances\\label{tbl-1}}\n\\tablewidth{0pt}\n\\tablehead{\n\\colhead{Instrument}&\\colhead{Duration}&\\colhead{Periods (day)}\n&\\colhead{Periods in small segments} \\nl\n\\colhead{(energy band)}&\\colhead{(days)}&\\colhead{(false alarm prob.)}\n&\\colhead{(false alarm prob.)} \\nl\n}\n\n\\startdata\n& & {\\bf Cyg X-2} & \\nl\n\\nl\nRXTE-ASM & 1078 & 40.4 (1 E-20), 68.8 (7 E-25) & 39.5 (4 E-9), 70.1 (1 E-12) \\nl\n(1.5--12 keV) & & & 39.6 (9 E-6), 56.3 (7 E-8), 72.4 (3 E-7) \\nl\n & & & 41.8 (2 E-7), 56.8 (5 E-7), 73.7 (1 E-10) \\nl\nGINGA-ASM & 1645 & 53.7 (1 E-4), 61.3 (1 E-7) & \\nl\n(1--20 keV) & \\nl\nARIEL-5 & 1963 & 41.3, 46.2, 53.9\\tablenotemark{a}, 77.4 (1 E-16) & 45.7 (3 E-3), 55.3 (1 E-5), 78 (0.9)\\tablenotemark{b} \\nl\n(3--6 keV) & & & 43.2 (0.015), 68.6 (4 E-5), 78 (0.8)\\tablenotemark{b} \\nl\n\t & & & 41 (0.025), 53 (1 E-4), 78 (0.07)\\tablenotemark{b} \\nl\nVELA-5B & 3675 & 33.9 (0.4), 77.4 (0.03) \\nl\n(3--12 keV) & \\nl\n\\nl\n& & {\\bf LMC X-3} & \\nl\n\\nl\nRXTE-ASM & 1080 & 104 (3 E-38), 169 (2 E-27), 216 (1 E-28) &\n104 (3 E-27), 178 (2 E-35) \\nl\n(1.5--12 keV) & & & 102 (6 E-12), 222 (1 E-11) \\nl\nGINGA-ASM & 1682 & 105 (1.5 E-3), 214 (1 E-10), 328 (2 E-5) \\nl\n(1--20 keV) & \\nl\nHEAO 1 & 506 & 99 (2 E-16), 203 (4 E-12) \\nl\n(1--13 keV) \\nl\nARIEL-5 & 1903 & 96 (8 E-3), 130 (0.03) \\nl\n(3--6 keV) \\nl\n\n\n\\tablenotetext{a}{41.3 (1 E-15), 46.2 (7 E-20), 53.9 (2 E-23)}\n\\tablenotetext{b}{In the periodograms generated from the segments of\nARIEL 5 light curve, the peaks near 78 days are barely visible, but\nin the periodogram of the complete light curve it is highly significant\n(see Figure 2).}\n\\enddata\n\\end{deluxetable}\n\n\\end{document}\n\n\\figcaption[fig1.ps]{The {\\it RXTE-ASM} (1.5--12 keV) and {\\it GINGA-ASM}\n(1--20 keV) light curves of Cyg X-2. The days of the observations are given\nin truncated Julian days in the figure.}\n\n\\figcaption[fig2.ps]{The Lomb-Scargle periodograms obtained from the\n{\\it RXTE-ASM, GINGA-ASM, ARIEL 5} and {\\it VELA 5B} light curves of\nCyg X-2. The horizontal dashed line represent the 99\\% confidence limits\n(see text for details).}\n\n\\figcaption[fig3.ps]{Three segments of the {\\it RXTE-ASM} light curve of\nlength 358 days each and the corresponding Lomb-Scargle periodograms are\nshown on the left and right hand sides respectively. The 99\\% confidence\nlimits are shown with the dashed horizontal lines.}\n\n\\figcaption[fig4.ps]{The long term light curves of LMC X-3 obtained with\nthe {\\it RXTE-ASM, GINGA-ASM} and {\\it HEAO~1} satellites. The energy ranges\nare 1.5--12 keV, 1--20 keV and 1--13 keV respectively.}\n\n\\figcaption[fig5.ps]{The Lomb-Scargle periodograms generated from the light\ncurves of LMC X-3 obtained with the {\\it RXTE-ASM, GINGA-ASM, HEAO~1} and\n{\\it ARIEL 5} detectors. The dashed horizontal lines indicate the 99\\%\nconfidence limits.}\n\n\\figcaption[fig6.ps]{The Lomb-Scargle periodograms obtained from two segments\nof the {\\it RXTE-ASM} light curve of LMC X-3. Each segment of the light curve\nis of 540 days duration. The dashed horizontal lines indicate the 99\\%\nconfidence limits.}\n\n\\figcaption[fig9.ps]{Hardness ratios HR1 (3-5 keV / 1.5-5 keV) and HR2\n(5-12 keV/ 3-5 keV) of Cyg X-2 and LMC X-3 obtained from the {\\it RXTE-ASM}\ndata are plotted against the total intensity. Cyg X-2 data points are averaged\nfor 3 days and LMC X-3 data points are averaged for 10 days.}\n\n"
}
] |
[
{
"name": "astro-ph0002219.extracted_bib",
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}
] |
astro-ph0002220
|
Study of the Long Term Stability of two Anomalous X-ray Pulsars \axpa\ and \axpb\ with \asca
|
[
{
"author": "B. Paul"
},
{
"author": "\\footnotemark[1] M. Kawasaki"
},
{
"author": "T. Dotani"
},
{
"author": "and F. Nagase"
}
] |
We present new observations of two anomalous X-ray pulsars (AXP) \axpa\ and \axpb\ made in 1998 with the \asca. The energy spectra of these two AXPs are found to consist of two components, a power-law and a blackbody emission from the neutron star surface. These observations, when compared to earlier \asca\ observations in 1994 show remarkable stability in the intensity, spectral shape and pulse profile. However, we find that the spin-down rate in \axpb\ is not constant. In this source, we have clearly identified three epochs with spin-down rates different from each other and the average value. This has very strong implications for the magnetar hypothesis of AXPs. We also note that the spin-down rate and its variations in \axpb\ are much larger than what can normally be produced by an accretion disk with very low mass accretion rate corresponding to its low X-ray luminosity.
|
[
{
"name": "ms.tex",
"string": "\\documentstyle[epsfig,aas2pp4]{article}\n\n\\lefthead{B. Paul et al.}\n\\righthead{Long term emission stability of two AXPs}\n\n\\newcommand\\asca{{\\it ASCA}}\n\\newcommand\\exo{{\\it EXOSAT}}\n\\newcommand\\xte{{\\it RXTE}}\n\\newcommand\\ros{{\\it ROSAT}}\n\\newcommand\\gin{{\\it GINGA}}\n\\newcommand\\ein{{\\it Einstein}}\n\\newcommand\\sax{{\\it BeppoSAX}}\n\\newcommand\\axpa{4U~0142+61}\n\\newcommand\\axpb{1E~1048.1$-$5937}\n\\newcommand\\sgra{SGR~1806$-$20}\n\\newcommand\\sgrb{SGR~1900+14}\n\n\\begin{document}\n\n\\title{Study of the Long Term Stability of two Anomalous X-ray Pulsars\n\\axpa\\ and \\axpb\\ with \\asca}\n\n\\author{B. Paul,\\footnotemark[1] M. Kawasaki, T. Dotani, and F. Nagase}\n\n\\affil{The Institute of Space and Astronautical Science,\\\\\n3-1-1 Yoshinodai, Sagamihara, Kanagawa 229-8510, Japan;\\\\\nbpaul@astro.isas.ac.jp, kawasaki@astro.isas.ac.jp,\ndotani@astro.isas.ac.jp, nagase@astro.isas.ac.jp}\n\\footnotetext[1]{On leave from the Tata Institute of Fundamental\nResearch, Homi Bhabha road, Mumbai, 400005, India}\n\n\\date{}\n\n\\begin{abstract}\n\nWe present new observations of two anomalous X-ray pulsars (AXP) \\axpa\\ and\n\\axpb\\ made in 1998 with the \\asca. The energy spectra of these two\nAXPs are found to consist of two components, a power-law and a blackbody\nemission from the neutron star surface.\nThese observations, when compared to earlier \\asca\\\nobservations in 1994 show remarkable stability in the intensity, spectral\nshape and pulse profile. However, we find that the spin-down rate\nin \\axpb\\ is not constant. In this source, we have clearly identified\nthree epochs with spin-down rates different from each other and the average\nvalue. This has very strong implications for the magnetar hypothesis of AXPs.\nWe also note that the spin-down rate and its variations in \\axpb\\ are\nmuch larger than what can normally be produced by an accretion disk with\nvery low mass accretion rate corresponding to its low X-ray luminosity.\n\n\\end{abstract}\n\n\\keywords{stars: neutron --- Pulsars:\nindividual (\\axpa, \\axpb) --- X-rays: stars}\n\n\\section{Introduction}\n\nSome X-ray pulsars are known to have remarkable similarity in their\nproperties which are different from other binary or isolated X-ray pulsars\n(\\cite{mere95b}).\nThe properties common to most of these objects are\na) pulse period in a small range of 5--12 s,\nb) monotonous spin down with ${\\rm P} / \\dot {\\rm P}$ in the range of\n$5\\times10^{11} - 1.3\\times10^{13}$ s\nc) identical X-ray spectrum consisting of steep power-law ($\\Gamma = 3-4$)\nand black body component (kT $\\sim 0.5$ keV), \nd) stable X-ray luminosity (10$^{34}-10^{36}$ ergs s$^{-1}$) for years,\ne) faint or unidentified optical counterpart,\nand f) no evidence of orbital motion.\nThe sources also have a galactic distribution, most of these are within\n$|{b}|\\leq 0.5^\\circ$\nand all are probably young ($\\sim 10^4$ yr) because of their association\nwith SNR or molecular clouds. The objects in which all the properties\nmentioned above have been observed are \\axpa, 1E~2259+586, \\axpb,\n1RXS~J170849.0$-$400910 and 1E~1841$-$045 (Kes~73). Two more objects,\nAX~J1845.0$-$0300 (\\cite{tori98}) and RX~J0720.4$-$3125\n(\\cite{habe96}),\nalso probably belong to the same class but to establish their AXP candidacy,\nmore X-ray observations are required to measure their pulse period variations,\nsearch for possible pulse arrival time delay and investigate the flux\nstability. Classification of an object as AXP only from some properties\nsimilar to the above is not very firm. 4U~1626$-$67, probably a binary system,\nshowed both spin-up and spin-down (\\cite{chak97}) and also has an optically\nbright accretion disk (\\cite{midd81}). Another one object RX~J1838.4$-$0301\n(\\cite{schw94}), does not have stable intensity and pulsations are also not\nalways detectable (\\cite{song99}). Therefore, these two objects are not AXPs.\n\nConsidering the strong similarity between these handful of sources, it\nhas been proposed that they have same physical nature and different\nscenarios have been proposed to explain the observed properties. The\nprominent models are\na) accretion from low mass binary companion (\\cite{mere95b}),\nb) single neutron star accreting from molecular cloud, or a product of\ncommon envelope evolution (Thorne-$\\rm \\dot{Z}$ytkov object) of close high mass\nX-ray binaries in which a solitary neutron star accretes matter from a\nfossil disk (van Paradijs, Taam, \\& van den Heuvel \\cite{vanp95a};\nGhosh, Angelini, \\& White \\cite{ghos97}), and\nc) extremely high magnetic field neutron star radiating X-rays due to magnetic\nfield decay (\\cite{thom96}). Unlike the radio pulsars and rotationally\npowered X-ray pulsars, in the AXPs, the spin-down rate is not large enough\nto power the observed X-ray emission.\n\nAmong the 90 or so known X-ray pulsars (\\cite{naga99}), direct evidence of\nbinary nature is known for more than 35 sources (\\cite{vanp95b}). Including\nthe indirect evidences this number can be upto about 65 and 7 pulsars are\nisolated stars in SNR and are powered by rotational energy losses. In the\nrest of the pulsars, in which no binary signature is known, it is often due\nto lack of sufficient observation. However, the 7 objects which are either\nAXPs or candidate AXPs (or 10 if we include the 3 Soft Gamma-ray Repeaters\nin which pulsations have been detected), no binary signature has been found\nin spite of extensive searches. The strong upper limit on pulse arrival time\ndelay that has been obtained in some of these sources strongly suggests\nnon-binary nature for the AXPs. In addition, the spin change behaviour of the\nAXPs is also remarkably different from accreting pulsars (\\cite{bild97}).\nIn almost all the accreting X-ray pulsars, both spin-up and spin-down\nepisodes have been seen which may be randomly distributed (in persistent\nsources) or spin-downs in quiescence followed by rapid spin-ups during bright\ntransient phases (in transient pulsars) or long monotonic spin-up and\nspin-down episodes accompanied by spectral and luminosity changes\n(e.g. 4U~1626$-$67, \\cite{yiiv99}).\n\nThe AXPs are in many respect also similar to the X-ray counterparts of the\nSoft Gamma-ray Repeaters (SGR). The X-ray spectral and timing properties\nof these two type of objects have strong similarities, half of the AXPs and\nSGRs are associated with supernova remnants. This has lead to the suggestion\nthat the AXPs are also magnetars in which the X-ray emission is due to\nmagnetic field decay (\\cite{thom96}). The main difference between\nthese two type of objects is the non detection of SGR bursts from the AXPs.\nHowever, considering the rarity of the SGR activity among the established\nSGRs (\\cite{kouv96}), the absence of bursts from AXPs is not a\nserious issue. From a relatively young age of the AXP, 1E~1841$-$045 in the\nsupernova remnant Kes~73, Gotthelf, Vasisht, \\& Dotani (\\cite{gott99})\nproposed that in the evolutionary track, the AXPs are an early quiescent\nstate of the SGRs. Stability of the X-ray emission properties (spin-down\nrate, luminosity, spectral shape and pulse shape and fraction) is usually\nmentioned as one important aspect of the AXPs though one has to compare\nbetween observations made with different instruments for which the energy\nband, energy resolution and sensitivity are not identical. To make\na rigorous comparison in the stability of the X-ray emission properties\nwe have made new observations of two AXPs with the \\asca, four years\nafter two previous observations reported by \\cite{whit96} and Corbet \\&\nMihara (\\cite{corb97}). The aim was to critically examine the\nstability of the X-ray emission pattern and more pulse period measurements\nwhich may provide support to either the accretion powered or the magnetar\nhypothesis for these objects.\n\nThe source \\axpa\\ is close to a long period binary pulsar RX J0146.9+6121\nand in the \\exo\\ observations of this field in which pulsations were first\ndiscovered, pulsations from both the sources were observed simultaneously\n(\\cite{isra94}). With \\exo, the 8.7 s pulsations in this\nsource were detected only in the 1.0--4.0 keV range.\nA binary nature of the system was preferred in spite of a large X-ray to\noptical flux ratio and absence of pulse arrival time delay.\nThe source was subsequently observed with \\ros\\ and the pulse period\nwas found to be very close to the \\exo\\ measurement (\\cite{hell94}).\n\\asca\\ observation in 1994 confirmed the steady spin-down trend and\ndefined the spectral character clearly. A model consisting a 0.4 keV\nblackbody and a power law with a photon index of 3.7 was found to\ndescribe the spectrum well. From a\nsmall radius of a few km of the black body emission zone\n(which probably is on the\nsurface of the neutron star) \\cite{whit96} suggested that the black-body\ncomponent is more likely to be due to a spherical accretion rather than\naccretion from a disk. A small\npulse fraction and energy dependent pulse profile, double peak at low energy\nand single peak at high energy is characteristic of this pulsar. From \\xte\\\nobservations, the upper limit on the pulse arrival time delay was determined\nto be 260 ms in the 70 s to 2.5 days range thereby ruling out all types of\nbinary companions except white dwarf or low mass He main sequence star\n(\\cite{wils99}). \\sax\\ observations during 1997--98 confirmed\nthe spectral characteristics, pulse profiles and spin-down trend\n(\\cite{isra99b}). Observations spanning 20 years during 1979--1998, with\nthe \\ein, \\exo, \\ros, \\asca, \\sax\\ and \\xte\\ show an overall constant\nspin-down trend with $\\dot {\\rm P} = 2.2 \\times 10^{-12}$ s s$^{-1}$.\n\nPulsations in the source \\axpb\\ were discovered from observations\nwith the \\ein\\ observatory in 1979 and was confirmed by \\exo\\ observation\nin 1985 (\\cite{sewa86}). The energy spectrum was found to be a\npower-law type ($\\Gamma$ = 2.26) with low energy absorption (N$_{\\rm H} = 1.6\n\\times 10^{22}$ atoms cm$^{-2}$). The relatively harder power-law spectrum and\na candidate optical counterpart lead to the speculation that this can be a Be\nstar binary. Several \\gin\\ observations established a secular spin-down trend\nwith $\\dot {\\rm P} = 1.5 \\times 10^{-11}$ s s$^{-1}$ similar to a few other\nsoft spectrum pulsars (\\cite{corb90}). Subsequent \\ros\\ observations\nhowever revealed an increase in the spin-down rate which is remarkably\ndifferent from other established AXPs (\\cite{mere95a}). The low energy part of\nthe spectrum was first accurately measured with the \\asca\\ in 1994 (Corbet \\&\nMihara \\cite{corb97}).\nHowever, it could not distinguish between power-law ($\\Gamma =\n3.34$) and a combination of power-law ($\\Gamma$ = 2.0) and black-body (kT =\n0.55 keV). During the \\ros\\ and the \\asca\\ observations, the spin-down rate\nremained at a higher level of $3.3 \\times 10^{-11}$ s s$^{-1}$. A decrease\nin intensity by a factor of 3 compared to the \\exo\\ observation was also\nnoticed. \\sax\\ observation in 1997 showed that a combined black-body and\npower-law model fits the data well. The size of the black-body emission\nzone was found to be of the order of km$^2$, identical to other AXPs\n(\\cite{oost98}). Compared to other AXPs, the pulse fraction was\nfound to be much larger ($\\sim$ 65\\%) in \\axpb\\ and has little energy\ndependence. The power-law component is also relatively harder ($\\Gamma = 2\n\\sim 2.5$) compared to the other AXPs ($\\Gamma = 3 \\sim 4$). \\xte\\ observations\nin 1996--97 showed yet another change in the spin down rate, now close to that\nin 1980's. Long \\xte\\ observations established a small upper limit of 60 ms for\nany pulse arrival time delay for orbital period in the range of 200 s to 1.5\ndays. Based on this, any binary companion other than low mass helium burning\nstar in a face on system has been ruled out (\\cite{mere98}).\n\n\\section{Observations and data analysis}\n\nBoth the sources were observed twice with \\asca, in 1994 and in 1998 with\nabout 4 years time difference between the two observations. \\asca\\ has two\nSolid-state Imaging Spectrometers (SIS) and Gas Imaging Spectrometers (GIS)\neach at the focal plane of four identical mirrors of typical photon\ncollecting area 250 cm$^2$ at 6 keV. The energy resolution is 120 eV and\n600 eV (FWHM) at 6 keV for the SIS and GIS detectors respectively. For more\ndetails about \\asca\\ please refer to \\cite{tana94}. Details of the 1994\nobservations are given in Corbet \\& Mihara (\\cite{corb97}) and\n\\cite{whit96}. In 1998, the GIS observations were made in normal PH\nmode in which the time resolution\nis 64 ms and 500 ms at high and medium bit rates respectively. The SIS\nobservations were made with one of the CCD chips, and has time resolution\nof 4 s. The standard data selection criteria of the \\asca\\ guest observer\nfacility, that comprises a cut-off rigidity of charged particles 6 GeV/c,\nmaximum rms deviation from nominal pointing of 0.01 degree, minimum angle\nfrom Earth's limb 10$^\\circ$, satellite outside the South Atlantic Anomaly\nregion etc were applied. Data were removed from the hot and flickering pixels\nof the SIS detectors and also the charged particle events were removed\nfrom the GIS detectors based on rise time discrimination. For the two\nobservations of \\axpa, the source photons were extracted from circular\nregions of radius 6 arc min and 4 arc min around the source for GIS and SIS\nrespectively. In the case of \\axpb, the source photons were\nextracted from relatively smaller regions of 5 and 3 arc min respectively.\nFor SIS, the background spectra were accumulated from the whole chip\nexcluding a circular region around the source and for GIS it was collected\nfrom regions diametrically opposite to the source location in the field of\nview.\n\n\\subsection{Period analysis}\n\nTo calculate the pulse periods accurately, barycentric correction was\napplied to the arrival time of each photon and light curves were extracted\nfrom the pair of GIS detectors with a time resolution of 0.5 s in the\nenergy band of 0.5-10.0 keV. Epoch\nfolding method was applied to obtain the pulse periods approximately and\ntemplates for the pulse profiles were created by folding the light curves\nat the approximate pulse periods. Subsequently, the light curves were\ndivided into eight segments of equal length and pulse profiles were created\nfrom each of these segments by applying the same epoch and pulsation period.\nThe relative phases of the pulses were then\nevaluated by cross correlating the pulse profiles with the respective\ntemplates. A linear fit to the relative phases with their pulse numbers gave\nthe correction necessary to obtain the accurate pulse period. The 1998\nobservations of the two AXPs resulted in new measurement of pulse periods\nat these epochs and from the 1994 observations we obtained similar pulse\nperiods as reported earlier, with reduced uncertainty for \\axpa. The\npulse periods obtained for the two sources are given in Table 1. The pulse\nprofiles of the two sources in three energy bands are shown in Figure 1\nand Figure 2. The pulse fraction, defined as the ratio of the pulsed to total\nflux, was calculated from background subtracted pulse profiles in the 0.5--10.0\nkeV band. Pulse fractions were found to be identical in both the observations,\n$\\sim 9\\%$ and $\\sim 75\\%$ in \\axpa\\ and \\axpb\\ respectively. In \\axpa, the\npulse profile shows energy dependence, from double peaked in low\n(0.5--1.5 keV) and medium (1.5--4.0 keV) energy to single peaked in high\n(4.0--8.0 keV) energy, associated with increase in the pulse fraction.\nIn \\axpb, on the other hand, the pulse profile and pulse fraction are almost\nidentical over the \\asca\\ energy range. Light curves of the two sources\ndid not show any intensity variations at minutes to days time scale.\n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=fig1.ps,width=2.3in,angle=-90}}\n\\caption\n{The background subtracted pulse profiles of \\axpa\\ obtained\nwith the GIS in three energy bands are plotted for two cycles. A change\nin the pulse profile, from double peaked at low energies to single peaked\nat high energies can be noticed.}\\label{fig1}\n\\end{figure}\n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=fig2.ps,width=2.3in,angle=-90}}\n\\caption\n{The background subtracted pulse profiles of \\axpb, similar\nto Figure 1. The pulse fraction of this source is $\\sim$75\\%, highest among\nthe AXPs.}\\label{fig2}\n\\end{figure}\n\n\\subsection{Spectral analysis}\n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=fig3.ps,width=2.3in,angle=-90}}\n\\caption\n{The observed SIS and GIS energy spectra of \\axpa\\ shown with\nhistograms for the model spectra folded through the responses matrices\nand the residuals.}\\label{fig3}\n\\end{figure}\n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=fig4.ps,width=2.3in,angle=-90}}\n\\caption\n{The SIS and GIS energy spectra of \\axpb\\ along with the\nresiduals. The histograms represent the best fitted model folded with the\nresponse matrices. A simultaneous fitting of the SIS and GIS spectra was\nperformed.}\\label{fig4}\n\\end{figure}\n\nIn \\axpa, a simple absorbed power-law fit shows large residuals at low\nenergy and addition of a black-body component results in acceptable fit.\nFor the 1998 observation, inclusion of the black-body component improved\nthe reduced $\\chi ^2$ from 2.88 to 0.94 and 1.23 to 0.76 for the GIS and SIS\nrespectively. Similar improvement in fitting was reported by \\cite{whit96}\nfor the 1994 observation.\nThe photon index of the power-law component obtained from the SIS data\nfor the two observations are identical, $\\Gamma = 3.3$. The photon index\nfrom the GIS data is slightly different from the SIS value, $\\Gamma = 3.9$,\nbut it is identical for the two observations. The temperature of the black\nbody component obtained from both SIS and GIS are identical, 0.39 keV,\nin both the observations and the flux in the two components are also\nidentical. The difference in the photon index between the SIS and GIS can\npossibly be attributed to calibration uncertainty, because the in-flight\nspectral calibration of the spectrometers are done with sources which have\nrelatively harder spectra. The SIS and GIS spectra of the 1998 observation\nare shown in Figure 3 along with the best fitted models for the respective\ndetectors and the residuals to the model spectra.\n\nFor the other source \\axpb, Corbet and Mihara (\\cite{corb97}) showed that\nthe power-law and black-body with power-law models could not be\ndistinguished from spectral analysis of the \\asca\\ data. We have found\ndifferent and deeper minima in the $\\chi ^2$ for the black-body with\npower-law model. The improvement in $\\chi ^2$, ($\\Delta\\chi^2$ of 41 for\n292 degrees of freedom and 28 for 261 degrees of freedom for the 1998 and\n1994 observations respectively, both indicating probability of chance\noccurrence less than 10$^{-3}$) therefore favours the inclusion of a\nblack-body component. The black-body component has also been detected with\n\\sax\\ (\\cite{oost98}). The best fitted power-law plus black-body model\ngives a photon index of $\\sim 3.0$, black body temperature of $\\sim 0.56$\nkeV and column density of $\\sim 1 \\times 10^{22}$ atoms cm$^{-1}$. The\nspectral parameters are identical in both the \\asca\\ observations and are\ngiven in Table 2. Due to relative weakness of this source, \nsimultaneous spectral fitting was carried out with the GIS and SIS data\nfor the 1998 observation (Figure 4). However, for the 1994 observation,\nthe SIS were operated in FAST mode and spectra were available only\nfrom the two GIS detectors.\n\n\\section{Discussion}\n\n\\subsection{Period changes and Emission stability}\n\nThe pulse period measurements of \\axpa\\ is rather scarce except for the\nlast two years (Figure 5). In spite of the source being very bright, with a\nflux of more than 10$^{-10}$ erg cm$^{-2}$ in the 2.0--10.0 keV band, a pulse\nfraction of only about 10\\% has restricted the individual pulse period\nmeasurements accurate to only about ${{\\Delta {\\rm P}} / {\\rm P}} \\sim \n$ 10$^{-5}$. A linear fit to the pulse period history\nshows that of the 10 measurements available, only during the 1994 \\asca\\\nobservation the pulse period measurement was slightly different (2.5$\\sigma$)\nfrom the linear trend. If the reported errors of all the measurements are\ntaken at their face value, the linear fit gives a reduced $\\chi^2$ of 1.7\nfor 8 degrees of freedom. It therefore can be concluded that the recent \\asca\\\nmeasurement together with the previous results is consistent with a\nconstant spin-down rate. The observations are not yet sufficient to clearly\nidentify any significant variation from a constant spin-down rate.\n\nIn the source \\axpb, departure from a linear spin-down is already\nknown (\\cite{mere95a}; \\cite{oost98}). In this source, an order of\nmagnitude larger spin-down rate and better pulse period measurements\n$({{\\Delta {\\rm P}} / {\\rm P}} \\sim $ 10$^{-6})$, owing to a high pulse\nfraction $(\\sim 75\\%)$, help us to identify three different epochs of\nspin-down history. Though the method adopted for calculating the errors\nin the pulse period is not known for all the observations and the\nuncertainty level is likely to be nonuniform, a constant spin-down\ntrend can be ruled out without any doubt. A linear fit to the pulse\nperiod history with the reported errors gives a reduced $\\chi ^2$ of\n4500 for 11 degrees of freedom. Including the 1998 \\asca\\ observation\n(see Figure 6) with the recent \\sax\\ and \\xte\\ observations, we\nfind that from 1996 the source has a spin-down rate of $(1.67 \\pm 0.02)\n\\times 10^{-11}$ s s$^{-1}$. This is a factor of 2 smaller than the\nspin-down rate of $(3.29 \\pm 0.03) \\times 10^{-11}$ s s$^{-1}$ during\nthe 1994--1996 period. The present spin-down rate is closer to the value\nof $(1.5 \\pm 0.5) \\times 10^{-11}$ s s$^{-1}$, measured during the \\ein,\n\\exo\\ and \\gin\\ observations made in the period 1979--1988. The spin-down\nrate is much closer to being constant during these three epochs with\nreduced $\\chi ^2$ of 0.8, 7.7, and 36 for 3, 3, and 1 degrees of freedom\nrespectively.\n\nThese two sources do not show flux variability on time scales from\na few minutes to days. In the \\asca\\ observations of both the sources\nseparated by 4 years we have found that the overall intensity and spectral\nparameters have remarkable stability. A difference between the GIS and SIS\nphoton index that has been found in \\axpa, is due to calibration\nuncertainties. The spectral parameters obtained from the 1998 GIS and\nSIS observations are identical to the 1994 values. The spectral parameters\nobtained from the simultaneous fitting of the GIS and SIS spectra are\nsimilar to the \\sax\\ values obtained during 1997--1998.\nIn \\axpa, the flux history shows a rms variation of 15\\% around\nthe average value (Figure 5), and multiple measurements with the same\ninstrument (\\asca\\ and \\sax) gave almost identical flux.\nIn \\axpb, the over all intensity during the two \\asca\\ observations\nand one \\sax\\ observation in between are within $10\\%$ of the average value.\nThe 2.0--10.0 keV fluxes during the \\ein\\ and \\ros\\ observations\nare estimated by extrapolating the measurements in the low energy\nbands of 0.2--4.0 keV and 0.5--2.5 keV respectively, and using a\nrather low photon index of 2.26, obtained by \\exo.\nThe flux during the \\gin\\ observation is estimated by comparing the\npulsed fluxes during the \\gin\\ and \\exo\\ observations and assuming\nthat the pulse fraction remained same.\nThe flux measurements from the previous observations as shown in\nthe bottom panel of Figure 6 are about a factor 3 higher than the recent\nmeasurements with \\asca\\ and \\sax.\nWe note that there is some overestimation in extrapolation of the soft\nX-ray measurements with \\ein\\ and \\ros\\ due to a smaller photon index used,\nand the flux estimates from \\exo\\ and \\gin\\ could be overestimated due\nto contribution from the nearby bright and variable source $\\eta$-Carina,\nwhich is only 0.4$^\\circ$ away and is about 15 times brighter than \\axpb\\\n(\\cite{corc98}; \\cite{ishi99}).\nIn view of the stability of the flux during\n1994--1998, as obtained from the imaging instruments \\asca\\ and\n\\sax, it is possible that the overall intensity of this source\ndoes not vary at a few years times scale. The spectral parameters from\nthe two \\asca\\ observations are also identical and consistent with the values\nobtained with \\sax\\ in between. However, we note that in \\axpb,\nthe absorption column density obtained from the two \\asca\\ observations are\nidentical and a factor of 1.5--2 larger than the \\sax\\ measurement in\nbetween. This difference is somewhat larger than the known calibration\ndifference between the two instruments (\\cite{orra98}).\n\nSome Low Mass X-ray Binaries (LMXB) have also been detected at low\nluminosity levels ($\\sim10^{33}$ erg s$^{-1}$; e.g, Cen~X$-$4, Aql~X$-$1,\nsee \\cite{tana96} and references therein), understood to be quiescent phase\nof the Soft X-ray Transients (SXT). Usually the LMXB sources show both short\nand long term irregular intensity variations and many also show quasi-periodic\noscillations, bursts, dips or orbital modulation. Even though the AXPs\ndo not show significant temporal variations other than the pulsations, which\nis somewhat different from typical characteristics of low-luminosity LMXBs,\nthis itself is not a strong argument against the AXPs being LMXBs. \nOne LMXB which has some properties similar to the AXPs is 4U 1626$-$67. The\nX-ray luminosity, magnitude of spin-change rate, pulse period, and flux\nstability over very short to years time scale of this source are similar\nto the AXPs. But, presence of both spin-up and spin-down, quasi-periodic\noscillations, optically bright accretion disk, and a hard X-ray spectrum\nmakes it different from the AXPs.\n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=fig5.ps,width=2.3in,angle=-90}}\n\\caption\n{The pulse period and flux history of \\axpa. The straight line\nshows the best fit for a constant spin-down. The pulse period\nmeasurements with {\\it ASCA} are marked with filled circles and\nthe open circles are for all the other observations mentioned in the\ntext.\\label{fig5}}\n\\end{figure}\n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=fig6.ps,width=2.3in,angle=-90}}\n\\caption\n{The pulse period and flux history of \\axpb. The lines are\nused to identify the different spin-down epochs. The pulse period\nmeasurements with {\\it ASCA} are marked with filled circles\nand other observations with open circles.}\\label{fig6}\n\\end{figure}\n\n\\begin{figure}[t]\n\\centerline{\\psfig{figure=fig7.ps,width=2.6in,angle=-90}}\n\\caption\n{The X-ray luminosity and pulse fraction of the AXPs and SGRs are\nplotted against the magnetic field strength assuming that these objects\nare magnetars. Two values of the luminosity are plotted for \\axpb\\\nto show the uncertainty in its distance and same has been done for \\sgrb\\\nto show the variability in its X-ray emission. Distance of\n1RXS~J170849.0$-$400910 is taken to be 10 kpc and that for other sources are the\nbest available estimates.}\\label{fig7}\n\\end{figure}\n\n\\subsection{Accretion torque in the common envelope evolution model}\n\nIt has been proposed that the AXPs are recent remnants of common-envelope\nevolution of high-mass X-ray binaries (van Paradijs et al. \\cite{vanp95a};\nGhosh et\nal. \\cite{ghos97}). In this model, the pulsar is rotating near its equilibrium\nperiod, close to the Keplerian period at the innermost part of the disk.\nIf the pulsar is rotating at the equilibrium period, small changes in the\nmass accretion rate cause alternate spin-up and spin-down episodes. The\nover all spin-down is explained with the assumption that in the absence of\na companion star as the source of mass accretion, the mass accretion rate\nfrom the disk decreases slowly on viscous time scale. The equilibrium period\nof the pulsar is inversely related to the mass accretion rate and shows\nsecular increase. For \\axpb, which has a pulse period of 6.5 s and\nluminosity of $6.3 \\times 10^{33}$ erg s$^{-1}$ for a distance of 3 kpc\n(or in a more favourable case, $7 \\times 10^{34}$ erg s$^{-1}$ if the\nsource is at a distance of 10 kpc), the magnetic field strength inferred\nfor an equilibrium rotator (\\cite{fran92}) is\n${\\rm B} = 10^{11}~({\\rm P / 3})^{7 / 6}~{\\rm L_{35}}^{1 / 2} = \n6.2 \\times 10^{10}$ (or $2.1 \\times 10^{11}$) gauss. Here, and in what\nfollows we have assumed a neutron star with mass M = 1.4 ${\\rm M}_{\\sun}$,\nradius R = $10^6$ cm, and moment of inertia I = $10^{45}$ gm cm$^2$. A\npulse period of P implies that if in equilibrium, the co-rotation radius or in\nthis case the radius of the inner disk is ${\\rm r_M} = ({\\rm GM})^{1 / 3}~\n({{\\rm P} / {2\\pi}})^{2 / 3}$. The infalling material from the disk\ncarries a positive angular momentum of $\\dot {\\rm M}~({\\rm GMr_M})^{1 / 2}$.\nThe torque can also be expressed in terms of the pulse period P and the\nX-ray luminosity ${\\rm L}_X$ as ${\\rm RL_X~{({\\rm P / {2\\pi GM}})}^{1\n/ 3}}$. Even if we assume that all of the X-ray emission is a result of\ndisk accretion, the accretion torque is only 1.1 $\\times 10^{31}$\n(or 1.2 $\\times 10^{32}$) gm cm$^2$ s$^{-2}$. To achieve the\nobserved spin-down rate for a neutron star with moment of inertia $10^{45}$\ngm cm$^2$, the negative torque required to be imparted onto the neutron star\nis I$\\dot \\Omega = 4.9 \\times 10^{33}$ gm cm$^2$ s$^{-2}$. This is a factor\nof 450 (or 40) larger than the accretion torque, and in the common envelope\nevolution model, a negative dimensionless torque of this magnitude is required\nto spin-down the pulsar at the observed rate. In other words, the spin-down\nrate of this source is much larger than what can be achieved with disk\naccretion onto a neutron star with a luminosity of less than $10^{35}$ erg\ns$^{-1}$. \\axpb\\ does not fit in the classical picture of $\\dot\n{\\rm P}~vs~{\\rm PL}^{3 / 7}$ of the equilibrium rotators (\\cite{ghos79}).\nIn addition, the two \\asca\\ observations made during the two epochs which have\na factor of 2 different spin-down rates, do not show significant difference\nin the luminosity or the spectral parameters.\n\nAmong the other AXPs, 1RXS~J170849.0$-$400910 (\\cite{sugi97}; \\cite{isra99a})\nand 1E~1841$-$045 (Kes~73, \\cite{vasi97}; Gotthelf et al. \\cite{gott99}) have relatively large spin-down rate of $2.2 \\times\n10^{-11}$ and $4.1\\times 10^{-11}$ s s$^{-1}$ respective, while the X-ray\nluminosity is in the range of $10^{35} - 10^{36}$ erg s$^{-1}$. In the common\nenvelope evolution model of the AXPs, a faster spin-down compared to the\ntorque provided by the accreting matter can be a potential problem for these\ntwo sources also. For this model to be correct for the AXPs, a very fine\ntuning of the mass accretion rate is required. All the sources need to have\ndisk accretion rate a tiny fraction larger than the propeller regime.\n\\cite{lixd99} have identified several other problems in the context of\napplicability of this model to the AXPs. Most notable is the limited lifetime\nof an accretion disk around a solitary neutron star compared to the response\ntime scale of the neutron star to changes in the accretion torque. One possible\nalternative is that the spin-down is due to magnetically driven wind from\nan accretion disk, proposed also for \\sgrb\\ (\\cite{mars99}), but this will\nrequire a harder X-ray spectrum than what has been observed. \\cite{chat99}\nproposed a scenario in which the AXPs are formed as single neutron stars\nwith fossil disks made from fallback material from the supernovae explosions.\nIn this model, the spin-down from an initial period of a few ms to $\\sim$6 s\nis due to strong propeller effect at some period when the accretion rate is\nvery low. But, if accretion is the correct phenomenon in the AXPs, as high\nspin-down goes on in presence of substantial accretion, spin-down due to\nwind outflow seems to be more plausible than accretion induced angular\nmomentum loss. However, it should be remembered that the classical equilibrium\ndisk picture assumed here is often found not to be the most appropriate\ndescription for the X-ray pulsars (\\cite{bild97}).\n\n\\subsection{Magnetar model}\n\nIn view of a very narrow mass and type allowed for any binary companion,\nand several arguments against the common envelope evolution model, the magnetar\nmodel seems to be the most likely one for the AXPs. If the spin-down is\ndue to magnetic braking, dipole field strength of the order of $10^{14}$\ngauss is estimated for these sources. A nearly constant spin-down property\nwas thought to favour the magnetar model over a binary scenario. In two\nAXPs, 1E~1841$-$045 (Gotthelf et al. \\cite{gott99}), and 1RXS~J170849.0$-$400910\n(Kaspi, Chakrabarty \\& Steinberger \\cite{kasp99}), there is very strong\nevidence for constant spin-down, whereas in \\axpb, deviation from a linear\ntrend is clear. Recently, a deviation has also been detected from \\sgrb\\\n(Woods et al. \\cite{wood99}). 1E~2259+586, the most frequently observed AXP,\nhas provided an interesting pulse period history. Observations made for\nabout 15 years with many instruments preceding \\xte\\ showed considerable\nvariation in the spin-down rate (\\cite{bayk96}). But, the pulse-coherent\ntiming observations with \\xte\\ proved it to be otherwise, at least for a\nperiod of last 2.6 yr (Kaspi et al. \\cite{kasp99}).\n\nTwo scenarios have been proposed which can explain the changing spin-down\nrate even when the overall braking is due to the ultrastrong magnetic field.\n\\cite{mela99} showed that for reasonable neutron star parameters, a\nradiative precession effect may take place which\ncan give the observed spin-down variations with time scale of about 10 years.\nIt will be possible to verify this scenario when more pulse period\nmeasurements become available in the next few years. Woods et al.\n(\\cite{wood99}) have \nidentified a possible {\\it braking glitch} in \\sgrb\\ close to the time\nwhen SGR activity was very strong. But if the spin-down variation is\nrelated to the SGR activity, similar activities should have been observed\nfrom \\axpb\\ and 1E 2259+586. We have found that all the gamma ray\nbursts observed with the BATSE for which the estimated positions are\nwithin $2\\sigma$ of these AXPs (about 30 GRBs around each AXP),\nhave strong high energy emission unlike the\nSGR bursts. \\cite{heyl99} have proposed\nthat the spin-down variations can be explained as glitches (similar to radio\npulsars) superposed on constant spin-down. But, with recent pulse period\nmeasurements of \\axpb\\ and \\sgrb, this will require too many\nglitches, one before almost every observation unless there are {\\it braking\nglitches}, never observed in radio pulsars. \n\nIn the magnetar model, the X-ray emission is due to decay of the magnetic\nfield. The energy generated at the core is transported to the crust along\nthe magnetic field direction. The black body component of the spectrum is\nthermal emission from the hot spots at the magnetic polar regions and the\npower-law component is part of the thermal emission reprocessed by the\nmagnetic field and the environment. Investigation is required about the\nexpected pulse profile and its energy dependence. Time and/or energy\ndependence of the pulse profile as has been observed in \\sgra\\\n(\\cite{kouv98}) and \\sgrb\\ (\\cite{hurl99};\n\\cite{kouv99}; \\cite{mura99}) also requires to be addressed. A double\npeaked pulse profile at low energy and single peaked profile at high energy\nare observed in \\axpa\\ (Figure 1). The pulsation is very weak in some\nsources (only 5--10$\\%$ in \\sgra\\ and \\axpa), and 75$\\%$\nin \\axpb. If the pulsation is due to confinement of the\nheat in the magnetic polar regions by the magnetic field, a correlation\nbetween magnetic field strength and pulse fraction should be observed.\nBut, it is likely to be smeared by the geometric effect of individual\nsources, i.e. the orientation of the spin and magnetic axes with respect to\nthe line of sight. In the magnetar model, there are two mechanisms by which\nX-rays can be generated. If the X-ray emission is powered by decaying\nmagnetic field, the luminosity is a very strong function of the magnetic\nfield strength, ${\\rm L_x \\propto B^4}$ (\\cite{thom96}). Alternate\nprocess of X-ray generation is particle acceleration by Alfven waves\nresulting from small scale fracture of the crust, in this case ${\\rm L_x\n\\propto B^2}$. The X-ray luminosity and pulse fraction of five confirmed\nAXPs and two SGR sources are shown in Figure 7. against the magnetic\nfield strength. The later is estimated from pulse period and the overall\nspin-down rate assuming ${\\rm B = 3.2 \\times 10^{19}~(P\\dot P)^{1 / 2}}$\ngauss. Though there is uncertainty in the luminosity of some\nsources (see the caption of Figure 7), a 2nd or 4th power correlation between\n${\\rm L_X}$ and B does not seem to be present. There is also no correlation\nbetween pulse fraction and the magnetic field.\n\nA clustering of the pulse period of 10 sources (7 AXPs and 3 SGRs) in the\n5--12 s range also needs to be addressed, when the magnetars are expected\nto be alive in X-ray until they have slowed down to a pulse period of about\n70 s (\\cite{dunc92}). The magnetars are expected to be radio quiet\ndue to suppression of pair creation at high magnetic field (\\cite{bari98}),\nand this seems to be true for most sources.\n\nChanges in luminosity or small changes in the spectral parameters can be a\nresult of varying activities in the core, the heat generated from which is\ntransported to the surface along the direction of the magnetic field at time\nscale of a few years. Variability study of AXPs with very high sensitivity\nmay rule out magnetar model if significant change in column density is\nobserved. This will indicate the presence of accretion disk and wind in the\nneighbouring area. The \\sax\\ and \\asca\\ observations give identical column\ndensity for \\axpa\\ but slightly different column density in case of\n\\axpb. However, multiple observation of the later source with the\nsame instrument is found to give identical value indicating that the\ndifference between the two instruments can also be a systematic effect.\n\n\\section{Conclusion}\n\nUsing multiple observations of two AXPs with the {\\it \\asca} we have found\nremarkable stability in the intensity, spectral shape and pulse profile\nover a 4 years period. For the source \\axpb, we have\nconfirmed that similar to other AXPs, the spectrum consists of a power-law\ncomponent and a black body component. The spin-down trend of \\axpa\\ is\nconsistent with a constant rate whereas in \\axpb\\ we have clearly\nidentified three different spin-down epochs. We have shown that the fast\nspin-down of some of the AXPs is difficult to achieve with disk accretion.\nHence the common envelope evolution scenario of AXPs is unlikely to be the case,\nunless the spin-down is due to wind outflow from the disk. In this case\nalso, the stability of X-ray emission in spite of varying spin-down rate\nremains unexplained. The significantly different spin-down rates of\n\\axpb\\ in different epochs are also difficult to reconcile in the\nmagnetar model, unless precession is at work. But the flux stability and\nlack of variation of the spectral parameters appear to favour the magnetar\nmodel.\n\n\\begin{acknowledgements}\n\nWe thank an anonymous referee for many suggestions which helped to improve\na previous version of the manuscript. B. Paul was supported\nby the Japan Society for the Promotion of Science through a fellowship.\n\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\n\\bibitem[Baring \\& Harding 1998]{bari98}\nBaring, M. G., \\& Harding, A. K. 1998, \\apj, 507, L55\n\n\\bibitem[Baykal \\& Swank 1996]{bayk96}\nBaykal, A., \\& Swank, J. 1996, \\apj, 460, 470\n\n\\bibitem[Bildsten et al. 1997]{bild97}\nBildsten, L., et al. 1997, \\apjs, 113, 367\n\n\\bibitem[Chakrabarty et al. 1997]{chak97}\nChakrabarty, D., et al. 1997, \\apj, 474, 414\n\n\\bibitem[Chatterjee, Hernquist \\& Narayan (1999)]{chat99}\nChatterjee, P., Hernquist, L., \\& Narayan, R. 1999, astro-ph, 9912137\n\n\\bibitem[Corbet \\& Day 1990]{corb90}\nCorbet, R. H. D., \\& Day, C. S. R. 1990, \\mnras, 243, 553\n\n\\bibitem[1997]{corb97}\nCorbet, R. D., \\& Mihara, T. 1997, \\apj, 475, L127\n\n\\bibitem[Corcoran et al. 1998]{corc98}\nCorcoran, M. F., et al. 1998, \\apj, 494, 381\n\n\\bibitem[Duncan \\& Thompson]{dunc92}\nDuncan, R. C., \\& Thompson, C. 1992, \\apj, 392, L9\n\n\\bibitem[Frank, King \\& Raine 1992]{fran92}\nFrank, J., King, A., \\& Raine, D. 1992, Accretion Power in Astrophysics\n(2nd ed; Cambridge: Cambridge University Press)\n\n\\bibitem[1997]{ghos97}\nGhosh, P., Angelini, L., \\& White, N. E. 1997, \\apj, 478, 713\n\n\\bibitem[Ghosh \\& Lamb 1979]{ghos79}\nGhosh, P., \\& Lamb, F. K. 1979, \\apj, 234, 296\n\n\\bibitem[1999]{gott99}\nGotthelf, E. V., Vasisht, G., \\& Dotani, T. 1999, \\apj, 522, L49\n\n\\bibitem[Haberl et al. 1996]{habe96}\nHaberl, F., Pietsch, W., Motch, C., \\& Buckley, D. A. H. 1996, \\iaucirc, 6445\n\n\\bibitem[Hellier 1994]{hell94}\nHellier, C. 1994, \\mnras, 271, L21\n\n\\bibitem[Heyl \\& Hernquist (1999)]{heyl99}\nHeyl, J. S., \\& Hernquist, L. 1999, \\mnras, 304, L37\n\n\\bibitem[Hurley et al. 1999]{hurl99}\nHurley, K., et al. 1999, \\apj, 510, L111\n\n\\bibitem[Ishibashi et al. 1999)]{ishi99}\nIshibashi, K., et al. 1999, \\apj, 524, 983\n\n\\bibitem[Israel et al. 1999a]{isra99a}\nIsrael, G. L., Covino, S., Stella, L., Campana, S., Haberl, F., \\&\nMereghetti, S. 1999a, \\apj, 518, L107\n\n\\bibitem[Israel et al. 1999b]{isra99b}\nIsrael, G. L., et al. 1999b, \\aap, 346, 929\n\n\\bibitem[Israel, Mereghetti \\& Stella 1994]{isra94}\nIsrael, G. L., Mereghetti, S., \\& Stella, L. 1994, \\apj, 433, L25\n\n\\bibitem[1999]{kasp99}\nKaspi, V. M., Chakrabarty, D., \\& Steinberger, J. 1999, \\apj, 525, L33\n\n\\bibitem[Kouveliotou et al. 1998]{kouv98}\nKouveliotou, C., et al. 1998, \\nat, 393, 235\n\n\\bibitem[Kouveliotou et al. 1999]{kouv99}\nKouveliotou, C., et al. 1999, \\apj, 510, L115\n\n\\bibitem[Kouveliotou et al. 1996]{kouv96}\nKouveliotou, C., et al. 1996, \\nat, 379, 799\n\n\\bibitem[Li (1999)]{lixd99}\nLi, X. D. 1999, \\apj, 520, 271\n\n\\bibitem[Marsden, Rothschild, \\& Lingenfelter 1999]{mars99}\nMarsden, D., Rothschild, R. E., \\& Lingenfelter, R. E., 1999, \\apj, 520, L107\n\n\\bibitem[Melatos (1999)]{mela99}\nMelatos, A. 1999, \\apj, 519, L77\n\n\\bibitem[Mereghetti 1995]{mere95a}\nMereghetti, S. 1995, \\apj, 455, 598\n\n\\bibitem[Mereghetti, Israel, \\& Stella 1998]{mere98}\nMereghetti, S., Israel, G. L., \\& Stella, L. 1998, \\mnras, 296, 689\n\n\\bibitem[Mereghetti \\& and Stella 1995]{mere95b}\nMereghetti, S., \\& Stella, S. 1995, \\apj, 442, L17\n\n\\bibitem[Middleditch et al. 1981]{midd81}\nMiddleditch, J., Mason, K. O., Nelson, J. E., \\& White, N. E. 1981,\n\\apj, 244, 1001\n\n\\bibitem[Murakami et al. 1999]{mura99}\nMurakami, T., Kubo, S., Shibazaki, N., Takeshima, T., Yoshida, A., \\&\nKawai, N. 1999, \\apj, 510, L119\n\n\\bibitem[Nagase 1999]{naga99}\nNagase, F. 1999, in Highlights in X-ray Astronomy in Honour of Joachim\nTruemper's 65th birthday, eds. B. Aschenbach \\& M. J. Freyberg\n(MPE rep. 272; Garching: MPE), 74\n\n\\bibitem[Oosterbroek et al. 1998]{oost98}\nOosterbroek, T., Parmar, A. N., Mereghetti, S., \\& Israel, G. L. 1998, \\aap,\n334, 925\n\n\\bibitem[Orr et al. 1998]{orra98}\nOrr, A., Yaqoob, T., Parmar, A. N., Piro, L., White, N. E., \\& Grandi, P.\n1998 \\aap, 337, 685\n\n\\bibitem[Schwentker 1994]{schw94}\nSchwentker, O. 1994, \\aap, 286, L47\n\n\\bibitem[Seward, Charles, \\& Smale 1986]{sewa86}\nSeward, F. D., Charles, P. A., \\& Smale, A. P. 1986, \\apj, 305, 814\n\n\\bibitem[Song et al. 1999]{song99}\nSong, L., Mihara, T., Matsuoka, M., Negoro, H., \\& Corbet, R.\n1999, \\pasj, in press\n\n\\bibitem[Sugizaki et al. 1997]{sugi97}\nSugizaki, M., Nagase, F., Torii, K., Kinugasa, K., Asanuma, T., Matsuzaki, K.,\nKoyama, K., \\& Yamauchi, S. 1997, \\pasj, 49, L25\n\n\\bibitem[Tanaka, Inoue \\& Holt (1994)]{tana94}\nTanaka, Y., Inoue, H., \\& Holt, S. S. 1994, \\pasj, 46, L37\n\n\\bibitem[Tanaka \\& Shibazaki 1996]{tana96}\nTanaka, Y., \\& Shibazaki. N. 1996, \\araa, 34, 607\n\n\\bibitem[Thompson \\& Duncan 1996]{thom96}\nThompson, C. \\& Duncan, R. C. 1996, \\apj, 473, 322\n\n\\bibitem[Torii et al. 1998]{tori98}\nTorii, K., Kinugasa, K., Katayama, K., Tsunemi, H., \\& Yamaguchi, S. 1998, \\apj,\n503, 843\n\n\\bibitem[1995]{vanp95a}\nvan Paradijs, J., Taam, R. E., \\& van den Heuvel, E. P. J. 1995, \\aap, 299, L41\n\n\\bibitem[van Paradijs 1995]{vanp95b}\nvan Paradijs, J. 1995, in X-ray Binaries, eds. W. H. G. Lewin, J. van\nParadijs, \\& E. P. J. van den Heuvel (Cambridge: Cambridge University Press)\n536\n\n\\bibitem[Vasisht \\& Gotthelf 1997]{vasi97}\nVasisht, G., \\& Gotthelf, E. V. 1997, \\apj, 486, L129\n\n\\bibitem[White et al. (1996)]{whit96}\nWhite, N. E., Angelini, L., Ebisawa, K., Tanaka, Y., \\& Ghosh, P. 1996, \\apj,\n463, L83\n\n\\bibitem[Wilson et al. 1999]{wils99}\nWilson, C. A., Dieters, S., Finger, M., Scott, D. M., \\& van Paradijs, J.\n1999, \\apj, 513, 464\n\n\\bibitem[1999]{wood99}\nWoods, P. M., et al. 1999, \\apj, 524, L55\n\n\\bibitem[Yi \\& Vishniac 1999]{yiiv99}\nYi, I., \\& Vishniac, E. T. 1999, \\apj, 516, L87\n\n\\end{thebibliography}{}\n\n\\clearpage\n\n\\begin{deluxetable}{ccc}\n\\footnotesize\n\\tablenum{1}\n\\tablecaption{The pulse periods from the \\asca\\ observations\\label{tbl-1}}\n\\tablewidth{0pt}\n\\tablehead{\n\\colhead{Date of Observation}&\\colhead{Source name}&\\colhead{Pulse period}\\nl\n\\colhead{(MJD)}&\\colhead{}&\\colhead{(s)}\\nl}\n\\startdata\n\t\t&\t{\\bf \\axpa}&\\nl\n49614.1\t\t&&\t8.687873 $\\pm$ 0.000034\t\\nl\n51046.7\t\t&&\t8.688267 $\\pm$ 0.000024\t\\nl\n\\nl\n\\hline\n\\nl\n\t\t&\t{\\bf \\axpb}&\\nl\n49416.5\t\t&&\t6.446645 $\\pm$ 0.000001\\nl\n51021.1\t\t&&\t6.450815 $\\pm$ 0.000002\\nl\n\\nl\n\n\\enddata\n\n\\end{deluxetable}\n\n\\begin{deluxetable}{lccccccc}\n\\footnotesize\n\\tablenum{2}\n\\tablecaption{The spectral parameters\\label{tbl-2}}\n\\tablewidth{0pt}\n\\tablehead{\n\\colhead{}&\\colhead{}&\\colhead{}&\\colhead{\\bf \\axpa}&\\colhead{}&\\colhead{}&\\colhead{}\\nl\n\\colhead{Obs. date}&\\colhead{}&\\colhead{1994/09/18-19}&\\colhead{}&\\colhead{}&\\colhead{1998/08/21}&\\colhead{}\\nl\n\\colhead{}&\\colhead{GIS}&\\colhead{SIS}&\\colhead{SIS+GIS}&\\colhead{GIS}&\\colhead{SIS}&\\colhead{SIS+GIS}\\nl\n}\n\n\\startdata\nN$_{\\rm H}$\\tablenotemark{a} & 1.03 $\\pm 0.08$ & 0.92 $\\pm 0.05$ & 1.10 $\\pm 0.04$ & 1.08 $\\pm 0.09$ & 0.97 $\\pm 0.08$ & 1.17 $\\pm 0.04$ \\nl\nPhoton index & 3.9 $\\pm 0.1$ & 3.3 $\\pm 0.1$ & 3.84$\\pm 0.08$ & 3.98 $\\pm 0.15$ & 3.3 $\\pm 0.2$ & 3.87 $\\pm 0.09$ \\nl\nPower-law norm\\tablenotemark{b} & 0.26 $\\pm 0.05$ & 0.12 $\\pm 0.03$ & 0.25 $\\pm 0.03$ & 0.30 $\\pm 0.06$ & 0.10 $\\pm 0.03$ & 0.24 $\\pm 0.03$ \\nl\nBB temp (keV) & 0.39 $\\pm 0.01$ & 0.380 $\\pm 0.006$ & 0.382 $\\pm 0.007$ & 0.399 $\\pm 0.014$ & 0.384 $\\pm 0.005$ & 0.378 $\\pm 0.009$ \\nl\nBB norm\\tablenotemark{c}~~~~~~~~~~~ & 1.4 $\\pm 0.2$ & 1.9 $\\pm 0.1$ & 1.5 $\\pm 0.1$ & 1.16 $\\pm 0.18$ & 1.97 $\\pm 0.15$ & 1.30 $\\pm 0.12$ \\nl \nReduced $\\chi ^2$ / dof & 0.95 / 691 & 1.11 / 356 & 1.35 / 1030 & 0.76 / 354 & 0.94 / 287 & 1.76 /645 \\nl\nObserved flux\\tablenotemark{d} && 13.0 &&& 13.4 \\nl\n\n\\nl\n\\hline\n\\nl\n\n&&&{\\bf \\axpb} \\nl\nObs. date&&1994/03/02-05&&&1998/07/26-27 \\nl\n&GIS&&&&&SIS+GIS \\nl\n\\nl\n\\hline\nN$_{\\rm H}$\\tablenotemark{a} & 1.0 $\\pm 0.2$ &&&&& 1.21 $ \\pm0.24$ \\nl\nPhoton index & 2.9 $\\pm 0.3$ &&&&& 3.2 $\\pm 0.5$ \\nl\nPower-law norm\\tablenotemark{b} & 5 $\\pm 3~10^{-3}$&&&&& 7 $\\pm 4~10^{-3}$ \\nl\nBB temp (keV) & 0.57 $\\pm 0.04$ &&&&& 0.56 $\\pm 0.06$ \\nl\nBB norm\\tablenotemark{c} & 0.05 $\\pm 0.02$ &&&&& 0.060 $\\pm 0.015$ \\nl\nReduced $\\chi ^2$ / dof & 0.98 /261 &&&&& 0.62 / 292 \\nl\nUnabsorbed flux\\tablenotemark{d} & 0.58 &&&&& 0.60 \\nl\n\n\\tablenotetext{a}{$10^{22}$ atoms cm$^{-2}$}\n\\tablenotetext{b}{photons cm$^{-2}$ s$^{-1}$ keV$^{-1}$ at 1 keV}\n\\tablenotetext{c}{$10^{-3}$ photons cm$^{-2}$ s$^{-1}$}\n\\tablenotetext{d}{$10^{-11}$ ergs cm$^{-2}$ s$^{-1}$, 2-10 keV}\n\\enddata\n\n\\end{deluxetable}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002220.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Baring \\& Harding 1998]{bari98}\nBaring, M. G., \\& Harding, A. K. 1998, \\apj, 507, L55\n\n\\bibitem[Baykal \\& Swank 1996]{bayk96}\nBaykal, A., \\& Swank, J. 1996, \\apj, 460, 470\n\n\\bibitem[Bildsten et al. 1997]{bild97}\nBildsten, L., et al. 1997, \\apjs, 113, 367\n\n\\bibitem[Chakrabarty et al. 1997]{chak97}\nChakrabarty, D., et al. 1997, \\apj, 474, 414\n\n\\bibitem[Chatterjee, Hernquist \\& Narayan (1999)]{chat99}\nChatterjee, P., Hernquist, L., \\& Narayan, R. 1999, astro-ph, 9912137\n\n\\bibitem[Corbet \\& Day 1990]{corb90}\nCorbet, R. H. D., \\& Day, C. S. R. 1990, \\mnras, 243, 553\n\n\\bibitem[1997]{corb97}\nCorbet, R. D., \\& Mihara, T. 1997, \\apj, 475, L127\n\n\\bibitem[Corcoran et al. 1998]{corc98}\nCorcoran, M. F., et al. 1998, \\apj, 494, 381\n\n\\bibitem[Duncan \\& Thompson]{dunc92}\nDuncan, R. C., \\& Thompson, C. 1992, \\apj, 392, L9\n\n\\bibitem[Frank, King \\& Raine 1992]{fran92}\nFrank, J., King, A., \\& Raine, D. 1992, Accretion Power in Astrophysics\n(2nd ed; Cambridge: Cambridge University Press)\n\n\\bibitem[1997]{ghos97}\nGhosh, P., Angelini, L., \\& White, N. E. 1997, \\apj, 478, 713\n\n\\bibitem[Ghosh \\& Lamb 1979]{ghos79}\nGhosh, P., \\& Lamb, F. K. 1979, \\apj, 234, 296\n\n\\bibitem[1999]{gott99}\nGotthelf, E. V., Vasisht, G., \\& Dotani, T. 1999, \\apj, 522, L49\n\n\\bibitem[Haberl et al. 1996]{habe96}\nHaberl, F., Pietsch, W., Motch, C., \\& Buckley, D. A. H. 1996, \\iaucirc, 6445\n\n\\bibitem[Hellier 1994]{hell94}\nHellier, C. 1994, \\mnras, 271, L21\n\n\\bibitem[Heyl \\& Hernquist (1999)]{heyl99}\nHeyl, J. S., \\& Hernquist, L. 1999, \\mnras, 304, L37\n\n\\bibitem[Hurley et al. 1999]{hurl99}\nHurley, K., et al. 1999, \\apj, 510, L111\n\n\\bibitem[Ishibashi et al. 1999)]{ishi99}\nIshibashi, K., et al. 1999, \\apj, 524, 983\n\n\\bibitem[Israel et al. 1999a]{isra99a}\nIsrael, G. L., Covino, S., Stella, L., Campana, S., Haberl, F., \\&\nMereghetti, S. 1999a, \\apj, 518, L107\n\n\\bibitem[Israel et al. 1999b]{isra99b}\nIsrael, G. L., et al. 1999b, \\aap, 346, 929\n\n\\bibitem[Israel, Mereghetti \\& Stella 1994]{isra94}\nIsrael, G. L., Mereghetti, S., \\& Stella, L. 1994, \\apj, 433, L25\n\n\\bibitem[1999]{kasp99}\nKaspi, V. M., Chakrabarty, D., \\& Steinberger, J. 1999, \\apj, 525, L33\n\n\\bibitem[Kouveliotou et al. 1998]{kouv98}\nKouveliotou, C., et al. 1998, \\nat, 393, 235\n\n\\bibitem[Kouveliotou et al. 1999]{kouv99}\nKouveliotou, C., et al. 1999, \\apj, 510, L115\n\n\\bibitem[Kouveliotou et al. 1996]{kouv96}\nKouveliotou, C., et al. 1996, \\nat, 379, 799\n\n\\bibitem[Li (1999)]{lixd99}\nLi, X. D. 1999, \\apj, 520, 271\n\n\\bibitem[Marsden, Rothschild, \\& Lingenfelter 1999]{mars99}\nMarsden, D., Rothschild, R. E., \\& Lingenfelter, R. E., 1999, \\apj, 520, L107\n\n\\bibitem[Melatos (1999)]{mela99}\nMelatos, A. 1999, \\apj, 519, L77\n\n\\bibitem[Mereghetti 1995]{mere95a}\nMereghetti, S. 1995, \\apj, 455, 598\n\n\\bibitem[Mereghetti, Israel, \\& Stella 1998]{mere98}\nMereghetti, S., Israel, G. L., \\& Stella, L. 1998, \\mnras, 296, 689\n\n\\bibitem[Mereghetti \\& and Stella 1995]{mere95b}\nMereghetti, S., \\& Stella, S. 1995, \\apj, 442, L17\n\n\\bibitem[Middleditch et al. 1981]{midd81}\nMiddleditch, J., Mason, K. O., Nelson, J. E., \\& White, N. E. 1981,\n\\apj, 244, 1001\n\n\\bibitem[Murakami et al. 1999]{mura99}\nMurakami, T., Kubo, S., Shibazaki, N., Takeshima, T., Yoshida, A., \\&\nKawai, N. 1999, \\apj, 510, L119\n\n\\bibitem[Nagase 1999]{naga99}\nNagase, F. 1999, in Highlights in X-ray Astronomy in Honour of Joachim\nTruemper's 65th birthday, eds. B. Aschenbach \\& M. J. Freyberg\n(MPE rep. 272; Garching: MPE), 74\n\n\\bibitem[Oosterbroek et al. 1998]{oost98}\nOosterbroek, T., Parmar, A. N., Mereghetti, S., \\& Israel, G. L. 1998, \\aap,\n334, 925\n\n\\bibitem[Orr et al. 1998]{orra98}\nOrr, A., Yaqoob, T., Parmar, A. N., Piro, L., White, N. E., \\& Grandi, P.\n1998 \\aap, 337, 685\n\n\\bibitem[Schwentker 1994]{schw94}\nSchwentker, O. 1994, \\aap, 286, L47\n\n\\bibitem[Seward, Charles, \\& Smale 1986]{sewa86}\nSeward, F. D., Charles, P. A., \\& Smale, A. P. 1986, \\apj, 305, 814\n\n\\bibitem[Song et al. 1999]{song99}\nSong, L., Mihara, T., Matsuoka, M., Negoro, H., \\& Corbet, R.\n1999, \\pasj, in press\n\n\\bibitem[Sugizaki et al. 1997]{sugi97}\nSugizaki, M., Nagase, F., Torii, K., Kinugasa, K., Asanuma, T., Matsuzaki, K.,\nKoyama, K., \\& Yamauchi, S. 1997, \\pasj, 49, L25\n\n\\bibitem[Tanaka, Inoue \\& Holt (1994)]{tana94}\nTanaka, Y., Inoue, H., \\& Holt, S. S. 1994, \\pasj, 46, L37\n\n\\bibitem[Tanaka \\& Shibazaki 1996]{tana96}\nTanaka, Y., \\& Shibazaki. N. 1996, \\araa, 34, 607\n\n\\bibitem[Thompson \\& Duncan 1996]{thom96}\nThompson, C. \\& Duncan, R. C. 1996, \\apj, 473, 322\n\n\\bibitem[Torii et al. 1998]{tori98}\nTorii, K., Kinugasa, K., Katayama, K., Tsunemi, H., \\& Yamaguchi, S. 1998, \\apj,\n503, 843\n\n\\bibitem[1995]{vanp95a}\nvan Paradijs, J., Taam, R. E., \\& van den Heuvel, E. P. J. 1995, \\aap, 299, L41\n\n\\bibitem[van Paradijs 1995]{vanp95b}\nvan Paradijs, J. 1995, in X-ray Binaries, eds. W. H. G. Lewin, J. van\nParadijs, \\& E. P. J. van den Heuvel (Cambridge: Cambridge University Press)\n536\n\n\\bibitem[Vasisht \\& Gotthelf 1997]{vasi97}\nVasisht, G., \\& Gotthelf, E. V. 1997, \\apj, 486, L129\n\n\\bibitem[White et al. (1996)]{whit96}\nWhite, N. E., Angelini, L., Ebisawa, K., Tanaka, Y., \\& Ghosh, P. 1996, \\apj,\n463, L83\n\n\\bibitem[Wilson et al. 1999]{wils99}\nWilson, C. A., Dieters, S., Finger, M., Scott, D. M., \\& van Paradijs, J.\n1999, \\apj, 513, 464\n\n\\bibitem[1999]{wood99}\nWoods, P. M., et al. 1999, \\apj, 524, L55\n\n\\bibitem[Yi \\& Vishniac 1999]{yiiv99}\nYi, I., \\& Vishniac, E. T. 1999, \\apj, 516, L87\n\n\\end{thebibliography}"
}
] |
astro-ph0002221
|
Long-term photometry of the Wolf-Rayet stars WR 137, WR 140, WR 148, and WR 153 \thanks{Based on observations collected at the National Astronomical Observatory Rozhen, Bulgaria}
|
[
{
"author": "Kiril P. Panov\\inst{1}"
},
{
"author": "Martin Altmann\\inst{2}"
},
{
"author": "Wilhelm Seggewiss\\inst{2}"
}
] |
In 1991, a long term $UBV$-photometry campaign of four Wolf-Rayet stars was started using the 60 cm telescope of the National Astronomical Observatory Rozhen, Bulgaria. Here we report on our observational results and discuss the light variations. The star WR\,137 was observed during 1991 - 1998. No indications of eclipses were found, though random light variations with small amplitudes exist, which are probably due to dynamical wind instabilities. WR\,140 was also monitored between 1991 and 1998. In 1993, a dip in the light curve in all passbands was observed shortly after periastron passage, with amplitude of 0.03\,mag in $V$. This is interpreted in terms of an ``eclipse'' by dust condensation in the WR-wind. The amplitude of the eclipse increases towards shorter wavelengths; thus, electron scattering alone is not sufficient to explain the observations. An additional source of opacity is required, possibly Rayleigh scattering. After the eclipse, the light in all passbands gradually increased to reach the ``pre-eclipse'' level in 1998. The very broad shape of the light minimum suggests that a dust envelope was built up around the WR-star at periastron passage by wind-wind interaction, and was gradually dispersed after 1993. Our observations of WR\,148 (WR + c?) confirm the 4.3 d period; however, they also show additional significant scatter. Another interesting finding is a long-term variation of the mean light (and, possibly, of the amplitude) on a time scale of years. There is some indication of a 4 year cycle of that long-term variation. We discuss the implications for the binary model. Our photometry of WR\,153 is consistent with the quadruple model of this star by showing that both orbital periods, 6.7 d (pair A) and 3.5 d (pair B), exist in the light variations. A search in the HIPPARCOS photometric data also reveals both periods, which is an independant confirmation. No other periods in the light variability of that star are found. The longer period light curve shows only one minimum, which might be due to an atmospheric eclipse; the shorter period light curve shows two minima, indicating that both stars in pair B are eclipsing each other. \keywords{stars: Wolf-Rayet -- stellar winds -- binaries: eclipsing -- binaries: spectroscopic -- techniques: photometric}
|
[
{
"name": "9201.tex",
"string": "%\\documentclass[referee]{aa}\n\\documentclass{aa}\n\n\\usepackage{graphics}\n\n\\begin{document}\n \n\\title{Long-term photometry of the Wolf-Rayet stars \nWR 137, WR 140, WR 148, and WR 153\n\\thanks{Based on observations collected at the National\nAstronomical Observatory Rozhen, Bulgaria}}\n\n\\author{Kiril P. Panov\\inst{1},\nMartin Altmann\\inst{2},\n\\and Wilhelm Seggewiss\\inst{2}}\n\n\\institute{Institute of Astronomy, Bulgarian Academy \nof Sciences, Sofia, Bulgaria \\and\nUniversit\\\"atssternwarte Bonn, Auf dem H\\\"ugel 71, D-53121 Bonn, Germany}\n\n\\date{Received 31 August 1999/18 Januar 2000}\n\n\\thesaurus{03.20.4:08.02.2;08.02.4;08.03.4;08.23.2}\n\n\\offprints{kpanov@astro.bas.bg}\n\n\\maketitle\n\n\\markboth{K.~P. Panov et~al., Long-term photometry of WR stars}\n \t{K.~P. Panov et~al., Long-term photometry of WR stars}\n\n\\begin{abstract}\nIn 1991, a long term $UBV$-photometry campaign of four Wolf-Rayet stars\nwas started using the 60 cm telescope of the National Astronomical \nObservatory Rozhen, Bulgaria.\nHere we report on our observational results and discuss the\nlight variations.\n\nThe star WR\\,137 was observed during 1991 - 1998. \nNo indications of eclipses were found, though random \nlight variations with small amplitudes\nexist, which are probably due to dynamical wind instabilities. \n\nWR\\,140 was also monitored between 1991 and 1998. \nIn 1993, a dip in the light curve in all passbands\nwas observed shortly after periastron passage, \nwith amplitude of 0.03\\,mag in $V$. This is interpreted \nin terms of an ``eclipse'' by dust condensation\nin the WR-wind. The amplitude \nof the eclipse increases towards shorter \nwavelengths; thus, electron scattering alone is \nnot sufficient to explain the observations. An additional \nsource of opacity is required, possibly Rayleigh \nscattering. After the eclipse, the light in all \npassbands gradually increased to reach the \n``pre-eclipse'' level in 1998.\nThe very broad shape of the light minimum suggests \nthat a dust envelope was built up around the WR-star \nat periastron passage by wind-wind interaction,\nand was gradually dispersed after 1993. \n\nOur observations of WR\\,148 (WR + c?) confirm \nthe 4.3 d period; however, they also show \nadditional significant scatter.\nAnother interesting finding is a long-term variation \nof the mean light (and, possibly, of the amplitude) on a time scale\nof years. There is some indication of a 4 year cycle of\nthat long-term variation. We discuss the \nimplications for the binary model. \n\nOur photometry of WR\\,153 is consistent \nwith the quadruple model of this star \nby showing that both orbital periods, \n6.7 d (pair A) and 3.5 d (pair B),\nexist in the light variations. A search in the HIPPARCOS \nphotometric data also reveals both\nperiods, which is an independant confirmation. \nNo other periods in the light variability of that \nstar are found. The longer period light curve shows \nonly one minimum, which might be due to an atmospheric eclipse; \nthe shorter period light curve shows two minima, \nindicating that both stars in pair B are eclipsing each other. \n\\keywords{stars: Wolf-Rayet -- stellar winds -- binaries: eclipsing \n-- binaries: spectroscopic -- techniques: photometric} \n\\end{abstract}\n\n%sec1\n\\section{Introduction}\n\n\n%tab1\n\\begin{table*}\n\\caption[]{Summary of data for the program stars. The last\ntwo columns contain\\\\ the emission line-contribution to the \ncolours (Pyper 1966)}\n\\label{summary}\n\\begin{tabular}{rrcrrrr}\n\\hline\\noalign{\\smallskip}\n WR & HD & Spectral & Comparison & Check & $\\delta(B-V)$ & $\\delta(U-B)$ \\\\ \n & & types & star, HD & star, HD & [mag] & [mag] \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n137 & 192641 & WC7+abs & 192538 & 192987 & +0.07 & $-0.11$ \\\\\n140 & 193793 & WC7+O4-5 & 193888 & 193926 & +0.05 & $-0.12$ \\\\\n148 & 197406 & WN7+c? & 197619 & 196939 & +0.01 & $-0.01$ \\\\\n153 & 211853 & 2$\\times$WN+O, or & 211430 & $---$ & +0.02 & $-0.02$ \\\\\n & & WN+O and O+O & & & & \\\\\n \\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table*}\n\n \nPhotometric studies of Wolf-Rayet (WR) stars \nduring the past decades (e.g. Moffat \\& Shara 1986; Lamontagne \n\\& Moffat 1987; van Genderen et al. 1987; Balona \net al. 1989; Robert et al. 1989; Gosset et al. 1990;\nAntokhin et al. 1995; Marchenko et al. 1998a;\nMarchenko et al. 1998b) have revealed \nlight variations of several per cent \n(up to 0.1 mag) on time-scales (typically) \nof days. WR stars are generally \nbelieved to be evolved Population I stars, \ndescendants of Of-type stars (Maeder 1996). \nThey exhibit strong, dense winds (mass loss rates \nof $10^{-5}$ to $10^{-4}$ M$_{\\sun}$ yr$^{-1}$) which, in most cases,\nhide the stellar surface. The wind-flow is \ndependant on time. Moffat et al. (1988,\n1994) and Robert (1994) discovered the existence \nof small, outward moving wind condensations, which they called\npropagating blobs. Unlike most O-type stars, the continuum \nlight of many WR stars originates from a layer\nin the dense wind ($\\tau = 1$), a ``pseudo-photosphere'' \n(van Genderen et al. 1987), which could be \ninhomogeneous because of dynamical wind instabilities. \nThe brightness variations of some WR stars proved to be periodic \nand are possibly due to binary or rotation \neffects. Core (photospheric) eclipses as well as\natmospheric eclipses have been observed. The \nlatter are characterized by only one V-shaped minimum on \nthe light curve, which is caused by the atmospheric \neclipse of an O-type star by the\nWR star's extended wind (Lamontagne et al. 1996). \nRandom light variations are common in WR stars \nand they are often superimposed on the regular \n(binary) variations, increasing the ``noise'' and\nsometimes even totally disturbing the underlying \nregular light variations. \nMarchenko et al. (1998b) suggested that random light\nvariations (light scatter) may be caused \nby short-lived, core-induced, multimode fluctuations,\npropagating in the wind. Other causes of variability, \nsuch as radial pulsations (Maeder 1985)\nnon-radial pulsations (Vreux 1985, Antokhin et al. \n1995, Rauw et al. 1996) and axial rotation \n(Matthews \\& Moffat 1994) have been proposed for WR stars. \nOccasional ``eclipses'' caused by dust formation in \nlate-type WC stars have been studied by Veen et al. (1998). \n\n\nWR\\,137 is a well known dust maker (Williams 1997; \nMarchenko et al. 1999). However little is known \nabout long-term light variations for that star and \nits binary status is still uncertain.\nWR\\,140 is another repeating dust maker \n(Williams 1997). The orbit is well determined.\nBecause of its high eccentricity ($e = 0.84$) the\nstrongest wind interaction occurs at periastron\npassage. During the last periastron passage in 1993,\nWR\\,140 received much attention and has been studied at\ndifferent wavelengths from X-ray to radio. \nHowever, only a few photometric studies in the\noptical were carried out so far and the long-term \nbehaviour of that star is not known. \nBoth stars WR\\,137 and WR\\,140 are included in the\ninfrared study by Williams et al. (1987a) and\nreported to have dust shells.\n\nWR\\,148 is a good candidate for a \nWR + c (WR plus compact companion) binary. There is some \ncontroversy about the light variations concerning the period\nand the shape of the light curve. Marchenko et al. \n(1998a) were not able to detect the 4.31 d\nbinary period in the HIPPARCOS photometry data, \notherwise well known from ground-based \nobservations (Marchenko et al. 1996). The very\n``noisy'' light curve and unusually broad \nminimum need further investigation.\n\nWR\\,153 is a quadruple system (Massey 1981), containing \na WN + O and an O + O system, or\ntwo WN + O pairs (Panov \\& Seggewiss\n1990). During the past years, several photometric \nstudies have been carried out. Yet the light \nvariability of the two pairs could not always be \nunambiguously separated (Lamontagne et al. 1996).\nOur aim is to try to solve some of these controversial questions.\n\n%sec 2\n\\section{Observations}\n\nIn 1991 we started a long-term photometric study of the\nfour WR stars at the National Astronomical Observatory Rozhen,\nBulgaria, using the 60 cm telescope and the UBV single channel,\nphoton counting photometer.\nThe photometric equipment has been used\nfor many years and proved to be very\nstable (cf. Panov et al. 1982).\n\nTable~1 contains the comparison and the check\nstars used. Generally, a 20\\arcsec\\,diaphragm and an integration\nof 10\\,s were used. Each measurement consists of four consecutive \nintegration cycles. An observing cycle was arranged in the \nfollowing way: Sky - Comp - WR - Comp - Sky\nand was repeated 3 to 5 times,\ndepending on the quality of the night. A separate\nmeasurement of the comparison star against\nthe check star in the same way was obtained\nbefore or after the WR star observation.\nThus a nightly mean was\ncalculated from the 3 to 5 individual measurements.\nThe standard error of the nightly mean is \n0.003 - 0.005 mag in most cases.\nReduction of the data was made taking into account\ndead-time effects, atmospheric extinction, and transformation\ninto the standard $UBV$ system. In the following tables\nwe present the magnitudes in the standard system; for WR\\,137,\nWR\\,140, and WR\\,148 the data are magnitude\ndifferences in the sense: comparison\nstar minus WR star. The contribution $\\delta(B-V)$ and $\\delta(U-B)$\nof emission lines to the respective colours are taken from\nPyper (1966) and included in Table~1 (last\ntwo columns). No corrections have been applied\nfor emission lines in our data. However, it does\nseem possible to distinguish the continuum\nlight from the emission line variations by\ncomparing the light in the $UBV$ passbands.\n \nMany WR stars show subtle short and long term variations \nas can be seen in the case of\nWR\\,148 (Sec. 3.3). Therefore it is preferable\nto use the same photometric equipment for long term studies. This reduces\npossible systematic effects caused by slightly different passbands or\nresponse curves. \n\n\n%fig1\n\\begin{figure}\n \\centering\n \\resizebox{08cm}{!}{\\includegraphics{9201-f1.eps}}\n \\hfill\n \\caption{Light curves of WR\\,137 (data from Table 2)}\n\\end{figure}\n\n%fig2\n\\begin{figure}%[h]\n \\centering\n \\resizebox{8cm}{!}{\\includegraphics{9201-f2.eps}}\n \\hfill\n \\caption{Random light variability correlations for WR\\,137\n (data from Table 2).}\n\\end{figure}\n \n\n\n%tab2\n\\begin{table}\n\\caption[]{Differential photometry of WR\\,137\n(= HD 192641) -- in the sense comparison\nstar HD 192538 minus WR\\,137}\n \\setlength\\tabcolsep{10pt}\n\\renewcommand{\\baselinestretch}{0.8}\n\\small\n\\begin{tabular}{rcccc}\n\\hline\n\\noalign{\\smallskip}\nYear & JD-2400000 & $\\Delta V$ & $\\Delta B$ & $\\Delta U$ \\\\\n & & [mag] & [mag] & [mag] \\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n1991 & 48563.225 & $-$1.483 & $-$1.734 & $-$1.382 \\\\\n & 48565.229 & $-$1.481 & $-$1.732 & $-$1.386 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n1992 & 48860.395 & $-$1.475 & $-$1.743 & $-$1.402 \\\\\n & 48861.395 & $-$1.464 & $-$1.731 & $-$1.394 \\\\\n & 48862.429 & $-$1.461 & $-$1.741 & $-$1.424 \\\\\n & 48863.410 & $-$1.472 & $-$1.737 & $-$1.409 \\\\\n & 48865.367 & $-$1.478 & $-$1.748 & $-$1.418 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n1993 & 49212.437 & $-$1.483 & $-$1.751 & $-$1.399 \\\\\n & 49220.396 & $-$1.491 & $-$1.740 & $-$1.402 \\\\\n & 49221.359 & $-$1.478 & $-$1.734 & $-$1.386 \\\\\n & 49222.392 & $-$1.481 & $-$1.744 & $-$1.392 \\\\\n & 49223.375 & $-$1.476 & $-$1.743 & $-$1.400 \\\\\n & 49224.392 & $-$1.477 & $-$1.746 & $-$1.405 \\\\\n & 49225.398 & $-$1.472 & $-$1.744 & $-$1.432 \\\\\n & 49233.341 & $-$1.483 & $-$1.741 & $-$1.386 \\\\\n & 49234.354 & $-$1.492 & $-$1.751 & $-$1.395 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n1995 & 49922.475 & $-$1.478 & $-$1.715 & $-$1.406 \\\\\n & 49947.449 & $-$1.467 & $-$1.728 & $-$1.385 \\\\\n & 49949.428 & $-$1.457 & $-$1.725 & $-$1.378 \\\\\n & 49976.379 & $-$1.466 & $-$1.732 & $-$1.371 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n1996 & 50313.390 & $-$1.474 & $-$1.740 & $-$1.383 \\\\\n & 50317.344 & $-$1.480 & $-$1.719 & $-$1.384 \\\\\n & 50317.361 & $-$1.471 & $-$1.715 & $-$1.377 \\\\\n & 50318.343 & $-$1.472 & $-$1.729 & $-$1.381 \\\\\n & 50318.363 & $-$1.473 & $-$1.734 & $-$1.385 \\\\\n & 50321.358 & $-$1.482 & $-$1.752 & $-$1.404 \\\\\n & 50321.375 & $-$1.476 & $-$1.743 & $-$1.408 \\\\\n & 50322.316 & $-$1.470 & $-$1.724 & $-$1.377 \\\\\n & 50322.338 & $-$1.470 & $-$1.729 & $-$1.383 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n1997 & 50676.374 & $-$1.460 & $-$1.710 & $-$1.377 \\\\\n & 50711.311 & $-$1.467 & $-$1.701 & $-$1.364 \\\\\n & 50714.272 & $-$1.470 & $-$1.707 & $-$1.372 \\\\\n & 50730.268 & $-$1.464 & $-$1.707 & $-$1.373 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n1998 & 51046.379 & $-$1.465 & $-$1.705 & $-$1.386 \\\\\n & 51049.343 & $-$1.462 & $-$1.720 & $-$1.393 \\\\\n & 51050.331 & $-$1.468 & $-$1.729 & $-$1.391 \\\\\n & 51053.334 & $-$1.457 & $-$1.721 & $-$1.395 \\\\\n & 51054.310 & $-$1.464 & $-$1.726 & $-$1.386 \\\\\n & 51058.364 & $-$1.484 & $-$1.736 & $-$1.398 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n%sec3\n\\section{Discussion}\n\n%sec31\n\\subsection{WR\\,137}\n\nWR\\,137 = HD 192641 (WC7 + ?) has been studied in the \ninfrared (IR) and peaks in brightness were \nreported in 1984.5 and in 1997, \nprobably caused by heated dust (Williams 1997). \nThe dust emission has been directly IR-imaged at two epochs\nrecently using the Hubble Space Telescope by\nMarchenko et al. (1999).\nThe repetition of IR maxima occurs with a $\\sim$13 yr\nperiod, suggesting a possible binary origin, as found\nfor other WR periodic dust makers. WR\\,137 was \ndiscovered to be a spectroscopic binary by Annuk (1995). \nHowever, Underhill (1992) did not find any evidence for \nbinary motion in her data. Therefore, the binary status of\nWR\\,137 remains uncertain. \n\nMarchenko \\& Pikhun (1992)\npublished a long-term photometric study for 1958 - 1989,\nbut it is based on photographic plates and the \naccuracy is insufficient to reveal light variations\nbelow a few per cent. Our photometry is presented\nin Table 2 and the light curves are shown in Fig 1. \nWe searched for periodicities using the procedure of Lafler \n\\& Kinman (1965), in the period range from 1 d to 100 d,\n but no period could be found.\nThe only photometric variations we can see in\nour data are random light variations with amplitudes\nof 0.02 mag (peak to peak) in $V$ during each observing \nseason and up to \n0.03 mag (peak to peak) when we compare different years. \n(However, the peak to peak amplitude from all data is\n0.05\\,mag in $B$, and 0.07\\,mag in $U$.)\nDuring 1991-1998 22 measurements of the check star HD\\,192987\nwere obtained. The mean values (N = 22) of the magnitude \ndifferences (HD\\,192538 minus HD\\,192987) and their standard\ndeviations are $\\Delta V = 0.002 \\pm0.008$ mag\nand $\\Delta B = 0.088 \\pm0.009$ mag. \nThe scatter in Fig.\\,1 is greater than the observational error\n($\\sim 5\\,\\sigma$\\,in\\,$B!$) and, therefore, probably contains real \nerratic variations with small amplitudes. \n\nIn 1997, when the last \npeak in the IR was observed (Williams 1997), no\nphotometric effect can be seen, apart\nfrom small-amplitude random variations. Their origin \nshould arise in the continuum, as the plots in Fig. 2 suggest:\nThere are some correlations ($r = 0.58$ for $B$ and $V$\nand $r = 0.64$ for $U$ and $B$) \nbetween the lightcurves in each of the three\npassbands, which would be difficult to explain\nby variability of emission lines. The origin \nof the small-amplitude random continuum \nvariations of WR\\,137 is possibly related to dynamical wind\ninstabilities, resulting in temperature effects \nat the ``pseudo-photospheric'' level.\n\n%tab3\n\\begin{table}\n\\caption[]{Differential photometry of WR\\,140\n(= HD 193793) -- in the sense comparison star\nHD 193888 minus WR\\,140. Orbital phases are\ncalculated with $P = 2900$ d and $T_0 = 1985.26$.}\n\\renewcommand{\\baselinestretch}{0.8}\n\\small\n\\begin{tabular}{rccccc}\n\\hline\n \\noalign{\\smallskip}\nYear & JD-2400000 & orb. & $\\Delta V$ & $\\Delta B$ & $\\Delta U$ \\\\\n & & phase & [mag] & [mag] & [mag] \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1991 & 48540.340 & 0.821 & 1.685 & 1.266 & 1.377 \\\\\n & 48563.250 & 0.829 & 1.650 & 1.247 & 1.354 \\\\\n & 48565.256 & 0.829 & 1.653 & 1.248 & 1.349 \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1992 & 48781.539 & 0.904 & 1.659 & 1.249 & 1.358 \\\\\n & 48860.432 & 0.931 & 1.672 & 1.255 & 1.359 \\\\\n & 48861.420 & 0.932 & 1.678 & 1.256 & 1.351 \\\\\n & 48862.457 & 0.932 & 1.680 & 1.268 & 1.349 \\\\\n & 48863.434 & 0.932 & 1.671 & 1.243 & 1.348 \\\\\n & 48865.387 & 0.933 & 1.686 & 1.267 & 1.349 \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1993 & 49212.469 & 0.053 & 1.652 & 1.232 & 1.333 \\\\\n & 49220.422 & 0.055 & 1.647 & 1.238 & 1.331 \\\\\n & 49221.379 & 0.056 & 1.649 & 1.243 & 1.333 \\\\\n & 49222.410 & 0.056 & 1.654 & 1.241 & 1.337 \\\\\n & 49223.396 & 0.056 & 1.645 & 1.228 & 1.323 \\\\\n & 49224.413 & 0.057 & 1.655 & 1.238 & 1.330 \\\\\n & 49233.362 & 0.060 & 1.647 & 1.236 & 1.344 \\\\\n & 49234.373 & 0.060 & 1.640 & 1.232 & 1.332 \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1994 & 49582.463 & 0.180 & 1.661 & 1.250 & 1.339 \\\\\n & 49584.433 & 0.181 & 1.669 & 1.252 & 1.347 \\\\\n & 49585.395 & 0.181 & 1.662 & 1.243 & 1.342 \\\\\n & 49586.402 & 0.182 & 1.679 & 1.259 & 1.345 \\\\\n & 49586.422 & 0.182 & 1.675 & 1.260 & 1.348 \\\\\n & 49587.385 & 0.182 & 1.665 & 1.246 & 1.343 \\\\\n & 49587.402 & 0.182 & 1.665 & 1.246 & 1.343 \\\\\n & 49589.392 & 0.183 & 1.670 & 1.252 & 1.343 \\\\\n & 49589.411 & 0.183 & 1.668 & 1.250 & 1.345 \\\\\n & 49594.392 & 0.184 & 1.664 & 1.250 & 1.342 \\\\\n & 49594.410 & 0.184 & 1.659 & 1.245 & 1.339 \\\\\n & 49594.428 & 0.184 & 1.665 & 1.247 & 1.340 \\\\\n & 49595.345 & 0.185 & 1.671 & 1.258 & 1.342 \\\\\n & 49596.352 & 0.185 & 1.670 & 1.246 & 1.329 \\\\\n & 49666.296 & 0.209 & 1.663 & 1.244 & 1.343 \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1995 & 49922.534 & 0.297 & 1.656 & 1.228 & 1.324 \\\\\n & 49947.473 & 0.306 & 1.672 & 1.259 & 1.350 \\\\\n & 49949.451 & 0.307 & 1.669 & 1.258 & 1.348 \\\\\n & 49953.368 & 0.308 & 1.675 & 1.249 & 1.360 \\\\\n & 49954.396 & 0.308 & 1.671 & 1.260 & 1.359 \\\\\n & 49958.414 & 0.310 & 1.676 & 1.242 & 1.342 \\\\\n & 49976.408 & 0.316 & 1.673 & 1.249 & 1.353 \\\\\n & 49977.368 & 0.316 & 1.663 & 1.242 & 1.350 \\\\\n & 49998.263 & 0.324 & 1.661 & 1.243 & 1.355 \\\\\n & 50001.288 & 0.325 & 1.661 & 1.240 & 1.352 \\\\\n & 50003.256 & 0.325 & 1.665 & 1.244 & 1.357 \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1996 & 50313.427 & 0.432 & 1.674 & 1.249 & 1.354 \\\\\n & 50317.392 & 0.433 & 1.675 & 1.250 & 1.362 \\\\\n & 50318.402 & 0.434 & 1.673 & 1.258 & 1.360 \\\\\n & 50321.401 & 0.435 & 1.677 & 1.259 & 1.354 \\\\\n & 50322.369 & 0.435 & 1.676 & 1.263 & 1.355 \\\\\n & 50359.295 & 0.448 & 1.668 & 1.248 & 1.361 \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1997 & 50676.407 & 0.557 & 1.677 & 1.277 & 1.372 \\\\\n & 50711.345 & 0.569 & 1.674 & 1.277 & 1.387 \\\\\n & 50714.301 & 0.570 & 1.672 & 1.277 & 1.391 \\\\\n & 50730.294 & 0.576 & 1.664 & 1.265 & 1.368 \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1998 & 51046.413 & 0.685 & 1.678 & 1.272 & 1.371 \\\\\n & 51049.369 & 0.686 & 1.689 & 1.278 & 1.381 \\\\\n & 51050.356 & 0.686 & 1.688 & 1.279 & 1.385 \\\\\n & 51053.389 & 0.687 & 1.689 & 1.275 & 1.377 \\\\\n & 51054.365 & 0.688 & 1.689 & 1.277 & 1.382 \\\\\n & 51059.329 & 0.689 & 1.683 & 1.280 & 1.387 \\\\\n \\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n%fig3\n\\begin{figure}\n \\centering\n \\resizebox{08cm}{!}{\\includegraphics{9201-f3.eps}}\n \\hfill\n \\caption{Long-term light variations of WR\\,140 (data from Table 3)}\n\\end{figure}\n\n%tab4\n\\begin{table}\n\\caption[]{Differential photometry of WR\\,148\n(= HD 197406)\\\\ -- in the sense comparison\nstar HD 197619 minus WR\\,148.\\\\ Orbital phases\nare calculated with $P = 4.317364$ d\\\\ and\n$T_0 =$ JD 2432434.4 (Drissen et al. 1986).}\n% \\setlength\\tabcolsep{10pt}\n\\renewcommand{\\baselinestretch}{0.8}\n\\small\n\\begin{tabular}{rccccc}\n\\hline\n \\noalign{\\smallskip}\nYear & JD-2400000 & orb. & $\\Delta V$ & $\\Delta B$ & $\\Delta U$ \\\\\n & & phase & [mag] & [mag] & [mag] \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1993 & 49212.502 & 0.19 & $-$1.908 & $-$2.313 & $-$2.231 \\\\\n & 49220.454 & 0.03 & $-$1.929 & $-$2.331 & $-$2.264 \\\\\n & 49221.402 & 0.25 & $-$1.900 & $-$2.287 & $-$2.209 \\\\\n & 49222.432 & 0.49 & $-$1.910 & $-$2.302 & $-$2.215 \\\\\n & 49223.419 & 0.72 & $-$1.896 & $-$2.288 & $-$2.213 \\\\\n & 49224.434 & 0.95 & $-$1.941 & $-$2.334 & $-$2.257 \\\\\n & 49233.384 & 0.03 & $-$1.913 & $-$2.309 & $-$2.234 \\\\\n & 49234.395 & 0.26 & $-$1.866 & $-$2.253 & $-$2.170 \\\\\n & 49235.373 & 0.49 & $-$1.878 & $-$2.288 & $-$2.215 \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1994 & 49582.507 & 0.89 & $-$1.987 & $-$2.382 & $-$2.307 \\\\\n & 49584.468 & 0.35 & $-$1.951 & $-$2.344 & $-$2.263 \\\\\n & 49585.424 & 0.57 & $-$1.884 & $-$2.222 & $-$2.134 \\\\\n & 49586.454 & 0.81 & $-$1.923 & $-$2.326 & $-$2.248 \\\\\n & 49587.429 & 0.03 & $-$1.955 & $-$2.348 & $-$2.270 \\\\\n & 49589.442 & 0.50 & $-$1.951 & $-$2.343 & $-$2.271 \\\\\n & 49594.476 & 0.67 & $-$1.928 & $-$2.329 & $-$2.251 \\\\\n & 49595.373 & 0.87 & $-$1.973 & $-$2.360 & $-$2.281 \\\\\n & 49596.375 & 0.10 & $-$1.962 & $-$2.353 & $-$2.272 \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1996 & 50313.505 & 0.21 & $-$1.942 & $-$2.337 & $-$2.263 \\\\\n & 50317.435 & 0.12 & $-$1.955 & $-$2.365 & $-$2.284 \\\\\n & 50318.436 & 0.35 & $-$1.964 & $-$2.346 & $-$2.266 \\\\\n & 50321.462 & 0.05 & $-$1.947 & $-$2.321 & $-$2.247 \\\\\n & 50322.404 & 0.27 & $-$1.922 & $-$2.307 & $-$2.222 \\\\\n & 50358.324 & 0.59 & $-$1.899 & $-$2.292 & $-$2.209 \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1997 & 50676.447 & 0.27 & $-$1.922 & $-$2.284 & $-$2.201 \\\\\n & 50714.327 & 0.05 & $-$1.913 & $-$2.281 & $-$2.212 \\\\\n & 50730.322 & 0.75 & $-$1.876 & $-$2.250 & $-$2.175 \\\\\n & 50731.317 & 0.98 & $-$1.905 & $-$2.272 & $-$2.199 \\\\\n & 50732.292 & 0.21 & $-$1.883 & $-$2.249 & $-$2.170 \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1998 & 51046.452 & 0.98 & $-$1.942 & $-$2.316 & $-$2.245 \\\\\n & 51049.406 & 0.66 & $-$1.933 & $-$2.303 & $-$2.229 \\\\\n & 51050.390 & 0.89 & $-$1.930 & $-$2.302 & $-$2.207 \\\\\n & 51050.405 & 0.89 & $-$1.924 & $-$2.304 & $-$2.212 \\\\\n & 51053.419 & 0.59 & $-$1.930 & $-$2.299 & $-$2.220 \\\\\n & 51054.392 & 0.81 & $-$1.924 & $-$2.288 & $-$2.218 \\\\\n & 51058.419 & 0.75 & $-$1.936 & $-$2.303 & $-$2.226 \\\\\n & 51059.399 & 0.97 & $-$1.949 & $-$2.321 & $-$2.245 \\\\\n \\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n%sec32\n\\subsection{WR\\,140}\n\nWR\\,140 = HD 193793 (WC7 + O4-5) is another \nperiodic dust maker.\nWilliams et al. (1978, 1987a, 1987b, 1990) and \nWilliams (1997) reported variations in the IR,\nrevealing brightenings in 1977, 1985, and in 1993,\nwhich they attributed to the building of dust \ngrains in the WR\\,140 wind with a period of\n7.94 yr. The re-occurrence of the heated dust has been\ninterpreted as due to wind-wind interaction in a binary\nsystem. Earlier spectroscopic studies failed to \nreveal the binary motion. However, a re-analysis \nof earlier published radial velocities and using the \nperiod in the IR (7.94 yr) led to a successful \ndetermination of the orbit (Williams et al. 1987c).\nIt was found that the grain formation coincides with \nthe periastron passage (PP) in the system (actually\noccurring before PP). This\ndiscovery was later confirmed by Moffat et al. (1987)\nand now presents the basic model for studies of\nWR\\,140. Williams et al. (1990) and van der Hucht et\nal. (1991) reported on variability of WR\\,140 at\nX-ray, UV, IR and radio-wavelengths.\nOur photometry of WR\\,140 is presented in Table 3\nand the light curves are shown in Fig. 3. From \nFig. 3, there is clear evidence for a dip in\nthe light in 1993, between orbital phases $\\sim$0.9\nand 1.1. The dip is seen in all passbands and should therefore be\ndue to continuum light attenuation. The amplitude\nof the ``eclipse'' in the $V$ passband is 0.03 mag.\n\n%fig4\n\\begin{figure}%[h]\n \\centering\n \\resizebox{8cm}{!}{\\includegraphics{9201-f4.eps}}\n \\hfill\n \\caption{WR\\,140. Random light variability correlations for 1994\n (data from Table 3)}\n\\end{figure}\n\nTwo remarkable features are to be mentioned. First, the very \nbroad shape of the light minimum, assuming a smooth trend \nbetween yearly data. After 1993, the light \ngradually increased to reach the ``pre-eclipse''\nlevel in 1997, or even 1998. Considering the ``eclipse'' to be caused by \nan obscuration of the star(s) by the wind, the light curves\nstrongly suggest that a dust envelope was built up\naround the WR star by the wind-wind interaction \nat the PP, which was gradually dispersed in\nthe following years. Possibly it is the same\ndust observed in the IR when still heated. \nSecond, it is apparent (Fig.~3) that the\namplitude of the eclipse increases towards\nshorter wavelengths. In the lower panel of Fig.~3, \nthe variation of the colour $\\Delta(U - V)$ is shown, \nwhich is in the sense: WR\\,140 colour gets redder\nwhen its light is attenuated. This conclusion is \neasily obtained when considering the magnitudes of \nthe comparison star HD 193888, which are: $V = 8.54$, \n$B-V = -0.07$, $U-B = -0.25$, and $U-V = -0.32$.\nThe amplitude of the colour variation in $U-V$ of WR\\,140 is \n0.04 mag (again Fig.~3). \nAs is well known, the main source of opacity, (non-relativistic) \nelectron scattering, has no effect on colours. \nThus, in this case electron scattering alone\nis not sufficient, and an additional opacity source should\nbe introduced, possibly Rayleigh (or Mie) scattering by small \ncarbon dust particles.\n\nOccasional ``eclipses'' have been observed in the carbon-rich\nlate-type WC stars WR\\,103, WR\\,113, and WR\\,121\n(for a history of ``eclipses'' see Veen et al. 1998).\nIn these cases the ``eclipses'' were caused by occasional\nformation of dust in the line-of-sight. Although dust\nformation in the winds of late-type WC stars is now\nwell established, the problem with grain condensation in the\nvery hostile environments where the grains are believed to form\nremains unsolved. Clearly, a trigger is needed to start \nthe grain formation. In the case of WR\\,140, this could be\nthe shock compression in the colliding winds at PP.\nWe assume that the fading of WR\\,140 shortly after PP is due to\ndust condensation in the wind of the WC star. \nAfter the condensation ceases the star brightens again because\nthe dust is blown away and gradually dispersed.\nThe ``eclipses'' studied by Veen et al. (1998) have typical\namplitudes of several tenths of a magnitude and last from\nseveral days up to a month. In contrast, the amplitude of the\nlight dip in WR\\,140 is much smaller and the recovery of\nbrightness lasts several years. This implies continuing\nsupply (expanding from the PP production + new?)\nof dust, even 2 -- 3 years after PP. If there is new dust,\nthis would be really surprising, since the trigger seems\nno longer to be effective. Following the procedure of \nVeen et al. (1998, using their equations (5), (6), and (7))\nand taking the terminal velocity $v_\\infty = \n2900\\,\\mathrm{km\\,s}^{-1}$ from Eenens \\& Williams (1994),\nwe obtain for the distance $R_\\mathrm{cc}$ of the dust\nformation region from the WC star in WR\\,140:\n$R_\\mathrm{cc} \\sim 300\\,000\\,R_{\\sun}$. This is only\na rough estimate, but it is much larger than the\nrespective distances for all ``eclipses'' studied by\nVeen and co-workers. It is also much larger than the radius\nof the shell of WR\\,140 obtained by Williams et al. (1987a)\nwhich is $R_{shell} = 1490\\,R_{\\sun}$. Taking for the\ncarbon particle density $1.85\\,\\mathrm{g\\,cm}^{-3}$\nwe get for the dust mass production rate (over unit area)\nthe value $\\dot{M}_{d} = 2\\,10^{-13}\\, \n\\mathrm{kg\\,m}^{-2}\\,\\mathrm{s}^{-1}$. These results should\nbe taken with caution because of the small amplitude of\nthe ``eclipse'' in WR\\,140 and of possible deviations from\nthe model used (e.g. continued supply of dust after PP).\n\nWR\\,140 was observed photometrically during PP in 1977 by\nFernie (1978) but no changes of brightness were found.\nThis is likely due to his low precision data.\n\nLike WR\\,137, the observations of WR\\,140 also\nshow small-amplitude, day-to-day random light\nvariations (amplitudes up to 0.02 mag), in addition\nto the eclipse variation. Fig.~4 shows the correlations \nof the random light variations in $UBV$, indicating \nthat they are likely due to continuum rather than emission \nline variations (similar to WR 137, Fig. 2). Dynamical\nwind instabilities could be the origin, as in WR\\,137.\nMoffat \\& Shara (1986) suggested a 6.25 d period \nfor the light variations they observed in WR\\,140, \nwhich, however, does not fit our data. \nOur observations during 1991 - 1998 cover 90\\%\nof the orbit. It remains to be seen whether\nthe forthcoming PP in 2001 will repeat the light\ncurve so far observed. \n\n\n\n%fig5\n\\begin{figure*}\n \\centering\n \\resizebox{17cm}{!}{\\includegraphics{9201-f5.eps}}\n \\hfill\n \\caption{Light curves of WR\\,148\n (data from Table 4)}\n\\end{figure*}\n\n\n%sec33\n\\subsection{WR\\,148}\n\n%tab5\n\\begin{table*}\n\\caption[]{ Photometry of WR\\,153 (= HD 211853).\nThe comparison star is HD 211430\\\\ with $V = 7.465$,\n$B - V = -0.054$, and $U - B = -0.490$.\\\\ Orbital\nphases \"1\" are calculated with $P1 = 6.6884$ d\nand $T_0 =$ JD 2443690.32 (Massey 1981),\\\\ orbital\nphases \"2\" with $P2 = 3.4696$ d and\n$T_0 =$ JD 2443689.16 (Annuk 1994)}\n \\setlength\\tabcolsep{12pt}\n\\renewcommand{\\baselinestretch}{0.8}\n\\small\n\\begin{tabular}{rcccccccc}\n\\hline \\noalign{\\smallskip}\nYear & JD-2400000 & \\multicolumn{2}{c}{Orb. Phase} & $V$ & $B$ & $U$ & $B-V$ & $U-B$ \\\\\n & & \"1\" & \"2\" & [mag] & [mag] & [mag] & [mag] & [mag] \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1991 & 48448.527 & 0.41 & 0.73 & 8.979 & 9.352 & 8.749 & 0.373 & $-$0.603 \\\\\n & 48510.472 & 0.67 & 0.59 & 9.001 & 9.373 & 8.765 & 0.372 & $-$0.608 \\\\\n & 48510.487 & 0.68 & 0.59 & 8.996 & 9.368 & 8.766 & 0.372 & $-$0.602 \\\\\n & 48510.504 & 0.68 & 0.60 & 8.995 & 9.372 & 8.769 & 0.377 & $-$0.603 \\\\\n & 48510.518 & 0.68 & 0.60 & 8.992 & 9.370 & 8.774 & 0.378 & $-$0.596 \\\\\n & 48511.524 & 0.83 & 0.89 & 8.992 & 9.372 & 8.771 & 0.380 & $-$0.601 \\\\\n & 48511.538 & 0.83 & 0.89 & 8.995 & 9.375 & 8.775 & 0.380 & $-$0.600 \\\\\n & 48511.551 & 0.83 & 0.90 & 8.995 & 9.372 & 8.777 & 0.377 & $-$0.595 \\\\\n & 48511.567 & 0.84 & 0.90 & 8.994 & 9.377 & 8.775 & 0.383 & $-$0.602 \\\\\n & 48511.580 & 0.84 & 0.91 & 8.996 & 9.379 & 8.784 & 0.383 & $-$0.595 \\\\\n & 48511.591 & 0.84 & 0.91 & 9.000 & 9.380 & 8.788 & 0.380 & $-$0.592 \\\\\n & 48512.519 & 0.98 & 0.18 & 9.042 & 9.428 & 8.818 & 0.386 & $-$0.610 \\\\\n & 48513.479 & 0.12 & 0.45 & 9.052 & 9.445 & 8.855 & 0.393 & $-$0.590 \\\\\n & 48514.502 & 0.28 & 0.75 & 8.978 & 9.353 & 8.737 & 0.375 & $-$0.616 \\\\\n & 48538.446 & 0.86 & 0.65 & 8.972 & 9.363 & 8.752 & 0.391 & $-$0.611 \\\\\n & 48539.464 & 0.01 & 0.94 & 9.068 & 9.462 & 8.862 & 0.394 & $-$0.600 \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1993 & 49220.514 & 0.83 & 0.23 & 8.979 & 9.367 & 8.751 & 0.388 & $-$0.616 \\\\\n & 49221.490 & 0.98 & 0.52 & 9.086 & 9.478 & 8.875 & 0.392 & $-$0.603 \\\\\n & 49222.523 & 0.13 & 0.81 & 8.972 & 9.363 & 8.743 & 0.391 & $-$0.620 \\\\\n & 49223.488 & 0.28 & 0.09 & 8.991 & 9.380 & 8.768 & 0.389 & $-$0.612 \\\\\n & 49224.519 & 0.43 & 0.39 & 8.972 & 9.361 & 8.750 & 0.389 & $-$0.611 \\\\\n & 49233.431 & 0.76 & 0.96 & 9.028 & 9.421 & 8.805 & 0.393 & $-$0.616 \\\\\n & 49233.446 & 0.77 & 0.96 & 9.929 & 9.418 & 8.808 & 0.389 & $-$0.610 \\\\\n & 49234.449 & 0.92 & 0.25 & 8.990 & 9.383 & 8.766 & 0.393 & $-$0.617 \\\\\n & 49234.462 & 0.92 & 0.25 & 8.986 & 9.382 & 8.761 & 0.396 & $-$0.621 \\\\\n & 49234.474 & 0.92 & 0.25 & 8.992 & 9.379 & 8.760 & 0.387 & $-$0.619 \\\\\n & 49234.490 & 0.92 & 0.26 & 8.994 & 9.382 & 8.764 & 0.388 & $-$0.618 \\\\\n & 49234.503 & 0.93 & 0.26 & 8.994 & 9.380 & 8.760 & 0.386 & $-$0.620 \\\\\n & 49234.517 & 0.93 & 0.27 & 8.989 & 9.382 & 8.764 & 0.393 & $-$0.618 \\\\\n & 49235.416 & 0.06 & 0.53 & 9.072 & 9.470 & 8.858 & 0.398 & $-$0.612 \\\\\n & 49235.429 & 0.06 & 0.53 & 9.076 & 9.478 & 8.862 & 0.402 & $-$0.616 \\\\\n & 49235.441 & 0.07 & 0.54 & 9.085 & 9.483 & 8.858 & 0.398 & $-$0.625 \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1994 & 49582.539 & 0.96 & 0.58 & 9.040 & 9.431 & 8.835 & 0.391 & $-$0.596 \\\\\n & 49584.494 & 0.25 & 0.14 & 8.993 & 9.381 & 8.770 & 0.388 & $-$0.611 \\\\\n & 49585.476 & 0.40 & 0.42 & 8.994 & 9.380 & 8.771 & 0.386 & $-$0.609 \\\\\n & 49586.502 & 0.55 & 0.72 & 8.976 & 9.368 & 8.763 & 0.392 & $-$0.605 \\\\\n & 49587.477 & 0.70 & 0.00 & 9.009 & 9.393 & 8.787 & 0.384 & $-$0.606 \\\\\n & 49589.498 & 0.00 & 0.58 & 9.051 & 9.448 & 8.844 & 0.397 & $-$0.604 \\\\\n & 49594.505 & 0.75 & 0.02 & 9.022 & 9.418 & 8.817 & 0.396 & $-$0.601 \\\\\n & 49595.417 & 0.89 & 0.29 & 8.985 & 9.375 & 8.763 & 0.390 & $-$0.612 \\\\\n & 49596.402 & 0.03 & 0.57 & 9.069 & 9.464 & 8.845 & 0.395 & $-$0.619 \\\\\n & 49666.396 & 0.50 & 0.74 & 8.984 & 9.379 & 8.767 & 0.395 & $-$0.612 \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n1995 & 49975.516 & 0.72 & 0.84 & 9.002 & 9.391 & 8.781 & 0.389 & -0.610 \\\\\n & 49977.524 & 0.02 & 0.42 & 9.054 & 9.436 & 8.832 & 0.382 & -0.604 \\\\\n \\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table*}\n\nWR\\,148 (= HD 197406, WN8 + c?) is a single-line \nspectroscopic binary, possibly hosting a compact companion.\nThe star has been studied by Bracher (1979). She \ndetermined the orbital period as $P = 4.3174$ d \nand also found light variations with the same \nperiod and an amplitude of 0.04 mag in $V$. Further \nspectroscopic studies by Moffat \\& Seggewiss \n(1979, 1980) revealed an unusually low mass \nfunction of the system, which was later \nconfirmed by Drissen et al. (1986): f(m) = 0.28 M$_{\\sun}$. \nWR\\,148 has also an exceptionally large \ndistance from the galactic plane, $z = 500 - 800$ pc \n(Moffat \\& Isserstedt 1980; Dubner et al. 1990).\nSmith et al. (1996) found that WR\\,148 is a WN8 star. \nThe low mass function and high $z$ value led\nMoffat \\& Seggewiss (1980) to advance the idea \nthat WR\\,148 harbours a compact companion as product\nof a supernovae explosion some 5 Myr \nago. In their model, the companion is orbiting\nwithin the WR envelope. As the companion orbits around the WR star\nthe projected envelope density varies. This is the origin of the\n light variations of WR\\,148, because electron scattering occurs in this \nenvelope. \nPhotometric studies by Antokhin (1984),\nMoffat \\& Shara (1986), and Marchenko et al. \n(1996) confirmed the light variations found by Bracher (1979) with an\namplitude of 0.03 mag in $V$ and also point\nto the very ``noisy'' appearence of\nthe light curve. (With the ephemeris \nof Drissen et al. (1986), the light minimum \noccurs at phase zero with the WR star in\nfront). Marchenko et al. (1996) noted the\nunusual wide-shaped light minimum, quite \ndifferent from other known WR + O systems \nwith atmospheric eclipses and a V-shaped light\nminimum (Lamontagne et al. 1996). For WR\\,148,\nMarchenko et al. suggested that the secondary \nlight arises from an extended hot cavity \nin the WR envelope, near the companion, \nand which is ionized by X-rays. According \nto Marchenko et al., the rather weak\nX-ray source observed in WR\\,148\n(Pollock et al. 1995)\nmay be explained by the hot X-ray \ncavity being locally embedded in the WR envelope. \nPresently, the evolutionary status of\nWR\\,148 remains unclear and the companion\ncould be either a B2-B4 III-V star or a \nrelativistic object (as deduced from the mass function,\nMarchenko et al. 1996). \n \nOur photometry is presented in Table 4 and\nthe light curves are shown in Fig.~5,\nplotted with the ephemeris of Drissen et al.\n(1986). From Fig.~5 it is apparent that our\nlight curves in 1993 are similar to the \nlight curves published by Moffat \\& Shara (1986).\nThe minimum occurs at phase zero. The \n1994 light curves, however, show a remarkable\nchange in their shape and mean light level.\nRandom light variations, already noted in \nother works, could well contribute to the \ndisturbance of the light curve shape, but\nit is unlikely that they would change the\nmean light. Furthermore, long-term changes \nin mean light appear to be \ncorrelated in $U$, $B$, and $V$ (Fig.~5). Therefore,\nthey too should be due to changes in \ncontinuum light. \n\nThere is a strong\nevidence for a long-term variation of the\nmean light. Although the time-base is too short, \nthere are some indications that the long-term variation \nis periodic, possibly with a cycle of about 4 years. \nMarchenko et al. (1998b) point to a possible\n``overall brightening'' of WR\\,148 in 1994 and \n1995. As shown in Fig.\\,5, it is obvious that\nin 1993 the mean light was even some 0.05 mag higher,\nas in 1994. This long-term variation completely masks \nthe short-term binary variations if the whole data set \nis depicted in one plot. Therefore we\nplotted the data separately for each year in Fig.~5.\n \nTaking into account the model of Marchenko et al.(1996), \nthe long-term light variations in WR\\,148 \ncould be due to variations of the size \nof the hot X-ray cavity.\nFurther conclusions at that time seem premature. \nA comment should be given on the observation at\nJD 2449585.4, phase = 0.57 (the companion $\\sim$ in front),\nwhich strongly deviates from the regular light curve of 1994. \nAs we can exclude observational errors as a reason for \nthis measurement, it has to have some astrophysical origin.\nFor instance, an event\nof accretion onto a compact companion could be \ninvoked to explain this flare-like burst. \n\nFlickering and flaring of\nWR\\,148 on different time-scales have been\nreported by Antokhin \\& Cherepashchuck (1989),\nZhilyaev et al. (1995) and\nKhalack \\& Zhilyaev (1995). Matthews et al.\n(1992) looked for flares in the WR star EZ Canis\nMajoris (WR\\,6 = HD 50896, WN5) and reported one\nflare event. Flare-type activity of EZ CMa was also\nobserved by Duijsens et al. (1996). This star is in many\nrespects similar to WR\\,148, e.g. showing\nlight variations with a 3.77 d period,\nlong-term changes in the light curve, and a\npossible WR + c binary status (Firmani et al. 1980;\nBalona et al. 1989; Duijsens et al. 1996). \n\n%fig6 \n\\begin{figure*} \n \\centering \n \\resizebox{12cm}{!}{\\includegraphics{9201-f6.eps}} \n \\hfill \n \\caption{Light curves of WR\\,153 with (a) $P1 = 6.6884$ d \n and (b) $P2 = 3.4696$ d (data from Table~5)}\n\\end{figure*}\n \n%sec34\n\\subsection{WR\\,153}\nWR\\,153 (= HD 211853 = GP Cep) is a quadruple system (Massey 1981) \nwith orbital periods 6.6884 d (pair A, WR + O) and\n3.4696 d (pair B, WR + O or O + O). Earlier spectroscopic\nstudies by Hiltner (1945) and Bracher (1968)\nrevealed radial velocity variations due to\nbinary motion with a period of 6.68 d. Panov \\&\nSeggewiss (1990) reanalysed Hiltner`s velocity\ndata and found evidence for two WR stars, one\nin each pair. WR\\,153 has been observed photometrically\nby Hjellming \\& Hiltner (1963), Stepien (1970),\nMoffat \\& Shara (1986), Panov \\& Seggewiss (1990),\nand Annuk (1994), all detecting eclipses\nwith both periods, 6.6884 d and 3.47 d.\nFinally, Annuk (1994) refined the second period\nto 3.4696 d, in agreement with the velocity\ndata of Massey (1981). However, in the recent \nanalysis of WR star light curves by Lamontagne et al. \n(1996) the 3.47 d variation of pair B could not\nunambiguously be extracted from their data. \n\nOur photometry of WR\\,153 is presented in\nTable 5 and the light curves are shown in\nFig.~6a and Fig.~6b, with the 6.6884 d and 3.4696 d\nperiods, respectively. From Fig.~6, our\ndata are consistent with the ephemeris of \nMassey (1981) and Annuk (1994), respectively.\nSince the true shape of both \nlight curves is unknown, no allowance is made for the\n3.47 d period in Fig.~6a, where it is\nsuperimposed on the 6.69 d light variations.\nIn Fig.~6b, the data points around the\n6.69 d period minimum (at phases from 0.96 to 0.13 in \nFig.~6a) have been removed. \n\nThe light curve with\nthe 6.69 d period (pair A) is probably due to\nan atmospheric eclipse (only one, V-shaped\nlight minimum!). In pair B, two light minima\nare seen due to a core eclipse in that pair.\nIndependent evidence can be obtained from \nthe HIPPARCOS photometry data. We made a period\nsearch, using 122 data-points from HIPPARCOS. The \nanalysis was performed with the PERIBM \nprocedure, developed at the Astronomical\nInstitute of the University of Vienna (latest version from:\\\\\nftp://dsn.astro.univie.ac.at./pub/PERIOD98/current/).\nOur analysis clearly shows that there are peaks at\n$f1 = 0.5763641$ d$^{-1}$, corresponding to a\n1.735 d period, and at $f2 = 0.1495867$ d$^{-1}$,\ncorresponding to the 6.69 d period. The \n1.735 d period is exactly 1/2 of the \n3.47 d period and the reason that it shows up \nin the amplitude spectrum is because of the\ndouble-wave light curve (two eclipses in pair B),\nconsistent with our ground-based photometry.\nMoffat \\& Shara (1986) also deduced that pair A had a\nsingle minimum at phase 0.00 ($P = 6.69$\\,d) and pair B\nhad a double minimum at phases 0.00 and 0.50\n($P = 3.47$ d).\n\n\n%sec4\n\\section{Conclusions}\n\nOur photometry of WR\\,137 reveals\nonly small amplitude ($\\le$ 0.03 mag in the\n$V$ passband) random light variations. No\nperiodicity could be found. These variations \nshould be attributed to the continuum and they are\nprobably due to dynamical wind instabilities. \n\nWR\\,140 exhibited remarkable light variations\nand a shallow light dip is seen in\nall passbands shortly after periastron\npassage in 1993. The light\nattenuation lasted until 1997 or even 1998, \nprobably because of a dust envelope built\naround the WR star by wind-wind interaction\nat periastron passage. The dust envelope was\ngradually dispersed. From the wavelength\ndependence of the light attenuation, we\nfind strong evidence for Rayleigh (Mie-like)\nscattering, contributing to the opacity,\nin addition to electron scattering. \n\nFor WR\\,148, our photometric study confirms \nthe 4.317364 d light variation, but \nreveals occasional scatter, disturbing the \nlight curve shape. On one occasion, we see a\nflare-like event at a phase when the companion\nis in front. Our photometry reveals long-term\nvariations of the mean light and, possibly, of\nthe amplitude of the regular variation. \nThere is some evidence for a periodicity of\nthe long-term light variation and a 4 year\ncycle cannot be ruled out. \n\nOur photometry of WR\\,153 is consistent \nwith the quadruple model for this star and\nboth the 6.6884 d and the 3.4696 d periods are seen \nin the light. In pair A (6.6884\\,d period) we found \nevidence for an atmospheric eclipse, in\nagreement with the results of other works, while in \npair B (3.4696 d period) the eclipse\nis probably photospheric (core eclipse).\n\n\\acknowledgements{\nThis research project was supported by the Deutsche \nForschungsgemeinschaft DFG,\\\\ grant 436\\,BUL 113/88/0.\nIn addition, M. Altmann is grateful to the DFG for grant Bo 779/21.\nK.P. Panov kindly acknowledges the support by the Bulgarian National \nScience Foundation, grant F\\,826. Thanks are due to J.S.W. Stegert \nfor his participation in the observations. The authors are thankful\nto the referee Dr. A.F.J. Moffat for his fruitful suggestions.\nFor our research we made with pleasure use of the SIMBAD data base \nin Strasbourg.}\n\n\\begin{thebibliography}{}\n\n\\bibitem[]{}\nAntokhin, I.I., 1984, Astron. Tsirk. 1350, 1\n\\bibitem[]{}\nAntokhin, I.I., Bertrand, J.F., Lamontagne, R., Moffat, A.F.J., Matthews, J.M.,\n 1995, AJ 109, 817 \n\\bibitem[]{}\nAntokhin, I.I., Cherepashchuck, A.M., 1989, Sov. Astron. Lett. 15(4), 303 \n\\bibitem[]{} \nAnnuk, K., 1994, A\\&A 282, 137 \n\\bibitem[]{} \nAnnuk, K., 1995, in: Wolf-Rayet Stars: Binaries, Colliding Winds, Evolution, \n IAU Symposium 163, K.A. van der Hucht, P.M. Williams (eds.), \nDordrecht, Kluwer Acad. Publ., p. 231 \n\\bibitem[]{} \nBalona, L.A., Egan, J., Marang, F., 1989, MNRAS 240, 103 \n\\bibitem[]{} \nBracher, K., 1968, PASP 80, 165 \n\\bibitem[]{} \nBracher, K., 1979, PASP 91, 827 \n\\bibitem[]{} \nDrissen, L., Lamontagne, R., Moffat, A.F.J., Bastien, P., Seguin, M., 1986,\n ApJ 304, 188 \n\\bibitem[]{} \nDubner, G.M., Niemela, V.S., Purton, C.R., 1990, AJ 99, 857 \n\\bibitem[]{} \nDuijsens, M.F.J., van der Hucht, K.A., van Genderen, A.M., Schwarz, H.E.,\n Linders, H.P.J., Kolkman, O.M., 1996, A\\&AS 119, 37\n\\bibitem[]{} \nEenens, P.R.J., Williams, P.M., 1994, MNRAS 269, 1082\n\\bibitem[]{} \nFernie, J.D., 1978, Inf. Bull. Variable Stars No. 1377\n\\bibitem[]{} \nFirmani, C., Koenigsberger, G., Bisiacchi, G.F., Moffat, A.F.J., Isserstedt, J., \n 1980, ApJ 239, 607 \n\\bibitem[]{} \nGosset, E., Vreux, J.-M., Manfroid, J., Remy, M., Sterken, C., 1990, \n A\\&AS 84, 377 \n\\bibitem[]{} \nHiltner, W.A., 1945, ApJ 101, 356 \n\\bibitem[]{} \nHjellming, R.M., Hiltner, W.A., 1963, ApJ 137, 1080 \n\\bibitem[]{} \nKhalack, V.R., Zhilyaev, B.E., 1995, Kinemat. Phys. Celest. Bodies 13 (2) \n\\bibitem[]{}\nLafler, J., Kinman, T.D., 1965, ApJS 11, 216 \n\\bibitem[]{} \nLamontagne, R., Moffat, A.F.J., 1987, AJ 94, 1008 \n\\bibitem[]{} \nLamontagne, R., Moffat, A.F.J., Drissen, L., Robert, C., Matthews, J.M., \n 1996, AJ 112, 2227 \n\\bibitem[]{} \nMaeder, A., 1985, A\\&A 147, 300 \n\\bibitem[]{} \nMaeder, A., 1996, in: Wolf-Rayet Stars in the Framework of Stellar Evolution, \n 33rd Li\\`ege Internat. Astrophys. Coll., J.M. Vreux, A. Detal, D. Fraipont-Caro, \n E. Gosset, G. Rauw (eds.), Li\\`ege, Universit\\'e de Li\\`ege, p. 39 \n\\bibitem[]{} \nMarchenko, S.V., Moffat, A.F.J., Eversberg, T., Hill, G.M., Tovmassian,\n G.H., Morel, T., Seggewiss, W., 1998b, MNRAS 294, 642 \n\\bibitem[]{} \nMarchenko, S.V., Moffat, A.F.J., Grosdidier, Y., 1999, ApJ 522, 433\n\\bibitem[]{} \nMarchenko, S.V., Moffat, A.F.J., Lamontagne, R., Tovmassian, G.H., \n 1996, ApJ 461, 386 \n\\bibitem[]{} \nMarchenko, S.V., Moffat, A.F.J., van der Hucht, K.A., Seggewiss, W., et al.,\n 1998a, A\\&A 331, 1022\n\\bibitem[]{} \nMarchenko, S.V., Pikhun, A.I., 1992, Kinemat. Phys. Celest. Bodies 8, 24 \n\\bibitem[]{} \nMassey, P., 1981, ApJ 244, 157 \n\\bibitem[]{} \nMatthews, J.M., Moffat, A.F.J., 1994, A\\&A 283, 493 \n\\bibitem[]{} \nMatthews, J.M., Moffat, A.F.J., Marchenko, S.V., 1992, A\\&A 266, 409 \n\\bibitem[]{} \nMoffat, A.F.J., Drissen, L., Lamontagne, R., Robert, C., 1988, ApJ 334, 1038 \n\\bibitem[]{} \nMoffat, A.F.J., Isserstedt, J., 1980, A\\&A 85, 201 \n\\bibitem[]{} \nMoffat, A.F.J., Lamontagne, R., Williams, P.M., Horn, J., Seggewiss, W., \n 1987, ApJ 312, 807 \n\\bibitem[]{} \nMoffat, A.F.J., L\\'epine, S., Henriksen, R.N., Robert, C., 1994, Ap\\&SS 216, 55 \n\\bibitem[]{} \nMoffat, A.F.J., Seggewiss, W., 1979, A\\&A 77, 128 \n\\bibitem[]{} \nMoffat, A.F.J., Seggewiss, W., 1980, A\\&A 86, 87 \n\\bibitem[]{} \nMoffat, A.F.J., Shara, M.M., 1986, AJ 92, 952 \n\\bibitem[]{} \nPanov, K.P., Pamukchiev, I.Ch., Christov, P.P., Petkov, D.I., Notev, P.T., \n Kotsev, N.G., 1982, C. R. Acad. Bulg. Sci. 36, 717 \n\\bibitem[]{} \nPanov, K.P., Seggewiss, W., 1990, A\\&A 227, 117 \n\\bibitem[]{} \nPollock, A.M.T., Haberl, F., Corcoran, M.F., 1995, in: Wolf-Rayet Stars: Binaries, \n Colliding Winds, Evolution, IAU Symposium 163, K.A. van der Hucht, \n P.M. Williams (eds.), Dordrecht, Kluwer Acad. Publ., p. 512 \n\\bibitem[]{} \nPyper, D.M., 1966, ApJ 144, 13 \n\\bibitem[]{}\nRauw, G., Gosset, E., Manfroid, J., Vreux, J.-M., Claeskens, J.-F., \n 1996, A\\&A 306, 783 \n\\bibitem[]{} \nRobert, C., 1994, Ap\\&SS 221, 137 \n\\bibitem[]{} \nRobert, C., Moffat, A.F.J., Bastien, P., Drissen, L., St-Louis, N., \n 1989, ApJ 347, 1034 \n\\bibitem[]{} \nSmith, L.F., Shara, M.M., Moffat, A.F.J., 1996, MNRAS 281, 163 \n\\bibitem[]{} \nStepien, K., 1970, Acta Astron. 20, 117 \n\\bibitem[]{} \nUnderhill, A.B., 1992, ApJ 398, 636 \n\\bibitem[]{} \nvan der Hucht, K.A., Williams, P.M., Pollock, A.M.T., Hidayat, B., McCain, \n C.F., Spoelstra, T.A.Th., Wamsteker, W.M., 1991, in: Wolf-Rayet Stars and \n Interrelations with other Massive Stars in Galaxies, IAU Symposium 143, \n K.A. van der Hucht, B. Hidayat (eds.), Dordrecht, Kluwer Acad. Publ.,\n p. 251\n\\bibitem[]{} \nvan Genderen, A.M., van der Hucht, K.A., Steemers, W.J.G., 1987, A\\&A 185, 131 \n\\bibitem[]{}\nVeen, P.M., van Genderen, A.M., van der Hucht, K.A., Li, A.,\nSterken, C., Dominik, C., 1998, A\\&A 329, 199\n\\bibitem[]{}\nVreux, J.-M., 1985, PASP 97, 274\n\\bibitem[]{}\nWilliams, P.M., 1997, Ap\\&SS 251, 321 \n\\bibitem[]{} \nWilliams, P.M., Beattie, D.H., Lee, T.J., Stewart, J.M., Antonopoulou, E., \n1978, MNRAS 185, 467 \n\\bibitem[]{} \nWilliams, P.M., van der Hucht, K.A., The, P.S., 1987a, A\\&A 182, 91 \n\\bibitem[]{} \nWilliams, P.M., van der Hucht, K.A., The, P.S., 1987b, QJRAS 28, 248 \n\\bibitem[]{} \nWilliams, P.M., van der Hucht, K.A., Pollock, A.M.T., Florkowski, D.R., \n van der Woerd, H., Wamsteker, W.M., 1990, MNRAS 243, 662 \n\\bibitem[]{} \nWilliams, P.M., van der Hucht, K.A., van der Woerd, H., Wamsteker, W.M., \n Geballe, T.R., Garmany, C.D., Pollock, A.M., 1987c, in: Instabilities \n in Luminous Early Type Stars, H.J.G.L.M. Lamers, C.W.H. de Loore (eds.), \n Dordrecht, Reidel, p. 221 \n\\bibitem[]{} \nZhilyaev, B.E., Khalack, V.R., Verlyuk, I.A., 1995, in: Wolf-Rayet Stars: \n Binaries, Colliding Winds, Evolution, IAU Symposium 163, K.A. van der \n Hucht, P.M. Williams (eds.), Dordrecht, Kluwer Acad. Publ., p. 550 \n \n\\end{thebibliography}{}\n\\end{document}\n\n\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002221.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[]{}\nAntokhin, I.I., 1984, Astron. Tsirk. 1350, 1\n\\bibitem[]{}\nAntokhin, I.I., Bertrand, J.F., Lamontagne, R., Moffat, A.F.J., Matthews, J.M.,\n 1995, AJ 109, 817 \n\\bibitem[]{}\nAntokhin, I.I., Cherepashchuck, A.M., 1989, Sov. Astron. Lett. 15(4), 303 \n\\bibitem[]{} \nAnnuk, K., 1994, A\\&A 282, 137 \n\\bibitem[]{} \nAnnuk, K., 1995, in: Wolf-Rayet Stars: Binaries, Colliding Winds, Evolution, \n IAU Symposium 163, K.A. van der Hucht, P.M. Williams (eds.), \nDordrecht, Kluwer Acad. Publ., p. 231 \n\\bibitem[]{} \nBalona, L.A., Egan, J., Marang, F., 1989, MNRAS 240, 103 \n\\bibitem[]{} \nBracher, K., 1968, PASP 80, 165 \n\\bibitem[]{} \nBracher, K., 1979, PASP 91, 827 \n\\bibitem[]{} \nDrissen, L., Lamontagne, R., Moffat, A.F.J., Bastien, P., Seguin, M., 1986,\n ApJ 304, 188 \n\\bibitem[]{} \nDubner, G.M., Niemela, V.S., Purton, C.R., 1990, AJ 99, 857 \n\\bibitem[]{} \nDuijsens, M.F.J., van der Hucht, K.A., van Genderen, A.M., Schwarz, H.E.,\n Linders, H.P.J., Kolkman, O.M., 1996, A\\&AS 119, 37\n\\bibitem[]{} \nEenens, P.R.J., Williams, P.M., 1994, MNRAS 269, 1082\n\\bibitem[]{} \nFernie, J.D., 1978, Inf. Bull. Variable Stars No. 1377\n\\bibitem[]{} \nFirmani, C., Koenigsberger, G., Bisiacchi, G.F., Moffat, A.F.J., Isserstedt, J., \n 1980, ApJ 239, 607 \n\\bibitem[]{} \nGosset, E., Vreux, J.-M., Manfroid, J., Remy, M., Sterken, C., 1990, \n A\\&AS 84, 377 \n\\bibitem[]{} \nHiltner, W.A., 1945, ApJ 101, 356 \n\\bibitem[]{} \nHjellming, R.M., Hiltner, W.A., 1963, ApJ 137, 1080 \n\\bibitem[]{} \nKhalack, V.R., Zhilyaev, B.E., 1995, Kinemat. Phys. Celest. Bodies 13 (2) \n\\bibitem[]{}\nLafler, J., Kinman, T.D., 1965, ApJS 11, 216 \n\\bibitem[]{} \nLamontagne, R., Moffat, A.F.J., 1987, AJ 94, 1008 \n\\bibitem[]{} \nLamontagne, R., Moffat, A.F.J., Drissen, L., Robert, C., Matthews, J.M., \n 1996, AJ 112, 2227 \n\\bibitem[]{} \nMaeder, A., 1985, A\\&A 147, 300 \n\\bibitem[]{} \nMaeder, A., 1996, in: Wolf-Rayet Stars in the Framework of Stellar Evolution, \n 33rd Li\\`ege Internat. Astrophys. Coll., J.M. Vreux, A. Detal, D. Fraipont-Caro, \n E. Gosset, G. Rauw (eds.), Li\\`ege, Universit\\'e de Li\\`ege, p. 39 \n\\bibitem[]{} \nMarchenko, S.V., Moffat, A.F.J., Eversberg, T., Hill, G.M., Tovmassian,\n G.H., Morel, T., Seggewiss, W., 1998b, MNRAS 294, 642 \n\\bibitem[]{} \nMarchenko, S.V., Moffat, A.F.J., Grosdidier, Y., 1999, ApJ 522, 433\n\\bibitem[]{} \nMarchenko, S.V., Moffat, A.F.J., Lamontagne, R., Tovmassian, G.H., \n 1996, ApJ 461, 386 \n\\bibitem[]{} \nMarchenko, S.V., Moffat, A.F.J., van der Hucht, K.A., Seggewiss, W., et al.,\n 1998a, A\\&A 331, 1022\n\\bibitem[]{} \nMarchenko, S.V., Pikhun, A.I., 1992, Kinemat. Phys. Celest. Bodies 8, 24 \n\\bibitem[]{} \nMassey, P., 1981, ApJ 244, 157 \n\\bibitem[]{} \nMatthews, J.M., Moffat, A.F.J., 1994, A\\&A 283, 493 \n\\bibitem[]{} \nMatthews, J.M., Moffat, A.F.J., Marchenko, S.V., 1992, A\\&A 266, 409 \n\\bibitem[]{} \nMoffat, A.F.J., Drissen, L., Lamontagne, R., Robert, C., 1988, ApJ 334, 1038 \n\\bibitem[]{} \nMoffat, A.F.J., Isserstedt, J., 1980, A\\&A 85, 201 \n\\bibitem[]{} \nMoffat, A.F.J., Lamontagne, R., Williams, P.M., Horn, J., Seggewiss, W., \n 1987, ApJ 312, 807 \n\\bibitem[]{} \nMoffat, A.F.J., L\\'epine, S., Henriksen, R.N., Robert, C., 1994, Ap\\&SS 216, 55 \n\\bibitem[]{} \nMoffat, A.F.J., Seggewiss, W., 1979, A\\&A 77, 128 \n\\bibitem[]{} \nMoffat, A.F.J., Seggewiss, W., 1980, A\\&A 86, 87 \n\\bibitem[]{} \nMoffat, A.F.J., Shara, M.M., 1986, AJ 92, 952 \n\\bibitem[]{} \nPanov, K.P., Pamukchiev, I.Ch., Christov, P.P., Petkov, D.I., Notev, P.T., \n Kotsev, N.G., 1982, C. R. Acad. Bulg. Sci. 36, 717 \n\\bibitem[]{} \nPanov, K.P., Seggewiss, W., 1990, A\\&A 227, 117 \n\\bibitem[]{} \nPollock, A.M.T., Haberl, F., Corcoran, M.F., 1995, in: Wolf-Rayet Stars: Binaries, \n Colliding Winds, Evolution, IAU Symposium 163, K.A. van der Hucht, \n P.M. Williams (eds.), Dordrecht, Kluwer Acad. Publ., p. 512 \n\\bibitem[]{} \nPyper, D.M., 1966, ApJ 144, 13 \n\\bibitem[]{}\nRauw, G., Gosset, E., Manfroid, J., Vreux, J.-M., Claeskens, J.-F., \n 1996, A\\&A 306, 783 \n\\bibitem[]{} \nRobert, C., 1994, Ap\\&SS 221, 137 \n\\bibitem[]{} \nRobert, C., Moffat, A.F.J., Bastien, P., Drissen, L., St-Louis, N., \n 1989, ApJ 347, 1034 \n\\bibitem[]{} \nSmith, L.F., Shara, M.M., Moffat, A.F.J., 1996, MNRAS 281, 163 \n\\bibitem[]{} \nStepien, K., 1970, Acta Astron. 20, 117 \n\\bibitem[]{} \nUnderhill, A.B., 1992, ApJ 398, 636 \n\\bibitem[]{} \nvan der Hucht, K.A., Williams, P.M., Pollock, A.M.T., Hidayat, B., McCain, \n C.F., Spoelstra, T.A.Th., Wamsteker, W.M., 1991, in: Wolf-Rayet Stars and \n Interrelations with other Massive Stars in Galaxies, IAU Symposium 143, \n K.A. van der Hucht, B. Hidayat (eds.), Dordrecht, Kluwer Acad. Publ.,\n p. 251\n\\bibitem[]{} \nvan Genderen, A.M., van der Hucht, K.A., Steemers, W.J.G., 1987, A\\&A 185, 131 \n\\bibitem[]{}\nVeen, P.M., van Genderen, A.M., van der Hucht, K.A., Li, A.,\nSterken, C., Dominik, C., 1998, A\\&A 329, 199\n\\bibitem[]{}\nVreux, J.-M., 1985, PASP 97, 274\n\\bibitem[]{}\nWilliams, P.M., 1997, Ap\\&SS 251, 321 \n\\bibitem[]{} \nWilliams, P.M., Beattie, D.H., Lee, T.J., Stewart, J.M., Antonopoulou, E., \n1978, MNRAS 185, 467 \n\\bibitem[]{} \nWilliams, P.M., van der Hucht, K.A., The, P.S., 1987a, A\\&A 182, 91 \n\\bibitem[]{} \nWilliams, P.M., van der Hucht, K.A., The, P.S., 1987b, QJRAS 28, 248 \n\\bibitem[]{} \nWilliams, P.M., van der Hucht, K.A., Pollock, A.M.T., Florkowski, D.R., \n van der Woerd, H., Wamsteker, W.M., 1990, MNRAS 243, 662 \n\\bibitem[]{} \nWilliams, P.M., van der Hucht, K.A., van der Woerd, H., Wamsteker, W.M., \n Geballe, T.R., Garmany, C.D., Pollock, A.M., 1987c, in: Instabilities \n in Luminous Early Type Stars, H.J.G.L.M. Lamers, C.W.H. de Loore (eds.), \n Dordrecht, Reidel, p. 221 \n\\bibitem[]{} \nZhilyaev, B.E., Khalack, V.R., Verlyuk, I.A., 1995, in: Wolf-Rayet Stars: \n Binaries, Colliding Winds, Evolution, IAU Symposium 163, K.A. van der \n Hucht, P.M. Williams (eds.), Dordrecht, Kluwer Acad. Publ., p. 550 \n \n\\end{thebibliography}"
}
] |
astro-ph0002222
|
Snapshot coronagraphy with an interferometer in space
|
[
{
"author": "Boccaletti A. (1"
},
{
"author": "2)"
},
{
"author": "Riaud P. (2"
},
{
"author": "4)"
},
{
"author": "Moutou C. (3)"
},
{
"author": "Labeyrie A. (2"
},
{
"author": "(1) DESPA"
},
{
"author": "Observatoire de Paris Meudon"
},
{
"author": "place J.Janssen"
},
{
"author": "92195 Meudon"
},
{
"author": "France"
},
{
"author": "(2) Coll{\\`e}ge de France"
},
{
"author": "11 Pl. M. Berthelot F-75321 Paris"
},
{
"author": "(3) ESO santiago"
},
{
"author": "Chile"
},
{
"author": "(4) Observatoire de Haute-Provence"
},
{
"author": "F-04870 St Michel l'Observatoire"
}
] |
Diluted arrays of many optical apertures will be able to provide high-resolution snapshot images if the beams are combined according to the densified-pupil scheme. We show that the same principle can also provide coronagraphic images, for detecting faint sources near a bright unresolved one. Recent refinements of coronagraphic techniques, i.e. the use of a phase mask, active apodization and dark-speckle analysis, are also applicable for enhanced contrast. Implemented in the form of a proposed 50-500m Exo-Earth Discoverer array in space, the principle can serve to detect Earth-like exo-planets in the infra-red. It can also provide images of faint nebulosity near stars, active galactic nuclei and quasars. Calculations indicate that exo-planets are detectable amidst the zodiacal and exo-zodiacal emission faster than with a Bracewell array of equivalent area, a consequence of the spatial selectivity in the image. \\ {Keywords}: extrasolar planets; instrumentation; image processing.
|
[
{
"name": "MS7409.tex",
"string": "\\documentclass[icarus,fleqn]{article}\n%\\documentclass[a4,fleqn]{article}\n%%%%%%%%%%%%%%%%%%%%%%\n%\\textwidth=18cm\n%\\textheight=22cm\n%\\topmargin=-0.5cm\n%\\oddsidemargin=-0.5cm\n%\\evensidemargin=0cm\n%\\columnwidth=9cm\n%\\columnsep=0.5cm\n%%%%%%%%%%%%%%%%%%%%%%%%%\n\\input epsf\n\\usepackage{amsmath}\n\\begin{document}\n%%%%%%%%%%%%%%%%%%%%%%%%%\n\\title{Snapshot coronagraphy with an interferometer in space}\n\\author{Boccaletti A. (1,2), Riaud P. (2,4), Moutou C. (3), Labeyrie A. \n(2,4) \\\\\n(1) DESPA, Observatoire de Paris Meudon, place J.Janssen, \\\\\n92195 Meudon, France, Boccalet@despa.obspm.fr \\\\\n(2) Coll{\\`e}ge de France, 11 Pl. M. Berthelot F-75321 Paris, France \\\\\n Riaud@mesioq.obspm.fr\\\\\n(3) ESO santiago, Chile, Cmoutou@eso.org\\\\\n(4) Observatoire de Haute-Provence, F-04870 St Michel l'Observatoire, \\\\\nFrance, Labeyrie@obs-hp.fr}\n%\\date{Received xxx; accepted yyy}\n\\date\n\\sloppy\n\\maketitle\n\\newpage\n\\begin{abstract}\nDiluted arrays of many optical apertures will be able to provide high-resolution snapshot images if the beams are combined according to the densified-pupil scheme. We show that the same principle can also provide coronagraphic images, for detecting faint sources near a bright unresolved one. Recent refinements of coronagraphic techniques, i.e. the use of a phase mask, active apodization and dark-speckle analysis, are also applicable for enhanced contrast. Implemented in the form of a proposed 50-500m Exo-Earth Discoverer array in space, the principle can serve to detect Earth-like exo-planets in the infra-red. It can also provide images of faint nebulosity near stars, active galactic nuclei and quasars. Calculations indicate that exo-planets are detectable amidst the zodiacal and exo-zodiacal emission faster than with a Bracewell array of equivalent area, a consequence of the spatial selectivity in the image. \\\\\n{\\it Keywords}: extrasolar planets; instrumentation; image processing.\n\\end{abstract}\n% *************************************************\n\\newpage\n\\section{Introduction}\n\\label{intro}\nAn early proposal for searching exo-planets involved coronagraphy aboard the \"Large Space Telescope\" (Bonneau {\\it et al.} 1975) which became the Hubble Space Telescope (HST). It was shown that telescope rotation and synchronous image subtraction could remove much of the coronagraphic residue, a speckled halo of star light expected to outshine the planet image by 3 or 4 orders of magnitude. The corresponding Faint Object Camera (FOC) was built by the European Space Agency, but the COSTAR corrector subsequently installed aboard HST to correct the figuring error of its main mirror destroyed the size matching of the Lyot stop in the FOC coronagraph and made it inoperable. Also, the aperture size had been shrunk from 3m to 2.4m, and the telescope rotation proved difficult to achieve. The FOC could however have succeeded since exo-planets brighter than expected were recently found by radial velocity measurements (Mayor and Queloz 1995, Marcy and Butler 1996, Delfosse {\\it et al.} 1998).\\\\ \n\nThe rotation modulation principle was later adopted, together with a form of coronagraphic field-selective attenuation, by Bracewell and McPhie (1979) for their proposed interferometer exploiting the improved contrast of a planet in the infrared. The concept has been refined by L\\'eger {\\it et al.} (1996) for the DARWIN proposal, and also adopted by Angel and Woolf (1997) for their Terrestrial Planet Finder. Both instruments are intended to observe in the 10$\\mu$m infra-red. At this wavelength, the Earth's luminosity is quoted to be $7.10^{6}$ times, or 17 magnitudes, fainter than the Sun's. \\\\\n\nCoronagraphic imaging is now also considered for the Next Generation Space Telescope (Gezari {\\it et al.} 1997, Moutou {\\it et al.} 1998, Trauger {\\it et al.} 1998, Le F\\`evre {\\it et al.} 1998). The added refinement of \"dark-speckle imaging\" can further improve the detection sensitivity 10 to 1000 times (Boccaletti {\\it et al.} 1998a), while the use of a phase mask and the active attenuation of residual starlight in the annular field push the sensitivity towards the exo-planet detection threshold at visible wavelengths.\\\\\n\nIn this article we analyze and confirm the suggestion (Labeyrie 1999b) that these techniques of apodized imaging are also usable with large multi-aperture interferometric arrays operating in the densified-pupil imaging mode. Indeed, it was recently shown that such arrays operated in this mode can produce snapshot images in a narrow field (Labeyrie 1996). We have studied the coronagraphic schemes applicable to such imaging conditions and find them suitable for exo-planet observing at infra-red wavelengths. At visible wavelengths they can provide higher angular resolution than NGST coronagraphy, allowing observations of fast orbiting exo-planets.\\\\\n\nOur numerical simulations of imaging with the \"Exo-Earth Discoverer\" (EED) sketched in Fig. \\ref{eedschema} verify the expected imaging performance. The EED is a 36-element space interferometer with size $D$ of the order of 100m. Having free-flying telescopes (Labeyrie 1985, B\\'ely {\\it et al.} 1996), it can be considered as a possible precursor of much larger instruments such as the 150 km Exo-Earth Imager proposed for the longer-term goal of making exo-planet portraits (Labeyrie 1999b). \n% *************************************************\n\\section{Science}\nThe proposed instrument is intended for imaging, in the infra-red, and possibly the visible, faint circumstellar environments with their diffuse component and their point sources, brown dwarf companions or exo-planets. Brown dwarfs are expected to be 10$^7$ to 10$^8$ times fainter in the optical range and 10$^{5}$ times in the near infra-red. Extra-solar planets are 10$^6$ times fainter than their parent star at 10 microns. Their detection may also be affected by the presence of extended emission, both zodiacal and exo-zodiacal in their vicinity.\\\\\n\nJets and disks, as well as extreme cases of circumstellar activity such as in SS 433 (Spencer 1979) are obviously also relevant to high-resolution coronagraphy. Extended sources in the vicinity of stars are of interest, especially at the birth and death stages of the star life: observations of nebulosities leading to the formation of a planetary system, ejected envelopes, accretion disks in binary systems, disks of small bodies and planetary debris will all benefit from high-resolution imaging coronagraphy, as well as high-velocity jets and supernova remnants.\\\\\n\nHigh-angular resolution can also access the inner parts of active galactic nuclei, inside the dust torus, and coronagraphy can improve the rejection of the bright unresolved core. In objects such as M81, QSO's and possibly gamma-ray bursters, where a central black hole is suspected, both the transverse and radial components of the gas velocity may become observable with milli-arcsecond angular resolution and the associated field spectrography. Also interesting is the observation of rings around supernovae in nearby galaxies.\n% *************************************************\n\\section{Concepts}\n\\label{concept}\n\\subsection{Pupil densification}\nFizeau interferometers, the equivalent of giant telescopes having a sparse mosaic mirror, produce an image, but its quality degrades catastrophically when the aperture size becomes much larger than the sub-apertures. A usable image can then be retrieved by densifying the exit pupil, i.e. distorting it to increase the relative size of the sub-pupils. Such instruments, which may be called \"hyper-telescopes\", evade a requirement long believed to be a \"golden rule of imaging interferometry\" (Traub and Davis 1982, Beckers 1997), namely that the exit pupil be identical to the entrance pupil. Instead, one preserves only the arrangement of sub-pupil centers, while magnifying each sub-pupil with respect to the inter-pupil spacings, thus making the exit pupil more densely packed than the highly diluted entrance pupil (Fig. \\ref{pupil}).\\\\\n\nThe result is a combined image where the interference pattern is magnified, with respect to the broad diffraction peak contributed by the sub-apertures. This broad peak acts as a window which limits the field but concentrates the energy in the useful central part of the interference pattern. The pupil densification mixes two different scales in the image: the low-resolution scale of the sub-images, or images contributed by a single sub-aperture, and the high-resolution scale of the interference pattern, which retains the classical convolution behaviour on extended objects. When the array is phased on a point source, a peak appears in the interference function, thus providing a direct image within the window.\\\\\nDepending on the baseline redundancy, snap-shot exposures obtained in this way can contain between $N$ and $N^2$ resolved elements, if $N$ is the number of apertures. Simulations of an exo-planet's image, showing clouds and continents, have been obtained assuming a 48 or 150-aperture \"Exo-Earth Imager\", a larger version of the EED with 150 km size (Labeyrie 1999b).\\\\\n\nHere we concentrate on the shorter-term goal of obtaining unresolved images of exo-planets, and the other goals mentioned in the previous section. It requires a smaller instrument, spanning 50m to 500m, so that the central source be unresolved, as required for phase-mask coronagraphy (Roddier and Roddier 1997, Guyon {\\it et al.} 1999) and for dark-speckle imaging (Labeyrie 1995, Boccaletti {\\it et al.} 1998a, Boccaletti {\\it et al.} 1998b). \\\\\nFor a sparse array geometry allowing full pupil densification, we assumed an entrance aperture shaped like an \"exploded\" hexagonal paving (Fig. \\ref{pupil}). The case of 36 elements, with concentric rings of 6, 12 and 18, was mostly used in the simulations, but a wider imaging field is obtainable with more elements, at no loss if the collecting area is conserved. Once densified, the 36-element pupil resembles the aperture of the Keck telescope (see Fig. \\ref{pupil}).\\\n \n% *************************************************\n\\subsection{Phase-mask coronagraphy with multi-aperture arrays}\nClassical coronagraphs since Lyot (1939) have an occulting mask in the first focal plane of a telescope, and, in a relayed pupil plane, a \"Lyot stop\" diaphragm. Slightly smaller than the pupil, it removes the double edge ring caused by diffraction, which contains most of the light propagated from the Airy rings (Malbet 1996). The focal mask is opaque, and has to cover at least the 4 or 5 central rings of the Airy pattern for efficient nulling. What remains in the final re-imaged field is a few attenuated Airy rings, becoming broken into random speckles at increasing distances from the vanished Airy peak. The speckles result mostly from the residual bumpiness of the telescope's mirror, but obscurations of spiders, segmentation, etc., on the pupil can contribute. \\\\\nWith Roddier and Roddier's proposal (1997) of a transparent phase-shifting mask, smaller than the Airy peak ($\\approx 0.5{\\lambda\\over D}$), similar extinction is achievable, but the usable field extends closer inwards, down to the very edge of the Airy peak. The phase mask is basically narrow-band. It can however be multiplexed for a wide spectral coverage by using a polychromatic Bragg hologram as a reflective phase mask (Labeyrie 1999b).\\\\\n\nWhen a star's Airy peak is properly focused and centered on a phase mask, most light is diffracted outside the geometric pupil, and is thus removable by a diaphragm, the Lyot stop, before re-imaging the focal plane. If made to match exactly the geometric pupil, including any central obscuration, spider arms and segmentation gaps, the Lyot stop can be nearly optimal. In the presence of obscurations or mirror segmentation such as shown on top of Fig. \\ref{pupil}, this is another advantage with respect to conventional Lyot coronagraphy, where the bright double fringe along edges requires masking a significant part of the geometric pupil area (typically 20\\% of the diameter is occulted).\\\\ \nPhase-mask coronagraphy for single telescopes such as the NGST (Moutou {\\it et al.} 1998) can be extended to the case of a densified-pupil interferometer. Whether the wavefront focused at the entrance of the coronagraph has natural continuity or is a dense mosaic of wavefront patches coming from widely spaced sub-apertures in the entrance aperture makes no difference indeed. A non-resolved star is therefore \"nulled\" identically in either case.\\\\\n\nAnother new coronagraphic scheme, the Achromatic Interfero-Coronagraph (Gay J. and Rabbia 1996, Rabbia {\\it et al.} 1998), also offers the capability of imaging a companion very close to the field center, and uses an ingenious solution for achromatism. Although not included in the present simulations, it would be of interest to assess its performance in the EED context. \n% *************************************************\n\\section{Numerical simulations}\n\\label{simu}\n\\subsection{The algorithm}\nWe have performed numerical simulations of the proposed interferometer and coronagraph, using various occulting and apodizing schemes. In accordance with the theory of densified-pupil interferometry (Labeyrie 1996), the complex amplitude distribution in the exit pupil is considered as a convolution of a sub-pupil with a \"fakir board\", i.e. an array of Dirac peaks representing the centers of the sub-pupils (the peaks can be complex numbers to represent phasing errors). The combined focal image of a point source is therefore a product of an interference function, the squared modulus of the fakir board's Fourier transform, and a diffraction function similarly transformed from the sub-aperture.\\\\ \n\nIf the array is correctly phased, the interference function resembles the classical Airy pattern with its central peak, although the outer rings here become broken into speckles. The usual phasing algorithms serving for adaptive optics in monolithic telescopes, using wavefront slope or curvature measurements, are not applicable to long baselines, but other approaches using sharpness criteria have been found usable on Earth and in space (Pedretti and Labeyrie 1999, Pedretti 1999). \\\\ \nAn extended incoherent source convolves the interference function, but affects negligibly the diffraction function if the interferometer is highly diluted. The interference function may therefore be considered as a spread function, while the diffraction function behaves like an envelope or field-limiting window applied to the convolved pattern.\\\\\n\nFor simulating the phase-mask coronagraph attachment, we introduced a $180^\\circ$ phase shift in the central part of the star's Airy-like interference peak. The mask size is quite critical and was adjusted by trial and error for minimal residual star light in the annular field. The Fourier transform of the resulting complex amplitude distribution is then multiplied by the Lyot stop, in most cases made to match exactly the geometric pupil, and again Fourier transformed to obtain the final image of the star. \\\\\nAdding the planet's image requires a similar calculation to be made for the planet. In the plane of the phase mask, this involves the same interference function, but attenuated and shifted off-axis before multiplication with the un-shifted diffraction function and the phase mask function. Since the planet's Airy peak falls outside of the phase mask, the mask affects very little the planet's final image. \\\\\nVarious sizes and shapes of the mask and pupil diaphragm were also experimented for optimizing the nulling of the star and its feet.\n% *************************************************\n\\subsection{Comparison of various pupil configurations}\nWe have considered diluted arrays of 36 elements, having either circular sub-apertures or, better, hexagonal ones allowing a full densification in the exit pupil. Although the interference functions are identical in both cases, we find that a darker coronagraphic field is achievable with the fully densified pupil. We therefore adopted this optimal pupil configuration for simulating the coronagraph in the following. The pupils and corresponding images are shown in Fig.\\ref{pupil}. \\\\ \n\nWhen working with hexagonal sub-apertures and full densification, the first-order secondary peaks of the star's interference function are exactly located on the envelope's dark ring. The field area, expressed on the sky in units of the array's Airy area (squared Airy radius) is approximately equal to the number of apertures. The secondary peaks of the star's interference function have the same intensity as the central peak, but have first-order lateral chromatism. Any stellar companion or planet present in the main field or in the extended field also has side-peaks. In this respect, in monochromatric light, the central field always contains a replica of the planet's image if the central image is outside (see Fig. 5a).\n% *************************************************\n\\subsection{Phase-mask size and shape}\nHere the sub-apertures of the interferometer are assumed perfectly phased. \\\\\nThe maximal nulling of starlight by the phase mask is reached when the amplitudes with opposite phases are balanced in the pupil, and this requires a careful adjustment of the phase mask diameter (Fig. \\ref{maskh}, top). A circular phase mask appears better than an hexagonal one. The calculated intensity profile in the coronagraphic image of the unresolved star (Fig. \\ref{maskh}, bottom) shows that the average attenuation of the annular field achieved by the phase-mask coronagraph is of the order of 20 to 50, a value comparable to that obtained by Roddier and Roddier (1997) for a monolithic telescope. Although not a large gain, this brings the average halo level to $\\approx 2.10^{-4}$ relative to the peak of the unmasked star image, a welcome improvement before applying the further darkening steps discussed below.\\\\\nResidual phase errors, both the intra-aperture errors caused by the bumpiness of the mirror elements and the inter-aperture errors caused by imperfect adjustment of the optical path differences among them, have the same effect as in monolithic telescopes: the feet of the diffraction pattern become distorted and intensified, both before and after the coronagraph. The intra-aperture bumpiness diffracts mostly outside of the imaging field and therefore contributes little to the image degradation. In the 10 micron infra-red, the inter-aperture path differences can be kept small compared to the wavelength. Our simulations indicate that wavefront bumpiness contributes little to the background. If its scale size is 10 times smaller than a sub-aperture and its RMS amplitude $59 nm$, corresponding to $\\lambda /8$ at $0.5 \\mu m$ and $\\lambda /170$ at $10 \\mu m$), the bumpiness contribution to the $2.10^{-4}$ background is only $10^{-8}$. Subtracting a reference star image, obtained with a different bumpiness, therefore leaves a speckled background at $10^{-8}$ level (Fig. \\ref{maskh}, bottom), and it can be smoothed if the actuators are re-ajusted many times during a long exposure. In the dark-speckle mode, the analysis is performed differently. \n% *************************************************\n\\subsection{Effect of full or partial pupil densification}\nAnother critical parameter is the amount of densification in the exit pupil, and numerical simulations have again served to characterize its effect (Fig. \\ref{ecart}). We varied the sub-pupil size and calculated the nulling in the annular coronagraphic field, extending from the second dark ring of the masked Airy peak $\\rho_m$, outward to the first dark ring of the sub-aperture's Airy peak $\\rho_f$. With 36 elements, its area is 25 times larger than the area of the first dark ring $\\rho_u$ in the unmasked Airy peak (Fig. \\ref{maskh}, bottom). \nThe residual intensity reaches $2.10^{-4}$ with full densification. It increases 10 times for 50\\% density. The optimal phase-mask size depends on the density and may be adjusted for optimal nulling\\\\\nNarrow gaps between elements, amounting to a few percents of the element size, are difficult to avoid in practice, but will not degrade significantly the field darkness. This is another advantage with respect to the classical Lyot coronagraph, where such amplitude patterns on the pupil can be disastrous.\n% *************************************************\n\\section{Application to exoplanet detection}\n\\subsection{Choice of wavelength }\nThe planet/star contrast improves a lot from the visible to the 10$\\mu$m infra-red, owing to the drop of the star's Planck function and the peaking thermal emissivity of the planet. Also, residual wavefront bumpiness causes smaller phase shifts and less scattered light at longer wavelengths. However, the angular separation of an 8m space telescope such as the NGST becomes sufficient to separate planets from their star in the visible, although not in all cases, and provides in principle the same planet detection performance as an EED of identical collecting area.\\\\ \n% *************************************************\n\\subsection{Performance of direct imaging}\nOptimal data reduction would involve a combination of the dark hole and dark speckle techniques mentioned below. The simulation routines are demanding of computer time however, and we have here simulated long-exposure images, a less sensitive method which smoothes the boiling speckles and thus cannot exploit the nulling achieved in the dark speckles, but nevertheless demonstrates the detectability of planets. The results shown in Fig. \\ref{result} assume 36 phased apertures of 0.6m, for a total collecting area similar to that of DARWIN (about 40 m$^2$) (L{\\'e}ger {\\it et al.} 1996, Mennesson and Mariotti 1997). We have simulated a twin of the solar system located at 20pc, with Venus, Earth and Mars near a $m_v=6.33$ star. At $10\\mu m$ the stellar magnitude is 11.5. The detector noise and photon noise were also included in the simulated 10 hours exposure. Planets $\\approx 7.10^6$ times fainter than the parent star are directly detected after subtracting a reference image.\\\\ \nPhasing errors, modelled to represent the bumpiness of the mirror segments, corresponding to $\\lambda/170$ rms, are included both for the planetary system and the reference star. A long exposure was fabricated by adding 60 images obtained with independant random phase maps, and this was repeated with different phase maps for the reference star. With larger wavefront errors of $\\lambda/80$ (at $10\\mu m$), the scattered light level is about $10^{-7}$ and is therefore higher than the Airy peak of Mars which remains undetected.\\\\\nWe have carried out the simulation at 3 different wavelengths (9.5, 10 and 10.5 $\\mu m$). Secondary peaks feature a 1$^{st}$ order chromatic dispersion and cannot be confused with the white primary peaks. Due to the interferometer geometry, an off-axis source has 3 peaks at $120^\\circ$ (1 primary and 2 secondary).\\\\\n% *************************************************\n\\subsection{Further gain with dark-hole and dark-speckle \ntechniques}\nMalbet {\\it et al.} 1995, and Trauger {\\it et al.} 1999, have shown how minor corrections of the wavefront shape, applied with active optics, can further improve the darkening of a coronagraphic image. Using a coronagraphic exposure, the dark-hole algorithm derives a phase correction map. Once applied to the actuators, it improves the average darkness of the selected annular field. \\\\ \nThe pattern of residual speckles changes randomly after each iteration, a consequence of noise in the servo loop. Although these speckles are here much fainter and slower than those caused by residual turbulence on Earth, the situation is similar, and dark-speckle imaging (Labeyrie 1995, Boccaletti {\\it et al.} 1998a) can similarly improve the star-light rejection if thousands of short exposures can be exploited. The actuators can be re-adjusted every 10s for example, and frozen in-between during the exposures.\\\\ \nDark-speckle observations performed on ground-based single-aperture telescopes (Boccaletti {\\it et al.} 1998b) with a CP20+ photon counting detector (Abe et al. 1998) have verified the theoretical expectations. Their extrapolation to the situation considered here suggests that exoplanets ($\\Delta m(10\\mu m)\\approx 16$ to $19$, $\\Delta m(1\\mu m)\\approx 22$ to $25$) can be detected with exposures lasting hours to a few tens of hours. A limitation is the imperfect cleaning of the image, with a few stellar speckles survfiving near the center. These can be removed with a reference star, but perhaps also by modifying the dark-hole algorithm.\n% *************************************************\n\\subsection{Signal to noise ratio}\nIn addition to the residual pattern of star-light, the image provided by a densified-pupil interferometer, contains light from the zodiacal and exo-zodiacal clouds. The part of these extended sources which lies outside of the narrow imaging field, but within the resolution patch of the sub-apertures, contaminates the image through the feet of the interference function.\\\\\n\nAn exo-planet peak in the image, with $J_p$ photo-events detected every second, is thus contaminated with : \\\\\n1- $J_s$ events/s from the residual speckled halo of starlight;\\\\\n2- $J_{ez}$ events/s from the image of the exo-zodiacal cloud;\\\\\n3- $J'_{ez}$ events/s from the feet of the exo-zodiacal image (the cloud being larger than the field, there is a contamination of the field from the missing parts of the cloud, through the feet of the spread function);\\\\\n4- $J_z$ events/s from the zodiacal cloud;\\\\\n5- $J_T$ events/s from the telescope thermal emission.\n\\smallskip\\\\\n\nTo calculate these quantities, we consider an entrance aperture of size D with N sub-apertures of size d. It receives $I_p$ photons/s per square meter from the planet; $I_s$ from the star; $L_z$ from the zodiacal cloud, per steradian; and $L_{ez}$ per steradian from the exo-zodiacal cloud of angular size $\\phi$, assumed unresolved by a sub-aperture. \\\\\nSince the planet's peak concentrates most entering photons, $J_p = I_p N d^2 $.\\\\\nWith the long-exposure mode using a reference star, the subtracted stellar contribution at the planet peak may be approximated by $J_s=I_s N d^2 g$.\\\\\nThe radial profile $g = \\rho^{-\\alpha}$ of starlight is estimated if $\\rho$ is the axial distance and $\\alpha$ the log slope of the coronagraphic halo, which is of the order of $\\alpha\\approx 1.5 \\sim 2$ according to the simulation results of Fig. \\ref{maskh} (bottom). $\\alpha$ decreases slowly as the number of speckle patterns is increased, as does the speckle noise.\\\\ \nThe remaining components may be expressed as :\n\\smallskip\\\\\n$J_z = L_z \\lambda^2 $ in the zodiacal cloud ;\\\\\n$J_{ez} = L_{ez} \\lambda^2 N d^2 D^{-2}$ in the image of the exo-zodiacal cloud; \\\\\n$J'_{ez} = L_{ez} \\phi^2 d^2$ in the halo of the exo-zodiacal image;\\\\\n$J_T=L_T\\lambda^2$ since the telescope thermal emission produces a background similar to the zodiacal cloud.\\\\\n\nThe last four quantities describe the respective contributions of the central peak and the infinitely wide pattern of secondary peaks in the interference function. This pattern adds a halo to the image of the exo-zodiacal disc. A similar halo is also added to the image of the zodiacal continuum, and dominates it completely.\\\\\nThese quantities are invariant when N varies at constant collecting area $ N d^2 $, except $J'_{ez}$ which decreases for increasing N. Increasing N, which is of interest to enlarge the field window, thus also improves the planet's discrimination against the halo of the exo-zodiacal image. In the $ N \\rightarrow + \\infty $ limit, the sparse array with densified exit pupil provides the same image as a filled telescope of similar diameter, although attenuated in the ratio of collecting areas.\\\\\nIn the long-exposure observing mode, noise components are: \n\\begin{itemize}\n\\item[1.]{ photon noise $P_n$ from the added photon contributions in the same speckle as the planet peak, amounting to $P_n= \\sqrt{( 2J_s+ J_p+ J_z+ J_{ez} + J'_{ez} )T }$ , where $T$ is the total exposure time (the factor 2 in the stellar term arises from the subtraction of a reference image);}\n\\item[2.]{speckle noise $S_n$ from the stellar contribution, $S_n=\\sqrt{2J_s^2 T^2 /n_s}$ (Angel 1994), if $n_s$ is the number of speckle patterns added in the long exposure. For $n_s > 20$ the speckle noise becomes negligible;}\n\\item[3.]{read-out noise, $R_n= \\sqrt{2\\sigma_{ron} n}$, where $\\sigma_{ron}$ is the detector's read-out noise per speckle area, whith n exposures made on both the object and reference star;}\n\\item[4.]{thermal emission within the telescope: Diner et al. (1991) calculated that a telescope at 70K provides, at $10\\mu m$, a 10\\% thermal contribution in the image of the zodiacal cloud. At 40K, the mirror temperature considered for DARWIN and TPF, the ratio is in the range $10^{-2}\\sim 10^{-3}$. Here, this ratio is unaffected when the Fizeau images goes through the densifier optics, provided its temperature is not higher than the primary mirror's. The image contamination from thermal emission is therefore negligible for planet searching at $10\\mu m$.}\n%thermal background from telescope, which is lower than zodical light emission if the telescope is cooled. Following the assumptions in Diner et al. 1991, the ratio telescope/zodiacal light is 0.1 for 70K at $10\\mu m$. For telescope passively cooled at 40K (DARWIN project), this value ranges between $10^{-2}\\sim 10^{-3}$, and is therefore negligible.}\n%Mariotti et al. ( ), Angel et al. () and Diner et al. (1991) found that the contamination of the exo-planet signal caused by thermal emission from the telescope is negligible with respect to zodiacal emission, given the mirror temperature $T_m=40$ to 70K, much lower than the $T_z=210K$ temperature of the zodiacal cloud. Owing to the classical throughput conservation law in optical systems, the analysis also applies to the hyper-telescope considered here since the pupil-densifying optics, if cooled like the main sparse mirror, does not increase the contamination of the planet peak observed in the Fizeau image (i.e. up-stream from the pupil densifier). The law further implies that the ratio of both contamination levels at the planet's location in the image is {\\epsilon_m}P(\\lambda,T_m)/{\\epsilon_z P(\\lambda,Tz)} were $\\epsilon_m=0.02$ and $\\epsilon_z=10^{-7}$ are emissivities of the mirror and zodiacal cloud, considered as grey bodies, at the wavelength considered, while P(\\lambda,T_m) and P(\\lambda,T_z) are the corresponding values of the Planck distribution. For $T_m=70K$ and $T_z=210K$, assuming identical emissivities for the mirror and zodiacal cloud, the ratio is 10. The hyper-telescope's thermal emission is therefore negligible. \n\\end{itemize}\nThe long-exposure signal/noise ratio is therefore :\n\\begin{equation}\nS/N_{EED}={I_p N d^2 T \\over \\sqrt{P_n^2+S_n^2+R_n^2 }}\n\\end{equation}\nor \n\\begin{equation}\n\\begin{split}\nS/N_{EED}=&I_pNd^2T[(2J_s+J_p+J_z+J_{ez}\\\\\n&+J'_{ez})T+2J_s^2T^2/n_s+2\\sigma_{ron}n]^{-1/2}\n\\end{split}\n\\end{equation}\n\nThe primary peak from the planet becomes attenuated if it moves towards the edge of the field. However this causes two secondary peaks to move inwards and become brighter. Because their location is known a priori, they can be added to the primary peak. The total signal thus obtained is invariant with respect to planet position, the energy being conserved. And the added contributions from uniform sky background within the planet's peaks are similarly invariant for the same reason. The same applies to the added contributions from the star's residual halo if it has the same radial attenuation as the envelope. The chromatic elongation of the secondary peaks does not necessarily affect the addition of the planet peaks since it is removable with a field spectroscopy arrangement. Therefore, the $S/N$ is little affected by a planet's motion in the field.\\\\\n \n%With respect to the angular distance, the primary peak is therefore attenuated by the envelope function. The total flux in the primary peak is thus a fraction $\\gamma$ of $I_p$ which is equal to 1 for on-axis object and 0 when $\\rho=rho_f$ (see Fig. 3 bottom). Owing to the shape of the array, 2 secondary peaks from off-axis objects appear very close to the center and contribute to the $SNR$ (see the case of Mars on Fig. 5). The total flux from the primary and secondary peaks is always equal to $I_p$.\nIn the dark-speckle mode, the stellar contribution to photon noise and speckle noise is decreased, as calculated by Boccaletti et al. (1998a). Also, no reference star is needed if the residual fixed speckles can be discriminated from planets by refining the dark-hole routine. Whether sensitive wave analyzer schemes, such as Zernike's phase contrast, can help remains to be investigated.\n% *************************************************\n\\subsection{Comparison with Bracewell nulling}\nIn a multi-aperture Bracewell interferometer, light from a field extending over the resolution patch of the sub-apertures is transmitted to \nthe single detector pixel, although with a field-dependant attenuation \ndefined by the high-resolution transmission map of the beam-splitter \narrangement. This map has a central dark minimum, designed to attenuate \nthe star, surrounded by brighter speckles which can be \nrotated or \"boiled\" for generating a planet signal. Like the procedure of Bracewell and Mac Phie (1979),\nthis is a single-pixel version of the rotation/subtraction algorithm originally proposed for exo-planet searching\nwith the Hubble Space Telescope by Bonneau {\\it et al.} (1975) (see also Davies 1980). The angular transmission map is such that the average transmission $\\tau$ of the planet's light and zodiacal light is of the order of $\\tau =0.2$.\\\\\n\nWith respect to the $J$ terms previously listed, the zodiacal and exo-zodiacal contributions must now be multiplied by $N\\tau$\nsince the detector pixel now receives all the energy from the part of these sources appearing in the sub-aperture's resolved patch.\nAlso, the exo-zodiacal image vanishes, as well as the speckle noise.\nThus, the signal/noise expression becomes: \n\\begin{equation}\n\\begin{split}\nS/N_{Bracewell}=&I_p N d^2 \\tau T [( J_s + J_p \\tau + J_z N \\tau \\\\\n&+ J'_{ez} N \\tau )T + \\sigma_{ron} n]^{-1/2} \n\\end{split}\n\\end{equation}\nwhere $g$ now describes the starlight rejection factor, expected to reach $10^{-6}$ in DARWIN.\n\nIncreasing the number of sub-apertures $N$ at constant collecting area \n$Nd^2$ changes only the zodiacal and exo-zodiacal signals, which increase in proportion to $N$. Unlike the EED,\nBracewell interferometers should thus remain limited to few apertures.\\\\\n\nUsing these expressions, we compared the performance of an EED having 36 apertures of 0.6m, and a DARWIN of equivalent area, both located at 1 A.U. from the Sun. The instrument's transmission combined with the quantum efficiency of the detector is 50\\% at $10 \\mu m$. An Earth at 20 parsecs provides 4 ph/$m^2$ in one hour of exposure.\\\\\nAt $ 10 \\mu m $, the luminosity of the solar zodiacal cloud varies between $7,6.10^{-7} W/(m^2.sr.\\mu m)$, at the ecliptic pole,\n\\sloppy\nthe value used by Mennesson et al. (1997) and $1,1.10^{-4}W/(m^2.sr.\\mu m)$.\nWe used the median value ($7,6.10^{-6} W/(m^2.sr.\\mu m)$ corresponding to 21 magnitudes per square arcsec.\nThe equivalent angular size $\\phi$ of the exo-zodiacal cloud is taken as $\\phi=0.25$arcsec, corresponding to 5 A.U.\nin the solar system, with $L_{ez}=10 L_z$. \\\\\n\nA 30 hr observation in the narrow spectral band ($\\lambda=10 \\mu m, \\Delta \\lambda=0.5 \\mu m$) provides a 0.5 $\\sigma$ detection with DARWIN,\nand a 5.8 $\\sigma$ detection with the EED in the long-exposure mode with \"boiling\" speckles.\nWith an achromatic phase-mask allowing a wider $6-18 \\mu m$ band, the DARWIN spectroscopy band,\nthe signal/noise ratio is 50.8 for the EED and 4.7 for DARWIN.\\\\\n \n\nThe gain in the EED case results from two effects:\\\\\n1- the fully constructive interference forming the planet peak in the image, as \nopposed to the 20\\% average intensity in the transmission map of \nDARWIN.\\\\\n2- the fact that the planet peak can be isolated from most of \nthe zodiacal contamination in the high-resolution image.\\\\ \n\nFor a given collecting area, the array size does not affect the signal/noise ratio. With the EED, the image is magnified, within its fixed window,\nwhen increasing the array size, and this can bring the planets optimally located in the field.\nIncreasing the sub-aperture count N from 36 to 100, their size being kept constant,\nincreases EED's signal/noise ratio nearly proportionally from 5.8 to 16.0.\nInstead, DARWIN's value of 0.5 in 30 hours increases to 0.8, as the square root of the aperture number.\\\\ \n\n% ************************************************\n\n\\section{Conclusion and future work}\nThe prospect for coronagraphic imaging with large interferometric \narrays, at\ninfrared and visible wavelengths, opens vast areas of science. The \nsimulations \npresented show that searches for exoplanets at 10$\\mu$m should be \nfeasible once the formation flight of mirror elements in space becomes \nmastered. We recall the main conclusions :\n\\begin{itemize}\n\\item{ Pupil densification allows direct imaging and coronagraphic nulling.}\n\\item{ A phase-mask, replacing the classical Lyot opaque mask, \ncleans the image closer to the attenuated star, and is more tolerant to the unavoidable narrow gaps between sub-pupils\nin the densified pupil. Both achromatisation of the \nmask and low-resolution spectroscopy ($\\lambda / \\Delta \\lambda = 20$) are desirable for analysing the images obtained.}\n\\item{At given collecting area, more sub-apertures is better in terms of image field and signal/noise ratio. }\n\\item{The optimal wavelength is a trade-off between resolution, \nstellar spill-off, planet contrast, background emission and detector \nperformance. At visible wavelengths, a monolithic 8m telescope often \nresolves the planet from its star and then has the same planet-searching \nefficiency as an EED of identical area.}\n\\item{ In addition to planet searches, direct imaging with the EED is also \nof interest for the other science goals briefly described above.}\n\\item{With respect to Bracewell's detection scheme, and its DARWIN and \nTPF proposed implementations, the image formation in the EED \nimproves markedly, at equal collecting area, the discrimination of an exo-planet amidst the zodiacal and \nexo-zodiacal nebulosity. The EED however requires 36 apertures at least,\nbut these are smaller and can be implemented with identical mirror segments compatible with the nano-satellite philosophy }.\n\n\\end{itemize} \nThe coronagraphic image is compatible with field spectrography.\n\nAdditional simulations are needed to compare the possible exposure routines,\nassess the desirability of a fine wavefront sensor, and refine the noise models.\nMore work is also needed to design optimal optical trains, including the\ncoronagraphic device and its spectro-imaging attachment. \n\\\\ \n\nAcknowledgments : \nJean-Marie Mariotti his constructive was among the first \nto understand our ideas and on densified-pupil imaging encouraged us to\nexplore their application.\nHis premature death deprived us of his insight\nand critical appreciation, particularly regarding these results. \n\n\\newpage\n\n% *************************************************\n\n\\Large{\\bf{Figure Captions}}\\\\[1cm]\n\\normalsize\n\nFigure \\ref{eedschema}: Possible optical train for the Exo-Earth Discoverer.\nMirror elements M1 focus starlight in the focal combiner C (detail below),\non field mirrrors FM, which form a densified image of the pupil on mirror segments PM.\nA combined image is focused in F at the entrance of a coronagraph Co.\nMirrors PM are carried by actuators for tip-tilt and piston corrections.\\\\ \n\nFigure \\ref{pupil}: Interferometer apertures (top row)\nwith disk (left) or hexagon (right) subpupils, and densified version of them\nobtained in the exit pupil (second row). The 100 to 200m Exo-Earth-Discoverer\nhas a sparse entrance aperture, but a fully densified exit pupil \nsuch as shown at right in the second row.\nThe star image (third row), with its diffractive envelope,\nhas most energy in the central Airy peak, as seen in the intensity profiles (bottom).\\\\\n\nFigure \\ref{maskh}: Top: Central darkening versus phase-mask size with a fully \ndensified \npupil of 36 adjacent hexagons, measured at the maximum ( dotted line) \nand across the area (solid line) of the \nAiry peak . The optimal mask size found is \n$(0.555 \\pm 0.005)\\lambda/D$. Bottom: Azimuthally averaged \nand normalized profiles of the unmasked Airy pattern (solid line), \ncoronagraphic pattern (dashed line) and residual scattered pattern after \nsubtraction of the reference frame (dotted line), including photon and \nreadout noise. Both long exposures incorporated 20 different maps of\n ($\\lambda/170$ rms) wavefront bumpiness. The radii of the \nfirst dark ring in the unmasked ($\\rho_u$), the masked ($\\rho_m$) and \nthe sub-aperture ($\\rho_f$) images are indicated. Also indicated is the \nlevel of Venus (dash-dot), Earth (dash-dot-dot-dot) and Mars (long \ndashes) multiplied by the sub-aperture's diffraction function .\\\\\n\nFigure \\ref{ecart}: Coronagraphic attenuation of star light versus exit-pupil \ndensity. The pupil density is measured as the relative area of the sub-\npupils in the exit pupil, while the attenuation is measured in the annular \nfield ($12\\lambda/D$) and normalized to the intensity of the unmasked peak. The dotted \ncurve indicates that the mask size was re-optimized for each density \nvalue, while the solid curve indicates that the initial value \n($0.555\\lambda/D$) was maintained . Numbers indicate the sizes of the \nre-optimized masks in units of $\\lambda/D$.\\\\\n\nFigure \\ref{result}: Coronagraphic image of a solar system twin observed at 20pc ($m_v=6,33$) with the Sun attenuated to detect Venus, Earth and Mars.\nThe magnitude differences at 10 $\\mu$m are respectively 16.4, 17.1, 19.8 relative to the parent star.\nThe simulated array has 36 telescopes of 0.6m, providing a collecting area similar to a DARWIN (40m$^2$).\nTo discriminate the dispersed secondary peaks from the white primary peaks, the final image was obtained\nwith a combination of 3 wavelengths (9.5, 10 and 10.5$\\mu m$).\\\\\nIn (a), the star is removed to show the Venus, Earth and Mars components of the image, with their primary (V, E, M) and secondary ($V_1$, $V_2$, $E_1$, $E_2$, $M_1$, $M_2$) peaks.\nThe peripheral attenuation by the diffraction envelope makes the secondary peaks of Mars brighter than the primary peak, since they are closer to the field center.\nNo photon noise is present here.\\\\\nThe separations are $1.75\\lambda/D$, $2.43\\lambda/D$ and $3.69\\lambda/D$, corresponding, for a 100m array, to 36, 50 and 76 milli-arcsecond at 10 $\\mu$m, respectively.\nA circle indicates the field limit, at the first dark ring of the\ndiffraction envelope of a single 0.6m-aperture.\nOn the sky, the corresponding field diameter is $12\\lambda/D$, amounting to 0.24 arc-second at 10 $\\mu$m with a 100m array of 36 elements.\\\\\nImage (b) shows a 10 hours exposure with subtraction of a reference star image similarly obtained. Photon noise and readout noise (100 e-/pix/frame) were included.\nA perfect wavefront was assumed. Image (c) is similar, but with 59 nm RMS wavefront bumpiness ($\\lambda /170$), of 10mn lifetime. Two different sets of 60 phase maps served for the object and the reference star.\nThis level of bumpiness has little effect in the usable field, within the white circle.\nA further gain in sensitivity is achievable in the dark-speckle mode.\\\\\n\n% *************************************************\n\n\\newpage\n\\begin{thebibliography}{}\n\\input{bib_MS7409.tex}\n\\end{thebibliography}\n\n\\onecolumn\n%\\newpage\n\\renewcommand{\\topfraction}{1.}\n\\begin{figure}[t]\n\\centerline{\\epsfxsize=7cm\\epsfbox{MS7409_fig1.eps}\n\\hspace{0.5cm}\\epsfxsize=8cm\\epsfbox{MS7409_fig2.eps}}\n\\caption[]{ }\n\\label{eedschema}\n\\end{figure}\n%\\newpage\n\\begin{figure}[b]\n\\centerline{\\epsfxsize=6cm\\epsfbox{MS7409_fig3.ps}}\n\\centerline{\\epsfxsize=7cm\\epsfbox{MS7409_fig4.eps}}\n\\caption[]{ }\n\\label{pupil}\n\\end{figure}\n\n\\newpage\n\\begin{figure}[t]\n\\centerline{\\epsfxsize=8cm\\epsfbox{MS7409_fig5.ps}}\n\\centerline{\\epsfxsize=8cm\\epsfbox{MS7409_fig6.ps}} \n\\caption[]{}\n\\label{maskh}\n\\end{figure}\n\n\\newpage\n\\begin{figure}[t]\n\\centerline{\\epsfxsize=8cm\\epsfbox{MS7409_fig7.ps}}\n\\caption[]{}\n\\label{ecart}\n\\end{figure}\n\n\\newpage\n\\begin{figure}\n\\centerline{\\epsfxsize=5.9cm\\epsfbox{MS7409_fig8B.ps}\n\\hspace{0.2cm} \\epsfxsize=5.9cm\\epsfbox{MS7409_fig9B.ps}\n\\hspace{0.2cm}\\epsfxsize=5.9cm\\epsfbox{MS7409_fig10B.ps}\n}\n\\caption[]{}\n\\label{result}\n\\end{figure}\n\n% *************************************************\n\\end{document}\n\n"
},
{
"name": "bib_MS7409.tex",
"string": "\\bibitem {abe98}\nAbe L., F. Vakili, I. Percheron, S. Hamma, J.P. Ragey and A. Blazit 1998. in Proc {\\it Catching the perfect wave}. Albuquerque June 1998\n\n\\bibitem {angel97}\nAngel J.R.P. and N.J Woolf 1997. An imaging nulling interferometer to study extrasolar planets. {\\it Astrophys. J.} {\\bf 475,} 373-379\n\n\\bibitem {beckers97}\nBeckers J. 1997. In {\\it Instrumentation for Large Telescopes}. (JJ Rodriguez Espinosa Ed.) Cambridge\n\n\\bibitem {bely96}\nB{\\'e}ly P.-Y., R.J. Laurance, S. Volonte et al. 1996. Kilometric baseline space interferometry. In SPIE Proc. {\\it Space Telescopes and Instruments IV} (P.-Y. B{\\'e}ly, J.B. Breckinridge Eds.), pp. 59-73. Vol 2807\n\n\\bibitem {boccaletti98a}\nBoccaletti A., A. Labeyrie and R. Ragazzoni 1998. Preliminary results of dark-speckle stellar coronagraphy. {\\it Astron. Astrophys.} {\\bf 338,} 106-110\n\n\\bibitem {boccaletti98b}\nBoccaletti A., C. Moutou , A. Labeyrie , D. Kohler and F. Vakili 1998. Present performance of the dark-speckle coronagraph {\\it Astron. Astrophys. Suppl. Ser.} {\\bf 133,} 395-402\n\n\\bibitem {bonneau75}\nBonneau D., M. Josse and A. Labeyrie 1975. In proc. Utrecht Symp. {\\it Image processing techniques in Astronomy} (de Jager/Nieuwenhuijzen eds) pp. 403-409. D. Reidel, Holland\n\n\\bibitem {bracewell79}\nBracewell R. and R.H. Mac Phie 1979. Searching for nonsolar planets. {\\it Icarus} {\\bf 38,} 136-147\n\n%\\bibitem {clampin91}\n%Clampin M., S.T. Durance, D.A. Golimowski and R.H. Barkhouser 1991. The Johns Hopkins Adaptive Optics Coronagraph. In SPIE Proc. {\\it Active and adaptive optical systems} pp. 165-174. Vol 1542\n\n\\bibitem {davies80}\nDavies D.W. 1980. Direct Imaging of Planetary Systems around Nearby Stars. {\\it Icarus} {\\bf 42,} 145-148\n\n\\bibitem {delfosse98}\nDelfosse X., T. Forveille, M. Mayor, C.Perrier, D. Naef and D. Queloz 1998. The Closest extrasolar planet. A giant planet around the M4 dwarf Gl876. {\\it Astron. Astrophys.} {\\bf 338,} L67-L70\n\n\\bibitem {diner91}\nDiner D.J., E.F. Tubbs, S.L. Gaiser and R.P. Korechoff 1991. Infrared imaging of extrasolar planets. {\\it J. Brit. Interplanetary Soc.} {\\bf 44,} 505-512\n\n\\bibitem {gay96}\nGay J. and Y. Rabbia 1996. Principe d'un coronographe interferentiel. {\\it CR. Acad. Sci. Paris} t. {\\bf 332,} Serie II b, 265-271\n\n\\bibitem {gezari97}\nGezari D. Y., A. Crotts, W. Danchi et al. 1997. An optimized coronagraph for Next Generation Space Telescope. Columbia University and Ball Aerospace Systems Division, proposal in response to NRA 98-GSFC-1\n\n\\bibitem {guyon99}\nGuyon O., C. Roddier, J.E. Graves, F. Roddier, S. Cuevas and C. Espejo 1999. Nulling coronagraph. Submitted to {\\it Applied Optics}.\n\n%\\bibitem {kenknight77}\n%KenKnight C.E. 1977. Methods of detecting extrasolar planets. I - Imaging. {\\it Icarus} {\\bf 30,} 422-433\n\n\\bibitem {labeyrie85}\nLabeyrie A., B. Authier, T. de Graauw, E. Kibblewhite and G. Weigelt 1985. \nTRIO: A kilometric array stabilized by solar sails. In ESA Colloq. {\\it Kilometric Optical Arrays in Space} pp. 27-33. Vol 226\n\n\\bibitem {labeyrie95}\nLabeyrie A. 1995. Images of exo-planets obtainable from dark speckles in adaptive telescopes. {\\it Astron. Astrophys.} {\\bf 298,} 544-548\n\n\\bibitem {labeyrie96}\nLabeyrie A. 1996. Resolved imaging of extra-solar planets with future 10-100km optical interferometric arrays. {\\it Astron. Astrophys. Suppl. Ser.} {\\bf 118,} 517-524\n\n\\bibitem {labeyrie99a}\nLabeyrie A. 1999, Direct Searches: Imaging, Dark-Speckle and Coronagraphy. in NATO ASI Cargese summer-school {\\it Planets outside the Solar System} pp. 261-279. (Mariotti J.-M. and Alloin D. Eds.) \n\n\\bibitem {labeyrie99b}\nLabeyrie A. 1999. Exo-Earth Imager for exoplanet snapshots with resolved details. to appear in ASP Conf Series {\\it Working on the Fringe}. (S. Unwin and R. Stachnik, Eds.) Dana Point, CA, May 24-27, 1999\n\n\\bibitem {lefevre98}\nLe F\\`evre O. 1998. Study of Payload Suite and Telescope for the NGST. in response to ESA AO/1-3405\n\n\\bibitem {leger96}\nL{\\'e}ger A., J-M. Mariotti, B. Menesson, M. Ollivier, J.-L. Puget, D. Rouan and J. Schneider 1996. Could we search for primitive life on extrasolar planets in the near future? the DARWIN project. {\\it Icarus} {\\bf 123,} 249-255\n\n\\bibitem {lyot39}\nLyot B. 1939. A study of the solar corona and prominences without eclipses. {\\it Mon. Not. Roy. Astron. Soc.} {\\bf 99,} 580-594\n\n\\bibitem {malbet95}\nMalbet F., J.W. Yu, and M. Shao 1995. High-Dynamic-Range Imaging Using a Deformable Mirror for Space Coronography. {\\it Publ. Astron. Soc. Pac.} {\\bf 107,} 386-398\n\n\\bibitem {malbet96}\nMalbet F. 1996. High angular resolution coronography for adaptive optics. {\\it Astron. Astrophys. Suppl. Ser.} {\\bf 115,} 161-174\n\n\\bibitem {marcy96}\nMarcy G.W. and R.P. Butler 1996. A Planetary Companion to 70 Virginis. {\\it Astrophys. J.} {\\bf 464} L147-151\n\n\\bibitem {mayor95}\nMayor M. and D. Queloz 1995. A Jupiter masss companion to a solar-type star. {\\it Nature} {\\bf 378,} 355-359 \n\n\\bibitem {mennesson97} \nMennesson B. and J.-M. Mariotti 1997. Array configurations for a space infrared nulling interferometer dedicated to the search for Earth-like extrasolar planets. {\\it Icarus} {\\bf 128,} 202-212\n\n\\bibitem {moutou98}\nMoutou C., A. Boccaletti and A. Labeyrie 1998. A Coronagraphic Dark-Speckle Imager for the NGST. In 34th Li\\`ege Astrophysics Colloq. {\\it NGST: Science Drivers and Technological Challenges} pp. 211-216.\n\n\\bibitem {pedretti99}\nPedretti E. and A. Labeyrie 1999. A hierarchical phasing algorithm for multi-element optical interferometers, {\\it Astron. Astrophys. Suppl. Ser.}, 137, 1-9\n\n\\bibitem{pedretti99b}\nPedretti E. 1999. Phasing algorithms for multi--element optical interferometers. to appear in ASP Conf Series {\\it Working on the Fringe}. (S. Unwin and R. Stachnik, Eds.) Dana Point, CA, May 24-27, 1999\n\n\\bibitem {rabbia98} \nRabbia Y., P. Baudoz and J. Gay 1998. Achromatic Interfero Coronagraphy and NGST. In 34th Li\\`ege Astrophysics Colloquium pp. 279- {\\it NGST: Science Drivers and Technological Challenges} pp. 279-284 \n\n\\bibitem {roddier97}\nRoddier F. and C. Roddier 1997. Stellar coronograph with phase-mask. {\\it Publ. Astron. Soc. Pac.} {\\bf 109,} 815-820\n\n\\bibitem {spencer79}\nSpencer R.E. 1979. A radio jet in SS433. {\\it Nature} {\\bf 282,} 483-484\n\n\\bibitem {traub82}\nTraub W.A. and W.F. Davis 1982. Coherent optical system of modular imaging collectors (COSMIC) telescope array - Astronomical goals and preliminary image reconstruction results. In SPIE Proc. {\\it International Conference on Advanced Technology Optical Telescopes} pp. 164-175. Vol 332\n\n\\bibitem {trauger98}\nTrauger J., D.E. Backman, C.A. Beichman et al. 1998. Strategies for High-Contrast Imaging with NGST. proposal in response to NRA 98-GSFC-1\n\n%\\bibitem {watson91}\n%Watson S.M., J.P. Mills, S.T. Gaiser and D.J. Diner 1991. Direct imaging of nonsolar planets with infrared telescopes using apodized coronographs. {\\it Applied Optics} {\\bf 30,} 3253-3262 \n \n\n"
}
] |
[
{
"name": "astro-ph0002222.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\input{bib_MS7409.tex}\n\\end{thebibliography}"
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] |
astro-ph0002223
|
A Near Infrared Polarized Bipolar Cone in the CIRCINUS Galaxy
|
[
{
"author": "D. M. Alexander$^2$"
},
{
"author": "S. Young$^1$"
},
{
"author": "J. Hough$^1$"
},
{
"author": "S. L. Lumsden$^3$"
},
{
"author": "C.A. Heisler$^4$\\thanks{We would like to dedicate this work to her memory }"
},
{
"author": "$^1$Department of Physical Sciences"
},
{
"author": "Hatfield"
},
{
"author": "Herts AL10 9AB"
},
{
"author": "UK."
},
{
"author": "$^2$International School for Advanced Studies"
},
{
"author": "SISSA"
},
{
"author": "Via Beirut 2-4"
},
{
"author": "34014 Trieste"
},
{
"author": "Italy."
},
{
"author": "$^3$Department of Physics and Astronomy"
},
{
"author": "Leeds LS2 9JT"
},
{
"author": "$^4$Mount Stromlo and Siding Spring Observatories"
},
{
"author": "Private Bag"
},
{
"author": "Weston Creek P.O."
},
{
"author": "Weston"
},
{
"author": "ACT 2611"
},
{
"author": "Australia"
}
] |
We present near--infrared broad--band polarization images of the nuclear regions of the Circinus galaxy in the J, H and K bands. For the first time the south--eastern reflection cone is detected in polarized light, which is obscured at optical wavelengths behind the galactic disk. This biconical structure is clearly observed in J and H band polarized flux whilst in the K band a more compact structure is detected. Total flux J--K and H--K colour maps reveal a complex colour gradient toward the south--east direction (where the Circinus galactic disk is nearer to us). We find enhanced extinction in an arc shaped structure, at about 200pc from the nucleus, probably part of the star-formation ring. We model the polarized flux images with the scattering and torus model of Young \etal, with the same basic input parameters as used by Alexander \etal in the spectropolarimetry modelling of Circinus. The best fit to the polarized flux is achieved with a torus radius of $\sim$16pc, and a visual extinction A$_V$, through the torus, to the near--infrared emission regions of $>$66 mags.
|
[
{
"name": "paper.tex",
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Ruiz et al.]{M. Ruiz$^1$\\thanks{email: mili@star.herts.ac.uk}, \nD. M. Alexander$^2$, S. Young$^1$, J. Hough$^1$, S. L. Lumsden$^3$, C.A. \nHeisler$^4$\\thanks{We would like to dedicate this work to her memory }\n\\\\ $^1$Department of Physical Sciences, University of Hertfordshire, \nHatfield, Herts AL10 9AB, UK. \n\\\\$^2$International School for Advanced Studies, SISSA, Via Beirut 2-4, \n34014 Trieste, Italy. \n\\\\$^3$Department of Physics and Astronomy, University of Leeds, Leeds \nLS2 9JT, UK.\n\\\\$^4$Mount Stromlo and Siding Spring Observatories, Private Bag,\nWeston Creek P.O., Weston, ACT 2611, Australia}\n\n\n\\pagerange{\\pageref{firstpage}--\\pageref{lastpage}}\n\\pubyear{2000}\n%\\usepackage{graphics}\n\\begin{document}\n\\setcounter{footnote}{0}\n\\maketitle\n\\label{firstpage}\n\\begin{abstract}\n \nWe present near--infrared broad--band polarization images of the nuclear\nregions of the Circinus galaxy in the J, H and K bands. For the first time\nthe south--eastern reflection cone is detected in polarized light, which is \nobscured at\noptical wavelengths behind the galactic disk. This biconical structure is\nclearly observed in J and H band polarized flux whilst in the K band a more\ncompact structure is detected. Total flux J--K and H--K colour maps reveal a\ncomplex colour gradient toward the south--east direction (where the\nCircinus galactic disk is nearer to us). We find enhanced extinction in an\narc shaped structure, at about 200pc from the nucleus, probably part of the\nstar-formation ring.\n\nWe model the polarized flux images with the scattering and torus model of\nYoung \\etal, with the same basic input parameters as used by Alexander \\etal \nin the spectropolarimetry modelling of Circinus.\nThe best fit to the polarized flux is achieved with a\ntorus radius of $\\sim$16pc, and a visual extinction A$_V$, through the torus,\nto the near--infrared emission regions of\n$>$66 mags.\n\n\\end{abstract}\n\n\\begin{keywords}\ngalaxies: active -- \ngalaxies: individual (Circinus) -- \ngalaxies: nuclei -- \ngalaxies: Starburst -- \ninfrared: galaxies\n\\end{keywords}\n\n\n\\section{Introduction} \n\n\n\\begin{figure*}\n% \\begin{center}\n% \\leavevmode\n\\centerline{\\epsfig{file=figure1a.ps,width=14cm,height=4cm,angle=0}}\n\\vspace{0.4cm}\n\\centerline{\\epsfig{file=figure1b.ps,width=14cm,height=4cm,angle=0}}\n\\vspace{0.4cm}\n\\centerline{\\epsfig{file=figure1c.ps,width=14cm,height=4cm,angle=0}}\n\\caption{Near-IR images of the Circinus galaxy, J band (top), \nH band (middle) and K band (bottom). Contours are arbitrarily scaled.}\n \\label{}\n\\end{figure*}\n\n The investigation of nearby Seyfert galaxies with \npolarimetric observations provides\nunique information on the nuclear \nstructure of these objects. This information is of \nparticular importance when studying unification models of Seyfert galaxies.\n\n\\begin{figure*}\n\\centerline{\\epsfig{file=figure2a.ps,width=14cm,height=4cm,angle=0}}\n\\vspace{0.4cm}\n\\centerline{\\epsfig{file=figure2b.ps,width=14cm,height=4cm,angle=0}}\n\\vspace{0.4cm}\n\\caption{Colour maps of the nuclear regions of the Circinus galaxy. J--K \n(top) and H--K (bottom). The dark areas correspond to regions of enhanced \nextinction.}\n\\label{}\n\\end{figure*}\n\nThe standard unified model for Seyfert galaxies proposes that all types of\nSeyfert galaxy are fundamentally the same, however, the presence of a dusty\nmolecular ``torus'' obscures the broad line emission in many systems. In\nthis picture the classification of Seyfert 1 or 2 depends on the\ninclination angle of the torus to the line of sight (Antonucci, 1993). The\nmost convincing evidence for this unified model comes from optical\nspectropolarimetry. Using this technique, the scattered radiation from the\nbroad line region (BLR) of many Seyfert~2 galaxies is revealed in the form\nof broad lines in the polarized flux (e.g.\\ Antonucci and Miller, 1985,\nYoung \\etal, 1996a, Heisler, Lumsden and Bailey, 1997).\n\nNear--IR imaging polarimetry provides valuable information on the nature of\nthe polarizing source (e.g.\\ Lumsden \\etal, 1999, Tadhunter \\etal, 1999,\nYoung \\etal, 1996b, Packham \\etal, 1996, 1997, 1998, 1999). For example, in\nNGC1068, bipolar scattering cones are clearly detected in polarized flux\n(Young \\etal 1996b, Packham \\etal 1997) and the torus itself has been\nviewed in silhouette in the H band (Young \\etal 1996b). Interestingly, the\nstructure of the scattering cones often coincide with ground-based \nnarrow band imaging (e.g.\nWilson and Tsvetanov, 1994) and high resolution HST imaging (e.g. Capetti\n\\etal 1997, Falcke, Wilson and Simpson, 1998). Since the unified model\ninfers the presence of a dusty torus obscuring the Seyfert 1 core, we\nexpect that longer wavelength polarimetry will be able to probe deeper into\nregions within the plane of the torus and to see scattering from the nucleus\nwhich might otherwise be shielded from view at optical wavelengths.\n \nCircinus is a nearby (4Mpc) highly inclined (65$\\deg$, Freeman \\etal 1977) \nSb-Sd galaxy. At this distance, the spatial scale is 20pc/arcsec. \nIt is seen through a low interstellar extinction window near\nthe Galactic plane (A$_V$ = 1.5 mag; Freeman \\etal 1977). The nuclear\noptical line ratios are typical of a Seyfert 2 galaxy. This classification\nas a type 2 is also supported by the detection of intense coronal lines\n(Oliva \\etal 1994), the intense X-ray Fe 6.4 keV line (Matt \\etal 1996),\nrapid variation of powerful H$_2$O maser emission and a prominent\nionization cone in [O\\,{\\sc iii}]5007 with filamentary supersonic outflows\n(Marconi \\etal 1994). Recent optical spectropolarimetry (Oliva \\etal, 1998\nand Alexander \\etal, 1999a) has shown a scattered polarized broad H$\\alpha$\nline and therefore a hidden Seyfert 1 nucleus. Other characteristics\ninclude enhanced star forming activity in the form of a star-forming ring\nof 200pc in size (Marconi \\etal 1994), a Compton thick nucleus at X-ray\nenergies (Matt \\etal 1996) and an unresolved nuclear source ($<$1.5pc) at\n2$\\mu$m (Maiolino \\etal 1998).\n\nSince it is already known from optical spectropolarimetry that the Circinus\ngalaxy harbours a hidden type 1 nucleus and the optical ionization cone\nsuggests the presence of an obscuring/collimating torus, this galaxy is an\nideal candidate to test the theoretical models of unified schemes. The\ndusty nature of the Circinus galaxy favours near-IR polarimetry over\noptical polarimetry due to the lower optical depth at near-IR wavelengths.\n\nIn this paper we present near--IR imaging polarimetry revealing, for the\nfirst time, a biconical emission region. We investigate the nature of this\nemission in the context of the standard unified model of Seyfert galaxies.\n\n\n\n\\begin{figure*}\n% \\begin{center}\n% \\leavevmode\n% {file=j.ps,width=3cm,height=14cm,angle=-90}\n\\centerline{\\epsfig{file=figure3a.ps,width=14cm,height=5cm,angle=0}}\n\\vspace{0.4cm}\n\\centerline{\\epsfig{file=figure3b.ps,width=14cm,height=5cm,angle=0}}\n\\vspace{0.4cm}\n\\centerline{\\epsfig{file=figure3c.ps,width=14cm,height=5cm,angle=0}}\n \\caption{Near-IR polarization maps of Circinus. The J band data is shown\nat the top, \nH band in the middle and K band at the bottom. The contours are of the\ntotal flux and are arbitrarily scaled. A 1 arcsec polarization vector \ncorresponds \nto a 10 percent polarization.}\n\n\\label{}\n \\end{figure*}\n\n\n\\begin{table}\n\\begin{minipage}[t]{5.5in}\n \\caption{Nuclear polarization}\n \\label{tab:table}\n \\leavevmode \n \\footnotesize\n \\begin{tabular}[h]{cccc}\n% \\hline \\\\[-5pt]\nWaveband & aperture & $\\%$ &angle\\\\\n & (arcsec)& & ($\\deg$)\\\\\n% \\hline \\hline \\\\[-5pt]\n &\t& & \\\\\n & 1 & 2.04$\\pm$0.38 & 34.1$\\pm$3.8\\\\\nJ & 2 & 1.71$\\pm$0.16 & 38.3 $\\pm$2.0 \\\\\n & 4 & 1.40$\\pm$0.08 & 46.3$\\pm$1.1 \\\\ \n &\t& & \\\\\n & 1 & 2.01$\\pm$0.15 & 33.4$\\pm$2.4 \\\\\nH & 2 & 1.75$\\pm$0.13 & 35.5$\\pm$1.9 \\\\\n\t& 4 & 1.34$\\pm$0.07 & 41.1$\\pm$1.1 \\\\ \n &\t& & \\\\\n & 1 & 3.25$\\pm$0.27 & 32.1$\\pm$3.1 \\\\\nK & 2 & 2.78$\\pm$0.25 & 33.7 $\\pm$2.9 \\\\\n\t& 4 & 1.99$\\pm$0.15 & 34.7 $\\pm$1.8 \\\\\n% \\hline\n \\end{tabular}\n\\end{minipage}\n\\end{table}\n\n\n\\section{Observations}\n\nThe data presented here were obtained on the nights of 22 May 1995 (H and K\nband data) and 11 August 1995 (J band) on the AAT with the common user camera\nIRIS, which uses a 128$^2$ HgCdTe array. \nWe used the cs/36 secondary, which results in a pixel scale of \napproximately 0.25 arcsec/pixel.\nThe May observations were made under\nnon-photometric conditions. Seeing as estimated in the infrared was $1-1.2$\narcsec for the May data, and $\\sim0.9$ arcsec for the August data. The IRIS\nphotometric standard star SA94-251 was observed at J for the August data. No\nphotometric standards are available for the May data given the conditions.\nInstead, we used a spectrum of the nucleus of Circinus, taken on 21 Feb 1997 \nwith the\nechelle grisms inside IRIS, to achieve an overall flux calibration as described\nbelow. The stability and instrumental polarization of the instrument were\nchecked using polarized and unpolarized standard stars. The measured\ninstrumental polarization is less than 0.1$\\%$, and the instrument is almost\ncompletely stable between the two dates when data were taken.\n\nThe polarimeter inside IRIS uses a Wollaston beam splitting prism inside the\ndewar to separate the $o-$ and $e-$rays. A mask in the focal plane prevents\nthe separate images from overlapping. The mask when used with the cs/36\nsecondary has dimensions on the sky of approximately \n30arcsec$\\times$8arcsec. A $\\lambda/2$ waveplate is positioned in front of \nthe dewar. Each\npolarimetry dataset is then comprised of exposures at four separate waveplate\npositions ($0^\\circ, 45^\\circ, 22.5^\\circ$ and $67.5^\\circ$).\n\nThe polarimetry data were reduced as follows. All frames were flatfielded using\ndome flats. Offset sky frames were taken with varying positions from the\nnucleus. These frames were median filtered to remove background sources,\nleaving four separate sky frames for each waveband, corresponding to the four\nwaveplate positions. The four sky frames were scaled to the median level of\nthe sky within each group of four individual object frames, and the result\nsubtracted from the object frames. The resultant images were then registered\nand combined into separate mosaics for each wave plate position. These final\nmosaics were combined to form the Q and U Stokes images (using the TSP package\nand the ratio method -- Bailey 1997) and hence polarization maps.\nTotal on-source exposure times for each waveplate position are \n960 seconds at J, and 300 seconds at both H and K.\n\nAs noted above, the May data were obtained under poor conditions. Therefore, \nwe did not\nattempt to perform an absolute flux calibration for this data therefore.\nInstead, we derived relative photometry from the flux-calibrated 1--2.4$\\mu$m\nspectrum. This calibration is performed by scaling the J total flux image\ncounts in a circular aperture of equivalent area to that of the spectrum\naperture (2arcsec$\\times$2arcsec). These counts correspond to the flux as\nmeasured in the spectrum at J. The count ratios H/J and K/J as measured from\nthe total flux images are then scaled to the corresponding ratios measured from\nthe spectrum.\nThe main error in this process is in the limited accuracy with which\nthe overall spectral shape is defined.\nWe therefore adopt a\nconservative error estimate of 30$\\%$ for the overall flux calibration\ntaken from this data. \n\n\\section{Results}\n\nIn this section we present the general results from our data and provide an \noverview \nof the features observed in the central regions of the Circinus galaxy. In \nFig. 1\nwe show the J, H and K total flux images of Circinus. \n\n\\subsection{Colour maps}\n\nThe J--K and H--K maps are shown in Fig. 2. These maps were generated by \nregistering the peaks of the total flux images, whose relative offsets did not\nexceed 2 pixels in RA or DEC. Darker areas correspond to redder colours.\n\nWe observe a complex colour structure clearly indicating a non--uniform \ndistribution of dust in the Circinus galactic disk. \n\nIn particular, we observe a colour gradient towards the south--east region \nwhich\nis due to an increase in extinction. As discussed by Quillen \\etal (1995),\nthe closest side of a galaxy disc undergoes the most efficient dust screening,\ntheu, the south-east region of the Circinus galactic disc is closest to us \n(see also section 4.2). \n\nAs previously observed by Maiolino \\etal (1998), we detect a dust lane close \nto the nucleus in a\nbar--like structure, running from the NE to SW which is also connected \nto the nucleus,\nbest seen in the J--K map. There is another dust lane\nin a bar--like structure, running parallel to the latter. \nAt about 180pc from the nucleus (9 arcsec), to the East, there is an arc of \nheavy extinction, which is likely to \nrepresent part of the star formation ring previously observed \nin an H$\\alpha$ image \n(Marconi \\etal 1994).\n\n\\begin{figure*}\n% \\begin{center}\n% \\leavevmode\n% {file=j.ps,width=3cm,height=14cm,angle=-90}\n\\centerline{\\epsfig{file=figure4a.ps,width=14cm,height=4cm,angle=0}}\n\\vspace{0.4cm}\n\\centerline{\\epsfig{file=figure4b.ps,width=14cm,height=4cm,angle=0}}\n\\vspace{0.4cm}\n\\centerline{\\epsfig{file=figure4c.ps,width=14cm,height=4cm,angle=0}}\n \\caption{Near-IR polarized flux images of Circinus, J band (top), \nH band (middle) and K band (bottom), showing the change in polarized \nstructure from \npredominantly scattering to predominantly dichroism.}\n \\label{}\n\\end{figure*}\n\n\n\\subsection{Polarized maps}\n\nThe polarization vector maps are shown \nin Fig. 3, superimposed are the continuum contours. Only those pixels with\na level of at least 3$\\sigma$ above the background of polarized intensity \nare displayed. \nThe J and H polarization vector maps are similar to each other but there is \nno obvious large--scale symmetry. The highest polarization for J and H is \nwithin\nthe 2 arcsec of the nucleus; at J it has a maximum value of 2.04$\\pm 0.38\\%$\nat a position angle of 34\\deg$\\pm$ 3.8\\deg and at H it has a \nmaximum of 2.01$\\pm 0.15\\%$ with a position angle of \n33.4\\deg $\\pm 2.4$\\deg. The E vectors at K are essentially parallel \nover the central 5 arcsec with a highest \npolarization of $\\sim$ 3.25$\\pm 0.27\\%$ at the nucleus a\n32\\deg$\\pm 3$\\deg and $\\sim$ 1.6$\\%$ elsewhere. Table 1 presents \npolarization and position\nangle values as measured in various aperture sizes. \nWe notice that the polarization position \nangle for a nuclear aperture of 1 arcsec is roughly perdendicular \nto the axis of the infrared \nscattering cones seen in the J band and the one--sided optical ionization cone \n(Marconi \\etal 1994) as well as to the the radio \ncontinuum emission (Elmouttie \\etal 1998). \nAt larger apertures, the polarization position angle changes, \ndue to different contributions\nto the total polarization such as galactic polarization. The largest \nchange in polarization position angle occurs in the J band. This is \nbecause the larger \naperture will have contributions from regions dominated by scattering \npolarization \ni.e., from the scattering cones.\nAt K, the polarization is dominanted by dichroism (see Section 4) \nat small and large apertures and the small change in the polarization \nposition angle is likely to be due to galactic polarization.\n\n\n\\subsection{Polarized flux images}\n\nThe near--infrared polarized--flux images are shown in Fig. 4.\nThe J band polarized image shows a double sided cone--like structure,\nwith axis approximately along the NW--SE direction. \nPrevious optical imaging of this \ngalaxy (Marconi \\etal 1994) showed a one-sided ionization cone in the light\nof the [O\\,{\\sc iii}]5007 line\nin the north--west direction. More recently, (Maiolino \\etal 1999) have shown\nan extended [Si\\,{\\sc vi}]1.95$\\mu$m emission in the south--eastern \nregion of the nucleus, \nproviding evidence for the existence of a counter--cone, whose existence was \npreviously inferred from radio maps (Elmouttie \\etal 1995, 1998). \nAdditionally, the presence of\npolarized emission to the south--east of the nucleus \n(the ``counter--cone'') is also indicated \nby the detection of polarized H$\\alpha$ emission at about 8arcsec \nto the SE (Oliva \\etal 1998).\n \nThe north--west polarization cone is presumably\nproduced by scattering in a region spatially coincident with the \nnorth--west ionization cone. The lack of an ionization cone to the \nsouth--east is due to the heavy extinction at optical wavelengths \ncaused by the galaxy disk ($\\imath \\simeq 65\\deg$), \nestimated at 5 mags in the visible (Oliva \\etal 1995; Maiolino \\etal 1998). \nIn addition, there is evidence for the \npresence of dust lanes in the south--east direction (Marconi \\etal 1994; \nMaiolino \\etal 1998) and as shown in Fig 2.\n\nAs the wavelength of the observations increases, at H and K bands, \nthe bipolar pattern tends to disappear as the amount of scattered \nlight reduces, as would\noccur for scattering from small dust grains, and with more nuclear \nlight being seen directly.\nFig. 5 shows cuts through the nucleus along the east--west direction of\nthe polarized flux images at J and K, showing the nuclear concentration \nof the K emission to the central 4 arcsec compared to the \nmore extended J emission.\n\n\\begin{figure*}\n\\centerline{\\epsfig{file=figure5.ps,width=14cm,height=8cm,angle=0}}\n\\vspace{0.4cm}\n\\caption{Polarized intensity cuts through the nucleus along the \neast--west direction for \nJ and K bands. The dashed line represents K and the dotted line \nrepresents J. The fluxes \nhave been normalized to unity.\n}\n \\label{}\n\\end{figure*}\n\n\\section{The scattering model}\n\nTo model\nthe observed polarization\ncharacteristics of the Circinus galaxy, we have used the standard \nSeyfert model of Young \\etal (1995), hereafter referred to as the Y95 model.\n\n\\subsection{Description of the model}\n\nThe Y95 model takes the standard unification of AGN approach, assuming a\nbare Seyfert~1 nucleus as the source function for the central source, in\nthis case NGC5548, surrounded by an optically thick torus. The nuclear\nradiation is collimated by the torus and scattered in a biconical\ncloud of electrons and/or dust grains. \nThe model also considers the direct view to the emission region, that can\nbe polarized via dichroic absorption by aligned grains within the torus.\nThe model was originally developed to reproduce\nspectropolarimetric data, and was used to successfully model the\npolarization of NGC1068 (Young \\etal 1995), other narrow line active\ngalaxies (e.g Young \\etal 1996a), and the Circinus galaxy \n(Alexander \\etal 1999a). The model was modified to produce images \nby integrating the\nscattered intensity over the size of a pixel at the distance of the galaxy\nin question, as illustrated for NGC1068 (Packham \\etal 1997).\n\nThe most important parameters for the model are the inclination of the\ncone axis to the line of sight (also the polar axis of the torus in this\nsimple model), the cone half opening-angle, the extinction through the\ntorus to the emission regions and the optical depth to scattering in the\ncones. The latter is defined in terms of inner and outer scattering\nradii, a number density of scatterers at the inner radius and the radial\ndependence of the number density of scatterers. In the case of spatially\nresolved imaging the inner scattering radius and the radial dependence for\nthe number density also determine the radial scattered light profile with\ndistance from the nucleus.\n\n\\subsection{Applying the model to the Circinus galaxy}\n\nTo reduce the number of free variables in the model we can fix some of these\nparameters. As in the spectropolarimetry modelling of Circinus (Alexander\n\\etal 1999a), we set the cone half opening-angle to 45\\deg, which is\nsimilar to the observed [O\\,{\\sc iii}]5007 emission line cone (Marconi \\etal\n1994). In order to reproduce the intrinsic scattered degree of\npolarization at 26$\\%$ (Oliva \\etal 1995; Alexander \\etal 1999a) the\ninclination of the scattering axis to the line of sight is 50\\deg.\nExcept for assuming a large outer scattering radius of 1$\\times 10^{20}$m, no\nother assumptions were made prior to the modelling.\n\nThe model output images were smoothed with a Gaussian filter with a FWHM\nchosen to match the seeing of the observations, 1 arcsec for J and H and\n1.5 arcsec for K, and then scaled by a factor to match the peak of the\npolarized image at J. As previously mentioned in section 2, \nthe images are not absolutely flux\ncalibrated but are in suitable units to represent relative fluxes, thus\nthe same scaling factor is used at all wavelengths. Comparisons of the\nmodel output with the observations are then made by producing\ncross--section cuts through the images in the SE--NW direction, in polarized\nflux. Modelling the polarized flux images, rather than the total flux, to\nthe first order removes the stellar population and the uncertainty of the\nstellar fraction.\n\nCross--sections through the observation images, however, show that the\npolarized nuclear flux has an underlying base, presumably resulting from\ndichroically polarized stellar emission. This base was fitted separately\nby a simple addition to the model output. At J this base is consistent\nwith a constant value over the model image size, whilst at H and K the\nexcess was taken as a linearly dependent ramp across the cut. With this\npedestal taken into account it is possible to determine the extinction to\nthe scattering regions away from the nucleus. For the south--east\n scattering cone\nthis is consistent with a visual extinction of A$_V$ =~5 mags, while for \nthe north--west cone away from the nucleus, \nthe extinction is A$_V$ = 1.5 mags. The\nlatter value of extinction is the same as that determined for the Galaxy\n(Freeman \\etal 1977), implying that the south--east scattering cone is actually\nviewed through an extinction of A$_V$ = 3.5 mags arising from the Circinus host\ngalaxy. This value is in agreement with the variation of extinction along\nthe cone--axis measured by Oliva \\etal (1999), as derived from optical \nspectral lines. \n\nTwo possible orientations for the model were investigated, the first has\nthe less obscured north--west scattering cone pointing towards \nthe observer and the\nsouth--east scattering region as the counter--cone, and the second model is the\nreverse with the forward pointing cone being to the south--east. However, \nno fit\nto the observations could be found using the first model and therefore,\nthis case will not be discussed further. Henceforth, the south--east\nscattering cone is considered to be forward pointing.\n\nTo match the radial distribution of the scattered flux from the nucleus,\nthe best fit was obtained with an inner scattering radius of 0.5pc and a\nradial dependence for the number density of scatterers as $r^{-1}$. This\nappears to be tightly constrained, with only a 10 percent alteration in\nthe inner radius being inconsistent with the observations. \nUnlike NGC1068 (Packham \\etal 1997),\nthe dichroically polarized direct view to the near--infrared emission region\nis only readily apparent in the K--band image, which suggests that the\nextinction through the postulated torus is higher than the A$_V$ = 37 mags\nfor NGC1068. However, because we only have one measurement of the direct\nview, it is not possible to determine absolutely the extinction through\nthe torus for the Circinus galaxy. It is possible to derive a lower limit\nfor this extinction in conjunction with an upper limit for the number\ndensity of scatterers. A visual extinction of A$_V$ = 66 mags was\nfound to be the lowest compatible with the observations, and the upper\nlimit for the required number density of the scattering electrons at the\ninner scattering radius were 3 $\\times 10^9$ m$^{-3}$ for the forward \ncone and 4.2 $\\times 10^9$ m$^{-3}$ for the counter--cone. \nIt should be noted that scattering using\nRayleigh--type dust grains did not provide a good fit to the observations.\n\nTo fully match the cross--sectional cuts through the observations it was\nnecessary to invoke extinction of the scattered flux from the\ncounter--cone by the torus, which was assumed to be an opaque disk. Also,\nit was found that the best match to the observations was achieved if the\ngalactic extinction of the forward cone extended partially across the\ncounter--cone and dropped off with distance away from the nucleus. The\nradius of the torus was found to be 16pc, and was well constrained, a\nsmaller torus being inconsistent at J and a larger torus was inconsistent\nat H. The galactic extinction tail--off was modelled as a simple step,\nwith the full extinction of A$_V$ = 3.5 mags stepping down to A$_V$ = 2.3 mags\nto a distance of 25 pc beyond the nucleus in addition to the Galactic\nextinction of 1.5 mags.\n\nThe model parameters are listed in Table 2. Comparison of the\ncross--sections through the model produce images and the observations in\npolarized flux are illustrated in Fig. 6 for the J, H and K bands.\n\n\\begin{figure*}\n\n\\centerline{\\epsfig{file=figure6a.ps,width=7cm,height=14cm,angle=-90}}\n\\vspace{0.4cm}\n\\centerline{\\epsfig{file=figure6b.ps,width=7cm,height=14cm,angle=-90}}\n\\vspace{0.4cm}\n\\centerline{\\epsfig{file=figure6c.ps,width=7cm,height=14cm,angle=-90}}\n\\vspace{0.4cm}\n\\caption{Cross-sections of polarized flux images along the NW--SE direction.\nJ band at the top, H band in the middle and K band at he bottom. \nThe solid line represents the data and the dashed line is the model fit.\n}\n\\label{}\n\\end{figure*}\n\n\n\\begin{table}\n\\begin{minipage}[t]{5.5in}\n \\caption{Model parameters.}\n \\label{tab:table}\n \\leavevmode \n \\footnotesize\n \\begin{tabular}[h]{lc}\n%\\hline \\\\[-5pt]\n\\hspace{1.2in}\n\\vspace{0.1in}\n\tInput parameters\\\\\n system inclination($\\deg$) & 50 \\\\\n SE or NW cone opening half-angle($\\deg$) & 45\\\\\n SE cone position angle($\\deg$) &125\\\\\n NW cone position angle($\\deg$) &305\\\\\n & \\\\\n%\\hline \\\\[-5pt]\n\\hspace{1.0in}\n\\vspace{0.1in}\n\tBest fitting parameters\\\\\n inner scattering radius (pc) & 0.5\\\\\n n$_{iscr}$(m$^{-3}$)\\footnote{number density at inner radius} &$< 3 \\times 10^9$\\\\\n n$_{cc}$(m$^{-3}$)\\footnote{number density at counter cone} &$< 4.2 \\times 10^{9}$\\\\\n $\\alpha$, power law decrement\\footnote{for number density $\\sim r^{\\alpha}$} &-1\\\\\n torus radius (pc) & 16\\\\\n A$_V$ through torus & $>$ 66\\\\\n A$_V$ through galactic disk & 3.5\\\\\n A$_V$ through Galactic disk & 1.5\\\\\n% \\hline\n \\end{tabular}\n\\end{minipage}\n\\end{table}\n\n\n\\subsection{Discussion}\n \nAlexander \\etal (1999a) modelled the optical and K--band spectropolarimetry \ndata of the\nCircinus galaxy with scattering, and a dichroic component through the dusty\ntorus corresponding to a visual extinction of A$_V$ = 35 mags. In the present \nstudy, we have\nthe advantage of being able to constrain the scattered flux with both the\nspatially resolved information of the images and the extra wavelength\ncoverage with the J and H band images. From this we determine that the\nratio of scattered intensity to that from the direct view is higher than\nthat found by Alexander \\etal (1999a), which explains the difference in\nthe modelled extinction.\n\nWe achieved a good fit to our polarized images with a torus radius of\napproximately 16~pc. This is substantially smaller than the size of the\ntorus determined for NGC1068 of $\\sim$ 180 pc (Efstathiou, Hough \\& Young 1995;\nYoung \\etal 1996b; Packham \\etal 1997), but larger than that estimated for \nCen A, $\\sim$2pc (Alexander \\etal 1999b). \n\nModelling the polarized flux images of Circinus only allowed us to place an\nupper limit for the electron scattering number density, together with a\nlower limit for the visual extinction through the torus to the near-IR\nemission region. However, the lower the scatterer's number density, the\nhigher the boost factor (the ratio of the actual luminosity of the source\nto the observed polarized luminosity). Scattering number densities\nsignificantly less than the upper limits, greater than a factor of 10--20,\nresult in a boost factor that, using the scattered broad \\ha~flux of\n4.3$\\times 10^{-15}$ erg s$^{-1}$ cm$^{-2}$ (Alexander \\etal 1999a), \nimplies a broad \\ha~luminosity in the top 40 percent of all Seyfert galaxies,\n while\nits infrared luminosity is in the lower 20 percent. This argues that the\nnumber density of scatterers must be within a factor of 10 of the upper\nlimit.\n\n\\section{Conclusions}\n\nWe have presented near--infrared polarimetric images of the\n Circinus galaxy showing\na clear bipolar scattering cone in the J band. The south--east cone was\npreviously undetected at optical\nwavelengths because it was hidden behind the heavy extinction of the galactic \ndisk. At longer wavelengths, the H and K band images show more compact \nstructures due to the dominance of dichroic absorption over scattered \nradiation.\nWe have successfully applied an adapted version of the Y95 \nmodel to\ninterpret the observed polarized flux distribution. This model includes two\ngeometrical identical scattering cones, diametrically opposite to each other, \nwith the forward cone in the south--east direction at a position angle of \n125$\\deg$ and an opening half angle of 45$\\deg$. The inclination of the system\nto the line of sight is 50$\\deg$. The estimated optical extinction \nA$_V$ to the \nnucleus through the torus is $>$66 mag. We estimate that the putative \ntorus in the Circinus galaxy has an outer radius of $\\sim$16pc.\n\n\n\\section{Acknowledgements}\nM.R. thanks PPARC for support through a postdoctoral assistanship.\nDMA thanks the TMR network (FMRX-CT96-0068) for a postdoctoral grant.\nWe thank Dolores P\\'erez-Ram\\'\\i rez for her valuable help on the\nproduction of this paper.\n\n\\vskip .3truecm\n\\leftskip=25pt\n\\parindent=-\\leftskip\n\n%\\section{References:}\n\n\\begin{thebibliography}{99}\n\n\\bibitem{}Alexander D. M., Heisler C., Young S., Lumsden S., Hough J. H., \nBailey J., 1999a, submitted to MNRAS\n\n\\bibitem{}Alexander D.M., Efstathiou A., Hough J.H., Aitken D.K., Lutz D., \nRoche P.F., Sturm E., 1999b, MNRAS, 310, 78\n\n\\bibitem{}Antonucci R., 1993, ARA\\&A, 31, 473\n\n\\bibitem{}Antonucci R., Miller J. S., 1985, ApJ, 297, 621\n\n\\bibitem{}Bailey J.A., 1997, TSP version 2.3. Starlink User Note 66.5\n\n\\bibitem{}Capetti A., Axon D., Macchetto F. D., 1997, ApJ, 487, 560\n\n\\bibitem{}Elmouttie M., Haynes R. F., Jones K. L., Ehle M., Beck R., \nWielebinski R., 1995, MNRAS, 275, L53\n\n\\bibitem{}Elmouttie M., Haynes R. F., Jones K. L., Sadler E. M., Ehle M., \n1998, MNRAS, 297, 1202\n\n%\\bibitem{}Efstathiou A., Rowan-Robinson M., 1990, MNRAS, 245, 275\n\n\\bibitem{}Efstathiou A., Hough J., Young S., 1995, MNRAS, 277, 1134\n\n\\bibitem{}Falcke H., Wilson A. S., Simpson C., 1998, ApJ, 502, 199\n\n\\bibitem{}Freeman K. C., Karlsson B., Lygna G., Burrell J. F., van Woerden H.\n, Goss W.M., Mebold U., 1977, A\\&A, 55, 445\n\n\\bibitem{}Heisler C. A., Lumsden S. L., Bailey J. A., 1997, Nature, 385, 700\n\n\\bibitem{}Lumsden S. L., Moore T. J. T., Smith C., Fujiyoshi T., \nBland-Hawthorn J., Ward M. J., 1999, MNRAS, 303, 209\n\n\\bibitem{}Maiolino R., Krabbe A., Thatte N., Genzel R., 1998, ApJ, 493, 650\n\n\\bibitem{}Maiolino R., Alonso--Herrero A., Anders S., Quillen A., Rieke M.J., \nRieke G.H., Tacconi--Garman L.E., 1999, astro--ph/99101160\n\n\\bibitem{}Marconi A., Moorwood A. F. M., Origlia L., 1994, Messenger, 78, 20\n\n\\bibitem{}Matt G., Fiore F., Perola G. C., Piro L., Fink G.G., Grandi P., \nMatsuoka M., Oliva E., Salvati M., 1996, A\\&A, 315, L109\n\n\\bibitem{}Oliva E., Salvati M., Moorwood A. F. M., Marconi A., 1994, \nA\\&A, 288, 457\n\n\\bibitem{}Oliva E., Origlia L., Kotilainen J. K., Moorwood A. F. M., \n1995, A\\&A, 301, 55\n\n\\bibitem{}Oliva E., Marconi A., Cimatti A., di Serego Alighieri S., \n1998, A\\&A, 329, L21\n\n\\bibitem{}Oliva E., Marconi A., Moorwood A. F. M., 1999, A\\&A, 342, 87\n\n\\bibitem{}Packham C., \\etal, 1999, in preparation\n\n\\bibitem{}Packham C., Hough J. H., Young S., Chrysostomou A., Bailey J. A., \nAxon D. J., Ward M. J., 1996, MNRAS, 278, 406\n\n\\bibitem{}Packham C., Young S., Hough J. H., Axon D. J., Bailey J. A., 1997, \nMNRAS, 288, 375 \n\n\\bibitem{}Packham C., Young S., Hough J. H., Tadhunter C. N., Axon D. J., \n1998, MNRAS, 297, 936\n\n\\bibitem{}Quillen A. C., Frogel J. A., Kuchinski L. E., Terndrup D. M., \n1995, AJ, 110, 156\n\n\\bibitem{}Tadhunter C. N., Packham C., Axon D. J., Jackson N. J., \nHough J. H., Robinson A., Young S., Sparks W., 1999, ApJ, 512, L91 \n\n\\bibitem{}Wilson A. S., Tsvetanov Z. I., 1994, AJ, 107, 1227\n\n\\bibitem{}Young S., Hough J., Axon D. J., Bailey J. A., Ward M. J., \n1995, MNRAS, 272, 513 (Y95)\n\n\\bibitem{}Young S., Hough J., Axon D. J., Ward M. J., Bailey J. A., \n1996a, MNRAS, 280, 291\n\n\\bibitem{}Young S., Packham C., Hough J., 1996b, MNRAS, 283, L1\n\n\\end{thebibliography}\n\n\\bsp\n\n\\label{lastpage}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002223.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{}Alexander D. M., Heisler C., Young S., Lumsden S., Hough J. H., \nBailey J., 1999a, submitted to MNRAS\n\n\\bibitem{}Alexander D.M., Efstathiou A., Hough J.H., Aitken D.K., Lutz D., \nRoche P.F., Sturm E., 1999b, MNRAS, 310, 78\n\n\\bibitem{}Antonucci R., 1993, ARA\\&A, 31, 473\n\n\\bibitem{}Antonucci R., Miller J. S., 1985, ApJ, 297, 621\n\n\\bibitem{}Bailey J.A., 1997, TSP version 2.3. Starlink User Note 66.5\n\n\\bibitem{}Capetti A., Axon D., Macchetto F. D., 1997, ApJ, 487, 560\n\n\\bibitem{}Elmouttie M., Haynes R. F., Jones K. L., Ehle M., Beck R., \nWielebinski R., 1995, MNRAS, 275, L53\n\n\\bibitem{}Elmouttie M., Haynes R. F., Jones K. L., Sadler E. M., Ehle M., \n1998, MNRAS, 297, 1202\n\n%\\bibitem{}Efstathiou A., Rowan-Robinson M., 1990, MNRAS, 245, 275\n\n\\bibitem{}Efstathiou A., Hough J., Young S., 1995, MNRAS, 277, 1134\n\n\\bibitem{}Falcke H., Wilson A. S., Simpson C., 1998, ApJ, 502, 199\n\n\\bibitem{}Freeman K. C., Karlsson B., Lygna G., Burrell J. F., van Woerden H.\n, Goss W.M., Mebold U., 1977, A\\&A, 55, 445\n\n\\bibitem{}Heisler C. A., Lumsden S. L., Bailey J. A., 1997, Nature, 385, 700\n\n\\bibitem{}Lumsden S. L., Moore T. J. T., Smith C., Fujiyoshi T., \nBland-Hawthorn J., Ward M. J., 1999, MNRAS, 303, 209\n\n\\bibitem{}Maiolino R., Krabbe A., Thatte N., Genzel R., 1998, ApJ, 493, 650\n\n\\bibitem{}Maiolino R., Alonso--Herrero A., Anders S., Quillen A., Rieke M.J., \nRieke G.H., Tacconi--Garman L.E., 1999, astro--ph/99101160\n\n\\bibitem{}Marconi A., Moorwood A. F. M., Origlia L., 1994, Messenger, 78, 20\n\n\\bibitem{}Matt G., Fiore F., Perola G. C., Piro L., Fink G.G., Grandi P., \nMatsuoka M., Oliva E., Salvati M., 1996, A\\&A, 315, L109\n\n\\bibitem{}Oliva E., Salvati M., Moorwood A. F. M., Marconi A., 1994, \nA\\&A, 288, 457\n\n\\bibitem{}Oliva E., Origlia L., Kotilainen J. K., Moorwood A. F. M., \n1995, A\\&A, 301, 55\n\n\\bibitem{}Oliva E., Marconi A., Cimatti A., di Serego Alighieri S., \n1998, A\\&A, 329, L21\n\n\\bibitem{}Oliva E., Marconi A., Moorwood A. F. M., 1999, A\\&A, 342, 87\n\n\\bibitem{}Packham C., \\etal, 1999, in preparation\n\n\\bibitem{}Packham C., Hough J. H., Young S., Chrysostomou A., Bailey J. A., \nAxon D. J., Ward M. J., 1996, MNRAS, 278, 406\n\n\\bibitem{}Packham C., Young S., Hough J. H., Axon D. J., Bailey J. A., 1997, \nMNRAS, 288, 375 \n\n\\bibitem{}Packham C., Young S., Hough J. H., Tadhunter C. N., Axon D. J., \n1998, MNRAS, 297, 936\n\n\\bibitem{}Quillen A. C., Frogel J. A., Kuchinski L. E., Terndrup D. M., \n1995, AJ, 110, 156\n\n\\bibitem{}Tadhunter C. N., Packham C., Axon D. J., Jackson N. J., \nHough J. H., Robinson A., Young S., Sparks W., 1999, ApJ, 512, L91 \n\n\\bibitem{}Wilson A. S., Tsvetanov Z. I., 1994, AJ, 107, 1227\n\n\\bibitem{}Young S., Hough J., Axon D. J., Bailey J. A., Ward M. J., \n1995, MNRAS, 272, 513 (Y95)\n\n\\bibitem{}Young S., Hough J., Axon D. J., Ward M. J., Bailey J. A., \n1996a, MNRAS, 280, 291\n\n\\bibitem{}Young S., Packham C., Hough J., 1996b, MNRAS, 283, L1\n\n\\end{thebibliography}"
}
] |
astro-ph0002224
|
An X-ray and optical study of the cluster A33
|
[
{
"author": "S. Colafrancesco \\inst{1}"
},
{
"author": "C.R. Mullis \\inst{2}"
},
{
"author": "A. Wolter \\inst{3}"
},
{
"author": "I.M. Gioia \\inst{2,10,11}"
},
{
"author": "T. Maccacaro \\inst{3}"
},
{
"author": "A. Antonelli \\inst{1}"
},
{
"author": "F. Fiore \\inst{1}"
},
{
"author": "J. Kaastra \\inst{4}"
},
{
"author": "R. Mewe \\inst{4}"
},
{
"author": "Y. Rephaeli \\inst{5}"
},
{
"author": "R. Fusco-Femiano \\inst{6}"
},
{
"author": "V. Antonuccio-Delogu \\inst{7}"
},
{
"author": "F. Matteucci \\inst{8} and P. Mazzotta \\inst{9}"
}
] |
We report the first detailed X-ray and optical observations of the medium-distant cluster A33 obtained with the Beppo-SAX satellite and with the UH 2.2m and Keck II telescopes at Mauna Kea. The information deduced from X-ray and optical imaging and spectroscopic data allowed us to identify the X-ray source 1SAXJ0027.2-1930 as the X-ray counterpart of the A33 cluster. The faint, $F_{2-10~keV} \approx 2.4 \times 10^{-13} \ergscm2$, X-ray source 1SAXJ0027.2-1930, $\sim 2$ arcmin away from the optical position of the cluster as given in the Abell catalogue, is identified with the central region of A33. Based on six cluster galaxy redshifts, we determine the redshift of A33, $z=0.2409$; this is lower than the value derived by Leir and Van Den Bergh (1977). The source X-ray luminosity, $L_{2-10~keV} = 7.7 \times 10^{43} \ergs$, and intracluster gas temperature, $T = 2.9$ keV, make this cluster interesting for cosmological studies of the cluster $L_X-T$ relation at intermediate redshifts. Two other X-ray sources in the A33 field are identified. An AGN at z$=$0.2274, and an M-type star, whose emission are blended to form an extended X-ray emission $\sim 4$ arcmin north of the A33 cluster. A third possibly point-like X-ray source detected $\sim 3$ arcmin north-west of A33 lies close to a spiral galaxy at z$=$0.2863 and to an elliptical galaxy at the same redshift as the cluster. \keywords{Cosmology: clusters of galaxies: individual: A33, observations: X-rays}
|
[
{
"name": "ds8573.tex",
"string": "% Da usare per la versione sottomessa\n%\\documentstyle[referee]{l-aa}\n%\n% Da usare per la versione accettata\n\\documentstyle{l-aa}\n% \n%\\documentclass{aa}\n\\input psfig\n%\\documentstyle[12pt,aasms4,epsfig]{article}%\n% Useful definitions%\n\\input{s.sty}\n\\def\\simlt{\\ \\raise -2.truept\\hbox{\\rlap{\\hbox{$\\sim$}}\\raise5.truept %MC\n\\hbox{$<$}\\ }} %\n\\def\\simgt{\\ \\raise -2.truept\\hbox{\\rlap{\\hbox{$\\sim$}}\\raise5.truept %\n\\hbox{$>$}\\ }} %\n\\newcommand{\\abu}{$Fe/H$}\n%\n\\begin{document}\n\n \\thesaurus{03 % A&A Section 3: extragalactic\n ( 11.03.4; %{\\bf Galaxies: clusters: individual:} $\\ldots$\n 11.09.3; %intergalactic medium\n 12.03.3; %Cosmology: observations\n% 12.04.1; %dark matter\n 11.01.2; %Galaxies: active\n 13.25.2)} % X-rays: galaxies\n% 13.25.3)} % X-rays: general\n\n \\title{An X-ray and optical study of the cluster A33}\n\n\n \\author{S. Colafrancesco\n \\inst{1}, C.R. Mullis \\inst{2}, A. Wolter \\inst{3}, I.M. Gioia\n\\inst{2,10,11}, \nT. Maccacaro \\inst{3}, A. Antonelli \\inst{1}, F. Fiore \\inst{1}, J. Kaastra \n\\inst{4}, R. Mewe \\inst{4}, Y. Rephaeli \\inst{5}, R. Fusco-Femiano \\inst{6},\nV. Antonuccio-Delogu \\inst{7}, F. Matteucci \\inst{8} and P. Mazzotta \\inst{9}}\n\n \\offprints{S. Colafrancesco}\n\n \\institute{Osservatorio Astronomico di Roma \n via dell'Osservatorio 2, I-00040 Monteporzio, Italy \\\\\n Email: cola@coma.mporzio.astro.it\n\\and \n Institute for Astronomy, University of Hawaii, \n 2680 Woodlawn Drive, Honolulu, HI 96822, USA\n\\and \n\tOsservatorio Astronomico di Brera, Via Brera 26,\n Milano, Italy\n\\and\n SRON, Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands \n\\and\n School of Physics and Astronomy, Tel Aviv University, Israel 69978\n\\and\n IAS - CNR, Via Fosso del Cavaliere, I00133, Roma, Italy\n\\and\n Osservatorio Astrofisico di Catania, Via A. Doria,\n Catania, Italy \n\\and\n Osservatorio Astronomico di Trieste, Via dell'Osservatorio, Trieste,\n Italy\n\\and\n Dipartimento di Fisica, Universit\\`a di Roma ``Tor Vergata'',\n Via della Ricerca Scientifica 1, I-00133 Roma, Italy\n\\and \n Home institution: Istituto di Radioastronomia del CNR, Via Gobetti \n 101, I-40129, Bologna - Italy\n\\and \n Visiting Astronomer at the W. M. Keck Observatory, jointly operated\n by the California Institute of Technology, the University of\n California and the National Aereonautics and Space Administration}\n\n\n\\date{received ; accepted }\n%\\markboth{S. Colafrancesco et al.}{An X-ray and optical study of A33}\n%\\authorrunning {Sergio Colafrancesco et al.}\n%\\titlerunning {An X-ray and optical study of the cluster A33}\n\n\\maketitle\n\\markboth{S. Colafrancesco et al.}{An X-ray and optical study of A33}\n\n\\begin{abstract}\n\nWe report the first detailed X-ray and optical observations of the \nmedium-distant cluster A33 obtained with the Beppo-SAX satellite and with the \nUH 2.2m and Keck II telescopes at Mauna Kea.\nThe information deduced from X-ray and optical imaging and spectroscopic \ndata allowed us to identify the X-ray source 1SAXJ0027.2-1930 as the X-ray \ncounterpart of the A33 cluster. \nThe faint, $F_{2-10~keV} \\approx 2.4 \\times 10^{-13} \\ergscm2$, X-ray source \n1SAXJ0027.2-1930, $\\sim 2$ arcmin away \nfrom the optical position of the cluster as given in the Abell catalogue,\nis identified with the central region of A33.\nBased on six cluster galaxy redshifts, we determine the \nredshift of A33, $z=0.2409$; this is lower \nthan the value derived by Leir and Van Den Bergh (1977). \nThe source X-ray luminosity, $L_{2-10~keV} = 7.7 \\times 10^{43} \\ergs$, \nand intracluster gas temperature, $T = 2.9$ keV, make this cluster \ninteresting for cosmological studies of the cluster \n$L_X-T$ relation at intermediate redshifts.\nTwo other X-ray sources in the A33 field are identified.\nAn AGN at z$=$0.2274, and an M-type star, whose emission are blended to\nform an extended X-ray emission $\\sim 4$ arcmin north of the A33 cluster. \nA third possibly point-like X-ray source detected $\\sim 3$ \narcmin north-west of A33 lies close to a spiral \ngalaxy at z$=$0.2863 and to an elliptical galaxy at the same redshift \nas the cluster.\n\n\\keywords{Cosmology: clusters of galaxies: individual: A33,\nobservations: X-rays}\n\n\\end{abstract}\n\n\\section{Introduction}\n\nA33 is a medium-distant Abell cluster of galaxies with\nvery few and sparse information in both the X-ray and the optical bands.\nThis cluster was claimed to have been detected by the \nHEAO1-A1 all sky survey (Johnson et al. 1983, Kowalski et al. 1984)\nwith a count rate of $3.77 \\pm 0.47$ counts cm$^{-2}$ s$^{-1}$ \nin the $2-6$ keV energy band.\nIts luminosity was estimated, with large uncertainties, \nto be $L_{2-6~keV} \\approx 2.34 \\times 10^{45}$ erg s$^{-1}$.\n\nA33 was also observed with the GINGA LAC detector from \nDecember 9 to December 10, 1988 (Arnaud \\ea 1991),\nbut no X-ray emission was found at the optical position of \nthe cluster. From such a non-imaging observation, Arnaud \\ea (1991) \nwere able to put an upper limit on the\nluminosity of A33, $L_{2-10~keV} < 6 \\times 10^{44}$ erg s$^{-1}$, \nassuming a temperature $T = 8.4$ keV.\nThe value of the X-ray luminosity derived from GINGA data\nis inconsistent with the one derived from the \nHEAO1-A1 observation (note, however, that A33 lies at the edge of \nthe error box for the position of the HEAO1 source).\n\nThe source 1RXSJ002709.5-192616 in the ROSAT Bright Source Catalog \n(BSC: Voges et al., 1996), \nat coordinates $\\alpha^x_{2000}= 00^h~ 27^m~ 09.50^s$ and\n$\\delta^x_{2000}=-19^o~ 26'~ 16\"$, has been observed for \n$317$ sec with a count rate of $0.062 \\pm 0.017$ cts/s. This source \nhas $19.6$ net counts in the $0.1-2.4$ keV energy band\ncorresponding to a flux \n$F_{0.2-2.4}=(9.3 \\pm 2.6) \\times 10^{-13}$ erg s$^{-1}$ cm$^{-2}$\n(assuming a nominal conversion factor of \n$1.5 \\times 10^{-11}$ erg cm$^{-2}$ s$^{-1}$ cts$^{-1}$) and does \nnot appear to be extended. This source is unrelated to the cluster\nand most probably associated with an AGN which is only $5.4''$ away\n(see Table 1, source 1SAXJ0027.1-1926, and Table 2, source A).\n\nIn the optical band there is no detailed \ninformation except from that derived from the extensive study\nof Leir \\& Van Den Bergh (1977), who \nclassified A33 as a distance class $D=6$, richness $R=1$, \nBautz-Morgan-class-III cluster. In the Abell (1958) catalog, A33 \nhas $69$ galaxies which lie within one Abell radius ($2.7 z^{-1}$ arcmin) \nand which are not more than 2 mag fainter than the third brightest galaxy.\nIts photometrically estimated redshift, $z = 0.28$, \nwas derived by Leir \\& Van Den Bergh (1977) from the cluster optical\ndiameter and the magnitude of the brightest and tenth-brightest\ncluster galaxies.\n\nIn this paper we present a new X-ray observation of A33 \nobtained with Beppo-SAX. \nThis observation enables us to derive detailed information on\nthe X-ray source, on its morphology and thermal properties.\nThe complex appearance of the X-ray emission in the field of \nA33 prompted us to obtain optical images and spectroscopic \ninformation for several objects in the field.\n\nThe plan of the paper is the following.\nIn Section 2 we present the basic information on the Beppo-SAX \nobservation and data reduction. In Section 3 we describe \nthe optical data and in Section 4 we discuss the X-ray spectroscopy\nof the various sources in the A33 field. \nWe summarize our results for A33 and discuss their implications in\nSection 5.\n\nThroughout the paper $H_0$=50 km sec$^{-1}$ Mpc$^{-1} $\nand $\\Omega_0=1$ are used unless otherwise noted.\n%\n{\\footnotesize\n\\begin{table*}[htbp]\n\\begin{center}\n\\caption{LECS ($0.1-2$ keV) and MECS ($2-10$ keV) count rates}\n\\label{tab_1}\n\\begin{tabular}{ccccccc}\n\\hline \\hline\nSource & $\\alpha_{2000}$ & $\\delta_{2000}$ & $t_{exp}$ &\nCount rate & Count rate & $R_{extr}$ \\\\ \\hline\n &$(^h~ ^m~ ^s)$ &$(^o~'~'')$ & ($s$) & ($10^{-3} s^{-1}$) & ($10^{-3} s^{-1}$) \n& arcmin \\\\ \n & & & & LECS & MECS & \\\\\n\\hline\\hline\n1SAXJ0027.1-1926 & $00~ 27~ 08$ &\n$-19~ 26~ 38$ & $77609$ & $7.6 \\pm 0.7$ & $7.8 \\pm 0.6$ & 2 \\\\\n1SAXJ0027.2-1930 & $00~ 27~ 12$ &\n$-19~ 30~ 32$ & $77609$ & -- & $1.76 \\pm 0.23$ & 2 \\\\\n1SAXJ0027.0-1928 & $00~ 27~ 01$ &\n$-19~ 28~ 30$ & $77609$ & -- & $ 1.14 \\pm 0.19$ & 1 \\\\\n\\hline \\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n}\n%\n\n\\section{Beppo-SAX Observation}\n\nThe A33 field was observed with the Narrow Field Instruments (NFI)\nof the Beppo-SAX satellite from November 23$^{\\rm th}$ to \n25$^{\\rm th}$, 1996. \nThe total effective exposure time is\n$t_{exp}= 3.8417 \\times 10^4$ s \nfor the LECS instrument and $t_{exp}= 7.7610 \\times 10^4$ s \nfor the MECS instrument (see \\eg Boella et al. 1997a and 1997b for a technical\ndescription of the Beppo-SAX mission and instrumentation). \n%\n\\begin{figure*}\n\\begin{center}\n%\\psfig{figure=ds8573f1_old.ps,height=10.cm,width=12.5cm,angle=0}\n\\psfig{figure=ds8573f1.ps,height=10.cm,width=11.cm,angle=0}\n\\end{center}\n\\caption{\\footnotesize {The Beppo-SAX image of A33 in the $2-10$ keV \nenergy band. The three different components of the emission are labeled\naccording to the text. The circles indicate the extraction area for each\nX-ray source. Note that 1SAXJ0027.2-1930 has also a diffuse, low-surface \nbrightness distribution which appears to be extended in the\nsouthern part of the image. The image has been deconvolved with a wavelet \ntransform using a smoothing length of 3.5 pixels (1 pixel = 8 arcsecs).\nNorth is up and East to the left.\n}}\n\\label{figure:fig_1}\n\\end{figure*}\n\nData preparation and linearization was performed using the \nSAXDAS v.1.3 package under the FTOOLS environment. \nThe imaging analysis was performed using the \nXIMAGE package (Giommi \\etal 1991).\nThe extraction of the source and background spectra was done \nwithin the XSELECT package.\nThe spectral analysis was performed using XSPEC v.9.0.\n\nThe only previous claimed X-ray detection of A33 was done with \nthe HEAO1 satellite (Johnson et al. 1983; Kowalski et al. 1984). \nDue to the large error box of the HEAO1 detectors, \nthe coordinates of the X-ray source were associated with the optical\ncoordinates of the A33 cluster. Thus the \nBeppo-SAX observation was centered on the optical coordinates\n$\\alpha^o_{2000}=$ $00^{h}26^{m}52.7^{s}$ and \n$\\delta^o_{2000}= -19^{o}32'29\"$.\nThe MECS $2-10$ keV X-ray image of the field is shown in \nFig.\\ref{figure:fig_1}, where three different subsystems are \nevident: a bright and apparently extended source, \n1SAXJ0027.1-1926, an extended but smaller source, 1SAXJ0027.2-1930, \nlocated to the south of the brightest source and an apparently \npoint-like source, 1SAXJ0027.0-1928, located to the west.\nPositions, count rates and extraction region radii, $R_{extr}$, \nare listed in Table \\ref{tab_1}.\nThe sources have sufficient count rates to be detected\nindividually at more than $4$ sigma level by the MECS instruments.\nThe poorer spatial resolution of the LECS instead allows only to determine the\ncount rate of the brightest source 1SAXJ0027.1-1926.\nIn the following we describe the spatial structure of each \nsource detected in the A33 field as derived from the MECS data.\n\n\nThe MECS PSF is $\\approx 1$ arcmin Half Energy Width, and this spatial resolution\nallows us to detect the sources 1SAXJ0027.1-1926 and 1SAXJ0027.2-1930 as extended in the\nMECS image of Fig.1.\n\nThe source 1SAXJ0027.1-1926 has an extension of $\\sim 2$ arcmin (radius).\nAs discussed in Sections 3 1nd 4, this source is most probably the result\nof the blending of two point-like sources not resolved by the MECS PSF.\nThe X-ray MECS image contours superposed onto the POSS II image of\nthe field plotted in Fig.\\ref{figure:fig_2}\nshow that there is no clear galaxy excess\nassociated to the X-ray source 1SAXJ0027.1-1926. \n\nThe source 1SAXJ0027.2-1930, located $\\sim 4.5$ arcmin \nsouth of the brightest source (see Fig. 1), has an extension of \n$\\simgt 1.5$ arcmin radius. Using a $\\beta$-model with values $\\beta=0.75$ \nand $r_c=260$ kpc ($H_0=50, \\Omega_0=1$) chosen as representative of such \nlow luminosity objects, and convolved with the MECS PSF\nwe find a central density of $\\approx 3.9 \\cdot 10^{-3}$ cm$^{-3}$.\nMoreover, an extended, low surface brightness X-ray emission \nis visible in the southern part of the image (see Fig. 1 and Fig. 2).\nSuch a low surface brightness source extends for a few arcminutes\nat levels of $\\sim 10^{-4}$ cts s$^{-1}$ cm$^{-2}$ arcmin$^{-2}$.\nThe extended source 1SAXJ0027.2-1930 is associated with A33 as shown\nin the POSS II image of the field (see Fig.\\ref{figure:fig_2} and \nSection 3).\n\nThe third source 1SAXJ0027.0-1928, located $\\sim 4$ arcmin south-west \nof the brightest source, has a point-like appearance.\nTwo faint objects in the POSS II are positionally consistent with\n1SAXJ0027.0-1928.\n\n%\n\\begin{figure}\n\\psfig{figure=ds8573f2.ps,height=9.cm,width=9.cm,angle=-90.}\n\\caption{\\footnotesize {The optical image of A33 taken from the\nPOSS II plate and the X-ray contours of the Beppo-SAX image obtained with the \nMECS detector in the $2-10$ keV energy band. Contours are taken from the image \nshown in Fig.1 and are logarithmically spaced.\nThe image has been deconvolved with a wavelet transform using\na smoothing length of 3.5 pixels (1 pixel = 8 arcsecs).\nThe white cross indicates the position of A33 from the Abell catalogue.\nThe first X-ray contour is at $3 \\sigma$ from the background level.\nNorth is up and East to the left.\n}}\n\\label{figure:fig_2}\n\\end{figure}\n\n\\section{Optical Imaging and Spectroscopy}\n%\n\\def\\arcdeg{\\hbox{$^\\circ$}}\n\\def\\arcsec{\\ifmmode^{\\prime\\prime}\\;\\else$^{\\prime\\prime}\\;$\\fi}\n\\def\\arcmin{\\hbox{$^\\prime$}}\n%\n%\n{\\footnotesize\n\\begin{table*}[htbp]\n\\begin{center}\n\\caption{Optical results}\n\\label{tab_o}\n\\begin{tabular}{ccccl}\n\\hline \\hline\nName & $\\alpha_{2000}$ & $\\delta_{2000}$ & $z$ & Identification and Comments \\\\ \n & $(^h~ ^m~ ^s)$ & $(^o~'~'')$ & & \\\\\n\\hline\\hline\n A & 00 27 09.8 & $-$19 26 12.6 & $0.2274 \\pm 0.0006$ & AGN \n ([OII], [OIII], [Ne III], broad Balmer) \\\\\n B & 00 27 07.3 & $-$19 26 36.4 & & M star \\\\\n C & 00 27 00.5 & $-$19 28 56.5 & $0.2420 \\pm 0.0005$ & galaxy (G-band, H$\\beta$, MgIb, NaId) \\\\\n D & 00 26 59.5 & $-$19 28 18.6 & $0.2863 \\pm 0.0015$ & galaxy (H+K, G-band, \nH$\\beta$, MgIb) \\\\\ng1 & 00 27 12.3 & $-$19 30 45.5 & $0.2406 \\pm 0.0008$ & galaxy (H+K, G-band, \nH$\\beta$, MgIb, NaId) \\\\\ng2 & 00 27 12.6 & $-$19 30 43.7 & $0.2380 \\pm 0.0012$ & galaxy (CaII-break, G-band, H$\\beta$, MgIb, NaId) \\\\\ng3 & 00 27 12.5 & $-$19 30 40.1 & $0.2395 \\pm 0.0017$ & galaxy (CaII-break, \nG-band, H$\\beta$, MgIb, NaId) \\\\\ng4 & 00 27 13.1 & $-$19 30 29.4 & $0.2445 \\pm 0.0004$ & galaxy (H+K, G-band, \nH$\\beta$, MgIb, NaId) \\\\\ng5 & 00 27 13.0 & $-$19 30 25.6 & $0.2406 \\pm 0.0005$ & galaxy (H+K, G-band, \nH$\\beta$, MgIb, NaId) \\\\\n\\hline \\hline\n\\end{tabular}\n\\end{center}\n%\\caption{Optical results}\n\\end{table*}\n}\n%\n\nDue to the lack of detailed optical information in the literature \nfor A33, we took I and B images of the cluster region on \nNovember 23 and 24 1997 at the Keck II telescope. \nThe images were obtained using the Low-Resolution and Imaging \nSpectrograph (LRIS) (Oke et al. 1995) in imaging mode, resulting in \na scale of 0.215\\arcsec pixel$^{-1}$ and a field of view of \n6\\arcmin$\\times$7.\\arcmin3. The I (B) images were taken in\n0.4\\arcsec$-$~0.5\\arcsec seeing on the first night and consist of \n3$\\times$300s (4$\\times$120s) dithered exposures \ncentered at $\\alpha$=00$^{h}$27$^{m}$10.$^{s}$5 and\n$\\delta=-19\\arcdeg29\\arcmin18\\arcsec$ (J2000), the southern region \nof the X-ray emission complex. On the second night (0.8\\arcsec seeing)\nwe took 2$\\times$120s I (2$\\times$300s B) exposures centered at \n$\\alpha$=00$^{h}$27$^{m}$09.$^{s}$8 and \n$\\delta=-19\\arcdeg26\\arcmin12.\\arcsec4$ (J2000), \nthe northern region of the X-ray emission system. \nThe optical position of A33 (Fig.\\ref{figure:fig_2}) is close to \nan open stellar cluster. \nFig.\\ref{figure:fig_10} \nshows the B images for both North (Fig.\\ref{figure:fig_10}a) and \nSouth (Fig.\\ref{figure:fig_10}b) regions. \nNo excess of galaxies is present in the northern region at the \nposition of 1SAXJ0027.1-1926 (Fig.\\ref{figure:fig_10}a), while \nFig.\\ref{figure:fig_10}b reveals an overdensity of galaxies\nin the region of the X-ray source 1SAXJ0027.2-1930.\n%\n\\begin{figure}\n\\begin{center}\n{\\vbox{\n\\psfig{figure=ds8573f3.ps,height=7.5cm,width=7.5cm,angle=0.}\n\\psfig{figure=ds8573f4.ps,height=7.5cm,width=7.5cm,angle=0.}\n}}\n\\end{center}\n\\caption{\\footnotesize {The two images are 1024x1024 (3.7x3.7 arcmin) \nsubarrays \nextracted from two B-band exposures taken at the Keck II telescope. \nThe image to the top shows the field around 1SAXJ0027.1-1926 and \n1SAXJ0027.0-1928 and the image to the botton shows the field around \n1SAXJ0027.2-1930. \nNorth is up and East to the left.\n}}\n\\label{figure:fig_10}\n\\end{figure}\n%\n\nSpectroscopic observations for several objects in the\nfield were carried out on August 16, 17\nand 19, 1998, with the Wide Field Grism Spectrograph and the \nTek2048$\\times$2048 CCD attached to the University of Hawaii 2.2m \ntelescope on Mauna Kea. We used the 420 l/mm grating which provided a \n$\\sim$3990-9900 \\AA\\ coverage and a pixel size of 3.6 \\AA/pix, and a \nlong-slit of 2.4$''$ which gives a low spectral resolution of about 24 \\AA.\nFor the reduction of the data we have used the IRAF package (Tody, 1993).\nIn the region of the northern X-ray emission we identified 2 objects\nlabeled as A and B in Fig.\\ref{figure:fig_10}a. \n\nIn the region to the west, where the X-ray source 1SAXJ0027.0-1928 is \npresent, we found two galaxies labeled C and D in the \nabove mentioned figure. In the region of the southern X-ray \nemission we obtained spectra for five galaxies which turned\nout to be members of the cluster. These galaxies are labeled g1 through \ng5 in Fig.\\ref{figure:fig_10}b. Table \\ref{tab_o} gives the results of the observations:\n\nBased on our imaging and spectroscopic results, we conclude that a\nblend of the AGN (A) and M-type star (B) X-ray emissions contribute\nto the extended source 1SAXJ0027.1-1926 to the north.\nThe Abell cluster A33 is the source of the southern X-ray emission\n1SAXJ0027.2-1930, while the identification of the source of the \nwestern X-ray emission, 1SAXJ0027.0-1928, remains unknown.\nThe two galaxies for which we measured the spectra,\nand which are the two brightest optical sources in the region,\nmight be responsible for part of the emission of\n1SAXJ0027.0-1928, but we need spectroscopic data for more objects to \nhelp in the identification. \nOne of the sources (C) is consistent with being part of A33.\nFrom the six cluster members listed in \nTable \\ref{tab_o} we obtain for A33 an average $<z>=$0.2409$\\pm$0.0009, \nand a very tentative velocity dispersion, given the few cluster galaxies,\n$\\sigma_{los}=$472$^{+295}_{-148}$ km s$^{-1}$.\nThis estimate includes the $1+z$ correction.\n\n%\n\\begin{figure}\n\\psfig{figure=ds8573f5.ps,height=9.cm,width=8.5cm,angle=-90.}\n\\caption{\\footnotesize {The combined LECS and MECS spectrum \nof the source 1SAXJ0027.1-1926 extracted from a $2$ arcmin radius \nregions. The spectrum shown in figure has been rebinned so that the \nsignificance of each bin is at least 3$\\sigma$. \nThe best fit model is a MEKAL thermal model (see text for details).\nThe spectrum has been further rebinned using XSPEC for graphical purposes. \n}}\n\\label{figure:fig_5}\n\\end{figure}\n%\n\n\\section{X-Ray Spectroscopy}\nThe Beppo-SAX concentrator/spectrometer system consists of four \nseparated concentrator mirrors, three of them covering the \n$1.6- 10$ keV range (Medium Energy Concentrator Spectrometer, or \nMECS) and the fourth extending to lower energies\ndown to $0.1$ keV (Low Energy Concentrator Spectrometer, or LECS). \nThe concentrators are designed to have a large \neffective area around the iron K$\\alpha$ line complex:\n$150$ and $50$ cm$^2$ for MECS and LECS, at $6$ keV. \nAlso, Beppo-SAX is able to provide spatially resolved spectra: its energy \nand angular resolution are $\\Delta E/E=8\\%$ at $6$ keV and \n$\\theta_{FWHM} \\approx 40''$, respectively. \n\n%\n{\\footnotesize\n\\begin{table*}[htbp]\n\\begin{center}\n\\caption{1SAXJ0027.1-1926}\n\\label{tab_2}\n\\begin{tabular}{ccccccc}\n\\hline \\hline\nModel & pho. index & $z$ & $T$ & bins & $\\chi^2$ & $\\chi^2_{red}$\\\\ \\hline\n & & & keV & & \\\\ \n\\hline\\hline\nRS & -- & $0.245 \\pm 0.023$ & $3.99^{+0.95(+1.83)}_{-0.77 (-0.98)}$\n & 61 & 56.12 & 0.97 \\\\\nMEKAL & -- & $0.245 \\pm 0.024$ & $3.90^{+0.99(+1.88)}_{-0.66 (-0.97)}$ & 61 & 55.98 & 0.97 \\\\\nPL & $2.05^{+0.17(+0.41)}_{-0.14 (-0.18)}$ & -- & -- \n& 61 & 62.55 & 1.06 \\\\\n\\hline \\hline\n\\end{tabular}\n\\end{center}\n%\\caption{1SAXJ0027.1-1926}\n\\end{table*}\n}\n%\n\nIn order to obtain the emission weighted spectral information \nof the three main sources in the A33 field,\nwe have extracted the photons from \ncircular regions drawn around each source \n(see Fig.\\ref{figure:fig_1}). The extraction radius, smaller than the \nsuggested $4$ arcmin radius region since the sources are separated by a small\nangular distance, might introduce a systematic uncertainty.\nWe have used the appropriate Ancillary Response File to correct for this\neffect. We fitted the source spectra using both a Raymond-Smith code\n(1977; hereafter RS) or a MEKAL code (Mewe, Kaastra \\& Liedahl 1995) \nto model the thermal intracluster gas emissivity and\na simple absorbed power-law, non-thermal model.\nBackground spectra have been extracted from library blank-sky images in \nthe same circular regions as the sources.\n%\n\\begin{figure}\n{\\vbox{\n\\psfig{figure=ds8573f6.ps,height=9.cm,width=8.5cm,angle=-90.}\n\\psfig{figure=ds8573f7.ps,height=9.cm,width=8.5cm,angle=-90.}\n}}\n\\caption{\\footnotesize {The SAX MECS spectra of 1SAXJ0027.2-1930 \nfitted with a \nthermal MEKAL model (upper panel) and with an absorbed power-law \nmodel (lower panel). Details of the spectral analysis are given in\nTable 4.\nThe spectrum has been further rebinned using XSPEC for graphical purposes. \n}}\n\\label{figure:fig_7}\n\\end{figure}\n%\n\n\\vskip 0.3truecm\n\\noindent\n{\\it a) 1SAXJ0027.1-1926}\n\n\\noindent\nThe spectrum of the brightest source in the field was extracted, both \nfor the LECS and the MECS instruments, from a circular region of $2$ \narcmin radius centered on the X-ray position of Table 1.\nThe combined LECS-MECS spectrum is shown in Fig.\\ref{figure:fig_5}: \nwe do not observe any low energy excess absorption in the spectrum,\nthus we keep $N_H$ fixed at the galactic value of 1.86 $\\times 10^{20}\ncm^{-2}$ (Dickey \\& Lockmann, 1990) relative to the source position.\n\nThe best fit spectral parameters for the MECS spectrum are listed in \nTable \\ref{tab_2} together with their uncertainties at $68.3 \\%$ (and $90 \\%$ \nin parentheses) confidence level.\nWe use $605$ source photons in this spectral fit.\n\nWithin $2$ arcmin from its center, the source has a flux of\n$F_{2-10 keV} = (4.20\\pm0.32) \\times 10^{-13}$ erg s$^{-1}$ cm$^{-2}$, evaluated using \nthe MEKAL best fit parameters. \nThe other models give similar fluxes.\nThis flux is also consistent, within the errors, with the flux of the X-ray source\n1RXSJ002709.5-192616 in the ROSAT band.\n\n\nThe optical magnitude of the M-star if $m_V \\approx 19$.\nAssuming that the X-ray flux of the M-star contributes to $50 \\%$ of the \ntotal flux of 1SAXJ0027.1-1926, we obtain $F_{2-10}/F_V \\approx 2.$ in the \n$2-10$ keV band and $F_{0.3-3.5}/F_V \\approx 6$ in the $0.3-3.5$ energy \nband (assuming a thermal emission at $T=1$ keV).\nThis ratio is almost one order of magnitude higher than the values of \n$F_{0.3-3.5}/F_V$ for X-ray selected stars in the EMSS \n(see Fig.1 in Maccacaro et al. 1988). \nThis means that the contribution of the M-star to the \nX-ray flux of 1SAXJ0027.1-1926 should be $\\simlt 8 \\%$ to be \nconsistent with the values of $F_X/F_V$ for normal stars.\nIf this is the case, then more than half \nof the X-ray emission of 1SAXJ0027.1-1926 is due to the AGN (listed \nas A in Table \\ref{tab_o}) at $z=0.2274$ with a luminosity\n$L_{2-10~keV} \\simlt 4.5 \\times 10^{43}$ erg s$^{-1}$.\nOtherwise, the source 1SAXJ0027.1-1926 should result from the blend of\nthe AGN and of a different unknown X-ray source.\n\n%\n{\\footnotesize\n\\begin{table*}[htbp]\n\\begin{center}\n\\caption{1SAXJ0027.2-1930}\n\\label{tab_3}\n\\begin{tabular}{ccccccc}\n\\hline \\hline\nModel & pho. index & $z$ & $T$ & bins & $\\chi^2$ & $\\chi^2_{red}$ \\\\ \\hline\n & & & keV & & \\\\ \n\\hline\\hline\nRS & -- & $0.2409$ & $2.91^{+1.25 (+2.44)}_{-0.54 (-0.83)}$ \n& 19 & 20.43 & 1.28 \\\\\nMEKAL & -- & $0.2409$ & $2.88^{+1.23 (+2.46)}_{-0.55 (-0.83)}$ & \n19 & 20.45 & 1.28 \\\\\nPL & $2.67^{+0.41 (+0.67)}_{-0.37 (-0.57)}$ & -- & -- \n& 19 & 22.05 & 1.30 \\\\\n\\hline \\hline\n\\end{tabular}\n\\end{center}\n%\\caption{1SAXJ0027.2-1930}\n\\end{table*}\n}\n%\n\n\\vskip 0.3truecm\n\\noindent\n{\\it b) 1SAXJ0027.2-1930}\n\n\\noindent\nThe average spectrum of 1SAXJ0027.2-1930 was extracted from a circular region of\n$2$ arcmin radius centered on the X-ray position of Table 1 (see also Fig.5).\nIn this region there is a clear excess of galaxies (see Fig. 3) which is\n$\\sim 1.5$ arcmin away from the Abell catalog position of A33.\nFitting the spectrum (which contains $140$ source photons) \nwith a RS thermal model with temperature, abundance and \nredshift as free parameters, the fit gives $\\chi^2_{red} = 1.22$. \nFixing the value of $N_H$ to the galactic value (1.86$\\times 10^{20}$ cm$^{-2}$)\nwe obtain an average temperature $T = 3.1\\pm0.9$ keV and a redshift \n$z_X = 0.72 \\pm 0.04$. The abundance is only marginally constrained at \n$Fe/H = 0.98 \\pm 0.71$ of the solar value. However, the fit results are \nmainly due to a marginally significant spectral feature at $E \\sim 4$ keV.\n\nTherefore, we fixed the redshift of the X-ray source at $z = 0.2409$, \nas measured from the optical spectra (see Section 3), and\nwe fitted the spectrum again, fixing the abundance to a value \nFe/H = 0.3 solar. The results of the fit are shown in Table 4.\nUncertainties in the temperature of 1SAXJ0027.2-1930 are given at $68.3 \\%$ \n(and $90 \\%$ in parentheses) confidence level.\nThe low count rate of the source does not allow a more accurate \ndescription of the X-ray emission.\n\nAssuming the MEKAL best fit parameters we obtain an integrated flux \nof $F_{2-10 keV} = (2.4\\pm0.3) \\times 10^{-13} \\ergscm2$ \nin the 2 arcmin radius extraction region (which corresponds to a\nlinear size of $\\approx 1 ~h^{-1}_{50}$ Mpc). The other models give \nconsistent fluxes. At the redshift of the cluster this \nflux corresponds to a luminosity $L_{2-10 ~keV} = (7.7\\pm0.9) \n\\times 10^{43} h^{-2}_{50}$ erg s$^{-1}$ and to a bolometric luminosity\n$L_{bol}=(2.2\\pm0.3)\\times 10^{44} h^{-2}_{50}$ erg s$^{-1}$.\n%\n\\begin{figure}\n\\psfig{figure=ds8573f8.ps,height=9.cm,width=8.5cm,angle=-90.}\n\\caption{\\footnotesize {The SAX MECS spectrum of 1SAXJ0027.0-1928 \nfitted with a non-thermal power-law model (see Table 4 for details).\nThe spectrum has been further rebinned using XSPEC for graphical purposes. \n}}\n\\label{figure:fig_9}\n\\end{figure}\n%\n%\n{\\footnotesize\n\\begin{table*}[htbp]\n\\begin{center}\n\\caption{1SAXJ0027.0-1928}\n\\label{tab_4}\n\\begin{tabular}{ccccccc}\n\\hline \\hline\nModel & pho. index & $z$ & $T$ & bins & $\\chi^2$ & $\\chi^2_{red}$ \\\\ \\hline\n & & & keV & & \\\\ \\hline\n\\hline\nRS & -- & $0.36 \\pm 0.09$ & $2.56\\pm 0.86$ & 13 & 14.70 & 1.47 \\\\\nMEKAL & -- & $0.35 \\pm 0.11$ & $2.45\\pm 0.85$ & 13 & 14.79 & 1.48 \\\\\nPL & $2.63 \\pm 0.60$ & -- & -- & 13 & 14.98 & 1.36 \\\\\n\\hline \\hline\n\\end{tabular}\n\\end{center}\n%\\caption{1SAXJ0027.0-1928}\n\\end{table*}\n}\n\n\\vskip 0.3truecm\n\\noindent\n{\\it c) 1SAXJ0027.0-1928}\n\n\\noindent\nWe extracted the spectrum of 1SAXJ0027.0-1928 from a circular region of $1$\narcmin radius centered on the X-ray position of Table 1 (see \nFig.\\ref{figure:fig_9}). Results of the fit are shown in Table 5\n(uncertainties on the best fit values are given here at 68.3 $\\%$ confidence\nlevel. Note that the spectrum of this source contains $90$ source photons).\nAssuming an absorbed power--law non--thermal model, we derived a flux of\n$F_{2-10 keV} = (4.74\\pm0.8) \\times 10^{-14} \\ergscm2$.\nThere are two galaxies, a spiral (C) at the same $z$ of A33, \nand an elliptical (D) in the \nregion for which we took an optical spectrum. \n\nThe identification of the source is not certain at the moment.\nAssuming that the galaxy D at $z = 0.2863$ is the X-ray emitter, its \nX-ray luminosity would be $L_{2-10~keV} = 1.9 \\times 10^{43}$ erg s$^{-1}$.\nSuch an X-ray luminosity seems to be sensibly higher than the X-ray luminosity\nof a ``normal'' galaxy. The possibility that the X-ray emission is due to a \nmore distant, unidentified object cannot be excluded at present.\n\n\\section{Discussion}\n\nIn this paper we presented the first detailed X-ray observation \nof the distant Abell cluster A33, obtained with the Beppo-SAX satellite.\nWe have closely examined and clarified the complex X-ray emission in the\ndirection of A33.\nThe analysis of the X-ray data revealed the presence of three different \nX-ray sources in the field of A33. \nThe X-ray counterpart of the cluster \nis 1SAXJ0027.2-1930.\nWe present a spectroscopic redshift for A33,\napplying a $\\sim 20\\%$ correction to the previous photometric estimate.\nFrom optical spectra of six cluster galaxies we measure\na redshift $z=0.2409\\pm0.0009$ and a velocity dispersion along the line of\nsight $\\sigma_{los}$=472$^{+295}_{-148}$ km s$^{-1}$.\nThe dominant X-ray component (incorrectly\nlinked with A33 in the past) is associated with a blend\nof an AGN and M star, while the X-ray emission\nfrom A33 is $\\sim 4$ times fainter.\nUsing the proper X-ray flux and measured redshift,\nwe determine a more realistic cluster luminosity of \n$L_{2-10 ~keV} = (7.7\\pm0.93) \\times 10^{43} ~h^{-2}_{50}$ erg s$^{-1}$, \none to two orders of magnitude lower than previous attempts.\nThe MECS spectral resolution also allows us to determine that \nthe intracluster gas temperature is $T = 2.91^{+1.25}_{-0.54}$\nkeV. \nNo useful information on the cluster abundance is given due to \nthe low count rate of the source in the MECS detector.\n\nIn the following we will focus on measured quantities \nsuch as the low temperature and low velocity dispersion. \nWe are dealing here with a moderately rich (R=1) and distant \n(D=3) Abell cluster but with X-ray luminosity and temperature more \ntypical of nearby (z$ < 0.1$) poor clusters. The temperature of A33 \nis commensurate with the predictions from its X-ray \nluminosity from the $L_{X}-T$ relation by David et al. (1993) and \nArnaud and Evrard (1999). There is an extensive literature on the \ncorrelation between these two basic and measurable quantities (Edge \\& \nStewart 1991, Ebeling 1993, David et al. 1993, Fabian et al. 1994, \nMushotzky \\& Scharf 1997, Markevitch 1998, Arnaud and Evrard, 1999).\nComparing the bolometric luminosity of A33 with the best\nfit relation, log(L$_{X}$)$=$(2.88$\\pm$0.15)\nlog(T/6keV) $+$(45.06$\\pm$0.03) obtained by Arnaud and Evrard (1999),\nanalyzing a sample of 24 low-z clusters with accurate temperature \nmeasurements and absence of strong cooling flows, we would expect for \nthe A33 a temperature of 3.4 keV, as compared with our deduced value\n2.9$^{+1.25}_{-0.54}$. \nThe $L_{X}-T$ relation does not seem to evolve much with \nredshift since z$=$0.4 (Mushotzky \\& Scharf 1997). Note however \nthat the ASCA data that they use show a strong bias at the low-luminosity\nend of the distribution due to the absence of objects in the lower \nluminosity range in the ASCA database. The present data on a cluster at\nabout 0.2 are thus important to fill in the gap in the $L_X-T$ relationship\nfound among rich clusters and groups (see Mushotzky \\& Scharf 1997). \n\nThe measured velocity dispersion of A33 is also commensurate with \nthe predictions from the $\\sigma-$T$_{X}$ relationship. \nA large number of authors (see Table 5 in Girardi et al., 1996, or\nTable 2 in Wu, Fang and Xu, 1998, for an exhaustive list of\npapers on the subject) have attempted to determine the\n$\\sigma-T$ using different cluster samples in order to test \nthe dynamical properties of clusters. \nGirardi et al. (1996) have derived a best fit\nrelation between the velocity dispersion and the X-ray temperature,\nwith more than 30$\\%$ reduced scatter with respect to previous work\n(Edge and Stewart 1991; Lubin and Bahcall 1993; Bird, Mushotzky and\nMetzler, 1995; Wu, Fang and Xu 1998, among others).\nIf we substitute the temperature of 1SAXJ0027.2-1930 in the \nbest fit relation log($\\sigma$)$=$(2.53$\\pm$0.04)+(0.61$\\pm$0.05)log(T),\nderived by Girardi et al. (1996) a value of 650 km s$^{-1}$\nwould be expected for the 1-D velocity dispersion, somewhat higher \nbut within the uncertainties of the measured value from six \ncluster members of A33.\nIf we assume energy equipartition between the galaxies and \nthe gas in the cluster ($\\beta$$=$1) and we use the \nmeasured temperature of 2.9 keV from the SAX data in the equation \n$\\beta = \\mu m_p \\sigma_v^{2} / k T_{gas} $ (where\n$\\mu m_p =0.62$, for solar abundance), we obtain a velocity dispersion \nof $665$ km/s. \n\nThe data for A33 are also consistent with the relation \n$\\sigma_{los} \\propto (T/keV)^{0.6\\pm0.1}$ found by Lubin \\& Bahcall (1993) \nand increase its statistical significance in the low temperature \n($T \\simlt 3$ keV) range and at intermediate redshifts ($z \\sim 0.2$) where \nonly a few clusters have measured values of $\\beta$. \nThis issue will be discussed in a forthcoming paper. \n\nWe have also found that the bright source 1SAXJ0027.1-1926 has an \nextended appearance which is due to the blending of two different sources: \nan AGN at $z = 0.227$ and approximate B magnitude $M_B \\approx -23.9$ \n(derived from the apparent B magnitude as given in the APM scans) and \nan M-type star. \nThe X-ray spectrum does not show any line features, and it is\ncontaminated by the emission of the M star. Given the\nlow statistics we did not try to disentangle the two contributions\nbut we consider an upper limit to the AGN emission using the $F_X/F_V$\nfor the M star.\nThe ROSAT BSC source found at a \nposition consistent with the coordinates of 1SAXJ0027.1-1926 is \nmost probably associated with the AGN. The distance between the foreground \nAGN and the cluster is $\\Delta ~d_L \\approx 89.2 h^{-1}_{50} Mpc$. \nAt the redshift of the AGN, the observed total flux corresponds to a \nluminosity \n$L_X \\simlt 4.5 \\times 10^{43}$ erg/s, which can be considered as an upper\nlimit to the AGN luminosity. \n\nWe also detected a point-like faint source, 1SAXJ0027.0-1928, for which \nno X-ray spectroscopic identification was possible. The $2-10$ keV \nspectrum of this source can be fitted by both thermal\nand non-thermal models (see Table 5) but we do not elaborate further given\nthe poor statistics.\n\n\n\\acknowledgements\n\nS.C. acknowledges useful discussions with G. Hasinger and C. Sarazin.\nPartial financial support from ASI, NASA (NAG5-1880 and NAG5-2523) and\nNSF (AST95-00515) grants is gratefully acknowledged.\nWe appreciate the generosity of B.Tully who allowed us to\ntake some images and spectra during his observing runs.\n\n\\begin{thebibliography}{}\n\n\\bibitem{} Abell, G.O. 1958, ApJS, 3, 211\n\n\\bibitem{} Abell, G.O., Corwin, H.G. and Olowin, R.P. 1989, ApJS, 70, 1\n\n\\bibitem{} Arnaud, M. and Evrard, A.E. 1999, MNRAS, 305, 631\n\n\\bibitem{} Arnaud M., Lachieze-Rey, M., Rothenflug, R., Yamashita, K. \n 1991, A\\&A, 243, 56 \n\n\\bibitem{} Bird, C.M., Mushotzky, R.F. and Metzler, C.A., 1995, ApJ, 453, 40\n\n\\bibitem{} Boella, G. \\ea 1997a, A\\&AS, 122, 299\n\n\\bibitem{} Boella, G. \\ea 1997b, A\\&AS, 122, 327\n\n\\bibitem{} Dickey, J.M. \\& Lockman, F.J. 180, ARAA, 28, 215 \n\n\\bibitem{} David, L.P., Slyz, A., Jones, C., Forman, W. and Vrtilek, \n S.D., 1993, ApJ, 412, 479\n\n\\bibitem{} Ebeling, H., 1993, PhD Thesis, MPE\n\n\\bibitem{} Edge, A.C., and Stewart,G.C., 1991, MNRAS, 252, 414\n\n\\bibitem{} Fabian, A.C., Crawford, C.S., Edge, A.C., Mushotzky, R.F., \n 1994, MNRAS, 267, 779\n\n\\bibitem{} Giommi, P., Angelini, L., Jacobs, P. and Tagliaferri, G. 1991,\n in \"Astronomical Data Analysis Software and Systems I\",\n Eds. D.M.Worrall, C. Biemesderfer and J. Barnes,\n A.S.P. Conf. Ser. 25, 100\n\n\\bibitem{} Girardi, M., Fadda, D., Giuricin, G., Mardirossian, F. and \n Mezzetti, M., 1996, ApJ, 457, 61\n\n\\bibitem{} Johnson, M.W. \\ea 1983, ApJ, 266, 425\n\n\\bibitem{} Leir, A.A. and Van Den Bergh, S. 1977, ApJS, 34, 381\n\n\\bibitem{} Lubin, L.M. \\& Bahcall, N.A. 1993, ApJ, 415, L20\n\n\\bibitem{} Kowalski, M.P. \\ea 1984, ApJS, 56, 403\n\n\\bibitem{} Maccacaro, T., Gioia, I.M., Wolter, A., Zamorani, G. \\&\nStocke, J.T. 1988, ApJ, 326, 680\n\n\\bibitem{} Markevitch, M., 1998, ApJ, 504, 27\n\n\\bibitem{} Mewe, R., Kaastra, J. and Liedahl, L. 1995, Legacy, 6, 16\n\n\\bibitem{} Mushotzky, R.F. and Scharf, C.A. 1997, ApJ, 482, L13\n\n\\bibitem{}Oke, J.B., Cohen, J.G., Carr, M., Cromer, J., Dingizian, A., Harris, F.H.,\n Labrecque, S., Lucinio, R., Schaal, W., Epps, H., and Miller, J., \n 1995, PASP, 107, 375\n\n\\bibitem{} Raymond J.C., Smith B.W., 1977, ApJS 35, 419\n\n\\bibitem{} Tody, D. 1993, \"IRAF in the Nineties\" in \nAstronomical Data Analysis Software and Systems II, A.S.P. Conference Ser., Vol 52, \neds. R.J. Hanisch, R.J.V. Brissenden, \\& J. Barnes, 173.\n\n\\bibitem{} Voges, W. et al., 1996 IAUC 6420\n \n\\bibitem{} Wu, X-P, Fang, L-Z and Xu, W., 1998, A\\&A, 338, 813\n\n\\end{thebibliography}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002224.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem{} Abell, G.O. 1958, ApJS, 3, 211\n\n\\bibitem{} Abell, G.O., Corwin, H.G. and Olowin, R.P. 1989, ApJS, 70, 1\n\n\\bibitem{} Arnaud, M. and Evrard, A.E. 1999, MNRAS, 305, 631\n\n\\bibitem{} Arnaud M., Lachieze-Rey, M., Rothenflug, R., Yamashita, K. \n 1991, A\\&A, 243, 56 \n\n\\bibitem{} Bird, C.M., Mushotzky, R.F. and Metzler, C.A., 1995, ApJ, 453, 40\n\n\\bibitem{} Boella, G. \\ea 1997a, A\\&AS, 122, 299\n\n\\bibitem{} Boella, G. \\ea 1997b, A\\&AS, 122, 327\n\n\\bibitem{} Dickey, J.M. \\& Lockman, F.J. 180, ARAA, 28, 215 \n\n\\bibitem{} David, L.P., Slyz, A., Jones, C., Forman, W. and Vrtilek, \n S.D., 1993, ApJ, 412, 479\n\n\\bibitem{} Ebeling, H., 1993, PhD Thesis, MPE\n\n\\bibitem{} Edge, A.C., and Stewart,G.C., 1991, MNRAS, 252, 414\n\n\\bibitem{} Fabian, A.C., Crawford, C.S., Edge, A.C., Mushotzky, R.F., \n 1994, MNRAS, 267, 779\n\n\\bibitem{} Giommi, P., Angelini, L., Jacobs, P. and Tagliaferri, G. 1991,\n in \"Astronomical Data Analysis Software and Systems I\",\n Eds. D.M.Worrall, C. Biemesderfer and J. Barnes,\n A.S.P. Conf. Ser. 25, 100\n\n\\bibitem{} Girardi, M., Fadda, D., Giuricin, G., Mardirossian, F. and \n Mezzetti, M., 1996, ApJ, 457, 61\n\n\\bibitem{} Johnson, M.W. \\ea 1983, ApJ, 266, 425\n\n\\bibitem{} Leir, A.A. and Van Den Bergh, S. 1977, ApJS, 34, 381\n\n\\bibitem{} Lubin, L.M. \\& Bahcall, N.A. 1993, ApJ, 415, L20\n\n\\bibitem{} Kowalski, M.P. \\ea 1984, ApJS, 56, 403\n\n\\bibitem{} Maccacaro, T., Gioia, I.M., Wolter, A., Zamorani, G. \\&\nStocke, J.T. 1988, ApJ, 326, 680\n\n\\bibitem{} Markevitch, M., 1998, ApJ, 504, 27\n\n\\bibitem{} Mewe, R., Kaastra, J. and Liedahl, L. 1995, Legacy, 6, 16\n\n\\bibitem{} Mushotzky, R.F. and Scharf, C.A. 1997, ApJ, 482, L13\n\n\\bibitem{}Oke, J.B., Cohen, J.G., Carr, M., Cromer, J., Dingizian, A., Harris, F.H.,\n Labrecque, S., Lucinio, R., Schaal, W., Epps, H., and Miller, J., \n 1995, PASP, 107, 375\n\n\\bibitem{} Raymond J.C., Smith B.W., 1977, ApJS 35, 419\n\n\\bibitem{} Tody, D. 1993, \"IRAF in the Nineties\" in \nAstronomical Data Analysis Software and Systems II, A.S.P. Conference Ser., Vol 52, \neds. R.J. Hanisch, R.J.V. Brissenden, \\& J. Barnes, 173.\n\n\\bibitem{} Voges, W. et al., 1996 IAUC 6420\n \n\\bibitem{} Wu, X-P, Fang, L-Z and Xu, W., 1998, A\\&A, 338, 813\n\n\\end{thebibliography}"
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astro-ph0002225
|
Extended X-ray emission from FRIIs and RL quasars
|
[
{
"author": "G. Setti"
},
{
"author": "G. Brunetti"
}
] |
We review the evidence that detectable fluxes of X-rays are produced by inverse Compton scattering of nuclear photons with the relativistic electrons in the radio lobes of strong FRII radio galaxies within the FRII-RL quasar unification scheme. We report here on the possible detection of this effect in two steep spectrum RL quasars. This may have important implications on the physics and evolution of powerful radio galaxies.
|
[
{
"name": "setti.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsfig]{article}\n\\markboth{Setti G. et al.}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{Extended X-ray emission from FRIIs and RL quasars}\n\\author{G. Setti, G. Brunetti}\n\\affil{Dipartimento di Astronomia, Universit\\'a di Bologna}\n\\affil{Istituto di Radioastronomia del CNR, Bologna}\n\\author{A. Comastri}\n\\affil{Osservatorio Astronomico di Bologna}\n\n\\begin{abstract}\n\nWe review the evidence that detectable fluxes of X-rays are produced\nby inverse Compton scattering of nuclear photons with the \nrelativistic electrons in the radio lobes of strong FRII \nradio galaxies within the FRII-RL \nquasar unification scheme. We report here on the possible detection of\nthis effect in two steep spectrum RL quasars. \nThis may have important implications on the \nphysics and evolution of powerful radio galaxies.\n\n\\end{abstract}\n\n\n\\section{Introduction}\n\nIt is well known that the synchrotron radio emission from the \nextended lobes of strong radio galaxies and radio-loud (RL) quasars\nsamples ultra relativistic electrons. It is a customary practice\nto estimate the average magnetic field intensity via the minimum\nenergy argument by making use of the emitted radio flux in the\n10 MHz -- 100 GHz band (source rest frame). Since the critical \nfrequency emitted in the synchrotron process is \n$\\nu(MHz) \\sim B(\\mu G) (\\gamma/10^3)^2$ \nand typically $B(\\mu G) > 10$, it then follows that\nonly electrons with Lorentz factor $\\gamma > 10^3$ are taken into\naccount. These electrons are also responsible for producing X-rays\nvia the inverse Compton (IC) scattering of the cosmic \nmicrowave background (CMB) photons \n[$\\epsilon(keV) \\sim (\\gamma/10^3)^2$]. \nWhen these X-rays are detected, \nthe number of ultra-relativistic electrons is fixed and from \nthe radio flux one can uniquely determine the average\nmagnetic field intensity. Up to now, because of the weakness and diffuse\nnature of the \npredicted X-ray emission, detection of X-ray fluxes due to this\nprocess has been possible for a few sources only, notably Fornax A\n(Feigelson et al. 1995; Kaneda et al. 1995) and \nCen B (Tashiro et al. 1998); \nthe derived magnetic field intensities are lower than \nthe classical equipartition values by factors 1.5--2.\n\nBrunetti, Setti \\& Comastri (1997) have pointed out that \nsizeable X-ray fluxes\ncan also be emitted by the IC scattering of relativistic electrons \nin the FRII's radio lobes with the IR photons from a quasar, \nand associated circumnuclear \ndusty/molecular torus, hidden in the galaxy's nucleus. \nSince the IR emission peaks at $50-100 \\mu m$ \nelectrons at lower energies ($\\gamma < 500$) \nare involved in this process. Of course there\nare no reasons why these lower energy particles shouldn't be present,\non the contrary one would expect them on physical grounds based on \nacceleration and loss mechanisms. In order to estimate the size\nof the expected X-ray flux, for a given quasar IR emission,\none may work out the equipartition by extrapolating downward \nthe electron spectrum derived from the synchrotron emission to a\nminimum energy ($\\gamma_{min}$) limited from below by possible Coulomb \nlosses. The equipartition fields ($B_{eq}$) so derived are stronger than\nthe classical one by factors from 1.5 to 3 \n(also Setti, Brunetti \\& Comastri 1999). \nWe have \nshown that the IC scattering of the IR nuclear photons may easily \naccount for a large fraction of the extended X-ray emission of several \npowerful FRIIs\nat large redshifts ($z \\sim 1$) detected by ROSAT in the 0.1--2.4 keV \ninterval. \n%It should be mentioned that at these large redshifts the\n%contribution from the IC scattering of the CMB is not negligeable, \n%typically \n\nMorphologically there are two important aspects that should be \nmentioned: firstly, for obvious geometrical reasons, the X-rays \nfrom the IC scattering of the quasar photons\nare more concentrated toward the nuclear region \nthan those from the IC scattering of the \nCMB photons and, secondly, given two symmetrical radio lobes the \nX-ray emission from the far lobe can be much larger than that \nfrom the near one, depending on the orientation of the radio\naxis with respect to the line of sight, due to the enhanced \nefficiency of head-on scatterings (Brunetti et al.1997). \nIt should also be mentioned that, while the X-rays from the IC \nscattering of the CMB photons must have a spectral slope coincident \nwith that of the synchrotron radio emission, the X-ray spectrum \nassociated with \nthe IC scattering of the nuclear photons may or may not have\nthe synchrotron slope simply because a different \nportion of the primary electron spectrum is being sampled\n(see also Brunetti 2000). \n\nDirect evidence of extended X-ray emission from the IC scattering \nof the IR photons from a hidden quasar has been gathered by \nBrunetti et al.(1999) making use of ROSAT HRI observations of \nthe powerful, double lobed radio galaxy 3C 219. The residual \nX-ray distribution after subtraction of the absorbed, unresolved \nnuclear source is remarkably coincident with the radio structure.\n%Combined ROSAT PSPC and ASCA observations lead to a power law\n%energy spectrum (0.1-10 keV)whose slope is very close to the low \n%frequency radio spectral index ($\\alpha \\sim 0.8$). \nThe central extended ($\\sim$ 100 kpc) X-ray emission, somewhat stronger\nin the counter-jet side as expected in our model, can be accounted for\nby assuming a magnetic field \n$\\sim 3$ times weaker than our equipartion value ($B_{eq} \n\\simeq 10\\mu G$, \n$\\gamma_{min} = 50$). Of course this estimate depends on the assumed\nIR power of the hidden quasar which we have derived by two, albeit\nindirect, approaches since 3C 219 has not been detected by IRAS \nand not observed by ISO. Observations with {\\it Chandra}, \nscheduled in the fall of the year 2000, will likely provide a check \nof our model.\n\n%We have also inspected the possible detection of IC X-rays\n%in steep spectrum RL quasars as described in the following\n%Section.\n\n\n\\begin{figure*}\n\\centerline{\n\\psfig{figure=3c215.ps,width=11cm,angle=270}\n}\n%\\caption{... ... ... ... ...}\n\\end{figure*}\n\n\n\\section{IC X-rays from the radio quasars 3C 215 and 3C 334} \n\nExtended X--ray emission around RL quasars \nhas been recently discovered from the analysis \nof ROSAT HRI observations\n(Crawford et al. 1999; Hardcastle \\& Worrall 1999).\n%The resulting wobble corrected (Harris et al.1998) \n%spatial profiles have been fitted\n%with a multi--component model including the inflight calibrated\n%PSF plus either a $\\beta$ model or a broken power--law model.\n%The resulting best--fit parameters have been employed to estimate\n%the percentage and linear size of the extended X--ray flux whose\n%intensity is generally rather weak. \nThe origin of the extended and rather weak component (5--15\\% of total \nintensity) is usually \nascribed to thermal emission from the surrounding\nintracluster medium (ICM), although a significant contribution\nfrom the IC scattering of the quasar's photons predicted\nby our model cannot be excluded (Crawford et al. 1999).\n\n\nIn order to test the IC hypothesis \nwe have carried out a detailed analysis of the spatial\nprofiles of the sources in the Crawford et al.(1999) sample.\nThe data retrieved from the public archive have been analyzed \nfollowing a procedure similar to that in Crawford et al.(1999),\nbut the azimuthal distribution has been investigated with the aim\nof checking for a possible correlation with the radio structure. \nAccordingly\nthe source counts have been subdivided in four quadrants centered\non the quasar (X-ray source peak) and so oriented that two opposite\nquadrants are aligned with the radio axis defined by the direction\nof the innermost radio lobes. We have then compared the source counts\nin the two quadrants along the radio axis with those collected in the\nperpendicular direction. \n%In order to increase the statistics \n%observations taken in different time periods, \n%when available, different roll angle intervals and phases have been \n%coadded after the de--wobbling procedure.\n\n\n%If the contribution from IC scattering with the nuclear photons \n%is important, then the extended emission is expected to be\n%aligned with the radio axis determined from the\n%direction of the innermost radio lobes. \n%Accordingly the azimuthal distribution has been investigated \n%as follows:\n\n\n%---- The source counts have been divided in four quadrants \n%determined from the radio--maps. \n%---- More specifically we have compared the \n%radio--axis (and roughly containing the radio--lobe\n%source counts within the two quadrants along the \n%with the counts in the opposite directions.\n\n\n\nWe find evidence of X--ray extension spatially \ncorrelated with the radio axis in two \nquasars: 3C 215 and 3C 334. For 3C 48, 254 and 273 our analysis is\ninconclusive since their radio angular sizes are lower then, or \ncomparable to, the HRI PSF. For 3C 215 (Fig.1) \nthe effect is strong : a KS test rejects at 99.9\\% level \nthe hypotesis that \nthe count distributions along (filled dots) and\nperpendicular to (open squares) the radio axis are extracted from\nthe same population. In the case of 3C 334 (not shown here),\nalthough the count distribution along the radio axis systematically\nexceeds that in the perpendicular direction, the effect is\nstatistically marginal (the same KS test gives $\\sim 92\\%$).\n\nIn order to check whether the elongation on $\\sim 10$ arcsec\nscale could be due to an intrinsic elongation of the\nHRI PSF and/or to an insufficient correction of the \nwobbling, we have analyzed several isolated stars (companion \nat least 6 mag fainter) \nwith similar count statistics extracted\nfrom the RASSDWARF catalogue (Huensch et al. 1998): no evidence\nof asymmetric distributions has been found. Moreover the count profiles\nof 3C 215 and 334 in the direction perpendicular to the radio axis\nare consistent with those of spatially unresolved sources.\n\nThe X--ray fluxes (0.1--2.4 keV, spectral index $\\alpha = 1$) \nassociated with the extended structures\nhave been estimated by \nsubtracting the counts within the \nquadrants in the direction perpendicular to the radio axis\nfrom those within the quadrants aligned with radio axis: the\nluminosity of 3C 215 is $\\sim 1.5 \\cdot 10^{45}$ erg s$^{-1}$ of which\n$\\sim 2.2 \\cdot 10^{44}$ erg s$^{-1}$ in the extended component,\nwhile for 3C 334 one has $\\sim 10^{45}$ erg s$^{-1}$\nand $\\sim 10^{44}$ erg s$^{-1}$, respectively \n[$H_o = 75$ km/s/Mpc, $q_o = 0$].\n\nKnowledge of the quasar IR radiation is of crucial importance for the\ncomputation of the expected IC X-ray fluxes. Unfortunately no FIR data \nare available \nfor 3C 215, while 3C 334 has been observed by IRAS with a \n60$\\mu m$ luminosity of $\\sim 10^{46}$erg s$^{-1}$\n(van Bemmel et al. 1998). By adopting typical quasar SEDs \nwe estimate a \n$1 - 100 \\mu m$ luminosity of $\\sim 10^{46}$ erg s$^{-1}$ \nand $\\sim 4 \\cdot 10^{46}$ erg s$^{-1}$ for 3C 215 and 3C 334,\nrespectively. Following Brunetti et al.(1997) model\nwe find that the magnetic field intensities \nrequired to fully account for the X-ray fluxes of the extended \ncomponents are $\\sim 5$ and $\\sim 3$ times smaller than $B_{eq}$ \nfor 3C 215 and 334, respectively. In each source $B_{eq}$ has been \ncalculated by extrapolating downward to $\\gamma_{min} = 50$ \nthe power law electron spectrum derived from the low frequency \nradio spectrum. It should be pointed out that by applying the \nstandard\nequipartition we would have obtained factors $\\sim 2.6$ (3C 215) and\n$\\sim 2$ (3C 334) below the corresponding equipartion fields, but this\nwould be conceptually wrong. \n\n\n\\section{Conclusions}\n\nThere is supportive observational evidence of \nextended X-ray emission from the IC scattering of quasar \nIR photons with relativistic electrons in the lobes \nof powerful radio galaxies. Besides being a \nconfirmation of the FRII--quasar unification, this may provide an \nimportant tool for the diagnostic of the relativistic plasma \nat particle energies not sampled by radio observations. \nThe unavoidable presence of lower energy particles implies \nstronger magnetic fields than derived by standard equipartition \nformulae and, consequently, a larger pressure inside the lobes. \nMoreover, accounting for the extended X-ray emission in sources \nfor which the quasar radiation can be constrained indicates \nmagnetic field strengths lower than equipartition. \nTherefore, confirmation of our IC model by {\\it Chandra} and \nXMM satellites may \nprovide important clues on the physics and evolution of radio \nsources. \n\n\\acknowledgments\nIt is a pleasure to thank C.S. Crawford, \nA.C. Fabian and I. Lehmann for informative discussions \nconcerning 3C 215 and 3C 334. \n\n\\begin{references}\n\\reference\\arg{Brunetti G., 2000, APh 13, 105}\n\\reference\\arg{Brunetti G., Setti G., Comastri A., 1997, A\\&A 325, 898}\n\\reference\\arg{Brunetti G., et al., 1999, A\\&A 342, 57}\n\\reference\\arg{Crawford C.S., et al., 1999, MNRAS 308, 1159}\n\\reference\\arg{Feigelson E.D., et al., 1995, ApJL 449, 149}\n\\reference\\arg{Hardcastle M.J., Worrall D.M., 1999, MNRAS 309, 969}\n%\\reference\\arg{Harris D.E., et al., 1998, A\\&AS 133, 431}\n\\reference\\arg{Huensch M., Schmitt J.H.M.M., Voges W., 1998, A\\&AS 132, 155}\n\\reference\\arg{Kaneda H., et al., 1995, ApJL 453, 13}\n\\reference\\arg{Setti G., Brunetti G., Comastri A., 1999, in 'Diffuse Thermal\nand Relativistic Plasma in Galaxy Clusters', eds. H.B\\\"ohringer,\nL.Feretti, P.Schuecker, MPE Report 271, p.55}\n%\\reference\\arg{Spinrad H., et al., 1985, PASP 97, 932}\n\\reference\\arg{Tashiro M., et al., 1998, ApJ 499, 713}\n\\reference\\arg{van Bemmel I.M., Barthel P.D., Yun M.S., 1998, A\\&A 334, 799}\n\\end{references}\n \n\\end{document}\n\n"
}
] |
[] |
astro-ph0002226
|
The Morphology, Color, and Gas Content of\\ Low Surface Brightness Galaxies
|
[
{
"author": "K. O'Neil"
}
] |
Recent surveys have discovered hundreds of low surface brightness galaxies, systems with central surface brightness fainter than 22.0 B mag arcsec$^{-2}$, in the local universe. Plots of the surface brightness distribution -- that is, the space density of galaxies plotted against central surface brightness -- show a flat space density distribution from the canonical Freeman value of 21.65 through the current observational limit of 25.0 B mag arcsec$^{-2}$. It is therefore extremely important to understand these diffuse systems if we wish to understand galaxy formation and evolution as a whole. This talk is a review of both the known properties of low surface brightness galaxies and of popular theories describing the formation and evolution of these enigmatic systems.
|
[
{
"name": "oneil.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\pagestyle{myheadings}\n\\newcommand{\\mss}{mag arcsec$^{-2}$}\n\\newcommand{\\Bmoi}{\\rm ${\\mu_{B_{i}}}$(0) }\n\\newcommand{\\plm}{$\\pm$ }\n\\newcommand{\\lb}{$\\langle \\:$}\n\\newcommand{\\gb}{$\\rangle \\:$}\n\\newcommand{\\lt}{$< \\:$}\n\\newcommand{\\gt}{$> \\:$}\n\\newcommand{\\lta}{$\\leq $}\n\\newcommand{\\gta}{$\\geq $}\n\\newcommand{\\Bmu}{\\rm $\\mu_B \\:$}\n\\newcommand{\\Rmu}{\\rm $\\mu_R \\:$}\n\\newcommand{\\Imu}{\\rm $\\mu_I \\:$}\n\\newcommand{\\Umu}{\\rm $\\mu_U \\:$}\n\\newcommand{\\Vmu}{\\rm $\\mu_V \\:$}\n\\newcommand{\\Bmo}{\\rm ${\\mu _B}$(0) }\n\\newcommand{\\Imo}{\\rm ${\\mu _I}$(0) }\n\\newcommand{\\Vmo}{\\rm ${\\mu _V}$(0) }\n\\newcommand{\\Ho}{\\rm H$_0$ }\n\\newcommand{\\Bmag}{\\rm B$\\rm _{mag}$ }\n\\newcommand{\\Bt}{\\rm B$\\rm _T$(0) }\n\\newcommand{\\mt}{\\rm m$\\rm _T$ }\n\\newcommand{\\muo}{\\rm ${\\mu}$(0) }\n\\newcommand{\\rts}{\\rm $\\rm r_{27}$ }\n\\newcommand{\\rtf}{\\rm $\\rm r_{25}$ }\n\\newcommand{\\Vc}{{V$_{circ}$\\ }}\n\\newcommand{\\Halp}{H$_{\\alpha}$\\ }\n\\newcommand{\\alp}{$\\alpha$\\ }\n\\newcommand{\\etal}{{\\it et.al.}\\ }\n\\newcommand{\\degree}{$^{\\circ}$ }\n\\newcommand{\\arcs}{\\rm arcsec$^2$}\n\\newcommand{\\teff}{\\rm T$_{eff}$\\ }\n\\newcommand{\\app}{$\\sim$}\n\\newcommand{\\eg}{{\\em e.\\ g.\\ }}\n\\newcommand{\\ie}{{\\em i.\\ e.\\ }}\n\\newcommand{\\mn}{{\\em MNRAS\\ }}\n\\newcommand{\\solarm}{$M_{\\odot}$\\ }\n\\newcommand{\\MLsol}{${M_{\\odot}}/{L_{\\odot}}$\\ }\n\\newcommand{\\Msol}{$M_{\\odot}$\\ }\n\\newcommand{\\Zsol}{$Z_{\\odot}$\\ }\n\\newcommand{\\Lsol}{$L_{\\odot}$\\ }\n%\\input{psfig}\n\\input{epsf}\n\\input{rotate}\n\\begin{document}\n\\markboth{K. O'Neil}{The Morphology, Color, and Gas Content of Low Surface Brightness Galaxies}\n\n\\title{The Morphology, Color, and Gas Content of\\\\\nLow Surface Brightness Galaxies}\n\\author{K. O'Neil}\n\\affil{Arecibo Observatory HC3 Box 53995 Arecibo, PR 00612\\\\ koneil@naic.edu}\n\n\\begin{abstract}\nRecent surveys have discovered hundreds of low surface brightness galaxies,\nsystems with central surface brightness fainter than 22.0 B mag arcsec$^{-2}$,\nin the local universe. Plots of the surface brightness distribution --\nthat is, the space density of galaxies plotted against central surface\nbrightness -- show a flat space density distribution from the canonical\nFreeman value of 21.65 through the current observational limit of\n25.0 B mag arcsec$^{-2}$. It is therefore extremely important\nto understand these diffuse systems if we wish to understand galaxy\nformation and evolution as a whole. This talk is a review of \nboth the known properties of low surface brightness galaxies and of \npopular theories describing the formation and evolution of these enigmatic systems.\n\\end{abstract}\n\n\\keywords{galaxies:morphology -- galaxies:evolution -- galaxies:formation --\ngalaxies:low surface brightness -- galaxies:surveys -- galaxies:stars}\n\n\\section{Introduction}\n\nThe importance of low surface brightness (LSB) galaxies in the local universe has\nrecently been emphasized in a study by O'Neil \\& Bothun (2000) which has extended\nthe known distribution of galaxies in the local universe.\nTheir result is a flat\nsurface brightness distribution function from the Freeman value of\n21.65 \\plm 0.30 to the survey limit of 25.0 B \\mss, more than\n10$\\sigma$ away (Figure~\\ref{fig:sbdist}a). This indicates that the majority of\nthe galaxies, and potentially the majority of the baryons in the local universe,\nare contained in gravitational potentials only dimly lit by the embedded galaxy.\nRealizing that most galaxies are optically diffuse, then, it becomes extremely\nimportant to understand these systems if we wish to understand galaxy \nformation and evolution as a whole. With this in mind I wish to undertake\na brief review both of our current understanding of LSB galaxy properties\nas well as a review of some popular ideas behind the formation of these \nenigmatic systems.\n\n\\begin{figure}[ht]\n\\centerline{\n\\sbox{1}{\n\\epsfxsize=2.3in\n\\epsffile{oneil_fig1a.ps}}\n\\rotr{1}\n\\sbox{1}{\n\\epsfxsize=2.3in\n\\epsffile{oneil_fig1b.ps}}\n\\rotr{1}\n}\n\\vskip 0.1in\n\\caption{(a) The number density of galaxies in the local universe, with $\\phi$ normalized to one\n(O'Neil \\& Bothun 2000). (b) A representative sample of LSB galaxy colors, from O'Neil, \n\\etal\\ (1997b).\\label{fig:sbdist}}\\vskip -0.1in\n\\end{figure}\n\n\\section{What We (think) We Know about LSB Galaxies}\n\n{\\bf LSB galaxy colors:} Contrary to what was first believed, the colors\nof LSB galaxies range across the entire high surface brightness (HSB) galaxy \nspectrum, including what may be the bluest galaxy known (UGC 12695, with \n$U - I\\:=\\:-0.2$) as well has some fairly red systems\n($B - V\\:>\\:1.0$) (Figure~\\ref{fig:sbdist}b) (O'Neil, \\etal\n1997a, 1997b, 1998). \nAlthough currently it appears that LSB galaxy colors do\nnot quite extend into the extremely\nred colors found in some HSB galaxies, this is likely due more to small\nnumber statistics rather than to an actual lack of extremely red LSB systems.\n\n{\\bf Gas-to-luminosity ratio of LSB galaxies:} The gas-to-luminosity ratio\n(M$_{HI}$/L$_B$) of LSB galaxies spans an extremely large range, from fairly low\n(M$_{HI}$/L$_B$ = 0.1 \\MLsol) through what may be the highest M$_{HI}$/L$_B$\ngalaxies known ([OBC97] N9-2, M$_{HI}$/L$_B$ = 46 \\MLsol).\nAdditionally, if any trend can be seen between\nthe galaxies' color and gas content it is that there may be an {\\it increase} in\ntheir M$_{HI}$/L$_B$ with redder color (Figure~\\ref{fig:gascol}a)\n(O'Neil, Bothun, \\& Schombert 2000, OBS from now on).\n\n{\\bf Tully-Fisher relation:} Although previous studies have shown LSB galaxies\nto follow a slightly broadened version of the standard Tully-Fisher (T-F)\nrelation defined by HSB galaxies (Zwaan, \\etal 1995), a recent study of over 40\nLSB galaxies found no significant correlation between LSB galaxy\nvelocity widths and absolute magnitudes, with\nonly 40\\% of the sample falling within 1$\\sigma$ of the previously defined\nLSB T-F relation (Figure~\\ref{fig:gascol}b). At the least, then,\nthere is a significant population of LSB galaxies which do not adhere to the \nT-F relation (OBS).\n \n{\\bf Rotation curves:} The rotation curves of LSB galaxies \nhave been shown to rise more slowly than similar HSB galaxies\nUsing `standard' values for the stellar mass-to-luminosity\nratio, as taken from HSB galaxies ($\\Upsilon_*$ = 1 -- 3), this leads to the conclusion\nthat many LSB galaxies have a baryonic mass fraction up to 3$\\times$ less than\nHSB galaxies with the same velocity width (i.e. Swaters, \\etal\\ 2000;\nVan Zee, \\etal\\ 1998; de Blok \\& McGaugh 1997). \n\n\\begin{figure}\n\\centerline{\n\\hskip 0.7in\n\\sbox{1}{\n\\epsfxsize=2.3in\n\\epsffile{oneil_fig2a.ps}}\n\\rotr{1}\n\\sbox{1}{\n\\epsfxsize=2.3in\n\\epsffile{oneil_fig2b.ps}}\n\\rotr{1}}\n\\vskip 0.1in\n\\caption{(a) Color versus mass-to-luminosity ratio for a variety of galaxy types (from\nOBS). (b) Galaxies from the sample of OBS.\nThe solid and dashed lines are the 1$\\sigma$ and 2$\\sigma$ fits\nto the LSB galaxy T-F relation of Zwaan, \\etal\\ (1995). \\label{fig:gascol}}\\vskip -0.1in\n\\end{figure}\n\n\\section{What Are LSB Galaxies?}\n\n{\\bf The faded version of HSB galaxies?} No. LSB galaxies often have both very blue colors \nand very low metallicities ($B-V$ $<$ 0.2, Z $<$ 0.01\\Zsol), precluding the possibility \nthat LSB galaxies are primarily composed of an old stellar population. As a caveat,\nthough, it should be noted that a number of very red LSB galaxies have now been\nfound, and these could be faded HSB galaxies. If this is\ncorrect, though, all other LSB galaxies (i.e. those which do not have extremely red colors)\nwould have to be explained, as well as why there are two separate populations of\nLSB galaxies (O'Neil, \\etal\\ 1997a, 1997b).\n\n{\\bf ``Stretched out'' HSB galaxies?} No. Current theories describing LSB\ngalaxies as extending further into their dark matter haloes than similar HSB\ngalaxies predict that LSB galaxies will follow either a universal T-F\nrelation or one which is unique at each \\muo.\nThese theories therefore cannot account for the galaxies of OBS\nwhich fall well off the T-F relation, with no correlation between\n\\muo\\ and residual error. Additional problems with the models can \n(depending on which models are considered) include:\ndifficulty matching the observed shape of LSB galaxy rotation curves;\ninability to allow for high gas fraction, red\nLSB galaxies, (i.e. Dalcanton, \\etal\\ 1997; McGaugh \\& de Blok 1998;\nAvila-Reese \\& Firmani 2000; McGaugh 1999).\n\n{\\bf A completely new type of galaxy?} No. Although this idea could justify \nignoring LSB galaxies when determining theories of galaxy formation and evolution,\nno evidence has been seen for LSB galaxies to be anything but a continuation\nof the HSB galaxy spectrum. There is a smooth transition between LSB and HSB galaxies\nin surface brightness\nand complete overlap in LSB and HSB galaxy colors, scale lengths, mass, \nluminosity, etc. (i.e. Bell \\& de Blok 2000; O'Neil, \\etal\\ 1997a, 1997b).\n\n{\\bf Galaxies with a different stellar population?} Maybe. Although this\nis not a popular idea, as having an IMF which depends on galaxy\nproperties (i.e. surface density) adds complication to models of\ngalaxy evolution, this theory has not yet been disproved. \nThe gas density of LSB galaxies is typically at or below the nominal \nthreshold for star formation, as set by the Toomre criterion (i.e. Van Zee, \\etal\\ 1998;\nde Blok, McGaugh, \\& Van der Hulst 1996).\nWith this in mind, it would be suprising if LSB galaxies' IMF was not at least\nsomewhat affected by their low density.\nAdditionally, recent HST WFPC-2 studies of three nearby LSB dE galaxies failed to find\nevidence for a significant number of red giants ($<$ 13 per 10 pc$^2$, as opposed\nto the 100s per 10 pc$^2$ typically found in HSB galaxies (O'Neil, \\etal\\ 1999)).\nUsing these two ideas -- the low gas density and the lack of evidence for significant\nnumbers of giant branch stars -- we can construct a toy model wherein no stars\ngreater than 2\\Msol are allowed to form. When this is done, not only are LSB\ngalaxy colors, gas fractions, etc. readily matched, but it is also remarkably\neasy to form both red and blue galaxies which do not follow the canonical \nT-F relation (see OBS). Additionally,\nthe addition of a large number of small stars to any galaxy dramatically increases\nthe galaxy's stellar mass-to-luminosity ratio ($\\Upsilon_*$) and can dramatically\ndecrease the total amount of dark matter needed in LSB systems (Swaters, \\etal\\ 2000;\nOBS). Although \nthese models are admittedly extremely oversimplified, they pave the way for\nfurther studies into this idea, and currently appear to be the best theory going.\n\n\\vskip -0.1in\n\\begin{references}\n\\vskip -0.1in\n\\reference Avila-Reese \\& Firmani 2000 RevMexAA 36, 1 \n\\reference Becker, \\etal\\ 1988 A\\&A 203, 21\n\\reference Bell \\& de Blok 2000 MNRAS 311, 668\n\\reference Bothun Sullivan, \\& Schommer 1982 AJ 87, 725\n\\reference Dalcanton, \\etal\\ 1997 ApJ 482, 659\n\\reference Davies 1990 MNRAS 244, 8\n\\reference de Blok \\& McGaugh 1997 MNRAS 290, 533\n\\reference de Blok, McGaugh, \\& Van der Hulst 1996 MNRAS 283, 18\n\\reference de Blok, Van der Hulst, \\& McGaugh 1996 BAAS 189, 8402\n\\reference de Blok, Van der Hult, \\& Bothun 1995 MNRAS 274, 235\n\\reference de Jong 1996 A\\&A 313, 46\n\\reference Matthews \\& Gallagher 1997 AJ 114, 1899\n\\reference McGaugh 1999 {\\it Galaxy Dynamics} ed. Meritt, \\etal\\ (San Francisco: ASP)\n\\reference McGaugh \\& de Blok 1998 ApJ 499, 41\n\\reference O'Neil \\& Bothun 2000 ApJ preprint\n\\reference O'Neil, Bothun, \\& Schombert 2000 AJ 119 136 (OBS)\n\\reference O'Neil, Bothun, \\& Impey 1999 AJ 118, 1618\n\\reference O'Neil, \\etal\\ 1998 AJ 116, 657\n\\reference O'Neil, \\etal\\ 1997b AJ 114, 2448\n\\reference O'Neil, Bothun, \\& Cornell 1997a AJ 113, 1212\n\\reference Phillipps, \\etal\\ 1987 MNRAS 229, 505\n\\reference Schombert, \\etal\\ 1995 AJ 110, 2067\n\\reference Swaters, Madore, \\& Trewhella 2000 ApJL preprint\n\\reference Van Zee, Skillman, \\& Salzer 1998 ApJ 497 L1\n\\reference Zwaan, \\etal\\ 1995 MNRAS 273 L35\n\\end{references}\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002227
|
A Single Circumbinary Disk in the HD~98800 Quadruple System
|
[
{
"author": "D.W. Koerner\\altaffilmark{1}"
},
{
"author": "E.L.N.Jensen\\altaffilmark{2}"
},
{
"author": "K.L. Cruz\\altaffilmark{1}"
},
{
"author": "T.B. Guild\\altaffilmark{1}"
},
{
"author": "and K. Gultekin\\altaffilmark{1}"
}
] |
We present sub-arcsecond thermal infrared imaging of HD~98800, a young quadruple system composed of a pair of low-mass spectroscopic binaries separated by 0.8$''$ (38 AU), each with a K-dwarf primary. Images at wavelengths ranging from 5 to 24.5 $\mu$m show unequivocally that the optically fainter binary, HD~98800B, is the sole source of a comparatively large infrared excess upon which a silicate emission feature is superposed. The excess is detected only at wavelengths of 7.9~$\mu$m and longer, peaks at 25 $\mu$m, and has a best-fit black-body temperature of 150~K, indicating that most of the dust lies at distances greater than the orbital separation of the spectroscopic binary. We estimate the radial extent of the dust with a disk model that approximates radiation from the spectroscopic binary as a single source of equivalent luminosity. Given the data, the most-likely values of disk properties in the ranges considered are $R_{in} = {5.0}\pm2.5$ AU, $\Delta R = 13\pm8$ AU, $\lambda_0 = {2}^{+4}_{-1.5}\mu$m, $\gamma = 0\pm2.5$, and $\sigma_{total} = 16\pm3$ AU$^2$, where $R_{in}$ is the inner radius, $\Delta R$ is the radial extent of the disk, $\lambda_0$ is the effective grain size, $\gamma$ is the radial power-law exponent of the optical depth, $\tau$, and $\sigma_{total}$ is the total cross-section of the grains. The range of implied disk masses is 0.001--0.1 times that of the moon. These results show that, for a wide range of possible disk properties, a circumbinary disk is far more likely than a narrow ring.
|
[
{
"name": "draft_finalpp.tex",
"string": "\\documentstyle[12pt,aaspp4,psfig]{article}\n%\\documentstyle[12pt,aasms4]{article}\n\\tighten\n\\newcommand{\\lsun}{\\mbox{$L_\\odot$}}\n\\newcommand{\\mearth}{\\mbox{$L_\\odot$}}\n\\begin{document}\n\n\\title {A Single Circumbinary Disk in the HD~98800 Quadruple System}\n\n\\author {D.W. Koerner\\altaffilmark{1}, E.L.N.Jensen\\altaffilmark{2}, \nK.L. Cruz\\altaffilmark{1}, T.B. Guild\\altaffilmark{1}, and \nK. Gultekin\\altaffilmark{1}}\n\\altaffiltext{1} \n{University of Pennsylvania, David Rittenhouse Laboratory, \n209 S. 33rd St., Philadelphia, PA 19104-6396}\n\\altaffiltext{2}\n{Dept. of Physics \\& Astronomy, Swarthmore College, Swarthmore, PA 19081}\n\n\\bigskip\n\\bigskip\n\n\\begin{abstract}\n\nWe present sub-arcsecond thermal infrared imaging \nof HD~98800, a young quadruple system composed of \na pair of low-mass spectroscopic binaries separated by 0.8$''$ \n(38 AU), each with a K-dwarf primary. Images at wavelengths\nranging from 5 to 24.5 $\\mu$m show unequivocally that\nthe optically fainter binary, HD~98800B, is the sole source of a\ncomparatively large infrared excess upon which a silicate\nemission feature is superposed. The excess is detected\nonly at wavelengths of 7.9~$\\mu$m and longer, peaks at 25 $\\mu$m,\nand has a best-fit black-body temperature of 150~K, indicating\nthat most of the dust lies at distances greater than the orbital\nseparation of the spectroscopic binary. We estimate \nthe radial extent of the dust with a disk model \nthat approximates radiation from the spectroscopic binary as a \nsingle source of equivalent luminosity. Given the data, \nthe most-likely values of disk properties in \nthe ranges considered are\n$R_{in} = {5.0}\\pm2.5$ AU, $\\Delta R = 13\\pm8$ AU, \n$\\lambda_0 = {2}^{+4}_{-1.5}\\mu$m, $\\gamma = 0\\pm2.5$,\nand $\\sigma_{total} = 16\\pm3$ AU$^2$, \nwhere $R_{in}$ is the inner radius,\n$\\Delta R$ is the radial extent of the disk, $\\lambda_0$\nis the effective grain size, $\\gamma$ is the radial\npower-law exponent of the optical depth, $\\tau$, and $\\sigma_{total}$\nis the total cross-section of the grains. The range of implied \ndisk masses is 0.001--0.1 times that of the moon.\nThese results show that, \nfor a wide range of possible disk properties, a\ncircumbinary disk is far more likely than a narrow ring.\n\n\\end{abstract}\n\nSubject headings: binaries: close --- binaries: spectroscopic --- \n circumstellar matter --- planetary systems --- \n stars: imaging --- stars: individual (HD 98800)\n\n\\vfill\n\\eject\n\n\\section {Introduction}\n\nThe evolution of circumstellar dust around young stars is \ntraced by a time-dependent signature in excess infrared emission.\nThe evidence lies primarily in the spectral distribution of \nradiation as it chronicles infall from a protostellar \nenvelope, viscous accretion in a gas-rich circumstellar disk, and \ndispersal in a dusty ``debris disk'' that survives as a \nlast vestige of planet formation \n(Adams, Lada, \\& Shu 1987; Backman \\& Paresce 1993). \nImaging has dramatically confirmed this interpretation,\nproviding support for a standard model of circumstellar evolution and \nelucidating the role of circumstellar disks throughout the process\n(Beckwith \\& Sargent 1996; Holland et al.\\ 1998;\nKoerner 1997; Koerner et al.\\ 1998). The\nco-existence of disks with stellar companions is attested by\ncomparison of high-resolution binary surveys (Ghez, Neugebauer, \n\\& Matthews 1993; Leinert et al.\\ 1993)\nwith the results of imaging and long-wavelength flux measurements \n(Jensen et al.\\ 1996a,b; Mathieu et al.\\ 2000). \nDisks are found to be reduced in mass for\nbinaries with separations in the 10--100 AU range, similar to the\ntypical disk size. However, \ncircumstellar disks in binaries wider than 100 AU\n(Beckwith et al.\\ 1990; Osterloh \\& Beckwith 1995; Jensen et al.\\ 1996a), \nand circum{\\em binary} disks around spectroscopic binaries\n(Jensen \\& Mathieu 1997) are not obviously different \nfrom disks around single stars with respect to either their \nglobal properties or frequency of occurrence. \nThese results argue strongly for the possibility of \nan abundant and diverse population of extra-solar planets.\n\nAmong pre--main-sequence spectroscopic binaries with \nseparations of 1 AU or less, there is growing evidence that\ncircumbinary disks are common. Massive circumbinary disks have\nbeen found in a handful of cases, demonstrating\nunequivocally that the presence of a small-separation binary is not an\nimpediment to the formation of a protoplanetary disk (Jensen \\&\nMathieu 1997). Examples include\nGW Ori (Mathieu et al.\\ 1991, 1995), UZ~Tau~E (Jensen et al.\\ 1996b;\nMathieu et al.\\ 1996), and DQ Tau (Mathieu et al.\\ 1997), all with\nprojected orbital separations of order 1 AU or\nless and disk masses that are comparable to or greater than that\nestimated for the minimum mass solar nebula. \n%While it has yet to be\n%confirmed, the recent discovery by microlensing of a circumbinary\n%planet (Bennett et al.\\ 1999) suggests that such disks may indeed\n%eventually form planets. \n\nThe degree of complexity possible for multiple star-disk\nsystems is perhaps nowhere better illustrated than in the \ncase of the post-T Tauri quadruple system, HD~98800. \nIt is composed of a pair of low-mass spectroscopic binaries, each with a\nK-dwarf primary, that have a projected separation of \n0.8$''$ (37.6 AU at the 47 pc\ndistance determined by {\\it Hipparcos}) and estimated ages\nof $\\sim10$~Myr (Soderblom et al.\\ 1998). Despite the presence of many\nstellar components, HD~98800 is associated with an unusually\nstrong IRAS signature of dust emission with a temperature similar\nto the solar zodiacal dust bands (Walker \\& Wolstencroft 1988;\nZuckerman \\& Becklin 1993; Sylvester et al.\\ 1996) and with\nevidence for silicate emission from dust grains (Skinner, Barlow,\n\\& Justtanont 1992). Until recently, there were no observations\nthat provided a hint as to how this dust was distributed among the stellar\ncomponents of the system. N-band imaging that marginally\nresolved the binary has now shown that most of the dust is\nassociated with the optical secondary and spectroscopic binary\nHD~98800B (Gehrz et al.\\ 1999). Here we present sub-arcsecond\nimages from 5 to 25 $\\mu$m that fully resolve\nthe 0.8$''$ binary components of the HD~98800 system.\n\n\n\\section{Observations and Results}\n\nHD~98800 was observed with JPL's mid-infrared camera MIRLIN at the f/40\nbent-Cassegrain focus of the Keck II telescope on UT 14 March 1998.\nMIRLIN employs a Boeing 128$\\times$128 pixel, high-flux Si:As BIB detector\nwith a plate scale at Keck II of 0.137$''$ per pixel \nand 17.5$''$ field of view. Background subtraction\nwas carried out by chopping the secondary mirror at a $\\sim$4 Hz rate with\n8$''$ throw in the north-south direction, and by nodding the telescope a\nsimilar distance east-west after coadding a few hundred chop\npairs. Images of the source on the \ndouble-differenced frames were shifted and added \nto make the final 32 $\\times$ 32 \n(4.4$''$ $\\times$ 4.4$''$) images. Observations were\ncarried out at wavelengths from 4.7 to 24.5 $\\mu$m in the\nspectral bands listed in Table I.\nSmall dither steps were taken between chop-nod cycles. \nInfrared standards $\\beta$ Leo (A3 V) and $\\alpha$ Hya (K3 III)\nwere observed in the same way at similar airmasses.\n\nThe resulting images of HD~98800 are displayed in Fig.\\ 1. \nSince the half-maximum width of the \npoint spread function (PSF) is between 0.3$''$ and 0.55$''$ over the full \nwavelength range, it is possible to identify unambiguously the relative\nflux densities of the mid-infrared emission for the first time.\nTwo point sources, separated by 0.81$''\\pm0.02''$, are detected at \nwavelengths up to $\\lambda$ = 12.5 $\\mu$m with an orientation that\ncorresponds to the binary optical components with A to the south and\nB to the north (cf.\\ Soderblom et al.\\ 1998). Only a single point source\nis detected at the longest wavelengths.\nIt is immediately apparent from the images that this \nemission arises predominantly from the northern source, \ncorresponding to the optical secondary HD~98800B. In contrast, emission\nfrom the optical primary decreases steadily towards longer wavelengths.\nSeparate-component flux densities were derived by fitting a \nmeasured PSF to each component and using the resulting\nflux component ratio to decompose the total flux into values \nfor HD~98800A and B. \nResults are listed in Table I and plotted as a spectral energy distribution \nin Fig.\\ 2 together with measurements from HST, IRAS, and the JCMT \n(Sylvester et al.\\ 1996; Soderblom et al.\\ 1998). Mid-infrared flux \ndensities measured for the total system are in excellent agreement with \nearlier values published in the literature (Zuckerman \\& Becklin 1993; \nSylvester et al.\\ 1996).\n\nThe distribution of mid-infrared flux between the components\nHD~98800A and B clearly indicates that the total infrared \nexcess of the system is dominated by the contribution from HD~98800B. \nValues for the flux density of HD~98800B at $\\lambda$ = 12.5 and 24.5 $\\mu$m \nagree very well with 12 and 25 $\\mu$m IRAS fluxes measured for the whole \nsystem. In contrast, flux densities for HD~98800A\ndecrease approximately as $\\lambda^{-2}$ between $\\lambda$ = 7.9 and \n12.5 $\\mu$m, consistent with origin in a stellar photosphere. At \n12.5 $\\mu$m, emission from HD~98800A contributes less \nthan 4\\% of the total emission. At 24.5~$\\mu$m, an\nupper limit to its contribution comprises only\n2\\% and an estimated photospheric contribution only 0.2\\% of the\ntotal flux.\nIt is thus a good approximation to ascribe all the \nemission from unresolved measurements at $\\lambda > 25\\ \\mu$m to HD~98800B \nand neglect any contribution from HD~98800A. This result is largely\nin agreement with the conclusion of Gehrz et al.\\ (1999), who\nnevertheless attributed some of the mid-infrared excess emission\nto HD~98800A on the basis of lower resolution imaging (1$''$ \nat $\\lambda$ = 9.8 $\\mu$m) which only marginally resolved the\n0.8$''$ separation of components A and B.\n\nA spectral signature of silicate emission \nat $\\lambda$ $\\approx$ 10~$\\mu$m is evident in the flux \nmeasurements of HD~98800B plotted in Fig.\\ 2. It is \ndisplayed in more detail in Fig.\\ 3, where the measurements at \n7.9 and 12.5 $\\mu$m have been assumed to represent featureless thermal \ncontinuum emission, and a simple linear extrapolation between the two\npoints has been subtracted off. The spectrum was then scaled to give \nthe 7.9 and 12.5 um points a value of one to facilitate\ncomparison with other data from the literature (see Hanner, Lynch, \\& \nRussell 1994 for comparison of different continuum removal techniques). \nSilicate features from comets and \ninterstellar dust are plotted in Fig.\\ 3 for comparison. \nIt is readily apparent that the circumstellar dust feature \nresembles that from comets more than that from\nthe interstellar medium. The feature is broader and does not show \na single narrow peak between 9 and 10 $\\mu$m as seen for interstellar grains \nin the Trapezium. For comets, this broadened line-shape has been \ninterpreted as diagnostic of a mixture of amorphous and crystalline \nsilicates that radiate predominantly at 9.8 and 11.2~$\\mu$m, respectively\n(Hanner, Lynch, \\& Russell 1994).\n\n\n\\section {Modeling and Discussion} \n\n%Mid-infrared imaging of HD~98800 presented here \n%demonstrates unequivocally that virtually all of the infrared excess \n%from the HD~98800 multiple system is associated with the optical\n%secondary, HD~98800B. A silicate feature is evident in flux measurements\n%in the 10~$\\mu$m band. It has more in common with cometary \n%spectra than with the signature from\n%grains in the interstellar medium. Its broad \n%shape may be due to the combined presence of amorphous\n%and crystalline components, with the latter perhaps arising after \n%processing in the circumstellar environment.\n\nTo better interpret the emission from HD~98800, we fit model emission\nfrom stellar photospheres to \noptical (WFPC2) and near infrared (NICMOS) HST imaging that resolved\ncomponents A and B (Soderblom et al.\\ 1998; Low et al.\\ 1999). \nThese were matched by reddened model atmospheres from Kurucz \nby varying only the stellar luminosity, as described by\nJensen \\& Mathieu (1997). Discrepant \nNICMOS measurements at roughly the \nsame wavelength were averaged and weighted\nas a single point in the fit. Stellar effective\ntemperatures were adopted from Case C of Soderblom et al.\\ (1998)\nwhere the single value $T_{\\rm eff} = 4350$ K was\ngiven for the spectroscopic binary HD~98800A, and\n$T_{\\rm eff} = 4250$ and 3700~K were reported for the two stars in the\ndouble-lined spectroscopic binary HD~98800B. Soderblom et al.\\ (1998)\nreported $A_{\\rm V} = 0.44$ mag for HD~98800B, but gave no $A_{\\rm V}$\nvalue for HD~98800A. We assumed $A_{\\rm V} = 0$ for HD~98800A and used\na standard interstellar extinction law with $A_{\\rm V} = 3.1 E_{\\rm\n(B-V)}$ to redden the model for HD~98800B. The luminosity ratio of the\ntwo components was fixed at 2.7 based on the absolute V magnitudes given by\nSoderblom et al.\\ (1998) and bolometric corrections from Kenyon \\& Hartmann\n(1995). The best-fit models gave $L_{\\rm star}$ = 0.78 \\lsun\\ and 0.56 \\lsun\\\nand are plotted as a dotted and dashed line in Fig.\\ 2 \nfor the A and B components, respectively. \n\nAn average dust temperature of 150 K was derived by fitting a\nPlanck function to the excess continuum emission from \nHD~98800B, omitting points associated with the silicate feature. \nFor grains 1-10 $\\mu$m in size, \nthis temperature corresponds to a 4-12 AU distance \nfrom a single star of luminosity 0.56 \\lsun.\nGiven the 1 AU orbital separation estimated \nfor the components of HD~98800B (Soderblom et al.\\ 1998), it \nimplies that most of the dust is located in a {\\it circumbinary}\nconfiguration around the spectroscopic binary. \nTo estimate the radial extent of the dust, we also fit\nthe spectral energy distribution with a model of a\ndisk around a single star of luminosity 0.56 \\lsun.\nThe model parametrization and fitting method are described in \nKoerner et al.\\ (1998). Five parameters were varied in the fit, \nincluding inner radius $R_{in}$, radial extent $\\Delta R$,\neffective particle size $\\lambda_0$, and the \nradial power-law index, $\\gamma$, of the optical depth,\n$\\tau(r) = {\\tau_0}(r/r_0)^{-\\gamma}$. The optical depth scaling, \n$\\tau_0$, was derived after varying the area-integrated optical depth,\n$\\sigma_{total} = {\\int^{R_{in}+\\Delta R}_{R_{in}}}\\ \n{\\tau_0}(r/r_0)^{-\\gamma}\\ 2 \\pi rdr$, an indicator of the total\ncross-sectional area of the grains.\n Parameter ranges considered were 0--9~AU for $R_{in}$, \n1--25~AU for $\\Delta R$, $10^{-1}$--$10^3~\\mu$m for $\\lambda_0$, \n-4.0--4.0 for $\\gamma$ and 5--50~AU$^2$ for $\\sigma_{total}$.\nA disk model with most-likely values of these \nparameters is displayed in Fig.\\ 2; these are\n$R_{in} = 5.0\\pm2.5$ AU, $ \\Delta R = 13\\pm8$ AU, \n$\\lambda_0 = {2}^{+4}_{-1.5}\\mu$m, $\\gamma = 0\\pm2.5$, \nand $\\sigma_{total} = 16\\pm3$ AU$^2$, where the values quoted are central\nwithin a range of probabilities enclosing the 68\\% confidence level. \nThe probability distribution is fairly flat within\nthese ranges and peak values are not always central \nbut lie at $R_{in} = 3.0$ AU, $ \\Delta R = 22$ AU, \n$\\lambda_0 = 1.8\\mu$m, $\\gamma = 1$, and $\\sigma_{total} = 16$ AU$^2$.\n\nMany of these values are not\nnarrowly constrained by the flux measurements alone,\nlargely because the temperature dependence on both\nparticle size and radial distance from the star makes\nit impossible to determine them uniquely.\nHowever, taken over the whole range of parameter space, there\nis greater than a 90\\% probability that the dust is distributed\nin a circumbinary {\\it disk}, with $\\Delta R/R_{in} > 1$, \nrather than a narrow ring like that around \nHR~4796A ($\\Delta R/R_{in} < 0.25$; Koerner et al.\\ 1998;\nSchneider et al.\\ 1999).\nWe emphasize the caveat that these estimates apply only \nunder the assumptions of this particular disk model.\nAn estimate of the true inner radius, for example, should take into \naccount radiation from the two stellar components, and some temperature\nbroadening may be due to a range of emissivities inherent\nin an unknown particle-size distribution.\nHowever, these effects are unlikely to alter our general \nconclusion about the disk vs ring-like nature of the dust.\n\nThe total cross section for dust grains around HD98800B, \n$\\sigma_{total} = 16\\pm3$ AU$^2$, is 2-3 orders of magnitude\nsmaller than for several other debris disks (e.g., $\\beta$ Pic, HR4796A,\nand 49 Cet). Thus, from the standpoint of\ncircumstellar mass, the disk around HD98800B is not as remarkable\nas suggested by the infrared excess alone \n(cf. Zuckerman \\& Becklin 1993). \nThe relatively high fractional luminosity is, instead,\na consequence of dust location \nclose to the star where grains intercept a greater \nfraction of the stellar radiation. Assuming a range of plausible grain \ndensities, $\\rho$ = 1.0-3.0 g cm$^{-3}$, values of $\\sigma_{total}$ and \n$\\lambda_0$ (grain radius $a$ = $\\lambda_0$/1.5; cf.\\ Backman et al. 1992)\nimply a disk mass in the range of 0.001--0.1 lunar masses.\n\n\nModels that\nincorporate a circumbinary disk surrounding an optically thin\nregion of warmer dust have served to explain the \nspectral energy distributions of \nyounger T-Tauri spectroscopic binaries (Jensen \\& Mathieu 1997).\nIt is likely that HD~98800B is a similar system in \na later phase of evolution. Modeling of the circumbinary dust emission \nindicates location of the dust in a radial zone\nassociated with planet building early in the life of our own solar system. \nConsequently, it may well represent the telltale signature of planet \nformation in a hierarchically ordered multiple star system.\nIf so, we can expect our\npicture of the plenitude and diversity of extra-solar planetary \nsystems to become increasingly rich as it is revealed by impending\nsurveys with high-resolution techniques now under development.\n\n\\acknowledgments\nWe gratefully acknowledge support of the NSF's ``Life in Extreme\nEnvironments'' program through grant AST 9714246.\nData presented herein were obtained at the W.M. Keck\nObservatory (WMKO), which is operated as a scientific partnership \namong the California Institute of Technology, the University of California \nand the National Aeronautics and Space Administration. \nThe Observatory was made possible by the generous financial support of the\nW.M. Keck Foundation. \nWe wish to thank an anonymous referee for useful comments. A great\ndebt is due, also, to Robert Goodrich and the WMKO summit staff for their \nmany hours of assistance in adapting MIRLIN to the Keck II visitor\ninstrument port. \n\n\\vfill\n\\eject\n\n\\begin{references}\n\n\\reference{als} Adams, F.C., Lada, C.J., \\& Shu, F.H., 1987, \\apj, 312, 788\n\n%\\reference{ada} Adams, F.C., Emerson, J.P., and Fuller, G.A., \n%1990, \\apj, 357, 606\n\n\\reference{art} Artymowicz, P. and Lubow, S.H., 1994, \\apj, 421, 651\n\n\\reference{bgw} Backman, D.E., Gillett, F.C., \\& Witteborn, F.C., 1992, \n\\apj, 385, 670\n\n\\reference{bp} Backman, D.E., \\& Paresce, F., 1993, in Protostars \\& \nPlanets III, (ed. E.H. Levy \\& J.I. 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V. Mannings, A. Boss, \\& S, Russell), \nTucson: University of Arizona Press, in press\n\n\n%\\reference{mom} Momose, M., Ohashi, N., Kawabe, R., Hayashi. M.,\n%\\& Nakano, T., 1996, \\apj, 470, 1001\n\n%\\reference{mlbr} Mouillet, A., Lagrange, A.-M., Beuzit, J.-L., \\& Renaud,\n%N., 1997, \\aap, 324, 1083\n\n\\reference{ost} Osterloh, M. \\& Beckwith, S.V.W., 1995, \\apj, 439, 288 \n\n%\\reference{pap} Papaloizou, J.C.B., \\& Pringle, J.E., 1977, \\mnras, 181, 441\n\n%\\reference{pla} Pantin, E., Lagage, P.O., \\& Artymowicz, P., 1997, \n%\\aap, 327, 1123\n\n\\reference{pol} Pollack, J.B., Hollenbach, D., Beckwith, S.,\nSimonelli, D.P., Roush, T., \\& Fong, W. 1994, \\apj, 421, 615\n\n%\\reference{sb} Sargent, A.I., \\& Beckwith, S.V.W., 1987, \\apj, 323, 294\n\n%\\reference{sch} Schwartz, P.R., Simon, T. \\& Campbell, R., 1986, \\apj, \n%303, 233\n\n%\\reference{shu} Shu, F.H., Najita, J., Galli, D., Ostriker, E., \\& Lizano,\n%S., 1993, in Protostars \\& Planets III, (ed. E.H. Levy \\& J.I. Lunine),\n%Tucson: University of Arizona Press, p. 3\n\n%\\reference{ski} Skinner, S.L. \\& Brown A., 1994, \\aj, 107, 1461\n\n\\reference{sbj} Skinner, S.L., Barlow, M.J., \\& Justtanont, K., 1992,\n\\mnras, 255, 31\n\n%\\reference{sft} Smith, B.A., Fountain, J.W., \\& Terrile R.J., 1992, \\aap, 261, \n%499\n\n%\\reference{sft} Smith, B.A., \\& Terrile R.J., 1984, Science, 226, \n%4681\n\n\\reference{sod} Soderblom, D.R., et al.\\ 1998, \\apj, 498, 385\n\n%\\reference{shb} Stauffer, J.R., Hartmann, L.W., \\& Barrado y Navascues, D.,\n%1995, \\apj, 454, 910\n\n%\\reference{str} Strom, K.M., Strom, S.E., Edwards, S., Cabrit, S., \\&\n%Skrutskie, M.F., 1989, \\aj, 97, 1451\n\n%\\reference{ssm} Sylvester, R.J., Skinner, C.J., \\& Mannings, V., 1995, \n%\\mnras, 279, 915\n\n\\reference{ssm} Sylvester, R.J., Skinner, C.J., Barlow, M.J.,\n\\& Mannings, V., 1996, \\mnras, 279, 915\n\n%\\reference{ter} Terebey, S., Ch\\&ler, C.J., \\& \\&r\\'e, P., \n%1993, \\apj, 414, 759\n\n%\\reference{tok} Tokunaga, A., 1998, in Astrophysical Quantities, (ed. Cox),\n%London: Dover, in press.\n\n\\reference{ww} Walker, H.J., \\& Wolstencroft R.D., 1988, \\pasp, 100, 1509\n\n%\\reference{wei} Weintraub, D.A., Kastner, J.H., Zuckerman, B. \\&\n%Gatley, I., 1992, \\apj, 391, 784\n\n%\\reference{wic} Wichmann, R., Bastian, U., Krautter, J., Jankovics, I.\n%\\& Ruci\\'nski, S., 1997, \\mnras, in press\n\n\\reference{zfk} Zuckerman, B., \\& Becklin, E.E., 1993, \\apjl, 406, L25\n\n%\\reference{zfk} Zuckerman, B., Forveille, T., \\& Kastner, J.H., 1995,\n%Nature, 373, 6514\n\n\\end{references}\n\n\n% Figure Captions here...\n\n\\ \\par \n\\bigskip\n\\psfig{figure=fig1.ps,width=6.4truein} % \\vskip -5.7truein\n\\medskip\n\n\\figcaption{\\small Keck/MIRLIN imaging of the thermal infrared emission\nfrom the HD~98800 quadruple system oriented with up axis aligned due North.\nThe spectroscopic binaries, HD~98800A and HD~98800B, \nare clearly resolved from each other and are identified, respectively,\nwith northern and southern point sources separated by 0.8$''$ (38 AU). \nEmission from HD~98800A steadily decreases with \nwavelength as $\\lambda^{-2}$ and is no longer detected in the 20 $\\mu$m \nimages. In contrast, radiation from the optical\nsecondary, HD~98800B, increases dramatically out to 24.5 $\\mu$m.}\n\n\\bigskip\n\\vfill\n\\eject\n\n\\psfig{figure=fig2.ps,width=6.4truein,angle=270}\n\n\\figcaption{\\small Spectral energy distributions for the separate\ncomponents of HD~98800. Filled circles in the left plot\nare HST (WFPC2 and NICMOS) fluxes for HD~98800A; triangles\nrepresent fluxes listed in Table 1. The dotted line is a\nmodel photosphere from a Kurucz fit to only the HST data. It \nclearly matches the mid-infrared fluxes presented in this work. \nOpen squares and diamonds\nare plotted in both panels and represent IRAS and JCMT sub-millmeter\nfluxes, respectively, for the whole system. Open circles in\nthe right-hand panel are HST fluxes for HD~98800B; open\ntriangles are from Table 1. The dashed line\nis a model photosphere fit to only the HST fluxes as for HD~98800A.\nThe dotted and dashed line represents emission from a model disk with\nparameters outlined in the text. Together\nwith the photospheric model, it was fit to measurements at 7.9 $\\mu$m,\n12.5 $\\mu$m, and all longer wavelengths.\nCombined photospheric and disk emission is plotted as a solid line.}\n\n\\bigskip\n\\vfill\n\\eject\n\n\\hskip 0.5truein\n\\psfig{figure=fig3.ps,width=5.0truein,angle=270}\n\n\n\\figcaption{\\small Plot of the emission from HD~98800B in the 10 $\\mu$m \nsilicate band. Filled circles are derived\nfrom flux densities listed in Table 1 by subtraction of continuum\nemission interpolated between the points at $\\lambda$ = 7.9 and \n12.5 $\\mu$m. Vertical error bars are derived from \nuncertainties listed in Table 1. Horizontal error bars refer only\nto the filter widths, also given in Table 1. Solid squares\ndepict the silicate emission feature as observed in the \ninterstellar medium toward the Trapezium. Solid triangles and open\ncircles refer to measurements taken from Hanner, Lynch, \\& Russell (1994)\nfor Comets Levy and Austin, respectively.}\n\n\n\n\\begin{deluxetable}{lcccccc}\n%\\tablewidth{33pc}\n\\tablewidth{0pc}\n\\tablecaption{Component Flux Densities for the HD~98800 System}\n\\tablehead{\n\\colhead{$\\lambda_{eff}$} & \n\\colhead{$\\delta\\lambda$} &\n\\colhead{Calibrator/Flux} & \n\\colhead{F$_\\nu$(HD~98800)} & \\colhead{Component} &\n\\colhead{F$_\\nu$(A)} & \\colhead{F$_\\nu$(B)} \\\\\n\\colhead{($\\mu$m)} &\n\\colhead{($\\mu$m)} &\n\\colhead{ \\ \\ \\ \\ \\ \\ \\ /(Jy)} &\n\\colhead{(Jy)} & \\colhead{Ratio (B/A)} &\n\\colhead{(Jy)} & \\colhead{(Jy)} }\n\\startdata\n4.68 & 0.57 & $\\beta$ Leo/28.95 & 1.03$\\pm$0.090$^1$ \n& 1.21 & 0.47$\\pm$0.04 & \n0.72$\\pm$0.04 \\nl\n7.91 & 0.59 & $\\beta$ Leo/10.68 & 0.62$\\pm$0.03 & 2.46 & 0.18$\\pm$0.02 & \n0.44$\\pm$0.02 \\nl\n8.81 & 0.87 & $\\beta$ Leo/8.67 & 0.10$\\pm$0.04 & 4.88 & 0.17$\\pm$0.01 & \n0.83$\\pm$0.03 \\nl\n9.69 & 0.93 & $\\beta$ Leo/7.21 & 1.78$\\pm$0.07 & 10.20 & 0.15$\\pm$0.02 & \n1.62$\\pm$0.07 \\nl\n10.27 & 1.01 & $\\beta$ Leo/6.44 & 2.02$\\pm$0.08 & 15.38 & 0.12$\\pm$0.01 & \n1.90$\\pm$0.08 \\nl\n11.70 & 1.11 & $\\beta$ Leo/5.00 & 2.28$\\pm$0.09 & 21.28 & 0.10$\\pm$0.01 & \n2.18$\\pm$0.09 \\nl\n12.49 & 1.16 & $\\beta$ Leo/4.40 & 2.19$\\pm$0.09 & 26.32 & 0.08$\\pm$0.01 & \n2.02$\\pm$0.08 \\nl\n17.93 & 2.00 & $\\alpha$ Hya/42.83 & 4.98$\\pm$0.20 & $> 27.78$ & $< 0.174$ \n& 4.98$\\pm$0.27 \\nl\n20.81 & 1.65 & $\\alpha$ Hya/31.74 & 5.53$\\pm$0.23 & $> 26.32$ & $< 0.210$ \n& 5.53$\\pm$0.31 \\nl\n24.48 & 0.76 & $\\alpha$ Hya/30.15 & 8.62$\\pm$0.35 & $> 47.62$ & $< 0.181$ \n& 8.62$\\pm$0.39 \\nl\n\\tablenotetext{1}{Total flux taken from Zuckerman \\& Becklin (1993)}\n\\enddata\n\\end{deluxetable}\n\n\\end{document}\n\n\n\n"
}
] |
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astro-ph0002228
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Coherent neutrino radiation in supernovae at two loops
|
[
{
"author": "A. Sedrakian and A. E. L. Dieperink"
}
] |
We develop a neutrino transport theory, in terms of the real-time non-equilibrium Green's functions, which is applicable to physical conditions arbitrary far from thermal equilibrium. We compute the coherent neutrino radiation in cores of supernovae by evaluating the two-particle-two-hole (2p-2h) polarization function with dressed propagators. The propagator dressing is carried out in the particle-particle channel to all orders in the interaction. We show that at two loops there are two distinct sources of coherence effects in the bremsstrahlung. One is the generically off-shell intermediate state propagation, which leads to the Landau-Pomeranchuk-Migdal type suppression of radiation. We extend previous perturbative results, obtained in the leading order in quasiparticle width, by deriving the exact non-perturbative expression. A new contribution due to off-shell finial/initial baryon states is treated in the leading order in the quasiparticle width. The latter contribution corresponds to processes of higher order than second order in the virial expansion in the number of quasiparticles. At 2p-2h level, the time component of the polarization tensor for the vector transitions vanishes identically in the soft neutrino approximation. Vector current thereby is conserved. The contraction of the neutral axial vector current with tensor interaction among the baryons leads to a non-vanishing contribution to the bremsstrahlung rate. These rates are evaluated numerically for finite temperature pure neutron matter at and above the nuclear saturation density.
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[
{
"name": "twoloop2.tex",
"string": "\\documentstyle[aps,preprint,epsf,graphicx]{revtex}\n%\\documentstyle[]{article}\n\n% functional abbreviations\n\n\\newcommand{\\nn}{\\nonumber}\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\bea}{\\begin{eqnarray}}\n\\newcommand{\\eea}{\\end{eqnarray}}\n\\newcommand{\\no}{\\noindent}\n\\newcommand{\\un}{\\underline}\n\\newcommand{\\sla}{\\! \\not \\!}\n\n\n% numerical syntax\n\n\\newcommand{\\Tr}{{\\rm Tr}}\n\\newcommand{\\anu}{\\bar\\nu}\n\\newcommand{\\omnu}{\\omega_{\\nu}}\n\\newcommand{\\ep}{\\varepsilon}\n%\\newcommand{\\bp}{\\vec p}\n%\\newcommand{\\bq}{\\vec q}\n%\\newcommand{\\vq}{\\vec q}\n\\newcommand{\\bp}{\\bbox{p}}\n\\newcommand{\\bP}{\\bbox{P}}\n\\newcommand{\\bq}{\\bbox{q}}\n\\newcommand{\\bk}{\\bbox{k}}\n\\newcommand{\\bK}{\\bbox{K}}\n\\newcommand{\\bv}{\\bbox{v}}\n\\newcommand{\\br}{\\bbox{r}}\n\\newcommand{\\bl}{\\bbox{l}}\n\\newcommand{\\bsigma}{\\bbox{\\sigma}}\n\\newcommand{\\Real}{\\Re{\\rm e}}\n\\newcommand{\\Img}{\\Im{\\rm m}}\n\n\\tighten\n\n\\begin{document}\n\n%\\preprint{KVI-preprint}\n\n\\title{Coherent neutrino radiation in supernovae at two loops}\n\n\\author{A. Sedrakian and A. E. L. Dieperink}\n\n\n\n\\address{\n Kernfysisch Versneller Instituut,\n NL-9747 AA Groningen,\n The Netherlands\n }\n\n\\maketitle\n\\begin{abstract}\nWe develop a neutrino transport theory, in terms of the real-time\nnon-equilibrium Green's functions, which\nis applicable to physical conditions arbitrary far from\nthermal equilibrium.\nWe compute the coherent neutrino radiation\nin cores of supernovae by evaluating the\ntwo-particle-two-hole (2p-2h) polarization function\nwith dressed propagators. The propagator dressing\nis carried out in the particle-particle channel to all orders\nin the interaction.\nWe show that at two loops\nthere are two distinct sources of coherence effects in the bremsstrahlung.\nOne is the generically off-shell intermediate state propagation,\nwhich leads to the Landau-Pomeranchuk-Migdal type\nsuppression of radiation.\nWe extend previous perturbative results, obtained in the leading\norder in quasiparticle width, by deriving the\nexact non-perturbative expression.\nA new contribution due to off-shell\nfinial/initial baryon states is treated in the\nleading order in the quasiparticle width. The latter contribution\ncorresponds to processes of higher order than second order in the\nvirial expansion in the number of quasiparticles.\nAt 2p-2h level, the time component of the polarization tensor\nfor the vector transitions vanishes identically in the soft\nneutrino approximation. Vector current thereby is conserved.\nThe contraction of the neutral\naxial vector current with tensor interaction among the baryons\nleads to a non-vanishing contribution to the bremsstrahlung rate.\nThese rates are evaluated numerically for finite temperature pure\nneutron matter at and above the nuclear saturation density.\n\\end{abstract}\n\n\\pacs{PACS 97.60.Jd; 26.60.+c; 47.37.+q}\n%\\vspace*{\\baselineskip}\n%]\n\n\\newpage\n\n\\section{Introduction}\n\n\nNeutrino production in baryon encounters is among the\nfundamental processes by which compact stars lose their\nenergy. The reactions can be arranged, in general,\naccording to the number of participating baryons,\nas the phase space arguments play the central role in\ncontrolling their temperature and density\ndependence\\cite{CHIU_SALPETER,BAHCALL_WOLF,FLOWERS_ETAL,FRIMAN_MAXWELL,VOSKRESENSKY,PETHICK}.\nIn the case of neutrino pair bremsstrahlung,\nthe leading order process in the density virial expansion\nis the two-body reaction\n\\be\\label{2BODY_BR}\nB_1+B_2\\to B_1+B_2+\\nu_f+\\overline\\nu_f,\n\\ee\nwhere $B$ stands for a baryon, $\\nu_f$ ($\\bar\\nu_f$) for a neutrino\n(anti-neutrino) of flavor $f = e, \\mu, \\tau$.\nNote that the subleading order process (i.e. the one\nin the absence of the spectator)\nvanishes for identical particles, as an on-shell propagating\nparticle cannot radiate.\n\nThe matter in neutron stars\nis highly degenerate for temperatures typically below a MeV\nand the elementary excitations are\nquasiparticles with well-defined energy-momentum relation. Produced\nneutrinos are typically ``soft\" with energies of order of\ntemperature. In this limit the\nintermediate quasiparticle propagator diverges as $1/\\omega$ and\nthe amplitudes of the neutrino absorption, scattering, and\nemission turn out formally divergent as $1/\\omega^2$.\nThe infrared behaviour of the in-medium rates, however, is\ndominated by the neutrino phase space factors, rather than\nthe infrared divergence of the amplitudes and\nthe rates of the bremsstrahlung and\nits space-like analogues remain finite. At the same time, at\nlow temperatures, the contribution from the infrared region to\nthe rate of the bremsstrahlung is negligible. The combined\neffect of the cancellation of the infrared divergence and the vanishing\ncontribution from the low frequency region\nmakes the quasiparticle approximation to eq. (\\ref{2BODY_BR})\napplicable in cold neutron stars.\n\nDuring the first several tens of seconds after a supernova explosion\nand core collapse the temperature of the dense nuclear matter\nis of the order of several tens of MeV. The neutrino\nbremsstrahlung is then suppressed,\nbecause the formation length of\nthe neutrino radiation is of the same order of magnitude as\nthe mean free path of a baryon\\cite{RAFFELT_SECKEL,JANKA,RAFFELT,HANESTAD}.\nThe collective effects become important on the radiation\nscale (i.e. the role of the spectator in the\nreaction (\\ref{2BODY_BR}) is taken over by the medium)\nbecause the baryon undergoes multiple scattering during the\nradiation.\nThe underlying mechanism is the Landau-Pomeranchuk-Migdal (LPM) quenching\nof the radiation, first introduced in the context of QED\\cite{LP}.\nThe central role in the theory is played by the\nformation length of radiation $l_{\\rm f}$. If the mean-free-path of a\nbaryon is much larger that the formation length $l_{\\rm mfp}\\gg l_{\\rm f}$\nthen the radiation reduces to a\nsum of separate radiation events, each of which is well described by\nthe Bethe-Heitler spectrum. In the opposite limit\n$l_{\\rm mfp}\\ll l_{\\rm f}$ the individual scattering\nevents are unresolved and the\nradiation spectrum takes the Bethe-Heitler form for a single\nscattering event.\nIn the intermediate regime, when $l_{\\rm mfp}\\sim l_{\\rm f}$,\nthe radiation amplitudes for scattering off various centers\ninterfere destructively and the radiation is suppressed\n(Landau-Pomeranchuk-Migdal effect; for\na review see refs. \\cite{RAFFELT,KNOLL_VOSKRESENSKY}).\n\nThe rates of neutrino-nucleon processes are commonly expressed\nthrough phase space integrals over the contraction of the\nweak currents with the polarization function of the nuclear\nmedium. The polarization function\n(or structure function) of the supernova/neutron star matter\nhas been subject of many\nstudies\\cite{RAFFELT,IWAMOTO_PETHICK,SAWYER,HOROWITZ,HAENSEL,BURROWS,REDDY_ETAL}.\nThe modifications of reactions rates by the spatial correlations among (on-shell)\nquasiparticles have been studied\nwithin the Fermi-liquid theory\\cite{IWAMOTO_PETHICK}, the\none-boson exchange interaction theory\\cite{SAWYER}, the\nrelativistic random phase\napproximation\\cite{HOROWITZ}, the variational approach\\cite{HAENSEL},\nand combinations thereof\\cite{BURROWS,REDDY_ETAL}.\nThe spatial correlations tend to suppress\nreaction rates in general, although their impact on the\nsupernova physics is model\ndependent\\cite{IWAMOTO_PETHICK,SAWYER,HOROWITZ,HAENSEL,BURROWS,REDDY_ETAL}.\n\n\nThe common strategy of incorporating the LPM effect in the\nneutrino-nucleon interaction processes is to add\na quasiparticle damping in the intermediate state propagator\nby replacing $\\omega$ by $\\omega +i\\gamma$\\cite{RAFFELT_SECKEL,JANKA,RAFFELT}.\nIn the soft neutrino limit the vector current coupling does not\ncontribute by virtue of the vector current conservation (CVC)\nand the net contribution comes from\nthe axial-vector transitions via baryon spin-flip.\nThe above modification of the intermediate state\npropagator then leads to an ansatz for\nthe nucleon spin structure function:\n$S_{\\sigma}\\propto \\gamma_{\\sigma}/(\\omega^2 + \\gamma_{\\sigma}^2)$\n\\cite{RAFFELT_SECKEL,JANKA,RAFFELT}, where $\\gamma_{\\sigma}$\nis the nucleon spin-flip collision rate.\nThe ansatz generalizes the quasiparticle picture, in a semi-phenomenological\nmanner, by including the temporal correlations\namong the quasiparticles in the leading order in\nthe quasiparticle width. The microscopic justification of this\nphenomenology emerges from the various formulations\nof the finite temperature quantum filed theory, e. g.\nthe thermo-field dynamics\\cite{BRAATEN} or the closed\ndiagram formalism in the Schwinger-Keldysh\ntechnique\\cite{KNOLL_VOSKRESENSKY}. A microscopic computation\nis not straightforward, however. For example,\nthe polarization function of the medium can be computed at\none-loop, including the quasiparticle width to all orders\nin $\\gamma$, however {\\it a priori} the current conservation\nis not guaranteed at this level. The reason,\nin part, is that the ``more complicated'' higher order\nin loop expansion\ndiagrams contribute at the same order as the single\nloop\\cite{KNOLL_VOSKRESENSKY}.\n\nIn a previous paper we carried out a microscopic computation\nof the bremsstrahlung, including the LPM effect, at\nthe one-loop level in a formalism based on the\nquasiclassical Kadanoff-Baym transport equation\\cite{SD}.\nHere we extend this computation to two-loops and partially modify our\napproach to include the propagator and vertex renormalization on the\nsame footing and to including the tensor force explicitly.\nThe extension to two-loops is motivated by the following.\nThe long\nrange phenomena, driven by the weaker attractive part of the\nbaryon-baryon interaction, are sensitive to the resummation\nin the particle-hole ($ph$) channel. On the other hand,\nas well known, one should fully resum the particle-particle ($pp$)\nchannel to treat the hard core of the baryon-baryon interaction.\nTherefore, the $ph$ channel can be treated perturbatively by expanding\nin the number of particle-hole loops, while the $pp$ channel must\nbe treated non-perturbatively by a full resummation of the ladder diagrams.\nThus, the separation of the long range and short range phenomena\ndictates the manner in which the diagrammatic expansion is carried out.\nThe dressing of the single particle propagators occurs in both channels and\ncan be treated either explicitly, say, by considering higher order\nself-energies attached to a propagator, or, alternatively, by condensing\nit in the width of the propagator spectral function.\nAs a consequence of the separation of the scales,\nthe short-range correlations\ncan be condensed in the propagator width on the scales relevant\nfor the long-range phenomena. The imaginary\npart of a single loop in the $ph$ channel vanishes in the time-like\nregion of the phase space, which is relevant for the particle\nproduction. A finite result emerges when one dresses the propagators\nby either extending the resummation in the $ph$ channel to two and higher\nloops and/or by dressing the propagators in the $pp$ channel to all orders.\nIgnoring the latter resummation, i.e. using the quasiparticle\npropagators in the two-loop expansion, misses a number of short-range\ncollective effects, such as the LPM quenching of the radiation due to\nmultiple scattering. On the other hand, summing only the ladders in\nthe $pp$ channel does not recover the vector current conservation\nin the radiation process (in, at least, a transparent manner).\nTherefore a natural choice, motivated by the separation\nof the short and long range phenomena, is to truncate the\n$ph$ channel at two-loops and\nto resum the $pp$ channel to all orders. The situation is\nreminiscent of the parquet resummation scheme in the first\niteration, where in both channels the driving force is the bare\nbaryon-baryon interaction.\n\n\nEarly studies of the bremsstrahlung at the quasiparticle level\nmodelled the strong force using\nthe $T$-matrix interaction\\cite{FLOWERS_ETAL}, the free-space\none-boson exchange interaction\\cite{FRIMAN_MAXWELL}\nand their in-medium modifications\n\\cite{VOSKRESENSKY} supplemented with a\nhard core modelled in the spirit of\nthe Fermi-liquid theory. The explicit use\nof the tensor interaction\nturned out to be crucial as there are\nsignificant cancellations among different\ndiagrams, and the surviving contribution\nis due to a non-trivial contraction\nbetween the operator structures of the weak and strong interactions\n(tensor force)~\\cite{FRIMAN_MAXWELL}.\nThis motivates our ansatz for the driving force in the\nparticle-hole ($ph$) channel of nuclear interaction,\nwhich includes explicitly the tensor force contribution.\nWe do not attempt, in the present work, to go beyond the\none-pion exchange approximation\nfor several reasons, one being that the non-perturbative\ntreatment of the interaction does not change the spin, isospin,\nand tensor operator structure of the interaction,\nand important cancellations\nin the radiation matrix elements will be preserved\nin a more advanced treatment.\nWe also want to be able to isolate the finite width effects\nin our comparisons to the earlier work done in the one-pion\nexchange approximation\\cite{FRIMAN_MAXWELL,RAFFELT}.\nThe situation is different in the particle-particle ($pp$)\nchannel, where the short-range correlations have to be treated in\na non-perturbative manner by summing up the ladder diagrams to\nall orders. We do this in the finite-temperature Brueckner\ntheory.\n\n\nThe paper is organized as follows. In Section 2, starting from\nthe Kadanoff-Baym formalism, we derive a single-time\ntransport equation for (anti)-neutrinos with\ncollision integrals driven by (anti)-neutrino coupling to\nbaryons via the polarization tensor of the medium. The polarization\ntensor is computed in the 2p-2h approximation in Section~3.\nThe summation of the ladder diagrams in the $pp$ channel\nwithin the finite temperature Brueckner theory is\ndescribed in Section 4.\nSection~5 evaluates the phase space integrals and\n neutrino bremsstrahlung emissivities.\nThe numerical results are presented in Section~6.\nSection 7 summarizes our main results.\n\n\n\\section{Neutrino Transport Formalism}\n\n\\subsection{Neutrino propagators}\n\nThe theory of neutrino radiation can be conveniently formulated in terms\nof the real-time quantum neutrino transport.\nLet us start by defining the various time-ordered\nGreens functions of massless Dirac neutrinos.\nThese can be written in the generic matrix form\n \\be\\label{MATRIX_GF}\n i \\underline{S}_{12} =i\\left( \\begin{array}{cc}\n S^{c}_{12} & S^{<}_{12} \\\\\n S^{>}_{12} & S^{a}_{12}\n \\end{array} \\right) =\n \\left( \\begin{array}{cc}\n\\left <T\\psi(x_1) \\bar \\psi(x_2)\\right > & -\\left <\\bar\\psi(x_2)\\psi(x_1)\\right > \\\\\n\\left <\\psi(x_1)\\bar\\psi(x_2)\\right > & \\left <\\tilde T\\psi(x_1)\\bar\\psi(x_2)\\right >\n \\end{array} \\right)= i\\left( \\begin{array}{cc}\n S^{--}_{12} & S^{-+}_{12} \\\\\n S^{+-}_{12} & S^{++}_{12}\n \\end{array} \\right),\n \\ee\nwhere $\\psi(x)$ are the neutrino field operators, $\\bar\\psi = \\gamma^0\\psi^*$,\n$T$ is the chronological time ordering operator, and $\\tilde T$\nis the anti-chronological time ordering operator; the indexes\n$1 = x_1$, $2=x_2$,...\ncollectively denote the space-time and discrete quantum numbers.\nThe neutrino matrix propagator is further assumed to obey\nthe Dyson equation,\n\\bea\\label{DYSON1}\n\\underline{S}(x_1,x_2) & = &\\underline{S}_0(x_1,x_2)\n + \\underline{S}_0(x_1,x_3)\n \\underline{\\Omega}(x_3,x_2) \\underline{S}(x_2,x_1) \\nonumber \\\\\n &=&\\underline{S}_0(x_1,x_2) + \\underline{S}(x_1,x_3)\n \\underline{\\Omega}(x_3,x_2) \\underline{S}_0(x_2,x_1),\n\\eea\nwhere $S_0(x_1,x_2)$ is the free neutrino\npropagator and $S_0^{-1}(x_1,x_2) S_0(x_1,x_2) = \\sigma_z \\delta(x_1-x_2)$,\n$\\sigma_z$ is the third component of the Pauli matrix,\n$\\underline\\Omega$ is the neutrino proper self-energy and\nwe assume integration (summation) over the repeated variables.\nThe self-energy $\\underline\\Omega$ is a $2\\times 2$ matrix with elements\ndefined on the contour in terms of the Dyson equation.\nThe quasiclassical neutrino transport equation follows from\nthe Dyson equation in the `conjugate subtracted' form\\cite{KADANOFF_BAYM,MALFLIET}:\n \\bea\n i\\underline{S}(x_1,x_2) \\not\\!\\partial_{x_2}\n -i \\not\\!\\partial_{x_1}\n \\underline{S}(x_1,x_2) =\n \\underline{S}(x_1,x_3)\n \\underline{\\Omega}(x_3,x_2)\n \\underline{ \\sigma_{z} }\n -\\underline{ \\sigma_{z} }\n \\underline{\\Omega}(x_1,x_3)\n \\underline{S}(x_3,x_2) ,\n \\label{DYSON}\n \\eea\nNote that the initial correlations are neglected in eq. (\\ref{DYSON}).\nThe set of the four Green's functions above can\nbe supplemented by the retarded and advanced Green's functions\nwhich are defined as\n\\bea\ni S^R_{12}=\\theta(t_1-t_2)\n \\langle \\left\\{ \\psi(x_1),\n \\overline{\\psi}(x_2) \\right\\}\\rangle ,\\quad\n i S^A_{12}=-\\theta(t_2-t_1)\n \\langle \\left\\{ \\psi(x_1),\n \\overline{\\psi}(x_2) \\right\\} \\rangle ,\n\\eea\nwhere $\\theta(x)$ is the Heaviside step function on the\nreal-time contour defined as $d \\theta(x)/dx = \\sigma_z \\delta(x)$.\nThe retarded and advanced Green's functions obey integral\nequations in the quasiclassical limit.\nThe relations between the six Green's functions are\nlisted in the Appendix A. The transport equation\nfor the off-diagonal elements of the matrix\nGreen's function reads\n \\bea\n&& \\left[ \\not\\!\\partial_{x_3} -\\Real\\, \\Omega^R(x_1,x_3),S^{>,<}(x_3,x_2)\\right]\n -\\left[\\Real\\, S^R(x_1,x_3),\\Omega^{>,<}(x_3,x_2)\\right]\\nonumber \\\\\n &&\\hspace{3cm} = \\frac{1}{2}\\left\\{S^{>,<}(x_1,x_3),\\Omega^{>,<}(x_3,x_2)\\right\\}\n +\\frac{1}{2}\\left\\{\\Omega^{>,<}(x_1,x_3),S^{>,<}(x_3,x_2)\\right\\},\n\\label{DYSON_OFF}\n\\eea\nwhere $[\\, ,\\,]$ and $\\{\\, ,\\, \\}$ stand for commutator and anti-commutator,\nrespectively.\nIn arriving at eq. (\\ref{DYSON_OFF}) we assumed the existence of the Lehmann\nrepresentation for the neutrino propagators; as a results we have\n$\\Real~ S^R = \\Real~ S^A\\equiv \\Real~ S$ and $\\Real~ \\Omega^R = \\Real~ \\Omega^A\\equiv \\Real~ \\Omega$.\n\nFor the present purposes the neutrino dynamics can\nbe treated semiclassically, by separating the slowly varying\ncenter-of-mass coordinates from the rapidly varying\nrelative coordinates. Carrying out a Fourier transform with\nrespect to the relative coordinates and keeping the first-order\ngradients in the slow variable we arrive at a quasiclassical neutrino\ntransport equation\n\\bea\n && i\\left\\{\\Real S^{-1}(q,x),S^{>,<}(q,x)\\right\\}_{P.B.}\n +i\\left\\{\\Real\\, S(q,x),\\Omega^{>,<}(q,x)\\right\\}_{P.B.} \\nonumber\\\\\n &&\\hspace{3cm} = S^{>,<}(q,x)\\Omega^{>,<}(q,x)\n +\\Omega^{>,<}(q,x)S^{>,<}(q,x),\n\\label{TRANS_EQ}\n\\eea\nwhere $q\\equiv (\\bq , q_0)$\nand $x$ are the neutrino four momentum and the center-of-mass\nspace-time coordinate, respectively,\n$\\{\\dots\\}_{P.B.}$ is the four-dimensional Poisson bracket.\nThe l.h.s. of eq. (\\ref{TRANS_EQ}) is the precursor of the drift term\nof the Boltzmann equation. The second Poisson bracket, however, does\nnot fit in the Boltzmann description and can be eliminated by an expansion\nof the neutrino propagator in the leading (quasi-particle) and next-to-leading\norder terms in the small neutrino damping: \n$S^{>,<}(q,x)=S_0^{>,<}(q,x)+S_{1}^{>,<}(q,x)$.\nA direct evaluation of the Poisson brackets decouples\n the l.h.s. of transport\nequation (\\ref{TRANS_EQ}) to the leading order with respect to the\nsmall damping of neutrino/anti-neutrino states ($\\Img\\Omega(q,x)\n/\\Real\\Omega(q,x) \\ll 1 $). The quasiparticle part of\nthe transport equation\n\\bea\\label{QPA_TRANS}\n i\\left\\{\\Real S^{-1}(q,x),S_0^{>,<}(q,x)\\right\\}_{P.B.}\n =S^{>,<}(q,x)\\Omega^{>,<}(q,x)+\\Omega^{>,<}(q,x)S^{>,<}(q,x)\n\\eea\ndescribes the evolution of the distribution\nfunction (Wigner function) of on-shell\nexcitations with the l.h.s. corresponding to the\ndrift term of the Boltzmann equation. The r.h.s. corresponds to\nthe collision integral with the self-energies $\\Omega^{>,<}(q,x)$\nhaving the meaning of the collision rates. The advantage of this form\nof the (generalized) collision integral is that it admits systematic\napproximations in terms of the Feynman perturbation theory. The remainder\npart of the transport equation\n\\bea\n i\\left\\{\\Real S^{-1}(q,x),S_{1}^{>,<}(q,x)\\right\\}_{P.B.}\n +i\\left\\{\\Real\\, S(q,x),\\Omega^{>,<}(q,x)\\right\\}_{P.B.} = 0,\n\\eea\nrelates the finite width part of the\nneutrino propagator to the self-energies in a form of a local\nfunctional which depends on the local (anti-)neutrino particle distribution\nfunction and their coupling to the matter.\n\n\\subsection{On-shell neutrino approximation}\n\nThe on-mass-shell neutrino propagator is related to the single-time\ndistribution functions (Wigner functions) of neutrinos and anti-neutrinos,\n$f_{\\nu}(q,x)$ and $f_{\\bar\\nu}(q,x)$, via the ansatz\n\\bea\nS_0^<(q,x)\n&=& \\frac{i\\pi\\sla q}{\\omnu(\\bq)}\n \\Big[ \\delta\\left(q_0-\\omnu(\\bq)\\right)f_{\\nu}(q, x)\n-\\delta\\left(q_0+\\omnu(\\bq)\\right) \\left(1-f_{\\bar \\nu}\n(-q,x)\\right) \\Big],\n\\eea\nwhere\n$\\omnu(\\bq)=c\\vert q\\vert$ is the on-mass-shell\nneutrino/anti-neutrino energy. Note that the ansatz\nincludes {\\it simultaneously} the neutrino particle states and\nanti-neutrino hole states, which propagate in, say, positive time\ndirection. Similarly, the on-shell propagator\n\\bea\nS_0^>(q,x)\n&=& - \\frac{i\\pi\\sla q}{\\omnu(\\bq)}\n \\Big[ \\delta\\left(q_0-\\omnu(\\bq)\\right)\n \\left(1-f_{\\nu}(q,x)\\right)\n-\\delta\\left(q_0+\\omnu(\\bq)\\right)f_{\\bar\\nu} (-q,x)\\Big],\n\\eea\ncorresponds to the states propagating in the reversed time\ndirection and, hence,\nincludes the anti-neutrino particle states and\nneutrino hole states.\n\nTo recover the Boltzmann drift term in the on-shell limit,\nwe take the trace on both\nsides of the transport equation (\\ref{TRANS_EQ})\nand integrate over the (anti-)neutrino energy $q_0$.\nThe first term on l.h.s. of eq. (\\ref{TRANS_EQ}) reduces then to the\ndrift term of the Boltzmann equation.\nThe single time Boltzmann equation (hereafter BE)\nfor neutrinos is obtained after integrating over the\npositive energy range:\n\\bea\\label{BE_NU}\n& & \\left[\\partial_t + \\vec \\partial_q\\,\\omnu (\\bq) \\vec\\partial_x\n\\right] f_{\\nu}(\\bq,x) =\n\\int_{0}^\\infty \\frac{dq_0}{2\\pi} {\\rm Tr} \\left[\\Omega^<(q,x)S_0^>(q,x)\n-\\Omega^>(q,x)S_0^<(q,x)\\right];\n\\eea\na similar equation follows for the anti-neutrinos if one integrates\nin eq. (\\ref{TRANS_EQ})\nover the range $[-\\infty , 0]$.\n\n%\\begin{figure}\n\\begin{center}\n\\includegraphics[height=.8in,width=3.2in]{fig1.eps}\n%\\mbox{\\epsfig{figure=fig1.eps,height=1.in,width=4in,angle=0}}\n\\end{center}\n%\\caption[]\n{\\footnotesize{Fig 1: The neutrino Dyson equation in terms of\nthe Feynman diagrams. The dashed curve corresponds to the $S$-propagator,\nwhich includes the neutrinos and anti-neutrino holes moving in the\nsame time direction; (reverting the time-direction one finds the\nDyson equation for anti-neutrinos and neutrino holes).\nThe shaded loop is the baryon\npolarization tensor. The wavy lines correspond to the $W^{\\pm},Z^0$ boson\npropagators.}}\n\\label{fig1}\n%\\end{figure}\n\n\n\\no\nThe different energy integration limits select from the r.h.s. of\nthe transport equations the processes leading to\nmodifications of the distribution functions of (anti-)neutrinos.\nThe separation of the transport equation into neutrino and anti-neutrino\nparts is arbitrary, however is motivated by the observation\nthat the fundamental quantities of neutrino radiative transport, as the\nenergy densities or neutrino fluxes, can be obtained by taking the\nappropriate moments of BEs. These quantities are not symmetric with\nrespect to the neutrino/anti-neutrino populations in general. E.g.\nthe neutrino emissivities (energy output per unit time per unit volume)\nfor processes based on $\\beta$-decay reactions are given by the\nzeroth order moment of the anti-neutrino BE, and it is sufficient\nto consider only the BE for anti-neutrinos.\nIn the case of the bremsstrahlung\nwe have to eventually sum these equations; still the relation of the\ntransport self-energies to particular processes becomes transparent\nif one treats the transport equations separately.\n\n\n\\subsection{Collision integrals}\n\nWe adopt the standard model for the description of\nthe neutrino-baryon interactions\nand write the neutral current interaction Hamiltonian in the from:\n\\bea\\label{HAM}\nH_{\\rm int} = \\frac{G}{2\\sqrt{2}} \\Gamma^H \\, \\Gamma^L, \\quad\n\\Gamma^H =\\overline \\phi \\gamma_{\\mu}\n(c_V - c_A\\gamma_5) \\phi ,\\quad \\Gamma^L\n= \\overline\\psi \\gamma^{\\mu}(1-\\gamma_5)\n\\psi,\n\\eea\nwhere $G$ is the weak coupling constant, $\\psi$ and $\\phi$ are the\nneutrino and baryon field operators, $c_V$ and $c_A$ are the\ndimensionless weak neutral-current vector and axial vector\ncoupling constants.\n\nThe diagrams contributing to the neutrino emission rates\ncan be arranged in a perturbation expansion with respect\nto the weak interaction. The lowest order in the weak interaction\nFeynman diagrams which contribute to scattering,\nemission, and absorption processes are shown in the Fig. 1.\nThe corresponding transport self-energies are read-off from\nthe diagram\n\\bea\n-i\\Omega^{>,<}(q_1,x) &=& \\int \\frac{d^4 q}{(2\\pi)^4}\n\\frac{d^4 q_2}{(2\\pi)^4}(2\\pi)^4 \\delta^4(q_1 - q_2 - q)\ni\\Gamma_{L\\, q}^{\\mu}\\, iS_0^{<}(q_2,x) i\\Gamma_{L\\, q}^{\\dagger\\, \\lambda}\ni \\Pi^{>,<}_{\\mu\\lambda}(q,x),\n\\eea\nwhere $\\Pi^{>,<}_{\\mu\\lambda}(q)$ are the off-diagonal elements\nof the matrix of the baryon polarization tensor,\n$\\Gamma_{L\\, q}^{\\mu}$ is the weak interaction vertex.\nThe contact interaction (\\ref{HAM}) can be used\nfor the energy-momentum\ntransfers much smaller than the vector boson mass, $q\\ll m_Z, m_W$.\nLet us first concentrate on the BE for neutrinos. Define the loss and\ngain terms of the collision integral as:\n\\bea\nI_{\\nu}^{>,<}(\\bq,x)=\\int_{0}^\\infty \\frac{dq_0}{2\\pi} {\\rm Tr}\n\\left[\\Omega^{>,<}(q,x)S_0^{>,<}(q,x)\\right].\n\\eea\nSubstituting the self-energies and the propagators in the collision\nintegrals we find for, e.g., the gain part:\n\\bea\\label{GAIN}\nI_{\\nu}^{\\rm <}(\\bq_1,x)&=& -i\\int_{0}^\\infty \\frac{dq_{10}}{2\\pi}\n {\\rm Tr}\n\\Biggl\\{ \\int_{-\\infty}^{\\infty} \\frac{d^4 q}{(2\\pi)^4}\n\\frac{d^4 q_2}{(2\\pi)^4}(2\\pi)^4\\delta^4(q_1 - q_2 - q)\n\\Gamma^{\\mu}_L\\frac{\\pi\\sla q_2}{\\omnu(\\bq_2)}\n\\Big[\\delta\\left(q_{02}-\\omnu( \\bq_2)\\right)f_{\\nu}(q_2, x)\\nonumber\\\\\n&-&\\delta\\left(q_{02}+\\omnu(\\bq_2)\\right) \\left(1-f_{\\bar \\nu}\n(-q_2,x)\\right) \\Big]\\Gamma^{\\dagger\\,\\lambda}_L\n\\frac{\\pi\\sla q_1}{\\omnu(\\bq_1)}\n\\delta\\left(q_{10}-\\omnu(\\bq_1)\\right)\\left(1-f_{\\nu}(q_1,x)\\right)\n\\Pi_{\\mu\\lambda}^{>}(q,x)\\Biggr\\}. \\nonumber \\\\\n\\eea\nThe loss term is obtained by replacing in eq. (\\ref{GAIN}) the\nneutrino Wigner functions by the neutrino-hole functions\n$f_{\\nu}(q, x) \\to (1-f_{\\nu}(q, x))$ and the anti-neutrino-hole\nWigner functions by the anti-neutrino functions\n$ \\left(1-f_{\\bar \\nu}(-q,x)\\right) \\to f_{\\bar \\nu}(q,x)$.\nThe terms proportional $(1-f_{\\nu}) f_{\\nu}$ and\n$(1- f_{\\nu})(1-f_{\\anu}) $ in the gain part of\nthe collision integral, $I_{\\nu}^<(\\bq)$, correspond to the\nneutrino scattering-in and emission contributions, respectively.\nThe terms proportional $f_{\\nu} (1-f_{\\nu})$ and $f_{\\nu}f_{\\anu}$\nin the loss part of the collision integral, $I_{\\nu}^>(\\bq)$, are the\nneutrino scattering-out and absorption contributions.\n\nThe loss and gain collision integrals for the anti-neutrinos can be defined\nin a manner, similar to the case of neutrinos, with the energy integration\nspanning the negative energy range\n\\bea\nI_{\\anu}^{>,<}(\\bq,x)=\\int^{0}_{-\\infty} \\frac{dq_0}{2\\pi} {\\rm Tr}\n\\left[\\Omega^{>,<}(q,x)S_0^{>,<}(q,x)\\right].\n\\eea\nUsing the above expressions for the\nself-energy and the propagators, we find, e.g.,\nfor the gain term:\n\\bea\\label{GAIN2}\nI_{\\anu}^{<}(\\bq_1,x)&=& i\\int^{0}_{-\\infty}\n\\frac{dq_{10}}{2\\pi} {\\rm Tr}\\Biggl\\{ \\int_{-\\infty}^{\\infty}\n\\frac{d^4 q}{(2\\pi)^4}\\frac{d^4 q_2}{(2\\pi)^4}(2\\pi)^4\\delta^4(q_1- q_2- q)\n\\Gamma^{\\mu}_L\\frac{\\pi\\sla q_2}{\\omnu(\\bq_2)}\\Big[\\delta\\left(q_{02}\n-\\omnu(\\bq_2)\\right)f_{\\nu}(q_2, x)\n\\nonumber \\\\\n&-&\\delta\\left(q_{02}+\\omnu(\\bq_2)\\right)\\left(1-f_{\\bar \\nu}(-q_2,x)\\right)\n\\Big]\\,\\Gamma^{\\dagger\\lambda}_L\\frac{\\pi\\sla q_1}{\\omnu(\\bq_1)}\n\\delta\\left(q_{10}+\\omnu(\\bq_1)\\right)f_{\\anu}(-q_1,x)\n\\Pi^{>}_{\\mu\\lambda}(q,x)\\Biggr\\}.\n\\eea\nThe loss term is obtained by making replacements in eq. (\\ref{GAIN2})\nanalogous to those applied to eq. (\\ref{GAIN}).\nThe terms proportional $ f_{\\nu}f_{\\anu}$ and\n$f_{\\anu}(1-f_{\\anu}) $ in the gain part of\nthe collision integral, $I_{\\anu}^<(\\bq)$, then correspond to the\nneutrino absorption and scattering-out contributions.\nThe terms proportional $(1-f_{\\anu}) (1-f_{\\nu})$ and\n$(1-f_{\\anu})f_{\\anu}$ in the loss part of the collision integral,\n$I_{\\anu}^>(\\bq)$, are the neutrino emission and scattering-in contributions,\nrespectively. Note that, when the neutrinos are in a thermal\nequilibrium with the baryons, the collision integrals for the\nscattering-in/scattering-out and for the absorption/emission cancel.\nUnder the conditions of detailed balance the (anti-)neutrino distribution\nfunction reduces to the Fermi-Dirac form.\n\n\\subsection{Bremsstrahlung emissivity}\n\nThe neutrino-pair emissivity (the power of the\nenergy radiated per volume unit)\nis obtained by multiplying the left-hand-sides of the\nneutrino and anti-neutrino\nby their energies, respectively, summing the BEs, and integrating over a\nphase space element:\n\\bea\n\\epsilon_{\\nu\\bar\\nu}&=&\\frac{d}{dt}\\int\\!\\frac{d^3q}{(2\\pi)^3}\n\\left[f_{\\nu}(\\bq) +f_{\\bar\\nu}(\\bq)\\right]\\omnu(\\bq)=\n\\int\\!\\frac{d^3q}{(2\\pi)^3}\\left[I_{\\nu}^{<, {\\rm em}}(\\bq)\n-I_{\\anu}^{>, {\\rm em}}(\\bq)\\right]\\omnu(\\bq),\n\\eea\nwhere in the collision integrals we kept only the terms\nwhich correspond to the processes with the\nneutrino and anti-neutrino in the final state (bremsstrahlung)\n\\bea\n&&\\int\\!\\frac{d^3q_1}{(2\\pi)^3}I_{\\nu}^{>,<, {\\rm em}}(\\bq_1)\\omnu(\\bq_1)\n= i \\int\\!\\frac{d^3q_1}{(2\\pi)^32 \\omnu(\\bq_1)}\n\\frac{d^3 q_2}{(2\\pi)^3 2\\omnu(\\bq_2)}\n\\frac{d^4 q}{(2\\pi)^4}(2\\pi)^4 \\delta^3(\\bq_1+\\bq_2-\\bq) \\nonumber\\\\\n\\label{COLL_INT1}\n&&\\hspace{1cm}\n\\delta(\\omnu(\\bq_1)+\\omnu(\\bq_2)-q_{0})\\omnu(\\bq_1)\n\\left[1-f_{\\nu}(\\omnu(\\bq_1))\\right]\n\\left[1-f_{\\anu}(\\omnu(\\bq_2))\\right]\\Lambda^{\\mu\\lambda}(q_1,q_2)\n\\Pi_{\\mu\\lambda}^{>,<}(q,x),\n\\label{COLL_INT2}\n\\eea\nand $\\Lambda^{\\mu\\lambda} = {\\rm Tr}\\left[\\gamma^{\\mu}\n(1 - \\gamma^5)\\sla q_1\\gamma^{\\nu}(1-\\gamma^5)\\sla q_2\\right]$.\nThe collision integrals for neutrinos and anti-neutrinos can be\ncombined if one uses the identities $\\Pi_{\\mu\\lambda}^{<}(q)\n=\\Pi_{\\lambda\\mu}^{>}(-q) = 2i g_B(q_0) {\\Img}\\,\n\\Pi_{\\mu\\lambda}^R(q)$; here $g_B(q_0)$ is the Bose distribution\nfunction and $\\Pi^R_{\\mu\\lambda}(q)$ is the retarded component\nof the polarization tensor. With these modifications\nthe neutrino-pair bremsstrahlung emissivity becomes\n\\bea\\label{EMISSIVITY}\n\\epsilon_{\\nu\\anu}&=& - 2\\left( \\frac{G}{2\\sqrt{2}}\\right)^2\n\\sum_f\\int\\!\\frac{d^3q_2}{(2\\pi)^32 \\omnu(\\bq_2)}\n\\int\\!\\frac{d^3 q_1}{(2\\pi)^3 2\\omnu(\\bq_1)}\n\\int\\!\n\\frac{d^4 q}{(2\\pi)^4}\n\\nonumber\\\\\n&&\\hspace{1cm}\n(2\\pi)^4 \\delta^3(\\bq_1 + \\bq_2 - \\bq)\n\\delta(\\omnu(\\bq_1)+\\omnu(\\bq_2)-q_{0})\\, \\left[\\omnu(\\bq_1)+\\omnu(\\bq_2)\\right]\n\\nonumber\\\\\n&&\\hspace{2cm}\n g_B(q_0)\\left[1-f_{\\nu}(\\omnu(\\bq_1))\\right]\n\\left[1-f_{\\anu}(\\omnu(\\bq_2))\\right]\n \\Lambda^{\\mu\\lambda}(q_1,q_2){\\Img}\\,\\Pi_{\\mu\\lambda}^R(q).\n\\eea\nWe note that eq. (\\ref{EMISSIVITY}) is applicable for arbitrary\ndeviation from equilibrium, as the equilibrium properties of the\nneutrinos and baryons have not been used in the derivation (e.g.\nthe temperature of the bath drops out if one assumes an\ninitially uncorrelated state). Therefore eq.\n(\\ref{EMISSIVITY}) is applicable beyond the boundaries\nof the linear response theory or the $S$-matrix theory which explicitly\nresort to the equilibrium properties of the system as a reference\npoint.\n\n\\section{Two-loop Baryon polarization function}\n\nIn this section we start the implementation\nof the perturbative scheme motivated in the\nintroduction. Our strategy is the separation\nof the long and short range phenomena in the\n$ph$ and $pp$ channels. Here we carry out the first step\nby expanding the particle-hole channel and truncating\nit at two loops. This fixes the amount of the long-range\ncorrelations in the theory. The short-range effects are\ncondensed in the width of the particle-hole propagators,\nwhich is specified in a later section by summing the ladder diagrams.\n\n\n\\subsection{Baryon propagators}\n\nAlthough we shall treat the baryon sector in the equilibrium limit,\nit is still useful to define the six Green's functions of the\nnon-equilibrium theory, as in the case of neutrinos.\nThe matrix Green's function of non-relativistic baryons\n is defined in the standard way\n\\be\\label{MATRIX_GFB}\n i\\underline{G}_{12} =i \\left( \\begin{array}{cc}\n G^{c}_{12} & G^{<}_{12} \\\\\n G^{>}_{12} & G^{a}_{12}\n \\end{array} \\right) =\n \\left( \\begin{array}{cc}\n\\left <T\\phi(x_1)\\phi^{\\dagger}(x_2)\\right > & -\\left <\\phi^{\\dagger}(x_2)\\phi(x_1)\\right > \\\\\n\\left <\\phi(x_1)\\phi^{\\dagger}(x_2)\\right > &\n\\left <\\tilde T\\phi(x_1)\\phi^{\\dagger}(x_2)\\right >\n \\end{array} \\right)=i \\left( \\begin{array}{cc}\n G^{--}_{12} & G^{-+}_{12} \\\\\n G^{+-}_{12} & G^{++}_{12}\n \\end{array} \\right),\n\\ee\nwhere $\\phi(x)$ are the baryon field operators. In terms of\nthese operators the retarded and advanced function are defined as\n\\bea\ni G^R_{12}=\\theta(t_1-t_2)\n \\langle \\left\\{ \\phi(x_1),\n \\phi^{\\dagger} (x_2) \\right\\}\\rangle ,\\quad\ni G^A_{12}=-\\theta(t_2-t_1)\n \\langle \\left\\{ \\phi(x_1),\n {\\phi}^{\\dagger} (x_2) \\right\\} \\rangle .\n\\eea\nThe structure of the proper self-energy matrix\n$\\underline{\\Sigma}$ is identical to eq.\n(\\ref{MATRIX_GFB}) and its elements\nare defined via the Dyson equation for baryons:\n\\bea\n\\underline{G}(x_1,x_2) & = &\\underline{G}_{0}(x_1,x_2)\n +\\underline{G}_{0}(x_1,x_3)\n \\underline{\\Sigma}(x_3,x_2) \\underline{G}(x_2,x_1) \\nonumber \\\\\n &=&\\underline{G}_{0}(x_1,x_2) + \\underline{G}(x_1,x_3)\n \\underline{\\Sigma}(x_3,x_2) \\underline{G}_{0}(x_2,x_1).\n\\eea\nIn a complete analogy to the neutrino sector, we approximate\nthe Green's functions by their quasiclassical counterparts\nby defining center-of-mass and relative space-time coordinates\nand Fourier transform with respect to the\nrelative space-time coordinates. In the equilibrium limit\nthe dependence of the quasiclassical Green's functions\non their center-of-mass space-time coordinate\nis trivial and can be dropped.\nThe distribution function of the baryons is related to the\noff-diagonal elements of the matrix Green function by\nthe exact relations\n\\bea\\label{ANSATZ}\n-iG^<(p) = a(p) f_N(p), \\quad iG^>(p) = a(p)[1- f_N(p)],\n\\eea\nwhere $a(p)=i[ G^R(p)-G^A(p)] = i[ G^>(p)-G^<(p)] $\nis the baryon spectral function,\n$f_N(p)=[{\\rm exp}(\\beta(\\omega-\\mu))+1]^{-1}$\nis the Fermi-Dirac distribution function, $\\beta = T^{-1}$ is the\ninverse temperature and $\\mu$ is the chemical potential\n(relations (\\ref{ANSATZ}) will be refereed\nto as the Kadanoff-Baym ansatz in the following). The\nquasiparticle energy, $\\varepsilon_p = p^2/2m\n+\\Real\\Sigma^R(p)\\vert_{\\omega=\\ep_p}$ follows from the\nsolution of the Dyson equation $G^R(p)=\\left[\\omega-\\varepsilon_p\n+i\\Img \\Sigma^R(p) \\right]^{-1}$.\nWhen damping of quasiparticle states\nis small,\n$\\Img \\Sigma^R(p) \\ll \\Real \\Sigma^R(p)$, the propagators can be\ndecomposed into quasiparticle and background contributions, e.g.,\n\\bea\n\\label{exp}\nG^<(p) &\\simeq& 2\\pi i z(\\bp)f_N(\\bp)\n\\delta(\\omega -\\ep_p) -\\Sigma^<(p)\n\\, \\frac{{\\cal P}}{(\\omega -\\ep_p)^2}+{\\cal O}(\\gamma^2).\n\\eea\nNote that the self-energy appearing in the\ndenominator of the second term of eq.~(\\ref{exp})\nvia the dispersion relation is restricted, to the\nleading order in damping, to the mass-shell.\nIn equilibrium,\n\\bea\ni\\Sigma^<(p) = \\gamma(p)f_N(p), \\quad -i\\Sigma^>(p) = \\gamma(p)[1-f_N(p)],\n\\eea\nwhere $\\gamma(p) = -2\\Img \\Sigma(p)$ is the width of the \nbaryon spectral function.\nThe wave-function renormalization, $z(\\bp)$, in the same approximation is\n\\bea\n\\label{Z} z(\\bp)\n=1-\\int\\!\\frac{d\\omega'}{2\\pi}\n\\Img \\Sigma(\\omega',\\bp)\\,\n\\frac{\\cal P}{(\\omega '-\\omega)^2}\\Big|_{\\omega=\\ep_p},\n\\eea\nwhere we used the integro-differential form of the Kramers-Kronig relation:\n\\bea\n\\frac{d}{d \\omega}{\\rm \\Real}\\, \\Sigma(\\omega,\\bp)&=&\n\\int\\!\\frac{d\\omega'}{\\pi} {\\rm \\Img}\\, \\Sigma(\\omega',\\bp)\n\\frac{{\\cal P}}{(\\omega-\\omega')^2}.\n\\eea\nOn inserting the expression of the wave-function renormalization\n(\\ref{Z}) in the expansion (\\ref{exp}) we find the final form\nof the propagator\n\\be\\label{exp1}\nG^<(p) \\simeq 2\\pi i f_N(\\bp) -2\\pi i \\int \\frac{d\\omega'}{2\\pi}\n\\, \\gamma(p')\\frac{{\\cal P}}{(\\omega' -\\ep_p)^2}\n\\left[\\delta(\\omega-\\ep_p)-\\delta(\\omega-\\omega')\\right]\nf_N(\\omega).\n\\ee\nNote that this form of propagator renders the strict\nfulfillment of the spectral sum rule,\n\\be \\label{sum_rule}\n\\int\\!\\frac{d\\omega}{2\\pi}~a(p) = 1,\n\\ee\nat any order in the expansion with respect to the damping.\n\nUsing the linear relations among the propagators, listed\nin Appendix A, we find for the causal propagator:\n\\bea\nG^{--}(p)\n&=& \\frac{\\omega-(\\epsilon_p+\\Real \\Sigma(p)-\\mu)}\n{\\left[\\omega-(\\epsilon_p+\\Real \\Sigma(p)-\\mu)\\right]^2+\n\\left[\\Img\\Sigma(p)\\right]^2}\\nonumber\\\\\n&-&\\frac{i\\Img\\Sigma(p)}\n{\\left[\\omega-(\\epsilon_p+\\Real \\Sigma(p)-\\mu)\\right]^2\n+ \\left[\\Img\\Sigma(p)\\right]^2}\n{\\rm tanh}\\left(\\frac{\\beta\\omega}{2}\\right),\n\\eea\nwhere ${\\rm tanh}\\left({\\omega}/{2}\\right)\\equiv [1-2f_N(\\omega)]$\nand $\\epsilon_p = p^2/2m$.\nAs the evaluation of the baryon polarization function requires\nthe causal and acausal Green's functions of the type $G^{--}(q+p)$,\nwe note here that, the denominator of such a function\ncan be expanded in the limit $vq\\ll\\omega$, where $v\\ll 1$ is the\ncharacteristic velocity of a baryon,\n\\be\\label{DENOM_EXP}\n(\\omega +\\varepsilon_p)-\\varepsilon_{\\vec p+\\vec q}\n\\simeq\n\\omega-\\bp\\cdot\\bq/m\n-q\\frac{\\partial}{\\partial p}~ \\Real\\Sigma(p)\n-\\epsilon_{q} \\simeq\\omega,\n\\ee\nto the leading order. The approximation (\\ref{DENOM_EXP}) will\nbe referred in the following as the {\\it soft-neutrino \napproximation}.\nWe also employed the non-relativistic limit for baryons.\nIf we use the ansatz $\\gamma(-\\omega)=\\gamma(\\omega)$,\nwhich is exact in the phenomenological Fermi-liquid theory and\nwill be verified in our microscopic calculations, then\n\\bea\nG^{--}(\\pm\\omega,\\bp) &=& \\pm\\frac{\\omega}{\\omega^2+\\gamma(\\omega,\\bp)^2/4}\n\\mp i\\frac{\\gamma(\\omega,\\bp)/2}{\\omega^2+\\gamma(\\omega,\\bp)^2/4}\n~{\\rm tanh}\\left(\\frac{\\beta\\omega}{2}\\right), \\\\\n-G^{++}(\\pm\\omega,\\bp) &=& \\pm\\frac{\\omega}{\\omega^2+\\gamma(\\omega,\\bp)^2/4}\n\\pm i\\frac{\\gamma(\\omega,\\bp)/2}{\\omega^2+\\gamma(\\omega,\\bp)^2/4}\n~{\\rm tanh}\\left(\\frac{\\beta\\omega}{2}\\right),\n\\eea\nwhere the second equation follows from the relation\n$[G^{--}(p)]^*=-G^{++}(p)$, valid in the momentum representation (see\nAppendix A).\nThus both propagators are odd under the exchange of the sign\nof $\\omega$, a property which will be important in establishing\nthe vector current conservation in the radiation processes\ndiscussed below. Since the dependence of the\nthe quasiparticle width on the momentum is weak in the density and\ntemperature range of interest it is useful\nto define momentum average quasiparticle width which a function\nonly of the frequency. This approximation is implemented in the\nphase space integrations below.\n\n\n\\subsection{The interactions}\n\nThe central ingredient of a bremsstrahlung\nprocess is the modelling of strong the interaction. For the\nparticle-hole interaction a reasonable, but\nnot unique, choice is the one-pion exchange interaction combined\nwith a contact interaction in the spirit of the Fermi-liquid\ntheory:\n\\be\\label{VBB}\nV_{[ph]}(k) = \\left(\\frac{f_{\\pi}}{m_{\\pi}}\\right)^2\n\\left(\\bsigma_1\\cdot \\bk \\right)D^{--}(\\bk)\\left(\\bsigma_2\\cdot \\bk \\right)\n+ f_0 + f_1 (\\bsigma\\cdot\\bsigma),\n\\ee\nwhere $f_{\\pi}$ is the pion decay constant, $m_{\\pi}$ is the pion mass,\n$D^{--}(\\bk)$ is the one-shell causal pion propagator,\n$f_0$ and $f_1$ are the coupling parameters of the Fermi-liquid\ntheory, $\\bsigma$ is the vector of the Pauli matrices.\nThe non-relativistic reduction of the neutrino-neutron \ninteraction vertex (\\ref{HAM}) is\n\\be\n\\Gamma_{\\mu}^H=-\\frac{G}{2\\sqrt{2}}\n\\left(\\delta_{\\mu 0} - g_A\\delta_{\\mu i}\\sigma_i\\right),\n\\ee\nwhere $g_A=1.25$ is the axial-vector coupling constant.\n\n\n\\subsection{Direct contribution to the polarization function}\n\nThe three topologically different {\\it direct} diagrams (i.e.\nthose which do not involve an exchange of outgoing\nparticles) are shown in Fig. 2a-c.\n\n\n%\\begin{figure}\n\\begin{center}\n\\includegraphics[height=1.in,width=5in,angle=0]{fig2.eps}\n\\end{center}\n%\\caption[]\n{\\footnotesize{Fig. 2: The Feynman diagrams for neutrino-nucleon\ninteraction in the 2p-2h approximation.\nThe vertical dashed lines correspond\nto the baryon-baryon interaction and the\nwavy lines to the $Z^0$ vector bosons.\nExchange diagrams are shown below in Fig. 3.\n}}\n\\label{fig2}\n%\\end{figure}\n\n\n\n\n\\no\nThe analytical expression, corresponding to the Fig. 2a, is\n\\bea\ni\\Pi^{-+\\, , \\, a}_{\\mu \\nu}(q) &=&\n\\int\\!\\!\\prod_{i=1}^4\n\\left[\\frac{d^4p_i}{(2\\pi)^4}\\right]\\frac{dk}{(2\\pi)^4} (2\\pi)^8\n\\delta(q+p_4-k-p_3) \\delta(k+p_2-p_1)\\Tr\\left[V(k) G^{-+}(p_1)\nV(k)G^{+-}(p_2)\\right]\\nonumber\\\\\n&&\\Tr\\Bigl[\\Gamma_{\\mu} G^{--}(q+p_4)V(k) D^{--}(k) G^{-+}(p_3)\nV(k) D^{++}(k)G^{++}(q+p_4)\\Gamma_{\\nu} G^{+-}(p_4)\\Bigr],\n\\label{diag_a}\n\\eea\nwhere $V(k)$ is the strong interaction vertex, which can be read-off\nfrom eq. (\\ref{VBB}).\nThe contribution of this diagram is readily recognized as a {\\it\npropagator dressing} in the $ph$ channel by means of a\nself-energy corresponding to an excitation\nof a single particle-hole collective mode.\nThe analytical expression,\ncorresponding to the Fig. 2b, is\n\\bea\ni\\Pi^{-+\\, ,\\, b}_{\\mu \\nu}(q) &=&\n\\int\\!\\!\\prod_{i=1}^4\n\\left[\\frac{d^4p_i}{(2\\pi)^4}\\right]\\, \\frac{dk}{(2\\pi)^4}\n(2\\pi)^8\\delta(q+p_4-k-p_3) \\delta(k+p_2-p_1)\n\\Tr\\left[V(k) G^{-+}(p_1)V(k)G^{+-}(p_2)\\right]\n\\nonumber\\\\\n&&\\Tr\\Bigl[\\Gamma_{\\mu} G^{--}(q+p_4)V(k) D^{--}(k) G^{-+}(p_3) \\Gamma_{\\nu}\nV(k) D^{++}(k)G^{++}(p_3-q)G^{+-}(p_4)\\Bigr].\n\\label{diag_b}\n\\eea\n\\noindent\nThe contribution of this diagram corresponds to a {\\it\nvertex correction} in the $ph$ channel by an\neffective interaction, which incorporates an intermediate\nparticle-hole collective mode excitation.\nThe contribution of the Fig. 2c reads\n\\bea\ni\\Pi^{-+\\, , \\, c}_{\\mu \\nu}(q) &=&\n\\int\\!\\!\\prod_{i=1}^4\\left[\\frac{d^4p_i}{(2\\pi)^4}\\right]\\,\n\\frac{dk}{(2\\pi)^4}\\, (2\\pi)^8\\delta(q+p_4-k-p_3)\\delta(k+p_2-p_1)\n\\nonumber\\\\\n&&\\Tr\\Bigl[\\Gamma_{\\mu} G^{--}(q+p_4)V(k)\nD^{--}(k)G^{-+}(p_3)V(k-q) G^{+-}(p_4)\\Bigr]\\nonumber\\\\\n&&\\Tr\\left[V(k) G^{-+}(p_1)\\Gamma_{\\nu}G^{++}(p_1-q)\nV(k-q) D^{++}(k-q) G^{+-}(p_2)\\right].\n\\label{diag_c}\n\\eea\nThe latter diagram may be interpreted as a particle-hole\nfluctuation. The diagrams $a$-$c$ are evaluated in the Appendix B.\nThere we show that (i) the vector\ncurrent contributions from diagrams $a$ and $b$ mutually\ncancel; (ii) the diagram $c$ does not contribute\nbecause the axial-vector contribution involves traces over odd number\nof $\\sigma$-matrices and the vector-current contribution\nis cancelled by an equal and of opposite sign contribution from\nthe diagram generated from $c$ by flipping one of the loops\nupside-down; (iii) all contributions due to the Fermi-liquid\ninteraction cancel after summing the diagrams $a$ and $b$.\nFor the contraction of the trace of the neutrino current with\nthe polarization function we find ($i,j,=1\\dots 3$)\n\\bea\\label{CONTR}\n{\\cal C}_{\\rm dir}(q, \\bq_1, \\bq_2)&=&\ni\\Tr(\\Lambda_{ij})\n\\left[\\Pi^{-+\\, ,\\, a}_{i j}(q)+\n\\Pi^{-+\\, ,\\, b}_{i j}(q)\\right] \\nonumber\\\\\n&=&{16} g_A^2G^2\n\\left(\\frac{f_{\\pi}}{m_{\\pi}}\\right)^4\\int\\!\\!\\prod_{i=1}^4\n\\left[\\frac{d^4p_i}{(2\\pi)^4}\\right]\\, \\frac{d^4k}{(2\\pi)^4}\nG^{--}(\\omega)^2 D^{--}(k)^2 \\nonumber\\\\\n&&\\bk^4\\left[\\omega_1\\omega_2 -\n\\frac{(\\bq_1\\cdot \\bk)(\\bq_2\\cdot \\bk)}{\\vert k\\vert^2}\\right]\nG^{-+}(p_1) G^{+-}(p_2)G^{-+}(p_3) G^{+-}(p_4) \\nonumber\\\\\n&&(2\\pi)^4\\delta(q+p_4-k-p_3)(2\\pi)^4 \\delta(k+p_2-p_1).\n\\eea\nThis result is valid in the soft-neutrino and\nnon-relativistic baryon limits.\nThe second term on the r.h.s. in the square\nbracket can be dropped, as it does not\ncontribute after the phase space integrations. Note that the\ntotal number of diagrams of the type $a$-$c$ is four, if one\nallows for all possible relabelling of incoming and outgoing\n(identical) baryons; this forfactor is equal to the symmetry factor\nby which the total rate must be reduced. We do not include\nthese factors explicitly.\n\n\n\\subsection{Exchange contribution to the polarization function}\n\nThe {\\it exchange} diagrams are generated from the direct ones\nby means of interchanging the outgoing propagators\nin a strong vertex. There is a complete set of diagrams analogous\nto $a$ and $b$ with exchanged labelling of the\nhole propagators. These contribute to the contraction\n\\bea\\label{CONTREX}\n{\\cal C_{\\rm ex}}(q) &=& 16 g_A^2\nG^2\\left(\\frac{f_{\\pi}}{m_{\\pi}}\\right)^4\n\\omega_1\\omega_2 G^{--}(\\omega)^2 \\int dk\\,\n\\bk^4 \\, \\, D^{--}(\\bk)^2\\nonumber\\\\\n&&\\int\\!\\!\\prod_{i=1}^4\n\\left[\\frac{d^4p_i}{(2\\pi)^4}\\right]\\,\n G^{-+}(p_1) G^{+-}(p_2)G^{-+}(p_3) G^{+-}(p_4) \\nonumber\\\\\n&&\\hspace{2cm}(2\\pi)^4\\delta(q+k+p_2-p_3)\\delta(k+p_4-p_1),\n\\eea\nin the soft neutrino approximation.\nThe skeleton diagrams which correspond to the\ninterference between the direct and exchange contributions\nare shown Fig. 3a-d. There are eight diagrams of each type\nif one allows for all possible relabelling of the propagators.\n\n\n%\\begin{figure}\n\\begin{center}\n\\includegraphics[height=2in,width=3.5in,angle=0]{fig3.eps}\n\\end{center}\n%\\caption[]\n{\\footnotesize{Fig. 3: The exchange Feynman diagrams for baryon-baryon\ninteraction in the 2p-2h approximation. Conventions are the same\nas in Fig. 2}}\n\\label{fig3}\n%\\end{figure}\n\n\n\n\\no\nThe analytical expressions for, e.g., the diagrams $a$ and $c$ are\n\\bea\ni\\Pi^{-+\\, , \\, a, {\\rm ex}}_{\\mu \\nu}(q) &=&\n\\int\\!\\!\\prod_{i=1}^4\n\\left[\\frac{d^4p_i}{(2\\pi)^4}\\right]\\frac{dk}{(2\\pi)^4} dk' (2\\pi)^8\n\\delta(q+p_4-k-p_3) \\delta(k'+p_2-p_3) \\delta(k+p_2-p_1) \\nonumber\\\\\n&& \\Tr\\Bigl[\\Gamma_{\\mu} G^{--}(q+p_4) V(k)D^{--}(k)G^{-+}(p_3)\\nonumber\\\\\n&&\\hspace{2cm}\nV(k') D^{++}(k) G^{+-}(p_2)V(k') G^{-+}(p_1) V(k')G^{++}(q+p_4)\n\\Gamma_{\\nu} G^{+-}(p_4)\\Bigr],\n\\label{diag_aex}\n\\eea\n\\bea\ni\\Pi^{-+\\, , \\, c, {\\rm ex}}_{\\mu \\nu}(q) &=&\n\\int\\!\\!\\prod_{i=1}^4\n\\left[\\frac{d^4p_i}{(2\\pi)^4}\\right]\\frac{dk}{(2\\pi)^4} dk' (2\\pi)^8\n\\delta(q+p_4-k-p_3) \\delta(k'+p_2-p_3) \\delta(k+p_2-p_1)\\nonumber\\\\\n&&\\Tr\\Bigl[\\Gamma_{\\mu} G^{--}(q+p_4) V(k)D^{--}(k)G^{-+}(p_3) \\nonumber\\\\\n&&\\hspace{2cm}\n V(k') D^{++}(k) G^{+-}(p_2)V(k') G^{-+}(p_1)\\Gamma_{\\nu}G^{++}(q+p_4)\nV(k') G^{+-}(p_4)\\Bigr],\n\\label{diag_cex}\n\\eea\nand their computation is a complete analogue of that for the\ndirect diagrams (Appendix B).\nThe vector current contribution again cancels among the diagrams\n$a$ and $c$ and, similarly, $b$ and $d$.\nThe contribution from the interference between the direct\nand exchange diagrams to the\ncontraction of neutrino and baryon currents is\n\\bea\\label{CONTREX2}\n{\\cal C_{\\rm int}}(q) &=& 16 g_A^2\nG^2\\left(\\frac{f_{\\pi}}{m_{\\pi}}\\right)^4\n\\omega_1\\omega_2 G^{--}(\\omega)^2 \\int dk\\int dk'\\, \\bk ^2\\,\n \\bk'^2 \\, D^{--}(\\bk)\\, D^{--}(\\bk')\\nonumber\\\\\n&&\\int\\!\\!\\prod_{i=1}^4\n\\left[\\frac{d^4p_i}{(2\\pi)^4}\\right]\\,\n G^{-+}(p_1) G^{+-}(p_2)G^{-+}(p_3) G^{+-}(p_4) \\nonumber\\\\\n&&\\hspace{2cm}(2\\pi)^4\\delta(q+p_4-k-p_3)\\delta(k+p_2-p_1)\n\\delta(k'+p_4-p_1),\n\\eea\nwhere we dropped the terms which vanish in the phase space\nintegrations.\nThe phase space integrations in the exchange contribution\nis complicated, since the momentum\nintegrations do not decouple into two separate loops.\nThe disentanglement can be achieved by constraining\nthe momentum transfer in one of the pion propagators at the\nvalue $\\vert k'\\vert = 2p_F$, as the main contribution to the\nintegral originates near this value of the momentum transfer.\n\n\n\\section{Quasiparticle width}\n\nThe purpose of this section is to specify\nthe width of baryon propagators.\nTo this end we carry out a full resummation in the\nparticle-particle ($pp$) channel by solving the scattering\n$T$-matrix at finite temperatures. Our approach is based on\nthe Brueckner theory with the continuous energy-momentum\nspectrum of baryons. The non-perturbative\ntreatment of the $pp$ channel is mandatory for including\nthe effects of the short-range correlations due to the\nrepulsive part of the nucleon-nucleon force. These\ncorrelations are then responsible for the width of quasiparticle\npropagators,\n$\\gamma$, in our perturbation expansion in the\nparticle-hole ($ph$) channel.\nThe $ph$ interactions are dominated by the weaker long-range\npart of the nucleon-nucleon interaction, which makes possible\nthe perturbative treatment of this channel by a truncation at\ntwo loops.\nThe contour ordered $T$-matrix in the configuration space is:\n\\bea\n\\label{TMATX}\n&&{\\underline T}(x_1,x_2;x_3,x_4)= {\\underline V}_{[pp]}(x_1,x_2;x_3,x_4)\n\\nonumber\\\\\n&&\\hspace{1cm}+ i {\\underline V}_{[pp]}(x_1,x_2;x_3,x_4)\n{\\underline G}(x_7,x_5)~ {\\underline G}(x_8,x_6)\n{\\underline T}(x_5,x_6;x_3,x_4),\n\\eea\nwhere ${\\underline V}_{[pp]}(x_1,x_2;x_3,x_4)\n= \\sigma_z\\, {V}_{[pp]}(x_1,x_2;x_3,x_4)$, is the\ntime-local baryon-baryon interaction in the particle-particle\nchannel. Note that the time locality\nimplies that the $pp$ propagator product\n$\\underline G\\,\\underline G \\equiv\n{\\underline G}_{[pp]}$ should\nbe considered as a single matrix. The components of the scattering\namplitudes, needed for complete specification of the self-energies,\ncan be chosen as the retarded/advanced ones; the remaining\ncomponents are provided by the optical theorem. In the\nquasiclassical limit the retarded/advanced $T$-matrices\nobey the integral equation\n\\bea\\label{TMIX}\nT^{R/A}(\\bp, \\bp'; P) &=&\nV_{[pp]}(\\bp, \\bp')+i\\int\\frac{d^3p''}{(2\\pi)^3} V_{[pp]}(\\bp , \\bp'')\nG_{[pp]}^{R/A}(\\bp'', P)T^{R/A}(\\bp'', \\bp', P) ,\n\\eea\nwhere we kept the leading order terms in the gradient expansion\nof the product ${G_{[pp]}}^{R/A} \\, T^{R/A}$.\nHere the subscript $[pp]$ indicates the particle-particle\nchannel and $\\bp$, $P$ are the relative momentum and total\nfour-momentum respectively. The two-particle Green's function,\nappearing in the kernel of equation (\\ref{TMIX}), is defined as\n\\bea \\label{G2}\nG_{[pp]}^{R/A}(\\bp_1, P_1) &=& \\int\\frac{d\\omega_1}{2\\pi}\n\\int\\frac{d^4P_2}{(2\\pi)^4}\n\\Big\\{G^{>}\\left(P_2/2+p_1\\right) \\,\nG^{>}\\left(P_2/2-p_1\\right) \\nonumber \\\\\n&&\\hspace{1cm}\n-G^{<}\\left(P_2/2+p_1\\right)\\, G^{<}\\left(P_2/2-p_1\\right)\\Big\\}\n\\frac{(2\\pi)^3\\, \\delta^3({\\bP_1}-{\\bP_2})}{E_1-E_2\\pm i\\delta},\n\\eea\nwhere we dropped the irrelevant dependence of the quasiclassical\nfunctions on their center-of-mass space-time coordinates.\nIf the particle-hole symmetry is kept in the kernel\nof the integral equation, the $T$-matrix diverges at the\ncritical temperature of the superfluid phase transition.\nTo be able to apply our computation to the low-temperature\nregime (and thereby avoid the pairing instability in the\n$T$-matrix) we drop the hole-hole propagators. This is a\ncommon approximation in the Brueckner theory and is justified\nin terms of the Bethe-Goldstone hole-line expansion. We treat the\nintermediate state two-particle propagation in the quasiparticle\nlimit. Using the angle averaging procedure for the\n$pp$ propagator and after partial wave expansion,\nthe thermodynamic retarded $T$-matrix is given by\n\\bea\\label{TMAT}\nT^{R\\alpha}_{ll'}( p, p', P, \\omega) &=&\nV^{\\alpha}_{[pp]\\, ll'}(p, p') \\nonumber\\\\\n&+&\\frac{2}{\\pi}\\sum_{l''}\n\\int\\!\\! dp''\\, p''^2 \\, V^{\\alpha}_{[pp]\\, ll''}(p, p'')\n\\langle G_{[pp]}^R(p'', P, \\omega)\\rangle\nT^{R\\alpha}_{l''l'}(p'', p', P,\\omega),\n\\eea\nwhere $\\alpha$ collectively denotes the quantum\nnumbers $(S,J,M)$ in a particular partial wave, $p$ and $P$\nare the magnitudes of the relative and total momentum\nrespectively, $V(p,p')$ is the bare nuclear interaction. Here\n$\\langle G_{[pp]}^R\\rangle$ is the angle averaged two-particle propagator\n\\bea\n\\langle G_{[pp]}^R(p, P, \\omega)\\rangle = \\int\\!\\frac{d\\Omega}{4\\pi}\n\\frac{\\left[1-f_N(\\ep(\\bP/2+\\bp))\\right]\n\\left[1-f_N(\\ep(\\bP/2-\\bp))\\right]}\n{\\omega -\\ep(\\bP/2+\\bp)-\\ep(\\bP/2-\\bp)+i\\delta },\n\\eea\nwith $\\ep(\\bp) = \\epsilon_p + {\\Real}\\Sigma(\\ep_p,\\bp)$, i.e.\nthe intermediate state propagation is treated in the\nquasiparticle approximation. The\n retarded self-energy is given by\n\\bea\\label{SELF_E}\n\\Sigma^R(p, \\omega) = \\frac{1}{\\pi}\\sum_{l\\alpha}(2J+1)\n\\int\\! dp'\\, p'^2 T^{R\\alpha}_{ll}(p,p';p,p';\\omega+ \\ep(p'))\nf_N(\\ep(p')),\n\\eea\nwhich also defines its real and imaginary parts.\nThe coupled equations (\\ref{TMAT}) and (\\ref{SELF_E})\nare subject to normalization to the total density at a given\ntemperature.\n\n\\section{Phase space integrations}\n\nLet us turn to the task of evaluating the phase space integrals in the\nexpressions for the current contractions.\nWe substitute the Kadanoff-Baym ansatz in eq. (\\ref{CONTR})\nand use the identity $f_N(\\ep_{1})f_N(-\\ep_{2})= g(\\ep_1-\\ep_2)\n\\left[f_N(\\ep_2)-f_N(\\ep_1)\\right]$,\nwhich is exact in the equilibrium limit. We then find that\nthe contributions from each loop decouple, i.e.,\n\\bea\n{\\cal C}_{\\rm dir}(q) &=& 16 g_A^2\nG^2\\left(\\frac{f_{\\pi}}{m_{\\pi}}\\right)^4\n\\omega_1\\omega_2 G^{--}(\\omega)^2 \\int\\!\\! \\frac{d^4k}{(2\\pi)^4}\n\\bk ^4 D^{--}(\\bk)^2\\, g(\\omega_k)\\,\ng(\\omega-\\omega_k)\\, L(k)\\, L(q-k),\n\\eea\nwhere $\\omega_k=k_0$ and the elementary loop is defined as\n\\bea\\label{L01}\nL(k) &=&\\int\\!\\!\n\\frac{d^4p_1}{(2\\pi)^4}\\,\\frac{d^4p_2}{(2\\pi)^4}\\,\na(p_1)a(p_2)[f_N(\\ep_2)-f_N(\\ep_1)] (2\\pi)^4\\delta(k+p_2-p_1).\n\\eea\nThe exchange contribution ${\\cal C}_{\\rm ex}$ leads to additional\nfactor of two. The interference contribution decouples only under certain\nconstrains.\nThe single loop, eq. (\\ref{L01}),\ncan be evaluated to arbitrary order in the spectral\nwidth in general\\cite{SD}. We shall restrict to the\nsmall quasiparticle damping limit and use the\nthe expansion with respect to the width\nof the spectral function given by eq. (\\ref{exp1}).\n\n\\subsubsection{Leading order}\n\nThe lowest order approximation corresponds to the quasiparticle\n(i.e. zero-width) limit. The contribution from a single loop\nvanishes in the time-like region of the phase space where\n$\\omega_k\\ge\\vert\\bk\\vert$. This result is found only if\nthe relativistic kinematics is applied; non-relativistic\nkinematics leads to spurious terms $\\propto m/q $. In the\nspace-like region of the phase space the result is finite.\nWe carry out the energy integrations keeping only the leading\norder term. Removing one of the trivial momentum delta functions\nwe find\n\\bea\nL_0(k) &=&\\int\\!\\!\n\\frac{d^3p}{(2\\pi)^3}\\,[f_N(\\ep_{p})-f_N(\\ep_{p+k})]\n(2\\pi)\\delta(\\omega_k+\\ep_{p}-\\ep_{p+k}).\n\\eea\nThe integrations can be carried out exactly \n\\bea\\label{LQPA}\nL_0(k)&=&\\int\\!\\!\n\\frac{d^3p}{(2\\pi)^3}\\,[f_N(\\ep_{p})-f_N(\\ep_{p+k})]\n(2\\pi)\\delta(\\omega_k+\\ep_{p}-\\ep_{p+k})\n=\\frac{m^{*\\, 2}}{2\\pi\\beta\\vert k\\vert}\n{\\cal L}(\\omega_k, \\bk),\n\\eea\nwhere $m^*$ is the effective\nmass of a quasiparticle and\n\\bea\\label{L0}\n{\\cal L}(\\omega_k,\\bk) ={\\rm ln}\n\\Bigg\\vert\\frac{1+{\\rm exp}\\left[-\\beta\\left(\\ep_-(k)-\\mu\\right)\\right]}\n{1+{\\rm exp}\\left[-\\beta\\left(\\ep_+(k)-\\mu\\right)\\right]}\\Bigg\\vert ,\n\\eea\nwith $\\varepsilon_{\\pm}(k)\n= (\\omega_k^2+\\varepsilon_k^2)/4\\varepsilon_k\\pm\\omega_k/2$. Note that\nthe quasiparticle loop (\\ref{LQPA}) is zero in the time like\nregion ($\\omega_k\\ge\\vert\\bk\\vert$), which sets a natural cut-off\nin the phase space integrations below.\n\n\n\\subsubsection{Next-to-leading order}\nThe next-to-leading order contribution (which is linear in $\\gamma$)\nis\n\\bea\nL_1(\\omega_k, k) &=& 2\\int\\!\\!\\frac{d^4 p}{(2\\pi)^4}\n(2\\pi)\\delta(\\ep+\\omega_k-\\ep_{p+k})\n\\int \\frac{d\\omega'}{2\\pi}\n\\gamma(p')\\frac{{\\cal P}}{(\\omega'-\\ep_{p})^2} \\nn \\\\\n&\\times&\n\\left\\{\\delta(\\ep -\\ep_p)-\\delta(\\ep-\\omega')\n\\right\\}\n\\left[f_N(\\ep) - f_N(\\ep+\\omega_k)\\right],\n\\eea\nwhere we summed the two term arising from the product of the\nleading and next-to-leading order contribution to\n$G^<(p)$. The angular integral can be carried out analytically\nto the accuracy ${\\cal O}(\\gamma^2)$. One finds\n\\bea\\label{L1}\nL_1(\\omega_k, k)=-\\frac{4m^{*\\, 2}}{k}\n\\int\\frac{d\\ep_p}{(2\\pi)^2}\n\\left[f_N(\\ep_p)-f_N(\\ep_p+\\omega)\\right]\n\\left\\{{\\cal Z}(\\ep_p, \\bk) - {\\cal F} (\\ep_p, \\bk,\\omega_k)\\right\\},\n\\eea\nwhere the first term in the curly brackets is due to the wave-function\nrenormalization\n\\bea\n {\\cal Z} (\\ep_p,\\bk) =\\theta(\\ep_p-\\ep_{\\rm min})\n \\int d\\omega \\gamma(\\omega)\\frac{{\\cal P}}{(\\omega-\\ep_{p})^2},\n\\quad \\ep_{\\rm min} = \\frac{(\\omega_k-\\ep_q)^2}{4\\ep_q}.\n \\eea\nThe second terms is the off-pole contribution and is given by\n\\bea\n {\\cal F} (\\omega_k, \\bk, \\ep_p)\n ={\\rm arctan}\\left[\n \\frac{\\epsilon_k-\\omega_k-\\mu\n +2\\sqrt{\\epsilon_p\\epsilon_k}}{\\gamma(\\ep_p+\\omega_k)/2}\\right]\n - {\\rm arctan}\\left[\n \\frac{\\epsilon_k-\\omega_k-\\mu-2\\sqrt{\\epsilon_p\\epsilon_k}}\n {\\gamma(\\ep_p+\\omega_k)/2}\n \\right].\n\\eea\n\n\nThe current contraction, which so far includes contributions\nto all orders in $\\gamma$, now can be decomposed in the\nleading and next-to-leading order terms with respect to\n$\\gamma$, employing the corresponding decomposition for the\nloops. E.g. for the direct contribution one finds\n\\bea\n{\\cal C}_{\\rm dir} (q) &=& 16 g_A^2\nG^2\\left(\\frac{f_{\\pi}}{m_{\\pi}}\\right)^4\n\\omega_1\\omega_2 G^{--}(\\omega)^2\n\\int \\frac{d^4k}{(2\\pi)^4}\n\\bk^4 D^{--}(\\bk)^2\\nn\\\\\n&& g(\\omega_k)\\, g(\\omega-\\omega_k)\\, \\left[\nL_0(k)\\, L_0 (q-k)+L_1(k)\\, L_0 (q-k) +\nL_0(k)\\, L_1 (q-k)\\right].\n\\eea\nThe exchange and interference terms can be decomposed in\na similar manner.\n\n\\subsubsection{Neutrino emissivity}\n\nAfter the preparatory work above, the computation of the neutrino\nemissivity is straightforward.\nWe first relate the current contraction to\nour original expression for the neutrino emissivity by\nusing the relation\n$-2 g_B(q_0) {\\Img} \\Pi^R_{\\mu\\nu}(q) = i \\Pi_{\\mu\\nu}^< (q)$.\nExpression (\\ref{EMISSIVITY}) takes the form:\n\\bea\n\\epsilon_{\\nu\\anu}&=&\n\\sum_f\\int\\!\\frac{d^3q_2}{(2\\pi)^32 \\omnu( q_2)}\n\\int\\!\\frac{d^3 q_1}{(2\\pi)^3 2\\omnu( q_1)}\n\\int\\!\\frac{d^4 q}{(2\\pi)^4}\n(2\\pi)^4 \\delta^4(q_1 + q_2 - q)\n\\left[\\omnu(\\bq_1)+\\omnu(\\bq_2)\\right]\\, {\\cal C}(q),\n\\eea\nwhere ${\\cal C}(q)$ is the sum of the direct, exchange and\ninterference contributions. Let us first compute the contribution\nfrom the direct term by substituting eq. (\\ref{CONTR}) for the\ncurrent contraction.\nWe carry out the integrations over the neutrino phase space\nand the summation over the three neutrino flavors to find:\n\\bea\\label{RESULT1}\n\\epsilon_{\\nu\\anu} &=& \\frac{16}{5(2\\pi)^7}\ng_A^2 {G_F}^2\\left(\\frac{f_{\\pi}}{m_{\\pi}}\\right)^4\n\\int_0^{\\infty}\\,\nd\\omega\\, \\omega^6 G^{--}(\\omega)^2\n\\int dk\nk ^6 D^{--}(\\bk)^2\\nn\\\\\n&& \\int d\\omega_k g(\\omega_k)\\, g(\\omega-\\omega_k)\\, \\left[\nL_0(k)\\, L_0 (q-k)+L_1(k)\\, L_0 (q-k) +\nL_0(k)\\, L_1 (q-k)\\right],\n\\eea\nwhere we used $d^4k = 4\\pi k^2 dk d\\omega_k$.\nNormalizing the energy scales by the temperature\nand the momenta by $2p_F$ we obtain\n\\bea\\label{RESULT2}\n\\epsilon_{\\nu\\anu} &=& \\frac{32}{5(2\\pi)^9} G_F^2 g_A^2\n\\left( \\frac{f_{\\pi}}{m_{\\pi}} \\right)^4\\,\n\\left(\\frac{m^*}{m}\\right)^4\\, p_F\\, I\\, T^8\n= 5.5 \\times 10^{19}\\, I_3 \\, T_9^8 ~({\\rm erg~cm^{-3}~s^{-1}})\n\\eea\nwhere $T_9$ is the temperature in units of $10^9$ K, $I_3$ is the\nintegral $I$ in units $10^3$ defined as\\footnote{It is understood that the functions\nof new variables are relabelled.}\n\\bea\\label{INT}\nI &=&\n\\int_0^{\\infty}d y\\, y^6 G^{--}(y)^2 {\\cal Q}(y)\n\\int^{\\infty}_0 dx x^4 D^{--}(x)^2\n\\int_{-\\infty}^{\\infty} dz ~g(z)~g(y-z)\n\\Biggl\\{{\\cal L}(z, x) {\\cal L}(y-z, x) \\nn\\\\\n&+&\\frac{2}{\\pi} z {\\cal L}(y-z, x)\\,\n[{\\cal F}(z, x)-{\\cal Z}(z,x)]\n+\\frac{2}{\\pi} (y-z) {\\cal L}(z, x) \\,\n[{\\cal F}(y-z, x)-{\\cal Z}(y-z,x)]\\Biggr\\}.\n\\eea\nThe explicit dependence of eq. (\\ref{RESULT2}) on the temperature\nand density is the generic one \\cite{CHIU_SALPETER,BAHCALL_WOLF,FLOWERS_ETAL,FRIMAN_MAXWELL,VOSKRESENSKY,PETHICK}. Additional\ndependence on these parameters is contained in the integral (\\ref{INT}).\nNote that to avoid spurious contributions from the quasiparticle\npart, (the first term in curly brackets in (\\ref{INT})),\none should restrict the $z$ integration to the space-like region.\nFor the numerical evaluation of the neutrino emissivity we use,\nfollowing ref. \\cite{FRIMAN_MAXWELL}, the free space pion propagator:\n$$\nD^{--}(k) = [\\bk^2+m_{\\pi}^2]^{-1}.\n$$\nThe free-space approximation should be valid in the vicinity\nof the nuclear saturation density. The softening\nof the one-pion exchange (a precursor of the pion-condensation)\nincreases the neutrino emissivity by large factors\n\\cite{VOSKRESENSKY}. We do not attempt to accommodate this\neffect as our main interest here is the role of the finite width\nof quasiparticles.\nThe Pauli blocking factor\n\\bea\n{\\cal Q}(y) = 30 \\int_0^1 d w~\n w^2~(1-w)^2 [1-f_{\\nu}(w y)] [1-f_{\\anu}((1-w)y)],\n\\eea\naccounts for the occupation of neutrino and anti-neutrino final states.\nIn the dilute (anti-)neutrino limit $\\beta\\mu_{\\nu_f}\\ll 1$\n(where $\\mu_{\\nu_f}$ is the chemical potential of neutrinos of\nflavor $f$) ${\\cal Q}(y) =1$.\n\nIn the low-temperature limit\n ${\\cal L}(z) = z$ and the $z$-integration\ndecouples from the $x$-integration. On imposing $\\gamma(\\omega)\\to 0$\n(quasiparticle limit)\none finds that ${\\cal F}=0$ and $G^{--}(\\omega)=\\omega^{-2}$.\nThen the $z$ integration can be carried analytically upon\ndropping the wave-function renormalization contribution:\n\\be\n\\int_{-\\infty}^{\\infty}\\!\\! dz ~g(z)\\, g(y-z)~ z ~(y-z)\n = \\frac{y~(y^2+4\\pi^2)}{6~(e^y-1)} .\n\\ee\nAfter these manipulations eq. (\\ref{RESULT2}) reduces\nto Friman and Maxwell's result [ref. \\cite{FRIMAN_MAXWELL}, eq. (47)].\nThe numerical coefficient in eq. (\\ref{RESULT2}), however,\nis by a factor 3 larger, since Friman and Maxwell do not carry out\nthe summation over the three neutrino flavors at that stage.\n\nThe contribution from the exchange current contraction, eq.\n(\\ref{CONTREX}), leads to a factor of 2 in the integral (\\ref{INT}).\nThe contribution of the interference term, in the approximation where\none of the momentum transfers is fixed at the characteristic value\n$2p_F$, is\n\\bea\\label{INT2}\nI_{\\rm int} &=&\n\\int_0^{\\infty}d y\\, y^6 G^{--}(y)^2 {\\cal Q}(y)\n\\int^{\\infty}_0 dx x^2 D^{--}(x) D^{--}(1)\n\\int_{-\\infty}^{\\infty} dz ~g(z)~g(y-z)\n\\Biggl\\{{\\cal L}(z, x) {\\cal L}(y-z, 1) \\nn\\\\\n&+&\\frac{2}{\\pi} z {\\cal L}(y-z, x)\\,\n[{\\cal F}(z, 1)-{\\cal Z}(z,1)]\n+\\frac{2}{\\pi} (y-z) {\\cal L}(z, 1) \\,\n[{\\cal F}(y-z, x)-{\\cal Z}(y-z,x)]\\Biggr\\}.\n\\eea\n\n\n\n\\section{Results}\nThe numerical calculations\nwere carried out for pure neutron matter using the\nParis $NN$ interaction keeping $J\\le 4 $ partial waves.\nFig. 4 displays the real part of\nthe on-shell self-energy and the\nhalf width of the spectral function as a function of the particle\nmomentum for several values of the temperature at the\nsaturation density $n_s=0.17$ fm$^{-3}$.\nThe width of the quasiparticle propagators can be parametrized\nin terms of the reciprocal of the quasiparticle life time in the\nFermi-liquid theory (damping of the zero sound):\n\\be\\label{ZERO_SOUND}\n\\gamma = a T^2\\left[1+\\left(\\frac{\\omega}{2\\pi T} \\right)^2 \\right],\n\\ee\nwhere $a$ is a density dependent phenomenological parameter. The parabolic\ndependence of the width on the frequency is justified for temperatures\nbelow 30 MeV in the range of the densities\n$n_s \\le n\\le 2 n_s$. The quadratic dependence\nof $\\gamma$ on the temperature breaks down at slightly lower temperatures.\nThe value of the parameter $a$ weakly depends on the density and is\napproximately 0.2 MeV$^{-1}$.\n\n\n%\\begin{figure}[b]\n\\begin{center}\n\\includegraphics[height=6.in,width=5.in,angle=0]{fig4.eps}\n\\end{center}\n%\\caption[]\n{\\footnotesize{Fig. 4: The real part of the on-shell\nself-energy and the half-width\nas a function of particle momentum at the saturation density $n_s=0.17$\nfm$^{-3}$ for different temperatures; the zero temperature\nFermi momentum is 1.7 fm $^{-1}$.}}\n\\label{fig4}\n%\\end{figure}\n\n\\no\nThe emergent neutrino spectrum can be caracterized by their spectral\nfunction \n\\bea\\label{SPEC}\nS(y) &=&\n G^{--}(y)^2 {\\cal Q}(y)\n\\int^{1}_0 dx x^4 D^{--}(x)^2\n\\int_{-\\infty}^{\\infty} dz ~g(z)~g(y-z)\n\\Biggl\\{{\\cal L}(z, x) {\\cal L}(y-z, x) \\nn\\\\\n&+&\\frac{2}{\\pi} z {\\cal L}(y-z, x)\\,\n[{\\cal F}(z, x)-{\\cal Z}(z,x)]\n+\\frac{2}{\\pi} (y-z) {\\cal L}(z, x) \\,\n[{\\cal F}(y-z, x)-{\\cal Z}(y-z,x)]\\Biggr\\}, \n\\eea\nwhich is depicted in Fig. 5. \nThe values of the integral are shown as\na function of neutrino frequency at $T = 20$ MeV\nand the saturation density $n_s=0.17$\nfm$^{-3}$ in the limit of vanishing width ({\\it dashed line}),\nincluding the leading order contribution in the width \n({\\it dashed-dotted line}) and full non-perturbative result\n({\\it solid line}). The energy carried by neutrinos is \nof order of $\\omega \\sim 5T$ in all three cases, \nas the peak in the spectral function is independent \nof the approximation to the width of the propagators.\nThe integral $I_3$ is show in Fig. 6.\nThe finite width of propagators \nleads to a suppression of the bremsstrahlung rate \nas a result of the LPM effect. \nKeeping the full non-perturbative\nexpression for the causal propagators enhances the value of the\nintegral, as the higher order terms contribute additively to the\nleading order result.\nThe LPM effect sets in roughly when\n$\\omega \\sim \\gamma$. As neutrinos are produced thermally,\nthe onset temperature of the LPM effect is\nof the order of $\\gamma$. Equation (\\ref{ZERO_SOUND})\nshows that the value of the parameter $a$ controls the onset temperature\nwhich turns out of the order of 5 MeV in agreement with the\nprevious results of\nrefs. \\cite{RAFFELT_SECKEL,JANKA,RAFFELT,HANESTAD}\nand our numerical computation (see Fig. 6).\n\n\n\n\n%\\begin{figure}\n\\begin{center}\n\\includegraphics[height=4.in,width=4.in,angle=-90]{fig5.eps}\n\\end{center}\n%\\caption[]\n{\\footnotesize{Fig. 5: The neutrino spectral function \n(\\ref{SPEC}) at the temperature $T=20$ MeV and \ndensity $n_s = 0.16$ fm$^{-3}$. \nThe dashed curve is the zero width limit, the \ndashed-dotted curve includes only the leading order in $\\gamma$ contribution\nfrom the causal propagator, the solid curve is the full non-perturbative\nresult.\n}}\n\\label{fig5}\n%\\end{figure}\n\n\n%\\begin{figure}\n\\begin{center}\n\\includegraphics[height=4.in,width=4.in,angle=-90]{fig6.eps}\n\\end{center}\n%\\caption[]\n{\\footnotesize{Fig. 6: The integral (\\ref{INT}) (including the exchange\nterms) as a function of temperature\nat the density $n_s = 0.16$ fm$^{-3}$.\nThe dashed curve is the zero width limit, the \ndashed-dotted curve includes only the leading order in $\\gamma$ contribution\nfrom the causal propagator, the solid curve is the full non-perturbative\nresult.\n}}\n\\label{fig6}\n%\\end{figure}\n\n\n\n\n\\section{Conclusions}\n\nIn this work we formulated a transport theory for neutrinos\nin the framework of real-time Green's functions\nformalism, with particular attention to the collision integrals\nfor the neutrino-pair bremsstrahlung. The main focus was\na first principle calculation of the bremsstrahlung emissivity\nincluding the width of propagators. This allows to answer\nquestions, not covered by the semi-phenomenological theory,\nsuch as the magnitude of the contribution\nof higher order terms in the expansion with respect to the\nquasiparticle width or the cancellation\nof the vector current contribution at all orders\nin the quasiparticle width.\nEven though the expression for the emissivity, which follows\nfrom our quasiclassical transport equation, is the same as the one found\nin the linear response theory, it is valid under conditions\narbitrary far from equilibrium. This is particularly important\nin the regime where the neutrinos decouple from matter and\ntheir distribution function strongly deviates from the Fermi-Dirac\nform.\n\n\nThe central quantity of the theory is\nthe particle-hole polarization tensor\nin the $ph$ channel truncated at two loops.\nThe $pp$ channel is treated non-perturbatively\nwithin the finite temperature Brueckner theory.\nWe find that the only contribution\nto the bremsstrahlung rate\ncomes from the contraction of the tensor force with the\naxial vector current to all orders in the\nquasiparticle width. Other contributions, which arise\nfrom the contraction of the Fermi-liquid\ntype interaction with the axial vector current\nand the contraction of the net strong interaction with the\nvector current, cancel when we take the sum\nof the diagrams corresponding to vertex corrections\nand propagator renormalization in the $ph$ channel. Thereby the\nvector current conservation is established at all orders\nin the quasiparticle width. These\ncancellations are independent of the approximations\nto the propagators and are effective both in the quasiparticle limit\nand beyond.\nThe three ingredients crucial to the cancellations are:\n(i) the anti-commutation of the\ntensor force with the axial vector current, (ii) the odd parity\nof the causal propagator under the exchange of its energy\nargument, (iii) the soft neutrino and non-relativistic\nbaryon approximations.\n\n\n\nOur numerical evaluation of the neutrino emissivity\nof hot neutron matter, carried out\nat two loops, shows that the LPM-type suppression sets in\nat temperatures $T\\ge \\gamma$, in agreement with the\nprevious work limited to the\nfirst order terms in the quasiparticle width (see ref. \\cite{RAFFELT}\nand references therein). The higher order terms\nenhance the magnitude of the neutrino emissivity compared to the\nleading order result. The non-perturbative result, however, is still\nsuppressed as compared to the quasiparticle limit. \n\nOur formalism can be extended in various ways. One obvious\nextension is allowing for two different chemical potentials\nof scattering baryons. This will include the Urca process\n(the $\\beta$-decay in the second order in the virial expansion)\nand the effects of the Pauli spin-paramagnetism,\nwhich become important in strong magnetic fields.\nThe formalism can be \nadapted, with minor changes, for a computation\nof the space-like analogous of the bremsstrahlung and,\nin particular, the neutrino opacities of\nthe supernova matter.\nThe perturbative scheme, employed here, itself requires\nfurther improvements in several direction, numerically\nthe most important one being the renormalization of the\none-boson exchange interaction in the $ph$ channel.\n\n\n\\section*{Acknowledgements}\n\nThis work has been supported by the Stichting voor\nFundamenteel Onderzoek der Materie\nwith financial support from the Nederlandse Organisatie\nvoor Wetenschappelijk Onderzoek.\nA.S. thanks the Institute for Nuclear Theory at the\nUniversity of Washington for its hospitality and the\nDepartment of Energy for partial support during the\ncompletion of this work.\n\n% send to Linda Vilett a copy of the preprint and the\n% published article.\n\n\\begin{appendix}\n\\section{Real-time Green's functions}\n\nThe six Green's functions of the non-equilibrium theory are\nnot independent. For completeness we summarize here the linear\nrelations among them, which can be easily verified from their\ndefinitions. The four components of the matrix Green's function\nare related to each other by the relations\n\\bea\n&& S^{--}(x_1,x_2)= \\theta(t_{1}-t_{2}) S^{+-}(x_1, x_2) +\n \\theta(t_{2}-t_{1}) S^{-+}(x_1, x_2) , \\\\\n\\label{GF1}\n&& S^{++}(x_1,x_2)= \\theta(t_{2}-t_{1}) S^{+-}(x_1,x_2) +\n \\theta(t_{1}-t_{2}) S^{-+}(x_1,x_2), \\\\\n\\label{GF2}\n&& S^{--}(x_1,x_2) + S^{++}(x_1,x_2)= S^{-+}(x_1,x_2) + S^{+-}(x_1,x_2).\n\\label{GF3}\n\\eea\nFollowing Hermitian conjugation relations hold:\n\\bea\nS^{--}(x_1,x_2)= - S^{++*}(x_2,x_1),\n\\label{HC1}\\\\\nS^{-+}(x_1,x_2)= - S^{-+*}(x_2,x_1),\n\\label{HC2}\\\\\nS^{--}(x_1,x_2)= - S^{+-*}(x_2,x_1).\n\\label{HC3}\n\\eea\nThe retarded and advanced Green's functions are\nrelated to the components of the matrix Green's function\nvia the relations\n\\bea\nS^{R}(x_1,x_2) &=& \\theta(t_{1}-t_{2})\n\\left[S^{+-}(x_1,x_2)-S^{-+}(x_1,x_2)\\right]\\nonumber \\\\\n&=&S^{--}(x_1,x_2)-S^{-+}(x_1,x_2)=S^{+-}(x_1,x_2)-S^{++}(x_1,x_2),\n\\label{APP:RET} \\\\\nS^{A}(x_1,x_2) &=& - \\theta(t_{2}-t_{1})\n\\left[S^{+-}(x_1,x_2)-S^{-+}( x,y ) \\right] \\nonumber \\\\\n&=& S^{--}(x_1,x_2)-S^{+-}(x_1,x_2)=S^{-+}(x_1,x_2)-S^{++}(x_1,x_2).\n\\label{APP:ADV}\n\\eea\nThey are Hermitian conjugates, i.e.\n\\be\nS^A(x_1,x_2) = S^{R*}(x_1,x_2).\n\\ee\nIn addition, we note that in the momentum representation\nthey satisfy the equations\n\\bea\\label{HC4}\nS^{--}(\\omega, \\bp) = - \\left[ S^{++}(\\omega,\\bp)\\right]^* ,\\quad\nS^{A}(\\omega, \\bp) = \\left[ S^{R}(\\omega,\\bp)\\right]^*.\n\\eea\n The relations above are valid for the baryon and pion propagators\n in general, and we do not repeat them here.\n\n Similar relations hold among the self-energies. These can be identified\n by performing a unitary orthogonal transformation affected by the\n matrix $R = (1+i\\sigma_y)/2$ by means of formula $S' = R^{-1}SR$.\n The form of the original Dyson equation in the matrix form (\\ref{DYSON1})\n is invariant against the transformation,\n \\be\n \\underline{S'}(x_1,x_2) = \\underline{S'}_0(x_1,x_2)\n + \\underline{S'}_0(x_1,x_3)\n \\underline{\\Omega'}(x_3,x_2) \\underline{S'}(x_2,x_1)\n \\ee\n where the primed quantities have the ``triangular'' form\n \\be\n S'_{12} = \\left( \\begin{array}{cc}\n 0 & S^{A}_{12} \\\\\n S^{R}_{12} & S^{K}_{12}\n \\end{array} \\right),\n \\quad\n \\Omega'_{12} =\\left( \\begin{array}{cc}\n \\Omega^K_{12} & \\Omega^{R}_{12} \\\\\n \\Omega^{A}_{12} & 0\\end{array} \\right).\n\\ee\nwhere\n\\be\n S^K(x_1,x_2) = S^c(x_1,x_2)+S^a(x_1,x_2) = S^>(x_1,x_2)+S^<(x_1,x_2),\n\\ee\n \\be\n\\Omega^R(x_1,x_2) = \\Omega^c(x_1,x_2) + \\Omega^{<}(x_1,x_2),\\quad\n \\Omega^A(x_1,x_2) = \\Omega^c(x_1,x_2) + \\Omega^{>}(x_1,x_2),\n \\ee\n \\be\n \\Omega^K(x_1,x_2) = \\Omega^c(x_1,x_2) +\\Omega^a(x_1,x_2)\n =-\\Omega^>(x_1,x_2)-\\Omega^<(x_1,x_2).\n \\ee\n\n\\section{Details of the computation of the polarization function}\n\nAs an example we compute here the direct contribution to the\npolarization function, represented by the diagrams $a$ and $b$\nin Fig. 2. The cancellation among the various contributions\nfrom these diagrams does not depend on the details of the structure\nof the baryon propagators (quasiparticle or dressed), but solely on the\nodd parity of the causal Green's function with respect to a\nchange of the sign of the energy argument in the soft neutrino\napproximation.\n\nIn the first step we substitute the vertices. As the contribution\nof the Landau Fermi-liquid part of the interaction\nwill cancel out, to save space, we shall drop its contribution\nfrom the outset. For the diagrams $a$ and $b$ (excluding the\nfactors for the topologically equivalent diagrams) we find\n\\bea\ni\\Pi^{-+, a}_{\\mu \\nu}(q) &=&\n\\left(\\frac{G}{2\\sqrt{2}}\\right)^2\\left(\\frac{f}{m_{\\pi}}\\right)^4\n\\int\\!\\!\\prod_{i=1}^4\n\\left[\\frac{d^4p_i}{(2\\pi)^4}\\right]\\, \\frac{dk}{(2\\pi)^4}\\nonumber\\\\\n&&\\Tr\\Bigl[\\left(\\delta_{\\mu 0}\n-g_A\\delta_{\\mu i}\\sigma_i\\right)\nG^{--}(q+p_4)\\left(\\bsigma\\cdot\\bk\\right) D^{--}(k)\\nonumber \\\\\n&&\\hspace{2cm} G^{-+}(p_3)\n\\left(\\bsigma\\cdot\\bk\\right) D^{++}(k)\nG^{++}(q+p_4)\\left(\\delta_{\\nu 0}-g_A\n\\delta_{\\nu j}\\sigma_j\\right) G^{+-}(p_4)\\Bigr]\\nonumber\\\\\n&&\\Tr\\left[\\left(\\bsigma\\cdot\\bk\\right)\nG^{-+}(p_1)\\left(\\bsigma\\cdot\\bk\\right)G^{+-}(p_2)\\right]\n(2\\pi)^8\\delta(q+p_4-k-p_3)\\delta(k+p_2-p_1),\n\\label{diag_a_app}\n\\eea\n\\bea\ni\\Pi^{-+, b}_{\\mu \\nu}(q) &=& \\left(\\frac{G}{2\\sqrt{2}}\\right)^2\n\\left(\\frac{f}{m_{\\pi}}\\right)^4\n\\int\\!\\!\\prod_{i=1}^4\n\\left[\\frac{d^4p_i}{(2\\pi)^4}\\right]\\, \\frac{dk}{(2\\pi)^4}\\nonumber\\\\\n&&\\Tr\\Bigl[\\left(\\delta_{\\mu 0}-g_A\\delta_{\\mu i}\\sigma_i\\right)\nG^{--}(q+p_4)\\left(\\bsigma\\cdot\\bk\\right) D^{--}(k)\\nonumber\\\\\n&&\\hspace{2cm} G^{-+}(p_3) \\left(\\delta_{\\nu 0}-g_A\\delta_{\\nu j}\\sigma_j\\right)\n\\left(\\bsigma\\cdot\\bk\\right) D^{++}(k)G^{++}(p_3-q)G^{+-}(p_4)\\Bigr]\\nonumber\\\\\n&&\\Tr\\left[\\left(\\bsigma\\cdot\\bk\\right) G^{-+}(p_1)\n\\left(\\bsigma\\cdot\\bk\\right)G^{+-}(p_2)\\right](2\\pi)^8\\delta(q+p_4-k-p_3)\n\\delta(k+p_2-p_1).\n\\label{diag_b_app}\n\\eea\nNext we apply the approximation (\\ref{DENOM_EXP}) to the causal and acausal\nGreen's functions and fix their momenta at the corresponding\nFermi momentum. Combining the diagrams $a$ and $b$, we find\n\\bea\ni\\Pi^{-+, a}_{\\mu \\nu}(q)+ i\\Pi^{-+, b}_{\\mu \\nu}(q) &=&\n\\left(\\frac{G}{2\\sqrt{2}}\\right)^2\\left(\\frac{f}{m_{\\pi}}\\right)^4\n \\int\\!\\!\\prod_{i=1}^4\n\\left[\\frac{d^4p_i}{(2\\pi)^4}\\right]\\, \\frac{dk}{(2\\pi)^4}\\nonumber\\\\\n&&G^{--}(\\omega)^2 D^{--}(k)^2\nG^{-+}(p_1) G^{+-}(p_2)G^{-+}(p_3) G^{+-}(p_4) \\nonumber\\\\\n&&\\Tr\\Bigl\\{\\left(\\delta_{\\mu 0}-g_A\\delta_{\\mu i}\\sigma_i\\right)\n\\left(\\bsigma\\cdot\\bk\\right)\n\\left(\\bsigma\\cdot\\bk\\right)\n\\left(\\delta_{\\nu 0}-g_A\\delta_{\\nu j}\\sigma_j\\right)\\nonumber\\\\\n&& -\\left(\\delta_{\\mu 0}-g_A\\delta_{\\mu i}\\sigma_i\\right)\n\\left(\\bsigma\\cdot\\bk\\right)\n \\left(\\delta_{\\nu 0}-g_A\\delta_{\\nu j}\\sigma_j\\right)\n\\left(\\bsigma\\cdot\\bk\\right)\\Bigr\\}\\nonumber\\\\\n&&\\Tr\\left[\\left(\\bsigma\\cdot\\bk\\right)\n\\left(\\bsigma\\cdot\\bk\\right)\\right]\n(2\\pi)^8\\delta(q+p_4-k-p_3) \\delta(k+p_2-p_1),\n\\label{diag_sum}\n\\eea\nwhere we used the conjugation relation (\\ref{HC4}).\nThe terms under the trace\n$\\propto \\delta_{0\\mu}, \\delta_{0\\nu}$\nvanish. The $\\Pi_{00}$ component of the polarization\nis hence zero and the vector current is conserved.\nThe remainder simplifies to\n\\bea\\label{APP:B1}\n&&i\\Pi^{-+,a}_{i j}(q)+i\\Pi^{-+,b}_{i j}(q)=\ng_A^2 \\left(\\frac{G}{2\\sqrt{2}}\\right)^2\n\\left(\\frac{f}{m_{\\pi}}\\right)^4\\int\\!\\!\\prod_{i=1}^4\n\\left[\\frac{d^4p_i}{(2\\pi)^4}\\right]\\,\\frac{dk}{(2\\pi)^4}\\nonumber\\\\\n&&[G^{--}(\\omega)^2 D^{--}(k)^2\nG^{-+}(p_1) G^{+-}(p_2)G^{-+}(p_3) G^{+-}(p_4) \\nonumber\\\\\n&&\\Tr\\Bigl[\\sigma_{i} \\left(\\bsigma\\cdot\\bk\\right)\n\\left(\\bsigma\\cdot\\bk\\right) \\sigma_{j}\n -\\sigma_{i} \\left(\\bsigma\\cdot\\bk\\right)\n\\sigma_{j}\\left(\\bsigma\\cdot\\bk\\right)\\Bigr]\n\\Tr\\left[\\left(\\bsigma\\cdot\\bk\\right)\n\\left(\\bsigma\\cdot\\bk\\right)\\right]\\nonumber\\\\\n&&\n(2\\pi)^8\\delta(q+p_4-k-p_3) \\delta(k+p_2-p_1).\n\\eea\nThe computation of the trace using the $\\bsigma$-algebra gives\n\\bea\n \\Tr\\left[\\left(\\bsigma\\cdot\\bk\\right)\n\\left(\\bsigma\\cdot\\bk\\right)\\right]\n\\Tr\\Bigl[\\sigma_{i} \\left(\\bsigma\\cdot\\bk\\right)\n\\left(\\bsigma\\cdot\\bk\\right) \\sigma_{j}\n -\\sigma_{i} \\left(\\bsigma\\cdot\\bk\\right)\n\\sigma_{j}\\left(\\bsigma\\cdot\\bk\\right)\\Bigr]\n= 8k^2 \\left(k^2\\delta_{ij} -k_ik_j \\right).\n\\eea\nThe contraction of the polarization tensor with the trace\nof neutrino currents,\ngiven by\n\\be\n\\Tr\\Lambda_{ij} = 8 \\left[q_{1i} q_{2j} + q_{1j} q_{2i}\n+\\left(\\omega_1\\omega_2+\\bq_1\\cdot\\bq_2\\right)\\delta_{ij}\n+\\epsilon_{injm} q_{1}^nq_{2}^m\\right],\n\\ee\nleads to\n\\be\\label{APP:B2}\n 8k^2 \\Tr\\Lambda_{ij}\\left(k^2\\delta_{ij} -k_ik_j \\right)\n = 128 k^4 \\left[\\omega_1\\omega_2 -\n \\frac{(\\bq_1\\cdot \\bk)(\\bq_1\\cdot \\bk)}{k^2} \\right].\n\\ee\nCombining eqs. (\\ref{APP:B1}) and (\\ref{APP:B2})\nwe recover eq. (\\ref{CONTR}).\n\nLet us turn to the fluctuation diagram in Fig. 1c. From the\noriginal diagram one can generate three additional ones\nby turning each of the loops upside-down.\nLet us combine the diagram in Fig. 1c with its counterpart, say $c'$,\nwhich results from $c$ by turning the upper loop upside-down.\nThe analytical expression corresponding to their sum is\n\\bea\ni\\Pi^{-+, c}_{\\mu \\nu}(q)+ i\\Pi^{-+, c'}_{\\mu \\nu}(q) &=&\n\\left(\\frac{G}{2\\sqrt{2}}\\right)^2\\left(\\frac{f}{m_{\\pi}}\\right)^4\n\\int\\!\\!\\prod_{i=1}^4\\left[\\frac{d^4p_i}{(2\\pi)^4}\\right]\\,\n\\frac{dk}{(2\\pi)^4}\\nonumber\\\\\n&&G^{--}(\\omega)^2 D^{--}(k)^2 G^{-+}(p_1)\nG^{+-}(p_2)G^{-+}(p_3)G^{+-}(p_4)\\nonumber\\\\\n&&\\Biggr\\{\\Tr\\Bigl[\\left(\\delta_{\\mu 0}\n-g_A\\delta_{\\mu i}\\sigma_i\\right)\n\\left(\\bsigma\\cdot\\bk\\right)\n\\left(\\bsigma\\cdot\\bk\\right)\n\\Bigr]\\Tr\\left[\\left(\\bsigma\\cdot\\bk\\right)\n\\left(\\delta_{\\nu 0}-g_A\\delta_{\\nu j}\\sigma_j\\right)\n\\left(\\bsigma\\cdot\\bk\\right)\\right]\\nonumber\\\\\n&-&\n\\Tr\\Bigl[ \\left(\\bsigma\\cdot\\bk\\right)\n\\left(\\delta_{\\mu 0}-g_A\\delta_{\\mu i}\\sigma_i\\right)\n\\left(\\bsigma\\cdot\\bk\\right)\\Bigr]\n\\Tr\\left[\\left(\\bsigma\\cdot\\bk\\right)\n\\left(\\delta_{\\nu 0}-g_A\\delta_{\\nu j}\\sigma_j\\right)\n\\left(\\bsigma\\cdot\\bk\\right)\\right]\n\\Biggr\\}\\nonumber\\\\\n&&(2\\pi)^8\\delta(q+p_4-k-p_3)\\delta(k+p_2-p_1),\n\\label{diag_1a1}\n\\eea\nwhere we dropped $\\bq$ compared with $\\bk$ in the strong interaction\nvertex. The contribution due to the axial-vector\ncurrent vanishes because the traces are over odd number of\n$\\bsigma$ matrices; the contribution due\nthe vector current cancels as these are identical for diagrams\n$c$ and $c'$ and are of opposite sign.\n\\end{appendix}\n\n\n\\begin{thebibliography}{99}\n\\bibitem{CHIU_SALPETER} H. Y. Chiu and E. E. Salpeter,\n Phys. Rev. Lett. {\\bf 12}, 413 (1964).\n\\bibitem{BAHCALL_WOLF} J. N. Bahcall and R. A. Wolf,\n Phys. Rev. Lett. {\\bf 14}, 343 (1965);\n Phys. Rev. {\\bf 140}, B1452 (1965).\n\\bibitem{FLOWERS_ETAL} E. G. Flowers, P. G. Sutherland and\n J. R. Bond, Phys. Rev. D {\\bf 12}, 315 (1975).\n\\bibitem{FRIMAN_MAXWELL}B. L. Friman and O. V. Maxwell,\n Ap. J. {\\bf 232}, 541 (1979).\n\\bibitem{VOSKRESENSKY} D. N. Voskresensky and A. V. Senatorov,\n Sov. Phys. JETP {\\bf 63}, 885 (1986);\n Sov. J. Nucl. Phys. {\\bf 45}, 411 (1987).\n\\bibitem{PETHICK} C. J. Pethick, Rev. Mod. Phys. {\\bf 64}, 1133 (1992).\n\\bibitem{RAFFELT_SECKEL} G. 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{
"name": "astro-ph0002228.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{CHIU_SALPETER} H. Y. Chiu and E. E. Salpeter,\n Phys. Rev. Lett. {\\bf 12}, 413 (1964).\n\\bibitem{BAHCALL_WOLF} J. N. Bahcall and R. A. Wolf,\n Phys. Rev. Lett. {\\bf 14}, 343 (1965);\n Phys. Rev. {\\bf 140}, B1452 (1965).\n\\bibitem{FLOWERS_ETAL} E. G. Flowers, P. G. Sutherland and\n J. R. Bond, Phys. Rev. D {\\bf 12}, 315 (1975).\n\\bibitem{FRIMAN_MAXWELL}B. L. Friman and O. V. Maxwell,\n Ap. J. {\\bf 232}, 541 (1979).\n\\bibitem{VOSKRESENSKY} D. N. Voskresensky and A. V. Senatorov,\n Sov. Phys. JETP {\\bf 63}, 885 (1986);\n Sov. J. Nucl. Phys. {\\bf 45}, 411 (1987).\n\\bibitem{PETHICK} C. J. Pethick, Rev. Mod. Phys. {\\bf 64}, 1133 (1992).\n\\bibitem{RAFFELT_SECKEL} G. Raffelt and D. Seckel, Phys. Rev. Lett.\n {\\bf 67}, 2605 (1991); Phys. Rev. D {\\bf 52},\n 1780 (1995).\n\\bibitem{JANKA} H.-T. Janka, W. Keil, G. Raffelt, D. Seckel, Phys. Rev.\n Lett. {\\bf 76}, 2621 (1996).\n\\bibitem{RAFFELT} G. Raffelt, {\\it Stars as Laboratories for\n Fundamental Physics}\n (Univ. Chicago Press, Chicago, 1996).\n\\bibitem{HANESTAD} S. Hannestad and G. Raffelt, Astrophys. J. {\\bf 507},\n 339 (1998).\n\\bibitem{LP} L. D. Landau and I. Ya. Pomeranchuk, Dokl. Akad. Nauk\n SSSR {\\bf 92} 535 (1953); {\\it ibidem} {\\bf 92}, 375 (1953).\nA. B. Migdal, Phys. Rev. {\\bf 103}, 1811 (1956).\n\\bibitem{KNOLL_VOSKRESENSKY} J. Knoll and D. N. Voskresensky,\n Ann. Phys. (NY) {\\bf 249}, 532 (1996).\n\\bibitem{IWAMOTO_PETHICK} N. Iwamoto and C. J. Pethick, Phys. Rev. D {\\bf 25},\n 313 (1982).\n\\bibitem{SAWYER} R. F. Sawyer, Phys. Rev. C {\\bf 40}, 865 (1989);\n Phys. Rev. Lett., {\\bf 75}, 2260 (1995).\n\\bibitem{HOROWITZ} C. J. Horowitz and K. Wehrberger,\n Nucl. Phys. A {\\bf 531}, 665 (1991).\n\\bibitem{HAENSEL} P. Haensel and A. J. Jerzak, Astron. Astrophys. {\\bf 179},\n 127 (1987).\n\\bibitem{BURROWS} A. Burrows and R. F. Sawyer, Phys. Rev. C\n {\\bf 58}, 554 (1998).\n\\bibitem{REDDY_ETAL} S. Reddy, M. Prakash and J. M. Lattimer,\n Phys. Rev. D {\\bf 58}, 013009 (1998).\n\\bibitem{BRAATEN} E. Braaten and R. D. Pisarski, Nucl. Phys. B {\\bf 337},\n 569 (1990).\n\\bibitem{SD} A. Sedrakian and A. Dieperink, Phys. Lett B {\\bf 463}, 145 (1999).\n\\bibitem{KADANOFF_BAYM} L. P. Kadanoff and G. Baym,\n {\\it Quantum Statistical Mechanics}\n (Benjamin, New York, 1962).\n\\bibitem{MALFLIET} W. Botermans and R. Malfliet, Phys. Rep. {\\bf 198},\n 115 (1990).\n\\end{thebibliography}"
}
] |
astro-ph0002229
|
BeppoSAX spectrum of GRB971214: evidence of a substantial energy output during afterglow
|
[
{
"author": "D. Dal~Fiume\\inst{1}"
},
{
"author": "L. Amati \\inst{1}"
},
{
"author": "L. A. Antonelli\\inst{2,3}"
},
{
"author": "F. Fiore\\inst{2,3}"
},
{
"author": "J. M. Muller\\inst{2,4}"
},
{
"author": "A. Parmar\\inst{5}"
},
{
"author": "N. Masetti\\inst{1}"
},
{
"author": "E. Pian\\inst{1}"
},
{
"author": "E. Costa\\inst{6}"
},
{
"author": "F. Frontera \\inst{1,7}"
},
{
"author": "L. Piro\\inst{6}"
},
{
"author": "J. Heise\\inst{4}"
},
{
"author": "R. C. Butler\\inst{8}"
},
{
"author": "A. Coletta\\inst{3}"
},
{
"author": "M. Feroci\\inst{6}"
},
{
"author": "P. Giommi\\inst{2}"
},
{
"author": "L. Nicastro\\inst{9}"
},
{
"author": "M. Orlandini\\inst{1}"
},
{
"author": "E. Palazzi\\inst{1}"
},
{
"author": "G. Pizzichini\\inst{1}"
},
{
"author": "M. Tavani\\inst{10}"
}
] |
We report the X/$\gamma$-ray spectrum of GRB971214 and of its afterglow. The afterglow was measured few hours after the main event and for an elapsed time of more than two days. The measure of this GRB and afterglow is relevant due to its extreme, cosmological distance (z=3.42). The prompt event shows a hard photon spectrum, consistent with a broken power law with photon indices $\Gamma_{X}\approx$0.1 below $\sim$20 keV and $\Gamma_\gamma\approx$1.3 above 60 keV. The afterglow spectrum, measured with the MECS and LECS BeppoSAX telescopes, is consistent with a power law with spectral photon index $\Gamma$=1.6. Within the statistical accuracy of our measure no spectral evolution is detected during the observation of the afterglow. When integrated during the time span covered by BeppoSAX observations, the power in the afterglow emission, even with very conservative assumptions, is at least comparable with the power in the main event. The IR-to-X rays broad band spectrum is also presented, collecting data from the literature and adding them to the BeppoSAX measure. It shows that the predictions from synchrotron emission models is qualitatively confirmed. The BeppoSAX measurement of the X and $\gamma$ ray spectrum of this GRB/afterglow is discussed in the framework of current theoretical models
|
[
{
"name": "grb971214.tex",
"string": "% \n% LATEX file for paper on \n% The energy spectrum of GRB971214\n% ddf et al.\n% \n% Tue Jan 11 10:36:01 MET 2000\n% Submitted to the Publisher\n% Thu Feb 10 16:28:36 MET 2000\n% Uploaded to LANL preprint archive\n% \n%\\documentstyle[referee,epsf,times]{aa} \n\\documentstyle[epsf,times]{aa} \n\\def\\Ldot{$L_0 \\ $} \n\\def\\Rdot{$R_0 \\ $} \n\\def\\ha{$cm^{-2}$} \n\\def\\Md{$\\dot M$} \n\\def\\Mdot{ \\dot M} \n\\def\\mdot{ \\dot m} \n\\def\\Ms{M_\\odot} \n\\def\\rerg{\\rm erg} \n\\def\\rs{\\rm s} \n\\def\\rs1{\\rm s$^{-1}$} \n\\def\\fxg{f_{X/\\gamma} } \n\\def\\fxgb{\\bf f_{X/\\gamma} } \n\\def\\rcm{\\rm cm} \n\\def\\rcm2{$\\rm cm^{-2}$} \n\\def\\deg{\\rm ^{\\circ}} \n\\def\\ergs{\\rerg\\ \\rcm2\\ \\rs1} \n\\def\\flux{\\mbox{ } {\\rm erg} \\mbox{ } {\\rm cm}^{-2}} \n\\def\\rkeV{\\rm keV} \n\\def\\reV{\\rm eV} \n\\def\\etal{{et al.}} \n\\def\\apj{{ApJ }\\ } \n\\def\\apjl{{ApJ }\\ } \n\\def\\apjs{{ApJS }\\ } \n\\def\\pasj{{PASJ }\\ } \n\\def\\nature{{Nat }\\ } \n\\def\\aa{{A\\&A}\\ } \n\\def\\aas{{A\\&AS}\\ } \n\\def\\mnras{{MNRAS}\\ } \n\\def\\iauc{{IAU Circ.}\\ }\n \n\\thesaurus{03(13.07.1; 13.07.2; 13.25.3)}\n\n\\title{BeppoSAX spectrum of GRB971214: evidence of a substantial energy\noutput during afterglow}\n \n\\author{D. Dal~Fiume\\inst{1}\n \\and L. Amati \\inst{1} \\and L. A. Antonelli\\inst{2,3} \\and F. Fiore\\inst{2,3}\n \\and J. M. Muller\\inst{2,4} \\and A. Parmar\\inst{5} \\and N. Masetti\\inst{1}\n \\and E. Pian\\inst{1}\n \\and E. Costa\\inst{6} \\and F. Frontera \\inst{1,7} \\and L. Piro\\inst{6}\n \\and J. Heise\\inst{4} \\and R. C. Butler\\inst{8} \\and A. Coletta\\inst{3}\n \\and M. Feroci\\inst{6} \\and P. Giommi\\inst{2}\n \\and L. Nicastro\\inst{9} \\and M. Orlandini\\inst{1}\n \\and E. Palazzi\\inst{1} \\and G. Pizzichini\\inst{1} \n \\and M. Tavani\\inst{10}}\n \n\\institute{\nIstituto di Tecnologie e Studio delle Radiazioni Extraterrestri\n (TeSRE), C.N.R., via Gobetti 101, I-40129 Bologna, Italy\n\\and Beppo-SAX Scientific Data Center, Via Corcolle 19, I-00131 \n Roma, Italy \n \\and\n Osservatorio Astronomico di Roma, Via Frascati 33, I-00044 Roma, Italy\n \\and\n Space Research Organization Netherlands, \n Sorbonnelaan 2, NL-3584 CA Utrecht, The Netherlands\n \\and\n Astrophysics Division, Space Science Department of ESA, \n ESTEC, P.O. Box 299, NL-2200 AG Noordwijk, The Netherlands\n \\and\n Istituto di Astrofisica Spaziale (IAS), C.N.R., Via Fosso del Cavaliere,\n I-00133 Roma, Italy\n \\and\n Dipartimento di Fisica, Universit\\`a di Ferrara, Via Paradiso 12,\n I-44100 Ferrara, Italy\n \\and\n Agenzia Spaziale Italiana, Viale Regina Margherita 202, \n I-00198 Roma, Italy\n \\and\n Istituto di Fisica Cosmica con Applicazioni all'Informatica (IFCAI),\n C.N.R., Via U. La Malfa 153, I-90139, Palermo, Italy\n \\and\n Istituto di Fisica Cosmica ``G. P. S. Occhialini'',\n C.N.R., via Bassini 15, I-20133 Milano, Italy\n }\n\\offprints{D.~Dal~Fiume --- daniele@tesre.bo.cnr.it}\n\\date{Received [date]; accepted [date]}\n\n\\begin{document} \n\n\\titlerunning{GRB971214 and its afterglow}\n\\authorrunning{D. Dal Fiume et al.}\n\\maketitle\n\n\\begin{abstract}\nWe report the X/$\\gamma$-ray spectrum of GRB971214 and of its afterglow.\nThe afterglow was\nmeasured few hours after the main event and for an elapsed time of more\nthan two days. The measure of this GRB and afterglow is relevant due to\nits extreme, cosmological distance (z=3.42). The prompt event shows a\nhard photon spectrum, consistent with a broken power law with photon\nindices $\\Gamma_{\\rm X}\\approx$0.1 below $\\sim$20 keV and\n$\\Gamma_\\gamma\\approx$1.3 above 60 keV.\nThe afterglow spectrum, measured with the MECS and LECS\nBeppoSAX telescopes, is consistent with a power law with spectral photon\nindex $\\Gamma$=1.6. Within the statistical accuracy of our measure no\nspectral evolution is detected during the observation of the afterglow.\nWhen integrated during the time span covered by BeppoSAX\nobservations, the power in the afterglow emission, even with very\nconservative assumptions, is at least comparable with the power in the\nmain event. The IR-to-X rays broad band spectrum is also presented,\ncollecting data from the literature and adding them to the BeppoSAX measure.\nIt shows that the predictions from synchrotron emission models is\nqualitatively confirmed. The BeppoSAX measurement of the X and $\\gamma$\nray spectrum of this GRB/afterglow is discussed in the framework of\ncurrent theoretical models\n\\end{abstract}\n\n\\keywords{Gamma rays: bursts - Gamma rays: \nobservations - X rays: general}\n\n\\section{Introduction}\n\nThe discovery of X-ray afterglows from Gamma-ray Bursts (GRBs) (Costa et\nal. \\cite{costa})\nis a major step forward to understand this still mysterious\nphenomenon. The detection of the faint, fading X-ray counterparts of GRBs\nposes tight constraints to the models for the emission. Multiwavelength\nstudies discovered optical, IR and radio transients associated with the\nX-ray afterglow, thanks to the unprecedented positioning accuracy\nobtained with BeppoSAX. The discovery of a substantial redshift\n(Kulkarni et al. \\cite{kulkarni_c,kulkarni_n}) in the absorption \nand emission lines in the spectra of the host galaxies associated\nwith the GRBs optical transients puts these catastrophic events at a\ncosmological distance and results in an extreme energy output from each\nGRB, if the emission is isotropic. \n\nThe recent advances in our knowledge about the cosmic events\nknown as GRBs were mainly due to the accurate positioning allowed by\nBeppoSAX (Boella et al. \\cite{boella}).\nThis satellite carries on board an optimal set of\ninstruments to detect GRBs (the Gamma Ray Burst Monitor - GRBM\nFrontera et al. \\cite{frontera}, Feroci et al. \\cite{ferocigrbm} ),\nto position them within a few arcminutes (the Wide\nField Cameras - WFC; Jager et al. \\cite{jager})\nand finally to pinpoint the positions\ndown to tens of arcseconds thanks to rapid (few hours) follow-up \nobservations with the\nNarrow Field Instruments (Low Energy Concentrator Spectrometer - LECS;\nParmar et al. \\cite{parmar};\nMedium Energy Concentrator Spectrometer - MECS; Boella et al.\n\\cite{boella2}; High Pressure Gas Scintillation Proportional Counter -\nHPGSPC; Manzo et al. \\cite{manzo};\nPhoswich Detection System - PDS; Frontera et al. \\cite{frontera} )\n\nThe positions given by BeppoSAX (e.g. Piro et al. \\cite{piro} for\n\\object{GRB960720}) allowed prompt ground based observations\nwith telescopes in optical, radio, IR. Up to now thirteen Optical\nTransients (OT) were discovered in the error boxes of the X-ray\nafterglows (van Paradijs et al. \\cite{ot_1}, Bond \\cite{ot_2},\nHalpern et al. \\cite{halpern}, Groot et al. \\cite{ot_3}, Palazzi et al.\n\\cite{ot_4}, Galama et al. \\cite{ot_5}, Jaunsen et al. \\cite{ot_6},\nHjorth et al. \\cite{ot_7}, Bloom et al. \\cite{ot_8},\nKulkarni et al. \\cite{ot_9}, Galama et al. \\cite{ot_10}, Palazzi et al.\n\\cite{ot_11}, Bakos et al. \\cite{ot_12}). \nAfter the fading of the OT in most cases a faint galaxy was detected.\nThe detection of the putative host galaxy of GRB971214 is particularly\nintriguing as the estimate of the\nredshift is z=3.42, locating this event at an extreme cosmological\ndistance (Kulkarni et al. \\cite{kulkarni_n}). \n\nWe observed with BeppoSAX a GRB on December 14.97272 UT 1997\n(Heise et al. \\cite{heise_grb}). A follow-up pointing performed 6.67 hours\nafter the main event detected the faint and fading X-ray source\n\\object{1SAX J1156.4+6513}\n(Antonelli et al. \\cite{antonelli}). After the fading\nof the optical transient, spectroscopic observations of the associated\nhost galaxy tentatively put it at cosmological distance, as the estimate of\nits redshift is z=3.42 (Kulkarni et al. \\cite{kulkarni_n}),\nthat corresponds to a luminosity distance $>$30 Gpc (for H$_0$=65 km s$^{-1}$ \nMpc$^{-1}$ and $\\Omega_0$=0.2). The\ncomplete evolutionary history of the emitted spectrum from X to $\\gamma$\nrays up to 2.5 days after the main event suggests that the afterglow in\nX-rays begins immediately. The energy output in the afterglow results to\nbe comparable to that in the prompt event.\nWith the new wealth of data on optical counterparts and X--ray\nafterglows, a major revamping of theoretical models is\noccurring. With the extragalactic origin firmly established on the basis\nof observations of host galaxies (Metzger et al. \\cite{metzger},\nKulkarni et al. \\cite{kulkarni_n, ot_9}), the cosmological fireball model\n(e.g. Cavallo \\& Rees \\cite{cavallo}, M\\'esz\\'aros \\& Rees\n\\cite{meszrees1}) gives predictions that reasonably fit to\nobservational data. In this paper we discuss\nthe details of the prompt and delayed emission from GRB971214, with\nemphasis on the X and $\\gamma$ ray spectrum and on its evolution with time.\nImplications on the models of the prompt event and of the afterglow\nare discussed.\n\n\\section{Observations}\n\\object{GRB971214} was detected in Lateral Shield 1 of GRBM and in WFC 1 on\nDecember 14.97272 UT. The burst lasted approximately 30 s, with two\nleading broad peaks (3s and 10 s FWHM) and a third fainter and sharper\npeak (1s FWHM) 34s after trigger. The GRB profile is shown in Fig.\n1, as measured by GRBM LS1 and WFC1.\n\n\\begin{figure}\n\\epsfxsize=\\columnwidth\n\\epsfbox{grb971214.f1}\n\\caption[]{\nGRB971214 as observed by BeppoSAX. Top panel: WFC1 (1 second time\nresolution -- E=1--26 keV).\nMiddle panel: GRBM LS1 ratemeter (1 second time resolution -- E=40--700 keV).\nBottom panel: GRBM LS1 AntiCoincidence ratemeter (1 second time\nresolution -- E$>$100 keV).\nZero time corresponds to the GRBM BeppoSAX trigger time.\nTop scale: time in the GRB reference frame (assuming z=3.42). Bottom\nscale: time in the Earth reference frame.}\n\\label{fig:lcurve}\n\\end{figure}\n\n\nThe analysis of the WFC data was performed using WFC\ndata reduction software version 103106.\nData reduction, background subtraction\nand spectral analysis of GRBM data were performed using dedicated SW\ntools (Amati et al. \\cite{amati})\nThe latest release of the WFC and GRBM response matrices were used.\nAll the spectral fits reported in this article were performed\nusing XSPEC, version 10.0 (Arnaud \\cite{xspec}).\n\n\\begin{figure}\n\\epsfxsize=\\columnwidth\n\\epsfbox{grb971214.f2}\n\\caption[]{\nTop panel: the emitted spectrum of GRB971214 in the $\\gamma$-ray \nand X-ray band. A fit with a broken power law is indicated as a \nsolid line. Bottom panel: the joint confidence contour for $\\Gamma_1$\nand $\\Gamma_2$. 68\\% and 90\\% confidence levels are shown.\n}\n\\label{fig:grbspectrum}\n\\end{figure}\n\nWe fitted the joint spectrum with the spectral shape of Band et al.\n(\\cite{band})\n($\\chi^2_{\\rm dof}$=1.99 for 22 degrees of freedom) and with a power law \nwith exponential cutoff ($\\chi^2_{\\rm dof}$=1.98 for 22 degrees of freedom).\nBoth give systematic residuals in the WFC energy band.\nThe best fit is obtained using a broken power law ($\\chi^2_{\\rm dof}$=1.6\nfor 21 degrees of freedom). An F--test shows that the improvement is not\nsignificant.\nThe average joint Wide Field Camera/Gamma Ray Burst Monitor spectrum \nduring the burst can be well described by a broken power\nlaw with photon indices $\\Gamma_1$=0.13 and $\\Gamma_2$=1.3 and a break energy \nat $\\sim$10 keV. Given the gap between WFC and GRBM spectra,\napproximately between 10 and 50 keV, a large uncertainty in the position\nof the break is present and must be added to the statistical uncertainty\nquoted in Table 1.\nThe fits with all the above functions are statistically unacceptable,\nbut we estimate that\na substantial contribution to the high value of $\\chi^2_{\\rm dof}$ is\ndue to systematic uncertainties in the spectral deconvolution. \nTherefore we do not consider to add further components to improve the fit.\nThe results from all the spectral fits we performed are reported in Table 1.\nIn Fig. 2 we report the count rate spectrum from WFC1 plus GRBM LS1.\nIn the same figure we report the joint confidence contours for the two\nspectral indices of the broken power law.\n\n\\begin{table*}\n\\caption{Spectral fit parameters}\n\\begin{flushleft}\n\\begin{tabular}{llllll}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\nStart$^{(1)}$ & End$^{(1)}$ & $\\Gamma_1$ & $\\Gamma_2$ & \nE$_{\\mbox{cut}}$ & $\\chi^2_{\\rm dof}$ \\\\\ntime & time & & & (keV) & (dof)\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n\\multicolumn{6}{c}{Average spectra}\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n0 & 35&0.13$^{+0.33}_{-0.47}$&1.33$\\pm$0.05&10$^{+2.3}_{-1.5}$&1.6(21)\\\\\n23300 & 215000 &1.6$\\pm 0.2$& & &0.94(20)\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n\\multicolumn{6}{c}{Time resolved spectra}\\\\\n\\hline\n\\noalign{\\smallskip}\n0 & 9 &0.37$\\pm$0.23&1.4$\\pm$0.11&95$\\pm$14&0.64(12)\\\\\n9 & 20&0.33$\\pm$0.27&1.0$\\pm$0.02&50$\\pm$4&0.63(12)\\\\\n23300 &75000&1.9$^{+0.39}_{-0.34}$& & &0.7(11)\\\\\n75000 &125000&1.42$^{+0.85}_{-0.68}$& & &0.28(5)\\\\\n125000&215000&1.23$^{+0.75}_{-0.91}$& & &0.44(2)\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n\\multicolumn{6}{l}{\\footnotesize (1) Seconds from trigger time}\\\\\n\\multicolumn{6}{l}{\\footnotesize NOTE: errors are single parameter 68\\%\nconfidence level}\n\\end{tabular}\n\\label{tab:spectralfits}\n\\end{flushleft}\n\\end{table*}\n\nThe joint confidence contour between $\\Gamma_2$ and the break energy\n(not reported in Fig. 2)\nsuggests that the GRB spectrum shows a bending above $\\approx$ 10 keV but\nthe hard X-ray/$\\gamma$ ray spectrum above 50 keV is consistent with a\nsingle power law. A fit with a power law plus exponential cutoff gives\nan e-folding energy of $\\sim$300 keV.\nThis is in the \"hard\" tail of the distribution from statistical studies of \nBATSE GRB spectra (Band et al. \\cite{band}),\nin which a broad interval of break energies from 50\nkeV to more than 1 MeV was found, with the majority of GRBs having a\ncutoff energy below 200 keV, and confirms that this GRB has a very hard\nspectrum.\n\nWe analyzed separately the spectra of the first and of the second peak.\nWe find evidence that the second peak is at least as hard as the first one.\nThis result is different from the hard-to-soft evolution that\nseems to be present in most GRBs (Preece et al. \\cite{preece}).\nIn this respect\nthe properties of GRB971214 are distinct from those observed on the\naverage in GRBs.\n\nThe burst fluences are 1.9\n$\\pm 0.4 \\times 10^{-7} \\flux$ in 2-10 keV and 8.8 \n$\\pm 0.8 \\times 10^{-6} \\flux$ in 40-700 keV.\nThe fluence in hard X-rays/$\\gamma$ rays is in good agreement with \nthat measured with BATSE (Kippen et al. \\cite{batse_fluence}).\nAssuming a redshift z=3.42 (Kulkarni et al. \\cite{kulkarni_n})\nin a standard Friedmann\ncosmology (with H$_0$=65 km s$^{-1}$ Mpc$^{-1}$ and $\\Omega_0$=0.2) the\nluminosity distance is 1.05$\\times 10^{29}$ cm. At this distance the\nobserved fluences correspond to 6 $\\pm 1.2 \\times 10^{51} $ ergs in\n2-10 keV and 2.8$\\pm 0.25 \\times 10^{53} $ ergs in 40-700 keV for an\nisotropically emitting source. Here we assume that\nL$_{\\rm grb}={\\rm F}_{\\oplus} 4\\pi {\\rm D}_{\\rm L}^2 (1+{\\rm z})^{-1}$\n(e. g. Hakkila et al. \\cite{hakkila}).\nIf we assume the measured slope of the GRB spectrum (see Table 1),\nL$_{\\rm grb}={\\rm F}_{\\oplus} 4\\pi {\\rm D}_{\\rm L}^2 (1+{\\rm z})^{-1.3}$\nand the luminosity is a factor 1.6 lower in the hard band.\nThe energy ranges correspond to 4.4-44\nkeV and 180-3090 keV at the source. The X-to-$\\gamma$ fraction\nis therefore 0.02. This can be compared to other fractions measured\nfor other GRBs as reported in Frontera et al. (\\cite{frontera_grb})\nthat range from 0.39 for \\object{GRB970508} to 0.01 for \n\\object{GRB980329}. Therefore this GRB\nshows one of the lowest ratios, i. e. the hardest spectrum, amongst those\nobserved with BeppoSAX. Of course such a comparison is made {\\it\nwithout} taking into account possible substantial differences in redshift\namongst the different GRBs.\nIf the emitted X-$\\gamma$ ray spectrum has a break somewhere above 10\nkeV, the redshift due to the extreme cosmological distance shifts this\nbreak to a lower energy in the spectrum as observed at earth, possibly\naffecting the fluence ratio.\n\n\\begin{figure}\n\\epsfxsize=\\columnwidth\n\\epsfbox{grb971214.f3}\n\\caption[]{\nTop panel: the emitted spectrum of 1SAX J1156.4+6513 in the \n0.7-10 keV energy band as measured with the LECS and MECS telescopes.\nBottom panel: the joint confidence contour for $\\Gamma$ and N$_{\\mbox{H}}$.\n68\\% and 90\\% confidence levels are shown.\\\\\nNote that the model assumes a redshift {\\it z}=3.42.}\n\\end{figure}\n\nAfter the detection of GRB971214 and its positioning using WFC1\n(Heise et al. \\cite{heise_grb}),\nBeppoSAX was rescheduled to point the center of the WFC error box.\nThe observation started on December 15.24583 UT ($\\sim$6.5 hours after the\ngamma--ray burst) and lasted until December 17.50069 UT for a total\nelapsed time of 2.25 days.\nA faint source, 1SAX J1156.4+6513 at $\\alpha_{2000}$=\n11$^{\\rm h}$ 56$^{\\rm m}$ 25$^{\\rm s}$ and \n$\\delta_{2000}$=+65$^{\\rm o}$ 13' 11'' (Antonelli et\nal. \\cite{antonelli}),\nwas clearly detected in the center of the MECS/LECS field of view. \nThe accuracy in the position is $\\sim$1'. This accuracy is largely\ndominated by uncertainties in the reconstructed BeppoSAX attitude in the\nnew 1-gyro mode that is implemented since summer 1997.\nThe S/N ratio for the entire observation is $\\sim$12 in the MECS. \nTherefore the source is detected with high significance.\nThe following data analysis was performed using the SAXDAS data\nreduction software, version 1.2, and\nthe latest release of the LECS and MECS response matrices.\n\nThe X-$\\gamma$ decay curve is discussed in more detail in Heise et al.\n(in preparation). The source faded smoothly during the observation.\nA S/N analysis of the count rates accumulated in twenty time intervals\nspanning the entire observation shows that the source is visible up to\nthe end of the NFI observation.\nA $\\chi^2$ test against constant count rate gives a chance probability\n$<10^{-5}$ ($\\chi^2_{\\rm dof}= 3.7$ for 19 dof).\nThe same test performed on a light curve extracted in a\nsource free region is consistent with a constant count rate ($\\chi^2_{\\rm dof}=\n0.76$ for 19 dof).\n\nThe spectrum averaged on the entire observing time is consistent with a\nsingle power law with spectral index $\\Gamma = 1.6\\pm 0.2$ (see Table 1).\nThe measured value of N$_{\\rm H}$ (1$^{+2.3}_{-1}\\times 10^{21}$) cm$^{-2}$\nis completely consistent with the expected value due to\ngalactic absorption along the line of sight N$_{\\rm H} \\approx 1.6\\times\n10^{20}$ cm$^{-2}$. To have a meaningful upper limit for N$_{\\rm H}$\nat the GRB frame,\nif the association of GRB971214 with the host galaxy is\ncorrect and therefore its redshift is 3.42, the measure of N$_H$ coming\nfrom the formal fit with a non-redshifted function is useless. We\ntherefore performed also an analysis using a redshifted model. The\npower law index is obviously unchanged, while the N$_{\\rm H}$ value is\ncompletely not determined. The measured 2-10 keV flux is 2.55$\\pm 0.2\\times\n10^{-13}$\\ergs, corresponding to a total 2-10 keV fluence of 4.9$\\times\n10^{-8}$ erg \\rcm2 from 23300 s to 215000 s after the GRB.\nIn Fig. 3 we show the count rate spectrum with the fitted power law\nand the joint confidence contours (68\\% and 90\\%) for $\\Gamma$ and\nN$_{\\rm H}$.\n\nWe analyzed separately the spectrum in three time intervals, to search for\nspectral variations. Within the accuracy of our detection, the three\ntime resolved spectra are consistent with no spectral variation.\n\n\n\\section{The broad band spectrum of the afterglow}\n\nFor the afterglow of GRB971214, we collected from the literature (see\ncaption of Fig. 4 for references) optical and near-IR data taken on 1997\nDec 15, 16 and 17 to construct broad-band spectra from IR to X-rays. To\ndetermine the magnitudes of the Optical Transient (OT), we first\nsubtracted from the measurements the contribution of the host galaxy, for\nwhich we considered V=26.5 (Odewahn et al. \\cite{odewahn}),\nR=25.6 (Kulkarni et al. \\cite{kulkarni_n}), I=25.4, J=25.0, K=24.5,\nestimated from H$_{\\rm host} = 23.7$ by Fruchter et al. (in preparation)\nassuming a flat IR spectrum. Next, we corrected the resulting OT\nmagnitudes for the foreground Galactic absorption using A$_{\\rm V}$ = 0.1\n(from Dickey \\& Lockman \\cite{dickey}) and the extinction law by Cardelli\net al. (\\cite{cardelli}). For each of the three\nconsidered epochs, we referred all data points taken on that night to the\ndates 1997 Dec 15.51 (t$_1$), 16.51 (t$_2$), and 17.50 (t$_3$),\nrespectively. If needed, we rescaled the data to the corresponding\nreference date using a power law decay with index $\\beta_{\\rm t\\_opt}$ =\n$-$1.2 $\\pm$ 0.02 (Diercks et al. \\cite{diercks}). \n\nWe also considered a possible dust obscuration at the source redshift,\nbased on the hypothesis that GRBs could be associated with star formation\n(e.g. Paczy\\'nski \\cite{paczynski}),\nand applied to the OT data the extinction law of\nCalzetti (\\cite{calzetti}) for a typical starburst galaxy at\nz=3.42 (details about this correction will be reported in Masetti et\nal. in preparation).The\ncorrected data together with the 2-10 keV fluxes observed at epochs t$_1$\nand t$_2$ and the extrapolation at epoch t$_3$ of the X-ray flux in the\nsame band are reported in Fig. 4. \n\n\\begin{figure}\n\\epsfxsize=\\columnwidth\n\\epsfbox{grb971214.f4}\n\\caption[]{\nNear-infrared, optical and X-ray data of the afterglow of GRB971214 at\nthree epochs. Optical/IR data are from Diercks et al. (\\cite{diercks}),\nHalpern et al. (\\cite{halpern}), Ramaprakash et al. (\\cite{ramaprakash})\nand Kulkarni et al. (\\cite{kulkarni_n}).\nThe IR and optical data have been corrected for Galactic and\nintrinsic absorption (see text). The X-ray data are corrected for\nGalactic extinction. The power law fits to the simultaneous\nJ-band-to-X-ray data are shown (solid lines) along with their 1$\\sigma$\nconfidence ranges (dotted lines). The GRB trigger time is defined as\nt$_0$.}\n\\end{figure}\n\nThe optical and X-ray data are well fitted, in a F$_\\nu$\nversus $\\nu$ diagram, by single power laws with slopes \n$\\alpha_{\\rm opt\\_X}$ = $-0.95 \\pm 0.02$ (t$_1$), \n$\\alpha_{\\rm opt\\_X}$ = $-0.90 \\pm 0.04$ (t$_2$), and \n$\\alpha_{\\rm opt\\_X}$ = $-0.88 \\pm 0.04$ (t$_3$). \nThese values are all marginally consistent among each other\nwithin the 1$\\sigma$ uncertainties\nand with the slope of the 2-10 keV X-ray spectrum $\\alpha_{\\rm X} =\n-0.6\\pm 0.2$, and are compatible with the value $\\alpha_{\\rm exp}$ =\n$-$0.8, expected for $\\beta_{\\rm t}$ = $-$1.2 if the peak frequency\n$\\nu_{\\rm m}$ of the afterglow multiwavelength spectrum, produced by a\nsingle synchrotron radiation component, has already passed the optical/IR\nband and the cooling frequency $\\nu_{\\rm c}$ has not ({\\it slow cooling\ncase}, Waxman \\cite{waxman_1,waxman_2}, Sari et al. \\cite{sari}). \n\nThe presence of a spectral turnover in the IR, already noted by\nRamaprakash et al. (\\cite{ramaprakash}), who applied {\\it a\nposteriori} an extinction correction to the optical/near-IR\nafterglow data, could be identified with the change of spectral slope at\nthe frequency $\\nu_{\\rm m}$ in the framework of the above-mentioned model\n(see however Wijers \\& Galama \\cite{wijers}).\nThe rather low statistical quality\nof the IR data prevents an accurate measure of the spectral index\n$\\alpha_{\\rm IR} = 0.75^{+1.05}_{-1.15}$ for epoch t$_1$, that is\nconsistent with the expected value 0.33. \n\nAfterglow data shown in Fig. 4 are quite remarkable.\nThe broad-band spectrum over four decades of\nphoton energy clearly shows that the optical and\nX-ray emission vary in a coordinated way.\nThe deduced broad-band energy index\n$\\alpha'_{\\rm opt\\_X} \\sim -1$ (within uncertainties)\nindicates a {\\it flat $\\nu \\, {\\rm F}_{\\nu}$ spectrum\nfor three decades of photon energy}.\nIn a model for which the optical and X-ray afterglow emission\nis produced by a single distribution of energized particles,\nthe flatness of the $\\nu \\, {\\rm F}_{\\nu}$ spectrum can be\nobtained only by a very efficient acceleration process\nthat has to operate despite the radiation and adiabatic losses.\nIn our data extending up to 2.5 days after the prompt burst \nemission,\nthere is no sign of a spectral break due to a transition\nbetween fast and slow cooling. Other bursts behave differently,\nwith breaks observed both in the lightcurves and spectra\nat late times (e.g. GRB990123, Akerlof et al. \\cite{rotse},\nGRB990510, Harrison et al. \\cite{harrison}).\n\n\n\\section{Discussion}\n\nVarious authors have discussed the emission in the afterglow (e.g.\nTavani \\cite{tavani}, Vietri \\cite{vietri}, M\\'esz\\'aros \\&\nRees \\cite{meszrees}, Sari et al. \\cite{sari}, Waxman \n\\cite{waxman_1,waxman_2}), giving a convincing answer to the\nproblem of light curve modeling.\\\\\nThe observed decay during the afterglow (Heise et al. in preparation)\nsmoothly reconnects\nwith the observed X-ray flux during the burst. In the hypothesis that\nthe afterglow starts a few seconds after the end of the main event,\nwe can\nestimate the total fluence in the afterglow, to be compared with\nthe X-ray luminosity during the prompt event. This hypothesis is\nsupported by the recent detection of an optical afterglow in GRB990123\na few seconds after the burst trigger (Akerlof et al. \\cite{rotse})\nand by the interpretation of the observed complex light curve (Sari \\&\nPiran \\cite{sapir_grb99}).\nAlso the detection of an early power--law--like tail from GRB920723\n(Burenin et al. \\cite{granat}) supports the hypothesis that the\nafterglow starts\nimmediately after the GRB, and probably without any interruption in the\nX--ray flux.\nOf course this assumption adds further uncertainty to the total\nestimate. As an example, assuming that the afterglow starts $\\sim$1000 s\nafter the trigger of the main event (and not a few seconds after {\\it the\nend} of the main event) the total integral differs by a factor $\\sim$2.\n\n\nIn doing this estimate we have to assume a spectral shape and slope.\nAssuming a time decay law $\\propto {\\rm t}^{-\\beta_{\\rm t\\_X}}$ with\n$\\beta_{\\rm t\\_X}\\sim$1.2 (Heise et al. in preparation), \nwe obtain that the total fluence in the afterglow between 2 and 10 keV\nuncorrected for redshift is 4.1 $\\times 10^{-7}$ erg \\rcm2. It\ncorresponds to a luminosity of 1.3$\\times 10^{52}$ erg.\nThis is 2 times the total luminosity in the same energy band during the\nburst. This is a lower limit, as we do not add any time evolution\nof the spectral shape, but we conservatively adopt the measured spectral\nindex during the afterglow, much steeper than that measured during the\nprompt event.\n\nIf we assume a similar, or even steeper, spectral slope in the 2-700\nkeV energy interval (uncorrected for redshift),\nthe total energy output from the afterglow is\nsubstantial. For the same power law index measured in the 2-10\nkeV energy band, we obtain a fluence in the afterglow\n$~4.5\\times 10^{-6} \\flux$. Using a more conservative assumption,\nadding an exponential cutoff with folding\nenergy $\\sim$50 keV, the total fluence in the afterglow up to 2.5 days\nafter the main event is 1.15$\\times 10^{-6} \\flux$.\nWe conclude that the {\\it radiated} X and $\\gamma$ total luminosity in \nthe afterglow may be estimated to be between 3.6$\\times\n10^{52}$ ergs and 1.4$\\times 10^{53}$ ergs.\nThis is comparable to the total radiated power in the main GRB event.\nThis estimate is only speculative, as the spectral data of the\nafterglow are consistent with any cutoff energy above $\\sim$2 keV\n(90\\% confidence) but it points out the need for prompt measurements of\nthe afterglow that can give a good estimate of the spectral shape above\n10 keV.\\\\\nUnfortunately the spectral evolution in hard X-rays\n(above 10 keV) of most GRBs seems unaccessible to the present generation of\ntelescopes operating in this energy band. This is a very important\nobservational point that cannot be fulfilled up to the next generation\nof focusing hard X-ray telescopes, maybe at least for a decade.\n\nThe time resolved spectral analysis of the afterglow reported in Table 1,\neven if of low statistical quality, do\nsuggest that the spectral shape remains stable during our observation\nof the afterglow. While these data cannot be profitably used to\nconstrain the spectral evolution of the afterglow in X--rays, they\nconfirm the stability of the {\\it engine } that is producing the\nobserved X--ray emission in spite of the substantial power--law decline\nwith time in the observed X--ray luminosity.\n\nThe spectral evolution from GRB to the X-ray afterglow indicates that\nthe energy distribution shifts towards lower energies, as expected from\ntheoretical models. The model for spectral evolution of Sari et\nal. (\\cite{sari}) suggests that the high energy tail of the emitted\nphoton spectrum of the afterglow has a power law slope\n$\\sim-\\frac{\\rm p}{2} - 1$ in the case of fast cooling,\nwhere p is the index of a power law distribution of the\nelectrons. Our measurement of a power law slope $\\sim -1.6$ implies\np$\\sim 1.2$, a value that would give a non-finite energy in the\nelectrons.\nIn this case the observations can be reconciled with theory\nassuming that a suitable cutoff, e.g. exponential, in the energy\ndistribution of the parent electron population is present. The\nobservation of this cutoff in the produced photon distribution is\nhowever beyond the capability of the present generation of X--ray\ntelescopes and may be accessible to the new missions like {\\it XMM} and\n{\\it Chandra} if it is substantially below 100 keV.\nOur data support (as\nsuggested also by Waxman \\cite{waxman_1,waxman_2})\nthat we observe a regime where the synchrotron cooling time is long\ncompared to the dynamical time. In this regime\n$\\Gamma = -\\frac{({\\rm p}-1)}{2} - 1$, and for a finite power in the electrons\none obtains $\\Gamma < -1.5$, definitely compatible with our measurement.\nA caveat must be added to this interpretation: as the adiabatic\nlosses become dominant in this regime, the observed {\\it radiated}\nluminosity is produced via synchrotron losses in much an inefficient\nway. This brings down the efficiency of the radiative process and in\nparallel rises accordingly the total energy budget in the afterglow.\n\nThe slope of the NIR-to-X-ray afterglow spectrum, corrected for Galactic\nand local extinction, and its temporal evolution are in fair agreement\nwith models of expanding fireballs. Our assumption on the intrinsic\nextinction reasonably conforms with the proposal that GRBs are connected\nwith star formation, and therefore expected to reside in star forming\nregions of their host galaxies (though not necessarily in extreme\nstarburst galaxies, see Odewahn et al. \\cite{odewahn}). We note that the\nlocal extinction correction we adopted has the advantage, with respect\nto other approaches, of using a specific model curve and\nof making the spectrum consistent with a single radiation component over\nmore than three decades of frequency.\n\nIf the emission is isotropic\nthe total X-$\\gamma$ luminosity in GRB971214, if at redshift z=3.42, is \nquite higher than 10$^{51}$ ergs, as already pointed out by\nKulkarni et al. (\\cite{kulkarni_n}). Our analysis shows that\na substantial fraction, more than 60\\%, of the total radiated energy\nin 2-10 keV is in the afterglow. In addition a reasonable guess of a high\nenergy exponential cutoff, with a folding energy of 50 keV, brings us to\nconclude that the total power in GRB971214 may be grossly underestimated\nif based only on the prompt event.\n\nIf the efficiency to convert the total energy output from the GRB in the\nafterglow is low, e.g. $\\sim$10\\%, as\nusually assumed in most theoretical models of fireball expansion,\nour measure of a substantial energy output in 2--10 keV during afterglow \nshows that the total energy balance of a GRB is grossly underestimated.\nFurthermore, if we consider the probable presence of a high energy tail\nof the afterglow, a conservative estimate may bring\nthe total energy output from GRB971214 to more than 10$^{54}$\nerg for an isotropically emitting source. Alternatively, one may more\ncomfortably stay with a luminosity of 10$^{53}$ erg assuming a more\nefficient mechanism to effectively extract radiative power from the\nexpanding fireball or assuming an extreme cutoff to the high energy\nspectrum.\n\nA way out of this deadlock may be beaming (Yi \\cite{yi}, Shaviv \\& Dar \n\\cite{shdar}).\nDifferent authors have discussed the ``beaming solution'' to the\nGRB/afterglow observational problem (Dar \\cite{dar1,dar2}, Rhoads\n\\cite{rhoads}, M\\'esz\\'aros \\& Rees \\cite{meszrees}, Drodzova \\&\nPanchenko\n\\cite{drodzova}, Panaitescu et al. \\cite{panait}). If the emitted\npower is strongly beamed, and therefore not isotropically distributed,\nthe total power in the GRB may be reduced by orders of magnitude, depending\non the beam open angle. Of course this has some major and obvious impacts.\nThe number of GRBs (not detected at earth) rises by the same orders of\nmagnitude. Limb darkening (due to the random distribution\nof viewing angles inside the emission cone), time dependent (due to\ndifferent beaming at different times after the main event) and energy\ndependent (due to the time--dependent photon energy distribution) effects\nshould be observable once the afterglow sample is large enough.\nExamples of such effects are discussed in Panaitescu et al.\n(\\cite{panait}), including a mixed case with a collimated jet and a\ncontribution from isotropic ejecta.\n\nAssuming a jetlike outflow, the models (Panaitescu et al. \\cite{panait},\nRhoads \\cite{rhoads2}, Sari et al. \\cite{sapir_jets})\npredict a steeper decay in the light curve,\ndepending on the jet opening angle. This steepening compared to an\nisotropic fireball expansion occurs for a 10$^{\\rm o}$ opening\nangle at approximately 6 days after the event, earlier for smaller\nangles. We do not detect such a steepening in the X--ray light curve up\nto 2.5 days after the main event.\nIf we assume a beam open angle $\\theta \\geq 10^{\\rm o}$ the total\nenergy in the event is reduced accordingly, compared to the isotropic case.\n\nAn argument to assess jetlike or spherical emission is proposed by\nSari et al. (\\cite{sapir_jets} ), using the decay slope of the\nhigh energy afterglow. As reported by other authors (see above), they\nsuggest that the power law decay for a jetlike emission is appreciably\nsteeper. For an isotropic fireball the expected decay is\nt$^{-\\beta_{\\rm X}}$ with $\\beta_{\\rm X} \\sim 1.1-1.3$, while for an\nexpanding jet the decay follows a power law with $\\beta_{\\rm X} \\sim$\n2.4 .\\\\\nThis effect is purely geometrical, as it is geometrical the effect\nof the jet {\\it ``spillover'' } (Rhoads \\cite{rhoads2}) expanding sideways\nat the\nlocal sound speed. In order to maintain the observed time decay power law\n$\\propto t^{-1.2}$, the Lorentz factor $\\gamma$ must be $> \\theta^{-1}$\nduring all the afterglow observation (see e.g. Piran \\cite{piran}).\nIn the case of GRB971214, this must hold up to the last observation of\nthe power law decay, performed approximately 2.5 days (60 hours)\nafter the prompt event.\nFollowing Sari et al. (\\cite{sapir_jets}) this translates in a lower\nlimit to the beam opening angle $\\theta_0 > 0.1 \\times (6.2 \\times 60\n\\times ({\\rm E}_{52}/ {\\rm n}_1)^\\frac{1}{3} )^\\frac{3}{8} \\approx 0.2$,\nassuming the total ``isotropic''\nenergy in the afterglow is $\\sim 10^{53}$ ergs.\nThis lower limit in beaming angle translates into a lower limit in the\ntotal radiated power from this GRB (prompt+afterglow) $\\sim 10^{52}$ ergs.\n\nIf the effect of beaming is comparable during the prompt event and the\nafterglow, the conclusions we draw on the relative {\\it observed} energy\noutput apply also directly to the total energy balance in the two cases.\nIf the effect of beaming is evolving from an extremely beamed emission\nduring the event to a relatively hollow beaming during the part\nof the afterglow we observed, the relative energy balance between the\ntwo cases should scale accordingly.\nAs a consequence, the energy budget in the\nafterglow may increase substantially with respect to that in the\nprompt event.\n\nIn conclusion the measurement of the spectrum during the prompt event\nand during the afterglow strongly supports the models for synchrotron\nemission from GRB afterglows, with an agreement both in the X-ray band\nand in a broader NIR-to-X-rays band (see Fig. 4). The measured\nspectral slope is in fair agreement with the requirements of the models\nof expanding fireballs, considering also the observed temporal decay. A\nsimple argument, based on recent models on jetlike emission and on the\nexpected temporal decay in this case, supports the observation of a\nspherical expanding shell or of a moderate beaming ($\\theta > 0.2$).\nIf this is the case, the observed radiated\npower in the afterglow is substantial and should be accordingly reproduced\nin any model for X-ray afterglow from GRBs.\n\n{\\bf Acknowledgements}. \nThis research is supported by the Agenzia Spaziale Italiana (ASI) and the\nConsiglio Nazionale delle Ricerche (CNR) of Italy. 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S., \\etal, 1998, \\apj 496,\n849\n%\n\\bibitem[1998]{ramaprakash}\nRamaprakash A.N., Kulkarni S.R., Frail D.A., et al., 1998, \\nature 393, 43\n%\n\\bibitem[1997]{rhoads}\nRhoads J. E., 1997, \\apjl 487, L1\n%\n\\bibitem[1999]{rhoads2}\nRhoads J. E., 1999, \\apj , submitted ({\\it astro-ph/9903399})\n%\n\\bibitem[1999]{sapir_grb99}\nSari R., Piran T., 1999a,\\apjl 517, L109\n%\n\\bibitem[1999]{sapir_jets}\nSari R., Piran T., Halpern J. P., 1999b, \\apjl 519, L17\n%\n\\bibitem[1998]{sari}\nSari R., Piran T., Narayan R., 1998,\\apjl 497, L17\n%\n\\bibitem[1995]{shdar}\nShaviv N. J., Dar A., 1995, \\apj 447, 863\n%\n\\bibitem[1997]{tavani}\nTavani M., 1997, \\apjl 483, L87\n%\n\\bibitem[1997]{ot_1}\nvan Paradijs J., Groot P. J., Galama T., \\etal, 1997,\\nature 386, 686\n%\n\\bibitem[1997]{vietri}\nVietri M., 1997, \\apjl 488, L105\n%\n\\bibitem[1997a]{waxman_1}\nWaxman E., 1997a, \\apjl 485, L5\n%\n\\bibitem[1997b]{waxman_2}\nWaxman E., 1997b, \\apjl 489, L33\n%\n\\bibitem[1999]{wijers}\nWijers R.A.M.J., Galama T.J., 1999, \\apj 523, 177\n%\n\\bibitem[1994]{yi}\nYi I., 1994, \\apj 431, 543\n%\n\\end{thebibliography}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002229.extracted_bib",
"string": "\\begin{thebibliography}{} \n\n\\bibitem[1999]{rotse}\nAkerlof C. W., Balsano R., Barthelmy S., \\etal, 1999, \\nature 398, 400\n%\n\\bibitem[1999]{amati}\nAmati L., Frontera F., Costa E., \\etal, 1999, \\aas 138, 403\n%\n\\bibitem[1997]{antonelli}\nAntonelli A., Butler R. C., Piro, L., \\etal, 1997, \\iauc 6792\n%\n\\bibitem[1996]{xspec}\nArnaud K.A. 1996, in Astronomical Data Analysis Software\nand Systems V, eds. Jacoby G. H., Barnes J., ASP Conf. Series\nvolume 101, p. 17 \n%\n\\bibitem[1999]{ot_12}\nBakos G., Sahu K., Menzies J., \\etal, 1999, GCN Circular 387\n%\n\\bibitem[1993]{band}\nBand D., Matteson J., Ford L., \\etal, 1993, \\apj , 413, 281\n%\n\\bibitem[1998]{ot_8}\nBloom J. S., Frail D. A., Kulkarni S. R., \\etal, 1998, \\apjl 508, L21\n%\n\\bibitem[1997a]{boella}\nBoella G., Butler R. C., Perola G. C., \\etal, 1997a, \\aas 122, 299\n%\n\\bibitem[1997b]{boella2}\nBoella G., Chiappetti L., Conti G., \\etal, 1997b, \\aas 122, 327\n%\n\\bibitem[1997]{ot_2}\nBond H. E. 1997, \\iauc 6654\n%\n\\bibitem[1999]{granat}\nBurenin R. A., Vikhlinin A. A., Gilfanov M. R., \\etal, 1999, \\aa 344, L53\n%\n\\bibitem[1997]{calzetti}\nCalzetti D., 1997, A. J. 113, 162\n%\n\\bibitem[1989]{cardelli}\nCardelli J.A., Clayton G.C., Mathis J.S., 1989, \\apj 345, 245\n%\n\\bibitem[1978]{cavallo}\nCavallo G., Rees M., 1978, \\mnras 183, 359\n%\n\\bibitem[1997]{costa}\nCosta E., Frontera F., Heise J., \\etal, 1997, \\nature 387, 783\n%\n\\bibitem[1998]{dar1}\nDar A., 1998, \\apjl 500, L93\n%\n\\bibitem[1999]{dar2}\nDar A., 1999, \\aas 138, 505\n%\n\\bibitem[1990]{dickey}\nDickey J.M., Lockman F.J., 1990, ARA\\&A 28, 215\n%\n\\bibitem[1998]{diercks}\nDiercks A., Deutsch E.W., Castander F.J., et al., 1998, \\apj 503, L105\n%\n\\bibitem[1997]{drodzova}\nDrodzova N. D., Panchenko I. E., 1997, \\aa 324, L17\n%\n\\bibitem[1997]{ferocigrbm}\nFeroci M., Frontera F., Costa E., \\etal, 1997, in EUV, X-Ray, and\nGamma-Ray\nInstrumentation for Astronomy VIII, eds. Siegmund O. H., Gummin M. A., SPIE\nProceedings 3114, p. 186\n%\n\\bibitem[1997]{frontera}\nFrontera F., Costa E., Dal Fiume D., \\etal, 1997, \\aas 122, 357\n%\n\\bibitem[1999]{frontera_grb}\nFrontera F., Amati L., Costa E., \\etal, 2000, \\apj in press\n%\n\\bibitem[1998]{ot_5}\nGalama T., Vreeswijk P. M., Van Paradijs J., \\etal, 1998, \\nature 395, 670\n%\n\\bibitem[1999]{ot_10}\nGalama T., Vreeswijk P. M., Rol E., \\etal, 1999, GCN Circular 313\n%\n\\bibitem[1998]{ot_3}\nGroot P. J., Galama T. J., Vreeswijk P. M., \\etal, 1998, \\apjl 502, L123\n%\n\\bibitem[1996]{hakkila}\nHakkila J., Meegan C. A., Horack J. M., \\etal, 1996, \\apj 462, 125\n%\n\\bibitem[1998]{halpern}\nHalpern J. P., Thorstensen J. R., Helfand D. J., \\etal, 1998,\n\\nature 393, 41\n%\n\\bibitem[1999]{harrison}\nHarrison F. A., Bloom, J. S., Frail, D. A., \\etal, 1999, \\apjl 523, L121\n%\n\\bibitem[1997]{heise_grb}\nHeise J., in't Zand J, Spoliti G., \\etal, 1997, \\iauc 6787\n%\n\\bibitem[1998]{ot_7}\nHjorth J., Andersen M. I., Pedersen H., \\etal, 1998, GCN Circular 109\n%\n\\bibitem[1997]{jager}\nJager R., Mels W. A., Brinkman A. C., \\etal, 1997, \\aas 125, 557\n%\n\\bibitem[1998]{ot_6}\nJaunsen A. V., Hjorth J., Andersen M. I., \\etal, 1998, GCN Circular 78\n%\n\\bibitem[1997]{batse_fluence}\nKippen R. M., Woods P., Connaughton V., et al. , 1997, \\iauc 6789\n%\n\\bibitem[1997]{kulkarni_c}\nKulkarni S. R., Adelberger K. L., Bloom J. S., \\etal, 1997, GCN Circular 029\n%\n\\bibitem[1998]{kulkarni_n}\nKulkarni S. R., Djorgovski S. G., Ramaprakash A. N., \\etal, 1998,\n\\nature 393, 35\n%\n\\bibitem[1999]{ot_9}\nKulkarni S. R., Djorgovski S. G., Odewahn S. C., \\etal, 1999, \\nature 398, 389\n%\n\\bibitem[1997]{manzo}\nManzo G., Giarrusso S., Santangelo A., \\etal, 1997, \\aas 122, 341\n%\n\\bibitem[1997a]{meszrees1}\nM\\'esz\\'aros P., Rees M. J. , 1997a, \\apj 476, 232\n%\n\\bibitem[1997b]{meszrees}\nM\\'esz\\'aros P., Rees M. J., 1997b, \\apjl, 482, L29\n%\n\\bibitem[1997]{metzger}\nMetzger M. R., Djorgovski S. G., Kulkarni S. R., \\etal, 1997,\n\\nature 387, 261\n%\n\\bibitem[1998]{odewahn}\nOdewahn S.C., Djorgovski S.G., Kulkarni S.R., et al., 1998, \\apj 509, L5\n%\n\\bibitem[1998]{paczynski}\nPaczy\\'nski B., 1998, \\apjl 494, L48\n%\n\\bibitem[1998]{ot_4}\nPalazzi E., Pian E., Masetti N., \\etal, 1998, \\aa 336, L95\n%\n\\bibitem[1999]{ot_11}\nPalazzi E., Masetti N., Pian E., \\etal, 1999, GCN Circular 377\n%\n\\bibitem[1998]{panait}\nPanaitescu A., M\\'esz\\'aros P., Rees M. J., 1998, \\apj 503, 314\n%\n\\bibitem[1997]{parmar}\nParmar A., Martin D. D. E., Bavdaz M., \\etal, 1997, \\aas 122, 309\n%\n\\bibitem[1995]{piran}\nPiran, T. 1995, Proceedings of the Second Huntsville Workshop,\nFishman G. J., Brainerd J. J., Hurley K. eds., AIP Conference Proceedings\n307, p. 495\n%\n\\bibitem[1998]{piro}\nPiro L., Heise J., Jager R., \\etal, 1998, \\aa 329, 906\n%\n\\bibitem[1998]{preece}\nPreece R. D., Pendleton, G. N., Briggs, M. S., \\etal, 1998, \\apj 496,\n849\n%\n\\bibitem[1998]{ramaprakash}\nRamaprakash A.N., Kulkarni S.R., Frail D.A., et al., 1998, \\nature 393, 43\n%\n\\bibitem[1997]{rhoads}\nRhoads J. E., 1997, \\apjl 487, L1\n%\n\\bibitem[1999]{rhoads2}\nRhoads J. E., 1999, \\apj , submitted ({\\it astro-ph/9903399})\n%\n\\bibitem[1999]{sapir_grb99}\nSari R., Piran T., 1999a,\\apjl 517, L109\n%\n\\bibitem[1999]{sapir_jets}\nSari R., Piran T., Halpern J. P., 1999b, \\apjl 519, L17\n%\n\\bibitem[1998]{sari}\nSari R., Piran T., Narayan R., 1998,\\apjl 497, L17\n%\n\\bibitem[1995]{shdar}\nShaviv N. J., Dar A., 1995, \\apj 447, 863\n%\n\\bibitem[1997]{tavani}\nTavani M., 1997, \\apjl 483, L87\n%\n\\bibitem[1997]{ot_1}\nvan Paradijs J., Groot P. J., Galama T., \\etal, 1997,\\nature 386, 686\n%\n\\bibitem[1997]{vietri}\nVietri M., 1997, \\apjl 488, L105\n%\n\\bibitem[1997a]{waxman_1}\nWaxman E., 1997a, \\apjl 485, L5\n%\n\\bibitem[1997b]{waxman_2}\nWaxman E., 1997b, \\apjl 489, L33\n%\n\\bibitem[1999]{wijers}\nWijers R.A.M.J., Galama T.J., 1999, \\apj 523, 177\n%\n\\bibitem[1994]{yi}\nYi I., 1994, \\apj 431, 543\n%\n\\end{thebibliography}"
}
] |
astro-ph0002230
|
Atomic data from the Iron Project
|
[
{
"author": "Sultana N. Nahar\\inst{1}"
},
{
"author": "Franck Delahaye\\inst{1}"
},
{
"author": "Anil K. Pradhan\\inst{1}"
},
{
"author": "C.J. Zeippen\\inst{2}"
}
] |
An extensive set of dipole-allowed, intercombination, and forbidden transition probabilities for Fe~V is presented. The Breit-Pauli R-matrix (BPRM) method is used to calculate $1.46 \times 10^6$ oscillator strengths for the allowed and intercombination E1 transitions among 3,865 fine-structure levels dominated by configuration complexes with $n \leq 10$ and $l \leq 9$. These data are complemented by an atomic structure configuration interaction (CI) calculation using the SUPERSTRUCTURE program for 362 relativistic quadrupole (E2) and magnetic dipole (M1) transitions among 65 low-lying levels dominated by the $3d^4$ and $3d^3 \ 4s$ configurations. Procedures have been developed for the identification of the large number of fine-structure levels and transitions obtained through the BPRM calculations. The target ion Fe~VI is represented by an eigenfunction expansion of 19 fine-structure levels of $3d^3$ and a set of correlation configurations. Fe~V bound levels are obtained with angular and spin symmetries $SL\pi$ and $J\pi$ of the (e~+~Fe~VI) system such that $2S+1$ = 5,3,1, $L \leq$ 10, $J \leq 8$ of even and odd parities. The completeness of the calculated dataset is verified in terms of all possible bound levels belonging to relevant $LS$ terms and transitions in correspondence with the $LS$ terms. The fine-structure averaged relativistic values are compared with previous Opacity Project $LS$ coupling data and other works. The 362 forbidden transition probabilities considerably extend the available data for the E2 and M1 transtions, and are in good agreement with those computed by Garstang for the $3d^4$ transitions. \keywords{ atomic data - radiative transition probabilities - fine-structure transitions}
|
[
{
"name": "astro-ph0002230.tex",
"string": "%\n%\n% Manuscript: Atomic data from the Iron Project XLIII.\n% Transition Probabilities For Fe V\n%\n%\n% l-aa.dem\n% Astronomy and Astrophysics, Supplement Series.\n%\n% L-AA vers. 3.0, LaTeX style file for Astronomy & Astrophysics\n% Demo file\n% (c) Springer-Verlag HD\n%\n%-----------------------------------------------------------------------\n%--------------------- REFEREE VERSION ---------------------\n\\documentstyle[referee]{l-aa}\n%--------------------- FINAL VERSION -----------------------\n%\\documentstyle{l-aa}\n%---------------------------------------------\n\n% `Thermodynamical' derivatives.\n\\newcommand{\\DXDYCZ}[3]{\\left( \\frac{ \\partial #1 }{ \\partial #2 }\n \\right)_{#3}}\n\n\\begin{document}\n\n \\thesaurus{06 % A&A Section 6: Form. struct. and evolut. of stars\n (03.11.1; % Cosmogony,\n 16.06.1; % Planets and satellites: general,\n 19.06.1; % Solar system: general,\n 19.37.1; % Stars: formation of,\n 19.53.1; % Stars: oscillations of,\n 19.63.1)} % Stars: structure of.\n%\n \\title{Atomic data from the Iron Project}\n\n \\subtitle{XLIII. Transition probabilities for Fe V}\n% * \\thanks{Tables of complete data are available\n%in electronic form at the CDS via anonymous ftp 130.79.128.5.}\n\n \\author{Sultana N. Nahar\\inst{1}, Franck Delahaye\\inst{1},\nAnil K. Pradhan\\inst{1} \\and C.J. Zeippen\\inst{2}}\n \\institute{ Department of Astronomy, The Ohio State University,\nColumbus, OH 43210, USA \\and\n UMR 8631 (associ\\'ee au CNRS et \\`a l'Universit\\'e Paris 7) et DAEC,\n Observatoire de Paris, F-92195 Meudon, France}\n \\offprints{S.N. Nahar}\n\n\n\\date{Received date; accepted date}\n\n\\def\\etal{{\\it et\\thinspace al.}\\ }\n \\maketitle\n\\markboth{S.N. Nahar \\etal: Transition probabilities for Fe V}{}\n\n\\begin{abstract}\n\n An extensive set of dipole-allowed, intercombination, and forbidden\ntransition probabilities for Fe~V is presented. The Breit-Pauli R-matrix\n(BPRM) method is used to calculate $1.46 \\times 10^6$ oscillator\nstrengths for the allowed and intercombination E1 transitions among\n3,865 fine-structure levels dominated by configuration complexes with\n$n \\leq 10$ and $l \\leq 9$. These data are complemented by an atomic\nstructure configuration interaction (CI) calculation using the\nSUPERSTRUCTURE program for 362 relativistic quadrupole (E2) and magnetic\ndipole (M1) transitions among 65 low-lying levels dominated by the\n$3d^4$ and $3d^3 \\ 4s$ configurations. Procedures have been developed\nfor the identification of the large number of fine-structure levels\nand transitions obtained through the BPRM calculations. The target\nion Fe~VI is represented by an eigenfunction expansion of 19 fine-structure\nlevels of $3d^3$ and a set of correlation configurations. Fe~V bound\nlevels are obtained with angular and spin symmetries $SL\\pi$ and\n$J\\pi$ of the (e~+~Fe~VI) system such that $2S+1$ = 5,3,1, $L \\leq$ 10,\n$J \\leq 8$ of even and odd parities. The completeness of the calculated\ndataset is verified in terms of all possible bound levels belonging to\nrelevant $LS$ terms and\ntransitions in correspondence with the $LS$ terms. The fine-structure\naveraged relativistic values are compared with previous Opacity Project\n$LS$ coupling data and other works. The 362 forbidden transition\nprobabilities considerably extend the available data for the\nE2 and M1 transtions, and are in good agreement with those computed by\nGarstang for the $3d^4$ transitions.\n\n\\keywords{ atomic data - radiative transition probabilities - fine-structure\ntransitions}\n\\end{abstract}\n\n%\n% 14.Sep.'90: Demo-Vs.\n%________________________________________________________________\n\n\\section {Introduction}\n\n Astrophysical and laboratory applications often require large\ndatasets that are complete and accurate for comprehensive model\ncalculations of opacities (Seaton \\etal 1994, the Opacity Project Team\n1995, 1996), radiative forces (e.g. Seaton 1997, Hui-Bon-Hoa and Alecian \n1998, Seaton 1999), radiation transport in high-density\nfusion plasmas, etc. \nThe Opacity Project (OP) (The Opacity Project 1995, 1996; Seaton \\etal\n1994) produced large\ndatasets of transition probabilities for most astrophysically abundant\natomic systems in the close coupling approximation using the powerful\nR-matrix method from atomic collision theory (Burke \\etal 1971, Seaton\n1987, Berrington \\etal 1987). However, the calculations were carried out\nin $LS$ coupling and the A-values were obtained neglecting relativistic\nfine-structure. The LS multiplets may be divided into fine-structure\ncomponents using algebraic transformations. This has been done for a\nnumber of atoms and ions using the OP data (or similar non-relativistic\ncalculations), including iron ions such as Fe~II (Nahar 1995), Fe~III\n(Nahar and Pradhan 1996), and Fe~XIII (Nahar 1999). However, for \nsuch complex and heavy ions the neglect of relativistic effects may \nlead to a significant lack of precision, especially for weak transitions.\n\nAs an extension of the OP to include relativistic effects, the\npresent Iron Project (IP) (Hummer \\etal 1993) employs relativistic\nextensions of the R-matrix codes in the Breit-Pauli approximation\n(Scott and Burke 1980, Scott and Taylor 1982, Berrington \\etal\n1995) to compute radiative and collisional atomic parameters.\nRecently, several relativistic calculations of\ntransition probabilities have been carried out using the Breit-Pauli\nR-matrix method (BPRM); e.g. for Fe~XXV and Fe~XXIV (Nahar and Pradhan\n1999a), C~III (Berrington \\etal 1998), Fe~XXIII ( Ram\\'{i}rez \\etal \n1999). These calculations produced highly accurate oscillator strengths for\nmost transitions considered, within a few percent of experimental data\nor other accurate theoretical calculations (where available).\n\nHowever, in these relatively simple atomic systems the electron\ncorrelation effects are weak and the configuration-interaction (CI,\nin the atomic structure sense) is easier to account for than in the more\ncomplex ions such as the low ionization stages of iron. In the present\nreport we present the results of a large-scale BPRM calculation for one\nsuch ion, Fe~V, and discuss the accuracy and completeness of the\ncalculated data. An earlier work (Nahar and Pradhan 1999b) has decribed\ncertain important aspects of these calculations, in particular the\ndifficulty with the identification of levels and completeness of\nfine-structure components within the LS multiplets. The general aim of the\npresent work is two-fold: (i) to extend the IP work to the calculation of\nrelativistic transition probabilities for the complex low-z iron ions,\nand (ii) to provide a detailed description of the extensive data tables\nthat should be essentially complete for most applications.\n\n\n\n\n\\section{Theory}\n\n\n\nThe theoretical scheme is described in earlier works (Hummer et al.\n1993, Nahar and Pradhan, 1999a,b). We sketch the basic points below.\nIn the coupled channel or close coupling (CC) approximation an atom\n(ion) is described in terms of an (e + ion) complex that comprises of\na `target' ion, with N bound electrons, and a `free' electron that may\nbe either bound or continuum. The total energy of the system is either\nnegative or positive; negative eigenvalues of the (N + 1)-electron\nHamiltonian correspond to bound states of the (e + ion) system. In the\nCC approximation the wavefunction expansion, $\\Psi(E)$, for\na total spin and angular symmetry $SL\\pi$ or $J\\pi$, of the (N+1)\nelectron system is represented in terms of the target ion states or\nlevels as:\n\n\\begin{equation}\n\\Psi_E(e+ion) = A \\sum_{i} \\chi_{i}(ion)\\theta_{i} + \\sum_{j} c_{j}\n\\Phi_{j},\n\\end{equation}\n\n\\noindent\nwhere $\\chi_{i}$ is the target ion wave function in a specific state\n$S_iL_i\\pi_i$ or level $J_i\\pi_i$, and $\\theta_{i}$ is the wave function\nfor the (N+1)th electron in a channel labeled as\n$S_iL_i(J_i)\\pi_i \\ k_{i}^{2}\\ell_i(SL\\pi) \\ [J\\pi]$; $k_{i}^{2}$ is the\nincident kinetic energy. In the second sum the $\\Phi_j$'s are\ncorrelation wavefunctions of the (N+1) electron system that (a)\ncompensate for the orthogonality conditions between the continuum and\nthe bound orbitals, and (b) represent additional short-range correlation\nthat is often of crucial importance in scattering and radiative CC\ncalculations for each $SL\\pi$.\n\nThe BPRM method yields the solutions of the relativistic CC equations\nusing the Breit-Pauli Hamiltonian for the (N+1)-electron system to\nobtain the total wavefunctions $\\Psi_E(e+ion)$ (Hummer \\etal 1993).\nThe BP Hamiltonian is\n\\begin{equation}\nH_{N+1}^{\\rm BP}=H_{N+1}+H_{N+1}^{\\rm mass} + H_{N+1}^{\\rm Dar}\n+ H_{N+1}^{\\rm so},\n\\end{equation}\nwhere $H_{N+1}$ is the nonrelativistic Hamiltonian,\n\\begin{equation}\nH_{N+1} = \\sum_{i=1}\\sp{N+1}\\left\\{-\\nabla_i\\sp 2 - \\frac{2Z}{r_i}\n + \\sum_{j>i}\\sp{N+1} \\frac{2}{r_{ij}}\\right\\},\n\\end{equation}\nand the additional terms are the one-body terms, the mass correction, the\nDarwin and the spin-orbit terms respectively. The spin-orbit interaction\nsplits the LS terms into fine-structure levels $J\\pi$, where\n$J$ is the total angular momentum. The positive and negative energy\nstates (Eq. 1) define continuum or bound (e~+~ion) states,\n\n\\begin{equation}\n \\begin{array}{l} E = k^2 > 0 \\longrightarrow\n{\\rm continuum~(scattering)~channel} \\\\ E = - \\frac{z^2}{\\nu^2} < 0\n\\longrightarrow {\\rm bound~state}, \\end{array}\n\\end{equation}\nwhere $\\nu$ is the effective quantum number relative to the core level.\nDetermination of the quantum defect ($\\mu(\\ell))$, defined as\n$\\nu_i = n - \\mu(\\ell)$ where $\\nu_i$ is relative to the core level\n$S_iL_i\\pi_i$, is helpful in establishing the $\\ell$-value associated\nwith a given channel level.\n\nThe $\\Psi_E$ represents a CI-type wavefunction over a large number of\nelectronic configurations depending on the target levels included\nin the eigenfunction expansion (Eq. 1). Transition matrix elements \nmay be calculated with these wavefunctions, and the electron dipole \n(E1), electric quadrupole (E2), magnetic dipole (M1) or other operators\nto obtain the corresponding transition probabilities. The present \nversion of the BPRM codes implements the E1 operator to enable the \ncalculation of dipole allowed and intercombination transition \nprobabilities. The oscillator strength is proportional to the \ngeneralized line strength defined, in either length form or velocity \nform, by the equations\n\\begin{equation}\nS_{\\rm L}=\n \\left|\\left\\langle{\\mit\\Psi}_f\n \\vert\\sum_{j=1}^{N+1} r_j\\vert\n {\\mit\\Psi}_i\\right\\rangle\\right|^2 \\label{eq:SLe}\n\\end{equation}\nand\n\\begin{equation}\nS_{\\rm V}=\\omega^{-2}\n \\left|\\left\\langle{\\mit\\Psi}_f\n \\vert\\sum_{j=1}^{N+1} \\frac{\\partial}{\\partial r_j}\\vert\n {\\mit\\Psi}_i\\right\\rangle\\right|^2. \\label{eq:SVe}\n\\end{equation}\nIn these equations $\\omega$ is the incident photon energy in Rydberg \nunits, and $\\mit\\Psi_i$ and $\\mit\\Psi_f$ are the bound wave\nfunctions representing the initial and final states respectively.\nThe line strengths are energy independent quantities.\n\nUsing the energy difference, $E_{ji}$, between the initial and final\nstates, the oscillator strength, $f_{ij}$, for the transition can be\nobtained from $S$ as\n\n\\begin{equation}\nf_{ij} = {E_{ji}\\over {3g_i}}S,\n\\end{equation}\n\n\\noindent\nand the Einstein's A-coefficient, $A_{ji}$, as\n\n\\begin{equation}\nA_{ji}(a.u.) = {1\\over 2}\\alpha^3{g_i\\over g_j}E_{ji}^2f_{ij},\n\\end{equation}\n\n\\noindent\nwhere $\\alpha$ is the fine structure constant, and $g_i$, $g_j$ are\nthe statistical weight factors of the initial and final states,\nrespectively. In cgs units,\n\\begin{equation}\nA_{ji}(s^{-1}) = {A_{ji}(a.u.)\\over \\tau_0},\n\\end{equation}\n\n\\noindent\nwhere $\\tau_0 = 2.4191 \\times 10^{-17}$s is the atomic unit of time.\n\n\n\n\n\\section{Computations}\n\n\n\\subsection{The BPRM calculations}\n\n\nThe Fe~V wavefunctions are computed with eigenfunction expansions over\nthe `target' ion Fe~VI.\nPresent work employs a 19-level eigenfunction expansion of Fe VI \ncorresponding to the 8-term $LS$ basis set of\n$3d^3 (^4F$, $^4P$, $^2G$, $^2P$, $^2D2$, $^2H$, $^2F$, $^2D1)$, as\nused in Nahar and Pradhan (1999b).\nThe target wavefunctions were obtained by Chen and Pradhan (1999) using\nthe Breit-Pauli version of the atomic structure code, SUPERSTRUCTURE \n(Eissner et al 1974). The bound channel set of\nfunctions ${\\Phi_j}$ in Eq. (1), representing additional (N+1)-electron \ncorrelation includes a number of Fe~V configurations, particularly from\nthe important n = 3 complex, i.e. $3s^23p^63d^4, 3p^63d^6, 3s^23p^53d^5,\n3s^23p^43d^6$; the complete list of ${\\Phi_j}$ for the n = 3 and 4\nconfigurations is given in Chen and Pradhan (1999).\n\nThe Breit-Pauli calculations consider all possible fine-structure\nbound levels of Fe V with (2$S$ + 1) = 1,3,5 and $L$ = 0 -- 10, \n$n\\leq 10, \\ \\ell \\leq n-1$, and $J \\leq$ 8, and the transitions among\nthese levels. In the R-matrix computations, the calculated energies \nof the target levels were replaced by\nthe observed ones. The calculations are carried out using the BPRM codes \n(Berrington et al. 1995) extended from the Opacity Project codes \n(Berrington et al. 1987). \n\nSTG1 of the BPRM codes computes the one- and two-electron radial\nintegrals using the one-electron target orbitals generated by\nSUPERSTRUCTURE. The number of continuum R-matrix basis functions \nis chosen to be 12. The intermediate coupling calculations are \ncarried out on recoupling these $LS$ symmetries in a \npair-coupling representation in stage RECUPD. The computer \nmemory requirement for this stage has been the\nmaximum as it carries out angular algebra of dipole matrix elements\nof a large number of levels due to fine-structure\nsplitting. The (e + Fe~VI) Hamiltonian is diagonalized for each\nresulting $J\\pi$ in STGH. \n\n\n\n\n\\subsubsection{Energy levels and identification}\n\n\nThe negative eigenvalues of the (e + Fe VI) Hamiltonian correspond to the bound \nlevels of Fe~V, determined using the code STGB.\nSplitting of each target LS term into its fine-structure components also\nincreases the number of Rydberg series of levels converging on to them.\nThese result in a large number of fine-structure levels in comparatively\nnarrow energy bands. An order of magnitude finer mesh of effective\nquantum number ($\\Delta \\nu$=0.001), compared to that needed for the\nlocating the bound $LS$ states, was needed to search for the\nBP Hamitonian eigenvalues in order to avoid missing energy levels. \nThe computational requirements\nwere, therefore, increased considerably for the intermediate coupling\ncalculations of bound levels over the LS coupling case by several \norders of magnitude. The calculations take up to several CPU hours per\n$J\\pi$ in order to determine the corresponding eigenvalues in the\nasymptotic program STGB.\n\nThe identification of the fine-structure bound levels computed in \nintermediate coupling using the collision theory BPRM method is rather \ninvolved, since they are labeled with quantum numbers related to\nelectron-ion scattering channels. The levels \nare associated with collision complexes of the (e + ion) system which, \nin turn, are initially identified only with their total angular momenta \nand parity, $J\\pi$. A scheme has been developed (Nahar and Pradhan \n1999b) to identify the levels with complete spectroscopic information \ngiving\n\\begin{equation}\nC_t (\\ S_t \\ L_t)\\ J_t~\\pi_t n\\ell \\ [K] {\\rm s}\\ \\ J \\ \\pi,\n\\end{equation}\nand also to designate the levels with a possible $SL\\pi$ symmetry\n($C_t$ is the target configuration).\n\nMost of the spectroscopic information of a computed level is extracted\nfrom the few bound channels that dominate the wavefunction of \nthat level. A new code PRCBPID has been developed to carry out the \nidentification, including quantum\ndefect analysis and angular momentum algebra of the dominant channels.\nTwo additional problems are addressed in the identification work:\n(A) correspondence of the computed fine-structure levels to the\nstandard $LS$ coupling designation, $SL\\pi$, and (B)\ncompleteness checks for the set of all fine-structure components\nwithin all computed $LS$ multiplets. A correspondence between\nthe sets of $SL\\pi$ and $J\\pi$ of the same configuration are\nestablished from the set of $SL\\pi$ symmetries, formed from the\ntarget term, $S_tL_t\\pi_t$, $nl$ quantum numbers of the valence\nelectron, and $J\\pi$ of the fine-structure level belonging to the $LS$\nterm. The identification procedure is described in detail in Nahar and \nPradhan (1999b).\n\nConsiderable effort has been devoted to a precise and unique \nidentification of levels.\nHowever, a complex ion such as Fe~V involves many highly mixed levels\nand it becomes difficult to assign a definite configuration and\nparentage to all bound states. Nonetheless, most of the levels have been\nuniquely identified. In particular all calculated levels corresponding \nto the experimentally observed ones are correctly (and independently) \nassigned to their proper spectroscopic designation by the\nidentification procedure employed.\n\n\n\\subsubsection{E1 oscillator strengths}\n\n\n\nThe oscillator strengths and transition probabilities were obtained\nusing STGBB of the BPRM codes. STGBB computed the transition matrix\nelements using the bound wavefunctions created by STGB, and the \ndipole operators computed by STGH. The\nfine structure of the core and the (N+1) electron system\nincreased the computer memory and CPU time requirements considerably\nover the LS coupling calculations.\nAbout 31 MW of memory, and about one CPU hour on the Cray T94, was required\nto compute the oscillator strengths for\ntransitions among the levels of a pair of $J\\pi$ symmetries.\nThese are over an order of magnitude larger than those\nneeded for $f$-values in $LS$ coupling. The number of $f$-values\nobtained from the BPRM calculations ranges from over 5,000, among \n$J$=8 levels, to over 123,000, among $J$=3 levels, for a pair of \nsymmetries.\n\nThese computations required over 120 CPU hours\non the Cray T94. Total memory size needed was over 42 MW to diagonalise\nthe BP Hamilitonian. Largest computations involved a single $J\\pi$ \nHamiltonian of matrix size 3555, 120 channels, and 2010 configurations.\n\nWe have included extensive tables of all computed bound levels, and \nassociated E1 A-values, with full spectroscopic identifications,\nas standardized by the U.S. National Institute for Standards and \nTechnology (NIST). In addition, rather elaborate (though rather\ntedious) procedures are implemented to check and ensure completeness \nof fine-structure components within all computed LS multiplets. The \ncomplete data tables are available in electronic format. A sample of \nthe datasets is described in the next section.\n\n\n\\subsection{SUPERSTRUCTURE calculations for the forbidden E2, M1\ntransitions}\n\nThe only available dataset by Garstang (1957) comprises of the E2,\nM1 A-values for transitions within the ground $3d^4$ levels. The CI \nexpansion for Fe~V consists of the configurations \n$(1s^22s^22p^63s^23p^6) \\ 3d^4,3d^34s,3d^34p$ as the spectroscopic \nconfigurations and\n$3d^34d,3d^35s,3d^35p,3d^35d,3d^24s^2,3d^24p^2,3d^24d^2,3d^24s4p,3d^24s4d$ as\ncorrelation configurations. The eigenenergies\nof levels dominated by the spectroscopic configurations are minimised\nwith scaling parameters $\\lambda_{n\\ell}$ in the Thomas-Fermi-Dirac\npotential used to calculate the one-electron orbitals in SUPERSTRUCTURE\n(see Nussbaumer and Storey 1978):\n$ { \\lambda_{[1s-5d]}} \\ = \\ {1.42912,1.13633,1.08043,1.09387,1.07756,0.99000,\n1.09616, 1.08171,}$\n\n\\noindent ${-0.5800,-0.6944,-1.0712,-3.0000} $.\n\nThere are 182 fine-structure levels dominated by the configurations\n$3d^4$, $3d^34s$ and $3d^34p$, and the respective number of LS terms is\n16, 32 and 80. The $\\lambda_{1s-3d}$ are minimised over the first\n16 terms of $3d^4$, $\\lambda_{4s}$ over 32\nterms including $3d^34s$, and $\\lambda_{4p}$, $\\lambda_{5p}$ over all 80\nterms. The $\\lambda_{5s}$ and $\\lambda_{5d}$ are optimised over the\n$3d^4$ terms to further improve the corresponding eigenfunctions.\n\n The numerical experimentation entailed a number of minimisation trials,\nwith the goal of optimisation over most levels. The final\nset of calculated energies agree with experiment to within 10\\%,\nalthough more selective optimisation can lead to much better agreement\nfor many (but not all) levels. Finally, semi-empirical term energy \ncorrections (TEC) (Zeippen \\etal 1977) were applied to obtain the \ntransition probabilities. This procedure has been successfully\napplied in a large number of studies (see e.g. Bi\\'emont \\etal 1994).\nThe electric quadrupole (E2) and the magnetic dipole (M1)\ntransition probabilites, A$^q$ and A$^m$, are obtained using observed \nenergies according to the expressions:\n\n\\begin{equation}\nA_{j,i}^q(E2) = 2.6733 \\times 10^3 (E_j - E_i)^5 {\\cal S}^q(i,j)\nsec^{-1},\n\\end{equation}\n\n\\noindent\nand\n\n\\begin{equation}\nA_{j,i}^m(M1) = 3.5644 \\times 10^4 (E_j - E_i)^3 {\\cal S}^m(i,j)\nsec^{-1},\n\\end{equation}\n\n\\noindent\nwhere $E_j > E_i$ (the energies are in Rydbergs), and ${\\cal S}$ is \nthe line strength for the corresponding transition.\n\n\n\n\\section {Results and discussion}\n\nWe have obtained nearly 1.5 $\\times 10^{6}$ oscillator strengths for \nbound-bound transitions in Fe~V. To our knowledge there are no previous \nab initio relativistic calculations for transition probabilities for \nFe~V. The previous\nOpacity Project data consists of approximately 30,000 LS\ntransitions. Therefore the new dataset of nearly 1.5 $\\times 10^{6}$\noscillator strengths should significantly enhance the database, and\nthe range and precision of related applications, some of which we\ndiscuss later.\n\nWe divide the discussion of energies and oscillator strengths in\nthe subsections below.\n\n\n\\subsection{Fine-structure levels from the BPRM calculations}\n\n\nA total of 3,865 fine-structure bound levels of Fe V have been\nobtained for $J\\pi$ symmetries, 0 $\\leq J \\leq$ 8 even and odd \nparities. These belong to symmetries $2S+1$ = 5,3,1, 0 $\\leq L \\leq$ \n9, with $n \\leq 10$ and 0 $\\leq l \\leq$ 9. The BPRM calculations \ninitially yield only the energies and the total symmetry, $J\\pi$, \nof the levels. Through an identification procedure based on the \nanalysis of quantum defects and percentage channel contributions \nfor each level in the region outside the R-matrix boundary \n(described in Nahar and Pradhan 1999b), the levels are assigned with \npossible designation of $C_t(S_tL_t)J_t\\pi_tnlJ(SL)\\pi$, which \nspecifies the core or target configuration, $LS$ term and parity, \nand total angular momentum; the principal and orbital angular momenta, \n$nl$, of the outer or the valence electron; the total angular momentum, \n$J$, and the possible $LS$ term and parity, $SL\\pi$, of the \n$(N+1)$-electron bound level. Table 1a presents a few partial sets \nof energy levels from the complete set available electronically.\n\n\n\n\\subsubsection{Computed order of levels according to $J\\pi$}\n\n\nExamples of fine structure energy levels are presented in sets of $J\\pi$ in Table\n1a where their assigned identifications are given. $N_J$ is the total \nnumber of energy levels for the symmetry $J\\pi$ (e.g. there are 80 \nlevels with $J\\pi$ = $0^e$, although the table presents only 25 of them). \nThe effective quantum number, $\\nu~=~z/\\sqrt(E-E_t)$ where $E_t$ is the\nenergy of the target state, is also given for each level. \nThe $\\nu$ is not given for any equivalent electron level as it is undefined. \nAn unidentifiable level is often assigned with a possible equivalent\nelectron level. In Table 1a, one level of $J\\pi$ = $0^o$ is assigned to the\nequivalent electron configuration, $3p^53d^5$. The assignment is based\non two factors: (a) the calculated $\\nu$ of the level does not match with\nthat of any valence electon, and (b) the wavefunction is represented \nby a number of channels of similar percentage weights, i.e., no dominant\nchannel. The configuration $3p^53d^3$ corresponds to a large number \nof $LS$ terms. However, the level can not be identified with any \nparticular term through quantum defect analysis. Hence it is \ndesignated as $^0S$, indicating an undetermined spectroscopic term.\n\n\n\\subsubsection{Energy order of levels}\n\n\n\nIn Table 1b a limited selection of energy levels is presented in a \nformat different from\nthat in Table 1a. Here they are listed in ascending energy order\nregardless of $J\\pi$ values, and are grouped together within the\nsame configuration to show the correspondence between the sets of\n$J$-levels and the $LS$ terms. This format provides a check of\ncompleteness of sets of energy levels in terms of $LS$ terms, and\nalso determines the missing levels. Levels grouped in such a manner also\nshow closely spaced energies, consistent with the fact that they are\nfine-structure components with a given $LS$ term\ndesignation. The title of each set in Table 1b lists all possible\n$LS$ terms that can be formed from the core or target term, and outer\nor the valence electron angular momentum. 'Nlv' is the total number\nof $J$-levels that correspond to the set of $LS$ terms. The spin \nmultiplicity ($2S+1$) and parity ($\\pi$) are given next. The $J$ values for\neach term is given with parentheses next to the corresponding $L$. At \nthe end of the set of levels, 'Nlv(c)' is the total number of $J$-levels\nobtained in the calculations. Hence, if Nlv = Nlv(c) for a set of levels\nof the same configuration the set is designated as `complete'.\n\nMost sets of fine-structure components between LS multiplets \nare found to be complete. High lying energy levels often belong to\nincomplete sets. The possible $LS$ terms for each level is specified \nin the last column. It is seen that a level may possibly belong to several\n$LS$ terms. In the absence any other criteriion, the proper term for the \nlevel may be assumed by\napplying Hund's rule: with levels of the same spin multiplicity,\nthe highest $L$-level is usually the lowest. For example, of the two \n$J$=4 levels with terms $^3(F,G)$ in the second set, the first or \nthe lower level could be $^3G$ while the second or the higher one \ncould be $^3F$. It may be noted that this criterion is violated for a\nnumber of cases in Fe~V due to strong CI. In Table 1b,\nthe upper sets of low energies are complete. The two lower sets are \nincomplete where a few levels are missing. The missing levels are \nalso specified by the program PRCBPID.\n\n\n\\subsubsection{Comparison with observed energies}\n\n\nOnly a limited number of observed energy levels of Fe~V are available (Sugar\nand Corliss 1985). All 179 observed levels were identified in a\nstraightforward manner by the program PRCBPID. The\npresent results are found to agree to about 1\\% with the observed\nenergies for most of the levels (Table III, Nahar and Pradhan 1999b).\nIn Table 2, a\ncomparison is presented for the $3d^4$ levels. The\nexperimentally observed levels are also the lowest calculated levels\nin Fe~V. The additional information in Table 2 is the level index,\n$I_J$, next to the J-values. As the BPRM levels are designated with\n$J\\pi$ values only, the level index shows the energy position, in\nascending order, of the level in the $J\\pi$ symmetry. It is necessary\nto use the level indices to make the correspondence among the\ncalculated and the observed levels for later use.\n\nAlthough the $LS$ term designation in general meets consistency checks,\nit is possible that there is some uncertainty in the designations. The\nspin multiplicities of the ion are obtained by the addition of\nthe angular momentum 1/2\nof the outer electron to the total spin, $S_t$, of the target. The\nhigher multiplicity corresponds to the addition of +1/2, and the\nlower one to the subtraction of -1/2. Typically the level with higher \nmultiplicity\nlies lower. Due to the large number of different channels representing the\nlevels of a $J\\pi$ symmetry, it is\npossible that this angular addition might have been interchanged for some\ncases where the channels themselves are incorrectly identified.\nTherefore, for example, a triplet could be represented by a singlet\nand vice versa. This can affect the $L$\ndesignation since a singlet can be assigned only to one single total $L$,\nwhereas a triplet can be assigned to a few possible $L$ values. For such\ncases, the $LS$ multiplets may not represent the correct transitions.\n\nWe emphasize, however, that the present calculations are all in\nintermediate coupling and the LS coupling designations attempted in\nthis work are carried out only to complete the full spectroscopic\nidentification that may be of interest for (a) specialized users\nsuch as experimentalists, and (b) as a record of all possible\ninformation (some of which may be uncertain) that can be derived from the\nBPRM calculations for bound levels.\n\n\n\\subsection{E1 oscillators strengths from the BPRM Calculations}\n\n\nThe bound-bound transitions among the 3865 fine-structure levels of Fe~V\nhave resulted in $1.46\\times 10^6$ oscillator strengths for dipole-allowed\nand intercombination transitions.\n\n\n\\subsubsection{Calculated f-values for the allowed transitions}\n\n\nTable 3 presents a partial set, in the format adopted, from the \ncomplete file of oscillator strengths. The two numbers at the \nbeginning of the table are the nuclear charge (i.e. Z = 26) and the \nnumber of electrons ($N_{elc}$ = 22) for Fe~V. Below this line are \nthe sets of transitions of a pair of symmetries $J\\pi~-~J'\\pi'$. \nThe first line of each set contains values of $2J$, parity $\\pi$ \n(=0 for even and =1 for odd), $2J'$ and $\\pi'$. Hence in Table 3, \nthe set of transitions given are among $J=0^e~-~J=1^o$.\nThe line following the transition symmetries specifies the number of\nbound levels, $N_{Ji}$ and $N_{Jj}$, of the symmetries among which\nthe transitions occur. This line is followed by $N_{Ji}\\times N_{Jj}$\ntransitions. The first two columns are the level indices, $I_i$ and\n$I_j$ (as mentioned above) for the energy indices of the levels, and\nthe third and the fourth columns are their energies, $E_i$ and $E_j$,\nin Rydberg units. The fifth and sixth columns are $gf_L$ and $gf_V$,\nwhere $f_L$ and $f_V$ are the oscillator strengths in\nlength and velocity forms, and $g~=~2J+1$ ($J$ is the total\nangular momentum of the lower level).\nFor the $gf$-values that are negative the lower level is $i$\n(absorption) and for the\npositive ones the lower level is $j$ (emission). The last column gives the\ntransition probability, $A_{ji}(sec^{-1})$. To obtain the identification\nof the levels, Table 1a should be referrred to following $I_i$ and $I_j$.\nFor example, the second transition of Table 3 corresponds to\nthe intercombination transition $3d^4(^5D^e)(I_i=1) \\rightarrow\n3d^3(^4F^e)4p(^3D^o)(I_j=3)$.\n\n\n\n\\subsubsection{f-values with experimental energies}\n\n\nAs the observed energies are much more precisely known that the\ncalculated ones, the $f$ and $A$-values can be reprocessed with the\nobserved energies for some improvement in accuracy. Using the\nenergy independent BPRM line strength, $S$ (Eq. 7), the $f$-value\ncan be obtained as,\n\\begin{equation}\nf_{ij} = S(i,j,BPRM){E_{ji}(obs)\\over (3g_{i})}.\n\\end{equation}\n\nTransitions among all observed levels have been so \nreprocessed. This recalculated subset consists of 3737 \ndipole-allowed and intercombination transitions among the 179 \nobserved levels (a relatively small part of the present transition \nprobabilities dataset). The calculated energy level indices \ncorresponding to the observed levels for each $J\\pi$ are \nlisted in Table 4. \n\nA sample set of $f$- and $A$-values from the reprocessed transitions\nare presented in Table 5a in $J\\pi-J'\\pi'$ order. Each transition is \ngiven with complete identification. The level index, $I_i$, for each energy\nlevel is given next to the $J$-value for easy linkage to the energy and\n$f$-files. In all calculations where large number of transitions are\nused, the reprocessed $f$- and $A$-values should replace those in the\ncomplete file (containing $1.46\\times 10^6$ transitions).\nFor example, the $f$- and $A$-values for the first transition\n$J=0^e(I_i=1)\\rightarrow J=1^o(I_j=1)$ in Table 3 should be replaced\nby those for the first transition in Table 5a. The overall replacement\nof transitions can be carried out easily using the level energy index set\nin Table 4.\n\n\n\\subsubsection{Spectroscopic designation and completeness}\n\nThe reprocessed transitions are further ordered in terms of their\nconfigurations for a completeness check, and to obtain the $LS$ multiplet\ndesignations.\nA partial set is presented in Table 5b (the complete table is\navailable electronically). The completeness\ndepends on the observed set of fine-structure levels since transitions\nhave been reprocessed only for the observed levels. The $LS$ multiplets\nare useful for various comparisons with existing values\nwhere fine-structure transitions can not be resolved. \n\n Semi-empirical atomic structure calculations have been carried out be\nother workers (Fawcett (1989), Quinet and Hansen (1995)).\nPresent oscillator strengths are compared with available \ncalculations by Fawcett (1989), the LS coupling R-matrix calculations from \nthe OP (Butler, TOPbase 1993) and from the IP (Bautista 1996), \nfor some low lying \ntransitions. Comparison in Table 5b shows various degrees of \nagreement. Present $f$-values agree very well (within 10\\%) with those \nby Fawcett for some fine-structure transitions while disagree \nconsiderably with the others within the same $LS$ multiplet. For example,\nthe agreement is good for most of the fine-structure transitions \nof $3d^4(^5D)\\rightarrow 3d^3(^4F)4p(^5D^o)$, $3d^4(^5D)\\rightarrow \n3d^3(^4P)4p(^5P^o)$, and $3d^42(^3P)\\rightarrow 3d^3(^4F)4p(^3D^o)$ \nwhile the disagreement is large with other as well as with those of \n$3d^4(^5D)\\rightarrow 3d^3(^4F)4p(^5F^o)$. \nThe agreement of the present $LS$ multiplets\nwith the others is good for strong transitions such as $3d^4(^5D)\\rightarrow\n3d^3(^4F)4p(^5F^o,^5D^o,^5P^o)$, and $3d^42(^3P)\\rightarrow\n3d^3(^4F)4p(^3D^o)$, but is poor for the weak ones.\n\n\n\n\\subsubsection{Estimate of uncertainities}\n\n\nThe uncertainties of the BPRM transition probabilities for the allowed\ntransitons are expected to be within 10 \\% percent for the\nstrong transitions, and 10-30\\% for the weak ones. A measure of\nthe uncertainty can be obtained from the dispersion of the $f$-values\nin length and velocity forms, which generally indicate deviations from\nthe `exact' wavefunctions (albeit with some exceptions).\nFig. 1 presents a plot of ${\\rm log}_{10}{gf}$ values,\nlength vs. velocity, for the transitions $(J=2)^e-(J=3)^3$\nof Fe~V. Though most of the points lie close to the $gf_L = gf_V$ line, \nsignificant\ndispersion is seen for $gf$ values smaller than 0.01. We should note\nthat the level of uncertainty may in fact be\nless than the dispersion shown in Fig. 1; in the close coupling R-matrix\ncalculations the length formulation is likely to be more accurate than the\nvelocity formulaton since the wavefunctions are better represented in the\nasymptotic region that dominates the contribution to the length form of\nthe oscillator strength.\n\n\n\\subsection{Forbidden transition probabilities}\n\n\nThe transition probabilities, $A^q$ and $A^m$, for 362 forbidden \nE2 and M1 transitions are obtained using some semi-empirical \ncorrections. The $A^q$ in general are much smaller than the $A^m$. \nAlthough $A^q$ is smaller, there are many cases where one \nor the other is negligible. Owing to the widespread use of the only \nother previous calculation by\nGarstang (1957), it is important to establish the\ngeneral level of differences with the previous work. Table 6 gives a\ndetailed comparison. The agreement between the two sets of data is\ngenerally good with a few noticeable discrepancies.\n\nA partial set of the transition \nprobabilities are given in Table 7 along with the observed wavelengths \nin microns. The full Table of forbidden transition probabilities is\navailable electronically.\n\n\n\\section {Conclusion}\n\n\nTo exemplify the future potential of computational spectroscopy with\nthe Breit-Pauli R-matrix method, complemented by related atomic structure\ncalculations, we present a fairly complete and large-scale set of\nmainly {\\it ab initio}\ntransition probabilities for a complex atomic system.\nLevel energies and fine-structure transition probabilities for Fe~V are\npresented\nin a comprehensive manner with spectroscopic identifications.\nWe should expect these data to be particularly useful\nfor the calculation of monochromatic opacities and in the analysis of\nspectra from astrophysical and laboratory sources where\nnon-local thermodynamic equilibrium (NLTE) atomic models with\nmany excited levels are needed.\n\n All data tables will be electronically available from the CDS archives, \nand via ftp from the first author at: nahar@astronomy.ohio-state.edu.\n\n\n\\begin{acknowledgements}\nWe would like to thank Dr. Werner Eissner for helpful comments and\ngeneral assistance with the BPRM codes.\nThis work was partially supported by\nU.S. National Science Foundation (AST-9870089) and the NASA (NAG5 7903).\nThe computational work was\ncarried out on the Cray\nT94 at the Ohio Supercomputer Center in Columbus, Ohio.\nThe collaboration between Columbus and Meudon benefitted from a visit to\nthe DAEC by AKP, with support from the Universit\\'e Paris 7.\n\n\n\\end{acknowledgements}\n\n\n\\def\\amp{{\\it Adv. At. Molec. Phys.}\\ }\n\\def\\apj{{\\it Astrophys. J.}\\ }\n\\def\\apjs{{\\it Astrophys. J. Suppl. Ser.}\\ }\n\\def\\apjl{{\\it Astrophys. J. (Letters)}\\ }\n\\def\\aj{{\\it Astron. J.}\\ }\n\\def\\aa{{\\it Astron. Astrophys.}\\ }\n\\def\\aasup{{\\it Astron. Astrophys. Suppl.}\\ }\n\\def\\adndt{{\\it At. Data Nucl. Data Tables}\\ }\n\\def\\cpc{{\\it Comput. Phys. Commun.}\\ }\n\\def\\jqsrt{{\\it J. Quant. Spectrosc. Radiat. Transfer}\\ }\n\\def\\jpb{{\\it Journal Of Physics B}\\ }\n\\def\\pasp{{\\it Pub. Astron. Soc. Pacific}\\ }\n\\def\\mn{{\\it Mon. Not. R. astr. Soc.}\\ }\n\\def\\pra{{\\it Physical Review A}\\ }\n\\def\\prl{{\\it Physical Review Letters}\\ }\n\\def\\zpds{{\\it Z. Phys. D Suppl.}\\ }\n\n\n\n%\\newpage\n\n\\begin{thebibliography}{}\n\n\\bibitem{} Bautista M.A., 1996, A\\&AS 119, 105\n\n\\bibitem{} Berrington K.A., Burke P.G., Butler K., Seaton M.J., Storey\nP.J., Taylor K.T., Yu Y., 1987, J. Phys. 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B 12, 4299\n\n\\bibitem{} Scott N.S., Taylor K.T., 1982, Comput. Phys. Commun. 25, 347\n\n\\bibitem{} Seaton M.J., 1987, J. Phys. B 20, 6363\n\n\\bibitem{} Seaton M.J., 1997, MNRAS 289, 700\n\n\\bibitem{} Seaton M.J., 1999, MNRAS 307, 1008\n\n\\bibitem{} Seaton M.J., Yu Y., Mihalas D., Pradhan A.K., 1994, MNRAS\n266, 805\n\n\\bibitem{} Sugar J., Corliss C., 1985, J. Phys. Chem. Ref. Data 14, Suppl.\n2\n\n\\bibitem{} {\\it The Opacity Project Team, Vol. 1}, 1995 (Institute of Physics \nPublishing, Bristol \\& Philadelphia, ISBN 0 7503 0288 7)\n\n\\bibitem{} {\\it The Opacity Project Team, Vol. 2}, 1996 (Institute of Physics \nPublishing, Bristol \\& Philadelphia, ISBN 0 7503 0174 0)\n\n\\bibitem{} Zeippen C.J., Seaton M.J., Morton D.C., 1977, MNRAS 181, 527\n\n\\end{thebibliography}\n\n\n%___________________________________ Two column table (place early!)\n\n\n\\pagebreak\n\n\n\\begin{table}\n\\noindent{Table Ia. Identified fine-strucuture energy levels of Fe V.\n$N_J$=total number of levels for the symmetry $J\\pi$.\n \\\\ }\n%\\small\n\\scriptsize\n\\begin{tabular}{rllrrrcrl}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n i & $C_t$ & $S_tL_t\\pi_t$ & $J_t$ & $nl$ & $J$ & $E_c(Ry)$ & $\\nu$ & $SL\\pi$\n\\\\\n \\noalign{\\smallskip}\n \\hline\n \\noalign{\\smallskip}\n \\multicolumn{9}{c}{$N_J$= 80,~~~~~$J\\pi$= $0^e$ } \\\\\n \\noalign{\\smallskip}\n \\hline\n \\noalign{\\smallskip}\n 1 & $3d4 $ & & & & 0 &-5.56210E+00& $^5 D e$ \\\\\n 2 & $3d4 2 $ & & & & 0 &-5.34705E+00& $^3 P e$ \\\\\n 3 & $3d4 2 $ & & & & 0 &-5.16997E+00& $^1 S e$ \\\\\n 4 & $3d4 1 $ & & & & 0 &-4.96162E+00& $^3 P e$ \\\\\n 5 & $3d4 1 $ & & & & 0 &-4.43020E+00& $^1 S e$ \\\\\n 6 & $3d3 $ & $^4P^e$&1/2 &$4s$& 0 &-3.47060E+00& 2.62&$^3 P e$ \\\\\n 7 & $3d3 $ & $^2P^e$&1/2 &$4s$& 0 &-3.44860E+00& 2.60&$^3 P e$ \\\\\n 8 & $3d3 $ & $^4F^e$&3/2 &$4d$& 0 &-2.28673E+00& 3.31&$^5 D e$ \\\\\n 9 & $3d3 $ & $^4F^e$&5/2 &$4d$& 0 &-2.24585E+00& 3.33&$^3 P e$ \\\\\n 10 & $3d3 $ & $^4P^e$&3/2 &$4d$& 0 &-2.08337E+00& 3.33&$^5 D e$ \\\\\n 11 & $3d3 $ & $^4P^e$&5/2 &$4d$& 0 &-2.07641E+00& 3.33&$^3 P e$ \\\\\n 12 & $3d3 2 $ & $^2D^e$&3/2 &$4d$& 0 &-2.03154E+00& 3.30&$^3 P e$ \\\\\n 13 & $3d3 $ & $^2P^e$&3/2 &$4d$& 0 &-1.94013E+00& 3.39&$^3 P e$ \\\\\n 14 & $3d3 2 $ & $^2D^e$&5/2 &$4d$& 0 &-1.84426E+00& 3.45&$^1 S e$ \\\\\n 15 & $3d3 $ & $^4P^e$&1/2 &$5s$& 0 &-1.76456E+00& 3.59&$^3 P e$ \\\\\n 16 & $3d3 $ & $^2F^e$&5/2 &$4d$& 0 &-1.73641E+00& 3.40&$^3 P e$ \\\\\n 17 & $3d3 $ & $^2P^e$&1/2 &$5s$& 0 &-1.70995E+00& 3.58&$^3 P e$ \\\\\n 18 & $3d3 1 $ & $^2D^e$&3/2 &$4d$& 0 &-1.54486E+00& 3.37&$^1 S e$ \\\\\n 19 & $3d3 1 $ & $^2D^e$&5/2 &$4d$& 0 &-1.32130E+00& 3.56&$^3 P e$ \\\\\n 20 & $3d3 $ & $^4F^e$&3/2 &$5d$& 0 &-1.27240E+00& 4.43&$^5 D e$ \\\\\n 21 & $3d3 $ & $^4F^e$&5/2 &$5d$& 0 &-1.25685E+00& 4.45&$^3 P e$ \\\\\n 22 & $3d3 $ & $^4P^e$&3/2 &$5d$& 0 &-1.11887E+00& 4.40&$^5 D e$ \\\\\n 23 & $3d3 $ & $^4P^e$&5/2 &$5d$& 0 &-1.08686E+00& 4.44&$^3 P e$ \\\\\n 24 & $3d3 $ & $^2P^e$&3/2 &$5d$& 0 &-1.03290E+00& 4.43&$^3 P e$ \\\\\n 25 & $3d3 2 $ & $^2D^e$&3/2 &$5d$& 0 &-1.02130E+00& 4.42&$^3 P e$ \\\\\n \\noalign{\\smallskip}\n \\hline\n \\noalign{\\smallskip}\n \\multicolumn{9}{c}{$N_J$= 85,~~~~~$J\\pi$ = $0^o$ } \\\\\n \\noalign{\\smallskip}\n \\hline\n \\noalign{\\smallskip}\n 1 & $3d3 $ & $^4F^e$ & 3/2&$4p$ &0 &-3.14690E+00& 2.82 & $^5 D^o$ \\\\\n 2 & $3d3 $ & $^4P^e$ & 1/2&$4p$ &0 &-2.97968E+00& 2.82 & $^5 D^o$ \\\\\n 3 & $3d3 $ & $^4P^e$ & 3/2&$4p$ &0 &-2.96755E+00& 2.82 & $^3 P^o$ \\\\\n 4 & $3d3 $ & $^2P^e$ & 1/2&$4p$ &0 &-2.94580E+00& 2.80 & $^1 S^o$ \\\\\n 5 & $3d3 $ & $^2P^e$ & 3/2&$4p$ &0 &-2.93098E+00& 2.81 & $^3 P^o$ \\\\\n 6 & $3d3 2$ & $^2D^e$ & 3/2&$4p$ &0 &-2.82995E+00& 2.84 & $^3 P^o$ \\\\\n 7 & $3d3 1$ & $^2D^e$ & 3/2&$4p$ &0 &-2.41156E+00& 2.85 & $^3 P^o$ \\\\\n 8 & $3d3 $ & $^4F^e$ & 3/2&$5p$ &0 &-1.68614E+00& 3.85 & $^5 D^o$ \\\\\n 9 & $3d3 $ & $^4F^e$ & 5/2&$4f$ &0 &-1.59067E+00& 3.96 & $^3 P^o$ \\\\\n 10 & $3d3 $ & $^4F^e$ & 7/2&$4f$ &0 &-1.58408E+00& 3.96 & $^5 D^o$ \\\\\n 11 & $3d3 $ & $^4P^e$ & 1/2&$5p$ &0 &-1.51986E+00& 3.84 & $^5 D^o$ \\\\\n 12 & $3d3 $ & $^4P^e$ & 3/2&$5p$ &0 &-1.51338E+00& 3.85 & $^3 P^o$ \\\\\n 13 & $3d3 $ & $^2P^e$ & 3/2&$5p$ &0 &-1.45761E+00& 3.84 & $^3 P^o$ \\\\\n 14 & $3d3 $ & $^2P^e$ & 1/2&$5p$ &0 &-1.45430E+00& 3.84 & $^1 S^o$ \\\\\n 15 & $3d3 2$ & $^2D^e$ & 3/2&$5p$ &0 &-1.41826E+00& 3.86 & $^3 P^o$ \\\\\n 16 & $3d3 $ & $^4P^e$ & 5/2&$4f$ &0 &-1.40953E+00& 3.97 & $^5 D^o$ \\\\\n 17 & $3d3 $ & $^2G^e$ & 7/2&$4f$ &0 &-1.39869E+00& 3.97 & $^3 P^o$ \\\\\n 18 & $3d3 2$ & $^2D^e$ & 5/2&$4f$ &0 &-1.34962E+00& 3.94 & $^3 P^o$ \\\\\n 19 & $3d3 $ & $^2F^e$ & 7/2&$4f$ &0 &-1.17207E+00& 3.96 & $^3 P^o$ \\\\\n 20 & $3d3 $ & $^2F^e$ & 5/2&$4f$ &0 &-1.16069E+00& 3.97 & $^1 S^o$ \\\\\n 21 & $3p53d5$ & & & &0 &-1.10428E+00& & $^0 S^o$ \\\\\n 22 & $3d3 $ & $^4F^e$ & 3/2&$6p$ &0 &-1.05635E+00& 4.86 & $^5 D^o$ \\\\\n 23 & $3d3 $ & $^4F^e$ & 5/2&$5f$ &0 &-1.01782E+00& 4.94 & $^5 D^o$ \\\\\n 24 & $3d3 1$ & $^2D^e$ & 3/2&$5p$ &0 &-1.01063E+00& 3.87 & $^3 P^o$ \\\\\n 25 & $3d3 $ & $^4F^e$ & 7/2&$5f$ &0 &-1.00821E+00& 4.95 & $^3 P^o$ \\\\\n \\noalign{\\smallskip}\n \\hline\n \\noalign{\\smallskip}\n \\multicolumn{9}{c}{$N_J$= 236,~~~~~$J\\pi$ = $1^o$ } \\\\\n \\noalign{\\smallskip}\n \\hline\n 1 & $3d3 $ & $^4F^e$ & 3/2&$4p$& 1 &-3.14950E+00& 2.82&$^5 DF o$ \\\\\n 2 & $3d3 $ & $^4F^e$ & 3/2&$4p$& 1 &-3.14082E+00& 2.82&$^5 DF o$ \\\\\n 3 & $3d3 $ & $^4F^e$ & 5/2&$4p$& 1 &-3.13088E+00& 2.82&$^3 D o$ \\\\\n 4 & $3d3 $ & $^4P^e$ & 3/2&$4p$& 1 &-2.99367E+00& 2.81&$^5 PD o$ \\\\\n 5 & $3d3 $ & $^4P^e$ & 1/2&$4p$& 1 &-2.97465E+00& 2.82&$^5 PD o$ \\\\\n 6 & $3d3 $ & $^4P^e$ & 3/2&$4p$& 1 &-2.96345E+00& 2.82&$^3 SPD o$ \\\\\n 7 & $3d3 $ & $^2P^e$ & 1/2&$4p$& 1 &-2.93263E+00& 2.81&$^3 SPD o$ \\\\\n 8 & $3d3 2$ & $^2D^e$ & 5/2&$4p$& 1 &-2.90308E+00& 2.82&$^1 P o$ \\\\\n 9 & $3d3 2$ & $^2D^e$ & 5/2&$4p$& 1 &-2.88417E+00& 2.82&$^3 PD o$ \\\\\n 10 & $3d3 $ & $^2P^e$ & 1/2&$4p$& 1 &-2.87902E+00& 2.83&$^3 SPD o$ \\\\\n 11 & $3d3 $ & $^2P^e$ & 3/2&$4p$& 1 &-2.86205E+00& 2.84&$^3 SPD o$ \\\\\n 12 & $3d3 $ & $^4P^e$ & 1/2&$4p$& 1 &-2.84777E+00& 2.88&$^3 SPD o$ \\\\\n 13 & $3d3 2$ & $^2D^e$ & 3/2&$4p$& 1 &-2.83128E+00& 2.84&$^3 PD o$ \\\\\n 14 & $3d3 $ & $^2P^e$ & 3/2&$4p$& 1 &-2.78217E+00& 2.88&$^1 P o$ \\\\\n 15 & $3d3 $ & $^4P^e$ & 5/2&$4p$& 1 &-2.77047E+00& 2.91&$^3 SPD o$ \\\\\n 16 & $3d3 $ & $^2F^e$ & 5/2&$4p$& 1 &-2.65585E+00& 2.85&$^3 D o$ \\\\\n 17 & $3d3 1$ & $^2D^e$ & 3/2&$4p$& 1 &-2.49355E+00& 2.82&$^3 PD o$ \\\\\n 18 & $3d3 1$ & $^2D^e$ & 3/2&$4p$& 1 &-2.41413E+00& 2.85&$^3 PD o$ \\\\\n 19 & $3d3 1$ & $^2D^e$ & 5/2&$4p$& 1 &-2.33944E+00& 2.89&$^1 P o$ \\\\\n 20 & $3d3 $ & $^4F^e$ & 3/2&$5p$& 1 &-1.68531E+00& 3.85&$^5 DF o$ \\\\\n \\noalign{\\smallskip}\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n\n%\\clearpage\n\n\n\n\\pagebreak \n\n \n\\begin{table}\n\\noindent{Table 1b. Ordered and identified fine-structure energy\nlevels of Fe V. Nlv=total number of levels expected for the possible\n$LS$ terms listed, and Nlv(c) = number of levels calculated. $SL\\pi$\nlists the possible $LS$ terms for each level (see text for details).\n \\\\ }\n%\\small \n\\scriptsize\n\\begin{tabular}{lcrrrcrl}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n$C_t$ & $S_tL_t\\pi_t$ & $J_t$ & $nl$ & $J$ & E(cal) & $\\nu$ & $SL\\pi$ \\\\\n \\noalign{\\smallskip}\n \\hline\n \\noalign{\\smallskip}\n\\multicolumn{1}{l}{Nlv=~ 5,~ 5,e:} &\n \\multicolumn{7}{l}{ F ( 5 4 3 2 1 )\n } \\\\\n%\\multicolumn{1}{l}{Nlv=~ 5~:} & \\multicolumn{7}{c}{ 5~ F e\n% } \\\\\n \\noalign{\\smallskip}\n 3d3 &(4Fe)& 3/2& 4s& 1& -3.73515E+00 & 2.59 & 5~ F e \\\\\n 3d3 &(4Fe)& 5/2& 4s& 2& -3.73238E+00 & 2.59 & 5~ F e \\\\\n 3d3 &(4Fe)& 5/2& 4s& 3& -3.72820E+00 & 2.59 & 5~ F e \\\\\n 3d3 &(4Fe)& 7/2& 4s& 4& -3.72275E+00 & 2.59 & 5~ F e \\\\\n 3d3 &(4Fe)& 9/2& 4s& 5& -3.71610E+00 & 2.59 & 5~ F e \\\\\n \\noalign{\\smallskip}\n \\multicolumn{8}{l}{Ncal=~ 5~ : set complete\n }\n\\\\\n \\noalign{\\smallskip}\n \\hline\n \\noalign{\\smallskip}\n \\multicolumn{1}{l}{Nlv=~ 3,~ 3,e:} &\n \\multicolumn{7}{l}{ F ( 4 3 2 )\n } \\\\\n%\\multicolumn{1}{l}{Nlv=~ 3~:} & \\multicolumn{7}{c}{ 3~ F e\n% } \\\\\n \\noalign{\\smallskip}\n 3d3 &(4Fe)& 3/2& 4s& 2& -3.63808E+00 & 2.62 & 3~ F e \\\\\n 3d3 &(4Fe)& 7/2& 4s& 3& -3.63107E+00 & 2.62 & 3~ F e \\\\\n 3d3 &(4Fe)& 9/2& 4s& 4& -3.62225E+00 & 2.62 & 3~ F e \\\\\n \\noalign{\\smallskip}\n \\multicolumn{8}{l}{Ncal=~ 3~ : set complete\n }\n\\\\\n \\noalign{\\smallskip}\n \\hline\n \\noalign{\\smallskip}\n \\multicolumn{1}{l}{Nlv=~ 3,~ 1,o:} &\n \\multicolumn{7}{l}{ P ( 1 ) D ( 2 ) F ( 3 )\n } \\\\\n%\\multicolumn{1}{l}{Nlv=~ 3~:} & \\multicolumn{7}{c}{ 1~ P D F o\n% } \\\\\n \\noalign{\\smallskip}\n 3d3 1 &(2De)& 3/2& 4p& 2& -2.45812E+00 & 2.83 & 1~ D o \\\\\n 3d3 1 &(2De)& 5/2& 4p& 3& -2.40581E+00 & 2.86 & 1~ F o \\\\\n 3d3 1 &(2De)& 5/2& 4p& 1& -2.33944E+00 & 2.89 & 1~ P o \\\\\n \\noalign{\\smallskip}\n \\multicolumn{8}{l}{Ncal=~ 3~ : set complete\n }\n\\\\\n \\noalign{\\smallskip}\n \\hline\n \\noalign{\\smallskip}\n \\multicolumn{1}{l}{Nlv=~23,~ 5,e:} &\n \\multicolumn{7}{l}{ P ( 3 2 1 ) D ( 4 3 2 1 0 ) F ( 5 4 3 2 1 ) G ( 6 5 4 3 2 )\n H ( 7 6 5 4 3) } \\\\\n%\\multicolumn{1}{l}{Nlv=~23~:} & \\multicolumn{7}{c}{ 5~ P D F G H e\n% } \\\\\n \\noalign{\\smallskip}\n 3d3 &(4Fe)& 3/2& 4d& 3& -2.37021E+00 & 3.25 & 5~ PDFGH e \\\\\n 3d3 &(4Fe)& 5/2& 4d& 4& -2.36647E+00 & 3.25 & 5~ DFGH e \\\\\n 3d3 &(4Fe)& 5/2& 4d& 5& -2.36189E+00 & 3.25 & 5~ FGH e \\\\\n 3d3 &(4Fe)& 3/2& 4d& 1& -2.35988E+00 & 3.25 & 5~ PDF e \\\\\n 3d3 &(4Fe)& 7/2& 4d& 6& -2.35651E+00 & 3.25 & 5~ GH e \\\\\n 3d3 &(4Fe)& 5/2& 4d& 2& -2.35541E+00 & 3.26 & 5~ PDFG e \\\\\n 3d3 &(4Fe)& 9/2& 4d& 7& -2.35041E+00 & 3.25 & 5~ H e \\\\\n 3d3 &(4Fe)& 5/2& 4d& 1& -2.34932E+00 & 3.26 & 5~ PDF e \\\\\n 3d3 &(4Fe)& 9/2& 4d& 3& -2.34736E+00 & 3.25 & 5~ PDFGH e \\\\\n 3d3 &(4Fe)& 9/2& 4d& 3& -2.34736E+00 & 3.25 & 5~ PDFGH e \\\\\n 3d3 &(4Fe)& 7/2& 4d& 2& -2.34633E+00 & 3.26 & 5~ PDFG e \\\\\n 3d3 &(4Fe)& 3/2& 4d& 2& -2.34397E+00 & 3.27 & 5~ PDFG e \\\\\n 3d3 &(4Fe)& 7/2& 4d& 4& -2.34329E+00 & 3.26 & 5~ DFGH e \\\\\n 3d3 &(4Fe)& 5/2& 4d& 3& -2.34092E+00 & 3.26 & 5~ PDFGH e \\\\\n 3d3 &(4Fe)& 9/2& 4d& 3& -2.33989E+00 & 3.26 & 5~ PDFGH e \\\\\n 3d3 &(4Fe)& 9/2& 4d& 5& -2.33822E+00 & 3.26 & 5~ FGH e \\\\\n 3d3 &(4Fe)& 7/2& 4d& 5& -2.33234E+00 & 3.27 & 5~ FGH e \\\\\n 3d3 &(4Fe)& 9/2& 4d& 6& -2.32699E+00 & 3.26 & 5~ GH e \\\\\n 3d3 &(4Fe)& 3/2& 4d& 4& -2.28772E+00 & 3.31 & 5~ DFGH e \\\\\n 3d3 &(4Fe)& 3/2& 4d& 0& -2.28673E+00 & 3.31 & 5~ D e \\\\\n 3d3 &(4Fe)& 7/2& 4d& 1& -2.28265E+00 & 3.30 & 5~ PDF e \\\\\n 3d3 &(4Fe)& 9/2& 4d& 2& -2.27468E+00 & 3.30 & 5~ PDFG e \\\\\n 3d3 &(4Fe)& 7/2& 4d& 3& -2.26346E+00 & 3.31 & 5~ PDFGH e \\\\\n 3d3 &(4Fe)& 9/2& 4d& 4& -2.25835E+00 & 3.31 & 5~ DFGH e \\\\\n \\noalign{\\smallskip}\n \\multicolumn{8}{l}{Ncal=~23~ : set complete\n }\n\\\\\n \\noalign{\\smallskip}\n \\hline\n \\noalign{\\smallskip}\n \\multicolumn{1}{l}{Nlv=~ 3,~ 1,e:} &\n \\multicolumn{7}{l}{ P ( 1 ) D ( 2 ) F ( 3 )\n } \\\\\n 3d3 &(2Pe)& 3/2& 4d& 1& -2.08815E+00 & 3.26 & 1~ P e \\\\\n 3d3 &(2Pe)& 1/2& 4d& 2& -1.95699E+00 & 3.41 & 1~ D e \\\\\n 3d3 &(2Pe)& 3/2& 4d& 3& -1.94667E+00 & 3.38 & 1~ F e \\\\\n \\noalign{\\smallskip}\n \\multicolumn{8}{l}{Ncal=~ 3~ : set complete\n }\n\\\\\n \\noalign{\\smallskip}\n \\hline\n \\noalign{\\smallskip}\n \\multicolumn{1}{l}{Nlv=~15,~ 3,e:} &\n \\multicolumn{7}{l}{ P ( 2 1 0 ) D ( 3 2 1 ) F ( 4 3 2 ) G ( 5 4 3 ) H ( 6 5 4 )\n } \\\\\n%\\multicolumn{1}{l}{Nlv=~15~:} & \\multicolumn{7}{c}{ 3~ P D F G H e\n% } \\\\\n \\noalign{\\smallskip}\n 3d3 &(4Fe)& 3/2& 4d& 1& -2.35634E+00 & 3.26 & 3~ PD e \\\\\n 3d3 &(4Fe)& 5/2& 4d& 2& -2.35219E+00 & 3.25 & 3~ PDF e \\\\\n 3d3 &(4Fe)& 7/2& 4d& 3& -2.34872E+00 & 3.25 & 3~ DFG e \\\\\n 3d3 &(4Fe)& 5/2& 4d& 4& -2.33701E+00 & 3.27 & 3~ FGH e \\\\\n 3d3 &(4Fe)& 5/2& 4d& 5& -2.28113E+00 & 3.31 & 3~ GH e \\\\\n 3d3 &(4Fe)& 3/2& 4d& 3& -2.28060E+00 & 3.31 & 3~ DFG e \\\\\n 3d3 &(4Fe)& 7/2& 4d& 4& -2.27417E+00 & 3.31 & 3~ FGH e \\\\\n 3d3 &(4Fe)& 9/2& 4d& 6& -2.27323E+00 & 3.30 & 3~ H e \\\\\n 3d3 &(4Fe)& 3/2& 4d& 2& -2.26789E+00 & 3.32 & 3~ PDF e \\\\\n 3d3 &(4Fe)& 7/2& 4d& 5& -2.26632E+00 & 3.31 & 3~ GH e \\\\\n 3d3 &(4Fe)& 5/2& 4d& 0& -2.24585E+00 & 3.33 & 3~ P e \\\\\n 3d3 &(4Fe)& 5/2& 4d& 1& -2.24483E+00 & 3.33 & 3~ PD e \\\\\n 3d3 &(4Fe)& 7/2& 4d& 2& -2.24278E+00 & 3.33 & 3~ PDF e \\\\\n 3d3 &(4Fe)& 7/2& 4d& 3& -2.23973E+00 & 3.33 & 3~ DFG e \\\\\n 3d3 &(4Fe)& 9/2& 4d& 4& -2.23571E+00 & 3.33 & 3~ FGH e \\\\\n \\noalign{\\smallskip}\n \\multicolumn{8}{l}{Ncal=~15~ : set complete\n }\n\\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n \\noalign{\\smallskip}\n \\multicolumn{1}{l}{Nlv=~13,~ 3,e:} &\n \\multicolumn{7}{l}{ S ( 1 ) P ( 2 1 0 ) D ( 3 2 1 ) F ( 4 3 2 ) G ( 5 4 3 )\n } \\\\\n \\noalign{\\smallskip}\n 3d3 2 &(2De) &5/2 &5d &1 & -1.05446E+00& 4.36 & 3~SPD e \\\\\n 3d3 2 &(2De) &5/2 &5d &5 & -1.04247E+00& 4.38 & 3~G e \\\\\n 3d3 2 &(2De) &3/2 &5d &3 & -1.04179E+00& 4.38 & 3~DFG e \\\\\n 3d3 2 &(2De) &3/2 &5d &1 & -1.03332E+00& 4.40 & 3~SPD e \\\\\n 3d3 2 &(2De) &5/2 &5d &4 & -1.03014E+00& 4.40 & 3~FG e \\\\\n 3d3 2 &(2De) &5/2 &5d &2 & -1.02889E+00& 4.40 & 3~PDF e \\\\\n 3d3 2 &(2De) &3/2 &5d &0 & -1.02130E+00& 4.42 & 3~P e \\\\\n 3d3 2 &(2De) &5/2 &5d &1 & -1.01682E+00& 4.43 & 3~SPD e \\\\\n 3d3 2 &(2De) &5/2 &5d &3 & -1.01420E+00& 4.43 & 3~DFG e \\\\\n 3d3 2 &(2De) &3/2 &5d &2 & -1.00936E+00& 4.44 & 3~PDF e \\\\\n 3d3 2 &(2De) &3/2 &5d &2 & -9.92578E-01& 4.47 & 3~PDF e \\\\\n 3d3 2 &(2De) &5/2 &5d &3 & -9.81500E-01& 4.49 & 3~DFG e \\\\\n \\noalign{\\smallskip}\n \\multicolumn{8}{l}{Ncal=~12~ , Nlv= 13 : set incomplete, level\nmissing: 4\n }\n\\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\n\n\n\n\n\\pagebreak\n\n\n\n\\begin{table}\n\\noindent{Table 2. Comparison of calculated BPRM energies, $E_c$, with\nthe observed ones (Sugar and Corliss 1985), $E_o$, of Fe V. $I_J$ is the\nlevel index for the energy position in symmetry $J\\pi$. \\\\\n}\n%\\label{TabSecInst}\n\\scriptsize\n\\begin{tabular}{llrrrr}\n\\hline\n\\noalign{\\smallskip}\n\\multicolumn{2}{c}{Level} & $J$ & $I_J$ & \\multicolumn{1}{c}{$E_c$(Ry)} &\n\\multicolumn{1}{c}{$E_o$(Ry)} \\\\\n\\hline\n \\noalign{\\smallskip}\n$3d^4 $ & $^5D$ & 4 & 1 & 5.5493 & 5.5015 \\\\\n$3d^4 $ & $^5D$ & 3 & 1 & 5.5542 & 5.5058 \\\\\n$3d^4 $ & $^5D$ & 2 & 1 & 5.5580 & 5.5094 \\\\\n$3d^4 $ & $^5D$ & 1 & 1 & 5.5607 & 5.5119 \\\\\n$3d^4 $ & $^5D$ & 0 & 1 & 5.5621 & 5.5132 \\\\\n$3d^42$ & $^3P$ & 2 & 2 & 5.3247 & 5.2720 \\\\\n$3d^42$ & $^3P$ & 1 & 2 & 5.3389 & 5.2856 \\\\\n$3d^42$ & $^3P$ & 0 & 2 & 5.3471 & 5.2940 \\\\\n$3d^4 $ & $^3H$ & 6 & 1 & 5.3074 & 5.2805 \\\\\n$3d^4 $ & $^3H$ & 5 & 1 & 5.3111 & 5.2833 \\\\\n$3d^4 $ & $^3H$ & 4 & 2 & 5.3143 & 5.2860 \\\\\n$3d^42$ & $^3F$ & 4 & 3 & 5.3043 & 5.2674 \\\\\n$3d^42$ & $^3F$ & 3 & 2 & 5.3064 & 5.2686 \\\\\n$3d^42$ & $^3F$ & 2 & 3 & 5.3076 & 5.2693 \\\\\n$3d^4 $ & $^3G$ & 5 & 2 & 5.2581 & 5.2359 \\\\\n$3d^4 $ & $^3G$ & 4 & 4 & 5.2614 & 5.2384 \\\\\n$3d^4 $ & $^3G$ & 3 & 3 & 5.2651 & 5.2415 \\\\\n$3d^42$ & $^1G$ & 4 & 5 & 5.2006 & 5.1798 \\\\\n$3d^4 $ & $^3D$ & 3 & 4 & 5.1950 & 5.1794 \\\\\n$3d^4 $ & $^3D$ & 2 & 4 & 5.1945 & 5.1782 \\\\\n$3d^4 $ & $^3D$ & 1 & 3 & 5.1928 & 5.1767 \\\\\n$3d^4 $ & $^1I$ & 6 & 2 & 5.1852 & 5.1713 \\\\\n$3d^42$ & $^1S$ & 0 & 3 & 5.1700 & 5.1520 \\\\\n$3d^42$ & $^1D$ & 2 & 5 & 5.1353 & 5.0913 \\\\\n$3d^4 $ & $^1F$ & 3 & 5 & 5.0476 & 5.0326 \\\\\n$3d^41$ & $^3P$ & 2 & 6 & 4.9756 & 4.9495 \\\\\n$3d^41$ & $^3P$ & 1 & 4 & 4.9663 & 4.9398 \\\\\n$3d^41$ & $^3P$ & 0 & 4 & 4.9616 & 4.9352 \\\\\n$3d^41$ & $^3F$ & 4 & 6 & 4.9719 & 4.9460 \\\\\n$3d^41$ & $^3F$ & 3 & 6 & 4.9706 & 4.9449 \\\\\n$3d^41$ & $^3F$ & 2 & 7 & 4.9712 & 4.9453 \\\\\n$3d^41$ & $^1G$ & 4 & 7 & 4.8830 & 4.8636 \\\\\n$3d^41$ & $^1D$ & 2 & 8 & 4.6609 & 4.6581 \\\\\n$3d^41$ & $^1S$ & 0 & 5 & 4.4302 & 4.4093 \\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\n\n\\pagebreak\n\n\n\\begin{table}\n\\noindent{Table 3. Transition probabilities for Fe V (see text for\nexplanation). \\\\ }\n%\\small\n\\scriptsize\n\\begin{tabular}{lrccccc}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n\\multicolumn{7}{l}{~~~26~~~~22} \\\\\n\\multicolumn{7}{l}{~~~~0~~~~0~~~~~~~~~2~~~~1} \\\\\n80 & 236 & $E_i(Ry)$ & $E_j(Ry)$ & $gf_L$ & $gf_V$ & $A_{ji}(sec^{-1})$ \\\\\n \\noalign{\\smallskip}\n 1& 1&-5.56210E+00&-3.14950E+00&-2.212E-01&-1.800E-01& 3.447E+09 \\\\\n 1& 2&-5.56210E+00&-3.14082E+00&-5.660E-03&-4.178E-03& 8.884E+07 \\\\\n 1& 3&-5.56210E+00&-3.13088E+00&-5.894E-02&-4.843E-02& 9.328E+08 \\\\\n 1& 4&-5.56210E+00&-2.99367E+00&-8.675E-02&-7.425E-02& 1.532E+09 \\\\\n 1& 5&-5.56210E+00&-2.97465E+00&-4.542E-03&-4.060E-03& 8.142E+07 \\\\\n 1& 6&-5.56210E+00&-2.96345E+00&-8.619E-05&-1.086E-04& 1.558E+06 \\\\\n 1& 7&-5.56210E+00&-2.93263E+00&-1.059E-03&-8.938E-04& 1.961E+07 \\\\\n 1& 8&-5.56210E+00&-2.90308E+00&-1.333E-08&-3.023E-07& 2.524E+02 \\\\\n 1& 9&-5.56210E+00&-2.88417E+00&-2.099E-06&-9.150E-07& 4.031E+04 \\\\\n 1& 10&-5.56210E+00&-2.87902E+00&-1.268E-03&-9.286E-04& 2.444E+07 \\\\\n 1& 11&-5.56210E+00&-2.86205E+00&-4.284E-06&-4.003E-06& 8.362E+04 \\\\\n 1& 12&-5.56210E+00&-2.84777E+00&-4.484E-06&-5.049E-06& 8.845E+04 \\\\\n 1& 13&-5.56210E+00&-2.83128E+00&-3.114E-05&-2.131E-05& 6.217E+05 \\\\\n 1& 14&-5.56210E+00&-2.78217E+00&-2.470E-06&-1.789E-06& 5.111E+04 \\\\\n 1& 15&-5.56210E+00&-2.77047E+00&-6.248E-05&-4.283E-05& 1.304E+06 \\\\\n 1& 16&-5.56210E+00&-2.65585E+00&-4.772E-06&-4.614E-06& 1.079E+05 \\\\\n 1& 17&-5.56210E+00&-2.49355E+00&-4.898E-06&-5.125E-06& 1.235E+05 \\\\\n 1& 18&-5.56210E+00&-2.41413E+00&-3.274E-07&-6.115E-07& 8.688E+03 \\\\\n 1& 19&-5.56210E+00&-2.33944E+00&-2.223E-09&-4.905E-09& 6.181E+01 \\\\\n 1& 20&-5.56210E+00&-1.68531E+00&-1.110E-02&-7.389E-03& 4.466E+08 \\\\\n 1& 21&-5.56210E+00&-1.68346E+00&-1.821E-02&-1.320E-02& 7.334E+08 \\\\\n 1& 22&-5.56210E+00&-1.67450E+00&-9.466E-05&-9.518E-05& 3.830E+06 \\\\\n 1& 23&-5.56210E+00&-1.59625E+00&-5.222E-03&-3.143E-03& 2.199E+08 \\\\\n 1& 24&-5.56210E+00&-1.59532E+00&-1.810E-03&-1.229E-03& 7.624E+07 \\\\\n 1& 25&-5.56210E+00&-1.58926E+00&-1.444E-03&-1.553E-03& 6.100E+07 \\\\\n 1& 26&-5.56210E+00&-1.58695E+00&-2.143E-01&-1.527E-01& 9.066E+09 \\\\\n 1& 27&-5.56210E+00&-1.58282E+00&-1.247E-01&-8.966E-02& 5.285E+09 \\\\\n 1& 28&-5.56210E+00&-1.56818E+00&-3.245E-03&-2.354E-03& 1.386E+08 \\\\\n 1& 29&-5.56210E+00&-1.52505E+00&-1.908E-02&-1.419E-02& 8.326E+08 \\\\\n 1& 30&-5.56210E+00&-1.51857E+00&-4.315E-03&-3.201E-03& 1.889E+08 \\\\\n 1& 31&-5.56210E+00&-1.51106E+00&-9.942E-04&-7.265E-04& 4.369E+07 \\\\\n 1& 32&-5.56210E+00&-1.48630E+00&-1.718E-05&-1.163E-05& 7.641E+05 \\\\\n 1& 33&-5.56210E+00&-1.45506E+00&-1.579E-04&-1.075E-04& 7.130E+06 \\\\\n 1& 34&-5.56210E+00&-1.45100E+00&-7.533E-06&-4.042E-06& 3.409E+05 \\\\\n 1& 35&-5.56210E+00&-1.44432E+00&-5.868E-04&-3.975E-04& 2.664E+07 \\\\\n 1& 36&-5.56210E+00&-1.44049E+00&-1.021E-01&-7.036E-02& 4.642E+09 \\\\\n 1& 37&-5.56210E+00&-1.43765E+00&-3.304E-04&-2.278E-04& 1.505E+07 \\\\\n 1& 38&-5.56210E+00&-1.43257E+00&-3.309E-05&-2.303E-05& 1.511E+06 \\\\\n 1& 39&-5.56210E+00&-1.42555E+00&-2.467E-07&-1.329E-07& 1.130E+04 \\\\\n 1& 40&-5.56210E+00&-1.41678E+00&-2.418E-05&-1.832E-05& 1.112E+06 \\\\\n 1& 41&-5.56210E+00&-1.41009E+00&-1.689E-02&-1.254E-02& 7.797E+08 \\\\\n 1& 42&-5.56210E+00&-1.40208E+00&-5.592E-05&-3.657E-05& 2.591E+06 \\\\\n 1& 43&-5.56210E+00&-1.40135E+00&-1.642E-05&-1.154E-05& 7.613E+05 \\\\\n 1& 44&-5.56210E+00&-1.39712E+00&-1.010E-04&-6.246E-05& 4.691E+06 \\\\\n 1& 45&-5.56210E+00&-1.39057E+00&-1.312E-05&-9.621E-06& 6.115E+05 \\\\\n 1& 46&-5.56210E+00&-1.37572E+00&-1.298E-05&-8.241E-06& 6.089E+05 \\\\\n 1& 47&-5.56210E+00&-1.36381E+00&-1.730E-04&-1.098E-04& 8.166E+06 \\\\\n 1& 48&-5.56210E+00&-1.34841E+00&-5.225E-07&-1.695E-06& 2.484E+04 \\\\\n 1& 49&-5.56210E+00&-1.33149E+00&-2.354E-06&-1.675E-06& 1.128E+05 \\\\\n 1& 50&-5.56210E+00&-1.32616E+00&-5.604E-05&-3.284E-05& 2.692E+06 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n\n\n\\begin{table}\n\\noindent{Table 4. Calculated energy level indices for various $J\\pi$\nsymmetries; all allowed transitions have been reprocessed \nusing observed energies. $n_j$ is the total number of $J\\pi$\nlevels observed.\n\\\\ }\n\\scriptsize\n\\begin{tabular}{ccrl}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n$J$ & $\\pi$ & $n_j$ & level indices \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n 0& e& 6 & 1,2,3,4,5,6 \\\\\n 0& o& 6 & 1,2,3,4,6,7 \\\\\n 1& e& 11 & 1,2,3,4,5,6,7,8,9,10,11 \\\\\n 1& o& 19 & 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19 \\\\\n 2& e& 18 & 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18 \\\\\n 2& o& 24 & 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25 \\\\\n 3& e& 14 & 1,2,3,4,5,6,7,8,9,10,11,12,13,14 \\\\\n 3& o& 24 & 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24 \\\\\n 4& e& 13 & 1,2,3,4,5,6,7,8,9,10,11,12,13 \\\\\n 4& o& 18 & 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18 \\\\\n 5& e& 6 & 1,2,3,4,5,6 \\\\\n 5& o& 11 & 1,2,3,4,5,6,7,8,9,10,11 \\\\\n 6& e& 3 & 1,2,3 \\\\\n 6& o& 5 & 1,2,3,4,5 \\\\\n 7& o& 1 & 1 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n\n\n\\pagebreak\n\n\n\\begin{table}\n\\noindent{Table 5a. Sample set of reprocessed $f$- and $A$-values with\nobserved transition energies. $I_i$ and $I_j$ are the level indices.\n\\\\ }\n\\scriptsize\n\\begin{tabular}{llllcrcrcccc}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n\\multicolumn{1}{c}{$C_i$} &\\multicolumn{1}{c}{$C_j$} &\n\\multicolumn{1}{c}{$S_iL_i\\pi_i$} & \\multicolumn{1}{c}{$S_jL_j\\pi_j$} &\n$2J_i+1$ & $I_i$ & $2J_j+1$ & $I_j$ & $E_i(Ry)$ & $E_j(Ry)$\n& $f$ & $A(sec^{-1})$ \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n $3d^4 $ & $-~3d^3(4F)4p $ & $^5D^e$ & $^5D^o$ & 1 & 1 & 3 & 2 & 5.5132 & 3.1540 & 5.515E-03 & 8.22E+07 \\\\\n $3d^4 $ & $-~3d^3(4F)4p $ & $^5D^e$ & $^3D^o$ & 1 & 1 & 3 & 3 & 5.5132 & 3.1439 & 5.744E-02 & 8.63E+08 \\\\\n $3d^4 $ & $-~3d^3(4P)4p $ & $^5D^e$ & $^5P^o$ & 1 & 1 & 3 & 4 & 5.5132 & 3.0195 & 8.420E-02 & 1.40E+09 \\\\\n $3d^4 $ & $-~3d^3(4P)4p $ & $^5D^e$ & $^5D^o$ & 1 & 1 & 3 & 5 & 5.5132 & 3.0058 & 4.401E-03 & 7.41E+07 \\\\\n $3d^4 $ & $-~3d^3(4P)4p $ & $^5D^e$ & $^3P^o$ & 1 & 1 & 3 & 6 & 5.5132 & 2.9911 & 8.365E-05 & 1.42E+06 \\\\\n $3d^4 $ & $-~3d^3(2P)4p $ & $^5D^e$ & $^3P^o$ & 1 & 1 & 3 & 7 & 5.5132 & 2.9439 & 1.035E-03 & 1.83E+07 \\\\\n $3d^4 $ & $-~3d^3(2D2)4p $ & $^5D^e$ & $^1P^o$ & 1 & 1 & 3 & 8 & 5.5132 & 2.9073 & 1.306E-08 & 2.38E+02 \\\\\n $3d^4 $ & $-~3d^3(2D2)4p $ & $^5D^e$ & $^3D^o$ & 1 & 1 & 3 & 9 & 5.5132 & 2.8826 & 2.062E-06 & 3.82E+04 \\\\\n $3d^4 $ & $-~3d^3(2P)4p $ & $^5D^e$ & $^3D^o$ & 1 & 1 & 3 & 10 & 5.5132 & 2.9274 & 1.222E-03 & 2.19E+07 \\\\\n $3d^4 $ & $-~3d^3(2P)4p $ & $^5D^e$ & $^3S^o$ & 1 & 1 & 3 & 11 & 5.5132 & 2.9052 & 4.138E-06 & 7.54E+04 \\\\\n $3d^4 $ & $-~3d^3(4P)4p $ & $^5D^e$ & $^3D^o$ & 1 & 1 & 3 & 12 & 5.5132 & 2.8991 & 4.318E-06 & 7.90E+04 \\\\\n $3d^4 $ & $-~3d^3(2D2)4p $ & $^5D^e$ & $^3P^o$ & 1 & 1 & 3 & 13 & 5.5132 & 2.8652 & 3.020E-05 & 5.67E+05 \\\\\n $3d^4 $ & $-~3d^3(2P)4p $ & $^5D^e$ & $^1P^o$ & 1 & 1 & 3 & 14 & 5.5132 & 2.8161 & 2.397E-06 & 4.67E+04 \\\\\n $3d^4 $ & $-~3d^3(4P)4p $ & $^5D^e$ & $^3S^o$ & 1 & 1 & 3 & 15 & 5.5132 & 2.8282 & 6.009E-05 & 1.16E+06 \\\\\n $3d^4 $ & $-~3d^3(2F)4p $ & $^5D^e$ & $^3D^o$ & 1 & 1 & 3 & 16 & 5.5132 & 2.7003 & 4.619E-06 & 9.78E+04 \\\\\n $3d^4 $ & $-~3d^3(2D1)4p $ & $^5D^e$ & $^3D^o$ & 1 & 1 & 3 & 17 & 5.5132 & 2.5285 & 4.765E-06 & 1.14E+05 \\\\\n $3d^4 $ & $-~3d^3(2D1)4p $ & $^5D^e$ & $^3P^o$ & 1 & 1 & 3 & 18 & 5.5132 & 2.4580 & 3.177E-07 & 7.94E+03 \\\\\n $3d^4 $ & $-~3d^3(2D1)4p $ & $^5D^e$ & $^1P^o$ & 1 & 1 & 3 & 19 & 5.5132 & 2.3924 & 2.152E-09 & 5.61E+01 \\\\\n $3d^4 2 $ & $-~3d^3(4F)4p $ & $^3P^e$ & $^5F^o$ & 1 & 2 & 3 & 1 & 5.2940 & 3.1644 & 2.317E-02 & 2.81E+08 \\\\\n $3d^4 2 $ & $-~3d^3(4F)4p $ & $^3P^e$ & $^5D^o$ & 1 & 2 & 3 & 2 & 5.2940 & 3.1540 & 1.751E-02 & 2.15E+08 \\\\\n $3d^4 2 $ & $-~3d^3(4F)4p $ & $^3P^e$ & $^3D^o$ & 1 & 2 & 3 & 3 & 5.2940 & 3.1439 & 6.702E-02 & 8.29E+08 \\\\\n $3d^4 2 $ & $-~3d^3(4P)4p $ & $^3P^e$ & $^5P^o$ & 1 & 2 & 3 & 4 & 5.2940 & 3.0195 & 7.726E-05 & 1.07E+06 \\\\\n $3d^4 2 $ & $-~3d^3(4P)4p $ & $^3P^e$ & $^5D^o$ & 1 & 2 & 3 & 5 & 5.2940 & 3.0058 & 2.863E-03 & 4.01E+07 \\\\\n $3d^4 2 $ & $-~3d^3(4P)4p $ & $^3P^e$ & $^3P^o$ & 1 & 2 & 3 & 6 & 5.2940 & 2.9911 & 1.907E-02 & 2.71E+08 \\\\\n $3d^4 2 $ & $-~3d^3(2P)4p $ & $^3P^e$ & $^3P^o$ & 1 & 2 & 3 & 7 & 5.2940 & 2.9439 & 9.377E-02 & 1.39E+09 \\\\\n $3d^4 2 $ & $-~3d^3(2D2)4p $ & $^3P^e$ & $^1P^o$ & 1 & 2 & 3 & 8 & 5.2940 & 2.9073 & 6.430E-03 & 9.81E+07 \\\\\n $3d^4 2 $ & $-~3d^3(2D2)4p $ & $^3P^e$ & $^3D^o$ & 1 & 2 & 3 & 9 & 5.2940 & 2.8826 & 7.067E-03 & 1.10E+08 \\\\\n $3d^4 2 $ & $-~3d^3(2P)4p $ & $^3P^e$ & $^3D^o$ & 1 & 2 & 3 & 10 & 5.2940 & 2.9274 & 7.538E-02 & 1.13E+09 \\\\\n $3d^4 2 $ & $-~3d^3(2P)4p $ & $^3P^e$ & $^3S^o$ & 1 & 2 & 3 & 11 & 5.2940 & 2.9052 & 2.193E-03 & 3.35E+07 \\\\\n $3d^4 2 $ & $-~3d^3(4P)4p $ & $^3P^e$ & $^3D^o$ & 1 & 2 & 3 & 12 & 5.2940 & 2.8991 & 3.284E-02 & 5.04E+08 \\\\\n $3d^4 2 $ & $-~3d^3(2D2)4p $ & $^3P^e$ & $^3P^o$ & 1 & 2 & 3 & 13 & 5.2940 & 2.8652 & 6.023E-03 & 9.51E+07 \\\\\n $3d^4 2 $ & $-~3d^3(2P)4p $ & $^3P^e$ & $^1P^o$ & 1 & 2 & 3 & 14 & 5.2940 & 2.8161 & 1.578E-04 & 2.59E+06 \\\\\n $3d^4 2 $ & $-~3d^3(4P)4p $ & $^3P^e$ & $^3S^o$ & 1 & 2 & 3 & 15 & 5.2940 & 2.8282 & 2.772E-04 & 4.51E+06 \\\\\n $3d^4 2 $ & $-~3d^3(2F)4p $ & $^3P^e$ & $^3D^o$ & 1 & 2 & 3 & 16 & 5.2940 & 2.7003 & 1.347E-03 & 2.43E+07 \\\\\n $3d^4 2 $ & $-~3d^3(2D1)4p $ & $^3P^e$ & $^3D^o$ & 1 & 2 & 3 & 17 & 5.2940 & 2.5285 & 4.641E-03 & 9.50E+07 \\\\\n $3d^4 2 $ & $-~3d^3(2D1)4p $ & $^3P^e$ & $^3P^o$ & 1 & 2 & 3 & 18 & 5.2940 & 2.4580 & 3.200E-04 & 6.89E+06 \\\\\n $3d^4 2 $ & $-~3d^3(2D1)4p $ & $^3P^e$ & $^1P^o$ & 1 & 2 & 3 & 19 & 5.2940 & 2.3924 & 1.102E-05 & 2.48E+05 \\\\\n $3d^4 2 $ & $-~3d^3(4F)4p $ & $^1S^e$ & $^5F^o$ & 1 & 3 & 3 & 1 & 5.1520 & 3.1644 & 7.493E-06 & 7.93E+04 \\\\\n $3d^4 2 $ & $-~3d^3(4F)4p $ & $^1S^e$ & $^5D^o$ & 1 & 3 & 3 & 2 & 5.1520 & 3.1540 & 7.672E-06 & 8.20E+04 \\\\\n $3d^4 2 $ & $-~3d^3(4F)4p $ & $^1S^e$ & $^3D^o$ & 1 & 3 & 3 & 3 & 5.1520 & 3.1439 & 2.529E-05 & 2.73E+05 \\\\\n $3d^4 2 $ & $-~3d^3(4P)4p $ & $^1S^e$ & $^5P^o$ & 1 & 3 & 3 & 4 & 5.1520 & 3.0195 & 1.024E-05 & 1.25E+05 \\\\\n $3d^4 2 $ & $-~3d^3(4P)4p $ & $^1S^e$ & $^5D^o$ & 1 & 3 & 3 & 5 & 5.1520 & 3.0058 & 1.932E-04 & 2.38E+06 \\\\\n $3d^4 2 $ & $-~3d^3(4P)4p $ & $^1S^e$ & $^3P^o$ & 1 & 3 & 3 & 6 & 5.1520 & 2.9911 & 2.404E-05 & 3.01E+05 \\\\\n $3d^4 2 $ & $-~3d^3(2P)4p $ & $^1S^e$ & $^3P^o$ & 1 & 3 & 3 & 7 & 5.1520 & 2.9439 & 7.035E-03 & 9.18E+07 \\\\\n $3d^4 2 $ & $-~3d^3(2D2)4p $ & $^1S^e$ & $^1P^o$ & 1 & 3 & 3 & 8 & 5.1520 & 2.9073 & 8.021E-03 & 1.08E+08 \\\\\n $3d^4 2 $ & $-~3d^3(2D2)4p $ & $^1S^e$ & $^3D^o$ & 1 & 3 & 3 & 9 & 5.1520 & 2.8826 & 2.263E-01 & 3.12E+09 \\\\\n $3d^4 2 $ & $-~3d^3(2P)4p $ & $^1S^e$ & $^3D^o$ & 1 & 3 & 3 & 10 & 5.1520 & 2.9274 & 1.305E-03 & 1.73E+07 \\\\\n $3d^4 2 $ & $-~3d^3(2P)4p $ & $^1S^e$ & $^3S^o$ & 1 & 3 & 3 & 11 & 5.1520 & 2.9052 & 1.968E-04 & 2.66E+06 \\\\\n $3d^4 2 $ & $-~3d^3(4P)4p $ & $^1S^e$ & $^3D^o$ & 1 & 3 & 3 & 12 & 5.1520 & 2.8991 & 2.048E-03 & 2.78E+07 \\\\\n $3d^4 2 $ & $-~3d^3(2D2)4p $ & $^1S^e$ & $^3P^o$ & 1 & 3 & 3 & 13 & 5.1520 & 2.8652 & 1.148E-02 & 1.61E+08 \\\\\n $3d^4 2 $ & $-~3d^3(2P)4p $ & $^1S^e$ & $^1P^o$ & 1 & 3 & 3 & 14 & 5.1520 & 2.8161 & 7.864E-02 & 1.15E+09 \\\\\n $3d^4 2 $ & $-~3d^3(4P)4p $ & $^1S^e$ & $^3S^o$ & 1 & 3 & 3 & 15 & 5.1520 & 2.8282 & 2.714E-02 & 3.92E+08 \\\\\n $3d^4 2 $ & $-~3d^3(2F)4p $ & $^1S^e$ & $^3D^o$ & 1 & 3 & 3 & 16 & 5.1520 & 2.7003 & 5.453E-07 & 8.78E+03 \\\\\n $3d^4 2 $ & $-~3d^3(2D1)4p $ & $^1S^e$ & $^3D^o$ & 1 & 3 & 3 & 17 & 5.1520 & 2.5285 & 6.569E-05 & 1.21E+06 \\\\\n $3d^4 2 $ & $-~3d^3(2D1)4p $ & $^1S^e$ & $^3P^o$ & 1 & 3 & 3 & 18 & 5.1520 & 2.4580 & 2.050E-07 & 3.98E+03 \\\\\n $3d^4 2 $ & $-~3d^3(2D1)4p $ & $^1S^e$ & $^1P^o$ & 1 & 3 & 3 & 19 & 5.1520 & 2.3924 & 2.421E-04 & 4.94E+06 \\\\\n $3d^4 1 $ & $-~3d^3(4F)4p $ & $^3P^e$ & $^5F^o$ & 1 & 4 & 3 & 1 & 4.9352 & 3.1644 & 9.362E-05 & 7.86E+05 \\\\\n $3d^4 1 $ & $-~3d^3(4F)4p $ & $^3P^e$ & $^5D^o$ & 1 & 4 & 3 & 2 & 4.9352 & 3.1540 & 2.852E-05 & 2.42E+05 \\\\\n $3d^4 1 $ & $-~3d^3(4F)4p $ & $^3P^e$ & $^3D^o$ & 1 & 4 & 3 & 3 & 4.9352 & 3.1439 & 1.131E-04 & 9.72E+05 \\\\\n $3d^4 1 $ & $-~3d^3(4P)4p $ & $^3P^e$ & $^5P^o$ & 1 & 4 & 3 & 4 & 4.9352 & 3.0195 & 4.206E-04 & 4.13E+06 \\\\\n $3d^4 1 $ & $-~3d^3(4P)4p $ & $^3P^e$ & $^5D^o$ & 1 & 4 & 3 & 5 & 4.9352 & 3.0058 & 1.295E-02 & 1.29E+08 \\\\\n $3d^4 1 $ & $-~3d^3(4P)4p $ & $^3P^e$ & $^3P^o$ & 1 & 4 & 3 & 6 & 4.9352 & 2.9911 & 1.009E-02 & 1.02E+08 \\\\\n $3d^4 1 $ & $-~3d^3(2P)4p $ & $^3P^e$ & $^3P^o$ & 1 & 4 & 3 & 7 & 4.9352 & 2.9439 & 7.813E-03 & 8.29E+07 \\\\\n $3d^4 1 $ & $-~3d^3(2D2)4p $ & $^3P^e$ & $^1P^o$ & 1 & 4 & 3 & 8 & 4.9352 & 2.9073 & 3.255E-04 & 3.58E+06 \\\\\n $3d^4 1 $ & $-~3d^3(2D2)4p $ & $^3P^e$ & $^3D^o$ & 1 & 4 & 3 & 9 & 4.9352 & 2.8826 & 3.644E-04 & 4.11E+06 \\\\\n $3d^4 1 $ & $-~3d^3(2P)4p $ & $^3P^e$ & $^3D^o$ & 1 & 4 & 3 & 10 & 4.9352 & 2.9274 & 2.974E-03 & 3.21E+07 \\\\\n $3d^4 1 $ & $-~3d^3(2P)4p $ & $^3P^e$ & $^3S^o$ & 1 & 4 & 3 & 11 & 4.9352 & 2.9052 & 2.856E-04 & 3.15E+06 \\\\\n $3d^4 1 $ & $-~3d^3(4P)4p $ & $^3P^e$ & $^3D^o$ & 1 & 4 & 3 & 12 & 4.9352 & 2.8991 & 4.236E-04 & 4.70E+06 \\\\\n $3d^4 1 $ & $-~3d^3(2D2)4p $ & $^3P^e$ & $^3P^o$ & 1 & 4 & 3 & 13 & 4.9352 & 2.8652 & 5.201E-02 & 5.97E+08 \\\\\n $3d^4 1 $ & $-~3d^3(2P)4p $ & $^3P^e$ & $^1P^o$ & 1 & 4 & 3 & 14 & 4.9352 & 2.8161 & 1.028E-02 & 1.24E+08 \\\\\n $3d^4 1 $ & $-~3d^3(4P)4p $ & $^3P^e$ & $^3S^o$ & 1 & 4 & 3 & 15 & 4.9352 & 2.8282 & 4.824E-02 & 5.73E+08 \\\\\n $3d^4 1 $ & $-~3d^3(2F)4p $ & $^3P^e$ & $^3D^o$ & 1 & 4 & 3 & 16 & 4.9352 & 2.7003 & 1.648E-01 & 2.20E+09 \\\\\n $3d^4 1 $ & $-~3d^3(2D1)4p $ & $^3P^e$ & $^3D^o$ & 1 & 4 & 3 & 17 & 4.9352 & 2.5285 & 2.144E-08 & 3.33E+02 \\\\\n $3d^4 1 $ & $-~3d^3(2D1)4p $ & $^3P^e$ & $^3P^o$ & 1 & 4 & 3 & 18 & 4.9352 & 2.4580 & 4.867E-02 & 8.00E+08 \\\\\n $3d^4 1 $ & $-~3d^3(2D1)4p $ & $^3P^e$ & $^1P^o$ & 1 & 4 & 3 & 19 & 4.9352 & 2.3924 & 4.875E-05 & 8.44E+05 \\\\\n $3d^4 1 $ & $-~3d^3(4F)4p $ & $^1S^e$ & $^5F^o$ & 1 & 5 & 3 & 1 & 4.4093 & 3.1644 & 8.262E-08 & 3.43E+02 \\\\\n $3d^4 1 $ & $-~3d^3(4F)4p $ & $^1S^e$ & $^5D^o$ & 1 & 5 & 3 & 2 & 4.4093 & 3.1540 & 3.663E-08 & 1.55E+02 \\\\\n $3d^4 1 $ & $-~3d^3(4F)4p $ & $^1S^e$ & $^3D^o$ & 1 & 5 & 3 & 3 & 4.4093 & 3.1439 & 1.626E-07 & 6.97E+02 \\\\\n $3d^4 1 $ & $-~3d^3(4P)4p $ & $^1S^e$ & $^5P^o$ & 1 & 5 & 3 & 4 & 4.4093 & 3.0195 & 8.343E-08 & 4.31E+02 \\\\\n $3d^4 1 $ & $-~3d^3(4P)4p $ & $^1S^e$ & $^5D^o$ & 1 & 5 & 3 & 5 & 4.4093 & 3.0058 & 1.509E-09 & 7.96E+00 \\\\\n$3d^4 1 $ & $-~3d^3(4P)4p $ & $^1S^e$ & $^3P^o$ & 1 & 5 & 3 & 6 & 4.4093 & 2.9911 & 2.573E-07 & 1.39E+03 \\\\\n $3d^4 1 $ & $-~3d^3(2P)4p $ & $^1S^e$ & $^3P^o$ & 1 & 5 & 3 & 7 & 4.4093 & 2.9439 & 1.238E-05 & 7.12E+04 \\\\\n $3d^4 1 $ & $-~3d^3(2D2)4p $ & $^1S^e$ & $^1P^o$ & 1 & 5 & 3 & 8 & 4.4093 & 2.9073 & 2.067E-05 & 1.25E+05 \\\\\n $3d^4 1 $ & $-~3d^3(2D2)4p $ & $^1S^e$ & $^3D^o$ & 1 & 5 & 3 & 9 & 4.4093 & 2.8826 & 3.442E-04 & 2.15E+06 \\\\\n $3d^4 1 $ & $-~3d^3(2P)4p $ & $^1S^e$ & $^3D^o$ & 1 & 5 & 3 & 10 & 4.4093 & 2.9274 & 1.868E-05 & 1.10E+05 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n\n\n\\pagebreak\n\n\n\n\\begin{table}\n\\noindent{Table 5b. Fine-structure transitions, ordered in $LS$\nmultiplets, compared with previous values.\n\\\\ }\n\\scriptsize\n\\begin{tabular}{llllrrrrll}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n\\multicolumn{1}{c}{$C_i$} &\\multicolumn{1}{c}{$C_j$} & $S_iL_i\\pi_i$ &\n$S_jL_j\\pi_j$ & $2J_i+1$ & $I_i$ & $2J_j+1$ & $I_j$ & $f_{ij}(present)$ &\n$f_{ij}(others)$ \\\\\n \\noalign{\\smallskip}\n\\hline\n \\noalign{\\smallskip}\n 3d4 & -3d3(4F)4p & 5D0 &5F1 & 1 &1& 3 &1& 0.2154&0.163$^a$\\\\\n 3d4 & -3d3(4F)4p & 5D0 &5F1 & 3 &1& 3 &1& 3.790E-04& \\\\\n 3d4 & -3d3(4F)4p & 5D0 &5F1 & 3 &1& 5 &3& 0.00136& \\\\\n 3d4 & -3d3(4F)4p & 5D0 &5F1 & 5 &1& 3 &1& 0.04617&0.0126$^a$\\\\\n 3d4 & -3d3(4F)4p & 5D0 &5F1 & 5 &1& 5 &3& 0.05967&0.0596$^a$\\\\\n 3d4 & -3d3(4F)4p & 5D0 &5F1 & 5 &1& 7 &3& 0.01462&0.0138$^a$\\\\\n 3d4 & -3d3(4F)4p & 5D0 &5F1 & 7 &1& 5 &3& 0.006895&0.0274$^a$\\\\\n 3d4 & -3d3(4F)4p & 5D0 &5F1 & 7 &1& 7 &3& 0.05889&0.0544$^a$\\\\\n 3d4 & -3d3(4F)4p & 5D0 &5F1 & 9 &1& 7 &3& 0.001966&0.00756$^a$\\\\\n 3d4 & -3d3(4F)4p & 5D0 &5F1 & 7 &1& 9 &3& 0.03262&0.0414$^a$\\\\\n 3d4 & -3d3(4F)4p & 5D0 &5F1 & 9 &1& 9 &3& 0.05139&0.03$^a$\\\\\n 3d4 & -3d3(4F)4p & 5D0 &5F1 & 9 &1&11 &2& 0.07548&0.0686$^a$\\\\\n & & & & & & & & & \\\\\n 3d4 &-3d3(4F)4p & 5D0 &5F1 &25 & &35 &&0.107&0.0804$^b$,0.0915$^c$\\\\\n & & & & & & & & & \\\\\n 3d4 & -3d3(4F)4p &5D0&5D1 &1 &1 &3 &2 &0.00551&0.041$^a$\\\\\n 3d4 & -3d3(4F)4p &5D0&5D1 &3 &1 &1 &1 &0.06255&0.0607$^a$\\\\\n 3d4 & -3d3(4F)4p &5D0&5D1 &3 &1 &3 &2 &0.03888&0.0343$^a$\\\\\n 3d4 & -3d3(4F)4p &5D0&5D1 &3 &1 &5 &2 &0.1360&0.1257$^a$\\\\\n 3d4 & -3d3(4F)4p &5D0&5D1 &5 &1 &3 &2 &0.01704&0.0532$^a$\\\\\n 3d4 & -3d3(4F)4p &5D0&5D1 &5 &1 &5 &2 &0.01372&0.0092$^a$\\\\\n 3d4 & -3d3(4F)4p &5D0&5D1 &5 &1 &7 &2 &0.1087&0.1006$^a$\\\\\n 3d4 & -3d3(4F)4p &5D0&5D1 &7 &1 &5 &2 &0.04155&0.0247$^a$\\\\\n 3d4 & -3d3(4F)4p &5D0&5D1 &7 &1 &7 &2 &0.04936&0.0517$^a$\\\\\n 3d4 & -3d3(4F)4p &5D0&5D1 &9 &1 &7 &2 &0.02644&0.0222$^a$\\\\\n 3d4 & -3d3(4F)4p &5D0&5D1 &7 &1 &9 &2 &0.07311&0.0588$^a$\\\\\n 3d4 & -3d3(4F)4p &5D0&5D1 &9 &1 &9 &2 &0.1168&0.130$^a$\\\\\n & & & & & & & & & \\\\\n 3d4 & -3d3(4F)4p& 5D0&5D1&25&& 25&& 0.1541&0.1708$^b$,0.192$^c$\\\\\n & & & & & & & & & \\\\\n 3d4 & -3d3(4P)4p& 5D0&5P1 &1 &1 &3 &4 &0.08420& 0.076$^a$\\\\\n 3d4 & -3d3(4P)4p& 5D0&5P1 &3 &1 &3 &4 &0.06281& 0.057$^a$\\\\\n 3d4 & -3d3(4P)4p& 5D0&5P1 &3 &1 &5 &6 &0.02114& 0.019$^a$\\\\\n 3d4 & -3d3(4P)4p& 5D0&5P1 &5 &1 &3 &4 &0.02926& 0.0266$^a$\\\\\n 3d4 & -3d3(4P)4p& 5D0&5P1 &5 &1 &5 &6 &0.04831& 0.0442$^a$\\\\\n 3d4 & -3d3(4P)4p& 5D0&5P1 &5 &1 &7 &7 &0.00622& 0.0054$^a$\\\\\n 3d4 & -3d3(4P)4p& 5D0&5P1 &7 &1 &5 &6 &0.05555& 0.0499$^a$\\\\\n 3d4 & -3d3(4P)4p& 5D0&5P1 &7 &1 &7 &7 &0.03105& 0.0264$^a$\\\\\n 3d4 & -3d3(4P)4p& 5D0&5P1 &9 &1 &7 &7 &0.08782& 0.0758$^a$\\\\\n & & & & & & & & & \\\\\n 3d4 & -3d3(4P)4p& 5D0&5P1&25& & 15& &0.0861 &0.076$^b$,0.0893$^c$\\\\\n\n & & & & & & & & & \\\\\n 3d4 & -3d3(4P)4p &5D0&5D1 &1 &1 &3 &5 &4.401E-03 &\\\\\n 3d4 & -3d3(4P)4p &5D0&5D1 &3 &1 &1 &2 &4.902E-04& \\\\\n 3d4 & -3d3(4P)4p &5D0&5D1 &3 &1 &3 &5 &7.201E-04& \\\\\n 3d4 & -3d3(4P)4p &5D0&5D1 &3 &1 &5 &7 &2.402E-03& \\\\\n 3d4 & -3d3(4P)4p &5D0&5D1 &5 &1 &3 &5 &1.502E-03& \\\\\n 3d4 & -3d3(4P)4p &5D0&5D1 &5 &1 &5 &7 &2.248E-03& \\\\\n 3d4 & -3d3(4P)4p &5D0&5D1 &5 &1 &7 &8 &1.474E-03& \\\\\n 3d4 & -3d3(4P)4p &5D0&5D1 &7 &1 &5 &7 &2.675E-03& \\\\\n 3d4 & -3d3(4P)4p &5D0&5D1 &7 &1 &7 &8 &1.048E-03& \\\\\n 3d4 & -3d3(4P)4p &5D0&5D1 &9 &1 &7 &8 &2.846E-06& \\\\\n 3d4 & -3d3(4P)4p &5D0&5D1 &7 &1 &9 &7 &1.408E-03& \\\\\n 3d4 & -3d3(4P)4p &5D0&5D1 &9 &1 &9 &7 &4.558E-03& \\\\\n & & & & & & & & & \\\\\n 3d4 & -3d3(4P)4p & 5D0&5D1&25&& 25&& 0.0047&0.00436$^b$,0.00564$^c$\\\\\n & & & & & & & & & \\\\\n 3d4 2& -3d3(4F)4p& 3P0&3D1& 1& 2& 3& 3& 6.702E-02&0.061$^a$\\\\\n 3d4 2& -3d3(4F)4p& 3P0&3D1& 3& 2& 3& 3& 1.585E-02&0.0147$^a$\\\\\n 3d4 2& -3d3(4F)4p& 3P0&3D1& 3& 2& 5& 4& 6.279E-02&0.057$^a$\\\\\n 3d4 2& -3d3(4F)4p& 3P0&3D1& 5& 2& 3& 3& 6.685E-04&\\\\\n 3d4 2& -3d3(4F)4p& 3P0&3D1& 5& 2& 5& 4& 1.144E-02&0.011$^a$\\\\\n 3d4 2& -3d3(4F)4p& 3P0&3D1& 5& 2& 7& 4& 7.753E-02&0.0756$^a$\\\\\n & & & & & & & & & \\\\\n 3d4 2& -3d3(4F)4p& 3P0&3D1& 9&& 15&& 0.0833&0.0973$^b$,0.106$^c$\\\\\n & & & & & & & & & \\\\\n 3d4 2& -3d3(4P)4p& 3P0&3P1& 1& 2& 3& 6 &1.907E-02&\\\\\n 3d4 2& -3d3(4P)4p& 3P0&3P1& 3& 2& 1& 3 &3.593E-03&\\\\\n 3d4 2& -3d3(4P)4p& 3P0&3P1& 3& 2& 3& 6 &3.409E-03&\\\\\n 3d4 2& -3d3(4P)4p& 3P0&3P1& 3& 2& 5& 8 &3.037E-03&\\\\\n 3d4 2& -3d3(4P)4p& 3P0&3P1& 5& 2& 3& 6 &3.742E-03&\\\\\n 3d4 2& -3d3(4P)4p& 3P0&3P1& 5& 2& 5& 8 &2.134E-03&\\\\\n & & & & & & & & & \\\\\n 3d4 2& -3d3(4P)4p& 3P0&3P1& 9&& 9&& 0.0087&0.00542$^b$,0.0127$^c$\\\\\n & & & & & & & & & \\\\\n 3d4 2& -3d3(2P)4p& 3P0&3S1& 1& 2& 3&11& 2.193E-03&\\\\\n 3d4 2& -3d3(2P)4p& 3P0&3S1& 3& 2& 3&11& 5.853E-03&\\\\\n 3d4 2& -3d3(2P)4p& 3P0&3S1& 5& 2& 3&11& 3.582E-04& \\\\\n & & & & & & & & & \\\\\n 3d4 2& -3d3(2P)4p& 3P0&3S1& 9&& 3&& 0.00239&0.00142$^b$,0.056$^c$\\\\\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n\\multicolumn{10}{l}{a~~Fawcett (1989),~b~~Butler, ~c~~Bautista (1996) }\\\\\n\\end{tabular}\n\\end{table}\n\n\n\\pagebreak\n\n\n\\begin{table*}\n\\noindent{Table 6. Comparison of $A$-values for forbidden transitions,\n$A_{fi}^{cal}$, among $3d^4$ fine-structure levels with those,\n$A_{fi}^G$, by Garstang (1957). \\\\ }\n%\\label{TabSecInst}\n\\begin{tabular}{llrrrrr}\n\\hline\n\\noalign{\\smallskip}\n Transition & & $\\lambda_{vac}$ & $E_{i}(cm^{-1})$\n& $E_{f}(cm^{-1})$ & $A_{fi}^G(s^{-1})$ &\n$A_{fi}^{cal}(s^{-1})$ \\\\\n \\noalign{\\smallskip}\n \\hline\n \\noalign{\\smallskip}\n$^5D_{1}$ & $^3P2_{0}$ & 4181.8 & 142.1 & 24055.4 & 1.30E+00 & 1.39E+00\\\\\n$^5D_{0}$ & $^3P2_{1}$ & 4004.3 & 0.0 & 24972.9 & 1.30E-01 & 1.23E-01 \\\\\n$^5D_{2}$ & $^3P2_{1}$ & 4072.4 & 417.3 & 24972.9 & 1.10E+00 & 1.07E+00 \\\\\n$^5D_{1}$ & $^3P2_{2}$ & 3798.5 & 142.1 & 26468.3 & 3.60E-02 & 3.54E-02 \\\\\n$^5D_{3}$ & $^3P2_{2}$ & 3896.3 & 803.1 & 26468.3 & 7.10E-01 & 7.08E-01 \\\\\n$^5D_{4}$ & $^3H_{4}$ & 4228.4 & 1282.8 & 24932.5 & 1.10E-03 & 4.34E-03 \\\\\n$^5D_{1}$ & $^3F2_{2}$ & 3756.8 & 142.1 & 26760.7 & 1.00E-01 & 1.04E-01 \\\\\n$^5D_{2}$ & $^3F2_{2}$ & 3796.0 & 417.3 & 26760.7 & 2.00E-01 & 2.01E-01 \\\\\n$^5D_{3}$ & $^3F2_{2}$ & 3852.4 & 803.1 & 26760.7 & 4.70E-02 & 5.25E-02 \\\\\n$^5D_{2}$ & $^3F2_{3}$ & 3784.3 & 417.3 & 26842.3 & 1.60E-01 & 1.78E-01 \\\\\n$^5D_{3}$ & $^3F2_{3}$ & 3840.4 & 803.1 & 26842.3 & 4.00E-01 & 4.66E-01 \\\\\n$^5D_{4}$ & $^3F2_{3}$ & 3912.4 & 1282.8 & 26842.3 & 6.60E-02 & 6.43E-02 \\\\\n$^5D_{3}$ & $^3F2_{4}$ & 3821.0 & 803.1 & 26974.0 & 1.60E-01 & 1.66E-01 \\\\\n$^5D_{4}$ & $^3F2_{4}$ & 3892.4 & 1282.8 & 26974.0 & 7.40E-01 & 7.92E-01 \\\\\n$^5D_{2}$ & $^3G_{3}$ & 3401.4 & 417.3 & 29817.1 & 7.00E-03 & 6.76E-03 \\\\\n$^5D_{3}$ & $^3G_{3}$ & 3446.6 & 803.1 & 29817.1 & 1.70E-02 & 1.62E-02 \\\\\n$^5D_{4}$ & $^3G_{3}$ & 3504.6 & 1282.8 & 29817.1 & 2.60E-03 & 2.32E-03 \\\\\n$^5D_{3}$ & $^3G_{4}$ & 3407.9 & 803.1 & 30147.0 & 7.80E-03 & 7.20E-03 \\\\\n$^5D_{4}$ & $^3G_{4}$ & 3464.5 & 1282.8 & 30147.0 & 3.20E-02 & 2.58E-02 \\\\\n$^5D_{2}$ & $^3D_{3}$ & 2761.5 & 417.3 & 36630.1 & 9.70E-02 & 9.76E-02 \\\\\n$^5D_{3}$ & $^3D_{3}$ & 2791.2 & 803.1 & 36630.1 & 8.90E-02 & 9.15E-02 \\\\\n$^5D_{4}$ & $^3D_{3}$ & 2829.1 & 1282.8 & 36630.1 & 3.70E-01 & 3.80E-01 \\\\\n$^5D_{1}$ & $^3D_{2}$ & 2731.0 & 142.1 & 36758.5 & 2.00E-01 & 1.96E-01 \\\\\n$^5D_{2}$ & $^3D_{2}$ & 2751.7 & 417.3 & 36758.5 & 1.80E-01 & 1.60E-01 \\\\\n$^5D_{3}$ & $^3D_{2}$ & 2781.2 & 803.1 & 36758.5 & 1.10E-01 & 1.05E-01 \\\\\n$^5D_{0}$ & $^3D_{1}$ & 2708.2 & 0.0 & 36925.4 & 2.20E-01 & 2.37E-01 \\\\\n$^5D_{1}$ & $^3D_{1}$ & 2718.6 & 142.1 & 36925.4 & 1.90E-01 & 2.11E-01 \\\\\n$^5D_{2}$ & $^3D_{1}$ & 2739.1 & 417.3 & 36925.4 & 1.90E-03 & 2.73E-03 \\\\\n$^3H_{4}$ & $^3G_{3}$ & 20472.5 & 24932.5 & 29817.1 & 3.60E-02 & 3.98E-02\\\\\n$^3H_{4}$ & $^3G_{4}$ & 19177.3 & 24932.5 & 30147.0 & 3.30E-02 & 3.33E-02 \\\\\n$^3H_{4}$ & $^3G_{5}$ & 18189.8 & 24932.5 & 30430.1 & 1.20E-03 & 8.77E-04 \\\\\n$^3H_{5}$ & $^3G_{5}$ & 19215.2 & 25225.9 & 30430.1 & 4.10E-02 & 4.40E-02 \\\\\n$^3H_{6}$ & $^3G_{5}$ & 20401.5 & 25528.5 & 30430.1 & 4.10E-02 & 4.39E-02 \\\\\n$^3H_{5}$ & $^1I_{6}$ & 8139.5 & 25225.9 & 37511.7 & 1.10E-01 & 1.16E-01 \\\\\n$^3H_{6}$ & $^1I_{6}$ & 8345.0 & 25528.5 & 37511.7 & 1.40E-01 & 1.52E-01 \\\\\n$^3F2_{2}$ & $^3G_{3}$ & 32718.2 & 26760.7 & 29817.1 & 3.00E-02 & 3.03E-02 \\\\\n$^3F2_{3}$ & $^3G_{3}$ & 33615.7 & 26842.3 & 29817.1 & 3.70E-02 & 3.76E-02 \\\\\n$^3F2_{4}$ & $^3G_{4}$ & 31515.9 & 26974.0 & 30147.0 & 2.70E-02 & 2.80E-02 \\\\\n$^3F2_{4}$ & $^3G_{5}$ & 28934.3 & 26974.0 & 30430.1 & 3.70E-02 & 3.74E-02 \\\\\n$^3F2_{3}$ & $^3D_{3}$ & 10216.8 & 26842.3 & 36630.1 & 6.40E-03 & 5.97E-03 \\\\\n$^3F2_{4}$ & $^3D_{3}$ & 10356.1 & 26974.0 & 36630.1 & 6.90E-03 & 6.37E-03 \\\\\n$^3F2_{2}$ & $^3D_{2}$ & 10002.2 & 26760.7 & 36758.5 & 1.70E-02 & 1.44E-02 \\\\\n$^3F2_{3}$ & $^3D_{2}$ & 10084.5 & 26842.3 & 36758.5 & 1.60E-03 & 1.21E-03 \\\\\n$^3F2_{2}$ & $^3D_{1}$ & 9838.0 & 26760.7 & 36925.4 & 1.40E-02 & 1.36E-02 \\\\\n$^3F2_{2}$ & $^1D2_{2}$ & 5120.2 & 26760.7 & 46291.2 & 2.10E-01 & 2.28E-01 \\\\\n$^3F2_{3}$ & $^1D2_{2}$ & 5141.7 & 26842.3 & 46291.2 & 4.20E-01 & 4.48E-01 \\\\\n$^3G_{3}$ & $^1F_{3}$ & 4363.8 & 29817.1 & 52732.7 & 1.20E-01 & 1.23E-01 \\\\\n$^3G_{4}$ & $^1F_{3}$ & 4427.6 & 30147.0 & 52732.7 & 1.70E-01 & 1.70E-01 \\\\\n$^3D_{3}$ & $^1D2_{2}$ & 10350.8 & 36630.1 & 46291.2 & 9.00E-02 & 1.08E-01 \\\\\n$^3D_{2}$ & $^1D2_{2}$ & 10490.2 & 36758.5 & 46291.2 & 1.70E-02 & 2.00E-02 \\\\\n$^3D_{1}$ & $^1D2_{2}$ & 10677.1 & 36925.4 & 46291.2 & 8.00E-02 & 9.60E-02 \\\\\n$^3D_{3}$ & $^1F_{3}$ & 6210.2 & 36630.1 & 52732.7 & 1.50E-01 & 1.65E-01 \\\\\n$^3D_{2}$ & $^1F_{3}$ & 6260.1 & 36758.5 & 52732.7 & 7.00E-02 & 7.41E-02 \\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\n\n\\begin{table*}\n\\noindent{Table 7. Forbidden transitions in Fe V. \\\\ \\\\}\n%\\label{TabSecInst}\n\\begin{tabular}{llllllrrrrr}\n\\hline\n\\noalign{\\smallskip}\n $C_{i}$ & $C_{j}$ & $S_{i}L_{i}\\Pi_{i}$ & $S_{j}L_{j}\\Pi_{j}$ & $J_{i}$ & $J_{j}$ & $\\lambda_{vac}$ & $E_{i} (cm^{-1})$ & $E_{j}(cm^{-1})$ & $A_{ji}^{M1}(s^{-1})$ & $A_{ji}^{E2}(s^{-1})$ \\\\\n \\noalign{\\smallskip}\n \\hline\n \\noalign{\\smallskip}\n$3d^4$ & $3d^4$ & $^5D$ & $^5D$ & 0 & 1 & 703729.8 & 0.0 & 142.1 & 1.55E-04 & 0.00E+00\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^5D$ & 0 & 2 & 239635.8 & 0.0 & 417.3 & 0.00E+00 & 1.17E-10\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^5D$ & 1 & 2 & 363372.1 & 142.1 & 417.3 & 1.18E-03 & 1.10E-11\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^5D$ & 1 & 3 & 151285.9 & 142.1 & 803.1 & 0.00E+00 & 1.00E-09\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^5D$ & 2 & 3 & 259201.7 & 417.3 & 803.1 & 2.65E-03 & 1.29E-10\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^5D$ & 2 & 4 & 115540.2 & 417.3 & 1282.8 & 0.00E+00 & 1.84E-09\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^5D$ & 3 & 4 & 208463.6 & 803.1 & 1282.8 & 2.98E-03 & 4.19E-10\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3P2$ & 2 & 0 & 4230.5 & 417.3 & 24055.4 & 0.00E+00 & 4.75E-04\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3P2$ & 1 & 1 & 4027.3 & 142.1 & 24972.9 & 8.72E-05 & 2.01E-04\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3P2$ & 3 & 1 & 4137.4 & 803.1 & 24972.9 & 0.00E+00 & 7.02E-05\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3P2$ & 0 & 2 & 3778.1 & 0.0 & 26468.3 & 0.00E+00 & 6.83E-05\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3P2$ & 2 & 2 & 3838.6 & 417.3 & 26468.3 & 3.52E-05 & 2.00E-05\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3P2$ & 4 & 2 & 3970.5 & 1282.8 & 26468.3 & 0.00E+00 & 2.04E-05\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3H$ & 2 & 4 & 4079.1 & 417.3 & 24932.5 & 0.00E+00 & 1.44E-07\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3H$ & 3 & 4 & 4144.3 & 803.1 & 24932.5 & 8.32E-04 & 1.15E-09\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3H$ & 3 & 5 & 4094.5 & 803.1 & 25225.9 & 0.00E+00 & 2.15E-06\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3H$ & 4 & 5 & 4176.6 & 1282.8 & 25225.9 & 1.25E-05 & 1.09E-07\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3H$ & 4 & 6 & 4124.4 & 1282.8 & 25528.5 & 0.00E+00 & 1.67E-05\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3F2$ & 0 & 2 & 3736.8 & 0.0 & 26760.7 & 0.00E+00 & 3.67E-05\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3F2$ & 4 & 2 & 3925.0 & 1282.8 & 26760.7 & 0.00E+00 & 2.54E-06\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3F2$ & 1 & 3 & 3745.3 & 142.1 & 26842.3 & 0.00E+00 & 1.28E-05\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3F2$ & 2 & 4 & 3765.5 & 417.3 & 26974.0 & 0.00E+00 & 1.14E-06\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3G$ & 1 & 3 & 3369.8 & 142.1 & 29817.1 & 0.00E+00 & 5.37E-05\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3G$ & 2 & 4 & 3363.6 & 417.3 & 30147.0 & 0.00E+00 & 8.67E-05\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3G$ & 3 & 5 & 3375.3 & 803.1 & 30430.1 & 0.00E+00 & 8.86E-05\\\\\n$3d^4$ & $3d^4$ & $^5D$ & $^3G$ & 4 & 5 & 3430.8 & 1282.8 & 30430.1 & 5.93E-04 & 2.13E-04\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 0 & 1 & 536.4 & 0.0 & 186433.6 & 6.97E-05 & 0.00E+00\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 1 & 1 & 536.8 & 142.1 & 186433.6 & 1.59E-04 & 1.54E+04\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 2 & 1 & 537.6 & 417.3 & 186433.6 & 6.48E-05 & 1.09E+04\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 3 & 1 & 538.7 & 803.1 & 186433.6 & 0.00E+00 & 1.09E+03\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 0 & 2 & 535.5 & 0.0 & 186725.5 & 0.00E+00 & 7.79E+03\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 1 & 2 & 536.0 & 142.1 & 186725.5 & 1.77E-05 & 1.90E-04\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 2 & 2 & 536.7 & 417.3 & 186725.5 & 1.26E-04 & 1.26E+04\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 3 & 2 & 537.9 & 803.1 & 186725.5 & 5.30E-05 & 6.83E+03\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 4 & 2 & 539.3 & 1282.8 & 186725.5 & 0.00E+00 & 3.51E+02\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 1 & 3 & 534.7 & 142.1 & 187157.5 & 0.00E+00 & 1.01E+04\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 2 & 3 & 535.5 & 417.3 & 187157.5 & 4.29E-07 & 1.19E+03\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 3 & 3 & 536.6 & 803.1 & 187157.5 & 8.40E-05 & 1.35E+04\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 4 & 3 & 538.0 & 1282.8 & 187157.5 & 2.36E-05 & 2.94E+03\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 2 & 4 & 533.9 & 417.3 & 187719.0 & 0.00E+00 & 1.01E+04\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 3 & 4 & 535.0 & 803.1 & 187719.0 & 3.95E-05 & 6.97E+03\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 4 & 4 & 536.4 & 1282.8 & 187719.0 & 4.06E-05 & 1.09E+04\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 3 & 5 & 533.1 & 803.1 & 188395.3 & 0.00E+00 & 7.09E+03\\\\\n$3d^4$ & $3d^3(4F)$ & $^5D$ & $^5F$ & 4 & 5 & 534.4 & 1282.8 & 188395.3 & 1.56E-04 & 2.10E+04\\\\\n$3d^4$ & $3d^4$ & $^3P2$ & $^3P2$ & 0 & 1 & 108991.8 & 24055.4 & 24972.9 & 1.38E-02 & 0.00E+00\\\\\n$3d^4$ & $3d^4$ & $^3P2$ & $^3P2$ & 0 & 2 & 41443.9 & 24055.4 & 26468.3 & 0.00E+00 & 8.70E-09\\\\\n$3d^4$ & $3d^4$ & $^3P2$ & $^3P2$ & 1 & 2 & 66871.7 & 24972.9 & 26468.3 & 4.52E-02 & 1.97E-09\\\\\n$3d^4$ & $3d^4$ & $^3P2$ & $^3F2$ & 0 & 2 & 36964.5 & 24055.4 & 26760.7 & 0.00E+00 & 3.47E-07\\\\\n$3d^4$ & $3d^4$ & $^3P2$ & $^3F2$ & 1 & 2 & 55934.7 & 24972.9 & 26760.7 & 2.22E-05 & 4.87E-08\\\\\n$3d^4$ & $3d^4$ & $^3P2$ & $^3F2$ & 2 & 2 & 341997.3 & 26468.3 & 26760.7 & 7.92E-07 & 1.19E-12\\\\\n$3d^4$ & $3d^4$ & $^3P2$ & $^3F2$ & 1 & 3 & 53493.1 & 24972.9 & 26842.3 & 0.00E+00 & 6.78E-08\\\\\n$3d^4$ & $3d^4$ & $^3P2$ & $^3F2$ & 2 & 3 & 267379.7 & 26468.3 & 26842.3 & 3.55E-07 & 1.48E-11\\\\\n$3d^4$ & $3d^4$ & $^3P2$ & $^3F2$ & 2 & 4 & 197745.7 & 26468.3 & 26974.0 & 0.00E+00 & 1.38E-10\\\\\n$3d^4$ & $3d^4$ & $^3P2$ & $^3G$ & 1 & 3 & 20643.2 & 24972.9 & 29817.1 & 0.00E+00 & 7.16E-08\\\\\n$3d^4$ & $3d^4$ & $^3P2$ & $^3G$ & 2 & 3 & 29861.4 & 26468.3 & 29817.1 & 1.16E-05 & 1.36E-08\\\\\n$3d^4$ & $3d^4$ & $^3P2$ & $^3G$ & 2 & 4 & 27183.5 & 26468.3 & 30147.0 & 0.00E+00 & 1.00E-08\\\\\n$3d^4$ & $3d^3(4F)$ & $^3P2$ & $^5F$ & 0 & 1 & 615.8 & 24055.4 & 186433.6 & 6.41E-08 & 0.00E+00\\\\\n$3d^4$ & $3d^3(4F)$ & $^3P2$ & $^5F$ & 1 & 1 & 619.3 & 24972.9 & 186433.6 & 6.00E-07 & 1.12E+00\\\\\n$3d^4$ & $3d^3(4F)$ & $^3P2$ & $^5F$ & 2 & 1 & 625.1 & 26468.3 & 186433.6 & 9.64E-08 & 3.48E-01\\\\\n$3d^4$ & $3d^3(4F)$ & $^3P2$ & $^5F$ & 0 & 2 & 614.7 & 24055.4 & 186725.5 & 0.00E+00 & 2.06E-01\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\n\\begin{table*}\n\\noindent{Table 7. Forbidden transitions in Fe V (Contd.) \\\\ \\\\}\n\\label{}\n\\begin{tabular}{llllllrrrrr}\n\\hline\n\\noalign{\\smallskip}\n $C_{i}$ & $C_{j}$ & $S_{i}L_{i}\\Pi_{i}$ & $S_{j}L_{j}\\Pi_{j}$ & $J_{i}$ &\n$J_{j}$ & $\\lambda_{vac}$ & $E_{i} (cm^{-1})$ & $E_{j}(cm^{-1})$ &\n$A_{ji}^{M1}(s^{-1})$ & $A_{ji}^{E2}(s^{-1})$ \\\\\n \\noalign{\\smallskip}\n \\hline\n \\noalign{\\smallskip}\n\n$3d^4$ & $3d^3(4F)$ & $^3P2$ & $^5F$ & 1 & 2 & 618.2 & 24972.9 & 186725.5 & 1.68E-07 & 1.63E-01\\\\\n$3d^4$ & $3d^3(4F)$ & $^3P2$ & $^5F$ & 2 & 2 & 624.0 & 26468.3 & 186725.5 & 3.12E-07 & 6.09E-01\\\\\n$3d^4$ & $3d^3(4F)$ & $^3P2$ & $^5F$ & 1 & 3 & 616.6 & 24972.9 & 187157.5 & 0.00E+00 & 4.94E-02\\\\\n$3d^4$ & $3d^3(4F)$ & $^3P2$ & $^5F$ & 2 & 3 & 622.3 & 26468.3 & 187157.5 & 6.44E-07 & 3.56E-01\\\\\n$3d^4$ & $3d^3(4F)$ & $^3P2$ & $^5F$ & 2 & 4 & 620.2 & 26468.3 & 187719.0 & 0.00E+00 & 5.32E-03\\\\\n$3d^4$ & $3d^4$ & $^3H$ & $^3P2$ & 4 & 2 & 65112.6 & 24932.5 & 26468.3 & 0.00E+00 & 6.81E-10\\\\\n$3d^4$ & $3d^4$ & $^3H$ & $^3H$ & 4 & 5 & 340831.6 & 24932.5 & 25225.9 & 6.60E-04 & 1.09E-13\\\\\n$3d^4$ & $3d^4$ & $^3H$ & $^3H$ & 4 & 6 & 167785.2 & 24932.5 & 25528.5 & 0.00E+00 & 2.54E-12\\\\\n$3d^4$ & $3d^4$ & $^3H$ & $^3H$ & 5 & 6 & 330469.3 & 25225.9 & 25528.5 & 6.12E-04 & 6.75E-15\\\\\n$3d^4$ & $3d^4$ & $^3H$ & $^3F2$ & 4 & 2 & 54698.6 & 24932.5 & 26760.7 & 0.00E+00 & 9.98E-08\\\\\n$3d^4$ & $3d^4$ & $^3H$ & $^3F2$ & 4 & 3 & 52361.5 & 24932.5 & 26842.3 & 1.55E-03 & 1.85E-08\\\\\n$3d^4$ & $3d^4$ & $^3H$ & $^3F2$ & 5 & 3 & 61865.9 & 25225.9 & 26842.3 & 0.00E+00 & 6.77E-08\\\\\n$3d^4$ & $3d^4$ & $^3H$ & $^3F2$ & 4 & 4 & 48983.6 & 24932.5 & 26974.0 & 6.05E-03 & 1.10E-10\\\\\n$3d^4$ & $3d^4$ & $^3H$ & $^3F2$ & 5 & 4 & 57205.0 & 25225.9 & 26974.0 & 9.40E-04 & 1.17E-08\\\\\n$3d^4$ & $3d^4$ & $^3H$ & $^3F2$ & 6 & 4 & 69180.2 & 25528.5 & 26974.0 & 0.00E+00 & 3.72E-08\\\\\n$3d^4$ & $3d^4$ & $^3H$ & $^3G$ & 5 & 3 & 21780.8 & 25225.9 & 29817.1 & 0.00E+00 & 4.24E-06\\\\\n$3d^4$ & $3d^4$ & $^3H$ & $^3G$ & 5 & 4 & 20320.7 & 25225.9 & 30147.0 & 4.59E-04 & 9.52E-05\\\\\n$3d^4$ & $3d^4$ & $^3H$ & $^3G$ & 6 & 4 & 21652.1 & 25528.5 & 30147.0 & 0.00E+00 & 3.21E-06\\\\\n$3d^4$ & $3d^3(4F)$ & $^3H$ & $^5F$ & 4 & 2 & 618.1 & 24932.5 & 186725.5 & 0.00E+00 & 1.66E+01\\\\\n$3d^4$ & $3d^3(4F)$ & $^3H$ & $^5F$ & 4 & 3 & 616.4 & 24932.5 & 187157.5 & 1.72E-06 & 3.91E+00\\\\\n$3d^4$ & $3d^3(4F)$ & $^3H$ & $^5F$ & 5 & 3 & 617.5 & 25225.9 & 187157.5 & 0.00E+00 & 2.08E+01\\\\\n$3d^4$ & $3d^3(4F)$ & $^3H$ & $^5F$ & 4 & 4 & 614.3 & 24932.5 & 187719.0 & 2.68E-06 & 2.75E-01\\\\\n$3d^4$ & $3d^3(4F)$ & $^3H$ & $^5F$ & 5 & 4 & 615.4 & 25225.9 & 187719.0 & 5.44E-07 & 6.70E+00\\\\\n$3d^4$ & $3d^3(4F)$ & $^3H$ & $^5F$ & 6 & 4 & 616.6 & 25528.5 & 187719.0 & 0.00E+00 & 1.47E+01\\\\\n$3d^4$ & $3d^3(4F)$ & $^3H$ & $^5F$ & 4 & 5 & 611.8 & 24932.5 & 188395.3 & 1.06E-07 & 3.46E-03\\\\\n$3d^4$ & $3d^3(4F)$ & $^3H$ & $^5F$ & 5 & 5 & 612.9 & 25225.9 & 188395.3 & 3.70E-06 & 2.25E-01\\\\\n$3d^4$ & $3d^3(4F)$ & $^3H$ & $^5F$ & 6 & 5 & 614.0 & 25528.5 & 188395.3 & 3.61E-07 & 8.33E+00\\\\\n$3d^4$ & $3d^4$ & $^3F2$ & $^3F2$ & 2 & 3 & 1225490.2 & 26760.7 & 26842.3 & 1.34E-05 & 4.26E-15\\\\\n$3d^4$ & $3d^4$ & $^3F2$ & $^3F2$ & 2 & 4 & 468823.3 & 26760.7 & 26974.0 & 0.00E+00 & 5.33E-15\\\\\n$3d^4$ & $3d^4$ & $^3F2$ & $^3F2$ & 3 & 4 & 759301.4 & 26842.3 & 26974.0 & 4.60E-05 & 2.91E-14\\\\\n$3d^4$ & $3d^4$ & $^3F2$ & $^3G$ & 4 & 3 & 35172.9 & 26974.0 & 29817.1 & 1.89E-04 & 1.37E-07\\\\\n$3d^4$ & $3d^4$ & $^3F2$ & $^3G$ & 2 & 4 & 29530.8 & 26760.7 & 30147.0 & 0.00E+00 & 1.13E-07\\\\\n$3d^4$ & $3d^4$ & $^3F2$ & $^3G$ & 3 & 4 & 30259.9 & 26842.3 & 30147.0 & 7.94E-04 & 1.22E-06\\\\\n$3d^4$ & $3d^4$ & $^3F2$ & $^3G$ & 3 & 5 & 27872.2 & 26842.3 & 30430.1 & 0.00E+00 & 8.99E-08\\\\\n$3d^4$ & $3d^4$ & $^3G$ & $^3G$ & 3 & 4 & 303122.2 & 29817.1 & 30147.0 & 9.18E-04 & 5.80E-13\\\\\n$3d^4$ & $3d^4$ & $^3G$ & $^3G$ & 3 & 5 & 163132.1 & 29817.1 & 30430.1 & 0.00E+00 & 3.11E-12\\\\\n$3d^4$ & $3d^4$ & $^3G$ & $^3G$ & 4 & 5 & 353232.1 & 30147.0 & 30430.1 & 4.69E-04 & 5.41E-13\\\\\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\n\n\\begin{figure}\n\\caption{Comparison between the length and the velocity forms of\nf-values for $(J=2)^e-(J=3)^3$ transitions in Fe V.}\n\\end{figure}\n\n\n\\end{document}\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002230.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem{} Bautista M.A., 1996, A\\&AS 119, 105\n\n\\bibitem{} Berrington K.A., Burke P.G., Butler K., Seaton M.J., Storey\nP.J., Taylor K.T., Yu Y., 1987, J. Phys. B 20, 6379\n\n\\bibitem{} Berrington K.A., Eissner W.B., Norrington P.H., 1995, Comput.\nPhys. Commun. 92, 290\n\n\\bibitem{} Berrington K.A., Pelan J., Quigley L., 1998, Physica Scripta\n57, 549 \n\n\\bibitem{} Bi\\'emont E., Delahaye F., Zeippen C.J., 1994, J. Phys. B 27, 5841\n\n\\bibitem{} Burke P.G., Hibbert A., Robb W.D., 1971, J. Phys. B 4, 153\n\n\\bibitem{} Butler K. (unpublished); data are available through the OP \ndatabase, TOPbase (Cunto W., Mendoza C., Ochsenbein F., Zeippen C.J., 1993,\nAstron. Astrophys, 275, L5) \n\n\\bibitem{} Chen G.X., Pradhan A.K., 1999, J. Phys. B 32, 1809\n\n\\bibitem{} Eissner W., Jones M., Nussbaumer H., 1974, Comput. Phys.\nCommun 8, 270\n\n\\bibitem{} Eissner, W., Jones, M., Nussbaumer, H., Comput. Phys. \nCommun {\\bf 8}, 270 (1974); Eissner W., 1991, J. Phys. IV (Paris) C1, 3\n\n\\bibitem{} Fawcett B.C., 1989, At. Data Nucl. Data Tables 41, 181\n\n\\bibitem{} Garstang R.H., 1957, MNRAS 117, 393\n\n\\bibitem{} Hui-Bon-Hoa A., Alecian G., 1998, A\\&A 332, 224\n\n\\bibitem{} Hummer D.G., Berrington K.A., Eissner W., Pradhan A.K, Saraph H.E.,\nTully J.A., 1993, A\\&A, 279, 298\n\n\n\\bibitem{} Nahar S.N., 1995, A\\&A 293, 967\n\n\\bibitem{} Nahar S.N., 1999, At. Data Nucl. Data Tables 72, 129\n\n\\bibitem{} Nahar S.N., Pradhan A.K., 1996, A\\&A Suppl. Ser. 119, 509\n\n\\bibitem{} Nahar S.N., Pradhan A.K., 1999a, A\\&A Suppl. Ser. 135,\n347\n\n\\bibitem{} Nahar S.N., Pradhan A.K., 1999b (Physica Scripta, in press)\n\n\\bibitem{} Quinet P., Hansen , 1995, J. Phys. B 28, L213\n\n\\bibitem{} Ram\\'{i}rez J.M., Nahar S.N., Mendoza C., Berrington K.A., 1999\n(in preparation) \n\n\\bibitem{} Nussbaumer H., Storey P.J., 1978, A\\&A 64, 139\n\n\\bibitem{} Sawey P.M.J., Berrington K.A., 1992, J.Phys. B 25, 1451\n\n\\bibitem{} Scott N.S., Burke P.G., 1980, J. Phys. B 12, 4299\n\n\\bibitem{} Scott N.S., Taylor K.T., 1982, Comput. Phys. Commun. 25, 347\n\n\\bibitem{} Seaton M.J., 1987, J. Phys. B 20, 6363\n\n\\bibitem{} Seaton M.J., 1997, MNRAS 289, 700\n\n\\bibitem{} Seaton M.J., 1999, MNRAS 307, 1008\n\n\\bibitem{} Seaton M.J., Yu Y., Mihalas D., Pradhan A.K., 1994, MNRAS\n266, 805\n\n\\bibitem{} Sugar J., Corliss C., 1985, J. Phys. Chem. Ref. Data 14, Suppl.\n2\n\n\\bibitem{} {\\it The Opacity Project Team, Vol. 1}, 1995 (Institute of Physics \nPublishing, Bristol \\& Philadelphia, ISBN 0 7503 0288 7)\n\n\\bibitem{} {\\it The Opacity Project Team, Vol. 2}, 1996 (Institute of Physics \nPublishing, Bristol \\& Philadelphia, ISBN 0 7503 0174 0)\n\n\\bibitem{} Zeippen C.J., Seaton M.J., Morton D.C., 1977, MNRAS 181, 527\n\n\\end{thebibliography}"
}
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astro-ph0002231
|
FORMATION OF DISK GALAXIES: ON THE ANGULAR \protect\\ MOMENTUM PROBLEM, THE TULLY-FISHER \protect\\ RELATION AND MAGNETOHYDRODYNAMICS
|
[
{
"author": "JESPER SOMMER-LARSEN"
}
] |
Two ways of possibly solving the angular momentum problem plaguing cold dark matter (CDM) {ab initio} simulations of disk galaxy formation are discussed: 1) Stellar feedback processes and 2) Warm dark matter (WDM) rather than CDM. In relation to the chemical evolution of disk galaxies our simulations indicate that in case 1) the first generation of {disk} stars formed in disk galaxies like the Milky Way should have an abundance about two dex below solar, in fairly good agreement with the lowest observed abundance of the metal-weak tail of the Galactic thick disk. For the second case no such statements can be made without further assumptions about the star-formation history of the galaxies. We find that the $I$-band Tully-Fisher relation can be matched by WDM disk galaxy formation simulations provided $(M/L_I) \sim$ 0.8 for disk galaxies, which Sommer-Larsen \& Dolgov (1999) argue is a reasonable value. Finally it is discussed how the magnetic field strengths observed in galactic disks can be obtained through disk galaxy {formation}, as an alternative to the conventional dynamo hypothesis.
|
[
{
"name": "vul_sissa.tex",
"string": "% The CRCKAPB.STY should be in your LaTeX directory.\n\n% Begin your text file with:\n\n%\\documentstyle[editedvolume]{crckapb} \n\n% Alternatives:\n% \\documentstyle[proceedings]{crckapb} \n% \\documentstyle[monograph]{crckapb} \n \\documentstyle[nato,psfig,namedreferences]{crckapb} \n\n\\newcommand{\\stt}{\\small\\tt}\n\\newcommand{\\etal}{et~al.~}\n\\newcommand{\\Msun}{\\ifmmode{M_\\odot}\\else$M_\\odot$~\\fi}\n\\newcommand{\\TSPH}{{\\sc TreeSPH~}}\n\\def\\ga{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr>\\cr\\noalign{\\vskip1.5pt}\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr>\\cr\n\\noalign{\\vskip1.0pt}\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr>\\cr\n\\noalign{\\vskip0.5pt}\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\n\\cr>\\cr\\noalign{\\vskip0.5pt}\\sim\\cr}}}}}\n\\def\\la{\\mathrel{\\mathchoice {\\vcenter{\\offinterlineskip\\halign{\\hfil\n$\\displaystyle##$\\hfil\\cr<\\cr\\noalign{\\vskip1.5pt}\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\textstyle##$\\hfil\\cr<\\cr\n\\noalign{\\vskip1.0pt}\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptstyle##$\\hfil\\cr<\\cr\n\\noalign{\\vskip0.5pt}\\sim\\cr}}}\n{\\vcenter{\\offinterlineskip\\halign{\\hfil$\\scriptscriptstyle##$\\hfil\n\\cr<\\cr\\noalign{\\vskip0.5pt}\\sim\\cr}}}}}\n\n% This document needs the CRCKAPB.STY file to create a \n% document with font size 12pts. \n% The title, subtitle, author's name(s) and institute(s) \n% are handled by the `opening' environment.\n\n\\begin{opening}\n\\title{FORMATION OF DISK GALAXIES: ON THE ANGULAR \\protect\\\\\nMOMENTUM PROBLEM, THE TULLY-FISHER \\protect\\\\\nRELATION AND MAGNETOHYDRODYNAMICS}\n%\\subtitle{Basic Instructions}\n\n% You can split the title and subtitle by putting \n% two backslashes at the appropriate place. \n\n\\author{JESPER SOMMER-LARSEN}\n\\institute{Theoretical Astrophysics Center\\\\\n\t Juliane Maries Vej\\\\\n\t DK-2100 Copenhagen {\\O}, Denmark}\n% If there are more authors at one institute, you should first\n% use \\author{...} for each author followed by \\institute{...}.\n\n\\end{opening}\n\n\\runningtitle{FORMATION OF DISK GALAXIES}\n\n\\begin{document}\n\n% The \\begin{document} command comes after the \\end{opening}\n% command.\n\n\\begin{abstract}\nTwo ways of possibly solving the angular momentum \nproblem plaguing cold dark matter (CDM) {\\it ab initio} simulations of disk \ngalaxy formation are discussed: 1) Stellar\nfeedback processes and 2) Warm dark matter (WDM) rather than CDM.\n\nIn relation to the chemical evolution of disk galaxies\nour simulations indicate that in case 1) the first generation of \n{\\it disk} stars formed in disk galaxies like the\nMilky Way should have an abundance about two dex below solar, in fairly \ngood agreement with the lowest observed abundance of the metal-weak tail of\nthe Galactic thick disk. For the second case no such statements can be made\nwithout further assumptions about the star-formation history of the \ngalaxies.\n\nWe find that the $I$-band Tully-Fisher relation can be matched by \nWDM disk galaxy formation simulations provided $(M/L_I) \\sim$ 0.8 for disk\ngalaxies, which Sommer-Larsen \\& Dolgov (1999) argue is a reasonable \nvalue.\n\nFinally it is discussed how the magnetic field strengths observed in galactic\ndisks can be obtained through disk galaxy {\\it formation}, as an alternative\nto the conventional dynamo hypothesis. \n\n\n\\end{abstract}\n \n\\section{Introduction}\n\\label{s:intro}\n\nThe formation of galactic disks is one of the most important unsolved\nproblems in astrophysics today. In the currently favored hierarchical\nclustering framework, disks form in the potential wells of dark matter\nhalos as the baryonic material cools and collapses dissipatively. Fall \\& \nEfstathiou (1980) have shown that\ndisks formed in this way can be expected to possess the observed\namount of angular momentum (and therefore the observed spatial extent\nfor a given mass and profile shape), but only under the condition that the\ninfalling gas retain most of its original angular momentum.\n\nHowever, numerical simulations of this collapse scenario in the cold dark \nmatter (CDM) cosmological context \n(e.g., \nNavarro \\& Benz 1991,\nNavarro \\& White 1994,\nNavarro, Frenk, \\& White 1995)\nhave so far consistently indicated that when only cooling processes are\nincluded the infalling gas loses too much angular momentum (by over\nan order of magnitude) and the resulting disks are accordingly much\nsmaller than required by the observations.\nThis discrepancy is known as the {\\em angular momentum problem} of\ndisk galaxy formation.\nIt arises from the combination of the following two facts:\na) In the CDM scenario the magnitude of linear density fluctuations \n$\\sigma(M) = \\langle(\\delta M/M)^2\\rangle^{1/2}$ increases steadily with \ndecreasing\nmass scale $M$ leading to the formation of non-linear, virialized structures\nat increasingly early epochs with decreasing mass i.e.~the hierarchical\n``bottom-up'' scenario. b) Gas cooling\nis very efficient at early times due to gas densities being generally\nhigher at high redshift as well as the rate of inverse Compton cooling also \nincreasing very rapidly with redshift. a) and b)\ntogether lead to rapid condensation of small, dense gas clouds,\nwhich subsequently lose energy and (orbital) angular momentum by dynamical\nfriction against the surrounding dark matter halo before they\neventually merge to form the central disk.\nA mechanism is therefore needed that prevents, or at least delays,\nthe collapse of protogalactic gas clouds and allows the gas to\npreserve a larger fraction of its angular momentum as it settles into\nthe disk. Two such possible solutions are discussed in section 2. \n\nIn section 3 we present some new results from our WDM disk galaxy formation\nsimulations on the Tully-Fisher relation\nand in section 4 we discuss how the magnetic field strengths of a few $\\mu$G\nobserved in galactic disks can be obtained\nvia disk galaxy {\\it formation}, as an alternative to disk dynamo \namplification.\n\n\\section{Towards solving the angular momentum problem}\n\n Two ways of possibly solving the angular momentum problem have recently been\n discussed in the literature: a) by invoking the effects of stellar\n feedback processes from either single, more or less uniformly distributed\n stars or star-bursts and b) by assuming that the dark matter is ``warm''\n rather than cold. Both options lead to the suppression of the formation\n of early, small and dense gas clouds, for a) because the small gas clouds\n may be disrupted due to the energetic feedback of primarily type II\n super-nova explosions and for b) simply because fewer of the small and\n dense gas clouds form in the first place for WDM free-streaming masses\n $M_{f,{\\rm WDM}} \\sim 10^{10}$-$10^{11} \\Msun$. \n\n\\subsection{Stellar feedback processes}\n\n\\begin{figure}\n\\psfig{file=fig1.ps,height=12cm,width=12cm}\n\\caption[]{The initial disk oxygen abundance resulting from infall of a \nmixture of enriched and unenriched gas onto the disk of a forming, Milky Way \nsized model galaxy. This abundance should be representative of the oxygen \nabundance of the first generation of {\\it disk} stars formed and is fairly\nconsistent with the lowest found observationally for the metal-weak tail of\nthe Galactic thick disk.}\n\\end{figure}\n\nSommer-Larsen \\etal (1999)\n showed that the feedback caused by a putative, early epoch of more or\n less uniformly distributed population III star formation was not\n sufficient to solve the angular momentum problem. Based on test \n simulations they showed, however, that effects of feedback from star-bursts in\n small and dense protogalactic clouds might do that. Preliminary results of\n more sophisticated simulations incorporating stellar feedback processes\n in detail indicate that this is at least partly the case. Considerable\n fine-tuning seems to be required, however: About 2-3\\% of the gas in\n the proto-galactic region of a forming disk galaxy should be turned into \nstars. If less\n stars are formed the feedback is not strong enough to cure the angular\n momentum problem and, vice versa, if more stars are formed during this\n fairly early phase of star-formation, the energetic feedback causes the\n formation of the main disks and thereby the bulk of the stars to be delayed \ntoo much compared to the observed star-formation history of the Universe.\n\nThis requirement of fine-tuning is advantageous, however, in relation to the \nearly chemical evolution of disk galaxies, since the early star-formation\nhistories of the galaxies are then well constrained. Furthermore, as it \nis possible to track the elements produced and ejected by (primarily) type II\nsupernovae in the star-bursts one can determine the fraction of these\nelements, which ultimately settle on the forming disk and hence\ndetermine the rate and metallicity of the gas falling onto the disk.\nIn Figure 1 we show the time evolution of the oxygen abundance in a forming\ndisk as a result of infall of a mixture of enriched and unenriched gas\n(neglecting the contribution of ejecta from stars formed subsequently in \nthe disk). We have assumed a Salpeter IMF with $M_{low}=0.1 \\Msun$ and\n$M_{up}=60 \\Msun$ and that a typical type II supernova ejects $\\sim 2 \\Msun$\nof oxygen. This abundance can be regarded as the initial\nabundance of the disk, its value depending on when star-formation \nsubsequently commenced in the disk (note that such two-epoch star-formation\nmodels have been advocated by, e.g., Chiappini, Matteucci \\& Gratton \n1997).\nAs can be seen from the figure this initial disk abundance is of the\norder $[O/H] \\sim -2$. This is similar to the lowest abundance of the \nlow-metallicity\ntail of the Galactic thick disk -- see Beers \\& Sommer-Larsen (1995).\n\n\\begin{figure}\n\\psfig{file=fig2.ps,height=12cm,width=12cm}\n\\caption[]{Face-on view of a disk galaxy with characteristic circular velocity\n$V_c \\sim$ 300 km/s formed in a warm dark matter simulation with no conversion\nof gas into stars (so the disk is purely gaseous). The mass of the disk is\n$M_{disk} \\sim 2\\cdot 10^{11} \\Msun$ and its specific angular momentum is\n$j_{disk} \\sim$ 2000 kpc km/s.}\n\\end{figure}\n\n\\subsection{Warm dark matter}\n\nAnother, more radical way of solving the angular momentum problem is to\nabandon CDM altogether and assume instead that dark matter is ``warm''. Such\na rather dramatic measure not only proves very helpful in this respect, as \nwill be discussed below, but may also be additionally motivated:\nRecently, various possible shortcomings of the CDM cosmological scenario \nin relation to structure formation on galactic scales have been \ndiscussed\nin the literature: 1) CDM possibly leads to the formation of too many\nsmall galaxies relative to what is observed, i.e. the {\\em missing satellites\nproblem} (e.g., Klypin \\etal 1999). 2) Even if galactic winds due\nto star-bursts can significantly reduce the number of visible dwarf\ngalaxies formed, sufficiently many of the small and tightly bound dark matter \nsystems left behind can still survive to the present day in the dark matter\nhalos of larger galaxies like the Milky Way to possibly destroy the large,\ncentral disks via gravitational heating, as discussed by Moore \\etal \n(1999a). 3) The dark matter halos produced in CDM cosmological\nsimulations tend to have central cusps with $\\rho_{DM}(r) \\propto r^{-N},\nN \\sim 1-2$ (Dubinski \\& Carlberg 1991, Navarro \\etal 1996,\nFukushige \\& Makino 1997, Moore \\etal 1998, Kravtsov \\etal \n1998, Gelato \\& \nSommer-Larsen 1999). This is in disagreement with the flat, central\ndark matter density profiles (cores) inferred from observations of the \nkinematics of dwarf and low surface brightness galaxies (e.g., Burkert \n1995, de Blok \\& McGaugh 1997,\nKravtsov \\etal 1998, Moore \\etal 1999b, but see also \nvan den Bosch \\etal 1999).\n\nThe first two problems may possibly be overcome by invoking warm dark\nmatter (WDM) instead of CDM: On mass scales less than the free-streaming mass,\n$M \\la M_{f,{\\rm WDM}}$,\nthe growth of the initial density fluctuations in the Universe is suppressed\nrelative to CDM due to relativistic free-streaming of the warm dark matter\nparticles. In conventional WDM theory these become non-relativistic at\nredshifts $z_{nr} \\sim 10^6$-$10^7$ for $m_{{\\rm WDM}} \\sim$ 1 keV, which is the\ncharacteristic WDM particle mass required to give sub-galactic to galactic \nfree-streaming masses.\nAs a consequence of this suppression, fewer low mass galaxies (or \n``satellites'') are formed\ncf., e.g., Moore \\etal (1999a) and Sommer-Larsen \\& Dolgov \n(1999, SD99). The \ncentral cusps problem may be more generic (Huss \\etal 1999 and\nMoore \\etal 1999b),\nbut WDM deserves further attention also on this point.\n\nSD99 show that the angular momentum problem\nmay be resolved by going from cold to warm dark matter,\nwith characteristic free-streaming mass $M_{f,{\\rm WDM}} \\sim \n10^{10}$-$10^{11} \\Msun$, and without having to invoke\neffects of stellar feedback processes at all.\nThe reason why this kind of warm dark matter leads to a solution of the\nangular momentum problem is that because of the suppression of density \nfluctuations on sub-galactic scales relative to CDM the formation of a\ndisk galaxy becomes a much more coherent and gentle process enabling the\ninfalling, disk-forming gas to retain much more of its original angular\nmomentum. In fact SD99 find it \nlikely that the angular momentum problem can be {\\it completely} resolved\nby going to the WDM structure formation scenario, which is more than can\nbe said for the CDM+feedback approach so far. In Figure 2 we show a\nface-on view of a disk galaxy with characteristic circular velocity (where the\nrotation curve is approximately constant) $V_c \\sim$\n300 km/s formed in a WDM simulation (in this simulation\ngas was not converted into stars). Clearly it is no\nlonger a problem to form extended, high angular momentum disks in fully\ncosmological simulations. In comparison the extent of typical disks formed\nin ``passive'' CDM simulations (i.e. simulations not incorporating the effects\nof stellar feedback processes) is less than 1 kpc -- see, e.g., Sommer-Larsen\n\\etal (1999).\n\nUnlike the CDM+feedback solution, one does not get a constraint\non the early star-formation histories of the proto-galaxies, so no statements \nabout the abundance of the first generation of disk stars can be made without \nfurther assumptions.\n\nSD99 discuss possible physical candidates for WDM \nparticles and find that\nthe most promising are neutrinos with weaker or stronger interactions than\nnormal, majorons (light pseudogoldstone bosons), or mirror or shadow world\nneutrinos.\n\n\\begin{figure}\n\\psfig{file=fig3.ps,height=12cm,width=12cm}\n\\caption[]{The mass vs. characteristic circular velocity ``Tully-Fisher'' \nrelation for the final disks formed in 16 WDM simulations of Sommer-Larsen \n\\& Dolgov (for $H_0$=70 km/s/Mpc).\nAlso shown is the observed $I$-band TF relation of\nGiovanelli \\etal converted to mass assuming ($M/L_I$) = 0.25 ({\\it dashed\nline}), 0.5 ({\\it solid line}) and 1.0 ({\\it dotted line}) and $H_0$=70 \nkm/s/Mpc. Finally, the\nsymbol ``MW'' with errorbars shows the likely range of the total, baryonic mass\nand characteristic circular velocity of the Milky Way.}\n\\end{figure}\n\n\\section{The Tully-Fisher relation}\nIn Figure 3 we show the cooled-out disk mass $M_{disk}$ at redshift $z$=0 as\na function of the characteristic circular velocity $V_c$ of model galaxies\nformed in our WDM simulations (assuming a Hubble parameter $H_0$=70 km/s/Mpc).\nAlso shown is the $I$-band Tully-Fisher (TF)\nrelation of Giovanelli \\etal (1997) converted to mass assuming $I$-band\nmass-to-light ratios $(M/L_I)$=0.25, 0.5 and 1.0 in solar units and \n$H_0$=70 km/s/Mpc. Finally, the baryonic mass of the\nMilky Way, estimated in a completely independent way, is shown (see SD99 for \ndetails). As can be seen from the figure we can match\nthe slope of the TF relation very well assuming a constant $(M/L_I)$. To get\nthe normalization right a $(M/L_I) \\sim 0.8$ is required. SD99 argue that this\nis quite a reasonable value in comparison\nwith various dynamical and spectrophotometric estimates. Moreover, it is \nclearly gratifying that the Milky Way data point falls right on top of the\ntheoretical as well as observational $M_{disk}$-$V_c$ relations (for\n$(M/L_I) \\sim 0.8$, $H_0$=70 km/s/kpc).\n\nSteinmetz \\& Navarro (1999) and Navarro \\& Steinmetz (1999)\nfind a discrepancy between the observed and ``theoretical'' TF on the basis\nof CDM simulations of disk galaxy formation. It is hence possible that\nWDM helps out also on this point, but this has to be checked with more\ndetailed simulations.\n\n\\begin{figure}\n\\psfig{file=fig4.ps,height=9cm,width=12cm}\n\\caption[]{The temporal evolution of the average field strength in the disk\nfor two values of $\\langle\\beta_0\\rangle$.}\n\\end{figure}\n\n\\begin{figure}\n\\psfig{file=fig5.ps,height=9cm,width=12cm}\n\\caption[]{The azimuthally averaged field strength in the disk at various\ntimes for the $\\langle\\beta_0\\rangle$=400 experiment.}\n\\end{figure}\n\n\\section{Magnetic fields in galactic disks and disk galaxy formation}\n\nR{\\\"o}gnvaldsson (1999) showed how the typical magnetic field strengths\nobserved in galactic disks can be explained as a result of disk galaxy\n{\\it formation}, as an alternative to the usually assumed dynamo amplification\nof an initially very weak magnetic field in the disk: Hot, virialized gas \n($T \\sim 2\\cdot 10^6$ K) in a dark matter halo is\nassumed to initially follow the dark matter distribution and to be\nrotating slowly, corresponding to a spin-parameter $\\lambda \\sim$ 0.05,\ntypical of galactic, dark matter halos. The hot gas is assumed to be threaded\nby a weak and random magnetic field. As the hot gas cools \nradiatively, gravity forces it to flow inwards and due to the spin it forms\na growing, cold, galactic disk in the central parts of the dark matter halo. \nThe\nmagnetic field follows the cooling gas inwards and is strongly amplified by\ncompression and shear in the forming disk. R{\\\"o}gnvaldsson (1999) carried\nout magnetohydrodynamical (MHD) simulations of this process using an eulerian\nmesh MHD code. The simulations were run with various \ninitial magnetic field strengths\nin the hot gas, parameterized by the initial ratio between the\ngas pressure and magnetic pressure\n$\\langle\\beta_0\\rangle = \\langle\\frac{P_{gas}}{B^2/8\\pi}\\rangle_0$.\nThe temporal evolution of the average magnetic field strength in the disk\ngas is shown in Figure 4. For weak initial fields \n($\\langle\\beta_0\\rangle$=100-400 was taken as a starting point, since\nthese values are typical values in the hot, \nintergalactic gas in clusters of galaxies) the\naverage magnetic field strength grows gradually from about $t$=1 Gyr (after\nan initial relaxation phase). The average values of 1-2$\\mu$G reached after\nabout 5 Gyr are quite reasonable for typical disk galaxies, indicating a \nroute to the explanation of the magnetic field strengths observed\nin galactic disks alternative to the usual dynamo one.\n\nAnother aspect of the growth of the field strength is reflected in the radial\naverage in the disk, shown in Figure 5 at various times for \na simulation with $\\langle\\beta_0\\rangle$=400.\nThe field strength is always highest in the outermost part of the growing \ndisk, since \nthe fieldlines brought in with the cooling flow are stacked on top of the \nalready existing field there and the field is further amplified by the disk \nshear. \n\n\n\n\\section{Acknowledgements}\n\nI have\nbenefited from comments by {\\\"O}rn{\\'o}lfur R{\\\"o}gnvaldsson,\nSasha Dolgov and Jens Schmalzing and\nthank the organizers for a magnificent \nconference. This work was supported by Danmarks Grundforskningsfond through \nits support for the establishment of the Theoretical Astrophysics \nCenter.\n\n\\begin{thebibliography}{}\n\\bibitem[1999]{} Beers, T. C., \\& Sommer-Larsen, J. 1995, \n{\\it Astrophys. J. Suppl.}, {\\bf 96}, 175\n\\bibitem[1999]{} van den Bosch, F. C., \\etal 1999, {\\it Astron. J.}, submitted \n(astro-ph/9911372)\n\\bibitem[1995]{} Burkert, A. 1995, {\\it Astrophys. J.}, {\\bf 488}, L55\n\\bibitem[1997]{} de Blok, W. \\ J. \\ G., \\& McGaugh, S. \\ S. 1997, {\\it MNRAS}, {\\bf 290}, 533\n\\bibitem[1997]{} Chiappini, C., Matteucci, F, \\& Gratton, R. 1997, \n{\\it Astrophys. J.}, {\\bf 477}, 765\n\\bibitem[1991]{} Dubinski, J., \\& Carlberg, R. 1991, {\\it Astrophys. J.}, {\\bf 378}, 496\n\\bibitem[1980]{} Fall, S. M., \\& Efstathiou, G. 1980, {\\it MNRAS}, {\\bf 193}, 189 \n\\bibitem[1997]{} Fukushige, T., \\& Makino, J. 1997, {\\it Astrophys. J.}, {\\bf 477}, L9\n\\bibitem[1999]{} Gelato, S., \\& Sommer-Larsen, J. 1999, {\\it MNRAS}, {\\bf 303}, 321\n\\bibitem[1997]{} Giovanelli, R., \\etal 1999, {\\it Astrophys. J.}, {\\bf 477}, L1\n\\bibitem[1999]{} Huss, A., Jain, B., \\& Steinmetz, M. 1999, {\\it Astrophys. J.}, {\\bf 517}, 64\n\\bibitem[1999]{} Klypin, A., Kravtsov, A. V., Valenzuela, O., \\& Prada, F.\n1999, {\\it Astrophys. J.}, {\\bf 523}, 32\n\\bibitem[1998]{} Kravtsov, A. \\ V., Klypin, A. \\ A., Bullock, J. \\ S., \\&\nPrimack, J. \\ R. 1998, {\\it Astrophys. J.}, {\\bf 502}, 48\n\\bibitem[1998]{} Moore, B., Governato, F., Quinn, T., Stadel, J., \\& Lake, G. 1998, {\\it Astrophys. J.}, {\\bf 499}, L5\n\\bibitem[1999a]{} Moore, B., Ghinga, S., Governato, F., Lake, G., Quinn, T., Stadel, J., \\& Tozzi, P. 1999a, {\\it Astrophys. J.}, {\\bf 524}, L19\n\\bibitem[1999b]{} Moore, B., Quinn, T., Governato, F., Stadel, J., \\& Lake, G. 1999b, {\\it MNRAS}, submitted (astro-ph/9903164)\n\\bibitem[1991]{} Navarro, J. F., \\& Benz, W. 1991, {\\it Astrophys. J.}, {\\bf 380}, 320\n\\bibitem[1994]{} Navarro, J. F., \\& White, S. D. M. 1994, {\\it MNRAS}, {\\bf 267}, 401\n\\bibitem[1995]{} Navarro, J. F., Frenk, C. S., \\& White, S. D. M. 1995, {\\it MNRAS}, {\\bf 275}, 56\n\\bibitem[1996]{} Navarro, J. F., Frenk, C. S., \\& White, S. D. M. 1996, {\\it MNRAS}, {\\bf 462}, 563\n\\bibitem[1999]{} Navarro, J. F., \\& Steinmetz, M. 1999, {\\it Astrophys. J.}, in press (astro-ph/9908114)\n\\bibitem[1999]{} R{\\\"o}gnvaldsson, {\\\"O}. 1999, PhD thesis, University of\nCopenhagen\n\\bibitem[1999]{} Sommer-Larsen, J., Gelato, S., \\& Vedel. H.\n1999, {\\it Astrophys. J.}, {\\bf 519}, 501 \n\\bibitem[1999]{} Sommer-Larsen, J., \\& Dolgov, A. 1999, {\\it Astrophys. J.}, submitted\n(astro-ph/9912166, SD99)\n\\bibitem[1999]{} Steinmetz, M., \\& Navarro, J. F. 1999, {\\it Astrophys. J.}, {\\bf 513}, 555\n\\end{thebibliography}\n\n\n\\end{document}\n\n"
}
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[
{
"name": "astro-ph0002231.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[1999]{} Beers, T. C., \\& Sommer-Larsen, J. 1995, \n{\\it Astrophys. J. Suppl.}, {\\bf 96}, 175\n\\bibitem[1999]{} van den Bosch, F. C., \\etal 1999, {\\it Astron. J.}, submitted \n(astro-ph/9911372)\n\\bibitem[1995]{} Burkert, A. 1995, {\\it Astrophys. J.}, {\\bf 488}, L55\n\\bibitem[1997]{} de Blok, W. \\ J. \\ G., \\& McGaugh, S. \\ S. 1997, {\\it MNRAS}, {\\bf 290}, 533\n\\bibitem[1997]{} Chiappini, C., Matteucci, F, \\& Gratton, R. 1997, \n{\\it Astrophys. J.}, {\\bf 477}, 765\n\\bibitem[1991]{} Dubinski, J., \\& Carlberg, R. 1991, {\\it Astrophys. J.}, {\\bf 378}, 496\n\\bibitem[1980]{} Fall, S. M., \\& Efstathiou, G. 1980, {\\it MNRAS}, {\\bf 193}, 189 \n\\bibitem[1997]{} Fukushige, T., \\& Makino, J. 1997, {\\it Astrophys. J.}, {\\bf 477}, L9\n\\bibitem[1999]{} Gelato, S., \\& Sommer-Larsen, J. 1999, {\\it MNRAS}, {\\bf 303}, 321\n\\bibitem[1997]{} Giovanelli, R., \\etal 1999, {\\it Astrophys. J.}, {\\bf 477}, L1\n\\bibitem[1999]{} Huss, A., Jain, B., \\& Steinmetz, M. 1999, {\\it Astrophys. J.}, {\\bf 517}, 64\n\\bibitem[1999]{} Klypin, A., Kravtsov, A. V., Valenzuela, O., \\& Prada, F.\n1999, {\\it Astrophys. J.}, {\\bf 523}, 32\n\\bibitem[1998]{} Kravtsov, A. \\ V., Klypin, A. \\ A., Bullock, J. \\ S., \\&\nPrimack, J. \\ R. 1998, {\\it Astrophys. J.}, {\\bf 502}, 48\n\\bibitem[1998]{} Moore, B., Governato, F., Quinn, T., Stadel, J., \\& Lake, G. 1998, {\\it Astrophys. J.}, {\\bf 499}, L5\n\\bibitem[1999a]{} Moore, B., Ghinga, S., Governato, F., Lake, G., Quinn, T., Stadel, J., \\& Tozzi, P. 1999a, {\\it Astrophys. J.}, {\\bf 524}, L19\n\\bibitem[1999b]{} Moore, B., Quinn, T., Governato, F., Stadel, J., \\& Lake, G. 1999b, {\\it MNRAS}, submitted (astro-ph/9903164)\n\\bibitem[1991]{} Navarro, J. F., \\& Benz, W. 1991, {\\it Astrophys. J.}, {\\bf 380}, 320\n\\bibitem[1994]{} Navarro, J. F., \\& White, S. D. M. 1994, {\\it MNRAS}, {\\bf 267}, 401\n\\bibitem[1995]{} Navarro, J. F., Frenk, C. S., \\& White, S. D. M. 1995, {\\it MNRAS}, {\\bf 275}, 56\n\\bibitem[1996]{} Navarro, J. F., Frenk, C. S., \\& White, S. D. M. 1996, {\\it MNRAS}, {\\bf 462}, 563\n\\bibitem[1999]{} Navarro, J. F., \\& Steinmetz, M. 1999, {\\it Astrophys. J.}, in press (astro-ph/9908114)\n\\bibitem[1999]{} R{\\\"o}gnvaldsson, {\\\"O}. 1999, PhD thesis, University of\nCopenhagen\n\\bibitem[1999]{} Sommer-Larsen, J., Gelato, S., \\& Vedel. H.\n1999, {\\it Astrophys. J.}, {\\bf 519}, 501 \n\\bibitem[1999]{} Sommer-Larsen, J., \\& Dolgov, A. 1999, {\\it Astrophys. J.}, submitted\n(astro-ph/9912166, SD99)\n\\bibitem[1999]{} Steinmetz, M., \\& Navarro, J. F. 1999, {\\it Astrophys. J.}, {\\bf 513}, 555\n\\end{thebibliography}"
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astro-ph0002232
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NEUTRON STAR STRUCTURE AND \\ THE EQUATION OF STATE
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[
{
"author": "J. M. LATTIMER AND M. PRAKASH"
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The structure of neutron stars is considered from theoretical and observational perspectives. We demonstrate an important aspect of neutron star structure: the neutron star radius is primarily determined by the behavior of the pressure of matter in the vicinity of nuclear matter equilibrium density. In the event that extreme softening does not occur at these densities, the radius is virtually independent of the mass and is determined by the magnitude of the pressure. For equations of state with extreme softening, or those that are self-bound, the radius is more sensitive to the mass. Our results show that in the absence of extreme softening, a measurement of the radius of a neutron star more accurate than about 1 km will usefully constrain the equation of state. We also show that the pressure near nuclear matter density is primarily a function of the density dependence of the nuclear symmetry energy, while the nuclear incompressibility and skewness parameters play secondary roles. In addition, we show that the moment of inertia and the binding energy of neutron stars, for a large class of equations of state, are nearly universal functions of the star's compactness. These features can be understood by considering two analytic, yet realistic, solutions of Einstein's equations, due, respectively, to Buchdahl and Tolman. We deduce useful approximations for the fraction of the moment of inertia residing in the crust, which is a function of the stellar compactness and, in addition, the presssure at the core-crust interface. \\ \ni {\em Subject headings:} structure of stars -- equation of state -- stars: interiors -- stars: neutron
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"name": "lp.tex",
"string": "\\documentstyle[12pt,aasms4,epsfig]{article}\n\\def\\in{\\indent}\n\\def\\ni{\\noindent}\n\\def\\simge{%\n \\mathrel{\\rlap{\\raise 0.511ex\n \\hbox{$>$}}{\\lower 0.511ex \\hbox{$\\sim$}}}}\n\\def\\simle{%\n \\mathrel{\\rlap{\\raise 0.511ex\n \\hbox{$<$}}{\\lower 0.511ex \\hbox{$\\sim$}}}}\n\n\\begin{document}\n\\title{NEUTRON STAR STRUCTURE AND \\\\ THE EQUATION OF STATE}\n\\author{J. M. LATTIMER AND M. PRAKASH}\n\n\\affil{Department of Physics and Astronomy, State University of New\nYork at Stony Brook \\\\ Stony Brook, NY 11974-3800}\n\n%\\date{\\today}\n%\\maketitle\n\\begin{abstract}\nThe structure of neutron stars is considered from theoretical and\nobservational perspectives. We demonstrate an important aspect of\nneutron star structure: the neutron star radius is primarily\ndetermined by the behavior of the pressure of matter in the vicinity\nof nuclear matter equilibrium density. In the event that extreme\nsoftening does not occur at these densities, the radius is virtually\nindependent of the mass and is determined by the magnitude of the\npressure. For equations of state with extreme softening, or those\nthat are self-bound, the radius is more sensitive to the mass. Our\nresults show that in the absence of extreme softening, a measurement\nof the radius of a neutron star more accurate than about 1 km will\nusefully constrain the equation of state. We also show that the\npressure near nuclear matter density is primarily a function of the\ndensity dependence of the nuclear symmetry energy, while the nuclear\nincompressibility and skewness parameters play secondary roles. \n\nIn addition, we show that the moment of inertia and the binding energy\nof neutron stars, for a large class of equations of state, are nearly\nuniversal functions of the star's compactness. These features can be\nunderstood by considering two analytic, yet realistic, solutions of\nEinstein's equations, due, respectively, to Buchdahl and Tolman. We\ndeduce useful approximations for the fraction of the moment of inertia\nresiding in the crust, which is a function of the stellar compactness\nand, in addition, the presssure at the core-crust interface. \\\\\n\n\n\\ni {\\em Subject headings:} structure of stars -- equation of state --\nstars: interiors -- stars: neutron \n\\end{abstract}\n%\\tableofcontents\n%\\newpage\n\\section{INTRODUCTION}\n\n\nThe theoretical study of the structure of neutron stars is crucial if\nnew observations of masses and radii are to lead to effective\nconstraints on the equation of state (EOS) of dense matter. This\nstudy becomes ever more important as laboratory studies may be on the\nverge of yielding evidence about the composition and stiffness of\nmatter beyond the nuclear equilibrium density\n$\\rho_s\\cong2.7\\cdot10^{14}$ g cm$^{-3}$. Rhoades \\& Ruffini (1974)\ndemonstrated that the assumption of causality beyond a fiducial\ndensity $\\rho_f$ sets an upper limit to the maximum mass of a neutron\nstar: $4.2\\sqrt{\\rho_s/\\rho_f}{\\rm~M}_\\odot$. However, theoretical\nstudies of dense matter have considerable uncertainty in the\nhigh-density behavior of the EOS largely because of the poorly\nconstrained many-body interactions. These uncertainties have\nprevented a firm prediction of the maximum mass of a beta-stable\nneutron star.\n\nTo date, several accurate mass determinations of neutron stars are\navailable from radio binary pulsars (Thorsett \\& Chakrabarty 1998), and\nthey all lie in a narrow range ($1.25-1.44$ M$_\\odot$). One neutron\nstar in an X-ray binary, Cyg X-2, has an estimated mass of $1.8\\pm0.2$\nM$_\\odot$ (Orosz \\& Kuulkers 1999), but this determination is not as\nclean as for a radio binary. Another X-ray binary, Vela X-1, has a reported\nmass around 1.9 M$_\\odot$ (van Kerkwijk et\nal. 1995a), although Stickland et al. (1997) argue it to be about 1.4\nM$_\\odot$. A third object, the eclipsing X-ray binary 4U 1700-37,\napparently contains an object with a mass of $1.8\\pm0.4$ M$_\\odot$ (Heap \\&\nCorcoran 1992), but Brown, Weingartner \\& Wijers (1996) have argued that\nsince this source does not pulse and has a relatively hard X-ray\nspectrum, it may contain a low-mass black hole instead. It would\nnot be surprising if neutron stars in X-ray binaries had\nlarger masses than those in radio binaries, since the latter have\npresumably accreted relatively little mass since their formation.\nAlternatively, Cyg X-2 could be the first of a new and rarer\npopulation of neutron stars formed with high masses which could\noriginate from more massive, rarer, supernovae. If the high masses\nfor Cyg X-2 or Vela X-1 are confirmed, significant constraints on the\nequation of state would be realized.\n\nOn the other hand, there is a practical, albeit theoretical, lower mass limit\nfor neutron stars, about $1.1-1.2$ M$_\\odot$, which follows from the minimum\nmass of a protoneutron star. This is estimated by examining a\nlepton-rich configuration with a low-entropy inner core of $\\sim0.6$\nM$_\\odot$ and a high-entropy envelope (Goussard, Haensel \\& Zdunik\n1998). This argument is in general agreement with the theoretical\nresult of supernova calculations, in which the inner homologous\ncollapsing core material comprises at least 1 M$_\\odot$.\n\nAlthough accurate masses of several neutron stars are available, a\nprecise measurement of the radius does not yet exist. Lattimer\net al. (1990) (see also Glendenning 1992) have shown that the\ncausality constraint can be used to set a lower limit to the\nradius: $R\\simge3.04GM/Rc^2$. For a 1.4 M$_\\odot$ star, this is about\n4.5 km.\n\nEstimates of neutron star radii from observations have given a wide\nrange of results. Perhaps the most reliable estimates stem from\nobservations of thermal emissions from neutron star surfaces, which\nyield values of the so-called ``radiation radius''\n\\begin{equation}\nR_\\infty=R/\\sqrt{1-2GM/Rc^2}\\,, \n\\label{rinfty}\n\\end{equation}\na quantity resulting from redshifting the stars luminosity and\ntemperature. A given value of $R_\\infty$ implies that $R<R_\\infty$\nand $M<0.13(R_\\infty/{\\rm~km})$ M$_\\odot$. Thus, a 1.4 M$_\\odot$ neutron\nstar requires $R_\\infty>10.75$ km. Those pulsars with at least some\nsuspected thermal radiation generically yield effective values of\n$R_\\infty$ so small that it is believed that a significant part of the\nradiation originates from polar hot spots rather than from the surface\nas a whole. For example, Golden \\& Shearer (1999) found that upper\nlimits to the unpulsed emission from Geminga, coupled with a\nparallactic distance of 160 pc, yielded values of $R_\\infty\\simle9.5$\nkm for a blackbody source and $R_\\infty\\simle10$ km for a magnetized H\natmosphere. Similarly, Schulz (1999) estimated emission radii of less\nthan 5 km, assuming a blackbody for eight low mass X-ray binaries.\n\nOther attempts to deduce a radius include analyses (Titarchuk 1994) of\nX-ray bursts from sources 4U 1705-44 and 4U 1820-30 which implied\nrather small values, $9.5<R_\\infty<14$ km. Recently, Rutledge et\nal. (1999) found that thermal emission from neutron stars of a\ncanonical 10 km radius was indicated by the interburst emission.\nHowever, the modeling of the photospheric expansion and touchdown on\nthe neutron star surface requires a model dependent relationship\nbetween the color and effective temperatures.\n\nAbsorption lines in X-ray spectra have also been investigated (Inoue\n1992) with a view to deducing the neutron star radius. Candidates for\nthe matter producing the absorption lines are either the accreted\nmatter from the companion star or the products of nuclear burning in\nthe bursts. In the former case, the most plausible element is thought\nto be Fe, in which case the relation $R\\approx3.2GM/c^2$, only\nslightly larger than the minimum possible value based upon causality\n(Lattimer et al. 1990; Glendenning 1992) is inferred. In the latter\ncase, plausible candidates are Ti and Cr, and larger values of the\nradius would be obtained. In both cases, serious difficulties remain\nin interpreting the large line widths, of order 100--500 eV, in the\n$4.1 \\pm 0.1$ keV line observed from many sources.\n\nA first attempt at using light curves and pulse fractions from pulsars\nto explore the $M-R$ relation suggested relatively large radii, of\norder 15 km (Page 1995). However, this method, which assumed dipolar\nmagnetic fields, was unable to satisfactorily reconcile the calculated\nmagnitudes of the pulse fractions and the shapes of the light curves\nwith observations.\n\nThe discovery of Quasi-Periodic Oscillations (QPOs) from X-ray\nemitting neutron stars in binaries provides a possible way of limiting\nneutron star masses and radii. These oscillations are manifested as\nquasi-periodic X-ray emissions, with frequencies ranging from tens to\nover 1200 Hz. Some QPOs show multiple frequencies, in particular, two\nfrequencies $\\nu_1$ and $\\nu_2$ at several hundred Hz. These\nfrequencies are not constant, but tend to both increase with time\nuntil the signal ultimately weakens and disappears. In the beat\nfrequency model (Alpar \\& Shaham 1985, Psaltis et al. 1998), the\nhighest frequency $\\nu_2$ is associated with the Keplerian frequency\n$\\nu_K$ of inhomogeneities or blobs in an accretion disc. The largest\nsuch frequency measured to date is $\\nu_{max}=1230$ Hz. However,\ngeneral relativity predicts the existence of a maximum orbital\nfrequency, since the inner edge of an accretion disc must remain\noutside of the innermost stable circular orbit, located at a radius of\n$r_s=6GM/c^2$ in the absence of rotation. This corresponds to a\nKeplerian orbital frequency of $\\nu_s=\\sqrt{GM/r_s^3}/2\\pi$ if the\nstar is non-rotating. Equating $\\nu_{max}$ with $\\nu_s$, and since\n$R<r_s$, one deduces\n\\begin{equation}\nM\\simle1.78{\\rm~M}_\\odot;\\qquad R\\simle8.86 (M/{\\rm\nM}_\\odot){\\rm~km}.\\label{qpo}\n\\end{equation}\nCorrections due to stellar rotation are straightforward to deduce and\nproduce small changes in these limits (Psaltis et al. 1998). The\nlower frequency $\\nu_1$ is associated with a beat frequency between\n$\\nu_2$ and the spin frequency of the star. This spin frequency is\nlarge enough, of order 250-350 Hz, to alter the metric from a\nSchwarzschild geometry, and increases the theoretical mass limit in\nequation (\\ref{qpo}) to about 2.1 M$_\\odot$ (Psaltis et al. 1998).\nThis remains strictly an upper limit, however, unless further\nobservations support the interpretation that $\\nu_{max}$ is associated\nwith orbits at precisely the innermost stable orbit.\n\nIf the frequency $\\nu_2-\\nu_1$ is to be associated with the spin of\nthe neutron star, it should remain constant in time. However, recent\nobservations reveal that it changes with time in a given source.\nOsherovich \\& Titarchuk (1999) proposed a model in which $\\nu_1$ is\nthe Keplerian frequency and $\\nu_2$ is a hybrid frequency of the\nKeplerian oscillator under the influence of a magnetospheric Coriolis\nforce. In this model, the frequencies are related to the neutron star\nspin frequency $\\nu$ by\n\\begin{equation}\n\\nu_2=\\sqrt{\\nu_1^2+(\\nu/2\\pi)^2}.\n\\label{ko}\n\\end{equation}\nOsherovich \\& Titarchuk argue that this relation fits the observed\nvariations of $\\nu_2$ and $\\nu_1$ in several QPOs. The Keplerian\nfrequency in Osherovich \\& Titarchuk's model, being associated with\nthe lower frequency $\\nu_1$, however, is at most 800 Hz, leading to an\nupper mass limit that is nearly 3 M$_\\odot$ and is therefore of little\npractical use to limit either the star's mass or radius.\n\nAn alternative model, proposed by Stella \\& Vietri (1999), associates\n$\\nu_2$ with the Keplerian frequency of the inner edge of the disc,\n$\\nu_K$, and $\\nu_2-\\nu_1$ with the precession frequency of the\nperiastron of slightly eccentric orbiting blobs at radius $r$ in the\naccretion disc. In a Schwarzschild geometry,\n$\\nu_1=\\nu_K\\sqrt{1-6GM/rc^2}$. Note that\n$(\\nu_K-\\nu_1)^{-1}$ is the timescale that an orbiting blob\nrecovers its original orientation relative to the neutron star and the\nEarth, so that variations in flux are expected to be observed at both\nfrequencies $\\nu_K$ and $\\nu_K-\\nu_1$. Presumably, even\neccentricities of order $10^{-4}$ lead to observable effects. This\nmodel predicts that\n\\begin{equation}\n\\nu_1/\\nu_2=1-\\sqrt{1-6(GM\\nu_2)^{2/3}/c^2},\n\\label{sv}\n\\end{equation}\na relation that depends only upon $M$. Equation~(\\ref{sv}) can also fit\nobservations of QPOs, but only if $1.9\\simle M/{\\rm M}_\\odot\\simle\n2.1$. This result is not very sensitive to complicating effects due\nto stellar rotation: the Lense-Thirring effect and oblateness. This\nmechanism only depends on gravitometric effects, and may apply also to\naccreting black hole systems (Stella, Vietri \\& Morsink 1999).\n\nProspects for a radius determination have improved in recent years\nwith the discovery of a class of isolated, non-pulsing, neutron stars.\nThe first of these is the nearby object RX J185635-3754, initially\ndiscovered in X-rays (Walter, Wolk \\& Neuha\\\"user 1996) and confirmed\nwith the Hubble Space Telescope (Walter \\& Matthews 1997). The\nobserved X-rays, from the ROSAT satellite, are consistent with\nblackbody emission with an effective temperature of about 57 eV and\nrelatively little extinction. The fortuitous location of the star, in\nthe foreground of the R CrA molecular cloud, coupled with the small\nlevels of extinction, limits the distance to $D<120$ pc. The fact\nthat the source is not observable in radio and its lack of variability\nin X-rays implies that it is not a pulsar, unlike other identified\nradio-silent isolated neutron stars. This gives the hope that the\nobserved radiation is not contaminated with non-thermal emission as in\nthe case for pulsars. \n\nThe X-ray flux of RX~J185635-3754, combined with a best-fit blackbody\n$T_{eff}=57$ eV, yields $R_\\infty\\approx 7.3 (D/120 {\\rm~pc}){\\rm~\nkm}$. Such a value for $R_\\infty$, even coupled with the maximum\ndistance of 120 pc, is too small to be consistent with any neutron\nstar with more than 1 M$_\\odot$. But the optical flux is about a\nfactor of 4 brighter than what is predicted by the X-ray blackbody.\nThe reconciliation the X-ray and optical fluxes through atmosphere\nmodeling naively implies an increase in $R_\\infty$ of approximately\n$4^{2/3}\\cong2.5$. (This results since the X-ray flux is proportional\nto $R_\\infty^2T_{eff}^4$, while the optical flux is on the\nRayleigh-Jeans tail of the spectrum and is hence proportional to\n$R_\\infty^2T_{eff}$. One seeks to enhance the predicted optical flux\nby 4 while keeping the X-ray flux fixed, as this is approximately\nequal to the total flux.) An et al. (2000) determined for\nnon-magnetized heavy element atmospheres that $R_\\infty/D\\cong\n0.18\\pm0.05$ km pc$^{-1}$, which is rough agreement with the above\nnaive expectations. However, uncertainties in the atmospheric\ncomposition and the quality of the existing data precluded obtaining a\nmore precise estimate of $R_\\infty/D$. An et al. concluded, in\nagreement with expectations based upon the general results of Romani\n(1987) and Rajagopal, Romani \\& Miller (1997), \nthat the predicted spectrum of a\nheavy element atmosphere, but not a light element atmosphere, was\nconsistent with all the observations. This is in contrast to the\nconclusions of Pavlov et al. (1996), whose results for RX J185635-3754\nimplied that the observations in the optical and X-ray bands were\nincompatible with atmospheric modelling for both heavy element and\nlight element non-magnetized atmospheres, unless the distance to this\nstar is greater than the presumed maximum of 120 pc based upon the\nstar's location in front of the R Cor Aus molecular cloud. Future\nprospects for determining the radius of this neutron star are\ndiscussed in \\S 7.\n\nOur objectives in this paper are 1) to demonstrate specifically how\nthe accurate measurement of a neutron star radius would constrain the\ndense matter EOS, and 2) to provide general relationships for other\nstructural quantities, such as the moment of inertia and the binding\nenergy, that are relatively EOS-independent, and which could be used\nto constrain the neutron star mass and/or radius. We will examine a\nwide class of equations of state, including those that have extreme\nsoftening at high densities. In addition, we will examine analytic\nsolutions to Einstein's equations which shed light on the results we\ndeduce empirically. In all cases, we will focus on non-rotating,\nnon-magnetized neutron stars at zero temperature.\n\nLindblom (1992) had suggested that a series of mass and radius\nmeasurements would be necessary to accurately constrain the dense\nmatter equation of state. His technique utilizes a numerical\ninversion of the neutron star structure equation. Our results instead\nsuggest that important constraints on the EOS can be achieved with\neven a single radius measurement, if it is accurate enough, and that\nthe quality of the constraint is not very sensitive to the mass. The\nfact that the range of accurately determined neutron star masses is so\nsmall, only about 0.2 M$_\\odot$ to date, further implies that\nimportant constraints can be deduced without simulaneous mass-radius\nmeasurements. Of course, several measurements of neutron star masses\nand radii would greatly enhance the constraint on the equation of\nstate.\n\n\nIn \\S~2, the equations of state selected in this paper are discussed.\nIn \\S~3, the mass-radius relation for a sample of these equations of\nstate are discussed. A quantitative relationship between the radii of\nnormal neutron stars and the pressure of matter in the vicinity of\n$n_s$ is empirically established and theoretically justified. In\nturn, how the matter's pressure at these densities depends upon\nfundamental nuclear parameters is developed. In \\S~4, analytic\nsolutions to the general relativistic equations of hydrostatic\nequilibrium are explored. These lead to useful approximations for\nneutron star structure and which directly correlate other observables\nsuch as moments of inertia and binding energy to the mass and radius.\nIt is believed that the distribution of the moment of inertia inside\nthe star is crucial in the interpretation of glitches observed in the\nspin down of pulsars, so that measurements of the sizes and\nfrequencies of glitches can constrain neutron star masses and radii\n(Link, Epstein \\& Lattimer 1999). In \\S~5, expressions for the\nfraction of moment of inertia contained within the stellar crust, as a\nfunction of mass, radius, and equation of state, are derived. In\n\\S~6, expressions for the binding energy are derived. \\S~7 contains a\nsummary and outlook.\n\n\\section{EQUATIONS OF STATE}\n\n\\def\\lsim{\\mathrel{\\rlap{\n\\lower3pt\\hbox{\\hskip-3pt$\\sim$}}\n\\raise1pt\\hbox{$<$}}}\n\nThe composition of a neutron star chiefly depends on the nature of\nstrong interactions, which are not well understood in dense matter.\nMost models that have been investigated can be conveniently grouped\ninto three broad categories: nonrelativistic potential models,\nrelativistic field theoretical models, and relativistic\nDirac-Brueckner-Hartree-Fock models. In each of these approaches, the\npresence of additional softening components such as hyperons, Bose\ncondensates or quark matter, can be incorporated. Details of these\napproaches have been further considered in Lattimer et al. (1990) and\nPrakash et al. (1997). A representative sample, and some general\nattributes, including references and typical compositions, of\nequations of state employed in this paper are summarized in Table\n1.\n\nWe have used four equations of state taken from Akmal \\& Pandharipande\n(1998). These are: AP1 (the AV18 potential), AP2 (the AV18 potential\nplus $\\delta v_b$ relativistic boost corrections), AP3 (the AV18\npotential plus a three-body UIX potential ), and AP4 (the AV18\npotential plus the UIX potential plus the $\\delta v_b$ boost). Three\nequations of state from M\\\"uller \\& Serot (1996), labelled MS1--3,\ncorrespond to different choices of the parameters $\\xi$ and $\\zeta$\nwhich determine the strength of the nonlinear vector and isovector\ninteractions at high densities. The numerical values used are\n$\\xi=\\zeta=0; \\xi=1.5, \\zeta=0.06$; and $\\xi=1.5, \\zeta=0.02$,\nrespectively. Six EOSs from the phenomenological non-relativistic\npotential model of Prakash, Ainsworth \\& Lattimer (1988), labelled\nPAL1--6, were chosen, which have different choices of the symmetry\nenergy parameter at the saturation density, its density dependence,\nand the bulk nuclear matter incompressibility parameter $K_s$. The\nincompressibilities of PAL1--5 were chosen to be $K_s=180$ or 240 MeV,\nbut PAL6 has $K_s=120$ MeV. Three interactions from the\nfield-theoretical model of Glendenning \\& Moszkowski (1991) are taken\nfrom their Table II; in order, they are denoted GM1--3. Two\ninteractions from the field-theoretical model of Glendenning \\&\nSchaffner-Bielich (1999) correspond, in their notation, to GL78 with\n$U_K(\\rho_0)=-140$ MeV and TM1 with $U_K=-185$ MeV. The labels\ndenoting the other EOSs in Table I are identical to those in the\noriginal references.\n\nThe rationale for exploring a wide variety of EOSs, even some that are\nrelatively outdated or in which systematic improvements are performed,\nis two-fold. First, it provides contrasts among widely different\ntheoretical paradigms. Second, it illuminates general relationships\nthat exist between the pressure-density relation and the macroscopic\nproperties of the star such as the radius. For example, AP4\nrepresents the most complete study to date of Akmal \\& Pandharipande\n(1998), in which many-body and special relativistic corrections are\nprogressively incorporated into prior models, AP1--3. AP1--3 are\nincluded here because they represent different pressure-energy\ndensity-baryon density relations, and serve to reinforce correlations\nbetween neutron star structure and microscopic physics observed using\nalternative theoretical paradigms. Similarly, several different\nparameter sets for other EOSs are chosen.\n\nIn all cases, except for PS (Pandharipande \\& Smith 1975), the\npressure is evaluated assuming zero temperature and beta equilibrium\nwithout trapped neutrinos. PS only contains neutrons among the\nbaryons, there being no charged components. We chose to include this\nEOS, despite the fact that it has been superceded by more\nsophisticated calculations by Pandharipande and coworkers, because it\nrepresents an extreme case producing large radii neutron stars.\n\nThe pressure-density relations for some of the selected EOSs are shown\nin Figure \\ref{fig:P-rho}. There are two general classes of equations\nof state. First, {\\em normal} equations of state have a pressure\nwhich vanishes as the density tends to zero. Second, {\\em self-bound}\nequations of state have a pressure which vanishes at a significant\nfinite density.\n\nThe best-known example of self-bound stars results from Witten's\n(1984) conjecture (also see Fahri \\& Jaffe 1984, Haensel, Zdunik \\&\nSchaeffer 1986, Alcock \\& Olinto 1988, and Prakash et al. 1990) that\nstrange quark matter is the ultimate ground state of matter. In this\npaper, the self-bound EOSs are represented by strange-quark matter\nmodels SQM1--3, using perturbative QCD and an MIT-type bag model, with\nparameter values given in Table 2. The existence of an energy ceiling\nequal to the baryon mass, 939 MeV, for zero pressure matter requires\nthat the bag constant $B\\le94.92$ MeV fm$^{-3}$. This limiting value\nis chosen, together with zero strange quark mass and no interactions\n($\\alpha_c=0$), for the model SQM1. The other two models chosen, SQM2\nand SQM3, have bag constants adjusted so that their energy ceilings\nare also 939 MeV.\n\nFor normal matter, the EOS is that of an interacting nucleon gas above\na transition density of 1/3 to 1/2 $n_s$. Below this density, the\nground state of matter consists of heavy nuclei in equilibrium with a\nneutron-rich, low-density gas of nucleons. In general, a\nself-consistent evaluation of the equilibrium that exists below the\ntransition density, and the evaluation of the transition density\nitself, has been carried out for only a few equations of state (e.g.,\nBethe, Pethick \\& Sutherland 1972, Negele \\& Vautherin 1974, Lattimer\net al. 1985; Lattimer and Swesty 1990). We have therefore not\nplotted the pressure below about 0.1 MeV fm$^{-3}$ in Figure\n\\ref{fig:P-rho}. For densities $0.001 < n < 0.08$ fm$^{-3}$ we employ\nthe EOS of Negele \\& Vautherin (1974), while for densities $n<0.001$\nfm$^{-3}$ we employ the EOS of Bethe, Pethick \\& Sutherland (1972).\nHowever, for most of the purposes of this paper, the pressure in the\nregion $n<0.1$ fm$^{-3}$ is not relevant as it does not significantly\naffect the mass-radius relation or other global aspects of the star's\nstructure. Nevertheless, the value of the transition density, and the\npressure there, are important ingredients for the determination of the\nsize of the superfluid crust of a neutron star that is believed to be\ninvolved in the phenomenon of pulsar glitches (Link, Epstein \\&\nLattimer 1999).\n\nThere are three significant features to note in Figure \\ref{fig:P-rho}\nfor normal EOSs. First, there is a fairly wide range of predicted\npressures for beta-stable matter in the density domain $n_s/2<n<2n_s$.\nFor the EOSs displayed, the range of pressures covers about a factor\nof five, but this survey is by no means exhaustive. That such a wide\nrange in pressures is found is somewhat surprising, given that each of\nthe EOSs provides acceptable fits to experimentally-determined nuclear\nmatter properties. Clearly, the extrapolation of the pressure from\nsymmetric matter to nearly pure neutron matter is poorly constrained.\nSecond, the {\\em slopes} of the pressure curves are rather similar. A\npolytropic index of $n\\simeq1$, where $P=Kn^{1+1/n}$, is implied.\nThird, in the density domain below $2n_s$, the pressure-density\nrelations seem to fall into two groups. The higer pressure group is\nprimarily composed of relativistic field-theoretical models, while the\nlower pressure group is primarily composed of non-relativistic potential\nmodels. As we show in \\S~3, the pressure in the vicinity of $n_s$ is\nmostly determined by the symmetry energy properties of the EOS, and it\nis significant that relativistic field-theoretical models generally\nhave symmetry energies that increase proportionately to the density\nwhile potential models have much less steeply rising symmetry\nenergies.\n\nA few of the plotted normal EOSs have considerable softening at high\ndensities, especially PAL6, GS1, GS2, GM3, PS and PCL2. PAL6 has an\nabnormally small value of incompressibility ($K_s=120$ MeV). GS1 and\nGS2 have phase transitions to matter containing a kaon condensate, GM3\nhas a large population of hyperons appearing at high density, PS\nhas a phase transition to a neutral pion condensate and a neutron\nsolid, and PCL2 has a phase transition to a mixed phase containing\nstrange quark matter. These EOSs can be regarded as representative of\nthe many suggestions of the kinds of softening that could occur at\nhigh densities.\n\n\\section{NEUTRON STAR RADII}\n\nFigure \\ref{fig:M-R} displays the mass-radius relation for cold,\ncatalyzed matter using these EOSs. The causality constraint described\nearlier and contours of $R_\\infty$ are also indicated in Figure\n\\ref{fig:M-R}. With the exception of model GS1, the EOSs used to\ngenerate Figure~\\ref{fig:M-R} result in maximum masses greater than 1.442\nM$_\\odot$, the limit obtained from PSR 1913+16. From a theoretical\nperspective, it appears that values of $R_\\infty$ in the range of\n12--20 km are possible for normal neutron stars whose masses are\ngreater than 1 M$_\\odot$.\n\nCorresponding to the two general types of EOSs, there are two general\nclasses of neutron stars. {\\em Normal} neutron stars are\nconfigurations with zero density at the stellar surface and which have\nminimum masses, of about 0.1 M$_\\odot$, that are primarily determined\nby the EOS below $n_s$. At the minimum mass, the radii are generally\nin excess of 100 km. The second class of stars are the so-called\n{\\em self-bound} stars, which have finite density, but zero pressure, at\ntheir surfaces. They are represented in Figure \\ref{fig:M-R} by \nstrange quark matter stars (SQM1--3).\n\nSelf-bound stars have no minimum mass, unlike the case of normal\nneutron stars for which pure neutron matter is unbound. Unlike normal\nneutron stars, the maximum mass self-bound stars have nearly the\nlargest radii possible for a given EOS. If the strange quark mass\n$m_s=0$ and interactions are neglected ($\\alpha_c=0$), the maximum\nmass is related to the bag constant $B$ in the MIT-type bag model by\n$M_{max}=2.033~(56{\\rm~MeV~fm}^{-3}/B)^{1/2}~{\\rm M}_\\odot$. Prakash\net al. (1990) and Lattimer et al. (1990) showed that the addition of a\nfinite strange quark mass and/or interactions produces larger maximum\nmasses. The constraint that $M_{max}>1.44$ M$_\\odot$ is thus\nautomatically satisfied for all cases by the condition that the energy\nceiling is 939 MeV. In addition, models satisfying the energy ceiling\nconstraint, with any values of $m_s$ and $\\alpha_c$, have larger radii\nfor every mass than the case SQM1. For the MIT model, the locus of\nmaximum masses of self-bound stars is given simply by $R\\cong1.85\nR_s$~(Lattimer et al. 1990), where $R_s=2GM/Rc^2$ is the Schwarzschild\nradius, which is shown in the right-hand panel of\nFigure~\\ref{fig:M-R}. Strange quark stars with electrostatically\nsupported normal-matter crusts~(Glendenning \\& Weber 1992) have larger\nradii than those with bare surfaces. Coupled with the additional\nconstraint $M>1{\\rm M}_\\odot$ from protoneutron star models, MIT-model strange\nquark stars cannot have $R<8.5$ km or\n$R_\\infty<10.5$ km. These values are comparable to the possible\nlower limits for a Bose (pion or kaon) condensate EOS.\n\nAlthough the $M-R$ trajectories for normal stars can be strikingly\ndifferent, in the mass range from 1 to 1.5 M$_\\odot$ or more it is\nusually the case that the radius has relatively little dependence upon\nthe stellar mass. The major exceptions illustrated are the model GS1,\nin which a mixed phase containing a kaon condensate appears at a\nrelatively low density and the model PAL6 which has an extremely small\nnuclear incompressibility (120 MeV). Both of these have considerable\nsoftening and a large increase in central density for $M>1$ M$_\\odot$.\nPronounced softening, while not as dramatic, also occurs in models GS2\nand PCL2, which contain mixed phases containing a kaon condensate and\nstrange quark matter, respectively. All other normal EOSs in this\nfigure, except PS, contain only baryons among the hadrons.\n\nWhile it is generally assumed that a stiff EOS implies both a large\nmaximum mass and a large radius, many counter examples exist. For\nexample, GM3, MS1 and PS have relatively small maximum masses but have\nlarge radii compared to most other EOSs with larger maximum masses.\nAlso, not all EOSs with extreme softening have small radii for $M>1$\nM$_\\odot$ (e.g., GS2, PS). Nonetheless, for stars with masses greater than\n1 M$_\\odot$, only models with a large degree of softening (including\nstrange quark matter configurations) can have\n$R_\\infty<12$ km. Should the radius of a neutron star ever be\naccurately determined to satisfy $R_\\infty<12$ km, a strong case could\nbe made for the existence of extreme softening.\n\nTo understand the relative insensitivity of the radius to the mass for\nnormal neutron stars, it is relevant that a Newtonian polytrope with\n$n=1$ has the property that the stellar radius is independent of both\nthe mass and central density. Recall that most EOSs, in the density\nrange of $n_s-2n_s$, have an effective polytropic index of about one (see\nFigure \\ref{fig:P-rho}). An $n=1$ polytrope also has the property that the\nradius is proportional to the square root of the constant $K$ in the\npolytropic pressure law $P=K\\rho^{1+1/n}$. This suggests that there\nmight be a quantitative relation between the radius and the pressure\nthat does not depend upon the EOS at the highest densities, which\ndetermines the overall softness or stiffness (and hence, the maximum\nmass).\n\nIn fact, this conjecture may be verified. Figure~\\ref{fig:P-R} shows\nthe remarkable empirical correlation which exists between the radii of\n1 and 1.4 M$_\\odot$ normal stars and the matter's pressure evaluated\nat fiducial densities of 1, 1.5 and 2 $n_s$. Table~1 explains the EOS\nsymbols used in Figure~\\ref{fig:P-R}. Despite the relative\ninsensitivity of radius to mass for a particular EOS in this mass\nrange, the nominal radius $R_M$, which is defined as the radius at a\nparticular mass $M$ in solar units, still varies widely with the EOS\nemployed. Up to $\\sim 5$ km differences are seen in $R_{1.4}$, for\nexample. Of the EOSs in Table 1, the only severe violations of this\ncorrelation occurs for PCL2 and PAL6 at 1.4 M$_\\odot$ for $n_s$, and\nfor PS at both 1 and 1.4 M$_\\odot$ for $2n_s$. In the case of PCL2,\nthis is relatively close to the maximum mass, and the matter has\nextreme softening due to the existence of a mixed phase with quark\nmatter. (A GS model intermediate between GS1 and GS2, with a maximum\nmass of 1.44 M$_\\odot$, would give similar results.) In the case of\nPS, it is clear from Figure~\\ref{fig:P-rho} that extensive softening\noccurs already by $1.5n_s$. We emphasize that this correlation is\nvalid only for cold, catalyzed neutron stars, i.e., not for\nprotoneutron stars which have finite entropies and might contain\ntrapped neutrinos.\n\nNumerically, the correlation has the form of a power law:\n\\begin{equation}\nR_M \\simeq C(n,M)~[P(n)]^{0.23-0.26}\\,,\n\\label{correl}\n\\end{equation}\nwhere $P(n)$ is the total pressure inclusive of leptonic contributions\nevaluated at the density $n$, and $C(n,M)$ is a number that depends on\nthe density $n$ at which the pressure was evaluated and the stellar\nmass $M$. An exponent of 1/4 was chosen for display in\nFigure~\\ref{fig:P-R}, but the correlation holds for a small range of\nexponents about this value. Using an exponent of 1/4, and ignoring\npoints associated with EOSs with phase transitions in the density\nranges of interest, we find values for $C(n,M)$, in units of km\nfm$^{3/4}$ MeV$^{-1/4}$, which are listed in Table 3. The error bars\nare taken from the standard deviations.\nThe correlation is seen to be somewhat tighter for the baryon density\n$n=1.5 n_s$ and $2 n_s$ cases.\n\nThe fact that the exponent is considerably less than the Newtonian\nvalue of 1/2 can be quantitatively understood by considering a relativistic\ngeneralization of the $n=1$ polytrope due to Buchdahl (1967). He\nfound that the EOS\n\\begin{equation}\n\\rho=12\\sqrt{p_*P}-5P\\,,\\label{buch}\n\\end{equation}\nwhere $p_*$ is a constant fiducial pressure independent of density,\nhas an analytic solution of Einstein's equations. This solution is\ncharacterized by the quantities $p_*$ and $\\beta\\equiv GM/Rc^2$, and\nthe stellar radius is found to be\n\\begin{equation}\nR=(1-\\beta)c^2\\sqrt{\\pi\\over288p_*G(1-2\\beta)}\\,.\n\\label{p*}\n\\end{equation}\nFor completeness, we summarize below the metric functions, the\npressure and the mass-energy density as functions of coordinate radius\n$r$:\n\\begin{eqnarray}\ne^\\nu &\\equiv& g_{tt}=\n(1-2\\beta)(1-\\beta-u)(1-\\beta+u)^{-1}\\,;\\cr \ne^\\lambda &\\equiv& g_{rr}=\n(1-2\\beta)(1-\\beta+u)(1-\\beta-u)^{-1}(1-\\beta+\\beta\\cos Ar^\\prime)^{-2}\\,;\\cr\n8\\pi PG/c^4 &=& A^2u^2(1-2\\beta)(1-\\beta+u)^{-2}\\,;\\cr\n8\\pi\\rho G/c^2&=& 2A^2u(1-2\\beta)(1-\\beta-3u/2)(1-\\beta+u)^{-2}\\,. \n\\label{buch1}\n\\end{eqnarray}\nwhere\n\\begin{eqnarray}\nr &=& r^\\prime(1-\\beta+u)(1-2\\beta)^{-1}\\,;\\cr\nu &=& \\beta(Ar^\\prime)^{-1}\\sin Ar^\\prime\\,;\\cr\nA^2 &=& 288\\pi p_*Gc^{-4}(1-2\\beta)^{-1}.\n\\label{buch2}\n\\end{eqnarray}\nNote that $R\\propto p_*^{-1/2}(1+\\beta^2/2+\\dots)$, so for a given\nvalue of $p_*$, the radius increases very slowly with mass.\n\nTo estimate the exponent, it is instructive to analyze the response of\n$R$ to a change of pressure at some fiducial density $\\rho$, for a\nfixed mass $M$. (At the relatively low densities of interest, the\ndifference between using $n$ or $\\rho$ in the following analysis is\nnot significant.) We find the exponent to be\n\\begin{eqnarray}\n{d\\ln R\\over d\\ln P}\\Biggr|_{\\rho,M} &=& {d\\ln R\\over d\\ln\np_*}\\Biggr|_\\beta {d\\ln p_*\\over d\\ln P}\\Biggr|_{\\rho}\\Biggl[1+{d\\ln\nR\\over d\\ln\\beta}\\Biggr|_{p_*}\\Biggr]^{-1} \\cr\n &=& \\frac 12 \\Biggl(1-{5\\over6}\\sqrt{P\\over p_*}\\Biggr)\n{(1-\\beta)(1-2\\beta)\\over(1-3\\beta+3\\beta^2)}\\,. \n\\end{eqnarray}\nIn the limit $\\beta\\rightarrow0$, one has $P\\rightarrow0$ and the\nexponent $d\\ln R/d\\ln P\\Bigr|{\\rho, M}\\rightarrow1/2$, the value\ncharacteristic of an $n=1$ Newtonian polytrope. Finite values of\n$\\beta$ and $P$ render the exponent smaller than 1/2. If the\nstellar mass and radius are about 1.4 M$_\\odot$ and 15 km,\nrespectively, for example, equation~(\\ref{p*}) gives\n$p_*=\\pi/(288 R^2)\\approx4.85\\cdot10^{-5}$ km$^{-2}$ (in geometrized\nunits). Furthermore, if the fiducial density is $\\rho\\approx\n1.5m_bn_s\\approx2.02\\cdot10^{-4}$ km$^{-2}$ (also in geometrized\nunits, with $m_b$ the baryon mass), equation~(\\ref{buch}) implies that in\ngeometrized units $P\\approx8.5\\cdot10^{-6}$ km$^{-2}$. Since the\nvalue of $\\beta$ in this case is 0.14, one then obtains $d\\ln R/d\\ln\nP\\simeq0.31$. This result, while mildly sensitive to the choices for\n$\\rho$ and $R$, provides a reasonable explanation of the correlation,\nequation~(\\ref{correl}). The fact that the exponent is smaller than 1/2 is\nclearly an effect due to general relativity.\n\nThe existence of this correlation is significant because the pressure\nof degenerate neutron-star matter near the nuclear saturation density\n$n_s$ is, in large part, determined by the symmetry properties of the\nEOS, as we now discuss. Thus, the measurement of a neutron star\nradius, if not so small as to indicate extreme softening, could\nprovide an important clue to the symmetry properties of matter. In\neither case, valuable information will be obtained.\n\nStudies of pure neutron matter strongly suggest that the specific\nenergy of nuclear matter near the saturation density may be expressed\nas an expansion quadratic in the asymmetry $(1-2x)$, where $x$ is the\nproton fraction, which can be terminated after only one term (Prakash,\nAinsworth \\& Lattimer 1988). In this case, the energy per particle\nand pressure of cold, beta stable nucleonic matter is\n\\begin{eqnarray}\nE(n,x) &\\simeq& E(n,1/2) + S_v(n)(1-2x)^2 \\,, \\nonumber \\\\\nP(n,x) &\\simeq& n^2[E^\\prime(n,1/2)+ S_v^\\prime (1-2x)^2] \\,,\n\\label{enuc}\n\\end{eqnarray}\nwhere $E(n,1/2)$ is the energy per particle of symmetric matter and\n$S_v(n)$ is the bulk symmetry energy (which is density dependent).\nPrimes denote derivatives with respect to density. At $n_s$, the\nsymmetry energy can be estimated from nuclear mass systematics and has\nthe value $S_v\\equiv S_v(n_s) \\approx 27-36~{\\rm MeV}$. Attempts\nto further restrict this range from consideration of fission\nbarriers and the energies of giant resonances have led to ambiguous\nresults. Both the magnitude of $S_v$ and its density dependence\n$S_v(n)$ are currently uncertain. Part of the symmetry energy is due\nto the kinetic energy for noninteracting matter, which for degenerate\nnucleonic matter is proportional to $n^{2/3}$, but the remainder of\nthe symmetry energy, due to interactions, is also expected to\ncontribute significantly to the overall density dependence.\n\nLeptonic contributions must to be added to equation~(\\ref{enuc}) to obtain the\ntotal energy and pressure; the electron energy per baryon is $(3/4)\\hbar\ncx(3\\pi^2nx)^{1/3}$.\nMatter in neutron stars is in beta equilibrium, i.e., $\\mu_e =\n\\mu_n - \\mu_p = - \\partial E/\\partial x$, which permits the evaluation\nof the equilibrium proton fraction and the total pressure \n$P$ may be written at a particular density\nin terms of fundamental nuclear parameters (Prakash 1996). \nFor example, the pressure at the saturation density is simply\n\\begin{eqnarray}\nP_s=n_s(1-2x_s)[n_sS_v^\\prime(1-2x_s)+S_v x_s]\\,,\n\\end{eqnarray}\nwhere $S_v^\\prime\\equiv(\\partial S_v(n)/\\partial n)_{n=n_s}$\nand the equilibrium proton fraction at $n_s$ is\n\\begin{eqnarray}\nx_s\\simeq(3\\pi^2 n_s)^{-1}(4S_v/\\hbar c)^3 \\simeq 0.04\\,,\n\\end{eqnarray}\nfor $S_v=30$ MeV. Due to the small value of $x_s$, we find that\n$P_s\\simeq n_s S_v^\\prime$. The inclusion of muons, which generally\nbegin to appear around $n_s$, does not qualitatively affect these results.\n\nWere we to evaluate the pressure at a larger density, contributions\nfeaturing other nuclear\nparameters, including the nuclear incompressibility $K_s=9(dP/dn)|n_s$\nand the skewness $K_s^\\prime=-27n_s^3(d^3E/dn^3)|_{n_s}$, also become\nsignificant. For analytical purposes, the nuclear matter energy per\nbaryon, in MeV, may be expanded in the vicinity of $n_s$ as\n\\begin{eqnarray}\nE(n,1/2) = -16 + \\frac {K_s}{18} \\left(\\frac {n}{n_s}-1 \\right)^2 \n- \\frac {K_s^\\prime}{27} \\left(\\frac {n}{n_s}-1 \\right)^3\\,.\n\\label{eexp}\n\\end{eqnarray}\nExperimental constraints to the compression modulus $K_s$, most\nimportantly from analyses of giant monopole resonances (Blaizot et\nal. 1995; Youngblood et al. 1999), give $K_s\\cong 220$ MeV. The\nskewness parameter $K_s^\\prime$ has been estimated to lie in the range\n1780--2380 MeV (Pearson 1991, Rudaz et al. 1992), but in these calculations\ncontributions from the surface symmetry energy were neglected.\nFor values of $K_s^\\prime$ this large, equation~(\\ref{eexp}) cannot be used\nbeyond about 1.5$n_s$. Evaluating the pressure for\n$n=1.5n_s$, we find\n\\begin{eqnarray}\nP(1.5n_s)= 2.25n_s [K_s/18-K_s^\\prime/216 + n_s(1-2x)^2S_v^\\prime] \\,.\n\\end{eqnarray}\nAssuming that $S_v(n)$ is approximately proportional to the density,\nas it is in most relativistic field theoretical models,\n$S_v^\\prime(n)\\cong S_v/n_s$. Since the $K_s$ and $K_s^\\prime$ terms\nlargely cancel, the symmetry term comprises most of the total.\nOnce again, the result that the pressure is mostly sensitive to the\ndensity dependence of the symmetry energy is found.\n\nThe sensitivity of the radius to the symmetry energy can further\ndemonstrated by the parametrized EOS of PAL (Prakash, Ainsworth \\&\nLattimer 1988). The symmetry energy function $S_v(n)$ is a direct\ninput in this parametrization and can be chosen to reproduce the\nresults of more microscopic calculations. Figure~\\ref{fig:alp9} shows\nthe dependence of mass-radius trajectories as the quantities $S_v$ and\n$S_v(n)$ are alternately varied. Clearly, of the two variations, the\ndensity dependence of $S_v(n)$ is more important in determining the\nneutron star radius. Note also the weak sensitivity of the maximum\nneutron star mass to $S_v$, and that the maximum mass depends more\nstrongly upon the function $S_v(n)$.\n\nAt present, experimental guidance concerning the density dependence of\nthe symmetry energy is limited and mostly based upon the division of\nthe nuclear symmetry energy between volume and surface contributions.\nUpcoming experiments involving heavy-ion collisions which might sample\ndensities up to $\\sim (3-4)n_s$, will be limited to analyzing\nproperties of the nearly symmetric nuclear matter EOS through a study\nof matter, momentum, and energy flow of nucleons. Thus, studies of\nheavy nuclei far off the neutron drip lines using radioactive ion\nbeams will be necessary in order to pin down the properties of the\nneutron-rich regimes encountered in neutron stars.\n\n\\section{MOMENTS OF INERTIA}\n\nBesides the stellar radius, other global attributes of neutron stars\nare potentially observable, including the moment of inertia and the\nbinding energy. These quantities depend primarily upon the ratio\n$M/R$ as opposed to details of the EOS, as can be readily seen by\nevaluating them using analytic solutions to Einstein's equations.\nAlthough over 100 analytic solutions to Einstein's equations are known\n(Delgaty \\& Lake 1998), nearly all of them are physically unrealistic.\nHowever, three analytic solutions are of particular interest in\nnormal neutron star structure.\n\nThe first is the well-known Schwarzschild interior solution for an\nincompressible fluid, $\\rho=\\rho_c$, where $\\rho$ is the mass-energy\ndensity. This case, hereafter referred to as ``Inc'', is mostly of\ninterest because it determines the minimum compactness $\\beta=GM/Rc^2$\nfor a neutron star, namely 4/9, based upon the central pressure being\nfinite. Two aspects of the incompressible fluid that are physically\nunrealistic, however, include the fact that the sound speed is\neverywhere infinite, and that the density does not vanish on the\nstar's surface.\n\nThe second analytic solution, due to Buchdahl (1967), is described in\nequation~(\\ref{buch1}). We will refer to this solution as ``Buch''.\n\nThe third analytic solution (which we will refer to as ``T VII'') was\ndiscovered by Tolman (1939) and corresponds to the case when the\nmass-energy density $\\rho$ varies quadratically, that is,\n\\begin{equation}\n\\rho=\\rho_c[1-(r/R)^2].\n\\end{equation}\nOf course, this behavior is to be expected at both extremes\n$r\\rightarrow0$ and $r\\rightarrow R$. However, this is also an\neminently reasonable representation for intermediate regions, as\ndisplayed in Figure~\\ref{fig:prof}, which contains results for neutron\nstars more massive than 1.2 M$_\\odot$. A wide variety of EOSs are\nsampled in this figure, and they are listed in Table~1.\n\nBecause the T VII solution is often overlooked in the literature (for\nexceptions, see, for example, Durgapal \\& Pande 1980 and Delgaty \\&\nLake 1998), it is summarized here. It is useful in establishing\ninteresting and simple relations that are insensitive to the EOS. In\nterms of the variable $x=r^2/R^2$ and the compactness parameter\n$\\beta=GM/Rc^2$, the assumption $\\rho=\\rho_c(1-x)$ results in\n$\\rho_c=15\\beta c^2/(8\\pi GR^2)$. The solution of Einstein's\nequations for this density distribution is:\n\\begin{eqnarray}\ne^{-\\lambda} &=& 1-\\beta x(5-3x)\\,,\\qquad e^\\nu =\n(1-5\\beta/3)\\cos^2\\phi\\,, \\cr P &=& {c^4\\over4\\pi R^2\nG}\\left[\\sqrt{3\\beta\ne^{-\\lambda}}\\tan\\phi-{\\beta\\over2}(5-3x)\\right]\\,, \\qquad n= {(\\rho\nc^2+P)\\over m_bc^2}{\\cos\\phi\\over\\cos\\phi_1}\\,, \\cr \\phi &=&\n(w_1-w)/2+\\phi_1\\,,\\qquad w =\n\\log\\left[x-5/6+\\sqrt{e^{-\\lambda}/(3\\beta)}\\right]\\,,\\cr \\phi_c &=&\n\\phi(x=0)\\,, \\quad \\phi_1 =\\phi(x=1)=\n\\tan^{-1}\\sqrt{\\beta/[3(1-2\\beta)]}\\,, \\quad w_1 = w(x=1)\\,.\n\\end{eqnarray}\nThe central values of $P/\\rho c^2$ and the square of the sound speed\n$c_s^2$ are\n\\begin{equation}\n{P\\over\\rho c^2}\\Biggr|_c={2\\over15}\\sqrt{3\\over\\beta}\\Bigr({c_{s}\\over\nc}\\Bigr)^2\\,,\\quad \\Bigr({c_{s}\\over \nc}\\Bigr)^2=\\tan\\phi_c\\left(\\tan\\phi_c+\\sqrt{\\beta\\over3}\\right)\\,.\n\\end{equation}\nThis solution, like that of Buchdahl's, is scale-free, with the\nparameters $\\beta$ and $\\rho_c$ (or $M$ and $R$). There are obvious\nlimitations to the range of parameters for realistic models: when\n$\\phi_c=\\pi/2$, or $\\beta\\approx0.3862$, $P_c$ becomes infinite, and\nwhen $\\beta\\approx0.2698$, $c_{s}$ becomes causal ({i.e., $c$).\nRecall that for an incompressible fluid, $P_c$ becomes infinite when\n$\\beta=4/9$, and this EOS is acausal for all values of $\\beta$. For\nthe Buchdahl solution, $P_c$ becomes infinite when $\\beta=2/5$ and the\ncausal limit is reached when $\\beta=1/6$. For comparison, the causal\nlimit for realistic EOSs is $\\beta\\cong0.33$ (Lattimer et al. 1990,\nGlendenning 1992), as previously discussed.\n\nThe general applicability of these exact solutions can be gauged by analyzing\nthe moment of inertia, which, for a star uniformly\nrotating with angular velocity $\\Omega$, is\n\\begin{equation}\nI=(8\\pi/3)\\int_0^R r^4(\\rho+P/c^2)e^{(\\lambda-\\nu)/2}\n(\\omega/\\Omega) dr\\,.\n\\label{inertia}\n\\end{equation}\nThe metric function $\\omega$ is a solution of the equation\n\\begin{equation}\nd[r^4e^{-(\\lambda+\\nu)/2}\\omega^\\prime]/dr + 4r^3\\omega\nde^{-(\\lambda+\\nu)/2}/dr=0\n\\label{diffomeg}\n\\end{equation}\nwith the surface boundary condition\n\\begin{equation}\\omega_R=\\Omega-{R\\over3}\\omega^\\prime_R\n=\\Omega\\left[1-{2GI\\over R^3c^2}\\right].\n\\label{boundary}\n\\end{equation}\nThe second equality in the above follows from the definition of $I$ and the TOV\nequation. Writing $j=\\exp[-(\\nu+\\lambda)/2]$, the\nTOV equation becomes\n\\begin{equation}\nj^\\prime=-4\\pi Gr(P/c^2+\\rho)je^\\lambda/c^2\\,.\n\\end{equation}\nThen, one has\n\\begin{equation}\nI=-{2c^2\\over3G}\\int {\\omega\\over\\Omega}r^3dj =\n{c^2R^4\\omega^\\prime_R\\over6G\\Omega} \\,. \\end{equation}\n\nUnfortunately, an\nanalytic representation of $\\omega$ or the moment of inertia for any of the\nthree exact solutions is not available. However, approximations which are\nvalid in the causal regime to within 0.5\\% are\n\\begin{eqnarray}\nI_{Inc}/MR^2 &\\simeq& 2(1-0.87\\beta-0.3\\beta^2)^{-1}/5\\,,\\label{iinc} \\\\\nI_{Buch}/MR^2 &\\simeq& \n(2/3-4/\\pi^2)(1-1.81\\beta+0.47\\beta^2)^{-1}\\,,\\label{ibuc} \\\\\nI_{T VII}/MR^2 &\\simeq& 2(1-1.1\\beta-0.6\\beta^2)^{-1}/7\\,.\\label{itol}\n\\end{eqnarray}\nIn each case, the small $\\beta$ limit gives the corresponding\nNewtonian result. Figure~\\ref{mominert} indicates that the T VII\napproximation is a rather good approximation to most EOSs without\nextreme softening at high densities, for $M/R\\ge0.1$ M$_\\odot$/km.\nThe EOSs with softening fall below this trajectory. \nRavenhall \\& Pethick (1994) had suggested the expression\n\\begin{equation}\nI_{RP}/MR^2\\simeq0.21/(1-2\\beta)\n\\end{equation}\nas an approximation for the moment of inertia; however, we find\nthat this expression is not a good overall fit, as shown in\nFigure~\\ref{mominert}. \n\nFor low-mass stars, none of the analytic approximations are suitable,\nand the moment of inertia deviates substantially from the behavior of\nan incompressible fluid. Although neutron stars of such small mass\nare unlikely to exist, it is interesting to examine the behavior of\n$I$ in the limit of small compactness, especially the suprising result\nthat $I/MR^2\\rightarrow0$ as $\\beta\\rightarrow0$. It is well known\nfrom the work of Baym, Bethe \\& Pethick (1971) that the adiabatic\nindex of matter below nuclear density is near to, but less than 4/3.\nAs the compactness parameter $\\beta$ decreases, a greater fraction of\nthe star's mass lies below $n_s$. To the extent that these stars can\nbe approximated as polytropes (i.e., having a constant polytropic\nindex $n$), Table 4 shows how the quantity $I/MR^2$ varies with $n$.\nFor a polytropic index of 3, corresponding to an adiabatic exponent of\n4/3, $I/MR^2\\simeq0.075$, considerably lower than the value of 0.4 for\nan incompressible fluid. Calculations of matter at subnuclear density\nagree on the fact that the adiabatic exponent of matter further\ndecreases with decreasing density, until the neutron drip point (near\n$4.3\\times10^{11}$ g cm$^{-3}$) is approached and the exponent is near\nzero. Although the central densities of minimum mass neutron stars\nare about $2\\times10^{14}$ g cm$^{-3}$, much of the mass of the star\nis at considerably lower density, unlike the situation for solar\nmass-sized neutron stars which are relatively centrally condensed.\nThus, as $\\beta$ decreases, the quantity $I/MR^2$ rapidly decreases,\napproaching the limiting value of zero as an effective polytropic\nindex of nearly 5 is achieved.\n\n\nAnother interesting result from Figure~\\ref{mominert} concerns the\nmoments of inertia of strange quark matter stars. Such stars are\nrelatively closely approximated by incompressible fluids, this\nbehavior becoming exact in the limit of $\\beta\\rightarrow0$. This\ncould have been anticipated from the $M\\propto R^3$ behavior of the\n$M-R$ trajectories for small $\\beta$ strange quark matter stars as\nobserved in Figure~\\ref{fig:M-R}.\n\n\\section{CRUSTAL FRACTION OF THE MOMENT OF INERTIA}\n\nA new observational constraint involving $I$ concerns pulsar\nglitches. Occasionally, the spin rate of a pulsar will suddenly\nincrease (by about a part in $10^6$) without warning after years of\nalmost perfectly predictable behavior. However, Link, Epstein \\&\nLattimer (1999) argue that these glitches are not completely random:\nthe Vela pulsar experiences a sudden spinup about every three years,\nbefore returning to its normal rate of slowing. Also, the size of a\nglitch seems correlated with the interval since the previous glitch,\nindicating that they represent self-regulating instabilities for which\nthe star prepares over a waiting time. The angular momentum\nrequirements of glitches in Vela imply that $\\ge 1.4$\\% of the\nstar's moment of inertia drives these events.\n\nGlitches are thought to represent angular momentum transfer between\nthe crust and another component of the star. In this picture, as a\nneutron star's crust spins down under magnetic\ntorque, differential rotation develops between the stellar crust and\nthis component. The more rapidly rotating component then acts as an\nangular momentum reservoir which occasionally exerts a spin-up torque\non the crust as a consequence of an instability. A popular notion at\npresent is that the freely spinning component is a superfluid flowing\nthrough a rigid matrix in the thin crust, the region in which\ndripped neutrons coexist with nuclei, of the star. As the solid\nportion is slowed by electromagnetic forces, the liquid continues to\nrotate at a constant speed, just as superfluid He continues to spin\nlong after its container has stopped. This superfluid is usually\nassumed to locate in the star's crust, which thus must contain at least\n1.4\\% of the star's moment of inertia. \n\nThe high-density boundary of the crust is naturally set by the phase\nboundary between nuclei and uniform matter, where the pressure is\n$P_t$ and the density $n_t$. The low-density boundary is the neutron\ndrip density, or for all practical purposes, simply the star's surface\nsince the amount of mass between the neutron drip point and the\nsurface is negligible. One can utilize equation~(\\ref{inertia}) to\ndetermine the moment of inertia of the crust alone with the\nassumptions that $P/c^2<<\\rho$, $m(r)\\simeq M$, and $\\omega\nj\\simeq\\omega_R$ in the crust. Defining $\\Delta R$ to be the crust\nthickness, that is, the distance between the surface and the point\nwhere $P=P_t$,\n\\begin{equation}\n\\Delta I\\simeq{8\\pi\\over3}{\\omega_R\\over\\Omega}\\int_{R-\\Delta\nR}^R \\rho r^4e^\\lambda dr\\simeq\n{8\\pi\\over3GM}{\\omega_R\\over\\Omega}\\int_0^{P_t}r^6dP\\,,\n\\label{deltaip}\n\\end{equation}\nwhere $M$ is the star's total mass and the TOV equation was used in\nthe last step. In the crust, the\nfact that the EOS is of the approximate polytropic form $P\\simeq\nK\\rho^{4/3}$ can be used to find an approximation for the integral\n$\\int r^6dP$, {\\em viz.}\n\\begin{equation}\n\\int_0^{P_t}r^6dP\\simeq P_tR^6\\left[1+\n%{8P_t\\over n_t m_nc^2}{4.5+(\\Lambda-1)^{-1}\\over\\Lambda-1}\n{2P_t\\over n_t m_nc^2}{(1+7\\beta)(1-2\\beta)\\over\\beta^2}\\right]^{-1}\\,.\n\\end{equation}\nFor most neutron stars, the approximation equation~(\\ref{itol}) gives\n$I$ in terms of $M$ and $R$, and equation~(\\ref{boundary}) gives\n$\\omega_R/\\Omega$ in terms of $I$ and $R$, the quantity $\\Delta I/I$\ncan thus be cast as a function of $M$ and $R$ with the only\ndependences upon the EOS arising from the values of $P_t$ and $n_t$;\nthere is no explicit dependence upon the EOS at any other density.\nHowever, the major dependence is mostly upon the value of $P_t$, since\n$n_t$ enters only as a correction. We then find\n\\begin{equation}{\\Delta I\\over I}\\simeq{28\\pi P_t\nR^3\\over3 \nMc^2}{(1-1.67\\beta-0.6\\beta^2)\\over\\beta}\\left[1+{2P_t(1+5\\beta-14\\beta^2)\\over \nn_t\nm_bc^2\\beta^2}\\right]^{-1}.\n\\label{dii}\n\\end{equation} \n\nIn general, the EOS parameter $P_t$, in the units of MeV fm$^{-3}$,\nvaries over the range $0.25<P_t<0.65$ for realistic EOSs. The\ndetermination of this parameter requires a calculation of the\nstructure of matter containing nuclei just below nuclear matter\ndensity that is consistent with the assumed nuclear matter EOS.\nUnfortunately, few such calculations have been performed. Like the\nfiducial pressure at and above nuclear density which appears in\nequation~(\\ref{correl}), $P_t$ should depend sensitively upon the behavior\nof the symmetry energy near nuclear density.\n\nSince the calculation of the pressure below nuclear density has not\nbeen consistently done for most realistic EOSs, we arbitrarily choose\n$n_t=0.07$ fm$^{-3}$ and compare the approximation equation~(\\ref{dii})\nwith the results of full structural calculations in\nFigure~\\ref{fig:M-R-2}. Two extreme values of $P_t$ were assumed in\nthe full structural calculations to identify the core-crust boundary.\nIrrespective of this choice, the agreement between the analytical\nestimate equation~(\\ref{dii}) and the full calculations appears to be\ngood for all EOSs, including ones with extreme softening. We\nalso note that Ravenhall \\& Pethick (1994) developed a different, but\nnearly equivalent, analytic formula for the quantity $\\Delta I/I$ as a\nfunction of $M, R, P_t$ and $\\mu_t$, where $\\mu_t$ is the neutron\nchemical potential at the core-crust phase boundary. This prediction\nis also displayed in Figure~\\ref{fig:M-R-2}.\n\nLink, Epstein \\& Lattimer (1999) established a lower limit to the\nradius of the Vela pulsar by using equation~(\\ref{dii}) with $P_t$ at\nits maximum value and the glitch constraint $\\Delta I/I\\ge0.014$. A\nminimum radius can be found by combining this constraint with the\nlargest realistic value of $P_t$ from any equation of state, namely\nabout 0.65 MeV fm$^{-3}$. Stellar models that are compatible with\nthis constraint must fall to the right of the $P_t=0.65$ MeV fm$^{-3}$\ncontour in Figure~\\ref{fig:M-R-2}. This imposes a constraint upon the\nradius, which is approximately equivalent to\n\\begin{equation}\nR>3.9+3.5 M/{\\rm M}_\\odot-0.08 (M/{\\rm M}_\\odot)^2{\\rm~km}\\,. \n\\label{glitch}\n\\end{equation}\nAs shown in the figure,\nthis constraint is somewhat more stringent than one based upon causality.\nBetter estimates of the maximum value of $P_t$ should make this\nconstraint more stringent.\n\n\\section{BINDING ENERGIES}\n\nThe binding energy formally represents the energy gained by assembling\n$N$ baryons. If the baryon mass is $m_b$, the binding energy is\nsimply $BE=Nm_b-M$ in mass units. However, the quantity $m_b$ has\nvarious interpretations in the literature. Some authors take it to be\n939 MeV/$c^2$, the same as the neutron or proton mass. Others take it\nto be about 930 MeV/$c^2$, corresponding to the mass of C$^{12}$/12 or\nFe$^{56}$/56. The latter choice would be more appropriate if $BE$ was\nto represent the energy released in by the collapse of a\nwhite-dwarf-like iron core in a supernova explosion. The difference\nin these definitions, 10 MeV per baryon, corresponds to a shift of\n$10/939\\simeq0.01$ in the value of $BE/M$. This energy, $BE$, can be deduced \nfrom neutrinos detected from a supernova\nevent; indeed, it might be the most precisely determined aspect of the\nneutrino signal.\n\nLattimer \\& Yahil (1989) suggested that the binding energy could be\napproximated as\n\\begin{equation}\nBE\\approx 1.5\\cdot10^{51} (M/{\\rm M}_\\odot)^2 {\\rm~ergs} = 0.084\n(M/{\\rm M}_\\odot)^2 {\\rm~M}_\\odot\\,.\n\\label{lybind}\n\\end{equation}\nPrakash et al. (1997) also concluded that such a formula was a\nreasonable approximation, based upon a comparison of selected\nnon-relativistic potential and field-theoretical \nmodels. In Figure~\\ref{bind}, this formula is compared to exact\nresults, which shows that it is accurate at best to about $\\pm20$\\%.\nThe largest deviations are for stars with extreme softening or large mass.\n\nHere, we propose a more accurate representation of the binding\nenergy:\n\\begin{equation}\nBE/M \\simeq 0.6\\beta/(1-0.5\\beta)\\,, \\label{newbind}\n\\end{equation}\nwhich incorporates some radius dependence. Thus, the observation of supernova\nneutrinos, and the estimate of the total radiated neutrino energy, will yield\nmore accurate information about $M/R$ than about $M$ alone.\n\nIn the cases of the incompressible fluid and the Buchdahl solution, analytic\nresults for the binding energy can be found:\n\\begin{eqnarray}\nBE_{Inc}/M &=& {3\\over4\\beta}\\Bigl({\\sin^{-1}\\sqrt{2\\beta}\\over\n\\sqrt{2\\beta}}-\\sqrt{1-2\\beta}\\Bigr)-1\\approx{3\\beta\\over5}+{9\\beta^2\\over14}+{5\n\\beta^3\\over6}+\\cdots\\,; \\\\\nBE_{Buch}/M &=& \n(1-1.5\\beta)(1-2\\beta)^{-1/2}(1-\\beta)^{-1}-1\\approx{\\beta\\over2}+{\\beta^2\\over2\n}+{3\\beta^3\\over4}+\\cdots\\,.\n\\end{eqnarray}\nIn addition, an expansion for the T VII solution can be found:\n\\begin{eqnarray}\nBE_{T VII}/M \\approx\n{11\\beta\\over21}+{7187\\beta^2\\over18018}+{68371\\beta^3\\over306306}+\\cdots\\,.\n\\end{eqnarray}\nThe exact results for the three analytic solutions of Einstein's\nequations, as well as the fit of equation~(\\ref{newbind}), are\ncompared to some EOSs in Figure~\\ref{bind1}. It can be seen\nthat for stars without extreme softening both the T VII and Buch\nsolutions are rather realistic. However, for EOSs with softening, the\ndeviations from this can be substantial. Thus, until information\nabout the existence of softening in neutron stars is available, the\nbinding energy alone provides only limited information about the\nstar's structure or mass.\n\n\\section{SUMMARY AND OUTLOOK}\n\nWe have demonstrated the existence of a strong correlation between the\npressure near nuclear saturation density inside a neutron star and the\nradius which is relatively insensitive to the neutron star's mass and\nequation of state for normal neutron stars. In turn, the pressure\nnear the saturation density is primarily determined by the isospin\nproperties of the nucleon-nucleon interaction, specifically, as\nreflected in the density dependence of the symmetry energy, $S_v(n)$.\nThis result is not sensitive to the other nuclear parameters such as\n$K_s$, the nuclear incompressibility parameter, or $K^\\prime_s$, the\nskewness parameter. This is important, because the value of the\nsymmetry energy at nuclear saturation density and the density\ndependence of the symmetry energy are both difficult to determine in\nthe laboratory. Thus, a measurement of a neutron star's radius would\nyield important information about these quantities.\n\nAny measurement of a radius will have some intrinsic uncertainty. In\naddition, the empirical relation we have determined between the\npressure and radius has a small uncertainty. It is useful to display\nhow accurately the equation of state might be established from an\neventual radius measurement. This can be done by inverting equation\n(\\ref{correl}), which yields\n\\begin{equation}\nP(n) \\simeq [R_M/C(n,M)]^4\\,.\n\\label{correli}\n\\end{equation}\nThe inferred ranges of pressures, as a function of density and for\nthree possible values of $R_{1.4}$, are shown in Figure~\\ref{fig:err}.\nIt is assumed that the mass is 1.4 M$_\\odot$, but the results are\nrelatively insensitive to the actual mass. Note from Table 3 that the\ndifferences between $C$ for 1 and 1.4 M$_\\odot$ are typically less than the\nerrors in $C$ itself. The light shaded areas show the pressures\nincluding only errors associated with $C$. The dark shaded areas show\nthe pressures when a hypothetical observational error of 0.5 km is\nalso taken into account. These results suggest that a useful\nrestriction to the equation of state is possible if the radius of a\nneutron star can be measured to an accuracy better than about 1 km.\n\nThe reason useful constraints might be obtained from just a single\nmeasurement of a neutron star radius, rather than requiring a series\nof simultaneous mass-radii measurements as Lindblom (1992) proposed,\nstems from the fact that we have been able to establish the empirical\ncorrelation, equation (\\ref{correl}). In turn, it appears that this\ncorrelation exists because most equations of state have slopes $d \\ln\nP/d \\ln n\\simeq2$ near $n_s$.\n\nThe best prospect for measuring a neutron star's radius may be\nthe nearby object RX J185635-3754. It is anticipated that parallax\ninformation for this object will be soon available (Walter, private\ncommunication). In addition, it may be possible to identify spectral\nlines with the Chandra and XMM X-ray facilities that would not only\nyield the gravitational redshift, but would identify the atmospheric\ncomposition. Not only would this additional information reduce the\nuncertainty in value of $R_\\infty$, but, {\\em both} the mass and\nradius for this object might thereby be determined. It is also\npossible that an estimate of the surface gravity of the star can be\nfound from further comparisons of observations with atmospheric\nmodelling, and this would provide a further check on the mass and\nradius.\n\nWe have presented simple expressions for the moment of inertia, the\nbinding energy, and the crustal fraction of the moment of inertia for\nnormal neutron stars which are largely independent of the EOS. \nIf the magnitudes of observed glitches from Vela are connected with the \ncrustal fraction of moment of inertia, the formula we derived establishes \na more stringent limit on the radius than causality. \n\n\nWe thank A. Akmal, V. R. Pandharipande and J. Schaffner-Bielich for\nmaking the results of their equation of state calculations available\nto us in tabular form. 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Lett.,\n82, 691 \\\\\n\n%\\end{thebibliography}\n\\newpage\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%\\begin{table}\n\\begin{center}\n\\centerline{TABLE 1}\n\\vspace*{0.15in}\n\\centerline{EQUATIONS OF STATE }\n\\begin{tabular}{l|l|l|l} \\hline\\hline\nSymbol & Reference & Approach & Composition \\\\ \\hline\nFP & Friedman \\& Pandharipande (1981) & Variational & np \\\\\nPS & Pandharipande \\& Smith (1975) & Potential & n$\\pi^0$ \\\\\nWFF(1-3) & Wiringa, Fiks \\& Fabrocine (1988) & Variational & np \\\\\nAP(1-4) & Akmal \\& Pandharipande (1998) & Variational & np \\\\\nMS(1-3) & M\\\"uller \\& Serot (1996) & Field Theoretical & np \\\\ \nMPA(1-2) & Mu\\\"ther, Prakash \\& Ainsworth (1987) & Dirac-Brueckner HF & np \\\\\nENG & Engvik et al. (1996) & Dirac-Brueckner HF & np \\\\\nPAL(1-6) & Prakash, Ainsworth \\& Lattimer (1988) & Schematic Potential & np \\\\\nGM(1-3) & Glendenning \\& Moszkowski (1991) & Field Theoretical & npH \\\\\nGS(1-2) & Glendenning \\& Schaffner-Bielich (1999) & Field Theoretical & npK\\\\\nPCL(1-2) & Prakash, Cooke \\& Lattimer (1995) & Field Theoretical & npHQ\n\\\\ \nSQM(1-3) & Prakash, Cooke \\& Lattimer (1995) & Quark Matter & Q $(u,d,s)$\\\\\n\\hline\n\\end{tabular}\n%\\label{eosname}\n\\end{center}\n\\vspace*{0.15in}\nNOTES.---- Approach refers to the\nunderlying theoretical technique. Composition refers to strongly\ninteracting components (n=neutron, p=proton, H=hyperon, K=kaon,\nQ=quark); all models include leptonic contributions.\n%\\end{table}\n\n\\newpage\n%\\begin{table}\n\\begin{center}\n\\centerline{TABLE 2}\n\\vspace*{0.15in}\n\\centerline{PARAMETERS FOR SELF-BOUND STRANGE QUARK STARS}\n\\begin{tabular}{l|c|c|c} \\hline\\hline\nModel & $B$ (MeV fm$^{-3})$ & $m_s$ (MeV) & $\\alpha_c$ \\\\ \\hline\nSQM1 & 94.92 & 0 & 0 \\\\\nSQM2 & 64.21 & 150 & 0.3 \\\\\nSQM3 & 57.39 & 50 & 0.6 \\\\ \\hline\n\\end{tabular}\n\\end{center}\n\\vspace*{0.15in} NOTES.---- Numerical values employed in the MIT bag\nmodel as described in Fahri \\& Jaffe (1984).\n%\\end{table}\n\n\\vspace*{1.5in}\n%\\begin{table}\n\\begin{center}\n\\centerline{TABLE 3}\n\\vspace*{0.15in}\n\\centerline{THE QUANTITY $C(n,M)$ OF EQUATION \\ref{correl}}\n\\begin{tabular}{l|l|l}\\hline\\hline\n$n$ & 1 M$_\\odot$ & 1.4 M$_\\odot$ \\\\ \\hline\n$n_s$ & $9.53\\pm0.32$ & $9.30\\pm0.60$ \\\\\n$1.5n_s$ & $7.14\\pm0.15$ & $7.00\\pm0.31$ \\\\\n$2n_s$ & $5.82\\pm0.21$ & $5.72\\pm0.25$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n\\vspace*{0.15in} NOTES.---- The quantity $C(n,M)$, in units of km\nfm$^{3/4}$ MeV$^{-1/4}$, which relates the pressure (evaluated at density\n$n$) to the radius of neutron stars of mass $M$. The errors are\nstandard deviations.}\n%\\end{table}\n\n\\newpage\n%\\begin{table}\n\\begin{center}\n\\centerline{TABLE 4}\n\\vspace*{0.15in}\n\\centerline{MOMENTS OF INERTIA FOR POLYTROPES }\n\\begin{tabular}{l|l|l|l}\\hline\\hline\nIndex $n$ & $I/MR^2$ & Index $n$ & $I/MR^2$ \\\\ \\hline\n0 & 0.4 & 3.5 & 0.045548 \\\\\n0.5 & 0.32593 & 4.0 & 0.022573 \\\\\n1.0 & 0.26138 & 4.5 & 0.0068949 \\\\ \n1.5 & 0.20460 & 4.8 & 0.0014536 \\\\\n2.0 & 0.15485 & 4.85 & 0.00089178 \\\\\n2.5 & 0.11180 & 4.9 & 0.0004536 \\\\\n3.0 & 0.075356 & 5.0 & 0 \\\\ \\hline\n\\end{tabular}\n\\end{center}\n\\vspace*{0.15in}\nNOTES.---- The quantity $I/MR^2$ for polytropes, which satisfy \nthe relation $P=K\\rho^{1+1/n}$ ($\\rho$ is the mass-energy density), \nas a function of the polytropic index $n$. \n%\\end{table}\n\\newpage\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section*{FIGURE CAPTIONS}\n\n\\ni FIG. 1.----The pressure-density relation for a selected\nset of EOSs contained in Table 1. The pressure is in units of\nMeV fm$^{-3}$ and the density is in units of baryons per cubic fermi.\nThe nuclear saturation density is approximately $0.16$ fm$^{-3}$.\n\n\\vspace*{.2in}\n\n\\ni FIG. 2.----Mass-radius curves for several EOSs listed in Table 1.\nThe left panel is for stars containing nucleons and, in some cases,\nhyperons. The right panel is for stars containing more exotic\ncomponents, such as mixed phases with kaon condensates or strange\nquark matter, or pure strange quark matter stars. In both panels, the\nlower limit causality places on $R$ is shown as a dashed line, a\nconstraint derived from glitches in the Vela pulsar is shown as the\nsolid line labelled $\\Delta I/I=0.014$, and contours of constant\n$R_\\infty=R/\\sqrt{1-2GM/Rc^2}$, are shown as dotted\ncurves. In the right panel, the theoretical trajectory of maximum\nmasses and radii for pure strange quark matter stars is marked by the\ndot-dash curve labelled $R=1.85R_s$.\n\n\\vspace*{0.2in}\n\n\\ni FIG. 3.----~Empirical relation between pressure, in units of MeV fm$^{-3}$,\nand radius, in km, for EOSs listed in Table 1. The upper panel shows\nresults for 1 M$_\\odot$ (gravitational mass) stars; the lower panel is\nfor 1.4 M$_\\odot$ stars. The different symbols show values of\n$RP^{-1/4}$ evaluated at three fiducial densities.\n\n\\vspace*{0.2in}\n\n\\ni FIG. 4.----~Left panel: Mass-radius curves for selected PAL (Prakash,\nAinsworth \\& Lattimer 1988) forces showing the sensitivity to symmetry\nenergy. The left panel shows variations arising from different\nchoices of $S_v$, the symmetry energy evaluated at $n_s$; the right\npanel shows variations arising from different choices of $S_v(n)$, the\ndensity dependent symmetry energy. In this figure, the shorthand\n$u=n/n_s$ is used.\n\n\\vspace*{0.2in}\n\n\\ni FIG. 5.----~Profiles of mass-energy density ($\\rho$), relative to central\nvalues ($\\rho_c$), in neutron stars for several EOSs listed in Table 1.\nFor reference, the thick black lines show the simple quadratic\napproximation $1-(r/R)^2$.\n\n\\vspace*{0.2in}\n\n\\ni FIG. 6.----~The moment of inertia $I$, in units of $MR^2$, for several\nEOSs listed in Table 1. The curves labelled ``Inc'', ``T VII'', ``Buch''\nand ``RP'' \nare for an incompressible fluid, the Tolman (1939) VII solution, the\nBuchdahl (1967) solution,\nand an approximation of Ravenhall \\& Pethick (1994), \nrespectively. The inset shows details of $I/MR^2$ for $M/R \\rightarrow 0$.\n\n\\vspace*{0.2in}\n\n\\ni FIG. 7.----~Mass-radius curves for selected EOSs from Table 1, comparing\ntheoretical contours of $\\Delta I/I=0.014$ from approximations\ndeveloped in this paper, labelled ``LP'', and from Ravenhall \\&\nPethick (1994), labelled ``RP'', to numerical results (solid dots).\nTwo values of $P_t$, the transition pressure demarking the\ncrust's inner boundary, which bracket estimates in the literature, are\nemployed. The region to the left of the $P_t=0.65$ MeV fm$^{-3}$\ncurve is forbidden if Vela glitches are due to angular momentum transfers\nbetween the crust and core, as discussed in Link, Epstein \\& Lattimer\n(1999). For comparison, the region excluded by causality alone lies\nto the left of the dashed curve labelled ``causality'' as determined\nby Lattimer et al. (1990) and Glendenning (1992).\n\n\\vspace*{0.2in}\n\n\\ni FIG. 8.----~The binding energy of neutron stars as a function of stellar\ngravitational mass for several EOSs listed in Table 1. The\npredictions of equation~(\\ref{lybind}), due to Lattimer \\& Yahil\n(1989), are shown by the line labelled ``LY'' and the shaded region.\n\n\\vspace*{0.2in}\n\n\\ni FIG. 9.----~The binding energy per unit gravitational mass as a\nfunction of compactness for the EOSs listed in Table 1. Solid lines\nlabelled ``Inc'', ``Buch'' and ``T VII'' show predictions for an\nincompressible fluid, the solution of Buchdahl (1967), and the Tolman\n(1939) VII solution, respectively. The shaded region shows the\nprediction of equation~(\\ref{newbind}).\n\n\\ni FIG. 10.---The pressures inferred from the empirical correlation\nequation (\\ref{correl}), for three hypothetical radius values (10, 12.5\nand 15 km) overlaid on the pressure-density relations shown in Figure\n~\\ref{fig:P-rho}. The light shaded region takes into account only the\nuncertainty associated with $C(n,M)$; the dark shaded region also\nincludes a hypothetical uncertainty of 0.5 km in the radius\nmeasurement. The neutron star mass was assumed to be 1.4 M$_\\odot$.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{figure}[hbt]\n\\epsfig{file=prho_1.eps, height=7.5in}\n\\caption{The pressure-density relation for a selected set of EOSs\ncontained in Table 1. The pressure is in units of MeV fm$^{-3}$ and\nthe density is in units of baryons per cubic fermi. The nuclear\nsaturation density is approximately $0.16$ fm$^{-3}$.}\n\\label{fig:P-rho}\n\\end{figure}\n\n\\begin{figure}[hbt]\n%\\vspace{25pc}\n%\\begin{center}\n%\\leavevmode\n\\epsfig{file=mrrad_1.eps, angle=90, height=5.5in}\n%\\end{center}\n%\\special{psfile=mrrad.ps hoffset=490 voffset=-50 hscale=70 vscale=65\n%angle=90}\n\\caption{Mass-radius curves for several EOSs listed in Table 1. The\nleft panel is for stars containing nucleons and, in some cases,\nhyperons. The right panel is for stars containing more exotic\ncomponents, such as mixed phases with kaon condensates or strange\nquark matter, or pure strange quark matter stars. In both panels, the\nlower limit causality places on $R$ is shown as a dashed line, a\nconstraint derived from glitches in the Vela pulsar is shown as the\nsolid line labelled $\\Delta I/I=0.014$, and contours of constant\n$R_\\infty=R/\\sqrt{1-2GM/Rc^2}$ are shown as dotted\ncurves. In the right panel, the theoretical trajectory of maximum\nmasses and radii for pure strange quark matter stars is marked by the\ndot-dash curve labelled $R=1.85R_s$.}\n\\label{fig:M-R}\n\\end{figure}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{figure}[hbt]\n%\\vspace{27pc}\n\\epsfig{file=p-r_1.ps, angle=90, height=5in}\n%\\special{psfile=p-r.ps hoffset=500 voffset=-28 hscale=70 vscale=65\n%angle=90}\n\\caption{Empirical relation between pressure, in units of MeV fm$^{-3}$,\nand $R$, in km, for EOSs listed in Table 1. The upper panel shows\nresults for 1 M$_\\odot$ (gravitational mass) stars; the lower panel is\nfor 1.4 M$_\\odot$ stars. The different symbols show values of\n$RP^{-1/4}$ evaluated at three fiducial densities.}\n\\label{fig:P-R}\n\\end{figure}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\begin{figure}[hbt]\n%\\vspace{26pc}\n\\epsfig{file=alp9.ps, height=6in}\n%\\special{psfile=alp9.ps hoffset=50 voffset=-80 hscale=65 vscale=58}\n\\caption{Left panel: Mass-radius curves for selected PAL (Prakash, Ainsworth\n\\& Lattimer 1988) forces showing the sensitivity to symmetry energy.\nThe left panel shows variations arising from different choices of\n$S_v$, the symmetry energy evaluated at $n_s$; the right panel shows\nvariations arising from different choices of $S_v(n)$, the density\ndependent symmetry energy. In this figure, the shorthand $u=n/n_s$ is\nused.}\n\\label{fig:alp9}\n\\end{figure}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{figure}[hbt]\n%\\vspace{27pc}\n\\epsfig{file=rhorad.ps, angle=90, height=5in}\n%\\special{psfile=rhorad.ps hoffset=510 voffset=-30 hscale=70 vscale=65\n%angle=90}\n\\caption{Profiles of mass-energy density ($\\rho$), relative to central\nvalues ($\\rho_c$), in neutron stars for several EOSs listed in Table 1.\nFor reference, the thick black lines show the simple quadratic\napproximation $1-(r/R)^2$.}\n\\label{fig:prof}\n\\end{figure}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{figure}[hbt]\n%\\vspace{27pc}\n\\epsfig{file=mominert_1.ps, angle=90, height=5.5in}\n%\\special{psfile=mominert.ps hoffset=520 voffset=-20 hscale=70 vscale=65\n%angle=90}\n\\caption{The moment of inertia $I$, in units of $MR^2$, for several\nEOSs listed in Table 1. The curves labelled ``Inc'', ``T VII'', ``Buch''\nand ``RP'' \nare for an incompressible fluid, the Tolman (1939) VII\nsolution, the Buchdahl (1967) solution, \nand an approximation of Ravenhall \\& Pethick (1994), \nrespectively. The inset shows details of $I/MR^2$ for $M/R \\rightarrow 0$.}\n\\label{mominert}\n\\end{figure}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{figure}[hbt]\n%\\vspace{25pc}\n\\epsfig{file=mrmom_1.ps, angle=90, height=5.5in}\n%\\special{psfile=mrmom.ps hoffset=490 voffset=-50 hscale=70 vscale=65\n%angle=90}\n\\caption{Mass-radius curves for selected EOSs from Table 1, comparing\ntheoretical contours of $\\Delta I/I=0.014$ from approximations\ndeveloped in this paper, labelled ``LP'', and from Ravenhall \\&\nPethick (1994), labelled ``RP'', to numerical results (solid dots).\nTwo values of $P_t$, the transition pressure demarking the\ncrust's inner boundary, which bracket estimates in the literature, are\nemployed. The region to the left of the $P_t=0.65$ MeV fm$^{-3}$\ncurve is forbidden if Vela glitches are due to angular momentum transfers\nbetween the crust and core, as discussed in Link, Epstein \\& Lattimer\n(1999). For comparison, the region excluded by causality alone lies\nto the left of the dashed curve labelled ``causality'' as determined\nby Lattimer et al. (1990) and Glendenning (1992).}\n\\label{fig:M-R-2}\n\\end{figure}\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{figure}[hbt]\n%\\vspace{27pc}\n\\epsfig{file=bind0_1.ps, angle=90, height=5.5in}\n%\\special{psfile=bind0.ps hoffset=520 voffset=-10 hscale=70 vscale=65\n%angle=90}\n\\caption{The binding energy of neutron stars as a function of stellar\ngravitational mass for several EOSs listed in Table 1. The\npredictions of equation~(\\ref{lybind}), due to Lattimer \\& Yahil\n(1989), are shown by the line labelled ``LY'' and the shaded region.}\n\\label{bind}\n\\end{figure}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{figure}[hbt]\n%\\vspace{27pc}\n\\epsfig{file=bind1_1.ps, angle=90, height=5.5in}\n%\\special{psfile=bind1.ps hoffset=520 voffset=-20 hscale=70 vscale=65\n%angle=90}\n\\caption{The binding energy per unit gravitational mass as a function\nof compactness ($\\beta=GM/Rc^2$) for several EOSs listed in Table 1.\nSolid lines labelled ``Inc'', ``Buch'' and ``T VII'' show predictions for an\nincompressible fluid, the solution of Buchdahl (1967), and the Tolman (1939)\nVII solution, respectively. The dotted curve and shaded region\nlabelled ``FIT'' is the approximation given by equation~(\\ref{newbind}).}\n\\label{bind1}\n\\end{figure}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{figure}[hbt]\n\\epsfig{file=err.ps, height=7.5in}\n\\caption{The pressures inferred from the empirical correlation\nequation (\\ref{correl}), for three hypothetical radius values (10, 12.5\nand 15 km) overlaid on the pressure-density relations shown in Figure\n~\\ref{fig:P-rho}. The light shaded region takes into account only the\nuncertainty associated with $C(n,M)$; the dark shaded region also\nincludes a hypothetical uncertainty of 0.5 km in the radius\nmeasurement. The neutron star mass was assumed to be 1.4 M$_\\odot$. }\n\\label{fig:err}\n\\end{figure}\n\n\\end{document}\n\n\n\n\n\n\nIn\nparticular, the formula for the crustal fraction of the moment of\ninertia can be used together with glitch observations, if the glitch\nmagnitudes are connected with the crustal fraction, to provide a new\nlimit on the masses and radii of neutron stars that is more stringent\nthan the most stringent general limit presently available, namely that\ndue to causality.\n"
}
] |
[
{
"name": "astro-ph0002232.extracted_bib",
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}
] |
astro-ph0002233
|
The Progenitor Masses of Wolf-Rayet Stars and Luminous Blue Variables Determined from Cluster Turn-offs. I. Results from 19 OB Associations in the Magellanic Clouds
|
[
{
"author": "PHILIP MASSEY\\altaffilmark{1}"
}
] |
We combine new CCD {UBV} photometry and spectroscopy with that from the literature to investigate 19 Magellanic Cloud OB associations that contain Wolf-Rayet (WR) and other types of evolved massive stars. Our spectroscopy reveals a wealth of newly identified interesting objects, including early O-type supergiants, a high mass double-lined binary in the SMC, and, in the LMC, a newly confirmed LBV (R~85), a newly discovered WR star (Sk$-69^\circ$194), and a newly found luminous B[e] star (LH85-10). We use these data to provide precise reddening determinations and construct physical H-R diagrams for the associations. We find that about half of the associations may be highly coeval, with the massive stars having formed over a short period ($\Delta \tau <$ 1~Myr). The (initial) masses of the highest mass {unevolved} stars in the coeval clusters may be used to estimate the masses of the progenitors of WR and other evolved stars found in these clusters. Similarly the bolometric luminosities of the highest mass unevolved stars can be used to determine the bolometric corrections for the evolved stars, providing a valuable observational basis for evaluating recent models of these complicated atmospheres. What we find is the following: (1) Although their numbers are small, it appears that the WRs in the SMC come from only the highest mass ($>70 \cal M_\odot$) stars. This is in accord with our expectations that at low metallicities only the most massive and luminous stars will have sufficient mass-loss to become WRs. (2) In the LMC, the early-type WN stars (WNEs) occur in clusters clusters whose turn-off masses range from 30$\cal M_\odot$ to 100 $\cal M_\odot$ or more. This suggests that possibly all stars with mass $>30 \cal M_\odot$ pass through an WNE stage at LMC metallicities. (3) The one WC star in the SMC is found in a cluster with a turn-off mass of 70$\cal M_\odot$, the same as for the SMC WNs. In the LMC, the WCs are found in clusters with turn-off masses of 45$\cal M_\odot$ or higher, similar to what is found for the LMC WNs. Thus we conclude that WC stars come from essentially the same mass range as do the WNs, and indeed are often found in the same clusters. This has important implications for interpreting the relationship between metallicity and the WC/WN ratio found in Local Group galaxies, which we discuss. (3) The LBVs in our sample come from very high mass stars ($>85 \cal M_\odot$), similar to what is known for the Galactic LBV $\eta$~Car, suggesting that only the most massive stars go through an LBV phase. Recently, Ofpe/WN9 stars have been implicated as LBVs after one such star underwent an LBV-like outburst. However, our study includes two Ofpe/WN9 stars, BE~381 and Br~18, which we find in clusters with much lower turn-off masses ($25-35 \cal M_\odot$). We suggest that Ofpe/WN9 stars are unrelated to ``true" LBVs: not all ``LBV-like outbursts" may have the same cause. Similarly, the B[e] stars have sometimes been described as LBV-like. Yet, the two stars in our sample appear to come from a large mass range ($>30-60 \cal M_\odot$). This is consistent with other studies suggesting that B[e] stars cover a large range in bolometric luminosities. (4) The bolometric corrections of early WN and WC stars are found to be extreme, with an average BC(WNE)=$-6.0$~mag, and an average BC(WC4)=$-5.5$~mag. These values are considerably more negative than those of even the hottest O-type stars. However, similar values have been found for WNE stars by applying Hillier's ``standard model" for WR atmospheres. We find more modest BCs for the Ofpe/WN9 stars (BC=$-2$ to $-4$~mag), also consistent with recent analysis done with the standard model. Extension of these studies to the Galactic clusters will provide insight into how massive stars evolve at different metallicities.
|
[
{
"name": "Massey.tex",
"string": "%Shortened, revised version resubmitted 9 Feb 2000\n%Origial submission: 12 Oct 1999\n\\documentstyle[12pt,aasms4]{article}\n\\begin{document}\n\\setcounter{secnumdepth}{4}\n\\def\\arcsec{\\ifmmode^{\\prime\\prime}\\;\\else$^{\\prime\\prime}\\;$\\fi}\n\\def\\arcmin{\\ifmmode^{\\prime}\\;\\else$^{\\prime}\\;$\\fi}\n\\def\\kms{~km~s$^{-1}$}\n\\title{The Progenitor Masses\nof Wolf-Rayet Stars and\nLuminous Blue Variables\nDetermined from Cluster Turn-offs. I. Results from 19 OB Associations in\nthe Magellanic Clouds}\n\n\\author{PHILIP MASSEY\\altaffilmark{1}}\n\\affil{Kitt Peak National Observatory, National Optical Astronomy\nObservatories\\altaffilmark{2}\n\\\\ P.O. Box 26732, Tucson, AZ 85726-6732}\n\n\n\\author{ELIZABETH WATERHOUSE\\altaffilmark{3} and\nKATHLEEN DEGIOIA-EASTWOOD}\n\\affil{Department of Physics and Astronomy, Northern Arizona University,\nP.O. Box 6010, Flagstaff, AZ 86011-6010.}\n\n\\altaffiltext{1}{Visiting Astronomer, Cerro Tololo Inter-American\nObservatory, National Optical Astronomy Observatories, which is operated by\nthe Association of Universities for Research in Astronomy, Inc.\\ (AURA) under\ncooperative agreement with the National Science Foundation.}\n\\altaffiltext{2}{Operated by AURA\nunder cooperative agreement with the\nNational Science Foundation.} \n\\altaffiltext{3}{Participant in Research Experiences\nfor Undergraduates program, Northern Arizona University, Summer 1998. \nPresent address:\nHarvard University, 436 Eliot House Mail Center, 101 Dunster St., Cambridge, MA 02138.}\n\n\\begin{abstract}\n\nWe combine new CCD {\\it UBV} photometry and spectroscopy with that from the\nliterature to investigate 19 Magellanic Cloud OB associations that contain\nWolf-Rayet (WR) and other types of evolved massive stars. \nOur spectroscopy reveals a wealth of newly identified\ninteresting objects,\nincluding early O-type supergiants, a high mass double-lined binary in the\nSMC, and, in the LMC, a newly confirmed LBV (R~85), a newly discovered\nWR star (Sk$-69^\\circ$194), and a newly found luminous B[e] star (LH85-10). \nWe use these data to provide\nprecise reddening determinations and construct physical H-R diagrams for\nthe associations. We find that about half of the associations may be\nhighly coeval, with the massive stars having formed\nover a short period ($\\Delta \\tau <$ 1~Myr). The (initial) masses\nof the highest mass {\\it unevolved} stars in the\ncoeval clusters may be used to estimate the masses of the progenitors of\nWR and other evolved stars found in these clusters.\nSimilarly the bolometric luminosities of the highest mass unevolved stars\ncan be used to determine the bolometric corrections for the evolved\nstars, providing a valuable observational basis for evaluating recent \nmodels of these complicated atmospheres.\nWhat we find is the following: \n(1) Although their numbers are small, it appears that the WRs\nin the SMC come from only the highest mass ($>70 \\cal M_\\odot$) stars.\nThis is in\naccord with our expectations that at low metallicities only the most massive\nand luminous stars\nwill have sufficient mass-loss to become\nWRs. \n(2) In the LMC, the early-type WN stars (WNEs) occur in clusters\nclusters whose turn-off masses range from 30$\\cal M_\\odot$\nto 100 $\\cal M_\\odot$ or more. \nThis suggests that possibly all stars with mass $>30 \\cal M_\\odot$ pass\nthrough an WNE stage at LMC metallicities.\n(3) The one WC star in the SMC is found in a cluster\nwith a turn-off mass of 70$\\cal M_\\odot$, the same as for the SMC WNs.\nIn the LMC, the WCs\nare found in clusters\nwith turn-off masses of 45$\\cal M_\\odot$ or higher, similar to what is found\nfor the LMC WNs. Thus we conclude that WC stars \ncome from essentially the same mass range\nas do the WNs, and indeed are often found in the same clusters. This\nhas important implications for interpreting the relationship between\nmetallicity and the WC/WN ratio found in Local Group galaxies, which\nwe discuss. (3) The LBVs in our\nsample come from very high mass stars ($>85 \\cal M_\\odot$), similar to what is known\nfor the Galactic LBV $\\eta$~Car, suggesting that only the most massive stars\ngo through an LBV phase. Recently, Ofpe/WN9 stars have been implicated\nas LBVs after one such star underwent an LBV-like outburst. However,\nour study includes two Ofpe/WN9 stars,\nBE~381 and Br~18, which we find in clusters with much lower turn-off masses\n($25-35 \\cal M_\\odot$). We \nsuggest that Ofpe/WN9 stars \nare unrelated to ``true\" LBVs: not all ``LBV-like outbursts\" may have the\nsame cause. Similarly, the B[e] stars have sometimes been\ndescribed as LBV-like. Yet, the two stars in our sample appear to come\nfrom a large mass range ($>30-60 \\cal M_\\odot$). This is\nconsistent with other studies\nsuggesting that B[e] stars cover a large range in bolometric luminosities.\n(4)\nThe bolometric corrections of early WN and WC stars are found to be \nextreme, with an average BC(WNE)=$-6.0$~mag, and an average BC(WC4)=$-5.5$~mag.\nThese values are considerably more negative than those of even the hottest\nO-type stars. However, similar values have been found for WNE stars by\napplying Hillier's\n``standard model\" for WR atmospheres. We find more modest BCs for the\nOfpe/WN9 stars (BC=$-2$ to $-4$~mag), also consistent with recent analysis done\nwith\nthe standard model. Extension of these studies\nto the Galactic clusters will provide insight into how massive stars evolve\nat different metallicities.\n\n\\end{abstract}\n\n\\keywords{Magellanic Clouds --- stars: early-type --- stars: evolution ---\nstars: Wolf-Rayet}\n\n\\section{Introduction}\n\nConti (1976) first proposed that Wolf-Rayet (WR) stars might be a normal, late\nstage in the evolution of massive stars.\nIn the modern version of the \n``Conti scenario\" (Maeder \\&\nConti 1994), strong stellar\nwinds gradually \nstrip off the H-rich outer layers of the most massive stars during the course\nof their\nmain-sequence lifetimes. \nAt first the H-burning CNO products He and N are revealed,\nand the star is called a WN-type WR star; this stage occurs either near the\nend of core-H burning or after core-He burning has begun, depending upon\nthe luminosity of the star and the initial metallicity. Further mass-loss\nduring the He-burning phases exposes the triple-$\\alpha$ products C and O, and results in a WC-type WR star. \nSince the fraction of mass that a star loses during\nits main-sequence evolution depends upon luminosity (mass), we\nwould expect that at somewhat lower masses evolution proceeds only\nas far as the WN stage. At still lower masses a star never loses \nsufficient mass to become a Wolf-Rayet at all, but spends its\nHe-burning life as a red supergiant (RSG). Mass-loss rates also scale with\nmetallicity as the stellar winds are driven by radiation \npressure acting through highly ionized metal lines. Thus the \nmass-limits for becoming WN or\nWC stars should vary from galaxy to galaxy, and with location within a galaxy\nthat has metallicity variations. \n\nStudies of mixed-age populations in the galaxies of the Local Group have \nconfirmed some of the predictions of the Conti scenario. For instance, the\nnumber ratio of WC and WN stars is a strong function of metallicity\n(Massey \\& Johnson 1998 and references therein), with proportionally more WC stars seen at higher\nmetallicities, suggesting that the mass-limit for becoming WC stars is somewhat\nlower in these galaxies. Similarly the relative number of WRs and RSGs is correlated with metallicity, and there\nis a paucity of high luminosity RSGs at high metallicities (Massey 1998a),\nsuggesting that these high luminosity stars have become WRs rather than RSGs.\n\nHowever, fundamental questions remain concerning the evolution of massive stars:\n\n\\noindent\n(1) What is the role of the luminous blue variables (LBVs)? These stars are\nhighly luminous objects that undergo photometric ``outbursts\" associated with\nincreased mass-loss (Humphreys \\& Davidison 1994). Are LBVs a short\nbut important stage in the lives of {\\it all} high mass stars that occur at\nor near the end of core-H burning? Recent efforts have linked some of\nthe LBVs to binaries, as Kenyon \\& Gallagher (1985) first suggested. \nThe archetype LBV, $\\eta$ Car, may be a binary with a highly eccentric orbit\n(Damineli, Conti, \\& Lopes 1997), but whether its outbursts\nhave anything to do with the binary nature remains controversial\n(Davidson 1997), as does the orbit itself (Davidson et al.\\ 2000).\nSimilarly, the WR star HD~5980 in the SMC underwent an\n``LBV-like\" outburst (Barba et al 1995); this star is also\nbelieved to be a binary with an eccentric orbit, although the nature\n(and multiplicity?)\nof the companion(s) remains unclear (Koenigsberger et al.\\ 1998; Moffat 1999).\n\n\\noindent\nThe\nOfpe/WN9 type WRs, and the high-luminosity B[e] stars have recently\nbeen implicated in the LBV phenomenon. \nThe former have spectral\nproperties intermediate between ``Of\" and ``WN\" (Bohannan \\& Walborn 1989).\nOne of the prototypes of this class, R~127, underwent an LBV outburst in 1982\n(Walborn 1982; Stahl et al.\\ 1983; see discussion in Bohannan 1997). \nSimilarly some B[e] stars have been described\nas having LBV-like outbursts. Var~C, a well-known LBV in M~33,\nhas a spectrum indistinguishable from B[e] stars: compare\nFig.~8a of\nMassey et al.\\ (1996) with Fig.~8 of Zickgraf et al. (1986). \nDo all B[e] stars undergo an LBV phase or not? Conti (1997) has\nprovided an insightful review.\n\n\\noindent\n(2) What is the evolutionary connection between WN and WC stars? \nWe expect only the highest mass stars become WCs, while\nstars of a wider range in mass become WNs. The changing proportion of\nWCs and WNs within the galaxies of the Local Group have been\nattributed to the expected dependence of these mass ranges on\nmetallicity. However, the relative\ntime spent in the WN and WC stages may also change with metallicity,\ncomplicating the interpretation of such \nglobal measures drawn from mixed-age populations.\n\n\\noindent\n(3) Is there any evolutionary significance to the excitation subtypes?\nBoth WN and WC stars are subdivided into numerical classes, or more\ncoarsely into ``early\" (WNE, WCE) or ``late\" (WNL, WCL) based upon\nwhether higher or lower excitation ions dominate. \nRecent modeling by Crowther (2000) suggests that the distinction between\nWNL and WNE is not actually due to temperature differences\nbut primarily metal abundance.\nArmandroff \\& Massey (1991) and Massey \\& Johnson (1998) have argued that\nthis true for the WC excitation classes based upon the metallicity\nof the regions where these stars are found.\n\nIf we knew the progenitor masses of LBVs and the various kinds of WRs\nwe would have our answers to the above.\nHowever, here recourse to stellar evolution models\nfails us. \nStellar evolutionary models show that a star's path in the HRD\nduring core-He burning is strongly dependent upon the amount of mass-loss that\nhas preceded this stage. Thus the nature of the LBV phenomenon becomes very\nimportant in understanding where WRs come from, \nas the amount of mass ejected by LBVs is large, but\ngiven the episodic nature of LBVs, hard to\ninclude in the evolutionary models.\nIn addition, the locations of WRs and LBVs\nin the H-R diagram are highly uncertain. LBVs have pronounced UV-excesses\nand ``pseudo-photospheres\" (Humphreys \\& Davidson 1994).\nFor WR stars, neither\nthe effective temperatures nor\nbolometric corrections are established, as none of the standard\nassumptions of stellar atmospheres hold in the non-LTE,\nrapidly expanding, ``clumpy\" stellar winds where \nboth the stellar continua and emission-lines arise (e.g., Conti 1988).\nWhile the WR subtypes represent some sort\nof excitation sequence in the stellar winds, the relationship, if any, to\nthe effective temperature of the star remains unclear. \n \nThere has been recent success in modeling WR atmospheres, with\nconvincing matches to the observed\nline profiles and stellar continua from the UV to the near-IR. \nThese models have the potential for determining the\nbolometric luminosities and effective temperatures.\nThe ``standard WR model\" (Hillier 1987, 1990) assumes a spherical geometry and\nhomogeneity, and then iteratively solves the equations for statistical\nequilibrium and radiative equilibrium for an adopted velocity law, mass-loss\nrate, and chemical composition. (See also Hillier \\& Miller 1998, 1999.) Comparison with observations then permits \ntweaking of the parameters. Although the solutions may not be unique, good\nagreement is often achieved with observations, and in a series of papers,\nCrowther and collaborators have offered the ``fundamental\" parameters \n(effective temperatures, luminosities, chemical abundances, \nmass-loss rates, etc.) of WN\nstars obtained with this model (Crowther, Hillier \\& Smith 1995a, 1995b; Crowther,\nSmith, \\& Hillier 1995c; Crowther et al. 1995d; Crowther, Smith, \\& Willis 1995e; \nCrowther \\& Smith 1997; Bohannan \\& Crowther 1999). \n\nHere we utilize a complementary, observational\napproach to the problem, one that can not only\nanswer the question of the progenitor masses of LBVs and WRs, but also provide\ndata on the BCs that can help constrain and evaluate the WR\natmosphere models. \n\n\\subsection{The Use of Cluster Turn-offs}\n\nA time-honored method of understanding the nature of evolved stars is to determine the turn-off luminosities in clusters containing such objects \n(Johnson \\& Sandage 1955; Schwarzschild 1958). \nThis was first applied by Sandage (1953)\nto determine the masses of RR~Lyrae stars in the globular clusters M~3 \nand M~92, with a result that was at variance with\nthat given by \ntheory (Sandage 1956). \nSimilarly, the turn-off masses of intermediate-age open clusters were used\nby Anthony-Twarog (1982) to determine the progenitor masses of white dwarfs.\nHowever, it is one thing to apply this to clusters with ages\nof $10^{10}$ yr,\nas was done for the RR~Lyrae stars, or to clusters whose ages are\n$2\\times 10^{7}$---$7\\times 10^{8}$ yr,\nas was done for white dwarfs.\nCan we safely extend this \nto clusters whose ages are only of order 3--5$\\times 10^6$~yr in order to\ndetermine the progenitor masses of WRs and LBVs?\n\nWhen stars form in a cluster or association, stars of intermediate mass appear\nto form over a significant time span---perhaps over several million years\n(Hillenbrand et al.\\ 1993; Massey \\& Hunter 1998). However,\nmodern spectroscopic and photometric studies have shown that the massive stars\ntend to form in a highly coeval fashion. For instance, in their study of the\nstellar content of NGC~6611, Hillenbrand et al.\\ (1993) \nfound a {\\it maximum} age spread of 1~Myr for the massive stars, and\nnoted that the data were consistent with {\\it no} discernible age spread.\nfor all one could tell ``the highest-mass stars could have all been born\non a particular Tuesday.\" Similarly, the high mass stars in the R136 cluster\nhave clearly formed over $\\Delta \\tau < 1$~Myr, given the large number of\nO3~V stars and the short duration that stars would have in this phase\n(Massey \\& Hunter 1998).\n\nSuch short time scales for star formation are consistent with recent \nstudies by Elmegreen (1997, 2000a, 2000b), who argues \nthat star formation takes place not over tens of crossing times but \nover one or two. \nFor regions with large spatial extent (such as 100~pc\ndiameter OB associations) star formation in the general region may occur\nover a prolonged time ($\\leq$10~Myr). \nHowever, large OB associations can contain subgroups that have formed independently\n(Blaauw 1964), and are small enough so that a high degree of coevality\n($<1-2$~Myr) is expected. The stars from such a subgroup need not be\nspatially coincident. Rather, a star with a random motion of 10~km~s$^{-1}$\nwill have traveled 30~pc in just 3~Myr. Thus in an OB association we may\nfind intermediate-mass stars which have formed from a number of\nsubgroups over time, but massive stars which may have\nformed from a single subgroup and hence are coeval---even though these \nmassive stars may now be spread out throughout the OB association.\nOr, it may be that massive stars of different\nages are present, in which case the ``turn-off mass\" will not be relevant\nto the evolved object. We take an optimistic approach in our search for\nturn-off masses, but will insist that coevality be established empirically\nfor the massive stars in the region in question.\n\nFor massive stars, the mass-luminosity relationship is much flatter than for\nsolar-type stars ($L\\sim M^{2.4}$ for 30~$\\cal M_\\odot$ and $L\\sim M^{1.5}$ for\n120~$\\cal M_\\odot$). As a result, the lifetimes of massive stars do not change as drastically with mass as one might expect. A 120 $\\cal M_\\odot$ will have a main-sequence\nlifetime of 2.6~Myr, a 60 $\\cal M_\\odot$ still will have a main-sequence lifetime of 3.5~Myr, and a 25 $\\cal M_\\odot$ star will have a main-sequence\nlifetime of 6.4~Myr. (These numbers are based on the $z=0.02$ models of Schaller et al.\\ 1992.)\n\nThus it should be possible to use clusters and OB associations to pin down the\n``minimum mass\" of various unevolved massive stars. If the highest mass\nstar still on the main-sequence is 60$\\cal M_\\odot$, and its associated\nstellar aggregate contains a WC-type WR star, then we might reasonably\nconclude that the progenitor mass of the WC star was at least 60 $\\cal M_\\odot$.\nOf course, if coevality does not hold, then this answer may be wrong---the WC star might have come from a 25 $\\cal M_\\odot$ that formed earlier. But were that the case, \nit would have to have formed {\\it much} \nearlier---at least 3~Myr earlier, according to the lifetimes given above,\nand such an age spread should be readily apparent.\n\nWe can in principle also find the BCs from the cluster turn-offs. \nIt is straightforward to \ndetermine the absolute visual magnitude of the WR, making\nsome modest correction for the emission lines.\nSince massive stars evolve at nearly constant bolometric luminosity, \nwe expect that the bolometric luminosity of the WR\nwill be at least as great as the bolometric luminosity of the highest\nmass main-sequence object. With modern stellar models we can improve on this\nby making first-order correction for modest luminosity evolution.\n\nWe are, of course, not the first to have trod on this ground. \nSchild \\& Maeder\n(1984) attempted to provide links between the different WR \nsubtypes using this sort of analysis of Galactic clusters, concluding that\nstars with masses as low as $18 \\cal M_\\odot$ became WN stars, while WC stars\ncame from stars of $35 \\cal M_\\odot$ and higher, and proposing various evolutionary relationships between the various subtypes.\nHumphreys, Nichols,\n\\& Massey (1985) also used data drawn from the literature on (mostly the same)\nGalactic clusters, and found a considerably higher minimum mass for becoming\na WR star (30 $\\cal M_\\odot$), with no difference between the masses required\nto become a WN or a WC. They were also\nthe first to apply this method to determining the minimum\nbolometric corrections for WR stars, concluding that WNE stars have BCs $<-5.5$~mag,\nWNL stars have BCs $<-3.5$~mag, and WCs have BCs $<-5.0$~mag. (These BCs\nare considerably more negative than had been commonly assumed.) Smith, Meynet, \\& Mermilliod (1994) re-addressed the\nissue of BCs by analyzing the same data from the literature on what was also\nmostly the same clusters, finding BCs for WNs that were typically $-4$ mag\n(WNL) to $-6$ mag (WNE), and $-4.5$ for WCs, essentially unchanged from the\nHumphreys et al.\\ findings.\n\nThere were\nproblems, however, with these earlier studies.\nThe most significant one was the reliance upon (the same) literature data\nfor the spectral types of the main-sequence stars in these clusters and\nassociations.\nOver the past decade we have examined the stellar content of numerous clusters\nand OB associations in the Milky Way, and invariably discovered stars of\nhigh mass that had been previously missed either due to reddening or simple\noversight (Massey, Johnson, \\& DeGioia-Eastwood 1995a).\nA related problem is that some of the literature spectral types were\n``outdated\" for the O-type stars, particularly for stars of type O7 and earlier,\nwhich would lead to an incorrect assignment of bolometric\ncorrections and hence luminosities and masses.\nIn addition, our understanding of massive star evolution has improved to\nthe point where we can do a considerably better job in assigning masses,\nand in particular understand the errors associated with this procedure\n(see, for example, Massey 1998b). Another problem was that the spectral information was sufficiently sparse that\nno test of coevality could be applied to the cluster. In addition, poor photometry---often photographic---led to poor reddening corrections.\nAnd, finally, a significant limitation in these earlier studies\nwas that all were restricted to the Milky Way. \nIt would be most interesting to understand the origin of evolved\nmassive stars as a function of metallicity; for this, extension to the\nMagellanic Clouds is a logical step.\n\nWe have attempted to rectify these problems by carrying out a modern analysis\nof OB associations containing WR and other evolved massive stars in galaxies\nof the Local Group, obtaining new spectroscopic and photometric data where\nwarranted, and combining this with studies drawn form the recent literature.\nIn this first paper we will determine the progenitor masses of WR and LBVs\nin 19 associations of the Magellanic Clouds. \nThese two galaxies have \nabundances which are low compared to the solar neighborhood.\nIn the next paper we will compare these to\nnew results obtained for OB associations in our\nown Galaxy. In a third paper we will combine {\\it HST} photometric and\nspectroscopic data with large-aperture ground-based studies to\nextend this work to the more\ndistant members of the Local Group as an addition check on metallicity effects.\n\nThroughout this paper we will assume the\ntrue distance modulus of the SMC is 18.9, and that of LMC is 18.5\n(Westerlund 1997; van den Bergh 2000). \n\n\\section{Sample Selection and Observing Strategy}\n\n\nIn selecting this sample, we first compared the locations of known WRs and\nLBVs to that of the cataloged OB associations in the SMC and LMC.\nThe probability of a chance supposition of a rare evolved object\nagainst one of these associations is, of course, low.\n\nThere are nine known WR stars in the SMC (Azzopardi \\& Breysacher 1979;\nMorgan, Vassiliadis, \\& Dopita 1991). Four of these are within three of the\nOB associations identified by\nHodge (1985). We list these in Table~1. The WR star\nHD~5980 underwent an ``LBV-like outburst\" in 1994 (Barba et al.\\ 1995). \nThis star is located in NGC~346, which is included in\nour study. Three\nother SMC stars described as LBV-like in some way are R~40, which is not a\nmember of any association: R~4, a B[e] star with ``brightness variations\ntypical for LBVs\" (Zickgraf et al.\\ 1996), located in Hodge~12, but not included\nhere, and AV~154 (aka S~18), another B[e] star tied to LBVs\n(Morris et al.\\ 1996), located just outside of Hodge~35, also not included here.\nOne other high luminosity B[e] star, R~50 (aka S~65=Sk~193), is listed by Zickgraf et al.\\ (1986),\nbut is well outside any OB association.\n\n\nFor the LMC, Breysacher (1981) cataloged 100 Wolf-Rayet stars; an occasional\nadditional one has been found spectroscopically (e.g., Conti \\& Garmany 1983;\nTestor, Schild, \\& Lortet 1993), plus components of R~136 and other\ncrowded clusters have been successfully resolved, which brought \nthe total of known WR stars in the LMC to 134 (Breysacher,\nAzzopardi, \\& Testor 1999).\nAs part of the present study, we discovered a new WR star, Sk$-69^\\circ$~194,\nlocated in LH~81.\nWe compared the positions of WRs\nagainst the Lucke-Hodge OB associations \n(Lucke \\& Hodge 1970; Lucke 1972), using only those associations with\n``A1\" classifications. Not all were included in the\ncurrent study; we list in Table~1 the 16 associations that are, along\nwith their WR stars.\n\nNext we considered the LMC LBVs. Six \nare listed by \nBohannan (1997): S~Dor, R~71, R~127, HD~269582, R~110, and R~143. To this\nlist we propose that R~85 be considered a seventh, based upon our discovery\nhere of spectral variability\n(Section~\\ref{Sec-r85}) and a recent characterization of its\nphotometric variability (van Genderen, Sterken, \\& de Groot 1998; see also\nStahl et al.\\ 1984). Of these seven, S~Dor and R~85 are in LH~41, which is \nincluded here, and R~143 is in LH~100, which is not. We \nargue later that one of the LH~85 stars may also be an LBV based upon its spectral\nsimilarity to other LBVs, but further monitoring is needed to establish\nvariability; we include it in Table~1 as a previously unknown,\nhigh luminosity B[e] star. \nThree other ``LBV candidates\" are\nlisted by Parker (1997) : \nR~99, \nS~61 (BE~153=Sk$-67^\\circ 266$), and\nS~119 (HD~269687=Sk$-69^\\circ 175$). Of these, only one is located near\nan OB association (R~99 near LH~49), and it is not included here.\nFinally, we also considered the location\nof the high luminosity \nB[e] stars (Table~1 of Lamers et al.\\ 1998;\nsee also\nZickgraf et al.\\ 1986, Zickgraf 1993, and \nin particular Fig.~10 in Gummersbach, Zickgraf, \\& Wolf 1995).\nOnly S~134, \nis found in one of our regions (LH~104), although several \nare found in other\nOB associations; i.e., S~22 in LH~38 and R~82 in LH~35.\n\n\nWe have referred to all of these stellar aggregates as ``OB associations\",\nalthough the distinction\nbetween an OB association, and a bona-fide ``cluster\" young enough\nto contain O-type stars, is hard to quantify.\nThe classical distinction, that clusters are gravitationally bound,\nis hard to establish, as it requires\na census down to the low-mass components, plus detailed\nradial velocity studies. Semantics aside, our\nprimary concern is to what degree these regions are coeval. Certainly\nmost of the OB associations studied as part of our efforts to determine the\nIMFs are (Massey et al.\\ 1995b). \nFor the new ones studied here, we will establish the\ndegree of coevality directly from the data.\n\n\nOur observing strategy had similarities to our work \nthat determined the initial mass functions in the LMC \n(e.g., Massey et al.\\ 1989a, 1995b). \nIt is possible to infer masses of main-sequence\nO- and B-type stars using their position in the physical H-R diagram\n($\\log T_{\\rm eff}$ vs. $M_{bol}$) and comparing these with modern evolutionary models. There may be systematic problems with the masses thus inferred,\nalthough there is good agreement with the overlap of masses determined\ndirectly from spectroscopic binaries up to 25$\\cal M_\\odot$ (Burkholder,\nMassey, \\& Morrell 1997), above which mass there is a scarcity of suitable\ndata on binaries. Massey (1998b) discusses the errors in the inferred mass\nwith temperature; since the BC is a steep function of the effective temperature,\naccurate knowledge of the latter is needed for this procedure to work. \nSufficient accuracy cannot be achieved from photometry alone, but knowledge of\nthe spectral type of the star yields adequate information in most cases.\nThe sort of error bars associated with this can be found in Fig.~1(c) and 1(d)\nof Massey et al.\\ (1995b). We will revisit this issue in Section~\\ref{Sec-coeval}.\n\nFor this project we considered relying simply on the photographic photometry\nor aperture photoelectric photometry that was available; e.g., Lucke (1972)\nor Azzopardi \\& Vigneau (1982), for the Large and Small Clouds respectively.\nAfter all, for the stars with spectroscopy (and hence accurate BC \ndeterminations)\nan error of 0.1 mag in the $B-V$ color will lead to a 0.3 mag error in $M_V$,\ngiven $A_V=3.1\\times E(B-V)$. An error of 0.3 mag in $M_V$ translates to an\nerror of 15\\% in the derived mass (see details in Massey 1998b).\n(For comparison, if we were relying upon the colors alone and were dealing with\na 0.1 mag uncertainty in $B-V$ we would have a 2 mag uncertainty in the BC,\nand thus a 0.4 dex uncertainty in the log of the mass (i.e.,\na factor of 2.5 uncertainty in the mass of the star).\n\nFor determining the IMF, it is necessary to pursue spectroscopy down the main-sequence until spectral-type of early B or later, after which good\nphotometry provides as accurate information. \nYet, in the case of determining\nthe turn-off masses in principle we need to only ascertain that we have obtained\nspectra of the most massive unevolved object in the association. In a \nstrictly coeval population with uniform reddening, this will be equivalent to\nknowing the spectral type of the visually brightest member. However, given \nfinite\nphotometric errors, slight non-coevality,\nreddening which is spatially variable across a cluster, the\npresence of other evolved supergiants (either members or field interlopers),\nand the\nneed to demonstrate coevality, our initial aim was to obtain spectra for the\nsix or seven visually brightest stars in each of these associations. \nStill, this is far fewer than what would be needed to construct the\nIMF.\n\nSome of these associations had extensive CCD photometry and modern\nspectroscopy in the literature, and for these we constructed H-R diagrams\nand obtained a few additional spectra where warranted. In other cases,\nwe already had existing unpublished CCD photometry (and in some cases\neven spectroscopy) that had been aimed at determining the IMF; the complete\ndata for these associations, and the IMF analysis, will be published \nseparately elsewhere.\nFor the most part, though,\nwe began with published photographic photometry, using this list to\nselect the appropriate (brightest and bluest) stars for spectroscopy, and\nsubsequently obtained new CCD {\\it UBV} data in order to better correct\nfor reddening. In all cases we examined the preliminary H-R diagrams and\nthen obtained spectra of the few remaining interesting stars, as needed.\n\n\\section{New Data}\nWe list in Table~1 the source of the data we used, be they new or from the\nliterature, or both. For the new data, we identify the year in\nwhich it was obtained.\n\nFor most of the associations (LMC) we began with the photographic iris photometry of Lucke (1972) or older sources, and\nobtained spectra of the brightest and bluest stars during a run on the\nCTIO 1.5-m telescope during 1996 Oct 27-31. \nGrating 58 was used in second\norder with a CuSO$_4$ blocking filter, yielding wavelength coverage from\n$\\lambda 3750$ to $\\lambda 5070$ with approximately 3\\AA\\ (2.8 pixels)\nresolution. The Loral chip was formated to\n500 $\\times$ 1200 (15--$\\mu$m) pixels. The slit was opened to 1.5 arcsec\n(85$\\mu$m) and oriented EW, except for crowded regions,\nwhere the slit angle was adjusted and/or the slit narrowed. A typical\nS/N of 100 per 3\\AA\\ spectral resolution \nelement was achieved in a 5 min exposure\nat $V=12$. \n\nOn the night following this run (i.e., 1996 Nov 1)\nwe obtained {\\it UBV} images of any OB associations without previous CCD\ndata, using the Tektronix 2048$\\times 2048$ CCD imager on the CTIO 0.9-m. \nThe field-of-view (FOV) was 13.5~arcmin by 13.5~arcmin, quite ample\nfor the typical 3 arcminute diameter OB associations in our sample. Exposure times were \nusually 100 sec in $U$ and 50 sec in each of $B$ and $V$.\nThe night was mostly\nphotometric, although the alert observing assistant reported seeing a\nsingle cloud pass by part way through the night; later we will argue\nthat this affected the {\\it U} photometry of two regions but nothing else.\nStandard stars were \nobserved at the beginning, middle, and end of the night, and reduced\nsatisfactorily (0.01 mag rms residuals in $U$, $B$, and $V$ in the fits to\nthe solutions). Nevertheless,\nwe treat the data as potentially non-photometric, comparing the derived\nreddening-free index $Q=(U-B)-0.72\\times (B-V)$ with that expected on the\nbasis of spectral type as a check, as described in Section \\ref{Sec-hrd}.\nAs we discussed above, our photometric requirements are in any event modest,\ngiven our extensive spectroscopy. \n\nAbout half of the OB associations in our sample had previously been imaged\nwith an RCA CCD on the CTIO 0.9-m in 1985 October by two of the present\nauthors (PM and KDE). The full details of these data are given in \nMassey et al.\\ (1989a). Although the FOV was only $2.5\\times 4.0$ arcmin\nin size, overlapping frames were taken when needed in order to \ninclude the whole\nof an\nOB association. The photometric integrity of these 1985 data is very\nhigh, as standard star observations were obtained over 10 photometric nights\nand used for precise determinations of zero-points and color-terms. \n\nSimilarly, some of the stars have\npreviously unpublished spectroscopy obtained as part of our program to\ndetermine IMFs in the Clouds. Data obtained in 1989-1992 (Table~1) were\ntaken on the CTIO 4-m telescope with the RC spectrograph. The details of\nthese data were given by Massey et al.\\ (1995b); here we will simply note that\nthey were of comparable spectral resolution (3\\AA), and covered at least the\nwavelength region from Si~$\\lambda 4089$ through He~II~$\\lambda 4686$. The\nS/N were typically 75 per 3\\AA\\ spectral resolution element.\n\nAfter our preliminary HRDs were constructed, we had two\nobserving opportunities to obtain additional spectra where warranted.\nOn 1999 Jan 3-7 we used the CTIO 4-m for significantly higher resolution\nand better S/N data. Grating KPGLD was used in second order\nwith a CuSO$_4$ filter resulting in a resolution of 1\\AA\\ (2.5 pixels) and\na wavelength coverage of 3730\\AA\\ to 4960\\AA\\ using the Loral\n$1024\\times 3100$ (15~$\\mu$m) CCD. The S/N obtained was typically 160 per\n1\\AA\\ resolution element.\nWe obtained one final observation for this project on 1999 Oct 21\nusing the CTIO 1.5-m. \n\n\\subsection{Analysis}\n\n\\subsubsection{Spectroscopy}\n\\label{Sec-spectra}\n\nWe classified the spectra with reference to the Walborn \\& Fitzpatrick (1990)\nspectral atlas of O and B stars. Based upon our internal consistency and previous experience\nwe expect that the spectral subtypes are\ndetermined to an accuracy of one subclass and one luminosity class (e.g.,\nsupergiant vs giant), \nexcept for the earliest O-type stars, for which there is little or no\nambiguity in subclass. (See discussion in Massey et al.\\ 1995a, 1995b.)\n\nThere is no metallicity dependence\nin classifying hot stars as to spectral subclass, as the primary spectral type\n(effective temperature) indicators are the relative strengths of different\nionization states of the same ion; e.g., He~I vs. He~II for the O-type stars,\nand Si~IV vs. Si~III for the early B-type stars; however, it is our experience\nthat the luminosity indicators are metallicity dependent, even for the O-type\nstars. This makes physical sense---in fact, it would be hard to see how this \nwould fail to be the case---as the O-type luminosity indicators are primarily\nindicators of the strength of the stellar wind (i.e., He~II emission vs. He~II\nabsorption). The B-type luminosity indicators rely upon how strong certain\nmetal lines are relative to, say, He, and again we expect this to have a \nmetallicity dependence. We therefore always checked the ``MK\" \nluminosity class with that expected on the basis of the absolute magnitudes,\nas described below; we note cases where we have adjusted the luminosity class\nbased upon the absolute magnitudes.\n\nAll told, we classified slightly over 200 stars. We include our classification,\nas well as those from the literature, in the catalog we describe in Section~\\ref{Sec-catalog}. Here we will illustrate and comment\non just a few of the more\ninteresting spectra. \n\n\\paragraph{R~85.}\n\\label{Sec-r85}\n\nWe propose that the luminous star R~85 in LH~41 be\nconsidered an LBV. Based upon their characteristic of its {\\it photometric}\nvariability, van Genderen et al.\\ (1998) state that the star is ``undoubtedly\nan active LBV.\"\nWe show in Fig.~\\ref{fig:r85} some of the\n{\\it spectral} changes that have taken place in recent years; we\nagree with van Genderen et al.'s characterization.\nFeast, Thackeray, \\& Wesselink\n(1960) classify the star as ``B5~Iae\", and note the presence of H$\\beta$\nemission, H$\\gamma$ and H$\\delta$ absorption, as well as \nits photometric variability. Our 1996 spectra did not appear totally\nconsistent with this description, as Mg~II $\\lambda 4481$ was present but\nthere was\nlittle or no He~I~$\\lambda 4471$; for a B5 star the latter should be somewhat\nstronger. We took a very high signal-to-noise spectrum with the CTIO 4-m in\nJanuary 1999, and were surprised by the rapid and strong changes present since\n1996;\nthe newer spectrum shows the star to be hotter (based upon He~I to Mg~II)\nwith much stronger lines.\nDr.~B. Bohannan was kind enough to make available a photographic spectrogram\nhe obtained in 1985 on the Yale 1-m, along with a sensitometer exposure; there\nis very good agreement between his exposure, and what we obtained 11 \nyears later. The recent change in the spectrum of R~85 suggests that further monitoring would be of interest. The photometry \nlisted in Table~2 comes from the 1 Nov 1996 \nobservation; e.g., $V=10.53$, $B-V=0.16$, and $U-B=-0.81$. In the\n1985 data (28 Nov) the star was slightly brighter: $V=10.44$, $B-V=0.12$,\nand $U-B=-0.71$.\n\n\\paragraph{Newly Identified O3 Stars.} \n\\label{Sec-o3s}\n\nAs part of this investigation we came across\na number of previously unrecognized O3 stars, stars whose effective temperatures\nare at the extreme of the \nspectral sequence of luminous stars. We show examples\nin Figs.~\\ref{fig:o31} and ~\\ref{fig:o32}.\n\nFirst, let us consider the O3 supergiants (O3~If*) and giants\n[O3~III(f*)]. These evolved stars are still in the \ntemperature regime covered by the O3 classification,\nand thus all such stars must be extremely massive. \nWalborn et al.\\ (1999) classify the star LH90$\\beta$-13 as O4~If+ on the\nbasis of an FOS spectrum obtained with {\\it HST}, but\nour higher signal-to-noise spectrum (with higher resolution) \nreveals N~V $\\lambda \\lambda 4603,19$\nabsorption; this, combined with the lack of He~I makes this an O3 star\n(Fig.~\\ref{fig:o31}).\nThe star ST5-31 in LH~101 was classified as O3~If* by Testor \\& Niemela (1998);\nour spectrum is in good agreement with that.\nWe consider the star W16-8 in LH~64 an O3~III(f*) owing to the relative\nweakness of He~II $\\lambda 4686$, despite the extremely strong N~IV $\\lambda\n4058$ emission and very strong N~V $\\lambda 4603, 19$, usually indicative of\nhigh luminosity; the absolute magnitude we derive in the next section is\n$M_V=-5.4$, consistent with this classification, and reminding us that \nslight abundance anomalies can mask as luminosity effects in early-type stars.\nA detailed atmospheric analysis\nof this star is in progress in collaboration with Rolf Kudritzki. \n\nAmong the O3 dwarfs (Fig.~\\ref{fig:o32}) we include ST2-22 (in LH~90).\nThis star was previously recognized as an O3, but called a \ngiant by Testor et al.\\ (1993). The lack of emission at\nHe~II $\\lambda 4686$, and the weakness of N~IV $\\lambda$~4058, \nsuggest a lower luminosity\nclass. We classify W28-23 in LH~81\nas an O3~V((f)). The star ST5-27 in LH~101 was called an O4~V by \nTestor \\& Niemela (1998). \nThe spectrum of this star is strongly contaminated by nebular\nemission lines. We tentatively adopt an O3~V((f)) spectral type, but our data\nare not inconsistent with the O4~V((f)) designation; we do not show the\nspectrum as the nebular lines makes casual\ncomparisons difficult.\nAnother star in LH~81, W28-5, appears to be intermediate\nbetween O3((f)) and O4~V((f)): the strength of He~I $\\lambda 4471$ relative\nto He~II~$\\lambda 4542$ would argues that the star is a little bit later than\nO3, but there is N~V~$\\lambda 4602,19$ present on our high signal-to-noise\nspectra, and this\nhas usually been taken as characteristic of O3s.\n\nThe presence of He~I $\\lambda 4471$ is easy to discern on the O3 stars in\nFig.~\\ref{fig:o32} because of the extraordinarily high S/N (160 per 1\\AA\\ \nresolution element). The O3 class was introduced \nby Walborn (1971) to describe\nfour stars in Carina which showed\nno He~I $\\lambda 4471$\non well-widened IIa-O emulsion spectrograms obtained\nat modest resolution (2\\AA). When finer-grain plates were used at higher\nresolution, He~I $\\lambda 4471$was detected with equivalent widths of 120-250~m\\AA\\ by Kudritzki (1980) and Simon et al.\\ (1984) for three of the\nCarina stars. Here we find that\nHe~I~$\\lambda 4471$ lines have equivalent widths of\n75~m\\AA\\ in W28-23, and 105~m\\AA\\ in ST2-22, significantly smaller than\nthat measured for the stars which first defined the class. Yet modern\nspectroscopy makes it possible to readily detect these lines. \n\n\\paragraph{Other O-type Stars.}\n\\label{Sec-Os}\n\nThere are clearly other exceptions to the premise that N~V $\\lambda 4603,19$\nabsorption is indicative of a luminous O3 star. \nIn Fig.~\\ref{fig:oms} we show the spectrum\nof ST5-52, a star in LH~101 classified by Testor \\& Niemela (1998) as\nO3~V. However, the strength of He~I suggests a considerably later O5.5 type.\nIt is easy to infer the basis for the Testor \\& Niemela classification of\nthis star: our spectrum shows both NIV $\\lambda 4058$\nemission and N~V $\\lambda 4603,19$ absorption, typically assumed to be\n{\\it only} characteristic of luminous O3 stars.\nOne possibility is that this star is a spectrum\nbinary, consisting of an O3~III(f*) plus a later O-type companion, which\ncontributes the He~I. However, we propose instead that this is\n a ``nitrogen enhanced\" star, and classify it as ON5.5V((f)).\nWe prefer this latter explanation because we have identified another LMC star,\nnot connected with the present study, whose He~I to He~II ratios are\nconsistent with an O5 type, but which also shows N~IV emission and\nN~V absorption. Detailed atmospheric analysis is underway for\nboth stars, pending {\\it HST} data.\n\nThe star LH58-496 was classified as ``O3-4~V\" by Garmany, Massey,\n\\& Parker (1994). Our high S/N spectrum (Fig.~\\ref{fig:oms})\nobtained with the CTIO 4-m shows a somewhat later spectral type,\nO5V((f)).\nIn Fig.~\\ref{fig:oms} \nwe also show two other early-type dwarfs, an O5~V((f)) star\nand an O4~V((f)) star. \n\nWe illustrate a few newly discovered\nluminous O-type supergiants in Fig.~\\ref{fig:osgs}. Examples shown here\ninclude supergiants from O4 through O8.\n\n\n\\paragraph{A Reconsideration of Br~58 as a WR star, and A Newly Discovered\nWR Star.}\n\\label{Sec-wrs}\n\n\nThe star Br~58 in LH~90, has long been recognized as\na WN Wolf-Rayet star.\nTestor et al. (1993)\nclassify it as WN6-7, while earlier work has classified it as WN5-6 (Conti \\& Massey 1989). We illustrate its spectrum in Fig.~\\ref{fig:wrs} from a new\nhigh-dispersion, high S/N observation.\nWe note that our ground-based spectrum shows strong \nN~V $\\lambda 4603, 19$ {\\it absorption}; this, plus the considerable strength\nof its absorption line spectrum, would tempt us to reclassify this as an\nextreme O3~If* star, i.e., O3If*/WN6. (See Fig.~3 in Massey \\& Hunter 1998.)\nThese stars are believed to be young, H-burning hot stars whose very high\nluminosities result in sufficiently strong stellar winds to mimic the\nstrong emission characteristic of a WR.\n\nThe star Sk$-69^\\circ194$=W28-10 in \nLH~81 is a newly discovered WR star, of type B0~I+WN.\nThe spectroscopic\ndiscovery of another WR star in the LMC is not surprising, particularly\ngiven the weakness of the emission in this object. (The equivalent width\nof He~II~$\\lambda 4686$ is $-2$\\AA, compared to typical $-30$\\AA\\ for a\nvery weak-lined WN star; presumably this is due to the continuum \nbeing dominated by the\nB0~I component.)\nWe question below whether all B0~I+WN are truly binaries. \n\n\\subsubsection{Photometry}\n\n{\\it UBV} photometry is needed only \n(a) to determine accurate $M_V$ values for the stars with spectra,\nand (b) to check that we obtained spectra for all of the likely ``most massive\nunevolved star\" candidates. In order to accomplish (a)\nwe typically needed \n$V$ and {\\it B-V} data for half a dozen stars or so in each association, and to\naccomplish (b) we also required {\\it U-B}, in order to construct a\nreddening-free index. Nevertheless, with modern techniques it proved just as\neasy to measure photometry for all stars on a frame, typically\n several {\\it thousand} stars.\nAt least we could then be assured that the brightest stars were well-measured,\nin the sense that their photometry was not contaminated by resolved neighbors.\n\nWe did this by fitting point-spread-functions (PSFs) using DAOPHOT\nimplemented under IRAF. The 1996 CCD frames were measured by E.W., while the\n1985 data were measured by P.M. The method used is similar to that described\nby Massey et al.\\ (1989a) and we will give only a brief overview here. Automatic\nstar-finding algorithms were used to identify stellar sources down to the\n``plate-limit\" (typically 4$\\sigma$ above the noise). \nAperture photometry through a small\ndigital aperture (with a diameter corresponding roughly to the full-width\nat half-maximum of the stellar images) were then run in order to determine the\nlocal sky values for each star (determined from the modal value in an annulus\nsurrounding each star) and to determine the instrumental magnitude to assign\nto the PSF stars. For each\nframe isolated, well-exposed stars were chosen to define the PSF. This PSF\nwas then simultaneously fit to all of the stars whose brightnesses could \npossibly overlap. In regions of nebulosity, the\nsky value was also fit separately; otherwise, an average sky value was adopted\nfor all the stars in a given fitting exercise. A frame in which the fitted\nPSFs had been subtracted was then examined to see how well the PSF matched and\nto look (by eye) for any stars that had been buried in the brightness of other\nstars. In addition, the $U$, $B$, and $V$ frames were blinked along with the\nfitted xy centers to make sure there was consistency. Missing stars were added\nback into the star list and a final run was made on each of the three colors.\nAperture corrections were then determined for each frame in order to correct\nthe instrument zero-point (based upon the small digital aperture) to the large\napertures used to measure the standard stars. These instrumental magnitudes\nwere then transformed to the standard system. In the case of the 1985 RCA CCD\ndata there were often overlapping frames involved in covering a region, and\nthe final photometry was combined to produce a single star list, with stars with\nmultiple entries averaged. \n\nOne region, Lucke-Hodge~41, was common to\nboth data sets, and thus served as an end-to-end\nindependent check on the final, transformed photometry. If we consider the twenty brightest\nstars (in $V$) we find a mean difference \n(new minus old data set)\nof $+0.015$ mag in $V$, $+0.011$ mag in $U-B$, and $+0.014$ in $B-V$, with\nsample standard deviations of 0.06 mag, \n0.02 mag, and 0.04 mag, respectively. If \ntwo outliers are removed from the $V$ data, and one from the $U-B$ data, the\nmean differences become +0.002 mag and $+0.001$ mag, respectively with\nstandard deviations of 0.03 mag and 0.04 mag. This agreement is excellent,\nand suggests that no systematic differences exist between the two data sets \nover the magnitude and color ranges of interest. \n\n\n\\subsection{The Catalog}\n\\label{Sec-catalog}\nWe list in Table~2 \nthe brightest stars in each of the 14 associations for which we have\nnew photometry; existing and new spectral types are also given. We include all stars\nof magnitudes $V=15$ or brighter; \nin several cases we extended this to fainter magnitudes\nto include additional stars with spectral types or, in the case of NGC~602c, to include\nat least 10 stars. For two of the associations \n(LH~58 and LH~101) we reply upon cited\nstudies (cf., Table~1) but have a few new spectral types; we include these in Table~2.\n(For three addition associations, NGC~346, LH~9, and LH~47, we reply purely on the cited\nworks in Table~1.) \n\nIn listing the stars we make use of published names where available\nfinding charts exist,\nalthough the celestial coordinates given in Table~2 should be of sufficient accuracy\nto remove the need for finding charts. For the\nLMC, we have kept with the star numbering given\nin the finding charts of Lucke (1972), with additional stars given designations\nof 1000+ so as to avoid confusion. The exceptions are those associations with\nmodern CCD studies, where we have kept with the numbering scheme employed by\nthe authors. In a few cases the associations contained stars that were\nsaturated on our CCDs (typically $V<10$); we include photometry of these \nstars from the literature.\nWe describe\nbelow details related to each association, making reference to\nthe results obtained in subsequent sections.\n\n\n\\subsubsection{Descriptions of Individual Associations}\n\n{\\it NGC~346:} We rely on the CCD\nphotometry and spectroscopy of Massey, Parker,\n\\& Garmany (1989b). The imaging data had their source in the same observing\nrun as the 1985 imaging used for many of the other associations studied\nhere. Four of the brightest stars were also subjected to detailed\nanalysis by Kudritzki et al.\\ (1989). Reanalysis of these stars by\nPuls et al.\\ (1996) was used in the spectral type to effective temperature\ncalibration of Vacca, Garmany, \\& Shull (1996), which we adopt\nin the next section; we note here that despite the different methodology\ninvolved, the masses determined by\nPuls et al.\\ for these stars are in good agreement with those we compute\nin the following sections.\nThe visually brightest star is HD~5980, the WN3+abs Wolf-Rayet that underwent\nan LBV-like outburst. The second\n brightest star is the O7If star Sk~80. More than a magnitude fainter visually are the very early O-type stars first\nfound by Walborn (1978), Walborn \\& Blades (1986), and Niemela, Marraco, \\& Cabanne (1986).\n\n\n{\\it Hodge~53:} Our photometry here is a comprehensive mosaic of several CCD frames and\nextensive spectroscopy obtained with the goal of determining the IMF. However, the \nthe region is not condensed, and there are several stars of type\nA-F and later, some of which are apparently foreground dwarfs or giants,\nand others which are SMC supergiants. Our spectrum of AV~331 shows it to be an\nSMC member of type\nA2~I, based both on its radial velocity, appearance of the hydrogen lines, and\nthe strength of Fe~II $\\lambda 4233$ (see Jaschek \\& Jascheck 1990, Fig~10.2).\nHowever, our spectrum of AV~339a shows it to be an F2 foreground star, probably\na dwarf, based both on its radial velocity and lack of\nluminosity-sensitive Sr~II $\\lambda 4077$. A fainter star, h53-144,\nis an A8 foreground dwarf.\nWe lack spectra for the other yellow\nstars, and so we cannot comment further on their membership.\nOur spectroscopy has also identified a double-lined spectroscopic\nbinary (O4~V+O6.5~V) which is among the most bolometric luminous members. \nWhen we construct the HRD, we will consider that each of the two components\ncontributes equally to the visual flux, consistent with the\nappearance of our double-lined\nspectrum, and the expected $M_V$s of stars of these spectral types.\nThe visually brightest member is the WR binary AV~332=Sk~108=R~31=AB~6 (WN3+O6.5) with\na 6.54 day orbit (Moffat 1982, 1988; Hutchings et al.\\ 1984; Hutchings, Bianchi, \\& Morris 1993). Hutchings et al.\\ (1984) argue convincingly that the O-type\ncompanion dominates the visual flux by a factor of 10 to 1 (making it of\nluminosity class ``I\"), and that its\nlocation in the HRD suggests an initial mass of $70-80 \\cal M_\\odot$,\nconsistent too with its Keplerian mass. Our analysis will yield a very\nsimilar value. The other WR member, AV~336a=AB~7, is quite a bit fainter. \nThe WR component is likely a WN3 (Moffat 1988), \nalthough all that is certain is that\nit is earlier \nthan WN7 (Conti, Massey, \\& Garmany 1989). An O-type absorption\nspectrum is also seen. \nRecent work by Niemela (1999)\nsuggests\na 19.6 day period. \n\n{\\it NGC~602c:} NGC~602 is located in the wing of the SMC; the\nregion was studied by Westerlund (1964), who identified three sub-components.\nComponents ``a\" and ``b\" are adjacent and are immersed in nebulosity known as\nN90 (Henize 1956); component ``a\" is also known as Lindsey~105 (Lindsey 1958).\nHere we are concerned with the third component, ``c\", which is an\nisolated condensation with little nebular emission. It was designated as a\nseparate association\nboth by Lindsey (1958) and Hodge (1985), and is known as ``Lindsey 107\", and \n``Hodge~69\". (See Plate 5 and Figure~1 in Westerlund 1964.) \nWe obtained new CCD photometry of NGC~602c. Its visually brightest star\nis the WR star AB~8, the only WC star known in the SMC.\nIt has enhanced oxygen, and was classified by Conti et al.\\ (1989) as\n``WO4 + abs\". (Crowther, De Marco, \\& Barlow 1998 instead \ncall the WR component\n``WO3\".) A new spectrum of the star obtained as part of the present program suggests\nthat the absorption spectrum is O4~V. Moffat, Niemela, \\& Marraco (1990) present an\norbit for this system with a period of 16.644 days. They propose spectral types of\nWO4+O4~V, with which we concur, although Kingsburgh, Barlow, \n\\& Storey (1995) suggest a somewhat later type for the O star.\n\n{\\it LH5:} Our photometry and spectroscopy are the first modern study of\nthis association. The visually brightest star is Sk~$-69^\\circ30$,\na G-type supergiant according to Feast et al.\\ (1960), \nwith the next brightest\nstar an O9~I. The WR star, Br4, was described as ``WN2\" by Conti \\& Massey \n(1989), as no N lines are visible, similar to the WN2 Galactic \nstar HD~6327. Like that star, Br~4 has a faint absolute magnitude.\nWe will find in subsequent sections that the star has a normal bolometric\nluminosity, and that its faintness is presumably due to a very high temperature,\nwhich shifts its light into the unobserved UV.\nIn constructing our HRD we find that the G5~Ia star Sk~$-69^\\circ~30$ is \ncoeval with the rest of the massive stars.\n\n{\\it LH9:} This association was\nstudied in detail by Parker et al.\\ (1992), \nusing the same 1985 imaging data and calibration that we employ\nhere for many of the other associations. The central object, HD~32228, was\nclearly an unresolved cluster of many early-type stars, with a composite\nWC+O spectral type. The region was recently\nexamined using {\\it HST}\nby Walborn et al.\\ (1999), and we adopt their photometry and spectroscopy\nhere, ignoring the region outside of the central 30 arcsec covered by the\nPC frame of WFPC2. \nAlthough they were able to spectroscopically\nobserve the WC component separately from\nits close neighbors for the first time, their spectral classification of WC4\nis based upon only a spectrum in the blue, which lacks the crucial classification lines O~V $\\lambda 5592$, C~III $\\lambda 5696$\nand C~IV $\\lambda 5812$ (e.g., Smith 1968a; van der Hucht et al.\\ 1981). \nWalborn (1977) had earlier classified the WR star as WC5, but this was also\nbased upon a blue spectrogram. Smith (1968b) called the star WC5, but this was\nbefore the earlier WC4 subclass was introduced. Breysacher et al.\\ (1999) \ncite a speckle study by Schertl et al.\\ (1995) for the spectral type, but no\nspectrum was actually taken as part of that study. We adopt WC4 as the\nspectral type, but note here that the type is uncertain. \nThe visually brightest stars\nin the LH~9 association are late-O supergiants (O9~I and O8.5~I).\n\n{\\it LH12:} Ours is the the first modern study of this association.\nIt contains\nthe WC4 star Br~10. The visually brightest stars are B-type supergiants,\nalthough our study has revealed a very early O-type star, with type O4~V(f).\nTo the extent that the association is coeval, the B-type\nsupergiants evolved from stars of spectral subtype O4~V or even earlier.\n\n{\\it LH31:} This association contains\ntwo Wolf-Rayet stars, Br~16 classified by Conti \\& Massey (1989) as\nWN2.5. A second WR star has been recently discovered by Morgan \\& Good (1985),\nwho classify the star as WC5+O. This star is BAT99-20 in the\ncatalog of Breysacher et al.\\ (1999), whose finding chart puts the star centrally located in the\nassociation boundary shown by Lucke (1972). \nNebulosity prevented Lucke from photographic photometry of any by the\nbrightest few stars. The visually\nbrightest stars include a B1~III, an O6~I(f), and two yellow stars. One\nbrighter of these, which we call LH31-1002, is apparently an LMC F2 supergiant,\nbased both upon our measured radial velocity and strong Sr~II $\\lambda 4077$\n(see Jaschek \\& Jaschek 1990). The other is clearly a late F-type foreground\ndwarf, based upon its radial velocity and its lack of Sr~II.\n\n{\\it LH39:} The cluster was examined by Schild (1987), and again by\nHeydari-Malayeri et al.\\ (1997). We obtained new photometry and a few\nadditional spectral types. The association contains one of the rare\nOfpe/WN9 stars, Br~18=Sk$-69^\\circ79$. Ardeberg et al.\\ (1972) list\nthe star Sk$-69^\\circ80$ as having a spectral type of F2~Ia; however,\nSchild (1987) suggests a type of B8:~I. Our photometry is\nconsistent with something intermediate between these two, and we will use\nits photometry to place it in the HR diagram. (The radial velocity of\nArdeberg et al.\\ does confirm it is an LMC member.) \nWe will find that two A supergiants classified by Schild (1987) appear to be\nmuch older than the rest of the cluster. We have independent spectroscopy for\none of these, LH39-22, and confirm Schild's type.\n\n{\\it LH41:} This association contains S Doradus, the prototype LBV,\nand the visually brightest star in the cluster. The second brightest\nstar, R~85=Sk-69$-69^\\circ92$ we propose as an LBV, based upon its \nspectral and photometric variability, as discussed earlier in \nSection~\\ref{Sec-r85}.\nThe third brightest star is the Wolf-Rayet\nstar Br~21, classified by Conti \\& Massey (1989) as B1Ia + WN3.\nThe star LH41-4 is of M-type, but we lack the radial velocity information\nthat would ascertain whether this is an M supergiant or foreground dwarf.\nThere are two lower luminosity but bona fide A-type supergiants, and an\nF5 supergiant. The latter has been confirmed based upon our radial velocity\nand the strength of Sr~II $\\lambda 4077$. (It is also an excellent match\nto the F5Iab star HD~9973 shown in the Jacoby, Hunter, \\& Christian 1984 atlas.)\nOurs is the first modern study of this association.\n\n{\\it LH43:} The visually brightest star is an early\nM-type, but again we lack the proper radial velocity information to\nascertain whether this is an LMC member or not. The second brightest\nstar is a newly discovered O4~If star. The WR star Br23 is classified\nWN3.\n\n{\\it LH47:} This association was studied by Oey \\& Massey (1995) and\nWill, Bomans \\& Dieball (1997). We adopt the photometry and spectroscopy\nof the former, who obtained spectral types for all the brighter components,\nprimarily of early to mid O-type. Oey \\& Massey (1995) suggest that there\nare two ages for the stars in the LH47/48 region: stars interior to the\nDEM~152 superbubble have an older age than stars in rim of the bubble.\nThe WR star and other\nmassive stars of interest are on the exterior, and we will restrict\nour analysis to those.\nIn agreement with Will et al.\\ we find no difference between the\nphotometric $Q$ and that expected on the basis of spectroscopy;\nwe cannot comment on their\nassertion that field-to-field differences exist in the individual $B-V$\nand $U-B$ colors at the 0.15 mag level, other than to note our value for\nthe reddening appears to be reasonable. \n\n{\\it LH58:} This association was recently studied by Garmany et al.\\ (1994).\nIt contains three WR stars, Br~32 (WC4+abs),\nBr~33 (WN3+abs), and Br~34 (B3I+WN3). The latter is the visually brightest\nstar. We did obtain a spectrum of the earliest-type star in the association,\nreclassifying it from O3-4~V to O5.5~V((f)), as described earlier\n(Section~\\ref{Sec-Os}).\nWe note that LH58-473 as B0.5V must be a giant based upon its\nM$_V$.\n\n{\\it LH64:} This association was studied by Westerlund (1961) as well\nas by Lucke (1972). Ours is the first modern study. The three visually\nbrightest stars have colors characteristic of mid-to-late type stars,\npresumably foreground, although spectroscopy is needed to\ndetermine if they are supergiants. The WR star Br~39 was not classified\nby Conti \\& Massey (1989), but was called WN3 by Breysacher (1981).\n\n{\\it LH81:} Also studied by Westerlund (1961) and Lucke (1972), ours is\nthe first CCD study of this interesting region. It contains\nthree WR stars: the WC4 star Br~50 (classified by Conti \\& Massey\n(1989), the WN4+OB star Br~53 (classified by Breysacher 1981), and\nSk$-69^\\circ$194, discovered as a WR star here (B0I+WN). The visually\nbrightest star is a foreground G dwarf. We identify two very\nearly-type stars in the association, W28-23, a O3~V((f)) star, and\nW28-5. As discussed in Section~\\ref{Sec-o3s}, we classify the latter as O4~V((f)) based upon its He~I to He~II\nstrengths, but our very high S/N spectrum \nshows the definite presence\nof N~V $\\lambda 4603,19$ absorption lines, previously associated only\nwith O3 stars. Possibly an intermediate type (O3.5) would be\nwarranted, but we leave that until we have been able to complete a\ndetailed analysis of this star.\n\n{\\it LH85:} We identify the star LH85-10 as a newly discovered\nB[e]. Our study is the first since Westerlund (1961)\nand Lucke (1972). The association also contains the WR star Br~63,\nclassified as WN4.5 (Breysacher et al.\\ 1999).\nWesterlund (1961) treated this association and the neighboring LH~89\nas one unit; we treat them separately here, following Lucke (1972), although\nthe ages and cut-off masses we derive will prove to be essentially the same.\nThe earliest spectral type we find in LH~85 is \nB0.5.\n\n{\\it LH89:} A section of LH89 was included in the study by\nSchild \\& Testor (1992) of stars in the general 30 Doradus region\n(their ``zone 3\"), in addition to the Westerlund (1961) and Lucke (1972)\nstudies. We have used their spectral types as a supplement to our own,\nbut use our own CCD photometry. \n%(The differences in our CCD photometry\n%with theirs\n%show a trend with magnitude, with an average difference (us minus them)\n%of $\\Delta V=-0.095$, $\\Delta(B-V)=+0.053$, and\n%$\\Delta(U-B)=-0.099$, with sample variances of 0.077,0.106, and 0.187 mag\n%respectively, for the 47 stars in common.)\nThe association contains Br6 (WN4) and\nBr~64=BE~381, the archetype of Ofpe/WN9 stars.\nThe visually brightest stars are three tenth magnitude \nstars of intermediate color; radial velocities\nof the two brightest demonstrate that they\nare LMC members (Ardenberg et al.\\ 1972). Our spectrum of the third shows\nit is a foreground F8 dwarf, based both on its radial velocity\nand the weakness of high-luminosity features in the spectrum,\nemphasizing once again the need for\nspectroscopy in determining membership of even bright stars in the Clouds.\nWe will find that the\ntwo confirmed A-F supergiants turn out to be coeval with the rest of\nthe association members.\n\n{\\it LH90:} Photometry of the LH~90 region was published by Schild \\& Testor\n(1992), who refer to the region as ``Zone 2\", and provide a finding\nchart in their Figure~3. (Only stars 2-33, 2-34, and and 2-45 fall\noutside the association boundary shown by Lucke 1972.) There are three\nclumps of stars, designated as ``clusters\" $\\alpha$, $\\beta$, and\n$\\delta$ by Loret \\& Testor (1984). The region was re-examined by\nTestor et al.\\ (1993), who provided new photometric and\nspectroscopic data on knots $\\alpha$ and $\\beta$.\nClusters $\\beta$ and $\\delta$ were also studied by\nHeydari-Malayeri et al. (1993).\nRecently, Walborn et\nal.\\ (1999) were largely successful in further unraveling the\n$\\beta$ knot of stars using\nWFPC-1 images and FOS spectroscopy with {\\it HST}. (They refer to\n$\\beta$ alternatively as ``NGC~2044 West\" and ``HDE 269828\".) To this,\nwe add our own {\\it UBV} photometry and spectroscopy. \nWe note that a comparison of the high resolution image of Testor et al.\\\n(his Fig.~1b) with that of Walborn et al.\\ (Fig.~5) suggest that \nground-based\nwork actually did a remarkably good job of resolving multiple components in\ncluster $\\beta$. The stars designated ``TSWR2\" and ``TSWR1\" are multiple,\nbut the others are actually well resolved with 1\" resolution.\nThe components found independently by our PSF-fitting are an exact\nmatch to those identified by Testor et al.\nThe most interesting star is the one Testor et al.\\ identify as ``6\" in\ncluster $\\beta$; this is the star labeled ``9\" by Heydari-Malayeri et al.,\nand split into two components (``9A\" and ``9B\") by Walborn et al., although\n9B is 1.5 mag fainter than 9A and hence the composite spectrum we obtained\nfrom the ground is a good representation of star 9A.\nWe have noted earlier (Section~\\ref{Sec-o3s}) that the star $\\beta-13$ is\nprobably better considered an O3~If* star rather than the O4If+ used by\nWalborn et al.\n\nIn our analysis of this region we will make use of our new ground-based data,\nbut defer to the {\\it HST} data of Walborn et al.\\ for stars for the\nthe group of stars called ``TSWR1\" (or $\\beta$-6) by Testor et al.,\nwhich is the star identified as\n``5\" by Heydari-Malayeri et al., split into multiple components by\nWalborn et al. (1999).\nOur ground-based (composite) spectrum would have resulted in\na ``B0I+WN\" designation, but the {\\it HST} work clearly shows that\nthese are separate stars, in accord with Testor et al.'s finding.\nOne wonders if other ``BI+WN\" systems might\nnot be similarly resolved. \nWe also note the need for a high-resolution study of the $\\delta$\nknot in this interesting region.\n\nIn addition to the WN4 component of ``TSWR1\", the association contains\nmany other WRs:\nBr~56 (WN6), Br~57 (WN7), Br~58 (WN5-6), and Br~65 (WN7), all of fairly\nlate type for the LMC, plus the WC4 star Br~62. The classifications are\nfrom Conti \\& Massey (1989), except for that of Br~65, which is from \nBreysacher (1981). Earlier (Section~\\ref{Sec-wrs}) we suggest \nthat Br~58 may be better classified as O3If*/WN6.\n\nIn analyzing this cluster in Section~\\ref{Sec-coeval}, we find that the\n$\\beta$ subclump is no more coeval than the association\nas a whole, as witness the fact that both a B0~I star of modest\nluminosity cohabits with an O3 star of high luminosity.\nThere is a significant range of ages.\n\n\n{\\it LH101:} This region has recent CCD photometry and spectroscopy by \nTestor \\& Niemela (1998). To this, we obtained our own spectra for\nthree of the stars, as discussed in Section~\\ref{Sec-spectra}. \nWe find that ST5-27 is an O3V((f)), as indicated both by\nthe lack of He~I and the weak presence of N~V $\\lambda 4609,19$ absorption; \nthe star was classified as O4~V\nby Testor \\& Niemela. We confirm that their star ST5-31 is indeed an O3If.\nAnd, we reclassify ST5-52 as an ON5.5V((f)) star, rather than O3~V (Section~\\ref{Sec-Os}).\nThe association contains Br~91, another of the rare Ofpe/WN9 objects.\n\n{\\it LH104:} This association was also studied by Testor \\& Niemela (1998).\nWe have obtained new CCD photometry, as well as additional spectroscopy.\nThe association contains three WRs, all of which are spectrum binaries\nas described by Testor \\& Niemela: Br~94 (WC5+O7), Br~95 (WN3+O7), and\nBr~95a (WC5+O6). The visually brightest star is the B[e] star, S~134\n(Zickgraf 1993). We note that one of the visually brighter stars is an M\nstar, confirmed by Testor \\& Niemela as a supergiant on the basis of its\nradial velocity; this agrees with the conclusion of\nMassey \\& Johnson (1998)\nthat WRs and M supergiants are sometimes found in the same associations, contrary\nto the prevailing wisdom.\n\n\\section{Construction of HRDs: \nCoevality and Uncovering the Most Massive Stars}\n\\label{Sec-hrd}\n\nIn order to identify the most massive stars, we construct ``physical\"\nH-R diagrams ($\\log T_{\\rm eff}$ vs. $M_{bol}$) for comparison with \nthe theoretical evolutionary tracks. These tracks will allow us to \ntest for coevality, and determine the masses for the\nhighest mass unevolved (H-burning) stars in these associations.\nFirst, we must correct the observed photometry for reddening, and second\nto convert the data (spectral types and photometry) to effective temperatures\nand bolometric magnitudes. Next we will construct the HRDs and uncover the\nmasses of the most massive stars.\n\n\\subsection{Corrections for Reddening and Testing the Reddening-free\nIndex $Q$}\n\nOur first step in constructing HRDs is to determine the reddening corrections\nfor each region. \nFor stars with spectral types, we adopt the intrinsic colors of FitzGerald\n(1970) as a function of spectral type and compute the color excess $E(B-V)$\ndirectly. Occasionally even a star with a spectral classification has a\nreddening which differs substantially from the other members in a region,\nand so we've chosen to\nconstrain the reddening \nto the range indicated\nby the majority of stars for which there are spectral types. We\nlist in Table~3 the average color excess $\\overline{E(B-V)}$ and ranges of\n$E(B-V)$ we adopt\nfor each of the 19 associations. (For consistency, we re-derived reddenings\neven for the associations with values already in the literature.)\n\nAlthough we obtained spectral types for most of the bright stars in each\nassociation, there are some stars for which we have only photometry.\nRather than de-redden these using $\\overline{E(B-V)}$ we \nemployed a relationship between $Q$ and $(B-V)_o$ to de-redden\neach star individually, using the star's photometry and $\\overline{E(B-V)}$\nas a gauge of whether the star's intrinsic colors were\nsufficiently blue for this method to work.\nWe found that for stars with $Q<-0.2$ for $(B-V)_o\\approx (B-V)-\\overline{E(B-V)}=-0.06$ we could de-redden star by star;\nfor stars with intrinsic colors redder than this amount, we adopted the\naverage reddening. We did further constrain\nthe reddening to the range determined by the majority of stars\nwith spectral types in a region.\n\nSince our earlier work (Massey et al.\\ 1989b, 1995b) it has become clear that\nthe intrinsic colors as a function of spectral type or effective temperatures\nare not extremely well know, particularly for the early B supergiants,\nand we\nhave therefore computed new relationships based $Q$ and $(B-V)_o$ (and\nthe intrinsic colors and effective temperatures) using the \nKurucz (1992) ATLAS9 models, using a metallicity of 0.8 times solar,\na compromise between SMC, LMC, and (local) Galactic abundances.\nWe find $$(B-V)_o=-0.005 + 0.317 \\times Q$$\nregardless of luminosity class.\n\nConstruction of the reddening-free index $Q$ for the stars with spectral type\nallows an independent check upon the accuracy of the photometry: is there\ngood agreement between the observed $Q$ and that $Q$ expected on the basis of\nthe intrinsic colors for that spectral type? We \ndetermine if there is a statistically significant shift in $Q$ for all the\nstars for which we have spectral types in each association. In general we find \ndeviations in $Q$ within 1$\\sigma$ of 0.0. The only exceptions for our new\nphotometry \nare LH~43, for which we adopt a shift $\\Delta Q=-0.13$, and LH~64, for\nwhich we adopt a shift $\\Delta Q=-0.15$ (i.e., in both cases the photometric\n$Q$ must be made more negative to agree with the expectations of the\nspectroscopy). The two regions were imaged within a few minutes of each\nother during the 1996 night at about the same time that the observing\nassistant reported seeing an isolated cloud. Interestingly, the reddening\nvalues we found for these two regions are each quite reasonable, suggesting\nthat it might have been only $U$ which was affected in the two fields.\nInspection of the observing logs confirms that the {\\it U} exposure of\nLH~43 was observed back-to-back with the {\\it U} exposure of LH~64.\nThe next regions observed, LH85/89, appears to have no significant\nphotometric problems. We see no problems with any of the 1985 data, either\npublished or new in this paper. We do find a shift of $\\Delta Q=-0.11$ for\nthe LH~101 photometry published by Testor \\& Niemela (1998).\nAlthough the large\nscatter (0.08~mag) makes this result marginal in significance, and nearly\nall the stars of interest to us have spectral types, we still apply this\ncorrection to their photometry. \n\nThe WFPC2 photometry of LH~9 (``HD 32228\") by Walborn\net al.\\ (1999) also shows a systematic shift in $Q$, with \n$\\Delta Q=-0.07\\pm0.01$(s.d.m.)~mag.\nPresumably this shift is an artifact of their reduction procedure. \nThis shift is larger\nthan any of the ground-based {\\it UBV} data reported here, other than the\ncases noted above, and so it is unlikely due to any problems with the\nspectral-class to $Q$ relationship we adopt. \nWe did not apply any correction to their data as\nwe used only the stars with spectral types in constructing the HRD, although\nthis could have some minor effect on the absolute magnitudes (0.2~mag) and\nhence masses we determine if the problem is in $B-V$ rather than in $U-B$.\n\n\\subsection{Conversion to $\\log T_{\\rm eff}$ and Bolometric Luminosity}\n\nThe final step in constructing the HRDs is to use the data to determine\nthe effective temperature and bolometric luminosity of each star.\n\nFor stars with spectral types, we begin by adopting the spectral type\nto effective temperature scale given by \nVacca et al.\\ (1996) for O-type stars, based as it is on the\nresults of modern hot-star models. This will yield results that are somewhat\nhotter and, thus, somewhat more luminous and massive than the older \neffective temperature scale of Chlebowski \\& Garmany (1991), say, or that\nof Conti (1973).\nFor the early B stars we were faced with a dilemma.\nAs discussed by Massey et al.\\ (1995a) \nthere is a discontinuity in the effective temperature scales of hot stars corresponding to roughly where\nthe modern work of Conti (1973) ended (i.e., O9.5) and earlier works took\nover. In order to smooth the transition, we have adopted the effective\ntemperatures of B0.5-B1 dwarfs and giants as given in Table 3-4 of Conti (1988),\nas those are in excellent agreement both with what we expect on the basis\nof the intrinsic colors from the model atmospheres, and with the spectral\nanalysis of Kilian (1992). For B1.5 and B2 dwarfs and giants, we compromised \nbetween the latter two. For the B-type supergiants, we made use of the\neffective temperatures suggested by Conti (1988),\nthe recent spectroscopic analysis of two early B supergiants by \nMcErlean, Lennon \\& Dufton (1998), a comparison of the intrinsic colors\nlisted by FitzGerald (1970) with those of the \nKurucz model atmospheres, and the effective temperature scale given by\nHumprheys \\& McElroy (1984). In the past we have relied exclusively on\nthe latter; we note here though that this disagrees with the more recent\nanalysis by 0.1 dex from B1~I through B5~I. It is clear that a consistent\neffective temperature scale that extends from O through the B-type stars is\ncurrently lacking, and the compromise we use here is only a stop-gap until\na comprehensive study can be done.\n\n\nFor stars with photometry alone, we rely upon a relationship between\nthe reddening-free parameter\n$Q$ and $\\log T_{\\rm eff}$ determined from the Kurucz models; this relationship\nis given in Table~4, and is appropriate for intrinsically blue stars\n[($Q<-0.6$ and either $(B-V)_o < 0.00$ or $(U-B)_o<-0.6$]. For redder stars,\nwe use a relationship between $(B-V)_o$ and $\\log T_{\\rm eff}$ also given\nin Table~4, based upon the Kurucz models. The latter relationship need not\nbe of high accuracy, as the BC becomes a less steep function of $\\log T_{\\rm eff}$.\n\nThe bolometric correction (BC)\nis a function primarily of effective temperature\nwith little dependence on $\\log g$; we adopt the approximation \n$BC=27.66-6.84\\times \\log{T_{\\rm eff}}$ appropriate to hot stars \n($\\log T_{\\rm eff}>4.2$) given by Vacca et al.\\ (1996).\nFor the cooler supergiants we find discrepancies between\nthe BCs listed by Humphreys \\& McElroy (1984) and the corresponding effective\ntemperatures when compared to the Kurucz models; we adopt the relationship\ngiven in Table~4 based upon a fit of the BCs with $\\log T_{\\rm eff}$ based\nupon the Kurucz models.\n\nWe show the resulting HRDs in Fig~\\ref{fig:hrds}. In these figures, we have\nindicated the stars with spectral types by filled circles, and those stars with\nonly photometry with open circles. Crosses represent stars with only\nphotometry whose placement in\nthe HRD are uncertain for one reason or another: either\ntheir transformations failed because of\nunrealistic colors, resulting in superfluously high effective temperatures\nand locations to the left of the ZAMS, or else\ntheir colors are too red to allow us to\ndetermine their reddening using $Q$, or the derived reddening falls outside\nthe range we adopted on the basis of our spectroscopy. \nWe also mark with\nan asterisk stars with spectral types but whose location is uncertain,\nsuch as the components of double-lined binaries.\nWe include in these diagrams the\nevolutionary tracks of Schaerer et al.\\ (1993) computed at $z=0.008$\n(appropriate for the LMC), and the tracks of Schaller et al.\\ (1992) at $z=0.001$, similar to the $z=0.002$ of the SMC.\n\nWe also show isochrones corresponding\nto ages of 2, 4, 6, 8, and 10~Myr (dashed curves), which we computed\nusing a program kindly provided\nby Georges Meynet. \n\n\\subsection{Identification of the Most Massive Stars, and the Limits of\nCoevality}\n\\label{Sec-coeval}\n\nUsing the results of our calculations in the previous section, we can now\nidentify the mass of the highest mass unevolved (H-burning) star\nin each association. We list the derived quantities ($\\log T_{\\rm eff}$,\n$M_{\\rm bol}$, mass, age) for the highest mass stars in Table~5.\n\nFor associations that are strictly coeval, we expect that the stars in the HRD\nwill follow a single isochrone, and in that case the highest mass would \ncorrespond to a ``turn-off\" mass and we could be confident that any evolved\nmembers of these associations were descended from stars with masses greater\nthan this value. Alas, the HRDs of Fig.~\\ref{fig:hrds}\ndo not for the most part yield\nsuch an unambiguous picture. In all cases there is some spread across\nisochrones. If real, such spreads would tell us that the massive stars formed\nover some period of time.\n\nHow significant are these age spreads? We can answer this quantitatively by\nconsidering the errors associated with the placement of stars in the HRD.\nLet us first consider the {\\it systematic} errors.\nIn Fig.~\\ref{fig:err}(a) \nwe show the location of the spectral type calibration data\nin the HRD. The huge gap among the supergiants \n(upper-most string of points) corresponds to the difference in the\nadopted effective temperature of a B5~I and a B8~I star, which is a realistic\nuncertainty in spectral classification. Smaller gaps\nlikewise correspond to differences of a single spectral type.\nWe have adopted an absolute magnitude corresponding to each type;\nof course, our stars, with $M_V$ computed from the photometry, will fall\nboth above and below the points shown. It is instructive to see the\nsystematic deviation of these stars from the ZAMS as one approaches cooler\ntemperatures among the dwarfs. By log~T$_{\\rm eff}=4.2$ the locations\nof the dwarfs are nearly coincident with the {\\it terminal} main-sequence,\nas indicated by the first switch-back in the tracks.\nIn this region the isochrones are\ntightly spaced, and a large error in the age spread would result if we\ncompared the ages of a high mass luminosity class ``V\" stars with one of\nlower mass; for this reason we should exclude stars below 20$\\cal M_\\odot$\nunless they are of high {\\it visual} luminosity, such as \nan A-type supergiant.\n\nWe note that this progression away from the ZAMS is intrinsic to the spectral\ntype to $\\log T_{\\rm eff}$ calibration we've adopted and/or the\nabsolute visual magnitude scale we've used for the purposes of this\nillustration. Transformations to effective \ntemperatures on the basis of {\\it colors} are usually often based on the use\nof spectral types as an intermediate step, rather than going directly from\nmodel atmosphere colors to effective temperatures. In these cases, the\napparent presence of stars to the right of the ZAMS might be misconstrued as\nevidence of pre-main-sequence objects. \nWe emphasize the need for spectroscopic followups\nto establish the authenticity of such discoveries. \n\nNext, let us consider the\n{\\it random} errors caused by misclassifying stars by a single spectral type\nand/or major \nluminosity class; i.e., calling a star an ``O8~III\" when in fact it is\nan ``O9~I\". (The absolute visual magnitudes of these two subclasses overlap,\nand so our photometry would pose no warning.)\nWe would overestimate the star's luminosity by 0.1~mag simply by assuming a\nslightly too negative $(B-V)_o$, which will lead to too large a value for\n$A_V$. More significant, however, is the fact that we will\noverestimate the star's \neffective temperature by 0.05~dex, and thus overestimate the star's bolometric\ncorrection by 0.4~mag, for a net error of 0.5~mag. The age we calculate might\nbe 3.80~Myr (6.58~dex) if the actual age were 5.25~Myr (6.72~dex). We expect\nmisclassification by a single spectral subtype to be common.\nThe size of the errors we make will depend of course upon the spectral type.\nWe show in Fig.~\\ref{fig:err}(b) \nthe errors associated with misclassification of a star\nby one spectral type and/or luminosity class. (We have not included in this\nfigure the modest addition error caused by the change in reddening adopted;\nthis will increase these errors.)\n\nGiven this discussion, we can ask the question: what fraction of stars\nof 20$\\cal M_\\odot$ and above, and lower-mass supergiants, \nare in fact consistent with some median age for\nthe association? \nWe assume here that our error in spectral sub-typing is only\n1 subtype, except for uncertain cases. We compute the youngest and oldest ages of each star associated with such a misclassification; \nif the cluster's median age falls\nwithin this range, we consider that the star is coeval with the rest of\nthe cluster. We use only the stars for which there\nare spectral information, as the errors in the HRD are much greater for\nstars with only photometry. (Compare Figures~1c and 1d of Massey\net al.\\ 1995b.) \nWe list the fraction of stars that we find to be coeval\nin Table~6, along with the median\nages of the clusters. \n\n\nEven for the clusters that have a large percentage \nof stars whose ages are within 1$\\sigma$ of the \nmedian cluster age, we might well\nask the question if the ages of the\nhighest mass stars are in accord with this value.\nAfter all, we know that in some clusters intermediate mass stars form over\nsome period of time (several million years), \nwith the highest mass stars forming over a shorter\ntime, e.g., NGC~6611 (Hillenbrand et al.\\ 1993) and R136 (Massey \\& Hunter\n1998). We include the median\nage of the three highest mass stars in Table~6. \n\nInspection of the HRDs in Fig.~\\ref{fig:hrds}, \nand of the numbers in Table~6, suggests\nthat there is a natural division, and that some of these associations are\nhighly coeval while the coevality of the\nothers are more questionable. \nIf the match between\nthe median cluster age and the age of the 3 highest mass stars is good\n($<0.2$ dex, comparable to the individual errors), and a large percentage\nof stars ($>80\\%$) lie within 1$\\sigma$ of the median cluster age, we consider\nthat degree of coevality is high. Clusters that fail to meet one or the \nother criterion we consider the degree of coevality questionable. We\nconsider the coevality high in 11 of our clusters, and questionable in four.\nWe regard the other five associations as non-coeval. This could be\nevidence that massive stars have formed over a prolonged period, possibly\nwith several subgroups of different ages contributing, but it may also be simply\ndue to line-of-sight \ncontamination within the Magellanic Clouds.\n\nThe age structure\nof the LH~47/48 was discussed by Oey \\& Massey (1995); as mentioned earlier,\nwe restrict ourselves here to the stars on the periphery of the associated\nsuperbubble, and confirm that these stars at least form a coeval unit.\nLH~90 is a very interesting association located near 30~Doradus, and its\nage structure was explicitly discussed by Testor et al.\\ (1993),\nwho found ``at least\" two distinct age groups (3-4~Myr and 7-8~Myr).\nThey attempted\nto assign membership of the evolved stars to one or the other of these\npopulations based, not upon spatial locale, but on the basis of bolometric\nluminosity, which then assumes an answer about the progenitor masses\n{\\it a priori}. They found that the $\\alpha$ clump itself was not coeval.\nWe have separately examined the $\\beta$ sub-cluster using the improved data\nobtained by Walborn et al.\\ (1999) and find that the same age spread apparent\nin the cluster as a whole is also apparent in this subclump; the $\\beta$\ncluster contains both a B0~I star of modest luminosity and a high luminosity\nO3~If* star. We are, therefore, forced\nto abandon this very interesting region with its large number of WR stars.\n\nWe can perform one other ``reasonability test\" of whether the turn-off\nmasses are relevant for the evolved objects. What is the spatial separation between the three highest mass stars (which typically define the turn-off)\nand the evolved objects? We computed the projected distances, and include the\n{\\it median} of these three values in Table~7, which we discuss in the next\nsection. (We note cases where the turnoff is actually due to the binary\ncompanion.) Here we find that the median separation is 25~pc. As this is the\nmedian, there is always some massive star nearer the evolved object than the\nnumbers shown here. This is consistent with the notion expressed in \nSection~1.1 that coeval massive stars may have originated in the same place,\nas drifts of this order are just what we expect over 3~Myr.\n\nWe can now proceed with some confidence to assign progenitor\nmasses to the evolved stellar content of the coeval regions. \n\n\n\\section{The Progenitor Masses and BCs}\n\n\\subsection{Progenitor Masses}\n\nIn Table~7 we present the main results of this investigation: what are the\nprogenitor masses of various evolved massive stars? We enclose in \nparenthesis values derived from clusters whose coevality is in question,\nand exclude the WR stars from the associations which are non-coeval.\n\nWhat can be conclude from these values? First, \nwe find that the masses of\nthe progenitors of WRs in the SMC are higher than those of the LMC. \nThe data are admittedly sparse, and this conclusion rests to some extent\non what mass we assign to the progenitor of AB7: the three stars with the\nhighest mass in Hodge~53 are all components of spectroscopic binaries.\nWe can be fairly certain that the progenitor mass of AV~332 was greater\nthan that of its companion (i.e., $>80\\cal M_\\odot$), although this\nsupposes that binary evolution itself did not play an important role in\nthis system.\n\nTurning to the WRs in the LMC, we find that there is a considerable\nrange of progenitor masses for the WNEs, with\nminimum masses of 30$\\cal M_\\odot$ through 60$\\cal M_\\odot$. If the\nmore questionable cases were included this would increase the mass range.\nIt appears that stars covering a range of masses pass through\na WNE stage, at least at LMC metallicities.\n\nBoth of the Ofpe/WN9 stars come from associations with very low lower limits---\nin fact, among the lowest in our sample. There is a third Ofpe/WN9 star, one\nlocated in LH~101, which also contains evolved stars of similarly low mass\n(as well as higher mass evolved stars). We might conclude then that the\nOfpe/WN9 stars in fact are not extremely high-mass stars at all, as their\nassociation with (other) LBVs has led others to speculate. \nOur conclusion that Ofpe/WN9 stars are actually ``low-mass\" (30$\\cal M_\\odot$)\nin origin is not\nnew with us: St-Louis et al.\\ (1998) examined five LMC associations containing\nOfpe/WN9 stars, including LH~89 and LH~101, and suggested much the same,\nalthough coevality was a concern for 3 of her 5 clusters. \nSchild (1987) had earlier studied LH~39, and also noticed the relative \nhigh age and low mass for this cluster containing an Ofpe/WN9 star.\nUsing the WR standard atmosphere model, Crowther et al.\\ (1995a) derive\nbolometric luminosities for Br~18 (R~84) and BE~381 that suggest (present)\nmasses of 25 $\\cal M_\\odot$ and 15 $\\cal M_\\odot$ respectively.\n\nThree BI + WN3 stars appear in our sample. Stars with this (composite?)\ntype are among the brightest stars when M~33 was imaged at $\\lambda 1500$\nwith the {\\it Ultraviolet Imaging Telescope} (Massey et al.\\ 1996).\nTo our knowledge, no BI + WN3 star has ever been demonstrated to have a\nspectroscopic orbit. We note with some interest the relatively high minimum\nmasses for the progenitors suggested by our study here, and we believe that\nonly radial velocity studies can resolve the nature of these objects.\n\nThe WCs come from high mass stars, but, interestingly,\nnot significantly higher than do the\nWNs. Naively this would suggest that most massive stars of mass 45-50\nand above go through both a WN {\\it and} a WC stage. Similarly the WC\nstar in the SMC, AB8, has a high minimum mass ($>70\\cal M_\\odot$), not\ntoo different from the WNs in the SMC. \n\nFor the LBVs in the LMC and SMC we find extremely high minimum masses---among the highest of any stars in our study. This is in accord with the\nprevailing notion that they are among the highest mass stars, and owe their\nphotometric outbursts and dramatic spectral changes to instabilities \ninherent to high luminosity. \nThe two B[e] stars in our sample have substantially different masses, in\naccord with the suggestion B[e] stars come from a large range of luminosity\n(Gummersbach et al.\\ 1995).\n\nAlthough the cluster turn-offs provide only {\\it lower limits} to the masses\nof the progenitors of the evolved stars, the mass functions of these and\nother OB associations we've studied are generally well populated\n(cf. Massey 1995a, 1995b). Thus these cluster turn-offs should provide substantial clues to the {\\it actual} masses of the progenitors. \n\n\n\\subsection{The Bolometric Corrections}\nWe next turn to computing the BCs for these evolved\nstars, using the {\\it observed} $M_V$ of the star, and the $M_{bol}$ of\nthe cluster turn-off stars. Previous efforts to do this (cf.\\ Humphreys et al.\\ 1985)\nrelied on the fact that little change occurs in the bolometric luminosity of\na massive star as it evolves, a fact simply traced to the fact that the core\nmass remains relatively unaffected during main-sequence evolution. Here we\npropose to do somewhat better, by using the evolutionary models to make\na modest correction for evolution.\n\nSmith (1968b) introduced a narrow-band \nphotometric system to reduce the\neffect of WR emission lines on photometry; her {\\it ``v\"} filter is centered\nat $\\lambda 5160$ has has a zero-point tied to the system of \nspectrophotometric standards. For a lightly reddened star with no emission,\nbroad-band Johnson {\\it V} and Smith's \n{\\it v} are equivalent. ($V-v=-0.02-0.36\\times(b-v)$ according to Conti\n\\& Smith 1972; a typical $b-v$ value\nfor a MC WR star is -0.1~mag, e.g. Table~VI of Smith 1968b. See also\nTurner 1982.) We therefore\nuse the {\\it ``v\"} mags listed by Breysacher et al.\\ (1999)\nwhen available to compute $M_V$, using the average reddenings we find\nfor each association. We list these values in Table~7.\n\nWe can make two assumptions for computing the BCs. The first\nof these is to assume that the bolometric luminosity of the WR star is the\nsame as that of the cluster turn-off. The second is to attempt to make a\ncorrection for the luminosity evolution that the models predict. The \ndifficulty with the latter is that what the evolutionary models predict \nis a very sensitive function of how mass-loss is treated, and, as we\nemphasized earlier in this paper, the episodic shedding of mass during the\nLBV phase can play an appreciable role and is difficult to model. The\nGeneva models do not produce WR stars when standard mass-loss rates are\napplied except at the very highest masses, and for this reason mass-loss\nrates twice that of the observed values have been assumed in some of the\nmodel calculations (e.g., Meynet et al.\\ 1994). From the end of core H-burning\n(similar to the stage of the highest mass stars near the cluster turn-off) to\nthe end of the WR phase, the evolution amounts to -1.1~mag to +0.5~mag\nat LMC metallicities, and +0.1~mag to +0.2~mag at SMC metallicities in\nthe sense of $M_{\\rm bol}$ at the end of core H-burning {\\it minus}\n$M_{\\rm bol}$ at the end of stellar models. \nWe include the BCs in Table~7 computed both ways, using the $M_{\\rm bol}$\ncorresponding to the end of core-H burning (i.e., the terminal age\nmain-sequence, or TAMS) and corresponding to the adopted mass of the cluster\nturn-off. \n\nWe see that the BCs for the WNE stars are indeed very negative, approximately\n$-6$~mag, whether evolution is taken into account or not. This is in good\naccord with similar analysis of Galactic clusters by Humphreys et al.\\ (1985)\nand Smith et al.\\ (1994), although this is considerably more negative than \nthat of even\nthe earliest O-type stars ($-5$~mag). However, recent applications\nof the ``standard WR model\" applied to ``weak-lined\" \nWNE stars\nby Crowther et al. (1995c) have found similar values for the BCs, giving us\nconfidence both in our method, and providing yet another indication that\nthe models provide a solid basis for interpreting the spectra of WR stars.\nThere is a large range present for the BCs of WNE stars shown in Table~7,\nwith perhaps some trend with spectral subclass; i.e., more negative with\nearlier type. It will be interesting to see if additional atmosphere\nanalysis produces similar results when applied to WN2 stars.\n\nThe Ofpe/WN9 stars have far more modest BCs ($-2$ to $-4$~mag); analysis\nby Crowther et al.\\ (1995a)\nof Br~18 (R~84) BE~381 using the ``standard WR model\" derives BCs of $-2.6$ and\n$-2.7$~mag, also in good agreement with what we find.\n\nTurning to the WCs, we find BCs of order $-5.5$~mag. This is a little more\nnegative than what Humphreys et al.\\ (1995) and Smith et al.\\ (1994) found,\nalthough none of the WCs in their samples were as early as those studied\nhere.\n\nThe BCs for S~Dor and R~85 are very modest ($-2$~mag). \nCrowther (1997) computes a similar BC for the LBV R~127, although we note\nthat this star is another Ofpe/WN9, or was until its outburst. We have used\nour own photometry obtained of HD~5980 obtained in 1985 (Massey et al.\\ 1989b)\nto compute its absolute visual magnitude; given the complicated nature of\nthis (multiple) star, it is unclear what to make if its value. The bolometric\nluminosity of S~134 computed by Zickgraf et al.\\ (1986) is $\\sim -10$,\nin excellent agreement with the assumptions here.\n\n\\section{Conclusions, Discussion, and Summary}\n\nOur photometric and spectroscopic investigation of 19 OB associations in the\nMagellanic Clouds has found that most of the massive stars have\nformed within a short time ($<$1~Myr) in about half of the regions\nin our sample. Their degree of coevality is similar to that found\nby Hillenbrand et al.\\ (1993) for NGC~6611, i.e., that the data are\n{\\it consistent} with all of the massive stars ``having been born on a\nparticular Tuesday.\" In other regions,\nstar-formation of the massive stars may have proceeded over a longer time,\nas suggested by\n the presence of evolved stars of 15-20$\\cal M_\\odot$ (suggesting\nages of 10~Myr) along with unevolved stars of high mass (60 $\\cal M_\\odot$)\nwith ages of only 2~Myr. In some cases such apparent non-coevality may be due\nto chance line-of-sight coincidences within the Clouds, or to drift of lower\nmass stars into the space occupied by a truly coeval OB association, but\nin other cases, such as the $\\beta$ subcluster of LH~90, one is forced to\nconclude that star-formation itself was not very coeval, but proceeded over \nseveral million years.\n\nThe turn-off masses of the coeval associations have provided considerable\ninsight into the evolution of massive stars. We find that only the\nhighest mass stars ($>70 \\cal M_\\odot$) become WRs in the SMC.\nThe numbers are admittedly sparse, and an additional\ncomplication is the fact that most SMC WRs show the presence of absorption\nlines. Are these absorption lines indicative of a weak stellar wind \n(as evidenced by the weakness\nof the WR emission lines) or are these all due to binary companions? \nConti et al.\\ (1989) discuss this without reaching any conclusions, and we note\nhere that the issue of the binary frequency of the SMC WR stars requires\nfurther\ninvestigation. Possibly a strong stellar wind due to very high luminosity\n{\\it and}\nbinary-induced mass-loss is needed to become a WR star in the low metallicity\nof the SMC.\n\nIn the LMC the mass limit for becoming a WR star would appear to be a great deal\nlower, possibly 30$\\cal M_\\odot$. Stars with a large range of initial masses\n(30-60 $\\cal M_\\odot$), and possibly {\\it all} massive stars with a mass\nabove 30$\\cal M_\\odot$ go through a WNE stage in the LMC. Most WR stars in the\nLMC are of early WN type; this is not true at the higher metallicity of the\nMilky Way, where WN3 and WN4 stars are relatively rare. This is consistent\nwith recent theoretical work \nof Crowther (2000), who finds that varying only\nthe abundance in synthetic WN models \n(holding all other physical parameters consist) changes the spectral subtype,\nwith WNEs characteristic of low abundances, and WNLs characteristic of higher\nabundances. Thus, it may be the excitation classes are related neither to\nthe masses nor to stellar temperatures.\n\nThe true LBVs \noccurs in clusters with very high turn-off masses ($\\approx 85\\cal M_\\odot$),\nboth in the LMC and the SMC. This is very similar to the turn-off mass in\nthe Trumpler 14/16 complex with which the Galactic LBV $\\eta$~Car is associated\n(Massey \\& Johnson 1993). This supports the standard picture, that LBVs are\nan important, if short-lived, phase in the evolution of the most massive stars,\nat least at the metallicities that characterize the Magellanic Clouds and the\nMilky Way. We note with interest the important study by King, Gallagher, \\& Walterbos (2000), who find that some LBV stars in M~31 appear to be found in\nrelative isolation, leading them to question whether these are all high\nmass stars, at least at the higher metallicity of M~31.\n\nThe Ofpe/WN9 stars, some of which go through some sort of outburst, cannot\nbe ``true\" LBVs, if the nature of the latter is tied to extremely high\nbolometric luminosities. We find that the Ofpe/WN9 stars have the {\\it lowest}\nmasses of {\\it any} WRs, with the progenitors possibly as low as 25$\\cal M_\\odot$. Similarly, the connection of the B[e] stars to LBVs seems tenuous\non the basis of mass or bolometric luminosities.\n\nWe know that the relative\nnumber of WC and WN stars change drastically throughout the Local Group, in\na manner well-correlated with metallicity (Massey \\& Johnson 1998). \nOne obvious\ninterpretation of this is that it is much harder to lose enough mass to\nbecome a WC star in a low-metallicity environment; i.e., only the most\nluminous and massive stars have sufficiently high mass-loss rates to achieve\nthis. And, similarly, the limit for WN stars should be higher in lower\nmetallicity systems. As long as the bar is somewhat lower for achieving WN\nstatus compared to WC status, then the IMF assures that the WC/WN ratio will\nchange. Thus our finding here that WCs and WNs come from similar mass\nranges (although higher in the SMC than in the LMC), suggest that an\nalternative explanation is needed.\nInstead, it may be that it is the relative lifetimes of the WC and\nWN stages which are different at different masses; i.e.,\nat very high masses the WC stage is shorter compared to the length of the WN\nstage than at lower masses. Or, it could be that the metallicity itself\naffects the relative lifetimes of the WC and WN stages. We note that we\nfound luminous red supergiants (RSGs) cohabiting with both WNs and WCs in many\nOB associations in more distant galaxies of the Local Group (Massey \\& Johnson\n1998; see for example their\nFigs.~14-16). While we were unable to evaluate the degree of coevality\nof these associations, the statistics suggest that these stars\nhave similar progenitor mass at a given metallicity, \nand that variations in the relative number of\nRSGs to WRs are due primarily to changes in the relative lifetimes due to\nthe effect of metallicity on the mass-loss rates (Azzopardi, Lequeux, \n\\& Maeder 1988).\n\nWe conclude that the BCs of WNE stars are quite substantial,\n$-6$ mag. This value is in very good accord with that determined from\nweak-lined WNE stars using the WR ``standard model\" of Hillier (1987, 1990)\nby Crowther et al.\\ (1995c). The earliest-type\nWN star known (of type WN2) \nis included in our sample, and our data suggest an even\nmore striking BC ($<-7.5$~mag); a full analysis of Br~4 via the standard model\nwould be of great interest.\nFor the Ofpe/WN9 stars we find BCs of $-2$ to\n$-4$~mag, again in good agreement with the atmospheric analysis of several\nsuch stars by Crowther et al.\\ (1995a). We find here that the BCs of WC4\nstars are typically about $-5.5$~mag.\n\nIn the next paper, we will extend this study to the higher metallicities found\nin our own Milky Way galaxy.\n\n\\acknowledgements\n\nWe are grateful to Nichole King for correspondence on the issue of LBVs\nand their native environments, as well as useful comments on the manuscript.\nDeidre Hunter was also kind enough to provide a critical reading of\nthe paper.\nWe thank Bruce Elmegreen for correspondence and helpful preprints concerning coevality in extended regions. Comments by an anonymous referee resulted in\nimproved discussion.\nClassification of some of the older spectra\nwere done in collaboration with C. D. Garmany.\nBruce Bohannan kindly allowed us to use his\nphotographic spectrum of R~85 in this work. The participation of one of the authors (E.W.) was made possible through\nthe Research Experiences for Undergraduate Program, which \nwas supported by the National Science Foundation under Grant No. 9423921.\nP.M. acknowledges the excellent support provided by the CTIO TELOPS group.\n\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table1a.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table1b.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table2a.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table2b.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table2c.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table2d.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table2e.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table2f.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table2g.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table2h.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table2i.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table3.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table4.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table5a.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table5b.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table5c.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table5d.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table6.ps}\n\\end{figure}\n\n\\clearpage\n\\begin{figure}\n\\epsscale{1.15}\n\\plotone{table7.ps}\n\\end{figure}\n\\begin{references}\n\\reference {} Anthony-Twarog, B. 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Lequeux (Berlin: Springer-Verlag), 257\n\\reference {} Zickgraf, F.-J., Kovacs, J., Wolf, B., Stahl, O., Kaufer, A.,\n\\& Appenzeller, I. 1996, A\\&A, 309, 505\n\\reference {} Zickgraf, F.-J., Wolf, B., Stahl, O., Leitherer, C., \\& Appenzeller, I. 1986, \nA\\&A, 163, 119\n\n\\end{references}\n\\clearpage\n\n\\figcaption{Three spectra of the suspected LBV R~85 are shown. The star was classified by Feast et al.\\ (1960) as an B5~Iae, roughly consistent with the \nspectrum we obtained in January 1999. Spectra from two earlier times show a veiled appearance, with a spectral type that is cooler, based upon the lack of He~I $\\lambda 4771$ compared to neighboring Mg~II $\\lambda 4481$.\n\\label{fig:r85}}\n\n\\figcaption{The spectra of two O3~If* stars are shown\n(LH90$\\beta-13$ and ST5-31 in LH~101), along with\nthat of an O3~III(f*) star (W16-8 in LH~64).\n\\label{fig:o31}}\n\n\\figcaption{The spectra of two O3~V(f*) stars, ST2-22 in LH~90 [previously\nclassified as O3 ~III(f) by Testor et al.\\ 1993], and W28-23 \nin LH~81. The\nthird star, W28-5, also in LH~81, appears to be intermediate between O3~V and\nO4~V, as the He~I $\\lambda 4471$ strength would imply an O4 \nclassification, while the presence of N~V $\\lambda 4603,19$ \nabsorption would suggest an O3 description.\n\\label{fig:o32}}\n\n\\figcaption{The spectra of several early O-type dwarfs are show.\n\\label{fig:oms}}\n\n\\figcaption{The spectra of several O-type supergiants are shown.\n\\label{fig:osgs}}\n\n\\figcaption{The star Br~58 in LH~90 \nhas previously been called a WR star of type\nWN5-6 or WN6-7. We suggest here that it may be better described as one of\nthe H-rich transition objects of type O3~If*/WN6, i.e., an O3~If* star that\nis so luminous that its stellar wind has come to resemble a WR star. (See\ndiscussion in Massey \\& Hunter 1998.) The B0I+WN star W28-10, in LH~81, is\nnewly discovered here.\n\\label{fig:wrs}}\n\n\\figcaption{The H-R diagrams for the 19 OB associations studied here are shown. Stars for which spectral types were available are shown by\nfilled circles; stars for which only photometry was available are shown by\nopen circles. Asterisks represent stars with spectral types but whose location\nin the HRD is considered particularly uncertain, usually the components of\nspectroscopic binaries. The location of the stars\ndenoted by the ``+\" symbol are particularly\nuncertain in the HRD. The solid lines show the evolutionary tracks for\nthe various (initial) masses as indicated. The dashed lines are isochrones\nat 2~Myr, 4~Myr, 6~Myr, and 10~Myr. The tracks and isochrones come from\nthe $z=0.001$ models of Schaller et al.\\ (1992) for the SMC associations, and\nfor the $z=0.008$ models of Schaerer et al.\\ (1993) for the LMC associations.\n\\label{fig:hrds}}\n\n\\figcaption{How much of an error in age or mass is made by misclassifying a\nstar by a single spectral type? The tracks and isochrones shown in these\nHRDs are the same as in Fig.~\\ref{fig:hrds} computed for LMC metallicity.\nIn (a) we show explicitly the discontinuities and gaps associated with \nadjacent spectral classification, as well as the systematic deviation\nfrom the ZAMS at lower masses. The upper sequence (supergiants) include\nspectral \ntypes O3, O4, O5, O5.5, O6, O6.5, O7, O7.5, O8, O8.5, O9, O9.5, B0, B0.2,\nB0.5, B1, B1.5, B2, B3, B5, B8, A0, A2, A5, A9, and F2.\nThe middle sequence (giants) include the same spectral types, but\nterminating at B2. The bottom sequence (dwarfs)\ninclude the same sequence as the supergiants, but terminating at B3.\nIn (b) we show the errors that would\nresult for a misclassification by a single spectral subtype and/or\nluminosity class for representative\npoints drawn from (a). The points shown correspond to \nO3~I, O6~I, O8~I, B0~I, B1.5~I, B8~I, and A5~I among the upper sequence. \nThe four giants shown in the middle sequence are: O5.5~III, O7.5~III, O9.5~III,\nand B1~III. The five dwarfs shown along the bottom sequences are:\nO4~V, O6.5~V, O8.5~V, B0.2~V, and B2~V. The error bars extend considerably\nfurther than adjacent points in (a) because we have also included the\npossibility of misclassification by a luminosity class; e.g., the possibility\nthat a star classified as an O7~III might actually be an O8~V.\n\\label{fig:err}}\n\n%\\input{figs}\n\\end{document}\n"
}
] |
[] |
astro-ph0002234
|
The SCUBA Local Universe Galaxy Survey I. First Measurements of the Submillimetre Luminosity and Dust Mass Functions
|
[
{
"author": "Loretta Dunne$^{1}$"
},
{
"author": "Stephen Eales$^{1}$"
},
{
"author": "Michael Edmunds$^1$"
},
{
"author": "Rob Ivison$^2$"
},
{
"author": "\\cr Paul Alexander$^3$ and David L. Clements$^1$"
},
{
"author": "$^1$Department of Physics and Astronomy"
},
{
"author": "PO Box 913"
},
{
"author": "Cardiff"
},
{
"author": "CF2 3YB"
},
{
"author": "$^2$ Department of Physics and Astronomy"
},
{
"author": "Gower Street"
},
{
"author": "London WC1E 6BT"
},
{
"author": "$^3$ Department of Astrophysics"
},
{
"author": "Cavendish Laboratory"
},
{
"author": "Madingley Road"
},
{
"author": "Cambridge CB3 0HE"
}
] |
%\end{center} %\bigskip %\parindent = 20pt This is the first of a series of papers presenting results from the SCUBA Local Universe Galaxy Survey (SLUGS), the first statistical survey of the submillimetre properties of the local universe. As the initial part of this survey, we have used the SCUBA camera on the James Clerk Maxwell Telescope to observe 104 galaxies from the IRAS Bright Galaxy Sample. We present here the 850$\mu$m flux measurements. The 60, 100, and 850$\mu$m flux densities are well fitted by single-temperature dust spectral energy distributions, with the sample mean and standard deviation for the best-fitting temperature being $T_{{d}}= 35.6\, \pm\, 4.9\,{K}$ and, for the dust emissivity index $\beta=1.3\, \pm\, 0.2$. The dust temperature was found to correlate with 60$\mu$m luminosity. The low value of $\beta$ may simply mean that these galaxies contain a significant amount of dust that is colder than these temperatures. We have estimated dust masses from the 850$\mu$m fluxes and from the fitted temperature, although if a colder component at around 20 K is present (assuming a $\beta$ of 2) then the estimated dust masses are a factor of 1.5--3 too low. We have made the first direct measurements of the submillimetre luminosity function (LF) and of the dust mass function. Unlike the {\em IRAS\/} 60$\mu$m LF, these are well fitted by Schechter functions. The slope of the 850$\mu$m LF at low luminosities is steeper than $-2$, implying that the LF must flatten at luminosities lower than we probe here. We show that extrapolating the 60$\mu$m LF to 850$\mu$m using a single temperature and $\beta$ does not reproduce the measured submillimetre LF. A population of `cold' galaxies ($T_{{d}} < 25 {K}$) emitting strongly at submillimetre wavelengths would have been excluded from the $60 \mu$m selected sample. {\em IF\/} such galaxies do exist then this estimate of the 850$\mu$m is biased (it is underestimated). Whether such a population does exist is unknown at present. We have correlated many of the global galaxy properties with the FIR/submillimetre properties. We find that there is a tendency for less luminous galaxies to contain hotter dust and to have a greater star-formation efficiency (cf. Young 1999). The average gas-to-dust ratio for the sample is $581\pm 43$ (using both the atomic and molecular hydrogen) which is significantly higher than the Galactic value of 160. We believe this discrepancy is likely to be due to a `cold dust' component at $T_{{d}}\leq 20\, K$. There is a surprisingly tight correlation between dust mass and the mass of molecular hydrogen, estimated from CO measurements, with an intrinsic scatter of $\simeq$50 per cent.
|
[
{
"name": "abstract.tex",
"string": "%\\documentclass[a4paper,12pt,fleqn]{article}\n%\\pagestyle{empty}\n%\\setlength{\\textwidth}{38em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\addtolength{\\oddsidemargin}{-10mm}\n%\\addtolength{\\evensidemargin}{-10mm}\n\n%\\begin{document}\n%\\parindent = 0pt\n\n%\\centerline{\\bf The SCUBA Local Universe Galaxy Survey I. First Measurements}\n%\\centerline{\\bf of the Submillimetre Luminosity and Dust Mass \n%Functions}\n\n%\\vspace{0.4in}\n\n%\\centerline{Loretta Dunne$^1$, Stephen Eales$^1$, Michael Edmunds$^1$, \n%Robert Ivison$^2$,}\n%\\centerline{Paul Alexander$^3$ \\& David Clements$^1$, }\n\n%\\vspace{1.0in}\n%\\centerline{Received\\underline{\\hspace{3.5cm}}; Accepted\\underline{\\hspace{3.5cm}}}\n%\\vspace{3.5in}\n\n%\\underline{\\hspace{8.5cm}}\n%\\bigskip\n\n%1 Department of Physics and Astronomy, Cardiff University,\n%P.O. Box 913, Cardiff CF2 3YB\n\n%\\bigskip\n\n%2 Department of Physics and Astronomy, University College London, Gower\n%Street, London WC1E 6BT\n\n%\\bigskip\n\n%3 Department of Astrophysics, Cavendish Laboratory, Madingley Road,\n%Cambridge CB3 0HE\n\n%\\vspace{1.0in}\n%\\centerline{Received\\underline{\\hspace{3.5cm}}; Accepted\\underline{\\hspace{3.5cm}}}\n%\\vspace{3.5in}\n\n%\\underline{\\hspace{8.5cm}}\n%\\bigskip\n\n%\\vspace{1.0in}\n\\title[The SCUBA Local Universe Galaxy Survey I]{The SCUBA Local Universe Galaxy Survey I. First Measurements of the Submillimetre Luminosity and Dust Mass Functions}\n\\author[Loretta Dunne et al.]\n{Loretta Dunne$^{1}$, \nStephen Eales$^{1}$, \nMichael Edmunds$^1$,\nRob Ivison$^2$,\\cr \nPaul Alexander$^3$ \nand David L. Clements$^1$\\\\\n$^1$Department of Physics and Astronomy, University of Wales Cardiff,\nPO Box 913, Cardiff, CF2 3YB\\\\\n$^2$ Department of Physics and Astronomy, University College London, Gower\nStreet, London WC1E 6BT\\\\\n$^3$ Department of Astrophysics, Cavendish Laboratory, Madingley Road,\nCambridge CB3 0HE\\\\ }\n\n\\maketitle\n\n%\\newpage\n\n%\\begin{center}\n\\begin{abstract}\n%\\end{center}\n\n%\\bigskip\n\n%\\parindent = 20pt\n\nThis is the first of a series of papers\npresenting results from the SCUBA Local Universe Galaxy Survey\n(SLUGS), the first statistical survey of the\nsubmillimetre properties of the local universe. As the initial part\nof this survey, we have used the SCUBA camera on the James Clerk Maxwell\nTelescope to observe 104 galaxies from the IRAS Bright Galaxy Sample.\nWe present here the 850$\\mu$m flux measurements.\n\nThe 60, 100, and 850$\\mu$m flux densities are well fitted by\nsingle-temperature dust spectral energy distributions, with the sample\nmean and standard deviation for the best-fitting temperature being\n$T_{\\rm{d}}= 35.6\\, \\pm\\, 4.9\\,\\rm{K}$ and, for the dust emissivity index\n$\\beta=1.3\\, \\pm\\, 0.2$. The dust temperature was found to correlate with\n60$\\mu$m luminosity. The low value of $\\beta$ may simply mean that\nthese galaxies contain a significant amount of dust that is colder\nthan these temperatures. We have estimated dust masses from the\n850$\\mu$m fluxes and from the fitted temperature, although if a colder\ncomponent at around 20 K is present (assuming a $\\beta$ of 2) then\nthe estimated dust masses are a factor of 1.5--3 too low.\n\nWe have made the first direct measurements of the submillimetre\nluminosity function (LF) and of the dust mass function. Unlike the\n{\\em IRAS\\/} 60$\\mu$m LF, these are well fitted by Schechter\nfunctions. The slope of the 850$\\mu$m LF at low luminosities is\nsteeper than $-2$, implying that the LF must flatten at luminosities\nlower than we probe here. We show that extrapolating the 60$\\mu$m LF\nto 850$\\mu$m using a single temperature and $\\beta$ does not reproduce\nthe measured submillimetre LF. A population of `cold' galaxies ($T_{\\rm{d}} <\n25 \\rm{K}$) emitting strongly at submillimetre wavelengths would have\nbeen excluded from the $60 \\mu$m selected sample. {\\em IF\\/} such\ngalaxies do exist then this\nestimate of the 850$\\mu$m is biased (it is underestimated). Whether\nsuch a population does exist is unknown at present. \n\nWe have correlated many of the global galaxy properties with the\nFIR/submillimetre properties. We find that there is a tendency for\nless luminous galaxies to contain hotter dust and to have a greater\nstar-formation efficiency (cf. Young 1999). The average gas-to-dust\nratio for the sample is $581\\pm 43$ (using both the atomic and molecular\nhydrogen) which is significantly higher than the Galactic value of\n160. We believe this discrepancy is likely to be due to a `cold dust'\ncomponent at $T_{\\rm{d}}\\leq 20\\, \\rm K$. There is a surprisingly\ntight correlation between dust mass and the mass of molecular\nhydrogen, estimated from CO measurements, with an intrinsic scatter of\n$\\simeq$50 per cent.\n\\end{abstract}\n\n\\begin{keywords}\ndust, extinction;galaxies -- ISM -- galaxies;luminosity\nfunction, mass function -- galaxies;starburst -- infrared;galaxies\n-- submillimetre.\n\\end{keywords}\n \n\n%\\end{document}\n\n"
},
{
"name": "bib.tex",
"string": "%\\documentclass[a4paper,12pt,fleqn]{article}\n%\\pagestyle{empty}\n%\\setlength{\\textwidth}{38em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\addtolength{\\oddsidemargin}{-10mm}\n%\\addtolength{\\evensidemargin}{-10mm}\n\n\n%\\begin{document}\n\n\n\\begin{thebibliography}{}\n\n\\bibitem{} Alton P. B. et al., 1998a, A\\&A, 335, 807\n\n\\bibitem{} Alton P. B., Bianchi S., Rand R. J., Xilouris E., Davies\nJ. I., Trewhella M., 1998b, ApJ, 507, L125\n\n\\bibitem{} Avni Y., Bahcall J. N., 1980, ApJ, 235, 694\n\n\\bibitem{} Barger A. J., Cowie L. L., Sanders D. B., Fulton E.,\nTaniguchi Y., Sato Y., Kawara K., Okuda H., 1998, Nat., 394, 248\n\n\\bibitem{} Barger A. J., Cowie L. L., Sanders D. B., 1999, ApJ, 518,\nL5\n\n\\bibitem{} Blain A. W., Kneib J.-P., Ivison R. J., Smail I., 1999a,\nApJ, 512, L87 \n\n\\bibitem{} Blain A. W., Smail I., Ivison R. 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},
{
"name": "conc.tex",
"string": "%\\documentclass[a4paper,12pt,fleqn]{article}\n%%\\pagestyle{empty}\n%\\setlength{\\textwidth}{38em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\addtolength{\\oddsidemargin}{-10mm}\n%\\addtolength{\\evensidemargin}{-10mm}\n\n%\\begin{document}\n\\parindent = 1em\n\n\\section{CONCLUSIONS}\n\nWe have undertaken the first statistical survey of the local universe\nwith the SCUBA bolometer array on the JCMT. We present here the\ninitial results from the first of the samples we are surveying: a\nsample of 104 galaxies selected at 60$\\mu$m from the {\\em IRAS\\/}\nBright Galaxy Sample.\\\\\n\n(i) The 60, 100 and 850$\\mu$m fluxes are well fitted by single\ntemperature SEDs. The mean and standard deviation (S.D.) in the\nbest-fitting dust temperature is $\\overline{T_{\\rm{d}}} = 35.6\\, \\pm\\, 4.9$ K with the mean and S.D. for the\nemissivity index being $\\overline{\\beta} = 1.3\\, \\pm\\, 0.2$. We\ndo not however, rule out the possibility of colder dust and a steeper\nemissivity. If $\\beta = 2$ and we assume there is a cold dust\ncomponent with a temperature of 20 K, we then obtain dust masses a\nfactor of 1.5--3 higher. The 450$\\mu$m data obtained for 30 per cent\nof the galaxies may eventually constrain the submillimetre emissivity index\nand therefore the presence of a cold component.\n\n(ii) We have presented the first direct measurements of the\nsubmillimetre luminosity and dust mass functions. They are well fitted\nby Schechter functions, in contrast to the {\\em IRAS\\/} 60$\\mu$m LFs\n(Lawrence et al. 1986; Rieke \\& Lebofsky 1986) which do not have the\nexponential cut-off required by the Schechter function. The slope of\nthe 850$\\mu$m LF at low luminosities is steeper than $-2$ implying that the\nLF must flatten at lower luminosities than were probed by this\nsurvey. The optically selected sample currently being observed will\ntake the submillimetre LF to lower luminosities and constrain the\n`knee' of the LF. The shape of the dust mass function is affected by\nthe model assumed for the temperature distribution.\n\n(iii) We have shown that a simple extrapolation of the {\\em IRAS\\/}\n60$\\mu$m LF to 850$\\mu$m using a single dust temperature and\nemissivity index does not reproduce the measured submillimetre LF, both in\nterms of normalisation and shape. \n\n(iv) A correlation was found between the fitted dust temperature and \n60$\\mu$m luminosity. This is best explained by the sensitivity of\nthe 60$\\mu$m flux to temperature (due to its position on the Wien side\nof the grey-body curve) rather than by a dependence on galaxy\nmass. Accounting for this temperature dependence when extrapolating\nthe 60$\\mu$m LF to submillimetre wavelengths produces a much better\nmatch to the observed 850$\\mu$m LF.\n\n(v) If there is a population of cold ($T_{\\rm{d}} < 25$ K) galaxies\nwhich are also luminous submillimetre sources, then our submillimetre\nLF is likely to be biased, as these objects would not have appeared in\nthe original {\\em IRAS\\/} bright galaxy sample which was selected at\n60$\\mu$m. The question of a missing population will be addressed by\nthe optically selected sample. \n\n(vi) We find an average value for the gas-to-dust ratio ($G_{\\rm{d}}$)\nof $581 \\pm 43$ where the gas mass is taken to be $M_{\\rm{HI}} +\nM_{\\rm{H_2}}$. This is lower than previous values determined using\n{\\em IRAS\\/} fluxes alone ($\\sim 1000$) indicating that the\nsubmillimetre is a better place to measure the dust mass. It is still,\nhowever, a factor of $\\sim 3.5$ higher than the value obtained for the\nGalaxy (Sodroski et al. 1994). Using `cold dust masses', calculated on\nthe basis of there being a $20 \\rm{K}$ component in addition to the warm\ndust, $G_{\\rm{d}}$ was reduced to 293. This supports the idea that the\nprevious large discrepancies in $G_{\\rm{d}}$ for our own Galaxy (using\n{\\em COBE\\/} data), and that of other galaxies (which use {\\em IRAS\\/}\nmeasurements), are due to a cold dust component which has gone\nundetected by {\\em IRAS\\/}.\n\n(vii) The relationship between the mass of molecular hydrogen (as\ndetermined from CO observations) and dust mass shows very little\nintrinsic scatter ($\\leq 50$ per cent) which implies that the CO to\nH$_2$ conversion, `$X$', depends on metallicity in the same way as the\ndust mass.\n\n(vii) The star formation efficiency as traced by\n$L_{\\rm{fir}}/M_{\\rm{H_2}}$ was found to be anti-correlated with\ngalaxy size (as measured by blue luminosity), a result also found by\nYoung (1999) using a different technique. The star formation\nefficiency for these galaxies is higher on average than that for the\nGalaxy by a factor of $\\sim 3$ (13.3 for the sample compared to 4 for\nthe Milky Way).\\\\\n\n\\subsubsection*{FUTURE WORK}\n\nObservations which would further our understanding of the properties\nof dust in galaxies and refine our initial estimates of the LF are as follows:\n\n\\begin{itemize} \\item Shorter wavelength (300 -- 600$\\mu$m) data from\nSCUBA and from SHARC on the CSO will allow us to ascertain the presence\nof any cold dust component in these galaxies and whether it is\nuniform (i.e. is the cold component similar in all the\ngalaxies or does it vary as a function of some other\nproperty). Determining the existence of such a cold dust will allow a\nmuch more accurate estimate of the dust mass (and hence the dust mass\nfunction) to be made.\n\n\\item In order to resolve some of the questions unanswered by this paper we\nwill need to complete the survey of an optically selected sample. This\nwill help to constrain the behaviour of the low luminosity end of the\n850$\\mu$m LF (i.e. the turn-over) and also establish whether there is\na population of `cold' galaxies missing from this {\\em IRAS}\nsample. We will then be able to investigate the differences between\nthe {\\em IRAS} galaxies when compared to `normal' optically selected\ngalaxies in terms of their dust properties.\n\n\\item The 850$\\mu$m LF also requires more data points at the high\nluminosity end. This sample contained only a few very luminous objects\nbecause of the high flux limit for the BGS. Observations of a complete\nsample of ULIRGS at 850$\\mu$m would prove very useful in this respect.\n\n\\item More CO and HI measurements, for those galaxies in both the {\\em\nIRAS} and optically selected samples which do not have them already,\nwould increase the statistical significance of the gas and dust\ncomparisons. In addition, detailed mapping in both HI and CO would be\nof great importance in determining the relationship of the dust to the \ndifferent gas phases of the ISM. Work on obtaining this data is in\nprogress.\n\n\\item Optical imaging would enable a\ncomparison of the optical structures with those in the\nsubmillimetre. Of importance is the radial profile and scale height of \nthe dust compared to the stars. Extinction maps could be created from\nmulti-colour optical data and compared with the submillimetre maps, a\ntechnique described by Trewhella (1998).\n\\end{itemize}\n\n\\section*{ACKNOWLEDGMENTS}\n\nWe would like to thank all of the support staff at the JCMT as well as\nany observers who took data on our behalf when the conditions were too\npoor for their own projects. In particular, we are grateful to Wayne\nHolland for the 'out of hours' support after our runs were over. We\nalso thank Paul Alton for useful discussions and information about NGC\n891. The work of L. Dunne, S. Eales, M. Edmunds, R. Ivison and\nD. Clements is supported by PPARC.\n \n\n%\\end{document}"
},
{
"name": "gas.tex",
"string": "%\\documentclass[a4paper,12pt,fleqn]{article}\n%\\pagestyle{empty}\n%\\setlength{\\textwidth}{38em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\addtolength{\\oddsidemargin}{-10mm}\n%\\addtolength{\\evensidemargin}{-10mm}\n%\\addtolength{\\topmargin}{-20mm}\n\n%\\begin{document}\n\n\\section{DISCUSSION}\n\n\\subsection{Correlations}\n\\subsubsection{Dust temperature}\n\n\\begin{figure}\n \\vspace{6cm}\n \\special{psfile='Fig11.ps' hoffset=0 voffset=0 hscale=30\nvscale=30}\n\\caption{\\label{md2tdF} Plotting dust temperature versus dust mass shows no\ncorrelation. This means that $L_{60}$--$T_{\\rm{d}}$ relationship\n(Fig.~\\ref{60TF}) is not a function of dust mass.}\n\\end{figure}\n\n\\begin{figure}\n \\vspace{6cm}\n \\special{psfile='Fig12.ps' hoffset=0 voffset=0 hscale=30\nvscale=30}\n\\caption{\\label{lb2tdF} A plot of dust temperature against blue luminosity\nshows an anti-correlation ($r=0.2$). This is quite surprising as\ninitially it was thought that the $L_{60}$--$T_{\\rm{d}}$ correlation\nwas due to galaxy mass (i.e. larger galaxies have more 60$\\mu$m\nluminosity and therefore higher dust temperatures).}\n\\end{figure}\n\nLuminosity is often strongly correlated with mass in astrophysical\nsituations, and so at first sight the $L_{60}-T_{\\rm{d}}$ correlation\n(Fig.~\\ref{60TF}) suggests that the more luminous systems are\nhotter. We can test this by plotting dust temperature versus dust mass\nand blue luminosity, often used as a measure of the mass of a\ngalaxy. In the first case (Fig.~\\ref{md2tdF}) there is no significant\ncorrelation (see Table~\\ref{fitsT} for coefficients), so there is no\ntendency for galaxies with lots of dust to be hotter, and in the\nsecond case (Fig.~\\ref{lb2tdF}) there is an inverse correlation. The\n$L_{60}-T_{\\rm{d}}$ correlation is therefore most naturally explained\nby the sensitivity of the 60$\\mu$m flux to the dust temperature. If,\nfor whatever reason (and not because of its mass) the dust is hotter,\nthis will greatly increase the 60$\\mu$m luminosity. What is rather\nmore interesting (and perhaps surprising) is the anti-correlation of\nthe corrected $L_{\\rm{B}}$ versus $T_{\\rm{d}}$\n(Fig.~\\ref{lb2tdF}). The significance is at the 98 per cent level,\nmaking it the least secure of the correlations we present here and the\nprobable link is with the star formation efficiency rather than\ndust temperature itself. Using $L_{\\rm{fir}}/M_{\\rm{H_2}}$ as a\nmeasure of star formation efficiency, Young (1999) has recently found\nthat the star formation efficiency of galaxies in many different types\nof environment decreases as galaxy size increases (as measured by the\noptical linear diameter $D_{25}$). If we now plot\n$L_{\\rm{fir}}/M_{\\rm{H_2}}$ against $L_{\\rm{B}}$ for our galaxies a\nmuch better correlation is seen than with $T_{\\rm{d}}$, indicating\nthat this is where the true dependence lies (see Fig.~\\ref{sfe2lbF}\nand Table~\\ref{fitsT}). The explanation Young gives for this\nrelationship is that larger galaxies have flatter rotation curves over\nmore of their disks and so experience more shear. She suggests that\nthe effect of this would be to reduce the ability of molecular clouds\nto form stars by increasing the turbulence within them, and to dampen\nthe effects of star-formation triggers.\n\n\\begin{figure}\n \\vspace{7.7cm}\n \\special{psfile='Fig13.ps' hoffset=0 voffset=0 hscale=30\nvscale=30}\n\\caption{\\label{sfe2lbF} A stronger anti-correlation is seen when the dust\ntemperature from Fig.~\\ref{lb2tdF} is replaced by a measure of the star\nformation efficiency ($L_{\\rm{fir}}/M_{\\rm{H_2}}$). This is the\nexplanation for the weak dependence on dust temperature in Fig.~\\ref{lb2tdF},\nas $L_{\\rm{fir}}$ is a function of $T_{\\rm{d}}$. This figure suggests\nthat smaller galaxies have larger star formation efficiencies, a trend\nfirst noticed by Young (1999).}\n\\end{figure}\n\n\\input{table8}\n\n\\subsubsection{\\label{7714}Gas and dust masses}\n\nWe compared the dust masses, derived from the submillimetre fluxes\nusing a single temperature, to the H$_2$, H{\\sc i} and H$_2$ + H{\\sc\ni} masses as shown in Figure~\\ref{d2gF}a-c. The strongest correlation\nis with the molecular gas which suggests that the dust is primarily\nfound in molecular clouds. The larger scatter on the H{\\sc i} plots\nmay be because we are using global H{\\sc i} values which may include\ngas at very large radii where there would be much less dust than in\nthe inner disk. Devereux \\& Young (1990) found that if\nthey only used the H{\\sc i} in the inner disk, in addition to the\nmolecular gas, then the correlation between gas and dust was\nimproved. We cannot, however, investigate the spatial connection between\ndust and atomic gas in the region they both occupy as we do not yet\nhave H{\\sc i} maps. We repeated the process using the `cold dust masses' but\nfound no differences in the correlations or slopes of the plots and so\nhave not included these.\n\n\\begin{figure*}\n \\vspace{8.5cm}\n \\special{psfile='Fig14a.ps' hoffset=0 voffset=0 hscale=30\nvscale=30}\n \\special{psfile='Fig14b.ps' hoffset=160 voffset=8 hscale=32\nvscale=28}\n \\special{psfile='Fig14c.ps' hoffset=320 voffset=0 hscale=30\nvscale=30}\n\\caption[a]{\\label{d2gF} a) Dust mass versus H$_2$ mass, a solar symbol\nindicates the Milky Way values (Sodroski et al. 1994). The line is the\nbest least squares fit (see Table~\\ref{fitsT} for fit parameters).\\\\\nb) Dust mass versus H{\\sc i} mass, the line indicates the best least\nsquares fit to the data. There is much more dispersion than for\nFig.~\\ref{d2gF}a.\\\\ c) Dust mass versus H$_2$ + H{\\sc i} mass.}\n\\end{figure*}\n\nWe would like to try to address the reasons behind the tightness of\nthe relationship between dust and molecular gas. The scatter in this\nplot (Fig.~\\ref{d2gF}a) is very small, the r.m.s dispersion about the\nline of best fit is only $\\sim 60$ per cent. Some of this is due to\nobservational errors; if we assume 30 per cent errors in the fluxes and\nsubtract this in quadrature from the overall value then we are left\nwith 52 per cent as the intrinsic scatter. There are some\nobservational-type errors which are hard to account for, such as\naperture corrections and the probability that our assumption of a\nsingle dust temperature is wrong, but the small scatter does suggest\nthat any aperture effects must be similar for all the galaxies and\nthat if our assumption about temperature is wrong then it must be\nwrong in the same way for all of the galaxies. This is borne out be\nthe similarity of the relationship when the `cold dust masses' are\nused.\n\nIn order to determine the physical meaning of the 50 per cent scatter\nwe will review the current views on the formation of dust and CO and\nthe expected dependences on metallicity.\n\nThere are no firm conclusions about how dust grains form. Suggested\nsites of formation range from post-AGB stars to supernova remnants\n(Whittet 1992). The grains are thought to grow in the darkest molecular\nclouds by accretion of icy mantles and are probably destroyed by\nsputtering in the diffuse ISM, after the dispersion of the molecular\ncloud by supernova shocks and HII regions. Despite the complications\nin determining how and where the various stages of dust evolution\noccur, there is some evidence that the fraction of metals bound up in\ndust grains is a constant, both from observations of nearby galaxies\n(Issa et al. 1990) and from observations in our own Galaxy, where the\ncarbon and oxygen abundances (the main constituents of dust) are\nconstant over a wide range ISM densities (Cardelli et al. 1996; Meyer\net al. 1998). This suggests that $M_{\\rm{d}}\n\\propto Z M_{g}$ where $M_g$ is the total mass of gas and $Z$ is the metallicity.\n\nThe formation of CO is better understood than that of dust and is\nbelieved to occur through a network of gas-phase reactions in the\ngiant molecular clouds (GMCs). CO will form readily, the rate\nincreasing with density, but is easily destroyed by UV radiation. In\norder to remain intact, the CO needs to be shielded by dust grains\nand/or large column densities of H$_2$. Assuming that the dominant\nmass in the GMCs is in the form of H$_2$, then since CO forms from the\nC and O available in the gas-phase, (and O is always more abundant\nthan C in the ISM), a metallicity dependence is suggested where\n$L_{\\rm{CO}} \\propto Z M_{\\rm{H_2}}$. However, since most of the\nshielding required to form the CO is produced by dust rather than\nH$_2$, the true metallicity dependence may be even higher than\nthis. When there is insufficient dust in a molecular cloud to provide\nadequate shielding from the UV radiation field, the volume of the\ncloud occupied by CO may not be as large as that occupied by H$_2$,\nbecause H$_2$ is more efficient at self-shielding. This is the likely\ncase in low metallicity systems such as the LMC or where the volume\nand/or column densities are low. The possibilities that CO and H$_2$\nmay not always be co-extensive, and that there may be a dependence of\nCO luminosity on metallicity, can lead to problems with the\napplication of the $X$ factor to CO observations in order to determine\nthe mass of H$_2$. For systems with significantly lower densities\nand/or metallicities a larger conversion may be needed relative to\ngalaxies such as the Milky Way. Observations do indicate a dependence\nof $X$ on metallicity for low metallicity systems (Wilson 1995) with\n$X/X_G= (Z/Z_{\\odot})^{-0.7}$ for systems with less than solar\nmetallicity and staying roughly constant for higher than solar\nmetallicities (Frayer \\& Brown 1997). This observed dependence is less\nsteep than one would have imagined from the above simplistic\narguments. It could be argued that for metallicities above some\ncritical value, where there is sufficient shielding, the $X$ factor\nmay show less dependence on metallicity, as the abundance of CO\nrelative to H$_2$ depends on the availability of C and O and not on\ndust any longer. While the formation of CO should still be greater for\nhigher metallicities, H$_2$ formation is also dependent on dust grains\nas catalysts so it is possible that this could cause the $X$ factor to\nsaturate : more metals lead to more CO, but they also lead to more\ndust and thus more H$_2$ formed from atomic hydrogen, producing the\nobservation that the $X$ factor is constant with metallicity above a\nthreshold value. Theory does predict significant depletion of CO onto\ndust grains (forming mantles) for favourable conditions in the cloud\nwhich would make $X$ smaller with increasing metallicity, possibly\noffsetting any trend for an increase but in the Milky Way this\ndepletion is only observed to be 5 to 40 per cent (Whittet 1992), much\nless than predicted, indicating that there is still much which is not\nunderstood about the interaction of dust and molecules in the GMCs.\n\nWe do not have metallicity measurements for our galaxies, but the\nrange of metallicities of spiral galaxies of similar absolute\nmagnitudes is 2--3 (Henry \\& Worthey 1999). Thus the small scatter in\nthe H$_2$--dust mass diagram strongly suggests that the metallicity\ndependence of dust mass and of the CO $X$ factor is very similar. An\nadditional test of this will be extending our study to galaxies likely\nto have a larger range of metallicity.\n\n\n\\subsubsection{Star formation efficiency}\n\nThe ratio of $L_{\\rm{fir}}/M_{\\rm{H_2}}$ is often used as a measure of\nthe star formation efficiency of a galaxy since $L_{\\rm{fir}}$ is\nbelieved to trace the star formation rate and so this ratio gives the\nstar formation rate per unit gas mass. Figure~\\ref{lfir2h2F} shows the\nstrong correlation between molecular gas and $L_{\\rm{fir}}$ and gives\nsome idea of the range of $L_{\\rm{fir}}/M_{\\rm{H_2}}$ values for these\ngalaxies. The L/M = 4 line represents `normal' galaxies such as the\nMilky Way (Scoville \\& Good 1989) and most of the galaxies in our\nsample show elevated star formation efficiencies relative to the Milky\nWay. Many of the galaxies lying above the general trend (SFE$\\geq 20$)\nare often interacting or have suspected active nuclei (e.g. IR 0857+39\nwith SFE $\\sim 100$). Values of $L_{\\rm{fir}}/M_{\\rm{H_2}}$ are\ngiven in Table~\\ref{massT}.\n\n\\subsection{\\label{g2dS}Gas to dust ratios}\n\nThe average gas-to-dust ratios (using the single temperature dust\nmasses) for the three components are\n$M_{\\rm{H_2}} /M_{\\rm{d}} = 293\\pm19$, $M_{\\rm{HI}} /M_{\\rm{d}}\n=304\\pm24$ and $M_{\\rm{H_2 + HI}} /M_{\\rm{d}} = 581\\pm43$, where the\n$\\pm$ indicates the error in the mean. In future, we will refer to\n$M_{\\rm{H_2 + HI}} /M_{\\rm{d}}$ as the gas-to-dust ratio $G_{\\rm{d}}$\nand the values are listed in Table~\\ref{massT}. In order to compare our\n$G_{\\rm{d}}$ with the Galactic value, we must be careful that we\naccount for the differences in $\\kappa_{d}(\\nu)$ and $X$ used by\nothers and ourselves. The gas-to-dust ratio for the Milky Way was\nmeasured by Sodroski et al. (1994), using {\\em COBE\\/} data at 140 and\n240$\\mu$m, therefore in order to compare our measurement with theirs\nwe must also scale the $\\kappa_{d}(240)$ value of the opacity\ncoefficient they used to 850$\\mu$m, using an assumed value for\n$\\beta$. Sodroski et al. use a $\\kappa_{d}(240)=0.72\\,\n\\rm{m}^{2}\\,\\rm{kg}^{-1}$; taking this to 850$\\mu$m gives\n$\\kappa_{d}(850)=0.2-0.057\\,\\rm{m}^{2}\\,\\rm{kg}^{-1}$ for\n$\\beta=1-2$. Comparing this to our value of 0.077 m$^2$ kg$^{-1}$ and\naccounting for the differences in $X$ factors (theirs being 0.71 times\nours) gives a range of Galactic $G_{\\rm{d}}$ values of 85--302 for a\n$\\beta$ of $1\\rightarrow 2$. The middle of the range at $\\beta=1.5$ is\n$G_{\\rm{d}}=160$ and this is the nominal value we will make\ncomparisons with. It can now be seen that our average gas-to-dust\nratio of 581 is more than a factor of three larger than the Galactic\nvalue of 160 (at the least a factor of 2 larger if $\\beta=2$). Of\ncourse, the measurement made by Sodroski et al. is a very difficult\none to make, but it is supported by arguments based on element\nabundances and depletions which predict a ratio of $\\sim 130$ (Eales\net al. in prep). The Galaxy has a FIR luminosity of\n$1.1\\times 10^{10}\\, \\rm{L_{\\odot}}$ and a dust mass of $\\sim\n2.9\\times 10^{7}\\,\\rm{M_{\\odot}}$ (Sodroski et al. 1994) which assumes\nthe same value for $\\kappa_{d}(\\nu)$ that gives a $G_{d}=160$. This\nplaces the Galaxy at the bottom end of the range of luminosities and\ndust masses found in this IR bright sample. Previous determinations\nof the gas-to-dust ratios in IR luminous objects using {\\em IRAS\\/}\ndata have always been high $\\sim 1000$ (Young et al. 1989; Devereux \\&\nYoung 1990; Sanders et al. 1991) which has been attributed to the lack\nof sensitivity of {\\em IRAS} to cold dust. It would seem that our\nsubmillimetre observations have reduced this tendency, giving a lower\ngas-to-dust value, but when the gas-to-dust ratios are re-calculated\nusing the `cold dust masses' we find a further reduction to\n$M_{\\rm{H_2}} /M_{\\rm{d}}^{cold} = 143\\pm9$, $M_{\\rm{HI}}\n/M_{\\rm{d}}^{cold} =158\\pm14$ and $M_{\\rm{H_2 + HI}}\n/M_{\\rm{d}}^{cold} = 293\\pm24$. This is now just within the range of\nvalues we calculated for the Galaxy, and in good agreement if the\n$\\beta=2$ case is taken. We perform the calculations with the `cold\nmasses' simply to illustrate the effect of overlooking this\ncomponent. A slightly colder temperature (say 15--18 K) would increase\nthe dust masses by a larger amount, further reducing the observed\ngas-to-dust ratios and so giving better agreement with the Galactic\nvalues.\n\n\\begin{figure}\n \\vspace{8cm}\n \\special{psfile='Fig15.ps' hoffset=0 voffset=0 hscale=35\nvscale=30}\n\\caption{\\label{lfir2h2F} FIR luminosity versus H$_2$ mass. The\nquantity $L_{\\rm{fir}}/M_{\\rm{H_2}}$ is taken as a measure of the star\nformation efficiency of the galaxy. The galaxies lying above the trend\nare mostly interacting or with suspected active nuclei. Our Galaxy is\nbelieved to lie on the L/M$\\sim4$ line and so most of the galaxies in\nour sample would appear to be more efficient than the Milky Way.}\n\\end{figure}\n\nThe gas-to-dust ratios calculated using the single temperature dust\nmasses vary from 1700 to 200, the large range being mostly due to the\nvariations in $M_{\\rm{HI}} /M_{\\rm{d}}$ as discussed in\nSection~\\ref{7714}. Some of the larger values of $M_{\\rm{H_2}}\n/M_{\\rm{d}}$ could be due to the large angular sizes of some of the\nnearer galaxies, meaning that our dust masses are underestimated when\ncompared to the CO fluxes produced from multi-positional single dish\nmeasurements (this particularly applies to NGC 772 and NGC 7479);\nhowever this is not always the case as there are some galaxies of\nsmall angular size which have high $M_{\\rm{H_2}} /M_{\\rm{d}}$ ratios\nbut more normal $M_{\\rm{HI}} /M_{\\rm{d}}$, (e.g. IR 0335+15, UGC 4881\nand Mkn 331). These galaxies are interacting or have Seyfert nuclei\nand typically have high dust temperatures, which may suggest that the\nlack of apparent dust mass is simply due to using a high temperature\nwhen calculating $M_{\\rm{d}}$ and not accounting for any colder\ndust. High temperatures cannot be the sole explanation, however, as\nother galaxies with high $T_{\\rm{d}}$ and signs of\ninteraction/activity have rather low values of $M_{\\rm{H_2}}\n/M_{\\rm{d}}$ (e.g. Arp 220). It could be that an enhanced\n$M_{\\rm{H_2}} /M_{\\rm{d}}$ is a stage that some merging/starburst\ngalaxies pass through, either by an enhancement of CO relative to\ndust, or a decrease in dust emission. A change in the $X$ factor,\ncausing the H$_2$ to be overestimated could also be responsible (this\nhas been suggested for many extreme active/starburst nuclei (Solomon\net al. 1997)). It is also possible that CO which was depleted from the\ngas phase onto grain mantles in dark clouds could, at a certain stage\nin the starburst evolution, become vaporized back into the gas phase,\ngiving a higher CO flux while keeping the atomic, dust and H$_2$\ncontent the same. One particular case which deserves a mention here is\nNGC 7714 which has $M_{\\rm{HI}}/M_{\\rm{d}} \\sim 1300$, causing its\nabnormally high gas-to-dust ($G_{\\rm{d}}$) value of 1700 (see column 9\nof Table~\\ref{massT}). NGC 7714 is interacting with NGC 7715 although\nthey are widely spaced enough (1.9 arcmin) that only NGC 7714 was\nobserved with SCUBA and the {\\em IRAS\\/} flux is due entirely to NGC\n7714 (Surace et al. 1993). The H{\\sc i} maps of Smith et al. (1997)\nshow rings and bridges of gas connecting the two galaxies, so it is\nprobable that some of the H{\\sc i} listed for NGC 7714 in the single\ndish measurement (Table~\\ref{massT}) is really associated with the\nwhole region and cannot be compared with what we observed. The amount\nof H{\\sc i} contained in the 50 $\\times$ 50 arcsec region centred on\nNGC 7714 (similar to the area of the dust emission) is given as only\n$1.7\\times10^9$ M$_{\\odot}$ compared to $7\\times10^9$ M$_{\\odot}$ for\nthe whole system. Using this lower value would give a more reasonable\nvalue of 355 for $M_{\\rm{HI}} /M_{\\rm{d}}$, bringing $G_{\\rm{d}}$ down\nto 802.\n\nOne further caveat to the whole $M_{\\rm{H_2}}/M_{\\rm{d}}$ business is\nthe large discrepancies in the CO fluxes between single-dish\nmeasurements and interferometer mappings. Maps have been found for\nfour of our galaxies (Sanders et al. 1988; Yun \\& Hibbard 1999;\nLaine et al. 1999) and always the flux is considerably less ($\\leq\n1/2$) than the single-dish measurement (Young et al. 1995). This is\nusually explained by resolution effects as these interferometer\nmeasurements are insensitive to structures larger than $\\sim 30$\narcsec but even in sources unresolved by the interferometer at $cz\\geq\n10,000$ km s$^{-1}$ (which are not expected to have large scale angular\nstructure), the difference in flux is still as large. If we used the\ninterferometer measurements for NGC 520, NGC 7469, NGC 7479 and UGC\n4881, the corresponding H$_2$ masses would decrease by factors of 2,\n2, 4, and 2 and bringing the $M_{\\rm{H_2}}/M_{\\rm{d}}$ ratios down to\n229, 195, 163 and 260 respectively.\n\n\n\n\n%\\end{document}"
},
{
"name": "intro.tex",
"string": "%\\documentclass[a4paper,12pt]{article}\n%\\pagestyle{empty}\n%\\setlength{\\textwidth}{38em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\addtolength{\\oddsidemargin}{-10mm}\n%\\addtolength{\\evensidemargin}{-10mm}\n%\\begin{document}\n\n%\\parindent = 1em\n\n\\section{Introduction}\n\nWith the advent of the SCUBA bolometer array (Holland et al. 1999) on\nthe James Clerk Maxwell Telescope\\footnote{The JCMT is operated by the\nJoint Astronomy Center on behalf of the UK Particle Physics and\nAstronomy Research Council, the Netherlands Organization for\nscientific Research and the Canadian National Research Council.} it\nhas, for the first time, become feasible to map the submillimetre\n(100$\\mu$m$<\\lambda<$1 mm) emission of a large ($>$100) sample of\ngalaxies. While this may seem a paltry feat in comparison to surveys\nconducted at other wavelengths, submillimetre astronomy has lagged\nbehind the rest due to the technical difficulties of building\nsensitive enough instruments. Until recently, all that existed were a\nhandful of submillimetre fluxes of nearby galaxies made with single\nelement bolometers (Eales, Wynn-Williams \\& Duncan 1989; Stark et al.\n1989; Clements, Andreani\n\\& Chase 1993). No information about the distribution of the dust was\navailable and even the fluxes themselves were subject to considerable\nuncertainty, especially when beam corrections had to be made in order\nto compare with measurements in the far infra-red (FIR :\n10$\\mu$m$<\\lambda<$100$\\mu$m) made with the {\\em IRAS\\/}\nsatellite. Quite surprisingly, even before SCUBA, there had been some\nsuccessful submillimetre observations of high redshift objects (Dunlop\net al. 1994; Isaak et al. 1994; Ivison 1995) but interpretation of the\nmeasurements, particularly the high implied dust masses, was hampered\nby a lack of knowledge of local submillimetre properties, such as\nluminosity and dust mass functions (Eales \\& Edmunds 1996, 1997\nhereafter EE96,97). We have started to use SCUBA to carry out a survey\nof a large number of nearby galaxies and hope that this first\nstatistical submillimetre survey will answer a number of questions.\n\n\n\\subsection{How much dust does a galaxy contain?}\n\nThe amount of dust in a galaxy is a measure of the quantity of heavy\nelements in the interstellar medium (ISM), since $\\sim$ 50 per cent of\nthe heavy elements are locked up in dust and there is some evidence\nthat this fraction is constant from galaxy to galaxy (EE96). This is a\ndifferent and complementary way of investigating the heavy element\ncontent from simply measuring the metallicity, which is of course, the\nmass of heavy elements {\\em per unit mass\\/} of gas not including that\nwhich is locked up in dust. EE96 have shown that the way in which the\ndust mass of a galaxy evolves depends critically on the mode of\nevolution:-- whether the galaxy can be treated as a closed box or\nwhether gas is inflowing onto or outflowing from it. Dust masses have\nbeen estimated from {\\em IRAS\\/} measurements but the resulting\ngas-to-dust ratios are a factor of $\\sim$ 5--10 higher than for our\nown Galaxy (Devereux \\& Young 1990; Sanders et al. 1991) suggesting a\nproblem with the method. The submillimetre offers a number of\nadvantages for estimating dust masses. At longer submillimetre\nwavelengths ($\\lambda>350\\mu$m) we are sampling the Rayleigh-Jeans\npart of the Planck function, where the flux is least sensitive to\ntemperature and most sensitive to the mass of the emitting\nmaterial. This is a good thing because accurate dust temperatures\n($T_{\\rm{d}}$) are difficult to estimate. Dust radiates as a `grey\nbody', which is a Planck function modified by an emissivity term\nQ$_{em}\\propto\n\\nu^{\\beta}$, where the emissivity index ($\\beta$) is believed to lie between 1 and 2\n(Hildebrand 1983). To derive the temperature, an assumption must be\nmade about $\\beta$ or vice-versa. If an incorrect temperature is\nassumed at say 850$\\mu$m, then the dust mass will be wrong by\napproximately the fractional error in $T_{\\rm{d}}$, but at shorter FIR\nwavelengths (100$\\mu$m) the error will be much larger as flux goes as\n$T_{\\rm{d}}^{(4+\\beta)}$. Generally, using {\\em IRAS\\/} measurements\nalone to determine the temperature and mass will always over-estimate\nthe first and so under-estimate the second. The reason for this is\nthat because of the sensitivity to temperature of emission on the Wien\nside of the grey-body curve, the FIR emission from a galaxy is\ndominated by warm dust, even when there is relatively little mass in\nthis component. Thus fits of grey-body curves to FIR fluxes are biased\ntowards higher temperatures than is warranted by the relative masses\nof warm and cold dust. This is, of course, the probable explanation of\nthe high gas-to-dust ratios observed by Devereux \\& Young (1990), and\nalso explains why it has been so difficult to demonstrate the presence\nof cold dust in galaxies. Longer wavelength studies (200$\\mu$m --\n850$\\mu$m) using {\\em COBE\\/}, {\\em ISO\\/} and SCUBA (Sodroski et al.\n1994; Reach et al. 1995; Alton et al. 1998a,b; Davies et al. 1999;\nFrayer et al. 1999; Papadopoulos \\& Seaquist 1999) have now confirmed\nthe existence of cold dust components at 15 $< T_{\\rm{d}} <$ 25 K in\nnearby spiral galaxies as predicted for grains heated by the general\ninterstellar radiation field (Cox, Kr\\\"{u}gel \\& Mezger 1986), rather\nthan in star forming regions.\n\nThere is one further difficulty in estimating dust masses\nat any wavelength:-- our poor knowledge of the dust mass opacity\ncoefficient $\\kappa_d(\\nu)$, which is needed to give absolute values\nfor mass. This varies with frequency in the same way as the\nemissivity, and so current measurements at 120--200$\\mu$m (Hildebrand\n1983, Draine \\& Lee 1984) must be extrapolated to the wavelength of\ninterest using the assumed value of $\\beta$, raising the possibility\nof large errors since $\\beta$ itself is poorly known. Hughes, Dunlop\n\\& Rawlings (1997) estimate the uncertainty in this coefficient to be a factor\n$\\sim$8 at 850$\\mu$m. For many issues, including galaxy evolution,\nabsolute values of mass are not important (EE96) provided the relative\nmasses are correct.\n\n\n\\subsection{How much optical light is absorbed by dust?}\n\nThere is an increasing need to understand the effects of dust on our\noptical view of the universe. Optical astronomers have recently shown\nthat the UV luminosity density in the universe may rise from now to\n$z\\sim1$ and then fall off at higher redshifts (Lilly et al. 1996;\nMadau et al. 1996). There have been claims that this represents the\n`star-formation history of the universe' but how much is this affected\nby dust? In general, how important are selection effects caused by\ndust, and is the high redshift universe significantly attenuated by\nforeground dusty objects? (Davies et al. 1997). Mapping large numbers of\ngalaxies at submillimetre wavelengths will help determine how the dust\nis distributed relative to the stars, and how effective it is at\nabsorbing optical light.\n\n\n\\subsection{How much cosmological evolution is seen in the \\protect\\newline submillimetre?}\n\nWith the deep SCUBA surveys now taking place (Smail, Ivison \\& Blain\n1997; Hughes et al. 1998; Barger et al. 1998,1999; Blain et al. 1999a;\nEales et al. 1999; Lilly et al. 1999), there is now probably more\ninformation about the submillimetre properties of the distant universe\nthan the local universe. The galaxies in the deep submillimetre\nsurveys appear very similar to the ULIRGs found nearby (Smail et\nal. 1998; Hughes et al. 1998; Lilly et al. 1999). If the dust in these\nhigh-redshift objects is heated by young stars, as seems to be largely\nthe case for nearby ULIRGs (Genzel et al. 1998) then, since these\nsources make up $>$20 per cent of the total extra-galactic background\nemission, this implies that $\\geq$10 per cent of all the stars that\nhave ever formed did so in in this kind of extreme object (Eales et\nal. 1999). Studies of the cosmological evolution of this population\nsuggests that it is very similar to that seen at optical wavelengths\nin the Lilly-Madau curve. What is derived for the cosmological\nevolution, however, depends critically on what is assumed about the\nsubmillimetre properties of the local universe (cf. results of Eales\net al. 1999 and Blain et al. 1999b). Currently, rather than working\nfrom a local submillimetre luminosity function, most investigations\nhave perforce started from a local {\\em IRAS\\/} 60$\\mu$m luminosity\nfunction and extrapolated to submillimetre wavelengths using some\nassumptions about the average FIR-submm SED. The lack of a direct\nsubmillimetre luminosity function has been a severe limitation when\ninterpreting the results of deep surveys. Even before SCUBA,\nsubmillimetre observations of high-redshift radio galaxies and quasars\nhave found unusually high dust masses. Here again, explanation has\nbeen restricted by our ignorance of the local universe, in this case\nthe statistics of dust masses in galaxies (EE 96).\n\n\n\\subsection{Is CO a good tracer of molecular hydrogen?}\n\nCarbon monoxide (CO) has long been used as a tracer for molecular gas\n(H$_2$). The conversion factor between CO and H$_2$ (known as the `$X$'\nfactor) is quite uncertain\nand may be a function of physical environment such as density,\ntemperature and metallicity (Maloney 1990; Wilson 1995). Dust is an\nalternative tracer of H$_2$, and may help support the case for or\nagainst CO. Any variations of the ratio of CO to dust would provide insight\non the way in which the $X$ factor depends on galaxy properties.\n\n\n\\subsection{The scope of the survey}\n\nThe ideal way to carry out the survey would be to do a blank field\nsurvey of large parts of the sky and measure the redshifts of all\nobjects detected, a method which would be largely free of any\nselection effects. Unfortunately, this is impractical at the moment\nbecause the field of view of SCUBA is only $\\sim $2 arcmins, making\nthe time needed for such a survey prohibitively long. Instead, we\ndecided to use the less ideal but more practical method of observing\ngalaxies drawn from as many different complete samples selected in as\nmany different wavebands as possible. This procedure still allows us\nto produce unbiased estimates of the submillimetre luminosity function\nand of the dust mass function using `accessible volume' techniques\n(Avni \\& Bahcall 1980). These will not be biased unless there is a\nclass of galaxies which is not represented in any of the\nsamples. Provided at least one member of such a class of objects is\npresent in one of the samples then the estimates will be unbiased\nalthough clearly with large random errors.\n\nIn this paper we present the results from a sample selected at\n60$\\mu$m. We present first estimates of the luminosity and dust\nmass functions, and examine the extent to which these may be\nbiased. Subsequent papers on other samples, in particular a sample\nselected at optical wavelengths, will allow us to refine these\nestimates. We will also begin to address the other questions raised in this\nsection.\n\nSection 2 describes the observations and the methods used to reduce\nthe data. In Section 3 we present the results from the {\\em IRAS\\/}-selected\nsample, in Section 4 we discuss the submillimetre\nluminosity and dust mass functions while in Section 5 we compare our results\nwith other data (gas masses, optical properties) taken from the\nliterature.\\\\\n\nWe assume a Hubble constant of 75 km s$^{-1}$ Mpc$^{-1}$ throughout.\n\n\n%\\end{document}\n"
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"string": "%\\documentclass[a4paper,fleqn,10pt]{article}\n%\\pagestyle{empty}\n%\\setlength{\\textwidth}{40em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{2.0}\n%\\addtolength{\\oddsidemargin}{-5mm}\n%\\addtolength{\\evensidemargin}{-5mm}\n%\\setlength{\\oddsidemargin}{25mm}\n%\\addtolength{\\topmargin}{-10mm}\n%\\usepackage{longtable}\n\\documentstyle[psfig,longtable,epsf]{mn}\n\\def\\mic{\\,\\mu\\rm m}\n\\begin{document}\n\n\\input{abstract}\n\\input{intro}\n\\input{obs}\n\\input{results}\n\\input{gas}\n\\input{conc}\n\\input{bib}\n%\\include{paper1_tab12000}\n%\\include{paper1_tab22000}\n%\\include{fluxerrTable}\n%\\include{paper1_tab3}\n%\\include{paper1_tab4}\n%\\include{convTable}\n%\\include{lfTable}\n%\\include{fitsTable}\n%\\include{paper1_caps}\n\n\\end{document}"
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"name": "obs.tex",
"string": "%\\documentclass[a4paper,12pt]{article}\n%\\pagestyle{empty}\n%\\setlength{\\textwidth}{6in}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\begin{document}\n%\\parindent = 1em\n\n\\section{OBSERVATIONS AND DATA REDUCTION}\n\\subsection{The Sample}\n\nThe {\\em IRAS\\/}-selected sample was taken from the revised Bright\nGalaxy Sample (BGS), which is complete to a flux limit of\n$S_{60}>5.24$ Jy at all $\\mid b \\mid>30^\\circ$ and $\\delta >\n-30^\\circ$ (Soifer et al. 1989). We observed a subset of this sample\nwith SCUBA, consisting of all galaxies with declination from\n$-10^\\circ <\\delta< 50^\\circ$ and with velocity $>$ 1900 km s$^{-1}$,\na limit imposed to try to ensure the galaxies fitted within the SCUBA\nfield of view. The SCUBA sample covers an area of $\\approx$ 10,400\nsq$^\\circ$ and contains 104 objects. Many of these are interacting\npairs and although most were resolved by SCUBA they were not by {\\em\nIRAS\\/}, even with subsequent HIRES processing (Surace et\nal. 1993). Table~\\ref{fluxT} lists the sample.\n\n\\subsection{Observations}\n\nWe observed the galaxies between July 1997 and September 1998 using\nthe SCUBA bolometer array at the 15-m James Clerk Maxwell Telescope\n(JCMT) on Mauna Kea, Hawaii. SCUBA has two arrays of 37 and 91\nbolometers for operation at long (850$\\mu$m) and short (450$\\mu$m)\nwavelengths respectively. They operate simultaneously with a field of\nview of $\\sim$ 2.3 arcmins (slightly smaller at 450$\\mu$m). The arrays\nare cooled to 0.1 K and have typical sensitivities (NEFDs) of 90 mJy\nHz$^{-1/2}$ at 850$\\mu$m and 700 mJy Hz$^{-1/2}$ at 450$\\mu$m (Holland\net al. 1999). Beam sizes were measured to be $\\sim 15$ arcsec and 8\narcsec at 850 and 450$\\mu$m respectively, depending on chop throw and\nconditions. We made our observations in `jiggle-map' mode, which is\nthe most efficient mapping mode for sources smaller than the field of\nview. The arrangement of the bolometers is such that the sky is\ninstantaneously under-sampled and so the secondary mirror is stepped\nin a 16-point pattern to `fill in the gaps'. For observations using\nboth arrays, a 64 offset pattern is required to fully sample the sky as\nthe spacing/size of the feedhorns is larger for the long wavelength\narray. Generally we used the 64-point jiggle, except in some cases\nwhere it was clear that the atmospheric conditions were too poor to\nobtain useful 450$\\mu$m data, when we instead used the 16-point jiggle\nto give better sky cancellation.\n\nThe telescope has a chopping secondary mirror operating at 7.8 Hz\nwhich provides cancellation of rapid sky variations. To compensate for\nlinear sky gradients (the effect of a gradual increase or decrease in\nsky brightness), the telescope is nodded to the `off' position when in\n`jiggle' mode. We used a chop throw of 120 arcsec in azimuth in all\nobservations, except for galaxies with nearby companions, when we\nchose a chop direction which avoided the second galaxy. Skydips were\nperformed regularly to measure the zenith opacity $\\tau_{850}$. This varied\nover the course of the observations resulting in some data being taken\nin excellent conditions with $\\tau_{850}< 0.2$ while others done in\n`back-up' mode had $\\tau_{850}\\sim$ 0.5--0.6. Due to the large range\nof observing conditions, only about one third of the galaxies have\nuseful 450$\\mu$m data and, in fact, we will not consider the 450$\\mu$m\ndata further in this paper although they will be presented in another\npaper at a later date. We checked the pointing regularly\nand found it generally to be good to $\\sim 2$ arcsec. Due to the\nuncertainty of the {\\em IRAS\\/} positions, we centred our observations\non the optical coordinates taken from the {\\em Digitised Sky Survey}\n(DSS)\\footnote{The Digitised Sky Surveys were produced at the Space\nTelescope Science Institute under U.S. Government grant NAGW-2166. The\nimages of these surveys are based on photographic data obtained using\nthe Oschin Schmidt Telescope on Palomar Mountain and the U.K. Schmidt\nTelescope. The plates were processed into the present digital form\nwith the permission of these institutions.}.\n\nIntegration times differed depending on conditions and source\nstrength. For bright sources in good weather we typically used 6\nintegrations (15 mins), but many sources had to be observed on more\nthan one occasion due to poor S/N or because the galaxy fell on noisy\nbolometers. In total we integrated for $\\sim 44$ hours, mostly in\nweather band 3 ($0.3\\leq\\tau_{850}\\leq0.5$). We calibrated our data by\nmaking jiggle maps of planets (Uranus and Mars) and, when they were\nunavailable, of the secondary calibrators CRL 618 and HL Tau. Planet\nfluxes were taken from the JCMT {\\sc fluxes} program and we assumed\nthat CRL 618 and HL Tau had fluxes of 4.56 Jy beam$^{-1}$ and 2.32 Jy\nbeam$^{-1}$ respectively. The calibration error at $850 \\mu$m was\ntaken to be 10 per cent (except for 7 galaxies observed in very poor\nconditions where 15 per cent was used instead. These are denoted by a\n* in Table~\\ref{fluxT}.). This calibration error is included in the\nflux error quoted in Table~\\ref{fluxT}.\n\n\\subsection{Data reduction}\n\nWe reduced the data using the standard {\\sc surf} package (Jenness \\& Lightfoot\n1998). This consisted of flat-fielding the data after the on-off\npositions had been subtracted and then correcting for atmospheric\nextinction using opacities derived from skydip measurements. Any noisy\nbolometers were flagged as `bad' and large spikes removed.\n\n\\input{table1}\n\\vspace{2mm}\nExcept on the most dry and stable nights a residual sky noise was seen\nwhich was correlated across all the pixels. In most cases we removed\nthis using the {\\sc surf} task {\\sc remsky}, which uses bolometers\nchosen by the user to define a sky region, and then subtracts this sky\nlevel from the other bolometers. The bolometers used to measure the\n`sky' were chosen to be those away from the source emission using a\nrough submillimetre map and optical information as a guide. After sky\nnoise removal, the data was despiked and regridded to form an image on\n1 arcsec pixels. If an object had more than one dataset, a co-add was\nmade in which each map was weighted as the inverse square of its\nmeasured noise.\n\nThe nodding and chopping should ideally leave a background with zero\nmean and some correlated noise superimposed on top. In reality\nthe background level was not zero and could, in bad conditions, become\nquite large (either positive or negative). Often this residual sky\nlevel would vary linearly across the array giving a `tilted sky\nplane', the {\\sc surf} task {\\sc remsky}, which was designed to remove\nthe sky noise is rather simplistic and cannot remove these sky planes\n(Jenness, Lightfoot \\& Holland 1998). Due to the short integration\ntimes of most of our objects and the poor conditions in which many\nwere observed, this problem of sky planes became the limiting factor\nin obtaining sufficient S/N in many observations. To this end a\nprogram was written to remove spatially varying sky backgrounds from\nthe array as well as the temporal `sky noise' dealt with by {\\sc\nremsky}.\n\nTwo fairly typical 850$\\mu$m images are shown in Figure~\\ref{jmapF} along\nwith optical images from the DSS. The SCUBA\nimages clearly contain large amounts of structural information, which\nwe will delay considering until a later paper. Here we will simply\nconsider the 850$\\mu$m flux measurements.\n\n\\begin{figure*}\n \\vspace{7cm}\n \\special{psfile='Fig1a.ps' hoffset=-40 voffset=-60 hscale=50 vscale=50}\n \\special{psfile='Fig1b.ps' hoffset=200 voffset=-60 hscale=50 vscale=50}\n \\caption{\\label{jmapF}a) SCUBA contours ($2, 4, 6 ... \\sigma$) overlaid on an optical DSS\nimage for the Seyfert 1 galaxy NGC 7469 (lower), and its companion IC\n5283. There appears to be extended emission between the two galaxies.\nb) SCUBA contours ($2,3,4 ... \\sigma$) overlaid over the optical DSS image for\nNGC 958. The companion satellite $\\sim 1$ arcmin to the east is a\nsurprise detection ($\\sim 35$ mJy) as it has no 1.49 GHz flux.}\n\\end{figure*}\n\n\\input{table2}\n\n\\subsection{Flux measurement and error analysis}\n\nWe used the submillimetre images to choose an aperture over which to\nintegrate the flux, trying to ensure that it contained all the flux\nassociated with the galaxy and as little of the surrounding sky as possible.\\\\\n\nThe noise /error on the flux measurement has two components.\\\\\n\ni) The error in subtracting the background sky level which, despite\nour best attempts at removing it, often had a non-zero value that\nvaried over the image. A number of smaller apertures were placed on\nregions containing no source emission and used to estimate the mean\nsky level. The standard deviation between the sky levels in each\naperture was then used to find the error in the mean sky as\n$\\sigma_{ms} = S.D./\\sqrt{\\rm{No.\\, aps}}$, where `No. aps' is the number of\nsky apertures used to determine the mean sky value. The noise in the\nobject aperture due to this sky error is then\n$\\sigma_{sky}=\\sigma_{ms}N_{ap}$ where $N_{ap}$ is the number of\npixels in the object aperture.\\\\\n\nii) Shot/Poisson noise from pixel to pixel variations within the sky\naperture, which would usually be determined from the standard\ndeviation of the pixels within the sky aperture and contribute to the\nflux error as $\\sigma_{shot}=\\sigma_{pix}\\,\\sqrt{N_{ap}}$. In ordinary\nCCD astronomy this would be the only error estimated and we will refer\nto it as the `theoretical error'. It is actually quite a large\nunderestimate of the true shot noise because the noise is correlated\nacross pixels. This is because, unlike a CCD image, the pixels of a\nSCUBA image do not contain independent samples of the sky, i.e. two\nneighbouring pixels on a SCUBA image are constructed from overlapping\nsets of bolometer measurements, (also the pixels on the SCUBA maps are\n`artificial' as they are smaller than the size of the beam). To\nquantify this effect, simulations of blank SCUBA fields were made by\nreplacing the data for each bolometer in an observation by the output\nof a Gaussian random number generator. A large number of artificial\nmaps were made in this way, and on each map the noise in an aperture\nof given size was measured in the traditional way using\n$\\sigma_{shot}=\\sigma_{pix}\\,\\sqrt{N_{ap}}$. This was compared with\nthe standard deviation of all the fluxes (in that size aperture)\nbetween the different maps, deemed to be the `real shot noise'. For the\nrange of aperture sizes actually used in measuring fluxes, the ratio\nof real to predicted noise was $\\sim 8$. The total error for each flux\nwas calculated from\\\\\n\n\\[\n\\sigma_{tot}=(\\sigma_{cal}^{2} + \\sigma_{sky}^{2} +\n\\sigma_{shot}^{2})^{1/2}\n\\]\n\nwhere $\\sigma_{cal}\\approx 10\\%$\n\n\\[\n\\sigma_{sky} = \\sigma_{ms}N_{ap}\n\\]\n\n\\[\n\\sigma_{shot} = 8\\,\\sigma_{pix}\\,\\sqrt{N_{ap}}\n\\]\n\nTo convert the aperture flux in volts to Janskys, a measurement of the\ncalibrator flux for that night was made using the same aperture as was\nused for the object. The orientation of the aperture relative to the\nchop throw was also translated to the calibrator map (this did have a\nsignificant effect for more elliptical apertures).\n\nFluxes were found to have total errors $\\sigma_{tot}$ in the range\n10--25 per cent at 850$\\mu$m and these are listed in Table~\\ref{fluxT}. All\nobjects were detected at $> 3 \\sigma$ except for IR 0857+39, which was\nonly detected at $2.4 \\sigma$, although the flux is in good agreement\nwith that measured by Rigopoulou et al. (1996). Where the system is\ninteracting and not resolved by {\\em IRAS\\/}, the 850$\\mu$m fluxes\ngiven are for both galaxies combined. For those paired galaxies which\nwere resolved by SCUBA, the individual fluxes are listed in\nTable~\\ref{pfluxT}.\n\nA few objects were detected with good signal to noise on more\nthan one occasion and these could be used to keep check on the\nconsistency of our flux measuring and calibration procedures. These\nobjects and their relative flux errors are detailed in\nTable~\\ref{calT} and it can be seen that the differences in measured\nfluxes are within the errors calculated in the manner described above.\n\n\\input{table3}\n\n%\\end{document}"
},
{
"name": "results.tex",
"string": "%\\documentclass[a4paper,12pt,fleqn]{article}\n%\\pagestyle{empty}\n%\\setlength{\\textwidth}{38em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\addtolength{\\oddsidemargin}{-10mm}\n%\\addtolength{\\evensidemargin}{-10mm}\n\n%\\begin{document}\n\\parindent = 1em\n\n\\section{RESULTS}\n\n\\subsection{Spectral fits}\n\nWe have fitted the {\\em IRAS\\/} 60, 100 and 850$\\mu$m fluxes with a\nsingle-component temperature model by minimising the sum of the\nchi-squared residuals. The best fit was found for both the emissivity\nindex $\\beta$ and temperature $T_{\\rm{d}}$, with the values given in\nTable~\\ref{fluxT}. Some examples of fits are shown in Fig.~\\ref{sedF}\nalong with the $1 \\sigma$ ranges. The uncertainty of each fitted value\nof $T_{\\rm{d}}$ and $\\beta$ was estimated in the following way. For\neach galaxy, a Gaussian random number generator was used to create 100\nartificial flux sets from the original fluxes and measurement\nerrors. These new data sets were then fitted in the same way and the\nstandard deviation in the new parameters was taken to represent the\nuncertainty in the parameters found from the real data set. Average\nvalues and standard deviations (S.D.) for the whole sample (i.e. using\nonly the best fitting parameters for the real data sets) are\n$\\overline{T_{\\rm{d}}} = 35.6\\, \\pm\\, 4.9$ K and $\\overline{\\beta} =\n1.3\\, \\pm\n\\,0.2 $.\n\n%\\input{sedfig}\n\\begin{figure*}\n\\vspace{23cm}\n\\special{psfile='Fig2.ps' hoffset=-30 voffset=-80 hscale=90 vscale=90}\n\\caption{\\label{sedF} Representative SEDs showing the range of $\\beta$ \nand $T_{\\rm{d}}$ for the sample. Data points are the 60 and\n100$\\mu$m {\\em IRAS} fluxes and the 850$\\mu$m point is from our\nsurvey 10 \n. The solid lines are the best-fitting lines relating to the SED\nparameters shown. The dashed and dot-dashed lines are the $\\pm 1\n\\sigma$ fits.}\n\\end{figure*}\n\nThe value of $\\beta$ is remarkably uniform (the overall S.D. for the\nwhole sample is of the same order as the individual uncertainties,\nderived from the above technique), and lower than the value of\n1.5--2.0 obtained from multi-wavelength studies of our Galaxy (Masi et\nal. 1995; Reach et al. 1995), and also of NGC 891 (Alton et\nal. 1998b). The number of galaxies at $\\beta \\geq 1.5$ is equivalent\nto those at $\\beta \\leq 1.1$, and in fact, the distribution of $\\beta$\nabout the mean is well represented by a Gaussian, with those galaxies\nat $\\beta > 1.5$ being the tail of that Gaussian. The\ndistribution of $\\beta$ values for the sample is shown in\nFig.~\\ref{betahistF}. In fact, when the fluxes of the Milky Way and\nNGC 891 are fitted in the same way as we have fitted the {\\em IRAS\\/}\ngalaxies (i.e. a single temperature model using only the 60,100 and\n850$\\mu$m points) the $\\beta$ value we find is 0.7. It is only when\nthe full SED is used (which inlcudes fluxes between 200 and 800$\\mu$m) \nthat the colder component at $< 20$ K can be\nidentified, leading to the higher $\\beta$ of 1.5--2. So rather than\nimplying that $\\beta$ truly does have a low value, our results\nprobably indicate that there is dust in these galaxies at colder\ntemperatures than is indicated by a single-component fit. The\nuniformity of the $\\beta$ values in the sample could be indicative of\nsimilar cold component properties in all of the {\\em IRAS\\/}\ngalaxies. \n\n\\begin{figure}\n \\vspace{6cm}\n \\special{psfile='Fig3.eps' hoffset=-20 voffset=200 hscale=40\nvscale=35 angle=-90}\n \\caption{\\label{betahistF} The distribution of $\\beta$ values for the\nsample, note that the value determined for the Galaxy with a\nmulti-component model is 1.5--2.0}\n\\end{figure}\n\nThe lower $\\beta$ of 0.7 determined in this way for the\nMilky Way and NGC 891, which are optically selected, may be due to\nthem having larger fractions of colder dust than the {\\em\nIRAS\\/} galaxies. We can partially test this using preliminary data \nfrom the optically selected sample. Figure~\\ref{colplotF} shows a\ncolour-colour plot for the {\\em IRAS\\/} galaxies (stars) plus the galaxies\nobserved so far from the optical sample (circles). There is clear evidence that\nthe optically selected galaxies occupy a different area of the space,\nimplying that they are not merely the less luminous equivalent of {\\em\nIRAS\\/} galaxies. We can make a more thorough investigation\nwhen the optically selected sample is completed and we have 350 and\n450$\\mu$m data for the samples. \n\n\\begin{figure}\n \\vspace{6cm}\n \\special{psfile='Fig4.ps' hoffset=0 voffset=0 hscale=40 vscale=40}\n \\caption{\\label{colplotF} A plot of the 100/850 versus 60/850 colours\nfor the {\\em IRAS\\/} sample described in this paper (solid symbols)\nplus the optically selected galaxies observed so far (open\nsymbols). The two samples clearly have different FIR-submm properties.}\n\\end{figure}\n\n\\subsection{Dust masses}\n\nUsing the 850$\\mu$m flux and the temperature derived in\nthe above way the dust mass is calculated from\n \n\\begin{equation}\nM_{\\rm{d}} = \\frac{S_{850}\\,D^2}{\\kappa_d(\\nu)\\,B(\\nu,\\, T_{\\rm{d}})}\n\\label{MdE}\n\\end{equation}\n\n\\parindent=0pt\nwhere $\\kappa_d(\\nu)$ is the dust mass opacity\ncoefficient, $B(\\nu,\\, T_{\\rm{d}})$ is the\nvalue of the Planck function at 850$\\mu$m for a temperature\n$T_{\\rm{d}}$, and $D$ for $\\Omega_0 =$1 is given by\n\n\\begin{equation}\nD = \\frac{2c}{H_0}\\left(1-\\frac{1}{\\sqrt{1+z}}\\right) \\label{DE}\n\\end{equation}\n\\parindent=1em\n\nThe dust masses are listed in Table~\\ref{massT}, with values for\nindividual members of pairs in Table~\\ref{pmassT}. We have assumed a\nvalue of 0.077 m$^2$ kg$^{-1}$ for $\\kappa_d(\\nu)$, which is\nintermediate between values for graphite and silicates as given by\nDraine \\& Lee (1984) and by Hughes et al. (1993), and also that\n$\\kappa_d(\\nu)$ has the same value at 850$\\mu$m for all our\ngalaxies. Even though the value of $\\kappa_d(\\nu)$ is notoriously\nuncertain, the relative values of our dust masses will be correct as\nlong as the dust has similar properties in all galaxies. The\nuncertainties in the relative dust masses then depend only on the\nerrors in $S_{850}$ and $T_{\\rm{d}}$. The formal statistical\nuncertainties in $T_{\\rm{d}}$ are only $\\sim$ a few K, but there is\nthe possibility that our assumption of a single temperature has biased\nour estimates of $T_{\\rm{d}}$ to higher values, and thus our mass\nestimates to lower values. We can estimate the size of this effect in\nthe following way: A single temperature fit will produce a lower value\nfor $\\beta$ than is actually true if more than one component is\npresent. In their {\\em COBE\\/}--FIRAS study of our Galaxy, Reach et\nal. (1995) concluded that the highest observed value of $\\beta$ in any\nregion was likely to be closest to the true value, with any excess\nemission in other regions due to a colder component. If we adopt the\nsame approach and assume that all our galaxies have a true $\\beta$ of\n2 (our highest observed value is 1.9) and a uniform cold dust\ntemperature of 20 K, we can then fit a two-component temperature model\nand calculate a new dust mass. We find that for the same mass\ncoefficient as before, the masses of dust estimated from this\ntwo-component model are between 1.5 and 3 times higher than those\nderived from a single temperature fit. The discrepancy is larger for\ngalaxies with lower $\\beta$ and higher temperatures and some galaxies\nwhich have steep SEDs and cold temperatures have little extra dust\nwhen modelled in this way (e.g. NGC 5371, NGC 772). The dust masses\ncalculated assuming this form for the cold component are listed\nalongside the single temperature masses in Table~\\ref{massT}. They\nwill be referred to as `cold dust masses' in future.\n\n\\subsection{Gas masses}\n\nNeutral hydrogen (H{\\sc i}) fluxes were taken from the\nliterature\\footnote{See notes to Table~\\ref{massT}} and converted to\nmasses (in solar units) using\n\n\\begin{equation}\nM_{\\rm{HI}}=2.36\\times 10^5\\, D^2\\, S_{\\rm{HI}} \\label{HImE}\n\\end{equation}\n\\parindent=0pt\n\nwhere $D^2$ (Eqn.~\\ref{DE}) is in Mpc and $S_{\\rm HI}$ is in Jy km s$^{-1}$\\\\\n\\parindent=1em\n\nMolecular gas (H$_2$) masses were calculated using CO fluxes taken\nfrom the literature$^3$ and scaled to telescope independent units (Jy\nkm s$^{-1}$). When an object appeared in more than one reference, an\naverage flux was used to determine the mass. Conversion factors used\nfor different telescopes are given in Table~\\ref{convT}. Molecular\nmasses in M$_{\\odot}$ are given by\n\n\\begin{equation}\nM_{\\rm{H_2}}=1.1\\times 10^4\\, D^2\\, S_{\\rm{CO}} \\label{H2mE}\n\\end{equation}\n\\parindent=0pt\n(Kenny \\& Young 1989), in which the parameters have the same units as in\nEqn.~\\ref{HImE}. This assumes a CO to H$_2$ conversion factor of\n$X=2.8\\times10^{20}$ H$_2$ cm$^{-2}$/[K($T_R$)km s$^{-1}]$. Atomic and\nmolecular gas masses are also given in Table~\\ref{massT}.\n\n\\subsection{Optical luminosities}\n\nBlue magnitudes were taken from the Lyon-Meudon Extra-galactic Database\n(LEDA) and converted to luminosities using $M_{B\\odot}=5.48$. Blue\nluminosities are given in Table~\\ref{massT} and are corrected for\nGalactic extinction but not for internal extinction or inclination\neffects. In future discussions involving $L_{\\rm{B}}$, mention will be\nmade of `corrected' blue luminosities. This will refer to the values\nin Table~\\ref{massT} after further correction for the internal effects\nof dust in the galaxy, and for inclination, following the prescription\ngiven in the 3rd Reference Catalogue of Bright Galaxies (RC3) (de\nVaucouleurs et al. 1991).\n\n\\subsection{Far Infra-Red Luminosities}\n\nThe FIR luminosity ($L_{\\rm{fir}}$) is usually calculated using the 60\nand 100$\\mu$m {\\em IRAS\\/} fluxes, as described in the\nAppendix of {\\em Catalogued Galaxies and Quasars Observed in the IRAS\nSurvey\\/} (Version 2, 1989):\n\n\\[ FIR = 1.26 \\times 10^{-14}(2.58S_{60}+S_{100})\\]\n\nand\n\n\\[L_{\\rm{fir}}=4\\pi D^2 \\times FIR \\times C\n\\]\n\n\\input{table4}\n\\vspace{2mm}\nwhere $D$ is defined in Eqn.~\\ref{DE} and $C$ is a colour correction\nfactor which depends on the ratio of $S_{60}/S_{100}$ and the assumed\nvalue of the emissivity index. The correction factor, designed to\naccount for emission outside the {\\em IRAS\\/} bands, varies between\n1.3 and 2.4 and is explained in more detail by Helou et al. (1988).\nHaving submillimetre fluxes, we can use our derived temperatures and\n$\\beta$ to integrate the total flux under the SED directly out to\n1000$\\mu$m, hopefully leading to more accurate values for\n$L_{\\rm{fir}}$ since no general assumptions are being made. We\nintegrate from $40-1000\\mu$m, since if we were integrating to shorter\nwavelengths we should really include the {\\em IRAS\\/} 12 and 25$\\mu$m\ndata points which would require a multi-component temperature model,\nbeyond the scope of what we are doing here. However, for our objects\nthe ratio of $S_{60}/S_{25}$ is greater than 2.4, meaning that the\ncontribution to the integral at $\\lambda < 40\\mu$m is not very\nsignificant (if we integrate our SED with only the three data points\nout to 1$\\mu$m we find increases in $L_{\\rm{fir}}$ of only a few per\ncent). Our values for $L_{\\rm{fir}}$ are similar to those calculated\nusing the standard {\\em IRAS\\/} formulation described above, although\nslightly lower ($\\sim 10$ per cent) than if the appropriate value of\n$C$ were chosen for an emissivity index of one. This is probably\nbecause calculating a temperature from the 60/100 flux ratio tends to\noverestimate the temperature and therefore the correction factor\nrequired. It must be noted that the true SED of these galaxies may not\nbe well represented by a single temperature model and the values of\n$L_{\\rm{fir}}$ would change accordingly. Our integrated values for\n$L_{\\rm{fir}}$ are listed in Table~\\ref{massT}.\n\n\\input{table5}\n\n\\section{LUMINOSITY AND DUST MASS FUNCTIONS}\n\n\\input{table6}\n\\input{table7}\n\nThe luminosity function (LF) is given by\n\n\\begin{equation}\n\\Phi(L)\\Delta L = \\sum_i \\frac{1}{V_i} \\label{lfE}\n\\end{equation}\n\nwhere $\\Phi(L)\\Delta L$ is the number density of sources (Mpc$^{-3}$)\nin the luminosity range $L$ to $L+\\Delta L$, the sum is over all the\nsources in the sample in this luminosity range, and $V_i$ is the\naccessible volume of the {\\em i}th source in the original sample (Avni\n\\& Bahcall 1980). For this sample, the accessible volume is the\nmaximum volume in which the object could be seen and still be in the\n{\\em IRAS} Bright Galaxy Sample and so to calculate this, the 60$\\mu$m\nluminosity of each galaxy is used. In Equation~\\ref{lfE}, however, the\nluminosity is the luminosity at 850$\\mu$m, the wavelength of our\nsurvey. The volume from $cz=0$ to $cz=$ 1900 km s$^{-1}$ is not included\nin the calculation of $V_i$ as galaxies with velocities less than this\nwere excluded from our sample. $\\Phi(L)$ has been normalised to\ndex$^{-1}$ by dividing by $\\Delta L$. The dust mass function is\nestimated in the same way as the luminosity function but substituting\ndust mass for luminosity in Eqn.~\\ref{lfE}. This was done for both\nvalues of the dust mass; using a single temperature, and assuming a colder\ncomponent at $T_{\\rm{d}}=20$ K. The luminosity function at\n850$\\mu$m and both of the dust mass functions are shown in\nFig.~\\ref{lf850F}, and tabular forms for the functions are given in\nTable~\\ref{lfT}.\n\n\\begin{figure*}\n \\vspace{6.5cm}\n \\special{psfile='Fig5a.ps' hoffset=-150 voffset=10 hscale=30\nvscale=35}\n \\special{psfile='Fig5b.ps' hoffset=230 voffset=10 hscale=30\nvscale=35}\n\\caption{\\label{lf850F}a) Luminosity function at 850$\\mu$m shown with\nbest-fitting Schechter function, $\\alpha=-2.18$,\n$L_{\\ast}=8.3\\times10^{21}$ W Hz$^{-1}$ sr$^{-1}$. b) Dust mass\nfunction. Solid line:-- dust masses calculated from the submillimetre\nfluxes using the best-fitting $\\beta$ and $T_{\\rm{d}}$. Schechter\nparameters shown are $\\alpha=-1.23$, $M_{\\ast}=2.5\\times10^7$\nM$_{\\odot}$. Dashed line:-- `cold dust mass' function using\n$T_{\\rm{cold}}=20\\,\\rm{K}$ and $\\beta=2$. Schechter parameters are\n$\\alpha=-1.91$ and $M_{\\ast}^{cold}=8.5\\times10^{7}$ M$_{\\odot}$.}\n\\end{figure*}\n\n\\parindent=1em\n\nThe BGS contains many close pairs which are resolved at 850$\\mu$m but\nnot at the {\\em IRAS\\/} wavelengths. A few do have HIRES fluxes\n(Surace et al. 1993) and, when the resolved 60$\\mu$m flux is still\nabove the 5.24 Jy limit of the sample, can be treated as separate\nobjects for the purposes of calculating the luminosity and dust mass\nfunctions. The effect on the luminosity function of separating sources\nin this way would be to steepen it, as one luminous source with a\nlarge accessible volume becomes two less luminous sources with smaller\nvolumes. We attempted to quantify this in the following way. For\ngalaxies without HIRES fluxes, we estimated 60$\\mu$m fluxes for the\nindividual galaxies in each pair using the FIR-radio correlation\n(Helou et al. 1985). We removed any galaxy whose flux fell below the\nflux limit of the sample and re-calculated the luminosity\nfunction. Figure~\\ref{lfpF} shows this luminosity function compared\nwith our original one (calculated using the sum of the 850$\\mu$m\nemission from a pair of galaxies unresolved at 60$\\mu$m). There is\nonly a significant difference in the highest luminosity bin, which\nsuffers from noise anyway due to the small number of objects. In\nfuture, we will refer only to the luminosity function constructed\nusing the combined pair fluxes (Fig.~\\ref{lf850F}a), since this can be\nmost readily compared with the 60$\\mu$m LF.\n\n\\begin{figure}\n \\vspace{8cm}\n \\special{psfile='Fig6.ps' hoffset=0 voffset=0 hscale=35\nvscale=30}\n\\caption{\\label{lfpF} Luminosity function at 850$\\mu$m for combined\npair fluxes (Table~\\ref{fluxT}) -- solid symbols, compared to the\nluminosity function when the fluxes for the resolved pairs are\nseparated (Table~\\ref{pfluxT}) -- open symbols.}\n\\end{figure}\n\nThe luminosity function estimator (Eqn.~\\ref{lfE}) is unbiased\nproviding there is no population of submillimetre emitting galaxies\nwhich have a high space density, yet are completely absent from the\noriginal {\\em IRAS} sample. The only conceivable type of galaxy to\nwhich this could apply would be a hypothetical `cold' population with\n$T_{\\rm{d}} < 25$ K. To investigate this possibility, let us assume\nthat there are two populations of galaxies with equal space\ndensities and 850$\\mu$m luminosities, one with dust temperatures\nat 20 K and the other at 35 K. The relative numbers in an 850$\\mu$m\nflux-limited survey would be given by\\\\\n\n\\[ \\frac{N_{A}}{N_{B}}\\, = \\:\\frac{\\Phi_{A}}{\\Phi_{B}}\\times\n\\frac{V_{A}}{V_{B}}\\, \\approx \\:\n\\frac{\\Phi_{A}}{\\Phi_{B}}\\,\\frac{(L_{850,A})^{3/2}}{(L_{850,B})^{3/2}}\n\\]\n\\parindent=0pt\nwhere A and B refer to the two populations, $\\Phi$ is the space\ndensity, $V$ is the `accessible volume' in which one of the galaxies\nwould have been detected by the survey, and $L_{850}$ is the\nluminosity at 850$\\mu$m. Given the assumptions we have made, $N_A /\nN_B =1$ and therefore equal numbers of the two populations should be\nfound by the survey.\n\n\\parindent=1em\n\nNow let us consider the relative numbers that would be found by a\n60$\\mu$m flux-limited survey (the BGS). Replacing the 850$\\mu$m\nluminosity in the above equation with 60$\\mu$m luminosity, we now\npredict that the ratio $N_{35K} / N_{20K}$ will be $\\sim\n724$. Clearly, in a sample of $\\sim100$ {\\em IRAS\\/} galaxies, finding\na member of this hypothetical cold population would be unlikely and so\nour attempt to construct the 850$\\mu$m LF from our\nsample would be an underestimate. Making a similar calculation for galaxies\nat $T_{\\rm{d}}=25$ K and 35 K we now expect to find\n$\\sim$ 32 times as many warm galaxies as cold ones, so in our sample\nwe would expect to see around 3 objects at $T_{\\rm{d}}=25$ K. There\nare actually two galaxies with $T_{\\rm{d}} \\sim25$ K in our sample,\nwhich is consistent with the idea that we could be missing a significant\ncold population.\n\nIs there truly a possibility that there is a missing population of\ngalaxies? An important point to realise is that our dust temperatures\nare merely those corresponding to a best-fitting single-component\nmodel and are not {\\em actual\\/} dust temperatures. One way to assess\nthe possibility that we are missing galaxies is to carry out precisely\nthe same fitting procedure for optically-selected galaxies. For\nexample, NGC 891 has been studied at many submillimetre wavelengths\n(Alton et al. 1998b), but if we throw away all the measurements except\nthose at 60, 100 and 850$\\mu$m, and carry out our fitting procedure,\nwe obtain $T_{\\rm{d}}=34$ K and $\\beta =0.7$. While this temperature\nis similar to the average temperature for our sample, indicating that\nthere is a warm component in NGC 891, the value of 0.7 for $\\beta$ is\nsignificantly lower than for most of our galaxies suggesting a large\namount of colder dust, and when the full submillimetre data-set was\nused the bulk of the dust in NGC 891 was found to be at 15 K. Consider now\nour own Galaxy : if the {\\em IRAS\\/} FIR and ARGO submillimetre data\n(Sodroski et al. 1989; Masi et al. 1995) for the Milky Way is combined\nand fitted in our usual way we find a temperature of 28 K with a\n$\\beta$ of 0.7, so again the SED of the Milky Way would not\nnecessarily have excluded it from our sample. The question of whether\nwe are missing cold galaxies remains open (primarily how many cold\ngalaxies there are to miss). To address this properly, and to\nconstrain the luminosity function better at low luminosities we will\nneed to complete the survey of an optically-selected sample, which\nwill not be biased by temperature selection as is the\nBGS.\n\n\\begin{figure}\n \\vspace{8.8cm}\n \\special{psfile='Fig7.eps' hoffset=0 voffset=0 hscale=35\nvscale=35}\n\\caption{\\label{602850F} The measured 850$\\mu$m luminosity\nfunction (solid symbols with error bars) along with extrapolations of the\n60$\\mu$m LF from Soifer et al. (1987), using the following fixed\nparameters:- $\\beta=2,\\,T_{\\rm{d}}=24$ K -- open triangles; $\\beta=1.5,\n\\, T_{\\rm{d}}=38$ K -- solid diamonds; $\\beta=1, \\,T_{\\rm{d}}=45$ K -- open\ncircles.}\n\\end{figure}\n\nThe 60$\\mu$m luminosity function of the BGS from Soifer et al. (1987),\ncan be compared to the 850$\\mu$m LF by making an extrapolation based\non an assumption about a galaxy's SED from the far-infrared to the\nsubmillimetre. In fact, all of the 60$\\mu$m LFs using {\\em IRAS} data\nare consistent with each other (with the exception the one from Saunders et\nal. (1990), see Lawrence et al. 1999) and so it does not really matter\nwhich one we use. We have used the Soifer et al. one as it represents\nthe same sample of galaxies which we observed. In the past this\nextrapolation has been done by assuming a single temperature and\n$\\beta$ for all galaxies, which for 60 and 850$\\mu$m gives the\nfollowing\n\n\\begin{equation}\nL_{850}=L_{60} \\times \\left(\\frac{\\nu_{850}}{\\nu_{60}}\\right)^{3+\\beta}\n\\times\n\\left(\\frac{e^{240.2/T_{\\rm{d}}}-1}{e^{16.8/T_{\\rm{d}}}-1}\\right)\n\\label{602850E}\n\\end{equation}\n\\parindent=0pt\nExtrapolations of the 60$\\mu$m LF using a range of plausible values of\n$\\beta$ and $T_{\\rm{d}}$ are shown over the measured 850$\\mu$m LF in\nFig~\\ref{602850F}. As one would expect, an 850$\\mu$m luminosity\nfunction obtained by extrapolating in wavelength from a 60$\\mu$m LF\nis highly dependent on the values assumed for $T_{\\rm{d}}$ and\n$\\beta$. In practice, luminosity functions obtained in this way have\nhad much lower amplitudes than the one we actually measure,\nessentially because dust temperatures deduced from {\\em IRAS\\/} data\nalone are always higher than the temperatures we estimate here. This\ncan have significant consequences when trying to model the evolution\nrequired to fit the observed submillimetre number counts from deep\nsurveys and the submillimetre background and the implications will be\ndiscussed in a future paper (Eales et al. in prep). The other\ndifference in the luminosity functions is the slope: the luminosity\nfunction we measure is steeper than the ones extrapolated from the\n60$\\mu$m LF. The difference in slope between the two LFs is due to the\ncorrelation of dust temperature with 60$\\mu$m luminosity\n(Fig.~\\ref{60TF}). As the temperature changes with 60$\\mu$m\nluminosity, extrapolating every $L_{60}$ to 850$\\mu$m with an average\n$T_{\\rm{d}}$ will underestimate the 850$\\mu$m luminosity at lower\n$L_{60}$ and overestimate it at high $L_{60}$. Using the fitted\ndependences of $L_{60}$ on $T_{\\rm{d}}$ and also $\\beta$ on\n$T_{\\rm{d}}$ (see Table~\\ref{fitsT}) we again extrapolate the 60$\\mu$m\nLF and this time the agreement with the 850$\\mu$m LF is much better\n(Fig.~\\ref{602850bF}).\n\n\\begin{figure}\n \\vspace{8.8cm}\n \\special{psfile='Fig8.ps' hoffset=0 voffset=0 hscale=35\nvscale=35}\n\\caption{\\label{60TF} Dust temperature $T_{\\rm{d}}$ versus 60$\\mu$m\nluminosity, showing that the most luminous galaxies have the hottest\ntemperatures, the abrupt cutoff at the low luminosity end is due to\nthe lower velocity limit in the selection of the sample at 60$\\mu$m.}\n\\end{figure}\n\n\\begin{figure}\n \\vspace{8.8cm}\n \\special{psfile='Fig9.ps' hoffset=0 voffset=0 hscale=35\nvscale=35}\n\\caption{\\label{602850bF} 850$\\mu$m LF (solid symbols)\nalong with the extrapolation of the Soifer et al. (1987) 60$\\mu$m LF\nusing variable $\\beta$ and $T_{\\rm{d}}$ given by the relationships in\nTable~\\ref{fitsT}. This produces a better match to the measured\n850$\\mu$m LF than extrapolations made using single values for\n$T_{\\rm{d}}$ and $\\beta$ (see Fig.~\\ref{602850F}).}\n\\end{figure}\n\nThe 850$\\mu$m luminosity and dust mass functions are well fitted by\nSchechter functions of the form (Press \\& Schechter 1974; Schechter 1975)\n\n\\[ \n\\Phi(L)dL =\\phi(L)\\left(\\frac{L}{L_{\\ast}}\\right)^{\\alpha}e^{-(L/L{\\ast})}\\,dL/L_{\\ast} \n\\]\n \nThe best fitting parameters for the 850$\\mu$m LF and the dust mass\nfunctions along with the reduced chi-squared values ($\\chi^{2}_{\\nu}$) \nfor the fits, are given in Table~\\ref{lfT}. The $\\chi^2$ contours\nshowing the joint confidence intervals on $\\alpha$ and $L_{\\ast}$ for\nall the functions are shown in Figs.~\\ref{chicontF}(a--c).\n\n\\begin{figure*}\n \\vspace{5cm}\n \\special{psfile='Fig10a.ps' hoffset=-10 voffset=-120 hscale=30\nvscale=35}\n \\special{psfile='Fig10b.ps' hoffset=150 voffset=-120 hscale=30\nvscale=35}\n \\special{psfile='Fig10c.ps' hoffset=310 voffset=-120 hscale=30\nvscale=35}\n\\caption{\\label{chicontF}a) Joint confidence $\\chi^2$contours for the\n850$\\mu$m LF parameters $\\alpha$ and $L_{\\ast}$. Contours are at the\n68, 90 and 95\\% confidence level, d.o.f = 2. b) Joint confidence\ncontours for the single temperature dust mass function parameters\n$\\alpha$ and $M_{\\ast}$. Same contour levels as a). c) Joint\nconfidence contours for the `cold' dust mass function, same parameters\nand levels as b).}\n\\end{figure*}\n\nThere are several points to note here. Firstly, the 60$\\mu$m LF cannot\nbe fitted by a simple Schechter function (Lawrence et al. 1986; Rieke\n\\& Lebofsky 1986) as the high luminosity end does not fall off steeply \nenough. The fact that the 850$\\mu$m LF and the dust mass\nfunction can, suggests that the Schechter function is surprisingly\nuniversal and that in the case of the 60$\\mu$m LF, the Schechter\nfunction exponential fall-off is concealed by the sensitivity of the\n60$\\mu$m emission to dust temperature. Secondly, the slope of the\n850$\\mu$m LF is steeper than $-2$ ($\\alpha=-2.18$ ) at lower submillimetre\nluminosities. This is significant because if this slope continued to\nzero luminosity, the submillimetre sky would be infinitely bright (a\nsubmillimetre Olbers Paradox). Of course, this means that the slope\nmust flatten out at lower luminosities not yet probed by our\nsurvey. The shape of the dust mass function is strongly affected by\nthe temperature distribution assumed, i.e. all of the dust at a single\ntemperature, or most of the dust at some colder temperature with a\nsmall warmer component being responsible for the 60$\\mu$m flux. The\nshape of the `cold dust mass' function bears more resemblance to the\n850$\\mu$m LF simply because of our assumption of a common universal\ntemperature for the cold component. We do believe however, that the\ntrue distribution of the dust masses lies somewhere between the two;\nthe temperature of a cold component may not be the same in all\ngalaxies but will probably vary less than the temperature of the warm\ncomponents and this degree of variation along with the relative\namounts of cold and warm dust will determine how similar the dust mass\nfunction is in shape to the 850$\\mu$m LF.\n\n%\\end{document}"
},
{
"name": "table1.tex",
"string": "%\\documentclass[a4paper,10pt]{article}\n%\\pagestyle{empty}\n%\\setlength{\\textwidth}{35em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\addtolength{\\oddsidemargin}{-25mm}\n%\\addtolength{\\evensidemargin}{-25mm}\n%\\marginparwidth=0mm\n%\\usepackage{longtable}\n%\\begin{document}\n\n%\\parindent=0pt\n\\onecolumn\n\\begin{longtable}{lccccccccccc} \n\\caption{\\label{fluxT}Flux densities and SED parameters}\\\\\n\\hline\n\\\\[-2.5ex]\n\\multicolumn{1}{c}{(1)}&\\multicolumn{1}{c}{(2)}&\\multicolumn{1}{c}{(3)}&\\multicolumn{1}{c}{(4)}&\\multicolumn{1}{c}{(5)}&\\multicolumn{1}{c}{(6)}&\\multicolumn{1}{c}{(7)}&\\multicolumn{1}{c}{(8)}&\\multicolumn{1}{c}{(9)}&\\multicolumn{1}{c}{(10)}&\\multicolumn{1}{c}{(11)}&\\multicolumn{1}{c}{(12)}\\\\\n\\\\[-1ex]\n\\multicolumn{1}{c}{Name}&\\multicolumn{1}{c}{R.A.}&\\multicolumn{1}{c}{Decl.}&\\multicolumn{1}{c}{$cz$}&\\multicolumn{1}{c}{$S_{60}$}&\\multicolumn{1}{c}{$S_{100}$}&\\multicolumn{1}{c}{$S_{850}$}&\\multicolumn{1}{c}{$\\sigma_{850}$}&\\multicolumn{1}{c}{$T_{\\rm{d}}$}&\\multicolumn{1}{c}{$\\sigma(T_{\\rm{d}})$}&\\multicolumn{1}{c}{$\\beta$}&\\multicolumn{1}{c}{$\\sigma(\\beta)$}\\\\\n\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{(J2000)}&\\multicolumn{1}{c}{(J2000)}&\\multicolumn{1}{c}{(km\ns$^{-1}$)}&\\multicolumn{1}{c}{(Jy)}&\\multicolumn{1}{c}{(Jy)}&\\multicolumn{1}{c}{(mJy)}&\\multicolumn{1}{c}{(mJy)}&\\multicolumn{1}{c}{(K)}&\\multicolumn{1}{c}{(K)}&\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{}\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\n\\endfirsthead\n\\caption{... continued}\\\\\n\\hline\n\\\\[-2.5ex]\n\\multicolumn{1}{c}{(1)}&\\multicolumn{1}{c}{(2)}&\\multicolumn{1}{c}{(3)}&\\multicolumn{1}{c}{(4)}&\\multicolumn{1}{c}{(5)}&\\multicolumn{1}{c}{(6)}&\\multicolumn{1}{c}{(7)}&\\multicolumn{1}{c}{(8)}&\\multicolumn{1}{c}{(9)}&\\multicolumn{1}{c}{(10)}&\\multicolumn{1}{c}{(11)}&\\multicolumn{1}{c}{(12)}\\\\\n\\\\[-1ex]\n\\multicolumn{1}{c}{Name}&\\multicolumn{1}{c}{R.A.}&\\multicolumn{1}{c}{Decl.}&\\multicolumn{1}{c}{$cz$}&\\multicolumn{1}{c}{$S_{60}$}&\\multicolumn{1}{c}{$S_{100}$}&\\multicolumn{1}{c}{$S_{850}$}&\\multicolumn{1}{c}{$\\sigma_{850}$}&\\multicolumn{1}{c}{$T_{\\rm{d}}$}&\\multicolumn{1}{c}{$\\sigma(T_{\\rm{d}})$}&\\multicolumn{1}{c}{$\\beta$}&\\multicolumn{1}{c}{$\\sigma(\\beta)$}\\\\\n\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{(J2000)}&\\multicolumn{1}{c}{(J2000)}&\\multicolumn{1}{c}{(km\ns$^{-1}$)}&\\multicolumn{1}{c}{(Jy)}&\\multicolumn{1}{c}{(Jy)}&\\multicolumn{1}{c}{(mJy)}&\\multicolumn{1}{c}{(mJy)}&\\multicolumn{1}{c}{(K)}&\\multicolumn{1}{c}{(K)}&\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{}\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\n\\endhead\n\\\\[-2.5ex]\n\\hline\n\\endfoot\n\\\\[-2.5ex] \n\\hline \n%\\\\[-2.5ex]\n%\\multicolumn{12}{p{50em}}{\\small (1) Most commonly used name taken\n%from the IRAS BGS}\\\\\n%\\multicolumn{12}{p{50em}}{\\small (2) Right ascension J2000 epoch}\\\\\n%\\multicolumn{12}{p{50em}}{\\small (3) Declination J2000 epoch}\\\\\n%\\multicolumn{12}{p{50em}}{\\small (4) Recession velocity taken from\n%NED (The NASA/IPAC Extragalactic Database (NED) is operated by\n%the Jet Propulsion Laboratory, California Institute of Technology,\n%under contract with the National Aeronautics and Space\n%Administration.)}\\\\\n%\\multicolumn{12}{p{50em}}{\\small (5) 60$\\mu$m flux from Soifer et\n%al. 1989}\\\\\n%\\multicolumn{12}{p{50em}}{\\small (6) 100$\\mu$m flux from Soifer et\n%al. 1989}\\\\\n%\\multicolumn{12}{p{50em}}{\\small (7) 850$\\mu$m flux (this work)}\\\\\n%\\multicolumn{12}{p{50em}}{\\small (8) error on 850$\\mu$m flux,\n%calculated in the manner described in Section 2.4 and inclusive of a\n%10\\% calibration uncertainty. A * indicates that a 15\\% calibration\n%uncertainty was used.}\\\\\n%\\multicolumn{12}{p{50em}}{\\small (9) Dust temperature derived from a\n%single component fit to the 60, 100 and 850$\\mu$ data points as\n%described in Section 3.1}\\\\\n%\\multicolumn{12}{p{50em}}{\\small (10) Statistical uncertainty in the\n%dust temperature as described in Section 3.1}\\\\\n%\\multicolumn{12}{p{50em}}{\\small (11) Emissivity index derived fron\n%the single component fit, described in Section 3.1}\\\\\n%\\multicolumn{12}{p{50em}}{\\small (12) Statistical uncertainty in the\n%emissivity index as described in Section 3.1}\\\\ \n%\\multicolumn{12}{p{50em}}{\\small $^p$ indicates a close or interacting\n%pair which was resolved by SCUBA. Individual fluxes are listed in\n%Table~\\ref{pfluxT}.}\\\\\n\\endlastfoot\nNGC 23 & 0 09 53.4 & $+$25 55 26 & 4565 & 8.77 & 14.96 & 144 & 25 &\n34.4 & 3.0 & 1.3 & 0.2\\\\ \nUGC 556 & 0 54 50.3 & $+$29 14 47 & 4629 & 5.36 & 9.99 & 79 & 15\n& 32.0 & 2.6 & 1.5 & 0.2\\\\ \nNGC 470 & 1 19 44.8 & $+$03 24 35 & 2374 & 7.09 & 12.01 &\n213 & 30 & 38.0 & 3.0 & 0.9 & 0.2\\\\ \nMCG+02-04-025 & 1 20 02.7 & $+$14 21 43 & 9362 & 10.72 & 9.60 & 39 & 8\n& 44.6 & 4.6 & 1.4 & 0.2 \\\\ \nUGC 903 & 1 21 47.9 & $+$17 35 34 & 2518 & 7.91 & 14.58 & 178 & 26 &\n34.4 & 3.1 & 1.2 & 0.2\\\\\nNGC 520 & 1 24 34.9 & $+$03 47 31 & 2281 & 31.55 & 46.56 & 325 & 50 &\n36.2 & 3.1 & 1.4 & 0.2\\\\\nIII ZW 035 & 1 44 30.5 & $+$17 06 08 & 8215 & 11.86 & 13.75 & 76 & 15\n& 39.2 & 3.8 & 1.4 & 0.2\\\\ \nNGC 695 & 1 51 14.3 & $+$22 34 56 & 9735 & 7.61 & 13.80 & 136 & 21 &\n33.8 & 2.8 & 1.3 & 0.2\\\\\nNGC 697 & 1 51 17.5 & $+$22 21 30 & 3117 & 5.62 & 16.54 & 221 & 48* &\n27.8 & 2.2 & 1.5 & 0.2\\\\ \nUGC 1351 & 1 52 59.6 & $+$12 42 31 & 4558 & 6.12 & 11.71 & 141 & 21 &\n34.4 & 2.8 & 1.2 & 0.2\\\\ \nUGC 1451 & 1 58 30.0 & $+$25 21 36 & 4916 & 6.75 & 12.20 & 107 & 18 &\n33.2 & 2.6 & 1.4 & 0.2\\\\ \nNGC 772 & 1 59 19.5 & $+$19 00 30 & 2472 & 6.78 & 24.11 & 288 & 43 &\n25.4 & 1.7 & 1.7 & 0.2\\\\\nNGC 877 & 2 17 59.5 & $+$14 32 42 & 3913 & 11.76 & 23.34 & 332 & 43 &\n34.4 & 2.8 & 1.1 & 0.2\\\\\nNGC 958 & 2 30 42.8 & $-$02 56 23 & 5738 & 5.90 & 14.99 & 262 & 34 &\n30.8 & 2.0 & 1.2 & 0.2\\\\ \nNGC 992 & 2 37 25.5 & $+$21 06 03 & 4141 & 10.96 & 15.63 & 146 & 26 &\n38.0 & 3.5 & 1.2 & 0.2\\\\\nUGC 2238 & 2 46 17.5 & $+$13 05 48 & 6436 & 8.16 & 15.22 & 104 & 14 &\n31.4 & 2.9 & 1.6 & 0.2\\\\ \nIR 0243+21 & 2 46 39.2 & $+$21 35 11 & 6987 & 5.50 & 6.25 & 40 & 8 &\n41.0 & 4.5 & 1.3 & 0.2\\\\ \nNGC 1134 & 2 53 41.5 & $+$13 00 53 & 3651 & 8.99 & 16.07 & 242 & 31 &\n36.2 & 3.4 & 1.0 & 0.2\\\\ \nUGC 2369 & 2 54 01.8 & $+$14 58 14 & 9400 & 7.68 & 11.10 & 72 & 13 &\n36.2 & 3.4 & 1.4 & 0.2\\\\\nUGC 2403 & 2 55 57.2 & $+$00 41 33 & 4161 & 7.51 & 11.77 & 111 & 18 &\n36.8 & 2.9 & 1.2 & 0.2\\\\ \nNGC 1222 & 3 08 56.8 & $-$02 57 18 & 2452 & 12.86 & 15.15 & 84 & 16 &\n39.2 & 4.0 & 1.4 & 0.2\\\\ \nIR 0335+15 & 3 38 47.1 & $+$15 32 53 & 10600 & 5.77 & 6.53 & 44 & 9 &\n42.2 & 4.9 & 1.2 & 0.2\\\\ \nUGC 2982 & 4 12 22.5 & $+$05 32 51 & 5305 & 8.70 & 17.32 & 176 & 34* &\n32.0 & 2.8 & 1.4 & 0.2\\\\\nNGC 1614 & 4 34 00.0 & $-$08 34 45 & 4778 & 33.12 & 36.19 & 219 & 32 &\n41.6 & 4.2 & 1.3 & 0.2\\\\ \nNGC 1667 & 4 48 37.2 & $-$06 19 12 & 4547 & 6.24 & 16.54 & 163 & 22 &\n28.4 & 1.7 & 1.6 & 0.2\\\\ \nNGC 2623 & 8 38 24.1 & $+$25 45 16 & 5535 & 25.72 & 27.36 & 91 & 14 & 39.8\n& 4.1 & 1.6 & 0.2\\\\ \nIR 0857+39 & 9 00 24.5 & $+$39 03 55 & 17480 & 7.66 & 5.06 & 17 & 7 &\n50.6 & 9.0 & 1.4 & 0.4\\\\\nNGC 2782 & 9 14 05.1 & $+$40 06 49 & 2562 & 9.60 & 14.65 & 237 & 32 &\n39.2 & 3.6 & 0.9 & 0.2\\\\\nNGC 2785 & 9 15 15.4 & $+$40 55 03 & 2734 & 9.21 & 16.78 & 201 & 33 &\n34.4 & 3.1 & 1.2 & 0.2\\\\ \nUGC 4881 & 9 15 54.7 & $+$44 19 52 & 11782 & 6.53 & 10.21 & 65 & 13 &\n34.4 & 3.1 & 1.5 & 0.2\\\\ \nNGC 2856 & 9 24 16.2 & $+$49 14 58 & 2638 & 6.15 & 10.28 & 89 & 16 &\n35.0 & 2.9 & 1.3 & 0.2\\\\\nMCG+08-18-012 & 9 36 37.2 & $+$48 28 28 & 7777 & 6.39 & 8.83 & 42 & 10 &\n35.6 & 3.4 & 1.6 & 0.2\\\\ \nNGC 2966 & 9 42 11.5 & $+$04 40 23 & 2044 & 5.76 & 8.69 & 136 & 28 &\n39.8 & 4.9 & 0.9 & 0.2\\\\\nNGC 2990 & 9 46 17.2 & $+$05 42 33 & 3088 & 5.49 & 10.16 & 110 & 19 &\n33.8 & 3.2 & 1.3 & 0.2\\\\\nIC 563/4 $^p$ & 9 46 20.7 & $+$03 03 31 & 6020 & 5.35 & 12.43 & 228 & 35\n& 32.0 & 3.0 & 1.1 & 0.2\\\\\nUGC 5376 & 10 00 26.8 & $+$03 22 26 & 2050 & 5.94 & 11.49 & 148 & 23 &\n33.8 & 2.9 & 1.2 & 0.2\\\\\nNGC 3094 & 10 01 26.0 & $+$15 46 13 & 2404 & 11.54 & 15.10 & 152 & 31 &\n40.4 & 3.8 & 1.1 & 0.2\\\\\nNGC 3110 & 10 04 02.0 & $-$06 28 31 & 5048 & 11.68 & 23.16 & 188 & 28\n& 32.0 & 2.3 & 1.5 & 0.2\\\\\nIR 1017+08 & 10 20 00.2 & $+$08 13 34 & 14390 & 6.08 & 5.97 & 36 & 6 &\n44.0 & 4.3 & 1.2 & 0.2\\\\\nNGC 3221 & 10 22 20.1 & $+$21 34 09 & 4110 & 7.44 & 19.56 & 253 & 37 &\n29.6 & 2.2 & 1.4 & 0.2\\\\\nNGC 3367 & 10 46 34.6 & $+$13 45 03 & 3037 & 6.06 & 12.49 & 132 & 21 &\n31.4 & 2.6 & 1.4 & 0.2\\\\\nIR 1056+24 & 10 59 18.2 & $+$24 32 34 & 12912 & 12.53 & 16.06 & 61 & 13\n& 35.6 & 3.3 & 1.7 & 0.2\\\\\nARP 148 & 11 03 54.0 & $+$40 50 59 & 10350 & 6.95 & 10.99 & 92 & 20 & 35.6\n& 3.0 & 1.3 & 0.2\\\\\nNGC 3583 & 11 14 12.2 & $+$48 18 56 &2136 & 7.18 & 19.50 & 185 &\n31 & 28.4 & 2.2 & 1.6 & 0.2\\\\\nMCG+00-29-023 & 11 21 10.9 & $-$02 59 13 & 7646 & 5.40 & 8.87 & 84 &\n13 & 35.0 & 3.6 & 1.3 & 0.2\\\\\nUGC 6436 & 11 25 46.6 & $+$14 40 26 & 10243 & 5.60 & 9.80 & 106 & 18 &\n35.0 & 3.2 & 1.2 & 0.2\\\\\nNGC 3994/5 $^p$ & 11 57 39.4 & $+$32 17 08 & 3170 & 8.26 & 16.94 & 232 &\n31 & 33.2 & 2.5 & 1.2 & 0.2\\\\\nNGC 4045 & 12 02 42.2 & $+$01 58 37 & 1981 & 6.50 & 13.57 & 142 & 25 &\n31.4 & 2.6 & 1.4 & 0.2\\\\\nIR 1211+03 & 12 13 46.1 & $+$02 48 40 & 21703 & 8.39 & 9.10 & 49 & 10\n& 42.2 & 5.2 & 1.3 & 0.2\\\\\nNGC 4273 & 12 19 56.1 & $+$05 20 37 & 2378 & 10.52 & 21.02 & 324 & 46\n& 33.8 & 3.2 & 1.1 & 0.2\\\\\nIR 1222-06 & 12 25 03.9 & $-$06 40 53 & 7902 & 5.79 & 7.53 & 74 & 15 &\n40.4 & 4.9 & 1.1 & 0.2\\\\\nNGC 4418 & 12 26 54.7 & $-$00 52 39 & 2179 & 42.32 & 30.76 & 255 & 37\n& 55.4 & 8.0 & 0.9 & 0.2\\\\\nNGC 4433 & 12 27 38.7 & $-$08 16 42 & 3000 & 14.15 & 22.42 & 220 & 47\n& 36.8 & 3.5 & 1.2 & 0.2\\\\\nNGC 4793 & 12 54 41.1 & $+$28 56 21 & 2484 & 12.49 & 27.99 & 258 & 42\n& 30.2 & 2.5 & 1.5 & 0.2\\\\\nNGC 4922 & 13 01 25.3 & $+$29 18 49 & 7071 & 6.20 & 7.30 & 53 & 12 &\n41.6 & 4.4 & 1.2 & 0.2\\\\\nNGC 5020 & 13 12 39.8 & $+$12 35 58 & 3362 & 5.39 & 10.01 & 206 & 34 &\n36.2 & 3.1 & 0.9 & 0.2\\\\\nIC 860 & 13 15 03.5 & $+$24 37 08 & 3347 & 17.66 & 17.66 & 118 & 20 &\n43.4 & 4.4 & 1.2 & 0.2\\\\\nUGC 8387 & 13 20 35.3 & $+$34 08 22 & 7000 & 13.69 & 24.90 & 113 & 15 &\n30.8 & 2.4 & 1.8 & 0.2\\\\\nNGC 5104 & 13 21 23.2 & $+$00 20 32 & 5578 & 6.69 & 12.77 & 91 & 20* &\n31.4 & 2.9 & 1.6 & 0.2\\\\\nNGC 5256 & 13 38 17.5 & $+$48 16 36 & 8353 & 7.19 & 10.35 & 82 & 17 &\n36.8 & 4.6 & 1.3 & 0.2\\\\\nNGC 5257/8 $^p$ & 13 39 55.5 & $+$00 50 09 & 6770 & 10.68 & 20.80 &\n283 & 39* & 33.2 & 2.4 & 1.2 & 0.2\\\\\nUGC 8739 & 13 49 14.0 & $+$35 15 24 & 5032 & 5.90 & 14.32 & 187 & 27 &\n30.8 & 2.4 & 1.3 & 0.2\\\\\nNGC 5371 & 13 55 39.0 & $+$40 27 31 & 2553 & 5.40 & 18.16 & 136 & 24 &\n25.4 & 1.5 & 1.9 & 0.2\\\\\nNGC 5394/5 $^p$ & 13 58 38.1 & $+$37 26 27 & 3470 & 9.07 & 21.51 & 269\n& 36 & 30.2 & 2.6 & 1.4 & 0.2\\\\\nNGC 5433 & 14 02 36.0 & $+$32 30 38 & 4354 & 6.34 & 11.26 & 163 & 28 &\n35.6 & 3.4 & 1.1 & 0.2\\\\\nNGC 5426/7 $^p$ & 14 03 26.0 & $-$06 01 50 & 2678 & 9.93 & 24.81 & 548\n& 86* & 32.0 & 2.8 & 1.0 & 0.2\\\\\nZW 247.020 & 14 19 43.3 & $+$49 14 12 & 7666 & 5.91 & 8.25 & 36 & 8 &\n34.4 & 3.4 & 1.7 & 0.2\\\\\nNGC 5600 & 14 23 49.2 & $+$14 38 22 & 2319 & 5.35 & 11.46 & 112 & 22 &\n31.4 & 2.6 & 1.4 & 0.2\\\\\nNGC 5653 & 14 30 10.2 & $+$31 12 56 & 3562 & 10.27 & 21.86 & 205 & 32\n& 30.8 & 2.0 & 1.5 & 0.2\\\\\nNGC 5665 & 14 32 25.9 & $+$08 04 47 & 2228 & 6.18 & 11.67 & 157 & 27 &\n35.0 & 3.4 & 1.1 & 0.2\\\\\nNGC 5676 & 14 32 46.7 & $+$49 27 29 & 2114 & 12.00 & 29.78 & 481 & 69\n& 30.8 & 1.8 & 1.2 & 0.2\\\\\nNGC 5713 & 14 40 11.4 & $-$00 17 26 & 1900 & 20.69 & 36.27 & 359 & 44\n& 34.4 & 3.1 & 1.3 & 0.2\\\\\nUGC 9618 $^p$ & 14 57 00.5 & $+$24 36 42 & 9900 & 6.68 & 14.54 & 215 &\n31 & 32.0 & 2.6 & 1.2 & 0.2\\\\\nNGC 5792 & 14 58 22.7 & $-$01 05 29 & 1924 & 9.45 & 18.31 & 383 & 56 &\n35.6 & 3.2 & 0.9 & 0.2\\\\\nZW 049.057 & 15 13 13.1 & $+$07 13 31 & 3927 & 21.06 & 29.88 & 200 &\n27 & 36.2 & 3.2 & 1.4 & 0.2\\\\\nNGC 5900 & 15 15 05.2 & $+$42 12 36 & 2511 & 7.36 & 16.69 & 179 & 23 &\n30.8 & 2.6 & 1.4 & 0.2\\\\\n1 Zw 107 & 15 18 06.1 & $+$42 44 45 & 11946 & 9.15 & 10.04 & 60 & 14 &\n41.6 & 4.6 & 1.3 & 0.2\\\\\nNGC 5929/30 $^p$ & 15 26 06.3 & $+$41 40 24 & 2617 & 9.14 & 13.69 &\n119 & 22 & 36.2 & 3.1 & 1.3 & 0.2\\\\\nIR 1525+36 & 15 26 59.4 & $+$35 58 37 & 16009 & 7.20 & 5.78 & 43 & 10\n& 50.6 & 6.9 & 1.0 & 0.2\\\\\nNGC 5936 & 15 30 00.9 & $+$12 59 21 & 4004 & 8.56 & 16.84 & 152 & 28 &\n32.6 & 2.9 & 1.4 & 0.2\\\\\nNGC 5937 & 15 30 46.1 & $-$02 49 46 & 2758 & 10.23 & 20.56 & 247 & 39\n& 32.6 & 2.7 & 1.3 & 0.2\\\\\nNGC 5953/4 $^p$ & 15 34 33.7 & $+$15 11 50 & 1960 &11.55 & 19.50 & 306\n& 31 & 36.8 & 4.1 & 1.0 & 0.2\\\\\nARP 220 & 15 34 57.2 & $+$23 30 11 & 5452 & 103.33 & 113.95 & 832 & 86\n& 42.2 & 5.7 & 1.2 & 0.2\\\\\nIR 1533-05 & 15 36 11.7 & $-$05 23 52 & 8186 & 5.25 & 8.96 & 79 & 15 &\n35.0 & 3.0 & 1.3 & 0.2\\\\\nNGC 5962 & 15 36 32.0 & $+$16 36 22 & 1963 & 8.99 & 20.79 & 317 & 37 &\n32.0 & 2.7 & 1.2 & 0.2\\\\\nNGC 5990 & 15 46 16.4 & $+$02 24 55 & 3839 & 9.20 & 15.46 & 110 & 23 &\n33.2 & 2.7 & 1.5 & 0.2\\\\\nNGC 6052 & 16 05 13.0 & $+$20 32 34 & 4712 & 6.46 & 10.18 & 95 & 15 &\n35.6 & 3.5 & 1.3 & 0.2\\\\\nMCG+01-42-008 & 16 30 56.5 & $+$04 04 58 & 7342 & 7.38 & 12.48 & 95 &\n18 & 34.4 & 2.8 & 1.4 & 0.2\\\\\nNGC 6181 & 16 32 21.2 & $+$19 49 30 & 2379 & 9.35 & 21.00 & 228 & 37 &\n30.8 & 2.6 & 1.4 & 0.2\\\\\nNGC 7448 & 23 00 03.6 & $+$15 58 56 & 2192 & 8.32 & 17.08 & 193 & 32 &\n32.6 & 2.8 & 1.3 & 0.2\\\\\nNGC 7469 $^p$ & 23 03 16.4 & $+$08 52 50 & 4892 & 27.68 & 34.91 & 264 & 30 &\n40.4 & 3.9 & 1.2 & 0.2\\\\\nNGC 7479 & 23 04 56.5 & $+$12 19 19 & 2381 & 15.35 & 24.60 & 335 & 56\n& 38.0 & 3.8 & 1.0 & 0.2\\\\\nZW 453.062 & 23 04 56.5 & $+$19 33 08 & 7524 & 7.06 & 10.39 & 69 & 14\n& 36.2 & 3.5 & 1.4 & 0.2\\\\\nNGC 7541 & 23 14 43.4 & $+$04 32 04 & 2665 & 20.59 & 40.63 & 427 & 60\n& 33.2 & 2.4 & 1.3 & 0.2\\\\\nZW 475.056 & 23 16 00.6 & $+$25 33 25 & 8197 & 8.75 & 11.64 & 77 & 15\n& 37.4 & 3.8 & 1.4 & 0.2\\\\\nNGC 7591 & 23 18 16.3 & $+$06 35 10 & 4956 & 7.82 & 13.52 & 135 & 21 & 34.4\n& 2.8 & 1.3 & 0.2\\\\\nNGC 7592 & 23 18 22.1 & $-$04 24 58 & 7350 & 8.02 & 10.50 & 108 & 19 &\n39.8 & 3.8 & 1.1 & 0.2\\\\\nNGC 7674 & 23 27 56.7 & $+$08 46 44 & 8713 & 5.28 & 7.91 & 108 & 20 &\n38.6 & 4.2 & 1.0 & 0.2\\\\\nNGC 7678 & 23 28 26.2 & $+$22 25 02 & 3489 & 7.01 & 14.84 & 195 & 26 &\n33.2 & 2.7 & 1.2 & 0.2\\\\\nNGC 7679 & 23 28 46.7 & $+$03 30 41 & 5138 & 7.28 & 10.65 & 93 & 15 &\n38.0 & 3.6 & 1.2 & 0.2\\\\\nNGC 7714 & 23 36 14.1 & $+$02 09 18 & 2798 & 10.52 & 11.66 & 72 & 13 &\n41.0 & 6.9 & 1.3 & 0.2\\\\\nNGC 7771 & 23 51 24.9 & $+$20 06 42 & 4256 & 20.46 & 37.42 & 377 & 42\n& 33.8 & 3.0 & 1.3 & 0.2\\\\\nMRK 331 & 23 51 26.8 & $+$20 35 10 & 5541 & 17.32 & 20.86 & 132 & 25 &\n40.4 & 4.3 & 1.3 & 0.2\\\\\nUGC 12914/5 $^p$ & 00 01 39.6 & $+$23 29 33 & 4350 & 6.27 & 13.40 &\n191 & 30 & 32.6 & 2.6 & 1.2 & 0.2\\\\\n\n\\end{longtable}\n\\twocolumn\n{\\bf Notes to Table~\\ref{fluxT}:}\\\\\n(1) Most commonly used name taken from the IRAS BGS (2) Right\nascension J2000 epoch (3) Declination J2000 epoch (4) Recession\nvelocity taken from NED\\footnote{The NASA/IPAC Extragalactic Database\n(NED) is operated by the Jet Propulsion Laboratory, California\nInstitute of Technology, under contract with the National Aeronautics\nand Space Administration.} (5) 60$\\mu$m flux from Soifer et al. 1989\n(7) 850$\\mu$m flux (this work) (8) error on 850$\\mu$m flux, calculated\nin the manner described in Section 2.4 and inclusive of a 10\\%\ncalibration uncertainty. A * indicates that a 15\\% calibration\nuncertainty was used. (9) Dust temperature derived from a single\ncomponent fit to the 60, 100 and 850$\\mu$ data points as described in\nSection 3.1 (10) Statistical uncertainty in the dust temperature as\ndescribed in Section 3.1 (11) Emissivity index derived fron the single\ncomponent fit, described in Section 3.1 (12) Statistical uncertainty\nin the emissivity index as described in Section 3.1 $^p$ indicates a\nclose or interacting pair which was resolved by SCUBA. Individual\nfluxes are listed in Table~\\ref{pfluxT}.\n\n%\\end{document}\n\n"
},
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"name": "table2.tex",
"string": "%\\documentclass[a4paper,11pt]{article}\n%\\pagestyle{empty}\n%\\setlength{\\textwidth}{35em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\addtolength{\\oddsidemargin}{-10mm}\n%\\addtolength{\\evensidemargin}{-20mm}\n%\\marginparwidth=0mm\n%\\begin{document}\n\n%\\parindent=0pt\n\\begin{table*}\n\\centering\n\\caption{\\label{pfluxT}Fluxes for pairs resolved by SCUBA}\n\\begin{tabular}{lcccrrcccccc}\n\\\\[-2ex] \n\\hline\n\\\\[-2.5ex]\n\\multicolumn{1}{c}{Name}&\\multicolumn{1}{c}{R.A.}&\\multicolumn{1}{c}{Decl.}&\\multicolumn{1}{c}{$cz$}&\\multicolumn{1}{c}{$S_{60}$}&\\multicolumn{1}{c}{$S_{100}$}&\\multicolumn{1}{c}{$S_{850}$}&\\multicolumn{1}{c}{$\\sigma_{850}$}&\\multicolumn{1}{c}{$T_{\\rm{d}}$}&\\multicolumn{1}{c}{$\\sigma(T_{\\rm{d}})$}&\\multicolumn{1}{c}{$\\beta$}&\\multicolumn{1}{c}{$\\sigma(\\beta)$}\\\\\n\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{(J2000)}&\\multicolumn{1}{c}{(J2000)}&\\multicolumn{1}{c}{(km\ns$^{-1}$)}&\\multicolumn{1}{c}{(Jy)}&\\multicolumn{1}{c}{(Jy)}&\\multicolumn{1}{c}{(mJy)}&\\multicolumn{1}{c}{(mJy)}&\\multicolumn{1}{c}{(K)}&\\multicolumn{1}{c}{(K)}&\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{}\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\nIC 563 & 9 46 20.3 & $+$03 02 46 & 6093 & $^h$2.90 & $^h$5.87 & 103 & 24 & 34.4\n& 2.7 & 1.0 & 0.2\\\\\nIC 564 & 9 46 21.0 & $+$03 04 19 & 6026 & $^h$2.46 & $^h$6.56 & 125 &\n26 & 30.8 & 2.0 & 1.1 & 0.2\\\\\n\\\\[-2ex]\nNGC 3994 & 11 57 36.9 & $+$32 16 38 & 3096 & $^h$5.00 & $^h$10.31 & 106 & 20 &\n32.0 & 2.3 & 1.4 & 0.2\\\\\nNGC 3995 & 11 57 44.0 & $+$32 17 37 & 3254 & $^h$3.27 & $^h$6.63 & 126 & 24 &\n34.4 & 3.1 & 1.0 & 0.2\\\\\n\\\\[-2ex]\nNGC 5257 & 13 39 52.1 & $+$00 50 27 & 6798 & U & U & 114 & 23 & ... &... \\\\\nNGC 5258 & 13 39 57.4 & $+$00 49 51 & 6757 & U & U & 169 & 32 & ... &... \\\\\n\\\\[-2ex]\nNGC 5394 & 13 58 33.7 & $+$37 27 13 & 3451 &U &U & 71 & 17 &... & ... \\\\\nNGC 5395 & 13 58 37.6 & $+$37 25 42 & 3491 &U & U & 198 & 32 &... &...\\\\\n\\\\[-2ex]\nNGC 5426 & 14 03 24.7 & $-$06 04 13 & 2621 & $^h$3.06 & $^h$8.50 & 287\n& 63 & 32.0 & 2.6 & 0.8 & 0.2\\\\\nNGC 5427 & 14 03 26.0 & $-$06 01 50 & 2730 & $^h$6.87 & $^h$16.31 &\n261 & 59 & 31.4 & 2.8 & 1.2 & 0.3\\\\\n\\\\[-2ex] \nUGC 9618 ({\\sc n}) & 14 57 00.7 & $+$24 36 58 & 10094 &U & U & 135 & 24 &... &... \\\\\nUGC 9618 ({\\sc s}) & 14 57 00.0 & $+$24 36 20 & 9776 &U & U & 80 & 20 &... &... \\\\\n\\\\[-2ex]\nNGC 5929 & 15 26 06.1 & $+$41 40 15 & 2561 & U & U & $\\sim$24 & 12\n&...&...\\\\\nNGC5930 & 15 26 07.9 & $+$41 40 34 & 2672 & U& U& 95 & 18 &... &...\\\\\n\\\\[-2ex]\nNGC 5953 & 15 34 32.4 & $+$15 11 40 & 1965 &U & U & 182 & 23 &... &... \\\\\nNGC 5954 & 15 34 35.1 & $+$15 12 04 & 1959 &U &U & 124 & 21 & ... &... \\\\\n\\\\[-2ex]\nNGC 7469 & 23 03 15.6 & $+$08 52 29 & 4916 &U &U & 192 & 27 & ... & ... \\\\\nIC 5283 & 23 03 18.2 & $+$08 53 36 & 4894 & U & U & 72 & 12 &... &...\\\\ \n\\\\[-2ex]\nUGC 12914 & 00 01 38.3 & $+$23 29 02 & 4371 &U & U& 131 & 22 &... & ... \\\\\nUGC 12915 & 00 01 42.1 & $+$23 29 23 & 4336 & U& U& 160 & 21 & ... &...\n\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\n\\multicolumn{10}{p{40em}}{\\small {\\sc notes\\/} -- $h$ :- {\\it IRAS\\/}\nfluxes resovled using HIRES (Surace et al 1993), U :- unresolved by {\\it\nIRAS\\/}. Columns have the same meanings as Table~\\ref{fluxT}}\n\\end{tabular}\n\\end{table*}\n%\\end{document}"
},
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"name": "table3.tex",
"string": "%\\documentclass[a4paper,11pt,twoside]{article}\n%\\pagestyle{empty}\n%\\setlength{\\textwidth}{35em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\addtolength{\\oddsidemargin}{-10mm}\n%\\addtolength{\\evensidemargin}{-20mm}\n%\\marginparwidth=0mm\n%\\begin{document}\n\n\\parindent=0pt\n\\begin{table*}\n\\centering\n\\caption{\\label{calT} Galaxies with repeat flux measurements and\ntheir errors}\n\\begin{tabular}{lcccccc} \n\\\\[-2ex]\n\\hline\n\\\\[-2ex]\n\\multicolumn{1}{c}{(1)}&\\multicolumn{1}{c}{(2)}&\\multicolumn{1}{c}{(3)}&\\multicolumn{1}{c}{(4)}&\\multicolumn{1}{c}{(5)}&\\multicolumn{1}{c}{(6)}&\\multicolumn{1}{c}{(7)}\\\\\n\\\\[-2.5ex]\n\\multicolumn{1}{c}{Object}&\\multicolumn{1}{c}{Date}&\\multicolumn{1}{c}{Ints.}&\\multicolumn{1}{c}{Weather}&\\multicolumn{2}{c}{\\% error on individual\nobservations}&\\multicolumn{1}{c}{Actual difference}\\\\\n\\\\[-2ex]\n\\multicolumn{3}{c}{}&\\multicolumn{1}{c}{($\\tau_{850}$)}&\\multicolumn{1}{c}{Theoretical\nnoise}&\\multicolumn{1}{c}{`True' noise}&\\multicolumn{1}{c}{\\%}\\\\\n\\\\[-2ex]\n\\hline\n\\\\[-2ex]\nArp 220 & 2.7.97 & 5 & 0.2 & 0.3 \\hspace{2ex} (10.0)& 2.6 \\hspace{2ex} (10.3) & 1.7\\\\\n & 5.3.98 & 4 & 0.2 & 0.3 \\hspace{2ex} (10.0)& 3.0 \\hspace{2ex} (10.4) & \\\\\n\\\\[-2ex]\nNGC 1134 & 7.8.97 & 10 & 0.3 & 0.9 \\hspace{2ex} (10.0)& 8.8 \\hspace{2ex} (13.3)& 5.0 \\\\\n & 7.8.97 & 10 & 0.3 & 1.1 \\hspace{2ex} (10.1) & 11.6 \\hspace{2ex} (15.3)& \\\\\n\\\\[-2ex]\nUGC 2238 & 14.8.97 & 10 & 0.4--0.5 & 1.9 \\hspace{2ex} (10.2)& 15.7 \\hspace{2ex} (18.6)& 13.3\\\\\n & 25.8.97 & 10 & 0.4--0.5 & 1.3 \\hspace{2ex} (10.1)& 11.0 \\hspace{2ex} (14.9)& \\\\\n\\\\[-2ex]\nUGC 903 & 14.8.97 & 10 & 0.4--0.5 & 1.2 \\hspace{2ex} (10.1)& 10.6 \\hspace{2ex} (14.6)& 10.6\\\\\n & 7.10.98 & 6 & 0.2 & 1.0 \\hspace{2ex} (10.0)& 8.3 \\hspace{2ex} (13.0)& \\\\\n\\\\[-2ex]\n\\hline\n\\\\[-2ex]\n\\multicolumn{7}{p{40em}}{\\small (1) Galaxy name. (2) Date of each\nobservation. (3) Number of integrations in observation. (4) Weather in \nterms of $850\\mu$m opacity. (5) The `theoretical' noise on the\nindividual observations, equivalent to shot noise on a CCD. Brackets\ngive the error inclusive of 10\\% calibration uncertainty. (6) The `true' noise on\nthe individual observations, consisting of $\\sigma_{sky}$ and the\n`real' $\\sigma_{shot}$ as described in Section 2.4, brackets again\ngive error inclusive of 10\\% calibration uncertainty. (7) The\nactual percentage difference between the fluxes for both observations. }\n\\end{tabular}\n\\end{table*}\n\n\n%\\end{document} "
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"name": "table4.tex",
"string": "%\\documentclass[a4paper,10pt]{article}\n%\\pagestyle{plain}\n%\\setlength{\\textwidth}{38em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\addtolength{\\oddsidemargin}{-25mm}\n%\\addtolength{\\evensidemargin}{-25mm}\n%\\marginparwidth=0mm\n%%\\setcounter{page}{33}\n%\\usepackage{longtable}\n%\\begin{document}\n\n%\\parindent=0pt\n\\onecolumn\n\\begin{longtable}{lcccccccccc}\n\\caption{\\label{massT} Luminosities and masses}\\\\\n\\hline\n\\\\[-2.5ex]\n\\multicolumn{1}{c}{Name}&\\multicolumn{1}{c}{log $L_{60}$}&\\multicolumn{1}{c}{log\n$L_{850}$}&\\multicolumn{1}{c}{log $L_{\\rm{fir}}$}&\\multicolumn{1}{c}{log $M_{\\rm{d}}$}&\\multicolumn{1}{c}{log\n$M_{\\rm{d}}^{cold}$}&\\multicolumn{1}{c}{log\n$M_{\\rm{HI}}$}&\\multicolumn{1}{c}{log\n$M_{\\rm{H_2}}$}&\\multicolumn{1}{c}{log\n$L_{\\rm{B}}$}&\\multicolumn{1}{c}{$G_{\\rm{d}}$}&\\multicolumn{1}{c}{$L_{\\rm{fir}}/M_{\\rm{H_2}}$}\\\\\n\\\\[-2ex]\n\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{(W\nHz$^{-1}$}&\\multicolumn{1}{c}{(W Hz$^{-1}$}&\\multicolumn{1}{c}{(L$_{\\odot}$)}&\\multicolumn{1}{c}{(M$_{\\odot}$)}&\\multicolumn{1}{c}{(M$_{\\odot}$)}&\\multicolumn{1}{c}{(M$_{\\odot}$)}&\\multicolumn{1}{c}{(M$_{\\odot}$)}&\\multicolumn{1}{c}{(L$_{\\odot}$)}&\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{(L$_{\\odot}$/M$_{\\odot}$)}\\\\\n\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{sr$^{-1}$)}&\\multicolumn{1}{c}{sr$^{-1}$)}&\\multicolumn{7}{c}{}\\\\\n\\\\[-2ex]\n\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{(1)}&\\multicolumn{1}{c}{(2)}&\\multicolumn{1}{c}{(3)}&\\multicolumn{1}{c}{(4)}&\\multicolumn{1}{c}{(5)}&\\multicolumn{1}{c}{(6)}&\\multicolumn{1}{c}{(7)}&\\multicolumn{1}{c}{(8)}&\\multicolumn{1}{c}{(9)}&\\multicolumn{1}{c}{(10)}\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\n\\endfirsthead\n\\caption{ ... continued}\\\\\n\\hline\n\\\\[-2.5ex]\n\\multicolumn{1}{c}{Name}&\\multicolumn{1}{c}{log $L_{60}$}&\\multicolumn{1}{c}{log\nL$_{850}$}&\\multicolumn{1}{c}{log $L_{\\rm{fir}}$}&\\multicolumn{1}{c}{log $M_{\\rm{d}}$}&\\multicolumn{1}{c}{log\n$M_{\\rm{d}}^{cold}$}&\\multicolumn{1}{c}{log\n$M_{\\rm{HI}}$}&\\multicolumn{1}{c}{log $M_{\\rm{H_2}}$}&\\multicolumn{1}{c}{log\n$L_{\\rm{B}}$}&\\multicolumn{1}{c}{$G_{\\rm{d}}$}&\\multicolumn{1}{c}{$L_{\\rm{fir}}/M_{\\rm{H_2}}$}\\\\\n\\\\[-2ex]\n\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{(W\nHz$^{-1}$}&\\multicolumn{1}{c}{(W\nHz$^{-1}$}&\\multicolumn{1}{c}{(L$_{\\odot}$)}&\\multicolumn{1}{c}{(M$_{\\odot}$)}&\\multicolumn{1}{c}{(M$_{\\odot}$)}&\\multicolumn{1}{c}{(M$_{\\odot}$)}&\\multicolumn{1}{c}{(M$_{\\odot}$)}&\\multicolumn{1}{c}{(L$_{\\odot}$)}&\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{(L$_{\\odot}$/M$_{\\odot}$)}\\\\\n\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{sr$^{-1}$)}&\\multicolumn{1}{c}{sr$^{-1}$)}&\\multicolumn{7}{c}{}\\\\\n\\\\[-2ex]\n\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{(1)}&\\multicolumn{1}{c}{(2)}&\\multicolumn{1}{c}{(3)}&\\multicolumn{1}{c}{(4)}&\\multicolumn{1}{c}{(5)}&\\multicolumn{1}{c}{(6)}&\\multicolumn{1}{c}{(7)}&\\multicolumn{1}{c}{(8)}&\\multicolumn{1}{c}{(9)}&\\multicolumn{1}{c}{(10)}\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\n\\endhead\n\\\\[-2.5ex]\n\\hline\n\\endfoot\n\\\\[-2.5ex]\n\\hline\n\\endlastfoot\n\nNGC 23 & 23.51 & 21.68 & 10.82 & 7.49 & 7.79 & 9.88 & 9.95 & 10.73 & 746 & 7.5\\\\\nUGC 556 & 23.31 & 21.43 & 10.86 & 7.28 & 7.57 & 9.64 & 9.61 & 9.72 & 444 & 10.9\\\\\nNGC 470 & 23.32 & 21.30 & 10.16 & 7.05 & 7.43 & 9.61 & 9.29 & 10.30 & 536 & 7.4\\\\\nMCG+02-04-025 & 24.21 & 21.71 & 11.38 & 7.39 & 7.76 & 9.54 &...& 10.40 & ... & ...\\\\\nUGC 903 & 22.94 & 21.27 & 10.27 & 7.08 & 7.38 & 9.52 &...& 9.44 & ... & ...\\\\\nNGC 520 & 23.45 & 21.45 & 10.73 & 7.22 & 7.53 & 9.77 & 9.88 & 10.35 & 809 & 7.0\\\\\nIII ZW 035 & 24.15 & 21.90 & 11.36 & 7.64 & 7.96 & 9.36 & 9.90 & 9.97 & 238 & 28.6\\\\\nNGC 695 & 24.12 & 22.29 & 11.42 & 8.11 & 8.41 & 10.33 & 10.55 & 10.86 & 443 & 7.8\\\\\nNGC 697 & 22.98 & 21.55 & 10.49 & 7.47 & 7.66 & 10.37 & ...& 10.43 & ... & ...\\\\\nUGC 1351 & 23.35 & 21.67 & 10.68 & 7.48 & 7.79 & 9.79 & ...& 10.24 & ... & ...\\\\\nUGC 1451 & 23.46 & 21.62 & 10.78 & 7.44 & 7.71 & 9.63 & ...& 10.11 & ... & ...\\\\\nNGC 772 & 22.86 & 21.46 & 10.46 & 7.44 & 7.56 & 10.36 & 10.15 & 10.81 & 1344 & 2.0\\\\\nNGC 877 & 23.50 & 21.92 & 10.85 & 7.72 & 8.04 & 10.31 & 10.00 & 10.67 & 573 & 7.2\\\\\nNGC 958 & 23.54 & 22.14 & 10.97 & 8.01 & 8.27 & 10.59 & 10.21 & 10.75 & 544 & 5.8\\\\\nNGC 992 & 23.51 & 21.61 & 10.78 & 7.36 & 7.72 & 10.07 & 9.83 & 9.58 & 809 & 8.8\\\\\nUGC 2238 & 23.78 & 21.83 & 11.11 & 7.69 & 7.90 & 10.02 & 10.22 & 10.20 & 550 & 7.9\\\\\nIR 0243+21 & 23.67 & 21.48 & 10.88 & 7.20 & 7.58 & 9.13 & ...& ...& ... & ...\\\\\nNGC 1134 & 23.32 & 21.72 & 10.65 & 7.50 & 7.85 & 10.28 & ...& 10.34 & ... & ...\\\\\nUGC 2369 & 24.09 & 21.98 & 11.33 & 7.77 & 8.07 &... & ...& 10.49 & ... & ...\\\\\nUGC 2403 & 23.36 & 21.49 & 10.64 & 7.26 & 7.60 & ...& ...& 9.82 & ... & ...\\\\\nNGC 1222 & 23.12 & 20.92 & 10.36 & 6.66 & 6.98 & 9.38 & ...& 9.98 & ... & ...\\\\\nIR 0335+15 & 24.06 & 21.87 & 11.25 & 7.57 & 7.98 &...&10.44 & 9.95 & ... & 6.4\\\\\nUGC 2982 & 23.64 & 21.90 & 10.99 & 7.74 & 8.00 & 10.07 & 10.23 & 9.98 & 520 & 5.8\\\\\nNGC 1614 & 24.12 & 21.90 & 11.33 & 7.61 & 8.00 & 9.54 & 10.09 & 10.34 & 389 & 17.2\\\\\nNGC 1667 & 23.36 & 21.73 & 10.81 & 7.65 & 7.82 & 9.75 & 9.98 & 10.50 & 342 & 6.7\\\\\nNGC 2623 & 24.13 & 21.66 & 11.33 & 7.39 & 7.67 & 9.25 & 9.97 & 10.32 & 456 & 22.7\\\\\nIR 0857+39 & 24.55 & 21.85 & 11.68 & 7.46 & 8.00 &...& 9.69 & 11.12 & ... & 98.0\\\\\nNGC 2782 & 23.04 & 21.41 & 10.34 & 7.14 & 7.54 & 9.62 & 9.36 & 10.45 & 465 & 9.5\\\\\nNGC 2785 & 23.08 & 21.39 & 10.42 & 7.20 & 7.51 & 8.99 &...& 9.42 & ... & ...\\\\\nUGC 4881 & 24.22 & 22.12 & 11.50 & 7.94 & 8.21 & 10.25 & 10.65 & 10.68 & 723 & 6.6\\\\\nNGC 2856 & 22.87 & 21.01 & 10.18 & 6.80 & 7.11 & 9.15 & ... & ... & ...\\\\\nMCG+08-18-012 & 23.84 & 21.59 & 11.07 & 7.38 & 7.65 & ...& ...& 10.21 & ...&...\\\\\nNGC 2966 & 22.62 & 20.97 & 9.91 & 6.70 & 7.10 & 9.14 & ...& 9.63 & ... & ...\\\\\nNGC 2990 & 22.96 & 21.23 & 10.30 & 7.05 & 7.35 & 9.69 & ... & 10.05 & ... & ...\\\\\nIC 563/4 & 23.54 & 22.11 & 10.95 & 7.96 & 8.25 & 10.10 & ... & 10.53 & ...&...\\\\\nUGC 5376 & 22.63 & 21.01 & 10.00 & 6.83 & 7.13 & 9.41 & ... & 9.54 & ...&...\\\\\nNGC 3094 & 23.06 & 21.16 & 10.31 & 6.88 & 7.27 & 9.35 & ...& 9.99 & ...&...\\\\\nNGC 3110 & 23.72 & 21.88 & 11.06 & 7.73 & 7.98 & ...& 10.34 & 10.52 & ...& 5.2\\\\\nIR 1017+08 & 24.35 & 22.03 & 11.52 & 7.71 & 8.16 & ...& 10.38 & ... & ...& 13.8\\\\\nNGC 3221 & 23.35 & 21.84 & 10.79 & 7.73 & 7.96 & 10.33 & 9.99 & 10.14 & 581 & 6.3\\\\\nNGC 3367 & 22.99 & 21.30 & 10.38 & 7.16 & 7.40 & 9.77 &... & 10.68 & ... & ...\\\\\nIR 1056+24 & 24.58 & 22.16 & 11.78 & 7.96 & 8.18 &... & 10.36 & 10.92 & ...& 26.2\\\\\nARP 148 & 24.13 & 22.17 & 11.39 & 7.96 & 8.32 & ...& 10.21 & ... & ... & 15.4\\\\\nNGC 3583 & 22.96 & 21.14 & 10.22 & 7.06 & 7.23 & 9.68 & 9.49 & 10.49 & 694 & 5.3\\\\\nMCG+00-20-023 & 23.75 & 21.88 & 11.04 & 7.68 & 7.99 &...& ...& 10.38 & ... &...\\\\\nUGC 6436 & 24.03 & 22.23 & 11.32 & 8.02 & 8.36 & 9.88 & 10.30 & 10.45 & 260 & 10.5\\\\\nNGC 3994/5 & 23.16 & 21.58 & 10.53 & 7.41 & 7.70 & 10.25 & ... & 10.65 & ...& ...\\\\\nNGC 4045 & 22.64 & 20.97 & 10.04 & 6.82 & 7.07 & 9.13 & ...& 10.02 & ... &...\\\\\nIR 1211+03 & 24.86 & 22.48 & 12.00 & 8.19 & 8.60 &...& 10.64 & 10.47 & ...& 22.9\\\\\nNGC 4273 & 23.01 & 21.48 & 10.39 & 7.30 & 7.61 & 9.64 & 9.63 & 10.37 & 435 & 5.8\\\\\nIR 1222-06 & 23.80 & 21.86 & 11.04 & 7.58 & 7.98 & ...& ...& 9.84 & ... & ...\\\\\nNGC 4418 & 23.50 & 21.30 & 10.68 & 6.86 & 7.41 & 8.75 & 9.12 & 9.68 & 261& 36.4\\\\\nNGC 4433 & 23.34 & 21.51 & 10.64 & 7.28 & 7.62 & 9.86 & 9.63 & 10.20 & 600 & 10.2\\\\\nNGC 4793 & 23.12 & 21.42 & 10.54 & 7.30 & 7.51 & 9.79 & 9.67 & 10.41 & 550 & 7.4\\\\\nNGC 4922 & 23.73 & 21.62 & 10.95 & 7.32 & 7.73 & 9.15 & ...& 10.67 & ... & ...\\\\\nNGC 5020 & 23.03 & 21.58 & 10.38 & 7.36 & 7.71 & 10.07 & ...& 10.44 & ...& ...\\\\\nIC 860 & 23.51 & 21.33 & 10.72 & 7.01 & 7.43 &... & 8.91 & 9.68 & ...& 64.1\\\\\nUGC 8387 & 24.08 & 21.93 & 11.39 & 7.81 & 7.96 & ...& 10.17 & 10.35 & ...& 16.5\\\\\nNGC 5104 & 23.57 & 21.65 & 10.90 & 7.51 & 7.74 & 9.83 & ...& 10.34 & ...& ...\\\\\nNGC 5256 & 23.95 & 21.94 & 11.20 & 7.72 & 8.04 & ...& 10.36 & 10.87 & ...& 6.9\\\\\nNGC 5257/8 & 23.94 & 22.31 & 11.24 & 8.14 & 8.44 & 10.55 & ...& 11.04 & ...&...\\\\\nUGC 8739 & 23.43 & 21.88 & 10.84 & 7.75 & 8.00 & 10.12 & ... & 10.47 & ...&...\\\\\nNGC 5371 & 22.79 & 21.16 & 10.34 & 7.14 & 7.18 & 10.05 & ...& 10.80 & ...&...\\\\\nNGC 5394/5 & 23.28 & 21.72 & 10.71 & 7.60 & 7.84 & 10.35 & ... & 10.86 & ...& ...\\\\\nNGC 5433 & 23.32 & 21.70 & 10.65 & 7.49 & 7.83 & 9.67 & ...& 10.21 & ...& ...\\\\\nNGC 5426/7 & 23.09 & 21.81 & 10.55 & 7.66 & 7.94 & 10.42& ...& 10.83 & ...&...\\\\\nZW 247.020 & 23.79 & 21.51 & 11.03 & 7.32 & 7.57 & ...& ...& 10.14 & ...&...\\\\\nNGC 5600 & 22.70 & 21.03 & 10.09 & 6.89 & 7.13 & 9.11 & 8.97 & 10.22 & 286& 13.3\\\\\nNGC 5653 & 23.36 & 21.63 & 10.74 & 7.49 & 7.72 & 9.23 & 9.76 & 10.49 & 240 & 9.5\\\\\nNGC 5665 & 22.72 & 21.11 & 10.07 & 7.20 & 6.91 & 8.88 & 9.05 & 10.25 & 234 & 10.6\\\\\nNGC 5676 & 22.97 & 21.55 & 10.42 & 7.42 & 7.68 & 9.77 & 9.96 & 10.42 & 577 & 2.9\\\\\nNGC 5713 & 23.11 & 21.33 & 10.43 & 7.14 & 7.43 & 9.91 & 9.68 & 10.41 & 982 & 5.7\\\\\nUGC 9618 & 24.09 & 22.51 & 11.45 & 8.35 & 8.65 & $>$10.26 &...& 10.65 & ...& ...\\\\\nNGC 5792 & 22.78 & 21.37 & 10.15 & 7.16 & 7.50 & 10.01 & ...& 10.32 & ...&...\\\\\nZW 049.057 & 23.75 & 21.70 & 11.02 & 7.48 & 7.76 & ...& 9.55 & 9.71 & ...&29.5\\\\\nNGC 5900 & 22.91 & 21.70 & 10.32 & 7.14 & 7.37 & 9.63 & ...& 9.42 & ...& ...\\\\\n1 ZW 107 & 24.36 & 22.10 & 11.55 & 7.81 & 8.22 &...& 10.27 & 10.57 & ...& 19.2\\\\\nNGC 5929/30 & 23.05 & 21.15 & 10.34 & 6.92 & 7.24 & 9.34 & 10.19 & 9.42 & 575 & \n8.3\\\\\nIR 1525+36 & 24.46 & 22.20 & 11.61 & 7.80 & 8.34 &...& ...& 10.48 & ... & ...\\\\\nNGC 5936 & 23.38 & 21.60 & 10.73 & 7.43 & 7.69 & 9.41 & 9.80 & 10.54 & 330 & 8.4\\\\\nNGC 5937 & 23.45 & 21.49 & 10.83 & 7.33 & 7.61 & 9.21 & ...& 10.39 & ... & ...\\\\\nNGC 5953/4 & 22.88 & 21.29 & 10.21 & 7.06 & 7.42 & 9.30 & 9.48 & 10.21 & 437 & 5.4\\\\\nARP 220 & 24.73 & 22.60 & 11.94 & 8.29 & 8.69 & 10.48 & 10.41 & 10.44 & 285 &33.5\\\\\nIR 1533-05 & 23.80 & 21.91 & 11.09 & 7.71 & 8.02 & ...& ...& 10.01 & ... & ...\\\\\nNGC 5962 & 22.78 & 21.31 & 10.19 & 7.15 & 7.43 & 9.48 & 9.46 & 10.34 &418 & 5.3\\\\\nNGC 5990 & 23.37 & 21.42 & 10.69 & 7.25 & 7.49 & 9.23 & ...& 10.62 & ... & ...\\\\\nNGC 6052 & 23.40 & 21.53 & 10.69 & 7.32 & 7.64 & 9.88 & ...& 10.53 & ... & ...\\\\\nMCG+01-42-088 & 23.85 & 21.90 & 11.14 & 7.71 & 8.00 & 9.48 & ...& 10.46 & ...& ...\\\\\nNGC 6181 & 22.96 & 21.33 & 10.37 & 7.20 & 7.44 & 9.75 & 9.79 & 10.38 & 746 & 3.9\\\\\nNGC 7448 & 22.84 & 21.19 & 10.22 & 7.02 & 7.29 & 9.75 & 9.06 & 10.39 & 640 & 14.4\\\\\nNGC 7469 $^p$ & 24.06 & 22.01 & 11.30 & 7.73 & 8.11 & 9.47 & 10.33 & 10.90 & 460& 9.2\\\\\nNGC 7479 & 23.18 & 21.50 & 10.48 & 7.25 & 7.62 & 9.94 & 10.06 & 10.64 & 1141 & 2.6\\\\\nZW 453.062 & 23.85 & 21.78 & 11.10 & 7.56 & 7.88 & 9.46 & ...& 10.29 & ... & ...\\\\\nNGC 7541 & 23.40 & 21.70 & 10.76 & 7.52 & 7.80 & 10.19 & 9.95 & 10.44 &726 & 6.5\\\\\nZW 475.056 & 24.02 & 21.90 & 11.25 & 7.66 & 7.99 & 9.74 & 10.03 & 10.44& 348 & 16.7\\\\\nNGC 7591 & 23.53 & 21.73 & 10.84 & 7.53 & 7.83 & 10.23 & 9.96 & 10.40 & 771 & 7.6\\\\\nNGC 7592 & 23.88 & 21.96 & 11.12 & 7.69 & 8.09 & 10.07 & 10.32 & 10.69 & 677 & 6.3\\\\\nNGC 7674 & 23.86 & 21.10 & 11.12 & 7.84 & 8.24 & 10.33 & 10.61 & 10.83 & 891 & 3.2\\\\\nNGC 7678 & 23.17 & 21.59 & 10.54 & 7.41 & 7.71 & 9.82 & 9.52 & 10.66 & 389 & 10.5\\\\\nNGC 7679 & 23.53 & 21.59 & 10.79 & 7.35 & 7.70 & 9.80 & ...& 10.64 & ... & ...\\\\\nNGC 7714 & 23.15 & 20.97 & 10.37 & 6.68 & 7.06 & 9.79 & 9.33 & 10.25 & 1739 & 11.0\\\\\nNGC 7771 & 23.81 & 22.04 & 11.14 & 7.86 & 8.15 & 9.95 & 10.18 & 10.58 & 332 & 9.3\\\\\nMRK 331 & 23.97 & 21.81 & 11.18 & 7.53 & 7.90 & 9.96 & 10.37 & 10.07 & 964 & 6.5\\\\\nUGC 12914/5 & 23.32 & 21.77 & 10.70 & 7.60 & 7.89 & 10.27 & ...& 10.68 & ... & ...\\\\\n\n\\end{longtable}\n\\twocolumn\n{\\bf Notes to Table~\\ref{massT}}\\\\ (1) 60$\\mu$m luminosity. (2)\n850$\\mu$m luminosity. (3) FIR luminosity calculated by integrating the\nmeasured SED from 40-1000$\\mu$m. (4) Dust mass calculated using a\nsingle temperature, derived from fitting the 60,100 and 850$\\mu$m\nfluxes. (5) Dust mass ($M_{\\rm{d}}^{cold}$) calculated using a\ntwo-component temperature fit to the data, assuming a cold\n$T_{\\rm{d}}=20$ K and $\\beta=2$. (6) H{\\sc i} refs:- Bottinelli et\nal. (1990), Huchtmeier \\& Richter (1989), Theureau et al. (1998) (7)\nH$_2$ refs:- Young et al. (1995), Solomon et al. (1997), Sanders et\nal. (1991), Chini, Kr\\\"{u}gel \\& Lemke (1996), Maiolino et al. (1997),\nCasoli et al. (1996), Lavezzi \\& Dickey (1998), Sanders et al. (1986),\nSanders \\& Mirabel (1985). (8) Blue luminosity calculated from\nB$_{\\rm{T}}$ taken from the LEDA database and corrected for galactic\nextinction but not for internal extinction or inclination effects. (9)\n$G_{\\rm{d}}$ is the gas-to-dust ratio calculated from H{\\sc i} +\nH$_{2}$ and the single temperature dust mass. (10) The FIR luminosity\nper unit gas mass (molecular); often used as a measure of the star\nformation efficiency of a galaxy. {$^p$ NGC 7469 includes masses for IC\n5283, except for H{\\sc i} which is for NGC 7469 only.\n\n%\\end{document}"
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"name": "table5.tex",
"string": "%\\documentclass[a4paper,11pt]{article}\n%\\pagestyle{empty}\n%\\setlength{\\textwidth}{35em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\addtolength{\\oddsidemargin}{-10mm}\n%\\addtolength{\\evensidemargin}{-20mm}\n%\\marginparwidth=0mm\n%\\begin{document}\n\n%\\parindent=0pt\n\\begin{table*}\n\\centering\n\\caption{\\label{pmassT}Luminosities and masses for pairs resolved by SCUBA}\n\\begin{tabular}{lccccccccc}\n\\\\[-2ex] \n\\hline\n\\\\[-2.5ex]\n\\multicolumn{1}{c}{Name}&\\multicolumn{1}{c}{log $L_{60}$}&\\multicolumn{1}{c}{log\n$L_{850}$}&\\multicolumn{1}{c}{log\n$L_{\\rm{fir}}$}&\\multicolumn{1}{c}{log\n$M_{\\rm{d}}$}&\\multicolumn{1}{c}{log $M_{\\rm{d}}^{cold}$}&\\multicolumn{1}{c}{log\n$M_{\\rm{HI}}$}&\\multicolumn{1}{c}{log $M_{\\rm{H_2}}$}&\\multicolumn{1}{c}{log\n$L_{\\rm{B}}$}&\\multicolumn{1}{c}{$G_{\\rm{d}}$}\\\\\n\\\\[-2ex]\n\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{(W Hz$^{-1}$\nsr$^{-1}$)}&\\multicolumn{1}{c}{(W Hz$^{-1}$\nsr$^{-1}$)}&\\multicolumn{1}{c}{(L$_{\\odot}$}&\\multicolumn{1}{c}{(M$_{\\odot}$)}&\\multicolumn{1}{c}{(M$_{\\odot}$)}&\\multicolumn{1}{c}{(M$_{\\odot}$)}&\\multicolumn{1}{c}{(M$_{\\odot}$}&\\multicolumn{1}{c}{(L$_{\\odot}$)}&\\multicolumn{1}{c}{}\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\nIC 563 & 23.28 & 21.78 & 10.65 & 7.59 & 7.92 &\\shortstack{10.10\\\\[-2ex] } & ... & 10.09 & ...\\\\\nIC 564 & 23.21 & 21.86 & 10.66 & 7.73 & 8.00 & & ... & 10.35& ...\\\\\n\\\\[-2ex]\nNGC 3994 & 23.04 & 21.22 & 10.29 & 7.07 & 7.33 & 9.75 & ... & 9.86 & ...\\\\\nNGC 3995 & 23.11 & 21.34 & 10.16 & 7.14 & 7.47 & 10.09 & ... & 10.33 & ...\\\\\n\\\\[-2ex]\nNGC 5257 &... & 21.92 & ... & 7.69 & ... &10.27 & ... & 10.69 & ...\\\\\nNGC 5258 & ... &22.09 & ... & 7.85 & ... &10.23 & ... & 10.71 & ...\\\\\n\\\\[-2ex]\nNGC 5394 & ... &21.14 & ... & 7.02 & ... & 9.95 & ... & 10.06 & ...\\\\\nNGC 5395 & ... &21.59 & ... & 7.47 & ... & 10.13 & ... & 10.49 & ...\\\\\n\\\\[-2ex]\nNGC 5426 & 22.56 & 21.51 & 10.06 & 7.36 & 7.64 & 10.16 & ... & 10.22 & ...\\\\\nNGC 5427 & 22.95 & 21.51 & 10.38 & 7.36 & 7.63 & 10.08 & ... & 10.62 & ...\\\\\n\\\\[-2ex] \nUGC 9618 (N) & ...& 22.32 & ... & 8.17 & ... &\\shortstack{$>$10.26\\\\[-2ex] } & ... & 10.59&...\\\\\nUGC 9618 (S) & ...& 22.07 & ... & 7.91 & ... & & ... & 10.28 & ...\\\\\n\\\\[-2ex]\nNGC 5929 & ... &20.41 & ... & 6.19 & ... & 8.93 & 9.06 & 9.61 & 1291\\\\\nNGC 5930 & ... &21.05 & ... & 6.83 & ... & 9.08 & 9.14 & 9.85 & 373\\\\\n\\\\[-2ex]\nNGC 5953 & ... &21.07 & ... & 6.84 & ... & 9.06 & 9.27 & 9.70 & 435\\\\\nNGC 5954 & ... &20.90 & ... & 6.67 & ... & 8.93 & 9.05 & 9.54 & 423\\\\\n\\\\[-2ex]\nNGC 7469 & ... &21.87 & ... & 7.52 & ... & 9.48 & 10.11 & 10.62 & 480\\\\\nIC 5283 & ... &21.44 & ... & 7.27 & ... & ... & 9.94 & 9.78 & ...\\\\ \n\\\\[-2ex]\nUGC 12914 & ...&21.61 & ... & 7.44 & ... & 9.99 & ... & 10.49 & ...\\\\\nUGC 12915 & ...&21.69 & ... & 7.52 & ... & 9.95 & ...& 10.13 & ...\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\n\\multicolumn{7}{p{34em}}{\\small{Columns have the same meanings as in Table~\\ref{massT}}}\\\\\n\\end{tabular}\n\\end{table*}\n%\\end{document}"
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{
"name": "table6.tex",
"string": "%\\documentclass[a4paper,11pt,twoside]{article}\n%\\pagestyle{empty}\n%\\setlength{\\textwidth}{35em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\addtolength{\\oddsidemargin}{-10mm}\n%\\addtolength{\\evensidemargin}{-20mm}\n%\\marginparwidth=0mm\n%\\begin{document}\n\n%\\parindent=0pt\n\\begin{table}\n\\centering\n\\caption{\\label{convT} Conversion factors used for CO data}\n\\begin{tabular}{lclcc} \n\\\\[-2ex]\n\\hline\n\\\\[-2.5ex]\n\\multicolumn{1}{c}{Telescope}&\\multicolumn{1}{c}{Beam\nsize}&\\multicolumn{1}{c}{Scale}&\\multicolumn{1}{c}{Conversion}&\\multicolumn{1}{c}{Refs}\\\\\n\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{\\small{$^{\\prime\\prime}$}}&\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{(Jy\nK$^{-1}$)}&\\multicolumn{1}{c}{}\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\nFCRAO & 45 & $T^{\\ast}_A$ & 42 & a\\\\\n & & $T^{\\ast}_R$ & 31.5 & d, h, i\\\\\nSEST & 45 & $T_{mb}$ & 19 & b\\\\\nIRAM & 22 & $T_{mb}$ & 4.5 & c\\\\\nNRAO & 55 & $T^{\\ast}_R$ & 35 & d, e, i\\\\\n & & $T_{mb}$ & 30 & f, g\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\n\\multicolumn{5}{p{26em}}{\\small {Reference Key :- (a) Young et al. (1995), (b) Chini et\nal. (1996), (c) Solomon et al. (1997), (d) Sanders et\nal. (1991), (e) Maiolino et al. (1997), (f) Casoli et\nal. (1996), (g) Lavezzi \\& Dickey (1998), (h) Sanders\net al. (1986), (i) Sanders \\& Mirabel (1985)}}\\\\\n\\end{tabular}\n\\end{table}\n%\\end{document}\n \n\n"
},
{
"name": "table7.tex",
"string": "%\\documentclass[a4paper,11pt]{article}\n%\\pagestyle{empty}\n%\\setlength{\\textwidth}{35em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\addtolength{\\oddsidemargin}{-10mm}\n%\\addtolength{\\evensidemargin}{-20mm}\n%\\marginparwidth=0mm\n%\\begin{document}\n\n%\\parindent=0pt\n\\begin{table}\n\\centering\n\\caption{\\label{lfT}Local luminosity function at 850$\\mu$m}\n\\begin{tabular}{cccc}\n\\\\[-2ex] \n\\hline\n\\\\[-2.5ex]\n\\multicolumn{1}{c}{log $L_{850}$}&\\multicolumn{1}{c}{$\\phi(L)$}&\\multicolumn{1}{c}{$\\sigma_{\\phi}$}\\\\\n\\multicolumn{1}{c}{(W Hz$^{-1}$\nsr$^{-1}$)}&\\multicolumn{1}{c}{(Mpc$^{-3}$\ndex$^{-1}$)}&\\multicolumn{1}{c}{(Mpc$^{-3}$\ndex$^{-1}$)}\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\n21.04 & 2.43e-3 & 7.69e-4 & \\\\\n21.28 & 1.33e-3 & 3.32e-4 & \\\\\n21.52 & 7.00e-4 & 1.37e-4 &\\\\\n21.76 & 2.13e-4 & 4.65e-5 &\\\\\n22.00 & 6.02e-5 & 1.38e-5 &\\\\\n22.24 & 2.34e-5 & 7.8e-6 &\\\\\n22.48 & 1.60e-6 & 9.2e-7 &\\\\\n\\\\[-2ex]\n\\hline\n\\\\[-2ex]\n\\multicolumn{1}{c}{$\\alpha$}&\\multicolumn{1}{c}{$L_{\\ast}$}&\\multicolumn{1}{c}{$\\phi_{\\ast}$}&\\multicolumn{1}{c}{$\\chi^{2}_{\\nu}$}\\\\\n\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{(W Hz$^{-1}$\nsr$^{-1}$)}&\\multicolumn{1}{c}{(Mpc$^{-3}$\ndex$^{-1}$)}&\\multicolumn{1}{c}{}\\\\\n\\\\[-2ex]\n\\hline\n\\\\[-2ex]\n$-2.18^{+0.22}_{-0.24}$ &\n$8.3^{+2.5}_{-2.0}\\times 10^{21}$ & $2.9^{+4.1}_{-1.5}\\times 10^{-4}$ & \n0.68\\\\\n\\\\[-2ex]\n\\hline\n & & \\\\\n\\multicolumn{3}{l}{Single temperature dust mass function}\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\n\\multicolumn{1}{c}{log $M_{\\rm{d}}$}&\\multicolumn{1}{c}{$\\phi(M)$}&\\multicolumn{1}{c}{$\\sigma_{\\phi}$}\\\\\n\\multicolumn{1}{c}{(M$_{\\odot}$)}&\\multicolumn{1}{c}{(Mpc$^{-3}$\ndex$^{-1}$)}&\\multicolumn{1}{c}{(Mpc$^{-3}$ dex$^{-1}$)}\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\n6.78 & 2.00e-3 & 6.68e-4 & \\\\\n7.02 & 1.05e-3 & 3.16e-4 &\\\\\n7.26 & 1.01e-3 & 2.10e-4 &\\\\\n7.50 & 4.82e-4 & 9.28e-5 &\\\\\n7.75 & 1.32e-4 & 2.75e-5 &\\\\\n7.99 & 2.27e-5 & 8.0e-6 &\\\\\n8.23 & 1.58e-6 & 9.1e-7 &\\\\\n\\\\[-2ex]\n\\hline\n\\\\[-2ex]\n\\multicolumn{1}{c}{$\\alpha$}&\\multicolumn{1}{c}{$M_{\\ast}$}&\\multicolumn{1}{c}{$\\phi_{\\ast}$}&\\multicolumn{1}{c}{$\\chi^{2}_{\\nu}$}\\\\\n\\multicolumn{1}{c}{}&\\multicolumn{1}{c}{(M$_{\\odot}$)}&\\multicolumn{1}{c}{(Mpc$^{-3}$\ndex$^{-1}$)}&\\multicolumn{1}{c}{}\\\\\n\\\\[-2ex]\n\\hline\n\\\\[-2ex]\n$-1.23^{+0.44}_{-0.59}$ &\n$2.50^{+0.95}_{-0.82}\\times 10^7$ & $1.64^{+0.69}_{-0.48}\\times\n10^{-3}$ & 0.56\\\\\n\\\\[-2ex]\n\\hline\n & & \\\\\n\\multicolumn{3}{l}{Cold component dust mass function}\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\n\\multicolumn{1}{c}{log $M_{\\rm{d}}^{cold}$}&\\multicolumn{1}{c}{$\\phi(M)$}&\\multicolumn{1}{c}{$\\sigma_{\\phi}$}\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\n7.10 & 2.30e-3 & 7.67e-4 & \\\\\n7.34 & 1.18e-3 & 3.04e-4 &\\\\\n7.59 & 7.91e-4 & 1.61e-4 &\\\\\n7.83 & 2.74e-4 & 5.99e-5 &\\\\\n8.08 & 7.63e-5 & 1.63e-5 &\\\\\n8.32 & 2.57e-5 & 8.13e-6 &\\\\\n8.57 & 1.56e-6 & 9.02e-7 &\\\\\n\\\\[-2ex]\n\\hline\n\\\\[-2ex]\n\\multicolumn{1}{c}{$\\alpha$}&\\multicolumn{1}{c}{$M^{cold}_{\\ast}$}&\\multicolumn{1}{c}{$\\phi_{\\ast}$}&\\multicolumn{1}{c}{$\\chi^{2}_{\\nu}$}\\\\\n\\\\[-2ex]\n\\hline\n\\\\[-2ex]\n$-1.91^{+0.21}_{-0.24}$ & $\n8.5^{+2.2}_{-1.9}\\times 10^7$ & $ 4.9^{+3.3}_{-2.2}\\times 10^{-4}$ & 0.62\\\\\n\\\\[-2.5ex]\n\\hline\n\\end{tabular}\n\\end{table}\n\n%\\end{document}"
},
{
"name": "table8.tex",
"string": "%\\documentclass[a4paper,11pt,twoside]{article}\n%\\pagestyle{empty}\n%\\setlength{\\textwidth}{35em}\n%\\setlength{\\textheight}{235mm}\n%\\renewcommand{\\baselinestretch}{1.0}\n%\\addtolength{\\oddsidemargin}{-10mm}\n%\\addtolength{\\evensidemargin}{-20mm}\n%\\marginparwidth=0mm\n%\\begin{document}\n\n%\\parindent=0pt\n\\begin{table*}\n%\\centering\n\\caption{\\label{fitsT} Parameters for fits and correlations}\n\\begin{tabular}{llcrrrr} \n\\\\[-2ex]\n\\hline\n\\\\[-2.5ex]\n\\multicolumn{1}{c}{$y$}&\\multicolumn{1}{c}{$x$}&\\multicolumn{1}{c}{Number}&\\multicolumn{1}{c}{$r_{s}$}&\\multicolumn{1}{c}{significance}&\\multicolumn{2}{c}{linear\nfit: $y=mx+c$}\\\\\n\\multicolumn{5}{l}{}&\\multicolumn{1}{c}{$m$}&\\multicolumn{1}{c}{$c$}\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\n$T_{\\rm{d}}$ & log $L_{60}$ & 104 & 0.44 & $2.5e-6$ & $4.57\\pm 0.82$ &\n$-71.9\\pm 19.4$\\\\\n$T_{\\rm{d}}$ & log $M_{\\rm{d}}$ & 104 & $-0.02$ & 0.8 & &\\\\\n$T_{\\rm{d}}$ & log $L_{\\rm{B}}$ $^c$ & 91 & $-0.25$ & 0.02 & & \\\\\n$\\beta$ & $T_{\\rm{d}}$ & 104 & 0.44 & $3.7e-6$ & $-0.0184\\pm 0.004$ &\n$1.95\\pm 0.13$\\\\\nlog $M_{\\rm{d}}$ &log $M_{\\rm{H_2}}$ & 59 & 0.89 & $6.2e-21$ & $0.82\\pm\n0.04$ & $-0.67\\pm 0.38$\\\\\nlog $M_{\\rm{d}}$ &log $M_{\\rm{HI}}$ & 84 & 0.64 & $3.6e-11$ & $0.94\\pm 0.09$\n& $-1.81\\pm 0.68$\\\\\nlog $M_{\\rm{d}}$ &log $M_{\\rm{H_{2}+HI}}$ & 47 & 0.86 & $7e-15$ &\n$0.96\\pm 0.06$ & $-2.32\\pm 0.53$\\\\\nlog $L_{\\rm{fir}}$ &log$M_{\\rm{H_2}}$ & 59 & 0.81 & $1.4e-14$ &\n$1.14\\pm 0.09$ & $-0.39\\pm 0.78$\\\\\nlog $L_{\\rm{fir}}/M_{\\rm{H_2}}$ & log $L_{\\rm{B}}$ $^c$ & 52 & $-0.39$ &\n$3.9e-4$ & $-1.04\\pm 0.20 $ & $11.89\\pm 0.59$\\\\\n\\\\[-2.5ex]\n\\hline\n\\\\[-2.5ex]\n\\multicolumn{7}{p{35em}}{\\small {\\sc notes} -- {\\it Column(4)}--\nSpearman rank correlation coefficient. {\\it Column(5)}-- probability\nthat $x$ and $y$ are unrelated. $c$ :- luminosity corrected for galactic and\ninternal extinction and for inclination effects.}\\\\\n\n\\end{tabular}\n\\end{table*}\n%\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002234.extracted_bib",
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}
] |
astro-ph0002235
|
Problems encountered in the Hipparcos variable stars analysis
|
[
{
"author": "Laurent Eyer"
}
] |
Among the 17 volumes of results from the Hipparcos space mission, two are dedicated to variable stars. These two volumes arose from the work of two groups, one at the Geneva Observatory and one at RGO (Royal Greenwich Observatory), on the 13 million photometric measurements produced by the satellite for 118~204 stars. The analysis of photometric time series permitted us to identify several instrumental and mathematical problems: overestimation of the precision, offsets in the zero-points depending on the field of view, mispointing effects, image superpositions, trends in the magnitudes, binarity effects (spurious periods and amplitudes) and time-sampling effects. In this article we summarize some of the problems encountered by the Geneva group.
|
[
{
"name": "leyer.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsfig,subfigure]{article}\n\\setcounter{page}{147}\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n%\\marginparwidth 1.25in\n%\\marginparsep .125in\n%\\marginparpush .25in\n%\\reversemarginpar\n\\markboth{Eyer \\& Grenon}{Problems encountered in the Hipparcos variable\n stars analysis}\n\\begin{document}\n\\title{Problems encountered in the Hipparcos variable stars analysis}\n \\author{Laurent Eyer}\n\\affil{Instituut voor Sterrenkunde,\n Katholieke Universiteit Leuven,\n Celestijnenlaan 200 B, B-3001 Leuven,\n Belgi\\\"e}\n\\author{Michel Grenon}\n\\affil{Observatoire de Gen\\`eve,\n CH-1290 Sauverny,\n Suisse}\n\\begin{abstract}\nAmong the 17 volumes of results from the Hipparcos space mission,\ntwo are dedicated to variable stars. These two volumes arose\nfrom the work of two groups, one at the Geneva Observatory\nand one at RGO (Royal Greenwich Observatory), on the 13 million\nphotometric measurements produced by the satellite for\n118~204 stars.\n\nThe analysis of photometric time series permitted us to identify\nseveral instrumental and mathematical problems: overestimation\nof the precision, offsets in the zero-points depending on the field \nof view, mispointing effects, image superpositions, trends in the \nmagnitudes, binarity effects (spurious periods and amplitudes)\nand time-sampling effects. In this article we summarize some of the \nproblems encountered by the Geneva group.\n\\end{abstract}\n\n\\section{Introduction}\nThe variable star analysis of the Hipparcos photometric data was \nan iterative process in interaction with the FAST and NDAC data\nreduction consortia. We started with data extracts from FAST, then\nfrom NDAC and finally worked on the whole merged data set, that is \non the 118~204 time series.\n\nThe result of variable star analysis is a beautiful by-product of \nthe mission and it was clear that it had to be published at the same\ntime as the astrometric results (ESA 1997). The time available for the photometric \nanalysis was then short in order to match the deadlines. The teams were\nput under strong pressure. The approach was then to produce a robust \nanalysis restricting the analysis to statistically well-confirmed \nvariables, leaving suspected variables and ambiguous cases for further\nanalysis.\n\nBecause several instrumental problems were identified and solved, the \nvariable star study definitely improved the overall quality of the \nHipparcos photometry available now on the CD-ROMs.\n\n\\section{Hipparcos main-mission photometry}\nAlthough the telescope diameter is small (29\\,cm), Hipparcos\nachieved a high photometric precision in the wide $H\\!p$ band (335 to \n895~nm), thanks to the chosen time allocation strategy and to the \nfrequent on-orbit photometric calibrations, making use of a large set \nof standard stars. The time allocated for a star observation was adapted \nto its magnitude in order to homogenize the astrometric precision. The \nphotometric reduction was made in time slices of 10 hours, called \nreduced great circles (RGC). During that time interval, the satellite \nscanned a closed strip in the sky, measuring about 2600 stars, among \nthem 600 standard stars.\n\nThe FAST and NDAC consortia independently reduced the photometry. They\nhad to map the time evolution of the spatial and chromatic response of\nthe detection chains for both fields of view (FOV), the preceding and\nthe following. In Fig.~1, a zero-point problem between FOV magnitude\nscales is shown, before and after its correction.\n\n\n\\begin{figure}\n\\centering%\n \\mbox{\n% \\subfigure{\\psfig{file=leyer1a.eps,height=70mm,width=70mm}}\n% \\subfigure{\\psfig{file=leyer1b.eps,height=70mm,width=70mm}}\n \\subfigure{\\psfig{file=leyer1a.eps,height=66mm,width=66mm}}\n \\subfigure{\\psfig{file=leyer1b.eps,height=66mm,width=66mm}}\n }\n \\caption{HIP~96647. Left: magnitudes before the\n data merging, open squares are for the following FOV, crosses for the\n preceding FOV. Right: the corrected final solution.}\n\\end{figure}\n\nThe light of the star was modulated by a grid for astrometric\npurposes. The transmitted signal was modeled by a Fourier\nseries of 5 parameters. From this model two estimates of the\nintensity were done: one, measuring the integrated signal, the\n``DC mode'', was robust to the duplicity but more dependent on\nthe background, and the second, measuring the amplitude of the\nmodulation, the ``AC mode'', was sensitive to the duplicity but\nnot to the background (cf. van Leeuwen et al. 1997). These two\nestimates and their accuracies are given in the Epoch\nPhotometry Annex (CD-ROM 2) and in the Epoch Photometry Annex\nExtension (CD-ROM 3).\n\n\n\\section{Noise and magnitude}\nThe precision of the magnitude is a function of the magnitude itself. \nIn addition, for a star of constant magnitude, the errors may be \nvariable. The data are then heteroscedastic. The correlation between \nthe error and the magnitude, may generate some problems. For instance, \nthe weighted mean cannot be used to estimate the central value of the \nmagnitude distribution, if the amplitude is large as for the Miras. \nThe global loss of precision as the satellite ages (Eyer \\& Grenon \n2000) also needs to be considered. The usual period search algorithms are \nalso sensitive to the inhomogeneity of the data.\n\n\\subsection{Quoted transit errors}\nDuring a single transit, a star was measured 9 times on average,\nthe transit error $\\sigma_{H\\!p}$ was derived in a first \napproximation from the spread of these measurements. However,\nthe estimation did not include offsets which might have affected\na whole transit, e.g., due to a mispointing or to a superposition of \na star from the other FOV. In our first analysis, an empirical law \nwas determined to correct the transit error underestimation, \notherwise the number of candidate variable stars did not appear credible.\n\nDuring the phase of data merging, ad-hoc corrections were computed\n(Evans 1995). The errors were studied with different methods,\ncomparing first the ``average'' error estimated from the $\\sigma_{H\\!p}$\nwith the dispersion of the measurements on $H\\!p$. Another study by \nEyer \\& Genton (1999) was made on the quoted errors using variograms;\nit showed a good general agreement with the Evans results, with some mild \nunderestimations for faint magnitudes and some mild overestimations \nfor the bright magnitudes in Evans' approach.\n\n\\subsection{Time sampling}\nThe time sampling was determined by the satellite rotation speed and \nby the scanning law which were optimized to reach the most uniform \nastrometric precision over the whole celestial sphere. The total number\nof transits per star is a function mainly of the ecliptic latitude.\nThe time intervals between successive transits are 20-108-20-etc\\ldots \nminutes. The transits form groups which are separated by about one month, \nbut the number of consecutive measurements as well as the time separation \nbetween groups of transits can vary strongly from one star to another.\n\n\\subsection{Chromatic aging}\nThe irradiation by cosmic particles reduced the optical transmission\nwith time. This aging was chromatic; it was worse than expected\nbecause the satellite had to cross the two van Allen Belts twice per\norbit. Furthermore, the satellite was operational during a maximum of \nsolar activity. For instance, the magnitude loss over 3.3 years was 0.8 \nmag for the bluest stars and only 0.15 mag for the reddest.\n\nThe aging of the image dissector tubes were not uniform and distinct\nfor both FOVs, therefore the aging corrections had to be calibrated\nas functions of the star location on the grid for each FOV.\n\n\\subsubsection{Magnitude trends:}\nAn odd effect of the chromatic aging was the production of magnitude \ntrends in the $H\\!p$ time series. As the transmission loss was colour \ndependent, the magnitude correction had to be a function of the star \ncolour. A colour index, monotonically growing with the effective\nwavelength of $H\\!p$ band, had to be evaluated from heterogeneous sources.\nThe precision of the equivalent $V-I$ was highly variable. For stars with\n``bad'' $V-I$ colour, the magnitude correction was erroneous and produced\na trend. A colour bluer than true generates a spurious increase of the \nluminosity with the time. An example of a trend is given in\nFig.~2.\n\\begin{figure}\n \\centering%\n \\mbox{\\psfig{file=leyer2.eps,height=80mm,width=80mm}}\n \\caption{HIP~29862, an example of trend induced by aging}\n\\end{figure}\n\\subsubsection{Selection of trends:}\n\nStars like Be stars may also show quasi-linear trends over the mission\nduration. The identification of spurious trends was iterative. LPVs,\nshowing Gaussian residuals when modeled with a trend on top of their\nsemi-periodic light-curve, were sorted first. But there was much more\ndiversity in the data showing trends, true or spurious. So we used an\nAbbe test (Eyer \\& Grenon 2000) for a global detection. Stars with an\nAbbe test close to 1, or with a large trend or with very long periods,\nwere flagged. Stars with possible envelopes were not retained. After\nvisual inspection of the time series by Grenon, the number of stars\nselected by these different procedures was 2412.\n\n\\subsubsection{Correction of the star colour:}\nThe amplitude of the magnitude drift was used to correct the star colour.\nIndeed, if a time series shows a trend $\\alpha$ which may be imputed to\nan incorrect initial colour, there is a possibility to recover the true \nstar colour by the relation:\n $$(V-I)_{new} = (V-I)_{old} - 14290 \\, \\alpha $$\nwhere $\\alpha$ is expressed in magnitude per day.\n\nEvery selected case was investigated to decide whether the trend could \nbe a consequence of an incorrect colour; 965 $V-I$ indices were corrected\nthis way with certainty and the origin of the errors on the colours was\ntraced back.\n\n\\section{Outlying values}\nWhen studying variable stars, outlying values and anomalous data\ndistributions are of great interest. Namely, it is important to\ndistinguish outliers of instrumental origin from those due to stellar\nphysical phenomena. Some stars show luminosity changes on very short\ntime scales. For Algol eclipsing binaries, the duration of the eclipse\nis short with respect to their period. With non-continuous time sampling,\neclipses may appear as low luminosity points. UV Ceti stars show strong\nbursts in the U band on very short time scales. However, because of the\nwidth of the $H\\!p$ band, the photospheric flux in the redder part of\nthe band largely dominates that of the burst, with the result that no\nburst was detected with certainty in the M dwarfs.\n\nIn Fig.~3 we present two cases of outlying values of instrumental origin.\n\\begin{figure}\n\\centering%\n \\mbox{\n \\subfigure{\\psfig{file=leyer3a.eps,height=66mm,width=66mm}}\n \\subfigure{\\psfig{file=leyer3b.eps,height=66mm,width=66mm}}\n }\n \\caption{\n Two examples of series with outlying values. Left: HIP~35527 the case\n of a light pollution from the other FOV, where Sirius is the perturbing \n star (this case is not flagged); Right: HIP~57437 an example of\n mispointing effect with low values correctly flagged (open circles).}\n\\end{figure}\n\n\n\\subsection{Instrumental outliers: Mispointing effect}\nThe pointing precision of the satellite was normally better than 1 arcsec.\nHowever after Earth or Moon eclipses and especially near the end of the \nmission when most gyroscopes were faulty, the problems of mispointing were\nmore acute. The radius of the photocathode was 15 arcsec, with a lower \nsensitivity towards the edge. An inaccurate pointing was inducing a loss of\ncounted photons, leading to dimmer points in the time series.\n\nThe problems with extended objects were even worse, depending on their sizes.\nA similar situation happened with visual double systems when the separation \nwas around 10 arcsec. In this case the target was either the primary or the \nphotocenter of the system. From time to time the companion was on the edge \nor out of the FOV, diminishing the amount of collected light. Even when the \ntwo components were measured alternatively, the not-measured star might have\nsometimes entered in the FOV producing a luminosity excess mimicking a burst.\n\n\\subsection{Instrumental outliers: Light pollution}\n\nA neighbour star could contaminate the observed star, although most of the \nidentified cases were rejected during the Input Catalogue compilation.\nThe perturbing star was possibly a real neighbour or, more often, a star \nbelonging to the other FOV. Several configurations are possible:\n\\begin{itemize}\n \\item A star from the other FOV was added to the measured star. That is \n called a superposition effect. Stars in the Galactic plane were \n more often perturbed because of the higher star density.\n \\item The perturbing star was very bright and caused scattered light in \n the detection chain. This veiling glare could be felt even if the \n disturbing star was further than 15 arcsec. \n \\item When the separation was greater that 15 arcsec, the two effects\n of pollution and mispointing could produce high values of fluxes\n of the dim component.\n\\end{itemize}\n\nFig.~4 shows the correlation between the asymmetry of \nthe time series for double systems and the angular separation $\\rho$. The \nasymmetry is positive for dimmer outlying values, and negative for pollution \nby the primary (bright outlying values).\n\\begin{figure}\n \\centering%\n \\mbox{\\psfig{file=leyer4.eps,height=80mm,width=80mm}}\n \\caption{Light pollution and mispointing effects\nfor double stars as a function of the angular separation $\\rho$.}\n\\end{figure}\n\n\\subsection{Selection of outliers}\nThe problems caused by the outliers were very acute at the beginning of \nthe analysis; we had then to take drastic measures before searching for \nperiods and amplitudes. We removed:\n\\begin{itemize}\n \\item all measurements with a non-null flag.\n \\item the end of the mission, if the dispersion of the data was smaller \n than 0.3 before the day 8883. (the data for large amplitude \n variables were kept up to the end of the mission).\n \\item high luminosity values if there was a magnitude jump in consecutive \n transits.\n \\item bad-quality measurements with transit errors higher than \n $\\epsilon(DC) = 0.0005*10^{0.167\\: H\\!p_{\\tiny DC}}+0.0014.$\n \\item temporarily one or two outliers to check their impact on the \n result of an analysis based on truncated time series.\n\\end{itemize}\nThis removal represents a reduction by 6\\% of the number of measurements\nwith non-zero flag.\n\nSuspect transits from the analysis of outliers were transmitted to the \nreduction consortia, who flagged them according to the origin of the\ndisturbance.\n\n\\section{Alias and spurious periods}\n\nThe spectral window produces spurious periods when it is convoluted \nwith the true spectrum. As a result, spurious periods around 0.09 d\nwere frequently found for long periods or irregular variables as \nwell as for stars showing magnitude trends. Periods of about 5 d for\nSR variables turned out to be nearly all spurious. With the Hipparcos \ntime sampling the spectral window changes from one star to another \nand the alias effect had to be studied on a per star basis. \n\nA 58 day periodicity was found in many time series when applying the \nperiod search algorithm. This period corresponds to the time interval \nbetween consecutive measurements of double systems under the same \nangle with respect to the modulating grid (the modulated signal is \nhigher when the components are parallel to the grid).\n\n\\section{Advice about the use of the data}\nWe want to stress that caution should be taken in handling the epoch\nphotometry, especially when the signal to noise ratio or when the \nnumber of retained measurements are small. The effects of multiperiodicity \nare generally very tricky. The spectral window should be investigated \nin detail and periods near sampling frequencies should be taken with \ncare, in particular in the range 5 to 20 d where the Hipparcos photometry\nhas the weakest detection capability.\n\nThe selection of photometric data can be made according to their flags,\nthe estimates of the transit errors and the background intensities.\nIn case of doubt about outlying data, a look to the magnitude difference\n$AC-DC$ will reveal problems related to duplicity and image superpositions\nsince the amplitude of the modulated signal is reduced in the case of\nmisaligned sources with respect to the grid orientation. The contents of\nthe opposite FOV can be investigated thanks to their published positions.\nIt is suggested to correct rather than to eliminate data since a loss\nof information might twist statistics. For an example of a successful\nselection procedure applied to the data of HIP~115510, see Lampens et\nal. (1999).\n\n\\section{Conclusion}\nPerforming accuracy photometry in space is not free from problems. The\nsame is true for the data analysis. Once the origin of the encountered \nproblems is identified, it is possible to cope with them and determine\nprecisely the domains of validity of the algorithms for search of periods\nand amplitudes. Globally the ratio quantity-quality generated by this \nmission for the study of variability has no equivalent up to now.\n\n\\begin{references}\n \\reference ESA 1997, {\\it The Hipparcos and Tycho catalogues}, ESA SP-1200\n \\reference Evans, D.W. 1995, {\\em Hipparcos Photometry Merging Report},\n RGO/NDAC 95.01\n \\reference Eyer, L., and Genton, M.G. 1999, A\\&AS 136, 421 \n \\reference Eyer, L. and Grenon, M., 2000, in preparation\n \\reference Lampens, P., van Camp, M., Sinachopoulos, D. 1999 \\aap, accepted\n \\reference van Leeuwen, F., Evans, D.W., Grenon, M.,\n Grossmann, V., Mignard, F., Perryman, M.A.C. 1997, \\aap 323, L61\n \\end{references}\n\n\\end{document}\n\n\n"
}
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astro-ph0002236
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The Schweizer$-$Middleditch star revisited
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[
{
"author": "M. R. Burleigh \\inst{1}"
},
{
"author": "U. Heber \\inst{2}"
},
{
"author": "D. O'Donoghue \\inst{3}"
},
{
"author": "M. A. Barstow \\inst{1}"
}
] |
We have re-observed and re-analysed the optical spectrum of the Schweizer$-$Middleditch star, a hot subdwarf which lies along almost the same line-of-sight as the centre of the historic SN1006 supernova remnant (SNR). Although this object is itself unlikely to be the remnant of the star which exploded in 1006AD, Wellstein et~al. (1999) have demonstrated that it could be the remnant of the donor star in a pre-supernova Type Ia interacting binary, if it possesses an unusually low mass. We show that, if it had a mass of 0.1$-$0.2$\Msun$, the SM star would lie at the same distance ($\approx$800pc) as the SNR as estimated by Willingale et~al. (1995). However, most distance estimates to SN1006 are much larger than this, and there are other convincing arguments to suggest that the SM star lies behind this SNR. Assuming the canonical subdwarf mass of 0.5$\Msun$, we constrain the distance of the SM star as 1050~pc$<$d$<$2100~pc. This places the upper limit on the distance of SN1006 at 2.1~kpc. \keywords{Stars: supernovae: individual: SN 1006}
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{
"name": "h1878.tex",
"string": "% l-aa.dem\n% L-AA vers. 3.0, LaTeX style file for Astronomy & Astrophysics\n% Demo file\n% (c) Springer-Verlag HD\n%rhubarb\n%-----------------------------------------------------------------------\n%\\documentclass[referee]{aa}\n\\documentclass[times]{aa}\n\\usepackage{epsfig}\n\\def\\Msun{\\hbox{$\\rm\\thinspace M_{\\odot}$}}\n\\newcommand{\\lapprox }{{\\lower0.8ex\\hbox{$\\buildrel <\\over\\sim$}}}\n%\n\\def\\la{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}{\\raise2pt\\hbox{$<$}}\n}}}\n\\def\\ga{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}{\\raise2pt\\hbox{$>$}}\n}}}\n\n\n\\begin{document}\n\n \\thesaurus{06(08.19.4 SN 1006)}% A&A Section 6: Form. struct. and evolut. \n %of stars\n \n%\n \\title{The Schweizer$-$Middleditch star revisited}\n\n \\author{M. R. Burleigh \\inst{1} \\and U. Heber \\inst{2} \n\\and D. O'Donoghue \\inst{3} \\and M. A. Barstow \\inst{1}}\n\n \\offprints{Matt Burleigh, mbu@star.le.ac.uk}\n\n \\institute{Department of Physics and Astronomy, University of\n Leicester, Leicester LE1 7RH, UK\n\\and Dr. Remeis-Sternwarte Bamberg, Universit\\\"at\nErlangen-N\\\"urnberg, Sternwartstrasse 7, D-96049 Bamberg, Germany\n%\\and Institut f\\\"ur Physik, Universit^�t Potsdam, Am Neuen Palais 10,\n%D-14415 Potsdam, Germany\n%\\and Institut f\\\"ur Astronomie und Astrophysik der Universit^�t M^�nchen,\n%Scheinerstrasse 1, D-81679 M^�nchen, Germany\n\\and South African Astronomical Observatory, PO Box 9, Observatory 7935,\nCape Town, South Africa }\n\n%Last revised 10th February 2000\n\n \\date{Received 30 November 1999 / Accepted 9 February 2000}\n\n \\titlerunning{The Schweizer$-$Middleditch Star Revisited} \n\n \\authorrunning{M. R. Burleigh et~al.}\n\n\\maketitle\n\n\\begin{abstract}\n\nWe have re-observed and re-analysed the optical spectrum of the \nSchweizer$-$Middleditch star, a hot subdwarf which lies along almost \nthe same line-of-sight as the centre of the historic SN1006 supernova\nremnant (SNR). \nAlthough this object is itself unlikely to be the remnant of the star \nwhich exploded in 1006AD, Wellstein et~al. (1999) have demonstrated that\nit could be the remnant of the donor star in a pre-supernova Type Ia \ninteracting binary, if it possesses an unusually low mass. We show that,\nif it had a mass of 0.1$-$0.2$\\Msun$, \nthe SM star would lie at the same distance\n($\\approx$800pc) as the SNR as estimated by Willingale et~al.\n(1995). However, most distance estimates to SN1006 are much larger than\nthis, and there are other convincing arguments to \nsuggest that the SM star lies behind this SNR. Assuming the \ncanonical subdwarf mass of 0.5$\\Msun$, we constrain the distance of the \nSM star as 1050~pc$<$d$<$2100~pc. This places the upper limit on the \ndistance of SN1006 at 2.1~kpc. \n\n\n \\keywords{Stars: supernovae: individual: SN 1006}\n \\end{abstract}\n\n%\n% 14.Sep.'90: Demo-Vs.\n%________________________________________________________________\n\n\\section{Introduction}\n\nSN 1006 was the brightest supernova witnessed in recorded history. The\nestimated peak magnitude (V$=$$-$9.5$\\pm$1, Clark \\& Stephenson\n1977), reported visibility for nearly two years, and the lack of a nearby\nOB association strongly suggests a Type Ia origin (SNIa, Minkowski 1966).\nAlmost all current models of Type Ia supernova involve the nuclear\nexplosion of a white dwarf induced by rapid mass accretion in a binary\nsystem. However, no stellar remnant from this supernova explosion \nhas ever been conclusively identified, \nincluding a pulsar, or the remains of any companion star.\n\n\n\\begin{figure*}\n\\vspace{8.5cm}\n%\\special{psfile=newspectrum.ps\n%\\special{psfile=figure1.ps\n\\special{psfile=1878.f1\nhscale=65 vscale=50 hoffset=75 voffset=25}\n\\caption{Optical spectrum of the SM star, smoothed with a 3 pixel Gaussian.}\n\\end{figure*}\n\nIn 1980, Schweizer \\& Middleditch searched for just such \na stellar remnant from SN 1006 and discovered a faint (V$=$16.7) \nblue star $\\approx$2.5' from the projected \ncentre of the supernova remnant (SNR). \nThey identified this object (now known as the\nSchweizer$-$Middleditch star, SM star or SM80) \nas a hot subdwarf sdOB\nstar, and estimated its effective temperature \nT$_{eff}$$=$38,500$\\pm$4500K, and surface \ngravity log g$=$6.7$\\pm$0.6. From an estimate\nof the absolute magnitude, M$_v$$=$6.2$\\pm$1.8, Schweizer and\nMiddleditch (1980) derived a distance to their subdwarf of 1.1 ($+$1.4,\n$-$0.6) kpc. \nSince chance projection seemed unlikely, and the distance estimate was in\nrough agreement with the then exisiting estimates of the distance to the\nSNR itself, Schweizer \\& Middleditch (1980) suggested that\ntheir subdwarf may in fact \nbe the remnant star, or at least associated with it. \n\nSavedoff and Van Horn (1982) later \nshowed conclusively that the SM star could not be the remnant of the \nsupernova itself, since the time to cool to the observed effective \ntemperature was simply too long, $\\sim$10$^6$ years compared to the SNR age of \n10$^3$ years. However, this does not rule out the SM star as a stellar remnant \nof the {\\it donor} star in a pre-SNIa interacting binary system. \n\n\nSubsequent far ultra-violet (far-UV) \nobservations with IUE and HST/FOS revealed the presence\nof strong Fe II and Si II, III and IV lines \nsuperimposed on the continuum of the SM star (Wu et~al. 1983, Fesen\net~al. 1988, Wu et~al. 1993). The iron lines have symmetrical \nvelocity profiles, broadened up to $\\sim$8000 km\ns$^{-1}$ FWHM. The Si features are asymmetric, redshifted \nand centred at a radial\nvelocity of $\\sim$5000 km s$^{-1}$. These features have been used to\nestimate the mass of iron in the remnant and to map the positions of\nvarious shock regions. Importantly, though, the presence of redshifted\nlines in the supernova ejecta suggests that the SM star must\nlie {\\it behind} the SNR, since they are assumed to originate in material \nmoving away from us on the far side of the remnant.\n\nMeasurements of the widths of these aborption lines, coupled with the\nangular size of the remnant, led Wu et~al. (1993) to derive a {\\it lower\nlimit} to the SNR distance of 1.9 kpc. This contrasts strongly with the\nestimate of Willingale et~al. (1995) of 0.7$\\pm$0.1 kpc, derived from \nmodelling X-ray emission detected in \nROSAT PSPC observations. Therefore, we were motivated to\nre-observe and re-analyse the SM star in order to place tighter\nconstraints on its distance, and hence on the distance to the SNR itself.\nSecondly, we learnt of the study by Wellstein et~al. (1999) \nwhich suggests that the prior donor star in an\nSN Ia progenitor system (an interacting binary) may appear subsequently\nas a {\\it low mass} hot subdwarf star. This new theoretical result re-opens \nthe question first posed by Schweizer \\& Middleditch (1980) in the conclusion \nto their discovery paper: \"Can one component of a\nbinary system that forms a Type Ia supernova end up being a hot subdwarf\nor white dwarf?\". In the light of Wellstein et~al.'s recent \nwork, we re-address this question. \n\n\n\\section{Spectroscopy}\n\nThe SM star was observed for a total of \n4000 seconds on 1996 April 14 with the South\nAfrican Astronomical Observatory's 1.9-m Ratcliffe Telescope, the Unit\nspectrograph and the Reticon photon counting system (RPCS). The RPCS had\ntwo arrays, one which accumulates energy from the source, while the other\nrecords sky background through an adjacent aperture. The target was\nobserved for 2000 seconds through one aperture, then for a further 2000\nseconds through the second aperture, in order to average out variations\nbetween the two light paths. The grating (number\n6) was blazed to cover a wavelength range of \n$\\sim$3700{\\AA}$-$5200{\\AA} with a\nresolution of $\\approx$4{\\AA}. Flat fields were obtained at the start and\nend of the night, and wavelength calibration was provided by a CuAr lamp, \nwhich was observed before and after the target. A blue spectro-photometric\nstandard (LTT 6248) was also observed. The reduced, calibrated spectrum is \nshown in Fig. 1.\n\n\n\n\\section{High speed photometry}\n\n\\begin{figure}\n\\vspace{11cm}\n%\\special{psfile=diffphot.ps\n%\\special{psfile=figure2.ps\n\\special{psfile=1878.f2\nhscale=50 vscale=50 hoffset=-30 voffset=-40}\n\\caption{Differential light curve for the SM Star (\\#8) and four \ncomparison stars in the same field.}\n\\end{figure}\n\n\n\n\\begin{figure}\n\\vspace{6cm}\n%\\special{psfile=smstar_ft.ps\n%\\special{psfile=figure3.ps\n\\special{psfile=1878.f3\nhscale=100 vscale=100 hoffset=-20 voffset=-20}\n\\caption{Amplitude spectrum determined from the SM Star's light curve.}\n\\end{figure}\n\n\n\nRecently, multi-periodic pulsations have been discovered in a number of \nsubdwarf sdB stars (the EC14026 stars, Kilkenny et~al., 1997). Both radial \nand non-radial modes are present, although the cause of these pulsations \nis not fully understood. \nTheoretical studies have shown that these oscillations may be excited by \nan opacity bump due to heavy element ionization, giving rise to a \nmetal-enrichment in this driving region (Charpinet et~al., 1996). \nHowever, why pulsations \nare observed in some sdBs and not in others remains a mystery. \n\nWe observed the SM Star on 1999 September 4th with the South African \nAstronomical Observatory's 0.75m telescope, together with the \nUniversity of Cape Town's CCD photometer in high speed mode, in \norder to search for pulsations. A $\\approx$2600 second light curve \nwas obtained, consisting of 20 second exposures separated \nby essentially zero seconds of dead time. \nFour comparison stars were also observed at the same time. \nThe differential light curve is shown in Fig. 2. \nThe SM star (star \\#8 in Fig. 2) shows no evidence of \npulsations; the fluctuations in Fig. 2 are merely random noise. \nThe amplitude spectrum (Fig. 3), which has been calculated out to the \nNyquist frequency, also shows no evidence for pulsations. However, \nat V$\\approx$16.7 we are clearly unable to detect fluctuations below \n$\\approx$0.05 mags. with this telescope. Many of the known sdB pulsators \nvary at the level of 0.001$-$0.05 mags., and so clearly we cannot rule out \nlow level pulsations in this object. We suggest that it should be re-observed \non a larger telescope.\n\n\n\\section{Analysis}\n\n\\subsection{Spectral analysis}\n\nThe H Balmer series is\nvisible in the calibrated optical spectrum (Fig. 1)\nto H11. HeI is detected at 4026{\\AA}, 4144{\\AA}, 4472{\\AA} and\nmarginally at 4922{\\AA}. There is also a marginal detection of HeII at\n4686{\\AA}. \n\nA grid of synthetic spectra derived from H \\& He line blanketed NLTE \nmodel atmospheres (Napiwotzki 1997) was matched to the data to \nsimultaneously determine the effective temperature, surface gravity \nand He abundance (see Heber et~al. 1999). We find T$_{eff}$$=$32,900K, \nlog g$=$6.18 and log (N(He)$/$N(H))$=$$-$1.7. While formal statistical errors \nfrom the fitting procedure are relatively small (1$\\sigma$:\n$\\Delta$(T$_{eff}$$=$)=340K, $\\Delta$(log\\,g)$=$$\\Delta$(log(He/H))$=$0.1dex),\nsystematics dominate the error budget and are estimated from varying the \nspectral windows for the profile fitting and the continuum setting to be \n$\\Delta$(T$\\_{eff}$)$=$$\\pm$1500K, $\\Delta$(log g)$=$$\\pm$0.3 dex and \n$\\Delta$(log (N(He)$/$N(H))$=$$\\pm$0.3 dex. These best-fit \nparameters are unchanged if H$_\\epsilon$ is omitted \nfrom the fit (since it might be contaminated by CaII). \nA more precise error estimate \nwould, however, require repeat observations.\n\nTherefore, we find that both the temperature and \ngravity are at the low end of the large range estimated \nby Schweizer \\& Middleditch (1980). With these parameters the\nSM star resembles an ordinary subdwarf B star \nclose to the zero-age extended horizontal branch (ZAEHB). \n\n\n\\subsection{Extinction}\n\nUsing the Matthews \\& Sandage (1963) calibration, combined with our model \nfit parameters, we estimate the colour excess E$_{(B-V)}$$=$0.16$\\pm$0.02. \nFrom Whitford (1958) we then estimate the visual extinction \nA$_v$$=$3.0$\\times$E$_{(B-V)}$$=$0.48$\\pm$0.06. Schweizer \\& Middleditch \nmeasured the V magnitude from photoelectric photometry as 16.74$\\pm$0.02. \nTherefore, we take the \nredening corrected magnitude as \n\\newline V$_0$$=$16.26$\\pm$0.07.\n\n\n\\subsection{Distance}\n\nSince bolometric corrections for hot subluminous stars are large and \nsomewhat uncertain, we prefer not to make use of them for the distance \ndetermination. Instead we calculate the angular radius from the \nratio of the observed (dereddened) flux at the effective wavelength of the \nV filter and the corresponding model flux.\nAssuming the canonical mass for hot subdwarf \nstars, M$=$0.5$\\Msun$, we determine the stellar radius from the \ngravity and finally derive the distance from the angular diameter and the \nstellar radius. \n%(we note that no mass-radius relation exists for \n%hot subdwarfs, unlike white dwarfs, and thus we cannot derive a mass estimate \n%from the gravity measurement)\nWe obtain a distance of d$=$1485pc which corresponds to an absolute \nmagnitude of M$_V$$=$5.4. However, the error on log g \nis large ($\\pm$0.3 dex), translating to d$=$1050pc for log g$=$6.48, or \nd$=$2100pc for log g$=$5.88. \n\nIf the SM star has a much lower mass than usually assumed for these \nobjects, as suggested by Wellstein \net~al. (1999), then the absolute magnitude will be lower \nand hence the star will be much closer to us. For example, \nif M$=$0.2$\\Msun$ then we find M$_V$$=$6.4 and \nd$=$940pc (assuming log g$=$6.18). \nIf M$=$0.1$\\Msun$, then M$_V$$=$7.2 and d$=$650pc. \n\n\n\\begin{figure}\n\\vspace{11cm}\n%\\special{psfile=newuli4.ps\n%\\special{psfile=figure4.ps\n\\special{psfile=1878.f4\nhscale=45 vscale=45 hoffset=-20 voffset=-15}\n\\caption{NLTE model fit to the H Balmer lines and He lines detected in the \nSM Star's optical spectrum.}\n\\end{figure}\n\n\n\\begin{figure}\n\\vspace{11cm}\n%\\special{psfile=newuli5.ps\n%\\special{psfile=figure5.ps\n\\special{psfile=1878.f5\nhscale=45 vscale=45 hoffset=-15 voffset=-15}\n\\caption{Position of the SM star in the T$_{eff}$/log g plane (large cross). \nThe zero-age \nextended horizontal branch (ZAEHB) \nand He main sequence are marked. Loci showing how \nstars of various masses evolve away from the ZAEHB are also shown.}\n\n\\end{figure}\n\n\n\\section{Discussion}\n\nA new analysis of the Schweizer-Middleditch star, a hot subdwarf which lies \nalong the same line-of-sight as the centre of the SN1006 SNR, has allowed \nus to place tighter constraints on its atmospheric parameters, and re-assess \nits distance. Since Wellstein et~al. (1999) have demonstrated that the \nremnant of \nthe donor star in a pre-SNIa binary system could appear as a hot subdwarf, \nalbeit with an abnormally low mass, we can now re-address Schweizer \\&\nMiddleditch's original question: is the SM star the stellar remnant of one \ncomponent of the SNIa progenitor binary?\n\nIn order to begin answering this question, we need to convice ourselves\nthat the SM star lies at the same distance as the SN1006 SNR.\nUnfortunately, there is a large range in the SNR distance estimates\nquoted in the literature. \nIn Table 1, we list the various distance estimates to the SN1006 SNR \nitself and the method used to obtain that distance. Early estimates, \nbased for example on the historical record of its brightness (e.g. Minkowski \n1966) and early models of the X-ray emission, gave distances $\\sim$1kpc. \nMost of the more recent estimates, based on a variety of theoretical\nmodels or measurements of e.g.~the expansion velocity or proper motion of\noptical filaments, place the SNR at a distance of $\\sim$1.5$-$2.0kpc. The\none glaring exception is the estimate of Willigale et~al. (1995),\n0.7$\\pm$0.1kpc, based on an analysis of the ROSAT PSPC X-ray image of the\nSNR. \n\nWe find the distance to the SM star 1050$<$d$<$2100 pc, \nassuming that it is an\nordinary hot subdwarf. If Willingale et~al's distance estimate is correct,\nthen \nthe SM star would lie a long way behind the remnant. In order\nfor it to lie within the remnant, it would have to be of unusually low\nmass. A mass of 0.1$-$0.2$\\Msun$ gives a distance compatible with \nWillingale et~al's estimate, and \nin that scenario the SM star could indeed then be\na remnant of the donor star in an SNIa progenitor system. \n\nHowever, if Willingale et~al's SNR distance estimate is wildly inaccurate, \nand \nthe more conservative estimates of $\\sim$1.5$-$2.0kpc are correct, then\nthe SM star cannot be a low mass remnant of the donor star in a \npre-SNIa binary. \n\n\n\\begin{table*}\n\\begin{center}\n\\caption{Distance estimates to the SN1006 SNR from the literature}\n\\begin{tabular}{lcll}\nAuthor & Year & Distance & Method \\\\\n & & (kpc) & \\\\\nMinkowski & 1966 & 1.3 & Historical record of brightness \\\\\nStephenson et~al. & 1977 & 1.0$\\pm$0.3 & Historical record of brightness \\\\\nWinkler & 1977 & 0.9$-$1.3 & Reverse shock model of x-ray emission \\\\\nHamilton et~al. & 1986 & 1.7 & Reverse shock model \\\\\nKirshner et~al. & 1987 & 1.4$-$2.1 & Shock velocity \\& proper motions \\\\\nHamilton \\& Fesen & 1988 & 1.5$-$2.0 & Spherically symmetric hydrodynamic \nsimulations \\\\\nFesen et~al. & 1988 & 1.5$-$2.3 & Fe line widths, age \\& angular size of \nremnant \\\\\nLong et~al. & 1988 & 1.7$-$3.1 & Proper motion of optical filaments \\\\\nWu et~al. & 1993 & $>$1.9 & FeII line widths \\& angular size of \nremnant \\\\\nWillingale et~al. & 1995 & 0.7$\\pm$0.1 & Analysis of x-ray emitting material \\\\\nLaming et~al. & 1996 & 1.8$\\pm$0.3 & Modelling non-radiative shocks \\\\\n\\end {tabular}\n\\end{center}\n\\end{table*}\n\n\nIn fact, there are two more compelling arguments against the SM star\nhaving any relation to SN1006. Firstly, it is located $\\approx$2.5' south\nof the projected centre of the remnant, and would have to possess a\nproper motion of 0.15\" per year and a velocity of $\\approx$800km\nsec$^{-1}$ to have reached its current location. Unfortunately, the star\nsimply does not possess this motion or velocity. Secondly, the presence\nof red-shifted metal absorption lines superimposed on the SM star's UV \nspectrum strongly indicate that the star is behind the remnant, since\nthese features almost certainly originate at a shock front on the\nremnant's far side. Confirmation of this may come \nfrom observations of other nearby objects with strong UV fluxes and generally\nfeatureless far-UV continuums. Indeed, P.F. Winkler has an HST/STIS\nprogram to observe four such objects behind SN1006 during Cycle 8\n(two QSOs and two A0 stars, program ID 8244), and one of these objects\nis even closer to the projected centre of SN1006 than the SM star. \nThese targets are not scheduled to be observed until\nJune-July 2000, but the detection of the same red-shifted features \nas seen in the SM star (and the non-detection of any \nadditional features with separate velocities) would effectively\nrule out any exotic origin for these lines, and confirm the location of\nthe SM star behind the SN1006 SNR.\n\nThus, the SM star can only be the remnant of the donor star in a pre-SNIa\nbinary, such as might have produced SN1006, if the following four\ncriteria are fulfilled: (1) The star has an unusually low mass for a hot\nsubdwarf ($\\approx$0.1$\\Msun$), (2) the low distance estimate to the SN1006\nSNR of Willingale et~al. (1995) is correct, (3) the red-shifted metal\nlines seen in the SM star's far-UV spectrum originate somewhere other\nthan on the far side of the SNR, and (4) the SM star has a high proper\nmotion and transverse velocity. Unfortunately, at the time of writing,\nnone of these conditions can convincingly shown to be true.\nHowever, the tighter constraint we have been able to place on the distance \nto the\nSM star in this analysis can now be used to place an upper limit on the\ndistance to the SN1006 SNR itself, and hence constrain the models and\nmethods used to estimate the distances of supernova remnants.\n\n\n\\begin{acknowledgements}\n\nMRB acknowledges the support of PPARC, UK. We thank Pete Wheatley (Leicester \nUniversity) for generating the Fourier transform of the SM Star's light \ncurve.\n\n\\end{acknowledgements}\n\n\n\\begin{thebibliography}{}\n\n%\\bibitem{} Blair W.P., Long K.S., Raymond J.C., 1996, ApJ 468, 871\n\n\\bibitem{} Charpinet S., Fontaine G., Brassard P., Dorman B., 1996, ApJ \n471, L103\n\n\\bibitem{} Clark D.H., Stephenson F.R., 1977, {\\it The Historical Supernovae} \n(Oxford: Pergamon)\n\n\\bibitem{} Fesen R.A., Wu C.-C., Leventhal M., Hamilton A.J.S., 1988, \nApJ 327, 164\n\n\\bibitem{} Hamilton A.J.S., Fesen R.A., 1988, ApJ 327, 178\n\n\\bibitem{} Hamilton A.J.S., Sarazin C.L., Szymkowiak A.E., 1986, ApJ 300, 698\n\n\\bibitem{} Heber U., Reid I.N., Werner K., 1999, A\\&A 348, L25\n\n\n\\bibitem{} Kilkenny D., Koen C., O'Donoghue D., Stobie R.S., 1997, MNRAS \n285, 640\n\n\\bibitem{} Kirshner R.P., Winkler P.F., Chevalier R.A., 1987, ApJ 315, L135\n\n\\bibitem{} Laming J.M., Raymond J.C., McLaughlin B.M., Blair W.P., 1996, ApJ \n472, 267\n\n\\bibitem{} Long, K.S., Blair W.P., van den Bergh S., 1988, ApJ 333, 749\n\n\\bibitem{} Matthews T.A., Sandage A.R., 1963, ApJ 138, 30\n\n\\bibitem{} Minkowski R., 1966, AJ 71, 371\n\n\\bibitem{} Napiwotzki R., 1997, A\\&A 322, 256\n\n\\bibitem{} Savedoff M.P, Van Horn H.M., 1982, A\\&A 107, L3\n\n\\bibitem{} Schweizer, F., Middleditch, J., 1980, ApJ 241, 1039 \n\n%\\bibitem{} Simon K.P., Hunger K., Kudritzki R.P., 1981, A\\&A 98, 211\n\n\\bibitem{} Stephenson F.R., Clark D.H., Crawford D.F., 1977, MNRAS 180, 567\n\n\\bibitem{} Wellstein S., Langer N., Gehren T., Burleigh M.R., \nHeber U., 1999, AGM 15, 3\n\n\\bibitem{} Whitford A.E., 1958, AJ 63, 201\n\n\\bibitem{} Willigale R., West R.G., Pye J.P, Stewart, G.C., 1995, \nMNRAS 278, 749\n\n\\bibitem{} Winkler P.F., 1977, ApJ 211, 562\n\n\\bibitem{} Wu C.-C., Leventhal M., Sarazin C.L., Gull T.R., 1983, ApJ 269, \nL5\n\n\\bibitem{} Wu C.-C., Crenshaw D.M., Fesen R.A., Hamilton A.J.S., Sarazin C.L., \n1993, ApJ 416, 247\n\n\n\n\\end{thebibliography}\n\n\n\\end{document}\n"
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[
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"name": "astro-ph0002236.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n%\\bibitem{} Blair W.P., Long K.S., Raymond J.C., 1996, ApJ 468, 871\n\n\\bibitem{} Charpinet S., Fontaine G., Brassard P., Dorman B., 1996, ApJ \n471, L103\n\n\\bibitem{} Clark D.H., Stephenson F.R., 1977, {\\it The Historical Supernovae} \n(Oxford: Pergamon)\n\n\\bibitem{} Fesen R.A., Wu C.-C., Leventhal M., Hamilton A.J.S., 1988, \nApJ 327, 164\n\n\\bibitem{} Hamilton A.J.S., Fesen R.A., 1988, ApJ 327, 178\n\n\\bibitem{} Hamilton A.J.S., Sarazin C.L., Szymkowiak A.E., 1986, ApJ 300, 698\n\n\\bibitem{} Heber U., Reid I.N., Werner K., 1999, A\\&A 348, L25\n\n\n\\bibitem{} Kilkenny D., Koen C., O'Donoghue D., Stobie R.S., 1997, MNRAS \n285, 640\n\n\\bibitem{} Kirshner R.P., Winkler P.F., Chevalier R.A., 1987, ApJ 315, L135\n\n\\bibitem{} Laming J.M., Raymond J.C., McLaughlin B.M., Blair W.P., 1996, ApJ \n472, 267\n\n\\bibitem{} Long, K.S., Blair W.P., van den Bergh S., 1988, ApJ 333, 749\n\n\\bibitem{} Matthews T.A., Sandage A.R., 1963, ApJ 138, 30\n\n\\bibitem{} Minkowski R., 1966, AJ 71, 371\n\n\\bibitem{} Napiwotzki R., 1997, A\\&A 322, 256\n\n\\bibitem{} Savedoff M.P, Van Horn H.M., 1982, A\\&A 107, L3\n\n\\bibitem{} Schweizer, F., Middleditch, J., 1980, ApJ 241, 1039 \n\n%\\bibitem{} Simon K.P., Hunger K., Kudritzki R.P., 1981, A\\&A 98, 211\n\n\\bibitem{} Stephenson F.R., Clark D.H., Crawford D.F., 1977, MNRAS 180, 567\n\n\\bibitem{} Wellstein S., Langer N., Gehren T., Burleigh M.R., \nHeber U., 1999, AGM 15, 3\n\n\\bibitem{} Whitford A.E., 1958, AJ 63, 201\n\n\\bibitem{} Willigale R., West R.G., Pye J.P, Stewart, G.C., 1995, \nMNRAS 278, 749\n\n\\bibitem{} Winkler P.F., 1977, ApJ 211, 562\n\n\\bibitem{} Wu C.-C., Leventhal M., Sarazin C.L., Gull T.R., 1983, ApJ 269, \nL5\n\n\\bibitem{} Wu C.-C., Crenshaw D.M., Fesen R.A., Hamilton A.J.S., Sarazin C.L., \n1993, ApJ 416, 247\n\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002237
|
High-resolution spectroscopy of V854\,Cen in decline -- Absorption and emission lines of C$_2$ molecules
|
[
{
"author": "N. Kameswara Rao"
},
{
"author": "$^1$ David L. Lambert"
},
{
"author": "$^2$"
},
{
"author": "Bangalore 560034"
},
{
"author": "India"
},
{
"author": "$^2$Department of Astronomy"
},
{
"author": "Austin"
},
{
"author": "TX 78712-1083"
},
{
"author": "USA"
}
] |
High-resolution optical spectra of the R Coronae Borealis (RCB) star V854\,Centauri in the early stages of a decline show, in addition to the features reported for other RCBs in decline, narrow absorption lines from the C$_2$ Phillips system. The low rotational temperature, T$_{rot}$ = 1150K, of the C$_2$ ground electronic state suggests the cold gas is associated with the developing shroud of carbon dust. These absorption lines were not seen at a fainter magnitude on the rise from minimum light nor at maximum light. This is the first detection of cold gas around a RCB star.
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Kameswara Rao \\& David L. Lambert]\n {N. Kameswara Rao,$^1$ David L. Lambert,$^2$\\\\ \n $^1$Indian Institute of Astrophysics, Bangalore 560034, India\\\\\n $^2$Department of Astronomy, University of Texas, Austin, TX 78712-1083, USA\\\\}\n\\date{Accepted .\n Received ;\n in original form 1999 }\n\n\\pagerange{\\pageref{firstpage}--\\pageref{lastpage}}\n\\pubyear{1999}\n\n\n\\maketitle\n\n\\label{firstpage}\n\n\\begin{abstract}\nHigh-resolution optical spectra of the R Coronae Borealis (RCB)\n star V854\\,Centauri\nin the early stages of a decline show, in addition to the features\nreported for other RCBs in decline, narrow absorption lines \nfrom the C$_2$ Phillips system. The low rotational temperature,\nT$_{\\rm rot}$ = 1150K, of the C$_2$ ground electronic state suggests\nthe cold gas is associated with the developing shroud of carbon dust.\nThese absorption lines were not seen at a fainter magnitude on the rise\nfrom minimum light nor at maximum light. This is the first detection of\ncold gas around a RCB star.\n \n\n\\end{abstract}\n\n\\begin{keywords}\nStar: individual: V854\\,Cen: variables: other\n\\end{keywords}\n\n\n\n\n\n\\section{Introduction}\n\n\nR Coronae Borealis stars are H-poor F-G type supergiants that decline\nin brightness unpredictably by up to 8 magnitudes and\nremain below their normal brightness for several weeks to\nmonths. It is generally accepted that these declines \nare due to formation of a cloud of carbon soot that obscures the\nstellar photosphere. Unanswered questions remain: `What triggers\ncloud formation?' and `Where does the soot form?' High-resolution\nspectroscopic monitoring of RCBs from maximum light into\ndecline will likely be necessary to refine schematic\nideas into answers that are\naccorded widespread acceptance. We report \nthe first detection of cool gas (T $\\simeq 1100$K) during the early decline of \na RCB star and, hence, evidence for a site of soot formation.\nCold dust is, of course, known around RCBs \nthrough detection of an infrared excess.\n\n The RCB in\nquestion is V854\\,Cen, which at maximum light is the\nthird brightest RCB variable after R\\,CrB and RY\\,Sgr.\nV854\\,Cen is presently the most variable of all Galactic RCBs.\nDespite the combination of favorable apparent magnitude and propensity to\nfade, there is a dearth of high-quality spectroscopic observations of\nthis star in decline. The sole report of a high-resolution optical\nspectrum covering a broad bandpass\nin a deep decline is that by Rao \\& Lambert (1993) taken\nwhen the star had faded by about 8 mag. Low resolution\nspectra are described by Kilkenny \\& Marang (1989) and spectropolarimetric\nobservations are discussed by Whitney et al. (1992). \nSpectra at high-resolution at maximum light were used by Asplund et al (1998)\nfor their abundance analysis that confirmed that V854\\,Cen has a somewhat\nunusual composition among the RCBs for which abundance anomalies are\na {\\it sine qua non}. In particular, V854\\,Cen, although hydrogen-poor\nrelative to normal stars, is the most hydrogen-rich RCB by a clear margin.\nDespite limited temporal coverage, our new spectra of V854\\,Cen in decline\nprovide a novel result - the detection of cold C$_2$ gas. \nOur spectra otherwise closely resemble\nthose of the RCBs extensively studied in decline:\nR\\,CrB (Rao et al. 1999) and RY\\,Sgr (Alexander et al. 1972).\nThis concordance, which suggests that RCBs have a common general\nstructure of their upper atmospheres and circumstellar\nregions, is briefly demonstrated here but we focus \non the novel lines of the C$_2$ molecule.\n\n\\section{Observations}\n\nV854\\,Cen was observed on four occasions \nfrom the W.J. McDonald Observatory with the\n2.7m Harlan J. Smith reflector and the {\\it 2dcoud\\'{e}} spectrograph\n(Tull et al. 1995). Details of the observations\nare given in Table 1. Figure 1 shows the light curve and the epochs of\nour spectra. The first two spectra at\neffectively the same epoch were taken when the\nstar was at V $\\sim$ 10.3 about 55 days after the onset of a decline\nthat saw the star fade to V $\\sim$ 13.6 by 1998 late-May.\nWe reobserved the star on 1998 June 6 at V $\\sim$ 11.7 in its \nrecovery to maximum brightness, and again on\n1999 February 10 when the star had returned to maximum\nbrightness. Observations by amateur observers show that\nthe recovery from the deep decline in mid-1998 to maximum brightness in\nearly 1999 was rapid, unbroken by subsidiary declines, and faster\nthan the fall from maximum to minimum brightness which may have\nbeen interrupted by brief halts.\n\n\n\n\\begin{table}\n\\centering\n\\begin{minipage} {140mm}\n\\caption{Spectroscopic observations of V854\\,Centauri.}\n%\\begin{center}\n\\begin{tabular}{lrrrr} \\hline\nDate & {XJD}\\footnote{XJD = JD - 245000.0}& V & {S/N}\n\\footnote{S/N ratio in continuum near 6560\\AA.} &{Phase}%\n \\footnote{Pulsation phase from Lawson et al.'s (1999) ephemeris\\\\ where zero phase is light maximum.} \\\\ \\hline\n1998 April 8 & 911.887& 10.3& 69& 81.227 \\\\\n1998 April 10 & 913.832& 10.3& 53& 81.272\\\\\n1998 June 6 & 970.679& 11.7& 61& 82.587\\\\\n1999 Feb 10 & 1219.988& 7.3& 149& 88.354\\\\ \\hline\n\\end{tabular}\n\\end{minipage}\n%\\end{center}\n\\end{table}\n\n\\begin{figure}\n\\epsfxsize=8truecm\n\\epsffile{pinkfig1.ps}\n\\caption{The lightcurve for V854\\,Cen from early 1998 to early 1999. Dots refer to\nV magnitudes\n from Lawson et al. (1999), open squares and dashes are visual estimates from\nthe AAVSO. The Julian dates of our observations are\nindicated by arrows.}\n\\end{figure}\n\nThe cross-dispersed echelle spectra are at a resolving power of 60,000 with nominal\ncoverage from 3800\\AA\\ to 10200\\AA. Echelle orders are incompletely\ncaptured on the CCD for wavelengths longward of 5500\\AA. In addition,\nthe star's southerly declination (Dec. = - 39$^{\\circ}$) and the observatory's\n northerly \nlatitude (Lat. = 31$^{\\circ}$) result in\nsevere atmospheric dispersion and loss of signal in the blue such that\nthe spectra are not useable for wavelengths shorter than about 4100\\AA.\n%A Th-Ar hollow cathode lamp provided a wavelength calibration which\n%was checked using telluric absorption and emission lines. Spectra\n%were reduced using the IRAF package.\n\n\\section{V854\\,Centauri in decline}\n\nWell-observed RCBs in decline -- R\\,CrB and RY\\,Sgr -- show common spectral\ncharacteristics that are shared with V854\\,Cen. As a star fades,\nthe first prominent addition to its optical spectrum are two sets of\nsharp emission lines: E1 (Alexander et al. 1972) or `transient'\n(Rao et al. 1999) appear shortly after onset of a decline and\ndisappear after a couple of weeks, and E2 or `permanent' lines\nare prominent for a longer period and may be present in some or all\ndeclines at all times, even at maximum light (Lambert, Rao, \\& Giridhar 1990a).\n A \nmark of E1 lines is that they include high-excitation lines (C\\,{\\sc i},\nO\\,{\\sc i}, and Si\\,{\\sc ii}, for example) not found among E2 lines.\nSingly-ionised metals (e.g., Ti\\,{\\sc ii} and Fe\\,{\\sc ii}) are prominent\ncontributors of E1 and E2 lines.\nThe E1 and E2 lines are sharp (FWHM $\\sim 14$ km s$^{-1}$ in R\\,CrB). In\ndeep declines, a few broad emission lines are seen with FWHM $\\sim 300$\nkm s$^{-1}$ with the Na\\,D being the strongest. \n\nIn our spectra of V\\,854 Cen,\nE1 lines, especially C\\,{\\sc i}\nlines, are present in 1998\nApril: 46 C\\,{\\sc i} lines from 6400\\AA\\ to 8800\\AA\\ give a velocity of\n-16.7 $\\pm$ 2.8 km s$^{-1}$. Emission had gone by 1998 June with the same\nlines appearing\n in absorption at a velocity of -24.0 $\\pm$ 2.4 km s$^{-1}$ which\nis the (out-of-decline) mean velocity of -25 km s$^{-1}$ \nthat is maintained to\nabout 2 km s$^{-1}$ as the star undergoes small semi-regular\nbrightness variations (Lawson \\& Cottrell 1989).\n The velocity of infall of the C\\,{\\sc i}\nemission lines is similar to that seen for\nR\\,CrB (Rao et al. 1999). Lines of higher excitation such as the\nN\\,{\\sc i} lines beyond 8000\\AA\\ also appear affected by emission, i.e.,\nthe N\\,{\\sc I} 8216\\AA\\ line has an equivalent width of 59 m\\AA\\ and a \nFWHM of 0.36\\AA\\ in April but its normal values, as in the 1999 February\nspectrum, are 164 m\\AA\\ and 0.69\\AA, respectively. It seems probable that\n emission has reduced the equivalent width, narrowed the line, and shifted\nthe apparent absorption velocity to the blue with the mean absorption\nvelocity at -34 $\\pm$ 2 km s$^{-1}$ in 1998 April. Some C\\,{\\sc i}\nemission lines show P Cygni profiles with absorption also at -34 km s$^{-1}$.\nEmission from E1 and E2 lines affects almost all photospheric lines\nin 1998 April. With the decay of E1 lines, the photospheric\nvelocity is measureable from the 1998 June spectrum: the result\n-27 $\\pm$ 1 km s$^{-1}$ is consistent with the systemic velocity.\nLines of low and high excitation potential are at the systemic velocity on the\n1999 February spectrum.\n% (-24 $\\pm$ 1 km s$^{-1}$).\n \n\nThe E2 lines on the 1998 April and June spectra\nare slightly blue-shifted with respect to the mean\nphotospheric velocity. The peak velocity which is unchanged between \nApril and June is -30 $\\pm 1$ km s$^{-1}$ corresponding to a\nblue shift of about 5 km s$^{-1}$, a typical value for the E2 lines\nof R\\,CrB and RY\\,Sgr. The degree of excitation appears to be\nsimilar to that of R\\,CrB in its 1995-1996 decline, and the\nline widths are also similar.\nThe line fluxes dropped by about a factor of 30 from 1998 April\nto June, as the V flux dropped by a factor of only 4. This contrasts\nwith the 1995-1996 decline of R\\,CrB when the line fluxes dropped by\nless than the V magnitude.\n\nThe only detectable broad lines are the Na\\,D lines. Other\nbroad lines reported by Rao \\& Lambert (1993) are not present. We \nattribute their absence to the fact that our observations were taken at\nV = 11.7 (and 10.3) but the spectrum on which our earlier report\nwas based was obtained when the star was about 3 magnitudes fainter. \nSimilarly, R\\,CrB's broad lines appeared only in the deepest part of\nits decline.\n\n\nLow-excitation lines of neutral metals are in absorption without discernible\nemission but with their weak absorption red-shifted relative to the\nsystemic velocity: the mean velocity of +15 $\\pm$ 2 km s$^{-1}$ from 7\nlines on the 1998 April spectra implies infall at 40 km s$^{-1}$ relative\nto the photosphere. Similar red-shifted\nlines were seen in R\\,CrB. This red-shifted\nabsorption, which is also clearly seen in the red wing of prominent\nsharp (blue-shifted) emission lines, is unlikely to be the residual\nof the photospheric line (assumed to be at the systemic velocity) because\nthe red-shifted absorption occurs outside the normal photospheric profile and\nmany lines lack accompanying emission. The fact that the red-shifted\nabsorption appears in lines of different excitation potentials indicates \nthat the responsible gas is warm. By 1998 June, the same lines were\nat -13 $\\pm$ 2 km s$^{-1}$ and at the systemic velocity (i.e., photospheric\nin origin) by 1999 February. \n\nThese snapshots of V\\,854 Cen's spectrum suggest its\ndecline from onset to beyond minimum light largely behaved similarly\nto R\\,CrB's 1995-1996 decline.\nThere is one exciting novel feature revealed for V854\\,Cen.\n\n\\section{C$_2$ Swan and Phillips System Lines}\n\n\n Previous detections of C$_2$ in spectra of\nRCBs are\nfor the Swan system which provides photospheric\n absorption lines at maximum light in all but the hottest\nRCBs, and sharp and broad emission lines in decline spectra (Rao \\&\nLambert 1993; Rao et al. 1999). Swan photospheric and E2 lines are seen here. \nThe novel feature is the detection of low excitation (non-photospheric)\n Phillips lines in absorption.\n\nThe Phillips system's lower state is the\n C$_2$ molecule's ground state (X\\,$^1\\Sigma^+_g$, Ballik \\& Ramsay 1963;\nHuber \\& Herzberg 1979) and its upper \nstate (A\\,$^1\\Pi_u$) has the excitation energy T$_{\\rm e}$ = 8391 cm$^{-1}$.\nThe Swan system's lower level is the lowest and very\nlow-lying {\\it triplet} state \n(a\\,$^3\\Pi_u$) with T$_{\\rm e}$ = 716 cm$^{-1}$ and the upper state \n(d\\,$^3\\Pi_g$) is at T$_{\\rm e}$ = 20022 cm$^{-1}$. Other low-lying \nstates exist but no other\nband systems from the ground or low-lying states provide lines in our\nbandpass. Radiative transitions between singlet and triplet states\noccur with a low transition probability relative to the Phillips\nsinglet-singlet and Swan triplet-triplet transitions. \n\nResolved rotational structure in the Swan system 0-0 band is shown in Figure 2.\n The velocity,\nas measured from clean 0-0 lines is -27 km s$^{-1}$ which is that of the\nE2 sharp emission atomic lines. The line width, which is slightly greater than\nthe instrumental resolution, is\nalso equal to that of E2 atomic lines. The rotational temperature \nestimated following Lambert et al. (1990b) is T$_{\\rm rot} = 4625 \\pm $ 300K \n(see Figure 3).\nMany bands from the $\\Delta v$ = 0, $\\pm$1, and +2 sequences are present.\n Semi-quantitative comparisons of the band profiles\nin the $\\Delta v$ = +1 sequence with predicted profiles (Lambert \\& Danks\n1983) indicate a vibrational temperature near 5000K and, hence,\nlikely equal to the rotational temperature. Rao \\& Lambert (1993 - see\nalso Rao et al. 1999 for R\\,CrB) in a deeper decline found the Swan lines\nto be broad but in our spectra any broad component must be very weak.\n\n\\begin{figure}\n\\epsfxsize=8truecm\n\\epsffile{pinkfig2.ps}\n\\caption{The C$_2$ Swan 0-0 P branch bandhead on 1998 April 8. A few lines and\nblends of are identified.}\n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize=8truecm\n\\epsffile{pinkfig3.ps}\n\\caption{A standard Boltzmann plot compiled from Swan 0-0 lines and blends\n(see key on figure). The solid line is a least-squares fitted line corresponding\nto a rotational temperature of 4625K.}\n\\end{figure}\n\n\nWeak absorption lines identified as Phillips system lines are present\non the 1998 April spectra but absent from the 1998 June spectrum. Figure 4 \nshows a portion of the 2-0 band and includes a spectrum of the post-AGB \nstar IRAS 22223+4327 in which circumstellar C$_2$ lines\nare strong. Many lines from the 2-0 and 3-0 bands were detected in\nV854\\,Cen with equivalent widths of up to 50 m\\AA.\n A search for 3-1 and 4-1 lines was unsuccessful; this is not\nsurprising given the low excitation temperature found from the detected\nlines. No search was made for either 1-0 or 4-0 lines. Rest wavelengths\nfrom Bakker et al. (1997) give the radial velocity of \n-30.4 $\\pm$ 1.3 km s$^{-1}$ from 15 lines,\n i.e., a small expansion velocity relative to the\nsystemic velocity of -25 km s$^{-1}$. The velocity\ndiffers considerably from that (+15 km s$^{-1}$)\n of the red-shifted absorption component\nof low-excitation atomic lines.\n In contrast to photospheric lines,\nthe C$_2$ absorption lines are not resolved. \nBoltzmann plots for 2-0 and 3-0 lines give a mean rotational temperature \nof T$_{\\rm rot} = 1150 \\pm$ 70K from levels J$^{\\prime\\prime}$ =\n4 to 28. We interpret this as a close approximation to the\ngas kinetic temperature. If, as occurs in interstellar diffuse clouds,\nthe C$_2$ molecule's excitation is greatly influenced by\nradiative pumping in the Phillips bands (and X\\,$^1\\Sigma^+_g$\n $\\rightleftharpoons$ a\\,$^3\\Pi_u$ radiative transitions), the\nBoltzmann plot is expected to be curved with lowest rotational levels\ngiving a temperature close to the kinetic temperature and higher levels\na higher temperature dependent on the ratio of the gas density and\nthe photon flux in the near-infrared, for example, the ground state\npopulations for $\\zeta$\\,Oph's diffuse clouds give T$_{\\rm rot} \\simeq\n40$K from the lowest levels and 785K from levels J$^{\\prime\\prime}\n\\simeq 20$ (Lambert, Sheffer \\& Federman 1995). A linear Boltzmann\nplot, as here, suggests that the observed levels may be in\nequilibrium with the gas, i.e., our C$_2$ molecules are in \ngas at a temperature below that at which carbon dust grains form,\nand the molecules may well be mixed in with the fresh dust. \nThe molecular column density is about 2 $\\times 10^{15}$ cm$^{-2}$.\n\n \n\n\\begin{figure}\n\\epsfxsize=8truecm\n\\epsffile{pinkfig4.ps}\n\\caption{Spectra from 8770-8826\\AA\\ of V854\\,Cen and IRAS2223+4327.\nLocations of C$_2$ Phillips 2-0 lines are indicated at the top of the\nfigure and below the 1998 April 10 spectrum of V854\\,Cen. The Phillips\nlines are strongly present in IRAS22223+4327 and the 1998 April spectra\nof V854\\,Cen but not in the 1998 June 6 spectrum. Two R\\,CrB spectra\nare shown superimposed: the spectrum from 1995 September 30 (dash-dot\nline) was taken at\nmaximum light just prior to the 1995 decline;\n the spectrum from 1995 October 13 (solid line) was taken when the star was about 3 magnitudes below maximum bightness, i.e., the star had faded by about the\nsame amount as V854\\,Cen had on 1998 April 10.}\n\\end{figure}\n\n\\begin{figure}\n\\epsfxsize=8truecm\n\\epsffile{pinkfig5.ps}\n\\caption{Standard Boltzmann plots for the C$_2$ Phillips absorption\nlines. Stars, dots and crosses refer to P, Q and R branch lines, \nrespectively. The line is the least-squares fitted\nline corresponding to the rotational temperature indicated on the\nfigure.}\n\\end{figure}\n\nFive questions arise directly from these observations of C$_2$ lines:\nWhy is an absorption component not seen in the C$_2$ Swan lines? Why is\nan emission component not seen in the C$_2$ Phillips lines? How are the\nSwan emission lines excited? Where is the emitting gas? Where is the\ncold absorbing gas?\n\n\nThe apparent absence of Swan absorption lines is easily explained. In the\nweak-line limit, the equivalent width \n$W_{\\lambda} \\propto f\\lambda^2NL$ where $f$ and $\\lambda$ are\n the line's oscillator strength and wavelength respectively and $NL$ is the\ncolumn density of molecules in the lower level of the transition. If the\ncolumn densities in the lowest singlet and triplet states are equal, the\nSwan system lines are favored by a factor of about 7 with the system's\ngreater $f$-value being a major factor (Grevesse et al. 1991; Bakker \\&\nLambert 1998) but considering that the Phillips absorption lines\nare at almost the same velocity as the Swan emission lines (-30 km s$^{-1}$\nversus -27 km s$^{-1}$), we suppose that the Swan absorption\nlines are masked by the strong emission lines. A large\nincrease in the column density of the lowest triplet state relative to\nthe ground triplet state would be required to provide detectable\nabsorption. \n\nA plausible explanation may be offered for the absence of Phillips\nemission lines. An approximate flux calibration of our spectrum gives\nthe detection limit for a sharp Phillips system line at about 0.2 that\nof a single sharp Swan line.\nThe predicted relative fluxes in Swan and Phillips\nlines depends on the assumed mode of excitation. If the molecule is \nin thermal equilibrium at the measured T$_{\\rm rot}$ = 4625K,\nit is readily shown that the flux in a Phillips 2-0 line is about 15\\%\nthat of the Swan 0-0 of a similar J-value in the event that\nreddening may be neglected, i.e., the line would not\nappear in emission in our spectrum. The great difference in the $f$-values of\nthe 0-0 Swan band and the 2-0 Phillips band is a major contributor to the\nlow flux of the Phillips lines. In the case of resonance\nfluorescence, as occurs for comets, the Phillips line is similarly\nweak unless the population in the X\\,$^1\\Sigma^+_g$ state is very\nmuch greater than in a\\,$^3\\Pi_u$ state. At low particle densities,\nas in the interstellar medium, the latter state is not populated;\nelectric-quadrupole transitions drain population to the lowest \nlevels of the X state. This situation is, however, unlikely to\nprevail in V854\\,Cen. For R\\,CrB, which may be taken as similar to\nV854\\,Cen, the sharp emission lines come from a region of high\nparticle density (Rao et al. 1999) such that the a to X populations\nmust be close to their equilibrium value, i.e., sharp Phillips emission lines\nare almost certainly below our detection limit. \n\nRao et al. (1999) assembled a wealth of data on the E2 lines including\nC$_2$ Swan system lines seen\nthroughout R\\,CrB's 1995-1996 decline to determine that the emitting gas\nwas warm and dense. The location of the gas relative to the star and the\nobscuring dust cloud could not be definitively established.\n Similarities between the atomic E2 lines of the two stars strongly suggest that\n V854\\,Cen's\nE2 Swan lines originate in the region providing its atomic E2 lines, and\nthat this region resembles that around R\\,CrB. Differences in physical\ncondition and chemical composition may account for the fact that\nthe Swan lines are more strongly in emission from V854\\,Cen. \n \nOur temporal coverage of V854\\,Cen's decline is limited but encourages\nthe speculations that (i) the narrow C$_2$ absorption lines appear\nonly in decline, and (ii) the appearance of the E1 (transient) atomic\n lines and the\nC$_2$ absorption lines may be related. The C$2$ Swan lines appear as\nweak photospheric absorption lines at maximum light. Their Phillips\nsystem counterparts are too weak to detect. The 1100K absorption\nlines are absent from our 1999 February spectrum. \n The E1 lines and\nPhillips absorption are both present in 1998 April but are\nseen neither in 1998 June when the star was fainter and\n E2 lines remained prominent.\n This suggests that the 1100K absorption\nis not merely related to the dust but more to the early\nstages of the decline. A possible connection is the\npresence of a shock, as considered by Woitke, Goeres \\& Sedlmayr\n(1996) and Woitke (1997) to be the trigger for a RCB decline. In their\nscenario, E1 lines originate in the hot gas immediately\nbehind the shock and dust forms in cool dense gas further behind the outwardly\nmoving shock front. Here, as for R\\,CrB, the shock may propagate through\nthe infalling gas betrayed by the red-shifted absorption lines of low\nexcitation atomic lines. \n\n In light of the detection of the Phillips absorption lines,\n we have reexamined spectra\n of R\\,CrB obtained in its 1995-1996 decline (Rao et al.\n1999). R\\,CrB appears not to have shown these absorption lines in\nits decline (Figure 4) but did show the E1 high-excitation lines.\nThis difference between V854\\,Cen and R\\,CrB may reflect\ndifferences in physical conditions\nin the upper atmospheres or in chemical compositions. Such differences\nmay also account for the far greater propensity of V854\\,Cen to\ngo into decline.\nThe high hydrogen to carbon ratio of V854\\,Cen \nhas led Goeres (1996) to predict that formation of carbon-containing molecules\nand dust grains is controlled by acetylene (C$_2$H$_2$) rather than the\n C$_3$ molecules that act as the throttle for `normal' RCBs.\n\n\n\\section{Concluding Remarks}\n\nFor the first time, cold gas below the temperature required for\nsoot formation has been detected around a RCB in its decline to\na deep minimum. Our detection of absorption by cold C$_2$ molecules\naround V854\\,Cen now needs to be followed by synoptic observations\nof this active RCB variable in order to trace the evolution of the\n cold gas and to place it relative to the star. Is the gas located behind\na shock where, as some theories would suppose, dust formation is\ntriggered? Or is it merely an innocent companion to the dust? We\nrecognise that providing synoptic observations at an adequate\nspectral resolution and high temporal frequency is a \nsubstantial challenge. If the challenge can be met, the result\nwill be a window into the time and place of dust formation, and,\nperhaps, provie the long-sought understanding of how\n the characteristic declines of RCBs\nare initiated.\n\n\n\\section{Acknowledgements}\nWe would like to thank Jocelyn Tomkin and Gulliermo Gonzalez for obtaining\nthe spectra of V854\\,Cen in decline, and Gajendra Pandey for\nconsiderable help in the reduction and presentation of the\nspectra.\nThis research has been supported in part by the US National Science\nFoundation (grant AST 9618414.\n\n\n\n\n\\begin{thebibliography}{99}\n\\bibitem{b1} Alexander J.B., Andrews P.J., Catchpole R.M., Feast M.W.,\n Lloyd Evans T., Menzies J.W., Wisse P.N.J., Wisse P., 1972,\n MNRAS, 158, 305\n\\bibitem {} Asplund, M., Gustafsson, B., Rao, N.K., Lambert, D.L.,\n 1998, A\\&A, 332, 651\n\\bibitem {} Bakker, E.J., Lambert, D.L., 1998, ApJ, 508, 387\n\\bibitem {} Bakker, E.J., van Dishoeck, E.F., Waters. L.B.F.M., Schoenmaker, T.\n 1997, A\\&A, 323, 469\n\\bibitem {} Ballik, E.A., Ramsay, D.A. 1963, ApJ, 137, 84\n%\\bibitem{} Clayton G.C., 1996, PASP, 108, 225\n\\bibitem {} Goeres, A., 1996, in Jeffery, C.S., Heber, U., eds., \n Hydrogen-deficient Stars, ASP Conf. Ser., 96, 69\n\\bibitem {} Grevesse, N., Lambert, D.L., Sauval, A.J., van Dishoeck, E.F.,\n Farmer, C.B., Norton, R.H., 1991, A\\&A, 242, 488\n\\bibitem {} Huber, K.P., Herzberg, G. 1979, Molecular Spectra and \n Molecular Structure, IV. Constants of Diatomic Molecules, Van Nostrand\n Reinhold Company, New York\n\\bibitem {} Kilkenny, D., Marang, F., 1989, MNRAS, 238, 1p\n\\bibitem {} Lambert, D.L., Danks, A.C., 1983, ApJ, 268, 428\n\\bibitem {} Lambert D.L., Rao N.K., Giridhar S., 1990a, JAA, 11, 475\n\\bibitem {} Lambert, D.L., Sheffer, Y., Danks, A.C., Arpigny, C.,\n Magain, P., 1990b, ApJ., 353, 640\n\\bibitem {} Lambert, D.L., Sheffer, Y., Federman, S.R., 1995, ApJ, 438, 740\n\\bibitem {} Lawson W.A., Cottrell P.L., 1989, MNRAS, 240, 689 \n\\bibitem {} Lawson, W.A., Maldoni, M.M., Clayton, G.C., Valencic, L.,\n Jones, A.F., Kilkenny, D., van Wijk, F., Roberts, G., Marang, F., 1999,\n AJ, 117, 3007\n\\bibitem {} Rao N.K., Lambert D.L., 1993, AJ, 105, 1915\n\\bibitem {} Rao, N.K., Lambert, D.L., Adams, M.T., Doss, D.R., Gonzalez, G.,\n Hatzes, A.P., James, C.R., Johns-Krull, C.M., Luck, R.E., Pandey, G.,\n Reinsch, K., Tomkin, J., Woolf, V.M., 1999, MNRAS, in press\n\\bibitem {} Tull R.G., MacQueen P.J., Sneden C., Lambert D.L.,\n 1995, PASP, 107, 251\n\\bibitem {} Whitney B.A., Clayton G.C., Schulte-Ladbeck R.E.,\n Meade M.R., 1992, AJ, 103, 1652\n\\bibitem {} Woitke P., 1997, Thesis, Tech. Univ. Berlin\n\\bibitem {} Woitke P., Goeres A., Sedlmayr E., 1996, A\\&A, 313, 217\n\\end{thebibliography}\n\n\\label{lastpage}\n\n\\end{document}"
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[
{
"name": "astro-ph0002237.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{b1} Alexander J.B., Andrews P.J., Catchpole R.M., Feast M.W.,\n Lloyd Evans T., Menzies J.W., Wisse P.N.J., Wisse P., 1972,\n MNRAS, 158, 305\n\\bibitem {} Asplund, M., Gustafsson, B., Rao, N.K., Lambert, D.L.,\n 1998, A\\&A, 332, 651\n\\bibitem {} Bakker, E.J., Lambert, D.L., 1998, ApJ, 508, 387\n\\bibitem {} Bakker, E.J., van Dishoeck, E.F., Waters. L.B.F.M., Schoenmaker, T.\n 1997, A\\&A, 323, 469\n\\bibitem {} Ballik, E.A., Ramsay, D.A. 1963, ApJ, 137, 84\n%\\bibitem{} Clayton G.C., 1996, PASP, 108, 225\n\\bibitem {} Goeres, A., 1996, in Jeffery, C.S., Heber, U., eds., \n Hydrogen-deficient Stars, ASP Conf. Ser., 96, 69\n\\bibitem {} Grevesse, N., Lambert, D.L., Sauval, A.J., van Dishoeck, E.F.,\n Farmer, C.B., Norton, R.H., 1991, A\\&A, 242, 488\n\\bibitem {} Huber, K.P., Herzberg, G. 1979, Molecular Spectra and \n Molecular Structure, IV. Constants of Diatomic Molecules, Van Nostrand\n Reinhold Company, New York\n\\bibitem {} Kilkenny, D., Marang, F., 1989, MNRAS, 238, 1p\n\\bibitem {} Lambert, D.L., Danks, A.C., 1983, ApJ, 268, 428\n\\bibitem {} Lambert D.L., Rao N.K., Giridhar S., 1990a, JAA, 11, 475\n\\bibitem {} Lambert, D.L., Sheffer, Y., Danks, A.C., Arpigny, C.,\n Magain, P., 1990b, ApJ., 353, 640\n\\bibitem {} Lambert, D.L., Sheffer, Y., Federman, S.R., 1995, ApJ, 438, 740\n\\bibitem {} Lawson W.A., Cottrell P.L., 1989, MNRAS, 240, 689 \n\\bibitem {} Lawson, W.A., Maldoni, M.M., Clayton, G.C., Valencic, L.,\n Jones, A.F., Kilkenny, D., van Wijk, F., Roberts, G., Marang, F., 1999,\n AJ, 117, 3007\n\\bibitem {} Rao N.K., Lambert D.L., 1993, AJ, 105, 1915\n\\bibitem {} Rao, N.K., Lambert, D.L., Adams, M.T., Doss, D.R., Gonzalez, G.,\n Hatzes, A.P., James, C.R., Johns-Krull, C.M., Luck, R.E., Pandey, G.,\n Reinsch, K., Tomkin, J., Woolf, V.M., 1999, MNRAS, in press\n\\bibitem {} Tull R.G., MacQueen P.J., Sneden C., Lambert D.L.,\n 1995, PASP, 107, 251\n\\bibitem {} Whitney B.A., Clayton G.C., Schulte-Ladbeck R.E.,\n Meade M.R., 1992, AJ, 103, 1652\n\\bibitem {} Woitke P., 1997, Thesis, Tech. Univ. Berlin\n\\bibitem {} Woitke P., Goeres A., Sedlmayr E., 1996, A\\&A, 313, 217\n\\end{thebibliography}"
}
] |
astro-ph0002238
|
Large-Scale Sunyaev-Zel'dovich Effect: Measuring Statistical Properties with Multifrequency Maps
|
[
{
"author": "Asantha Cooray$^1$"
},
{
"author": "Wayne Hu$^2$"
},
{
"author": "and Max Tegmark$^3$"
}
] |
We study the prospects for extracting detailed statistical properties of the Sunyaev-Zel'dovich (SZ) effect associated with large scale structure using upcoming multifrequency CMB experiments. The greatest obstacle to detecting the large-angle signal is the confusion noise provided by the primary anisotropies themselves, and to a lesser degree galactic and extragalactic foregrounds. We employ multifrequency subtraction techniques and the latest foregrounds models to determine the detection threshold for the Boomerang, MAP (several $\mu$K) and Planck CMB (sub $\mu$K) experiments. Calibrating a simplified biased-tracer model of the gas pressure off recent hydrodynamic simulations, we estimate the SZ power spectrum, skewness and bispectrum through analytic scalings and N-body simulations of the dark matter. We show that the Planck satellite should be able to measure the SZ effect with sufficient precision to determine its power spectrum and higher order correlations, e.g. the skewness and bispectrum. Planck should also be able to detect the cross correlation between the SZ and gravitational lensing effect in the CMB. Detection of these effects will help determine the properties of the as yet undetected gas, including the manner in which the gas pressure traces the dark matter.
|
[
{
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We employ multifrequency\nsubtraction techniques and the latest foregrounds models to determine\nthe detection threshold for the Boomerang, MAP (several $\\mu$K) \nand Planck CMB (sub $\\mu$K) experiments.\nCalibrating a simplified biased-tracer model of the gas pressure \noff recent hydrodynamic simulations, we estimate the SZ power spectrum,\nskewness and bispectrum through analytic scalings and N-body\nsimulations of the dark matter. We show that the Planck satellite should\nbe able to measure the SZ effect with sufficient precision to determine\nits power spectrum and higher order correlations, e.g. the skewness\nand bispectrum. Planck should also be able to detect the\ncross correlation between the SZ and gravitational lensing effect\nin the CMB. Detection of these effects will help determine the properties \nof the as yet undetected gas, including the manner in which the gas pressure\ntraces the dark matter.\n\\end{abstract}\n\n%------------------------------------------------------------------------------\n% User-supplied List of keywords.\n\n\\keywords{cosmic microwave background --- cosmology: theory --- large\nscale structure of universe}\n]\n%------------------------------------------------------------------------------\n\\section{Introduction}\n\nIt is by now well established that the precision measurements of the cosmic\nmicrowave background expected from upcoming experiments, especially \nMAP and Planck satellite missions, will provide a gold mine of information \nabout the early universe and the fundamental cosmological parameters\n(e.g., \\cite{Junetal96} 1996). \nThese experiments can in fact do so much more. With all-sky maps across\nthe wide range of uncharted frequencies from $20$GHz-$900$GHz, the secondary science\nfrom these missions will arguably be as interesting as the primary science.\n\nIn this paper, we examine the prospects for extracting the large-scale\nproperties of the hot intergalactic gas from multifrequency observations of the CMB. \nInverse-Compton scattering of CMB photons by hot gas, known as\nthe Sunyaev-Zel'dovich (SZ; \\cite{SunZel80} 1980) \neffect, leaves a characteristic distortion\nin the spectrum of the CMB, which fluctuates in the sky with the gas\ndensity and temperature. \nIn the Rayleigh-Jeans (RJ) regime, it produces\na constant decrement and with only low frequency measurements, the\nmuch larger primary anisotropies in the CMB itself obscure the\nfluctuations on scales greater than a few arcminutes (e.g., \n\\cite{GolSpe99} 1999). \nThe upscattering in frequency implies an increment at high frequencies\nand a null around $217$GHz. This behavior provides a potential tool for the separation\nof\nSZ effect from other temperature anisotropy contributors.\n\n\nSince both the SZ spectrum and the CMB spectrum are accurately known,\none can expect that foreground removal techniques developed to isolate\nthe primary anisotropies can be reversed to recover the SZ signal in the presence \nof noise from the primary anisotropies. Galactic and extragalactic\nforegrounds will be more challenging to remove. Here we use the latest\nforeground models from \\cite{Tegetal99} (1999) that takes into account the fact\nthat imperfect correlations in the foregrounds between frequency\nchannels inhibits our \nability to remove them. Using foreground information together with the\nexpected noise properties of individual experiments,\none can determine the minimal detectable\nsignal in each experiment and the upper limit\nachievable in the absence of\ndetection. Experiments with sufficient signal-to-noise can \nextract precision measurements for the power spectrum \nand higher order statistics such as the skewness. Ultimately, they can\nprovide detailed maps of the large-angle SZ effect. \n\n\nTo assess the prospects for an actual detection, we must model the\nSZ signal itself. \nThe SZ effect is now routinely imaged\nin massive galaxy clusters (e.g., \\cite{Caretal96} 1996; \\cite{Jonetal93} 1993),\nwhere the temperature of the scattering medium can reach as high as\n10 keV, producing temperature changes in the CMB of order 1 mK at\nRJ wavelengths. The possibility for detection of massive clusters in\nCMB satellite data has already been discussed in several studies\n(e.g., \\cite{Aghetal96}, \\cite{HaeTeg96} 1996, \\cite{Poietal98} 1998).\nHere, however, we are interested in the SZ effect produced by\nlarge-scale structure in the general intergalactic medium (IGM) where \nthe gas is expected to be at $\\lesssim 1$keV in mild overdensities, \nleading to CMB contributions in the $\\mu$K range. \n\nIt is now widely believed that at least $\\sim$ 50\\% of the\npresent day baryons, when compared to the total baryon budget from\nbig bang nucleosynthesis, are present in gas associated with hot large-scale\nstructure which has remained undetected given its\ntemperature and clustering properties\n(e.g., \\cite{Fuketal98} 1998; \\cite{CenOst99} 1999; \\cite{Pen99} 1999). \nRecently, \\cite{Schetal00} (2000) has provided a tentative detection of\nX-ray emission from a large-scale filament in one of the deep\nROSAT PSPC fields; previous attempts \nyielding upper limits are described in\n\\cite{KulBoh99} (1999) and \\cite{BriHen95} (1995). \nThese results are consistent with current predictions for the X-ray\nsurface brightness based on numerical simulations (e.g.,\n\\cite{Cenetal95} 1995). \n\\cite{Pen99} (1999) argued that non-gravitational heating of the\ngas to $\\sim 1$keV is required to evade bounds from the soft X-ray background.\nThese results suggest that the X-ray emission from this gas \nmay be detectable in the near future with \nwide-field observations with Chandra X-ray\nObservatory\\footnote{http://asc.harvard.edu} and X-ray Multiple Mirror\nMission\\footnote{http://astro.estec.esa.nl/XMM}.\n\nOn the theoretical front, hydrodynamic simulations\nof the SZ effect continue to improve \n(\\cite{daS99} 1999; \\cite{Refetal99} 1999; \\cite{Seletal00} 2000). As a consensus from these simulations of basic\nproperties such as the opacity weighted gas temperature and average\nCompton distortion is still lacking, we will base our assessment \nof the detectability of the\nlarge-scale SZ effect on a simple parameterization of the\neffect, based on a gas pressure bias model\n(\\cite{Refetal99} 1999), \ncrudely calibrated with the recent hydrodynamic simulations.\nWe employ perturbation theory, non-linear scaling relations, and N-body simulations for the dark matter to assess the statistical properties of the\nsignal.\nProperly calibrated, these techniques can complement hydrodynamic \nsimulations by extending their dynamic range and sampling volume. \nCurrently, they should simply be \ntaken as order of magnitude estimates of the potential signal.\n\nThroughout this paper, we will take an adiabatic cold dark matter (CDM)\nmodel as our fiducial cosmology. We assume cosmological\nparameters $\\Omega_c=0.30$ for the cold dark matter density, \n$\\Omega_b=0.05$ for the baryon density, $\\Omega_\\Lambda=0.65$ for the\ncosmological constant, $h=0.65$ for the dimensionless Hubble \nconstant and a COBE-normalized scale invariant spectrum of\nprimordial fluctuations (\\cite{BunWhi97} 1997). \n\nThe layout of the paper is as follows.\nIn \\S~\\ref{sec:cleaning}, we describe the foreground and primary anisotropy \nremoval method and assess their efficacy for upcoming CMB experiments. \nIn \\S~\\ref{sec:sz}, we detail the bias model for the SZ effect\nand calculate through perturbation theory, analytic approximations and\nnumerical simulations, \nthe low order statistics of the SZ effect: its power spectrum, skewness \nand bispectrum.\nIn \\S~\\ref{sec:sn}, having estimated the noise and the signal, we \nassess the prospects for measuring these low order statistics in \nupcoming experiments. \nWe conclude in \\S~\\ref{sec:discussion} with a discussion of\nour results.\n\n\n\\begin{figure*}\n\\centerline{\\psfig{file=figure1.eps,width=6.5in,angle=0}}\n\\caption{Top: foreground contributions to temperature anisotropies \n$(\\Delta T/T)^2 = l(l+1)C_l/2\\pi$ from the various foregrounds\n(dust, free-free, synchrotron, radio and infrared point sources,\nand rotating dust) at three fiducial frequencies as labeled.\nThe SZ signal (solid, unlabeled) is estimated with the simplified model of \\S~3.\nBottom: residual foregrounds after multifrequency subtraction for\nBoomerang, MAP and Planck. The total includes detector noise and residual CMB.\n}\n\\label{fig:clean}\n\\end{figure*}\n \n\\section{Modeling the CMB and Foreground Noise}\n\\label{sec:cleaning}\n\nThe main obstacle for the detection of the SZ effect from large-scale\nstructure for angular scales above a few arcminutes is the CMB itself.\nHere the primary anisotropies dominate the SZ effect for frequencies\nnear\nand below the peak in the CMB spectrum (see Fig.~\\ref{fig:clean}). \nFortunately, the known\nfrequency dependence and statistical properties of primary\nanisotropies allows \nfor extremely\neffective subtraction of their contribution (e.g., \n\\cite{Hobetal98} 1998; \\cite{BouGis99} 1999). \nIn particular, primary anisotropies obey Gaussian\nstatistics\nand follow the blackbody spectrum precisely.\n \nPerhaps more worrying are the galactic and extragalactic foregrounds,\nsome of which are expected to to be at least comparable to the SZ\nsignal in\neach frequency band. These foregrounds typically have spatial and/or\ntemporal\nvariations in their frequency dependence leading to imperfect\ncorrelations \nbetween\ntheir contributions in different frequency bands. We attempt here to\nprovide\nas realistic an estimate as possible of the prospects for CMB and\nforeground\nremoval, given our incomplete understanding of\nthe foregrounds. \n\n \n\\begin{table}[tb]\\footnotesize\n\\caption{\\label{tab:specs}}\n\\begin{center}\n{\\sc CMB Experimental Specifications}\n\\begin{tabular}{rcccc}\n\\tableskip\\hline\\hline\\tableskip\nExperiment & $\\nu$ & FWHM & $10^6 \\Delta T/T$ & \\\\\n\\tableskip\\hline\\tableskip\nBoomerang\n& 90 & 20 & 7.4 \\\\\n& 150 & 12 & 5.7 \\\\\n& 240 & 12 & 10 \\\\\n& 400 & 12 & 80 \\\\\n\\tableskip\\hline\\tableskip\nMAP\n& 22 & 56 & 4.1 \\\\\n& 30 & 41 & 5.7 \\\\\n& 40 & 28 & 8.2 \\\\\n& 60 & 21 & 11.0 \\\\\n& 90 & 13 & 18.3 \\\\\n\\tableskip\\hline\\tableskip\nPlanck\n& 30 & 33 & 1.6 \\\\\n& 44 & 23 & 2.4 \\\\\n& 70 & 14 & 3.6 \\\\\n& 100 & 10 & 4.3 \\\\\n& 100 & 10.7 & 1.7 \\\\\n& 143 & 8.0 & 2.0 \\\\\n& 217 & 5.5 & 4.3 \\\\\n& 353 & 5.0 & 14.4 \\\\\n& 545 & 5.0 & 147 \\\\\n& 857 & 5.0 & 6670 \\\\\n\\tableskip\\hline\n\\end{tabular}\n\\end{center}\nNOTES.---%\nSpecifications used for \nBoomerang, MAP and Planck.\nFull width at half maxima (FWHM) of the beams are in arcminutes and\nshould be converted to radians for the noise formula. \nBoomerang covers a fraction $\\sim$ 2.6\\% of the sky, while we assume\na usable fraction of 65\\% for MAP and Planck. In \\S~\\ref{sec:sn}, in\norder to calculate the maximum signal-to-noise, we define a {\\it perfect}\nexperiment as one with no instrumental noise and full sky coverage.\n\\end{table}\n\n\\subsection{Foreground Model and Removal}\n\\label{sec:foregmodel}\n\nWe use the ``MID'' foreground model of \n\\cite{Tegetal99} (1999) and adapt the subtraction techniques found\nthere for the purpose of extracting the SZ signal. \nThe assumed level of the foreground signal in the power spectrum\nfor three fiducial frequencies is shown in Fig.~\\ref{fig:clean}.\n\nThe foreground model is defined in terms of the covariance between\nthe multipole moments at different frequency \nbands\\footnote{A potential caveat for this type of modeling is that it \nassumes the foregrounds are statistically\nisotropic whereas we know that the presence of the Galaxy violates\nthis assumption at least for the low order multipoles. We assume that\n$1-f_\\sky \\sim 0.35$ of the sky is lost to this assumption even with\nan all-sky experiment. }\n\\begin{equation}\n\\left< a_{l' m'}^{\\fore *}(\\nu') a_{l m}^{\\fore} (\\nu) \\right> = \nC_l^{\\fore}(\\nu',\\nu)\n \\delta_{l l'} \\delta_{m m'}\\,,\n\\end{equation}\nin thermodynamic temperature units as set by the CMB blackbody. \nIn this section, we will speak of the primary\nanisotropies and detector noise simply as other foregrounds with very\nspecial \nproperties:\n\\begin{eqnarray}\nC_l^{\\rm CMB}(\\nu',\\nu)&=& C_l\\,, \\nonumber\\\\\nC_l^{\\rm noise}(\\nu',\\nu)&=& 8\\ln 2 \\theta(\\nu)^2 e^{\\theta^2(\\nu) l(l+1)}\n\t\\left({\\Delta T\\over T}\\right)^2\\Big|_{\\rm noise}\n\\delta_{\\nu,\\nu'}\\,. \\nonumber \\\\\n\\label{eqn:clnoise}\n\\end{eqnarray}\nThe FWHM$=\\sqrt{8\\ln 2} \\theta$ and noise specifications \nof the Boomerang, MAP and Planck frequency channels \nare given in Tab.~1. True foregrounds generally fall in \nbetween these extremes of perfect and no frequency correlation.\n\n \nThe difference between extracting the SZ signal and the primary signal\nis \nsimply\nthat one performs the subtraction referenced to the\nSZ frequency dependence\n\\begin{equation}\ns(\\nu) = 2 - {x \\over 2}\\coth {x \\over 2}\\,,\n\\end{equation}\nwhere $x = h\\nu/kT_{\\rm cmb} \\approx \\nu/56.8$GHz. Note that\nin the RJ limit \n$s(\\nu) \\rightarrow 1$ such that\n\\begin{equation}\nC_l^{\\rm SZ}(\\nu,\\nu') = s(\\nu)s(\\nu') C_l^{\\rm SZ}\n\\end{equation}\nwhere $C_l^{\\rm SZ}$ is the SZ power spectrum in the RJ\nlimit.\n \nConsider an arbitrary linear combination of the channels,\n\\begin{equation}\nb = \\sum_{\\nu_{i}} {1 \\over s(\\nu_i)} w(\\nu_i) a(\\nu_i)\\,.\n\\end{equation}\nSince the subtraction is done multipole by multipole, we have\ntemporarily\nsuppressed the multipole index.\nThe covariance of this quantity is\n\\begin{equation}\n\\left< b^2 \\right> = C^{\\sz}[\\sum_{\\nu_i} w(\\nu_i)]^2\n + \\sum_{\\nu_i,\\nu_j} w(\\nu_i) w(\\nu_j)\n \\sum_{\\fore} {C^\\fore(\\nu_i,\\nu_j) \\over\ns(\\nu_i)s(\\nu_j)} \n\\,.\n\\end{equation}\nMinimizing the variance contributed by the foregrounds subject to the\nconstraint that the SZ estimation be unbiased, we obtain\n\\begin{equation}\n\\sum_{\\nu_i} w(\\nu_j) \\sum_{\\fore} {C^\\fore(\\nu_i,\\nu_j) \\over \ns(\\nu_i)s(\\nu_j)} =\n{\\rm const.}\\,\n\\end{equation}\nDefining the scaled foreground covariance matrix as\n\\begin{eqnarray}\n\\tilde C(\\nu_i,\\nu_j) &=&\n\\sum_{\\fore} {C^\\fore(\\nu_i,\\nu_j) \\over s(\\nu_i)s(\\nu_j)}, \n\\nonumber\\\\\n&\\equiv& \\sum_{\\fore} \\tilde C^\\fore(\\nu_i,\\nu_j) \\,,\n\\end{eqnarray}\nwe solve for the weights that minimize the noise variance\n\\begin{equation}\n{\\bf w} \\propto {\\tilde {\\bf C}^{-1} {\\bf e}} \\, ,\n\\label{eqn:weights}\n\\end{equation}\nwhere ${\\bf e}$ is the vector of all ones $e(\\nu_i)=1$. Finally we\nnormalize the sum of the weights to unity $\\sum w(\\nu_i)=1$ to obtain\nan unbiased estimator.\nOur approach is same as minimizing the foreground variance subject to\nthe constraint that the recovered multipole is an unbiased estimate of\nthe true SZ signal. As each channel is rescaled such that SZ signal\ncorresponds to the RJ level, the weights sum to unity.\n\nThe total residual noise variance in the map from the foregrounds per\nmultipole \nis then\n\\begin{equation}\nN_l = {\\bf w}_l^t {\\tilde {\\bf C}_l} {\\bf w}_l\\,,\n\\label{eqn:nl}\n\\end{equation}\nand from each foreground component\n\\begin{equation}\nN_l^\\fore = {\\bf w}_l^t {\\tilde {\\bf C}_l^\\fore} {\\bf w}_l\\,.\n\\label{eqn:residualcomponent}\n\\end{equation}\nNote that the residual noise in the map is independent of assumptions\nabout the\nSZ signal including whether it is Gaussian or not. However if the\nforegrounds\nthemselves are non-Gaussian, then this technique only minimizes the\nvariance\nand may not be optimal for recovery of non-Gaussian features in the SZ\nmap \nitself. \\cite{Bouetal95} (1995) have shown that similar techniques are quite\neffective \neven\nwhen confronted with non-Gaussian foregrounds. \nThis is a potential caveat especially for cases in which \nthe residual noise is not dominated by the primary anisotropies \nor detector noise. We shall discuss methods to alleviate this\nconcern in the next section.\n\n\\begin{figure}[t]\n\\centerline{\\psfig{file=figure2.eps,width=3.5in,angle=0}}\n\\caption{Dependence of the residual noise rms on foreground\nassumptions expressed as a ratio to the fiducial model of Fig.~\\protect\\ref{fig:clean}. (a) Falsely assuming the foregrounds have perfect\nfrequency coherence not only underpredicts the residual noise by a substantial\nfactor but also leads to substantially more actual residual noise.\n(b) Multiplying the foreground amplitudes by 2 (power by\n4) produces less than a factor of 2 increase in the residual noise.\n}\n\\label{fig:simul}\n\\end{figure}\n\\subsection{Detection Threshold}\n\nThe residual noise sets the detection threshold for the\nSZ effect for a given experiment. \nIn Fig.~\\ref{fig:clean}, \nwe show the rms of the residual noise after\nforeground subtraction for the Boomerang, MAP and Planck\nexperiments assuming the ``MID'' foreground model from\n\\cite{Tegetal99} (1999). With the Boomerang and Planck channels,\nelimination of the primary anisotropies is excellent up to the beam\nscale where detector noise dominates. As expected, the MAP channels,\nwhich are all on the RJ side of the spectrum, do not\nallow good elimination of the primary anisotropies.\n\nIt is important not to assume that the foregrounds are \nperfectly correlated in frequency, which is the usual \nassumption in the literature (\\cite{Hobetal98} 1998; \n\\cite{BouGis99} 1999). There are two types of errors\nincurred by doing so. The first is that one underpredicts\nthe amount of residual noise in the SZ map (see Fig.~\\ref{fig:simul}).\nThe second is that if one calculates the optimal weights in\nequation~(\\ref{eqn:weights}) based on this assumption the actual\nresidual noise increases. For Planck it can actually increase the noise\nbeyond the level in which it appears in the $100$GHz maps with no\nforeground subtraction at all. The reason is that the cleaning \nalgorithm then erroneously uses the contaminated high and low\nfrequency channels to subtract out the small foreground contamination\nin the central channels. In Planck, the difference between the predicted\nand actual rms noise from falsely assuming perfect frequency coherence\ncan be more than two orders of magnitude. \n\n\n\nFor Boomerang and Planck, the largest residual noise component,\naside from detector noise, is dust emission and is sufficiently\nlarge that one might worry that current uncertainties in our knowledge\nof the foreground model may affect\nthe implications for the detection of the SZ effect. It is therefore\nimportant to explore variations on our fiducial foreground \nmodel. \n\nMultiplying\nthe foreground rms amplitudes uniformly by a factor of 2 (and hence\nthe power by a factor of 4), produces less than a factor of 2 increase\nin the residual noise rms as shown in Fig.~\\ref{fig:simul}. \nLikewise, as discussed in \\cite{Tegetal99} (1999), minor\nvariations in the frequency coherence do not effect the residual noise much\nin spite of the fact that it is crucial not to assume perfect\ncorrelation. \nWe conclude that uncertainties in the properties of currently known\nforegrounds are unlikely to change our conclusions qualitatively.\nThere is however always the possibility that some foreground that does not\nappear in the currently-measured frequency bands will affect our\nresults.\n\nThe fact that the residual dust contributions are comparable to those \nof the detector noise for Boomerang and Planck is problematic for\nanother reason. Since the algorithm minimizes\nto total residual variance, it attempts to keep these two main\ncontributors roughly comparable. However the dust will clearly \nbe non-Gaussian to some extent and one may prefer instead to trade\nmore residual detector noise for dust contamination. One can\nmodify the subtraction algorithm to account for this by artificially\nincreasing the rms amplitude of the dust when calculating the weights in\nequation~(\\ref{eqn:weights}) while using the real amplitude \nin calculating the residual noise in equation~(\\ref{eqn:residualcomponent}).\nFor example we have explored increasing the amplitude by a factor of\n4 (power by 16) for the weights. The result is an almost negligible increase \nin total residual noise rms but an improvement in dust rejection by \na factor of 3-4 in rms. For Planck this brings the ratio of \ndust to total rms to $\\sim 10\\%$ and recall that the noise adds\nin quadrature so that the total dust contribution is really \n$\\sim 1\\%$ of the total.\nThis more conservative approach is thus advisable but since\nit leaves the total residual noise rms essentially unchanged, we\nwill adopt the minimum variance noise to estimate the\ndetection threshold.\n\nFig.~\\ref{fig:clean} directly tells us the detection threshold per\n$(l,m)$ multipole moment. Since the SZ signal is likely to have a smooth \npower spectrum in $l$,\none can average over bands in $l$ to beat down the residual noise. \nAssuming Gaussian-statistics, the residual noise variance $ 2N_l^2$ for\nthe power spectrum estimate is then given by\n\\begin{equation}\nN_l^{-2}\\Big|_{\\rm band} = \n{f_\\sky} \\sum_{l_{\\rm band}} (2l+1) N_l^{-2}\\,,\n\\end{equation}\nwhere $f_\\sky$ accounts for the reduction of the number of independent \nmodes due to the fraction of sky covered.\nThe result for the three experiments is shown in Fig.~\\ref{fig:error}.\nIn the absence of a detection, they can be interpreted as the optimal\n1 $\\sigma$ upper limits on SZ bandpowers achievable by the experiment.\nBoomerang and MAP can place upper limits on the SZ signal in the interesting\n$\\mu$K regime whereas Planck can detect signals well below a $\\mu$K.\n\nThis noise averaging procedure in principle implicitly assumes that the \nstatistical properties of the residual noise, and by implication the\nfull covariance matrix of the other foregrounds, is precisely \nknown. In reality, they too must be estimated from the multifrequency data \nitself through\neither through the subtraction techniques discussed here or\nby direct modeling of the foregrounds in the maps. \\cite{Tegetal99} (1999)\nfound that direct modeling of the foregrounds with hundreds of fitted\nparameters did not appreciably degrade our ability to extract the\nproperties of the primary anisotropies. The main source of variance there\nwas the cosmic variance of the primary anisotropies themselves whose \nproperties are precisely known.\nSimilarly here the main source of residual variance is either the \nprimary anisotropies (for MAP) or detector noise (for Boomerang and Planck)\nand their statistical properties may safely be considered known.\n\n\n\\begin{figure}[b]\n\\centerline{\\psfig{file=figure3.eps,width=3.5in,angle=0}}\n\\caption{Detection thresholds for the SZ effect. Error boxes represent the\n1-$\\sigma$ rms residual noise in multipole bands and can be interpreted \nas the detection threshold. Also shown (dotted) is the level of the primary\nanisotropies that have been subtracted with the technique and the signal\n(dashed) expected in the simplified model of \\S \\ref{sec:sz}.}\n\\label{fig:error}\n\\end{figure}\n\n\n\n\n\n\\section{Modeling the SZ Signal}\n\\label{sec:sz}\n\n\nIn order to estimate how well the statistical properties of \nthe SZ effect might be recovered with multifrequency CMB maps, \nwe need to model the large-angle SZ effect itself. \nThe current state-of-the-art in hydrodynamic simulations\n(\\cite{daS99} 1999; \\cite{Refetal99} 1999; \\cite{Seletal00} 2000)\nhas reached a qualitative but not quantitative consensus on the\nstatistical properties of the SZ effect. In addition,\nquestions as to the heating of the gas from non-gravitational\nsources may even change the results qualitatively (\\cite{Pen99} 1999).\nHydrodynamic simulations are also severely limited in the \ndynamic range and volume sampled. \n\nGiven the current\nstate of affairs, we believe it is useful to explore a \nparameterized model of the effect whose consequences are\nsimple to calculate and which may be calibrated against hydrodynamic\nsimulations as they continue to improve.\n\n\n\\subsection{Bias Prescription}\n\n\nIn general, the SZ temperature fluctuation $\\Theta=\\Delta T/T$ \nis given by\nthe opacity weighted\nintegrated pressure fluctuation along \nthe line of sight:\n\\begin{eqnarray}\n\\Theta^\\sz(\\bn,\\nu) \n%i&=& -2 s(\\nu) {\\sigma_T \\over m_e} \n%\t\\int_0^{\\rad_0} d\\rad\\, a \\delta p_\\gas(\\rad,\\bn \\rad) \\nonumber\\\\\n\t &=& -2 s(\\nu) \\int_0^{\\rad_0} d\\rad\\\n\t\t\t\\dot\\tau \\pi(r,\\bn r) \\,,\n\\end{eqnarray}\n$\\rad$ is the the comoving distance, $\\tau$ is the Thomson optical depth, \noverdots are derivatives with respect to $\\rad$ and\nthe dimensionless electron pressure fluctuation is\n\\begin{equation}\n\\pi = \\delta p_e/\\rho_e\\,.\n\\end{equation}\nOne needs to model the statistical properties of $\\pi$, in particular\nits power spectrum and bispectrum\n\\begin{eqnarray}\n\\left< \\pi(\\bfk)^* \\pi(\\bfk') \\right> &=& (2\\pi)^3 \\deld(\\bfk -\\bfk')P_\\pi(k) \n\t\t\\,, \\\\\n\\left< \\pi(\\bfk)\\pi(\\bfk')\\pi(\\bfk'') \\right> &=& (2\\pi)^3 \\deld(\\bfk+\\bfk'+\\bfk'')\n\t\tB_\\pi(k,k',k'')\\,,\\nonumber\n\\end{eqnarray}\nas a function of lookback time or distance $r$. In principle we also need the\nunequal time correlators, but in practice these do not play a role \nas we shall see.\n\nBy analogy to the familiar case of galaxy clustering, \nit is reasonable to \nsuppose that the pressure fluctuations depend locally\non the dark matter density and hence are biased\ntracers of the dark matter density in the {\\it linear} regime (\\cite{GolSpe99} 1999).\nHence the statistical properties follow from those of the dark matter distribution\n\\begin{eqnarray}\nP_\\pi(k;r) &\\approx& b_\\pi(r)^2 P_\\delta(k;r)\\,, \\nonumber\\\\\nB_\\pi(k,k',k'';r) &\\approx& b_\\pi(r)^3 B_\\delta(k,k',k'';r) \\,. \n\\end{eqnarray}\nWe have restored the time dependence since the bias will be time dependent\neven in the linear regime and must be extracted from simulations. \nIn general, the bias parameter for the power spectrum and bispectrum\nneed not be the same even in the linear regime since the bispectrum\nautomatically involves higher order corrections (\\cite{FryGaz93} 1993). \nFor estimation purposes here we will take them to be equal. \n\nFollowing \\cite{GolSpe99} (1999), we chose the form\n\\begin{eqnarray}\nb_\\pi(r) = b_\\pi(0) /(1+z) \\, ,\n\\end{eqnarray}\nas motivated by findings that the average gas temperature \ndrops off roughly by this factor. We normalize the value of \nthe bias parameter today by comparison with recent\nhydrodynamic simulations. It is conceptually useful to separate\nthe bias into two factors: \n\\begin{equation}\nb_\\pi(0) = {k_B T_e(0) \\over m_e c^2} b_{\\delta} \\,,\n\\end{equation}\ni.e. an opacity-weighted average temperature and a bias parameter\nfor the gas density at that temperature.\nIn \\cite{Refetal99} (1999), for our fiducial $\\Lambda$CDM cosmology,\nthe bias $b_\\delta$ was found to be \n$\\sim$ 8 to 9, while in \\cite{Seletal00} (2000) it was\nfound to be in the range $\\sim$ of $3$ to $4$. \nIn both these papers, $T_e(0) \\sim$ 0.3 to 0.4 keV; \nthese values are lower than the $\\sim$ 1 keV found by\n\\cite{CenOst99} (1999) using hydrodynamical simulations with\nfeedback effects. \nAs a compromise between these results, we take \n$T_e(0)=0.5$keV and $b_\\delta=4$, which corresponds to \n\\begin{equation}\nb_\\pi(0) = 0.0039\\,.\n\\end{equation}\nNote that this is a factor of 2 lower than used in\n\\cite{GolSpe99} (1999) and \\cite{CooHu99} (1999).\n\nNeedless to say, the resulting predictions should be taken\nas order-of-magnitude estimates only.\nAs simulations \nimprove, one can expect better values for the bias today and a more detailed \nmodeling of its redshift and perhaps even scale dependence.\n\n\n\\subsection{Multipole Moments}\n\nThe multipole moments of the SZ effect under these simplifying assumptions\ncan then be expressed \nas a weighted projection of the\ndensity field (\\cite{CooHu99} 1999):\n\\begin{eqnarray}\n\\almn^\\sz(0) &\\equiv&\n\t\\int d \\bn Y_l^{m*}(\\bn)\\Theta^\\sz(\\bn,0)\\nonumber\\\\\n &\\approx& i^l \\int {d^3{\\bf k } \\over 2\\pi^2} \\delta({\\bf k},r_l) I_l^\\sz(k) \n \\Ylmn{}^*(\\bk) \\, ,\n\\label{eqn:szsource}\n\\end{eqnarray}\nwhere \n\\begin{eqnarray}\nI_l^\\sz(k) &\\approx& W^{\\sz}(\\rad_l) \\sqrt{{\\pi \\over 2l}}{1\n\\over k} F_l(k) \\, , \\nonumber\\\\\nW^\\sz(r) & = & -2 b_\\pi(r) \\dot\\tau\\,,\n\\end{eqnarray}\nin the Limber approximation\nand\n(\\cite{Hu00a} 2000a)\n%\\begin{eqnarray}\n%I_l^\\sz(k) &=& \\int d\\rad W^{\\sz}(\\rad)\\alpha_l(k,\\rad) \\,, \n%\\label{eqn:isz}\n%\\end{eqnarray}\n%where the weight function for the SZ effect is \n%\\begin{eqnarray}\n%\\end{eqnarray}\n%$\\alpha_l$ is the \n%spherical Bessel function in a flat universe or the \n%ultra spherical Bessel function in a curved\n%universe $\\Omega_K = 1-\\Omega_c-\\Omega_b-\\Omega_\\Lambda >0$.\n%The present day density field can be scaled back in time using the\n%growth factor $G$ in linear theory $\\delta(\\bfk,r) =\n%G(r)\\delta(\\bfk,0)$. \n%In the Limber approximation limit (\\cite{Lim54} 1954)\n%where the weight function varies with \n%$r$ much more slowly than the Bessel functions, we can approximate the\n%integral as\n%where \n\\begin{eqnarray}\n\\rad_l & = & \\Omega_K^{-1/2} H_0^{-1} \\sinh^{-1} (\\Omega_K^{1/2} H_0 l/k) \\,,\\nonumber\\\\\nF_l & = & (1 +\\Omega_K H_0^2 l^2/k^2)^{-1/4} \\,.\n\\label{eqn:Limber}\n\\end{eqnarray}\nThe quantities take on a simple forms for a flat universe: $\\rad_l \\rightarrow l/k$ and\n$F_l(k) \\rightarrow 1$. \nThe Limber approximation breaks down for $l \\la 50$ but is sufficient for our purposes. \n\n\\begin{figure}[t]\n\\centerline{\\psfig{file=figure4.eps,width=3.5in,angle=0}}\n\\caption{{\\it top:} SZ power spectrum from simulations\ncompared to analytical predictions based on linear perturbation \ntheory (PT) and the non-linear scaling relations of \\protect\\cite{PeaDod96} (1996; PD96). {\\it bottom:} \nErrors on the binned power spectrum estimators for a single \n$6^\\circ\\times 6^\\circ$ field; for a given experiment\nthe errors should be scaled by $\\sim 0.03 f_\\sky^{-1/2}$. \nThe sampling errors in the simulations is nearly equal to\nthose of a Gaussian random field with the same power spectrum.\nThe total noise including residual foregrounds and detector noise\nis also given for Planck. }\n\\label{fig:simultwopt}\n\\end{figure}\n\n\\subsection{Power Spectrum}\n\nThe power spectrum of the SZ effect in this simplified model follows\nfrom equation~(\\ref{eqn:szsource}),\n\\begin{eqnarray}\nC_l^{\\sz} &=& {2 \\over \\pi} \\int {dk \\over k} {k^3\nP_\\delta\\left(k;r_l\\right)} [I_l^\\sz(k)]^2 \n\t\t\\nonumber\\,,\\\\\n\t &\\approx& \\int_0^{\\rad_0}d\\rad {[W^\\sz(r)]^2 \\over \\da^2 }\n\t\tP_\\delta(l/\\da;r) \\,,\n\\label{eqn:clsz}\n\\end{eqnarray}\nIn the second line we have transformed the integration variable \nunder the Limber correspondence: $k=l/\\da$ and \n\\begin{equation}\n\\int {d k\\over k} F_l^2\\ldots = \\int {d\\rad \\over \\da}\\ldots \\; .\n\\end{equation}\nWe see that to go from the flat to curved cosmologies in the Limber\napproximation one simply replaces the radial distance with the angular\ndiameter distance in the integrand. \n\nIn evaluating the SZ power spectrum, we have extended the SZ model\nto the non-linear regime \nby using the scaling formulae for the nonlinear dark matter power\nspectrum of \\cite{PeaDod96} (1996).\nHowever, modeling the SZ effect with a scale-independent bias factor will clearly break\ndown deep in the non-linear regime. \\cite{Refetal99} (1999) have shown that it is \na reasonable approximation in the weakly non-linear regime (overdensities $\\la 10$)\nfor $z \\la 1$ but can be in serious error outside of this range. As \nthe weakly non-linear regime is the one of interest for \nanisotropies at $l \\la 1000$, we will use this\napproximation to test the effects of non-linearities.\nThe predicted power spectrum in our fiducial model is shown \nin Fig.~\\ref{fig:simultwopt}.\n\n\n\n\\subsection{Bispectrum}\n\\label{sec:bispectrum}\n\nThe bispectrum of the SZ effect also follows from\nexpression~(\\ref{eqn:szsource}) \n\\begin{eqnarray}\n\\bilm &\\equiv& \\left<a_{l_1m_1} a_{l_2m_2} a_{l_3m_3}\\right> \\nonumber\\\\\n&=&\n\\left[ \\prod_{j=1}^3 i^{l_j} \\int \\frac{d^3 k_j}{2\\pi^2} \nI_{l_j}^\\sz(k_j) Y_l^{m\\ast}(\\hat{\\bf k}_j) \\right]\n\\nonumber \\\\\n&& \n(2\\pi)^3 \\deld(\\veck_1+\\veck_2+\\veck_3)\nB_\\delta(k_1,k_2,k_3) \\,.\n\\nonumber\n\\end{eqnarray}\nHere the density bispectrum should be understood as arising from the full \nunequal time correlator\n\\begin{equation}\n\\left< \\delta(\\bfk_1;r_1) \\delta(\\bfk_2;r_2) \\delta(\\bfk_3;r_3) \\right> \\,,\n\\end{equation} \nwhere the temporal coordinate, which we temporarily suppress,\n is evaluated in the Limber approximation\n(\\ref{eqn:Limber}). \n\nTo further simplify this expression, we expand the delta function \n\\begin{equation}\n\\deld(\\veck_1+\\veck_2+\\veck_3) = \\frac{1}{(2 \\pi)^3} \\int e^{i\n(\\veck_1+\\veck_2+\\veck_3) \\cdot \\bn r} d^3x \\, ,\n\\end{equation}\nand employ the Rayleigh expansion\n\\begin{equation}\ne^{i \\veck \\cdot \\bn r} = 4 \\pi \\sum_{lm} i^l j_l(k r) Y_l^{m\n\\ast}(\\hat{\\veck}) Y_l^m(\\bn) \\, .\n\\end{equation}\nWe have assumed here a flat universe to simplify the derivation; as we\nhave seen in the last section, we can promote the final result to a \ncurved universe by replacing radial distances with angular diameter \ndistances.\n\nWith these relations, the angular integral over the directions of\n$\\bfk_j$ collapse to give\n\\begin{eqnarray}\n\\bilm\n&=& \\int r^2 dr \\left[ \\prod_{j=1}^3 {2 \\over \\pi} \\int k_j^2 dk_j\nI_{l_j}^\\sz(k_j) j_{l_j}(k_j r) \\right] \\nonumber\\\\\n&& \\times B(k_1,k_2,k_3) G_{l_1 l_2 l_3}^{m_1 m_2 m_3}\\,,\n\\end{eqnarray}\nwhere the Gaunt integral is\n\\begin{eqnarray}\nG_{l_1 l_2 l_3}^{m_1 m_2 m_3} &\\equiv& \\int d\\bn\n \\Ylm{1} \\Ylm{2} \\Ylm{3} \\\\\n&=&\\sqrt{(2l_1+1)(2l_2+1)(2l_3+1) \\over 4\\pi}\n\\nonumber\\\\ &&\\times\n \\wj \\wjm \\,. \\nonumber \n\\label{eqn:harmonicsproduct}\n\\end{eqnarray}\nHere, the quantities in parentheses are the Wigner-3$j$ symbols\nwhose properties are described in Appendix A of \\cite{CooHu99} (1999).\nThe integrals over the Bessel functions can again be done in \nthe Limber approximation \nleaving\n\\begin{eqnarray}\n\\bilm\n&=& G_{l_1 l_2 l_3}^{m_1 m_2 m_3} \\int dr \n\t{[W^\\sz(r)]^3 \\over r^4} \n%\\nonumber\\\\ &&\\times \nB_\\delta({l_1 \\over r},{l_2 \\over r},{l_3\\over r};r)\\,, \\nonumber\n\\end{eqnarray}\nNote that only equal time contributions contribute in the Limber approximation.\n\nWe can promote this result to a curved universe by \nreplacing radial distances with angular diameter distances\n\\begin{eqnarray}\n\\bilm \n&=& G_{l_1 l_2 l_3}^{m_1 m_2 m_3} \n\t\\int dr {[W^\\sz(r)]^3 \\over \\da^4} \n%\\nonumber\\\\ &&\\times \n\t\tB_\\delta({l_1 \\over \\da},{l_2 \\over \\da},{l_3\\over \\da};r) \\,.\n\\nonumber\n\\end{eqnarray}\nFinally, we can introduce the angular averaged bispectrum as\n\\begin{eqnarray}\n\\bi = \\sum_{m_1 m_2 m_3} \\wjm \\bilm\\,,\n\\end{eqnarray}\nto obtain the final result\n\\begin{eqnarray}\n\\bi &=& \\sqrt{(2l_1+1)(2l_2+1)(2l_3+1) \\over 4\\pi} \\wj\n\t\\nonumber\\\\\n&&\\times \\int dr {[W^\\sz(r)]^3 \\over \\da^4} B_\\delta({l_1 \\over \\da},{l_2 \\over \\da},{l_3\\over \\da};r) \\,.\n\\label{eqn:szbispectrum}\n\\end{eqnarray}\t\nOne can alternately derive this relation by taking a flat-sky \napproach and using the general relation between the flat-sky and\nall-sky bispectra (see Appendix C, \\cite{Hu00b} 2000b).\n\nEquation (\\ref{eqn:szbispectrum}) gives the SZ angular bispectrum in\nterms of the underlying density bispectrum. In second order\nperturbation theory, the density bispectrum is in turn given by\n\\begin{eqnarray}\nB_\\delta (k_1,k_2,k_3;r) &=& F_2(\\bfk_1,\\bfk_2) P_\\delta (k_1;r) P_\\delta (k_2;r) \\nonumber\\\\\n&& + 5\\; {\\rm perm.}\\,,\n\\end{eqnarray}\nwhere\n\\begin{eqnarray}\nF_2(\\bfk_1,\\bfk_2) = \\frac{5}{7} + \\frac{\\veck_1 \\cdot \\veck_2}{k_2^2}\n+ \\frac{2}{7} \\frac{(\\veck_1 \\cdot \\veck_2)^2}{k_1^2\\ k_2^2}\\,.\n\\end{eqnarray}\n\nUnfortunately, there exists no accurate fitting formula for the bispectrum of the\ndensity field in the mildly non-linear regime; we will employ simulations in \\S \\ref{sec:sims}\nto address this regime. In the deeply non-linear regime,\nthe density field obeys the hierarchical ansatz\n\\begin{eqnarray}\nB_\\delta (k_1,k_2,k_3;r) = {Q_3 \\over 2} [P(k_1;r)P(k_2;r)+{\\rm 5\\; perm.}]\\,,\n\\end{eqnarray}\nwhere the power \nspectra are given by the non-linear scaling of \\cite{PeaDod96} (1996).\n\\cite{ScoFri99} (1999) find that for power law power spectrum\n\\begin{eqnarray}\nQ_3 (n) = [4 - 2^n]/[1+2^{n+1}] \\,. \n\\end{eqnarray}\n\\cite{Hui99} (1999) suggests that for a general power spectrum\none should replace $n$ with the local linear power spectral index at $(k_1+k_2+k_3)/3$. \n\n\n\\begin{figure}[b]\n\\centerline{\\psfig{file=figure5.eps,width=3.5in,angle=0}}\n\\caption{{\\it top:} Skewness in the simulations \ncompared with second order perturbation theory\n(PT) and hyper-extended perturbation theory (HEPT). \nThe smoothing is performed with an \nangular\ntophat of radius $\\sigma$.\n{\\it bottom:}\nErrors on the skewness measurement for a single\n$6^\\circ\\times 6^\\circ$ field due to sampling errors\nand residual noise from Planck.}\n\\label{fig:skewness}\n\\end{figure}\n\n\n\\subsection{Skewness}\n\nThe simplest aspect of the bispectrum that can be measured is the\nthird moment of the map smoothed on some scale with a window $W(\\sigma)$\n\\begin{eqnarray}\n\\left< \\Theta^3(\\bn;\\sigma) \\right> &=& \n%\t\t{1 \\over 4\\pi}\n%\t\t\\sum_{l_1 l_2 l_3}\\sum_{m_1 m_2 m_3}\n%\t\t \\bilm G_{l_1 l_2 l_3} W_{l_1} W_{l_2} W_{l_3}\\nonumber \\,,\\\\\n\t\t{1 \\over 4\\pi} \\sum_{l_1 l_2 l_3}\n\t\t\\sqrt{(2l_1+1)(2l_2+1)(2l_3+1) \\over 4\\pi} \\nonumber\\\\\n\t\t&&\\times \\wj \\bi W_{l_1}(\\sigma)W_{l_2}(\\sigma)W_{l_3}(\\sigma)\n\t\t\\,,\n\\end{eqnarray}\nwhere $W_l$ are the multipole moments (or Fourier transform in a flat-sky approximation)\nof the window. For simplicity, we will choose windows which are either\ntop hats in real or multipole space.\n\nIt is useful to define the skewness parameter\n\\begin{equation}\nS_3(\\sigma) = {\\left< \\Theta^3(\\bn;\\sigma) \\right> \\over \\left< \\Theta^2(\\bn;\\sigma) \\right>^2}\\,,\n\\end{equation}\nwhere \nthe second moment is that of the SZ signal\n\\begin{equation}\n\\left< \\Theta^2(\\bn;\\sigma) \\right> = \n{1 \\over 4\\pi} \\sum_l (2l+1) C_l^\\sz W_l^2(\\sigma)\\,.\n\\end{equation}\nThe skewness in our fiducial model is shown \nfor both the perturbation theory and HEPT predictions in\nFig.~\\ref{fig:skewness}.\n\n\nSince the {\\it density} bispectrum in both the perturbative and non-linear\nregime scale as $[P_\\delta(k)]^2$, the amplitude of the underlying density \nfluctuations roughly scale out of $S_3$. However, the pressure bias $b_\\pi$\ndoes {\\it not}: $S_3 \\propto b_\\pi^{-1}$. \n$S_3$ thus provides an observable handle on the bias.\nThis general point applies even if the bias is non-linear although its\ninterpretation will be not be as straightforward (see \\cite{FryGaz93} 1993 and\n\\cite{MoJinWhi97} 1997 for its application in galaxy biasing). \n\n\\begin{figure}[b]\n\\centerline{\\psfig{file=figure6.eps,width=2.2in,angle=0}}\n\\caption{One of 500 simulations \nof the SZ effect in the $\\Lambda$CDM model for a \n$6^\\circ\\times 6^\\circ$ \nfield-of-view. The range of the map is $-100\\mu K , 25\\mu K$ with an\nrms of $9\\mu K$ and has an approximate angular resolution of $2'$.\nNote the lack of obvious filamentary structures.}\n\\label{fig:simulmap}\n\\end{figure}\n\n\\begin{figure*}\n\\centerline{\n\\psfig{file=figure7a.eps,width=2.2in,angle=0}\n\\psfig{file=figure7b.eps,width=2.2in,angle=0}\n\\psfig{file=figure7c.eps,width=2.2in,angle=0}\n\t}\n\\caption{Recovery of the SZ signal with Planck: left to right, model\nSZ signal, signal $+$ noise from primary anisotropies and foregrounds, and\nfinal recovered map from Planck. The signal map is that\nof Fig.~\\protect\\ref{fig:simulmap} smoothed with a top-hot of\nradius $20'$.\n}\n\\label{fig:recovery}\n\\end{figure*}\n\n\\subsection{Numerical Simulations}\n\\label{sec:sims}\n\nSince we are interested in the properties of the SZ effect in the \nweakly-nonlinear regime, \ncosmological simulations are required to recover the complete statistical\nproperties of the signal and calibrate\nsemi-analytic approaches for its low-order statistics. \nThe simplified SZ model employed in this paper \nhas the virtue that it is easy to simulate as it requires only dark matter \nand not the gas to model. Its main drawback of course is that results must\nbe taken with a grain of salt due to missing physics.\n\nThe realism of the basic\napproach can be improved by better calibrating the bias model \nagainst hydrodynamic simulations. One can envision \ngoing beyond the simple redshift dependent bias approach taken \nhere to include scale dependence and stochasticity. Even accounting\nfor these additional complications, simple dark matter simulations can\ncontinue to complement full hydrodynamic simulations. \nHydrodynamic simulations will always\nbe more limited in dynamic range and sampling volume. \nIndeed, the current state of the art is limited\na handful of realizations across one order of magnitude in physical scale \n(\\cite{Refetal99} 1999; \\cite{Seletal00} 2000). A single simulation\nis then ``stacked'' on the line-of-sight.\nGiven the range of redshifts at which the SZ effect contributes, the\nsimulation volume is traced many times for each line-of-sight. Moreover,\nthe angular resolution decreases monotonically as one approaches the\norigin at $z=0$. \n\nThe reduction in dynamic range due to the angular projection is a\nserious but not unfamiliar problem in cosmology. It occurs whenever\nthe kernel for the projection spans cosmological distances. \n\\cite{WhiHu99} (1999) introduced a technique of tiling multiple particle-mesh simulations which\ntelescope along the line of sight to maintain a fixed angular resolution for\nthe analogous problem in weak lensing. \nThis also avoids the problem of over-representing the filamentary structure of\nthe map noted by \\cite{Refetal99} (1999). \n\nWe refer the reader to \n\\cite{WhiHu99} (1999) for details of the approach and tests of the method.\nThe simulation all have a \n$256^3$ mesh with $256^2$ lines of sight for the ray tracing on a $6^\\circ \\times 6^\\circ$ field. \nOther relevant parameters are given in Tab.~\\ref{tab:sims}:\nthe box size $L_{\\rm box}$, the number of particles $N_{\\rm part}$, the number of simulations run\n$N_{\\rm sim}$, the number of tiles of the given box size used $N_{\\rm tile}$, the maximum\nredshift to which a given box is used, and the angular resolution of the mesh the maximum and\nminimum redshift used $\\theta_{\\rm mesh}$. \nNote that we cannot shrink the box size along the line-of-sight indefinitely since\nthe fundamental mode of the box must be in the linear regime to provide accurate evolution.\nThis implies that we lose angular resolution near the origin where a fixed physical scale\nsubtends a large angle on the sky. \nFurthermore at the higher redshift the number of particles must be increased to eliminate\nshot noise from the initial conditions. Nonetheless, the tiling technique does a good\njob of maintaining angular resolution at all but the lowest redshifts.\n\nWe construct 500 SZ maps from random combinations of the tiles in Tab.~1 for our \nstatistical analysis; one realization is shown in Fig.~\\ref{fig:simulmap}.\nThe average power spectrum is shown in\nFig.~\\ref{fig:simultwopt} (top panel) and compared with the linear perturbation\ntheory prediction and the non-linear scaling relation of \\cite{PeaDod96} (1996).\nWe have tested that the deficit of power at the low\nmultipoles is an artifact of the finite field-of-view through monte-carlo\nrealizations of the predicted power spectrum. The roll-off at high\nmultipoles is due to the spatial resolution in the simulations. This \nalso explains the $\\sim 10\\%$ deficit at intermediate scales which \ncomes from highly non-linear structure close to the origin. Agreement\nis restored if one eliminates contributions from overdensities $>10$ in\nthe predictions. Since our SZ model is at best valid in the weakly \nnon-linear regime, these contributions should not be included anyway. \n\nFig.~\\ref{fig:skewness} (top panel) shows the results for the skewness\nin the simulations compared with the second order perturbation theory\nand HEPT predictions. The agreement here is worse, but is still\nsufficient for our purposes, given the crudeness of the underlying\nmodel for the SZ effect itself. \n\nWe can address sample variance questions from the scatter of the\nresults in the individual realizations. Sampling errors for\nthe power spectrum and skewness are shown in the bottom panels of\nFig.~\\ref{fig:simultwopt} and \\ref{fig:skewness} respectively.\nSince these are for individual $6^\\circ \\times 6^\\circ$ planes,\nthey should be scaled by $\\sim 0.03 f_\\sky^{-1/2}$ for a given \nexperiment. Sampling errors are one source of noise that\nwe will include in the signal-to-noise calculations in the\nnext section.\n\n\n\n\\begin{table}[tb]\\footnotesize\n\\caption{\\label{tab:sim}}\n\\begin{center}\n{\\sc Details of Numerical Simulations}\n\\begin{tabular}{cccccc}\n\\tableskip\\hline\\tableskip\n$L_{\\rm box}$ & $N_{\\rm part}$ & $N_{\\rm sim}$ & $N_{\\rm tile}$ & $z_{\\rm max}$ & $\\theta_{\\rm mesh}$ \\\\\n\\tableskip\\hline\n445 &$256^3$ & 5 & 2 & 3.00 & $1.4'-1.8'$ \\\\\n355 &$256^3$ & 5 & 2 & 1.87 & $1.4'-1.8'$ \\\\\n280 &$256^3$ & 5 & 2 & 1.27 & $1.4'-1.8'$ \\\\\n220 &$256^3$ & 5 & 2 & 0.90 & $1.4'-1.8'$ \\\\\n175 &$128^3$ & 6 & 2 & 0.66 & $1.4'-1.8'$ \\\\\n140 &$128^3$ & 6 & 2 & 0.50 & $1.4'-1.8'$ \\\\\n110 &$128^3$ & 6 & 2 & 0.38 & $1.4'-1.8'$ \\\\\n85 &$128^3$ & 6 & 2 & 0.29 & $1.4'-1.8'$ \\\\\n70 &$128^3$& 10 & 9& 0.22 & $1.4'-\\infty$ \\\\\n\\tableskip\\hline\n\\end{tabular}\n\\end{center}\nNOTES.---%\nNumerical simulations in our $\\Lambda$CDM cosmological model; see\ntext for a description of these quantities.\n\\label{tab:sims}\n\\end{table}\n\n\n\n\\begin{figure}[t]\n\\centerline{\\psfig{file=figure8.eps,width=3.5in,angle=-90}}\n\\caption{Cumulative signal-to-noise in the measurement of the SZ\npower spectrum with Boomerang, MAP and Planck as a function of maximum\n$l$. The solid line\nis the maximum signal-to-noise achievable in a perfect experiment\n(see text).\n%The signal-to-noise is adequate in Planck satellite for a clear\n%detection\n%of the SZ effect while Boomerang and MAP will only allow reasonable\n%limits to be placed on any SZ contribution.\n}\n\\label{fig:clsn}\n\\end{figure}\n\n\n\\section{Estimating the Signal-to-Noise}\n\\label{sec:sn}\nWith the SZ signal estimated from the simple bias model of \\S \\ref{sec:sz}\nand residual noise calculated from the foreground model and subtraction\ntechniques of \\S \\ref{sec:cleaning}, we can now estimate the signal-to-noise\nfor the detection of the SZ effect. \nIn Fig.~\\ref{fig:recovery}, we illustrate the foreground subtraction\ntechnique on simulated Planck maps. The signal-to-noise in the maps\nis of order one for features spanning tens of arcminutes. We shall here\nshow that this level of signal-to-noise is more than sufficient for\nthe purpose of extracting measurements of the low order statistics\nof the SZ signal. \n\n\\subsection{Power Spectrum}\n\nThe signal-to-noise in the power spectrum per multipole $(l,m)$ mode is simply\n\\begin{equation}\n\\left( {S \\over N} \\right)_{l m}^2 = {1 \\over 2} \n\t\\left( {C_l^\\sz \\over {C_l^\\tot}}\\right)^2 \\, .\n\\end{equation}\nHere, $C_l^\\tot$ is the power spectrum of all contributions in \nthe SZ map,\n\\begin{eqnarray}\nC_l^{\\rm tot} = C_l^\\sz + N_l\\,,\n\\label{eqn:cltot}\n\\end{eqnarray}\nwhere recall that the residual noise $N_l$ \nwas defined in equation (\\ref{eqn:nl}) and includes contributions\nfrom detector noise.\n\nAssuming Gaussian statistics for the signal and noise, each mode\nis independent so that the total signal-to-noise is the quadrature\nsum \n\\begin{equation}\n\\left( {S \\over N} \\right)^2 = {f_\\sky \\over 2}\\sum_l (2l+1) \\left( \n\t{C_l^\\sz \\over {C_l^\\tot}} \\right)^2 \\, .\n\\end{equation}\nThis quantity gives the variance of the total power measurement in the\nSZ effect, including sample variance. ${\\rm S/N} \\gg 1$ means that \none has a precise measurement of the power spectrum not simply\na highly significant detection.\nIn Fig.~\\ref{fig:clsn}, for the Boomerang, MAP\nand Planck experiments as a function of the maximum $l$ mode included\nin the sum. We also show the ultimate limit of perfect foreground and\nnoise removal where $C_l^{\\rm tot}=C_l^\\sz$ and $f_\\sky=1$. \nWe will refer to this case here and below as a ``perfect experiment''.\n\nWith our fiducial\nchoice of the gas bias, Planck should have a highly significant\ndetection of the total signal. One should\nbear in mind that the bias parameter $b_\\pi$ is still highly\nuncertain and that the $S/N$ scales as $b_\\pi^2$. Nevertheless even a \nrelatively large reduction in the average gas temperature\nor density bias will not make the signal undetectable in principle. \nIn practice, however remember that one is then relying on a precise \nsubtraction of the noise bias in the measurement of $C_l^\\tot$, \nwhich in turn requires that the power spectrum of the dust and other \nresidual foregrounds lurking at least at the $10\\%$ \nlevel in rms (1\\% in power)\nare determined comparably precisely. \n\nIf the fiducial SZ bias is close to correct, the high total single-to-noise \nin Planck can be used to break\nthe measurement into\nbands in $l$ and recover the band power with errors \n\\begin{equation}\n\\left( \\Delta C_l^\\sz \\over C_l^\\sz \\right)^{-2} = {f_\\sky \\over 2}\n\\sum_{l_{\\rm band}} (2l+1)\n\\left( { C_l^\\sz \\over C_l^\\tot}\\right)^2 \\,.\n\\end{equation}\nWe give an example from monte carlo realizations of the Gaussian noise\nand sample variance from the simulations in Fig.~\\ref{fig:simultwopt}.\nNote that these are errors for a $6^\\circ \\times 6^\\circ$ section\nof the sky and should be scaled by $\\sim 0.03 f_\\sky^{-1/2} \\approx\n0.04$ for Planck.\n\nThese signal-to-noise estimates assume that both the signal and noise\nare Gaussian. Of course in reality the SZ signal is non-Gaussian.\nIn general, gravitational collapse correlates the amount of power \nin density fluctuations across all scales in the non-linear regime.\nHowever since the SZ effect probes many \nindependent density fluctuations along the line-of-sight, the central\nlimit theorem ensures that the SZ signal is far more Gaussian than\nthe density field. We can test how much this affects the signal-to-noise \nwith our simulations. Shown in Fig.~\\ref{fig:simultwopt} is the \nsampling errors on the band powers from the simulations themselves \nas compared with those from Gaussian realizations of the same power spectrum. \nThe excess variance over the Gaussian limit is small on the relevant scales \ngiven detector\nnoise limitations from Planck. \n\n\\begin{figure}[t]\n\\centerline{\\psfig{file=figure9.eps,width=3.5in,angle=-90}}\n\\caption{Cumulative signal-to-noise in the measurement of the third\nmoment, $\\Theta^3$, with top hat smoothing in multipole space (i.e. truncation\nabove $l_{\\rm max}$). The HEPT approximation to the bispectrum\nis assumed here. MAP and Boomerang (not shown) have signal-to-noise\nvalues less than $0.1$ everywhere.}\n\\label{fig:t3}\n\\end{figure}\n\n\\subsection{Skewness}\n\\label{sec:skewness}\n\nThe overall signal-to-noise for the measurement of the third moment of\nSZ effect is\n\\begin{equation}\n\\left( {S \\over N} \\right)^2 = {f_\\sky}\n\t\t{ \\left< \\Theta^3(\\bn;\\sigma) \\right>^2 \\over {\\rm Var}}\n\\end{equation}\nwhere the variance is given by \n\\begin{eqnarray}\n{\\rm Var} &=& { 1 \\over (4\\pi)^2 } \\sum_{l_1 l_2 l_3}\n\t\t{(2l_1+1)(2l_2+1)(2l_3+1) \\over 4\\pi} \\wj^2 \\nonumber\\\\\n\t\t&& \\times W_{l_1}^2(\\sigma) W_{l_2}^2(\\sigma) W_{l_3}^2(\\sigma)\n\t\t\t\t6 C_{l_1}^\\tot C_{l_2}^\\tot C_{l_3}^\\tot\\,.\n\\label{eqn:t3var}\n\\end{eqnarray}\nIn Fig.~\\ref{fig:t3}, we show the signal-to-noise for a measurement of\nthe third moment as calculated under the HEPT. We compare the\nsignal-to-noise in Planck with the ideal case of perfect\nremoval of foregrounds and detector noise, and full sky coverage. We use here a tophat window\nin multipole space out to $l_{\\rm max}$ \nto conform with other signal-to-noise considerations.\nCosmic variance and Planck detector\nnoise reduces the signal-to-noise values both at the\nlow and high end for $l_{\\rm max}$ values respectively. For Planck, the $l$ values in the\nrange of few hundred to $\\sim$ 1000 provides the maximal signal-to-noise for a\nmeasurement of the skewness. This corresponds to smoothing scales $\\sigma \n\\sim$ 10'-30' for tophat windows in angular space \n(c.f.~Fig.~\\ref{fig:skewness}). For MAP and Boomerang, the\nsignal-to-noise values are $\\lesssim$ 0.1, suggesting that a\ndetection of SZ skewness is not likely to be possible in these two experiments.\n\nAgain equation~(\\ref{eqn:t3var}) assumes Gaussian statistics for\nthe variance and ignores the sample variance of the third moment \nitself. We test this approximation in Fig.~\\ref{fig:skewness} and\nfind that it is reasonable given the level of residual noise for Planck. \nIn constructing an estimator for $S_3$, it is important\nto remove the noise bias since noise variance will always reduce the\nskewness in the map. We do this by multiplying the estimator by\n$(\\left<\\Theta_{\\rm tot}^2 \\right>/\\left<\\Theta_{\\rm SZ}^2 \\right>)^2$.\n\nFinally, note that in the noise-dominated regime\nthe signal-to-noise in $S_3$ scales strongly with the gas bias\n$S/N \\propto b_\\pi^3$, so that the detectability of this effect\ndepends strongly on currently uncertain assumptions.\n\n\n\n\n\\begin{figure}[t]\n\\centerline{\\psfig{file=figure10.eps,width=3.5in,angle=-90}}\n\\caption{Cumulative signal-to-noise for the detection of \nSZ bispectrum as a function of $l_3$ multipole. The solid line\nis the maximum signal-to-noise achievable in a perfect experiment.\n%The other curves are based on the\n%separation of SZ effect in Planck, Boomerang and MAP data. As shown,\n%Planck has a strong possibility to detect the bispectrum due to\n%SZ effect.\n}\n\\label{fig:szbispec}\n\\end{figure}\n\n\\subsection{Bispectrum}\n\nThe full bispectrum of the SZ effect contains all of the information\nabout its three-point correlations induced by the growth of structure\nbeyond the linear approximation. The skewness is simply one,\neasily measured, aspect of the bispectrum.\nThe full signal-to-noise ratio of the bispectrum is\n\\begin{equation}\n\\left( {S \\over N} \\right)^2 = \nf_\\sky \\sum_{l_1,l_2,l_3} \n\t{\\bi^2 \\over \n\t\t 6 C_{l_1}^\\tot C_{l_2}^\\tot C_{l_3}^\\tot } \\, ,\n\\label{eqn:bispecnoise}\n\\end{equation}\nwhere $C_l^\\tot$ follows Eq.~(\\ref{eqn:cltot}). We plot the bispectrum\ncumulative signal-to-noise as a function of signal $l_3$, summed over\n$l_1$ and $l_2$.\nWe refer the reader to \\cite{CooHu99} (1999) for a detailed discussion on the \nbispectrum, its variance and the calculation of signal-to-noise ratio.\n\nIn Fig.~\\ref{fig:szbispec}, we show the expected cumulative \nsignal-to-noise for the SZ bispectrum in Boomerang, MAP and Planck data and\na perfect experiment.\nThe signal-to-noise is\ncalculated\nunder the HEPT approximation for the underlying density field. \nAs shown, MAP and Boomerang\nallow reasonable limits to be placed on any non-Gaussian signal in the SZ\neffect while Planck allows a strong possibility for a detection.\n\nAgain the same caveats as to the sensitivity of the $S/N$ estimate\nto the underlying assumptions\nthat applied for the skewness also apply here. Moreover, measuring\nall the configurations of the bispectrum will be a formidable \ncomputational challenge as will control over systematic effects in the\nexperiments.\n\n\n\\subsection{Lensing Correlation}\n\nThe SZ effect and weak\ngravitational lensing of the CMB both trace large-scale structure in\nthe underlying density field. \nBy measuring the correlation, one can directly test the\nmanner in which gas pressure fluctuations trace the dark matter\ndensity fluctuations. \nThe correlation vanishes in the two-point functions since the\nlensing does not affect an isotropic CMB due to conservation\nof surface brightness. \n\nThe correlation manifests itself as a \nnon-vanishing bispectrum in the CMB at RJ\nfrequencies (\\cite{GolSpe99} 1999; \\cite{CooHu99} 1999). \nAgain\nthe cosmic variance from the primary anisotropies presents an \nobstacle for detection of the effect above the several arcminute\nscale ($l\\sim 2000$).\nWith the multifrequency cleaning of the\nSZ map presented here one can enhance the detectability of the\neffect. \n\nConsider the bispectrum composed of one $a_{l m}$ from the cleaned\nSZ map and the other two from the CMB maps. Call this the SZ-CMB-CMB\nbispectrum. The noise variance of this term will be reduced\nby a factor of $C_l^\\tot / C_l^\\cmb$ compared with the\nCMB-CMB-CMB bispectrum. As one can see from Fig.~\\ref{fig:clean}\nthis can be up to a factor of $10^3$ in the variance.\nDetails for the calculation of the CMB-CMB-CMB bispectrum\nare given in \\cite{CooHu99} (1999). Here we \nhave updated the normalization for SZ effect, taken\n$f_{\\sky}=0.65$ for Planck's useful sky coverage, and\ncompared the $S/N$ of the two bispectra.\nAs shown, the measurement using foreground cleaned Planck SZ and CMB\nmaps has a substantially higher signal-to-noise than that from\nusing the Planck CMB map alone for multipoles $l \\sim 10^2-10^3$. \n\n\nBeyond the improvement in signal-to-noise, however, \nthere is an important \nadvantage in constructing the SZ-lensing bispectrum using SZ and CMB\nmaps. A mere measurement of the bispectrum in CMB data can lead to\nsimultaneous detection of non-Gaussianities through processes other than just\nSZ-lensing cross-correlation. As discussed in \\cite{GolSpe99} (1999)\nand extended in \\cite{CooHu99} (1999), gravitational lensing\nalso correlates with other late time secondary anisotropy contributors\nsuch as integrated Sachs-Wolfe (ISW; \\cite{SacWol67} 1967) effect\nand the reionized Doppler effect. In addition to lensing correlations,\nnon-Gaussianities can also be generated through reionization and\nnon-linear growth of perturbations (\\cite{SpeGol99} 1999;\n\\cite{GolSpe99} 1999; \\cite{CooHu99} 1999). \nBispectrum measurements at a signle frequency can result in a confusion as to the relative contribution from\neach of these scenarios. In \\cite{CooHu99} (1999), we\nsuggested the possibility of using differences in individual bispectra as\na function of multipoles, \nhowever, such a separation can be problematic \ngiven that these differences are subtle (e.g.,\nFig~6 of \\cite{CooHu99} 1999). \n\nThe construction\nof the SZ-lensing bispectrum using SZ and CMB maps has the advantage\nthat one eliminates all possibilities, other than SZ, that result in a\nbispectrum. For effects related to SZ,\nthe cross-correlation of lensing and SZ should produce the dominant\nsignal; as shown in \\cite{CooHu99} (1999), bispectra signal through SZ\nand reionization effects, such as Ostriker-Vishniac (OV;\n\\cite{OstVis86} 1986), are considerably smaller.\n\nConversely, multifrequency cleaning also eliminates the SZ \ncontribution from the CMB maps and hence a main contaminant of \nthe CMB-CMB-CMB bispectrum.\nThis assists in the detection of smaller signals such as\nthe \nISW-lensing correlation, Doppler-lensing correlation or the \nnon-Gaussianity of the initial conditions. \nSuch an approach is\nhighly desirable and Planck will allow such detailed studies to be\ncarried out.\n\nA potential caveat is that as noted above, the full bispectrum \nin an all-sky satellite experiment will be difficult to measure.\n\\cite{ZalSel99} (1999) have developed a reduced set of three-point statistics\noptimized for lensing studies, based on a two point reconstruction of\nthe lensing-convergence maps from temperature gradient information. \nThey show that most of the information\nis retained in these statistics. Multifrequency cleaning improves\nthe signal-to-noise for these statistics by exactly the same factor\nas for the full bispectrum.\n\n\\begin{figure}\n\\centerline{\\psfig{file=figure11.eps,width=3.5in,angle=-90}}\n\\caption{Cumulative signal-to-noise in the measurement of the SZ-weak\ngravitational lensing cross-correlation through the bispectrum\nmeasurement in CMB data. Compared are the\nexpected signal-to-noise with (SZ-CMB-CMB) and without (CMB-CMB-CMB) \nmultifrequency isolation\nof the SZ effect for Planck and a perfect/cosmic variance limited\nexperiment. \nMultifrequency isolation provides additional\nsignal-to-noise and the opportunity to uniquely identify the bispectrum\ncontribution with the SZ effect.}\n\\label{fig:szlens}\n\\end{figure}\n\n\\section{Discussion}\n\\label{sec:discussion}\n\nWe have studied the prospects for extracting the statistical properties\nof the Sunyaev-Zel'dovich (SZ) effect associated with hot gas in \nlarge-scale structure using upcoming multifrequency CMB experiments. \nThis gas currently remains undetected but may comprise a substantial\nfraction of the present day baryons. \nThe SZ effect has a distinct spectral dependence with a null at a frequency of\n$\\sim$ 217 GHz compared with true temperature anisotropies. \nThis frequency dependence is what allows for effective separation\nof the SZ contribution with multifrequency\nCMB measurements. \n\nAs examples, we have employed the frequency and noise specifications \nof the Boomerang, MAP, Planck experiments. \nThe MAP satellite only covers frequencies at \nRJ part of the frequency spectrum. Consequently, only\nBoomerang and Planck can take full advantage of multifrequency separation of\nthe SZ and primary anisotropies. We have evaluated the\ndetection threshold for SZ power\nspectrum measurements (see Fig.~\\ref{fig:error}).\nBoomerang and MAP should provide limits on the degree\nscale fluctuations at the several \n$\\mu$K level in rms; Planck should be able to detect sub $\\mu$K signals.\n\nThe expected level of the SZ signal in the fiducial $\\Lambda$CDM\nmodel is still somewhat uncertain. We have employed a simple\nbias model for the pressure fluctuations, roughly normalized\nto recent hydrodynamic simulations\n(\\cite{Refetal99} 1999; \\cite{Seletal00} 2000), and calculated\nthe resulting signal using analytic scaling relations and particle-mesh \ndark matter simulations.\nAs hydrodynamic simulations improve, these techniques \ncan be extended with more sophisticated modeling of the\nbias. They complement hydrodynamic simulations by\nextending the dynamic range and simulated volume, the latter\nbeing important for questions of sample variance. \n\nAssuming this simplified model of the SZ signal, Planck should\nhave signal-to-noise per multipole of order unity\nfor $l < 1000$. Although the recovered maps are then somewhat \nnoisy, they are sufficient for precise determinations of \nlow order statistics such as the SZ power spectrum, bispectrum\nand skewness (see Figs.~\\ref{fig:simultwopt}-\\ref{fig:szbispec}).\nThe skewness in principle can be used to separate the pressure bias\nfrom the underlying amplitude of the density fluctuations.\nThe full bispectrum contains significantly more information but will\nbe difficult to extract in its entirety.\nCurrent methods for measuring the bispectrum, tested with the \nCOBE data, have concentrated at measuring specific modes such as\n$l_1 = l_2 =l_3 = l$ (\\cite{Feretal98} 1998). \nMore work will clearly be required, \nespecially in understanding the systematic errors at a \nsufficient level, but the wealth of information potentially\npresent in the bispectrum should motivate efforts.\n\nNote however that the non-Gaussianity in the SZ signal is not very strong\ndue to the fact that it is constructed from many independent pressure\nfluctuations along the line of sight. As a consequence, we expect that\nsignal-to-noise ratios can be estimated by Gaussian approximations, \nbut that techniques that try to improve the SZ-primary separation\nbased on non-Gaussianity (\\cite{Hobetal98} 1998; \\cite{AghFor99} 1999)\nmay not be particularly effective for this signal. \n\nWe caution the reader that our oversimplification of the SZ signal\ncan cause problems for a naive interpretation of future detections.\nFor example, \\cite{Seletal00} (2000) find that the SZ power spectrum\nin their simulations is dominated by shot noise from the rare hot \nclusters not included in our modeling.\nFortunately since these contributions are highly non-Gaussian, they can \ncan readily be identified and removed. At the very least, $X$-ray\nbright clusters can be externally identified and removed; this has\nbeen shown to substantially reduce the shot noise contribution (\\cite{KomKit99} 1999).\nThe effect we are modeling should be understood as the signal\nin fields without such clusters. \n\nAnother means of separating the SZ signal from large-scale structure\nfrom that of massive clusters is to cross correlate it with other \ntracers of large-scale structure that are less sensitive to highly\noverdense regions. \nAn added benefit is that such a cross-correlation will \nalso empirically measure the extent to which pressure fluctuations\nfollow mass fluctuations.\nThe CMB anisotropies themselves\ncarry one such tracer in the form of the convergence from \nweak lensing. It manifests itself as a three-point correlation \nor bispectrum (\\cite{GolSpe99} 1999) but without frequency\ninformation it is severely sample-variance limited due to \nconfusion noise from primary anisotropies. \nMeasuring the SZ-lensing correlation using the cleaned SZ maps\nimproves the signal-to-noise for the detection by over an order\nof magnitude at degree scales. Furthermore, the techniques\nintroduced by \\cite{ZalSel99} (1999) provide a concrete algorithm\nfor extracting most of the three-point signal without\nrecourse to measuring all the configurations of the bispectrum. \nConversely, SZ removal from\nthe CMB maps themselves can assist in the detection of\nother smaller bispectrum signals by eliminating one source\nof confusion noise. \n\n\nThe cross-correlation coefficient between the SZ effect and CMB weak\nlensing is relatively \nmodest ($\\sim$ 0.5, see \\cite{Seletal00} 2000). This is due to\nthe fact that the SZ effect is a tracer of the nearby universe while CMB\nlensing is maximally sensitive to structure at $z\\sim 3$. A higher\ncorrelation is expected if SZ is cross-correlated with an\nexternal probe of low redshift structure.\n\\cite{PeiSpe00} (2000)\nsuggested the cross-correlation of MAP CMB data and\nSloan\\footnote{http://www.sdss.org} galaxy data.\nAn improved approach would be to use the Planck derived SZ map\nrather than a CMB map.\nUsing a SZ map reduces noise from the primary anisotropies\nand guarantees that any\ndetection is due to correlations with the SZ effect. \nExtending the calculations in\n\\cite{PeiSpe00} (2000) with the Planck generated\nSZ map, we\nfind signal-to-noise ratios which are on average greater by a factor of\n$\\sim$ 10 when compared to signal-to-noise values using MAP CMB map.\nIn fact with redshifts for galaxies, Planck SZ map can be\ncross-correlated in redshifts bins to study the \nredshift evolution of the gas. \nOther promising possibilities include cross correlation with \nsoft X-ray background measurements,\nas well as ultraviolet and soft X-ray absorption line studies. \n\n\nAll these considerations imply a bright future for\nSZ studies of the hot gas associated with large-scale structure\nwith wide-field multifrequency CMB observations. \nIts detailed properties should be revealed in its non-Gaussianity and\ncorrelation with other tracers of large-scale structure. \n\n\n\\acknowledgments\nWe thank Martin White for permission to adapt his PM ray tracing \ncode for these purposes. We acknowledge \nuseful discussions with Lloyd Knox, Joe Mohr, Roman Scoccimarro, Ned Wright and\nMatias Zaldarriaga. ARC is grateful to John \nCarlstrom, Michael Turner and Don York for helpful advice and financial\nsupport. WH is supported by the Keck Foundation, a Sloan Fellowship,\nand NSF-9513835. MT acknowledges NASA grant NAG5-6034 and Hubble\nFellowship HF-01084.01-96A from STScI, operate by AURA, Inc. under\nNASA contract NAS5-26555. We acknowledge the use of CMBFAST\n(\\cite{SelZal96} 1996).\n\n\n\n\\begin{thebibliography}{99}\n\\frenchspacing\n \n\\bibitem[Aghanim et al.]{Aghetal96}\n Aghanim, N., Desert, F.X., Puget, J.L, \\& Gispert, R. 1996, A\\&A, 311 1\n\n \n%\\bibitem[Banday et al.]{Banetal99}\n% Banday, A.J., Zaroubi, S. \\& Gorski, K.M., ApJ submitted\n% (astro-ph/9908070)\n \n%\\bibitem[Bernardeau]{Ber95}\n%\tBernardeau, F. 1995, A\\&A, 301, 309\n\n%\\bibitem[Bernardeau et al]{Beretal97}\n%\tBernardeau, F., Van Waerbeke, L., Mellier, Y. 1997, A\\&A, 322, 1\n\\bibitem[Aghanim \\& Forni]{AghFor99}\n Aghanim, N., Forni, O. 1999, A\\&A, 347 409 \n\n\\bibitem[Bouchet \\& Gispert]{BouGis99}\n\tBouchet, F., Gispert, R., 1999, NewA, 4 443 \n\n\\bibitem[Briel \\& Henry]{BriHen95}\n Briel, U. G., Henry, J. P., 1995, A\\&A, 302, L9\n\n%\\bibitem[Bromley \\& Tegmark]{BroTeg99}\n% Bromley, B., Tegmark, M. ApJL in press (astro-ph/9904254)\n \n%\\bibitem[Bruscoli et al]{Bruetal99}\n%\tBruscoli, M., Ferrara, A., Fabbri, R., Ciardi, B. 1999, astro-ph/991146%7\n\n\\bibitem[Bouchet et al]{Bouetal95}\n\tBouchet, F. R. et al. 1995, Space Sci Rev., 84, 37\n\n\\bibitem[Bunn \\& White]{BunWhi97}\n Bunn, E. F., White, M. 1997, ApJ, 480, 6\n \n\\bibitem[Carlstrom et al]{Caretal96}\n Carlstrom, J. E., Joy, M., Grego, L. 1996, ApJ, 456, L75\n\n%\\bibitem[Carlstrom et al]{Caretal99}\n% Carlstrom, J. E., Joy, M., Grego, L., Holder, G. P., Holzapfel,\n%W. L., Mohr, J. J., Patel, S. K., Reese, E. D. 1999, astro-ph/9905255\n\n\\bibitem[Cen et al]{Cenetal95}\n Cen, R., Kang, H., Ostriker, J. P., Ryu, D. 1995, ApJ, 451,\n436\n\n\\bibitem[Cen \\& Ostriker]{CenOst99}\n Cen, R., Ostriker, J. P. 1999, ApJ, 514, 1\n \n\\bibitem[Cooray \\& Hu]{CooHu99}\n\tCooray, A. R., Hu, W. 1999, ApJ in press, astro-ph/9910397\n\n\\bibitem[da Silva et al.]{daS99}\n da Silva, A. C., Barbosa, D., Liddle, A. R., Thomas,\nP. A. 1999, MNRAS, submitted, astro-ph/9907224\n \n%\\bibitem[Eisenstein et al]{Eisetal99}\n% Eisenstein, D.J. Hu, W., Tegmark, M. 1999, ApJ, 518, 2\n\n%\\bibitem[Eisenstein \\& Hu]{EisHu99}\n% Eisenstein, D.J. \\& Hu, W. 1999, ApJ, 511, 5\n \n%\\bibitem[Falk et al.]{Falk93}\n% Falk, T., Rangarajan, R., Frednicki, M. 1993, ApJ, 403, L1\n \n \n\\bibitem[Ferreira et al.]{Feretal98}\n Ferreira, P.G., Magueijo, J., Gorksi, K.M. 1998, ApJ, 503, 1\n \n%\\bibitem[Fry]{Fry84}\n%\tFry, J. N., ApJ, 277, L5 \n\n\\bibitem[Fry \\& Gaztanaga]{FryGaz93}\n\tFry, J.N., Gaztanaga, E. 1993, ApJ, 413 447\n\n\\bibitem[Fukugita et al]{Fuketal98}\n Fukugita, M., Hogan, C. J., Peebles, P. J. E. 1998, ApJ, 503, 518\n\n\n%\\bibitem[Gangui \\& Martin]{GanMar99}\n% Gangui, A., Martin, J., MNRAS submitted\n% (astro-ph/9908009)\n \n%\\bibitem[Gangui et al]{Ganetal94}\n% Gangui, A., Lucchin, F., Matarrese, S. \\& Mollerach, S.\n% 1994, ApJ, 430, 447\n \n\\bibitem[Goldberg \\& Spergel]{GolSpe99}\n Goldberg, D. M., Spergel, D. N. 1999, PRD, 59, 103002\n\n%\\bibitem[Gnedin \\& Hui]{GneHui98}\n%Gnedin, N. Y., Hui, L. 1998, MNRAS, 296, 44\n\n%\\bibitem[Griffiths et al.]{Grietal99}\n% Griffiths, L. M., Barbosa, D., Liddle, A. R. 1999, MNRAS, 308, 845.\n \n%\\bibitem[Gruzinov \\& Hu]{GruHu98}\n% Gruzinov, A., Hu, W. 1998, ApJ, 508. 435 \n \n\\bibitem[Haehnelt \\& Tegmark]{HaeTeg96}\n\tHaehnelt M. G., Tegmark, M. 1996, MNRAS, 279, 545\n\n\n\n%\\bibitem[Haiman \\& Knox]{HaiKno99}\n% Haiman, Z., \\& Knox, L. 1999, in {\\it Microwave Foregrounds,}\n%ed. A. de Oliveira-Costa \\& M. Tegmark (ASP: San Fransisco), astro-ph/9902311\n \n%\\bibitem[Hinshaw et al]{Hinetal95}\n% Hinshaw, G., Banday, A.J., Bennett, C.L., Gorski, K.M.,\n% \\& Kogut, A 1995, ApJ, 446, 67\n \n%\\bibitem[Heavens]{Hea98}\n% Heavens, A. 1998, MNRAS, 299, 805\n \n\\bibitem[Hobson et al]{Hobetal98}\n\tHobson, M. P., Jones, A. W., Lasenby, A. N., Bouchet,\nF. R. 1998, MNRAS, 299, 895\n\n%\\bibitem[Holzapfel et al]{Holetal99}\n%\tHolzapfel, W. L., Carlstrom, J. E., Grego, L., Holder, G.,\n%Joy, M., Reese, E. D. 1999, astro-ph/9912010\n\n\\bibitem[Hu]{Hu00a}\n Hu, W. 2000a, ApJ, 529, 12\n\n\\bibitem[Hu]{Hu00b}\n Hu, W. 2000b, PRD submitted, astro-ph/0001303\n \n%\\bibitem[Hu \\& White]{HuWhi96}\n% Hu, W. \\& White M. 1996, A\\&A, 315, 33\n\n\\bibitem[Hui]{Hui99}\n Hui, L. 1999, ApJ, 519, L9\n \n\\bibitem[Jones et al]{Jonetal93}\nJones, M. Saunders, R., Alexander, P., et al. 1993, Nat, 365, 320\n\n\\bibitem[Jungman et al.]{Junetal96}\n\tJungman, G., Kamionkowski, M., Kosowsky, A., \n\tSpergel, D.N., 1996, Phys. Rev. D, 54, 1332\t\n\n%\\bibitem[Kaiser]{Kai84}\n% Kaiser, N. 1984, ApJ, 282, 374\n \n%\\bibitem[Kaiser]{Kai92}\n% Kaiser, N. 1992, ApJ, 388, 286\n \n \n%\\bibitem[Kendall \\& Stuart]{KenStua69}\n% Kendall, M. G., Stuart, A. 1969, Advanced Theory of\n%Statistics, Vol. II (London: Griffin)\n \n \n%\\bibitem[Knox]{Kno95}\n% Knox, L. 1995, PRD, 48, 3502\n \n%\\bibitem[Knox et al.]{KnoScoDod98}\n% Knox, L., Scoccimarro, R., \\& Dodelson, S. 1998, Phys. Rev. Lett.,\n% 81, 2004\n \n\n\\bibitem[Komatsu \\& Kitayama]{KomKit99}\nKomatsu, E. Kitayama, T., 1999, ApJ, 526, L1\n\n\\bibitem[Kull \\& B\\\"ohringer]{KulBoh99}\n Kull, A., B\\\"ohringer, H. 1999, A\\&A, 341, 23\n\n\\bibitem[Limber]{Lim54}\n Limber, D. 1954, ApJ, 119, 655\n \n%\\bibitem[Luo]{Luo94}\n% Luo, X. 1994, ApJ, 1994, ApJ, 427, 71\n \n%\\bibitem[Luo \\& Schramm]{LuoSch93}\n% Luo, X. \\& Schramm, D.N 1993, PRL, 71,1124\n \n%\\bibitem[Matarrese et al]{Matetal97}\n%\tMatarrese, S., Verde, L., Heavens, A. F. 1997, MNRAS, 290, 651\n\n\\bibitem[Mo, Jing \\& White]{MoJinWhi97}\n\tMo, H.J., Jing, Y.P., White, S.D.M. 1997, MNRAS, 284, 189\n\n\\bibitem[Ostriker \\& Vishniac]{OstVis86}\n Ostriker, J.P., Vishniac, E.T. 1986, Nature, 322, 804\n \n%\\bibitem[Pando et al.]{Pando98}\n% Pando, J. Vallas-Gabaud D. \\& Fang, L. 1998, PRL, 79, 1611\n \n\n%\\bibitem[Peacock \\& Dodds]{PeaDod94}\n% Peacock, J.A., Dodds, S.J. 1994, MNRAS, 267, 1020\n\n\\bibitem[Peacock \\& Dodds]{PeaDod96}\n Peacock, J.A., Dodds, S.J. 1996, MNRAS, 280, L19\n \n%\\bibitem[Peebles]{Pee80}\n% Peebles, P.J.E. 1980, The Large-Scale Structure of the\n%Universe, (Princeton: Princeton Univ. Press)\n \n\\bibitem[Pen]{Pen99}\n Pen, U.-L. 1999, ApJ, 510, 1\n\n\n\\bibitem[Persi et al]{Peretal95}\nPersi, F. M., Spergel, D. N., Cen, R., Ostriker, J. P. 1995, ApJ, 442,\n1\n\n\\bibitem[Peiris \\& Spergel]{PeiSpe00}\n\tPeiris, H. V., Spergel, D. N. 2000, ApJ submitted, astro-ph/001393\n\n\\bibitem[Pointecouteau et al]{Poietal98}\nPointecouteau, E., Giard, M., Barret, D. 1998, A\\&A, 336, 44\n\n\n%\\bibitem[Rees \\& Sciama]{ReeSci68} Rees, M. J., Sciama, D. N. 1968,\n%Nature. 519. 611\n \n\\bibitem[Refregier et al.]{Refetal99}\n\tRefregier, A., Komatsu, E., Spergel, D. N., Pen, U.-L. 1999,\n PRD submitted, astro-ph/9912180\n \n\\bibitem[Sachs \\& Wolfe]{SacWol67} Sachs, R. K., Wolfe, A. M.,\n1967, ApJ, 147, 73\n \n\\bibitem[Scharf et al]{Schetal00}\n Scharf, C., Donahue, M., Voit, G. M., Rosati, P., Postman,\nM. 2000, ApJ, 528, L73\n\n\n%\\bibitem[Schulten \\& Gordon]{SchGor75}\n% Schulten, K. \\& Gordon, R.G. 1975, J. Math. Phys., 16, 1971\n \n\\bibitem[Scoccimarro \\& Frieman]{ScoFri99}\n\tScoccimarro, R., Frieman, J. A. 1999, ApJ, 520, 35\n\n\\bibitem[Seljak et al.]{Seletal00}\n\tSeljak, U, Burwell, J., Pen, U.-L. 2000, PRD submitted, astro-ph/001120\n\n\n%\\bibitem[Seljak]{Sel96}\n% Seljak, U. 1996, ApJ, 460, 549\n \n\\bibitem[Seljak \\& Zaldarriaga]{SelZal96}\n Seljak, U., Zaldarriaga, M. 1996,\n ApJ, 469, 437\n \n%\\bibitem[Seljak \\& Zaldarriaga]{SelZal99}\n% Seljak, U. \\& Zaldarriaga, M. 1999,\n% preprint, astro-ph/9811123\n \n \n\\bibitem[Spergel \\& Goldberg]{SpeGol99}\n Spergel, D. N., Goldberg, D. M. 1999, PRD, 59, 103001\n \n%\\bibitem[Subrahmanyan et al]{Subetal98}\n%\tSubrahmanyan, R., Kesteven, M. J., Ekers, R. D., Sinclair, M.,\n%Silk, J. 1998, MNRAS, 298, 1189\n\n\\bibitem[Sunyaev \\& Zel'dovich]{SunZel80}\n Sunyaev, R.A., Zel'dovich, Ya. B. 1980, MNRAS, 190, 413\n \n\\bibitem[Tegmark et al.]{Tegetal99}\n Tegmark, M., Eisenstein, D.J., Hu, W., de Oliveira-Costa, A.\n ApJ, 1999, in press, astro-ph/9905257\n \n%\\bibitem[Vishniac]{Vis87}\n% Vishniac, E.T. 1987, ApJ, 322, 597\n \n%\\bibitem[Wang \\& Kamionkowski]{WanKam99}\n% Wang, L. \\& Kamionkowski, M. 1999, preprint, astro-ph/9907431\n\n\\bibitem[White \\& Hu]{WhiHu99}\n\tWhite, M., Hu, W., 1999, ApJ in press, astro-ph/9909165 \n\n%\\bibitem[White et al.]{Whietal99}\n% White, M., Carlstrom, J.E., Dragovan, M. \\& Holzapfel, W.L. 1999\n% ApJ, 514, 12\n \n\\bibitem[Zaldarriaga \\& Seljak]{ZalSel99}\n Zaldarriaga, M., Seljak, U. 1999, Phys. Rev. D. 59, 123507 \n \n\\end{thebibliography}\n\n\n\n\\end{document}\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002238.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\frenchspacing\n \n\\bibitem[Aghanim et al.]{Aghetal96}\n Aghanim, N., Desert, F.X., Puget, J.L, \\& Gispert, R. 1996, A\\&A, 311 1\n\n \n%\\bibitem[Banday et al.]{Banetal99}\n% Banday, A.J., Zaroubi, S. \\& Gorski, K.M., ApJ submitted\n% (astro-ph/9908070)\n \n%\\bibitem[Bernardeau]{Ber95}\n%\tBernardeau, F. 1995, A\\&A, 301, 309\n\n%\\bibitem[Bernardeau et al]{Beretal97}\n%\tBernardeau, F., Van Waerbeke, L., Mellier, Y. 1997, A\\&A, 322, 1\n\\bibitem[Aghanim \\& Forni]{AghFor99}\n Aghanim, N., Forni, O. 1999, A\\&A, 347 409 \n\n\\bibitem[Bouchet \\& Gispert]{BouGis99}\n\tBouchet, F., Gispert, R., 1999, NewA, 4 443 \n\n\\bibitem[Briel \\& Henry]{BriHen95}\n Briel, U. G., Henry, J. P., 1995, A\\&A, 302, L9\n\n%\\bibitem[Bromley \\& Tegmark]{BroTeg99}\n% Bromley, B., Tegmark, M. ApJL in press (astro-ph/9904254)\n \n%\\bibitem[Bruscoli et al]{Bruetal99}\n%\tBruscoli, M., Ferrara, A., Fabbri, R., Ciardi, B. 1999, astro-ph/991146%7\n\n\\bibitem[Bouchet et al]{Bouetal95}\n\tBouchet, F. R. et al. 1995, Space Sci Rev., 84, 37\n\n\\bibitem[Bunn \\& White]{BunWhi97}\n Bunn, E. F., White, M. 1997, ApJ, 480, 6\n \n\\bibitem[Carlstrom et al]{Caretal96}\n Carlstrom, J. E., Joy, M., Grego, L. 1996, ApJ, 456, L75\n\n%\\bibitem[Carlstrom et al]{Caretal99}\n% Carlstrom, J. E., Joy, M., Grego, L., Holder, G. P., Holzapfel,\n%W. L., Mohr, J. J., Patel, S. K., Reese, E. D. 1999, astro-ph/9905255\n\n\\bibitem[Cen et al]{Cenetal95}\n Cen, R., Kang, H., Ostriker, J. P., Ryu, D. 1995, ApJ, 451,\n436\n\n\\bibitem[Cen \\& Ostriker]{CenOst99}\n Cen, R., Ostriker, J. P. 1999, ApJ, 514, 1\n \n\\bibitem[Cooray \\& Hu]{CooHu99}\n\tCooray, A. R., Hu, W. 1999, ApJ in press, astro-ph/9910397\n\n\\bibitem[da Silva et al.]{daS99}\n da Silva, A. C., Barbosa, D., Liddle, A. R., Thomas,\nP. A. 1999, MNRAS, submitted, astro-ph/9907224\n \n%\\bibitem[Eisenstein et al]{Eisetal99}\n% Eisenstein, D.J. Hu, W., Tegmark, M. 1999, ApJ, 518, 2\n\n%\\bibitem[Eisenstein \\& Hu]{EisHu99}\n% Eisenstein, D.J. \\& Hu, W. 1999, ApJ, 511, 5\n \n%\\bibitem[Falk et al.]{Falk93}\n% Falk, T., Rangarajan, R., Frednicki, M. 1993, ApJ, 403, L1\n \n \n\\bibitem[Ferreira et al.]{Feretal98}\n Ferreira, P.G., Magueijo, J., Gorksi, K.M. 1998, ApJ, 503, 1\n \n%\\bibitem[Fry]{Fry84}\n%\tFry, J. N., ApJ, 277, L5 \n\n\\bibitem[Fry \\& Gaztanaga]{FryGaz93}\n\tFry, J.N., Gaztanaga, E. 1993, ApJ, 413 447\n\n\\bibitem[Fukugita et al]{Fuketal98}\n Fukugita, M., Hogan, C. J., Peebles, P. J. E. 1998, ApJ, 503, 518\n\n\n%\\bibitem[Gangui \\& Martin]{GanMar99}\n% Gangui, A., Martin, J., MNRAS submitted\n% (astro-ph/9908009)\n \n%\\bibitem[Gangui et al]{Ganetal94}\n% Gangui, A., Lucchin, F., Matarrese, S. \\& Mollerach, S.\n% 1994, ApJ, 430, 447\n \n\\bibitem[Goldberg \\& Spergel]{GolSpe99}\n Goldberg, D. M., Spergel, D. N. 1999, PRD, 59, 103002\n\n%\\bibitem[Gnedin \\& Hui]{GneHui98}\n%Gnedin, N. Y., Hui, L. 1998, MNRAS, 296, 44\n\n%\\bibitem[Griffiths et al.]{Grietal99}\n% Griffiths, L. M., Barbosa, D., Liddle, A. R. 1999, MNRAS, 308, 845.\n \n%\\bibitem[Gruzinov \\& Hu]{GruHu98}\n% Gruzinov, A., Hu, W. 1998, ApJ, 508. 435 \n \n\\bibitem[Haehnelt \\& Tegmark]{HaeTeg96}\n\tHaehnelt M. G., Tegmark, M. 1996, MNRAS, 279, 545\n\n\n\n%\\bibitem[Haiman \\& Knox]{HaiKno99}\n% Haiman, Z., \\& Knox, L. 1999, in {\\it Microwave Foregrounds,}\n%ed. A. de Oliveira-Costa \\& M. Tegmark (ASP: San Fransisco), astro-ph/9902311\n \n%\\bibitem[Hinshaw et al]{Hinetal95}\n% Hinshaw, G., Banday, A.J., Bennett, C.L., Gorski, K.M.,\n% \\& Kogut, A 1995, ApJ, 446, 67\n \n%\\bibitem[Heavens]{Hea98}\n% Heavens, A. 1998, MNRAS, 299, 805\n \n\\bibitem[Hobson et al]{Hobetal98}\n\tHobson, M. P., Jones, A. W., Lasenby, A. N., Bouchet,\nF. R. 1998, MNRAS, 299, 895\n\n%\\bibitem[Holzapfel et al]{Holetal99}\n%\tHolzapfel, W. L., Carlstrom, J. E., Grego, L., Holder, G.,\n%Joy, M., Reese, E. D. 1999, astro-ph/9912010\n\n\\bibitem[Hu]{Hu00a}\n Hu, W. 2000a, ApJ, 529, 12\n\n\\bibitem[Hu]{Hu00b}\n Hu, W. 2000b, PRD submitted, astro-ph/0001303\n \n%\\bibitem[Hu \\& White]{HuWhi96}\n% Hu, W. \\& White M. 1996, A\\&A, 315, 33\n\n\\bibitem[Hui]{Hui99}\n Hui, L. 1999, ApJ, 519, L9\n \n\\bibitem[Jones et al]{Jonetal93}\nJones, M. Saunders, R., Alexander, P., et al. 1993, Nat, 365, 320\n\n\\bibitem[Jungman et al.]{Junetal96}\n\tJungman, G., Kamionkowski, M., Kosowsky, A., \n\tSpergel, D.N., 1996, Phys. Rev. D, 54, 1332\t\n\n%\\bibitem[Kaiser]{Kai84}\n% Kaiser, N. 1984, ApJ, 282, 374\n \n%\\bibitem[Kaiser]{Kai92}\n% Kaiser, N. 1992, ApJ, 388, 286\n \n \n%\\bibitem[Kendall \\& Stuart]{KenStua69}\n% Kendall, M. G., Stuart, A. 1969, Advanced Theory of\n%Statistics, Vol. II (London: Griffin)\n \n \n%\\bibitem[Knox]{Kno95}\n% Knox, L. 1995, PRD, 48, 3502\n \n%\\bibitem[Knox et al.]{KnoScoDod98}\n% Knox, L., Scoccimarro, R., \\& Dodelson, S. 1998, Phys. Rev. Lett.,\n% 81, 2004\n \n\n\\bibitem[Komatsu \\& Kitayama]{KomKit99}\nKomatsu, E. Kitayama, T., 1999, ApJ, 526, L1\n\n\\bibitem[Kull \\& B\\\"ohringer]{KulBoh99}\n Kull, A., B\\\"ohringer, H. 1999, A\\&A, 341, 23\n\n\\bibitem[Limber]{Lim54}\n Limber, D. 1954, ApJ, 119, 655\n \n%\\bibitem[Luo]{Luo94}\n% Luo, X. 1994, ApJ, 1994, ApJ, 427, 71\n \n%\\bibitem[Luo \\& Schramm]{LuoSch93}\n% Luo, X. \\& Schramm, D.N 1993, PRL, 71,1124\n \n%\\bibitem[Matarrese et al]{Matetal97}\n%\tMatarrese, S., Verde, L., Heavens, A. F. 1997, MNRAS, 290, 651\n\n\\bibitem[Mo, Jing \\& White]{MoJinWhi97}\n\tMo, H.J., Jing, Y.P., White, S.D.M. 1997, MNRAS, 284, 189\n\n\\bibitem[Ostriker \\& Vishniac]{OstVis86}\n Ostriker, J.P., Vishniac, E.T. 1986, Nature, 322, 804\n \n%\\bibitem[Pando et al.]{Pando98}\n% Pando, J. Vallas-Gabaud D. \\& Fang, L. 1998, PRL, 79, 1611\n \n\n%\\bibitem[Peacock \\& Dodds]{PeaDod94}\n% Peacock, J.A., Dodds, S.J. 1994, MNRAS, 267, 1020\n\n\\bibitem[Peacock \\& Dodds]{PeaDod96}\n Peacock, J.A., Dodds, S.J. 1996, MNRAS, 280, L19\n \n%\\bibitem[Peebles]{Pee80}\n% Peebles, P.J.E. 1980, The Large-Scale Structure of the\n%Universe, (Princeton: Princeton Univ. Press)\n \n\\bibitem[Pen]{Pen99}\n Pen, U.-L. 1999, ApJ, 510, 1\n\n\n\\bibitem[Persi et al]{Peretal95}\nPersi, F. M., Spergel, D. N., Cen, R., Ostriker, J. P. 1995, ApJ, 442,\n1\n\n\\bibitem[Peiris \\& Spergel]{PeiSpe00}\n\tPeiris, H. V., Spergel, D. N. 2000, ApJ submitted, astro-ph/001393\n\n\\bibitem[Pointecouteau et al]{Poietal98}\nPointecouteau, E., Giard, M., Barret, D. 1998, A\\&A, 336, 44\n\n\n%\\bibitem[Rees \\& Sciama]{ReeSci68} Rees, M. J., Sciama, D. N. 1968,\n%Nature. 519. 611\n \n\\bibitem[Refregier et al.]{Refetal99}\n\tRefregier, A., Komatsu, E., Spergel, D. N., Pen, U.-L. 1999,\n PRD submitted, astro-ph/9912180\n \n\\bibitem[Sachs \\& Wolfe]{SacWol67} Sachs, R. K., Wolfe, A. M.,\n1967, ApJ, 147, 73\n \n\\bibitem[Scharf et al]{Schetal00}\n Scharf, C., Donahue, M., Voit, G. M., Rosati, P., Postman,\nM. 2000, ApJ, 528, L73\n\n\n%\\bibitem[Schulten \\& Gordon]{SchGor75}\n% Schulten, K. \\& Gordon, R.G. 1975, J. Math. Phys., 16, 1971\n \n\\bibitem[Scoccimarro \\& Frieman]{ScoFri99}\n\tScoccimarro, R., Frieman, J. A. 1999, ApJ, 520, 35\n\n\\bibitem[Seljak et al.]{Seletal00}\n\tSeljak, U, Burwell, J., Pen, U.-L. 2000, PRD submitted, astro-ph/001120\n\n\n%\\bibitem[Seljak]{Sel96}\n% Seljak, U. 1996, ApJ, 460, 549\n \n\\bibitem[Seljak \\& Zaldarriaga]{SelZal96}\n Seljak, U., Zaldarriaga, M. 1996,\n ApJ, 469, 437\n \n%\\bibitem[Seljak \\& Zaldarriaga]{SelZal99}\n% Seljak, U. \\& Zaldarriaga, M. 1999,\n% preprint, astro-ph/9811123\n \n \n\\bibitem[Spergel \\& Goldberg]{SpeGol99}\n Spergel, D. N., Goldberg, D. M. 1999, PRD, 59, 103001\n \n%\\bibitem[Subrahmanyan et al]{Subetal98}\n%\tSubrahmanyan, R., Kesteven, M. J., Ekers, R. D., Sinclair, M.,\n%Silk, J. 1998, MNRAS, 298, 1189\n\n\\bibitem[Sunyaev \\& Zel'dovich]{SunZel80}\n Sunyaev, R.A., Zel'dovich, Ya. B. 1980, MNRAS, 190, 413\n \n\\bibitem[Tegmark et al.]{Tegetal99}\n Tegmark, M., Eisenstein, D.J., Hu, W., de Oliveira-Costa, A.\n ApJ, 1999, in press, astro-ph/9905257\n \n%\\bibitem[Vishniac]{Vis87}\n% Vishniac, E.T. 1987, ApJ, 322, 597\n \n%\\bibitem[Wang \\& Kamionkowski]{WanKam99}\n% Wang, L. \\& Kamionkowski, M. 1999, preprint, astro-ph/9907431\n\n\\bibitem[White \\& Hu]{WhiHu99}\n\tWhite, M., Hu, W., 1999, ApJ in press, astro-ph/9909165 \n\n%\\bibitem[White et al.]{Whietal99}\n% White, M., Carlstrom, J.E., Dragovan, M. \\& Holzapfel, W.L. 1999\n% ApJ, 514, 12\n \n\\bibitem[Zaldarriaga \\& Seljak]{ZalSel99}\n Zaldarriaga, M., Seljak, U. 1999, Phys. Rev. D. 59, 123507 \n \n\\end{thebibliography}"
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astro-ph0002239
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One-Line Redshifts and \\ Searches for High-Redshift \lya\ Emission\altaffilmark{1}
|
[
{
"author": "Daniel Stern\\altaffilmark{2}"
},
{
"author": "Andrew Bunker\\altaffilmark{3}"
},
{
"author": "Hyron Spinrad"
}
] |
We report the serendipitous discovery of two objects close in projection with fairly strong emission lines at long wavelength ($\lambda\sim 9190$\,\AA). One (A) seems not to be hosted by any galaxy brighter than $V_{555}=27.5$, or $I_{814}=26.7$ (Vega-based 3$\sigma$ limits in 1\farcs0 diameter apertures), while the other line is associated with a faint ($I_{814}\simeq 24.4$) red galaxy (B) offset by 2\farcs7 and 7 \AA\ spectrally. Both lines are broad (FWHM $\approx 700$\,km\,s$^{-1}$), extended spatially, and have high equivalent widths ($W_\lambda^{obs}({A}) > 1225$ \AA, 95\% confidence limit; $W_\lambda^{obs}({B}) \approx 150$ \AA). No secondary spectral features are detected for galaxy A. Blue continuum and the marginal detection of a second weak line in the spectrum of galaxy B is consistent with \oxytwo\ (the strong line) and \magtwo\ (the weak line) at $z = 1.466$. By association, galaxy A is likely at $z=1.464$, implying a rest-frame equivalent width of the \oxytwo\ emission line in excess of 600\,\AA\ and a projected separation of 30~$h_{50}^{-1}$~kpc for the galaxy pair. Conventional wisdom states that isolated emission lines with rest-frame equivalent widths larger than $\sim 200$ \AA\, are almost exclusively \lya. This moderate-redshift discovery therefore compromises recent claims of high-redshift \lya\ emitters for which other criteria (\ie line profile, associated continuum decrements) are not reported. We discuss observational tests to distinguish \lya\ emitters at high redshift from foreground systems.
|
[
{
"name": "stern.tex",
"string": "\n%% --------------------------------------------------------------------\n%% Fri Dec 17 13:17:48 1999\n%% This file was generated automagically from the files\n%% ser2pap.bbl and ser2pap.tex using\n%% nat2jour.pl\n%% All citations have been inlined and dependencies on the natbib\n%% package have been removed so that this file (together with\n%% ser2pap-aas.bbl) should be suitable for submission to journals with\n%% the citation styles of ApJ or MNRAS.\n%% --------------------------------------------------------------------\n\n%\\documentstyle[12pt,aasms4]{article}\n\\documentstyle[11pt,aaspp4,flushrt]{article}\n%\\citestyle{aa}\n\n\\slugcomment{\\it to appear in The Astrophysical Journal (July 1, 2000)}\n\\lefthead{Stern et al.}\n\\righthead{Cosmological One-Liners }\n\n%GOOD AASTEX DEFINITIONS\n\\def\\cf{{c.f.,~}}\n\\def\\ie{{i.e.,~}}\n\\def\\eg{{e.g.,~}}\n\\def\\etal{{et al.~}}\n\n\\def\\deg{\\ifmmode {^{\\circ}}\\else {$^\\circ$}\\fi}\n\\def\\hr{$^{h}$}\n\\def\\min{$^{m}$}\n\\def\\secper{\\ifmmode \\rlap.{^{s}}\\else $\\rlap{.}{^{s}} $\\fi}\n\\def\\ew{equivalent width}\n\n\\def\\kms{\\ifmmode {\\rm\\,km\\,s^{-1}}\\else\n ${\\rm\\,km\\,s^{-1}}$\\fi}\n\\def\\kmsMpc{\\ifmmode {\\rm\\,km\\,s^{-1}\\,Mpc^{-1}}\\else\n ${\\rm\\,km\\,s^{-1}\\,Mpc^{-1}}$\\fi}\n\\def\\ergcm2s{\\ifmmode {\\rm\\,ergs\\,cm^{-2}\\,s^{-1}}\\else\n ${\\rm\\,ergs\\,cm^{-2}\\,s^{-1}}$\\fi}\n\\def\\ergsHz{\\ifmmode {\\rm\\,ergs\\,s^{-1}\\,Hz^{-1}}\\else\n ${\\rm\\,ergs\\,s^{-1}\\,Hz^{-1}}$\\fi}\n\\def\\ergs{\\ifmmode {\\rm\\,ergs\\,s^{-1}}\\else\n ${\\rm\\,ergs\\,s^{-1}}$\\fi}\n\\def\\WHz{\\ifmmode {\\rm\\,W\\,Hz^{-1}}\\else\n ${\\rm\\,W\\,Hz^{-1}}$\\fi}\n\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\def\\simlt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}}\n\\def\\simgt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}}\n\n\\def\\hone{\\ion{H}{1}}\n\\def\\htwo{\\ion{H}{2}}\n\\def\\lya{Ly$\\alpha$}\n\\def\\oxytwo{[\\ion{O}{2}]}\n\\def\\magtwo{\\ion{Mg}{2}}\n\\def\\hbeta{H$\\beta$}\n\\def\\oxythree{[\\ion{O}{3}]}\n\\def\\halpha{H$\\alpha$}\n\\def\\oiipair{[\\ion{O}{2}] $\\lambda \\lambda 3726,3729$}\n\n\\def\\loxytwo{L_{\\rm [OII]}}\n\\def\\soxytwo{\\sigma_{\\rm [OII]}}\n\\def\\woxytwo{W_{\\rm [OII]}}\n\\def\\lmm{lines mm$^{-1}$}\n\n%END OF GOOD AASTEX DEFINITIONS\n\n%\\received{4 August 1988}\n%\\accepted{23 September 1988}\n%\\journalid{337}{15 January 1989}\n%\\articleid{11}{14}\n\n\\begin{document}\n\n\\title{One-Line Redshifts and \\\\\nSearches for High-Redshift \\lya\\ Emission\\altaffilmark{1}}\n\n\\author{Daniel Stern\\altaffilmark{2}, Andrew Bunker\\altaffilmark{3}, Hyron Spinrad}\n\\affil{Department of Astronomy, University of California at Berkeley \\\\\nBerkeley, CA 94720 }\n\\and\n\\author{Arjun Dey\\altaffilmark{4}}\n\\affil{KPNO/NOAO \\\\\n950 N. Cherry Avenue, P.O. Box 26732 \\\\\nTucson, AZ 85726 }\n\n\\altaffiltext{1}{Based on observations at the W.M. Keck Observatory,\nwhich is operated as a scientific partnership among the University of\nCalifornia, the California Institute of Technology, and the National\nAeronautics and Space Administration. The Observatory was made possible\nby the generous financial support of the W.M. Keck Foundation.}\n\n\\altaffiltext{2}{Current address: Jet Propulsion Laboratory, California\nInstitute of Technology, Mail Stop 169-327, Pasadena, CA 91109; {\\tt\nstern@zwolfkinder.jpl.nasa.gov}}\n\n\\altaffiltext{3}{Current address: Institute of Astronomy, Madingley Road,\nCambridge, CB3 OHA, England}\n\n\\altaffiltext{4}{Hubble Fellow}\n\n\\begin{abstract}\n\nWe report the serendipitous discovery of two objects close in\nprojection with fairly strong emission lines at long wavelength\n($\\lambda\\sim 9190$\\,\\AA). One (A) seems not to be hosted by any galaxy\nbrighter than $V_{555}=27.5$, or $I_{814}=26.7$ (Vega-based 3$\\sigma$\nlimits in 1\\farcs0 diameter apertures), while the other line is\nassociated with a faint ($I_{814}\\simeq 24.4$) red galaxy (B) offset by\n2\\farcs7 and 7 \\AA\\ spectrally. Both lines are broad (FWHM $\\approx\n700$\\,km\\,s$^{-1}$), extended spatially, and have high equivalent\nwidths ($W_\\lambda^{\\rm obs}({\\rm A}) > 1225$ \\AA, 95\\% confidence\nlimit; $W_\\lambda^{\\rm obs}({\\rm B}) \\approx 150$ \\AA). No secondary\nspectral features are detected for galaxy A. Blue continuum and the\nmarginal detection of a second weak line in the spectrum of galaxy B is\nconsistent with \\oxytwo\\ (the strong line) and \\magtwo\\ (the weak line)\nat $z = 1.466$. By association, galaxy A is likely at $z=1.464$,\nimplying a rest-frame equivalent width of the \\oxytwo\\ emission line in\nexcess of 600\\,\\AA\\ and a projected separation of 30~$h_{50}^{-1}$~kpc\nfor the galaxy pair. Conventional wisdom states that isolated emission\nlines with rest-frame equivalent widths larger than $\\sim 200$ \\AA\\,\nare almost exclusively \\lya. This moderate-redshift discovery\ntherefore compromises recent claims of high-redshift \\lya\\ emitters for\nwhich other criteria (\\ie line profile, associated continuum\ndecrements) are not reported. We discuss observational tests to\ndistinguish \\lya\\ emitters at high redshift from foreground systems.\n\n\\end{abstract}\n\n\\keywords{galaxies: distances and redshifts -- galaxies: evolution\n-- galaxies : formation -- early universe}\n\n\\section{Introduction}\n\nSerendipitous detections of emission line galaxies are common on\nlow-dispersion spectrograms taken with large ground-based telescopes.\nIndeed, finding distant galaxies through blank sky slit spectroscopy is\nfully complementary to narrow-band imaging searches for distant\nline-emitting galaxies: rather than probing a large area of sky for\nobjects over a limited range of redshift, deep slit spectroscopy\nsurveys a smaller area of sky for objects at a larger range in redshift\n\\markcite{Pritchet:94, Thompson:95}(\\eg Pritchet 1994; Thompson \\&\nDjorgovski 1995). Also, since the resolution of optical spectra is\nbetter matched to narrow line emission than filters with widths of\n$\\approx 3000$ \\kms, deep slit spectroscopy is vastly more sensitive\nthan narrow-band imaging. In a 1.5 hour spectrum with the Keck\ntelescope at moderate dispersion ($\\lambda / \\Delta \\lambda \\simeq\n1000$), the limiting flux density probed for spectrally unresolved line\nemission in a 1 arcsec$^2$ aperture is $S_{\\rm lim} (3 \\sigma) \\approx\n6 \\times 10^{-18} \\ergcm2s$ at $\\lambda \\approx 9300$ \\AA. The first\ngalaxy confirmed at $z > 5$ was found serendipitously during\nspectroscopic observations of a galaxy at $z = 4.02$\n\\markcite{Dey:98}(Dey {et~al.} 1998). Since then, several other $z >\n5$ galaxies have been reported \\markcite{Hu:98, Weymann:98, Spinrad:98,\nvanBreugel:99a, Chen:99, Hu:99}(Hu, Cowie, \\& McMahon 1998; Weymann\n{et~al.} 1998; Spinrad {et~al.} 1998; van Breugel {et~al.} 1999; Chen,\nLanzetta, \\& Pascarelle 1999; Hu, McMahon, \\& Cowie 1999).\n\nIn both narrow-band imaging and slit spectroscopy surveys, the\nequivalent width of detected emission lines is a standard redshift\nindicator \\markcite{Cowie:98, Hu:98}(\\eg Cowie \\& Hu 1998; Hu {et~al.}\n1998). \\lya\\ at high redshift can have a very large rest-frame\nequivalent width \\markcite{Charlot:93}(up to $W_\\lambda^{\\rm rest}\n\\approx 200$ \\AA\\ if driven by star formation; Charlot \\& Fall 1993),\nwhile \\oxytwo $\\lambda$3727\\AA\\ at low to moderate redshift, the other\nprimary strong, solitary emission feature in UV/optical galaxy spectra,\nrarely has a rest-frame equivalent width exceeding 100 \\AA\\, in\nmagnitude-limited surveys \\markcite{Songaila:94, Guzman:97, Hammer:97,\nHogg:98}(\\eg Songaila {et~al.} 1994; Guzm\\`an {et~al.} 1997; Hammer\n{et~al.} 1997; Hogg {et~al.} 1998). Equivalent width selection is also\nhelped by $W_\\lambda^{\\rm obs} = W_\\lambda^{\\rm rest} (1 + z)$, which\nboosts \\lya\\ more than \\oxytwo. The other strong UV/optical emission\nfeatures in galaxies, \\eg \\hbeta,\n\\oxythree$\\lambda\\lambda$4959,5007\\AA, \\halpha, are generally easily\nidentified spectroscopically from their wavelength proximity to other\nemission features, though \\halpha\\ can also have extremely high\nequivalent widths, up to 3000 \\AA\\ \\markcite{Leitherer:95}(Leitherer,\nCarmelle, \\& Heckman 1995), leading to some confusion between\nlow-redshift, young, dwarf starbursts and high-redshift \\lya-emitters\n\\markcite{Stockton:98}(\\eg Stockton \\& Ridgway 1998).\n\nHere we report the discovery of two emission lines in the approximate\ndirection of the Abell~2390 cluster. The equivalent widths of these\nlines are rather large, with $W_\\lambda^{\\rm obs} (\\rm A) > 1225$\n\\AA\\ (95\\% confidence limit) for the first object and $W_\\lambda^{\\rm\nobs} (\\rm B) \\approx 150$ \\AA\\, for the second object. However, as we\nargue below, \\oxytwo\\ at $z=1.46$ is the most likely identification for\nthese features, indicating an atypical system.\n\nIn \\S 2 $-$ \\S 4 we discuss the observations, redshift determination,\nand properties of these galaxies. In \\S 5 we consider the implications\nof this discovery for narrow-band searches for \\lya\\ emission from\ndistant protogalaxies, including a detailed discussion of the\nobservational criteria useful for distinguishing high-redshift\n\\lya\\ from foreground emission-line galaxies. \n\nThroughout this paper, unless otherwise indicated, we adopt $H_0 = 50~\nh_{50}~ \\kmsMpc, q_0 = 0.1$, and $\\Lambda = 0$. For these parameters,\nthe luminosity distance, $d_L$, at $z=1.46$ is 13.88 $h_{50}^{-1}$ Gpc\nand 1\\arcsec\\ subtends 11.1 $h_{50}^{-1}$ kpc.\n\n\n%FIG 1\n\n\\begin{figure}[t!]\n\\plotfiddle{stern.fig1.eps}{2.0in}{0}{91}{91}{-220}{0}\n\n\\caption{{\\it HST} $I$-band (F814W; 10500 s) image of the\nserendipitously discovered galaxies in the field of Abell~2390. Galaxy\nA, marked by dotted circle, is undetected ($I_{814} > 26.7, 3\\sigma$).\nGalaxy B has $I_{814} = 24.4$ (1\\arcsec\\ diameter aperture). Slit\npositions for our three observations are indicated. The images shown\nare 30\\arcsec\\ on a side, oriented with north upwards and east to the\nleft. Galaxy B is located at $\\alpha = 21^h53^m35\\secper16$, $\\delta =\n+17\\deg42\\arcmin56\\farcs66$ (J2000) and is 2\\farcs7 SE of galaxy A.\nThe bright elliptical galaxy south of galaxy B is a member of the Abell\n2390 galaxy cluster ($z=0.241$).}\n\n\\label{hstslit}\n\\end{figure}\n\n\n\n\\section{Observations}\n\nOn UT 1997 July 31, an observation of a pair of lensed arcs close to\nthe core of the rich galaxy cluster Abell~2390 \\markcite{Frye:98,\nBunker:00a}(Frye \\& Broadhurst 1998; Bunker, Moustakas, \\& Davis 2000) resulted in the serendipitous detection of a strong emission\nline at 9185 \\AA\\ approximately 70\\arcsec\\ NNE of the arcs along the\nlong slit spectrogram. These observations were made with the Low\nResolution Imaging Spectrometer \\markcite{Oke:95}(LRIS; Oke {et~al.} 1995) at the\nCassegrain focus of the Keck~II Telescope, using the 400\n\\lmm\\ grating ($\\lambda_{\\rm blaze} \\approx 8500$ \\AA). The detector\nis a Tek $2048^2$ CCD with $24 \\mu$m pixels, corresponding to\n0\\farcs212 pix$^{-1}$. The GG495 filter was used to block second\norder light and the observations sample $\\lambda\\lambda 6100 - 9900$\n\\AA. The slit width was 1\\arcsec, yielding an effective resolution of\n$\\Delta \\lambda_{\\rm FWHM} \\approx 8$ \\AA, and the data were binned by\na factor of two spatially during the data acquisition. Reductions were\ndone with IRAF and followed standard spectroscopic procedures.\nWavelength calibration was verified against telluric emission lines.\nThe night was photometric with a seeing of $\\approx$ 0\\farcs7 FWHM, and the\ndata were calibrated using observations of BD+174708 \\markcite{Massey:88,\nMassey:90}(Massey {et~al.} 1988; Massey \\& Gronwall 1990) procured on the same night. The total integration time was\n3600 s with the slit oriented at a position angle of $23$\\deg\\ (see\nFig.~1). The emission line source (Fig.~2), which we refer to as\ngalaxy A, was spatially extended by 3\\arcsec\\ in this discovery\nspectrogram and no associated continuum was detected, implying an\nequivalent width $W_\\lambda^{\\rm obs} > 400$ \\AA\\ (95\\% confidence\nlimit). The wavelength of the emission line does not correspond to any\nprominent lines at the redshift of Abell~2390 ($z = 0.24$). Throughout we have\ncorrected for foreground Galactic extinction using the dust maps of\n\\markcite{Schlegel:98}Schlegel, Finkbeiner, \\& Davis (1998) which have an optical reddening of $E(B-V) = 0.11$\nin the direction of Abell~2390, equivalent to extinctions of $A_{555} =\n0.33$ and $A_{814} = 0.20$.\n\n\n%FIG 2\n\n\\begin{figure}[t!]\n\\plotfiddle{stern.fig2.eps}{2.0in}{0}{91}{91}{-160}{0}\n\n\\caption{Two-dimensional, flattened, sky-subtracted spectra near the\nemission lines from our discovery (July; left) and final (September;\nright) observations. The abscissa indicates wavelength and the\nordinate indicates spatial position. The July data do not sample the\nentire spatial range. Both data sets have been convolved with a\nGaussian of width 1 pixel. Galaxy~A is detected in both observations\nand is the upper emission feature in the September data. Galaxy~B is\nonly visible in the September data (lower emission feature). Note the\nlack of continuum associated with galaxy~A in both data sets, while\ngalaxy~B has faint continuum blue-ward of the emission line, indicating\nthat the emission line is unlikely to be \\lya. The horizontal feature\nin the July data set is continuum emission from an Abell~2390 cluster\nmember ($z=0.241$). The negative horizontal feature in the September\ndata is an artifact of our fringe suppression algorithm (see text); it\nis the negative of a different Abell~2390 cluster member ($z=0.232$).\nFaint negatives of galaxies A and B are also evident.}\n\n\\label{twod}\n\\end{figure}\n\n\n\nA comparison with archival {\\it Hubble Space Telescope} ({\\it HST}) Wide\nField/Planetary Camera~2 \\markcite{Trauger:94}(WFPC2; Trauger {et~al.} 1994) images secured\nby Fort \\etal (HST-GO~5352) finds no obvious optical identification for\nobject A. The {\\it HST} imaging was undertaken on UT 1994 December 10 in\nthe F555W ($V_{555}$) and F814W ($I_{814}$) filters. The data comprised\nfour orbits in F555W and five in F814W, with each orbit consisting of\na single integration of 2100 s. For the combined F555W image (8400 s),\nthe 1$\\sigma$ limiting magnitude reached in 1 square arcsecond is $V_{555}\n= 28.4$ mag arcsec$^{-2}$, and for the combined F814W image (10500 s),\nit is $I_{814} = 27.6$ mag arcsec$^{-2}$ (Vega-based magnitudes are\nadopted throughout). This is consistent with the predicted sensitivity\nbased on the Poissonian counting statistics and the WF readout noise\n(5 $e^-$). The 3$\\sigma$ limits on the brightness of the host of\ngalaxy A are $V_{555} > 27.5$ and $I_{814} > 26.7$ for a 1\\arcsec\\\ndiameter aperture. A faint red galaxy, which we refer to as galaxy\nB, was found nearby ($\\approx$ 2\\farcs7 to the SE) but {\\em not} coincident\nwith our estimate of the galaxy A position based on our spectroscopic\nslit observations (see Fig.~1). Galaxy B is faintly detected in F555W\n($V_{555} = 27.63 \\pm 0.54$) and has $I_{814} = 24.36 \\pm 0.05$, where\nboth magnitudes are quoted for 1\\arcsec\\ diameter apertures.\n\nOn UT 1997 August 24 \\& 26 we observed galaxy B using LRIS in slitmask\nmode at a position angle of $-$10.4\\deg\\ (Fig.~1). The\n1.4\\arcsec\\ wide slitlet was 42\\arcsec\\, long, and observations were\nmade with both the 600 \\lmm\\ grating (UT 1997 August 24; 3600 s;\n$\\lambda_{\\rm blaze} = 5000$\\AA; $\\Delta\\lambda_{\\rm FWHM} \\approx\n7.5$\\AA; $\\lambda\\lambda 7050 - 9550$\\AA) and the 300 \\lmm\\ grating (UT\n1997 August 26; 4800 s; $\\lambda_{\\rm blaze} = 5000$\\AA;\n$\\Delta\\lambda_{\\rm FWHM} \\approx 14$\\AA; $\\lambda\\lambda 3800 -\n8800$\\AA). Moderate cirrus affected these observations. Our\nspectrogram of galaxy B shows a {\\em weak} emission line at $\\lambda \\simeq 9196$\n\\AA, nearly the same wavelength as for galaxy A. However, galaxy B\nalso shows weak continuum blue-ward of the emission line extending down\nto wavelengths of $\\sim 4000$\\AA.\n\n\n%FIG 3\n\n\\begin{figure}[t!]\n\\plotfiddle{stern.fig3.eps}{4.8in}{0}{75}{75}{-240}{-130}\n\n\\caption{Spectra of galaxies A and B in the Abell~2390 field from the\nUT 1997 Sep 11 observations, illustrating the high equivalent width\nemission lines observed at 9185 \\AA\\ (galaxy A) and 9191 \\AA\\ (galaxy\nB). The total exposure time was 5400 s, and the spectrum was extracted\nusing a 1\\farcs5 $\\times$ 1\\farcs5 aperture.}\n\n\\label{oned}\n\\end{figure}\n\n\nFinally, on UT 1997 September 11, we attempted to put the LRIS 1\\farcs0\nwide slit across both galaxies, as well as could be determined from\ntheir spectroscopic positions (Fig.~1). These observations were\nobtained with the 400 \\lmm\\ grating ($\\lambda_{\\rm blaze} = 8500$ \\AA)\nat a position angle of 80\\deg\\ and sample $\\lambda\\lambda 5950 - 9730$\n\\AA. The seeing was $\\approx 0\\farcs7$. As the night was not\nphotometric, we applied the UT 1997 July 31 sensitivity function,\nscaled to maintain the same total flux in the galaxy A emission line.\nThe total integration time was 5400 s. In Fig.~2 we present the July\nand September two-dimensional, flattened, sky-subtracted spectra near\nthe emission lines. In order to suppress the fringing which adversely\naffects long wavelength ($\\lambda \\simgt 7200$ \\AA) optical spectra, we\ndithered the telescope between individual exposures and subtract\ntemporally adjacent frames prior to co-adding the data sets. This\nprocedure, which is essential for recovering information on faint\nobjects in the telluric OH bands, should not affect the object spectra,\nbut does leave negative holes in the final two-dimensional spectra (see\nFig.~2). Fig.~3 presents the extracted, one-dimensional spectra from\nthe September data and Table~1 summarizes the observed properties of\ngalaxies A and B.\n\n\n% TABLE THE FIRST\n\\begin{deluxetable}{lrcrr}\n\\tablewidth{0pt}\n\\tablecaption{Observed Properties of Galaxies A and B in the Abell~2390 Field.}\n\\tablehead{\n\\colhead{Parameter} &\n\\colhead{Galaxy A} &\n\\colhead{~~~~~~} &\n\\colhead{} &\n\\colhead{Galaxy B}}\n\\startdata\nLine ID \\dotfill & \\oxytwo & & \\magtwo & \\oxytwo \\nl\n$\\lambda_{\\rm obs}$ (\\AA) \\dotfill & $9184.8\\pm0.8$ & & $\\simeq$ 6895 & $9191.3\n\\pm1.4$ \\nl\n$z$ \\dotfill & 1.464 & & 1.463 & 1.466 \\nl\n$f_{\\rm line}$ ($10^{-17}$ ergs~ cm$^{-2}$ s$^{-1}$) \\dotfill & $8.7\\pm0.8$ & &\n0.9 & $7.3\\pm0.9$ \\nl\n$L_{\\rm [OII]}$ ($h_{50}^{-2}~ 10^{42}$ ergs~ s$^{-1}$) \\dotfill & $2.02 \\pm 0.2\n$ & & & $1.70 \\pm 0.2$ \\nl\n$f_{\\rm cont}$ ($10^{-20}$ ergs~ cm$^{-2}$ s$^{-1}$ \\AA$^{-1}$) \\dotfill & $-2.2\n\\pm4.2$ & & & $51.4\\pm4.5$ \\nl\n$W_\\lambda^{\\rm obs}$ (\\AA) \\dotfill & $> 1225$ & & 90 & $102 - 189$ \\nl\nFWHM (km s$^{-1}$) \\dotfill & $627\\pm62$ & & 300 & $785\\pm94$ \\nl\n$V_{555}$ (mag) \\dotfill & $>27.5$ & & & $27.63 \\pm 0.54$ \\nl\n$I_{814}$ (mag) \\dotfill & $>26.7$ & & & $24.36 \\pm 0.05$ \\nl\n\\enddata\n\\tablecomments{Magnitudes are in the Vega system and quoted for\n1\\farcs0 circular apertures. $3 \\sigma$ limits are presented for the\nmagnitude of galaxy A. Spectroscopic measurements derive from UT 1997\nSeptember 11 data and have been corrected for Galactic extinction using\nan optical reddening of $E(B-V) = 0.11$ \\markcite{Schlegel:98}(Schlegel\n{et~al.} 1998). The \\magtwo\\ line is weakly detected. Parameters for\nthe \\oxytwo\\ lines have been measured using the SPECFIT contributed\npackage within IRAF \\markcite{Kriss:94}(Kriss 1994) with a flat (in\n$F_\\lambda$) continuum and a single Gaussian emission line. Equivalent\nwidths have been calculated with a Monte Carlo analysis using the\nmeasured line flux and continuum amplitude with errors subject to the\nconstraint that both must be $> 0$. We quote the 95\\% confidence limit\nfor galaxy A and the 95\\% confidence interval for galaxy B. Line\nwidths (FWHM) are deconvolved by the instrumental resolution ($\\approx$\n8 \\AA).}\n\n\\label{specprop}\n\\end{deluxetable}\n\n\n\n\\section{Redshift Determination }\n\nUnderstanding objects A and B requires first determining their\nredshifts. Speculations on one-line redshifts are common among faint\ngalaxy observers. Here we have been spared that fate by the presence\nof the second {\\em weak} emission line in the spectrum of object~B at\n$\\lambda \\simeq 6895$ \\AA. The wavelength ratio with the stronger line\nat $\\lambda = 9191$ \\AA\\ is 1.333, close to the laboratory measured\n[\\ion{O}{2}]$\\lambda3727$\\AA\\ /\n\\ion{Mg}{2}$\\lambda\\lambda$2796,2803\\AA\\ = 1.332. This implies a\nredshift $z = 1.466$ for galaxy B with the stronger line identified, as\nis usually the case, with [\\ion{O}{2}]$\\lambda$3727\\AA\\ (hereinafter\n\\oxytwo). For non-active galaxies it is slightly unusual to observe\n\\ion{Mg}{2}$\\lambda\\lambda$2796,2803\\AA\\ (hereinafter \\magtwo) in\nemission. For example, \\markcite{Guzman:97}Guzm\\`an {et~al.} (1997) report on a spectroscopic\nstudy of 51 compact field galaxies in the flanking fields of the Hubble\nDeep Field. Of the 9 galaxies at redshifts sufficient for \\magtwo\\ to\nbe sampled by their observations, only 2 (22\\%) show \\magtwo\\ in {\\em\nemission}. Active galaxies, of course, often show \\magtwo\\ in\nemission. The velocity offset between the \\magtwo\\ and \\oxytwo\\ lines\nare cause for slight concern, but similar offsets are common in radio\ngalaxy spectra \\markcite{Stern:99a}(\\eg Stern {et~al.} 1999b). As discussed below, the\ncontinuum blueward of the long wavelength, isolated line\nmakes alternate redshift identifications unconvincing.\n\nThe question then remains: what is the redshift of object A? Previous\nexperience might suggest that isolated optical emission lines with\n$W_\\lambda^{\\rm obs} > $ several $\\times 100$ \\AA\\ are exclusively\nidentified with \\lya\\ at high redshift. For example, 0140+326~RD1 at\n$z=5.34$ has $W_{Ly\\alpha}^{\\rm obs} = 600 \\pm 100$\\AA\\ \\markcite{Dey:98}(Dey {et~al.} 1998)\nwhile HDF~4-473.0 at $z=5.60$ has $W_{Ly\\alpha}^{\\rm obs} \\approx\n300$\\AA\\ \\markcite{Weymann:98}(Weymann {et~al.} 1998). Magnitude-limited redshift surveys find\nthe $W_\\lambda^{\\rm obs}$ distribution for \\oxytwo, typically the\nprimary doppelg\\\"anger for high redshift \\lya, rarely has a rest-frame\nequivalent width exceeding 100\\AA\\ \\markcite{Songaila:94,\nGuzman:97, Hammer:97, Hogg:98}(\\eg Songaila {et~al.} 1994; Guzm\\`an {et~al.} 1997; Hammer {et~al.} 1997; Hogg {et~al.} 1998). High values of $\\woxytwo$ are\noccasionally seen in AGN, however. The $3^{rd}$ Cambridge/Molonglo\nRadio Catalog (3C/MRC) composite radio galaxy spectrum of\n\\markcite{McCarthy:93}McCarthy (1993) has $\\woxytwo = 128$\\AA\\ while the lower radio\npower MIT-Green Bank (MG) composite radio galaxy spectrum of\n\\markcite{Stern:99a}Stern {et~al.} (1999b) has $\\woxytwo = 142$\\AA. Since the surface density\nof luminous active galaxies is relatively low, \nour July data suggested at first that the\nemission line in object A was enticingly identified\nwith \\lya\\ at the extremely high redshift of $z = 6.55$. Although this\ninterpretation cannot be {\\em completely} ruled out, the\nrobust identification of the emission line in object B \nwith \\oxytwo\\ at $z = 1.466$ coupled with its projected proximity\nto object A strongly argues that we are witnessing associated galaxies\nat moderate redshift. The projected separation at $z = 1.466$ is\n$30~ h_{50}^{-1}$ kpc. The radial velocity difference between the\nobjects is 220 km s$^{-1}$.\n\n%doppelg\\\"anger (German: ``double goer''): in German folklore, a wraith\n%or apparition of a living person, as distinguished from a ghost ... a\n%spirit double, an exact replica ...}\n\n\n\\section{Galaxies A and B as Active Galaxies}\n\nAssociating the \\oxytwo\\ emission in this system with recent star\nformation activity is likely inappropriate. The \\oxytwo\\ luminosities\nimply star formation rates of $\\approx 90~h_{50}^{-2}~M_\\odot~{\\rm\nyr}^{-1}$ \\markcite{Kennicutt:92}(Kennicutt 1992) which seems improbable given the\nfaintness of the hosts. Using the SPECFIT contributed package within\nIRAF \\markcite{Kriss:94}(Kriss 1994) to fit the emission lines with the\n\\oiipair\\ doublet, we derive deconvolved circular velocities $v_c\n\\simgt 200 / \\sin i$ km s$^{-1}$ for both galaxies. Applying the\nhigh-redshift Tully-Fisher relation \\markcite{Vogt:97}(Vogt {et~al.} 1997), these line widths\nsuggest apparent $I$-band magnitudes $I \\simlt 23.4$, much more\nluminous than the observed galaxies.\n\nA more natural explanation for the spectral character of this system is\nto associate the line emission from galaxies A and B with active\ngalactic nuclei (AGN). The line widths are consistent with those seen\nin radio galaxies and Seyfert galaxies: the deconvolved FWHM of\ngalaxies A and B are $\\approx 650$ and $\\approx 800$ km s$^{-1}$\nrespectively (fit as a single line), while the composite radio galaxy\nspectra have FWHM$_{\\rm [OII]} \\simgt 1000$ km s$^{-1}$\n\\markcite{McCarthy:99a, Stern:99a}(McCarthy \\& Lawrence 1999; Stern {et~al.} 1999b). This interpretation also presents a\nnatural explanation for the high equivalent widths, similar to those\nseen in other active systems.\n\nComparison with the FIRST radio catalog \\markcite{Becker:95}(Faint Images of the\nRadio Sky at Twenty-one cm; Becker, White, \\& Helfand 1995) reveals no radio source\nwithin 1 arcminute of either galaxy to a limiting flux density of\n$f_{\\rm 1.4 GHz} \\simeq 1$ mJy ($5 \\sigma$). The traditional\ndemarcation between radio-loud and radio-quiet systems is $\\log L_{\\rm\n1.4 GHz} ({\\rm ergs\\ s}^{-1} {\\rm Hz}^{-1}) = 32.5$. For an emitted\nluminosity density $L_\\nu \\propto \\nu^\\alpha$, this demarcation\ncorresponds to $S_{\\rm 1.4 GHz} = 1.36 h_{50}^2 (1 + z)^{1 + \\alpha}$\nmJy for $z = 1.46$. The FIRST non-detection therefore\ndoes not preclude a weak radio-loud source.\n\n\n\\section{Tests for Cosmological One-liners}\n\nSeveral programs are currently underway to search for high-redshift\nprimeval galaxies through deep narrow-band imaging\n\\markcite{Stern:99e}(\\eg see Stern \\& Spinrad 1999). Table~2 lists\nseveral recently discovered high-redshift ($z > 5$) sources and\nincludes lower-redshift, strong line-emitters. The previous generation\nof narrow-band surveys failed to confirm any field \\lya-emitting\nprotogalaxy candidates \\markcite{Pritchet:94, Thompson:95}(Pritchet\n1994; Thompson \\& Djorgovski 1995). Examples of new programs include\nthe Calar Alto Deep Imaging Survey \\markcite{Thommes:98,\nThommes:99}(CADIS, Thommes {et~al.} 1998; Thommes 1999) which uses a\nFabry-P\\'erot interferometer ($S_{\\rm lim} (5 \\sigma) \\approx 3 \\times\n10^{-17} \\ergcm2s $), the Keck-based narrow-band, interference filter\nimaging program of Cowie, Hu, and McMahon \\markcite{Cowie:98, Hu:98}\n(Cowie \\& Hu 1998; Hu, Cowie, \\& McMahon 1999; $S_{\\rm lim}\n(5 \\sigma) \\approx 1.5 \\times 10^{-17} \\ergcm2s$),\nand serendipitous searches on deep slit spectra\n\\markcite{Manning:00}(\\eg this paper; Manning {et~al.} 2000).\n\n\n% TABLE THE SECOND\n\\begin{deluxetable}{lccccl}\n\\tablewidth{0pt}\n\\tablecaption{Galaxies Reported/Considered at $z > 5$.}\n\\tablehead{\n\\colhead{Galaxy} &\n\\colhead{$z$} &\n\\colhead{$W_\\lambda^{\\rm obs}$} &\n\\colhead{asymmetric} &\n\\colhead{continuum} &\n\\colhead{Reference} \\nl\n\\colhead{} &\n\\colhead{} &\n\\colhead{(\\AA)} &\n\\colhead{line profile} &\n\\colhead{decrement} &\n\\colhead{}}\n\\startdata\nSTIS parallel gxyA & 6.68 & $\\approx 120$ & \\nodata & x & \\markcite{Chen:99}Chen\n {et~al.} (1999) \\nl\nSSA22-HCM1 & 5.74 & 350 & x & x & \\markcite{Hu:99}Hu {et~al.} (1999) \\nl\nBR 1202$-$0725 ser & 5.64 & $>600$ & \\nodata & x & \\markcite{Hu:98}Hu {et~al.} \n(1998) \\nl\nHDF 4-473.0 & 5.60 & $\\approx 300$ & x & xx & \\markcite{Weymann:98}Weymann \n{et~al.} (1998) \\nl\n0140+326 RD1 & 5.34 & $600\\pm100$ & x & x & \\markcite{Dey:98}Dey {et~al.} \n1998) \\nl\nHDF 3-951.0 & 5.34 & N/A & N/A & xx & \\markcite{Spinrad:98}Spinrad {et~al.}\n(1998) \\nl\nTN J0924$-$2201 & 5.19 & $\\approx 150$ & 1/2 & \\nodata & \\markcite{vanBreugel:99a}\nvan Breugel {et~al.} (1999)\n\\nl\n\\nl\nAbell 2390 serA & 1.46 & $>1225$ & no & \\nodata & this paper \\nl\nERO~J164502+4626.4 & 1.44 & 115 & \\nodata & x & \\markcite{Dey:99a}Dey {et~al.} \n(1999) \\nl\n3C212 B08 & 0.31 & $\\approx 640$ & \\nodata & no & \\markcite{Stockton:98}\nStockton \\& Ridgway (1998) \\nl\n\\enddata\n\n\\tablecomments{Symbols indicate reliability of the criterion\nconsidered. Ellipses (`...') refer to unreported criteria. `x' refers\nto a positive result and `xx' refers to an extremely positive result\n--- namely, the two $z > 5$ confirmed galaxies in the HDF whose\nspectral energy distributions are confirmed flat (in $f_\\nu$) into the\nnear-infrared. The source HDF 3-951.0 lacks \\lya\\ emission; we\ntherefore list some of its criteria not applicable, `N/A'. The `1/2'\nfor the high-redshift radio galaxy TN J0924$-$2201 refers to the\nenigmatic result that one observation illustrates asymmetric\n\\lya\\ emission while a second observation does not.}\n\n\\label{comp5}\n\\end{deluxetable}\n\n\nSelecting objects on the basis of strong line emission may sample a\ndifferent galaxy population from the traditional magnitude-limited\nsurveys. In particular, emission-line surveys are much more sensitive\nto active galaxies and objects undergoing massive bursts of star\nformation. Determining the redshift and physical origin of line\nemission is challenging; comparison to field surveys selected on the\nbasis of continuum magnitude is perhaps inappropriate. Samples of\nline-emitting protogalaxy candidates will shortly become available. We\ntherefore present below a timely and detailed discussion of the\nobservational criteria which can be used to distinguish high-redshift\n\\lya\\ emission from low-redshift interlopers.\n\n\\subsection{Equivalent Width}\n\nThe stellar population synthesis models of \\markcite{Charlot:93}Charlot \\& Fall (1993) predict\nrest-frame \\lya\\ equivalent widths of $50 - 200$ \\AA\\ for dust-free\nyoung galaxies. For a constant star formation history, the \\lya\\\nluminosity and equivalent width are only somewhat dependent on the star\nformation rate and are greatest at times less than 10 Myr after the\nonset of the burst. For comparison, the spectral atlas of nearby\ngalaxies by \\markcite{Kennicutt:92}Kennicutt (1992) shows that the rest-frame equivalent\nwidth of the H$\\alpha$ + [\\ion{N}{2}] complex rarely exceeds 200 \\AA,\nthat of [\\ion{O}{3}]$\\lambda$5007 \\AA\\ rarely exceeds 100 \\AA, H$\\beta$\nrarely exceeds 30 \\AA, and [\\ion{O}{2}] rarely exceeds 100 \\AA. With\nthe $(1 + z)$ amplification of observed equivalent widths, emission\nlines in the optical with measured equivalent widths larger than\n$\\approx 300$ \\AA\\ should be almost exclusively identified with \\lya.\nSee Table~2 for a list of the equivalent widths of several recently\nreported protogalaxy candidates at $z > 5$.\n\nA number of caveats temper sole reliance on equivalent width arguments\nto discriminate \\lya\\ from foreground emission. First, high-ionization\n\\ion{H}{2} dwarf galaxies can have strong H$\\alpha$ emission with very\nweak continuum. \\markcite{Stockton:98}Stockton \\& Ridgway (1998) report an object (3C212 B08) with\na single strong emission line at 8567 \\AA\\ and $W_\\lambda^{\\rm obs}\n\\approx 640$ \\AA. They eventually identify the line as H$\\alpha$ at $z =\n0.305$ due to a secondary feature at 2\\% of the strong line whose\nwavelength matches redshifted \\ion{He}{1}$\\lambda$5876 \\AA. Starburst\nmodels \\markcite{Leitherer:95}(Leitherer {et~al.} 1995) with continuous star formation and a\nSalpeter initial mass function over the mass range $0.1 - 100$\nM$_\\odot$ can have H$\\alpha$ equivalent widths as high as 3000 \\AA\\ up\nto ages of 3 Myr and can remain above $\\sim 300$ \\AA\\ up to ages of 100\nMyr. Furthermore, extreme \\ion{H}{2} galaxies with very hot ($>$\n60,000 K) stars and low metal abundances can have suppressed\nlow-ionization metallic emission lines such as [\\ion{N}{2}] and\n[\\ion{S}{2}], making H$\\alpha$ identification difficult \\markcite{Terlevich:91}(\\eg Tol\n1214$-$277; Fig.~4o in Terlevich {et~al.} 1991). Such galaxies tend to show\n\\ion{He}{1}$\\lambda$5876 \\AA\\ in emission.\n\nAGN offer another potential source of ionizing radiation to stimulate\nline emission: photoionization by a power law continuum emitted near\nthe central engine combined with shock-excited emission can produce\nvery high equivalent width emission. The composite radio galaxy\nspectrum in \\markcite{McCarthy:93}McCarthy (1993) shows several lines with rest-frame\nequivalent widths in excess of 50 \\AA. As argued earlier, however, the\nspectral proximity of several features make the most likely\nidentification of an observed, isolated, high-equivalent width emission\nfeature an ambiguous selection between \\lya\\ and \\oxytwo. Composite\nradio galaxy spectra have $\\woxytwo \\approx 135$\n\\AA\\ \\markcite{McCarthy:93, Stern:99a}(McCarthy 1993; Stern {et~al.} 1999b). Occasional sources show extremely\nhigh equivalent width \\oxytwo. For example, \\markcite{McCarthy:91}McCarthy (1991)\nreports \\oxytwo\\ emission from the radio galaxy B3~0903+428 ($z =\n0.907$) with $\\woxytwo = 251 \\pm 55$ \\AA\\ (rest-frame) and the northern\nknot in 3C368 has a rest-frame $\\woxytwo = 485$ \\AA\\ \\markcite{Dey:99c}(Dey 1999).\nLuminous, narrow-lined, radio-quiet AGN, the so-called quasar-II\npopulation, are another potential active galaxy source of confusion for\none-lined sources, though they remain largely unidentified in\nobservational surveys.\n\n\\subsection{Asymmetric Line Profile}\n\nStar formation at low and high redshift is associated with large-scale\noutflows. Resonant scattering processes in the outflowing gas will\ntrap \\lya\\ photons short-ward of the systemic velocity of the emission\nand potentially destroy them through dust absorption. This results in\na P-Cygni profile for the \\lya\\ line. At the low signal-to-noise ratio\nobservations typically obtained on objects at $z \\simgt 5$, this causes\nan asymmetric \\lya\\ line profile with a broad red wing and a steep\ncut-off on the blue wing. This asymmetric profile is seen in many of\nthe confirmed $z > 5$ \\lya-emitting sources \\markcite{Dey:98}(\\eg Dey {et~al.} 1998)\nthough similar asymmetries might be mimicked by low signal-to-noise\nratio observations of \\oxytwo\\ in the low-density limit\n([\\ion{O}{2}]$\\lambda$3726\\AA\\ / [\\ion{O}{2}]$\\lambda$3729\\AA\\ $ =\n0.7$).\n\nIs an asymmetric line profile a necessary condition for high-redshift\n\\lya, or merely a sufficient condition? In addition to the local\nstar-forming galaxies with (1) broad damped \\lya\\ absorption centered\nat the wavelength corresponding to the redshift of the \\ion{H}{2}\nemitting gas and (2) galaxies with \\lya\\ emission marked by blueshifted\nabsorption features, \\markcite{Kunth:98b}Kunth {et~al.} (1999) notes a third morphology of\n\\lya\\ line that is occasionally observed in the local Universe: (3)\ngalaxies showing `pure' \\lya\\ emission, \\ie galaxies which show no\n\\lya\\ absorption whatsoever. \\markcite{Terlevich:93}Terlevich {et~al.} (1993) present {\\it IUE}\nspectra of two examples of `pure' emitters: C0840+1201 and\nT1247$-$232, both of which are extremely low-metallicity \\ion{H}{2}\ngalaxies. \\markcite{Thuan:97a}Thuan \\& Izotov (1997) present a high signal-to-noise ratio {\\it\nHST} spectrum of the latter galaxy, noting that with $Z = Z_\\odot /\n23$, it is the lowest metallicity local star-forming galaxy showing\n\\lya\\ in emission. At high signal-to-noise ratio, the emission line\nshows multiple superposed narrow absorption features, bringing into\nquestion the `pure' designation.\n\n%Tenorio-Tagle \\etal (1999; see also Kunth \\etal 1998b) have proposed a\n%scenario to explain the variety of \\lya\\ profiles based on the\n%hydrodynamical evolution of superbubbles powered by massive\n%starbursts. In brief, the large flux of ionizing photons during the\n%first few ($3 - 4$) Myr after onset of a massive starburst establishes\n%an ionized conical \\ion{H}{2} region in the low density \\hone\\ halo.\n%The apex of this cone coincides with the starburst, and it extends to\n%the galaxy outer edge. The ionized gas is transparent to the UV\n%photons and will result in `pure' \\lya\\ emission for the first few Myr\n%after onset of the burst. E.g., in the absence of large columns of\n%neutral hydrogen near the galaxy, the \\lya\\ emission during this stage\n%will not show any absorption features. However, the burst also creates\n%a shell, or blowout, of hot gas into the galaxy halo. Shocks formed\n%along the outer edge of this expanding bubble compress and cool the\n%gas, allowing recombination to occur. Eventually, sufficient\n%scattering and absorption of \\lya\\ photons occurs to cause blueshifted\n%\\lya\\ absorption. At later times, geometric dilution of the UV flux as\n%the superbubble continues to grow combined with the drop in UV photon\n%production as the most massive stars evolve and die will deplete the\n%\\lya\\ emission strength. The column density of neutral material will\n%continue to grow as hydrogen recombines and eventually \\lya\\ will be\n%seen primarily in absorption.\n\nObservations of local star-forming galaxies have two implications for\nstudies of high-redshift \\lya\\ emission. First, they provide a natural\nexplanation for asymmetric profiles which seem to characterize\nhigh-redshift \\lya, but also imply that although the asymmetric profile\nmay be a sufficient condition for identification of a strong line with\n\\lya, it is not a necessary one. Second, if \\lya\\ emission is\nprimarily a function of kinematics and perhaps evolutionary phase of a\nstarburst as suggested by the scenario of \\markcite{TenorioTagle:99}Tenorio-Tagle {et~al.} (1999),\nattempts to derive the comoving star-formation rate at high redshifts\nfrom \\lya\\ emission will require substantial and uncertain assumptions\nregarding the relation of observed \\lya\\ properties to the intrinsic\nstar-formation rate.\n\n\\subsection{Continuum Decrements}\n\nActively star-forming galaxies should, in the absence of dust absorption,\nhave blue continua, nearly flat in $f_\\nu$, at rest-frame ultraviolet\nwavelengths long-ward of \\lya. This radiation derives from the hot,\nmassive, short-lived stars and can therefore be used as indicator of\nthe instantaneous star formation rate of a galaxy modulo uncertainties\nin dust absorption, age, metallicity, and stellar initial mass function.\nShort-ward of the Lyman limit (912 \\AA), the spectral energy distributions\nshould drop steeply. This is due both to photospheric absorption in\nthe UV-emitting stars themselves, as well as photoelectric absorption by\nneutral hydrogen along the line of sight to the galaxy. Between\nthe Lyman limit and \\lya, photoelectric absorption from neutral hydrogen\nin the intergalactic medium attenuates the emitted spectrum. \n\nIn terms of emission line surveys, this discontinuity serves as a\nuseful foil for identifying observed lines with high-redshift \\lya,\nprovided the data are sufficiently sensitive to detect continuum.\nObjects which show evidence of a flat spectral energy distribution\nacross an emission line can immediately be ruled out as distant galaxy\ncandidates. The presence of a discontinuity, however, is {\\em not\nsufficient} for classifying the observed emission line with \\lya,\nunless the amplitude is extreme (see below). In particular, \\oxytwo,\nthe other strong, solitary emission feature in the UV/optical spectra\nof star-forming galaxies, lies short-ward of the Balmer and 4000\n\\AA\\ breaks. The former is strongest in young systems dominated by an\nA-star population, while the latter arises from metal-line blanketing\n(predominantly \\ion{Fe}{2}) in late-type stars. At high\nsignal-to-noise ratio, the morphology of the break can be used to\ndistinguish the \\lya\\ forest from the Balmer break from the 4000\n\\AA\\ break. At low signal-to-noise ratio, however, the continuum\ndecrement across \\oxytwo\\ can mimic that across high-redshift \\lya.\nFor example, \\markcite{Dey:99a}Dey {et~al.} (1999) report an optical\nspectrogram of the extremely red object ERO~J164502+4626.4\n\\markcite{Hu:94}(HR10 in Hu \\& Ridgway 1994), showing a single, strong\nemission feature at 9090.6 \\AA\\ and a drop in the continuum level by a\nfactor of $\\approx 3$ across the emission line. The optical data alone\nis suggestive of \\lya\\ emission at $z = 6.48$. However, near-infrared\nimages show the source to be extremely red, with a steeper spectral\nenergy distribution than expected for a high-redshift, star-forming\ngalaxy. Furthermore, a near-infrared spectrum shows a second emission\nat 1.603$\\mu$m, solidying the emission line identifications as\n\\oxytwo\\ and H$\\alpha$ at $z = 1.44$. Extremely dusty,\nmoderate-redshift galaxies such as ERO~J164502+4626.4 may be\nmisidentified as high-redshift \\lya-emitters by {\\em solely} optical\nsurveys.\n\nThe amplitude of a continuum discontinuity may be used as a tool for\ndistinguishing the identification of that discontinuity. In order of\ndecreasing wavelength, discontinuities are commonly observed in\nUV/optical spectra of galaxies at rest wavelengths of 4000\n\\AA\\ [$D(4000)$], 2900 \\AA\\ [$B(2900)$], 2640 \\AA\\ [$B(2640)$], 1216\n\\AA\\ (\\lya), and 912 \\AA\\ (the Lyman limit). The hydrogen\ndiscontinuities derive from associated and foreground absorption and\nthus have no theoretical maximum. The longer rest-wavelength\ndiscontinuities derive from metal absorption in the stars and galaxies\nand are thus dependent on the age and metallicity of the galaxy\n\\markcite{Fanelli:92}(\\cf Fanelli {et~al.} 1992). The largest measured\nvalues of $D(4000)$ are $\\sim 2.6$ \\markcite{Hamilton:85,\nDressler:90}(Hamilton 1985; Dressler \\& Gunn 1990), while {\\it IUE}\nspectra of main-sequence stars exhibit $B(2900) \\simlt 3$ and $B(2640)\n\\simlt 3$ \\markcite{Spinrad:97}(Spinrad {et~al.} 1997). The example of\nERO~J164502+4626.4 illustrates the utility of break amplitudes for\nredshift identifications. The amplitude of the continuum break in\nERO~J164502+4626.4 is $\\approx 3$ across an emission line at 9090.6\n\\AA. Were the emission line \\lya, the implied redshift would be $z =\n6.48$. Models and measurements of the strength of the \\lya\\ forest\nimply decrements $\\simgt 10$ at $z \\simgt 6$ \\markcite{Madau:95,\nStern:99e}(Madau 1995; Stern \\& Spinrad 1999), incompatible with the\nobserved decrement and arguing for a lower redshift line\nidentification.\n\n\n\\section{Conclusions}\n\nWe report the serendipitous discovery of two faint galaxies with high\nequivalent width emission lines at long wavelength ($\\lambda \\approx\n9190$ \\AA). For one source, galaxy B, faint blue continuum and a weak\nsecondary line emission feature implies the source is at $z = 1.466$.\nThe spatial proximity and similar emission wavelength of object A\npersuasively argues that this is an unusual \\oxytwo-emitter at $z =\n1.464$. It had been thought that serendipitous one-lined sources with\nrest-frame equivalent widths larger than a few $\\times$ 100 \\AA\\ are\nexclusively identified with high-redshift \\lya. Our observations have\nshown that this is demonstrably not the case. Both sources are unlike\nlocal star-forming galaxies, and we suggest that the observations are\nmost consistent with the discovery of a moderate-redshift active system.\n\nSeveral programs are currently underway to find high-redshift \\lya\\\nemitters using a combination of narrow- and broad-band imaging\n\\markcite{Thommes:98, Hu:98}(\\eg Thommes {et~al.} 1998; Hu {et~al.}\n1998) and serendipitous long slit surveys \\markcite{Manning:00}(\\eg\nManning {et~al.} 2000). The moderate-redshift system discussed herein\nhas serious implications for those surveys. In particular we expect\nthe line-emission surveys to uncover a population of strong line\nemitters and we emphasize that comparison of this sample with\nmagnitude-limited surveys could be misleading.\n\nWe discuss various criteria which can be used to assess whether a\nsolitary, high-equivalent width emission feature is associated with\nhigh-redshift \\lya. In Table~2 we consider how recently reported $z >\n5$ spectroscopic candidates fare with respect to these criteria. Some\nsources are reliably confirmed at $z > 5$, while others are confirmed\nat low-redshift and yet others remain ambiguous with the current data.\nWe conclude that some criteria are necessary, but not sufficient, to\nconclude that a source is at $z > 5$, such as a continuum decrement\nacross the emission feature, while other criteria are sufficient, but\nnot necessary, such as an asymmetric line profile. We suggest that\nmultiple criteria are necessary to convincingly demonstrate that a\nsingle-lined source is at high-redshift.\n\n\\acknowledgments\n\nWe thank Alex Filippenko, Doug Leonard, and Aaron Barth for obtaining\nthe July 1997 observations, and Tom Broadhurst and Brenda Frye for the\nfollow-up observations during August 1997. We are indebted to the\nexpertise of the staff of Keck Observatory for their help in obtaining\nthe data presented herein, and to the efforts of Bev Oke and Judy Cohen\nin designing, building, and supporting LRIS. The work presented here\nhas been aided by discussions with Mike Liu, Curtis Manning, Gordon\nSquires, and Chuck Steidel. We are also grateful to Trinh Thuan for\nsharing the {\\it HST}/GHRS spectrum of T1214$-$277 and to Carlos\nDe~Breuck and Adam Stanford for carefully reading the manuscript. This\nwork has been supported by the following grants: IGPP/LLNL 98-AP017\n(DS), NICMOS/IDT grant NAG~5-3042 (AJB), NSF grant AST~95-28536 (HS),\nand NASA HF-01089.01-97A (AD). A preliminary version of this work was\npresented at the January 1999 AAS meeting in Austin under the title\n``Cosmological One-Liners: A Cautionary Tale''\n\\markcite{Stern:99d}(Stern {et~al.} 1999a).\n\n% REFERENCES\n\n%\\bibliographystyle{apj}\n%% \\bibliography\n\\begin{thebibliography}{}\n\n\\bibitem[Becker, White, \\& Helfand 1995]{Becker:95}\nBecker, R.~H., White, R.~L., \\& Helfand, D.~J. 1995, \\apj, 450, 559\n\n\\bibitem[Bunker, Moustakas, \\& Davis 2000]{Bunker:00a}\nBunker, A.~J., Moustakas, L.~A., \\& Davis, M. 2000, \\apj, in press (March)\n\n\\bibitem[Charlot \\& Fall 1993]{Charlot:93}\nCharlot, S. \\& Fall, S.~M. 1993, \\apj, 378, 471\n\n\\bibitem[Chen, Lanzetta, \\& Pascarelle 1999]{Chen:99}\nChen, H.-W., Lanzetta, K.~M., \\& Pascarelle, S. 1999, \\nat, 398, 586\n\n\\bibitem[Cowie \\& Hu 1998]{Cowie:98}\nCowie, L. \\& Hu, E.~M. 1998, \\aj, 115, 1319\n\n\\bibitem[Dey 1999]{Dey:99c}\nDey, A. 1999, in {\\it The Most Disant Radio Galaxies}, ed. H.~R\\\"ottgering, P.~N. Best, \\& M.~D. Lehnert (Dordrecht: Kluwer), 19\n\n\\bibitem[Dey, Graham, Ivison, Smail, Wright, \\& Liu 1999]{Dey:99a}\nDey, A., Graham, J.~R., Ivison, R.~J., Smail, I., Wright, G.~S., \\& Liu, M.~C. 1999, \\apj, 519, 610\n\n\\bibitem[Dey, Spinrad, Stern, Graham, \\& Chaffee 1998]{Dey:98}\nDey, A., Spinrad, H., Stern, D., Graham, J.~R., \\& Chaffee, F. 1998, \\apj, 498, L93\n\n\\bibitem[Dressler \\& Gunn 1990]{Dressler:90}\nDressler, A. \\& Gunn, J.~E. 1990, in {\\it Evolution of the Universe of Galaxies: the Edwin Hubble Centennial Symposium}, ed. R.~G. Kron, Vol.~10 (San Francisco: ASP Conference Series), 200\n\n\\bibitem[Fanelli, O'Connell, Burstein, \\& Wu 1992]{Fanelli:92}\nFanelli, M.~N., O'Connell, R.~W., Burstein, D., \\& Wu, C.~C. 1992, \\apjs, 82, 197\n\n\\bibitem[Frye \\& Broadhurst 1998]{Frye:98}\nFrye, B. \\& Broadhurst, T.~J. 1998, \\apj, 499, 115\n\n\\bibitem[Guzm\\`an {et~al.} 1997]{Guzman:97}\nGuzm\\`an, R. {et~al.} 1997, \\apj, 489, 559\n\n\\bibitem[Hamilton 1985]{Hamilton:85}\nHamilton, D. 1985, \\apj, 297, 371\n\n\\bibitem[Hammer {et~al.} 1997]{Hammer:97}\nHammer, F. {et~al.} 1997, \\apj, 481, 49\n\n\\bibitem[Hogg {et~al.} 1998]{Hogg:98}\nHogg, D.~W. {et~al.} 1998, \\apj, 504, 622\n\n\\bibitem[Hu, Cowie, \\& McMahon 1998]{Hu:98}\nHu, E.~M., Cowie, L.~L., \\& McMahon, R.~G. 1998, \\apj, 502, 99\n\n\\bibitem[Hu, McMahon, \\& Cowie 1999]{Hu:99}\nHu, E.~M., McMahon, R.~G., \\& Cowie, L.~L. 1999, \\apj, 522, 9\n\n\\bibitem[Hu \\& Ridgway 1994]{Hu:94}\nHu, E.~M. \\& Ridgway, S.~E. 1994, \\aj, 107, 1303\n\n\\bibitem[Kennicutt 1992]{Kennicutt:92}\nKennicutt, R. 1992, \\apj, 388, 310\n\n\\bibitem[Kriss 1994]{Kriss:94}\nKriss, G. 1994, in {\\it Astronomical Data Analysis Software and Systems III }, Vol.~61 (San Francisco: ASP Conference Series), 437\n\n\\bibitem[Kunth, Terlevich, Terlevich, \\& Tenorio-Tagle 1999]{Kunth:98b}\nKunth, D., Terlevich, E., Terlevich, R., \\& Tenorio-Tagle, G. 1999, in {\\it Dwarf Galaxies and Cosmology}, ed. T.~X. Thuan (Gif-sur-Yvette: Editions Frontieres), in press\n\n\\bibitem[Leitherer, Carmelle, \\& Heckman 1995]{Leitherer:95}\nLeitherer, C., Carmelle, R., \\& Heckman, T.~M. 1995, \\apjs, 99, 173\n\n\\bibitem[Madau 1995]{Madau:95}\nMadau, P. 1995, \\apj, 441, 18\n\n\\bibitem[Manning, Stern, Spinrad, \\& Bunker 2000]{Manning:00}\nManning, C., Stern, D., Spinrad, H., \\& Bunker, A.~J. 2000, \\apj, submitted\n\n\\bibitem[Massey \\& Gronwall 1990]{Massey:90}\nMassey, P. \\& Gronwall, C. 1990, \\apj, 358, 344\n\n\\bibitem[Massey, Strobel, Barnes, \\& Anderson 1988]{Massey:88}\nMassey, P., Strobel, K., Barnes, J.~V., \\& Anderson, E. 1988, \\apj, 328, 315\n\n\\bibitem[McCarthy 1991]{McCarthy:91}\nMcCarthy, P.~J. 1991, \\aj, 102, 518\n\n\\bibitem[McCarthy 1993]{McCarthy:93}\n---. 1993, \\araa, 31, 639\n\n\\bibitem[McCarthy \\& Lawrence 1999]{McCarthy:99a}\nMcCarthy, P.~J. \\& Lawrence, C.~R. 1999, \\apj, in preparation\n\n\\bibitem[Oke {et~al.} 1995]{Oke:95}\nOke, J.~B. {et~al.} 1995, \\pasp, 107, 375\n\n\\bibitem[Pritchet 1994]{Pritchet:94}\nPritchet, C.~J. 1994, \\pasp, 106, 1052\n\n\\bibitem[Schlegel, Finkbeiner, \\& Davis 1998]{Schlegel:98}\nSchlegel, D., Finkbeiner, D., \\& Davis, M. 1998, \\apj, 500, 525\n\n\\bibitem[Songaila, Cowie, Hu, \\& Gardner 1994]{Songaila:94}\nSongaila, A., Cowie, L.~L., Hu, E.~M., \\& Gardner, J.~P. 1994, \\apjs, 94, 461\n\n\\bibitem[Spinrad, Dey, Stern, Peacock, Dunlop, Jimenez, \\& Windhorst 1997]{Spinrad:97}\nSpinrad, H., Dey, A., Stern, D., Peacock, J.~A., Dunlop, J., Jimenez, R., \\& Windhorst, R.~A. 1997, \\apj, 484, 581\n\n\\bibitem[Spinrad, Stern, Bunker, Dey, Lanzetta, Yahil, Pascarelle, \\& Fern\\`andez-Soto 1998]{Spinrad:98}\nSpinrad, H., Stern, D., Bunker, A.~J., Dey, A., Lanzetta, K., Yahil, A., Pascarelle, S., \\& Fern\\`andez-Soto, A. 1998, \\aj, 116, 2617\n\n\\bibitem[Stern, Bunker, Spinrad, \\& Dey 1999a]{Stern:99d}\nStern, D., Bunker, A.~J., Spinrad, H., \\& Dey, A. 1999a, \\baas, 193, \\#122.09\n\n\\bibitem[Stern, Dey, Spinrad, Maxfield, Dickinson, Schlegel, \\& Gonz\\'alez 1999b]{Stern:99a}\nStern, D., Dey, A., Spinrad, H., Maxfield, L.~M., Dickinson, M.~E., Schlegel, D., \\& Gonz\\'alez, R.~A. 1999b, \\aj, 117, 1122\n\n\\bibitem[Stern \\& Spinrad 1999]{Stern:99e}\nStern, D. \\& Spinrad, H. 1999, \\pasp, 111, 1475\n\n\\bibitem[Stockton \\& Ridgway 1998]{Stockton:98}\nStockton, A. \\& Ridgway, S.~E. 1998, \\aj, 115, 1340\n\n\\bibitem[Tenorio-Tagle, Kunth, Terlevich, Terlevich, \\& Silich 1999]{TenorioTagle:99}\nTenorio-Tagle, G., Kunth, D., Terlevich, E., Terlevich, R., \\& Silich, S.~A. 1999, \\mnras, in press, astro-ph/9905324\n\n\\bibitem[Terlevich, D\\`iaz, Terlevich, \\& Garc\\`ia 1993]{Terlevich:93}\nTerlevich, E., D\\`iaz, A.~I., Terlevich, R., \\& Garc\\`ia, M.~L. 1993, \\mnras, 260, 3\n\n\\bibitem[Terlevich, Melnick, Masegosa, Moles, \\& Copetti 1991]{Terlevich:91}\nTerlevich, R., Melnick, J., Masegosa, J., Moles, M., \\& Copetti, M.~V.~F. 1991, \\aaps, 91, 285\n\n\\bibitem[Thommes 1999]{Thommes:99}\nThommes, E. 1999, in {\\it From Stars to Galaxies to the Universe}, in press, astro-ph/9812223\n\n\\bibitem[Thommes, Meisenheimer, Fockenbrock, Hippelein, R\\\"oser, \\& Beckwith 1998]{Thommes:98}\nThommes, E., Meisenheimer, K., Fockenbrock, R., Hippelein, H., R\\\"oser, H.~J., \\& Beckwith, S. 1998, \\mnras, 293, L6\n\n\\bibitem[Thompson \\& Djorgovski 1995]{Thompson:95}\nThompson, D. \\& Djorgovski, S.~G. 1995, \\aj, 110, 982\n\n\\bibitem[Thuan \\& Izotov 1997]{Thuan:97a}\nThuan, T.~X. \\& Izotov, Y.~I. 1997, \\apj, 489, 623\n\n\\bibitem[Trauger {et~al.} 1994]{Trauger:94}\nTrauger, S. {et~al.} 1994, \\apj, 435, 3\n\n\\bibitem[van Breugel, {De~Breuck}, Stanford, Stern, R\\\"ottgering, \\& Miley 1999]{vanBreugel:99a}\nvan Breugel, W., {De~Breuck}, C., Stanford, S.~A., Stern, D., R\\\"ottgering, H., \\& Miley, G. 1999, \\apjl, 518, L61\n\n\\bibitem[Vogt {et~al.} 1997]{Vogt:97}\nVogt, N. {et~al.} 1997, \\apj, 435, 3\n\n\\bibitem[Weymann, Stern, Bunker, Spinrad, Chaffee, Thompson, \\& Storrie-Lombardi 1998]{Weymann:98}\nWeymann, R., Stern, D., Bunker, A.~J., Spinrad, H., Chaffee, F., Thompson, R., \\& Storrie-Lombardi, L. 1998, \\apj, 505, L95\n\n\\end{thebibliography}\n\n\\eject\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002239.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Becker, White, \\& Helfand 1995]{Becker:95}\nBecker, R.~H., White, R.~L., \\& Helfand, D.~J. 1995, \\apj, 450, 559\n\n\\bibitem[Bunker, Moustakas, \\& Davis 2000]{Bunker:00a}\nBunker, A.~J., Moustakas, L.~A., \\& Davis, M. 2000, \\apj, in press (March)\n\n\\bibitem[Charlot \\& Fall 1993]{Charlot:93}\nCharlot, S. \\& Fall, S.~M. 1993, \\apj, 378, 471\n\n\\bibitem[Chen, Lanzetta, \\& Pascarelle 1999]{Chen:99}\nChen, H.-W., Lanzetta, K.~M., \\& Pascarelle, S. 1999, \\nat, 398, 586\n\n\\bibitem[Cowie \\& Hu 1998]{Cowie:98}\nCowie, L. \\& Hu, E.~M. 1998, \\aj, 115, 1319\n\n\\bibitem[Dey 1999]{Dey:99c}\nDey, A. 1999, in {\\it The Most Disant Radio Galaxies}, ed. H.~R\\\"ottgering, P.~N. Best, \\& M.~D. Lehnert (Dordrecht: Kluwer), 19\n\n\\bibitem[Dey, Graham, Ivison, Smail, Wright, \\& Liu 1999]{Dey:99a}\nDey, A., Graham, J.~R., Ivison, R.~J., Smail, I., Wright, G.~S., \\& Liu, M.~C. 1999, \\apj, 519, 610\n\n\\bibitem[Dey, Spinrad, Stern, Graham, \\& Chaffee 1998]{Dey:98}\nDey, A., Spinrad, H., Stern, D., Graham, J.~R., \\& Chaffee, F. 1998, \\apj, 498, L93\n\n\\bibitem[Dressler \\& Gunn 1990]{Dressler:90}\nDressler, A. \\& Gunn, J.~E. 1990, in {\\it Evolution of the Universe of Galaxies: the Edwin Hubble Centennial Symposium}, ed. R.~G. Kron, Vol.~10 (San Francisco: ASP Conference Series), 200\n\n\\bibitem[Fanelli, O'Connell, Burstein, \\& Wu 1992]{Fanelli:92}\nFanelli, M.~N., O'Connell, R.~W., Burstein, D., \\& Wu, C.~C. 1992, \\apjs, 82, 197\n\n\\bibitem[Frye \\& Broadhurst 1998]{Frye:98}\nFrye, B. \\& Broadhurst, T.~J. 1998, \\apj, 499, 115\n\n\\bibitem[Guzm\\`an {et~al.} 1997]{Guzman:97}\nGuzm\\`an, R. {et~al.} 1997, \\apj, 489, 559\n\n\\bibitem[Hamilton 1985]{Hamilton:85}\nHamilton, D. 1985, \\apj, 297, 371\n\n\\bibitem[Hammer {et~al.} 1997]{Hammer:97}\nHammer, F. {et~al.} 1997, \\apj, 481, 49\n\n\\bibitem[Hogg {et~al.} 1998]{Hogg:98}\nHogg, D.~W. {et~al.} 1998, \\apj, 504, 622\n\n\\bibitem[Hu, Cowie, \\& McMahon 1998]{Hu:98}\nHu, E.~M., Cowie, L.~L., \\& McMahon, R.~G. 1998, \\apj, 502, 99\n\n\\bibitem[Hu, McMahon, \\& Cowie 1999]{Hu:99}\nHu, E.~M., McMahon, R.~G., \\& Cowie, L.~L. 1999, \\apj, 522, 9\n\n\\bibitem[Hu \\& Ridgway 1994]{Hu:94}\nHu, E.~M. \\& Ridgway, S.~E. 1994, \\aj, 107, 1303\n\n\\bibitem[Kennicutt 1992]{Kennicutt:92}\nKennicutt, R. 1992, \\apj, 388, 310\n\n\\bibitem[Kriss 1994]{Kriss:94}\nKriss, G. 1994, in {\\it Astronomical Data Analysis Software and Systems III }, Vol.~61 (San Francisco: ASP Conference Series), 437\n\n\\bibitem[Kunth, Terlevich, Terlevich, \\& Tenorio-Tagle 1999]{Kunth:98b}\nKunth, D., Terlevich, E., Terlevich, R., \\& Tenorio-Tagle, G. 1999, in {\\it Dwarf Galaxies and Cosmology}, ed. T.~X. Thuan (Gif-sur-Yvette: Editions Frontieres), in press\n\n\\bibitem[Leitherer, Carmelle, \\& Heckman 1995]{Leitherer:95}\nLeitherer, C., Carmelle, R., \\& Heckman, T.~M. 1995, \\apjs, 99, 173\n\n\\bibitem[Madau 1995]{Madau:95}\nMadau, P. 1995, \\apj, 441, 18\n\n\\bibitem[Manning, Stern, Spinrad, \\& Bunker 2000]{Manning:00}\nManning, C., Stern, D., Spinrad, H., \\& Bunker, A.~J. 2000, \\apj, submitted\n\n\\bibitem[Massey \\& Gronwall 1990]{Massey:90}\nMassey, P. \\& Gronwall, C. 1990, \\apj, 358, 344\n\n\\bibitem[Massey, Strobel, Barnes, \\& Anderson 1988]{Massey:88}\nMassey, P., Strobel, K., Barnes, J.~V., \\& Anderson, E. 1988, \\apj, 328, 315\n\n\\bibitem[McCarthy 1991]{McCarthy:91}\nMcCarthy, P.~J. 1991, \\aj, 102, 518\n\n\\bibitem[McCarthy 1993]{McCarthy:93}\n---. 1993, \\araa, 31, 639\n\n\\bibitem[McCarthy \\& Lawrence 1999]{McCarthy:99a}\nMcCarthy, P.~J. \\& Lawrence, C.~R. 1999, \\apj, in preparation\n\n\\bibitem[Oke {et~al.} 1995]{Oke:95}\nOke, J.~B. {et~al.} 1995, \\pasp, 107, 375\n\n\\bibitem[Pritchet 1994]{Pritchet:94}\nPritchet, C.~J. 1994, \\pasp, 106, 1052\n\n\\bibitem[Schlegel, Finkbeiner, \\& Davis 1998]{Schlegel:98}\nSchlegel, D., Finkbeiner, D., \\& Davis, M. 1998, \\apj, 500, 525\n\n\\bibitem[Songaila, Cowie, Hu, \\& Gardner 1994]{Songaila:94}\nSongaila, A., Cowie, L.~L., Hu, E.~M., \\& Gardner, J.~P. 1994, \\apjs, 94, 461\n\n\\bibitem[Spinrad, Dey, Stern, Peacock, Dunlop, Jimenez, \\& Windhorst 1997]{Spinrad:97}\nSpinrad, H., Dey, A., Stern, D., Peacock, J.~A., Dunlop, J., Jimenez, R., \\& Windhorst, R.~A. 1997, \\apj, 484, 581\n\n\\bibitem[Spinrad, Stern, Bunker, Dey, Lanzetta, Yahil, Pascarelle, \\& Fern\\`andez-Soto 1998]{Spinrad:98}\nSpinrad, H., Stern, D., Bunker, A.~J., Dey, A., Lanzetta, K., Yahil, A., Pascarelle, S., \\& Fern\\`andez-Soto, A. 1998, \\aj, 116, 2617\n\n\\bibitem[Stern, Bunker, Spinrad, \\& Dey 1999a]{Stern:99d}\nStern, D., Bunker, A.~J., Spinrad, H., \\& Dey, A. 1999a, \\baas, 193, \\#122.09\n\n\\bibitem[Stern, Dey, Spinrad, Maxfield, Dickinson, Schlegel, \\& Gonz\\'alez 1999b]{Stern:99a}\nStern, D., Dey, A., Spinrad, H., Maxfield, L.~M., Dickinson, M.~E., Schlegel, D., \\& Gonz\\'alez, R.~A. 1999b, \\aj, 117, 1122\n\n\\bibitem[Stern \\& Spinrad 1999]{Stern:99e}\nStern, D. \\& Spinrad, H. 1999, \\pasp, 111, 1475\n\n\\bibitem[Stockton \\& Ridgway 1998]{Stockton:98}\nStockton, A. \\& Ridgway, S.~E. 1998, \\aj, 115, 1340\n\n\\bibitem[Tenorio-Tagle, Kunth, Terlevich, Terlevich, \\& Silich 1999]{TenorioTagle:99}\nTenorio-Tagle, G., Kunth, D., Terlevich, E., Terlevich, R., \\& Silich, S.~A. 1999, \\mnras, in press, astro-ph/9905324\n\n\\bibitem[Terlevich, D\\`iaz, Terlevich, \\& Garc\\`ia 1993]{Terlevich:93}\nTerlevich, E., D\\`iaz, A.~I., Terlevich, R., \\& Garc\\`ia, M.~L. 1993, \\mnras, 260, 3\n\n\\bibitem[Terlevich, Melnick, Masegosa, Moles, \\& Copetti 1991]{Terlevich:91}\nTerlevich, R., Melnick, J., Masegosa, J., Moles, M., \\& Copetti, M.~V.~F. 1991, \\aaps, 91, 285\n\n\\bibitem[Thommes 1999]{Thommes:99}\nThommes, E. 1999, in {\\it From Stars to Galaxies to the Universe}, in press, astro-ph/9812223\n\n\\bibitem[Thommes, Meisenheimer, Fockenbrock, Hippelein, R\\\"oser, \\& Beckwith 1998]{Thommes:98}\nThommes, E., Meisenheimer, K., Fockenbrock, R., Hippelein, H., R\\\"oser, H.~J., \\& Beckwith, S. 1998, \\mnras, 293, L6\n\n\\bibitem[Thompson \\& Djorgovski 1995]{Thompson:95}\nThompson, D. \\& Djorgovski, S.~G. 1995, \\aj, 110, 982\n\n\\bibitem[Thuan \\& Izotov 1997]{Thuan:97a}\nThuan, T.~X. \\& Izotov, Y.~I. 1997, \\apj, 489, 623\n\n\\bibitem[Trauger {et~al.} 1994]{Trauger:94}\nTrauger, S. {et~al.} 1994, \\apj, 435, 3\n\n\\bibitem[van Breugel, {De~Breuck}, Stanford, Stern, R\\\"ottgering, \\& Miley 1999]{vanBreugel:99a}\nvan Breugel, W., {De~Breuck}, C., Stanford, S.~A., Stern, D., R\\\"ottgering, H., \\& Miley, G. 1999, \\apjl, 518, L61\n\n\\bibitem[Vogt {et~al.} 1997]{Vogt:97}\nVogt, N. {et~al.} 1997, \\apj, 435, 3\n\n\\bibitem[Weymann, Stern, Bunker, Spinrad, Chaffee, Thompson, \\& Storrie-Lombardi 1998]{Weymann:98}\nWeymann, R., Stern, D., Bunker, A.~J., Spinrad, H., Chaffee, F., Thompson, R., \\& Storrie-Lombardi, L. 1998, \\apj, 505, L95\n\n\\end{thebibliography}"
}
] |
astro-ph0002240
|
Projected bispectrum in spherical harmonics and its application to angular galaxy catalogues
|
[
{
"author": "Licia Verde$^{1}$"
},
{
"author": "Alan F. Heavens$^{1}$"
},
{
"author": "Sabino Matarrese$^{2,3}$"
},
{
"author": "Royal Observatory"
},
{
"author": "Blackford Hill"
},
{
"author": "Edinburgh EH9 3HJ"
},
{
"author": "United Kingdom"
},
{
"author": "$^{2}$ Dipartimento di Fisica {\\em Galileo Galilei}"
},
{
"author": "Universit\\`{a} di Padova"
},
{
"author": "via Marzolo 8"
},
{
"author": "I-35131 Padova"
},
{
"author": "Italy"
},
{
"author": "$^{3}$ Max-Planck-Institut f\\\"ur Astrophysik"
},
{
"author": "Karl-Schwarzschild-Strasse 1"
},
{
"author": "D-85748 Garching"
},
{
"author": "Germany."
}
] |
We present a theoretical and exact analysis of the bispectrum of projected galaxy catalogues. The result can be generalized to evaluate the projection in spherical harmonics of any 3D bispectrum and therefore has applications to cosmic microwave background and gravitational lensing studies. By expanding the 2D distribution of galaxies on the sky in spherical harmonics, we show how the 3-point function of the coefficients can be used in principle to determine the bias parameter of the galaxy sample. If this can be achieved, it would allow a lifting of the degeneracy between the bias and the matter density parameter of the Universe which occurs in linear analysis of 3D galaxy catalogues. In previous papers we have shown how a similar analysis can be done in three dimensions, and we show here through an error analysis and by implementing the method on a simulated projected catalogue that ongoing three-dimensional galaxy redshift surveys (even with all the additional uncertainties introduced by partial sky coverage, redshift-space distortions and smaller numbers) will do far better than all-sky projected catalogues with similar selection function.
|
[
{
"name": "projbisp2.tex",
"string": "\\documentstyle[onecolumn,epsf,mnras_cite]{mn}\n\\input{epsf}\n\\newcommand{\\ba}{\\begin{eqnarray}}\n\\newcommand{\\ea}{\\end{eqnarray}}\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\nn}{\\nonumber \\\\}\n\\newcommand{\\vk}{{\\bf{k}}}\n\\newcommand{\\vkone}{{\\bf{k}_1}}\n\\newcommand{\\vktwo}{{\\bf{k}_2}}\n\\newcommand{\\vkthree}{{\\bf{k}_3}}\n\\newcommand{\\kvone}{{\\bf{k}_1}}\n\\newcommand{\\kvtwo}{{\\bf{k}_2}}\n\\newcommand{\\vr}{{\\bf{r}}}\n\\newcommand{\\vx}{{\\bf{x}}}\n\\newcommand{\\ls}{\\mathrel{\\raise1.16pt\\hbox{$<$}\\kern-7.0pt % <\n\\lower3.06pt\\hbox{{$\\scriptstyle \\sim$}}}} % ~\n\\newcommand{\\gs}{\\mathrel{\\raise1.16pt\\hbox{$>$}\\kern-7.0pt % >\n\\lower3.06pt\\hbox{{$\\scriptstyle \\sim$}}}} % ~\n%\n\\def\\VEV#1{{\\langle #1 \\rangle}}\n\\long\\def\\comment#1{}\n\\def\\hatn{{\\bf \\hat n}}\n\\def\\fun#1#2{\\lower3.6pt\\vbox{\\baselineskip0pt\\lineskip.9pt\n \\ialign{$\\mathsurround=0pt#1\\hfil##\\hfil$\\crcr#2\\crcr\\sim\\crcr}}}\n\\def\\lap{\\mathrel{\\mathpalette\\fun <}}\n\\def\\gap{\\mathrel{\\mathpalette\\fun >}}\n\\newcommand{\\vkappa}{\\mbox{\\boldmath $\\kappa$}}\n\\newcommand{\\vtheta}{\\mbox{\\boldmath $\\theta$}}\n%\n\\title{Projected bispectrum in spherical harmonics and its application to \nangular galaxy catalogues}\n\\author[Licia Verde, Alan F. Heavens, Sabino Matarrese]\n{Licia Verde$^{1}$, Alan F. Heavens$^{1}$, Sabino Matarrese$^{2,3}$\\\\\n$^{1}$ Institute for Astronomy, University of Edinburgh, Royal Observatory,\nBlackford Hill, Edinburgh EH9 3HJ, United Kingdom\\\\\n$^{2}$ Dipartimento di Fisica {\\em Galileo Galilei}, Universit\\`{a} di\nPadova, via Marzolo 8, I-35131 Padova, Italy\\\\\n$^{3}$ Max-Planck-Institut f\\\"ur Astrophysik, \nKarl-Schwarzschild-Strasse 1, D-85748 Garching, Germany. }\n%\\date{Accepted 2000 ???? ???; Received 2000 ???? ???;\n%in original form 2000 ???? ??}\n\\begin{document}\n%\\baselineskip=20pt\n\\maketitle\n\\begin{abstract}\nWe present a theoretical and exact analysis of the bispectrum of projected\ngalaxy catalogues. The result can be generalized to evaluate the projection \nin spherical harmonics of any 3D bispectrum and therefore has\napplications to cosmic microwave background and gravitational lensing studies.\n\nBy expanding the 2D distribution of galaxies on\nthe sky in spherical harmonics, we show how the 3-point function of\nthe coefficients can be used in principle to determine the bias\nparameter of the galaxy sample. If this can be achieved, it would\nallow a lifting of the degeneracy between the bias and the\nmatter density parameter of the Universe which occurs in linear\nanalysis of 3D galaxy catalogues. In previous papers we have shown\nhow a similar analysis can be done in three dimensions, and we show\nhere through an error analysis and by implementing the method on a\nsimulated projected catalogue that ongoing three-dimensional galaxy\nredshift surveys (even with all the additional uncertainties introduced by partial sky coverage, redshift-space distortions and smaller numbers) will do far better than all-sky\nprojected catalogues with similar selection function.\n\\end{abstract}\n\n\\begin{keywords}\ncosmology: theory - galaxies: clustering - bias -\nlarge-scale structure of the Universe\n\\end{keywords}\n\n\\section{Introduction}\n\nThe clustering of mass in the Universe is an important fossil record\nof the early perturbations which gave rise to large-scale structure\ntoday. Knowledge of the mass clustering puts powerful constraints on\nthe quantity and properties of dark matter in the Universe, and the\ngeneration mechanism for the perturbations. Most of our knowledge of\nthe mass clustering is, however, indirect, coming principally from the\ndistribution of galaxies. A major obstacle in interpretation is\ntherefore the uncertain relationship between galaxy and mass\nclustering - a relationship which is conventionally quantified by the\n`bias parameter', $b$. In particular, attempts based on linear\nperturbation theory to measure the density parameter of the Universe,\n$\\Omega_0$, through peculiar velocity or redshift-distortion studies,\nyield only the degenerate combination $\\beta=\\Omega_0^{0.6}/b$, making\nit impossible to determine $\\Omega_0$ without determining $b$. The\ndegeneracy can be lifted by going to second order in perturbation\ntheory, and this can be achieved most elegantly by studying the\nbispectrum, which is the three-point function in Fourier (or spherical\nharmonic) space. A major positive feature of the bispectrum method is\nthat it can provide error bars on the desired parameters. The method\nworks because gravitational instability leads to a density field which\nis progressively more skewed to high densities as it develops, and\nthis skewness appears as a non-zero bispectrum. This behaviour can\nalso be mimicked by biasing, if the galaxy density field is a local,\nnonlinear function of the underlying mass density field. This\npossibility must be dealt with. The two effects can, however, be\nseparated by the use of information about the shape of the structures:\nin essence the effect of biasing is to shift iso-density contours up\n(or down), while maintaining the shape of the contour; gravitational\nevolution, instead, changes the shape, usually leading to flattening\nof collapsing structures (e.g. Zel'dovich pancakes).\n\n\\scite{Fry94} recognized the role the bispectrum could play in\ndetermining the bias parameter, and \\scite{MVH97} (hereafter MVH97)\nand \\scite{VHMM98} have turned the idea into a practical proposition\nfor 3D galaxy redshift surveys by including analysis of selection\nfunctions, shot noise, and redshift distortions (see also\n\\pcite{SCF98}). The latter is potentially a serious problem for 3D\nsurveys, as the signal for bias comes from mildly nonlinear scales,\nwhere the redshift distortions are not trivial to analyze. However,\nexperiments on simulated catalogues \\cite{VHMM98} show that the method\nis successful. Note however that the theory has been developed only\nin the `distant-observer approximation' (see e.g. \\pcite{Kaiser92}), and is\napplicable to relatively deep surveys such as the Anglo-Australian\ntwo-degree field galaxy redshift survey (\\pcite{colles96,Colles99})\nand the Sloan Digital Sky Survey (\\pcite{SDSS}). Shallow surveys such\nas the IRAS PSCz should be analysed in spherical coordinates\n(cf Taylor \\& Heavens 1995; Tadros et al. 1999 for the \npower spectrum), and suffer from high shot noise, so cannot be usefully used\nfor bispectrum analysis based on a Fourier expansion (see also \n\\pcite{Bharadwaj}).\n\nThe absence of suitable existing 3D surveys prompts us to consider\nwhether the bias might be extracted from a projected galaxy catalogue,\nsuch as the APM galaxy survey (\\pcite{maddoxetal90,Lov92,JonAPMcat}).\nWith only angular positions, the information is more limited, but the\nsurvey is not complicated by redshift distortions, and contains a\nlarge number $\\sim 10^6$ of galaxies. The DPOSS catalogue\n(\\pcite{DPOSS}) will be even larger, with 50 million galaxies and\nnearly all-sky. \nThere are two important caveats to keep in mind: first, to have a\nmeasurement of $\\Omega_0$ we need to be able to measure the $\\beta$ parameter\nand the linear bias parameter. It is not possible to extract the $\\beta$\nparameter from a two-dimensional survey, $\\beta$ will need to be determined\nfrom a -{\\em different}- three-dimensional survey. The selection criteria will\nnecessarily be different for different catalogues, and so will be the galaxy\npopulation selected. Since different galaxy populations can have different bias\nwith respect to the underlying dark matter distribution, some care needs to be\ntaken in the interpretation of the final result i.e. the value for $\\Omega_0$.\nThe other caveat concerns the effect of the evolution along the line of sight\n(also referred to as the {\\it light-cone effect}). This is due to the fact\nthat galaxy clustering evolves gravitationally with time along the line of\nsight and depends on the (unknown) cosmology. For shallow surveys such as the\nAPM, this effect is smaller or comparable to the cosmic variance, in what follows we will neglect this effect for this\nreason. However, for deeper\nsurveys, this effect needs to be properly taken into account. Assuming these\nissues can be dealt with, the key requirement is to obtain an expression\nfor the projected bispectrum given an analytical formula for the spatial one.\nAn expression for the projected bispectrum in the small angle approximation\nhas been presented by \\scite{BKJ99}.\nHowever this might not be a good approximation for the bispectrum if the\nsample is close enough to the observer or if the scales under analysis are large. In fact it is not known {\\it a priori} whether, for the bispectrum, the small angle approximation is valid on large enough\nscales for the second order perturbation theory to hold:\nit is necessary to obtain an exact expression for the projected\nbispectrum using spherical harmonics expansion. Only then it will be possible to\ntest the limit of validity for the small-angle approximation bispectrum (Verde\net al. 2000).\n\nIn this paper, we develop the theory for projected catalogues in a\nfull treatment. The resulting expression for the spherical harmonic projected\nbispectrum can straightforwardly be\napplied to gravitational lensing and to cosmic microwave background (CMB)\nstudies, for comparison with observations such as the claimed detection by \\scite{FMG98}.\n\n In Section 2 we expand the sky density of galaxies in\nspherical harmonics with coefficients $a_\\ell^m$, and compute an\nexplicit expression for the bispectrum $\\langle a_{\\ell_1}^{m_1}\na_{\\ell_2}^{m_2} a_{\\ell_3}^{m_3}\n\\rangle$ accurate to second-order in perturbation theory. In\nparticular, we show how this quantity depends on the bias parameter.\nWe present in Section 3 an error analysis specific to the second-order\nperturbation theory bispectrum, which shows the expected\nuncertainty in the derived bias parameter, and test on a numerical\nsimulation. In the Appendices, we detail asymptotic results which are \nuseful for high-$\\ell$ spherical harmonics. The main conclusion of\n large-scale structure application in this paper is that 3D large scale\nstructure surveys (even with small sky coverage, smaller numbers, and the complications of\nredshift-space distortion, shot noise etc.) will do far better than all-sky \nprojected catalogues for the purpose of measuring the bias parameter. \n However the mathematics developed for this purpose has much wider applications: with\nappropriate radial weight functions, the analysis can be applied to the CMB\nbispectrum induced by lensing, Sunyaev-Zel'dovich effect, the integrated\nSachs-Wolfe effect or foreground point sources, and to gravitational lenses studies.\n\n\\section{Projected Bispectrum in Spherical Harmonics}\n\nLet the projected galaxy density field be $n(\\Omega)$, where $\\Omega$\nrepresents angular positions in the sky. If the three-dimensional\ngalaxy density field is $\\rho(\\vr)$ (with mean $\\overline{\\rho}$) and\nthe selection function is $\\psi(r)$, the projected density is\n\n\\be\nn(\\Omega)d\\Omega =\\left(\\int dr\\, r^2 \\rho(\\vr)\\psi(r)\\right)d\\Omega.\n\\ee\n\nWe expand the projected density in spherical harmonics (see Appendix A\nfor definitions)\n\\ba\na^m_{\\ell} & \\equiv &\\frac{1}{\\overline{n}}\\int d\\Omega\\,\nn(\\Omega)Y_{\\ell}^m(\\Omega)\\nn\n& =&\\frac{\\overline{\\rho}}{\\overline{n}}\\int\nd\\Omega dr \\, r^2 \\delta(r)\\psi(r) Y_{\\ell}^m(\\Omega)\\mbox{ for ${\\ell}\\neq 0$ }\n\\label{blm}\n\\ea\nwhere $\\delta \\equiv (\\rho-\\overline{\\rho})/\\overline{\\rho}$ is the\nfractional overdensity in galaxies. The average surface density is\n\\be\n\\overline{n}=\\int dr\\,r^2\\overline{\\rho}\\psi(r).\n\\ee\nand is inserted in the transform for convenience. The three-point function of the\ncoefficients may be factorised by isotropy (e.g. \\pcite{Luo94}) into\n\\be\n\\langle a_{\\ell_1}^{m_1} a_{\\ell_2}^{m_2} a_{\\ell_3}^{m_3}\\rangle=B_{\\ell_1\\ell_2\\ell_3}\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m_1m_2m_3} \\right)\n\\label{eq:2dbispluo}\n\\ee\nwhere $\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m_1m_2m_3} \\right)$ is the\nWigner 3J symbol. We refer to $B_{\\ell_1\\ell_2\\ell_3}$ as the\nangular bispectrum. From general considerations about rotational\ninvariance of the quantity $\\langle\na_{\\ell_1}^{m_1}a_{\\ell_2}^{m_2}a_{\\ell_3}^{m_3}\n\\rangle $ the indices $\\ell_i, m_i$ for $i=1,2,3$ must satisfy the\nfollowing conditions:\n\\begin{itemize}\n\\item[{\\it (i)}] $\\ell_j +\\ell_k\\geq\\ell_1 \\geq \\mid \\ell_j- \\ell_k \\mid$ (triangle rule)\n\\item[{\\it (ii)}] $\\ell_1 +\\ell_2+\\ell_3=$ even\n\\item[{\\it (iii)}] $m_1+m_2+m_3=0$.\n\\end{itemize}\nThe presence of the 3J symbol ensures that these conditions are\nsatisfied. \n\nIn order to be able\nto extract the bias parameter from projected catalogues, the effect of the\nprojection in the configuration dependence of the bispectrum needs to be\nunderstood (\\pcite{FryThomas99}).\n\nTo do so, we compute the angular bispectrum in terms of the 3D\nbispectrum, $B(\\vk_1,\\vk_2,\\vk_3)$ defined by $\\langle \\delta_{\\vk1}\n\\delta_{\\vk2}\\delta_{\\vk3}\\rangle=(2\\pi)^3 B(\\vk_1,\\vk_2,\\vk_3) \n\\delta^D(\\vk_1+\\vk_2+\\vk_3)$, where the Fourier transform of\n$\\delta$ is $\\delta_\\vk \\equiv \\int d^3\\vr ~\\delta(\\vr) \\exp(i\\vk\\cdot\n\\vr)$, and $\\delta^{D}$ denotes the Dirac delta function.\n\nWe proceed from (\\ref{blm}):\n\\be\n\\langle a_{\\ell_1}^{m_1} a_{\\ell_2}^{m_2} a_{\\ell_3}^{m_3}\\rangle=\n\\left(\\frac{\\overline{\\rho}}{\\overline{n}}\\right)^3\\int\nd\\Omega_1 d\\Omega_2 d\\Omega_3 dr_1 dr_2 dr_3 r_1^2 r_2^2r_3^2\n\\psi_1 \\psi_2 \\psi_3\n \\langle\\delta(\\vr_1)\\delta(\\vr_2)\\delta(\\vr_3) \\rangle\n Y_{\\ell_1}^{m_1}(\\Omega_1)Y_{\\ell_2}^{m_2}(\\Omega_2)Y_{\\ell_3}^{m_3}\n(\\Omega_3) \\;.\n\\ee\nThe 3D three-point function (in real space) is related to the 3D\nbispectrum by\n\\be\n\\langle \\delta(\\vr_1)\\delta(\\vr_2)\\delta(\\vr_3) \\rangle=\n\\frac{1}{(2\\pi)^6}\\int d^3\\vk_1 d^3\\vk_2 d^3\\vk_3 B(\\vk_1,\\vk_2,\\vk_3)e^{i(\\vk_1\\cdot\n\\vr_1+\\vk_2\\cdot \\vr_2+ \\vk_3\\cdot\n\\vr_3)}\\delta^{D}(\\vk_1+\\vk_2+\\vk_3) \\;.\n\\ee\nWe then define the quantity:\n\\be\nI(\\vr_1,\\vr_2,\\vr_3) \n\\equiv\\int_0^{\\infty}dk_1dk_2dk_3k_1^2k_2^2k_3^2\\int_{4\\pi}d\\Omega_{k_1}\nd\\Omega_{k_2} d\\Omega_{k_3} B(\\vkone,\\vktwo,\\vkthree)\ne^{i(\\vkone\\cdot\\vr_1+\\vktwo\\cdot\\vr_2+\\vkthree\\cdot\\vr_3)}\n\\delta^D(\\vkone+\\vktwo+\\vkthree)\n\\label{eq.I123}\n\\ee\nbecause we will later expand the exponential in spherical harmonics and\nperform the angular integrations in (\\ref{eq.I123}) explicitly.\n\nIn second order perturbation theory the bispectrum is:\n\\be\nB(\\vkone,\\vktwo,\\vkthree)= {\\cal K}(\\vkone,\\vktwo)P(k_1)P(k_2)+cyc. \\;,\n\\label{eq:2OPTbisp}\n\\ee\nwhere the shape-dependent factors ${\\cal K}$ can be found in\n\\scite{Fry84}, \\scite{CLMM95} and MVH97. The dependence of ${\\cal\nK}$ on the cosmology in negligible (e.g. \\scite{KB99}\nand references therein), so in what follows we\nassume an Einstein-de Sitter Universe. The factors are, however,\ndependent on the biasing model assumed. If we take a local biasing\nmodel, then for consistency with second-order perturbation theory, we\nexpand in a Taylor series the galaxy overdensity to second-order in\nthe matter overdensity $\\delta_m$:\n\\be\n\\delta(\\vx)=b_1\\delta_m(\\vx)+{1\\over 2}b_2\\delta_m(\\vx)^2,\n\\label{eq:nlbias}\n\\ee\n(a constant term $b_0$ is irrelevant except at $\\vk={\\bf 0}$ and is\nignored). Here $b_1$ is the linear bias parameter and $b_2$ is the\nquadratic bias parameter. The linear bias parameter $b$ that appears\nin the definition of $\\beta$ and that is needed to recover $\\Omega_0$,\nis $b = b_1$ on large scales, under fairly general conditions\n(\\pcite{HMV98}). Note that we take the bias function to be\ndeterministic, not stochastic (cf\n\\pcite{CO92,DL99,TegBrom99,Matsu99,Somervilleetal99}); \nit has been shown (\\pcite{Taruyaetal99})\nthat the effect of stochastic bias on the bispectrum is very similar\nto that of nonlinear bias (Eq. \\ref{eq:nlbias}). \nThis formalism might be straightforwardly extended to the case when the\nbias process operates in Lagrangian, rather than Eulerian, space \n(\\pcite{Catelanetal98}). \n\nWith these assumptions, a typical cyclical term can be written\n\\be\n{\\cal\nK}(\\vkone,\\vktwo)=A_0+A_1\\cos(\\theta_{12})+A_2\\cos^2(\\theta_{12})\n\\ee\nwhere $\\theta_{12}$ denotes the angle between $\\vkone$ and $\\vktwo$, and\n\\ba\nA_0 &=& \\frac{10}{7}c_1+c_2 \\nn\nA_1 &=& c_1\\left(\\frac{k_1}{k_2}+\\frac{k_2}{k_1}\\right) \\nn\nA_2 &=& \\frac{4}{7}c_1,\n\\label{eq.A0A1A2}\n\\ea\nand $c_1=1/b_1$; $c_2=b_2/b_1^2$. Through these relations, the\nprojected bispectrum will depend on the bias parameters $b_1$ and $b_2$.\n\nUsing this, we will now calculate the theoretical expression for the\nprojected bispectrum in spherical harmonics in the mildly nonlinear\nregime. With substitution (\\ref{eq:2OPTbisp}) we find\n\\be\nI(\\vr_1,\\vr_2,\\vr_3)\\equiv I_{12}+I_{23}+I_{13}\n\\ee\n\nUsing the properties of spherical harmonics in Appendix A [equation\n(\\ref{eq.expspharm}), the orthogonality relation, (\\ref{eq.spharmorth})\nand (\\ref{eq.spharmconj})], we obtain that a typical cyclical term is:\n\n\\ba\n%\nI_{12}&=&(4\\pi)^4\\int_0^{\\infty}d^3\\vk_1d^3\\vk_2\n{\\cal K}(\\vk_1,\\vk_2)P(k_1)P(k_2)\\times \\nn\n%\n& &\\sum_{\\ell_1^{\\prime}m_1^{\\prime}}i^{\\ell_1^{\\prime}}j_{\\ell_1^{\\prime}}(k_1r_1)Y_{\\ell_1^{\\prime}}^{*m_1^{\\prime}}(\\Omega_{k_1})Y^{m_1^{\\prime}}_{\\ell_1^{\\prime}}(\\Omega_{r_1})\n\\sum_{\\ell_2^{\\prime}m_2^{\\prime}}i^{\\ell_2^{\\prime}}j_{\\ell_2^{\\prime}}(k_2r_2)Y_{\\ell_2^{\\prime}}^{*m_2^{\\prime}}(\\Omega_{k_2})Y^{m_2^{\\prime}}_{\\ell_2^{\\prime}}(\\Omega_{r_2})\\times \\nn\n%\n& & \\sum_{L_1 n_1}i^{L_1}j_{L_1}(k_1r_3)Y_{L_1}^{*n_1}(-\\Omega_{k_1}) Y^{n_1}_{L_1}(\\Omega_{r_3}) \\sum_{L_2n_2}i^{L_2}j_{L_2}(k_2r_3)Y_{L_2}^{*n_2}(-\\Omega_{k_2}) Y^{n_2}_{L_2}(\\Omega_{r_3}).\n%\n\\label{eq:I12} \n\\ea \n\nWe can now write \n\n\\be \n\\int_{4\\pi}d\\Omega Y^{*m_1}_{\\ell_1}(\\Omega )Y^{m_2}_{\\ell_2}(\\Omega\n)Y^{m_3}_{\\ell_3}(\\Omega)= {\\cal H}^{m_1m_2m_3}_{\\ell_1\\; \\ell_2\\; \\ell_3} \\;,\n\\ee\nwhich can be expressed\nin term of Clebsch-Gordan coefficients, and is non-zero only if\nthe following symmetry conditions are satisfied:\n\\begin{itemize}\n\\item $m_2+m_3=m_1$\n\\item $\\ell_1+\\ell_2+\\ell_3=$ even\n\\item $\\ell_1,\\ell_2,\\ell_3$ satisfy the triangle rule\n\\end{itemize}\nFrom equation (\\ref{eq:I12}) we thus obtain:\n\\be\n\\int_{4\\pi}d\\Omega_{r_1}d\\Omega_{r_2}d\\Omega_{r_3}\nY_{\\ell_1}^{m_1}\n(\\Omega_{r_1})Y_{\\ell_2}^{m_2}(\\Omega_{r_2})Y_{\\ell_3}^{m_3}(\\Omega_{r_3})I_{12}=(4\\pi)^4\\int dk_1\ndk_2k_1^2k_2^2P(k_1)P(k_2)F(r_1,r_2,r_3,k_1,k_2) \\;,\n\\ee\nwhere\n\\ba\n F(r_1,r_2,r_3,k_1,k_2)&=& \\int d\\Omega_{k_1}d\\Omega_{k_2} \\left(A_0\n +A_1\\cos\\theta_{12}+A_2\\cos^2\\theta_{12} \\right)i^{\\ell_1+\\ell_2}\n (-1)^{(m_1+m_2+m_3)}j_{\\ell_1}(k_1r_1)j_{\\ell_2}(k_2r_2) \\times \\nn & &\n \\sum_{\\ell_{6,7}m_{6,7}}i^{\\ell_6+\\ell_7}j_{\\ell_6}(k_1r_3)j_{\\ell_7}(k_2r_3)Y^{*-m_1}_{\\ell_1}(\\Omega_{k_1})Y^{*-m_2}_{\\ell_2}\n (\\Omega_{k_2})Y^{*m_6}_{\\ell_6}(-\\Omega_{k_1})Y^{*m_7}_{\\ell_7}(-\\Omega_{k_2}){\\cal H}^{-m_3m_6m_7}_{\\ell_3\\;\\ell_6\\;\\ell_7}\n\\ea\nand F can be written as $F_0+F_1+F_2$ where $F_0$ involves the term\n$A_0$ etc.\n\nThe $F_0$ term is easily calculated: \n\n\\be\nF_0=A_0i^{2(\\ell_1+\\ell_2)}j_{\\ell_1}(k_1r_1)j_{\\ell_2}(k_2r_2)j_{\\ell_1}(k_1r_3)j_{\\ell_2}(k_2r_3)\n{\\cal H}_{\\ell_3 \\;\\ell_1 \\; \\ell_2}^{-m_3 m_1 m_2} \n\\ee \nand therefore satisfies the symmetry rules.\n\nFor $F_1$ and $F_2$ we exploit the fact that:\n\\be\n\\cos\\theta_{12}=P_1(\\cos\\theta_{12}),\n\\ee\n\\be\n\\cos^2\\theta_{12}=\\frac{1}{3}\\left[2 P_2(\\cos\\theta_{12})+P_0(\\cos\\theta_{12}) \\right]\n\\ee\nand use the addition theorem for spherical harmonics:\n\\be\nP_n(\\cos\\theta_{12})=\\frac{4 \\pi}{2n+1}\\sum_{m=-n}^nY_n^m(\\Omega_{k_1})Y_n^{*m}(\\Omega_{k_2}).\n\\ee\nThe $F_1$ term then becomes:\n\\be\nF_1=A_1\\frac{4\\pi}{3}\ni^{\\ell_1+\\ell_2}(-1)^{m_1+m_3}j_{\\ell_1}(k_1r_1)j_{\\ell_2}(k_2r_2)\\sum_{\\ell_6m_6 \\ell_7m_7 M}\ni^{\\ell_6+\\ell_7}j_{\\ell_6}(k_1r_3)j_{\\ell_7}(k_2k_3) {\\cal H}^{-m_3 m_6\nm_7}_{\\ell_3 \\; \\ell_6 \\;\\ell_7}{\\cal H}^{-m_1 -m_6 M}_{\\ell_1 \\; \\ell_6\n\\;1}{\\cal H}^{M m_2 -m_7 }_{1\\; \\ell_2\\; \\ell_7}.\n\\label{eq.F1}\n\\ee\nIt is easy to see that $m_6+m_7=-m_3$. To demonstrate that the\nsymmetry conditions are all satisfied, consider the\nfollowing part of eq.(\\ref{eq.F1}):\n\\be\n\\sum_{m_6m_7M}{\\cal\nH}^{-m_3 m_6 m_7}_{\\ell_3 \\; \\ell_6 \\; \\ell_7}{\\cal H}^{-m_1 -m_6 M}_{\\ell_1\n\\;\\ell_6 \\; 1}{\\cal H}^{M m_2 -m_7}_{1\\; \\ell_2 \\; \\ell_7} \\;;\n\\ee\nlet's introduce a new\nquantity $h^{m_1m_2m_3}_{\\ell_1 \\; \\ell_2 \\; \\ell_3}$ that is symmetric for any\npermutation of the columns $\\left(^{m_i}_{\\ell_i}\\right)$. It is\nclear that:\n\\be\n{\\cal\nH}^{m_1m_2m_3}_{\\ell_1 \\; \\ell_2 \\; \\ell_3}=(-1)^{m_1}h^{-m_1m_2m_3}_{\\ell_1\n\\; \\ell_2 \\; \\ell_3}.\n\\ee\nThe quantity $h^{m_1m_2m_3}_{\\ell_1 \\; \\ell_2 \\; \\ell_3}$ can be written in terms of the $3J$ symbols:\n\\be\nh^{m_1m_2m_3}_{\\ell_1 \\; \\ell_2 \\; \\ell_3}=\\sqrt{(2 \\ell_1+1)(2\\ell_2+1)(2\\ell_3+1)/(4 \\pi)}\n\\left(^{\\ell_1\\; \\ell_2\\;\\ell_3}_{0\\;\\;\\;0\\;\\;\\;0}\\right)\n\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m_1m_2m_3} \\right).\n\\ee\nEquation (\\ref{eq.F1}) therefore contains the following multiplicative term:\n\\be\n\\sum_{m_6m_7M}(-1)^{-m3-m_1+M}\\left(^{\\ell_3\\;\\;\\;\\;\\ell_6\\;\\;\\;\\;\\ell_7}_{m_3\\;m_6\\;m_7}\\right)\n\\left(^{\\ell_1\\;\\;\\;\\;\\ell_6\\;\\;\\;\\;1}_{m_1\\;-m_6 \\;M} \\right)\n\\left(^{1\\;\\;\\;\\;\\;\\ell_2\\;\\;\\;\\;\\;\\;\\ell_7}_{-M\\;m_2\\;-m_7} \\right)=(-1)^{\\ell_6+\\ell_7+\\ell}\n\\left(^{\\ell_1\\;\\;\\;\\;\\ell_2\\;\\;\\;\\;\\ell_3}_{m_1\\;m_2\\;m_3} \\right)\n\\left\\{^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{\\ell_7\\;\\;\\; \\ell_6\\;\\;\\;\\; 1}\\right\\}\n\\label{eq.3j3j3j} \\;,\n\\ee\nwhere $\\left\\{^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{\\ell_7\\;\\;\\; \\ell_6\\;\\;\\;\\;\n1}\\right\\}$ denotes the 6J symbol.\nIn the last equality we used eq. (4.88) of \\scite{Sobelman}.\nThe properties of the 3J symbol ensure that the $F_1$ term\nsatisfies the symmetry conditions.\n\nSimilarly for the $F_2 $ term we obtain\n\\ba\nF_2 & = & A_2 i^{\\ell_1+\\ell_2}(-1)^{m_1+m_3}\\frac{4\\pi}{3}\nj_{\\ell_1}(k_1r_1)j_{\\ell_2}(k_2r_2)\n\\sum_{\\ell_{6,7}m_{6,7}M}(-i)^{\\ell_6+\\ell_7}j_{\\ell_6}(k_1r_3)j_{\\ell_7}(k_2r_3) \\times \\nn\n & & {\\cal H}^{-m3m_6 m_7}_{\\ell_3\\;\\;\\; \\ell_6\\;\\;\\; \\ell_7}\n\\left[ \\frac{2}{5}{\\cal H}^{-m1 M -m_6}_{\\ell_1\\;\\;\\; 2\\;\\;\\; \\ell_6}{\\cal H}^{M m_2\n-m_7}_{2\\;\\;\\; \\ell_2\\;\\;\\; \\ell_7} + {\\cal H}^{-m_1 0-m_6}_{\\ell_1\\;\\;\\;0\\;\\;\\; \\ell_6}\n{\\cal H}^{ 0 m_2 -m_7}_{0\\;\\;\\; \\ell_2\\;\\;\\; \\ell_7} \\right] \\;.\n\\ea\nThe second term in the square brackets does not present any\nproblem, in fact it is nonzero only if $\\ell_1=\\ell_6$, $\\ell_2=\\ell_7$,\n$m_1=m_6$, $m_2=m_7$, and satisfies the symmetry conditions.\nSimilar methods to those above complete the symmetry considerations.\n\nFactorising the Wigner 3J symbol, and collecting terms together, we\nfind the expression for the angular bispectrum, as\na sum of cyclical permutations:\n\\be\nB_{\\ell_1 \\ell_2\\ell_3}={\\cal B}_{12}+{\\cal B}_{13}+{\\cal B}_{23}\n\\label{eq:bisp1}\n\\ee\nwhere, writing $\\Psi_{\\ell}(k)=\\overline{\\rho}\\int dr r^2j_{\\ell}(kr)\\psi(r)$,\n\\ba\n{\\cal B}_{12}&=&\\frac{1}{\\overline{n}^3}\\frac{16}{\\pi}\\sqrt{\\frac{(2\\ell_1+1)(2\\ell_2+1)(2\\ell_3+1)}{(4\\pi)^3}}\\int dk_1 dk_2 i^{\\ell_1+\\ell_2} k_1^2\nk_2^2P(k_1)P(k_2)\\Psi_{\\ell_1}(k_1)\\Psi_{\\ell_2}(k_2) \\times \\nn\n& &\\!\\!\\!\\!\\!\\!\\!\\!\\!\\sum_{\\ell \\ell_6\\ell_7}i^{\\ell_6+\\ell_7}(-1)^{\\ell} B_{\\ell}(k_1,k_2)(2 \\ell_6+1)(2\\ell_7+1)\\overline{\\rho}\\!\\int dr r^2 \\psi(r)j_{\\ell_6}(k_1r)j_{\\ell_7}(k_2r)\n\\left(^{\\ell_1\\;\\;\\ell_6\\;\\;\\ell}_{0 \\;\\;\\;0\\;\\;\\; 0} \\right)\n\\left(^{\\ell_2\\;\\;\\;\\ell_7\\;\\;\\ell}_{0\\;\\;\\;\\; 0\\;\\;\\;\\; 0} \\right)\n\\left(^{\\ell_3\\;\\;\\ell_6\\;\\;\\ell_7}_{0\\;\\;\\;\\; 0\\;\\;\\;\\; 0} \\right)\n\\left\\{^{\\ell_1\\;\\ell_2\\;\\ell_3}_{\\ell_7\\;\\ell_6\\;\\,\\ell}\n\\right\\}\n\\label{eq.finalprojbisp}\n\\ea\nwhere $B_{\\ell}(k_1,k_2)$ for $\\ell=0,1,2$ are:\n\n\\ba\nB_0(k_1,k_2)&=& \\frac{34}{21}c_1+c_2 \\nn\nB_1(k_1,k_2)&=& c_1\\left(\\frac{k_1}{k_2}+\\frac{k_2}{k_1}\\right) \\nn\nB_2(k_1,k_2)&=& \\frac{8}{21}c_1,\n\\label{eq.B0B1B2}\n\\ea\nand the sum $\\sum_{\\ell\\ell_6\\ell_7}$ extends over $\\ell=0,1,2;$\n$\\ell_6=\\ell_1-\\ell.....\\ell_1+\\ell;$ \n$\\ell_7=\\ell_2-\\ell.....\\ell_2+\\ell$.\n\nThe above expression can easily be generalized for any 3D bispectrum. In\nfact, since a) the bispectrum is non-zero only if the three $k$ vectors form a\ntriangle, b) the bispectrum does not depend on the spatial orientation of the\ntriangle (isotropy) and c) a triangle is completely specified only by the\nmagnitude of two sides and the angle between them, the bispectrum can always\nbe expressed as a sum over three cyclical terms each involving only the\nmodulus of two $k$-vectors and the angle between them:\n\n\\be\nB(\\vk_1,\\vk_2,\\vk_3)={\\cal F}(k_1,k_2,\\theta_{12}).\n\\ee\nEach of the cyclical terms can therefore be expanded as:\n\\be\n{\\cal F}(k_1,k_2,\\theta_{12})=P(k_1)P(k_2)\\sum_{\\ell=0}^nB_{\\ell}(k_1,k_2)P_{\\ell}(\\cos\\theta_{12})\n\\ee\nwhere now $P(k_i)$ is an arbitrary function of $|\\vk_i|$, the\ncoefficients $B_{\\ell}$ can depend on any combination of $|\\vk_1|$ and\n$|\\vk_2|$ and the sum over $\\ell$ should in principle go to infinity,\nbut in practice will be truncated at $n$.\n\nWe find that the exact expression for the projected bispectrum $B_{\\ell_1\\ell_2\\ell_3}$ is still given by equations\n(\\ref{eq:bisp1}) and (\\ref{eq.finalprojbisp}) where now the sum over $\\ell$\ngoes up to $n$.\n\nThis, with equations (\\ref{eq:bisp1}) and (\\ref{eq.finalprojbisp}), is the major new result of this paper. \n\n\\subsection{Applications}\nEquation (\\ref{eq.finalprojbisp}) has therefore much wider applications\nthan the second-order gravitationally induced bispectrum considered so far.\nThe mathematics developed for this purpose can be straightforwardly applied to\nCMB and gravitational lensing studies. The\ngravitational fluctuations and cosmological structures along the path of the\nlast-scattering surface photons. \ndistort the CMB signal mainly through gravitational\nlensing, the integrated Sachs-Wolfe effect (Sachs \\& Wolfe 1967), the\nSunyaev-Zel'dovich effect (Sunyaev \\& Zel'dovich 1980), and through the\nRees-Sciama effect (Rees \\& Sciama 1968) and other second order\neffects (e.g. Mollerach \\& Matarrese 1997 and references therein). In particular, if the primordial\nfluctuations were Gaussian, many of these effects can introduce non gaussian features\nin the CMB signal. The bispectrum is a powerful tool for detecting these\neffects to probe the low-redshift Universe (Goldberg \\& Spergel 1998, Spergel\n\\& Goldberg 1998). Contributions to the CMB bispectrum induced\nby secondary anisotropies during reionization (Cooray \\& Hu 1999), non-linear\ngravitational evolution (Luo \\& Schramm 1994; Mollerach et al. 1995; Munshi,\nSouradeep \\& Starobinsky 1995) and foregrounds\n(e.g. Refregier, Spergel \\& Herbig 1998) imprint specific signatures on the CMB\nbispectrum which need to be subtracted from the signal in order to be able to test the gaussian nature of primordial\nfluctuations.\n\n%effects needs to be accurately calculated and subtracted from the CMB signal\n%in order to be able to test the gaussian nature of primordial fluctuations.\n\nOn the other hand, primordial fluctuations can induce nonzero bispectrum in\nthe CMB, that encloses information about the physical mechanism that generated\nthem (e.g. Falk, Rangarajan \\& Srednicki 1993; Luo \\& Schramm 1994, Gangui et\nal. 1994, Mollerach et al. 1995, Gangui \\& Mollerach 1996, Wang \\&\nKamionkowski 1999, Gangui \\& Martin 1999). The evaluation of all these contributions to the observed\nCMB bispectrum requires calculation of an integral as in our equation (5) and\n(6), where $r^2 \\psi(r)$ is replaced by an \nappropriate weight function.\n\nIn the local Universe, gravitational lensing provides a direct probe of the\nmass fluctuations.\nThe study of Fourier space correlation functions of the gravitational weak\nshear and convergence field is still in its infancy, but it is\npotentially fruitful: it could give us detailed knowledge of the correlation\nproperties of the projected mass distribution \n(e.g. Bernardeau et al. 1997 and references therein, Munshi 2000). \n\n \nIn the present paper we will use equation (\\ref{eq.finalprojbisp}) together\nwith (\\ref{eq:bisp1}) as an {\\em exact} expression for the second-order perturbation theory bispectrum\nof an angular catalogue with selection function $\\psi(r)$ and galaxy power spectrum $P(k)$, assuming a \nlocal bias model with parameters\n$b_1$ and $b_2$. In principle, one can estimate the angular\nbispectrum from a projected galaxy catalogue, and use likelihood\nmethods to constrain the bias parameters, which enter through the\n$B_\\ell$ terms. In Section 3, we compute the likely errors\nfrom such a study, to determine if it is worthwhile to undertake such\nan analysis with current catalogues. Before we do so, it is worth\nnoting that, in the current form, it is very expensive to compute: in\nthe following subsection we rewrite it in a form more suitable for\npractical evaluation.\n\n\\subsection{Practical evaluation of $B_{\\ell_1\\ell_2\\ell_3}$}\n\nFrom a computational point of view it is possible to speed up the\ncalculations considerably (and consequently make the problem\ncomputationally manageable) by rewriting equation\n(\\ref{eq.finalprojbisp}) in terms of the function $\\Theta^q_{\\ell}$\ndefined as:\n\\be\n\\Theta_{\\ell_i}^q(\\ell_j,r)\\equiv\\int dk \\Psi_{\\ell_i}(k)k^2P(k)j_{\\ell_j}(kr)k^q\n\\label{eq:theta}\n\\ee\nwhere $q=-1,0,1$ and $\\{i,j\\}=\\{1,6\\}$ or $\\{2,7\\}$. This function can be\nevaluated and tabulated in advance to speed up the analysis.\nWith this definition, we can write the components of the angular\nbispectrum as\n\\ba\n{\\cal B}_{12}&=&\\frac{1}{\\overline{n}^3}\\frac{16}{\\pi}\n\\sqrt{\\frac{(2\\ell_1+1)(2\\ell_2+1)(2\\ell_3+1)}{(4\\pi)^3}}i^{\\ell_1+\\ell_2}\\times\n\\nn\n& & \\int dr_3 r_3^2\\psi(r_3)\\left(\\frac{34}{21}c_1+c_2\\right)\\Theta^0_{\\ell_1}(\\ell_1,r_3)\\Theta^0_{\\ell_2}(\\ell_2,r_3)\n\\left(^{\\ell_1\\;\\;\\;\\ell_1\\;\\;\\;0}_{0\\;\\;\\;\\;0\\;\\;\\;\\; 0} \\right)\n\\left(^{\\ell_2\\;\\;\\;\\ell_2\\;\\;\\;0}_{0\\;\\;\\;\\; 0\\;\\;\\;\\; 0} \\right)\n\\left(^{\\ell_3\\;\\;\\;\\ell_1\\;\\;\\;\\ell_2}_{0\\;\\;\\;\\; 0\\;\\;\\;\\; 0} \\right)\n\\left\\{^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;0}\\right\\}\n+ \\nn\n& & c_1\\sum_{^{\\ell_1-1<\\ell_6<\\ell_1+1}_{\\ell_2-1<\\ell_7<\\ell_2+1}}\\left[\\Theta_{\\ell_1}^{-1}(\\ell_6,r_3)\\Theta_{\\ell_2}^{+1}(\\ell_7,r_3)+\\Theta_{\\ell_1}^{+1}(\\ell_6,r_3)\\Theta_{\\ell_2}^{-1}(\\ell_7,r_3)\\right]\n\\left(^{\\ell_1\\;\\;\\;\\ell_6\\;\\;\\;\\ell}_{0 \\;\\;\\;\\;0\\;\\;\\;\\; 0} \\right)\n\\left(^{\\ell_2\\;\\;\\;\\ell_7\\;\\;\\;\\ell}_{0\\;\\;\\;\\; 0\\;\\;\\;\\; 0} \\right)\n\\left(^{\\ell_3\\;\\;\\;\\ell_6\\;\\;\\;\\ell_7}_{0\\;\\;\\;\\; 0\\;\\;\\;\\; 0} \\right)\n\\left\\{^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{\\ell_7\\;\\;\\;\\ell_6\\;\\;\\;\\ell}\\right\\}\n+\\nn\n& & \\frac{8}{21}c_1\\sum_{^{\\ell_1-2<\\ell_6<\\ell_1+2}_{\\ell_2-2<\\ell_7<\\ell_2+2}}\n\\Theta^0_{\\ell_1}(\\ell_6,r_3)\\Theta^0_{\\ell_2}(\\ell_7,r_3)\n\\left(^{\\ell_1\\;\\;\\;\\ell_6\\;\\;\\;\\ell}_{0 \\;\\;\\;\\;0\\;\\;\\;\\; 0} \\right)\n\\left(^{\\ell_2\\;\\;\\;\\ell_7\\;\\;\\;\\ell}_{0\\;\\;\\;\\; 0\\;\\;\\;\\; 0} \\right)\n\\left(^{\\ell_3\\;\\;\\;\\ell_6\\;\\;\\;\\ell_7}_{0\\;\\;\\;\\; 0\\;\\;\\;\\; 0} \\right)\n\\left\\{^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{\\ell_7\\;\\;\\;\\ell_6\\;\\;\\;\\ell}\\right\\}.\n\\label{eq.biscomputational}\n\\ea\nNote that this analysis is appropriate for all-sky coverage, and\nignores shot noise. This is a good approximation for the high\nsurface-density catalogues such as APM, in the range where\nperturbation theory is valid. Estimators for noisy data and partial sky\ncoverage are presented in Heavens (1998) and Heavens (2000), see also \\scite{ganguimartin00}. Note also that numerical codes can run\ninto difficulties when computing the spherical harmonic expansion\nand 3J symbols for high $\\ell$. In Appendix C we give\nasymptotic expressions at high $\\ell$ for the 3J symbols that are\neasily evaluated, and we present a way to calculate spherical\nharmonics fast and accurately at high $\\ell$.\n\n\n\\section{Error analysis for the bias parameter}\n\nThe spherical harmonic bispectrum in second-order perturbation theory\nis a known function of the galaxy power spectrum, and depends on the\nbias parameters $b_1$ and $b_2$ through $B_0, B_1, B_2$ (equation\n\\ref{eq.B0B1B2}). Equation (\\ref{eq.finalprojbisp}) relates therefore\ntwo measurable quantities (the spherical harmonic bispectrum of\ngalaxies and the galaxy power spectrum) via the unknown bias\nparameters $b_1$ and $b_2$. The 3D power spectrum may be obtained\nfrom the projected catalogue either by deconvolution of the angular\ncorrelation function or the angular power spectrum\n(e.g. \\pcite{BE93,BE94}). \nIn practice this is done in the\nsmall-angle approximation. In Appendix B we show that this is\nperfectly adequate for the power spectrum. We therefore have a full\nprescription for the angular bispectrum in terms of observable\nquantities and parameters which we wish to measure [equation\n(\\ref{eq.finalprojbisp}) or the computationally manageable equation\n(\\ref{eq.biscomputational})]. The problem is therefore suitable for a \nlikelihood analysis to extract the bias parameter. Such a programme\nis a major undertaking, so it makes sense to compute the expected\nerror on the bias parameter first, to see whether the programme is likely to succeed.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Likelihood analysis for $c_1$ and $c_2$}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nWe assume we have full sky coverage unless otherwise stated.\nWe define the quantity\\footnote{{\\bf Re}[x]\ndenotes the real part of the complex number x.} $d_{\\alpha}$=${\\bf\nRe}[a_{\\ell_1}^{m_1}a_{\\ell_2}^{m_2}a_{\\ell_3}^{m_3}]$\nwith $\\ell_i$, $m_i$ such that $\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m_1 m_2\nm_3}\\right)\\neq 0$. For a given triplet\n$\\ell_1,\\ell_2,\\ell_3$ there are $(2\\ell_1+1)(2\\ell_2+1)$ distinct\n$d_{\\alpha}$.\nFrom $d_{\\alpha}$ we can build the unbiased estimator of\n$B_{\\ell_1\\ell_2\\ell_3}$,\n$\\hat{D}_{\\alpha}=\\frac{d_{\\alpha}}{\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m_1 m_2\nm_3}\\right)}$.\n\nSince $\\hat{D}_{\\alpha}$ is unbiased, any combination\n$D_{\\alpha}=(\\sum_{\\alpha '}w_{\\alpha '}\\hat{D}_{\\alpha '})/(\\sum_{\\alpha\n'}w_{\\alpha '})$,\nwhere $w_{\\alpha '}$ is a weight,\nis\nalso an unbiased estimator of $B_{\\ell_1\\ell_2\\ell_3}$.\n\nThe optimum weight $w_{\\alpha}$ that minimizes the variance\n$\\langle(D_{\\alpha}-B_{\\ell_1\\,\\ell_2\\,\\ell_3})^2 \\rangle $ is\n$w_{\\alpha}=1/\\sigma_{\\hat{D}_{\\alpha}}^2=\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m_1\\;\nm_2\\; m_3} \\right)^2/\\sigma^2_{d_{\\alpha}}$ (cf Gangui \\& Martin 2000).\nThe minimum variance estimator is\n\\be\nD_{\\alpha}=\\frac{\\sum_{m_1m_2m_3}\\frac{\n\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m_1\\;\nm_2\\; m_3}\\right)d_{\\alpha}}{\\sigma^2_{d_{\\alpha}}}}\n{\\sum_{m_1m_2 m_3}\\frac{\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m_1\\;\nm_2\\; m_3} \\right)^2}{\\sigma^2_{d_{\\alpha}}}}\n\\label{eq.estimatorB1}\n\\ee\nThe variance of $d_{\\alpha}$ does depend on $m$, but only weakly.\nThere is a leading term, independent of $m$, proportional to 3 angular\npower spectra \n($C_{\\ell_1}C_{\\ell_2}C_{\\ell_3}$), plus a sub-leading term proportional\nto $B_{\\ell_i\\ell_j\\ell_k}B_{\\ell_{p}\\ell_{q}\\ell_{r}}\\left(^{\\ell_i\\;\\;\\;\\ell_j\\;\\;\\;\\ell_k}_{m_i\\;\nm_j\\; m_k} \\right)\\left(^{\\ell_{p}\\;\\;\\;\\ell_{q}\\;\\;\\;\\ell_{r}}_{m_{p}\\;\nm_{q}\\; m_{r}} \\right)$, where $\\{i,j,k,p,q,r\\}$ is a permutation of\n$\\{1,2,3,1,2,3\\}$. If we ignore the $m$-dependence of this last \nterm, then the estimator simplifies to\n\\be\nD_{\\alpha}=\\sum_{m_i}d_{\\alpha}\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m_1\\;\nm_2\\; m_3} \\right), \\mbox{ $i=1,2,3$}.\n\\label{eq.estimatorB2}\n\\ee\nStrictly it is not the minimum variance estimator, but it is not far\nfrom it, is much simpler, and is unbiased.\n\n\\subsection{A priori error for the bias parameter}\n\nSince the quantity $\\langle a_{\\ell_1}^{m_1}a_{\\ell_2}^{m_2}a_{\\ell_3}^{m_3}\n\\rangle$ can be factorized as in equation (\\ref{eq:2dbispluo}) it is \npossible to evaluate the expected error on $c_1$ estimation by\napproximating the variance by its leading term, neglecting shot noise\nand by considering uncorrelated data, obtaining:\n\\be\n\\sigma^{-2}_{c_1}=-\\langle\\frac{\\partial^2{\\cal L}}{\\partial\nc_1^2}\\rangle\n\\simeq\\sum_{\\ell_i}\\frac{B_{\\ell_1\\ell_2\\ell_3}^2}{C_{\\ell_1}C_{\\ell_2}C_{\\ell_3}}\\sum_{m_i}\\frac{\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m_1\\;m_2\\;m_3}\\right)^2}{N_{\\ell_i}(m_i)}\n\\label{eq.sphharmapriorierror}\n\\ee\nwhere ${\\cal L}$ denotes the likelihood function.\n\nThe quantity $N_{\\ell_i}(m_i)$ denotes the number of terms like\n$C_{\\ell_1}C_{\\ell_2}C_{\\ell_3}$ present in the covariance. It depends\non the configuration i.e. on the choice of the triplets of ${\\ell}$'s.\nIt is useful to notice here that in the absence of $N_{\\ell_i}(m_i)$ we have\n\\be\n\\sum_{m_1m_2m_3}\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m_1\\;m_2\\;m_3}\n\\right)^2=1.\n\\ee\nEquation (\\ref{eq.sphharmapriorierror}) assumes that the covariance\nmatrix is diagonal, this means that different bispectrum estimators\n$\\langle a_{\\ell_1}^{m_1}a_{\\ell_2}^{m_2} a_{\\ell_3}^{m_3}\n\\rangle$ are uncorrelated. In the case of a survey with full sky coverage,\nsimilarly to the three-dimensional case treated in MVH97, the\ncovariance matrix is well approximated by a diagonal matrix if each\n$a_{\\ell}^m$ appears in one estimator only. However,\n% as we will seein section (4), \nin the presence of a mask, different $a_{\\ell}^m$ are\ncorrelated, therefore (\\ref{eq.sphharmapriorierror}) might no\nlonger be valid.\n\nFor an order-of-magnitude estimation of the expected error on the bias\nparameter, let us consider only equilateral configurations\n(i.e. configurations where $\\ell_1=\\ell_2=\\ell_3$), and assume full\nsky coverage for a survey with the APM selection function. It is easy to estimate the error achievable on $c_1$\nusing equation (\\ref{eq.sphharmapriorierror}) and considering that\nsecond order perturbation theory should hold up to $\\ell=35$. This\nchoice is justified by the following argument: in the\nthree-dimensional galaxy distribution, second-order perturbation\ntheory breaks down at $k\\sim 0.6$ (Mpc $h^{-1}$)$^{-1}$ (cf\n MVH97, although it depends on the power spectrum slope and can be\nsmaller, see e.g. \\scite{SCFFHM98}) that\ncorresponds to a scale of the order of 10 Mpc $h^{-1}$. At the medium\ndepth of the APM survey (335 Mpc $h^{-1}$), this subtends an angle of\nabout 0.03 radians (in agreement with the findings of \\pcite{GB98}),\ncorresponding with $\\ell \\sim 33$. This order of magnitude\ncalculation yields an estimate for the error on $c_1$ of about $\\pm\n3.5$, which is not really encouraging. However, this is only an\norder-of magnitude calculation: a more rigorous treatment\nis implemented in the next section.\n\n\\subsection{The choice of the triplets}\n\nAs already discussed in MVH97, the choice of the triplets to evaluate\nthe bispectrum is very wide, but, speed and memory considerations\nforce one to simplify the analysis by ensuring that the covariance\nmatrix is diagonal, for a full sky survey, this can be achieved by\nensuring that each $\\ell$ appears only in one triplet. \n%\\footnote{As explained in\n%MVH97, this choice throws away some information, but the resulting error-bar\n%is larger by a factor less than 1.7 for equilateral configurations and less\n%than 1.4 for degenerate. The factors will be $\\sqrt{3}$ and $\\sqrt{2}$ if all %the distinct\n%configurations were independent, which is not true.}. \nThe choice of\nthe ratio between the $\\ell$'s (the shape) of a triplet, is influenced\nby the behavior of the bispectrum: triplets with the same shape give\nan almost degenerate information on $c_1$ and $c_2$, in practice each\nshape can constrain a linear combination of $c_1$ and $c_2$: the\nlikelihood will be aligned along a straight line in the $c_1$,$c_2$\nplane. The best choice to try to lift this additional degeneracy is\nto combine the likelihood for equilateral triplets\n($\\ell_1=\\ell_2=\\ell_3$) with the likelihood for degenerate triplets\n($\\ell_1=\\ell_2$ and $\\ell_3=2\\ell_1$).\n\n\n\\subsection{Covariance}\nTo perform a likelihood analysis we need an expression for the covariance\nmatrix for our estimator $\\widehat{B}_{\\ell_1\\ell_2\\ell_3}$.\nIt is easy to verify that, if each $\\ell$ appears only in one\n$\\widehat{B}_{\\ell_1\\ell_2\\ell_3}$ then the\n$\\widehat{B}_{\\ell_1\\ell_2\\ell_3}$ are uncorrelated, that is:\n\\be\n\\langle\n\\widehat{B}_{\\ell_1\\ell_2\\ell_3}\\widehat{B}_{\\ell_4\\ell_5\\ell_6}\\rangle=\\langle\\widehat{B}_{\\ell_1\\ell_2\\ell_3}\\rangle\n\\langle\\widehat{B}_{\\ell_4\\ell_5\\ell_6} \\rangle\n\\ee\nif $\\ell_i\\neq \\ell_j$, where $i=1,2,3$ and $j=4,5,6$. This means that\nthe off-diagonal terms of the covariance matrix are zero. In fact:\n\\be\n\\langle\n\\widehat{B}_{\\ell_1\\ell_2\\ell_3}\\widehat{B}_{\\ell_4\\ell_5\\ell_6}\\rangle=\n\\sum_{m_1m_2m_3}\\sum_{m_4m_5m_6}\\langle a_{\\ell_1}^{m_1}a_{\\ell_2}^{m_2}a_{\\ell_3}^{m_3}a_{\\ell_4}^{m_4}a_{\\ell_5}^{m_5}a_{\\ell_6}^{m_6}\n\\rangle\\ \\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m_1\\;m_2\\;m_3} \\right) \\left(^{\\ell_4\\;\\;\\;\\ell_5\\;\\;\\;\\ell_6}_{m_4\\;m_5\\;m_6} \\right)\n\\label{eq.cov}\n\\ee\nwhere we used the fact that $a_{\\ell}^{*m}=(-1)^m a_{\\ell}^{-m}$.\nAnalogously to MVH97, the quantity $\\langle\na_{\\ell_1}^{m_1}a_{\\ell_2}^{m_2}a_{\\ell_3}^{m_3}a_{\\ell_4}^{m_4}a_{\\ell_5}^{m_5}a_{\\ell_6}^{m_6}\\rangle$\ncan be split into:\n\\begin{itemize}\n\\item[a)] 15 cyclical permutations of the kind $\\langle a_{\\ell_1}^{m_1}a_{\\ell_2}^{m_2}\\rangle\n\\langle a_{\\ell_3}^{m_3}a_{\\ell_4}^{m_4}\\rangle\n\\langle a_{\\ell_5}^{m_5}a_{\\ell_6}^{m_6}\\rangle$ that are all zero if\n$\\ell_i\\neq \\ell_j$, where $i=1,2,3$ and $j=4,5,6$,\n\n\\item[b)] 1 term\n$$B_{\\ell_1\\ell_2\\ell_3}B_{\\ell_4\\ell_5\\ell_6}\\sum_{m_1m_2m_3}\\sum_{m_4m_5m_6}\\left(\n^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m_1\\;m_2\\;m_3}\\right)^2\n\\left(^{\\ell_4\\;\\;\\;\\ell_5\\;\\;\\;\\ell_6}_{m_4\\;m_5\\;m_6} \\right)^2 =\n\\langle\\widehat{B}_{\\ell_1\\ell_2\\ell_3} \\rangle\n\\langle\\widehat{B}_{\\ell_4\\ell_5\\ell_6} \\rangle$$\n\n\\item[c)] 9 cyclical permutations of the kind:\n$$B_{\\ell_i\\ell_j^{\\prime}\\ell_k}B_{\\ell_i^{\\prime}\\ell_j\\ell_k^{\\prime}}\\sum_{m_im_jm_k}\\sum_{m_i^{\\prime}m_j^{\\prime}m_k^{\\prime}}\n%\n\\left(_{m_i\\; m_j^{\\prime}\\;m_k}^{\\ell_i\\;\\;\\;\\ell_j^{\\prime}\\;\\;\\;\\ell_k}\\right)\n%\n\\left(^{\\ell_i^{\\prime}\\;\\;\\;\\ell_j\\;\\;\\;\\ell_k^{\\prime}}_{m_i^{\\prime}\\;m_j\\; m_k^{\\prime}}\\right)\n%\n\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m_1\\;m_2\\;m_3}\\right)\n%\n\\left(_{m_4\\;m_5\\;m_6}^{\\ell_4\\;\\;\\;\\ell_5\\;\\;\\;\\ell_6}\\right)\n$$\nwhere $i,j,k$ is any permutation of 1,2,3 and $i^{\\prime}j^{\\prime}k^{\\prime}$\ndenotes any permutation of 4,5,6.\nThese terms in c) are all zero unless there are repeated $\\ell$ in two different $D_{\\alpha}$.\n\\end{itemize}\nThe term in b) cancels when subtracting the mean to obtain the covariance.\nLet us now consider the diagonal terms of the covariance matrix: these are\ngiven by equation (\\ref{eq.cov}) with the following identities for the indices:\n$1=4$, $2=5$, $3=6$.\nFor symmetry considerations we can restrict ourselves to consider\n$\\ell_1\\le\\ell_2\\le \\ell_3$.\nIn the case where $\\ell_1<\\ell_2<\\ell_3$ we have:\n\\begin{itemize}\n\\item[] in a) only one term surviving, giving $C_{\\ell_1}C_{\\ell_2}C_{\\ell_3}$.\n\\item[] in c) using (\\ref{eq.orth2}), $3B_{\\ell_1\\ell_2\\ell_3}^2$\n\\end{itemize}\n\nIn the case where $ \\ell_1=\\ell_2<\\ell_3$ we have:\n\\begin{itemize}\n\\item[ ]in a) $C_{\\ell_1}^2C_{\\ell_3}\\left[2+\\sum_{m\nm^{\\prime}}\\left(^{\\ell_1\\;\\;\\;\\ell_1\\;\\;\\;\\ell_3}_{m\\;-m\n\\;0}\\right)\\left(^{\\ell_1\\;\\;\\;\\ell_1\\;\\;\\;\\ell_3}_{m^{\\prime}\\;-m^{\\prime}\\;0}\\right) \\right]$\nin the particular case where $\\ell_3=2\\ell_1$ (degenerate configurations) as\nshown in Appendix C (eq. \\ref{eq:3j3jll2l}) we obtain to very good\napproximation: $C_{\\ell_1}^2C_{\\ell_3}\\left[2+\\sqrt{(2\\pi\n\\ell_1)}/(1+4\\ell_1)\\right]$\n\\item[ ] in c) $5 B_{\\ell_1\\ell_1\\ell_3}^2$\n\\end{itemize}\n\nFor equilateral configurations where $\\ell_1=\\ell_2=\\ell_3=\\ell$ we have:\n\\begin{itemize}\n\\item[]in a) $C_{\\ell}^3\\left[6+9\\sum_{m m^{\\prime}}\\left(^{\\ell\\;\\;\\;\\; \\ell\\;\\;\\;\\; \\ell}_{m\n-m\\; 0}\\right)\\left(^{\\ell\\;\\;\\;\\; \\ell \\;\\;\\;\\;\\ell}_{m^{\\prime} -m^{\\prime}\\; 0 }\\right) \\right]$\nwhich, to a very good approximation, is $\\simeq C_{\\ell}^3\\left[6+9\\times 1.15/(2\\ell+1)\\right]$\n\\item[ ]in c) $9 B_{\\ell\\ell\\ell}^2$\n\\end{itemize}\n\n\\subsection{Likelihood analysis of a simulated catalogue}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nWe created an all-sky catalogue with the APM selection function\n$\\phi(r)\\propto r^{-0.1}\\exp[(-r/335)^2]$ (e.g. \\scite{apmselfn95},\n\\scite{GB98}), by replicating an N-body simulation of 500\nMpc $h^{-1}$ side and then sparsely sampling and projecting to the\nplane of the sky 2303636 particles (galaxies for our purposes)\naccordingly to the APM selection function. The simulation was\nsupplied by J. Peacock using the AP$^3$M code (\\pcite{C91}). The\ncharacteristics are: $128^3$ particles, CDM transfer function\n(\\pcite{BBKS}), $\\Gamma=0.25$, $\\Omega=0.3$, $\\Lambda=0.7$, evolved to\n$\\sigma_8$=1 to best fit the observed cluster abundance; this \nchoice gives also a good fit to the COBE 4-year data (e.g. \\pcite{Teg96}). The rate of\nsampling used ensures that the probability of selecting the same\nparticle in the simulation more than once in the replicated box is\nnegligible.\n\nFigure \\ref{fig.clsim} shows the angular power spectrum for the\nsimulated projected catalogue. The solid line is the underlying \npower spectrum obtained from the 3D one by applying convolution with the\nselection function and full-treatment projection; the dashed line is the\nunderlying linear power spectrum. Deviations for\nlinear theory are already evident at $\\ell \\sim 40$.\n\\begin{figure}\n\\begin{center}\n\\setlength{\\unitlength}{1mm}\n\\begin{picture}(90,70)\n\\special{psfile=fig1.ps\nangle=00 hoffset=-10 voffset=0 hscale=50 vscale=50}\n\\end{picture}\n\\end{center}\n\\caption{The power spectrum in spherical harmonics for the simulated projected\ncatalogue. The points are the $C_{\\ell}$ measured for the catalogue, the solid\nline is the underlying power spectrum, and the dashed line is the underlying\nlinear power spectrum. The underlying power spectrum is obtained from the 3D\none by applying the selection function and the full-treatment projection. Deviations from linear theory are already evident at\n$\\ell \\sim 40$.}\n\\label{fig.clsim}\n\\end{figure}\nIn order to lift the degeneracy between $c_1$ and $c_2$ we consider\nequilateral and degenerate configurations.\nThe likelihood for equilateral configurations is shown in Figure\n\\ref{fig.likeq}; it does not give a strong constraint\non the bias: perturbation theory breaks down at $\\ell \\sim 40$: up to $\\ell\n< 40$ there are only 18 independent equilateral triplets\\footnote{18 is the\nnumber of independent $D_{\\alpha}$ as defined in eq. 35 with $\\ell_i=\\ell<40$, $i=1,2,3$. The\npresence of the 3-J symbol for equilateral configurations requires $\\ell$ to\nbe even, $\\ell=2$ is discarded because it would be contaminated by the galaxy\n%corresponds to the \nquadrupole.}.\n\\begin{figure}\n\\begin{center}\n\\setlength{\\unitlength}{1mm}\n\\begin{picture}(90,70)\n\\special{psfile=fig2.ps\n%\\special{psfile=likeq4-42.ps\nangle=00 hoffset=-10 voffset=0 hscale=50 vscale=50}\n\\end{picture}\n\\end{center}\n\\caption{Likelihood contours for equilateral triplets\nconfigurations. The two levels (where the downhill direction is indicated for\nclarity) are the 1$-\\sigma$ and 3-$\\sigma$ confidence\nlevels and the $+$ indicates where the true value for the parameters\nlies. Perturbation theory breaks down at $\\ell \\sim 40$ here $\\ell$ up to 42\nare considered even though the likelihood only for the triplets between\n$\\ell=40$ and $\\ell=42$ includes the true value just within the boundary of\nthe $3-\\sigma$ level. This configuration does not place strong constraints on\nthe bias parameter.}\n\\label{fig.likeq}\n\\end{figure}\nThe likelihood for degenerate configurations gives a better constraint on the\nbias. Perturbation theory for this configuration breaks down where the short\n$\\ell$ is\n$\\ell=40$. Likelihood contours for degenerate triplets configurations where\nthe short $\\ell$ is $20< \\ell\\leq 40$, are shown\nin Figure \\ref{fig.likdeg}.\nSince the likelihood for equilateral configurations is quite broad, even\ncombining it to the likelihood for degenerate configurations does not modify Figure \\ref{fig.likdeg} sensibly.\n\n\\begin{figure}\n\\begin{center}\n\\setlength{\\unitlength}{1mm}\n\\begin{picture}(90,70)\n\\special{psfile=fig3.ps\n%\\special{psfile=likdeg-20-40.ps\nangle=00 hoffset=-10 voffset=0 hscale=50 vscale=50}\n\\end{picture}\n\\end{center}\n\\caption{Likelihood contours for degenerate triplets\nconfigurations. The two levels are the 1$-\\sigma$ and 3-$\\sigma$ confidence\nlevels and the $+$ indicates where the true value for the parameters\nlies. Perturbation theory breaks down at $\\ell_{\\rm short}=40$.}\n\\label{fig.likdeg}\n\\end{figure}\n\nFrom this analysis we can conclude that from a two-dimensional galaxy survey\nwith the APM selection function, even if it is an all-sky survey, it is only\npossible to constrain a combination of the linear and quadratic bias\nparameter, or, alternatively, if we {\\em assume} (without\njustification) that the bias is linear (i.e. $b_2=0$), \n$0.7<c_1<1.4$ or $0.7<b_1<1.4$, at 68\\% confidence. \n\n\\section{Conclusions}\n\nIn this paper, we have presented the formalism for translating the 3D\nbispectrum of a sample population into the angular bispectrum in spherical\nharmonics. As discussed in section 2.1, this method has applications in a\nvariety of areas, such as microwave background studies, gravitational lensing\nand analysis of angular galaxy catalogues. We have investigated the last of these in\ndetail in this paper: since the bispectrum is a measurable quantity, and\nits theoretical expression depends on measurable quantities via the\nunknown bias parameter, it is possible to extract the bias parameter\nvia a likelihood analysis. We have therefore investigated its use as\na tool for measuring the bias parameter for projected galaxy surveys. In\nprinciple, it is an alternative method to using 3D galaxy redshift\nsurveys, without the complicating effects of redshift distortions and\nhigher shot noise. \nRecently, other methods based on second-order perturbation\ntheory have been proposed to measure the bias parameter from 2D galaxy\ncatalogues (see e.g. \\pcite{FG99,FryThomas99}).\nFrieman \\& Gaztanaga (1999) studied the reduced 3-point correlation\nfunction on the sky. The error analysis in real space is more\ncomplicated because of strong correlations between the estimates.\nFrieman \\& Gaztanaga conclude that $b_1 \\ll 1.5$ or so, giving a\ncomparable error to our analysis (section 3.5) if $b_2$ is assumed to\nbe zero. We emphasize that allowing a non-zero quadratic bias term\nopens up a wide range of acceptable linear bias parameters.\n\nThe analysis of Fry \\& Thomas (1999) is closest to ours. They consider\nthe bispectrum, but present results in the small-angle approximation\nonly. They do go some way in writing down the general expression for\nthe angular bispectrum in spherical harmonics in terms of the 3D\nbispectrum. In this paper, by expanding the (general) dependence of\nthe 3D bispectrum on angle between wavevectors in Legendre\npolynomials, we were able to derive a practical general relationship\nwhich is computable with few numerical integrations.\n\nWe have \ncalculated the expected\nerror on the linear bias parameter from an all-sky catalogue with a\nselection function similar to the APM survey. We find that the\nresults are not encouraging for projected catalogues, and that it is\npreferable to undertake a bispectrum study of 3D galaxy redshift\nsurveys such as the AAT 2dF or the Sloan Digital Sky Survey, using the\nmethods discussed in MVH97 and \\scite{VHMM98}. Tests on simulated\nprojected catalogues confirm our analytic findings. In a similar way as for 3D\nsurveys (see discussion in MVH97), one can reduce the\nerrors by subdividing the sky \\footnote{The procedure of subdivision to increase the S/N appears\ncounter-intuitive. In fact, nothing more is gained by this than by\nrelaxing the precise shape of the triangles. It is easiest to\ndemonstrate this in Fourier space in 3D. MVH97 considered the\nbispectrum $B({\\bf k}_1, {\\bf k}_2, {\\bf k}_3)$ and demonstrated that\nthe S/N increases $\\propto N^{1/2}$, where $N$ is the number of\nsubvolumes. Alternatively, in increasing the volume by a factor $N$,\none has more triangles to analyse. MVH97's analysis includes the\ndensity of ${\\bf k}_1$ states; relaxing the triangle shape\nconfiguration increases the number of ${\\bf k}_2$ states by the ratio\nof the density of states (i.e. $N$). ${\\bf k}_3$ is fixed at $-{\\bf\nk}_1-{\\bf k}_2$, so the number of triangles for given ${\\bf k_1}$ is\n$\\propto N$, giving the same increase of S/N (see Verde 2000). 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The definition we use here\nis expressed in terms of the associate Legendre functions\n$P_{\\ell}^{m}(\\cos\\theta)$:\n\\be\nY_{\\ell}^m(\\Omega)\\equiv\nY_{\\ell}^m(\\theta,\\phi)=\\sqrt{\\frac{(2\\ell+1)(\\ell-m)!}{4\\pi(\\ell+m)!}}P^m_{\\ell}(\\cos\\theta)e^{\\imath\nm\\phi}\\times\\left\\{^{(-1)^m\\mbox{ for $m\\geq 0$}}_{1 \\mbox{ for $m < 0$}}\\right.\n\\ee\nwhere $\\ell$ and $m$ are integers and $\\ell\\geq0$, $-\\ell<m<\\ell$.\nTheir orthogonality relation is:\n\\be\n\\int_{4 \\pi}d\\Omega Y_{\\ell_1}^{m_1}(\\Omega)\nY_{\\ell_2}^{*m_2}(\\Omega)=\\delta^K_{\\ell_1\\ell_2}\\delta^K_{m_1m_2}.\n\\label{eq.spharmorth}\n\\ee\nAny two dimensional pattern $f(\\Omega)$ on the surface of a sphere can be\nexpanded as:\n\\be\nf(\\Omega)=\\sum_{\\ell m}a_{\\ell}^{m}Y_{\\ell}^{m*}(\\Omega)\n\\ee\nwhere\n\\be\na_{\\ell}^{m}=\\int d\\Omega Y^{m}_{\\ell}(\\Omega)f(\\Omega).\n\\ee\n\nUseful relations involving the spherical harmonics are:\n\\be\nY_{\\ell}^{m*}(\\Omega)=(-1)^mY^{-m}_\\ell(\\Omega)\\mbox{ , }\nY_{\\ell}^{m}(-\\Omega)=(-1)^{m+\\ell}Y^{m}_\\ell(\\Omega).\n\\label{eq.spharmconj}\n\\ee\nand the identities:\n\\be\n\\sum_{\\ell m}Y_{\\ell}^{*m}(\\Omega)Y_{\\ell}^{m}(\\Omega^{\\prime})=\\delta(\\Omega-\\Omega^{\\prime})\n\\ee\n\n\\be\n\\exp(i \\vk\\cdot\\vr)=4\\pi\\sum_{\\ell\nm}i^{\\ell}j_{\\ell}(kr)Y_{\\ell}^{*m}(\\Omega_\\vk)Y_{\\ell}^{m}(\\Omega_\\vr)\n\\label{eq.expspharm}\n\\ee\n\\be\nP_{\\ell}(\\cos\\theta)=\\frac{4\\pi}{2\\ell+1}\\sum_{m=-\\ell}^{\\ell}Y_{\\ell}^{m}(\\Omega_{\\vr})Y^{*m}_{\\ell}(\\Omega_{\\vk})\n\\label{eq.legendrep}\n\\ee\nwhere $\\theta$ denotes the angle between the vectors $\\vr$ and $\\vk$.\nThe latter is the addition theorem for spherical harmonics.\n\n\\section*{Appendix B: the power spectrum and the small-angle approximation}\n\nThe power spectrum of a 2-D distribution on the plane on the sky is\ngiven by the set of $C_{\\ell}$\ndefined as:\n\\be\n\\langle a_{\\ell}^m a_{\\ell^{\\prime}}^{m^{\\prime}*} \\rangle=C_{\\ell} \n\\delta^{K}_{\\ell\\ell^{\\prime}}\\delta^{K}_{m m^{\\prime}}.\n\\ee\nThe corresponding angular two-point correlation function\ncan be expanded as\n\\be\nC(\\theta)=\\frac{1}{4\\pi}\\sum_{\\ell}(2\\ell+1)C_{\\ell}P_{\\ell}(\\cos\\theta)\n\\label{eq.ctheta}\n\\ee\nwith inverse relation is:\n\\be\nC_{\\ell}=2\\pi \\int_{-1}^{1}C(\\theta)P_{\\ell}(\\cos\\theta)d\\cos(\\theta)\n\\ee\nOn the other hand, for a plane two-dimensional distribution with \npower spectrum $P_{2D}(\\kappa)$\nthe two-point correlation function is:\n\\be\n%&\n w(\\theta)=\\frac{1}{(2\\pi)^2}\\int P_{2D}(\\kappa)\\exp(i {\\vkappa} \\cdot {\\vtheta})d^2{\\bf\n\\kappa}=% & \\nn\n%&\n\\frac{1}{(2\\pi)^2}\\int_{0}^{\\infty}\\int_{0}^{2\\pi}P_{2D}(\\kappa)\\cos(\\kappa\\theta\\cos\\phi)d\\phi\n\\kappa d\\kappa=\\frac{1}{(2\\pi)}\\int_0^{\\infty}P_{2D}(\\kappa) J_0(\\kappa\\theta) \\kappa\nd\\kappa %&\n\\ee\nIn the small angle approximation, i.e. in equation (\\ref{eq.ctheta})\nfor small $\\theta$, we have that $P_{\\ell}(\\cos\\theta)\\sim\nJ_0[(\\ell+1/2)\\theta]$, but, since small angular patches restrict us\nto high $\\ell$, $P_{\\ell}(\\cos\\theta)\\sim J_0(\\ell \\theta)$. We can\ntherefore conclude that in the small-angle approximation\n\\be\n\\ell\\longrightarrow \\kappa\\mbox{ ; }\n\\;\\;\\;\\;C_{\\ell}\\longrightarrow P_{2D}({\\ell})\n\\label{eq.smallanglemap}\n\\ee\nFor a real angular catalogue the two-dimensional galaxy density in the\nsky is obtained as follow. Let the true three-dimensional galaxy\ndensity field be $\\rho(\\vr)$ and the selection function be $\\psi(r)$,\nnormalized here to $\\int dr r^2 \\psi(r)=1$. It is straightforward to\nobtain an expression for the angular power spectrum given the\nthree-dimensional one:\n\\be\n\\langle a_{\\ell_1}^{m_1}a_{\\ell_2}^{m_2*}\\rangle =\\left\\{\\begin{array}{ll}\n\\frac{1}{\\overline{n}^2}\\frac{2}{\\pi}\\int dk k^2 P(k)\\left[\\int dr\nr^2 \\psi(r)j_{\\ell_1}(k_1 r)\\right]^2 & \\mbox{if $m_1=-m_2$ and $\\ell_1=\\ell_2$}\\\\\n0 &\\mbox{otherwise}\n\\end{array}\n\\right.\n\\label{eq.projpsexact}\n\\ee\nIn the small-angle approximation this is (\\pcite{Kaiser92}, \\pcite{BKJ99}):\n\\be\nP_{2D}(\\kappa)=\\int_{0}^{\\infty}dr P_{3D}(\\kappa/r)\\psi^2(r)r^2\n\\label{eq.projpssmallangle}\n\\ee\nAlso in the presence of the selection function we can check that mapping\n(\\ref{eq.smallanglemap}) is valid and we can asses the limit of validity for\nthe small angle approximation for the power spectrum.\n\nAssuming the APM selection function $\\phi(r)\\propto\nr^{-0.1}\\exp[(-r/335)^2]$, and a CDM power spectrum (\\pcite{EBW92})\nwith $\\Gamma= 0.25$, we compared the angular power spectrum obtained\nwith the exact projection as in equation (\\ref{eq.projpsexact}) and\nwith the small angle approximation [equation\n\\ref{eq.projpssmallangle}]. The result is shown in Figure\n\\ref{fig.smallangleps}: the small angle approximation introduces an\nerror smaller than 3\\% for $\\ell > 20$.\n\\begin{figure}\n\\begin{center}\n\\setlength{\\unitlength}{1mm}\n\\begin{picture}(90,70)\n\\special{psfile=fig4.ps\n%\\special{psfile=smallangl.ps\nangle=00 hoffset=-10 voffset=0 hscale=50 vscale=50}\n\\end{picture}\n\\end{center}\n\\label{fig.smallangleps}\n\\caption{The small-angle approximation for the angular power spectrum works\nvery well for $\\ell > 20$ introducing an error smaller that 3\\%.}\n\\end{figure}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5\n\n\n\\section*{Appendix C: Useful formulae for the high $\\ell$ regime.}\n\nLibrary routines dealing with spherical harmonics at high $\\ell$ can\nsometimes fail. In this appendix, we present some asymptotic results\nwhich can avoid problems.\n\nThe 3J symbol $\\left(^{\\ell_1\\ell_2\\ell_3}_{0\\;\\;0\\;\\;0}\\right)$ may be written\nas:\n\\be\n\\left(^{\\ell_1\\ell_2\\ell_3}_{0\\;\\;0\\;\\;0}\\right)=(-1)^L\n\\sqrt{\\frac{(L-2\\ell_1)!(L-2\\ell_2)!(L-2\\ell_3)!}{(L+1)!}}\n\\frac{(L/2)!}{(L/2-\\ell_1)!(L/2-\\ell_2)!(L/2-\\ell_3)!}\n\\label{eq:clebshzero}\n\\ee\nwhere $L=\\ell_1+\\ell_2+\\ell_3$.\n\nIn the special case where $\\ell_1=\\ell_2=\\ell$ and $\\ell_3=2\\ell$ this becomes:\n\\be\n\\frac{2[\\Gamma(2\\ell)]^2}{\\sqrt{\\ell} \\sqrt{1+4\\ell}[\\Gamma(\\ell)]^2\\sqrt{\\Gamma(4\\ell)}}\n\\label{eq:clebshzerodeg}\n\\ee\n\nNumerical routines to calculate the 3J symbols usually encounter\nproblems for large ${\\ell}$. We therefore evaluated an approximation\nbased on the Stirling approximation: i.e. $n!=\\Gamma(n+1)$ and\n(\\pcite{GR65})\n\\be\n\\Gamma(z)\\sim e^{-z}z^{z-1/2}(2\\pi)^{1/2} \\;\\;\\;\\mbox{ for large }\\;\\;\\; z.\n\\label{eq:gammastirling}\n\\ee\nThis approximation for the $\\Gamma$ function is quite good, in fact it\nintroduces an error of only 4\\% at $z=2$. Using this approximation we\nobtain for eq. (\\ref{eq:clebshzero}):\n\\be\n\\left(^{\\ell_1\\ell_2\n\\ell_3}_{0\\;\\;0\\;\\;0}\\right)\\longrightarrow \\frac{(-1)^{L/2}}{\\sqrt{2\\pi}}\n\\frac{2^{1/4}\\sqrt{e}}{(L+1)^{L/2+1/2+1/4}}\\frac{L^{L/2+1/2}}{[(L/2-\\ell_1)(L/2-\\ell_2)(L/2-\\ell_3)]^{1/4}}.\n\\ee\nThis approximation introduces a small error of a few percent at\n${\\ell}\\sim 20$. For equation (\\ref{eq:clebshzerodeg}) we obtain:\n\\be\n\\left(^{\\ell\\;\\;\\ell\\;\\;\n2\\ell}_{0\\;\\;0\\;\\;0}\\right)\\longrightarrow\\frac{1}{\\sqrt{1+4\\ell}}\\left(\\frac{4}{\\ell 2 \\pi}\\right)^{0.25}\n\\ee\nWhen the $m$'s are non-zero it is still possible to find a simple expression\nfor the 3J symbol in special cases. For example if\n$\\ell_3=\\ell_1+\\ell_2$ we have:\n\\be\n\\left(^{\\ell_1 \\;\\;\\ell_2\\;\\;\\;\\;\\; \\ell_1+\\ell_2}_{m_1 m_2 -m_1-m_2}\\right)=(-1)^{\\ell_1-\\ell_2+m_1+m_2}\\sqrt{\\frac{(2\\ell_1)!(2\\ell_2)!(\\ell_1+\\ell_2+m_1+m_2)!(\\ell_1+\\ell_2-m_1-m_2)!}{(2\\ell_1+2\\ell_2+1)!(\\ell_1+m_1)!(\\ell_2+m_2)!(\\ell_1-m_1)!(\\ell_2-m_2)!}}\n\\ee\nIn the special case where $\\ell_1=\\ell_2=\\ell$ the previous expression can be further\nsimplified and approximated --using (\\ref{eq:gammastirling})-- by:\n\\be\n\\left(^{\\ell \\;\\;\\;\\;\\ell\\;\\;\\;\\;\\;\\;\\;\\; 2\\ell}_{m_1 m_2\n-m_1-m_2}\\right)\\longrightarrow(-1)^{m_1+m_2}\\frac{(\\ell 2 \\pi)^{1/4}}{2^{2\\ell}\\sqrt{4\\ell+1}}\\sqrt{\\frac{(2\\ell+m_1+m_2)!(2\\ell-m_1-m_2)!}{(l+m_1)!(\\ell+m_2)!(\\ell-m_1)!(\\ell-m_2)!}}\n\\ee\nIn the calculation of the covariance matrix for ``degenerate''configurations\nfor the quantities $B_{\\ell\\ell2\\ell}$ we came across with the following sum\nover $m$ of a\nproduct of two 3J-symbols. An useful expression for it is\n%Another useful expression for the 3J symbol is\nthe following:\n\\be\n\\sum_{m_1,m_2}\\left(^{\\ell\\;\\;\\;\\;\\;\\;\\ell\\;\\;\\;\\;\\; 2\\ell}_{m_1\\;-m_1\\;0}\\right)\\left(^{\\ell\\;\\;\\;\\;\\;\\;\\ell\\;\\;\\;\\;\\;\n2\\ell}_{m_2\\;-m_2\\;0}\\right)=\\frac{2^{(2+4\\ell)}\\ell^3\\Gamma(2\\ell)^4}{(1+4\\ell)\\Gamma(4\\ell)\\Gamma(2\\ell+1)^2}\n\\equiv\\frac{2^{4\\ell}\\ell\n[(2\\ell-1)!]^2}{(1+4\\ell)(4\\ell-1)!}.\n\\label{eq:3j3jll2l}\n\\ee\n\nFor large $\\ell$ using the above approximation for the Gamma function we\nobtain:\n\\be\n\\frac{2^{4\\ell}\\ell[\\Gamma(2\\ell)]^2}{(1+4\\ell)\\Gamma(4\\ell)}\\longrightarrow\\frac{\\sqrt{2\\pi}\\sqrt{\\ell}}{(1+4\\ell)}\n\\mbox{ (for large $\\ell$)}\n\\ee\nthis approximation works very well also at low $\\ell$, in fact\nintroduces an error below 1\\% at $\\ell=6$.\n\nThe orthogonality relations for 3J-symbols are also widely used:\n\\be\n\\sum_{m_1\\;m_2\\;m_3}\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m1\\;\\;m2\\;\\;m3}\\right)^2=1\n\\label{eq.orth1}\n\\ee\nand\n\\be\n\\sum_{m_1\\;m_2}\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_3}_{m1\\;\\;m2\\;\\;m3}\\right)\\left(^{\\ell_1\\;\\;\\;\\ell_2\\;\\;\\;\\ell_4}_{m1\\;\\;m2\\;\\;m4}\\right)=\\frac{1}{(2\n\\ell_3+1)}\\delta^K_{\\ell_3\\;\\ell_4}\\delta^K_{m_3\\;m_4}\n\\label{eq.orth2}\n\\ee\nWhen calculating the spherical harmonic coefficients for a galaxy distribution\non the celestial sphere, numerical problems arise with the\nassociate Legendre polynomials at high $\\ell$. Routines based on the \nrecurrence relations used for\nexample by the numerical recipes routines (\\pcite{NUMREC}) \nfails at $\\ell \\sim 35$ if $m \\sim\n\\ell$, at slightly higher $\\ell$ for $m \\ll l$.\nThe asymptotic expansion for the associate Legendre polynomial\n(e.g.\\pcite{GR65}):\n\\be\nP_{\\ell}^{m}(\\cos\\theta)\\simeq\n\\frac{2}{\\sqrt{\\pi}}\\frac{\\Gamma(\\ell+m+1)}{\\Gamma(\\ell+3/2)}\\frac{\\cos[(\\ell+1/2)\\theta-\\pi/4+m\\pi/2]}{\\sqrt{2\\sin\\theta}}+{\\cal O}(1/\\ell)\n\\ee\n is valid for $\\mid \\ell\\mid \\gg\\mid m\\mid$, $\\mid \\ell \\mid \\gg 1$ and\n $\\epsilon<\\theta<\\pi-\\epsilon$.\n\nThe use of the recursive relations involve the calculation of\n$(2\\ell-1)!!$ that at high $\\ell$ can create numerical problems.\nUsing the following expression for the $\\Gamma$ function:\n\\be\n\\Gamma(n+1/2)=\\frac{\\sqrt{\\pi}}{2^n}(2n-1)!!\n\\ee\nand (\\ref{eq:gammastirling}) for the $\\Gamma$ function for big argument we\nobtain:\n\n\\be\n(2n-1)!!=\\frac{2^{n+1/2}(n+1/2)^n}{e^{n+1/2}}\n\\ee\n\nThis approximation introduces an error of only a few percent for $n \\sim\n10$.\n\nWhen calculating the spherical harmonics at higher $\\ell$, problems arise not\nonly with the associated Legendre polynomials, but also with the part that\ninvolves the ratio of two factorials.\nA better way to calculate the spherical harmonics, fast and accurate to high\n$\\ell$ is based on the algorithm proposed by \\cite{Muciacciaetal97}. In\nessence the numerical problems can be avoided by defining the normalized\nassociated Legendre polynomials $\\lambda_{\\ell}^m$:\n\\begin{equation}\n\\lambda_{\\ell}^{m}(\\cos\\theta)\\equiv\\sqrt{\\frac{2\\ell+1}{4\\pi}\\frac{(\\ell-m)!}{(\\ell+m)!}}P_{\\ell}^m(\\cos\\theta)\n\\end{equation}\nThe recurrence relation for $\\lambda_{\\ell}^m$ is:\n\\be\n\\lambda_{\\ell}^m(x)=\\left[x\\lambda_{\\ell-1}^m(x)-\\sqrt{\\frac{(\\ell+m-1)(\\ell-m-1)}{(2\\ell-3)(2\\ell-1)}}\\lambda_{\\ell-2}^m(x)\\right]\\sqrt{\\frac{4\\ell^2-1}{\\ell^2-m^2}}\n\\ee\nwith expressions for the starting values:\n\\be\n\\lambda_m^m(x)=(-1)^m\\sqrt{\\frac{2m+1}{4\\pi}}\\frac{(2m-1)!!}{\\sqrt{(2m)!}}(1-x)^{m/2}\n\\label{eq:lmm}\n\\ee\n\\be\n\\lambda_{m+1}^m(x)=x\\sqrt{2m+3}\\lambda_m^m(x)\n\\ee\nnumerical evaluation can be greatly speeded up by noticing that the factor in\n(\\ref{eq:lmm}) depends only on $m$ and can therefore be calculated and/or\ntabulated for $m\\leq \\ell_{max}$ only once.\n\n\n\\end{document}\n\n\n\n\n"
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}
] |
astro-ph0002241
|
A Serendipitous Search for High-Redshift Ly$\alpha$ Emission: \\ Two Primeval Galaxy Candidates at $z \simeq 3$\altaffilmark{1}
|
[
{
"author": "Curtis Manning"
},
{
"author": "Daniel Stern\\altaffilmark{2}"
},
{
"author": "Hyron Spinrad"
},
{
"author": "\\& Andrew J. Bunker\\altaffilmark{3}"
}
] |
In the course of our ongoing search for serendipitous high-redshift \lya\ emission in deep archival Keck spectra, we discovered two very high equivalent width ($W_{\lambda}^{obs} \simgt 450$ \AA, $2 \sigma$) \lya\ emission line candidates at $z \sim 3$ in a moderate dispersion ($\lambda / \Delta \lambda \simeq 1200$) spectrogram. Both lines have low velocity dispersions ($\sigma_v \sim 60\ \kms$) and deconvolved radii $r \approx 1\ h_{50}^{-1}$ kpc. We argue that the lines are \lya, and are powered by stellar ionization. The surface density of robust, high equivalent width \lya\ candidates is estimated to be $\sim 3 \pm 2\ {arcmin}^{-2}$ per unit redshift at $z \simeq 3$, consistent with the estimate of \citet{Cowie:98}. The \lya\ emission line source characteristics are consistent with the galaxies undergoing their first burst of star formation, \ie\ with being primeval. Source sizes and velocity dispersions are comparable to the theoretical primeval galaxy model of \citet{Lin:92} based on the inside-out, self-similar collapse of an isothermal sphere. In this model, star formation among field galaxies is a protracted process. Galaxies are thought to be able to display high equivalent widths for only the first $\sim$ few $\times 10^7$ yr. This time is short in relation to the difference in look back times between $z=3$ and $z=4$, and implies that a substantial fraction of strong line-emitting galaxies at $z=3$ were formed at redshifts $z \leq 4$. We discuss the significance of high-equivalent width \lya-emitting galaxies in terms of the emerging picture of the environment, and the specific characteristics of primeval galaxy formation at high redshift.
|
[
{
"name": "sersearch_emulnat.tex",
"string": "%\\documentstyle[11pt,aaspp4,flushrt,natbib209]{article}\n%\\documentstyle[12pt,aasms4,flushrt,natbib209]{article}\n%\\documentstyle[aas2pp4,flushrt, natbib209]{article}\n\\documentstyle[11pt,aaspp4,flushrt, natbib209]{article}\n\\citestyle{aa}\n\n\n\\def\\plotone#1{\\centering \\leavevmode\n\\epsfxsize=\\columnwidth \\epsfbox{#1}}\n\\def\\plottwo#1#2{\\centering \\leavevmode\n\\epsfxsize=.45\\columnwidth \\epsfbox{#1} \\hfil\n\\epsfxsize=.45\\columnwidth \\epsfbox{#2}}\n\\def\\plotfiddle#1#2#3#4#5#6#7{\\centering \\leavevmode\n\\vbox to#2{\\rule{0pt}{#2}}\n\\special{psfile=#1 voffset=#7 hoffset=#6 vscale=#5 hscale=#4 angle=#3}}\n\n\\slugcomment{\\it In press,\\\\\n The Astrophysical Journal}\n\\lefthead{Manning et al.}\n\\righthead{Primeval Galaxies}\n\n%GOOD AASTEX DEFINITIONS\n\\def\\cf{{c.f.,}}\n\\def\\ie{{i.e.,}}\n\\def\\eg{{e.g.,}}\n\\def\\etal{{et al.~}}\n\n\\def\\deg{\\ifmmode {^{\\circ}}\\else {$^\\circ$}\\fi}\n\\def\\hr{$^{h}$}\n\\def\\min{$^{m}$}\n\\def\\secper{\\ifmmode \\rlap.{^{s}}\\else $\\rlap{.}{^{s}} $\\fi}\n\\def\\ew{equivalent width}\n\n\\def\\kms{\\ifmmode {\\rm\\,km\\,s^{-1}}\\else\n ${\\rm\\,km\\,s^{-1}}$\\fi}\n\\def\\kmsMpc{\\ifmmode {\\rm\\,km\\,s^{-1}\\,Mpc^{-1}}\\else\n ${\\rm\\,km\\,s^{-1}\\,Mpc^{-1}}$\\fi}\n\\def\\ergAcm2{\\ifmmode {\\rm\\,ergs\\,cm^{-2}\\,s^{-1}\\,{\\rm \\AA}^{-1}}\\else\n ${\\rm\\,ergs\\,cm^{-2}\\,s^{-1}\\,\\AA^{-1}}$\\fi}\n\\def\\ergcm2s{\\ifmmode {\\rm\\,ergs\\,cm^{-2}\\,s^{-1}}\\else\n ${\\rm\\,ergs\\,cm^{-2}\\,s^{-1}}$\\fi}\n\\def\\ergsHz{\\ifmmode {\\rm\\,ergs\\,s^{-1}\\,Hz^{-1}}\\else\n ${\\rm\\,ergs\\,s^{-1}\\,Hz^{-1}}$\\fi}\n\\def\\ergs{\\ifmmode {\\rm\\,ergs\\,s^{-1}}\\else\n ${\\rm\\,ergs\\,s^{-1}}$\\fi}\n\\def\\ergsA{\\ifmmode {\\rm\\,ergs\\,s^{-1}\\,\\AA^{-1}}\\else\n ${\\rm\\,ergs\\,s^{-1}\\,\\AA^{-1}}$\\fi}\n\\def\\ergs{\\ifmmode {\\rm\\,ergs\\,s^{-1}}\\else\n ${\\rm\\,ergs\\,s^{-1}}$\\fi}\n\\def\\WHz{\\ifmmode {\\rm\\,W\\,Hz^{-1}}\\else\n ${\\rm\\,W\\,Hz^{-1}}$\\fi}\n\\def\\Msun{M_\\odot}\n\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\def\\simlt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}}\n\\def\\simgt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}}\n\n\\def\\hone{\\ion{H}{1}}\n\\def\\htwo{\\ion{H}{2}}\n\\def\\heii{\\ion{He}{2}}\n\\def\\lya{Ly$\\alpha$}\n\\def\\hbeta{H$\\beta$}\n\\def\\halpha{H$\\alpha$}\n\\def\\oii{[\\ion{O}{2}] $\\lambda3727$}\n\\def\\oiipair{[\\ion{O}{2}] $\\lambda \\lambda 3726,3729$}\n\\def\\oiii{[\\ion{O}{3}] $\\lambda5007$}\n\\def\\oiiipair{[\\ion{O}{3}] $\\lambda \\lambda 4959,5007$}\n\\def\\nv{\\ion{N}{5} $\\lambda$1240}\n\\def\\civ{\\ion{C}{4} $\\lambda$1549}\n\\def\\siii{\\ion{Si}{2} $\\lambda$1260}\n\\def\\alii{\\ion{Al}{2} $\\lambda$1670}\n\n\\def\\loxytwo{L_{\\rm [OII]}}\n\\def\\soxytwo{\\sigma_{\\rm [OII]}}\n\\def\\woxytwo{W_{\\rm [OII]}}\n\\def\\lmm{lines mm$^{-1}$}\n\n%END OF GOOD AASTEX DEFINITIONS\n\n%\\received{4 August 1988}\n%\\accepted{23 September 1988}\n%\\journalid{337}{15 January 1989}\n%\\articleid{11}{14}\n\n\\begin{document}\n\n\\title{A Serendipitous Search for High-Redshift Ly$\\alpha$ Emission: \\\\\nTwo Primeval Galaxy Candidates at $z \\simeq 3$\\altaffilmark{1}}\n\n\\author{Curtis Manning, Daniel Stern\\altaffilmark{2}, Hyron Spinrad,\n\\& Andrew J. Bunker\\altaffilmark{3} }\n\\affil{Department of Astronomy, University of California at Berkeley \\\\\nBerkeley, CA 94720 \\\\\n{\\tt email: (cmanning,dstern,spinrad,bunker)@bigz.berkeley.edu}}\n\n\\altaffiltext{1}{Based on observations at the W.M. Keck Observatory,\nwhich is operated as a scientific partnership among the University of\nCalifornia, the California Institute of Technology, and the National\nAeronautics and Space Administration. The Observatory was made possible\nby the generous financial support of the W.M. Keck Foundation.}\n\n\\altaffiltext{2}{Current address: Jet Propulsion Laboratory,\nCalifornia Institute of Technology, Mail Stop 169-327, Pasadena, CA\n91109; {\\tt stern@zwolfkinder.jpl.nasa.gov}}\n\n\\altaffiltext{3}{Current address: Institute of Astronomy, Madingley\nRoad, Cambridge, CB3 0HA, England; {\\tt email: bunker@ast.cam.ac.uk}}\n\n\\begin{abstract}\n\nIn the course of our ongoing search for serendipitous high-redshift\n\\lya\\ emission in deep archival Keck spectra, we discovered two very\nhigh equivalent width ($W_{\\lambda}^{\\rm obs} \\simgt 450$ \\AA, $2\n\\sigma$) \\lya\\ emission line candidates at $z \\sim 3$ in a moderate\ndispersion ($\\lambda / \\Delta \\lambda \\simeq 1200$) spectrogram. Both\nlines have low velocity dispersions ($\\sigma_v \\sim 60\\ \\kms$) and\ndeconvolved radii $r \\approx 1\\ h_{50}^{-1}$ kpc. We argue that the\nlines are \\lya, and are powered by stellar ionization. The surface\ndensity of robust, high equivalent width \\lya\\ candidates is estimated\nto be $\\sim 3 \\pm 2\\ {\\rm arcmin}^{-2}$ per unit redshift at $z \\simeq\n3$, consistent with the estimate of \\citet{Cowie:98}. The \\lya\\\nemission line source characteristics are consistent with the galaxies\nundergoing their first burst of star formation, \\ie\\ with being\nprimeval. Source sizes and velocity dispersions are comparable to the\ntheoretical primeval galaxy model of \\citet{Lin:92} based on the\ninside-out, self-similar collapse of an isothermal sphere. In this\nmodel, star formation among field galaxies is a protracted process.\n\nGalaxies are thought to be able to display high equivalent widths for\nonly the first $\\sim$ few $\\times 10^7$ yr. This time is short in\nrelation to the difference in look back times between $z=3$ and $z=4$,\nand implies that a substantial fraction of strong line-emitting\ngalaxies at $z=3$ were formed at redshifts $z \\leq 4$. We discuss the\nsignificance of high-equivalent width \\lya-emitting galaxies in terms\nof the emerging picture of the environment, and the specific\ncharacteristics of primeval galaxy formation at high redshift.\n\n\\end{abstract}\n\n\\keywords{Cosmology: observations --- galaxies: compact --- galaxies:\nevolution --- galaxies:formation --- galaxies: starburst --- line:\nprofiles}\n\n\\clearpage\n\n\\section{Introduction}\n\nEarly theoretical models of primeval galaxies suggested that their\n\\lya\\ lines would be highly luminous and diffuse. But searches on\n4m-class telescopes confirmed no such emission lines\n\\citep{Pritchet:94, Thompson:95} and the search for galaxies at large\nlook-back times turned to other strategies. One highly successful\ntechnique is color-selection of the Lyman break in galaxies of redshift\n$z \\simeq 3$ \\citep{Steidel:92, Steidel:96a}. Lyman-break galaxies\n(LBGs) are strongly star-forming, and compact relative to local ${\\cal\nL}^*$ galaxies \\citep{Giavalisco:96b}. However, LBGs are not generally\nthought to be primeval, in part because they have lower\n\\lya\\ equivalent widths than expected of primeval galaxies, in part\nbecause interstellar metallic absorption lines (\\eg\\ \\siii, \\alii) are\ncharacteristic of most LBG spectra.\n\nThe theoretical upper limit equivalent width for \\lya\\ emission\nproduced by stellar photoionization is thought to be\n$W_{\\lambda}^{\\rm rest} \\sim 100 - 200$ \\AA\\ \\citep{Charlot:93}, and\ncan be expected to last only a few$\\times 10^7$ yr for a constant star\nformation rate (SFR). Several examples of high-redshift, high\nequivalent width (non-AGN) \\lya\\ emission have been reported\n\\citep[\\eg][]{Dey:98, Weymann:98, Hu:99}. Few secure examples of\nisolated, high equivalent widths that are not \\lya\\ exist in the\nliterature \\citep[\\eg][]{Stockton:98, Stern:99b}. About half of LBGs\nhave \\lya\\ in emission \\citep{Steidel:96a, Steidel:98, Lowenthal:97},\nwith rest equivalent widths $\\sim 5 - 35$ \\AA. Likewise, about half\nof local actively star-forming galaxies have \\lya\\ in emission, with\nrest equivalent widths in the range $W_{\\lambda} \\simeq 10 - 35$ \\AA\\\n\\citep{Giavalisco:96a}, though a few have $W_{\\lambda} \\simgt 50\n\\mbox{ \\AA}$.\n\nLocal studies show that whether \\lya\\ is seen in emission or\nabsorption may depend heavily on the kinematics of the surrounding\nneutral \\hone\\ halo \\citep{Legrand:97, Kunth:98a} and the chance\ngeometry of neutral gas and dust \\citep{Giavalisco:96a}. However,\n$W_{\\lambda}^{\\rm rest}$ is shown to be weakly-correlated with\nmetallicity \\citep{Terlevich:93, Giavalisco:96a}. The selective\nabsorption of resonantly scattered \\lya\\ photons, whose path length in\nthe cloud is much longer than that of photons of modestly different\nwavelength, is thought to be the major factor in quenching the \\lya\\\nline. The partially extincted \\lya\\ line is characteristically\nasymmetric \\citep[\\eg][]{Dey:98, Kunth:98a, Legrand:97}, presumably\ncaused by the absorption of photons from the blue side of the line by\ndust in an expanding shell, and compounded by the addition of\nred-shifted backscattering off the neutral shell expanding away from\nthe observer \\citep[\\eg][]{Legrand:97}. Though dust-free galaxies are\nthe most likely to have high equivalent width \\lya\\ emission, it is\nclear that a more evolved galaxy can also have high equivalent width\n\\lya\\ emission emerging within specific zones of active star formation\ndue to an incomplete covering factor. Such emission may appear\nspatially offset from the region of star formation\n\\citep[\\eg][]{Bunker:00}. Averaged over the whole galaxy, the\ncontinuum supplied by recent star formation with locally quenched\n\\lya\\ emission will reduce the integrated line equivalent width.\n\nDeep spectra taken at the Keck telescopes regularly reveal\nserendipitous high-equivalent width, isolated emission lines\n\\citep[\\eg][]{Stern:99b}. Indeed, the first confirmed galaxy at $z >\n5$ was discovered in this manner \\citep{Dey:98}. \\citet{Steidel:98}\nobtained a serendipitous spectrum of a strong \\lya\\ line with\nextremely faint continuum near the $\\langle z \\rangle \\simeq 3.09$\nstructure in the SSA22 field. Strong emission lines can also be\neffectively targeted by using narrow band imaging, in conjunction with\nbroad band imaging. Recent observations, using narrow band imaging\nwith a ``strong equivalent width'' ($W_\\lambda^{\\rm obs} \\geq 77$ \\AA)\ncriterion \\citep{Cowie:98} and follow-up spectroscopy \\citep{Hu:98}\nhave disclosed a population of galaxies with what is thought to be\n\\lya\\ in emission. The galaxies tend to have very weak, sometimes\nundetectable, continua. They are also are quite compact, as noted of\nthe $z\\sim 2.4$ \\lya\\ emitters found in HST searches \n\\citep{Pascarelle:96, Pascarelle:98}. \\citet{Cowie:98} estimate a\nsurface density of 3.6 arcmin$^{-2}$ per unit redshift for flux\ndensities $j > 2 \\times 10^{-17}~\\ergcm2s$, corresponding to line\nluminosities ${\\cal L}_{\\rm Ly\\alpha} >1.8 \\times 10^{42} \\ergs$ for\nan Einstein-de Sitter Universe with $H_0 = 50 \\kmsMpc$ at $z \\approx\n3.4$.\n\nWe are conducting a search for serendipitous emission lines in deep\narchival Keck spectra. Such a serendipitous search is an emission-line\nflux-limited survey, and may find emission lines over a wide range of\nredshifts. Narrow-band surveys are sensitive to candidates over\nonly small redshift ranges, and require follow-up spectroscopy to\ndiscriminate stellar \\lya\\ lines from metal and AGN emission lines.\nThe identification of a population of primeval galaxies may provide\nimportant information about the epoch(s) of galaxy formation, including\ndata relevant to the integrated global star formation rate, and the\nluminsity function of galaxies to photometric limits fainter than\nthat accessible to color-selection surveys.\n\nOne drawback faced by all \\lya\\ emission line searches is possible\nconfusion with other isolated, high equivalent width lines such as\n\\oii\\ and H${\\alpha}$. Experience has shown that \\oii\\ is often\nmis-identified as \\lya. When continuum is detected, we may use the\nBalmer series or the continuum depression to discriminate, and when\nabsent we may search for another line, such as \\nv\\ or \\oiii.\nHowever, \\nv\\ is rarely detected in non-AGN, and the search for \\oiii\\\noften fails because these lines would either fall out of the range of\nthe spectrograph, or in the high-noise infrared part of the spectrum\nwhich, combined with the large intrinsic dispersion in \\oii/\\oiii\\\n\\citep{Kennicutt:92}, can make an unambiguous verification untenable.\nAlternatively, one may use the known tendency of \\lya\\ lines to\ndisplay a P-Cygni profile to identify this resonance line. However,\nasymmetry cannot be a completely necessary criterion for \\lya\\ emission\nlines since some local sources apparently have symmetric, or ``pure''\nprofiles \\citep{Kunth:98b}. When emission lines are unresolved, and\nhave undetected continua, the last recourse is the knowledge that\n\\oii\\ rarely has an equivalent width greater than 100 \\AA\\ \\citep[but\nsee][]{Stern:99b}. For these reasons, unambiguous \\lya\\ lines are\nrare, and worthy of extra scrutiny.\n\nWe serendipitously found two isolated emission lines on a single\nslitlet from a mask centered on the SSA22 field, andq determined that\nthey are in fact \\lya\\ lines --- examples of galaxies which are more\ncompact and have higher \\lya\\ equivalent widths than known LBGs. We\nreport on their equivalent widths, intrinsic radii, velocity\ndispersions, and surface/volume density in order to place them in the\npicture of the evolving Universe emerging from studies of\nhigh-redshift galaxies. The source targeted by the slitlet in which\nwe found our emission line galaxies is the color-selected Lyman-break\ngalaxy SSA22~C17; we analyze it in parallel for comparison. We adopt\n$H_0 = 50\\, h_{50}\\, \\kmsMpc, \\Omega_0 = 1,$ and $\\Lambda = 0$ unless\notherwise stated. At $z = 3$, for $\\Omega = 1 (0.1)$, 1\\farcs0\ncorresponds to $7.3\\, (12.3)\\, h_{50}^{-1}$ kpc.\n\n\n\\section{Observations and Data Reduction}\n\nWe have obtained deep, moderate-dispersion spectra of $z \\simeq 3$\nLBGs with the aim of making detailed studies of the ages, kinematics,\ndust-content, and abundances of the LBG population (Dey et. al., in\npreparation). The data were taken during the years 1997 to 1999 with\nthe Low Resolution Imaging Spectrometer \\citep{Oke:95} at the\nCassegrain focus on the Keck~II telescope. The camera uses a Tek\n$2048^2$ CCD detector with a pixel scale 0\\farcs212 pix$^{-1}$. On UT\n1997 September 10 we obtained moderate-dispersion multislit spectra of\nLBGs in the SSA22 field, using the 600 lines mm$^{-1}$ grating blazed\nat 5000 \\AA. Slitlet widths were 1\\farcs25, resulting in a spectral\nresolution of $\\sim$ 4.4 \\AA\\ (FWHM) for sources filling the slitlet,\nand a resolution $\\lambda/\\Delta \\lambda_{\\rm FWHM} \\sim 1200$.\nObjects not filling the slitlet will have higher spectral resolution.\nFor a spatially unresolved source -- one blurred only by atmospheric\nseeing -- we estimate a resolution of $\\sim$ 2.8 \\AA\\ (FWHM) based on\n\\lya\\ absorption systems in the quasar SSA22~D14 also observed on the\nslitmask reported herein. Four of the integrations totaling 7200$s$\nwere of excellent quality, with seeing along the spatial axis of\n$0\\farcs78$. Additional observations were made on UT 1997 September\n12 and UT 1999 June 14. Here we concentrate on the data of UT 1997\nSeptember 10 for which the signal-to-noise ratio ($S/N$) is highest.\n\nThe data reductions were performed using the {\\tt IRAF} package, and\nfollowed standard slit spectroscopy procedures. Flat-fielding, sky\nsubtraction, cosmic ray removal, and aperture extractions of the\nslitmask data were facilitated by the home-grown software package {\\tt\nBOGUS}, created by D.~Stern, A.~J.~Bunker \\& S.~A.~Stanford.\nWavelength calibration was performed using a HgNeAr lamp, employing\ntelluric sky lines to adjust the wavelength zero-point to the data\nframes, compensating for any drift in the wavelength coverage. Flux\ncalibration was performed using observations of Wolf 1346\n\\citep{Massey:90}.\n\n%[EDITOR: FIGURE 1 GOES NEAR HERE]\n\n\\begin{figure}[ht]\n\n\\plotfiddle{spec2d.eps}{2.0in}{0}{91}{91}{-190}{-21}\n\n\\caption{Two-dimensional spectrogram of the slitlet in the SSA22 field\ntargeting the LBG SSA22~C17 at $z=3.299$. Two strong line emitters are\nserendipitously identified, ser-1 and ser-2. The high-equivalent\nwidths, narrow velocity widths, and lack of secondary spectral features\nstrongly argue that these are \\lya\\ emitters at $z \\simeq 3$. Note the\nforeground continuum source and the residual of the\n[\\ion{O}{1}]$\\lambda$ 5577 \\AA\\ skyline.}\n\n\\end{figure}\n\n\\begin{figure}[ht]\n% prg for this in ~/fortran. find *.f, *.macro, *.eps\n\n\\plotfiddle{OIIres_noise.eps}{3.0in}{0}{45}{45}{-146}{-72}\n\n\\caption{The \\oiipair\\ doublet line profile from a source with a 50 \\kms\\\nvelocity dispersion, as it would appear in its rest frame, observed\nwith an effective 2.8 \\AA\\ resolution of a point-source emitter.\nPoisson noise has been added commensurate to that observed in the LRIS\nspectra. The observed emission lines of ser-1 and ser-2 have been\nreferred to the same wavelength, with their amplitude adjusted to\nagree with that of the \\oiipair\\ lines. The line profiles of ser-1\nand ser-2 are clearly incompatible with an \\oiipair\\ interpretation.}\n\n\\end{figure}\n\n\n%[EDITOR: FIGURE 2 GOES NEAR HERE]\n\n\\section{Spectroscopic Results}\n\nWe find two serendipitous, isolated emission lines, ser-1 and ser-2,\nin a 100\\arcsec\\ long slitlet centered on the LBG SSA22~C17 ($z =\n3.299$; see Fig.~1). In lower dispersion spectra, it is often\nimpossible to distinguish between high equivalent width forms of \\oii\\\nand \\lya, unless there is an evident continuum depression, a line\nasymmetry, or other distinguishing features. Though only one of these\ntwo serendipitously discovered sources (ser-2) displays evidence of\nthe asymmetry characteristic of high-redshift \\lya\\ emission in LBGs,\nwe argue that \\lya\\ is indeed the most likely interpretation for\nboth. We simulate the \\oiipair\\ doublet using our 2.8 \\AA\\ resolution\n(for an unresolved source) with 50 \\kms\\ intrinsic velocity\ndispersion, introducing the Poisson noise appropriate to the observed\nflux of the median of ser-1 and ser-2 (see Fig.~2). We conclude that\n\\oiipair\\ is inconsistent with our lines, as the oxygen doublet would\nbe marginally resolved and has a significantly greater FWHM. Further,\nthe absence of associated emission lines argues against H${\\beta}$ and\n\\oiiipair\\ interpretations. Finally, the lines are shortward of 6563\n\\AA\\, so H${\\alpha}$ is not a viable identification. In the\nfollowing, we assume what is most certainly the case --- that these\nare in fact \\lya\\ emission lines. Notably, these spectra display no\ndetectable continua.\n\n%[EDITOR: TABLE 1 GOES NEAR HERE]\n\n\\begin{table}\n\\caption{Emission Line Properties}\n\\scriptsize\n\\begin{center}\n\\begin{tabular}{cccccccccc}\n\\tableline\n\\tableline\nObject &\n$\\lambda^{\\rm obs}$ &\n$z$ &\n$j_{-17}^a$ &\n${\\cal L}_{42}^b$ &\n$W_{\\lambda}^{\\rm obs}$ &\n$W_\\lambda^{\\rm rest}$ &\n$r^c$ &\n$\\sigma_v^d$ \\\\\n&\n(\\AA) &\n& \n(cgs) &\n(cgs) &\n(\\AA) &\n(\\AA) &\n($h_{50}^{-1}$ kpc) &\n(\\kms) \\\\\n\\tableline\nser-1 & 4889.3 & 3.022 & 1.85 & 1.29 & $\\geq 550\\, (2\\sigma)$ & $\\geq 137\\,\n(2\\sigma)$ & $0.8 \\pm 0.6$ & $62 \\pm 9$ \\\\\nser-2 & 5296.8 & 3.357 & 1.35 & 1.19 & $\\geq 470\\, (2\\sigma) $ &$\\geq 109\\,\n(2\\sigma)$ & $1.1 \\pm 0.5$ & $47 \\pm 9$ \\\\\nC17 & 5226.4 & 3.299 & 2.60 & 2.20 & 35.6 & 8.3 & 2.8: & 82: \\\\\n\\tableline\n\\end{tabular}\n\\end{center}\n\\medskip\n\n\\emph{Notes.---} (a) Emission line fluxes are in units of $10^{-17}$\n\\ergcm2s. (b) The \\lya\\ line luminosities are in units of $10^{42}\\,\nh_{50}^{-2}\\, \\ergs$. (c) radius based on deconvolution of source\nFWHM. (d) Deconvolved velocity dispersion assumes sources fill the\n1\\farcs25 width of slitlets.\n\n\\normalsize\n\\end{table}\n\n\n\\begin{figure}[ht]\n\n\\plotfiddle{elspec3.eps}{2.0in}{0}{75}{75}{-235}{-369}\n\n\\caption{Spectra of two serendipitously identified \\lya-emitters in the\nfield of SSA22, with the known LBG SSA22~C17. The abscissa on the left\nrefers to the first two plots, while the abscissa on the right refers\nto the right-hand plot. Inserts illustrate the characteristic\nasymmetric \\lya\\ profile of C17 and ser-2.}\n\n\\end{figure}\n\n%[EDITOR: FIGURE 3 GOES NEAR HERE]\n\n\nThe spectra of the serendipitous emission lines ser-1 and ser-2 are\npresented in Fig.~3, together with that of the LBG SSA22~C17. The\nredshifts of these galaxies, their emission line wavelengths, fluxes\nand attributed luminosities are given in Table~1. It should be noted\nthat the fluxes and luminosities represent only that part of the\natmospherically smeared image of the galaxy falling within the slitlet,\nand are in all likelihood under-estimates as these\nserendipitously-identified sources are not necessarily centered in the\nslitlets. The sources ser-1 and ser-2 are at redshifts $z = 3.022$,\nand $z = 3.357$, respectively. We note that ser-2 is at nearly the\nsame redshift as the nearby quasar SSA22~D14 \\citep{Steidel:98}.\n\nTo date, our serendipitous search has reviewed five slitmasks ($\\simeq\n0.75$ arcmin$^{2}$) and five longslit spectra ($\\simeq 0.30$\narcmin$^{2}$). In addition to the two lines presented here, we have\nfound one other definite \\lya\\ line at $z = 2.946$ with a line flux\n$j = 3.32 \\times 10^{-17} ~\\ergcm2s$ and line luminosity ${\\cal\nL}_{\\rm Ly\\alpha} = 2.2 \\times 10^{42} h_{50}^{-2}\\, \\ergs$. In a\ntotal search area slightly over 1 arcmin$^{2}$, this suggests that the\nsurface density of robustly identified high equivalent width \\lya\\\nemission lines within the redshift range, $2.5 \\leq z \\leq 3.5$ is\nvery roughly of the order $3 \\pm 2$ arcmin$^{-2}$ per unit redshift.\nThis is consistent with the estimate of\n\\citet{Cowie:98} who find a surface density of $\\approx 3.6$\n\\lya-emitters arcmin$^{-2}$ per unit redshift to a higher limiting\nflux density of $2 \\times 10^{-17} ~\\ergcm2s$. The full survey\nincluding candidates at higher redshift will be discussed in a\nsubsequent paper.\n\n\\subsection{Intrinsic Angular Diameters and Velocity Dispersion}\n\nWe derive the intrinsic spatial FWHM assuming that the intrinsic,\natmospheric, and instrumental FWHM add in quadrature. Based on on the\nresults of multiple measurements, we assume the 1$\\sigma$\nobservational and intrinsic FWHM measurement errors to be $\\sim 0.25$\npix, and run 100 trials based on the observed central values. We find\ndeconvolved FWHM for ser-1 and ser-2 of 0\\farcs24 $\\pm$ 0\\farcs18 and\n0\\farcs36 $\\pm$ 0\\farcs15, respectively. At these redshifts, a\ncompact galaxy with $r=1 \\, h_{50}^{-1}$ kpc would have an intrinsic\nangular diameter of $\\sim 0 \\farcs 27 \\, / \\, 0 \\farcs 16$ ($\\Omega=1\n\\, / \\, 0.1$). We note, however, that the deconvolved spatial FWHM of\nC17 at the \\lya\\ line, and in the continuum redward of the line are\n$\\sim 0 \\farcs 90 \\, {\\rm and}\\, 0 \\farcs 40$, respectively. The\ndifference is likely due to scattering of \\lya\\ photons in the \\hone\\\nhalo. Hence it is conceivable that the intrinsic sizes of the stellar\ncomponents of ser-1 and ser-2 are $\\sim 50 \\%$ smaller than the values\nobtained above, or $r \\simlt 500 h_{50}^{-1}$ pc.\n\nWe measure the instrumental resolution (for objects filling the\nslitlet) from the line profile of lamp spectra. We find FWHM$_{\\rm\ninstr}^{\\rm lamp} \\simeq 4.4$ \\AA. For spatially unresolved sources,\nwe find FWHM$_{\\rm instr}^{\\rm QSO} \\simeq 2.8$ \\AA, measured from the\n\\lya\\ forest of the QSO SSA22~D14. The deconvolved velocity width is\ngiven by the equation, \n\\begin{equation} \\sigma_v = c \\frac{\\sqrt{({\\rm\nFWHM}_{\\rm obs})^2 - ({\\rm FWHM}_{\\rm instr})^2}} {2.354\\,\n\\lambda_{\\rm obs}}, \n\\end{equation} \nwhere $c$ is the velocity of light. We find that $\\sigma_v$ is\nconsistent with $\\sim 55 \\pm 8.5 ~ \\kms$ for both serendipitous\nobjects assuming the sources fill the slitlet (see Table 1). For\nunresolved sources, perhaps more appropriate for the small angular\nextent of these sources, $\\sigma_v \\lesssim 95 ~\\kms$. Bear in mind,\nhowever, that these values refer to the kinematics of the\ncircum-galactic H I cloud, rather than stellar velocity dispersion,\nwhich will be less (see related discussion in \\S5).\n\n\n\\subsection{\\lya\\ Equivalent Widths}\n\nThe measured continua for the serendipitously-identified \\lya-emitters\nwere consistent with zero counts, confirming the visual impression of\nser-1 and ser-2 seen in Figs.~1 and 3. Therefore, direct\nspectroscopic measure of the line equivalent widths is not possible.\nWe can, however, determine lower limits on the equivalent widths using\nthe $1 \\sigma$ uncertainty of the continua. The Poisson noise is the\nsquare root of the photon counts per pixel, and we denote its average\nper pixel by $\\sigma_{\\rm pix}$. The summed noise in a aperture of\nwidth $w$ and length $l$ is $\\sigma_{\\rm pix} \\sqrt{wl}$. We have $l$\ndifferent approximations of the value of the continuum, so the noise\nin the continuum $\\sigma_{\\rm cont}$ is, \\begin{equation} \\sigma_{\\rm\ncont} = \\sigma_{\\rm pix} \\sqrt{\\frac{w}{l}}. \\end{equation} However,\n$w$ is not a free parameter, but must be chosen so as to maximize the\n$S/N$. Since our sources are small, we assume their undetected\ncontinua have a Gaussian shape along a spatial cut, and that their\nFWHM is the same as the seeing ($\\sim$ 0\\farcs78). For the \\lya\\\nline, this would imply a source of zero intrinsic extension. But\nsince the FWHM of the continuum is probably significantly less than\nthat of the \\lya\\ line, as we found with SSA22~C17 (\\S3.1), it may in\nfact be a slight over-estimation of the continuum FWHM. We find the\n$S/N$ ratio is maximized when $w = 1.165 \\times$ FWHM. For $l$ we\nchose 100 pixels ($\\sim$ 126 \\AA). Then,\n\\begin{equation} W_{\\lambda}^{\\rm obs}\\, (2 \\sigma) \\simgt\n\\frac{j_{\\alpha}}{2 \\sigma_{\\rm cont}}. \n\\end{equation} \nFor the 1 $\\sigma$ continuum uncertainties, $\\sigma_{\\rm cont} \\simeq\n1.7 (1.4) \\times 10^{-20} ~\\ergAcm2$ for ser-1 (ser-2). We find the\n$2 \\sigma$ lower-limits on the observed equivalent widths are\n$W_{\\lambda}^{\\rm obs} \\geq 550$ \\AA\\ (ser-1), and $\\geq 470$ \\AA\\\n(ser-2). The rest-frame values are tabulated in Table~1. Considering\nthe apparent absence of \\nv\\ and \\civ\\, and the low ISM velocity\ndispersion of these sources, the data is consistent with stellar\nsources, and only marginally with a possible weak AGN. We discuss\nthis further in \\S4. SSA22~C17 has measured $W_{\\lambda}^{\\rm obs}\n\\simeq 35.6$ \\AA.\n\n\\subsection{Star Formation Rates}\n\nAssuming the \\lya\\ line flux is powered by star formation, the\nstrength of this line can be used to infer a star formation rate for a\nyoung galaxy. We first estimate the H$\\alpha$ luminosity\ncorresponding to the measured \\lya\\ luminsity: the low-density case B\nratio \\lya/H$\\beta$ is approximately 25 in the absence of dust\n\\citep{Ferland:85}, while H$\\alpha$/H$\\beta \\sim 2.8$ for hot stars\n\\citep[$T \\simeq 1.2 \\times 10^4$~K;][]{Osterbrock:89}.\n\\citet{Kennicutt:83} provides the conversion from H$\\alpha$ luminosity\nto the SFR, resulting in a SFR -- ${\\cal L}_{{\\rm Ly}\\alpha}$ relation\nof $\\dot{M}\\, (\\Msun$ yr$^{-1}) \\simeq 10^{-42} {\\cal L}_{{\\rm\nLy}\\alpha}$ (\\ergs). This results in SFRs of $\\sim 1.3/1.2 ~\\Msun$\nyr$^{-1}$ for ser-1/ser-2, respectively. Because of the possibility\nof dust, or incomplete absorption of ionizing radiation by the gaseous\nhalo, these numbers are lower limits. We believe slit losses are\nminimal as the lines are nearly unresolved and do not fill the slit.\nLine fluxes from two other nights of observations support this\nconclusion. The continuum flux of the LBG SSA22~C17 at 1500 \\AA\\ was\nused to determine the SFR of ${\\dot M} = 27.7 ~\\Msun$ yr$^{-1}$\n\\citep{Madau:98}, based on a Salpeter IMF with mass range $0.1 \\leq\nM/\\Msun \\leq 125$. However, based on the synthetic spectra of\n\\citet{Leitherer:95}, with a continuous SFR at $\\sim 10$ Myr of age,\nthe SFR is $\\sim 1.6$ times larger, or $\\sim 45 ~\\Msun$ yr$^{-1}$. We\nexpect that the true value is somewhere in between. The \\lya\\ line\nluminosity of C17 (Table 1) would imply a SFR of $2.2 ~\\Msun$ yr.\n\n\n\\subsection{Projected Photometric Magnitudes}\n\nWe use the spectral slope of a $10^7$ year old starburst with a rest\nequivalent width of 150~\\AA \\citep{Charlot:93} to calculate the\nexpected continua of ser-1 and ser-2. We would thus expect continuum\nmagnitudes of $V=27.8$/28.0 for ser-1/ser-2, or $V=27.4$/27.7 when the\n\\lya\\ line is in included. The $2 \\sigma$ upper limits on the\ncontinua of ser-1 and ser-2 (\\S3.2) are only $\\sim 30 \\%$ greater than\nthe continua implied by ${\\rm W}_{\\lambda}^{\\rm rest}=150$ \\AA.\n\n\\section{Discussion}\n\nWhat is the physical origin of these isolated, high equivalent width\nemission lines? \\nv\\ or \\civ\\ are not found in the spectra of ser-1 or\nser-2. The ratio of the high-ionization line flux relative to \\lya\\ is\n$\\simlt 1/15$ and $\\simlt 1/20$ for \\nv\\ and \\civ, respectively, significantly\nless than ratios measured from composite AGN spectra\n\\citep[\\eg~][]{Stern:99a}. The small velocity dispersions of ser-1 and\nser-2 ($\\sigma_v \\simeq 60 \\kms$) and the lack of associated\n\\nv\\ or \\civ\\ emission argue against the presence of an AGN, while the\nhigh surface brightness is inconsistent with photoionization by the\nmetagalactic flux \\citep[\\eg~][]{Bunker:98}. Thus we assume the lines\nowe their existence to stellar sources. Below we argue that the\ngalaxies are primeval, and attempt to fit them into a cogent picture of\nthe evolving Universe at $z \\simeq 3$.\n\n\\subsection{The Production of High Equivalent Width \\lya\\ Emission}\n\nThe production of a strong \\lya\\ line requires two things: first there\nmust be a large column of neutral hydrogen which can intercept almost\nall photons with $\\lambda \\leq 912$ \\AA, and second, \\lya\\ radiation\nmust escape the cloud. The large cross section of \\hone\\ for \\lya\\\nphotons makes \\lya\\ extremely vulnerable to dust quenching. We\nconsider the scenario of \\citet{TenorioTagle:99} in some detail as one\nmodel of the early phases of a starbursting protogalaxy.\n\\citet{TenorioTagle:99} suggest that after an initial stellar\nionization of dynamically quasi-relaxed gas and attendant high\nequivalent width ``pure'' \\lya\\ emission (\\ie\\ a symmetric\nline profile), enriched stellar winds sweep up gas. The compressed\ngas recombines, forming a shell of neutral gas which absorbs emerging\nLyman continuum radiation. \\lya\\ radiation is then emitted and\nscattered within the shell. The expansion of the compressed shell of\ngas results in the preferential scattering, and probable absorption,\nof the blue-wing of the \\lya\\ line. The LBG SSA22~C17 (Figs.~1, 3) is\na good example of this common feature of LBGs; in the insert we see a\ntrough with center $\\sim 350 ~\\kms$ blueward of the line center, while\nat $\\sim 650 ~\\kms$ we see a second maximum. Here, perhaps, is\npalpable proof of a strong wind and a neutral shell, with the blueward\nemission line probably caused by the recombination of shocked gas\nassociated with the expanding shell \\citep{TenorioTagle:99}. In this\nscenario, the time scale for high equivalent width \\lya\\ line emission\nmust be only modestly greater than the lifetime of the most massive\nstars (at most $\\sim 10^7$ yr).\n\nThis model is based upon a single, central starburst driving the \\lya\\\nemission --- an assumption which may not generally hold in real\ngalaxies. High-resolution VLA/optical observations of five local\nstar-forming blue compact dwarfs reveal a history of spatially\ndistinct star forming regions in various stages of evolution\n\\citep{vanZee:98}. Perhaps new star-forming regions in the same\ngalaxy could display high equivalent width \\lya\\ emission. This\neffect appears to be seen in a $z=4.04$ lensed galaxy whose star\nformation regions are subjected to a detailed lensing chromatography\nstudy by \\citet{Bunker:00}. Their color analysis shows a sequence of\nnon-coeval star formation sites with ages ranging from zero to $\\sim\n100$ Myr. ``Nodes'' of star formation, showing \\lya\\ in absorption,\nhave spectral energy distributions consistent with a burst age of $20\n- 30$ Myr. There is, however, an outlying region of very high\nequivalent width \\lya\\ emission ($W_{\\lambda}^{\\rm rest} > 100$ \\AA,\n$3 \\sigma$) thought to be resonantly-scattered \\lya\\ photons escaping\nfrom the adjacent star-forming node. Yet summed over the whole galaxy\n(as we would see it without the benefit of gravitational lensing), the\n\\lya\\ equivalent width is modest.\n\nWe therefore suggest that, for apertures containing entire young\nand compact galaxies, high equivalent width stellar \\lya\\ emission\n($W_{\\lambda}^{\\rm rest} \\simgt 100$ \\AA) indicates a primeval or\nnear-primeval galaxy. We conclude that it is very likely that ser-1\nand ser-2 are primeval galaxies --- by which we mean they are\nundergoing their first significant burst of star formation.\n\n\\subsection{The Surface Density of High-Redshift \\lya-Emitters}\n\nHow do ser-1 and ser-2 fit within the context of surveys of star\nforming galaxies at high redshift? The luminosity function (LF) of\ngalaxies at high redshift is a useful comparative tool for our\npurposes. \\citet{Steidel:99} find a steep faint-end slope ($\\alpha\n\\simeq -1.6$) for the observed ${\\cal R}$-band LF of star-forming\ngalaxies at $\\langle z \\rangle \\simeq 3.04$, implying that a large\nfraction of the UV luminosity density is produced by galaxies fainter\nthan the spectroscopic limits of current Earth-based photometric\nsurveys. By virtue of the association of UV luminosity with SFR, this\nimplies that a large fraction of the star formation history is\nunobserved. When integrated to the apparent magnitudes expected of\nthe continua our serendipitous emission-line galaxies (${\\cal\nR} \\simeq 28$ mag), their UV luminosity function implies number densities\n$\\sim 20$ times, and integrated star formation density $\\sim 4$\ntimes, higher than the classical LBGs integrated to the completeness\nlimits of their ground-based survey, ${\\cal R}=25$ mag.\n\nAs we have noted, because the \\lya\\ emission lines of such sources as\nour serendipitous objects are likely to be observable only for a very\nsmall fraction of 1~Gyr, the modest numbers of high equivalent width\n\\lya\\ sources are tangible evidence for this many-fold larger\npopulation of slightly older, faint continuum, star forming galaxies\nwith self-absorbed \\lya\\, inaccessible to even the deepest\nspectroscopic or color selection surveys. If we are to believe that\nhigh equivalent width \\lya\\ can only be exhibited for the first $\\sim\n5 \\times 10^{7}$ yr of a galaxy's life, and that their surface density\nis $\\sim 3\\ {\\rm arcmin}^{-2}$ per unit redshift, then if their\ndistribution is uniform between $3 \\leq z \\leq 4$, there must be $\\sim\n30$ (50) galaxies ($\\Omega=1~(0.1)$) per square arcminute formed in\nthat interval. This follows because there are 10 ~(17) intervals of\n$5 \\times 10^7$ yr between $z=3$ and $z=4$. The surface density of\nnewly formed galaxies would thus be $\\sim 30$ times larger than the\nLBG surface density. One must integrate the UVLF to ${\\cal R}=28.5$\nto achieve that surface density. Thus, available surface density\nestimates of primeval (high equivalent width \\lya\\ emission) galaxies\nare consistent with the claim that most galaxies at $z\\simeq 3$ were\nformed at redshifts less than $z=4$. However, the integration of the\n$z \\sim 4$ LF \\citep{Steidel:99} over luminosity limits identical to\nthat at $z=3$ shows that the implied co-moving number densities\nincrease only slightly for $\\Omega$ in the range of $0.1 \\leq \\Omega\n\\leq 1.0$, apparently consistent with very low net galaxy formation.\nThese two lines of research could be consistent if the merger rate was\nnearly equal to the galaxy formation rate. There is evidence that the\nepoch-dependent merger rate was higher in the past by $~(1+z)^m$ with\n$m \\sim 1.5-3.0$ \\citep{Windhorst:99}, and that mergers were more frequent\nfor the sub-${\\cal L}^*$ galaxies. However, determining the\nsize-dependent merger rate that would be needed to leave the shape of\nthe luminosity function unchanged while producing only a very modest\nincrease in comoving galaxy density, is beyond the scope of this\npaper.\n\n\\subsection{Environment}\n\nThe environment of high equivalent width \\lya-emitters is of\nconsiderable interest. In their study of Lyman-break candidates in\nthe SSA22 field, \\citet{Steidel:98} display convincing evidence for\nredshift ``spikes'' at $\\langle z \\rangle = 3.09$, and $\\langle z\n\\rangle = 3.35$. Ser-1 lies $\\sim 5000 \\kms$ from the former\nenhancement, a structure which they suggest is a proto-Abell cluster.\nThe latter redshift spike, which is substantially less massive than\nthe former, contains a quasar (SSA22~D14). Ser-2 is only $\\sim 190\n(320) h_{50}^{-1}$ kpc (projected), for $\\Omega = 1 ~(0.1)$, and\n$\\simlt 200 \\kms$ distant from the quasar, while both are on order 400\n\\kms\\ beyond the apparent center of the redshift spike\\footnote{ We\nmodeled the effect of the quasar on ser-2 by extending the observed\ncontinuum blueward of the \\lya\\ line. The extrapolated photon flux is\nsuch that its excitation of gas around ser-2 could account for at most\n$\\sim3 \\%$ of the \\lya\\ emission of ser-2.}. We note that the\nserendipitously-identified high equivalent width \\lya\\ line, SSA22-S1\n\\citep{Steidel:98} at $z=3.100$, is $\\sim 750 \\kms$ from the $\\langle\nz \\rangle = 3.09$ enhancement. Thus, this limited amount of data\nsuggests that high equivalent width \\lya\\ emitters tend to be loosely\nassociated with density enhancements some of which may be\nprotoclusters. Similar clustering of \\lya\\ emitters is seen in\nstudies at $z \\simeq 2.4$ \\citep{Keel:99}.\n\n\\section{A Primeval Galaxy Model}\n\nIn a speculative vein, we now consider what we have learned of\nprimeval galaxies in the light of observations, and the modeling of\nassociated phenomena. Our purpose is to emphasize the significance of\nthe above results to the wider field of cosmology. Our study suggests\nthe existence of a high volume density of tiny galaxies with high\nspecific SFRs, which may cumulatively have rivaled that of the LBGs.\nWe seek here to provide a galaxy formation scenario in which\nthis is plausible, and to place this scenario in the larger context of\nthe evolution of the universe.\n\nIn response to the very small effective radii of faint galaxies imaged\nby HST \\citep[\\eg][]{Giavalisco:96b, Pascarelle:98}, it has been shown\nthat an ``inside-out'' galaxy formation scenario may produce galaxies\nwith small scale-lengths \\citep{Bouwens:97, Cayon:96}. A theoretical\nframework for this hypothesis is presented in a paper by\n\\citet{Lin:92}, which seeks to model primeval galaxies using two\nalternative hypotheses of protogalactic clouds. In these models,\nrobust self--regulating star formation occurs at a rate inversely\nproportional to the cooling time for hydrogen number densities greater\nthan $n_c \\sim 4 \\,{\\rm cm}^{-3}$. Their model $A$ is a homogeneous\ncloud which collapses uniformly; the critical density is first reached\nat a size $R_c \\simeq 6 M_{11}^{1/3}$ kpc, where $M_{11}$ is the\ngalaxy mass in units of $10^{11} ~\\Msun$, creating a star-forming\nregion whose size is inconsistent with observations of either ser-1 or\nser-2. Model $B$ is an isothermal cloud with a core of $500$ pc,\nwhich collapses in an inside--out manner according to the\n\\citet{Shu:77} self-similar collapse model, and reaches the density\n$n_c$ at $R_c \\simeq 1 M_{11}^{1/2} R_{100}^{-1/2}$ kpc , where\n$R_{100}$ is the outer radius of the cloud in units of $100$ kpc.\nModel B predicts sizes that are very close to the constrained sizes of\nour serendipitous emission line regions, and makes their comparison\nwith the model appear quite promising. It also predicts that\nprotogalaxies will have a relatively constant bolometric luminosity\nfor a period of $\\sim 1.7$ Gyr. In their published simulation, the\nbolometric luminosity $\\log{\\cal L} \\sim {43.5}\\, (\\rm{ erg \\,\ns}^{-1})$, though the scale-free nature of isothermal spheres could be\nexpected to allow the somewhat more modest luminosities observed here.\nWe shall see that this luminosity is consistent with a SFR of $\\sim\n5.7 ~\\Msun \\, {\\rm yr}^{-1}$.\n\nAn isothermal cloud which is bounded by an external medium of pressure\n$P_{\\rm ext}$ may achieve a hydrostatic equilibrium if the ratio of\nthe external to the internal pressure is less than 14.3\n\\citep{Shu:77}. This cloud, known as a Bonnor-Ebert sphere, has a\njust-critical mass $M_{crit} \\simeq 0.8 a^4 G^{-3/2} P_{\\rm\next}^{-1/2}$, where $a$ is the sound speed. This mass may be\nconsistent with galactic masses when the intergalactic pressure is\nmodest (\\ie\\ $P_{\\rm ext} \\simlt 1 \\times 10^{-19} {\\rm dyne} ~{\\rm\ncm}^{-2}$). Such a sphere would become super-critical, and collapse\nfrom the inside out if it were part of a general over-density which\nhad pulled away from the Hubble flow and begun to collapse. Linear\ntheory shows that the turn-around radius moves outward at a rate of\n$\\sim$half the Hubble flow \\citep{Davis:80}, so that we could expect\nthe location of high equivalent width \\lya\\ emission to be somewhat\nwithin the turn-around radius, and to move outward with time. A more\nextensive discussion of this subject will be reserved for a future\npublication.\n\nIn order to link the model with observations, we made a rough\nsimulation of a galaxy undergoing a constant SFR over a period of up\nto 1 Gyr. We used a Salpeter IMF ($\\alpha = -2.35$) with lower mass\nlimit of $0.1 ~\\Msun$, and main sequence lifetimes and luminosities\n(Tables 3-6 and 3-9) from \\citet{Mihalas:81}, modeling them as black\nbodies, which is sufficiently accurate for metal-free, non-evolved\nstars. Unless otherwise stated, our upper mass limit is $125 ~\\Msun$,\nand we assume that the SFR is $1.2~\\Msun\\,{\\rm yr}^{-1}$. The \\lya\\\nphoton emission rate of a primeval galaxy is taken to be 2/3 of the\nstellar emission of photons more energetic than 13.6 eV, according to\nthe case B recombination \\citep{Spitzer:78}. We assume that $80\\%$ of\nall newly introduced gas (\\ie\\ over and above the $\\sim 10^{7} ~\\Msun$\nof gas of density $n_c$ within the central 500 pc) is transformed into\nstars immediately.\n\nThe continuum measured in the $75$ \\AA\\ region around the \\lya\\\nemission line, together with the \\lya\\ luminosity, is used to\ncalculate the equivalent width. We tested the derived equivalent\nwidths against the dust-free calculations of \\citet{Charlot:93} for\ncontinuous star formation and upper mass limits of 80 and $120\n~\\Msun$, and found values that were quite consistent with values\nattained by interpolating between the bracketing Salpeter slopes which\nthey employed. We find that for a 10 Myr old galaxy,\n$W_{\\lambda}^{\\rm{rest}} = 160/200/250$\\AA\\ respectively for\n80/100/120 $\\Msun$ upper limits. These derived values drop to $\\sim\n125/155/200$\\AA\\ by 100 Myr. The relation of the resulting \\lya\\ line\nluminosity to the SFR is in agreement with the case B predictions.\nThe model predicts a continuum in the observed visual band of $\\sim\n1.3 \\times 10^{-20} ~\\ergAcm2$ for a $z=3$ galaxy with ${\\dot M}=1.2\n~\\Msun ~{\\rm yr}^{-1}$. This is within the $1 \\sigma$ non-detection\nlimits of the continua of ser-1 and ser-2 ($1.7/1.4 \\times 10^{-20}\n~\\ergAcm2$).\n\nFor an upper mass limit of 100 $\\Msun$, and $\\dot{M}=1.0~\\Msun ~{\\rm\nyr}^{-1}$, the bolometric luminosity at 10 Myr is $\\sim 5.5 \\times\n10^{42}~\\ergs$. Thus, the luminosity of the \\citet{Lin:92} model B\ncorresponds to $\\dot{M}\\simeq 5.7~\\Msun ~{\\rm yr}^{-1}$. We calculate\nthe mass to bolometric luminosity ratio of our model by adding the\nmass in stars and dissipated gas, dividing it by the luminosity. The\ndark matter does not participate in the cloud's collapse since it is\nnot pressure supported. It will be compressed somewhat by the\ngradually increasing concentration of baryons in the center, however,\non the whole, the DM halo should have little effect on the velocity\ndispersion of stars formed out of dissipated gas in the first few tens\nof Myr since they are formed well within the core of the isothermal\nsphere. We find that the calculated ${\\cal M}/{\\cal L} \\simeq 0.01$,\n0.05, and 0.37 for $\\log {t} = 7$, 8, and 9 (Gyr) respectively. We\nnote that compact narrow emission line galaxies, which appear to be\nlikely lower-redshift counterparts, have mass-to-luminosity ratios,\n${\\cal M}/{\\cal L} \\approx 0.1$ \\citep{Phillips:97}.\n\nThe expected stellar velocity dispersion, $\\sigma_s = \\sqrt{G\nM_{stars+gas}/r}$, implies dispersions of model galaxies of from $\\sim\n14~/~ 37~/~$, and $110 ~\\kms$ for $\\log {t} =7$, 8, and 9 (yr),\nassuming a radius of 500 pc. The low $\\sigma_s$ for the 10 Myr old\ngalaxy is actually reasonable, in view of the finding that the very\nlarge cluster in the blue compact dwarf NGC 1705 \\citep{Ho:96} has\n$\\sigma_s \\sim 11\\kms$. A low $\\sigma_s$ is also not in conflict with\nour deconvolved velocity dispersions of $\\sigma_v \\sim 60 ~\\kms$\n(\\S3.1) since the latter is a measure of both the turbulence of gas\n(from infall and stellar winds) which give rise to the \\lya\\ resonance\nline, as well as the possibly spatially resolved structure within the\nslitlet. On the basis of the observed $\\sigma_v$ and deconvolved\nradius $r$ of the LBG C17 (Table 1), we find that the galaxy mass is\n$M_{\\rm{LBG}} = 4.3 \\times 10^9 ~\\Msun$. This galaxy would take\n$\\sim$1.2 Gyr to form at the SFR derived for ser-1 or ser-2. However,\nbetween $z=3.5$ and $z=3.0$, there are only $0.265/0.473$ Gyr for\n$\\Omega=1.0/0.1$. Thus, LBGs would not be formed in a reasonable\namount of time from low-SFR objects if SFRs remain constant. Below,\nwe consider the possibility that the SFR may increase with time\n\nOur simple galaxy model has assumed that ${\\dot M}$ is constant.\nHowever, a realistic isothermal sphere will have a baryonic core,\nassumed here to be $\\sim 500$ pc. In this case case the infall rate\nwill $not$ be constant in time, but given a sound speed of 10 $\\kms$,\nmay increase during the first $\\sim 5 \\times 10^7$ yr. In addition,\nthe negligible metallicity expected of primordial gas will make\ncooling times, and the Jeans mass, larger\\footnote{It has been\nsuggested \\citep{Lin:92} that the IMF of primeval galaxies may be\nheavily weighted in high-mass stars, which could result in rest \\lya\\\nequivalent widths significantly larger than $150$~\\AA. The truth of\nthis contention could be tested if spectroscopic observations deep\nenough to detect the continua were made.} during the first few tens of\nMyr of a galaxy's life. Thus the effect of metals ejected from\nevolved stars in aiding cooling, and of dust in catalyzing the\nproduction of molecules, is to compound the effect of increasing\ninfall; the SFR and its efficiency can be expected to rise\nsubstantially by a few tens of Myr.\n\nOn the other hand, recall that the high equivalent width of the \\lya\\\nemission line of primeval galaxies is expected to be quenched over\nessentially the same time scale. This means that the nature, and fate\nof these pre-LBG/post-primeval galaxies will be very difficult to\nlearn. With an ernhanced SFR, the post-primeval galaxies could\nplausibly grow by a factor of 10-40 into LBGs in a few tenths of a Gyr\nor, by virtue of competition from neighbors, have their growth\ntruncated while still in the dwarf stage, or even be cannibalized;\nenvironment may have a dominant role to play.\n\nWhile the mass and SFRs of our purportedly primeval galaxies are much\nsmaller than that of LBGs, the $specific$ SFR of the former is on\naverage 10 or 20 times greater than the latter. The large numbers of\nsmall, young galaxies which are thought to have been formed (\\S4.2) in\nthe interval $3 \\simlt z \\simlt 4$ might thus be expected to provide a\nsubstantial fraction of the star formation rate density. In fact, the\nsteep faint end slope of the $z \\sim 3$ UV luminosity function of\n\\citet{Steidel:99} implies that up to 40\\% of the SFR density may be\nsupplied by galaxies fainter than ${\\cal R} =27$ (${\\cal L} \\sim 0.1$)\nbut brighter than the projected continuum magnitudes of our\nserendipitous sources. \n\nIn addition to the formation of a galactic bulge according to the\nLin-Murray process, it is expected to be accompanied by the formation\nof the halo, as infalling clumps of gas dissipatively interact with\nthe already accreted gas \\citep{Binney:76, Manning:99a}.\n\n\\section{Conclusions}\n\nWe draw the following conclusions from this study:\n\n\\begin{itemize}\n\n\\item We suggest that the combination of high equivalent widths, low\nvelocity dispersions, and small intrinsic sizes seen in the \\lya\\\nlines of these two galaxies can be well-explained as their being\nextremely low-metallicity galaxies undergoing an initial burst of star\nformation--- hence, primeval galaxies. These characteristics,\nmarkedly different from earlier expectations, suggests an inside-out,\nrather than a monolithic collapse formation mechanism.\n\n\\item Our data, which imply that most galaxies at $z=3$ may have been\nformed at $z \\leq 4$, stand in apparent conflict with the $z=3$ and 4\nUVLFs \\citep{Steidel:99}, which suggest that the comoving galactic\ndensity remained relatively constant during this interval. These may\nbe reconciled, however, with a large merger rate that preserves the\nfaint-end slope of the luminosity function.\n \n\n\\item The agreement of the angular size, and the projected total\nluminosity of these emission line galaxies, with the predictions of\nthe inside-out collapse of a nearly-isothermal \\hone\\ halo\n\\citep{Lin:92} suggests that the latter is a promising basis for\nmodeling galaxy formation. Our discussion has suggested that a rising\nstar formation rate with a time-scale of $\\sim 5 \\times 10^7$ yr is\nplausible for many post-primeval galaxies.\n\n\\item The isothermal collapse model requires that protogalactic clouds\nform in relatively isolated regions. However, their collapse may be\nstimulated by the gradually increasing pressures of a protocluster\nenvironment, thus accounting for the apparent weak clustering on large\nscales noted of high-, as well as low-redshift \\lya\\ emission line\ngalaxies.\n\n\n\\end{itemize}\n\n\n\\acknowledgments\n\nWe thank C. Leitherer, and C. C. Steidel, for useful discussions. We\nare grateful to our referee, Dr. R. A. Windhorst, for valuable\nsuggestions. We also thank A. Dey for assistance with the\nobservations. We are grateful for the support of NSF grant AST\n95-28536.\n\n\\bibliographystyle{apj}\n% give path to manning.bib file as 2nd argument below. ie,\n% if manning.bib is at /moscow/kremlin/manning.bib, the\n% argument should be /moscow/kremlin/manning\n% you might use:\n%\\bibliography{apj-jour,/chakra/manning/serendip/SERsearch/dans_version/manning}\n% my version uses:\n%bibliography{apj-jour,/bigz1/manning/manning}\n\\bibliography{apj-jour,/chakra/manning/serendip/SERsearch/apj_replysubmit/manning}\n\n\n\n\\end{document}\n"
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[
{
"name": "sersearch_emulnat.bbl",
"string": "\\begin{thebibliography}{49}\n\\expandafter\\ifx\\csname natexlab\\endcsname\\relax\\def\\natexlab#1{#1}\\fi\n\n\\bibitem[{Binney(1976)}]{Binney:76}\nBinney, J. 1976, \\mnras, 177, 19\n\n\\bibitem[{Bouwens {et~al.}(1997)Bouwens, Cay\\'on, \\& Silk}]{Bouwens:97}\nBouwens, R.~J., Cay\\'on, L., \\& Silk, J. 1997, \\apj, 489, L21\n\n\\bibitem[{Bunker {et~al.}(1998)Bunker, Marleau, \\& Graham}]{Bunker:98}\nBunker, A.~J., Marleau, F.~R., \\& Graham, J.~R. 1998, \\aj, 116, 2086\n\n\\bibitem[{Bunker {et~al.}(2000)Bunker, Moustakas, \\& Davis}]{Bunker:00}\nBunker, A.~J., Moustakas, L.~A., \\& Davis, M. 2000, \\apj, in press\n\n\\bibitem[{Cay\\'on {et~al.}(1996)Cay\\'on, Silk, \\& Charlot}]{Cayon:96}\nCay\\'on, L., Silk, J., \\& Charlot, S. 1996, \\apj, 467, L53\n\n\\bibitem[{Charlot \\& Fall(1993)}]{Charlot:93}\nCharlot, S. \\& Fall, S.~M. 1993, \\apj, 451, 580\n\n\\bibitem[{Cowie \\& Hu(1998)}]{Cowie:98}\nCowie, L. \\& Hu, E.~M. 1998, \\aj, 115, 1319\n\n\\bibitem[{{Davis} {et~al.}(1980){Davis}, {Tonry}, {Huchra}, \\&\n {Latham}}]{Davis:80}\n{Davis}, M., {Tonry}, J., {Huchra}, J., \\& {Latham}, D.~W. 1980, \\apjl, 238,\n L113\n\n\\bibitem[{Dey {et~al.}(1998)Dey, Spinrad, Stern, Graham, \\& Chaffee}]{Dey:98}\nDey, A., Spinrad, H., Stern, D., Graham, J.~R., \\& Chaffee, F. 1998, \\apj, 498,\n L93\n\n\\bibitem[{Ferland \\& Osterbrock(1985)}]{Ferland:85}\nFerland, G.~J. \\& Osterbrock, D.~E. 1985, \\apj, 289, 105\n\n\\bibitem[{Giavalisco {et~al.}(1996{\\natexlab{a}})Giavalisco, Koratkar, \\&\n Calzetti}]{Giavalisco:96a}\nGiavalisco, M., Koratkar, A., \\& Calzetti, D. 1996{\\natexlab{a}}, \\apj, 466,\n 831\n\n\\bibitem[{Giavalisco {et~al.}(1996{\\natexlab{b}})Giavalisco, Steidel, \\&\n Macchetto}]{Giavalisco:96b}\nGiavalisco, M., Steidel, C.~C., \\& Macchetto, D. 1996{\\natexlab{b}}, \\apj, 470,\n 189\n\n\\bibitem[{Ho \\& Filippenko(1996)}]{Ho:96}\nHo, L.~C. \\& Filippenko, A.~V. 1996, \\apj, 472, 600\n\n\\bibitem[{Hu {et~al.}(1998)Hu, Cowie, \\& McMahon}]{Hu:98}\nHu, E.~M., Cowie, L.~L., \\& McMahon, R.~G. 1998, \\apj, 502, 99\n\n\\bibitem[{Hu {et~al.}(1999)Hu, McMahon, \\& Cowie}]{Hu:99}\nHu, E.~M., McMahon, R.~G., \\& Cowie, L.~L. 1999, \\apj, 522, 9\n\n\\bibitem[{{Keel} {et~al.}(1999){Keel}, {Cohen}, {Windhorst}, \\&\n {Waddington}}]{Keel:99}\n{Keel}, W.~C., {Cohen}, S.~H., {Windhorst}, R.~A., \\& {Waddington}, I. 1999,\n \\aj, 118, 2547\n\n\\bibitem[{Kennicutt(1983)}]{Kennicutt:83}\nKennicutt, R. 1983, \\apj, 282, 54\n\n\\bibitem[{Kennicutt(1992)}]{Kennicutt:92}\n---. 1992, \\apj, 388, 310\n\n\\bibitem[{Kunth {et~al.}(1998{\\natexlab{a}})Kunth, Mas-Hesse, Terlevich,\n Terlevich, \\& Fall}]{Kunth:98a}\nKunth, D., Mas-Hesse, J.~M., Terlevich, E., Terlevich, R., \\& Fall, S.~M.\n 1998{\\natexlab{a}}, \\aap, 334, 11\n\n\\bibitem[{Kunth {et~al.}(1998{\\natexlab{b}})Kunth, Terlevich, Terlevich, \\&\n Tenorio-Tagle}]{Kunth:98b}\nKunth, D., Terlevich, E., Terlevich, R., \\& Tenorio-Tagle, G.\n 1998{\\natexlab{b}}, in {\\it Dwarf Galaxies and Cosmology}, ed. T.~X. Thuan\n (Gif-sur-Yvette: Editions Frontieres), in press\n\n\\bibitem[{Legrand {et~al.}(1997)Legrand, Kunth, Mas-Hesse, \\&\n Lequeus}]{Legrand:97}\nLegrand, F., Kunth, D.~F., Mas-Hesse, J.~M., \\& Lequeus, J. 1997, \\aap, 326,\n 929\n\n\\bibitem[{Leitherer {et~al.}(1995)Leitherer, Carmelle, \\&\n Heckman}]{Leitherer:95}\nLeitherer, C., Carmelle, R., \\& Heckman, T.~M. 1995, \\apjs, 99, 173\n\n\\bibitem[{Lin \\& Murray(1992)}]{Lin:92}\nLin, D.~N.~C. \\& Murray, S.~D. 1992, \\apj, 394, 523\n\n\\bibitem[{Lowenthal {et~al.}(1997)}]{Lowenthal:97}\nLowenthal, J.~D. {et~al.} 1997, \\apj, 481, 673\n\n\\bibitem[{Madau {et~al.}(1998)Madau, Pozzetti, \\& Dickinson}]{Madau:98}\nMadau, P., Pozzetti, L., \\& Dickinson, M.~E. 1998, \\apj, 498, 106\n\n\\bibitem[{Manning(1999)}]{Manning:99a}\nManning, C. 1999, \\apj, 518, 226\n\n\\bibitem[{Massey \\& Gronwall(1990)}]{Massey:90}\nMassey, P. \\& Gronwall, C. 1990, \\apj, 358, 344\n\n\\bibitem[{Mihalas \\& Binney(1981)}]{Mihalas:81}\nMihalas, D. \\& Binney, J. 1981, {\\it Galactic Astronomy} (San Francisco: W. H.\n Freeman and Company)\n\n\\bibitem[{Oke {et~al.}(1995)}]{Oke:95}\nOke, J.~B. {et~al.} 1995, \\pasp, 107, 375\n\n\\bibitem[{Osterbrock(1989)}]{Osterbrock:89}\nOsterbrock, D. 1989, {\\it The Astrophysics of Gaseous Nebulae and Active\n Galactic Nuclei} (Mill Valley: Univ. Science Books)\n\n\\bibitem[{{Pascarelle} {et~al.}(1998){Pascarelle}, {Windhorst}, \\&\n {Keel}}]{Pascarelle:98}\n{Pascarelle}, S.~M., {Windhorst}, R.~A., \\& {Keel}, W.~C. 1998, \\aj, 116, 2659\n\n\\bibitem[{Pascarelle {et~al.}(1996)Pascarelle, Windhorst, Keel, \\&\n Odewahn}]{Pascarelle:96}\nPascarelle, S.~M., Windhorst, R.~A., Keel, W.~C., \\& Odewahn, S.~C. 1996, \\nat,\n 383, 45\n\n\\bibitem[{{Phillips} {et~al.}(1997){Phillips}, {Guzman}, {Gallego}, {Koo},\n {Lowenthal}, {Vogt}, {Faber}, \\& {Illingworth}}]{Phillips:97}\n{Phillips}, A.~C., {Guzman}, R., {Gallego}, J., {Koo}, D.~C., {Lowenthal},\n J.~D., {Vogt}, N.~P., {Faber}, S.~M., \\& {Illingworth}, G.~D. 1997, \\apj,\n 489, 543\n\n\\bibitem[{Pritchet(1994)}]{Pritchet:94}\nPritchet, C.~J. 1994, \\pasp, 106, 1052\n\n\\bibitem[{Shu(1977)}]{Shu:77}\nShu, F.~H. 1977, \\apj, 214, 488\n\n\\bibitem[{Spitzer(1978)}]{Spitzer:78}\nSpitzer, L. 1978, {\\it Physical Processes in the Interstellar Medium} (New\n Work: Wiley)\n\n\\bibitem[{Steidel {et~al.}(1998)Steidel, Adelberger, Dickinson, Giavalisco,\n Pettini, \\& Kellogg}]{Steidel:98}\nSteidel, C.~S., Adelberger, K.~L., Dickinson, M., Giavalisco, M., Pettini, M.,\n \\& Kellogg, M. 1998, \\apj, 492, 428\n\n\\bibitem[{Steidel {et~al.}(1999)Steidel, Adelberger, Giavalisco, Dickinson, \\&\n Pettini}]{Steidel:99}\nSteidel, C.~S., Adelberger, K.~L., Giavalisco, M., Dickinson, M., \\& Pettini,\n M. 1999, \\apj, 519, 1\n\n\\bibitem[{Steidel {et~al.}(1996)Steidel, Giavalisco, Dickinson, \\&\n Adelberger}]{Steidel:96a}\nSteidel, C.~S., Giavalisco, M., Dickinson, M., \\& Adelberger, K.~L. 1996, \\aj,\n 112, 352\n\n\\bibitem[{Steidel \\& Hamilton(1992)}]{Steidel:92}\nSteidel, C.~S. \\& Hamilton, D. 1992, \\aj, 104, 941\n\n\\bibitem[{Stern {et~al.}(2000)Stern, Bunker, Spinrad, \\& Dey}]{Stern:99b}\nStern, D., Bunker, A.~J., Spinrad, H., \\& Dey, A. 2000, \\apj, in press\n\n\\bibitem[{Stern {et~al.}(1999)Stern, Dey, Spinrad, Maxfield, Dickinson,\n Schlegel, \\& Gonz\\'alez}]{Stern:99a}\nStern, D., Dey, A., Spinrad, H., Maxfield, L.~M., Dickinson, M.~E., Schlegel,\n D., \\& Gonz\\'alez, R.~A. 1999, \\aj, 117, 1122\n\n\\bibitem[{Stockton \\& Ridgway(1998)}]{Stockton:98}\nStockton, A. \\& Ridgway, S.~E. 1998, \\aj, 115, 1340\n\n\\bibitem[{Tenorio-Tagle {et~al.}(1999)Tenorio-Tagle, Silich, Kunth, Terlevich,\n \\& Terlevich}]{TenorioTagle:99}\nTenorio-Tagle, G., Silich, S.~A., Kunth, D., Terlevich, E., \\& Terlevich, R.\n 1999, \\mnras, 309, 332\n\n\\bibitem[{Terlevich {et~al.}(1993)Terlevich, D\\`iaz, Terlevich, \\&\n Garc\\`ia}]{Terlevich:93}\nTerlevich, E., D\\`iaz, A.~I., Terlevich, R., \\& Garc\\`ia, M.~L. 1993, \\mnras,\n 260, 3\n\n\\bibitem[{Thompson \\& Djorgovski(1995)}]{Thompson:95}\nThompson, D. \\& Djorgovski, S.~G. 1995, \\aj, 110, 982\n\n\\bibitem[{van Zee {et~al.}(1998)van Zee, Skillman, \\& Salzer}]{vanZee:98}\nvan Zee, L., Skillman, E.~D., \\& Salzer, J.~J. 1998, \\aj, 110, 963\n\n\\bibitem[{Weymann {et~al.}(1998)Weymann, Stern, Bunker, Spinrad, Chaffee,\n Thompson, \\& Storrie-Lombardi}]{Weymann:98}\nWeymann, R., Stern, D., Bunker, A.~J., Spinrad, H., Chaffee, F., Thompson, R.,\n \\& Storrie-Lombardi, L. 1998, \\apj, 505, L95\n\n\\bibitem[{Windhorst {et~al.}(1999)Windhorst, Cohen, \\&\n Waddington}]{Windhorst:99}\nWindhorst, R.~A., Cohen, S.~H., \\& Waddington, I. 1999, in {\\it After the Dark\n Ages: When Galaxies were Young}, ed. S.~S. Holt \\& E.~P. Smith, Vol. 470 (New\n York: AIP), 202\n\n\\end{thebibliography}\n"
}
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astro-ph0002242
|
The RR Lyrae {U Com} as a test for nonlinear pulsation models
|
[
{
"author": "Giuseppe Bono\\altaffilmark{1}"
},
{
"author": "Vittorio Castellani\\altaffilmark{2}"
},
{
"author": "Marcella Marconi\\altaffilmark{3}"
}
] |
We use high precision multiband photometric data of the first overtone RR Lyrae \uc to investigate the predictive capability of full amplitude, nonlinear, convective hydrodynamical models. The main outcome of this investigation is that theoretical predictions properly account for the luminosity variations along a full pulsation cycle. Moreover, we find that this approach, due to the strong dependence of this observable and of the pulsation period on stellar parameters, supply tight constraints on stellar mass, effective temperature, and distance modulus. Pulsational estimates of these parameters appear in good agreement with empirical ones. Finally, the occurrence of a well-defined bump just before the luminosity maximum gave the unique opportunity to calibrate the turbulent convection model adopted for handling the coupling between pulsation and convection.
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"name": "ms.tex",
"string": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% AAS style double spaced\n\\documentstyle[12pt,aaspp4]{article}\n\n% AAS style single spaced\n%\\documentstyle[12pt,aasms4]{article}\n\n\n\\pagestyle{headings}\n%\\pagestyle{empty}\n%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n% abbreviations\n%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++\n\\newcommand{\\uc}{\\rm U Com~}\n\\newcommand{\\cdo}{$^{12}C(\\alpha ,\\gamma)^{16}O\\;$}\n\\newcommand{\\dydz}{$\\Delta Y / \\Delta Z\\;$}\n\\newcommand{\\kms}{$\\,km\\,s^{-1}$}\n\\newcommand{\\lsun}{log $L/L_{\\odot}\\,$}\n\\newcommand{\\msun}{$M/M_{\\odot}\\,$}\n\n%====================================================================\n\n\\begin{document}\n\n\\title{The RR Lyrae {\\rm U Com} as a test for nonlinear pulsation models}\n\n\n\\author{Giuseppe Bono\\altaffilmark{1}, Vittorio Castellani\\altaffilmark{2}, \nMarcella Marconi\\altaffilmark{3}}\n\n\\affil{1. Osservatorio Astronomico di Roma, Via Frascati 33,\n00040 Monte Porzio Catone, Italy; bono@coma.mporzio.astro.it}\n\\affil{2. Dipartimento di Fisica Universit\\`a di Pisa, Piazza Torricelli 2,\n56100 Pisa, Italy; vittorio@astr18pi.difi.unipi.it}\n\\affil{3. Osservatorio Astronomico di Capodimonte, Via Moiariello 16,\n80131 Napoli, Italy; marcella@na.astro.it}\n\n\\begin{abstract}\nWe use high precision multiband photometric data of the first\novertone RR Lyrae \\uc to investigate the predictive capability \nof full amplitude, nonlinear, convective hydrodynamical models. \nThe main outcome of this investigation is that theoretical predictions \nproperly account for the luminosity variations along a full pulsation \ncycle. Moreover, we find that this approach, due to the strong dependence \nof this observable and of the pulsation period on stellar parameters, \nsupply tight constraints on stellar mass, effective temperature, and \ndistance modulus. Pulsational estimates of these parameters appear \nin good agreement with empirical ones.\nFinally, the occurrence of a well-defined bump just before the luminosity \nmaximum gave the unique opportunity to calibrate the turbulent convection \nmodel adopted for handling the coupling between pulsation and convection. \n\\end{abstract}\n\n\\keywords{stars: distances -- stars: evolution -- stars: horizontal branch -- \nstars: individual (\\uc) -- stars: oscillations -- stars: variables: RR Lyrae} \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\pagebreak \n\\section{Introduction} \n \nVariable stars play a key role in many astrophysical problems, \nsince their pulsation properties do depend on stellar parameters, \nand therefore they can supply valuable and independent constraints \non a large amount of current evolutionary predictions. \nIn particular, the empirical evidence found long time ago in \nMagellanic Cepheids of the correlation between period and \nluminosity was the initial step for a paramount theoretical and \nobservational effort aimed at using variable stars as standard \ncandles to estimate cosmic distances. The current literature is still \nhosting a vivid debate on the intrinsic accuracy of the Cepheid distance \nscale (Bono et al. 1999; Laney 2000) and on the use of RR Lyrae \nvariables to evaluate the distance -and the age- of Galactic globulars \n(Caputo 1998; Gratton 1998, G98). \n\nTheoretical insights into the problem of radial stellar pulsations \ncame from the linearization of local conservation equations governing \nthe dynamical instability of stellar envelopes. Linear, nonadiabatic \nmodels typically supply accurate pulsation periods and plausible \nestimates (necessary conditions) on the modal stability of the \nlowest radial modes. \nHowever, a proper treatment of radial pulsations does require the \nsolution of the full system of hydrodynamic equations, including \na nonlocal and time-dependent treatment of turbulent convection \n(TC) to account for the coupling between radial and convective \nmotions (Castor 1968; Stellingwerf 1982, S82). \n \nThe development of nonlinear, convective hydrocodes (S82; Gehmeyr 1992; \nBono \\& Stellingwerf 1994, BS; Wuchterl \\& Feuchtinger 1998) \ngave the opportunity to provide plausible predictions on the properties \nof radial variables, and in particular on the topology of the instability \nstrip, as well as on the time behavior of both light and radial velocity \ncurves. This new theoretical scenario allowed to investigate, for the \nfirst time, the dependence of pulsation amplitudes and Fourier \nparameters on stellar mass, luminosity and effective temperature \n(see e.g. Kovacs \\& Kanbur 1997; Brocato et al. 1996; Feuchtinger 2000, F20).\nHowever, all these investigations dealt with parameters related to \nthe light curve, whereas nonlinear computations supply much more \ninformation, as given by the detailed predictions of the light \nvariation along a full pulsation cycle. Therefore, the direct \ncomparison between observed and predicted light curves appears as \na key test only partially exploited in the current literature \n(Wood, Arnold, \\& Sebo 1997, WAS). \n\nIn order to perform a detailed test of the predictive capability of our \nnonlinear, convective models we focused our attention on the photometric \ndata collected by Heiser (1996, H96) for the field, first \novertone -$RR_c$- variable \\uc. The reason for this choice relies \non the detailed coverage of the U, B, and V light curves, as well as \non the characteristic shape of the light curve, with a well-defined \nbump close to the luminosity maximum. This secondary feature provides \na tight observational constraint to be nailed down by theory. \nSince the period of the variable strongly depends on the structural \nparameters (mass, luminosity, and radius) of the pulsator, \nthe problem arises whether or not nonlinear pulsation models \naccount for the occurrence of similar pulsators, and in affirmative \nhow precisely the observed light curves can be reproduced by \ntheoretical predictions.\n\nIn \\S 2 we present the comparison between theory and observations, \nwhile in \\S 3 we discuss the calibration of the TC model. Finally,\nin \\S 4 we briefly outline the observables which can further \nvalidate this theoretical scenario. \n \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Comparison between theory and observations}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nOn the basis of spectroscopic measurements Fernley \\& Barnes (1997, FB97) \nestimated for \\uc a metallicity $[Fe/H]=-1.25\\pm0.20$, \nwhile Fernley et al. (1998, FB98) found a negligible interstellar \nextinction ($E(B-V)=0.015\\pm0.015$). \nAccording to these empirical evidence and to a well-established \nevolutionary scenario, we expect for a metal-poor RR Lyrae a \nstellar mass of the order of 0.6 $M_\\odot$ and a luminosity \nranging from \\lsun=1.6 to 1.7. At the same time, pulsation \npredictions on double-mode pulsators suggest similar mass values \n(Cox 1991; Bono et al. 1996). \nAs a consequence, we computed a sequence of nonlinear models at fixed \nchemical composition (Y=0.24, Z=0.001) and pulsation period \n$P_{FO}\\approx0.29$ d. \nAlong such an iso-period sequence the individual models were constructed \nat fixed mass value (\\msun = 0.60), while both the luminosity and the \neffective temperature were changed according to the pulsation relation \ngiven by Bono et al. (1997, BCCM). \nBoth linear and nonlinear models were computed by adopting the input\nphysics, and physical assumptions already discussed in BS, BCCM, \nand in Bono, Marconi \\& Stellingwerf (1999). According to S82, \ncurrent models were computed by assuming a vanishing efficiency \nof turbulent overshooting in the region where the superadiabatic \ngradient attains negative values. This means that the convective flux \ncan only attain positive or vanishing values ($F_c \\ge 0$). \nIn the next section we show that the assumption adopted \nin our previous investigations -i.e. $F_c$ can attain both \npositive and negative values- marginally affects the topology \nof the instability strip, but the predicted light curves are \nsomewhat at variance with empirical ones. \n\nThe top panels of Fig. 1 show that at fixed stellar mass (\\msun=0.60), \nthe double peak feature appears in models characterized by \nluminosities approximately equal to \\lsun$\\approx$1.61, and effective \ntemperatures ranging from 6950 to 7150 K. These models also present \n{\\rm B} amplitudes in reasonable agreement with empirical estimates \n($A_B=0.64$ mag). The bottom panels of Fig. 1 display the light \ncurves of models \nalong the iso-period sequence constructed by adopting a fixed effective \ntemperature ($T_e=7100$ K) but different assumptions on stellar mass \nand luminosity. A glance at these curves shows that the luminosity \namplitude is mainly governed by the stellar mass, whereas the shape \nof the light curve is only marginally dependent on this parameter. \n\nWe find that the best fit to the observed B light curve is obtained \nfor \\msun=0.6, \\lsun=1.607, $T_e=7100$ K, $P_{FO}=0.290$ d, together \nwith a distance modulus $(m_B-M_B) = 11.01$ mag. The fit -though not perfect- \nappears rather satisfactory, thus suppling a substantial support \nto the predictive impact of the adopted theoretical scenario.\nOn the basis of this finding, we are now interested in testing the \naccuracy of theoretical predictions in different photometric bands. \nFig. 2 shows from left to right the comparison between predicted \nlight curves (solid lines) and empirical data (open circles) in the \nU, B, V, and K band respectively. The comparison was performed by \nadopting the same distance modulus, i.e. by neglecting \nthe interstellar extinction, and the agreement between theory and \nobservations seems even better than for the B light curve. \nThus suggesting that nonlinear models account for luminosity \namplitudes which are a long-standing problem of pulsation theory. \n\n\nNot surprisingly, we also find that the time average colors predicted \nby our model appear, within current uncertainty on both reddening and \n photometry, in very good agreement with empirical estimates \n(see Table 1). This result supports the evidence that nonlinear models, \nat least in this case, can constrain stellar colors by best fitting \nthe light curve in a single photometric band. At the same time,\nthis agreement suggests that the pulsational constraints on the \ntemperature of the pulsator, as derived by the B light curve, are\nconsistent with the theoretical light curves in the other photometric \nbands.\n\n\\small \n\\begin{center}\n\\begin{tabular}{cccc}\n\\tablewidth{0pt}\\\\ \n\\multicolumn{4}{c}{TABLE 1. {\\rm U Com}: theoretical and empirical\ncolors$^a$}\\\\\n\\hline \nColor & Theory & Observ. & Observ. \\\\ \n% mag & & $E_{(B-V)}=0$ & $E_{(B-V)}=0.015$ \\\\ \n mag & & $E(B-V)=0$ & $E(B-V)=0.015$ \\\\ \n\\hline \n$<U>-<B>$ &$0.06\\pm0.01$ & $0.11\\pm0.02$ & $0.09\\pm0.02$ \\\\ \n$<B>-<V>$ &$0.23\\pm0.01$ & $0.21\\pm0.02$ & $0.19\\pm0.02$ \\\\ \n$<V>-<K>$ &$0.77\\pm0.01$ & $0.81\\pm0.07$ & $0.77\\pm0.07$ \\\\ \n\\hline \n\\end{tabular}\n\\end{center}\n\\normalsize \n\\begin{minipage}{1.00\\linewidth} \n\\noindent $^a$ Empirical estimates are based on photometric \ndata collected by H96 and by FB97. Theoretical colors refer to the best \nfit model, and the errors were estimated by assuming an uncertainty of \n50 K in the temperature of this model. \n\\end{minipage} \n\nHowever, we note that on the basis of both the period and the \nshape of the {\\rm B} light curve we predicted the effective temperature, \nthe intrinsic luminosity, and in turn the distance modulus of this object. \nThe plausibility of the theoretical constraints can be further tested\nby comparing them with independent evaluations available in the literature. \nWe find that the effective temperature predicted by nonlinear models \n-$T_e=7100\\pm50$ K- is in remarkable agreement with the empirical \ntemperature -$T_e=7100\\pm150$ K- derived by adopting the true intensity \nmean color $(<V>-<K>)_0=0.77\\pm0.07$ provided by FB97 and the \nCT relation by Fernley (1989). The same outcome applies by assuming \nE(B-V)=0, and indeed \n$(<V>-<K>)=0.81\\pm0.07\\,\\rightarrow\\,T_e=7050\\pm150$ K, while the \nsemi-empirical estimate provided by H96 suggests $T_e=7250\\pm150$ K. \nWe also note that the effective gravity of the best fit model \n(log $g\\approx3.0$) is also in very good agreement with both the \nphotometric estimate obtained by H96 (log $g=3.1\\pm0.2$) and the \nspectroscopic measurements for field RR Lyrae variables provided \nby Clementini et al. (1995) and by Lambert et al. (1996). \n\nAs far as the distance modulus is concerned, Fig. 3 shows the comparison \nof our pulsational estimates (filled circles) with empirical and \ntheoretical \\uc absolute magnitudes obtained by adopting different \nmethods. The top and the bottom panel refer to absolute magnitudes \nbased on visual and NIR magnitudes respectively. Data plotted in \nthis figure show that our estimates appear in satisfactory \nagreement with distances based on the Baade-Wesselink method, \non the statistical parallax method, on Hipparcos trigonometric \nparallaxes and proper motions, and on RR Lyrae {\\rm K} band \nPL relation. \n\nHowever, one also finds that the distance determination based on \nHB evolutionary models constructed by including the most recent\ninput physics (Cassisi et al. 1999, C99) seems to overestimate \nthe distance \nmodulus by approximately 0.18 mag when compared with the current \npulsation determination. A disagreement between evolutionary and \npulsation predictions concerning the luminosities of RR Lyrae \nstars was brought out by Caputo et al. (1999), and more recently by \nCastellani et al. (2000) who found that up-to-date\nHe-burning models seem too bright when compared with Hipparcos \nabsolute magnitudes. Data plotted in Fig. 3 confirm this discrepancy\nbetween evolutionary and pulsational predictions, possibly due to \nan overluminosity of HB models. Part of this discrepancy might be \ndue to the higher temperature of U Com when compared with the mean \ntemperature of RR Lyrae gap ($T_e=6800$ K) adopted in evolutionary \nestimates. \n\nFinally, we also constructed several sequences of models by increasing\nor decreasing the metal abundance by a factor of two. We find that the \nbump becomes more (less) evident at lower (higher) metal contents, and \nthat this change does not allow us to obtain a good fit between \ntheory and observations. This result is in satisfactory agreement with \nthe spectroscopic estimate by FB97 and supports the evidence that the \nshape of the light curve can also be used to constrain the $RR_c$ \nmetallicity (Bono, Incerpi, \\& Marconi 1996). \n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Calibration of the TC model}\n\nThe first set of models we constructed for fitting the empirical \nlight curves was characterized by an unpleasant feature: \nthe peak of the bump was, in contrast with empirical evidence, brighter\nthan the \"true\" luminosity maximum. According to Bono \\& Stellingwerf\n(1993) the bump along the rising branch presents a strong dependence \non the free parameters adopted in the TC model. However, in the \ncalibration of the TC model suggested by BS both the eddy viscosity \nand the diffusion scale lengths (see their equ. 4 and 9) were scaled \nto the value of the mixing length parameter. We performed several \nnumerical experiments by \nchanging along each sequence only one of the three free parameters. \nAs a result, we find that full amplitudes models constructed by adopting \nplausible changes of the free parameters do not simultaneously account \nfor the pulsation amplitude, the shape of the light curve, and the \ntemperature width of first overtone instability region. \n\nDue to the lack of a self-consistent theory of time-dependent, nonlocal, \nconvective transport, current investigations were mainly aimed at \ncalibrating the free parameters adopted for treating the coupling \nbetween pulsation and convection (Yecko et al. 1998; F20). This is not \na trivial effort, since the observables and the comparison between theory \nand observations are affected by the thorny problem of the transformation \ninto the observational plane and/or by systematic deceptive errors \nsuch as reddening and distance estimates. \nIn order to overcome some of these difficulties, F20 calibrated \nthe TC model by performing a detailed comparison between theoretical \nand observed luminosity amplitudes of field RR Lyrae variables. On the basis \nof the fine tuning of both mixing length and turbulent viscosity length, \nF20 found that the Fourier parameters of fundamental light curves agree \nwith observational data. The same outcome did not apply to $RR_c$ \nvariables, and indeed predicted values appear, at fixed period, \nsmaller than the empirical ones. \nA detailed comparison with the convective \nstructure of RR Lyrae models constructed by F20 is not possible because \nhe adopted a convective flux limiter in the turbulent source function \nand in the convective flux enthalpy, and neglected both the turbulent \npressure and the turbulent overshooting. As a consequence, we decided \nto test the dependence of full amplitude models on the last two \ningredients. \n\nInterestingly enough, we find that the models constructed\nby assuming a vanishing overshooting efficiency satisfy empirical \nconstraints i.e. the bump is dimmer than the luminosity maximum, the \nluminosity amplitudes attain values similar to the observed ones \nand the temperature width of the region in which the first overtone \nis unstable agrees with BCCM findings for cluster $RR_c$ variables. \nFig. 4 shows the \n{\\rm B} light curve of two models constructed by adopting \nthe same input parameters, but different assumptions on the efficiency \nof turbulent overshooting. It is noteworthy the simultaneous change in \nthe pulsation amplitude and in the shape of the light curve. \nThe dependence of the convective structure on both overshooting \nand turbulent pressure will be investigated in a forthcoming paper. \n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Discussion and Conclusions} \n\nThe comparison between theory and observations, namely the period and \nthe shape of the {\\rm B} light curve of U Com, allowed us to supply \ntight constraints on the structural parameters such as stellar mass, \neffective temperature, and gravity, as well as on the distance of this \nvariable. We also found that the occurrence of a well-defined bump \nclose to the luminosity maximum can be safely adopted for \nconstraining the metallicity of this object and for calibrating \nthe TC model adopted for handling the coupling between convection \nand pulsation. \n\nThe approach adopted in this investigation seems quite promising since \nit only relies on nonlinear, convective models and on stellar atmosphere \nmodels. In fact, the best fit model to the empirical data was found by \nconstructing sequences of iso-period models in which the stellar mass, \nthe luminosity and the effective temperatures were not changed according \nto HB models but to the pulsation relation (BCCM). \nThe comparison between theory and observations \nshows that both the structural parameters and the distance are \nin very good agreement with estimates available in the literature. \nNo evidence for a systematic discrepancy was found in pulsation estimates, \nthus supporting the evidence that the individual fit to light curves \ncan supply independent and firm constraints on the actual parameters \nand distances of variable stars. This finding confirms the results \nof a similar analysis on a LMC Bump Cepheid by WAS. \n\nAccurate radial velocity data for \\uc are not available in the \nliterature and therefore we could not constrain the accuracy of the \nvelocity variation along the pulsation cycle. The three radial velocity \npoints collected by FB98 agree quite well with the \npredicted curve. However, the radial velocity curve is a key \nobservable for constraining the consistency of the adopted TC \nmodel (F20), and therefore new spectroscopic measurements \nof \\uc would be of great relevance for assessing the \npredictive impact of nonlinear, convective models. \nTheoretical observables of the best fit model discussed in this \npaper, as well as both radius and radial velocity variations \nare available upon request to the authors. \n\n\n%\\acknowledgments\nIt is a pleasure to thank M. Groenewegen for providing us the\n\\uc distances based on the reduced parallax method and on \nthe modified Lutz-Kelker correction, as well as for insightful \ndiscussions on their accuracy. We are indebted to R. Garrido \nfor sending us radial velocity data and to T. Barnes for useful \nsuggestions on current data. We also acknowledge an anonymous \nreferee for some useful suggestions that improved the readability \nof the paper. This work was supported by MURST -Cofin98- under the \nproject \"Stellar Evolution\". Partial support by ASI and CNAA is \nalso acknowledged. \n\n\n\\begin{references}\n\\reference{} Barnes, T. G., \\& Hawley, S. L. 1986, \\apj, 307, L9 (BH) \n\\reference{} Bono, G., Caputo, F., Castellani, V., \\& Marconi, M. 1996, \\apj, 471, L33 \n\\reference{} Bono, G., Caputo, F., Castellani, V., \\& Marconi, M. 1997,\n\\aaps, 121, 327 (BCCM) \n\\reference{} Bono, G., Caputo, F., Castellani, V., \\& Marconi, M. 1999, \\apj, 512, 711 \n\\reference{} Bono, G., Incerpi, R., \\& Marconi, M. 1996, \\apj, 467, L97 \n\\reference{} Bono, G., Marconi, M., \\& Stellingwerf, R. F. 1999, \\apjs, 22, 167\n\\reference{} Bono, G., \\& Stellingwerf, R. F. 1993, Soc. Astr. Italiana Mem., 64, 559\n\\reference{} Bono, G., \\& Stellingwerf, R. F. 1994, ApJS, 93, 233 (BS) \n\\reference{} Brocato, E., Castellani, V. \\& Ripepi, V. 1996, \\aap, 111, 809\n\\reference{} Caputo, F. 1998, \\aapr, 9, 33 \n\\reference{} Caputo, F., Castellani, V., Marconi, M., \\& Ripepi, V. 1999,\n\\mnras, 306, 815 \n\\reference{} Carney, B. W., Fulbright, J. P., Terndrup, D. M., Suntzeff, N. B.,\n \\& Walker, A. R. 1995, \\aj, 110, 1674 (C95) \n\\reference{} Cassisi, S., Castellani, V., Degl'Innocenti, S., Salaris, M. \\& Weiss, A. 1999, \\aaps, 134, 103 (C99)\n\\reference{} Castellani, V., Degl'Innocenti, S., Girardi, L., Marconi, M.,\n Prada Moroni, P. G., \\& Weiss, A. 2000 \\aap, in press \n\\reference{} Castelli, F., Gratton, R. G., \\& Kurucz, R. L. 1997, \\aap, 324, 432\n\\reference{} Castor, J. I. 1968, unpublished \n\\reference{} Clementini, G., Carretta, E., Gratton, R., Merighi, R. 1995, \\aj, 110, 2319\n\\reference{} Cox, A. N. 1991, \\apj, 381, L71\n\\reference{} Fernley, J. 1989, MNRAS, 239, 905\n\\reference{} Fernley, J., \\& Barnes, T. G. 1997, \\aaps, 125, 313 (FB97) \n\\reference{} Fernley, J., et al. 1998, \\aap, 330, 515 (FB98) \n\\reference{} Fernley, J., Carney, B. W., Skillen, I., Cacciari, C., \\&\nJanes, K. 1998, \\mnras, 293, L61 (FC98) \n\\reference{} Fernley, J., Skillen, I., \\& Burki, G. 1993, \\aaps, 97, 815 \n\\reference{} Feuchtinger, M. U. 2000, \\aap, in press (F20) \n\\reference{} Gehmeyr, M. 1992, \\apj, 399, 272\n\\reference{} Gould, A. \\& Popowski, P. 1998, \\apj, 508, 844 (GP)\n\\reference{} Gratton, R. G. 1998, \\mnras, 296, 739 (G98) \n\\reference{} Groenewegen, M. A. T., \\& Salaris, M. 1999, \\aap, 348, L33 (GS) \n\\reference{} Heiser, A. M. 1996, \\aj, 112, 2142 (H96) \n\\reference{} Jones, R. V., Carney, B. W., Storm, J., \\& Latham, D. W.\n1992, \\apj, 386, 646 (J92) \n\\reference{} Kovacs, G., \\& Kanbur, S. 1997, \\mnras, 295, 834 \n\\reference{} Lambert, D. L., Heath, J. E., Lemke, M., Drake, J. 1996 \\apjs, 103, 183\n\\reference{} Laney C. D. 2000, in IAU Colloq. 176, The Impact of Large-Scale \nSurveys on Pulsating Star Research, ed. L. Szabados, \\& D. Kurtz \n(San Francisco: ASP), in press \n\\reference{} Layden, A. 1999 in Post-Hipparcos Cosmic Candles, ed. A. Heck,\n\\& F. Caputo (Dordrecht: Kluwer), 37 (L99) \n\\reference{} Layden, A., Hanson, R. B., Hawley, S. L., Klemola, A. R. \\&\nHanley, C. J. 1996, \\aj, 112, 2110 (L96) \n\\reference{} Longmore, A. J., Dixon, R., Skillen, I., Jameson, R. F., \\&\nFernley, J. 1990, \\mnras, 247, 684 (L90) \n\\reference{} Stellingwerf, R. F. 1982, \\apj, 262, 330 (S82) \n\\reference{} Tsujimoto, T., Miyamoto, M., \\& Yoshii, Y. 1998, \\apj,\n492, L79 (TMY) \n\\reference{} Wood, P. R., Arnold, A., \\& Sebo, K. M. 1997, ApJ, 485, L25 (WAS) \n\\reference{} Wuchterl, G., \\& Feuchtinger, M. U. 1998, 340, 419 \n\\reference{} Yecko, P. A., Kollath, Z., Buchler, J.R. 1998, A\\&A, 336, 553 \n\\end{references}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% Figure Captions\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\pagebreak\n% 1\n\\figcaption{Top panels: blue light curves of iso-period -$P=0.29$ d- RR Lyrae \nmodels constructed by adopting the same chemical composition (Y=0.24, \nZ=0.001) and stellar mass (\\msun=0.60), but different assumptions on \neffective temperatures and luminosities (see labeled values). \nBolometric curves where transformed into {\\rm B} magnitudes by \nadopting bolometric corrections and color-temperature (CT) relations \nby Castelli, Gratton \\& Kurucz (1997). \nBottom panels: similar to top panels, but for models constructed at \nfixed effective temperature ($T_e=7100$ K), and different assumptions \non stellar masses and luminosities (see labeled values).}\n\n% 2\n\\figcaption{Comparison between theory (solid lines) and observations \n(open circles). From left to right the panels refer to photometric \ndata in U, B, V (Heiser 1996), and K (Fernley, Skillen \\& Burki 1993). \nEmpirical data were plotted by assuming $E(B-V)=0$. Photometric errors \nin optical bands are equal to the symbol size.} \n\n% 3 \n\\figcaption{\\uc absolute magnitudes vs. time. Top and bottom panels \nshow {\\rm V} and {\\rm K} estimates respectively. The acronyms refer \nto different methods: \nBW: Baade-Wesselink (Jones et al. 1992); HB models: Horizontal Branch\nmodels (Cassisi et al. 1999, C99); SP: statistical parallax\n(Barnes \\& Hawley 1986, BH); TP: trigonometric parallax (Gratton 1998, G98);\nBW + PLK: zero point from BW and slope from {\\rm K} band Period-Luminosity\nrelation (Longmore et al. 1990, L90; J92; Carney et al. 1995, C95);\nLK + BW: zero point from modified Lutz-Kelker correction (Groenewegen \\&\nSalaris 1999, GS) and slope from BW (Fernley et al. 1998, FC98);\nRP + BW: zero point from reduced parallax (GS) and slope from BW (FC98);\nSP + BW: zero point from SP (Layden et al. 1996, L96; Fernley et al. 1998,\nFB98; Gould \\& Popowski 1998, GP; Tsujimoto, Miyamoto, \\& Yoshii 1998, TMY;\nLayden 1999, L99) and slope from BW (FC98).} \n\n% 4 \n\\figcaption{ {\\rm B} light curves of RR Lyrae models vs. phase. \nSolid lines refer to models constructed by adopting the calibration \nof the TC model suggested by BS, while dashed lines to models \nconstructed by assuming that the convective flux is vanishing in the \nregions in which the superadiabatic gradient is negative \n(see equ. 7 and \\S 3 in BS).} \n\\end{document}\n"
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astro-ph0002243
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Gamma-Ray Bursts, Cosmic-Rays and Neutrinos \thanks{Invited talk presented at TAUP99, the 6th International Workshop on Topics in Astroparticle and Underground Physics (September 1999, Paris, France).}
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The $\gamma$-ray burst (GRB) model for production of ultra-high-energy, $>10^{19}$~eV, cosmic-rays is based on the hypothesis that GRBs arise from the dissipation of the kinetic energy of relativistic fireballs at cosmological distances. Recent observations of delayed low energy emission, ``afterglow,'' from GRB sources strongly support the validity of this hypothesis. Observations also provide quantitative support for the model. The inferred physical fireball parameters imply that protons may be accelerated to $>10^{20}$~eV, and the inferred GRB energy generation rate is similar to that required to account for the observed flux of ultra-high-energy cosmic-rays (UHECRs). Strong suppression of cosmic-ray flux is expected in this model above $10^{19.7}$~eV, due to proton interaction with microwave background photons. Strong deviations from model flux derived under the assumption of uniform source distribution is expected above $10^{20}$~eV, due to source discreteness and due to inhomogeneities in source distribution. In particular, the flux above $10^{20.5}$~eV is expected to be dominated by few, narrow spectrum sources. While model predictions can not be tested (with high confidence level) using present data, the predicted signatures should be observed with the planned Auger and Telescope-Array UHECR detectors. A natural consequence of the GRB model of UHECR production is the conversion of a large fraction, $\sim10\%$, of the fireball energy to accompanying burst of $\sim10^{14}{eV}$ and $\sim10^{18}{eV}$ neutrinos. A ${km}^2$ neutrino detector would observe several tens of events per year correlated with GRBs, and test for neutrino properties (e.g. flavor oscillations, for which upward moving $\tau$'s would be a unique signature, and coupling to gravity) with an accuracy many orders of magnitude better than is currently possible.
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"string": "%\\documentstyle[twoside,fleqn,espcrc2]{article}\n\\documentclass[twoside]{article}\n\\usepackage{fleqn,espcrc2}\n\\usepackage{graphicx}\n\\input psfig\n\n\\title{Gamma-Ray Bursts, Cosmic-Rays and Neutrinos\n\\thanks{Invited talk presented at TAUP99, the 6th International Workshop\non Topics in Astroparticle and Underground Physics \n(September 1999, Paris, France).}\n}\n\n\\author{Eli Waxman\n\\thanks{Incumbent of the Beracha foundation career development chair}\n%e-mail address: waxman@wicc.weizmann.ac.il}\n\\thanks{Work supported in part \nby BSF Grant 9800343, AEC Grant 38/99 and MINERVA Grant.}\n\\address{Dept. of Condensed Matter Physics, Weizmann Institute of Science,\nRehovot 76100, Israel}}\n\n\\begin{document}\n\n\\begin{abstract}\n \nThe $\\gamma$-ray burst (GRB) model for production of ultra-high-energy, \n$>10^{19}$~eV, cosmic-rays is based on the hypothesis that GRBs arise from \nthe dissipation of the kinetic energy of relativistic fireballs at cosmological\ndistances. Recent observations of delayed low energy emission, ``afterglow,'' \nfrom GRB sources strongly support the validity of this hypothesis. \nObservations also provide quantitative support for the model.\nThe inferred physical fireball parameters\nimply that protons may be \naccelerated to $>10^{20}$~eV, and the inferred GRB \nenergy generation rate is similar to that required to account for the\nobserved flux of ultra-high-energy cosmic-rays (UHECRs).\n\nStrong suppression of cosmic-ray flux is expected in this model above \n$10^{19.7}$~eV, due to proton interaction with microwave background photons. \nStrong deviations from model flux derived under the assumption of uniform \nsource distribution is expected above $10^{20}$~eV, due to source discreteness \nand due to inhomogeneities in source distribution. In particular, the flux \nabove $10^{20.5}$~eV is expected to be dominated by few, narrow spectrum \nsources. While model predictions can not be tested (with \nhigh confidence level) \nusing present data, the predicted signatures should be observed with\nthe planned Auger and Telescope-Array UHECR detectors.\n\nA natural consequence of the GRB model of \nUHECR production is the conversion of \na large fraction, $\\sim10\\%$, of the fireball energy to accompanying burst\nof $\\sim10^{14}{\\rm eV}$ and $\\sim10^{18}{\\rm eV}$ neutrinos. A ${\\rm km}^2$ \nneutrino detector would observe several tens of events per year correlated \nwith GRBs, and test for neutrino properties (e.g. flavor oscillations,\nfor which upward moving $\\tau$'s would be a unique signature, and coupling\nto gravity) with an accuracy many orders \nof magnitude better than is currently possible.\n\n\\end{abstract} \n\n\\maketitle\n\n\n\\section{Introduction}\n\nThe origin of GRBs,\nbursts of 0.1 MeV---1 MeV photons lasting for a few seconds, \nremained unknown for over 20 years, primarily because GRBs \nwere not detected prior to 1997 at wave-bands other than $\\gamma$-rays \n(see \\cite{Fishman} for review of $\\gamma$-ray observations).\nThe isotropic distribution of bursts over the sky\nsuggested that GRB sources lie at cosmological distances, and\ngeneral phenomenological considerations were used to argue that the\nbursts are produced by the dissipation of the kinetic\nenergy of a relativistic expanding fireball (see \\cite{fireballs} for\nreview). \n\nAdopting the cosmological fireball hypothesis, it\nwas shown that the physical conditions in the fireball dissipation region \nallow Fermi acceleration of protons\nto energy $>10^{20}{\\rm eV}$ \\cite{W95a,Vietri95}, and that\nthe average rate at which energy is emitted as $\\gamma$-rays\nby GRBs is \ncomparable to the energy generation rate of UHECRs in a model where\nUHECRs are produced by a cosmological distribution of sources \\cite{W95b}. \nBased on these two facts, it was suggested that GRBs and UHECRs have\na common origin (see \\cite{Nobel_rev} for review). \n\nIn the last two years, afterglows of GRBs have been discovered in X-ray, \noptical, and radio wave bands (see \\cite{AG_review} for review).\nAfterglow observations confirmed the cosmological origin of the bursts,\nthrough the redshift determination of several GRB host-galaxies\n(see \\cite{Freedman} for an updated list), and\nconfirmed \\cite{AG_confirm} standard model predictions \n\\cite{AG_pred} of afterglows\nthat result from the collision of an expanding fireball with\nits surrounding medium. These observations therefore provide strong\nsupport for the GRB model of UHECR production.\n\nIn this review, UHECR and neutrino production in GRBs is discussed in the \nlight of recent GRB and UHECR observations. \nThe fireball model is briefly described in \\S2.1, and proton acceleration\nin GRB fireballs is discussed in \\S2.2. Recent claims, according to which\nprotons can not be accelerated to $>10^{20}$~eV in the fireball \n\\cite{Gallant98}, are shown in \\S2.2 to be erroneous.\nImplications of recent afterglow\nobservations to high energy particle \nproduction are discussed in \\S3. It is \nshown that, contrary to some recent claims \\cite{Stecker},\nthe GRB energy generation rate implied by afterglow observations is \nsimilar to the energy generation rate required to account for the flux of\n$>10^{19}$~eV cosmic-rays.\nModel predictions are shown to be consistent with the observed\nUHECR spectrum in \\S4. \n\nPredictions\nof the GRB model for UHECR production, that can be tested with future \nUHECR experiments, are discussed in \\S5. Implications of the\ndetection by the AGASA experiment of multiple high energy events with\nconsistent arrival directions \\cite{AGASA_pairs} is also discussed in \\S5.\nHigh energy neutrino production in fireballs and its implications for future\nhigh energy neutrino detectors are discussed in \\S6. \n\n\n\\section{UHECR from GRB fireballs}\n\n\\subsection{The fireball model}\n\nIn the fireball model of GRBs\n\\cite{fireball86}, a compact source, of linear scale\n$r_0\\sim10^7$~cm, produces a wind characterized by an average luminosity \n$L\\sim10^{52}{\\rm erg\\,s}^{-1}$ and mass loss rate $\\dot M=L/\\eta c^2$.\nAt small radius, \nthe wind bulk Lorentz factor, $\\Gamma$, \ngrows linearly with radius, until most of the wind energy is converted\nto kinetic energy and $\\Gamma$ saturates at $\\Gamma\\sim\\eta\\sim300$.\nVariability of the source on time scale $\\Delta t$, resulting\nin fluctuations in the wind bulk Lorentz factor $\\Gamma$ on similar\ntime scale, then leads to internal shocks \\cite{internal}\nin the expanding fireball at a radius\n\\begin{equation}\nr_i\\approx\\Gamma^2c\\Delta t=3\\times10^{13}\\Gamma^2_{300}\\Delta t_{\\rm10ms}\n{\\rm\\ cm},\n\\label{eq:r_i}\n\\end{equation}\nwhere $\\Gamma=300\\Gamma_{300}$, $\\Delta t=10\\Delta t_{\\rm10ms}$~ms.\nIf the Lorentz factor variability within the wind is significant,\ninternal shocks would reconvert a substantial \npart of the kinetic energy to internal energy. It is assumed that\nthis energy is then radiated as \n$\\gamma$-rays by synchrotron and inverse-Compton emission of\nshock-accelerated electrons.\n\nIn this model, the observed\n$\\gamma$-ray variability time, $\\sim r_i/\\Gamma^2 c\\approx\\Delta t$,\nreflects the variability time of the underlying source, and the GRB\nduration, $T\\sim10$s, \nreflects the duration over which energy is emitted from the\nsource. A large fraction of bursts detected by BATSE show variability\non the shortest resolved time scale, $\\sim10$~ms \\cite{Woods95}, and some show\nvariability on shorter time scales, $\\sim1$~ms \\cite{Bhat92}.\nThis sets the constraint on underlying source size, \n$r_0<c\\Delta t\\sim10^7$~cm. The wind must be expanding relativistically, \nwith a Lorentz factor $\\Gamma\\sim300$, \nin order that\nthe fireball pair-production optical depth be small for observed \nhigh energy, $\\sim100$~MeV, GRB photons \\cite{Gamma}.\n\nThe wind Lorentz factor is expected to fluctuate on\ntime scales ranging from the source dynamical time, $\\Delta t$, to the\nwind duration $T$, leading to internal collisions \nover a range of radii, $r\\sim r_i=\\Gamma^2c\\Delta t$ to $r\\sim\\Gamma^2cT$. \nInternal shocks are generally expected \nto be ``mildly'' relativistic in the fireball \nrest frame, i.e. characterized by Lorentz factor \n$\\gamma_i-1\\sim1$, since adjacent shells within the wind are expected to\nexpand with Lorentz factors which do not differ by more than an\norder of magnitude. \n\nAs the fireball expands, it drives a relativistic shock (blastwave)\ninto the surrounding gas. \nAt early time, the fireball is little affected by this external interaction. \nAt late time, most of the fireball energy is transferred to the \nsurrounding gas, and\nthe flow approaches self-similar expansion. \nFor typical fireball parameters, the transition to self-similar expansion\noccurs at a radius $r\\sim\\Gamma^2cT$. At this\nradius, mildly relativistic reverse shocks propagate into the fireball\nejecta and decelerate it \\cite{reverse}. \nThe reverse shocks disappear on (observed)\ntimes scale $T$, and the flow becomes self-similar at later time, with \na single, relativistic decelerating shock propagating into the surrounding \nmedium. Plasma conditions in the reverse shocks are similar to those of \ninternal shocks arising from variability on time scale $\\sim T$, since both \nare mildly relativistic and occur at similar radii. \nIn the discussion that follows\nwe therefore do not discuss the reverse shocks separately from the \ninternal shocks.\n\nThe shock driven into the ambient medium continuously heats new gas, and\naccelerates relativistic \nelectrons that may produce by synchrotron emission \nthe delayed radiation, ``afterglow,''\nobserved on time scales of\ndays to months.\nAs the shock-wave decelerates, the emission shifts with time to\nlower frequency. \n\n\n\\subsection{Fermi acceleration in GRBs}\n\nIn the fireball model, the observed GRB and afterglow radiation is produced\nby synchrotron emission of shock accelerated\nelectrons. In the region where electrons are accelerated, \nprotons are also expected to be\nshock accelerated. This is similar to what is thought to occur in supernovae \nremnant shocks \\cite{Bland87}. We consider below proton acceleration \nin internal (and reverse) fireball shocks.\nSince the internal shocks are mildly relativistic,\nwe expect results related to particle\nacceleration in sub-relativistic shocks (see, e.g.,\n\\cite{Bland87} for review) to be valid for the present\nscenario. In particular, the predicted energy distribution of accelerated\nprotons is $dN_p/dE_p\\propto E_p^{-2}$.\n\nTwo constraints must be satisfied by\nfireball wind parameters in order to allow proton acceleration to\n$E_p>10^{20}$~eV in internal shocks \\cite{W95a}:\n\\begin{equation}\n\\xi_B/\\xi_e>0.02\\Gamma_{300}^2 E_{p,20}^2L_{\\gamma,52}^{-1},\n\\label{eq:xi_B}\n\\end{equation}\nand\n\\begin{equation}\n\\Gamma>130 E_{20}^{3/4}\\Delta t^{-1/4}_{10\\rm ms}.\n\\label{eq:G_min}\n\\end{equation}\nHere, $E_p=10^{20}E_{p,20}$~eV, $L_{\\gamma}=10^{52}L_{\\gamma,52}{\\rm erg/s}$\nis the $\\gamma$-ray luminosity, $\\xi_B$ is the \nfraction of the wind energy density which is carried by magnetic field,\n$4\\pi r^2 c\\Gamma^2 (B^2/8\\pi)=\\xi_B L$, \nand $\\xi_e$ is the fraction of wind energy carried by shock\naccelerated electrons. Since the electron synchrotron cooling time is short \ncompared to the wind expansion time, electrons lose their energy radiatively \nand $L$ is related to the observed $\\gamma$-ray luminosity by\n$L_\\gamma\\approx\\xi_e L$. The first condition must be satisfied in order \nfor the proton acceleration time $t_a$ to be smaller than the wind expansion \ntime. The second condition must be satisfied in order for the \nsynchrotron energy loss time of the proton to be larger than $t_a$.\n\nFrom Eqs. (\\ref{eq:xi_B}) and (\\ref{eq:G_min}), we infer that \na dissipative ultra-relativistic wind,\nwith luminosity and variability time implied by GRB observations,\nsatisfies the constraints necessary to allow the acceleration of protons \nto energy $>10^{20}$~eV, provided that the wind bulk Lorentz factor is\nlarge enough, $\\Gamma>100$, and that the\nmagnetic field is close to equipartition with electrons. The former \ncondition, $\\Gamma>100$, is remarkably similar to that inferred based on\n$\\gamma$-ray spectra. There is no theory at present that allows a basic\nprinciples calculation of the strength of the magnetic field. However, \nmagnetic field close to equipartition, $\\xi_B\\sim1$, is required\nin order to account\nfor the observed $\\gamma$-ray emission (see also \\S3). \n\nWe have assumed in the discussion so far that the fireball is spherically \nsymmetric. However, since a jet-like fireball behaves as if it were\na conical section of a spherical fireball as long as the jet opening\nangle is larger than $\\Gamma^{-1}$, our\nresults apply also for a jet-like fireball \n(we are interested only in processes that occur when\nthe wind is ultra-relativistic, $\\Gamma\\sim300$, prior to \nsignificant fireball deceleration). For a jet-like wind, $L$ in our\nequations should be understood as the luminosity the fireball\nwould have carried had it been spherically symmetric.\n\nIt has recently been pointed out in \\cite{Gallant98} that\nconditions at the {\\it external, highly relativistic}\nshock driven by the fireball into the ambient\ngas are not likely to allow proton acceleration to ultra-high energy. \nAlthough correct, this observation\nis irrelevant to the scenario considered here based on \\cite{W95a}, \nsince in this scenario protons are accelerated in {\\it internal, mildly\nrelativistic} fireball shocks.\n\n\n\\section{Implications of afterglow observations}\n\nIn addition to providing support to the validity of the qualitative fireball \nscenario described in \\S2.1 \\cite{AG_review}, afterglow observations provide \nquantitative constraints on fireball model parameters.\n\nThe determination of GRB redshifts implies that\nthe characteristic GRB $\\gamma$-ray luminosity and emitted energy, \nin the 0.05 to 2~MeV band, are $L_\\gamma\\sim10^{52}{\\rm erg/s}$ and \n$E_\\gamma\\sim10^{53}{\\rm erg}$ respectively (e.g. \\cite{Freedman}), \nan order of magnitude higher than the values\nassumed prior to afterglow detection\n(here, and throughout the paper, we assume an open universe, \n$\\Omega=0.2$, $\\Lambda=0$, and $H_0=75{\\rm\\ km/s\\ Mpc}$). \nThe increased GRB luminosity scale implies that the constraint \n(\\ref{eq:xi_B}) on the fireball magnetic field \nis less stringent than previously assumed. \n\nDue to present technical limitations of the experiments, \nafterglow radiation is observed in most cases only on time scale $>>10$~s.\nAt this stage, radiation is produced by the\nexternal shock driven into the surrounding gas, and afterglow observations\ntherefore do not provide direct constraints on the magnetic field \nenergy fraction $\\xi_B$ at the internal and reverse shocks, where\nprotons are accelerated to ultra-high energy. In one case, however, \nthat of GRB~990123, reverse shock emission was detected over $\\sim10$~s\ntime scale \\cite{Akerlof99,SPMR_0123}. \nFor this case, the inferred value of $\\xi_B$ \\cite{WnD00} is consistent with\nthe constraint (\\ref{eq:xi_B}). Clearly, more observations are required\nto determine whether this condition is generally satisfied.\n\nThe observed GRB redshift distribution implies a GRB rate of \n$R_{\\rm GRB}\\sim10/{\\rm Gpc}^3{\\rm yr}$ at $z\\sim1$. \nThe present, $z=0$, rate is less well constrained, since most observed \nGRBs originate at redshifts $1\\le z\\le2.5$ \\cite{GRB_z}. \nPresent data\nare consistent with both no evolution of GRB rate with redshift, and \nwith strong evolution (following, e.g.,\nthe luminosity density evolution of QSOs or the evolution of\nstar formation rate), in which $R_{\\rm GRB}(z=1)/R_{\\rm GRB}(z=0)\\sim8$\n\\cite{GRB_z}.\nThe energy observed in $\\gamma$-rays reflect the fireball\nenergy in accelerated electrons. Afterglow observations imply that \naccelerated electrons and protons carry similar energy \\cite{Freedman}.\nThus, the inferred $z=0$ rate of cosmic-ray production by GRBs is\nsimilar to the generation rate of $\\gamma$-ray energy, \n\\begin{equation}\nE^2 (d\\dot n_{CR}/dE)_{z=0}= 10^{44}\\zeta {\\rm erg/Mpc}^3{\\rm yr},\n\\label{eq:cr_rate}\n\\end{equation}\nwhere $\\zeta$ is in the range of $\\sim1$ to $\\sim8$.\nThis energy generation rate is remarkably similar to that \nimplied by the observed UHECR flux (see \\S4).\\footnote{\nIt has recently been argued \\cite{Stecker} that\nthe $z=0$ GRB $\\gamma$-ray energy generation rate\nis much smaller, $\\sim10^{42}{\\rm erg/Mpc}^3{\\rm yr}$. \nMost of the discrepancy between this result and our result can be accounted \nfor by noting two errors made in the analysis of ref. \\cite{Stecker}: \nestimating the energy generation rate as the product of the GRB rate and \nthe {\\it median}, rather than {\\it average}, GRB energy, and using\n(following \\cite{MnM98}) the GRB\nenergy observed in the 50 to 300~keV band, where only a small fraction \nof the 0.05 to 2~MeV $\\gamma$-ray energy is observed.}\n\n\n\\section{Comparison with UHECR observations}\n\n\nFly's Eye \\cite{Bird934} and AGASA \\cite{Hayashida945,Takeda98} results\nconfirm the flattening of the cosmic-ray spectrum at $\\sim10^{19}$~eV,\n\\begin{figure}\n\\centerline{\\psfig{figure=cr_flux.ps,width=3in}}\n\\caption{\nThe UHECR flux expected in a cosmological model, where high-energy protons \nare produced at a rate $(E^2 d\\dot n_{CR}/dE)_{z=0}=0.8\\times10^{44}\n{\\rm erg/Mpc}^3{\\rm yr}$ as predicted in the GRB model \n[Eq. (\\ref{eq:cr_rate})], compared to the Fly's Eye, Yakutsk and AGASA data. \n$1\\sigma$ flux error bars are shown. The highest energy points are derived\nassuming the detected events (1 for Fly's Eye and Yakutsk, \n4 for AGASA) represent a\nuniform flux over the energy range $10^{20}$~eV--$3\\times10^{20}$~eV.}\n\\label{fig1}\n\\end{figure}\nevidence for which existed in previous experiments with weaker statistics\n\\cite{Watson91}. Fly's Eye data is well fitted in the energy range \n$10^{17.6}$~eV to $10^{19.6}$~eV by a sum of two power laws: A\nsteeper component, with differential number spectrum\n$J\\propto E^{-3.50}$, dominating at lower\nenergy, and a shallower component, $J\\propto E^{-2.61}$, \ndominating at higher energy, $E>10^{19}$~eV.\nThe flattening of the spectrum, combined with the lack of anisotropy \nand the evidence for a change in composition from heavy nuclei at low\nenergy to light nuclei (protons) at high energy \\cite{composition},\nsuggest that an extra-Galactic source of protons dominates the flux at\nhigh energy $E>10^{19}$~eV.\n\nIn Fig. 1 we compare the UHECR spectrum,\nreported by the Fly's Eye \\cite{Bird934}, the Yakutsk \\cite{Yakutsk}, \nand the AGASA \\cite{Takeda98} experiments, \nwith that predicted by the GRB model.\nThe proton generation rate is assumed to evolve in redshift \nfollowing QSO luminosity evolution \\cite{QSO}.\nNote, that the cosmic-ray spectrum at energy $>10^{19}$~eV is \nlittle affected by modifications of the cosmological parameters or of\nthe redshift evolution of cosmic-ray generation rate, since\ncosmic-rays at this energy originate from distances shorter than\nseveral hundred Mpc. The spectrum and flux at $E>10^{19}$~eV is mainly \ndetermined by the present ($z=0$) generation rate and spectrum.\nThe absolute flux measured at\n$3\\times10^{18}$~eV differs between the various experiments,\ncorresponding to a systematic $\\simeq10\\%$ ($\\simeq20\\%$) over-estimate \nof event energies in the AGASA (Yakutsk)\nexperiment compared to the Fly's Eye experiment (see also \\cite{Hayashida945}).\nIn Fig. 1, the Yakutsk energy normalization is used. \n\nThe suppression of model flux above $10^{19.7}$~eV is \ndue to energy loss of high energy protons\nin interaction with the microwave background, i.e. to the ``GZK cutoff''\n\\cite{GZK}. \nBoth Fly's Eye and Yakutsk data show a deficit in the number of events,\ncompared to the number expected based on extrapolation of the \n$J\\propto E^{-2.61}$ power-law fit, consistent with the predicted \nsuppression. The deficit is, however, only\nat a $2\\sigma$ confidence level \\cite{W95a}.\nThe AGASA data is consistent \nwith Fly's Eye and Yakutsk results below $10^{20}$~eV.\nA discrepancy may be emerging at higher energy, $>10^{20}$~eV, \nwhere the Fly's Eye and Yakutsk experiments detect 1 event each,\nand the AGASA experiment detects 6 events for similar exposure. \n\nThe flux above $10^{20}{\\rm eV}$ is\ndominated by sources at distances $<30\\ {\\rm Mpc}$ \\cite{W95b} \n(see \\S5). Since the distribution of known astrophysical systems\n(e.g. galaxies, clusters of galaxies) is inhomogeneous on scales of\ntens of Mpc, significant deviations from model predictions presented\nin Fig. 1 for a uniform source distribution are expected above \n$10^{20}{\\rm eV}$. It has recently been shown \\cite{CR_clustering}\nthat clustering of cosmic-ray sources leads\nto a standard deviation, $\\sigma$, in the expected number, $N$, of \nevents above $10^{20}$ eV, given by \n$\\sigma /N = 0.9(d_0/10 {\\rm Mpc})^{0.9}$, where $d_0$ is the unknown scale\nlength of the source correlation function and $d_0\\sim10$ Mpc \nfor field galaxies.\n\nAn order of magnitude increase in the exposure of UHECR experiments,\ncompared to that available at present, is required to test for\nthe existence of the GZK\ncutoff \\cite{W95b}. Such exposure would allow this test through an \naccurate determination of the spectrum in the energy range\nof $10^{19.7}$~eV to $10^{20}$~eV, where the effects of source inhomogeneities\nare expected to be small \\cite{W95b,CR_clustering}. \nMoreover, an order of magnitude\nincrease in exposure will also allow to determine the source correlation \nlength $d_0$, through the detection of anisotropies in the arrival directions\nof $\\sim10^{19.5}$~eV cosmic-rays over angular scales of \n$\\Theta\\sim d_0/30$~Mpc \\cite{CR_clustering}.\n\nFinally, we note that preliminary results from the HiRes experiment \nwere presented in this conference \\cite{Matthews99}, reporting 7 events beyond \n$10^{20}$~eV for an exposure similar to that of the Fly's Eye. It is difficult\nto decide how to interpret this result, since the discrepancy between \nHiRes and Fly's Eye results is present not only above $10^{20}$~eV but also \nat lower energy, where Fly's Eye, AGASA and Yakutsk experiments are in \nagreement: 13 events above $6\\times10^{19}$~eV are reported in the preliminary\nHiRes analysis, while only 5 events at that energy range are reported by the\nFly's Eye. We therefore believe that unambiguous conclusions based on the \nrecent HiRes data can only be drawn after a complete analysis of the HiRes \ndata is published. \n\n\n\\section{GRB model predictions for planned UHECR experiments}\n\nThe energy of the most\nenergetic cosmic ray detected by the Fly's Eye experiment is in excess of\n$2\\times10^{20}{\\rm eV}$, and that of the most\nenergetic AGASA event is $\\sim2\\times10^{20}{\\rm eV}$. On a\ncosmological scale, the distance traveled by such energetic particles is\nsmall: $<100{\\rm Mpc}$ ($50{\\rm Mpc}$) for the AGASA (Fly's Eye) event\n(e.g., \\cite{Aharonian94}). Thus, the detection of these events over a $\\sim5\n{\\rm yr}$ period can be reconciled with the rate of nearby GRBs, $\\sim1$\nper $100\\, {\\rm yr}$ out to $100{\\rm Mpc}$, only if\nthere is a large dispersion, $\\geq100{\\rm yr}$, in the arrival time of protons \nproduced in a single burst. \n\nThe required dispersion\nis likely to occur due to the combined effects of deflection \nby random magnetic fields and energy dispersion of the particles\n\\cite{W95a}. \nA proton of energy $E$ propagating over a distance $D$\nthrough a magnetic field of strength $B$ and correlation length\n$\\lambda$ is deflected by an angle\n$\\theta_s\\sim(D/\\lambda)^{1/2}\\lambda/R_L$, which results in a time\ndelay, compared to propagation along a straight line,\n$\\tau(E,D)\\approx\\theta_s^2D/4c\\propto B^2\\lambda$. \nThe random energy loss UHECRs suffer as they propagate, owing to the \nproduction of pions, implies that \nat any distance from the observer there is some finite spread\nin the energies of UHECRs that are observed with a given fixed energy.\nFor protons with energies $>10^{20}{\\rm eV}$ \nthe fractional RMS energy spread is of order unity\nover propagation distances in the range $10-100{\\rm Mpc}$ \n(e.g. \\cite{Aharonian94}).\nSince the time delay is sensitive to the particle energy, this implies that\nthe spread in arrival time of UHECRs with given observed energy is comparable\nto the average time delay at that energy, $\\tau(E,D)$.\n\nThe magnetic field required in order to produce a spread \n$\\tau(E=10^{20}{\\rm eV},D=100{\\rm Mpc})>100$~yr, is \nwell below the current upper bound on the inter-galactic magnetic \nfield, $B\\lambda^{1/2}\\le10^{-9}{\\rm G\\ Mpc}^{1/2}$ \\cite{IGM},\nwhich allows a spread $\\tau\\sim10^5$~yr. \nWe discuss below some implications, unique to the GRB model, of \ntime delays induced by magnetic-field deflection.\n\n\n\\subsection{The highest energy sources}\n\nThe rapid increase with energy of the pion production energy loss rate\neffectively\nintroduces a cutoff distance, $D_c(E)$, beyond which sources do not contribute\nto the flux above $E$. The function $D_c(E)$ is shown in Fig. 2. \nWe define a critical energy $E_c$, for which the average number of sources\nat $D<D_c(E_c)$ is 1, \n$\\frac{4\\pi}{5} R_{GRB}D_c(E_c)^3 \\tau\\left[E_c,D_c(E_c)\\right]=1$ \n\\cite{MnW96}.\nAlthough $E_c$ depends through $\\tau$ on the unknown properties of \nthe intergalactic magnetic field, the rapid\ndecrease of $D_c(E)$ with energy near $10^{20}{\\rm eV}$\nimplies that $E_c$ is only weakly dependent on the value of $B^2\\lambda$. \nIn The GRB model, the product $R_{GRB}\\tau(D=100{\\rm Mpc},E=10^{20}{\\rm eV})$\nis approximately limited to the range $10^{-6}{\\rm\\ Mpc}^{-3}$ to\n$10^{-3}{\\rm\\ Mpc}^{-3}$ (The lower limit is set by the requirement that \nat least a few GRB sources be present at $D<100$~Mpc, and the upper limit by \nthe Faraday rotation bound \n$B\\lambda^{1/2}\\le10^{-9}{\\rm G\\ Mpc}^{1/2}$ \\cite{IGM} and \n$R_{GRB}\\le10/{\\rm\\ Gpc}^3{\\rm yr}$). The corresponding range\nof values of $E_c$ is \n$10^{20}{\\rm eV}\\le E_c<3\\times10^{20}{\\rm eV}$.\n\nFig. 2 presents the flux obtained in one realization of\na Monte-Carlo simulation described in ref.\n\\cite{MnW96} of the total\n\\begin{figure}\n\\centerline{\\psfig{figure=difflux.ps,width=3in}}\n\\caption{Results of a Monte-Carlo realization of the bursting sources\nmodel, with $E_c=1.4\\times10^{20}$~eV: Thick solid line- overall \nspectrum in the realization;\nThin solid line- average spectrum, this\ncurve also gives $D_c(E)$;\nDotted lines- spectra of brightest sources at different energies.\n}\n\\label{figNc}\n\\end{figure}\nnumber of UHECRs received from GRBs at some fixed time for \n$E_c=1.4\\times10^{20}$~eV. \nFor each\nrealization the distances and\ntimes at which cosmological GRBs occurred were randomly drawn. \nMost of the realizations gave an overall spectrum similar to that presented\nin Fig. \\ref{figNc} when the brightest source of this \nrealization (dominating at $10^{20}{\\rm eV}$) is not included.\nAt $E < E_c$,\nthe number of sources contributing to the flux is very large, \nand the overall UHECR flux received at any\ngiven time is near the average flux (obtained for spatially and temporally\nhomogeneous UHECR volume emissivity).\nAt $E > E_c$, the flux will generally be much lower than the average,\nbecause there will be no burst within a distance $D_c(E)$ having taken\nplace sufficiently recently. There is, however, a significant probability\nto observe one source with a flux higher than the average.\nA source similar to the brightest one in Fig. \\ref{figNc}\nappears $\\sim5\\%$ of the time. \n\nAt any fixed time a given burst is observed in UHECRs only over a narrow\nrange of energy, because if\na burst is currently observed at some energy $E$ then UHECRs of much lower\n(higher) energy from this burst will arrive (have arrived) mainly in the \nfuture (past). For energies above the \npion production threshold, \n$E>10^{19.7}{\\rm eV}$, the dispersion in arrival times of UHECRs\nwith fixed observed energy is comparable to the average delay at that\nenergy. This implies that\nthe spectral width $\\Delta E$ of the source at a given time is of order\nthe average observed energy, $\\Delta E\\sim E$.\nThus, bursting UHECR sources should have narrowly peaked energy\nspectra,\nand the brightest sources should be different at different energies.\nFor steady state sources, on the other hand, the brightest\nsource at high energies should also be the brightest one at low\nenergies, its fractional contribution to the overall flux decreasing to\nlow energy only as $D_c(E)^{-1}$.\nA detailed numerical analysis of the time dependent energy spectrum of \nbursting sources is given in \\cite{Sigl_Lemoine97}.\n\nThe AGASA experiment reported the presence\nof one triplet and three doublets of UHECRs with angular separations \n(within each multiplet) \n$\\le2.5^\\circ$, roughly consistent with the measurement error,\namong a total of 47 UHECRs with $E\\ge4\\times10^{19}{\\rm eV}$ \n\\cite{AGASA_pairs}. The probability to have found such multiplets by chance\nis $\\sim1\\%$. Therefore, this observation favors\nthe bursting source model, although more data are needed to confirm it.\n\nTesting the GRB model predictions described above \nrequires an exposure 10 times larger than that of present\nexperiments. Such increase is expected to be provided by the planned\nAuger \\cite{Auger} and Telescope Array \\cite{TA} detectors.\n\n\n\n\\subsection{Spectra of Sources at $E<4\\times10^{19}{\\rm eV}$}\n\\label{subsec:Blambda}\n\nFor nearby, $D<100$~Mpc, sources contributing at $E\\le4\\times10^{19}{\\rm eV}$,\npion production energy loss is negligible, and particle energy may be \nconsidered constant along the propagation path. \nIn this case, the spectral shape of individual sources depends primarily on\nthe magnetic field correlation length \\cite{WnM96}. \n\nIf $\\lambda \\gg D\\theta_s(D,E)\n\\simeq D(D/\\lambda)^{1/2}\\lambda/R_L$, all UHECRs that arrive at the\nobserver are essentially deflected by the same magnetic field structures, \nand the absence of random energy loss during propagation implies that\nall rays with a fixed observed energy would reach the observer with exactly\nthe same direction and time delay. At a fixed time, therefore, the source would\nappear mono-energetic and point-like (In reality,\nenergy loss due to pair production\nresults in a finite but small spectral and angular width, \n$\\Delta E/E\\sim\\delta\\theta/\\theta_s\\le1\\%$ \\cite{WnM96}).\n\nIf, on the other hand, $\\lambda \\ll D\\theta_s(D,E)$,\nthe deflection of different UHECRs arriving at the observer\nare essentially independent. Even in the absence of any energy loss there \nare many paths from the source to the observer for UHECRs of fixed energy $E$\nthat are emitted from the source at an angle \n$\\theta\\le\\theta_s$ relative to the source-observer line of sight. Along\neach of the paths, UHECRs are deflected by independent magnetic field \nstructures. Thus, the source angular size would be of order $\\theta_s$\nand the spread in arrival times would be comparable to the characteristic \ndelay $\\tau$, leading to $\\Delta E/E\\sim1$ \n(The spectral shape of sources is given\nin analytic form for this case in \\cite{WnM96}).\n\nFor $D=30{\\rm Mpc}$ and $E\\simeq10^{19}{\\rm eV}$, \nthe $\\theta_s D=\\lambda$ line divides the\nallowed region (for the GRB model) \nin the $B$--$\\lambda$ plane at $\\lambda\\sim1{\\rm Mpc}$. Thus, \nmeasuring the spectral width of bright sources would allow to determine\nif the field correlation length is much larger, much smaller, or comparable\nto $1{\\rm Mpc}$.\n\n\n\\section{High energy Neutrinos}\n\n\\subsection{GRB neutrinos, $\\sim10^{14}$~eV}\n\nProtons accelerated in the fireball to high energy lose energy through\nphoto-meson interaction with fireball photons. The decay of charged\npions produced in this interaction, $\\pi^+\\rightarrow\\mu^++\\nu_\\mu\n\\rightarrow e^++\\nu_e+\\overline\\nu_\\mu+\\nu_\\mu$, \nresults in the production of high energy neutrinos \\cite{WnB97}. \nThe neutrino spectrum is determined by the observed gamma-ray\nspectrum, which is well described by a broken power-law,\n$dN_\\gamma/dE_\\gamma\\propto E_\\gamma^{-\\beta}$ \nwith different values of $\\beta$ at low and high energy \\cite{Fishman}. The\nobserved break energy (where $\\beta$ changes) is typically \n$E_\\gamma^b\\sim1{\\rm MeV}$, \nwith $\\beta\\simeq1$ at energies below the break and $\\beta\\simeq2$ \nabove the break. The interaction of protons accelerated to a power-law\ndistribution, $dN_p/dE_p\\propto E_p^{-2}$, \nwith GRB photons results in a broken power law\nneutrino spectrum, $dN_\\nu/dE_\\nu\\propto E_\\nu^{-\\beta}$ with\n$\\beta=1$ for $E_\\nu<E_\\nu^b$, and $\\beta=2$ for $E_\\nu>E_\\nu^b$. \nThe neutrino break energy $E_\\nu^b$ is fixed by the threshold energy\nof protons for photo-production in interaction with the dominant $\\sim1$~MeV\nphotons in the GRB \\cite{WnB97},\n\\begin{equation}\nE_\\nu^b\\approx5\\times10^{14}\\Gamma_{300}^2(E_\\gamma^b/1{\\rm MeV})^{-1}{\\rm eV}.\n\\label{Enu}\n\\end{equation}\n\nThe normalization of the flux is determined by the\nefficiency of pion production.\nAs shown in \\cite{WnB97}, the fraction of energy lost to pion production\nby protons producing the neutrino flux above the break, $E^b_\\nu$, is \nessentially independent of energy and is given by\n\\begin{equation}\nf_\\pi\\approx0.2{L_{\\gamma,52}\\over\n(E_\\gamma^b/1{\\rm MeV})\\Gamma_{300}^4 \\Delta t_{10\\rm ms}}.\n\\label{fpi}\n\\end{equation}\nThus, acceleration of protons to high energy in internal fireball\nshocks would lead to conversion of a significant fraction of\nproton energy to high energy neutrinos.\n\nIf GRBs are the sources of UHECRS, \nthen using Eq. (\\ref{fpi}) and the UHECR generation rate\ngiven by Eq. (\\ref{eq:cr_rate}) with $\\zeta\\simeq1$,\nthe expected GRB neutrino flux is \\cite{WnB99}\n\\begin{eqnarray}\nE_\\nu^2\\Phi_{\\nu_x}\\approx&&\n1.5\\times10^{-9}\\left({f_\\pi\\over0.2}\\right)\\times\\cr\n&&\\min\\{1,E_\\nu/E^b_\\nu\\}\n{{\\rm GeV}\\over{\\rm cm}^{2}{\\rm s\\,sr}},\n\\label{JGRB}\n\\end{eqnarray}\nwhere $\\nu_x$ stands for $\\nu_\\mu$, $\\bar\\nu_\\mu$ and $\\nu_e$.\n\nThe neutrino spectrum (\\ref{JGRB}) is\nmodified at high energy, where neutrinos are produced by the decay\nof muons and pions whose life time \nexceeds the characteristic time for\nenergy loss due to adiabatic expansion and synchrotron emission \n\\cite{WnB97,RnM98,WnB99}.\nThe synchrotron loss time is determined by the energy density of the\nmagnetic field in the wind rest frame.\nFor the characteristic parameters of a GRB wind, \nsynchrotron losses are the dominant effect, leading to strong suppression of\n$\\nu$ flux above\n$\\sim10^{16}$~eV.\n\nWe note, that the results presented above were derived using the \n``$\\Delta$-approximation,'' i.e.\nassuming that photo-meson interactions are dominated by the contribution of\nthe $\\Delta$-resonance.\nIt has recently been shown \\cite{Muecke98}, that for photon spectra harder\nthan $dN_\\gamma/dE_\\gamma\\propto E^{-2}_\\gamma$, the contribution of \nnon-resonant interactions may be important. Since in order to interact with\nthe hard part of the photon spectrum, $E_\\gamma<E_\\gamma^b$, the proton energy\nmust exceed the energy at which neutrinos of energy $E_\\nu^b$ are\nproduced, significant modification of the $\\Delta$-approximation results\nis expected only for $E_\\nu\\gg E_\\nu^b$, where the neutrino flux is \nstrongly suppressed by synchrotron losses.\n\n\n\\subsection{Afterglow neutrinos, $\\sim10^{18}$~eV}\n\nProtons are expected to be accelerated to \n$>10^{20}$~eV in both internal shocks due to variability of the underlying\nsource, and in the reverse shocks driven into the fireball ejecta at the\ninitial stage of interaction of the fireball with its surrounding gas, which\noccurs on time scale $T\\sim10$~s, comparable to the duration of the GRB itself.\nOptical--UV photons are radiated by electrons accelerated in shocks\npropagating backward into the ejecta, and may interact with accelerated\nprotons. The interaction of these low energy, 10~eV--1~keV, photons \nand high energy protons produces a burst of duration $\\sim T$ \nof ultra-high energy, $10^{17}$--$10^{19}$~eV, neutrinos [as indicated by\nEq. (\\ref{Enu})] via photo-meson interactions \\cite{AG_nus}.\n\nAfterglows have been detected in several cases; reverse\nshock emission has only been identified for GRB 990123 \\cite{Akerlof99}.\nBoth the detections and the non-detections are consistent with shocks\noccurring with typical model parameters \\cite{SPMR_0123},\nsuggesting that reverse shock emission may be common.\nThe predicted neutrino emission depends, however, upon parameters\nof the surrounding medium that\ncan only be estimated once\nmore observations of the prompt optical afterglow emission are available.\n\nIf the density of gas surrounding the fireball is \ntypically $n\\sim1{\\rm cm}^{-3}$,\na value typical to the inter-stellar medium and consistent with\nGRB 990123 observations, then the expected neutrino intensity is\n\\cite{AG_nus}\n\\begin{equation}\nE_\\nu^2\\Phi_{\\nu_x}\\approx 10^{-10}\n\\left({E_\\nu\\over10^{17}{\\rm eV}}\\right)^{\\beta}\n{{\\rm GeV}\\over{\\rm cm}^{2}{\\rm s\\, sr}},\n\\label{eq:Phinu}\n\\end{equation}\nwhere $\\beta=1/2$ for $\\epsilon_\\nu^{\\rm ob.}>10^{17}{\\rm eV}$\nand $\\beta=1$ for $\\epsilon_\\nu^{\\rm ob.}<10^{17}{\\rm eV}$.\nHere too, $\\nu_x$ stands for $\\nu_\\mu$, $\\bar\\nu_\\mu$ and $\\nu_e$.\nThe neutrino flux is expected to be strongly suppressed at energy\n$>10^{19}$~eV, since protons are not expected to be\naccelerated to energy $\\gg10^{20}$~eV. \n\nThe neutrino flux due to interaction with reverse shock photons may be \nsignificantly higher than that given in Eq. (\\ref{eq:Phinu}), if the\ndensity of gas surrounding the fireball is significantly higher than \nthe value we have assumed, i.e. if $n\\gg1{\\rm cm}^{-3}$.\n\n\n\\subsection{Implications}\n\nThe flux of $\\sim10^{14}$~eV neutrinos given in Eq. (\\ref{JGRB}) implies\nthat large area, $\\sim1{\\rm km}^2$, high-energy neutrino telescopes,\nwhich are being constructed to detect \ncosmologically distant neutrino sources (see \\cite{Halzen_review99}\nfor review), would\nobserve several tens of events per year correlated with GRBs. \nThe detection rate of ultra-high energy, $\\sim10^{18}$~eV, afterglow \nneutrinos implied by Eq. (\\ref{eq:Phinu}) is much lower. The\n$\\sim10^{18}$~eV neutrino flux depends,\nhowever, on parameters of the surrounding medium which can be estimated\nonly once more observations of reverse shock emission are available.\n\nOne may look\nfor neutrino events in angular coincidence, on degree scale, \nand temporal coincidence, on time scale of seconds, with GRBs \\cite{WnB97}. \nDetection of neutrinos from GRBs could be used to\ntest the simultaneity of\nneutrino and photon arrival to an accuracy of $\\sim1{\\rm\\ s}$\n($\\sim1{\\rm\\ ms}$ for short bursts), checking the assumption of \nspecial relativity\nthat photons and neutrinos have the same limiting speed.\nThese observations would also test the weak\nequivalence principle, according to which photons and neutrinos should\nsuffer the same time delay as they pass through a gravitational potential.\nWith $1{\\rm\\ s}$ accuracy, a burst at $100{\\rm\\ Mpc}$ would reveal\na fractional difference in limiting speed \nof $10^{-16}$, and a fractional difference in gravitational time delay \nof order $10^{-6}$ (considering the Galactic potential alone).\nPrevious applications of these ideas to supernova 1987A \n(see \\cite{John_book} for review), where simultaneity could be checked\nonly to an accuracy of order several hours, yielded much weaker upper\nlimits: of order $10^{-8}$ and $10^{-2}$ for fractional differences in the \nlimiting speed and time delay respectively.\n\nThe model discussed above predicts the production of high energy\nmuon and electron neutrinos. \nHowever, if the atmospheric neutrino anomaly has the explanation it is\nusually given, oscillation to $\\nu_\\tau$'s with mass $\\sim0.1{\\rm\\ eV}$\n\\cite{atmo}, then\none should detect equal numbers of $\\nu_\\mu$'s and $\\nu_\\tau$'s. \nUp-going $\\tau$'s, rather than $\\mu$'s, would be a\ndistinctive signature of such oscillations. \nSince $\\nu_\\tau$'s are not expected to be produced in the fireball, looking\nfor $\\tau$'s would be an ``appearance experiment.''\nTo allow flavor change, the difference in squared neutrino masses, \n$\\Delta m^2$, should exceed a minimum value\nproportional to the ratio of source\ndistance and neutrino energy \\cite{John_book}. 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{
"name": "astro-ph0002243.extracted_bib",
"string": "\\begin{thebibliography}{12}\n\n\\bibitem{Fishman} \n Fishman, G. J. \\& Meegan, C. A., ARA\\&A {\\bf 33}, 415 (1995).\n\\bibitem{fireballs} \n Piran, T., in Unsolved Problems In Astrophysics, eds.\n J. N. Bahcall and J. P. Ostriker, 343-377 (Princeton, 1996).\n\\bibitem{W95a} \n Waxman, E., Phys. Rev. Lett. {\\bf 75}, 386 (1995).\n\\bibitem{Vietri95} \n Vietri, M., Ap. J. {\\bf 453}, 883 (1995).\n\\bibitem{W95b} \n Waxman, E., Ap. J. {\\bf 452}, L1 (1995).\n\\bibitem{Nobel_rev}\n Waxman, E., in Proc. Nobel Symposium {\\it Particle Physics and\n The Universe} (Haga Slott, Sweden, August 1998), eds. L. Bergstrom, \n P. Carlson, \\& C. Fransson (astro-ph/9911395).\n\\bibitem{AG_review}\n M\\'esz\\'aros, P., in Proc. {\\it Cosmic Explosions} (Maryland, U.S.A.,\n Oct. 1999), ed. M. Livio (astro-ph/9912474).\n\\bibitem{Freedman}\n Freedman, D. L., \\& Waxman, E., submitted to Ap. J. (astro-ph/9912214).\n\\bibitem{AG_confirm}\n Waxman, E., Ap. J. {\\bf 485}, L5 (1997); \n Wijers, R. A. M. J., Rees, M. J. \\& M\\'esz\\'aros, P., \n MNRAS {\\bf 288}, L51 (1997).\n\\bibitem{AG_pred}\n Paczy\\'nski, B. \\& Rhoads, J., Ap. J. {\\bf 418}, L5 (1993);\n Katz, J. I., Ap. J. {\\bf 432}, L107 (1994);\n M\\'esz\\'aros, P. \\& Rees, M., Ap. J. {\\bf 476}, 232 (1997);\n Vietri, M., Ap. J. {\\bf 478}, L9 (1997).\n\\bibitem{Gallant98}\n Gallant, Y. A., \\& Achterberg, A., MNRAS {\\bf 305}, L6 (1999).\n\\bibitem{Stecker}\n Stecker, F. W. , Submitted to Ap. J. (astro-ph/9911269).\n\\bibitem{AGASA_pairs} \n Hayashida, N., {\\it et al.} Phys. Rev. Lett. {\\bf 77}, 1000 (1996);\n Takeda, M. {\\it et al.}, astro-ph/9902239.\n\\bibitem{fireball86}\n Paczy\\'nski, B., Ap. J. {\\bf 308}, L43 (1986);\n Goodman, J., Ap. J. {\\bf 308}, L47 (1986).\n\\bibitem{internal} \n Paczy\\'nski, B. \\& Xu, G., Ap. J. {\\bf 427}, 708 (1994);\n M\\'esz\\'aros, P., \\& Rees, M., MNRAS {\\bf 269}, 41P (1994).\n\\bibitem{Woods95}\n Woods, E. \\& Loeb, A., Ap. J. {\\bf 453}, 583 (1995).\n\\bibitem{Bhat92}\n Bhat, P. N., {\\it et al.}, Nature {\\bf 359}, 217 (1992).\n\\bibitem{Gamma}\n Krolik, J. H. \\& Pier, E. A., Ap. J. {\\bf 373}, 277 (1991);\n Baring, M., Ap. J. {\\bf 418}, 391 (1993).\n\\bibitem{reverse}\n M\\'esz\\'aros, P., Rees, M., and Papathanassiou, H., Ap. J. {\\bf 432}, 181 \n (1994).\n\\bibitem{Bland87} \n Blandford, R., \\& Eichler, D., Phys. Rep. {\\bf 154}, 1 (1987).\n\\bibitem{Akerlof99}\n Akerlof, C. W. {\\it et al.}, Nature, {\\bf 398}, 400 (1999).\n\\bibitem{SPMR_0123}\n Sari, R. \\& Piran, T., Ap. J. {\\bf 517}, L109 (1999);\n M\\'esz\\'aros, P. \\& Rees, M., MNRAS {\\bf 306}, L39 (1999).\n\\bibitem{WnD00}\n Waxman, E., \\& Draine, B. T., Ap. J., in press (astro-ph/9909020). \n\\bibitem{GRB_z}\n Krumholtz, M., Thorsett, S. E., \\& Harrison, F. A., Ap. J. {\\bf 506}, L81\n (1998);\n Hogg, D. W. \\& Fruchter, A. S., Ap. J. {\\bf 520}, 54 (1999).\n\\bibitem{MnM98}\n Mao, S. \\& Mo, H. J., A\\&A {\\bf 339}, L1 (1998).\n\\bibitem{Bird934} \n Bird, D. J., {\\it et al.}, Ap. J. {\\bf 424}, 491 (1994).\n\\bibitem{Hayashida945} \n Yoshida, S., {\\it et al.}, Astropar. Phys. {\\bf 3}, 151 (1995).\n\\bibitem{Takeda98} \n Takeda, M. {\\it et al.}, Phys. Rev. Lett. {\\bf 81}, 1163 (1998).\n\\bibitem{Watson91}\n Watson, A. A., Nucl. Phys. B (Proc. Suppl.) {\\bf 22B}, 116 (1991).\n\\bibitem{composition}\n Gaisser, T. K. {\\it et al.}, Phys. Rev. D {\\bf 47}, 1919 (1993);\n Dawson, B. R., Meyhandan, R., Simpson, K.M., Astropart. Phys. {\\bf 9}, \n 331 (1998).\n\\bibitem{Yakutsk}\n Efimov, N. N. {\\it et al.}, in {\\it Proceedings of the International\n Symposium on Astrophysical Aspects\n of the Most Energetic Cosmic-Rays}, edited by M. Nagano and F. Takahara\n (World Scientific, Singapore, 1991), p. 20.\n\\bibitem{QSO} \n Boyle, B. J. \\& Terlevich, R. J., MNRAS {\\bf 293}, L49 (1998).\n\\bibitem{GZK}\n Greisen, K., Phys. Rev. Lett. {\\bf 16}, 748 (1966); \n Zatsepin, G. T., \\& Kuzmin, V. A., JETP lett., {\\bf 4}, 78 (1966).\n\\bibitem{CR_clustering}\n Waxman, E., \\& Bahcall, J. N., submitted to Ap. J. (hep-ph/9912326)\n\\bibitem{Matthews99}\n Matthews, J. N., these proceedings\n\\bibitem{Aharonian94} \n Aharonian, F. A., \\& Cronin, J. W., Phys. Rev. D {\\bf 50}, 1892 (1994).\n\\bibitem{IGM} \n Kronberg, P. P., Rep. Prog. Phys. {\\bf 57}, 325 (1994).\n\\bibitem{MnW96}\n Miralda-Escud\\'e, J. \\& Waxman, E., Ap. J. {\\bf 462}, L59 (1996). \n\\bibitem{Sigl_Lemoine97}\n Sigl, G., Lemoine, M. \\& Olinto, A. V., Phys. Rev. {\\bf D56}, 4470 (1997);\n Lemoine, M., Sigl, G., Olinto, A. V. \\& Schramm, D. N., Ap. J. {\\bf 486},\n L115 (1997).\n\\bibitem{Auger}\n Cronin, J. W., Nucl. Phys. B (Proc. Suppl.) {\\bf 28B}, 213 (1992).\n\\bibitem{TA}\n Teshima, M. {\\it et al.}, Nuc. Phys. {\\bf 28B} (Proc. Suppl.), 169 (1992).\n\\bibitem{WnM96}\n Waxman, E. \\& Miralda-Escud\\'e, J., Ap. J. {\\bf 472}, L89 (1996).\n\\bibitem{WnB97} \n Waxman, E., \\& Bahcall, J. N., Phys. Rev. Lett. {\\bf 78}, 2292 (1997).\n\\bibitem{WnB99}\n Waxman, E., \\& Bahcall, J. N., Phys. Rev. {\\bf D59}, 023002 (1999).\n\\bibitem{RnM98} \n Rachen, J. P., \\& M\\'esz\\'aros, P., Phys. Rev. D {\\bf 58},\n 123005 (1998).\n\\bibitem{Muecke98}\n Muecke, A. {\\it et al.}, PASA {\\bf 16}, 160 (1999) (astro-ph/9808279).\n\\bibitem{AG_nus}\n Waxman, E., \\& Bahcall, J. N., submitted to Ap. J. (hep-ph/9909286)\n\\bibitem{Halzen_review99}\n Halzen, F., in Proc. 17th International Workshop on\n Weak Interactions and Neutrinos (Cape Town, South Africa, January 1999)\n (astro-ph/9904216). \n\\bibitem{John_book} \n Bahcall, J. N., {\\it Neutrino Astrophysics}, Cambridge \n University Press (NY 1989).\n\\bibitem{atmo} \n Fukuda, Y., {\\it et al.}, Phys. Lett. {\\bf B335}, 237 (1994);\n Casper, D., {\\it et al.}, Phys. Rev. Lett. {\\bf 66}, 2561 (1991); \n Fogli, G. L., \\& Lisi, E., Phys. Rev. {\\bf D52}, 2775 (1995).\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002244
|
The Elusive Active Nucleus of NGC 4945. \thanks{Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5--26555. Also based on observation collected at European Southern Observatory, La Silla, Chile.}
|
[
{
"author": "A. Marconi\\inst{1}"
},
{
"author": "E. Oliva\\inst{1}"
},
{
"author": "P.P. van der Werf\\inst{2}"
},
{
"author": "R. Maiolino\\inst{1}"
},
{
"author": "E.J. Schreier\\inst{3}"
},
{
"author": "F. Macchetto\\inst{3,4}"
},
{
"author": "A.F.M. Moorwood\\inst{5}"
}
] |
We present new HST NICMOS observations of NGC 4945, a starburst galaxy hosting a highly obscured active nucleus that is one of the brightest extragalactic sources at 100 keV. The HST data are complemented with ground based \FeII\ line and mid--IR observations. A 100pc-scale starburst ring is detected in \PA, while \Hmol\ traces the walls of a super bubble opened by supernova-driven winds. The conically shaped cavity is particularly prominent in \PA\ equivalent width and in the \PA/\Hmol\ ratio. Continuum images are heavily affected by dust extinction and the nucleus of the galaxy is located in a highly reddened region with an elongated, disk-like morphology. No manifestation of the active nucleus is found, neither a strong point source nor dilution in CO stellar features, which are expected tracers of AGN activity. Even if no AGN traces are detected in the near-IR, with the currently available data it is still not possible to establish whether the bolometric luminosity of the object is powered by the AGN or by the starburst: we demonstrate that the two scenarios constitute equally viable alternatives. However, the absence of any signature other than in the hard X-rays implies that, in both scenarios, the AGN is non-standard: if it dominates, it must be obscured in all directions, conversely, if the starburst dominates, the AGN must lack UV photons with respect to X-rays. An important conclusion is that powerful AGNs can be hidden even at mid-infrared wavelengths and, therefore, the nature of luminous dusty galaxies cannot be always characterized by long-wavelength data alone but must be complemented with sensitive hard X-ray observations. \keywords{ Galaxies: active -- Galaxies: individual: NGC4945 -- Galaxies: nuclei -- Galaxies: Seyfert -- Galaxies: Starburst -- Infrared: galaxies}
|
[
{
"name": "marconi.tex",
"string": "%\\documentclass[referee]{aa} % for a referee version\n\n\\documentclass{aa}\n\n\\usepackage{epsfig}\n\n\\newcommand{\\lesssim}{\\ensuremath{\\stackrel{<}{\\sim}}}\n\\newcommand{\\xten}[1]{\\ensuremath{\\times 10^{#1}}}\n\\newcommand{\\ten}[1]{\\ensuremath{10^{#1}}}\n\\newcommand{\\Hmol}{\\ensuremath{\\mathrm{H}_2}}\n\\newcommand{\\water}{\\ensuremath{\\mathrm{H_2O}}}\n\\newcommand{\\HA}{\\ensuremath{\\mathrm{H}\\alpha}}\n\\newcommand{\\PA}{\\ensuremath{\\mathrm{Pa}\\alpha}}\n\\newcommand{\\BA}{\\ensuremath{\\mathrm{Br}\\alpha}}\n\\newcommand{\\BG}{\\ensuremath{\\mathrm{Br}\\gamma}}\n\\newcommand{\\HNU}{\\ensuremath{\\mathrm{h}\\nu}}\n\\newcommand{\\AV}{\\ensuremath{A_\\mathrm{V}}}\n\\newcommand{\\AWL}{\\ensuremath{A_\\lambda}}\n\\newcommand{\\Lo}{\\ensuremath{\\mathrm{L}_\\odot}}\n\\newcommand{\\Mo}{\\ensuremath{\\mathrm{M}_\\odot}}\n\\newcommand{\\Zo}{\\ensuremath{\\mathrm{Z}_\\odot}}\n\\newcommand{\\LAGN}{\\ensuremath{L_\\mathrm{AGN}}}\n\\newcommand{\\LUV}{\\ensuremath{L_\\mathrm{UV}}}\n\\newcommand{\\LX}{\\ensuremath{L_\\mathrm{X}}}\n\\newcommand{\\LFIR}{\\ensuremath{L_\\mathrm{FIR}}}\n\\newcommand{\\LBOL}{\\ensuremath{L_\\mathrm{BOL}}}\n\\newcommand{\\QH}{\\ensuremath{Q(\\mathrm{H})}}\n\\newcommand{\\NH}{\\ensuremath{N_\\mathrm{H}}}\n\\newcommand{\\EV}{\\ensuremath{\\,\\mathrm{ev}}}\n\\newcommand{\\KEV}{\\ensuremath{\\,\\mathrm{keV}}}\n\\newcommand{\\ERG}{\\ensuremath{\\,\\mathrm{erg}}}\n\\newcommand{\\K}{\\ensuremath{\\,\\mathrm{K}}}\n\\renewcommand{\\S}{\\ensuremath{\\,\\mathrm{s}}}\n\\newcommand{\\YR}{\\ensuremath{\\,\\mathrm{yr}}}\n\\newcommand{\\MPC}{\\ensuremath{\\,\\mathrm{Mpc}}}\n\\newcommand{\\PC}{\\ensuremath{\\,\\mathrm{pc}}}\n\\newcommand{\\KM}{\\ensuremath{\\,\\mathrm{km}}}\n\\newcommand{\\CM}{\\ensuremath{\\,\\mathrm{cm}}}\n\\newcommand{\\MIC}{\\ensuremath{\\,\\mathrm{\\mu m}}}\n\\newcommand{\\MAG}{\\ensuremath{\\,\\mathrm{mag}}}\n\\newcommand{\\1}{\\ensuremath{^{-1}}}\n\\newcommand{\\2}{\\ensuremath{^{-2}}}\n\\newcommand{\\forb}[2]{\\ensuremath{[\\mathrm{#1}\\,\\textsc{\\lowercase{#2}}]}}\n\\newcommand{\\perm}[2]{\\ensuremath{\\mathrm{#1}\\,\\textsc{\\lowercase{#2}}}}\n\\newcommand{\\WL}{\\ensuremath{\\lambda}}\n\\newcommand{\\OIII}{\\forb{O}{III}}\n\\newcommand{\\NeV}{\\forb{Ne}{V}}\n\\newcommand{\\NeII}{\\forb{Ne}{II}}\n\\newcommand{\\FeII}{\\forb{Fe}{II}}\n\\newcommand{\\NII}{\\forb{N}{II}}\n\\newcommand{\\HeI}{\\perm{He}{I}}\n\n\n\\begin{document}\n\n\\thesaurus{11.01.2 -- 11.09.1 -- 11.14.1 -- 11.19.1 -- 11.19.3 -- 13.09.1}\n\n\\title{The Elusive Active Nucleus of NGC 4945.\n\\thanks{Based on observations made with the NASA/ESA Hubble Space Telescope,\nobtained at the Space Telescope Science Institute, which\nis operated by AURA, Inc., under NASA contract NAS 5--26555.\nAlso based on observation collected at European Southern Observatory,\nLa Silla, Chile.} }\n\n\\author{A. Marconi\\inst{1},\n\tE. Oliva\\inst{1},\n\tP.P. van der Werf\\inst{2},\n\tR. Maiolino\\inst{1},\n\tE.J. Schreier\\inst{3},\n\tF. Macchetto\\inst{3,4},\n\t\\and A.F.M. Moorwood\\inst{5}\n\t}\n\n\\offprints{A. Marconi}\n\n\\institute{\n\t Osservatorio Astrofisico di Arcetri,\n\t Largo E. Fermi 5, I-50125 Firenze, ITALY\n\t \\and\n\t Sterrewacht Leiden, P.O. Box 9513, 2300 RA Leiden, The Netherlands\n\t \\and\n\t Space Telescope Science Institute\n\t 3700 San Martin Drive, Baltimore, MD 21218, USA\n\t \\and\n\t Affiliated to ESA science division\n\t \\and\n\t European Southern Observatory\n\t Karl-Schwarzschild-Strasse 2, 85748 Garching bei M\\\"unchen, Germany\n}\n\n\\date{Received ... Accepted ... }\n\n\\authorrunning{Marconi et al.}\n\\titlerunning{The elusive AGN of NGC 4945}\n\\maketitle\n\n\n\\begin{abstract}\n\nWe present new HST NICMOS observations of NGC 4945, a starburst \ngalaxy hosting a highly obscured active nucleus that is\none of the brightest extragalactic sources at 100 keV.\nThe HST data are complemented with ground based \\FeII\\\nline and mid--IR observations. \n\nA 100pc-scale starburst ring is detected in \\PA, while \\Hmol\\ traces\nthe walls of a super bubble opened by supernova-driven winds.\nThe conically shaped cavity is particularly prominent in \\PA\\\nequivalent width and in the \\PA/\\Hmol\\ ratio.\nContinuum images are heavily affected by dust extinction and the\nnucleus of the galaxy is located\nin a highly reddened region with an elongated, disk-like morphology.\nNo manifestation of the active nucleus is found,\nneither a strong point source nor dilution in CO stellar features,\nwhich are expected tracers of AGN activity.\n\nEven if no AGN traces are detected in the near-IR,\nwith the currently available data it is still not possible\nto establish whether the bolometric luminosity of the object is\npowered by the AGN or by the starburst: we demonstrate\nthat the two scenarios constitute equally viable alternatives.\nHowever, the absence of any signature other than in the hard X-rays \nimplies that, in both scenarios, the AGN is non-standard: \nif it dominates, it must be obscured in all directions,\nconversely, if the starburst dominates, the AGN must lack UV photons\nwith respect to X-rays.\n\nAn important conclusion is that\npowerful AGNs can be hidden even at mid-infrared\nwavelengths and, therefore, the nature of luminous dusty galaxies\ncannot be always characterized by long-wavelength data alone\nbut must be complemented with sensitive hard X-ray observations.\n\n\\keywords{ Galaxies: active -- Galaxies: individual: NGC4945 -- \nGalaxies: nuclei -- Galaxies: Seyfert -- Galaxies: Starburst --\nInfrared: galaxies}\n\n\\end{abstract}\n\n\\section{Introduction}\n\nA key problem in studies of objects emitting most of their energy\nin the FIR/submm is to establish the\nrelative importance of highly obscured\nActive Galactic Nuclei (AGN) and starburst activity.\nIn particular, it is important to know if it is still\npossible to hide an AGN, contributing significantly to the bolometric\nemission, when optical to mid-IR spectroscopy and imaging \nreveal only a starburst component.\n\nSeveral pieces of evidence suggest that most cosmic\nAGN activity is obscured.\nMost, and possibly all, cores of large galaxies host a\nsupermassive black hole (\\ten{6}--\\ten{9}\\Mo;\ne.g. Richstone et al. \\cite{richstone}).\nTo complete the formation process in a Hubble time,\naccretion must proceed at high rates,\nproducing quasar luminosities ($L\\sim\\ten{12}\\Lo$).\nHowever the observed black hole density is an order of magnitude\ngreater than that expected from the observed quasar light,\nassuming accretion efficiency of 10\\%,\nsuggesting that most of the accretion history is obscured\n(e.g. Fabian \\& Iwasawa \\cite{fabian99}, and references therein).\nIt is estimated either that 85\\% of all AGNs are obscured (type 2)\nor that 85\\% of the accretion history of an object is hidden from view.\n\nIn addition, the hard X-ray background ($>1\\KEV$)\nrequires a large population of obscured AGNs\nat higher redshifts ($z\\sim1$) since the\nobserved spectral energy distribution cannot\nbe explained with the continua of Quasars, \ni.e. un--obscured (type 1) AGNs (Comastri et al. \\cite{comastri},\nGilli et al. \\cite{gilli99}).\nDespite the above evidence, detections of obscured AGNs at\ncosmological distances are still sparse (e.g. Akiyama et al. \\cite{akiyama}).\n\nUltra Luminous Infrared Galaxies (ULIRGs; see\nSanders \\& Mirabel \\cite{sanders96} for a review)\nand the sources detected in recent far-infrared and submm surveys \nperformed with ISO and SCUBA (e.g. Rowan-Robinson et al. \\cite{rowanrob},\nBlain et al. \\cite{blain} and references therein)\nare candidate to host the missing population of type 2 AGNs.\nHowever, mid-IR ISO spectroscopy\nhas recently shown that ULIRGs are mostly powered\nby starbursts and that no trace of AGNs is found in the majority of cases\n(Genzel et al. \\cite{genzel98}; Lutz et al. \\cite{lutz98}).\nYet, the emission of a hidden AGN could be heavily absorbed\neven in the mid-IR. Indeed, the obscuration of the AGN could be related\nto the starburst phenomenon, as observed for Seyfert 2s\n(Maiolino et al. \\cite{maiolino95}).\nFabian et al. (\\cite{fabian98}) proposed\nthat the energy input from supernovae and stellar winds prevents \ninterstellar clouds from collapsing into a thin disk, thus maintaining them \nin orbits that intercept the majority of the lines of sight from \nan active nucleus.\n\nIn this paper, we investigate the existence\nof completely obscured AGNs and the Starburst-AGN connection through\nobservations of NGC 4945, one of the closest galaxies where\nan AGN and starburst coexist.\nNGC 4945 is an edge-on ($i\\sim 80^\\circ$), nearby ($D=3.7\\MPC$) \nSB spiral galaxy hosting a\npowerful nuclear starburst (Koornneef \\cite{koorn}; \nMoorwood \\& Oliva \\cite{moorwood94a}).\nIt is a member\nof the Centaurus group and, like the more famous Centaurus A (NGC 5128),\nits optical image is marked by dust extinction\nin the nuclear regions. The ONLY evidence for a hidden AGN comes from the\nhard X-rays where NGC 4945 is characterized by a Compton-thick spectrum\n(with an absorbing column density of $\\NH=5\\xten{24}\\CM\\2$,\nIwasawa et al. \\cite{iwasawa93})\nand one of the brightest 100\\KEV\\ emissions among extragalactic sources\n(Done et al. \\cite{done96}).\nRecently, BeppoSAX clearly detected variability in the 13-200\\KEV\\ band\n(Guainazzi et al., \\cite{guainazzi}).\n\n\nIts total infrared luminosity derived from IRAS data\nis $\\sim 2.4\\xten{10}\\Lo$ (Rice et al. \\cite{rice88}),\n$\\sim 75\\%$ of which arises from\na region of $\\le 12\\arcsec\\times9\\arcsec$ centered on\nthe nucleus (Brock et al. \\cite{brock88}).\nAlthough its star formation and supernova rates are moderate,\n$\\sim 0.4\\,\\Mo\\YR\\1$\nand $\\sim 0.05\\YR\\1$ (Moorwood \\& Oliva \\cite{moorwood94a}),\nthe starburst activity is concentrated in the central $\\sim 100\\PC$ and\nhas spectacular consequences\non the circumnuclear region which is characterized by a conical cavity\nevacuated by a supernova-driven wind (Moorwood et al. \\cite{moorwood96a}). \n\nThe radio emission is characterized by a compact non-thermal core\nwith a luminosity of $\\simeq 8\\xten{38}\\ERG\\S\\1$\n(Elmouttie et al. \\cite{elmouttie}).\nIt is one of the first H$_2$O and OH megamaser sources detected\n(dos Santos \\& Lepine \\cite{dossantos}; Baan \\cite{baan85}) and\nthe H$_2$O maser was mapped by Greenhill et al. (\\cite{greenhill})\nwho found the emission linearly\ndistributed along the position angle of the galactic disk and with a \nvelocity pattern suggesting the presence of a \n$\\sim\\ten{6}\\Mo$ black hole.\nMauersberger et al. (\\cite{mauersberger}) mapped the $J=3-2$ line of $^{12}$CO\nwhich is mostly concentrated within the nuclear $\\sim 200\\PC$.\n\n\nWe present new line and continuum images obtained with the\n{\\it Near Infrared Camera and Multi\nObject Spectrograph} (NICMOS) on-board the Hubble Space Telescope (HST),\naimed at detecting AGN activity in the near-infrared.\nThese observations are complemented by recent ground based near- and\nmid-IR observations obtained at the European Southern Observatory.\nSection \\ref{sec:obs} describes the observations and data reduction techniques.\nResults are presented in Section \\ref{sec:res} and discussed\nin Section \\ref{sec:discuss}.\nFinally, conclusions will be drawn in Sec. \\ref{sec:conclus}.\nThroughout the paper we assume a distance of 3.7\\MPC\\\n(Mauersberger et al. \\cite{mauersberger}),\nwhence 1\\arcsec\\ corresponds to $\\simeq18$\\PC.\n\n\\begin{figure*}\n\\begin{center}\n\\begin{tabular}{cc}\n \\epsfig{figure=marconi_f1a.ps,width=0.45\\linewidth} &\n \\epsfig{figure=marconi_f1b.ps,width=0.45\\linewidth} \\\\\n & \\\\\n \\epsfig{figure=marconi_f1c.ps,width=0.45\\linewidth} &\n \\epsfig{figure=marconi_f1d.ps,width=0.45\\linewidth} \\\\\n & \\\\\n \\epsfig{figure=marconi_f1e.ps,width=0.45\\linewidth} &\n \\hspace{14pt}\\vspace*{-14pt}\n \\epsfig{figure=marconi_f1f.ps,width=0.38\\linewidth} \\\\\n\\end{tabular}\n\\end{center}\n\\caption{\\label{fig:cont}\n(a) F222M image (K band).\nNorth is up and East is left.\nThe cross marks the location of the K nucleus and\nthe circle represents the uncertainty on the position of the H$_2$O maser\ngiven by Greenhill et al. (1997).\nUnits of the frame box are seconds of arc.\nThe origin is at the nominal location of the H$_2$O maser.\n(b) F160W image (H). Notation as in panel (a).\n(c) F110W image (J). Notation as in panel (a).\nThe black contours are from the H-K color image at 1.8, 2 and 2.2 levels.\n(d) F606W image (R band). Notation as in panel (a) except for the contours\nwhich are from the K band image. (e) H-K image. Symbols are as in (a).\n(f) Truecolor (Red=F222M, Green=F110W, Blue=F606W) image.\n}\n\\end{figure*}\n\n\n\\begin{figure*}[!]\n\\begin{center}\n\\begin{tabular}{cc}\n \\epsfig{figure=marconi_f2a.ps,width=0.45\\linewidth} &\n \\epsfig{figure=marconi_f2b.ps,width=0.45\\linewidth} \\\\\n & \\\\\n \\epsfig{figure=marconi_f2c.ps,width=0.45\\linewidth} &\n \\epsfig{figure=marconi_f2d.ps,width=0.45\\linewidth} \\\\\n & \\\\\n \\epsfig{figure=marconi_f2e.ps,width=0.45\\linewidth} &\n \\hspace{14pt}\\vspace*{-14pt}\n \\epsfig{figure=marconi_f2f.ps,width=0.38\\linewidth} \\\\\n\\end{tabular}\n\\end{center}\n\\caption{\\label{fig:line}\n(a) Pa$\\alpha$ image. Symbols as in Fig. 1.\nThe black contours are from the \\HA+\\NII\\ image by Moorwood et al. (1996).\n(b) H$_2$ image. Black contours are from the blue ground-based \\FeII\\ image,\n(c) Equivalent width of Pa$\\alpha$.\n(d) \\PA/\\Hmol\\ image. Symbols as in Fig. 1.\n(e) CO index. Symbols as in Fig. 1.\n(f) Truecolor line image (Red=F222M, Green=\\Hmol, Blue=\\PA) image.\n}\n\\end{figure*}\n\n\n\\section{\\label{sec:obs} Observations and Data Reduction}\n\n\n\\begin{table}\n\\caption{\\label{tab:log} Log of HST observations.}\n\\begin{tabular}{lccl}\n\\hline\\hline\nDataset & Filter & T$_{exp}$ (sec) & Description \\\\\n\\hline\n\\\\\nn4mq01010 & F110W & 768\t & J \t\t\t \\\\\nn4mq02010 & F160W & 768\t & H \t\t\t \\\\\nn4mq01040 & F222M & 288 & K \t\t\t \\\\\nn4mq01070 & F237M & 288 & CO \t\t \\\\\nn4mqa1010 & F222M & 288 & K background \t \\\\\nn4mqa1020 & F237M & 288 & CO background \t \\\\\n\\\\\nn4mqb1nrq & F187N & 320 & \\PA\\\t\t \\\\\nn4mqb1nuq & F190N & 320 & \\PA\\ continuum\t \\\\\nn4mqb1o0q & F190N & 320 & \\PA\\ continuum\t \\\\\nn4mqb1o3q & F187N & 320 & \\PA\\\t\t \\\\\nn4mqb1o9q & F187N & 320 & \\PA\\\t\t \\\\\nn4mqb1odq & F190N & 320 & \\PA\\ continuum\t \\\\\nn4mqb1oiq & F190N & 320 & \\PA\\ continuum\t \\\\\nn4mqb1olq & F187N & 320 & \\PA\\\t\t \\\\\n\\\\\nn4mqb1opq & F212N & 320 & \\Hmol\\\t\t \\\\\nn4mqb1osq & F190N & 320 & \\Hmol\\ continuum\t \\\\\nn4mqb1ovq & F190N & 320 & \\Hmol\\ continuum\t \\\\\nn4mqb1ozq & F212N & 320 & \\Hmol\\\t\t \\\\\nn4mqb1p2q & F212N & 320 & \\Hmol\\\t\t \\\\\nn4mqb1p5q & F190N & 320 & \\Hmol\\ continuum\t \\\\\nn4mqb1p9q & F190N & 320 & \\Hmol\\ continuum\t \\\\\nn4mqb1pcq & F212N & 320 & \\Hmol\\\t\t \\\\\n\\\\\nu29r2p01t & F606W & 80\t & R archive\t \\\\\nu29r2p02t & F606W & 80 & R archive \\\\\nu2e67z01t & F606W & 500 & R archive \\\\\n\\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\n\\begin{table*}\n\\caption{\\label{tab:loggr}Log of Ground Based observations.}\n\\begin{tabular}{lcccl}\n\\hline\\hline\nImage & T$_{exp}$ (min) & Date & Instrument & Telescope\\\\\n\\hline\n\\\\\nL$^\\prime$ & 10 & May 30, 1996 & IRAC1 & ESO/MPI 2.2m \\\\\nN & 40 & May 27, 1996 & TIMMI & ESO 3.6m \\\\\n\\FeII\\ & 24 & April 1, 1998 & IRAC2B & ESO/MPI 2.2m \\\\\n\\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\nThe nuclear region of NGC 4945 was observed on March 17$^{th}$ and\n25$^{th}$, 1998, with NICMOS Camera 2 (MacKenty et al. \\cite{mackenty})\nusing narrow and broad band filters for imaging in lines and continuum.\nHST observations are logged in Tab. \\ref{tab:log}.\nAll observations were carried out with a MULTIACCUM sequence (MacKenty et al.\n\\cite{mackenty})\nand the detector was read out non-destructively several times\nduring each integration to remove cosmic rays hits and correct\nsaturated pixels.\nFor each filter we obtained several exposures with the object \nshifted by $\\sim 1\\arcsec$ on the detector to remove bad pixels.\nThe observations in the F222M and F237M filters\nwere also repeated on a blank sky area several arcminutes away\nfrom the source to remove thermal background emission.\nFor narrow band images, we obtained subsequent\nexposures in line and near continuum filters with the object\nat several positions on the detector.\n\nThe data were re-calibrated using the pipeline software CALNICA v3.2\n(Bushouse et al. \\cite{bushouse}). \nA small (few percent) drift in the NICMOS bias level caused an error\nin the flat-fielding procedure which resulted in spurious artifacts\nin the final images (the so-called \"pedestal problem\" -- Skinner,\nBergeron \\& Daou \\cite{skinner}). Given the strong signal from the galaxy,\nsuch artifacts are only visible in ratio or difference images.\nThis effect was effectively removed using the pedestal\nestimation and quadrant equalization software developed by Roeland\nP. van der Marel which subtracts a constant bias\nlevel times the flat-field, minimizing the standard deviation\nin the images. For each filter, the corrected\nimages were then aligned via cross-correlation and combined.\nFlux calibration of the images was achieved by multiplying the count rates\n(adu\\S\\1) for the PHOTFLAM (\\ERG\\CM\\2\\,adu\\1) conversion factors\n(MacKenty et al. \\cite{mackenty}).\n\nThe narrow band images obtained at wavelengths adjacent to the\n\\PA\\ and \\Hmol\\ lines where used for continuum subtraction.\nThe procedure was verified by rescaling\nthe continuum by up to $\\pm 10\\%$ before subtraction and establishing that this did not significantly affect the observed emission-line structure.\n\nWFPC2 observations in the F606W (R band) filter were retrieved from the\nHubble Data Archive and\\\\ re-calibrated with the\nstandard pipeline software (Biretta et al. \\cite{biretta}).\n\nGround-based observations were obtained at the European Southern\nObservatory at La Silla (Chile) in the continuum L$^\\prime$ (3.8\\MIC) and\nN (10\\MIC) bands, and in the \\FeII\\ 1.64\\MIC\\ emission line and\nare logged in Tab. \\ref{tab:loggr}. The L$^\\prime$ \nimage was obtained with IRAC1 (Moorwood et al. \\cite{moorwood94b})\nat the ESO/MPI 2.2\\,m telescope on May 30, 1996 using an SBRC 58$\\times$62 pixel\nInSb array with a pixel size of 0\\farcs45. Double beam-switching was used,\nchopping the telescope secondary mirror every 0.24\\S\\ and nodding the\ntelescope every 24\\S\\ to build up a total on-source integration time of\n10\\,minutes in a seeing of 0\\farcs9. The N-band image was obtained with\nTIMMI (K\\\"aufl et al. \\cite{kaufl}) at the ESO 3.6m telescope on May 27, 1996\nusing a 64$\\times$64 Si:Ga array with 0\\farcs46 pixels. Again using\ndouble beam switching, total on-source integration time was 40 minutes\nin 1\\arcsec\\ seeing. The \\FeII\\ 1.64\\MIC\\ image was taken with with the\nIRAC2B camera (Moorwood et al. \\cite{moorwood92})\non the ESO/MPI 2.2m telescope on April 1, 1998, using a\n256$\\times$256 Rockwell NICMOS3 HgCdTe array with 0\\farcs51 pixels. The\n\\FeII\\ line was scanned with a $\\lambda/\\Delta\\lambda=1500$ Fabry-Perot\netalon covering three independent wavelength settings on the line and\ntwo on the continuum on either side of the line, for a total integration\ntimes of 24\\,minutes on the line in 0\\farcs9 seeing. Standard procedures\nwere used for sky subtraction, flat fielding, interpolation of hot and\ncold pixels at fixed positions on the array, recentering and averaging\nof the data. For the \\FeII\\ data, the continuum was determined from the\ntwo off-line channels and subtracted from the on-line data.\nThe integrated \\FeII\\ line flux is in excellent agreement with the value\ndetermined by Moorwood and Oliva (\\cite{moorwood94a}).\n\n\\section{\\label{sec:res}Results}\n\n\\begin{figure*}\n\\begin{center}\n\\begin{tabular}{cc}\n \\epsfig{figure=marconi_f3a.ps,width=0.48\\linewidth} &\n \\epsfig{figure=marconi_f3b.ps,width=0.48\\linewidth} \\\\\n\\end{tabular}\n\\end{center}\n\\caption{\\label{fig:midir}\n(a) L band contours overlayed on the NICMOS K band image\n(displayed with a logarithmic look--up table).\nContours are 0.005 and from 0.01 to 0.14 with step of 0.01\n(units of \\ten{-16}\\ERG\\CM\\2\\S\\1\\AA\\1). The frame boxes are\ncentered on the nucleus, identified with the \\Hmol\\ maser position.\n(b) N band contours overlayed on the NICMOS K band image.\nContours are from 0.02 to 0.08 with step of 0.003\n(units and notation as above). }\n\\end{figure*}\n\n\\subsection{Morphology}\n\nPanels a--d in Figure \\ref{fig:cont}\nare the continuum images in the NICMOS\nK, H, J and WFPC2 R filters\\footnote{Color images are also available at\nhttp://www.arcetri.astro.it/$\\sim$marconi}.\nThe cross marks the position of the K band peak and the\ncircle is the position of the H$_2$O maser measured by\nGreenhill et al. (\\cite{greenhill}). The radius of the circle is the\n$\\pm1$\\arcsec\\ r.m.s. uncertainty of the astrometry performed on the\nimages and based on the Guide Star Catalogue (Voit et al. \\cite{voit}).\nThe position of the K peak is offset by $\\sim 0\\farcs5$\nfrom the location of the H$_2$O maser, hereafter identified with\nthe location of the nucleus of the galaxy. Note that \nthis offset is still within the absolute astrometric uncertainties\nof the GSC and the K peak could be coincident with the nucleus.\nThe continuum images are also shown with a \"true color\" RGB representation\nin Fig. \\ref{fig:cont}f (Red=F222M, Green=F110W, Blue=F606W).\nA comparison of photometry between our data and earlier published\nresults is not straightforward since the NICMOS filters are different \nfrom the ones commonly used.\nHowever, as shown in table \\ref{tab:comp}, our measured fluxes in\n6\\arcsec\\ and 18\\arcsec\\ circular apertures centered on the K band peak\nare within 15-30\\%\\ of the ones by Moorwood \\& Glass (\\cite{moorwood84})\nmeasured in the same areas.\n\n\\begin{table}\n\\caption{\\label{tab:comp}Comparison with ground based photometric data.}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n\\\\\n\t& \t& \\multicolumn{2}{c}{Moorwood \\& Glass 1984} & This work \\\\\nBand \t& $\\O$ (\\arcsec) & mag\t& Flux$^a$\t& Flux$^a$\t\t\\\\\n\\\\\n\\hline\n\\\\\nK\t& 6\\arcsec & 9.34\t& 7.1\\xten{-15} & 9.5\\xten{-15}\t\\\\\nK\t& 18\\arcsec & 8.12\t& 2.2\\xten{-14} & 2.5\\xten{-14}\t\\\\\nH\t& 6\\arcsec & 10.7\t& 5.7\\xten{-15} & 7.1\\xten{-15}\t\\\\\nH\t& 18\\arcsec & 9.15\t& 2.4\\xten{-14} & 2.7\\xten{-14}\t\\\\\nJ\t& 6\\arcsec & 12.70 & 2.4\\xten{-15}\t& 2.7\\xten{-15}\t\\\\\nJ\t& 18\\arcsec & 10.80 & 1.4\\xten{-14}\t& 1.6\\xten{-14}\t\\\\\n\\\\\n\\hline\\hline\n\\end{tabular}\n\\\\\n$^a$ In units of \\ERG\\S\\1\\CM\\2\\AA.\\\\\n$^b$ The K band of ground based observations corresponds to the F222M NICMOS\nfilter. Similarly H and J corresponds to F160W and F110W, respectively.\n\\end{table}\n\nFigure \\ref{fig:cont}e is the H-K color map. H-K contours are also \noverlayed on the J image in Fig. \\ref{fig:cont}c.\nAt the location of the maser, South-East of the K band peak,\nemission from galactic stars is obscured by a dust lane oriented \nalong the major axis of the galactic disk.\nThe morphology of this resembles an edge-on disk with a 4\\farcs5\nradius (80\\PC) and probably marks the region where high density \nmolecular material detected in CO\nis concentrated (e.g. Mauersberger et al. \\cite{mauersberger}).\nThe average H-K color is $\\sim 1.7$ with a peak value of 2.3.\nThe dust lane has a sharp southern edge which is not very evident in the color map and can be explained by\nsaturated absorption:\nbackground H and K emission becomes completely undetectable and the color\nis dominated by foreground stars. Therefore, the sharp K edge \nis evidence for a region with such high extinction that it is not detected\neven in the near-IR.\nWith this dust distribution, \nthe observed morphology in the continuum images is the result of\nan extinction gradient in the direction perpendicular to the\ngalactic disk. Patchy extinction is also\npresent all over the field of view.\nAt shorter wavelengths, the morphology is more irregular\nbecause dust extinction is more effective (the same effect seen so obviously in Centaurus A, cf. Schreier et al. \\cite{schreier98},\nMarconi et al. \\cite{marconi99}) and the\nconical cavity extensively mapped by Moorwood et al. (\\cite{moorwood96a})\nbecomes more prominent: there, the\ndust has been swept away by supernova-driven winds.\nIndeed, in the R image, significant emission is detected only in the wind-blown\ncavity which presents a clear conical morphology \nwith well defined edges and apex lying $\\simeq 3\\arcsec$\nfrom the K peak. Due to the above mentioned\nreddening gradient, the apex of the cone gets closer to the\nnucleus with increasing wavelength\n(compare with R band and Pa$\\alpha$/H$_2$ images -- see below).\n\nThe continuum-subtracted Paschen $\\alpha$ image\n(Fig. \\ref{fig:line}a) shows the presence of several strong emission line knots \nalong the galactic plane, very likely resulting from a circumnuclear \nring of star formation seen almost edge-on.\n\"Knot B\" of Moorwood et al. (\\cite{moorwood96a}) is clearly observed \nSouth East of the nucleus while \"Knot C\", North-West \nof the nucleus, is barely detected.\nBoth knots are also marked on the figure.\n\nDust extinction strongly affects the \\PA\\ morphology\nmaking very difficult to trace the ring and locate its center; \na likely consequence is \nthe apparent misalignment between the galaxy nucleus and the ring center.\nThe observed ring of star formation is similar to what has been found in other\nstarburst galaxies (cf. Moorwood \\cite{moorwood96b}).\n%and a nice example is given by the Circinus galaxy\n%(Marconi et al. \\cite{marconi94}, Maiolino et al. \\cite{maiolino98}).\nThe starburst ring could result from two alternative scenarios:\neither the starburst originates at the nucleus,\nand then propagates outward forming a ring\nin the galactic disk; or the\nring corresponds to the position of\nthe inner Lindblad resonance \nwhere the gas density is naturally increased\nby flow from both sides (see the review in Moorwood \\cite{moorwood96b}).\n\nPanel b shows the continuum-subtracted H$_2$ image which \ntraces the edges of the wind-blown cavity. As expected, the morphology is \ncompletely different from that of \\PA\\ which traces mainly starburst activity.\nNote the strong H$_2$ emission close to the nucleus at the\napex of the cavity with an elongated, arc-like morphology.\nThe \\Hmol\\ flux in a $6\\arcsec\\times 6\\arcsec$ aperture centered on the K \nband peak is 1.1\\xten{-13}\\ERG\\CM\\2\\S\\1\\ and corresponds to $\\sim 70\\%$ \nof the total integrated emission in the NICMOS field of view.\nThis is in good agreement with the 1.29$\\pm 0.05$ found by\nKoornneef \\& Israel (\\cite{koorn96}) in an equally sized aperture\nand the integrated 3.1\\xten{-13}\\ERG\\CM\\2\\S\\1\\ from the map by\nMoorwood \\& Oliva (\\cite{moorwood94a}).\nWe remark that contamination of \\Hmol\\ emission by \\HeI\\WL 2.112\\MIC\\\nis unlikely since the line was detected neither by Koornneef\n(\\cite{koorn}) nor by Moorwood \\& Oliva (\\cite{moorwood94a}) and\nfrom their spectra we can set an upper limit\nof 5-10\\%\\ to the \\HeI/\\Hmol\\ ratio.\n\nPanel c in Figure \\ref{fig:line} shows that the equivalent\nwidth of \\PA\\ is up to 150--200\\AA\\ in the star forming regions,\nbut much lower in the wind-blown cavity.\nSince near-IR continuum emission within the cone is not significantly\nhigher than in the surrounding medium,\nthe low equivalent width within the cone is due\nto weaker \\PA\\ emission, the likely consequence of low gas density. \n\nPanel d in Figure \\ref{fig:line} is the\nPa$\\alpha$/H$_2$ ratio image which also traces the wind-blown cavity.\nNote that the cone traced by Pa$\\alpha$ and H$_2$ is offset with respect\nto the light cone observed in R:\nthis is a result of the reddening gradient in the\ndirection perpendicular to the galactic plane.\n\nFig. \\ref{fig:line}f is a true color RGB representation \nof line and continuum images (Red=F222M, Green=\\Hmol, Blue=\\PA).\n\nL$^\\prime$ and N band ground based images are shown in Fig. \\ref{fig:midir}\na and b with contours overlayed on the NICMOS K band image.\nNo obvious point source is detected at the location of the nucleus\nand the extended emission is smooth and regular, elongated as\nthe galactic disk. \n\nThe \\FeII\\ emission shown in contours in Fig. \\ref{fig:line}b deviates from the\n\\PA\\ image in a number of interesting ways. First, the northern\nedge of the cavity outlined most clearly in \\Hmol\\ emission is also detected, although more\nfaintly, in \\FeII, presumably excited by the shocks resulting\nfrom the superwind. Otherwise, the \\FeII\\ emission displays two\nprominent peaks in the starburst region traced by \\PA, one peak\nclose to the nucleus and one offset at a position angle of about 250\ndegrees (counterclockwise from North). In both of these regions the\n\\FeII/\\PA\\ ratio is much higher than in the rest of the starburst region. The\n\\FeII\\ emission likely originates in radiative supernova remnants\n(SNRs). In the dense nuclear region of NGC4945 the radiative phase of\nthe SNRs will be short, and hence the \\FeII\\ emission will be much more\nstrongly affected by the stochastic nature of supernova explosions in\nthe starburst ring than \\PA. The regions of high\n\\FeII/\\PA\\ ratios thus simply trace recent supernova activity.\n\n\\subsection{Reddening}\n\nA lower limit and a reasonable estimate of reddening can be\nobtained from the H--K color image in the case of foreground screen extinction.\nIn this case, the extinction is simply\n\\begin{equation}\n\\AV = \\frac{E(H-K)}{c(H)-c(K)}\n\\end{equation}\nwhere the color excess is given by the difference between observed \nand intrinsic colour, $E(H-K)=(H-K)-(H-K)_\\circ$ and\nthe $c$ coefficients represent the wavelength dependence of the extinction law;\n$A_\\lambda = c(\\lambda) \\AV$.\nWe have assumed $\\AWL=A_{1\\MIC}(\\WL/1\\MIC)^{-1.75}$\n($\\lambda>1\\MIC$) and $\\AV=2.42 A_{1\\MIC}$.\nSpiral and elliptical galaxies have average intrinsic colours\n$(H-K)_\\circ\\sim 0.22$ with 0.1\\MAG\\ dispersion (Hunt et al. \\cite{hunt})\nand the color correction due to the non-standard filters used by NICMOS\nis negligible -- $(H-K)_\\circ\\sim 0.26$ instead of 0.22.\nIn the region of the \\PA\\ ring,\nthe average color $H-K=1.1$ yields $\\AV\\simeq 11$,\nin fair agreement with the estimate $\\AV>13$ from the Balmer\ndecrement presented below. In knot B $(H-K)=1.2$ yields $\\AV=12.5$, while\nin knot C $(H-K)=0.64$ yields $\\AV=5.2$. \n\nA different reddening estimate can be derived from the analysis\nof Hydrogen line ratios. We can estimate the reddening to \"Knot B\" and \"Knot C\"\nby using the images and spectra published by \nMoorwood et al. (\\cite{moorwood96a}).\nThe inferred reddening (assuming an intrinsic ratio Pa$\\alpha$/H$\\alpha$=0.18,\nand $A(\\HA)=0.81\\AV$, $A(\\PA)=0.137\\AV$) is \\AV=3.2 for Knot B and\n\\AV=3.8 for Knot C.\nWe can also estimate a lower limit to the reddening on the \n\\PA\\ ring. Considering a region $\\sim 11\\arcsec\\times5\\arcsec$ aligned\nalong the galactic plane, including all the stronger \\PA\\ emission, \nwe find $\\PA/\\HA>500$ which corresponds to $\\AV>13$mag, a value\nin agreement with the estimate given by Moorwood \\& Oliva (\\cite{moorwood88}),\n$\\AV=14\\pm3$, from the \\BA/\\BG\\ ratio in a $6\\arcsec\\times6\\arcsec$\naperture centered on the IR peak.\n\nWe note that the first approach measures the mean extinction of the starlight,\nwhile the second one measures the extinction toward the HII regions.\nTherefore, these \\AV\\ estimates indicate that in the case of Knot C\nthe star light and the emitting gas are located behind the same screen.\nConversely, Knot B has a lower extinction and must therefore be\nlocated in front of the screen hiding the star light.\nA likely interpretation is that Knot C is located within the galactic \nplane on the walls of the cavity farthest from us.\nwhereas Knot B is \nlocated above the galactic plane, toward the observer\n \nIt appears that the hypothesis of screen extinction\ncan provide reasonable results.\nOf course the true extinction, i.e. the optical depth at a\ngiven wavelength, is larger if dust is mixed with the emitting regions.\nHowever, it should be noted that the case in which dust is completely\nand uniformly mixed with the emitting regions does not apply here\nbecause the observed color excesses are larger than the maximum\nvalue expected in that case ($E(H-K)\\sim 0.6$).\n\n\\subsection{CO Index}\n\nA straight computation of the CO stellar index as\\\\\n$W(CO)=m(CO)-m(K)$,\nwhere $m(CO)$ and $m(K)$ are the magnitudes in the\nCO and K filters, is hindered by the high extinction\ngradients.\nTherefore we have corrected for the reddening using the \nprescription described above:\n\\begin{equation}\nW(CO) = m(CO)-m(K)+\\frac{c(K)-c(CO)}{c(H)-c(K)}E(H-K)\n\\end{equation}\nwhere, as above, the $c$ coefficients represent the wavelength dependence of\nthe reddening law. The correction is $0.145\\, E(H-K)$ which is important\nsince the expected CO index is $\\sim 0.2$.\n\nThe \"corrected\" photometric CO index map is displayed in Fig. \\ref{fig:line}e.\n\nAs a check, in the central $4\\arcsec\\times 4\\arcsec$ we derive\na photometric CO index of 0.18 which is in good\nagreement with the value 0.22 obtained from spectroscopic observations by\nOliva et al. (\\cite{oliva95}), when one takes into account the uncertainties\nof reddening correction.\n\nIn the central region there are three knots\nwhere the CO index reaches values $\\simeq 0.25$ aligned along\nthe galactic disk.\nHowever, we do not detect \nany clear indication of dilution by a spatially unresolved source,\nthat would be expected in the case of emission by hot \n($\\sim 1000\\K$) dust heated by the AGN.\nThere are regions close to the location of the H$_2$O maser where\nthe CO index is as low as 0.08 but that value is still consistent\nwith pure stellar emission or, more likely, with an imperfect\nreddening correction.\n\n\\subsection{\\label{sec:AGNactiv}AGN activity}\n\nThe NICMOS observations presented in this paper\nwere aimed at detecting near-IR traces of AGN activity\nin the central ($R<10\\arcsec$) region of NGC 4945. Indeed, recent NICMOS studies exploiting the high spatial resolution of HST\nshow that active galactic nuclei are usually\ncharacterized by prominent point sources in K, \ndetected e.g. in the Seyfert 2 galaxies\nCircinus (Maiolino et al. \\cite{maiolino99}) \nand NGC 1068, and the radio galaxy\nCentaurus A (Schreier et al. \\cite{schreier98}). \nNGC 4945 does not show any point-like emission at the position of the nucleus\n(identified by the \\water\\ maser) and the \nupper limit to the nuclear emission is\n$F_\\lambda(\\mathrm{F222M})<2\\xten{-13}\\ERG\\CM\\2\\S\\1\\MIC\\1$.\n\nWe also do not detect any dilution of the\nCO absorption features by hot dust emission, as observed in many \nactive galaxies (Oliva et al. \\cite{oliva99b}). \nFrom the analysis of the CO index image, non-stellar light contributes less\nthan $F_\\lambda(\\mathrm{F222M})<6\\xten{-14}\\ERG\\CM\\2\\S\\1\\MIC\\1$\nthus providing a tighter upper limit than above.\n\nThe lack of a point source in the ground based L and N observations \nalso places upper limits on the mid-IR emission, though less tight \ndue to the lower sensitivity and spatial resolution\n($F_\\lambda(\\mathrm{L})<1.2\\xten{-12}\\ERG\\CM\\2\\S\\1\\MIC\\1$ and\n$F_\\lambda(\\mathrm{N})<6.0\\xten{-13}\\ERG\\CM\\2\\S\\1\\MIC\\1$).\n\nFinally, type 2 AGNs are usually characterized by ionization cones \ndetected either in line images or in \nexcitation maps, i.e. ratios between high and\nlow excitation lines (usually \\OIII\\ and \\HA) revealing\nhigher excitation than the surrounding medium.\nIn NGC 4945 the equivalent width of \\PA\\ and the \\PA/\\Hmol\\ \nratio indeed show a cone morphology but the behaviour is the\nopposite of what expected, i.e. the excitation \nwithin the cone is lower than in the surroundings and\nthe H$_2$/Pa$\\alpha$ ratio increases up to $\\sim 5$ (see Fig. \\ref{fig:line}d).\nTwo processes could be responsible for the enhanced \\Hmol\\ emission --\neither shocks caused by the interaction between the supernova-driven wind\nand the interstellar medium or exposure to a strong X-ray dominated\nphoton flux emitted by the AGN. But in any case there is absolutely no\nindication of the strong UV flux which produces ``standard'' AGN ionization\ncones.\n\nWe find, therefore, no evidence for the expected AGN markers in our NICMOS\ndata.\n\n\\section{\\label{sec:discuss}Discussion}\n\nAlthough no trace of its presence has been found in these data,\nthe existence of an obscured AGN in the nucleus of\nNGC 4945 is unquestionably indicated by the\nX-rays (Iwasawa et al. \\cite{iwasawa93}, Done et al. \\cite{done96}).\nRecent, high signal-to-noise observations by BeppoSAX\n(Guainazzi et al., \\cite{guainazzi}) have confirmed the\nprevious indications of variability \nfrom Ginga observations (Iwasawa et al. \\cite{iwasawa93}):\nin the 13-200 keV band, where\nthe transmitted spectrum is observed, the light curve \nshows fluctuations with an\nextrapolated doubling/halving time scale of $\\tau\\sim 3-5\\xten{4}\\S$.\nThese time scales and amplitudes essentially exclude any known\nprocess for producing the high energy X-rays other than \naccretion onto a supermassive black hole.\n\nMaking the 3\\xten{42}\\ERG\\S\\1\\ observed in the\n2-10\\KEV\\ band with BeppoSAX would require about 10000\nof the most luminous X-ray binaries observed in our Galaxy \n(e.g. Scorpio-X1) and only a few of this objects are known.\n\nAlternatively, very hot plasma ($KT\\sim$ a few \\KEV), due to \nsupernovae, has been observed in the 2-10\\KEV\\ spectrum of starburst\ngalaxies, but at higher\nenergies ($>30\\KEV$) the emission is essentially negligible\n(Cappi et al. \\cite{cappi}; Persic et al. \\cite{persic});\nwhereas the\nemission of NGC4945 peaks between 30 and 100\\KEV. Also, given that the X-ray\nemission is observed through a gaseous absorbing column density\nof a few times \\ten{24}\\CM\\2, both\nthe 10000 superluminous X-ray binaries and the very hot SN wind should be\nhidden by this huge gaseous column. It is very difficult to find a geometry for\nthe gas distribution that could produce this effect. We\ntherefore conclude that the presence of an AGN provides \nthe only plausible origin of the hard X-ray emission.\n\nThe above considerations combined with the absence of any evidence for the\npresence of an AGN at other wavelengths\nhas important consequences irrespective of the relative,\nand unknown, contributions of the starburst and AGN to the total bolometric\nluminosity.\nThis is illustrated below by considering the extreme possibilities that the\nluminosity is dominated either by the starburst or the AGN.\n\n\\subsection{NGC 4945 as a starburst dominated object}\n\nMost previous studies have concluded that the FIR emission in NGC 4945\ncan be attributed solely to starburst activity (e.g. Koornneef \\cite{koorn},\nMoorwood \\& Oliva \\cite{moorwood94a}) without invoking \nthe presence of an AGN.\n\nWe note that, on average, active galaxies are characterized by \n$L_{FIR}/L_{Br\\gamma}$ ratios much larger than starbursts\nand this fact was sometimes invoked to discern starbursts\nfrom AGNs (see the discussion in Genzel et al. \\cite{genzel98}).\nIn this regard, NGC 4945 has a starburst-like ratio:\n$\\LFIR/L_\\mathrm{Br\\gamma}\\sim1.4\\xten{5}$\n(from observed \\PA\\ with \\AV=15mag). This is similar to the \nvalue for the prototypical starburst galaxy M82\n($\\LFIR/L_\\mathrm{Br\\gamma}\\sim3.4\\xten{5}$, Rieke et al. \\cite{rieke80}),\nsuggesting that the FIR emission of NGC 4945\nmay arise from the starburst.\n\nGenzel et al. (\\cite{genzel98})\nshowed that, when considering the reddening\ncorrection derived from the mid-IR -- usually much larger than from the optical\nand near-IR -- the observed H line emission from the\nstarburst translates into an\nionizing luminosity comparable to the FIR luminosity.\nIndeed, if in NGC 4945 the bulk of H emission is hidden by just \\AV=45mag,\n$\\LFIR/L_\\mathrm{ion}\\sim 1$ and the observed starburst activity\nis entirely responsible for the FIR.\n\n\n\\begin{figure*}\n\\centerline{\n\\epsfig{figure=marconi_f4.ps,width=\\linewidth}}\n\\caption{\\label{fig:sbmod} Properties of a burst of star formation as a\nfunction of the time elapsed from the beginning of the burst\n(models by Leitherer et al. 1999).\nThe thick solid line represents an instantaneous burst with mass\n$3.5\\xten{7}\\Mo$. The thick dashed line is a continuous star formation\nrate of $0.13\\Mo\\YR\\1$. See text for more details on the models.\nPanel 1 is the time dependence of the ionizing photon rate. The shaded\narea limits values consistent with observations. The thin dotted line is drawn \nat a time in which the \"instantaneous\" burst meets the observational\nconstraints. The crossed square represents the combination of the properties\nof the two models at $t=10^{7.4}\\YR$.\nPanel 2 gives the \\BG\\ equivalent width. The shading outline the lower limit \ngiven by observations. The other symbols are as in panel 1.\nPanel 3 gives the Supernova Rate. As above the shaded area limits\nthe range of values allowed from observations. Symbols as in panel 1.\nPanel 4 gives the mechanical luminosity. Symbols as in panel 1.\nPanel 5 gives the monochromatic luminosity\nin the K band (\\ERG\\S\\1\\AA). Symbols as in panel 1.\nPanel 6 gives the bolometric luminosity of the burst.\nThe shading marks the upper limit set by the total IRAS\nluminosity of the galaxy.}\n\\end{figure*}\n\nAlthough all the bolometric luminosity could be generated by a starburst \nit is also possible to construct starburst models which are consistent with the\nobserved near infrared properties but generate a much lower total luminosity.\nIt is important to recall that $\\LFIR/L_{\\BG}$\nrepresents the ratio between star formation rates\naveraged over two different timescales, i.e. $>10^8$yrs and $<10^7$yrs,\nrespectively. Therefore, this ratio strongly depends on the \npast star formation history. For example, objects which have not\nexperienced star formation in the past $10^7$yrs will emit\nlittle \\BG, but significant FIR radiation.\nA more quantitative approach is presented in\nFig. \\ref{fig:sbmod} where we compare the observed nuclear properties\nof NGC 4945 with \nsynthesis models by Leitherer et al. (\\cite{leitherer}).\nWe have considered two extreme cases of star formation history.\nThe thick solid line in the figure represents an instantaneous burst \nwith mass $3.5\\xten{7}\\Mo$ whereas the thick dashed line is a continuous \nstar formation rate of $0.13\\Mo\\YR\\1$.\nIn both cases a Salpeter initial mass function (i.e. $\\propto M^{-2.35}$),\nupper mass cutoff of 100\\Mo\\ and abundances $Z=\\Zo$ are chosen.\nPanel 1 shows the evolution of the ionizing photon rate\n(\\QH) as a function of time after the beginning of the burst.\nThe shaded region limits the values compatible with the observations;\n\\QH\\ is estimated from the total \\PA\\ flux in the \nNICMOS images ($5.6\\xten{-13}\\ERG\\S\\1\\CM\\2$),\ndereddened with $A_V=5$mag and $A_V=20$mag and converted \nusing case B approximation for H recombinations.\nPanel 2 gives the equivalent width\nof \\BG\\ ($W_\\lambda(\\BG)$); the observed value\noutlined by the shaded area is a lower limit\nfor the starburst models and was derived by rescaling the observed \\PA\\\nflux and dividing by the flux observed in the same aperture with the F222M\nfilter.\nPanel 3 is the evolution of the SuperNova Rate (SNR).\nEstimates of SNR from radio\nobservations suggest values $>0.3\\YR\\1$ (Koornneef \\cite{koorn}), $0.2\\YR\\1$ \n(Forbes \\& Norris \\cite{forbes}),\ndown to 0.05\\YR\\1 (Moorwood \\& Oliva \\cite{moorwood94a}). \nThe shaded region covers the 0.01-0.4\\YR\\1\\ range.\nPanel 4 is the mechanical luminosity produced by the Supernovae.\nFinally, panels 5 and 6 give the K-band and\nbolometric luminosity, respectively.\nThe allowed range for the K monochromatic luminosity\nis given by the total observed flux in a $6\\arcsec\\times 6\\arcsec$ aperture\ncentered on the K peak where photospheric emission from supergiants\nis known to dominate (Oliva et al. \\cite{oliva99b}).\nThe upper and lower limits represent\nthe values obtained after dereddening by $A_V=5$mag and $A_V=20$mag.\nThe upper limit to the bolometric\nluminosity is the {\\it total} NGC 4945 luminosity derived from IRAS observations\n(Rice et al. \\cite{rice88}).\nIn all cases the thin dotted line represents the time at which the properties\nof the instantaneous burst meet the observational constraints.\nThe crossed square represent the combination of the two models\nat $t=\\ten{7.4}\\YR$.\n\nIt is clear from the figure that an instantaneous burst of $t\\sim\\ten{6.8}\\YR$\nis capable of meeting all the observational constraints. It reproduces the\ncorrect supernova rate and K band luminosity and its bolometric luminosity\ndominates the total bolometric luminosity of the galaxy.\nConversely the continuous burst fails to reproduce the SNR and K luminosity.\nJust considering these two models alone it is tempting to infer\nthat the starburst\npowers the bolometric emission of NGC4945.\nHowever, the instantaneous and continuous SFR are two extreme and simplistic\ncases. More realistically the SF history is more complex since bursts\nhave a finite and limited length or are the combination of several \ndifferent events. As an example we consider\nthe case of two bursts of star formation taking place at\nthe same time: one instantaneous and the other continuous. Both have the\nsame characteristics as the bursts presented above.\nThe properties of this double burst model at $t=\\ten{7.4}\\YR$ are shown \nin the figure by the crossed squares. The choice of the time\nis arbitrary and any other value between $\\ten{7.2}\\YR$ and $\\ten{7.5}\\YR$\nmight do.\nEven in this case the starburst model meets all the observational\nconstraints: \\QH\\ is provided for by the continuous burst while\nSNR and K luminosity come from the instantaneous burst.\nThe important difference with respect to the single instantaneous\nburst is that the bolometric luminosity of the burst is\nnow $\\lesssim 20\\%$ of the total bolometric luminosity of the galaxy.\n\nThe mechanical luminosity injected by the SN in the \"instantaneous\"\nburst (which dominates also in the double burst model)\nis $\\sim \\ten{8.5}\\Lo$ over $\\sim \\ten{7.4}\\YR$. This results\nin a total injected energy of $\\sim 10^{57}\\ERG$ which is more than enough\nto account for the observed superwind.\nIndeed Heckman et al. (\\cite{heckman}) estimate\nan energy content of the winds\nblown cavity of $\\sim 1.5\\xten{55}\\ERG$\n(after rescaling for the different adopted distance of NGC 4945).\nBoth models agree with the constraints imposed by dynamical measurements \nthat the central mass in stars must be less than 6.6\\xten{8}\\Mo\\\n(Koornneef \\cite{koorn}, after rescaling for the different assumed distances of\nthe galaxy): the continuous SFR would require 5\\xten{9}\\YR\\\nto produce that mass of stars.\n\nIn conclusion, two different star formation histories can reproduce\nthe observed starburst properties but only in one case\ndoes the starburst dominate the bolometric luminosity of the galaxy.\nTherefore the available data\ndo not allow any constraints on the bolometric luminosity of the starburst.\n\nAs shown in the next section, the observed (\\LFIR/\\LX) ratio\nof NGC 4945 is equal to that of a \"normal\" AGN in which the\n\\LFIR\\ is reprocessed UV radiation. If the \\LFIR\\ in NGC 4945 is actually \ndominated by the starburst, therefore, it is clear that the AGN must\nbe strongly deficient in UV relative to X-rays.\n\nIn this starburst-dominant scenario for NGC4945, \nwith the black hole mass inferred from the \\water\\ maser\nmeasurements (Greenhill. et al. \\cite{greenhill}), the AGN is emitting\nat \\lesssim 10\\% of its Eddington Luminosity.\n\n\n\\subsection{NGC 4945 as an AGN dominated object}\n\n\\begin{figure}\n\\epsfig{figure=marconi_f5.ps,width=\\linewidth}\n\\caption{\\label{fig:compare}\nSpectral energy distributions of NGC 4945 (upper panel) and\nCircinus (lower panel). \"Stars\" are the IRAS\nphotometric points (except for the points with the highest wavelength\nwhich are from baloon-borne observations). \"K\", \"L\", \"M\" and \"N\"\nare the points in the standard photometric bands. The hatched areas\nlabeled as \"Starburst\" and \"AGN\" represent the continuum levels\nderived from the ionizing photon rates (see text) emitted by starburst \nand AGN, respectively. The \"100\\KEV\" points are from X-ray observations.\nThe IR spectrum of Circinus (solid line in lower panel) is plotted in the\nupper panel (dotted line) after rescaling to match the 100\\KEV\\ points.\nThe solid line in the upper panel is the same spectrum after extinction\nby an extra $\\AV=150\\MAG$ (see text for details). }\n\\end{figure}\n\nBy fitting the simultaneous 0.1-200 keV spectrum from BeppoSAX,\nthe absorption corrected luminosity in the 2-10 keV band\nis $\\LX(2-10\\KEV) = 3\\xten{42}\\ERG\\S\\1$ (Guainazzi et al., \\cite{guainazzi}).\nIf the AGN in NGC 4945 has an intrinsic spectral energy distribution\nsimilar to a quasar, then\n$\\LX(2-10\\KEV)/L_{\\rm bol}\\sim 0.03$ (Elvis et al. \\cite{elvis}) therefore\n$(L_{\\rm bol})_{\\rm AGN}\\sim \\ten{44}\\ERG\\S\\1 = 2.6\\xten{10}\\Lo$\nwhich is the {\\it total} far-IR luminosity of NGC 4945, measured by IRAS\n(Rice et al., \\cite{rice88}).\nThus, a \"normal\" AGN in NGC 4945 {\\it could} in principle\npower the total bolometric luminosity.\n\nFor this scenario, we compare NGC 4945 with a nearby obscured object,\nthe Circinus galaxy,\nnow considered an example of a ``standard'' Seyfert 2 galaxy\n(c.f. Oliva et al. \\cite{oliva94}, Oliva et al. \\cite{oliva98}, \nMaiolino et al. \\cite{maiolino98}, Matt et al. \\cite{matt99},\nStorchi-Bergmann et al. \\cite{storchi99}, Curran et al. \\cite{curran}).\nIn particular, Oliva, Marconi \\& Moorwood (\\cite{oliva99}) and,\npreviously, Moorwood et al. (\\cite{moorwood96c})\nshowed that the total energy output from the AGN required to \nexplain the observed emission line spectrum is comparable to the\ntotal FIR luminosity, concluding that any starburst contribution\nto the bolometric luminosity is small (\\lesssim 10\\%).\nThe choice of the Circinus galaxy is motivated by the \nsimilar distance (D=4\\MPC), FIR and hard X-ray luminosities as NGC 4945\n($\\LFIR\\sim1.2\\xten{10}\\Lo$; Siebenmorgen et al., \\cite{sieben} --\n$\\LX(2-10\\KEV)\\sim 3.4-17\\xten{41}\\ERG\\S\\1$; Matt et al., \\cite{matt99}).\nNote that its $\\LX (2-10\\KEV)/\\LFIR$ ratio ($\\sim 0.01-0.05$)\nis consistent with the average value for quasars (Elvis et al., \\cite{elvis}).\n\n\nThe overall spectral energy distributions of NGC 4945 and Circinus\nare compared in Fig. \\ref{fig:compare}.\nThe \"stars\" represent the IRAS photometric points (except for the\npoints with the largest wavelength which are the 150\\MIC\\\nmeasurements by Ghosh et al. \\cite{ghosh92}).\nIn NGC 4945 the points labeled with \"K\", \"L\" and \"N\" are the upper limits\nderived from our observations, while in Circinus they represent emission from\nthe unresolved nuclear source corrected for stellar emission\n(Maiolino et al. \\cite{maiolino98}).\nThe points labeled \"100 keV\" are from Done et al. \\cite{done96} (NGC 4945)\nand Matt et al. \\cite{matt99} (Circinus).\nThe bars between 13.6 and 54.4 eV are at a level given by\n$\\nu L_\\nu\\sim Q(\\mathrm{H}) <h\\nu>$, where $Q(\\mathrm{H})$ is the rate\nof H-ionizing photons and $<h\\nu>$ is the mean photon energy of the ionizing\nspectrum. For NGC 4945, $Q(\\mathrm{H})$ is derived from H recombination \nlines and thus represent \nthe energy which is radiated by the young starburst; \nwe assumed $<h\\nu>=16\\EV$.\nFor Circinus, the point labeled with \"Starburst\" is similarly derived\nfrom Br$\\gamma$ emission associated with the starburst\n(Oliva et al. \\cite{oliva94}) while that labeled \"AGN\"\nis from the estimate made by Oliva, Marconi \\& Moorwood (\\cite{oliva99}).\n\nIn the lower panel, we represent the IR spectrum of Circinus by connecting\nthe photometric points just described. We plot this same spectrum as a dotted line\nin the upper panel, rescaling to match the\n100 keV points. NGC 4945 and Circinus have similar X/FIR ratios:\\\\\n$\\nu L_\\nu(100 keV) / L_{FIR} \\simeq 2\\xten{-3}$ for Circinus\nand $\\simeq 3\\xten{-3}$ for NGC 4945.\nNote that, at each wavelength, both Circinus and NGC 4945 were observed\nwith comparable resolution.\n\nIf the AGN in NGC 4945 dominates the luminosity and its intrinsic spectrum\nis similar to that of Circinus, then the lack of AGN detections in the near-IR\nand mid-IR require larger obscuration.\nIn particular the non-detection of a K band point source or of dilution\nof the CO features can be used to estimate the extinction at 2.2\\MIC.\nIn Circinus from Maiolino et al. \\cite{maiolino98} (K band) and\nMatt et al. \\cite{matt99},\nwe can derive $\\nu L_\\nu (K) / \\nu L_\\nu (100 keV)\\simeq 0.5$.\nIf NGC 4945 has a similar near-IR over hard-X-rays ratio then,\ngiven $\\nu L_\\nu (K) / \\nu L_\\nu (100 keV) < 8\\xten{-4}$\n(K band upper limit from CO and X-ray data from\nDone et al. \\cite{done96}), \nthe extinction toward the nucleus is\n$\\Delta \\mathrm{A}_\\mathrm{K}>7$mag (i.e. $\\Delta\\AV>70$mag) \nlarger than in the case of Circinus.\nHot dust in NGC 4945 must be hidden by at least \n$\\AV>135\\MAG$, in agreement with the estimate by\nMoorwood \\& Glass (\\cite{moorwood84}),\n$\\AV>70$ and, more recently, with an analysis of ISO CVF spectra\nimplying $\\AV\\sim 100\\MAG$ (Maiolino et al., 2000, in preparation).\nWe note that the required extinction is not unexpected\nand in agreement with the X-ray measurements.\nThe measured column density in absorption in the X-rays is \n$N_\\mathrm{H}\\sim {\\rm few}\\xten{24}\\CM\\2$ therefore the expected $A_V$,\nassuming a galactic gas-to-dust ratio is:\n\\begin{equation}\nA_V\\sim 450 \\left( \\frac{N_\\mathrm{H}}{\\ten{24}\\CM\\2} \\right)\n\\end{equation}\nThe $A_V$ measured from optical/IR data is estimated smaller\nthan derived from X-rays ($A_V(\\mathrm{IR})\\sim 0.1-0.5\\, A_V(\\mathrm{X})$;\nGranato, Danese \\& Franceschini \\cite{granato}),\ntherefore the X-ray absorbing\ncolumn density is in excellent agreement with the required extinction.\nVery high extinction, expected in the frame of the unified AGN model\nare observed in many objects as discussed and summarized,\nfor instance, in Maiolino et al. \\cite{maiolino98b}\nand in Risaliti et al. \\cite{risaliti}. \n\nThe higher extinction can also qualitatively explain the redder\ncolors of the NGC 4945 FIR spectrum.\nThe solid line\nin the upper panel is the spectrum of Circinus after applying\nforeground extinction\nby $\\AV=150\\MAG$. We have applied the extinction law by Draine\n\\& Lee (\\cite{draine}) and the energy lost in the mid-IR has been reprocessed\nas 40\\K\\ dust emission (i.e. black body emission at 40\\K\\ corrected\nfor $\\WL^{-1.75}$ emissivity).\nThough a careful treatment requires a full radiation transfer calculation,\nthis simple plot demonstrates that (i) the redder color of NGC 4945 with\nrespect to Circinus can be explained with extra absorption and (ii) that \nthis is not energetically incompatible with the observed FIR luminosity,\ni.e. the absorbed mid-IR emission re-radiated\nin the FIR does not exceed the observed points.\n\nIf the FIR emission is powered by the AGN this is UV radiation re-processed\nby dust. However, if the AGN emits $\\sim 2\\xten{10}\\Lo$ in UV photons,\nhigh excitation gas emission lines should also be observed.\nThe absence of high ionization lines like\n\\OIII$\\lambda 5007,4959$\\AA\\ (Moorwood et al. \\cite{moorwood96a})\nor \\NeV$\\lambda 14.3\\MIC$ (Genzel et al. \\cite{genzel98}) \nand the low excitation observed in the wind-blown cone strongly\nargues that no ionizing UV photons\n(i.e. $13.6\\le \\HNU < 500\\EV$) escape from the inner\nregion.\nThe low excitation H$_2$/Pa$\\alpha$ map,\nassociated with the peak in H$_2$\nemission close to the nucleus location, indicates that \nALL ultraviolet photons must be absorbed within\n$R<1\\farcs5$, i.e. $R<30\\PC$ along ALL lines of sight.\nThis is in contrast with the standard unified model of AGN\nwhere ionizing radiation escapes\nalong directions close to the torus axis.\n\nIf the AGN is embedded in a thick dusty medium then two\neffects will contribute to its obscuration. First, \ndust will compete with the gas in absorbing UV photons\nwhich will be directly converted into infrared radiation\n(e.g. Netzer \\& Laor \\cite{netzer93},\nOliva, Marconi \\& Moorwood \\cite{oliva99}). Second,\nemission lines originating in this medium\nwill be suppressed by dust absorption. To estimate the amount of required\nextinction, note that in Circinus $\\NeV 14.3\\MIC/\\NeII 12.8\\MIC=0.4$\n(extinction corrected) and in NGC 4945 \\NeV/\\NeII$\\le 0.008$\n(both ratios are from Genzel et al. \\cite{genzel98}).\nIf NGC4945 has the same intrinsic ratio as Circinus, then the observed\n\\NeV/\\NeII\\ ratio requires $A(14.3\\MIC)>4.2$mag \ncorresponding to $\\AV>110$mag and in agreement\nwith the above estimates.\n\nWe conclude that the AGN can power the FIR emission if it is properly obscured. Inferring\nthe black hole mass from the \\water\\ maser\nobservations ($1.4\\xten{6}\\Mo$, Greenhill. et al. \\cite{greenhill}), we find in this scenario that\nthe AGN is emitting\nat $\\sim 50\\%$ of its Eddington Luminosity.\n\n\\subsection{On the existence of completely hidden Active Galactic Nuclei}\n\nAs discussed above, if an AGN powers the FIR\nemission of NGC 4945, it must be hidden up to mid-IR \nwavelengths and does not fit in the standard unified model. \nThe possible existence of such a class of Active Nuclei,\ndetectable only at $>10\\KEV$,\nwould have important consequences on the interpretation of\nIR luminous objects whose power source is still debated.\n\nGenzel et al. (\\cite{genzel98}) and Lutz et al. (\\cite{lutz98}) compared\nmid-IR spectra of Ultra Luminous IRAS galaxies (ULIRGs, see\nSanders \\& Mirabel \\cite{sanders96} for a review) with those of AGN and\nstarburst templates. They concluded that the absence of high excitation lines\n(e.g. \\NeV) and the presence of PAH features\nundiluted by strong thermal continuum in ULIRGs spectra\nstrongly suggest that the starburst component is dominant.\nThey also show that, after a proper extinction correction,\nthe observed star formation activity can power FIR emission.\nIn their papers, NGC 4945 is classified as a starburst \nbecause of its mid-IR properties but, as shown in the previous section, \nNGC 4945 could also be powered by a highly obscured AGN\nand the same scenario could in principle apply to all ULIRGs.\nTheir bolometric emission can be powered by an active nucleus\ncompletely obscured even at mid-IR wavelengths. \n\nThe same argument could be used for \nthe sources detected at submillimeter wavelengths by SCUBA\nwhich can be considered\nas the high redshift counterpart \nof local ULIRGs. If they are powered by hidden active nuclei then\ntheir enormous FIR emission would not require star formation\nrates in excess of $>100\\Mo\\YR\\1$ (e.g. Hughes et al. \\cite{hughes98}),\nand this would have important consequences for understanding the history\nof star formation in high redshift galaxies.\n\nIn addition, it is well known that in order to explain the X-ray background\na large fraction of obscured AGN is required. However\nGilli et al. (\\cite{gilli99}) have shown that, in order to reconcile\nthe observed X-ray background with hard X-ray counts, a rapidly\nevolving population of hard X-ray sources is required\nup to redshift $\\sim 1.5$. No such population is\nknown at the moment and the only class of objects which are known\nto undergo such a rapid density evolution are local ULIRGs\n(Kim et al. \\cite{kim98}) and, at higher redshift,\nthe SCUBA sources (Smail et al. \\cite{smail97}).\nSCUBA sources are therefore candidates to host a population\nof highly obscured AGNs.\n\nAlmaini et al. (\\cite{almaini99}) suggest that, if the SED of high redshift\nAGN is similar to those observed locally, one can explain\n10--20\\% of the 850\\MIC\\ SCUBA sources at 1 mJy.\nThis fraction could be significantly higher if a large\npopulation of AGN are Compton thick at X-ray wavelengths.\nTrentham, Blain \\& Goldader (\\cite{trentham}) show that if the SCUBA sources\nare completely powered by a dust enshrouded AGN then they may\nhelp in explaining the discrepancy between the local density in \nsuper massive black holes and the high redshift AGN component\n(see also Fabian \\& Iwasawa \\cite{fabian99}). \n\nEstablishing the nature of SCUBA sources could be extremely\ndifficult if the embedded AGNs are like NGC4945, i.e.\ncompletely obscured in all directions, because they would then not be\nidentifiable with the standard optical/IR diagnostics.\nIncidentally, this fact could possibly account for the sparse detections\nof type 2 AGNs at high redshifts (Akiyama et al. \\cite{akiyama}).\n\nThe best possibility for the detection of NGC4945-like AGNs is \nvia their hard X-ray emission but, unfortunately,\nthe sensitivity of existing X-ray surveys is still not high enough \nto detect high $z$ AGN and the low spatial resolution makes identifications\nuncertain in the case of faint optical/near-IR counterparts.\nMoreover, hard X-rays alone are not enough to establish if the AGN\ndominates the bolometric emission.\n\n\\section{\\label{sec:conclus}Conclusions}\n\nOur new HST NICMOS observations of NGC 4945, complemented by new ground\nbased near and mid-IR observations, have provided detailed morphology\nof the nuclear region. In \\PA, we detect a 100pc-scale starburst ring while\nin \\Hmol\\ we trace the walls of a conical cavity blown by\nsupernova driven winds. The continuum images are strongly affected by\ndust extinction but show that even at HST resolution and sensitivity,\nthe nucleus is completely obscured by a dust lane with an elongated, disk-like\nmorphology.\nWe detect neither a strong point source nor dilution in CO \nstellar features, expected signs of AGN activity.\n\nWhereas all the infrared properties of NGC 4945 are consistent with starburst\nactivity, its strong and variable hard X-ray emission cannot be plausibly \naccounted for without the presence also of an AGN.\nAlthough the starburst must contribute to the total bolometric luminosity\nwe have shown, using starburst models, that the actual amount is dependent on the star formation history. A major contribution from the AGN is thus not\nexcluded. Irrespective of the assumption made, however, our most important \nconclusion is that the observed variable hard X-ray emission combined\nwith the lack of evidence for reprocessed UV radiation in the\ninfrared is incompatible with the \"standard\" AGN model. If the AGN dominates\nthe bolometric luminosity, then its UV radiation must be totally obscured along all lines of sight. If the starburst dominates then the AGN must be \nhighly deficient in its UV relative to X-ray emission. The former case clearly raises the possibility that a larger fraction of ULIRGs than currently\nthought could actually be AGN rather than starburst powered.\n\n\\begin{acknowledgements}\nA.M. and A.R. acknowledge the partial support of the Italian Space Agency (ASI)\nthrough grants ARS--98--116/22 and ARS--99--44\nand of the Italian Ministry for University\nand Research (MURST) under grant Cofin98-02-32.\nE.J.S. acknowledge support from STScI GO grant O0113.GO-7865.\nWe thank Roeland P. van der Marel for the use of the pedestal\nestimation and quadrant equalization software.\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n%\n\\bibitem[1999]{akiyama}\nAkiyama M., et al., 1999, Proceeding of the first XMM workshop\n\"Science with XMM\", in press (astro-ph/9811012)\n%\n\\bibitem[1999]{almaini99}\nAlmaini O., Lawrence A., Boyle B.J., 1999, MNRAS, 305, L59 \n%\n\\bibitem[1985]{baan85}\nBaan W.A., 1985, Nature, 315, 26\n%\n\\bibitem[1996]{biretta}\nBiretta J.A., et al., 1996, {\\it WFPC2 Instrument Handbook}, \nVersion 4.0 (Baltimore:STScI)\n%\n\\bibitem[1999]{blain}\nBlain A.W., Kneib J.P., Ivison R.J., Smail I., 1999, ApJ, 512, L87\n%\n\\bibitem[1988]{brock88}\nBrock D., 1988, ApJ, 329, 208\n%\n\\bibitem[1997]{bushouse}\nBushouse H., Skinner C.J., MacKenty J.W., 1997,\n{\\it NICMOS Instrument Sci. Rept. 97-28} (Baltimore:STScI)\n%\n\\bibitem[1999]{cappi}\nCappi M., et al., 1999, A\\&A, 350, 777\n%\n\\bibitem[1995]{comastri}\nComastri A., Setti G., Zamorani G., Hasinger G., 1995, A\\&A, 296, 1\n%\n\\bibitem[1999]{curran}\nCurran S.J., et al., 1999, A\\&A, 344, 767\n%\n\\bibitem[1996]{done96}\nDone C., Madejski G.M., Smith D.A., 1996, ApJ, 463, L63\n%\n\\bibitem[1979]{dossantos}\nDos Santos P.M., Lepine J.R.D., 1979, Nature, 278, 34\n%\n\\bibitem[1984]{draine}\nDraine B.T., Lee H.M., 1984 ApJ, 285, 89\n%\n\\bibitem[1997]{elmouttie}\nElmouttie M., et al., 1997, MNRAS, 284, 830\n%\n\\bibitem[1994]{elvis}\nElvis M., et al., 1994, ApJS, 95, 1\n%\n\\bibitem[1998]{fabian98}\nFabian et al., 1998, MNRAS, 297, L11\n%\n\\bibitem[1999]{fabian99}\nFabian A.C., Iwasawa K., 1999, MNRAS, 303, L34\n%\n\\bibitem[1998]{forbes}\nForbes D.A, Norris R.P., 1998, MNRAS, 300, 757\n%\n\\bibitem[1998]{genzel98}\nGenzel R., Lutz D., Sturm E., Egami E., Kunze D., Moorwood A.F.M.,\nRigopoulou D., Spoon H.W.W., Sternberg A., Tacconi-Garman L.E.,\nTacconi L., Thatte N., 1998, ApJ, 498, 579\n%\n\\bibitem[1992]{ghosh92}\nGhosh S.K., et al., 1992, ApJ, 391, 111\n%\n\\bibitem[1999]{gilli99}\nGilli R., Risaliti R., Salvati M., 1999, A\\&A, 347, 424\n%\n\\bibitem[1997]{granato}\nGranato G.L., Danese L., Franceschini A., 1997, ApJ, 486, 14\n%\n\\bibitem[1997]{greenhill}\nGreenhill L.J., Moran J.M., Herrnstein J.R., 1997, ApJ, 481, L23\n%\n\\bibitem[2000]{guainazzi}\nGuainazzi M., et al., 2002000, A\\&A, in press (astro-ph/0001528)\n%\n\\bibitem[1990]{heckman}\nHeckman T.M., Armus L., Miley G.K., 1990, ApJS, 74, 833\n%\n\\bibitem[1998]{hughes98}\nHughes D.H., et al., 1998, Nature, 394, 241\n%\n\\bibitem[1997]{hunt}\nHunt L.K., Malkan M.A., Salvati M., et al., 1997 ApJS, 108, 229\n%\n\\bibitem[1993]{iwasawa93}\nIwasawa K., et al., 1993, ApJ, 409, 155\n%\n\\bibitem[1994]{kaufl}\nK\\\"aufl H.U., Jouan R., Lagage P.O., Masse P., Mestreau P., Tarrius A.,\n1994, Infrared Phys. Technol. 35, 203 \n%\n\\bibitem[1998]{kim98}\nKim D.-C., Sanders D.B., 1998, ApJS, 119, 41\n%\n\\bibitem[1993]{koorn}\nKoornneef J., 1993, ApJ, 403, 581\n%\n\\bibitem[1996]{koorn96}\nKoornneef J., Israel F.P., 1996, New Astronomy, 1, 271\n%\n\\bibitem[1999]{leitherer}\nLeitherer C., et al., 1999, ApJS, 123, 3\n%\n\\bibitem[1998]{lutz98}\nLutz D., Spoon H.W.W., Rigopoulou D., Moorwood A.F.M., Genzel R.,\n1998, ApJ, 505, L103\n%\n\\bibitem[1997]{mackenty}\nMacKenty J.W., et al., 1997, {\\it NICMOS Instrument Handbook}, \nVersion 2.0 (Baltimore:STScI)\n%\n\\bibitem[1995]{maiolino95}\nMaiolino R., Ruiz M., Rieke G.H., Keller L.D., 1995, ApJ, 446, 561\n%\n\\bibitem[1998a]{maiolino98}\nMaiolino R., Krabbe A., Thatte N., Genzel R., 1998, ApJ, 493, 650\n%\n\\bibitem[1998b]{maiolino98b}\nMaiolino R., Salvati M., Bassani L., Dadina M., della Ceca R., Matt G.,\nRisaliti G., Zamorani G., 1998, A\\&A 338, 781\n%\n\\bibitem[1999a]{maiolino99}\nMaiolino R., et al., 1999, ApJ, in press (astro-ph/9910160)\n%\n%\\bibitem[1994]{marconi94}\n%Marconi A., Moorwood A.F.M., Origlia L. and Oliva E., 1994, ESO Mess., 78, 20\n%\n\\bibitem[2000]{marconi99}\nMarconi A., Schreier E.J., Koekemoer A.,\nCapetti A., Axon D.J., Macchetto F.D., Caon N., 2000, ApJ, 528, 276\n%\n\\bibitem[1999]{matt99}\nMatt G., Guainazzi M., Maiolino R., Molendi S., Perola G.C., Antonelli L.A., \nBassani L., Brandt W.N., Fabian A.C., Fiore F., Iwasawa K., Malaguti G., \nMarconi A., Poutanen J., 1999, A\\&A, 341, L39\n%\n\\bibitem[1996]{mauersberger}\nMauersberger R., et al., 1996, A\\&A, 309, 705\n%\n\\bibitem[1984]{moorwood84}\nMoorwood A.F.M. and Glass I.S., 1984, A\\&A, 135, 281\n%\n\\bibitem[1988]{moorwood88}\nMoorwood A.F.M. and Oliva E., 1988, A\\&A, 203, 278\n%\n\\bibitem[1992]{moorwood92}\nMoorwood A.F.M., Finger G., Biereichel P., Delabre B.,\nVan Dijsseldonk A., Huster G., Lizon J. L., Meyer M., Gemperlein H.,\nMoneti A., 1992, The Messenger, 69, 61\n%\n\\bibitem[1994a]{moorwood94a}\nMoorwood A.F.M. and Oliva E., 1994a, ApJ, 429, 602\n%\n\\bibitem[1994b]{moorwood94b}\nMoorwood A.F.M., Finger G., Gemperlein H., 1994b, The Messenger, 77, 8\n%\n\\bibitem[1996a]{moorwood96a}\nMoorwood A.F.M., van der Werf P.P., Kotilainen J.K., Marconi A., Oliva E., \n1996a, A\\&A, 308, L1\n%\n\\bibitem[1996b]{moorwood96b}\nMoorwood A.F.M., Space Sci. Rev., 1996b, 77, 303\n%\n\\bibitem[1996c]{moorwood96c}\nMoorwood A.F.M., Lutz D., Oliva E., Marconi A., Netzer H., Genzel R., \nSturm E., de Graauw Th., 1996c, A\\&A, 315, L109\n%\n\\bibitem[1993]{netzer93}\nNetzer H., Laor A., 1993, ApJ, 404, L51\n%\n\\bibitem[1994]{oliva94}\nOliva E., Salvati M., Moorwood A.F.M., Marconi A., 1994, A\\&A, 288, 457\n%\n\\bibitem[1995]{oliva95}\nOliva E., Origlia L., Kotilainen J.K., Moorwood A.F.M., 1995, A\\&A, 301, 55\n%\n\\bibitem[1998]{oliva98}\nOliva E., Marconi A., Cimatti A., di Serego Alighieri S., 1998, 329, L21\n%\n\\bibitem[1999a]{oliva99}\nOliva E., Marconi A., Moorwood A.F.M., 1999a, A\\&A, 342, 87\n%\n\\bibitem[1999b]{oliva99b}\nOliva E., Origlia L., Maiolino R., Moorwood A.F.M., 1999b, A\\&A, 350, 9\n%\n\\bibitem[1998]{persic}\nPersic M., et al., 1998, A\\&A, 339, L33\n%\n\\bibitem[1988]{rice88}\nRice G.H., et al., 1988, ApJS, 68, 91\n%\n\\bibitem[1998]{richstone}\nRichstone D., et al., 1998, Nature, 395, 14\n%\n\\bibitem[1980]{rieke80}\nRieke G.H., et al., 1980, ApJ, 238, 24\n%\n\\bibitem[1999]{risaliti}\nRisaliti G., et al., 1999, ApJ 522, 157\n%\n\\bibitem[1997]{rowanrob}\nRowan-Robinson M., et al., 1997, MNRAS, 298, 490\n%\n\\bibitem[1996]{sanders96}\nSanders D.B., Mirabel I.F., 1996, ARA\\&A, 34, 749\n%\n\\bibitem[1998]{schreier98}\nSchreier E.J., Marconi A., Axon D.J., Caon N., Macchetto D., Capetti A.,\nHough J.H., Young S., Packham C., 1998, ApJ, 499, L143 (Paper~II)\n%\n\\bibitem[1997]{sieben}\nSiebenmorgen R., Moorwood A., Freudling W., Kaeufl H.U., 1997, A\\&A, 325, 450\n%\n\\bibitem[1998]{skinner}\nSkinner C.J., Bergeron L.E., Daou D., 1998, {\\it HST Calibration\nWorkshop}, ed. S. Casertano et al. (Baltimore:STScI), in press\n%\n\\bibitem[1997]{smail97}\nSmail I., Ivison R.J., Blain A.W., 1997, ApJ, 490, L5\n%\n\\bibitem[1999]{storchi99}\nStorchi-Bergmann T., et al., 1999, MNRAS, 304, 35\n%\n\\bibitem[1999]{trentham}\nTrentham N., Blain A.W., Goldader J., 1999, MNRAS, 305, 61\n%\n\\bibitem[1997]{voit}\nVoit, M., et al., 1997, {\\it HST Data Handbook - Vol. I}, Version 3.0\n(Baltimore:STScI)\n\\end{thebibliography}\n\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002244.extracted_bib",
"string": "\\begin{thebibliography}{}\n%\n\\bibitem[1999]{akiyama}\nAkiyama M., et al., 1999, Proceeding of the first XMM workshop\n\"Science with XMM\", in press (astro-ph/9811012)\n%\n\\bibitem[1999]{almaini99}\nAlmaini O., Lawrence A., Boyle B.J., 1999, MNRAS, 305, L59 \n%\n\\bibitem[1985]{baan85}\nBaan W.A., 1985, Nature, 315, 26\n%\n\\bibitem[1996]{biretta}\nBiretta J.A., et al., 1996, {\\it WFPC2 Instrument Handbook}, \nVersion 4.0 (Baltimore:STScI)\n%\n\\bibitem[1999]{blain}\nBlain A.W., Kneib J.P., Ivison R.J., Smail I., 1999, ApJ, 512, L87\n%\n\\bibitem[1988]{brock88}\nBrock D., 1988, ApJ, 329, 208\n%\n\\bibitem[1997]{bushouse}\nBushouse H., Skinner C.J., MacKenty J.W., 1997,\n{\\it NICMOS Instrument Sci. Rept. 97-28} (Baltimore:STScI)\n%\n\\bibitem[1999]{cappi}\nCappi M., et al., 1999, A\\&A, 350, 777\n%\n\\bibitem[1995]{comastri}\nComastri A., Setti G., Zamorani G., Hasinger G., 1995, A\\&A, 296, 1\n%\n\\bibitem[1999]{curran}\nCurran S.J., et al., 1999, A\\&A, 344, 767\n%\n\\bibitem[1996]{done96}\nDone C., Madejski G.M., Smith D.A., 1996, ApJ, 463, L63\n%\n\\bibitem[1979]{dossantos}\nDos Santos P.M., Lepine J.R.D., 1979, Nature, 278, 34\n%\n\\bibitem[1984]{draine}\nDraine B.T., Lee H.M., 1984 ApJ, 285, 89\n%\n\\bibitem[1997]{elmouttie}\nElmouttie M., et al., 1997, MNRAS, 284, 830\n%\n\\bibitem[1994]{elvis}\nElvis M., et al., 1994, ApJS, 95, 1\n%\n\\bibitem[1998]{fabian98}\nFabian et al., 1998, MNRAS, 297, L11\n%\n\\bibitem[1999]{fabian99}\nFabian A.C., Iwasawa K., 1999, MNRAS, 303, L34\n%\n\\bibitem[1998]{forbes}\nForbes D.A, Norris R.P., 1998, MNRAS, 300, 757\n%\n\\bibitem[1998]{genzel98}\nGenzel R., Lutz D., Sturm E., Egami E., Kunze D., Moorwood A.F.M.,\nRigopoulou D., Spoon H.W.W., Sternberg A., Tacconi-Garman L.E.,\nTacconi L., Thatte N., 1998, ApJ, 498, 579\n%\n\\bibitem[1992]{ghosh92}\nGhosh S.K., et al., 1992, ApJ, 391, 111\n%\n\\bibitem[1999]{gilli99}\nGilli R., Risaliti R., Salvati M., 1999, A\\&A, 347, 424\n%\n\\bibitem[1997]{granato}\nGranato G.L., Danese L., Franceschini A., 1997, ApJ, 486, 14\n%\n\\bibitem[1997]{greenhill}\nGreenhill L.J., Moran J.M., Herrnstein J.R., 1997, ApJ, 481, L23\n%\n\\bibitem[2000]{guainazzi}\nGuainazzi M., et al., 2002000, A\\&A, in press (astro-ph/0001528)\n%\n\\bibitem[1990]{heckman}\nHeckman T.M., Armus L., Miley G.K., 1990, ApJS, 74, 833\n%\n\\bibitem[1998]{hughes98}\nHughes D.H., et al., 1998, Nature, 394, 241\n%\n\\bibitem[1997]{hunt}\nHunt L.K., Malkan M.A., Salvati M., et al., 1997 ApJS, 108, 229\n%\n\\bibitem[1993]{iwasawa93}\nIwasawa K., et al., 1993, ApJ, 409, 155\n%\n\\bibitem[1994]{kaufl}\nK\\\"aufl H.U., Jouan R., Lagage P.O., Masse P., Mestreau P., Tarrius A.,\n1994, Infrared Phys. Technol. 35, 203 \n%\n\\bibitem[1998]{kim98}\nKim D.-C., Sanders D.B., 1998, ApJS, 119, 41\n%\n\\bibitem[1993]{koorn}\nKoornneef J., 1993, ApJ, 403, 581\n%\n\\bibitem[1996]{koorn96}\nKoornneef J., Israel F.P., 1996, New Astronomy, 1, 271\n%\n\\bibitem[1999]{leitherer}\nLeitherer C., et al., 1999, ApJS, 123, 3\n%\n\\bibitem[1998]{lutz98}\nLutz D., Spoon H.W.W., Rigopoulou D., Moorwood A.F.M., Genzel R.,\n1998, ApJ, 505, L103\n%\n\\bibitem[1997]{mackenty}\nMacKenty J.W., et al., 1997, {\\it NICMOS Instrument Handbook}, \nVersion 2.0 (Baltimore:STScI)\n%\n\\bibitem[1995]{maiolino95}\nMaiolino R., Ruiz M., Rieke G.H., Keller L.D., 1995, ApJ, 446, 561\n%\n\\bibitem[1998a]{maiolino98}\nMaiolino R., Krabbe A., Thatte N., Genzel R., 1998, ApJ, 493, 650\n%\n\\bibitem[1998b]{maiolino98b}\nMaiolino R., Salvati M., Bassani L., Dadina M., della Ceca R., Matt G.,\nRisaliti G., Zamorani G., 1998, A\\&A 338, 781\n%\n\\bibitem[1999a]{maiolino99}\nMaiolino R., et al., 1999, ApJ, in press (astro-ph/9910160)\n%\n%\\bibitem[1994]{marconi94}\n%Marconi A., Moorwood A.F.M., Origlia L. and Oliva E., 1994, ESO Mess., 78, 20\n%\n\\bibitem[2000]{marconi99}\nMarconi A., Schreier E.J., Koekemoer A.,\nCapetti A., Axon D.J., Macchetto F.D., Caon N., 2000, ApJ, 528, 276\n%\n\\bibitem[1999]{matt99}\nMatt G., Guainazzi M., Maiolino R., Molendi S., Perola G.C., Antonelli L.A., \nBassani L., Brandt W.N., Fabian A.C., Fiore F., Iwasawa K., Malaguti G., \nMarconi A., Poutanen J., 1999, A\\&A, 341, L39\n%\n\\bibitem[1996]{mauersberger}\nMauersberger R., et al., 1996, A\\&A, 309, 705\n%\n\\bibitem[1984]{moorwood84}\nMoorwood A.F.M. and Glass I.S., 1984, A\\&A, 135, 281\n%\n\\bibitem[1988]{moorwood88}\nMoorwood A.F.M. and Oliva E., 1988, A\\&A, 203, 278\n%\n\\bibitem[1992]{moorwood92}\nMoorwood A.F.M., Finger G., Biereichel P., Delabre B.,\nVan Dijsseldonk A., Huster G., Lizon J. L., Meyer M., Gemperlein H.,\nMoneti A., 1992, The Messenger, 69, 61\n%\n\\bibitem[1994a]{moorwood94a}\nMoorwood A.F.M. and Oliva E., 1994a, ApJ, 429, 602\n%\n\\bibitem[1994b]{moorwood94b}\nMoorwood A.F.M., Finger G., Gemperlein H., 1994b, The Messenger, 77, 8\n%\n\\bibitem[1996a]{moorwood96a}\nMoorwood A.F.M., van der Werf P.P., Kotilainen J.K., Marconi A., Oliva E., \n1996a, A\\&A, 308, L1\n%\n\\bibitem[1996b]{moorwood96b}\nMoorwood A.F.M., Space Sci. Rev., 1996b, 77, 303\n%\n\\bibitem[1996c]{moorwood96c}\nMoorwood A.F.M., Lutz D., Oliva E., Marconi A., Netzer H., Genzel R., \nSturm E., de Graauw Th., 1996c, A\\&A, 315, L109\n%\n\\bibitem[1993]{netzer93}\nNetzer H., Laor A., 1993, ApJ, 404, L51\n%\n\\bibitem[1994]{oliva94}\nOliva E., Salvati M., Moorwood A.F.M., Marconi A., 1994, A\\&A, 288, 457\n%\n\\bibitem[1995]{oliva95}\nOliva E., Origlia L., Kotilainen J.K., Moorwood A.F.M., 1995, A\\&A, 301, 55\n%\n\\bibitem[1998]{oliva98}\nOliva E., Marconi A., Cimatti A., di Serego Alighieri S., 1998, 329, L21\n%\n\\bibitem[1999a]{oliva99}\nOliva E., Marconi A., Moorwood A.F.M., 1999a, A\\&A, 342, 87\n%\n\\bibitem[1999b]{oliva99b}\nOliva E., Origlia L., Maiolino R., Moorwood A.F.M., 1999b, A\\&A, 350, 9\n%\n\\bibitem[1998]{persic}\nPersic M., et al., 1998, A\\&A, 339, L33\n%\n\\bibitem[1988]{rice88}\nRice G.H., et al., 1988, ApJS, 68, 91\n%\n\\bibitem[1998]{richstone}\nRichstone D., et al., 1998, Nature, 395, 14\n%\n\\bibitem[1980]{rieke80}\nRieke G.H., et al., 1980, ApJ, 238, 24\n%\n\\bibitem[1999]{risaliti}\nRisaliti G., et al., 1999, ApJ 522, 157\n%\n\\bibitem[1997]{rowanrob}\nRowan-Robinson M., et al., 1997, MNRAS, 298, 490\n%\n\\bibitem[1996]{sanders96}\nSanders D.B., Mirabel I.F., 1996, ARA\\&A, 34, 749\n%\n\\bibitem[1998]{schreier98}\nSchreier E.J., Marconi A., Axon D.J., Caon N., Macchetto D., Capetti A.,\nHough J.H., Young S., Packham C., 1998, ApJ, 499, L143 (Paper~II)\n%\n\\bibitem[1997]{sieben}\nSiebenmorgen R., Moorwood A., Freudling W., Kaeufl H.U., 1997, A\\&A, 325, 450\n%\n\\bibitem[1998]{skinner}\nSkinner C.J., Bergeron L.E., Daou D., 1998, {\\it HST Calibration\nWorkshop}, ed. S. Casertano et al. (Baltimore:STScI), in press\n%\n\\bibitem[1997]{smail97}\nSmail I., Ivison R.J., Blain A.W., 1997, ApJ, 490, L5\n%\n\\bibitem[1999]{storchi99}\nStorchi-Bergmann T., et al., 1999, MNRAS, 304, 35\n%\n\\bibitem[1999]{trentham}\nTrentham N., Blain A.W., Goldader J., 1999, MNRAS, 305, 61\n%\n\\bibitem[1997]{voit}\nVoit, M., et al., 1997, {\\it HST Data Handbook - Vol. I}, Version 3.0\n(Baltimore:STScI)\n\\end{thebibliography}"
}
] |
astro-ph0002245
|
A Model of Supernovae Feedback in Galaxy Formation
|
[
{
"author": "G. Efstathiou"
},
{
"author": "Madingley Road"
},
{
"author": "Cambridge"
},
{
"author": "CB3 OHA."
}
] |
A model of supernovae feedback during disc galaxy formation is developed. The model incorporates infall of cooling gas from a halo and outflow of hot gas from a multiphase interstellar medium (ISM). The star formation rate is determined by balancing the energy dissipated in collisions between cold gas clouds with that supplied by supernovae in a disc marginally unstable to axisymmetric instabilities. Hot gas is created by thermal evaporation of cold gas clouds in supernovae remnants, and criteria are derived to estimate the characteristic temperature and density of the hot component and hence the net mass outflow rate. A number of refinements of the model are investigated, including a simple model of a galactic fountain, the response of the cold component to the pressure of the hot gas, pressure induced star formation and chemical evolution. The main conclusion of this paper is that low rates of star formation can expel a large fraction of the gas from a dwarf galaxy. For example, a galaxy with circular speed $\sim 50\;\kms$ can expel $\sim 60$--$80\%$ of its gas over a time-scale of $\sim 1$ Gyr, with a star formation rate that never exceeds $\sim 0.1 M_\odot$/year. Effective feedback can therefore take place in a quiescent mode and does not require strong bursts of star formation. Even a large galaxy, such as the Milky Way, might have lost as much as $20\%$ of its mass in a supernovae driven wind. The models developed here suggest that dwarf galaxies at high redshifts will have low average star formation rates and may contain extended gaseous discs of largely unprocessed gas. Such extended gaseous discs might explain the numbers, metallicities and metallicity dispersions of damped Lyman alpha systems. \vskip 0.2 truein
|
[
{
"name": "mn_paper.tex",
"string": "\\documentstyle{mn}\n%\\input{epsf}\n\n%\\voffset = -0.6 truein\n\n\n\n\\newcounter{parentequation}\\setcounter{parentequation}{0}\n\\def\\beglet{\n \\addtocounter{equation}{1}%\n \\setcounter{parentequation}{\\value{equation}}%\n \\setcounter{equation}{0}%\n \\def\\theequation{\\arabic{parentequation}\\alph{equation}}%\n \\ignorespaces\n}\n\\def\\endlet{\n \\setcounter{equation}{\\value{parentequation}}%\n \\def\\theequation{\\arabic{equation}}%\n}\n\\def\\begletA{\n \\addtocounter{equation}{1}%\n \\setcounter{parentequation}{\\value{equation}}%\n \\setcounter{equation}{0}%\n \\def\\theequation{A\\arabic{parentequation}\\alph{equation}}%\n \\ignorespaces\n}\n\\def\\endletA{\n \\setcounter{equation}{\\value{parentequation}}%\n \\def\\theequation{\\arabic{equation}}%\n}\n\\def\\begletB{\n \\addtocounter{equation}{1}%\n \\setcounter{parentequation}{\\value{equation}}%\n \\setcounter{equation}{0}%\n \\def\\theequation{B\\arabic{parentequation}\\alph{equation}}%\n \\ignorespaces\n}\n\\def\\begletC{\n \\addtocounter{equation}{1}%\n \\setcounter{parentequation}{\\value{equation}}%\n \\setcounter{equation}{0}%\n \\def\\theequation{B\\arabic{parentequation}}%\n \\ignorespaces\n}\n\\def\\endletB{\n \\setcounter{equation}{\\value{parentequation}}%\n \\def\\theequation{\\arabic{equation}}%\n}\n\\def\\ltsima{$\\; \\buildrel < \\over \\sim \\;$}\n\\def\\gtsima{$\\; \\buildrel > \\over \\sim \\;$}\n\\def\\simlt{\\lower.5ex\\hbox{\\ltsima}}\n\\def\\simgt{\\lower.5ex\\hbox{\\gtsima}}\n\\def\\kms{{\\rm kms}^{-1}}\n\\def\\etal{{\\it et al.}\\rm}\n\n\n\n\\begin{document}\n\n\n\n\\title[Supernovae Feedback in Galaxy Formation]{A Model of Supernovae\nFeedback in Galaxy Formation}\n\n\n\n\\author[G. Efstathiou]{G. Efstathiou \\\\\nInstitute of Astronomy, Madingley Road, Cambridge, CB3 OHA.}\n\n\n\\maketitle\n\n\\begin{abstract}\nA model of supernovae feedback during disc galaxy formation is\ndeveloped. The model incorporates infall of cooling gas from a halo\nand outflow of hot gas from a multiphase interstellar medium\n(ISM). The star formation rate is determined by balancing the energy\ndissipated in collisions between cold gas clouds with that supplied by\nsupernovae in a disc marginally unstable to axisymmetric\ninstabilities. Hot gas is created by thermal evaporation of cold gas\nclouds in supernovae remnants, and criteria are derived to estimate\nthe characteristic temperature and density of the hot component and\nhence the net mass outflow rate. A number of refinements of the model\nare investigated, including a simple model of a galactic fountain, the\nresponse of the cold component to the pressure of the hot gas,\npressure induced star formation and chemical evolution. The main\nconclusion of this paper is that low rates of star formation can expel\na large fraction of the gas from a dwarf galaxy. For example, a\ngalaxy with circular speed $\\sim 50\\;\\kms$ can expel $\\sim 60$--$80\\%$\nof its gas over a time-scale of $\\sim 1$ Gyr, with a star formation\nrate that never exceeds $\\sim 0.1 M_\\odot$/year. Effective feedback\ncan therefore take place in a quiescent mode and does not require\nstrong bursts of star formation. Even a large galaxy, such as the\nMilky Way, might have lost as much as $20\\%$ of its mass in a\nsupernovae driven wind. The models developed here suggest that dwarf\ngalaxies at high redshifts will have low average star formation rates\nand may contain extended gaseous discs of largely unprocessed\ngas. Such extended gaseous discs might explain the numbers,\nmetallicities and metallicity dispersions of damped Lyman alpha\nsystems.\n\\vskip 0.2 truein\n\\end{abstract}\n\n\n%\\keywords{Galaxy formation; interstellar medium; cosmology}\n\n\n\\section{Introduction}\n\nSince the pioneering paper of White and Rees (1978), it has been clear\nthat some type of feedback mechanism is required to explain the shape\nof the galaxy luminosity function in hierarchical clustering theories.\nThe reason for this is easy to understand; if the power spectrum of\nmass fluctuations is approximated as a power law $P(k) \\propto k^n$,\nthe Press-Schechter (1974) theory for the distribution of virialized haloes\npredicts a power law dependence at low masses\n\\begin{equation}\n{d N(m) \\over dm} \\propto m^{-(9-n)/6}. \\label{Int1}\n\\end{equation}\nFor any reasonable value of the index $n$ ($n \\approx -2$ on the\nscales\nrelevant to galaxy formation in cold dark\nmatter (CDM) models), equation~(\\ref{Int1}) predicts a much steeper\nmass spectrum than the observed faint end slope of the galaxy\nluminosity function, $dN(L)/dL\n\\propto L^\\alpha$, with $\\alpha \\approx -1$ (Efstathiou, Ellis and\nPeterson 1988, Loveday \\etal$\\;$ 1992, Zucca \\etal$\\;$ 1997).\nFurthermore, the cooling times of collisionally ionised gas clouds\nforming at high redshift are short compared to the Hubble time (Rees\nand Ostriker 1977, White and Rees 1978). Thus, in the absence of\nfeedback, one would expect that a large fraction of the baryons would\nhave collapsed at high redshift into low mass dark matter haloes, in\ncontradiction with observations.\n\nIn reality, there are a number of complex physical mechanisms that can\ninfluence galaxy formation and these need to be understood if we are\nto construct a realistic model of galaxy formation. In the `standard'\ncold dark matter model ({\\it i.e.} nearly scale invariant adiabatic\nperturbations), the first generation of collapsed objects will form in\nhaloes with low virial temperatures ($T \\simlt 10^4$K, characteristic\ncircular speeds $v_c \\simlt 20 \\kms$). Molecular hydrogen is the\ndominant coolant at such low temperatures and so an analysis of the\nformation of the first stellar objects requires an understanding of\nthe molecular hydrogen abundance and how this is influenced by the\nambient ultraviolet radiation field (Haiman, Rees and Loeb 1997,\nHaiman, Abel and Rees 1999). As the background UV flux rises, the\ntemperature of the intergalactic medium will rise to $\\sim 10^4$K\n({\\it e.g.} Gnedin and Ostriker 1997) and the UV background will\nreduce the effectiveness of cooling in low density highly ionized gas\n(Efstathiou 1992). A UV background can therefore suppress the collapse\nof gas in regions of low overdensity. It is this\nlow density photoionized gas that we believe\naccounts for the Ly$\\alpha$ absorption lines (Cen \\etal$\\;$ 1994,\nHernquist \\etal$\\;$ 1996, Theuns \\etal$\\;$ 1998, Bryan \\etal$\\;$\n1999). Photoionization can also suppress the collapse of gas in haloes\nwith circular speeds of up to $v_c \\sim 20$--$30\\kms$. However,\nnumerical simulations have shown that a UV background cannot prevent\nthe collapse of gas in haloes with higher circular speeds, though it\ncan reduce significantly the efficiency with which low density gas is\naccreted onto massive galaxies (Quinn, Katz and Efstathiou 1996, Navarro and Steinmetz\n1997).\n\nTo explain the galaxy luminosity function, feedback is required in\ngalaxies with circular speeds $v_c \\simgt 50 \\;\\kms$ with\ncharacteristic virial temperatures of $\\simgt 10^5\\;$K. Energy\ninjection from supernovae is probably the most plausible feedback\nmechanism for systems with such high virial temperatures. Winds from\nquasars might also disrupt galaxy formation (Silk and Rees 1998) or,\nmore plausibly, limit the growth of the central black hole (Fabian\n1999). Here we will be concerned exclusively with supernova driven\nfeedback and will not consider feedback from an active nucleus.\nSimple parametric models of supernovae feedback were developed by\nWhite and Rees (1978) and White and Frenk (1991) and form a key\ningredient of semi-analytic models of galaxy formation ({\\it e.g.}\nKauffmann, White and Guiderdoni 1993, Lacey\n\\etal$\\;$ 1993, Cole \\etal$\\;$ 1994, Baugh \\etal$\\;$ 1996, 1998,\nSomerville and Primack 1999). In this paper, we develop a more\ndetailed model of the feedback process itself. Previous papers on\nsupernovae feedback include those of Larson (1974), Dekel and Silk\n(1986) and Babul and Rees (1992). These authors compute the energy\ninjected by supernovae into a uniform interstellar medium (ISM) and\napply a simple binding energy criterion to assess whether the ISM\nwill be driven out of the galaxy. The feedback process in these models\nis explosive, operating on the characteristic timescale of $\\sim 10^6$\n--$10^7$ yrs for supernova remnants to overlap. This is much shorter\nthan the typical infall timescale of hot gas in the halo, begging the\nquestion of how a resevoir of cold gas accumulated in the first place.\nThe present paper differs in that we model the ISM as a two-phase\nmedium consisting of cold clouds and a hot pressure confining medium,\n{\\it i.e.} as a simplified version of the three-phase model of the ISM\ndeveloped by McKee and Ostriker (1977, hereafter\nMO77). The cold component contains most of the gaseous mass of the\ndisc and is converted into a hot phase by thermal evaporation in\nexpanding supernovae remnants. In this type of model, the cold phase\ncan be lost gradually in a galactic wind as it is slowly converted into\na hot phase.\n\n\nThe main result of this paper is that low rates of star formation can\nexpel a large fraction of the baryonic mass in dwarf galaxies over a\nrelatively long timescale of $\\sim 1$ Gyr. We therefore propose that\neffective feedback can operate in an steady, unspectacular mode;\nstrong bursts of star formation and superwind-like phenomena ({\\it\ne.g.} Heckman, Armus and Miley 1990) are not required, although\ngalaxies may experience additional feedback of this sort. In fact,\nhydrodynamic simulations suggest that nuclear starbursts are\nineffective in removing the ISM from galaxies with gas masses $\\simgt\n10^6 M_\\odot$ (Mac Low and Ferrara 1999, Strickland and Stevens 1999)\nbecause hot gas generated in the nuclear regions is a expelled in a\nbipolar outflow without coupling to the cool gas in the rest of the\ndisc. This result provides additional motivation for investigating a\n``quiescent'' mode of feedback. Silk (1997) describes a model which\nis similar, in some respects, to the model described here. However,\nthe model described here is more detailed and allows a crude\ninvestigation of the radial properties of a disc galaxy during\nformation.\n\n\nThe layout of this paper is as follows. A simple model of star\nformation regulated by disc instabilities is described in Section\n2. This is applied to `closed box' ({\\it i.e.} no infall or outflow\nof gas) models of disc galaxies neglecting feedback. Section 3\ndescribes a model of the interaction of expanding supernovae shells in\na two-phase ISM. This section is based on the model of MO77, but\ninstead of focussing on equilibrium solutions that might apply to our\nown Galaxy, we compute the net rate of conversion of cold gas to hot\ngas incorporating the model for self-regulating star formation. This\nyields the temperature and density of the hot phase as a function of\ntime and radius within the disc. Section 4 revisits the model of\nSection 2, but includes simultaneous infall and outflow of gas. This\nmodel is extended in Section 5 to include a galactic fountain, the\npressure response of the cold ISM to the hot phase, and a model of\nchemical evolution. Section 6 describes some results from this model\nand discusses the effects of varying some of the input parameters. In\naddition, the efficiency of feedback is computed as a function of the\ncircular speed of the surrounding dark matter halo. Our conclusions\nare summarized in Section 7. Although we focus on disc galaxies in\nthis paper, a similar formalism could be applied to the formation of bulges\nif the assumption that gas conserves its angular momentum during\ncollapse is relaxed.\n\n\\section{Star Formation Regulated by Disc Instabilities}\n\n\\subsection{Rotation curve for the Disc and Halo}\n\nThe dark halo is assumed to be described by the Navarro, Frenk and White\n(1996, hereafter NFW) profile\n\\begin{equation}\n \\rho_H(r) = {\\delta_c \\rho_c \\over (cx) (1 + cx)^2}, \\qquad x\\equiv r/r_v,\n \\label{Rot1}\n\\end{equation}\nwhere $\\rho_c$ is the critical density, $r_v$ is the virial radius\nat which the halo has a mean overdensity of $200$ with respect to the\nbackground and $c$ is a concentration parameter (approximately $10$ for\nCDM models). The circular speed corresponding to this profile is\n\\begin{equation}\n v^2_H(r) = v^2_{v} {1 \\over x} { \\left [ {\\rm ln} (1 + cx) - cx/(1 + cx)\n\\right ] \\over \\left [ {\\rm ln} (1 + c) - c/(1 + c)\n\\right ]}, \\quad v^2_v \\equiv {G M_v \\over r_v}, \\label{Rot2}\n\\end{equation}\nwhere $M_v$ is the mass of the halo within the virial radius.\n\nWe assume that the disc surface mass density distribution\nis described by an exponential,\n\\begin{equation}\n \\mu_D(r) = \\mu_0 \\; {\\rm exp}(- r/r_D), \\qquad M_D \\equiv 2\\pi \\mu_0 r_D^2,\n\\label{Rot3}\n\\end{equation}\nwhere $M_D$ is the total disc mass. The rotation curve\nof a cold exponential disc is given by (Freeman 1970)\n\\begin{eqnarray}\n v^2_D(r) =2 v^2_c y^2\n\\left [I_0(y)K_0(y)- I_1(y)K_1(y)\\right], \\\\\n\\quad y \\equiv {1 \\over 2}{r \\over r_D}, \\quad v^2_c = {G M_D \\over r_D}. \\nonumber\n\\label{Rot4}\n\\end{eqnarray}\n\nTo relate the disc scale length, $r_D$, to the virial radius of the\n halo $r_v$, we assume that the angular momentum of the disc material\n acquired by tidal torques is approximately conserved during the\n collapse of the disc (see Fall and Efstathiou 1980). This fixes the\n collapse factor\n\\begin{equation}\n f_{coll} = {r_V \\over r_D} \n\\label{Rot5}\n\\end{equation}\nin terms of the dimensionless spin parameter $\\lambda_H \\equiv J \\vert\nE \\vert^{1/2} G^{-1}M^{-5/2}$ of the halo component. The spin\nparameter is found to have a median value of $\\approx 0.05$ from\nN-body simulations (Barnes and Efstathiou 1987), and for the models\ndescribed here, this value is reproduced for collapse factors of\naround $50$. A more detailed calculation of the collapse factor of\nthe disc is given in Section 4.\n\n\\subsection{Vertical scale height of the disc}\n\nThe velocity dispersion of the cold gas clouds in the vertical\ndirection is assumed to be constant and equal to $\\sigma^2_g$. The\nequations of stellar hydrodynamics then give the following solution\n\\begin{equation}\n \\rho(z) = {\\mu_g \\over 2 H_g} {\\rm sech}^2 \\left ( {z \\over H_g} \\right), \\label{Vert1}\n\\end{equation}\nwhere $\\mu_g$ is the surface mass density of the gas and the scale height\nis given by\n\\begin{equation}\n H_g = {\\sigma^2_g \\over \\pi G \\mu_g}. \\label{Vert2}\n\\end{equation}\nEquation (\\ref{Vert2}) must be modified to take into account the\nstellar disc. We do this approximately by assuming `disc pressure\nequilibrium' (Talbot and Arnett 1975)\n\\begin{equation}\n H_g = {\\sigma^2_g \\over \\pi G \\mu_g} { 1 \\over (1 + \\beta/\\alpha)}, \\label{Vert3}\n\\end{equation}\nwhere the quantities $\\alpha$ and $\\beta$ relate the vertical velocity\ndispersion $\\sigma^2_*$ and surface mass density $\\mu_*$ of the stars\nto those of the gas clouds\n\\beglet\n\\begin{eqnarray}\n\\sigma_* = \\alpha \\sigma_g, \\\\\n\\mu_* = \\beta \\mu_g. \n\\end{eqnarray}\n\\endlet\n\n\n\\subsection{Stability of a two-component rotating disc}\n\nThe stability of rotating discs of gas and collisionless particles\nto axisymmetric modes has been analysed in classic papers by Goldreich\nand Lynden-Bell (1965) and by Toomre (1964). Here we use the results of Jog\nand Solomon (1984) who analysed the stability of a rotating disc\n consisting of two isothermal fluids of sound speeds $c_1$, $c_2$\nand surface mass densities $\\mu_1$ and $\\mu_2$. These authors find\nthat such a disc is stable to axisymmetric modes of wavenumber $k$ if\n\\begin{equation}\n x = {2 \\pi G \\mu_1 \\over \\kappa^2} { k \\over ( 1 + k^2c_1^2/\\kappa^2)}\n+ {2 \\pi G \\mu_2 \\over \\kappa^2} { k \\over ( 1 + k^2c_2^2/\\kappa^2)} < 1,\n\\label{Stab1}\n\\end{equation}\nwhere $\\kappa$ is the epicyclic frequency\n\\begin{equation}\n \\kappa = 2\\omega \\left ( 1 + {1 \\over 2} {r \\over \\omega} {d\\omega \\over dr}\n\\right )^{1/2}. \\label{Stab2}\n\\end{equation}\nEquation (\\ref{Stab1}) yields a cubic equation for the most unstable\nmode $k_m$. Solving this equation in terms of the parameters $\\alpha$\nand $\\beta$ of equations (10), and ignoring the small differences\nbetween a gaseous and collisionless disc, we can write the stability\ncriterion for a two-component system as\n\\begin{equation}\n \\sigma_g = {\\pi G \\mu_g \\over \\kappa} g (\\alpha, \\beta). \\label{Stab3}\n\\end{equation} \nThis is identical to the Goldreich-Lynden-Bell criterion except for\nthe factor $g(\\alpha, \\beta)$. This factor is plotted in Figure 1 for\nvarious values of $\\alpha$ and $\\beta$.\n\n\\subsection{Star formation and supernovae energy input}\n\nWe assume a stellar initial mass function (IMF) of the standard\nSalpeter (1955) form\n\\begin{eqnarray}\n {dN_* \\over dm} = Am^{-(1+x)}, \\quad m_l < m < m_u, \\quad x = 1.35, \n\\label{SN1}\\\\\n m_l = 0.1 M_\\odot, \\quad m_u = 50M_\\odot, \\quad\\quad\\quad\\quad\\nonumber\n\\end{eqnarray} \nand that each star of mass greater than $8M_\\odot$ releases\n$10^{51}E_{51}$ ergs in kinetic energy in a supernova explosion. For\nthe IMF of equation~(\\ref{SN1}), one supernova is formed for every\n$125M_\\odot$ of star formation. The energy injection rate is\ntherefore related to the star formation rate by\n\\begin{equation}\n \\dot E_{sn} = 2.5 \\times 10^{41} E_{51}\\dot M_* \\; {\\rm erg/sec}, \\label{SN2}\n\\end{equation} \nwhere $\\dot M_*$ is the star formation rate in $M_\\odot$ per year.\n\n\n\n\n\\begin{figure}\n\n\\vskip 2.8 truein\n\n\\special{psfile=pgfig1.ps hscale=40 vscale=40 angle=-90 hoffset= -20\nvoffset=240}\n\n\\caption\n{The factor $g(\\alpha, \\beta)$ appearing in the stability criterion of\nequation (13) plotted against $\\beta$ for three values of $\\alpha$}\n\\label{figure1}\n\\end{figure}\n\n\\begin{table*}\n\\bigskip\n\\centerline{\\bf Table 1: Parameters of Model Galaxies}\n\\begin{center}\n\\begin{tabular}{ccccccccc} \\hline \\hline\n\\noalign{\\medskip}\n & $v_c$ (km/s) & $v_{\\rm max}$ (km/s) & $v_v/v_c$ & $r_D$ (kpc) &\n$M_D$ ($M_\\odot$) & $f_{coll}$ & $c$ & $\\lambda_H$ \\\\\nModel MW & $280$ & $212$ & $0.45$ & $3.0$ & $5.5 \\times 10^{10}$ &\n$50$ & $10$ & $0.065$ \\\\\nModel DW & $70$ & $53$ & $0.45$ & $0.2$ & $2.3 \\times 10^{8}$ &\n$50$ & $10$ & $0.065$\\\\ \\hline\n\\noalign{\\medskip}\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\subsection{Energy dissipated by cloud collisions}\n\nWe assume cold clouds of constant density \n$\\overline \\rho_c = 7 \\times10^{-23}$ g/cm$^3$ with a distribution of cloud radii\n\\begin{eqnarray}\n {dN_{ca} \\over da} = N_0a^{-4}, \n\\quad a_l < a < a_u, \\\\\n \\quad a_l = 0.5 \\;{\\rm pc}, \\quad a_u = 10\\;\n{\\rm pc}\n\\nonumber,\n\\label{Diss1}\n\\end{eqnarray} \n(MO77). Following MO77, the clouds are assumed to have an isotropic\nGaussian velocity distribution with velocity dispersion independent of\ncloud size and that they lose energy through inelastic collisions. The\nrate of energy loss per unit volume is given by\n\\begin{eqnarray}\n {dE_{coll} \\over dtdV} = 24 \\pi^{3/2} \\overline \\rho_c N_{cl}^2\na_l^5 \\sigma_g^3 I_a, \\\\\n I_a = {1 \\over 2} \\int_1^{a_u/a_l}\n\\int_1^{a_u/a_l} {(x+y)^2 \\over (x^3 + y^3)} {dx \\over x} {dy \\over y}\n\\nonumber \\label{Diss2},\n\\end{eqnarray} \nwhere $N_{cl}$ is the local cloud density $N_{cl} =\nN_0/3a_l^3$. Integrating equation (17) over the vertical\ndirection and using equation (\\ref{Vert3}) for the scale height, the\nrate of energy loss per unit surface area $\\dot E^\\Omega_{coll}$ is\n\\begin{eqnarray}\n \\dot E^\\Omega_{coll} = 5.0 \\times 10^{29} \\left ( 1 + {\\beta \\over \\alpha}\n\\right )\n\\mu_{g5}^3 \\sigma_{g5} \\;\\; {\\rm erg}/{\\rm sec}/{\\rm pc}^2 \\label{Diss3},\n\\end{eqnarray} \nwhere $\\mu_{g5}$ is the surface mass density of the gas component in\nunits of $5 M_\\odot/{\\rm pc}^2$ and $\\sigma_{g5}$ is the cloud\nvelocity dispersion in units of $5$ km/sec. These values are close to\nthose observed in the local solar neighbourhood. To estimate the\nefficiency with which supernovae accelerate the system of clouds, we\nnormalize to the observed net star formation rate of the Milky\nWay. Assuming that the gas distribution has a flat surface mass\ndensity profile to $R_{max} = 14$ kpc (Mihalas and Binney 1981),\n$\\beta \\approx 10$, $\\alpha \\approx 5$, and equating the integral\nof (\\ref{Diss3}) to $\\epsilon_c \\dot E_{sn}$ (equation \\ref{SN2}),\nwe find\n\\begin{equation}\n \\epsilon_c E_{51} \\dot M_* = 0.004. \\label{Diss4}\n\\end{equation} \nAn efficiency parameter of $\\epsilon_c = 0.01$ produces a net star\nformation rate of $0.4M_\\odot$/yr which is reasonable for a Milky\nWay-like galaxy. We will therefore adopt a constant value of\n$\\epsilon_c=0.01$ in the models of the next subsection. The value of\n$\\epsilon_c$ will, of course, depend on the properties of the clouds,\nISM and star formation rate. For example, in the model of MO77 the\nclouds are accelerated by interactions with the cold shells\nsurrounding supernova remnants and they find efficiencies $\\epsilon_c$\nof typically a few percent. We investigate the effect of varying\n$\\epsilon_c$ in Section 6.\n\n\n\n\\subsection{Self-regulating models without inflow or outflow}\n\nThe equations derived above allow us to evolve an initially gaseous\ndisc and to compute the local star formation rate, cloud velocity\ndispersion {\\it etc}. The system of stars and gas is constrained to\nsatisfy the stability criterion of equation (\\ref{Stab3}), which fixes\nthe cloud velocity dispersion $\\sigma_g$. There is some empirical\nevidence that star formation in nearby galaxies is regulated by a\nstability criterion of this sort ({\\it e.g.} Kennicutt 1998). The\nenergy lost in cloud collisions (equation \\ref{Diss3}) is balanced\nagainst the energy input from supernovae assuming a constant\nefficiency factor $\\epsilon_c = 0.01$. We assume further that $\\alpha\n= 5$ (equation 10a) {\\it i.e.} that stars are instantaneously\naccelerated to higher random velocities than the system of gas clouds,\nand that the properties of the gas clouds (mass spectrum, internal\ndensity, {\\it etc}) are independent of time. These are clearly\nrestrictive assumptions, but they allow us to generate simple models\nof self-regulating star formation with only one free parameter\n$\\epsilon_c$.\n\n\n We study the evolution of two model galaxies with parameters listed\nin Table 1. Model MW has parameters roughly similar to those of the\nMilky Way and model DW has parameters similar to those of a relatively\nhigh surface brightness dwarf galaxy.\n\n\n\n\\begin{figure*}\n\n\\vskip 3.8 truein\n\n\\special{psfile=pgfig2a.ps hscale=55 vscale=55 angle=-90 hoffset= -30\nvoffset=320}\n\\special{psfile=pgfig2b.ps hscale=55 vscale=55 angle=-90 hoffset= 220\nvoffset=320}\n\n\\caption\n{The evolution of the gas (solid lines) and stellar (dashed lines)\nsurface mass density distributions according to the simple\nself-regulating model described in this section. The results are\nshown for ages of $0$, $0.1$, $1$, $3$, $6$ and $10$ Gyr.}\n\\label{figure2}\n\\end{figure*}\n\n\nFigure 2 shows the evolution of the gas and stellar surface mass\ndensities of the two models. The net star formation rates, gas\nfractions and mean gas cloud velocity dispersion are plotted in Figure\n3. In model MW, the star formation rates are initially high ($> 100\nM_\\odot$/yr) and hence the timescale for star formation is short; half\nthe disc mass is converted into stars in $10^7$ years. The\nstar formation rate declines rapidly to less than $1 M_\\odot$/yr after\na few Gyr. As figure 2 shows, the star formation at early times is\nconcentrated to the inner parts of the disc which have a high surface\ndensity and hence the gas distribution develops a characteristic\nsurface density profile with an inner `hole', similar to what is seen\nin the HI distributions in real galaxies (see Burton 1991). The\nstellar disc is truncated at about the Holmberg (1958) radius ($r/r_D\n\\approx 5$), in rough agreement with observations. The truncation\narises because the gas disc becomes thick at large radii (equation\n\\ref{Vert3}) and the rate of energy lost in cloud collisions can be\nbalanced by a very low star formation rate. \n\n\n\\begin{figure*}\n\n\\vskip 4.5 truein\n\n\\special{psfile=pgfig3a.ps hscale=65 vscale=65 angle=-90 hoffset= -40\nvoffset=365}\n\\special{psfile=pgfig3b.ps hscale=65 vscale=65 angle=-90 hoffset= 200\nvoffset=365}\n\n\\caption\n{Evolution of the star formation rate, gas fraction and gas cloud\nvelocity dispersion in the self-regulating model.}\n\\label{figure3}\n\\end{figure*}\t\n\nThe evolution of model DW is qualitatively similar, though the star\nformation rate is scaled down roughly in proportion to the disc mass.\nHalf the gas is converted to stars by $3 \\times 10^7$ yr, and the gas\nfraction is $0.12$ after $10^{10}$ yr, similar to the final gas fraction\nof $0.13$ in model MW.\n\nNeither of these models is satisfactory. The star formation rate in\nmodel MW is too high at early times to be compatible with deep number\ncounts (see {\\it e.g.} Ellis 1997), which require more gentle star\nformation rates in typical $L^*$ galaxies. Model SW converts most of\nits gas into stars on a short timescale and so does not solve the\nproblem raised in the introduction of explaining the flat faint end\nslope of the luminosity function in CDM-like models. As we will see in\nlater sections, infall of gas provides the solution to the former\nproblem, since this allows the disc to build up gradually on a cooling\nor dynamical timescale. Outflow of hot gas heated by supernovae\nprovides a solution to the latter problem.\n\n\\section{Evolution of a two-phase ISM}\n\nIn this Section we consider the interaction of a multiphase\ninterstellar medium with expanding supernova remnants following the\nmodel of MO77 and discuss the conditions under which a protogalaxy can\nform a wind. The key ingredients of the model are as follows. Most of\nthe cold gaseous mass is assumed to be in cold clouds with properties\nas given in Section 2.5. Supernovae explode and their remnants\npropagate evaporating some of the cold clouds and forming a low\ndensity hot phase of the ISM. The star formation rate therefore\ndetermines the evaporation rate and hence the rate of conversion of\nthe cold phase to a hot phase. A wind from the galaxy can result if\nthe hot phase is: (i) sufficiently pervasive (filling factor of order\nunity), (ii) low density (so that radiative cooling is unimportant)\nand (iii) the temperature of the hot phase exceeds the virial\ntemperature of the galaxy. In this section we follow closely the\ntheory of the ISM developed by MO77 and we use their notation where\npossible.\n\n\\subsection{Evaporation of cold clouds}\n\nAn expanding supernovae remnant will evaporate a mass of \n\\begin{equation}\n M_{ev} \\approx 540\\; E_{51}^{6/5} \\Sigma^{-3/5} n_h^{-4/5} \\; M_\\odot,\n \\label{Eva1}\n\\end{equation}\nwhere $n_h$ is the density interior to the supernovae remnant and\n$\\Sigma$ (in pc$^2$) is the evaporation parameter introduced by MO77\n\\begin{equation}\n \\Sigma = { \\gamma \\over 4 \\pi a_l N_{cl} \\phi_\\kappa} .\n \\label{Eva2}\n\\end{equation}\nHere the parameter $\\gamma$ relates the blast wave velocity to the\nisothermal sound speed ($v_b = \\gamma c_h$, $\\gamma \\approx 2.5$) and\nthe parameter $\\phi_\\kappa$ quantifies the effectiveness of the\nclassical thermal conductivity of the clouds ($\\kappa_{eff} = \\kappa\n\\phi_\\kappa$) and so is less than unity if the conductivity is reduced\nby tangled magnetic fields, turbulence {\\it etc}. Using equations\n(\\ref{Vert1}) and (\\ref{Vert3}) to estimate the mean cloud density we\nfind\n\\begin{equation}\n \\Sigma \\approx 280 {\\sigma_{g5}^2 \\over \\mu_{g5}^2} {1 \\over (1+\n\\beta/\\alpha)} {1 \\over \\phi_\\kappa} \\;{\\rm pc}^2 =\nf_\\Sigma{\\Sigma_\\odot}, \\quad \\Sigma_\\odot \\approx 95\\; {\\rm pc}^2,\n\\label{Eva3}\n\\end{equation}\nwhere $\\Sigma_\\odot$ is the evaporation parameter characteristic of\nthe local solar neighbourhood ($\\beta/\\alpha \\approx 2)$. \n\nEvaluating equation (\\ref{Eva1}), we find\n\\begin{equation}\n M_{ev} \\approx 1390\\; E_{51}^{6/5} f_\\Sigma^{-3/5} \\phi_\\kappa^{3/5} n_{h-2}^{-4/5} \\; M_\\odot,\n \\label{Eva4}\n\\end{equation}\nwhere $n_{h-2}$ is $n_h$ in units of $10^{-2} {\\rm cm}^{-2}$ (a\ncharacteristic value for the hot component). Thus, provided thermal\nconduction is not highly suppressed, a single supernovae remnant can\nevaporate a much larger mass than the $125\\;M_\\odot$ formed in\nstars per supernovae for a standard Saltpeter IMF (Section 2.4). If a\nsignificant fraction of this evaporated gas can escape in a wind, then\nstar formation will be efficiently suppressed.\n\n\\subsection{Temperature and density of the hot phase}\n\nTo compute the properties of the hot phase we assume that the\ndisc achieves a state in which the porosity parameter $Q$\nis equal to unity. The disc is then permeated by a network of\noverlapping supernovae remnants. Ignoring cooling interior to the\nremnants (which we will see is a reasonable approximation for \nan ISM with low metallicity) the age, radius and temperature of\na SNR when $Q=1$ are given by\n\\beglet\n\\begin{eqnarray}\nt_o = 5.5 \\times 10^6 S_{13}^{-5/11} \\gamma^{-6/11} E_{51}^{-3/11} n_h^{3/11}\n\\;\\; {\\rm yr}, \\\\\nR_o = 100 S_{13}^{-2/11} \\gamma^{2/11} E_{51}^{1/11} n_h^{-1/11}\\;\\;\n {\\rm pc}, \\\\\nT_o = 1.2 \\times 10^{4} S_{13}^{6/11} \\gamma^{-6/11} E_{51}^{8/11} \nn_h^{-8/11}\\;\\; {\\rm K}.\n\\end{eqnarray}\n\\endlet\nwhere $S_{13}$ is the supernova rate in units of $10^{-13} {\\rm pc}^{-3}\n{\\rm yr}^{-1}$.\nThe density of a remnant at $t_o$ ($n_h^o \\approx M_{ev}/(4/3\\pi R_o^3)$),\ngives an approximate estimate of the density of the ambient hot phase\n\\begin{equation}\n n_h^o \\approx 4.3 \\times 10^{-3} S_{13}^{0.36} \\gamma^{-0.36} E_{51}^{0.61} \nf_\\Sigma^{-0.393}\\;\\; {\\rm cm}^{-3}.\n \\label{Temp2}\n\\end{equation}\nInserting this estimate into equations (24) we find\n\\beglet\n\\begin{eqnarray}\nt_o = 1.2 \\times 10^6 S_{13}^{-0.36} \\gamma^{-0.64} (E_{51}\nf_\\Sigma)^{-0.11}\n\\;\\; {\\rm yr}, \\\\\nR_o = 164 (S_{13}/\\gamma)^{-0.21} E_{51}^{0.04} f_\\Sigma^{0.035}\\;\\;\n {\\rm pc}, \\\\\nT_o = 6.6 \\times 10^{5} (S_{13} E_{51} f_\\Sigma/\\gamma)^{0.29}\\;\\; {\\rm K},\n\\end{eqnarray}\n\\endlet\nand the rate at which clouds are evaporated is\n\\begin{equation}\n \\dot M_{ev} = \n2.7 \\times 10^{-10} S_{13}^{0.71} \\gamma^{0.29} E_{51}^{0.71} \nf_\\Sigma^{-0.29}\\;\\; {\\rm M}_\\odot {\\rm pc}^{-3} {\\rm yr}^{-1}. \n \\label{Temp3}\n\\end{equation}\nIntegrating equation (\\ref{Temp3}) over the scale height of the disc gives\nthe evaporated mass per unit area,\n\\begin{eqnarray}\n \\dot M_{ev}^\\Omega \\approx \n1 \\times 10^{-7} \\left ({\\sigma_{g5}^2 \\over\n\\mu_{g5} (1 + \\beta/\\alpha) } \\right ) \\times \\qquad \\nonumber \\\\ \n\\qquad \\qquad S_{13}^{0.71} \\gamma^{0.29} E_{51}^{0.71} \nf_\\Sigma^{-0.29}\\;\\; {\\rm M}_\\odot {\\rm pc}^{-2} {\\rm yr}^{-1}. \n \\label{Temp4}\n\\end{eqnarray}\n\nAdopting a cooling rate of $\\Lambda \\approx 2.5 \\times 10^{-22}\nT_5^{-1.4}$ erg cm$^{3}$ s$^{-1}$\nfor $10^{5} \\simlt T \\simlt 10^{6}$ for a gas with primordial composition,\nthe ratio of $t_o$ to the cooling time $t_{\\rm cool}$ is\n\\begin{equation}\n {t_o \\over t_{\\rm cool} } \\approx 0.5 T_5^{-2.4} f_\\Sigma^{-0.5},\n \\label{Temp5}\n\\end{equation}\nThus if the temperature of the hot phase is higher than about $10^5$K,\nthe assumption that cooling can be neglected will be valid. A cooling\nfunction for a gas with primordial composition will be used throughout\nthis paper. As the metallicity of the gas builds up, the cooling time\nof the hot component will shorten and more of the supernovae energy\nwill be lost radiatively. This effect will reduce the efficiency of \nfeedback in galaxies with high metallicity but is not included in this\npaper.\n\n\n\n\\begin{figure*}\n\n\\vskip 7.0 truein\n\n\\special{psfile=pgfig4a.ps hscale=60 vscale=60 angle=-90 hoffset= 0\nvoffset=600}\n\\special{psfile=pgfig4b.ps hscale=60 vscale=60 angle=-90 hoffset= 0\nvoffset=360}\n\n\\caption\n{The left hand panels show the evolution of the gas (solid lines) and\nstellar (dashed lines) surface mass density distributions for ages of\n$0$, $0.1$, $1$, $3$, $6$ and $10$ Gyr as in figure 2. The panels to\nthe right show various properties of the hot gas component as a\nfunction of the disc radius $r/r_D$. The solid lines show the\ntemperature, dashed lines show the density and the dotted lines show\nthe ratio of overlap to cooling timescales, $t_o/t_{\\rm cool}$.}\n\\label{figure4}\n\\end{figure*}\n\n\n\\begin{figure*}\n\n\\vskip 4.8 truein\n\n\\special{psfile=pgfig5a.ps hscale=65 vscale=65 angle=-90 hoffset= -40\nvoffset=375}\n\\special{psfile=pgfig5b.ps hscale=65 vscale=65 angle=-90 hoffset= 200\nvoffset=375}\n\n\\caption\n{Evolution of the star formation rate, gas fraction and gas cloud\nvelocity dispersion for the models shown in figure 4.}\n\\label{figure5}\n\\end{figure*}\t\n\n\\subsection{Simple self-regulating model with outflow}\n\nIn this section we apply the results of the previous paragraphs to\nconstruct a simplified self-regulating model with outflow. The star\nformation rate is governed by the self-regulation algorithm as in\nSection 2.6 with the parameter $\\epsilon_c = 0.01$. This provides an\nestimate of the local supernova rate per unit volume which we insert\nin equations (26) to compute the properties of the hot phase, adopting\na value $\\phi_\\kappa = 0.1$ in equation (\\ref{Eva2}) for the\nconduction efficiency parameter. The hot gas will be lost from\nthe system if its specific enthalpy\n$$\n{1\\over 2} v^2 + {5 \\over 2} {p \\over \\rho} \n$$\nexceeds to within a factor of order unity\nits gravitational binding energy per unit mass. If the gas has\nan initial isothermal sound speed of $c_i = (kT/\\mu_p) = 37 T_5^{1/2}\n{\\rm km} {\\rm s}^{-1}$ (for a mean mass per particle of $\\mu_p = 0.61\nm_p$), conservation of specific enthalpy implies that the wind will\nreach a bulk speed of $v_w \\approx \\sqrt{5}c_i$. Some of the thermal\nenergy will be lost radiatively, and in fact the spherical steady\nwind solutions described in Appendix B suggest that a more accurate\ncriterion for the wind to escape from a galaxy is $v_w \\approx\n\\sqrt{2.5} c_i > v_{esc}$, where $v_{esc}$ \nis the escape speed from the centre of the halo (neglecting\nthe potential of the disc). If $\\sqrt{2.5} c_i < v_{esc}$, the\nhot phase is returned instantaneously to the cold phase. This type\nof binding energy criterion for outflow has been adopted in previous\nstudies ({\\it e.g.} Larson 1974, Dekel and Silk 1986) and is clearly\noversimplified, as are the assumptions of instantaneous mass loss and\nreturn of cold gas. These points will be discussed further in Section\n6, but for the moment these assumptions will be adopted to illustrate\nthe qualitative features of the model. As gas is lost from the system,\nthe circular speed of the disc component (equation 5) is simply\nrescaled by the square root of the mass of the disc that remains.\n\n\n\n\nThe evolution of the surface mass densities for the two disc models is\nillustrated in Figures 4 and 5. In model MW, the evolution is similar\nto that without outflow shown in Figure \\ref{figure2}. With the simple\nprescription for mass loss used here, no hot gas is lost unless the\ntemperature of the hot phase exceeds $T_{crit} \\approx 5 \\times\n10^6$K. This does happen at early times when the star formation rate\nis high, and about $25$\\% of the galaxy mass is lost within $10^7$\nyr. Thereafter, no more mass is lost and a nearly exponential disc is\nbuilt up with a gas distribution containing a central hole as in\nFigure 2. The star formation rate in this model declines strongly with\ntime, exceeding $100M_\\odot$/yr in the early phases of evolution.\n\nThe behaviour of model DW is qualitatively different. Here the\ncritical temperature for mass loss is much lower, $T_{crit} \\approx 3\n\\times 10^5$ K, hence half the mass of the galaxy is expelled by $\\sim\n10^8$ yr and and $66\\%$ by $1$ Gyr. After $1$ Gyr, the temperature of\nthe hot phase drops below $T_{crit}$ and the galaxy settles into a\nstable state with a low rate of star formation.\n\nThe wind prescription in these models, and particularly the assumption\nthat gas below the critical temperature necessary for escape is\nreturned instantaneously to the cold phase, is clearly oversimplified\nand so the mass loss fractions should not be taken too seriously. A\nmore detailed model is developed in Section 6. A more serious deficiency of\nthe model presented here is that the entire gas disc is assumed to\nhave formed instantaneously at $t=0$. This is unrealistic and leads\nto high rates of star formation and gas ejection at early times. A\nsimple infall model, similar to those adopted in semi-analytic models\n(White and Frenk 1991, Cole \\etal$\\;$ 1994) is included in the next\nSection.\n\n\\section{Infall Model}\n\n\\subsection{Conservation of specific angular momentum}\n\nFollowing Fall and Efstathiou (1980), the gas is assumed to follow the\nspatial distribution of the halo component with the same distribution\nof specific angular momentum prior to collapse. The halo is assumed to\nrotate cylindrically with rotation speed $v^{rot}_H(\\varpi_H)$, where\n$\\varpi_H$ is the radial coordinate in the cylindrical coordinate\nsystem. The gas is assumed to conserve its specific angular momentum\nduring its collapse, so that the final specific angular momentum of\nthe disc at radius $\\varpi_D$, $h_D = \\varpi_D v^{rot}_D$, is equal to\nthe specific angular momentum of the halo $h_D = \\varpi_H v^{rot}_H$\nat the radius $\\varpi_H$ from which the gas originated. Mass\nconservation relates the radii $\\varpi_H$ and $\\varpi_D$,\n\\begin{equation}\n {d \\varpi_H \\over d\\varpi_D} = {\\mu_D(\\varpi_D)\\over \\mu_H(\\varpi_H)}\n{M_H \\over M_D} {\\varpi_D \\over \\varpi_H}, \n \\label{Sam1}\n\\end{equation}\nwhere $M_H/M_D$ is the ratio of the halo to disc mass interior to the maximum\ninfall radius of the disc (see figure 6a below) and $\\mu_H$ is the projected\nsurface mass density of the halo\n\\begin{equation}\n \\mu_H(\\varpi) = 2 \\int_0^\\infty \\rho_H \\left ( ( \\varpi^2 + z^2)^{1/2}\n\\right ) dz.\n \\label{Sam2}\n\\end{equation}\nThe solution of equation (\\ref{Sam1}) yields $\\varpi_D(\\varpi_H)$\nand the rotation speed of the halo follows from the conservation of\nspecific angular momentum, $v^{rot}_H = \\varpi_D\nv^{rot}_D(\\varpi_D)/\\varpi_H$. The results for the parameters of\nmodels MW and DW are shown in figure\n\\ref{figure6}, where we have used the notation $s = \\varpi/r_D$. When\nexpressed in the dimensionless units of Figure \\ref{figure6}, the solutions\nfor models MW and DW are identical.\n\n\n\\begin{figure*}\n\n\\vskip 3.6 truein\n\n\\special{psfile=pgmofha.ps hscale=50 vscale=50 angle=-90 hoffset= -10\nvoffset=300}\n\\special{psfile=pgmofhb.ps hscale=50 vscale=50 angle=-90 hoffset= 230\nvoffset=300}\n\n\\caption\n{Figure 6a shows the solution of the mass conservation equation (30)\nrelating the initial halo radius $s_H = \\varpi_H/r_D$ to the final\ndisc radius $s_D = \\varpi_D/r_D$. The solid line in \nfigure 6b shows the derived rotation\ncurve of the halo in units of $v_c = (GM_D/r_D)^{1/2}$ assuming\nconservation of specific angular momentum $h_H = h_D$. The dashed line\nshows the fitting function of equation (39).}\n\\label{figure6}\n\\end{figure*}\n\n\\begin{figure*}\n\n\\vskip 3.5 truein\n\n\\special{psfile=pgcoola.ps hscale=50 vscale=50 angle=-90 hoffset= -10\nvoffset=300}\n\\special{psfile=pgcoolb.ps hscale=50 vscale=50 angle=-90 hoffset= 230\nvoffset=300}\n\n\\caption\n{The free-fall (solid lines) and cooling times (dashed lines) \nfor the two model galaxies plotted as a function of halo radius $r_H/r_D$.\nNote that for these models, the ratio of baryonic to dark mass within\nthe virial radius is $0.1$.}\n\\label{figure7}\n\\end{figure*}\n\nThis prescription is guaranteed to form an exponential disc with the\nrequired parameters. The derived rotation velocity of the halo is\nalmost independent of radius in general agreement with what is found\nin N-body simulations (Frenk \\etal$\\;$ 1988, Warren \\etal$\\;$\n1992). The upturn in the halo rotation speed at $s_H(max)\n\\approx 30$ is caused by the rapid decline in the mass of the input\nexponential disc at large radii and is of little consequence in the\ndiscussion that follows. The values of the spin parameter quoted in\nTable 1 were derived from the mass and binding energy of the halo and\nassuming that the the halo rotation velocity is constant at $0.095\nv_c$ at large radii.\n\n\\subsection{Mass infall rate}\n\n\n\n To determine the gas infall rate we compute the free fall time\nfor a gas element at rest at radius $r_i$, \n\\begin{equation}\n t_{\\rm ff} = \\int_0^{r_i} {dr \\over \\sqrt 2 [\\phi_H(r_i) - \\phi_H(r)]^{1/2}},\n \\label{Mir1}\n\\end{equation}\nand the cooling time\n\\begin{equation}\n t_{\\rm cool} = {3 \\over 2} {kT_v \\times 1.92 \\over \\Lambda(T_v) n_e(r)},\n \\label{Mir2}\n\\end{equation}\nwhere $n_e(r)$ is the electron density. The temperature $T_v$ in equation \n(\\ref{Mir2}) is set to the virial temperature derived from the equation\nof hydrostatic equilibrium assuming that the temperature is slowly\nvarying with radius\n\\begin{equation}\n T_v \\approx - v^2_H(r) {\\mu_p \\over k} {d {\\rm ln} r \\over d {\\rm ln} \\rho_b(r)},\n \\label{Mir3}\n\\end{equation}\nwhere we assume that the baryons follow the same spatial distribution\nas the halo. The infall rate is given by\n\\begin{equation}\n \\dot M_{inf} = 4 \\pi \\rho_b(r_H) r_H^2 \\Bigg \\{ \\begin{array}{ll}\n dr_H(t_{\\rm ff} = t)/dt & \\quad t_{\\rm ff} > t_{\\rm cool} \\\\\n dr_H(t_{\\rm cool} = t)/ dt & \\quad t_{\\rm cool} > t_{\\rm ff} \\end{array} . \n \\label{Mir4}\n\\end{equation}\nFinally, conservation of specific angular momentum specifies the final\nradius in the disc for each gas element. Since the halo is assumed to\nrotate on cylinders, the gas near to the poles in an infalling shell\nhas a lower specific angular momentum that the gas at the equator. The\ninfalling material is therefore distributed through the disc according\nto \n\\begin{equation} 2 \\pi \\varpi_D \\dot \\mu_D(\\varpi_D) d\\varpi_D =\n\\dot M_{inf} {\\varpi_H d\\varpi_H \\over r_H (r_H^2 - \\varpi_H^2)^{1/2}},\n \\label{Mir5}\n\\end{equation}\nwhere $\\varpi_D$ and $\\varpi_H$ are related by the solution of equation\n(\\ref{Sam1}).\n\nEquations (\\ref{Mir1}) -- (\\ref{Mir5}) specify the infall model. The\nfree-fall and cooling times of the two model galaxies are shown in\nFigure \\ref{figure7}. In the larger galaxy, gas within $r_H/r_D\n\\approx 10$ infalls on the free-fall timescale and ends up within one\nscale length of the final disc. The material in the outer parts of the\ndisc infalls on the cooling timescale. In contrast, apart from a small\namount of gas in the very central part of the halo\nwith virial temperature $< 10^4$ K, the gas in the dwarf\ngalaxy infalls on a free-fall timescale because the cooling time is so\nshort.\n\n\n\\subsection{Simple self-regulating model with inflow and outflow}\n\n The models described in this section are exactly the same as those\ndescribed in section 3.3, except that we grow the discs gradually\nusing the infall model of sections 4.1 and 4.2. In the models\ndescribed below, inflow and outflow are assumed to occur\nsimultaneously. This is often assumed in semi-analytic models\nof galaxy formation ({\\it e.g.} Cole \\etal$\\;$ 1994, Somerville and\nPrimack 1999) and may not be completely unrealistic if the\ninfalling gas is clumpy. The dark matter haloes will contain\nsignificant sub-structure ({\\it e.g.} Moore \\etal$\\;$ 1999) which may\ncontain pockets of cooled gas. Furthermore, if the cooling time is\nshort compared to\nthe dynamical time, the infalling gas will be thermally unstable (Fall\nand Rees 1985) and will fragment into clouds. These will fall to the\ncentre on a free-fall timescale if they are sufficiently dense and\nmassive that gravity dominates over the ram pressure of the wind. This\nrequires clouds with masses\n\\begin{eqnarray}\nm_{\\rm cloud} \\simgt 9.5 \\times 10^5 M_\\odot \\Big ( { a_{\\rm cloud} \\over 1{\\rm\nkpc}} \\Big ) \\Big ( {r \\over 10{\\rm kpc}} \\Big )^{-1} \\times \\nonumber \\\\\n\\qquad\n\\Big\n({\\dot M_w \\over 1 M_\\odot/{\\rm\nyr}} \\Big ) \\Big ( {v_w \\over 100 {\\rm km}/{\\rm s}} \\Big ) \\Big (\n{v_v \\over 100 {\\rm km}/{\\rm s} } \\Big )^{-2}, \\label{SR1}\n\\end{eqnarray}\nwhere $a_{\\rm cloud}$ is the radius of the cloud. However, even if\n(\\ref{SR1}) is satisfied, the clouds may be sheared and disrupted into\nsmaller clouds by Kelvin-Helmholtz instabilities on a timescale of a\nfew sound crossing times as they flow through the wind ({\\it e.g.}\nMurray \\etal $\\;$ 1993). The wind energy will be partially\nthermalized in shocks with the infalling clouds and dissipated in\nevaporating small clouds. But for the typical mass outflow rates\nexpected from dwarf galaxies ($\\dot M_w\n\\simlt 0.2 M_\\odot/{\\rm yr}$), the rate at which energy is supplied\nby the wind $\\dot E_w = {1/2}\\dot M_w v^2_w$ is much smaller than the\nenergy lost in radiative cooling,\n\\begin{eqnarray}\n{\\dot E_{\\rm cool} \\over \\dot E_w} \\approx 50 \\Lambda_{-23} \n\\left ( {v_v \\over 100 {\\rm km}/{\\rm s}} \\right )^{4}\n\\left ( {r_{\\rm cool} \\over 10 {\\rm kpc}} \\right)^{-1} \\times \\nonumber \\\\\n\\qquad \\left ( {v_w \\over 100 {\\rm km}/{\\rm s}} \\right )^{-2} \n\\left ({\\dot M_w \\over 1 M_\\odot/{\\rm\nyr}} \\right )^{-1}, \\label{SR2}\n\\end{eqnarray}\nwhere $r_{\\rm cool}$ is the radius at which the cooling time is equal to\nthe age of the system. \n\nThe qualitative picture that we propose is as follows. In \ngalaxies with a short cooling time, clouds formed by thermal\ninstabilities will infall ballistically if (\\ref{SR1}) is\nsatisfied. If (\\ref{SR1}) is not satisfied, the ram pressure of the\nwind will drive out the infalling gas and infall will be\nsuppressed. With infall suppressed, the star formation rate in the\ndisc and the wind energy will decline until infall can begin again.\nThe wind will be partially thermalised before reaching $r_{\\rm cool}$ and\ncompletely thermalised at $\\sim r_{\\rm cool}$, but the energy supplied by\nthe wind will be small compared to the energy radiated by the gas at\n$r \\simgt r_{\\rm cool}$ and so cannot prevent radiative cooling. If\n(\\ref{SR1}) is satisfied, some of the outflowing gas may fall back\ndown to the disc after shocking against infalling clouds. However, in\nthe models described here the efficiency of converting infalling gas\ninto stars is low in dwarf systems, so provided the gas does not cycle\naround the halo many times, neglecting return of some of the\noutflowing gas should not affect the qualitative features of the\nmodels. The global geometry of the system, {\\it e.g.} if the\nwind is weakly collimated perpendicular to the disc, may also \npermit simultaneous inflow and outflow of gas.\n\n\n\\begin{figure*}\n\\vskip 6.7 truein\n\n\\special{psfile=pgfig8a.ps hscale=60 vscale=60 angle=-90 hoffset= 0\nvoffset=590}\n\\special{psfile=pgfig8b.ps hscale=60 vscale=60 angle=-90 hoffset= 0\nvoffset=350}\n\n\\caption\n{The left hand panels show the evolution of the gas (solid lines) and\nstellar (dashed lines) surface mass density distributions for ages of\n$0$, $0.1$, $1$, $3$, $6$ and $10$ Gyr as in figure 2. The panels to\nthe right show the radial distribution of density, temperature and\nratio of overlap to cooling timescales for the hot gas component.}\n\\label{figure8}\n\\end{figure*}\n\n\n\\begin{figure*}\n\n\\vskip 4.5 truein\n\n\\special{psfile=pgfig9a.ps hscale=65 vscale=65 angle=-90 hoffset= -40\nvoffset=365}\n\\special{psfile=pgfig9b.ps hscale=65 vscale=65 angle=-90 hoffset= 200\nvoffset=365}\n\n\\caption\n{Evolution of the star formation rate, gas fraction and gas cloud\nvelocity dispersion for the models shown in figure 8.}\n\\label{figure9}\n\\end{figure*}\t \n \nThe interaction of an outflowing wind with an inhomogeneous infalling\ngas clearly poses a complex physical problem. In reality, the process\nmay be far from steady, with outflow occurring in bursts accompanied\nby infall from discrete sub-clumps containing cooled gas. In the\nmodels described below and in the rest of this paper, we will assume\nthat the infall and outflow occur simultaneously, steadily and without\nany interaction between the inflowing and outflowing gas. As the\ndiscussion of the preceeding two paragraphs indicates, this is\nobviously an over-simplification. It should be viewed as an\nidealization, on a similar footing to some of the other\nassumptions adopted in this paper ({\\it e.g.} spherical\nsymmetry, neglect of halo substructure and merging, steady star\nformation rates {\\it etc}) designed to give some insight into how a\nquiescent mode of feedback might operate.\n\n\n \nThe analogues of figures \\ref{figure4} and \\ref{figure5} for the\nmodels incorporating infall and outflow are shown in figures\n\\ref{figure8} and \\ref{figure9}. The discs build up \nfrom the inside out, as in the models of disc formation described by\nFall and Efstathiou (1980) and Gunn (1982). Most of the star\nformation occurs in a propagating ring containing the most recently\naccreted gas. The most significant differences from the models of\nsection 3.3, are the net rates of star formation (figure\n\\ref{figure9}) and the timescale of outflow. The initial high rates\nof star formation in the models of section 3.3 are suppressed in the\nmodels with infall, and the timescale for outflow is now much longer\nbecause it is closely linked to the gas infall timescale. Apart from\nthese differences, the final states, gas fractions and mass-loss\nfractions are similar to those in the models without infall. In model\nMW some outflow occurs when $t \\simlt 10^8$yrs and the temperature of\nthe hot gas is high enough that it can escape from the\nsystem. Thereafter, the hot component cannot escape and the disc\nbuilds up without further outflow. About 17\\% of the total galaxy\nmass is expelled in the early phases of evolution, but as we have\ndescribed above, this could be an overestimate since\nsome of this gas may be returned to the galaxy if the\nwind energy is thermalized before it reaches the virial radius. In\ncontrast, model DW drives a wind until $t \\sim 1$ Gyr and expels about\n74\\% of its mass. About half of the gas is lost within $3 \\times\n10^8$ yrs, {\\it i.e.} on about the infall timescale for most of the gas\nin the halo (see figure 7b).\n\n\n\n\\section{Refinements of the Model}\n\nThe models described in the previous sections contain a number of\nsimplifications, which we will attempt to refine in this section. We\ndo not address the problem of the interaction of a wind with the\ninfalling gas, which is well beyond the scope of this paper. Instead,\nwe introduce some simple improvements to the infall model (\\S 5.1),\nmodel for mass loss from the galactic disc (\\S 5.2, \\S 5.3) and the\npressure response of the cold ISM to the hot phase (\\S 5.4, \\S5.5).\n\n\\subsection{Infall Model}\n\nIn Section 4, we used a simplified model of infall that guarantees the\nformation of an exponential disc if angular momentum is conserved\nduring collapse. In this section, we assume a specific functional\nform for the rotation velocity of the halo,\n\\begin{equation}\n v^{rot}_H(s) = c_1v_c {(s/c_2) \\over (1 + (s/c_2))(1 + (s/c_3)^{c_4})},\n \\quad s \\equiv r/r_D\n \\label{Inf1}\n\\end{equation}\nwith $c_1 = 0.115$, $c_2= 0.6$, $c_3 = 16$, $c_4 = 0.25$. The functional form and\ncoefficients in equation (\\ref{Inf1}) have been chosen to provide a good\nfit to the halo rotation profile derived in section 4.1 from conservation\nof specific angular momentum and is plotted as the dashed line in \nfigure (6b). As in the previous section,\nthe gas is assumed to follow the same radial density\ndistribution and rotation velocity as the halo component, but its\nfinal radius in the disc is computed by assuming conservation of\nspecific angular momentum and self-consistently solving for the\nrotation speed of the disc component. The halo component\nis assumed to be rigid and the contribution of the disc component to\n$v^{rot}_D$ is computed using the\nFourier-Bessel theorem (see Binney and Tremaine 1987 \\S 2.6)\n\\begin{eqnarray}\nv^2(r) = - r \\int_0^\\infty S(k) J_1(kr)k\\;dk, \\quad \\nonumber \\\\ \nS(k) = \n- 2\\pi G \\int_0^\\infty J_0(kr) \\mu_D(r) r \\;dr. \\label{Inf2}\n% \\kappa^2(r) = 2 {v^2(r) \\over r^2} - \\int_0^\\infty S(k) k^2 J_0(kr)\\; dk.\n%\\qquad \\qquad \\qquad \\qquad \\qquad \\qquad\n\\end{eqnarray}\nEquation (\\ref{Inf2}) is time consuming to evaluate accurately and in\nour application $v^2(r)$ must be computed many times. A fast\nalgorithm has therefore been developed as described in Appendix A. The\nepicyclic frequency $\\kappa$ is required in equation (\\ref{Stab3}) to\ncompute the instantaneous star formation rate and is derived by\nnumerically differentiating the rotation speed.\n\n\nWith this formulation of the infall model, the infall rate is governed\nby the dark matter profile and the ratio of dark to baryonic mass\nwithin the virial radius, $M_v/M_D = (v_v/v_c)^2 f_{coll}$. For the\nmodels described here, we adopt $M_v/M_D = 10$, consistent with the\nparameters listed in Table 1. The final disc surface mass density will\nbe close to an exponential by construction, since the halo rotation\nvelocity (\\ref{Inf1}) has been chosen to match the rotation profile\nderived by assuming an exponential disc and conservation of specific\nangular momentum.\n\n\n\n\n%\\subsection{Response of the disc to mass changes}\n%\n%If the disc loses a significant fraction of its mass, it will expand\n%resulting in a disc of low surface mass density and surface brightness\n%(see {\\it e.g.} Dekel and Silk 1986). This is modeled under the\n%assumption that the disc\n%responds adiabatically to mass loss so that mass elements at radius\n%$r$ move according to\n%\\begin{equation}\n% {dr \\over dt} = - {r \\over v^{rot}_D} {dv^{rot}_D \\over dt},\n% \\label{Res1}\n%\\end{equation}\n%where $v^{rot}_D$ is the rotation curve of the disc, including the\n%contribution from the halo. \n\n\n\n\\subsection{Galactic Fountain}\n\n\nIn previous sections, we have assumed that gas is lost from the disc\nif the bulk velocity of the wind $v_w \\approx \\sqrt{2.5}c_i$, exceeds\nthe escape speed $v_{esc}$ from the halo, but is otherwise returned\ninstantaneously to the ISM. More realistically, gas with $v_w <\nv_{esc}$ will circulate in the halo along a roughly ballistic\ntrajectory and will cool forming a galactic fountain (Shapiro and Field 1976,\nBregman 1980). In the models described in this section, hot gas with\n$v_w < v_{esc}$ is returned to the disc at the radius from which it\nwas expelled after a time $t_{ret}$,\n\\begin{equation}\n t_{ret} = 2 t_{ff}(r_{max}), \\qquad v^2_w = 2[ \\phi_H(r_{max}) -\n\\phi_H(0)],\n \\label{Esc2}\n\\end{equation}\n{\\it i.e.} we ignore the gravity of the disc and the\nangular momentum of the gas in computing the ballistic trajectory\nof a gas element.\n\n\n\\subsection{Escape Velocity of the Wind}\n\nThe detailed dynamics of the hot corona itself is complicated and\nbeyond the scope of this paper. Type II supernovae at the upper and\nlower edges of the gas disc will be able to inject their energy\ndirectly into the hot gas, as will Type Ia supernovae forming in the\nthicker stellar disc. In addition, the hot component will interact\nwith the primordial infalling gas in a complicated way as sketched in\n\\S 4.3.\n\n\nIn the absence of radiative cooling, the hot gas will extend\nhigh above the galactic disc in an extended corona. For an\nisothermal corona, the equation of hydrostatic equilibrium in the \nz-direction has the following approximate solution,\n\\begin{eqnarray}\n {\\rho_H(\\varpi, z) \\over \\rho_H(0)} \\approx {\\rm sech}^{2p_g} \\left (\n{ z \\over H_g} \\right )\\; {\\rm sech}^{2p_s} \\\n\\left (\n{ z \\over H_s} \\right ) \\times \\nonumber \\qquad \\\\\n {\\rm exp} \\left ( -{1 \\over c_i^2}\n\\int_0^z {z v^2_H(r) \\over r^2}\\; dz \\right ), \\quad r^2 = \\varpi^2 +\nz^2, \\label{Win1}\n\\end{eqnarray}\n\\begin{eqnarray}\n p_g = {\\mu_g \\sigma^2_g \\sigma_s \\over c_i^2 (\\mu_g \\sigma_s + \n\\mu_s \\sigma_g)}, \\;\\; \n p_s = {\\mu_s \\sigma^2_s \\sigma_g \\over c_i^2 (\\mu_g \\sigma_s + \n\\mu_s \\sigma_g)}, \\;\\; \\qquad \\qquad \\nonumber\n\\end{eqnarray}\nwhere we have assumed that both the stars and the gas follow ${\\rm\nsech^2}$ vertical distributions (equation \\ref{Vert1}) and $c_i$ is\nthe isothermal sound speed of the hot gas. We define a characteristic\nscale height for the hot component, $H_{hot}(\\varpi)$, at which the\ndensity drops by a factor $\\sim e$ according to equation\n(\\ref{Win1}). If radiative cooling were negligible, we would expect a\nsonic point in the flow at about $z \\sim H_{hot}$.\nIt is interesting to compare some characteristic\nnumbers for the coronal gas:\n\\beglet\n\\begin{eqnarray}\n\\dot E_{in} \\approx 1.1 \\times 10^{40} T_{h6} \\dot M_{ev}\\; {\\rm erg}\\;{\\rm\ns}^{-1} \\qquad \\qquad\\qquad \\qquad \\quad \\\\\n\\dot E_{\\rm SNII} \\approx 5.7 \\times 10^{40} \\epsilon_{\\rm SNII} E_{51}\\dot M_* \\;{\\rm\nerg}\\;{\\rm s}^{-1} \\qquad \\qquad \\qquad \\;\\; \\\\\n\\dot E_{\\rm cool} \\approx 2 \\times 10^{39} n_{h-2}^{2} \\Lambda_{-23} \\left (\n{H_{hot} \\over 1\\;{\\rm kpc} } \\right ) \\left ( {R_{hot} \\over 3\\; {\\rm\nkpc}} \\right )^2 {\\rm erg}\\;{\\rm s}^{-1} \n \\label{Win2}\n\\end{eqnarray}\n\\endlet\nwhere the rates $\\dot M_{ev}$, $\\dot M_*$ are in $M_\\odot\\;/{\\rm yr}$.\nHere $\\dot E_{in}$ is the thermal energy injected into the hot corona\nby evaporating cold gas at a rate $\\dot M_{ev}$, $\\dot E_{\\rm SNII}$ is\nthe energy supplied to the corona by Type II supernovae forming above\nand below one scale height of the cold gas layer and the parameter\n$\\epsilon_{\\rm SNII}$ expresses the efficiency with which this energy\nis coupled to the hot coronal gas. $\\dot E_{\\rm cool}$ is the rate of\nenergy lost by a uniform density isothermal corona of scale height\n$H_{hot}$ within a cylinder of radius $R_{hot}$. For a large galaxy\nsuch as the Milky Way that can sustain an evaporation rate of $\\sim 10\nM_\\odot/{\\rm yr}$, $\\dot E_{\\rm cool}$ is small compared to $\\dot\nE_{in}$ and it is a good approximation to neglect radiative cooling in\nthe early stages of the flow (see Appendix B). However, in a dwarf\ngalaxy $\\dot E_{\\rm cool}$ is typically larger than $\\dot E_{in}$. In this\ncase, we expect that the hot component will develop a sonic point at a\ncharacteristic cooling scale height $H_{\\rm cool}$\n\\begin{equation}\n H_{\\rm cool} \\sim v_w t_{\\rm cool} \\sim 11 \\left ( {v_w \\over 100\\; {\\rm\n km}/{\\rm s}} \\right ) T_{h6} n_{h-2}^{-1} \\Lambda_{-23}^{-1} \\;\\;\n {\\rm kpc}. \\label{Win4}\n\\end{equation}\n(see {\\it e.g.} Kahn 1981 and Appendix B) and that most of the thermal\nenergy will be converted into kinetic energy by the time the gas flows\nto $H_{\\rm cool}$. We therefore ignore radiative cooling and estimate the \nbulk velocity of the wind at each radial shell in the disc from\n\\beglet\n\\begin{equation}\n {1 \\over 2} \\dot M_{out}^\\Omega v^2_w = \\dot E_{in}^\\Omega + \\dot\n E_{\\rm SNII}^\\Omega, \\qquad\\qquad \n \\label{Win3a}\n\\end{equation}\nand to close the equations we assume that\n\\begin{equation}\n\\dot M_{out}^\\Omega = \\dot M_{in}^\\Omega = \\dot M_{ev}^\\Omega.\n \\label{Win3b}\n\\end{equation}\n\\endlet\n(Note that the numerical coefficient in equation (43a) has been\nadjusted to give $v_w = \\sqrt{2.5}c_i$ if $\\dot E_{\\rm SNII} =0$ so\nthat the criterion for the wind to escape, $v_w > v_{esc}$, is the same\nas in the preceeding Section).\n\nEnergy input from Type II supernovae exploding high above the cold gas\nlayer will make a small contribution to the thermal energy of the hot\ncoronal gas. For values of $\\epsilon_{SNII} \\sim 1$, $\\dot\nE_{SNII}^\\Omega$ will be about $20\\%$ or so of $\\dot E_{in}$ and\ncannot be higher because $\\dot M_{ev}^\\Omega$ and the star formation\nrate are nearly proportional to each other (equation\n\\ref{Temp3}). Type Ia supernovae will also supply energy to the\ncorona, with a time lag of perhaps $\\simgt 1$ Gyr (Madau, Della Valle\nand Panagia 1998). However, this effect will also make a small\nperturbation to the energy budget of the corona and so it is ignored\nhere. Furthermore, in the models described here much of the gas is\nexpelled on a timescale of $\\simlt 1$ Gyr, thus feedback is likely to\nbe more or less complete before energy injection from Type Ia\nsupernovae becomes significant.\n\n\n\n\n\n\\subsection{Pressure equilibrium and cold cloud radii}\n\nIn the models of Section 3 and 4, the cold cloud radii were kept constant\nirrespective of the pressure of the confining hot phase. More\nrealistically, the cold cloud radii will adjust to maintain\napproximate pressure equilibrium with the hot phase. Thus\n\\begin{equation}\n {a \\over a_\\odot} \\approx 0.53 \\left ( {T_c \\over 80K} \\right )^{1/3}\n(n_{h-2} T_{h6})^{-1/3},\n \\label{Pe5}\n\\end{equation}\nwhere $a_\\odot$ denotes the cloud radii at the solar neighbourhood with\nvalues as given in equation (\\ref{Diss1}) and $T_c$ is the\ninternal temperature of the cold clouds. In our own Galaxy,\nphotoelectric heating of dust grains is believed to be the main\nheating mechanism of the cold clouds (see {\\it e.g.} Wolfire \\etal$\\;$\n1995) but other heating mechanisms may be important, for example,\ncosmic-ray heating (Field, Goldsmith and Habing 1969). We therefore\nexpect that $T_c$ varies in a complex (and uncomputable) way as a\ngalaxy evolves. To assess the effects of the pressure\nresponse of the cold clouds, $T_c$ will be assumed to remain constant at\n$80$K. The cloud radii are then determined solely by the pressure of\nthe hot component via equation (\\ref{Pe5}).\n\n\nThe energy lost through cloud collisions (equation \\ref{Diss2}) varies\nas $a^2$ (for fixed cloud masses). However, the cloud heating\nefficiency factor $\\epsilon_c$ will also change as the cloud radii\nchange in response to the pressure of the hot phase. In the model of\nMO77, the energy acquired from momentum exchange with cooling\nsupernovae shells varies as $a^4$. The net effect of these variations\nin the self-regulating star formation model is to introduce positive\nfeedback, since a higher rate of star formation is required to balance\nenergy lost through cloud collisions in regions where the ambient\npressure is higher. This is modelled by assuming $\\dot E_{coll}\n\\propto (a/a_\\odot)^2$ and $\\epsilon_c = \\epsilon_{c\\odot}\n(a/a_\\odot)^4$, where $\\epsilon_{c\\odot}$ is a fiducial efficiency\nfactor.\n\n\n\\subsection{Induced star formation}\n\nThe maximum mass for an isothermal cloud in pressure equilibrium with\nthe confining medium of pressure $p_h$ is given by the Bonner-Ebert\ncriterion (Bonner 1956, Ebert 1955, Spitzer 1968),\n\\begin{eqnarray}\n m_{\\rm BE} = 1.18 \\left ( {k T_c \\over \\mu_p} \\right )^2 G^{-3/2}\n p_h^{-1/2} \\qquad \\nonumber \\\\\n = 433 \\left (T_c \\over 80K \\right )^2 (n_{h-2} T_{h6})^{-1/2} M_\\odot.\n \\label{Be1}\n\\end{eqnarray}\nFor our own Galaxy (MO77), $n_h \\sim 1.5 \\times 10^{-3} {\\rm\ncm}^{-3}$, $T_h \\sim 4 \\times 10^5$ and $p_h \\sim 3 \\times 10^{-12}\n{\\rm dyne}\\;{\\rm cm}^{-2}$, hence $m_{\\rm BE} \\approx 1700\nM_\\odot$. This is reasonably close to the upper mass limit, $m_u =\n4300 M_\\odot$, for the cold cloud mass spectrum adopted in this paper\n($a_u = 10 {\\rm pc}$ with $\\rho_c = 7 \\times 10^{-23}\\; {\\rm\ng/cm^3}$). Gravitational stability requires $m_u \\approx m_{\\rm BE}$\nand we will henceforth impose this condition in determining the upper\nmass limit of the cold cloud spectrum. An increase in the pressure of\nthe hot phase will lead to a decrease in $m_u$ and hence to some\npressure induced star formation. If the over-pressured clouds fragment\ninto stars with an efficiency $\\epsilon_{\\rm BE}$, the induced star\nformation rate is given by\n\\begin{equation}\n{dM_s^\\Omega \\over dt} = \\epsilon_{\\rm BE} {M_g^\\Omega \\over 2 p_h \n{\\rm ln } (m_u/m_L)} \\Bigg \\{ \\begin{array}{ll}\n dp_h/dt & \\quad dp_h/dt > 0 \\\\\n 0 & \\quad dp_h/dt \\le 0 \\end{array} ,\n \\label{Be2}\n\\end{equation}\nwhere $m_L$ is the lower limit to the cloud mass spectrum, $m_L\n\\approx 0.5 M_\\odot$. This provides an additional source of positive\nfeedback, since as the pressure of the hot component rises the star\nformation rate of the self-regulating model is enhanced by pressure\ninduced star formation. \n\n\n\n\\subsection{Chemical evolution}\n\nIt is straightforward to include chemical evolution in the models using the\ninstantaneous recycling approximation. We distinguish between `primordial'\ninfalling gas accreting at a rate $d\\mu_I/dt$ with metallicity $Z_I$, and\nprocessed gas from the galactic fountain of metallicity $Z_F$ accreted at\na rate $d\\mu_F/dt$. The equation of chemical evolution is then\n\\begin{equation}\n \\mu_g dZ = p d\\mu_s + (Z_I - Z) d\\mu_I + (Z_F - Z) d\\mu_F,\n \\label{CE1}\n\\end{equation}\n(see {\\it e.g.} Pagel 1997), where $p$ is the yield. \n%The instantaneous\n%recycling approximation should be reasonably accurate except where the\n%gas density in the disc becomes low. \nWe adopt a yield of $p = 0.02$ and assume that the primordial gas has\nzero metallicity ($Z_I =0$). Gas ejected in a galactic fountain is\nassumed to have the same metallicity as the ISM at the time that \nthe gas was ejected. Within the disc, the ISM gas is assumed to be perfectly\nmixed at all times. We normalize the metallicities to the solar value,\nfor which we adopt $Z_\\odot = 0.02$.\n\n\\section{Results and Discussion}\n\n\\subsection{Variation of input parameters}\n\nIn addition to the many simplifying assumptions introduced in previous\nsections, the model described here has $4$ key parameters: (i)\n$\\phi_\\kappa$, determining the efficiency of heat conduction (equation\n\\ref{Eva1}); (ii) $\\epsilon_{c\\odot}$, controlling the star formation\nrate (equation \\ref{Diss4}); (iii) $\\epsilon_{\\rm SNII}$, determining the\nefficiency with which energy from Type II supernovae couples directly\nto the gas (equation \\ref{Win3a}) ; (iv) $\\epsilon_{\\rm BE}$, setting the\nefficiency with which over-pressured ISM clouds collapse to make stars\n(equation \\ref{Be2}). In addition, the ISM cloud radii can be allowed\nto vary in response to the pressure of the ISM as described in Section\n5.4.\n\n\\begin{table*}\n\\bigskip\n\\centerline{\\bf Table 2: Feedback Efficiency: Variation of Input Parameters}\n\\begin{center}\n\\begin{tabular}{|c|cc|cc|cc|} \\hline \\hline\nModel & MW1 & DW1 & MW2 & DW2 & MW3 & DW3 \\\\\n$\\phi_\\kappa$ & \\multicolumn{2}{c|}{$0.1$} & \\multicolumn{2}{c|}{$0.01$} & \\multicolumn{2}{c|}{$0.1$} \\\\\n$\\epsilon_{c\\odot}$ & \\multicolumn{2}{c|} {$0.01$} & \\multicolumn{2}{c|} {$0.01$} & \\multicolumn{2}{c|} {$0.03$} \\\\\n$\\epsilon_{\\rm SNII}$ & \\multicolumn{2}{c|} {$0.0$} & \\multicolumn{2}{c|} {$0.0$} &\\multicolumn{2}{c|} {$1.0$} \\\\\n$\\epsilon_{\\rm BE}$ & \\multicolumn{2}{c|} {$0.0$} & \\multicolumn{2}{c|} {$0.0$} &\\multicolumn{2}{c|} {$0.0$} \\\\\n\\S5.4 & \\multicolumn{2}{c|} {no} & \\multicolumn{2}{c|} {no} & \\multicolumn{2}{c|} {no} \\\\\n$M_s$ ($M_\\odot$) & $2.8\\times 10^{10}$ & $4.2 \\times 10^7$ & $2.3\n\\times10^{10}$& $7.1 \\times 10^7$ & $2.3 \\times 10^{10}$& $3.6 \\times\n10^7$ \\\\\n$M_g$ ($M_\\odot$) & $5.4\\times 10^{9}$ & $1.3\\times 10^8$ & $5.4\n\\times10^9$& $9.9 \\times 10^7$& $6.9 \\times 10^9$& $1.3 \\times 10^8$\\\\\n$M_{ej}$ ($M_\\odot$) & $4.6 \\times 10^9$& $2.6 \\times 10^8$ & $7.9\n\\times 10^9$ & $3.1 \\times 10^8$ & $6.5 \\times 10^9$& $3.0 \\times\n10^8$ \\\\\n$f_{ej}$ & $0.12$& $0.59$ & $0.22$ & $0.64$ & $0.18$& $0.64$ \\\\\n$\\tau_{ej}$ (Gyr) & $0.25$& $0.82$ & $0.40$& $1.8$ & $0.30$ &$1.24$ \\\\\n$f_{*}$ & $0.74$& $0.10$ & $0.63$ & $0.15$ & $0.63$ & $0.08$ \\\\\n$\\langle Z_g/Z_\\odot \\rangle$ & $0.65$& $0.03$ & $0.57$ & $0.04$ & $0.56$ & $0.02$ \\\\\n$\\langle Z_s/Z_\\odot \\rangle$ & $0.55$& $0.20$ & $0.43$ & $0.30$ & $0.42$ & $0.19$ \\\\\n$\\langle Z_{ej}/Z_\\odot \\rangle$ & $0.29$& $0.11$ & $0.38$ & $0.14$ & $0.26$ & $0.09$ \\\\\n\\hline\n\\noalign{\\medskip}\n\\end{tabular}\n\n\n\\begin{tabular}{|c|cc|cc|cc|} \\hline \\hline\nModel & MW4 & DW4 & MW5 & DW5 & MW6 & DW6 \\\\\n$\\phi_\\kappa$ & \\multicolumn{2}{c|}{$0.1$} & \\multicolumn{2}{c|}{$0.1$} & \\multicolumn{2}{c|}{$0.1$} \\\\\n$\\epsilon_{c\\odot}$ & \\multicolumn{2}{c|} {$0.01$} & \\multicolumn{2}{c|} {$0.01$} & \\multicolumn{2}{c|} {$0.01$} \\\\\n$\\epsilon_{\\rm SNII}$ & \\multicolumn{2}{c|} {$1.0$} & \\multicolumn{2}{c|} {$1.0$} &\\multicolumn{2}{c|} {$1.0$} \\\\\n$\\epsilon_{\\rm BE}$ & \\multicolumn{2}{c|} {$0.0$} & \\multicolumn{2}{c|} {$0.05$} &\\multicolumn{2}{c|} {$0.05$} \\\\\n\\S5.4 & \\multicolumn{2}{c|} {yes} & \\multicolumn{2}{c|} {no} & \\multicolumn{2}{c|} {yes} \\\\\n$M_s$ ($M_\\odot$) & $2.5\\times 10^{10}$ & $4.3 \\times 10^7$ & $2.4\n\\times10^{10}$ & $4.3 \\times 10^7$ & $2.5 \\times 10^{10}$& $4.5 \\times\n10^7$ \\\\\n$M_g$ ($M_\\odot$) & $2.1\\times 10^{9}$ & $3.5\\times 10^7$ & $4.9\n\\times10^9$& $9.5 \\times 10^7$& $1.9 \\times 10^9$& $2.9 \\times 10^7$\\\\\n$M_{ej}$ ($M_\\odot$) & $7.1 \\times 10^9$& $3.4 \\times 10^8$ & $6.8\n\\times 10^9$ & $3.1 \\times 10^8$ & $7.2 \\times 10^9$& $3.4 \\times\n10^8$ \\\\\n$f_{ej}$ & $0.21$& $0.82$ & $0.19$ & $0.69$ & $0.21$& $0.82$ \\\\\n$\\tau_{ej}$ (Gyr) & $0.30$& $1.19$ & $0.30$& $1.19$ & $0.21$ &$1.12$ \\\\\n$f_{*}$ & $0.73$& $0.10$ & $0.67$ & $0.09$ & $0.74$ & $0.11$ \\\\\n$\\langle Z_g/Z_\\odot \\rangle$ & $0.62$& $0.03$ & $0.59$ & $0.02$ & $0.64$ & $0.02$ \\\\\n$\\langle Z_s/Z_\\odot \\rangle$ & $0.47$& $0.17$ & $0.44$ & $0.21$ & $0.48$ & $0.19$ \\\\\n$\\langle Z_{ej}/Z_\\odot \\rangle$ & $0.26$& $0.09$ & $0.27$ & $0.10$ & $0.27$ & $0.10$ \\\\\n\\hline\n\\noalign{\\medskip}\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\noindent\n\n\n\\begin{figure*}\n\n\\vskip 6.7 truein\n\n\\special{psfile=pgmodule7_MW1_new.ps hscale=60 vscale=60 angle=-90 hoffset= 0\nvoffset=590}\n\\special{psfile=pgmodule7_DW1_new.ps hscale=60 vscale=60 angle=-90 hoffset= 0\nvoffset=350}\n\n\\caption\n{The left hand panels show the evolution of the stellar (dashed lines)\nand cold gas (solid lines) profiles\n in models MW1 and DW1. The right hand panels\nshow the temperature (solid lines) and density (dashed lines) of the\nhot component. The radius $r_D$ is the fiducial radius listed in\nTable 1. The results are plotted at ages of $0.1$, $1$, $3$, $6$,\n$10$ Gyr and (for MW1 only) at $15\\;$ Gyr.}\n\\label{figure10}\n\\end{figure*}\n\n\n\n\nThe effects of varying these parameters are summarised in Table\n2. Here we have run six models of galaxies MW and DW varying the input\nparameters. We list the final stellar mass $M_s$, gaseous disc mass\n$M_g$, and ejected mass $M_{ej}$ after $10$ Gyr for model DW (there is\nvery little evolution after this time) and after $15$ Gyr for model\nMW. The parameters $f_{ej}$ and $f_*$ are the final ejected and\nstellar masses divided by the total baryonic mass ($M_{ej} + M_* +\nM_g$). $\\tau_{ej}$ is the time when half the final ejected mass is\nlost. The last three numbers list the final mean metallicities of\nthe cold ISM, the stars and the ejected gas.\n\nThe most important result from this table is that the final parameters\nof the models are remarkably insensitive to variations of the input\nparameters. For models DW, the final stellar disc mass varies between\n$\\sim 4 \\times 10^7$ and $7 \\times 10^7 M_\\odot$ and the gas ejection\nfraction varies from $0.59$ to $0.82$. For models MW, the final\nstellar disc mass varies between $\\sim 2.3 \\times 10^{10}$ and $2.8\n\\times 10^{10} M_\\odot$ and the gas ejection fraction varies from\n$0.12$ to $0.22$. Figure \\ref{figure10} shows the evolution of the\nradial density profiles of models MW1 and DW1 and figure\n\\ref{figure11} shows the time evolution of the star formation rates,\ngas fractions and gas velocity dispersions. The models of Table 2 \nbehave in similar ways, and so these two figures are representative of\nthe behaviour of all of the models. These figures are qualitatively similar\nto those of the simple model of Section 4 (figure \\ref{figure8} and\n\\ref{figure9}). The main differences are:\n\n\\begin{figure*}\n\n\\vskip 4.5 truein\n\n\\special{psfile=pgfig11a_new.ps hscale=65 vscale=65 angle=-90 hoffset= -40\nvoffset=365}\n\\special{psfile=pgfig11b_new.ps hscale=65 vscale=65 angle=-90 hoffset= 200\nvoffset=365}\n\n\\caption\n{Evolution of the star formation rate, gas fraction and gas cloud\nvelocity dispersion for the models shown in figure 10.}\n\\label{figure11}\n\\end{figure*}\t\n\n\n\\smallskip\n\n\\noindent\n(a) The gas discs have a sharper outer edge. This is a consequence of the\ninfall model; the outer edge is determined by the final time of the model\nwhich sets the maximum cooling radius within the halo ({\\it cf.} figures\n\\ref{figure7}). \n\n\\smallskip\n\n\\noindent\n(b) The radial profiles of models MW show oscillatory behaviour near\ntheir centres, and the star formation rates and gas fractions show\noscillatory behaviour as a function of time. Both of these effects are\na consequence of the galactic fountain.\n\n\n\nIn these models, the star formation rate begins to rise as the gas\ndisc builds up from infalling gas. As the star formation rate rises,\nthe cold ISM is converted efficiently into a hot phase and this is\neither driven out of the halo or becomes part of the galactic\nfountain. In models MW, most of the gas that escapes from the system\nis lost within this early ($\\simlt 0.2$ Gyr) period of star formation\nwhen the net star formation rate is close to its peak of $\\sim 10\nM_\\odot$/yr. After about $0.2$ Gyr, the temperature of the hot phase \nin models MW settles to $\\sim 10^6$ K very nearly\nindependent of radius ({\\it cf} figure \\ref{figure10}), and\nso the galactic fountain cycles on a characteristic time-scale of\n$\\sim 4\\times 10^8$ yr. Models DW behave in much the same way as the\nsimpler models of Section 4.3, except that infall, by construction,\nextends over a longer period of time. In these models, the escape\ncriterion for the wind is satistfied over most of the lifetime of the\ndisc and hence the model of a galactic fountain is unimportant.\n\n\nWe discuss briefly the effects of varying the input parameters:\n\n\\smallskip\n\n\\noindent\n$\\phi_k$: The evaporation rate $\\dot M_{ev}$ has a weak dependence on\nthe evaporation parameter $\\phi_k$ ($\\propto \\phi_k^{0.29}$, equation\n\\ref{Temp4}) and obviously decreases as $\\phi_k$ is reduced. However,\nthe temperature of the hot component is proportional to\n$\\phi_k^{-0.29}$ and hence rises as $\\phi_k$ is reduced. The net\neffect is that the mass of gas ejected is relatively insensitive to\n$\\phi_k$, but the mass of the final stellar disc increases as \n$\\phi_k$ is reduced.\n\n\\smallskip\n\n\\noindent\n$\\epsilon_{c\\odot}$: Increasing this parameter reduces the\nstar formation rate in the self-regulating model for a fixed gas\nsurface density and velocity dispersion (equations \\ref{SN2} and\n\\ref{Diss3}). However, a lower past star formation rate leads to\na higher gas surface density which increases the star formation rate.\nThese effects tend to cancel and so the models are \ninsensitive to variations in $\\epsilon_{c\\odot}$.\n\n\n\\smallskip\n\n\\noindent\n$\\epsilon_{\\rm SNII}$: Setting this parameter to unity increases the\ntemperature of the hot component slightly and hence increases the efficiency\nof feedback. As explained in Section 5.3, energy injection by Type\nII supernovae at large vertical scale heights will always be small\ncompared to the internal energy of the hot phase.\n\n\n\\smallskip\n\n\\noindent\n$\\epsilon_{BE}$: Values of $\\epsilon_{\\rm BE} \\sim 0.05$ have little\neffect on the evolution. Provided that $\\epsilon_{\\rm BE}$ is not too\nlarge (so that it does not dominate the net star formation rate),\npressure enhanced star formation is self-limiting because it increases\nthe velocity dispersion of the cold clouds (reducing the star\nformation rate in the self-regulating model) and converts cold gas to\nhot gas. Both of these effects tend to reduce the net star formation\nrate.\n\n\\smallskip\n\n\\noindent\n{\\it Pressure response of cold cloud radii:} Allowing the cold gas\nradii to respond to the pressure of the hot phase provides strong\npositive feedback in the very early stages of galaxy formation when\nthe pressure of the hot phase is high. However, most of the cold ISM\nis ejected on a much longer timescale ({\\it cf.} values of $\\tau_{ej}$\nin Table 2) when the typical pressure of the ISM is similar to that in\nour own Galaxy. The pressure response of the cold cloud radii\ntherefore has little effect on the final feedback efficiency.\n\n\nThe models described here involve a complex set of coupled equations\nand a number of parameters. However, one of the most\ninteresting aspects of this study is that the equations interact in\nsuch a way that the evolution of the models is insensitive to the\nparameters. Most importantly, the efficiency of feedback is\ninsensitive to the thermal conduction parameter $\\phi_\\kappa$. The\npossible severe suppression of thermal conduction by tangled magnetic\nfields in astrophysical environments is a long standing theoretical\nproblem. However, our results show that even a reduction of $\\kappa$\nby a factor of $100$ or more will not significantly alter the\nefficiency of feedback.\n\n\\begin{figure*}\n\\vskip 4.05 truein\n\n\\special{psfile=pg_met1a.ps hscale=30 vscale=30 angle=-90 hoffset= 40\nvoffset=325}\n\\special{psfile=pg_met1b.ps hscale=30 vscale=30 angle=-90 hoffset= 230\nvoffset=325}\n\n\\special{psfile=pg_met1c.ps hscale=30 vscale=30 angle=-90 hoffset= 40\nvoffset=175}\n\\special{psfile=pg_met1d.ps hscale=30 vscale=30 angle=-90 hoffset= 230\nvoffset=175}\n\n\n\\caption\n{The distribution of stellar metallicities at four radii in model MW1\nat an age of $15$ Gyr.}\n\\label{figure12}\n\\end{figure*}\n\n\\begin{figure*}\n\\vskip 4.0 truein\n\n\\special{psfile=pg_met2a.ps hscale=30 vscale=30 angle=-90 hoffset= 40\nvoffset=325}\n\\special{psfile=pg_met2b.ps hscale=30 vscale=30 angle=-90 hoffset= 230\nvoffset=325}\n\n\\special{psfile=pg_met2c.ps hscale=30 vscale=30 angle=-90 hoffset= 40\nvoffset=175}\n\\special{psfile=pg_met2d.ps hscale=30 vscale=30 angle=-90 hoffset= 230\nvoffset=175}\n\n\n\\caption\n{The distribution of stellar metallicities at four radii in model DW1\nat an age of $10$ Gyr.}\n\\label{figure13}\n\\end{figure*}\n\n\\begin{figure*}\n\\vskip 3.0 truein\n\n\\special{psfile=pg_zgrad_stars.ps hscale=40 vscale=45 angle=-90 hoffset= -20\nvoffset=270}\n\n\\special{psfile=pg_zgrad_gas.ps hscale=40 vscale=45 angle=-90 hoffset= 220\nvoffset=270}\n\n\n\\caption\n{Metallicity gradients in the stars and gas at the final times in\nmodels MW1 and DW1}\n\\label{figure14}\n\\end{figure*}\n\n\n\n\\subsection{Chemical evolution}\n\n\nIn this section, we summarize some of the results relating to chemical\nevolution in these models. Our intention is not to present a detailed\nmodel of chemical evolution in disc systems along the lines of, for\nexample, Lacey and Fall (1983, 1985) but to investigate some of the\ngeneral features of chemical evolution with physically motivated\nmodels of inflow and outflow. The chemical evolution model is based on\nthe instantaneous recycling approximation as described in Section\n5.6. This is probably a reasonable approximation since the timescales\nof star formation and outflow are $\\sim 1\\;$Gyr, but will overestimate\nthe gas metallicities where the gas density is low. As in the previous\nSection, results from models MW1 and DW1 are used to illustrate the\ngeneral features of the models. The other models listed in Table 2\nbehave in very similar ways. \n\n\n\n\n\n\\subsubsection{Stellar metallicity distribution}\n\nThe final mean stellar metallicities are typically $Z_s/Z_\\odot\n\\approx 0.5$ in models MW and $\\approx 0.2$ in models DW. Models DW\nhave a lower stellar metallicity because a larger fraction of the ISM\nis expelled in a wind. The stellar metallicity distributions are shown\nin Figures (\\ref{figure12}) and (\\ref{figure13}). Figure\n(\\ref{figure12}c) is particularly interesting because this radius is\nclose to the solar radius. This metallicity distribution is quite\nsimilar to that of G-dwarfs in the solar cylinder (see {\\it e.g.}\nfigure 8.19 of Pagel 1997), showing that the infall model solves the\n`G-dwarf' problem of closed box models of chemical evolution. The\nmetallicity distributions of model DW1 plotted in figure\n(\\ref{figure13}) also show a lack of stars with low metallicities.\n\n\n\\subsubsection{Metallicity gradients}\n\nOver most of the stellar disc, model MW1 has a fairly weak stellar\nmetallicity gradient (figure \\ref{figure14}a) except at the very outer\nedge where the stellar density and metallicity fall abrubtly. This\ndiffers from the metallicity gradients seen in large disc systems\nwhich show linear gradients (see Vila-Costas 1998 for a recent review). It\nis possible that this problem might be resolved by including radial\ngas flows in the models (Lacey and Fall 1985, Pitts and Tayler 1985).\nThe stellar metallicity gradients in model DW1 are steeper, in\nqualitative with observations which indicate that the abundance\ngradients in Scd and Irr galaxies are steeper than those in earlier\ntype galaxies.\n\nThe radial gas metallicity profiles are shown in figure\n(\\ref{figure14}b). Model DW contains a gasesous disc extending well\nbeyond the edge of the stellar disc. This gas disc has a low\nmetallicity in the outer parts, with $Z/Z_\\odot \\simlt 10^{-2}$ at $r\n\\simgt 2\\;$kpc. At these large radii, the star formation rate is\nalways low and the gas disc can survive for much longer than a Hubble\ntime without converting into stars. This is unlikely to happen in all\ngalaxies for at least two reasons: (i) the energy injection from\nsupernovae into this gas will not be uniform as assumed in this paper;\n(ii) the extended gas disc is susceptible to external disturbances and\nso could be tidally stripped or transported towards the centre of the\nsystem in a tidal interaction. Nevertheless, it is possible that dwarf\ngalaxies at high redshift possess extended gaseous discs, some of\nwhich survive to the present day.\n\n\n\\begin{figure}\n\n\\vskip 3.0 truein\n\n\\special{psfile=pg_yield.ps hscale=40 vscale=40 angle=-90 hoffset= -10\nvoffset=240}\n\n\\caption\n{The effective yield for model DW1. For each radial ring in the galaxy\nwe plot the gas metallicty $Z_g$ against the gas fraction in that\nring. According to the simple closed box model of chemical evolution,\n$Z_g = -p{\\rm ln}(M_g/(M_g + M_s))$, where $p$ is the yield. The\ndashed line shows this relation, but using an effective yield $p_{\\rm\neff} = p/5$.}\n\\label{figure15}\n\\end{figure}\n\n\\subsubsection{Effective yields}\n\nAccording to the simple closed box model of chemical evolution, the\nmetallicity of the ISM is related to the gas fraction according to\n\\begin{equation}\nZ_g = -p\\;{\\rm ln}(M_g/(M_g + M_s)).\n \\label{Met1}\n\\end{equation}\nIt is well known that the yields\nderived from applying this relation to gas rich galaxies (usually\ndwarf systems) result in ``effective yields'', $p_{\\rm eff}$, that are\nmuch lower than the yield expected from a standard Salpeter-like IMF.\nFor example, Vila-Costas and Edmunds (1992) find effective yields in\nthe range $p_{\\rm eff} \\sim 0.004$--$0.02$ and that the effective yield\ndecreases with increasing radius.\n\nThe solid line in figure (\\ref{figure15}) shows the final gas\nmetallicity in radial rings in model DW1 plotted against the gas\nfraction within each ring. The dashed line shows equation (\\ref{Met1})\nwith an effective yield of $0.004$ ({\\it i.e.} one-fifth of the true\nyield). The strong outflows in this model suppress the effective yield\nwell below the true yield and produce a strong radial variation of the\neffective yield, in qualitative agreement with observations. \n\n\n\n\n\\subsubsection{Metallicity of ejected gas}\n\nThe last line in Table 2 lists the mean metallicity of the gas that\nescapes from the galaxy. The mean metallicity of the ejected gas is\nabout $0.3 Z_\\odot$ for model MW1 and about $0.1 Z_\\odot$ for model\nDW1. In model DW1 this value is about $3$ to $5$ times higher than the\nmean metallicity of the final gas disc. The ejected gas in this model\nis therefore `metal enhanced' relative to the gaseous disc. The\nmechanism for this metal enhancement is physically different to that\nin the models of Vader (1986, 1987) and Mac Low and Ferrara\n(1999). In the models of these authors, metal enhancement arises from\nincomplete local mixing between the supernovae ejecta and the ISM. In\nour models, the gas is assumed to be well mixed locally, but metal\nenhancement arises because the gas is lost preferentially from the\ncentral part of the galaxy, which has a higher metallicity than the gas\nin the outer parts of the system.\n\n\\subsection{Connection with damped Lyman alpha systems}\n\nThe column density threshold for the identification of damped\nLy$\\alpha$ systems is $N({\\rm HI}) \\simgt 2 \\times 10^{20}\\;{\\rm cm}^{-2}$\n(Wolfe 1995) corresponding to a neutral gas surface mass density of\n$\\sim 1.6\\; M_\\odot/{\\rm pc}^2$. Comparison with Figure 10 shows that the\nextended cold gasesous discs around dwarf galaxies would be detectable\nas damped Ly$\\alpha$ systems. Furthermore, in CDM-like models, such\nextended discs around dwarf galaxies would dominate the cross-section\nfor the identification of damped Ly$\\alpha$ systems at high redshift\nbecause the space density of haloes with low circular speeds is high\n(Kauffman and Charlot 1994, Mo and Miralda-Escude 1994). If this is\nthe case, then the metallicities of damped Ly$\\alpha$ systems would be\nexpected to be low at high redshift, $Z/Z_\\odot \\sim {\\rm few} \\times\n10^{-2}$, with occasional lines-of-sight intersecting the central\nregions of galaxies where the metallicity rises to $Z/Z_\\odot \\simgt\n0.1$. At lower redshifts, the metallicities of damped systems would \nbe expected to show a similarly large scatter, but with\nperhaps a trend for the mean metallicity to increase as disc\nsystems with higher circular speeds form and the extended gaseous\ndiscs around dwarfs are disrupted by tidal encounters.\n\nThis is qualitatively in accord with what is observed (Pettini\n\\etal$\\;$ 1997, Pettini \\etal$\\;$ 1999, Pettini 1999). These authors\nfind that the typical metallicity of a damped Ly$\\alpha$ system \nat $z \\sim 2$--$3$ is about\n$0.08Z_\\odot$ with a spread of about two orders of\nmagnitude. Comparing the metallicities of high redshift systems\nwith those of $10$ damped Ly$\\alpha$ systems with redshifts $z =\n0.4$--$1.5$, Pettini \\etal$\\;$ (1999) find no evidence for evolution\nof the column density weighted metallicity. Whether these and other\nproperties of the damped Ly$\\alpha$ systems can be reproduced with the\nfeedback model described here requires more detailed `semi-analytic'\ncalculations along the lines described by Kauffmann (1996). However,\nthe key point that we wish to emphasise is that according to the\nmodels described here, most of the cross-section at any given redshift\nwill be dominated by largely unprocessed gas in the outer parts of\ngalaxies that does not participate in the star formation\nprocess. The metallicity distributions and the evolution of\n$\\Omega_{\\rm HI}$ as a function of redshift are therefore more likely to\ntell us about feedback processes and the outer parts of dwarf\ngalaxies than about the history of star formation. Attempts to use \nthe properties of damped Ly$\\alpha$ systems to constrain the cosmic\nstar formation history ({\\it e.g.} Pei, Fall and Hauser 1999) should\ntherefore be viewed with caution.\n\n\n\\begin{figure}\n\n\\vskip 3.0 truein\n\n\\special{psfile=pgfig16.ps hscale=43 vscale=43\nangle=-90 hoffset= -10\nvoffset=250}\n\n\\caption\n{The solid line shows the retained baryonic fraction $1 - f_{ej}$ as a\nfunction of the halo circular speed $v_v$. The parameters\n$\\phi_\\kappa$, $\\epsilon_{c\\odot}$ {\\it etc.} adopted are the same as\nthose of models MW4 and DW4 listed in Table 2. The dotted line shows\nthe relation adopted by Cole \\etal$\\;$ (1994), equation (51) with\n$v_{hot} = 140\\; \\kms$ and $\\alpha_{hot} = 5.5$. The dashed line shows\nequation (51) with $v_{hot}=75\\; \\kms$ and $\\alpha_{hot}=2.5$.}\n\\label{figure16}\n\\end{figure}\n\n\n\n\\subsection{Feedback efficiency as a \nfunction of halo circular speed and semi-analytic\nmodels of galaxy formation}\n\n \nIn this section we investigate the efficiency of feedback as a\nfunction of halo circular speed. We have adopted the parameters of\nmodels 4 in Table 1 and run a series of models varying the halo\ncircular speed $v_v$. The virial radius of the halo is set to $r_v =\n150 (v_v/126\\; \\kms)^2\\;{\\rm kpc}$, the concentration parameter $c=10$\nand the ratio of gas to halo mass within the virial radius is set to\n$1/10$. The halo rotation speed is set by equation (\\ref{Inf1}) with\nthe fiducial disc scale length equal to $r_v/50$. With these\nparameters, the family of models has a constant value for the halo\nspin parameter of $\\lambda_H = 0.065$.\n\nThe retained baryonic fraction, $1-f_{ej}$, is plotted as a function\nof halo circular speed in Figure 16. The dotted line shows the\nrelation used by Cole {\\it et al.} (1994, hereafter C94) in their\nsemi-analytic models,\n\\begin{equation}\n1 - f_{hot} = {1 \\over 1 + \\beta(v_v)}, \\qquad \\beta(v_v) =\n\\left( {v_v \\over v_{hot} } \\right )^{-\\alpha_{hot}},\n \\label{Cole1}\n\\end{equation}\nwhere $f_{hot}$ is the fraction of the cooled gas that is reheated and\n$v_{hot}$ and $\\alpha_{hot}$ are parameters. C94\nadopt a severe feedback prescription with $\\alpha_{hot} = 5.5$\nand $v_{hot} = 140\\;\\kms$ to reproduce the flat faint end slope of the\nB-band galaxy luminosity function in a critical density CDM model. The\nC94 feedback model does not agree at all well with the models\ndescribed here. There is a slight ambiguity in the appropriate value\nof $v_v$ to use in equation (\\ref{Cole1}) because C94 adopt\nan isothermal rather than an NFW halo profile; the halo circular speed\nat $\\sim 0.1r_v$ may be $20 \\%$ higher than the circular speed at the\nvirial radius, but this is far too small a difference to reconcile\nthe C94 feedback prescription with the models of this paper.\n\n\nIn fact, the dashed line in Figure 16 shows that our models are\nreasonably well described by equation (\\ref{Cole1}) with $v_{hot} =\n75\\; \\kms$ and $\\alpha_{hot} = 2.5$. Our results therefore suggest a\nmuch gentler feedback prescription than assumed in C94.\nNote that with the C94 parameters, a Milky Way\ntype galaxy with $v_v \\approx 130 \\; \\kms$ would have lost about $60\n\\%$ of its baryonic mass in a wind. This is well outside the range\nfound from our models for plausible choices of the input parameters\n({\\it cf.} Table 2).\n\n\nRecently Baugh \\etal$\\;$ (1999) and Cole \\etal$\\;$ (1999) describe\nsemi-analytic models applied to $\\Lambda$-dominated CDM cosmologies\nthat employ a gentler feedback model. The prescription for their\nreference model is similar to that of equation (\\ref{Cole1}) with\n$v_{hot} = 150 \\; \\kms$ and $\\alpha_{hot} = 2.0$, but with $v_v$\nreplaced by the disc circular speed $v_{\\rm disc}$. This model is\ncloser to the results found here. Assuming angular momentum\nconservation, a halo with $\\lambda_H \\approx 0.06$ will produce a disc\nwith a circular speed $v_{\\rm disc} \\approx 1.7 v_v$ ({\\it cf.} Table\n1) and so their model can be approximated by equation (\\ref{Cole1})\nwith $v_{hot} \\approx 90 \\; \\kms$ and $\\alpha_{hot} = 2.0$. With these\nparameters, their model gives somewhat stronger feedback than found in\nour models, but is well within the range of physical\nuncertainties. Kauffmann \\etal$\\;$ (1993) and Kauffmann, Guiderdoni\nand White (1994) also adopt a much less severe feedback prescription\nthan C94 in their semi-analytic models. For a detailed analysis of the\neffects of varying the feedback prescription (and other parameters) in\nsemi-analytic models see Somerville and Primack (1999).\n\nThe change from an Einstein-de Sitter CDM cosmology in C94\nto a $\\Lambda$-dominated CDM model in Cole \\etal$\\;$ (1999) partly\nexplains why the revised models provide a reasonable match to\nobservations using less efficient feedback. However, the revised\nmodels predict a faint end slope for the B-band luminosity function\nthat is consistent with the observations of Zucca \\etal$\\;$ (1997) but not\nwith those of other authors ({\\it e.g.} Loveday \\etal$\\;$ 1992, Maddox\n\\etal$\\;$ 1998). (The earlier paper of Cole \\etal$\\;$ 1994 attempted to\nreproduce the flat faint end slope of the Loveday \\etal$\\;$ luminosity\nfunction). The observational differences in estimates of the faint\nend slope of the optical luminosity function are not properly\nunderstood and so it remains unclear whether a gentle feedback model,\nof the type proposed here and used in Cole \\etal$\\;$ (1999), can account\nfor galaxy formation in CDM-type models.\n\n\\bigskip\n\\centerline{\\bf Table 3: Dependence of Feedback Efficiency}\n\\centerline{\\bf of Model DW on Halo Angular Momentum}\n\\begin{center}\n\\begin{tabular}{cccc} \\hline \\hline\n\\noalign{\\medskip}\n $f_{coll}$ & $v_c$ (km/s) & $\\lambda_H$ & $f_{ej}$ \\\\\n $\\;\\;25$ & $\\;\\;50$ & $0.12$ & $0.64$ \\\\\n $\\;\\;50$ & $\\;\\;70$ & $0.065$ & $0.59$ \\\\\n $150$ & $120$ & $0.031$ & $0.82 $ \\\\ \\hline\n\\noalign{\\medskip}\n\\end{tabular}\n\\end{center}\n\n\nWith the Cole \\etal$\\;$ (1999) parameterization the efficiency of\n feedback depends, by construction, on the surface density of the\n galaxy and hence on the angular momentum of the parent halo. In\n their model, higher angular momentum haloes lead to more efficient\n feedback because they form low surface density discs with low disc\n circular speeds. This is not what is found in our models. Table 3\n lists the ejected gas fraction as a function of the halo spin\n parameter $\\lambda_H$. Here, the halo circular speed and virial\n radius, $v_v$ and $r_v$, are the same as for model DW in Table 1, but\n the amplitude of the halo rotation speed (or equivalently the\n parameter $f_{coll}$) is adjusted to change the spin parameter of the\n halo. The parameters of the feedback model are the same as those for\n model DW1 in Table 2. The feedback efficiency depends weakly (and\n non-monatonically) on $\\lambda_H$, and is greater in systems with low\n values of $\\lambda_H$. This is because higher surface densities in\n low $\\lambda$ galaxies result in higher star formation rates and a\n higher temperature hot component that can escape more easily from the\n halo.\n\nThe timescale for feedback in C94 and Cole \\etal$\\;$ 1999 is closely\nlinked to the star formation timescale which is assumed to be\nshorter in galaxies with high circular speeds. This is not what is\nfound in the models of Table 2. The timescale for star formation is \nof order several Gyr in models MW (which have a roughly constant star\nformation rate at late times, see Figure 11), yet the ejection of hot\ngas occurs only in the initial stages of formation with a\ncharacteristic timescale of $\\sim 0.3$ Gyr. In models DW, the\nsituation is reversed with star formation occuring on a somewhat shorter\ntimescale than that for outflow.\n\n\n\n\\section{Conclusions}\n\nThe main aim of this paper has been to show that supernovae driven\nfeedback can operate in a quiescent mode and that high rates of star\nformation are not required to drive efficient feedback. In dwarf\ngalaxies feedback occurs on an infalling timescale and so can extend\nover a period of $\\sim 1$ Gyr. In the feedback model developed here,\ncold gas clouds are steadily evaporated in expanding supernovae\nremnants and converted into a hot component. Critically, the rate at\nwhich cold gas is evaporated can exceed the rate at which mass is\nconverted into stars. If the temperature of the hot component is high\nenough, a wind will form and the hot gas can escape from the halo\n(provided the interaction with infalling gas can be ignored). If the\ntemperature of the hot component is not high enough for it to escape\nfrom the halo, it will cool and fall back down to the disc in\na galactic fountain. Some characteristic features of the models are as\nfollows:\n\n\\smallskip\n\n\\noindent\n(i) In a Milky Way type system, feedback from supernovae may drive out\nsome of the gas from the halo in the early phases of evolution ($t\n\\simlt 0.3$ Gyr) when the star formation rate is high and the\ntemperature of the hot phase exceeds $\\sim 5 \\times 10^6$ K. For\nplausible sets of parameters, perhaps $20$ -- $30 \\%$ of the final\nstellar mass might escape from the galaxy. At later times, the\ntemperature of the hot phase drops to $T \\sim 10^6$ K and the\nevaporated gas cycles within the halo in a galactic fountain.\n\n\\smallskip\n\n\\noindent\n(ii) In a dwarf galaxy with a circular speed $\\sim 50 \\; \\kms$, expanding\nsupernovae remnants can convert the cold interstellar medium\nefficiently into a hot component with a chacteristic temperature of a\nfew times $10^5$ K. This evaporated gas can escape from the halo in a\ncool wind. Typically, only about $10\\%$ of the baryonic material forms\nstars. Gas accreted from the halo at $\\simgt 1$ Gyr forms\nan extended gaseous disc which, according to the self-regulating star\nformation model used here, can survive for longer than a Hubble time\nwithout converting into stars.\n\n\\smallskip\n\n\\noindent\n(iii) The feedback model developed here is meant to provide a sketch\nof how feedback might operate in a multi-phase interstellar medium.\nThe model contains a number of obvious over-simplifications. For\nexample, we have neglected any interaction of the outflowing gas with\nthe infalling medium, we have not addressed the origin of the cold\ncloud spectrum, ignored the dense molecular cloud component of the ISM\nand neglected any local dissipation of supernovae energy in star\nforming regions. These effects, and other processes, are undoubtedly\nimportant in determining the efficiency of feedback. Nevertheless,\nthe simplified model presented here contains some interesting\nfeatures. Firstly, the model shows how positive feedback (via pressure\ninduced star formation) and negative feedback (via outflowing gas) can\noccur {\\it simultaneously}. Secondly, the models are remarkably\ninsensitive to uncertain physical parameters, in particular, thermal\nconduction would need to be suppressed relative to its ideal value by\nfactors of much more than $100$ to qualitatively change the model. If\nthermal conduction is highly suppressed, it may be possible to\nconstruct a qualitatively similar model to the one presented here in\nwhich cold gas is converted into hot gas in shocks.\n\n\\smallskip\n\n\\noindent\n(iv) The self-regulated star formation and feedback models described\nhere provide physically based models for the star formation timescale\nand feedback efficiency as a function of the parameters of the\nhalo. The star formation timescale and feedback efficiency (or\ntimescale) are taken as free parameters in semi-analytic models of\ngalaxy formation ({\\it e.g.} Cole \\etal$\\;$ 1999, Kauffmann \\etal$\\;$\n1994) and are critically important in determining some of the key\npredicted properties of these models, for example, the faint end slope\nof the galaxy luminosity function and the star formation history at\nhigh redshifts (see {\\it e.g.} Somerville and Primack 1999). It is\ntherefore important that we develop a theoretical understanding\nof these parameters (as attempted crudely here) and also that ways\nare found to constrain these parameters observationally. The results\npresented here show that supernovae feedback is much less effective\nthan assumed in some earlier semi-analytic models (Cole \\etal$\\;$\n1994, Baugh \\etal$\\;$ 1996) but is closer to the more gentler feedback\nprescriptions used in more recent models (Cole \\etal$\\;$ 1999,\nSomerville and Primack 1999).\n\nThe feedback model described in this paper has a number of consequences and\nraises some problems which are summarized below.\n\n\\smallskip\n\n\\noindent\n(i) {\\it Evidence for outflows:} According to the models described\nhere, outflows with speeds of $\\sim 200\\; T_{h6}^{1/2}\\kms$ should be\ncommon in high redshift galaxies. There is evidence for an outflow of\n$\\sim 200 \\; \\kms$, a mass loss rate of $\\sim 60 M_\\odot/{\\rm yr}$ and a star\nformation rate of $\\sim 40 M_\\odot/{\\rm yr}$ in the gravitationally lensed\nLyman break galaxy MS1512-cB58 (Pettini \\etal$\\;$ 2000). The outflow\nvelocity in this galaxy is consistent with our models, but the star\nformation and mass loss rates (which are highly uncertain) are high.\nThe most likely explanations are either that MS1512-cB58 is a massive galaxy\ndriving an outflow that will remain bound to the system, or that it is\na less massive system undergoing a burst of star formation. In\naddition to direct detection of outflowing gas, winds may have other\nobservational consequences. The winds from dwarf galaxies will cool\nrapidly (see Appendix B). Wang (1995b) has suggested that photoionized\ngas clouds formed in the cooling wind might contribute to the \nLy$\\alpha$ forest. Nulsen, Barcon and Fabian (1998) suggest that\noutflows caused by bursts of star formation in dwarf galaxies might\neven produce damped Ly$\\alpha$ systems.\n\n\n\\smallskip\n\n\\noindent\n(ii) {\\it Damped Ly$\\alpha$ systems:} The extended gaseous discs that\nform around dwarf galaxies in our models have low metallicities\nbecause they have low rates of star formation. If this is correct,\nthen this largely unprocessed gas would dominate the cross section for\nthe formation of damped Ly$\\alpha$ absorbers. The metallicities\nof most of these systems would be low, but would\nshow a large scatter because some lines of sight will pass close to\nthe central regions of galaxies containing gas of high\nmetallicity. This is broadly in agreement with what is\nobserved. Extended gaseous discs would be vulnerable in tidal\ninteractions. Some of the gas might be stripped and some might be\ntransported into the central regions to be converted into stars\nand hot gas. The evolution of $\\Omega_{\\rm HI}$ determined from damped\nLy$\\alpha$ systems ({\\it e.g.} Storrie-Lombardi, McMahon and Irwin\n1996) might have more to do with infall, feedback and tidal\ndisruption than with the cosmic star formation history.\n\n\\smallskip\n\n\\noindent\n(iii) {\\it Angular momentum conservation:} In hydrodynamic\nsimulations, \ngas is found to cool effectively in sub-units during the formation of\na protogalaxy. These sub-units lose their orbital angular momentum to\nthe halo as they spiral towards the centre and merge. Hence the gas\ndoes not conserve angular momentum during the formation of a massive\ngalaxy. (Navarro and Benz 1991, Navarro and Steinmetz 1997, Weil Eke\nand Efstathiou 1998, Navarro and Steinmetz 2000). In fact, in the\nabsence of feedback it has proved impossible to form discs with\nangular momenta similar to those of real disc galaxies starting from\nCDM initial conditions. In the models described here, it has been\nassumed for simplicity that the specific angular momentum of the gas\nis conserved during collapse. This assumption could easily be\nrelaxed. However, the feedback model decribed here suggests that the\nnumerical simulations miss some important physics. Firstly, it is\npreferentially the low angular momentum gas, infalling in the early\nstages of evolution, that is most likely to be ejected from a\ndeveloping protogalaxy. Secondly, supernovae driven feedback may help\nto solve the angular momentum momentum problem by ejecting gas\nefficiently from sub-units. The ejected gas may then infall at later\ntimes when the halo is less sub-structured, approximately conserving\nits angular momentum (Weil\n\\etal 1998, Eke, Efstathiou and Wright 2000).\n\n\n\n\\smallskip\n\n\\noindent\n(iv) {\\it Implementing feedback in numerical simulations:} There have\nbeen a number of attempts to implement supernovae feedback in gas\ndynamical numerical simulations ({\\it e.g.} Katz 1992, Navarro and\nWhite 1993, Navarro and Steinmetz 2000). These involve either heating\nthe gas around star forming regions (which is ineffective because the\nenergy is quickly radiated away) or reversing the flow of infalling\ngas. An implementation of the feedback model described here is well\nbeyond the capabilities of present numerical codes. It would require\nmodelling several gas phases, a cold interstellar medium, a hot\noutflowing medium and an infalling component, including \nmass transfer between each phase. It might be worth\nattempting simpler simulations in which cold high density gas is added\nto the halo beyond the virial radius at a rate that is determined by\nthe local star formation rate.\n\n\n\\smallskip\n\n\\noindent\n(vi) {\\it Starbursts vs quiescent feedback:} It is likely that\nstarburts are more common at high redshift because of the increased\nfrequency of galaxy interactions. Starbursts could contribute to\nsupernovae driven feedback in addition to the quiescent mode described\nhere. However, at any one time, our models suggest that the cold gas\ncomponent will have a mass of only $20$ -- $50\\%$ of the the mass of the\nstellar disk. Even if a substantial fraction of this gas is\ntransported towards the centre of a galaxy in a tidal encounter (see\n{\\it e.g.} Barnes and Hernquist 1996) and is subsequently ejected in\na superwind, this mode of feedback will be inefficient because the\nmass of gas involved is a small fraction of the total gas mass ejected\nin the quiescent feedback mode over the lifetime of the galaxy. \n\n\n\\smallskip\n\n\\noindent\n(vii) {\\it Metallicity ejection:} The mean metallicity of the gas\nejected from a dwarf galaxy is typically about $Z_\\odot/10$ in our\nmodels, and comparable to the mean metallicity of the stars in the\nfinal galaxy. Yet typically a dwarf galaxy is predicted to expel $5$\nto $10$ times its residual mass in stars. Dwarf galaxies can therefore\npollute the IGM with metals to a much higher level than might be\ninferred from their stellar content. 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This integral\nis convergent in the limit $\\epsilon \\rightarrow 0$.\nThe functions $I_<$ and $I_>$ can be evaluated once and stored, \nreducing the computation of $v^2(r)$ to a simple\nintegral over the surface density of the disc multiplied by the tabulated\nfunctions. We evaluate the epicyclic frequency by differentiating \nequation (A3) numerically.\n\n\n\n\n\\section{Steady Spherical Winds}\n\n\n\n\\begin{figure*}\n\n\\vskip 3.7 truein\n\n\\special{psfile=pgwind_MWa.ps hscale=55 vscale=55 angle=-90 hoffset= -30\nvoffset=320}\n\\special{psfile=pgwind_MWb.ps hscale=55 vscale=55 angle=-90 hoffset= 220\nvoffset=320}\n\n\\vskip 3.7 truein\n\n\\special{psfile=pgwind_DWa.ps hscale=55 vscale=55 angle=-90 hoffset= -30\nvoffset=320}\n\\special{psfile=pgwind_DWb.ps hscale=55 vscale=55 angle=-90 hoffset= 220\nvoffset=320}\n\n\\caption\n{Steady wind solutions for models MW and DW including radiative\ncooling. The curves show the wind velocity (figs a,c) and adiabatic\nsound speed (figs b, d) assuming that the flow begins at $r_i =\n0.04r_v$ with a Mach number of unity. The numbers give the initial\nisothermal sound speed in units of the escape speed $v_{esc}$ from the\ncentre of the halo. These curves are for a mass injection rate of $10\nM_\\odot/{\\rm yr}$ for model MW and $0.2 M_\\odot/{\\rm yr}$ for model\nDW.}\n\\label{figure17}\n\\end{figure*}\n\nThe equations governing a steady spherically symmetric wind are\n\\begletB\n\\begin{eqnarray}\n {1 \\over r^2} {d \\over dr}( \\rho v r^2) = q(r), \\\\\n \\rho v {dv \\over dr} = -{dp \\over dr} - \\rho {d \\Phi \\over dr} - q(r)v, \\\\ \n {1 \\over r^2} {d \\over dr} \\left [ \\rho v r^2 \\left ({1 \\over 2} v^2 + \n{5 \\over 2} {p \\over \\rho} \\right )\\right] + \\rho v {d \\Phi \\over dr}\n = {\\cal H} - {\\cal C},\n\\end{eqnarray}\n\\endletB\nwhere $q(r)$ is the mass density injected per unit time and ${\\cal H}$\nand ${\\cal C}$ are the heating and cooling rates per unit volume\n({\\it e.g.} Burke 1968, Holzer and Axford 1970). We assume that the\ngravitational force is given by the NFW halo potential (equation 3),\n$d\\Phi/dr = v^2_H(r)/r$, and rewrite these equations as two\ndimensionless first order equations\n\\begletB\n\\begin{eqnarray}\n {d v^2\\over dx} = {1 \\over 2 \\pi x^2 (c^2 - v^2)}\n\\Big [ - 8 \\pi x c^2 v^2 + 4 \\pi x v^2 v^2_H \\nonumber \\\\\n+ {4 \\over 3} \\gamma v^2\n+ \\gamma c^2_i - {2 \\over 3} \\kappa \\Big ]\n\\\\\n {d c^2\\over dx} = {-1 \\over 6 \\pi x^2 (c^2 - v^2) v^2}\n\\Big [ -8 \\pi x c^2 v^4 + 4 \\pi x c^2 v^2 v^2_H \\nonumber \\\\\n- \\gamma (v^2c^2\n- {3 \\over 2} c^4 - {5 \\over 6} v^4) \\cr\n- {3 \\over 2} \\gamma c^2_i (c^2 - {5 \\over 3} v^2 )\n+ \\kappa (c^2 - {5 \\over 3} v^2) \\Big ]\n\\end{eqnarray}\nwhere $c$ is the adiabatic sound speed, $x = r/r_v$, and all\nvelocities are expressed in units of $v_v$. The quanities $\\gamma$ and\n$\\kappa$ in these equations are related to the mass injection and\ncooling rates according to\n\\begin{eqnarray}\n\\gamma (x, v) = {q(r) \\dot M(r) \\over \\rho^2 r_v v_v^2}, \\quad\n\\kappa(x, c) = {\\dot M(r) \\Lambda(T) n_e^2 \\over \\rho^2 v_v^4 r_v}, \\cr\n \\dot M(r) = 4 \\pi \\int_0^r q(r) r^2 \\;dr.\n\\end{eqnarray}\n\\endletB\nand the injected gas is assumed to have a uniform initial isothermal\nsound speed of $c_i = (k T_i/(0.61 m_p))^{1/2}$.\n\n\n\n\n\n\n\n\n\n\nWe illustrate the behaviour of the wind solutions by studying two\nregimes. Firstly, we assume that $q=0$ beyond an initial radius $r_i =\n0.04r_v$ defining the base of the flow\n({\\it i.e.} two disc scale lengths for $f_{coll} = 50$).\n Equations (B2) do not have a transonic\npoint when $q=0$ (Wang 1995a, see also the discussion below) and so we\nbegin the integrations at a Mach number slightly greater than unity\nwith $c^2 = 5c_i^2/3$. We adopt the parameters of models MW and DW\ngiven in Table 1 and integrate the equations (B1) adopting $\\dot M =\n10 M_\\odot/{\\rm yr}$ for model MW and $\\dot M = 0.2 M_\\odot/{\\rm yr}$\nfor model DW. These mass injection rates are close to the maximum\nrates at times $t\n\\sim \\tau_{ej}$ for the models described in Section 6. The curves in\nFigure \\ref{figure17} show solutions for initial isothermal sound speeds of\n$0.75$, $1.0$ and $1.25$ times the escape velocity from the centre of\nthe halo ($v_{esc}=430\\;\\kms$ for model MW and $107\\;\\kms$ for model DW).\n\n\n\n\nThe figure shows that the criterion $v_w \\approx \\sqrt{2.5} c_i\n\\simgt v_{esc}$ is about\nright if the wind is to reach beyond the virial radius. For $c_i\n\\approx v_{esc}$ the wind in model MW begins at a high temperature of\n$T_i \\approx 1.4 \\times 10^7\\;{\\rm K}$ and cools almost adiabatically\ninitially, reaching a temperature of $\\sim 1.5 \\times 10^5\\;{\\rm K}$\nat the virial radius. The timescale for the flow to reach the virial\nradius, $\\sim 2 \\times 10^8 {\\rm yrs}$, is slightly longer than the\ncooling time at $r_v$. The behaviour of models DW is quite\ndifferent. For $c_i \\approx v_{esc}$ the initial temperature of the\ngas is $T_i \\approx 8 \\times 10^5{\\rm K}$ and cools to $\\simlt 10^4\n{\\rm K}$ by $r = 0.3r_v$. As expected from the discussion in Section\n6, cooling is important in outflows from dwarf galaxies (see {e.g.}\nKahn 1981, Wang 1995a, b).\n\nAn investigation of transonic solutions of equations (B2) require a\nmodel for $q(r)$. An example is illustrated in Figure \\ref{figure18}\nfor model DW,\nusing\n\\begletC\n\\begin{equation}\nq(r) = {\\dot M(\\infty) \\over 8 \\pi r_w^3} {\\rm exp}(- r/r_w),\n \\qquad r_w= 0.04r_v.\n\\end{equation}\n\\endletB\nIn this solution, $\\dot M(\\infty) = 0.2 M_\\odot/{\\rm yr}$ and the\ncentral gas density was adjusted to obtain a critical solution for the\ncase $c_i = v_{esc}$. If the gas is to escape from a dwarf galaxy the\ntransonic point must occur before cooling sets in. For such systems,\nthe wind parameters would adjust so that a sonic point exists at a\ncharacteristic cooling scale height as shown in Figure \\ref{figure18}. The wind\nwill then cool radiatively just beyond the sonic point forming a cold\nwind as discussed above. It is also likely that the wind will be\nheated to a temperature of $T \\sim 10^4$K by photoionizing radiation\nfrom the galaxy and the general UV background. These sources of\nheating have not been included in the models of Figures \\ref{figure17}\nand \\ref{figure18}.\n\nThe wind will be thermally unstable when cooling sets in, and may form\nclouds. However, in the absence of a confining medium, the clouds\nwould have a filling factor of order unity so the wind is likely to\nmaintain its integrity until it meets the surrounding IGM. The\nexternal pressure required to balance the ram pressure of the wind is\n\\begletC\n\\begin{eqnarray}\n{ p_{ext} \\over k} \\approx 80 \n\\left ( {\\dot M \\over 0.2 M_\\odot/{\\rm yr}} \\right ) \n\\left ( { r \\over 10\\;{\\rm kpc}} \\right ) ^{-2} \\times \\qquad \\nonumber \\\\\n\\left ( {v_w \\over 100 {\\rm km}/{\\rm s} } \\right ) \n\\; {\\rm cm}^{-3}\\; {\\rm K}, \n\\end{eqnarray}\n\\endletB\nwhich is about equal to the pressure of the IGM with a temperature of $10^4$K\nand an overdensity of\n\\begletC\n\\begin{eqnarray}\n\\Delta \\approx 4500 \\left ( {2 \\over 1+z} \\right )^3 T_4^{-1} \n\\left ( {\\dot M \\over 0.2 M_\\odot/{\\rm yr}} \\right ) \\times \\qquad \\nonumber\n\\\\\n\\left ( { r \\over 10\\;{\\rm kpc}} \\right ) ^{-2} \n\\left ( {v_w \\over 100 {\\rm km}/{\\rm s} } \\right ) .\n\\end{eqnarray}\n\\endletB\nProvided that the halo is devoid of high pressure gas, the cool wind\nwill propagate beyond the virial radius and will be halted either by\nthe ram pressure of infalling gas or after sweeping up a few times its\nown mass. As pointed out by Babul and Rees (1992), if a dwarf galaxy is \nembedded in a group or cluster of galaxies with a pressure exceeding\n$\\sim 100 \\; {\\rm cm}^{-3} {\\rm K}$, the bulk motion of the outflowing gas\nwould be thermalized in a shock and the cooled shocked gas could fall\nback onto the galaxy generating a new burst of star formation. The\nefficiency of feedback is therefore likely to be a function of\nlocal environment.\n\n\n \n\\begin{figure}\n\n\\vskip 3.2 truein\n\n\\special{psfile=pgwind_SP.ps hscale=45 vscale=45 angle=-90 \nhoffset= -10\nvoffset=270}\n\n\\caption\n{Critical solution for a wind in model DW with $c_i=v_{esc}$, $\\dot M(\\infty)\n= 0.2 M_\\odot/{\\rm yr}$, and $q(r)$ given by equation (B3).}\n\\label{figure18}\n\\end{figure}\n\n\\end{appendix}\n\n\n\n\\end{document}\n\\bye\n\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002245.extracted_bib",
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}
] |
astro-ph0002246
|
$IZ$ photometry of L dwarfs and the implications for brown dwarf surveys
|
[
{
"author": "I.A. Steele \\& L. Howells"
},
{
"author": "Liverpool"
},
{
"author": "CH41 1LD"
}
] |
The $I-Z$ colour has been recently shown to be a good temperature indicator for M dwarfs. We present the first $IZ$ photometry of a small sample of L dwarfs ranging in spectral type from L0.5V to L6.0V. We find that the $I-Z$ colour is not a good temperature indicator for objects between L1V and L5V, such objects having colours that overlap with mid M dwarfs. We attribute this to the reduction in the strength of the TiO and VO bands in the L dwarfs which are the dominant opacity source in the $I$ band for late M dwarfs. Beyond L5V, $I-Z$ appears to be a reasonable indicator. This has important implications for the planning of optical surveys for cool objects in clusters and the field. For example $I-Z$ will cease to be a good method of discriminating brown dwarfs in the Pleiades below around $0.04 M_\odot$, and at around $0.075 M_\odot$ in the Hyades and Praesepe.
|
[
{
"name": "pa.tex",
"string": "\\input epsf\n\\documentstyle[referee]{mn}\n\\begin{document}\n\\title[$IZ$ photometry of L dwarfs and the implications for\nbrown dwarf surveys]\n{$IZ$ photometry of L dwarfs and the implications for\nbrown dwarf surveys}\n\\author[I.A. Steele \\& L. Howells]\n{I.A. Steele \\& L. Howells \\\\\nAstrophysics Research Institute, Liverpool John Moores University, \nLiverpool, CH41 1LD\\\\\n}\n\\maketitle\n\\begin{abstract}\nThe $I-Z$ colour has been recently shown to be \na good temperature indicator for\nM dwarfs. We present the first $IZ$ photometry of\na small sample of L dwarfs ranging in spectral type from L0.5V to\nL6.0V. We find that the $I-Z$ colour is not a good temperature\nindicator for objects between L1V and L5V, such objects\nhaving colours that overlap with mid M dwarfs. \nWe attribute this\nto the reduction in the strength of the TiO and VO bands in the L dwarfs\nwhich are the dominant opacity source in the $I$ band for late M dwarfs. \nBeyond L5V,\n$I-Z$ appears to be a reasonable indicator. This has\nimportant implications for the planning of optical surveys for cool\nobjects in clusters and the field. For example $I-Z$ will\ncease to be a good method of discriminating brown dwarfs in the Pleiades\nbelow around $0.04 M_\\odot$, and at around $0.075 M_\\odot$ in the\nHyades and Praesepe.\n\\end{abstract}\n\\begin{keywords}\nstars: low mass, brown dwarfs\n\\end{keywords}\n\n\\section{Introduction}\n\nKirkpatrick et al. (1999) have recently identified and classified the\nfirst large sample of L dwarfs (objects cooler than M-dwarfs) from \nthe 2-micron all sky survey (2MASS). The optical spectra of these objects\nare characterised by the disappearance of the TiO and VO bands\nwhich dominate late M dwarfs, and their replacement by metallic\nHydrides and neutral alkali metals. This would be expected to \naffect the optical colours one observes for such objects. This is\nimportant as many surveys for low mass objects (specifically brown dwarfs) \nin clusters have relied\non colours such as $V-I$ (e.g. Stauffer, Hamilton \\& Probst 1994), \n$R-I$ (e.g. Jameson \\& Skillen 1989, Hambly et al. 1999), \nand $I-Z$ (e.g Pinfield et al. 1997, Cossburn et al. 1997, \nZapatero Osorio et al. 1999). The $I-Z$ \ncolour has been particularly favoured of late, as it has been found to\nbe an excellent method of picking late cluster M dwarfs from the\nfield. The lowest mass object so far detected in the Pleiades\nusing this technique is the $\\sim$ L1V dwarf Roque 25 \nwhich was recently identified by Martin et al. (1998).\nIt is therefore useful to see if the $I-Z$ colour\nwould remain useful as a method of picking out later $L$ dwarfs in cluster\nfields. For example at the distance of the Hyades \nan L3V dwarf would have $I\\sim 19$ based on the pseudo-photometry \n(derived from flux calibrated spectra) presented by Kirkpatrick et al. (1999).\nThis is easily obtained with 2-m class telescopes, and therefore\nan optical survey at $I$ and $Z$, at which wavelengths much larger\nfields of view are generally available than the near infrared $JHK$ bands,\nwould appear to be an excellent way of finding such objects. \n\nIn order to address this question of applicability to cluster surveys,\nas well as the more general question of the use of $I-Z$ as a temperature \nindicator we have carried out $I_{\\rm Harris}$ (hereafter $I_H$)\nand $Z_{RGO}$ photometry of a small number of L dwarfs ranging in spectral type\nfrom L0.5V to L6V. This paper presents the results of that photometry,\nand discusses the results in the context set out above.\n\n\\section{Observations}\n\nOur observations were obtained using the 1.0-m Jacobus Kapteyn Telescope\n(JKT), La Palma on the night of 1999 December 19. The photometric conditions\nwere excellent, with relative humidity always below 5\\% (giving \ngood stability, especially in the $Z$ band) and no\ncirrus or other cloud. The lunar phase was near full, however this\ndoes not affect the $I$ and $Z$ bands as much as the bluer optical bands.\nThrough the course of the night the seeing was reasonable, \nslowly varying between 1.1 and 1.3 arcsec FWHM. This was sufficient\nto adequately resolve the two of our program objects \n(2MASSW J0147334+345411 and 2MASSs J0850359+105716) that are\nclose ($\\sim 2$ arcsec) binaries. \nEach object in the\nprogramme was observed three times through each filter, with an\nintegration time of 600 seconds per observation (except for\nthe faintest object, 2MASSs J0850359+105716, where the integrations\nwere each 1200 seconds). The standard field PG0918 (Landolt 1992) was\nobserved between each object (i.e. roughly once per 90 minutes) throughout\nthe night.\n\nThe CCD employed was a SITE 2048x2048 pixel array, and the\nfilters used were $I_H$ and $Z_{RGO}$. These filters are\ntypically the ones used for the majority of $IZ$ surveys of\nclusters so far carried out.\nThey \nhave been calibrated using a TEK 1024x1024 CCD for a sample\nof Landolt (1992) \nstandards and M-dwarfs by Cossburn et al. (2000). A comparison\nof the measured \nquantum efficiency curves of the two CCDs shows that they are\nidentical to within $\\sim 2$\\% over the range 6000 - 10000 {\\AA}. The \nstandards and M-dwarfs from Cossburn et al. (2000) are therefore\ndirectly applicable to the newer SITE detector.\nIt is important to note that the Cossburn et al. (2000) calibration is\nbased on an assigned $I-Z$ colour of 0.0 for an unreddened A0 star and that\nthis is {\\em different} to the Gunn $z$ and Sloan $z^\\prime$ systems.\n\nData reduction was carried out in the usual manner, using a combination\nof twilight fields and the median of the programme frames in the\nappropriate bands to flat field and defringe the data. \n\nThe results of our photometry are presented in Table 1. Errors were\nestimated from the dispersion of the measurements of each object. \nOne object, 2MASSW J0918382+213406 has a very bright star roughly 1 arcminute\nSW, making background estimation difficult due to scattered light. This is\nreflected in the greater photometric errors for this object compared to\nthe fainter 2MASSW J0913032+184150.\n\n\\begin{table*}\n\\caption{Photometry of 2MASS L-dwarfs. Spectral types from Kirkpatrick \net al. (1999).}\n\\begin{tabular}{lllll}\n\\hline\nObject & Spectral Type & $I_H$ & $Z_{RGO}$ & $I_H-Z_{RGO}$ \\\\\n2MASSW J0147334+345311 & L0.5V & $18.20 \\pm 0.05$ & $17.40 \\pm 0.05$ \n& $0.80 \\pm 0.07$ \\\\\n2MASSW J0918382+213406 & L2.5V & $18.25 \\pm 0.20$ & $17.75 \\pm 0.10$ \n& $0.50 \\pm 0.22$ \\\\\n2MASSW J0913032+184150 & L3.0V & $19.30 \\pm 0.10$ & $18.60 \\pm 0.05$ \n& $0.70 \\pm 0.12$ \\\\\n2MASSs J0850359+105716 & L6.0V & $20.00 \\pm 0.20$ & $18.70 \\pm 0.20$ \n& $1.30 \\pm 0.30$ \\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n\n\\section{Discussion}\n\nIn Figure 1 we plot $I_{H}-Z_{RGO}$ (hereafter $I-Z$) versus spectral\ntype (Kirkpatrick et al. 1999) for our sample (circles). Also\nplotted as crosses are the M-dwarf data of Cossburn et al. (2000) and\ntheir observation of DENIS-P J1228.2-1547, which Kirkpatrick et al. (1999)\nclassify as L5V. Based purely on their \nM dwarf sample Cossburn et al. (2000) made the reasonable\nclaim that $I-Z$ was a good temperature indicator down\nto $\\sim 2000K$ (M9). \nHowever from the figure we see that between \n$\\sim$ L1V and $\\sim$ L5V the $I-Z$ colour of the L dwarfs \nis {\\em bluer} than the late M-dwarfs, and in fact overlaps with the\nmid-M dwarfs. $I-Z$ is therefore {\\em not}\na good temperature indicator in the range $\\sim 0.5 - 1$.\n\n\\def\\epsfsize#1#2{0.5#1}\n\\begin{figure}\n\\setlength{\\unitlength}{1.0in}\n\\centering\n\\begin{picture}(3.0,3.0)(0,0)\n\\put(-0.4,0.0){\\epsfbox[0 0 2 2]{fig1.ps}}\n\\end{picture}\n\\caption{Spectral Class, $I_H-Z_{RGO}$ diagram for our observations of\nL-dwarfs (circles). Also plotted (crosses) \nare the M-dwarf and DENIS-P J1228.2-1547\ndata of Cossburn et al. (2000)}\n\\end{figure}\n\nThe reason for the relatively blue $I-Z$ colour of the early-mid L dwarfs\ncan be understood by examining the spectra of Kirkpatrick et al. (1999).\nA comparison of the L0V spectra with (for example) \nthe L3V spectra shows that the\nTiO and VO band strengths are much reduced in the L3V objects. These \nopacity sources are especially strong between 7800-8000 {\\AA} (VO) and\n8400-8600 {\\AA} (TiO), i.e. in the region where the $I$ band\nfilter transmission is greatest. Overlaying the spectra\nnormalized at the pseudo-continuum point at $\\sim 8250$ {\\AA}\nshows that the regions longward of $\\sim 8600$ {\\AA} (where the\n$Z$ band transmission is greatest) overlap \nwell, but a significant flux excess for the L3V object shorter than\nthis wavelength. Therefore such objects will appear bluer than earlier\nobjects in $I-Z$. For objects later than $\\sim$ L5V $I-Z$ again\nbecomes a reasonable temperature indicator. Examination of the\nspectra shows that this is simply due to the extremely cool\ntemperature giving a very steep spectral slope through $I$ and $Z$ \nwhich `overwhelms' the effect of the lack of opacity in the\n$I$ band.\n\nAs stated previously, $I-Z$ has recently become the favoured\ncolour for cluster brown dwarf searches, often with considerable\nsuccess (e.g. Cossburn et al. 1997, Zapatero Osorio et al. 1999). However\nfrom Figure 1 it appears that if we wish to find cluster L dwarfs\n(which compared with field objects \nhave the advantage of known distance, age and metallicity,\nmaking mass derivations via. a comparison with isochrones feasible),\nthe $I-Z$ colour would not be appropriate. To confirm this in Figure 2\nwe plot the combined $I,I-Z$ diagram for the four fields containing\nour L dwarfs. It is apparent that only the earliest and\nlatest L dwarf would be identified from this diagram as\na potentially interesting object, the middle two objects\noverlapping with the background objects (which may be\ndistant M dwarfs, even more distant M giants or extragalactic)\nas would be expected from their bluer colours. It is therefore\napparent that $I,Z$ searches for L dwarfs in clusters (and the field) \nwill only be sensitive to objects earlier than $\\sim$L1V and later than \n$\\sim$L5V.\nUsing the objects listed in\nKirkpatrick et al. (1999) which have measured parallaxes\nto define an absolute $I$ magnitude, spectral type relation \nfor the L dwarfs, this indicates that\n$I-Z$ will not be a useful colour in the absolute magnitude range\n$M_I \\sim 15 - 17$. Assuming a Pleiades age of $\\sim 120 $Myr \nand using an extension (Baraffe, priv. comm.) of the Lyon Group \nabsolute magnitude-mass relationship presented by \nBaraffe et al. (1998) this\nimplies that for that cluster objects with masses lower than\n$\\sim 0.04M_\\odot$ will be difficult to pick out with $IZ$ photometry.\nThis is consistent with the lowest mass (spectroscopically\nconfirmed) object so far found using that\ntechnique (Roque 25) which has a spectral type\nof $\\sim$ L1V ($M\\sim 0.04M_\\odot$) \n(Martin et al. \n1998).\nFor older clusters such as the Hyades and Praesepe (age $\\sim 1$ Gyr), \nobjects in the range $\\sim 0.075 - 0.06 M_{\\odot}$ will be difficult to\ndetect using the $I-Z$ colour. This is consistent with\nthe lowest mass objects detected in Praesepe with this\ntechnique having $I \\sim 21.5$ (Pinfield et al. 1997, Magazzu et al. 1998),\ncorresponding to $M_I \\sim 15$.\n\n\\def\\epsfsize#1#2{0.49#1}\n\\begin{figure}\n\\setlength{\\unitlength}{1.0in}\n\\centering\n\\begin{picture}(3.0,4.6)(0,0)\n\\put(-0.4,0.0){\\epsfbox[0 0 2 2]{fig2.ps}}\n\\end{picture}\n\\caption{$I,I-Z$ diagram for all of the objects in our observed fields.\nThe L-dwarfs are indicated by circles with error bars \nand the other objects by crosses. Note that the photometry is based\non a single observation of each field, and therefore differs\nslightly from the average value presented in Table 1.}\n\\end{figure}\n\n\\section{Conclusions}\n\nWe have presented observations that show that the $I-Z$ \ncolour is not a good temperature indicator for\nL dwarfs between L1V and L5V, these objects having $I-Z$ colours\nwhich overlap with mid-late M dwarfs. We attribute this to\nthe decreasing blanketing of the $I$ band flux in L dwarfs due\nto the absence of strong TiO and VO bands in their spectra. This\nimposes limits on the use of $I-Z$ as an indicator of very cool\nobjects in cluster brown dwarf searches at around\n$0.04 M_\\odot$ for the Pleiades and $0.075 M_\\odot$ for\nPraesepe and the Hyades. For objects of lower mass than this\nnear infrared ($JHK$) surveys should be considered.\n \n\\section*{Acknowledgements}\n\nData reduction for this paper was carried out on the\nLiverpool John Moores STARLINK node. \nThe JKT is operated by\nthe ING on behalf of the UK Particle Physics and\nAstronomy Research Council (PPARC) at the ORM Observatory, La Palma. \nWe are pleased to thank Rachel Curran and the technical staff\nof the ING\nfor their assistance at the telescope. We gladly \nacknowledge the postscript genius of Andrew Newsam\nfor the addition of error bars to Fig. 2.\nLH acknowledges a PPARC research studentship.\n\n\\begin{thebibliography}{}\n\\bibitem[\\protect\\citename{b98}1998]{b98}\nBaraffe I., Chabrier G., Allard F., Hauschildt P.H., 1998, A\\&A, 337, 403\n\\bibitem[\\protect\\citename{c97}1997]{c97}\nCossburn M.R., Hodgkin S.T., Jameson R.F., Pinfield D.J., 1997,\nMNRAS, 288, L23\n\\bibitem[\\protect\\citename{c00}2000]{c00}\nCossburn M.R., Hodgkin S.T., Jameson R.F., 2000, MNRAS, in press \n\\bibitem[\\protect\\citename{j89}1989]{j89}\nJameson R.F., Skillen W.J.I., 1989, MNRAS, 239, 247.\n\\bibitem[\\protect\\citename{h99}1999]{h99}\nHambly N.C., Hodgkin S.T., Cossburn M.R., Jameson R.F., MNRAS,\n1999, 303, 835\n\\bibitem[\\protect\\citename{k99}1998]{k99}\nKirkpatrick J.D., et al., 1999, ApJ, 519, 802\n\\bibitem[\\protect\\citename{l92}1992]{l92}\nLandolt A.U., 1992, AJ, 104, 340\n\\bibitem[\\protect\\citename{m98}1997]{m98}\nMagazzu A., Rebolo R., Zapatero Osorio M.R., Martin E.L., Hodgkin S.T.,\n1998, ApJ, 497, L47\n\\bibitem[\\protect\\citename{ma98}1999]{ma98}\nMartin E.L., Basri G., Zapatero Osorio M.R., Rebolo R., Lopez Garcia R.J.,\nApJ, 1998, 507, L41 \n\\bibitem[\\protect\\citename{p97}1997]{p97}\nPinfield D.J., Hodgkin S.T., Jameson R.F., Cossburn M.R., von Hippel T., \n1997, MNRAS, 287, 180\n\\bibitem[\\protect\\citename{s94}1997]{s94}\nStauffer J.R., Hamilton D., \\& Probst R.G., 1994, AJ, 108, 155\n\\bibitem[\\protect\\citename{z99}1999]{z99}\nZapatero Osorio M.R., Rebolo R., Martin E.L., Hodgkin S.T., Cossburn M.R., \nMagazzu A., Steele I.A., Jameson R.F., 1999, A\\&AS, 134, 537\n\\end{thebibliography}\n\\end{document}\n\n\n\n"
}
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[
{
"name": "astro-ph0002246.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[\\protect\\citename{b98}1998]{b98}\nBaraffe I., Chabrier G., Allard F., Hauschildt P.H., 1998, A\\&A, 337, 403\n\\bibitem[\\protect\\citename{c97}1997]{c97}\nCossburn M.R., Hodgkin S.T., Jameson R.F., Pinfield D.J., 1997,\nMNRAS, 288, L23\n\\bibitem[\\protect\\citename{c00}2000]{c00}\nCossburn M.R., Hodgkin S.T., Jameson R.F., 2000, MNRAS, in press \n\\bibitem[\\protect\\citename{j89}1989]{j89}\nJameson R.F., Skillen W.J.I., 1989, MNRAS, 239, 247.\n\\bibitem[\\protect\\citename{h99}1999]{h99}\nHambly N.C., Hodgkin S.T., Cossburn M.R., Jameson R.F., MNRAS,\n1999, 303, 835\n\\bibitem[\\protect\\citename{k99}1998]{k99}\nKirkpatrick J.D., et al., 1999, ApJ, 519, 802\n\\bibitem[\\protect\\citename{l92}1992]{l92}\nLandolt A.U., 1992, AJ, 104, 340\n\\bibitem[\\protect\\citename{m98}1997]{m98}\nMagazzu A., Rebolo R., Zapatero Osorio M.R., Martin E.L., Hodgkin S.T.,\n1998, ApJ, 497, L47\n\\bibitem[\\protect\\citename{ma98}1999]{ma98}\nMartin E.L., Basri G., Zapatero Osorio M.R., Rebolo R., Lopez Garcia R.J.,\nApJ, 1998, 507, L41 \n\\bibitem[\\protect\\citename{p97}1997]{p97}\nPinfield D.J., Hodgkin S.T., Jameson R.F., Cossburn M.R., von Hippel T., \n1997, MNRAS, 287, 180\n\\bibitem[\\protect\\citename{s94}1997]{s94}\nStauffer J.R., Hamilton D., \\& Probst R.G., 1994, AJ, 108, 155\n\\bibitem[\\protect\\citename{z99}1999]{z99}\nZapatero Osorio M.R., Rebolo R., Martin E.L., Hodgkin S.T., Cossburn M.R., \nMagazzu A., Steele I.A., Jameson R.F., 1999, A\\&AS, 134, 537\n\\end{thebibliography}"
}
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astro-ph0002247
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Constraining reionization using the thermal history of the baryons
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[
{
"author": "Joop Schaye"
}
] |
The thermal evolution of the intergalactic medium (IGM) depends on the reionization history of the universe. Numerical simulations indicate that the low density IGM, which is responsible for the low column density \lya\ forest, follows a well defined temperature-density relation. This results in a cut-off in the distribution of line widths as a function of column density. We use hydrodynamic simulations to calibrate the relation between the cut-off and the temperature-density relation and apply this relation to Keck spectra spanning a redshift range $z=2$--4.5. We find that the temperature peaks at $z\sim 3$ and interpret this as evidence for reheating due to the reionization of helium.
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[
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"name": "schayej.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{J. Schaye et al.}{The thermal history of the baryons}\n\\pagestyle{myheadings}\n\\def\\plotone#1{\\centering \\leavevmode\\epsfxsize=0.55\\columnwidth \\epsfbox{#1}}\n\n% Some definitions I use in these instructions.\n\\newcommand{\\ion}[2]{{\\rm #1}\\,{\\small\\rm #2}}\n\\newcommand{\\HI}{\\ion{H}{I}}\n\\newcommand{\\HeII}{\\ion{He}{II}}\n\\newcommand{\\HeIII}{\\ion{He}{III}}\n\\newcommand{\\SiIV}{\\ion{Si}{IV}}\n\\newcommand{\\CIV}{\\ion{C}{IV}}\n\\newcommand{\\lya}{Ly$\\alpha$}\n\n\n\\begin{document}\n\n\\title{Constraining reionization using the thermal history of the baryons}\n\\author{Joop Schaye}\n\\affil{Institute of Astronomy, Madingley Road, Cambridge CB3~0HA, UK}\n\\author{Tom Theuns}\n\\affil{Max-Planck-Institut f\\\"ur Astrophysik, Postfach 1523, 85740\n Garching, Germany}\n\\author{Michael Rauch}\n\\affil{European Southern Observatory, Karl-Schwarzschild-Str.\\ 2,\n85748 Garching, Germany}\n\\author{George Efstathiou}\n\\affil{Institute of Astronomy, Madingley Road, Cambridge CB3~0HA, UK}\n\\author{Wallace L. W. Sargent}\n\\affil{Astronomy Department, California Institute of Technology,\nPasadena, CA 91125, USA}\n\n\\begin{abstract}\nThe thermal evolution of the intergalactic medium (IGM) depends on the\nreionization history of the universe. Numerical simulations indicate\nthat the low density IGM, which is responsible for the low column\ndensity \\lya\\ forest, follows a well defined temperature-density\nrelation. This results in a cut-off in the distribution of line widths\nas a function of column density. We use hydrodynamic simulations to\ncalibrate the relation between the cut-off and the temperature-density\nrelation and apply this relation to Keck spectra spanning a\nredshift range $z=2$--4.5. We find that the temperature peaks at\n$z\\sim 3$ and interpret this as evidence for reheating due to the\nreionization of helium.\n\\end{abstract}\n\n\\keywords{cosmology: miscellaneous --- galaxies: formation ---\nintergalactic medium --- quasars: absorption lines}\n\n\\section{Introduction}\nQuasars have provided us with a unique probe of the high redshift\nuniverse. These bright point sources shine like a flashlight through\nspace, revealing the presence of baryonic matter through the light it\nabsorbs. Thus every quasar spectrum contains a one-dimensional map of\nthe distribution of matter along the line of sight. The extraordinary\nquality of the spectra obtainable with the HIRES spectrograph on the\nKeck telescope, enables us to extract the wealth of information that\nhas been collected by the quasar's light along its journey through\nspace and time. Computer simulations of structure formation have been\nremarkably successful in reproducing these observations. They show\nthat the physics governing the high redshift intergalactic medium\n(IGM), which is responsible for the low column density absorption\nlines (the so-called \\lya\\ forest) is relatively simple. The IGM,\nwhich contains most of the baryons in the universe, is photoionized\nand photoheated by the collective UV radiation from young stars and\nquasars. On large scales its dynamics are determined by the\ngravitational field of the dark matter, while on small scales gas\npressure is important. The availability of superb data and a detailed\nphysical model, have made the \\lya\\ forest into a powerful probe of\nthe high-redshift universe.\n\nSince shock heating is unimportant in the low-density IGM, most of the\ngas follows a simple temperature-density relation which is the result\nof the interplay of photoionization heating and adiabatic cooling due\nto the expansion of the universe. For densities around the cosmic\nmean, this relation is well-described by a power-law,\n$T=T_0(\\rho/\\bar{\\rho})^{\\gamma-1}$ (Hui \\& Gnedin 1997). At\nreionization the gas is reheated, resulting in an increase in $T_0$\nand a decrease in $\\gamma$ (provided that the gas is reionized on a\ntimescale short compared to the Hubble time). In ionization\nequilibrium, $T_0$ decreases and the slope of the effective equation\nof state steepens (i.e.\\ $\\gamma$ increases). However, because the\ntimescale for recombination is long, the gas retains some memory of\nhow and when it was reionized (Miralda-Escud\\'e \\& Rees 1994).\n\nThe distribution of line widths ($b$-parameters) depends on various\nmechanisms. Thermal motions of the hydrogen atoms broaden\nthe \\HI\\ absorption lines and other processes, such as the differential\nHubble flow across the absorbing structure and bulk flows, also\ncontribute to the line widths. However, the minimum line width is set\nby the temperature of the gas, which in turn depends on the density.\nA standard way of analyzing \\lya\\ forest spectra is by decomposing\nthem into a set of Voigt profiles. Since the minimum line width\n($b$-parameter) depends on the temperature, and since column density\n($N$) correlates strongly with physical density, there is a cut-off in\nthe $b(N)$ distribution which traces the effective equation of state\nof the IGM (Schaye et al.~1999; Ricotti, Gnedin \\& Shull 2000; Bryan\n\\& Machacek 2000). We have used this relation to measure\nthe thermal evolution of the IGM from a set of nine \\lya\\ quasar\nabsorption line spectra.\n\nThis work is more fully described and discussed in a forthcoming\npublication (Schaye et al.\\ 2000).\n\n\\section{Method}\nWe have measured the $b(N)$ cut-off for a set of nine high-quality\n\\lya\\ forest spectra, spanning the redshift range 2.0--4.5, eight of\nwhich were taken with the HIRES spectrograph of the Keck telescope.\nWe used hydrodynamic simulations to calibrate the relations between\nthe $b(N)$ cut-off and the temperature-density relation. Except for\nthe two lowest redshift quasars, the \\lya\\ forest spectra were split\nin two in order to take into account the significant redshift\nevolution ($\\Delta z \\sim 0.5$) and signal-to-noise variation across\na single spectrum. The calibration was done separately for each half\nof each observed spectrum. The synthetic spectra were processed to\ngive them identical characteristics (resolution, pixel size, noise\nproperties, mean absorption) as the real data. The same Voigt profile\nfitting package (an automated version of VPFIT (Webb 1987)) was used\nfor both the simulated and the observed spectra.\n\n\\section{Results and discussion}\nThe measured evolution of the temperature at the mean density and the\nslope of the effective equation of state are plotted in Figure~1. From\n$z\\sim 3.5$ to $z\\sim 3.0$, $T_0$ increases and the gas \nbecomes close to isothermal ($\\gamma \\sim 1.0$). This behavior differs\ndrastically from that predicted by models in which helium is fully\nreionized at higher redshift. For example, the solid lines correspond\nto a simulation that uses a uniform metagalactic UV-background from\nquasars as computed by Haardt \\& Madau (1996) and which assumes the gas to\nbe optically thin. In this simulation, both hydrogen and helium are\nfully reionized by $z\\sim 4.5$ and the temperature of the IGM declines\nslowly as the universe expands. Such a model can clearly not account\nfor the peak in the temperature at $z\\sim 3$ (reduced $\\chi^2$ for the\nsolid curves are 6.9 for $T_0$ and 3.6 for $\\gamma$). Instead, we\nassociate the peak in $T_0$ and the low value of $\\gamma$ with reheating\ndue to the second reionization of helium (\\HeII\\ $\\rightarrow$\n\\HeIII). This interpretation is supported by measurements of the\n\\SiIV/\\CIV\\ ratio (Songaila 1998, but see also Boksenberg, Rauch, \\&\nSargent 1998 and Giroux \\& Shull 1997) and direct measurements of the\n\\HeII\\ opacity (Heap et al.\\ 2000 and references therein).\n\n\\begin{figure}\n\\mbox{\n\\hspace{-0.8cm}\n\\plotone{schayej_fig1a.eps}\n\\hspace{-0.8cm}\n\\plotone{schayej_fig1b.eps} \n}\n\\caption{The evolution of the temperature at the mean density (left\npanel) and the slope of the effective equation of state (right\npanel). Horizontal error bars indicate redshift interval spanned by\nthe absorption lines, vertical error bars are $1\\,\\sigma$\nerrors. Different symbols correspond to different quasars. See text\nfor a description of the models.}\n\\end{figure}\n\nThe dashed lines in Figure~1 are for a model that was designed to fit\nthe data (reduced $\\chi^2$ is 0.24 for $T_0$ and 1.38 for\n$\\gamma$). In this simulation, which has a much softer UV-background\nat high redshift, \\HeII\\ reionizes at $z\\sim 3.2$. Before\nreionization, when the gas is optically thick to ionizing photons, the\nmean energy per photoionization is much higher than in the optically\nthin limit (Abel \\& Haehnelt 1999). We have approximated this effect\nin this simulation by enhancing the photoheating rates during\nreionization, so raising the temperature of the IGM.\n\nSince the simulation assumes a uniform ionizing background, the\ntemperature has to increase abruptly (i.e.\\ much faster than the gas\ncan recombine) in order to make $\\gamma$ as small as observed. In\nreality, the low-density gas may be reionized by harder photons, which\nwill be the first ionizing photons to escape from the dense regions\nsurrounding the sources. This would lead to a larger temperature\nincrease in the more dilute, cooler regions, resulting in a decrease\nof $\\gamma$ even for a more gradual reionization. Furthermore,\nalthough reionization may proceed fast locally (as in our small\nsimulation box), it may be patchy and take some time to\ncomplete. Hence the steep temperature jump indicated by the dashed\nline, although compatible with the data, should be regarded as\nillustrative only. The globally averaged $T_0$ could well increase\nmore gradually which would also be consistent with the data. More data\nat $z \\ga 3$ is needed to determine whether the temperature rise is\nsharp or gradual. On the theoretical side, more realistic models\nshould include radiative transfer effects, which are important during\nreionization.\n\nTogether with measurements of the \\HeII\\ opacity, which probe the\nionization state in the voids, the thermal history of the IGM provides\nimportant constraints on models of helium reionization. Furthermore,\nthe temperature of the IGM before the onset of helium reionization can\nbe used to constrain the redshift of hydrogen reionization, which\nmarks the end of the dark ages of cosmic history.\n\n\\acknowledgments\nWe are grateful to Bob Carswell and Sara Ellison for giving us\npermission to use their spectra of the quasars Q1100$-$264 and\nAPM\\,08279+5255 respectively.\n\n\\begin{references}\n\\reference\nAbel, T., \\& Haehnelt, M. G. 1999, ApJ, 520, L13\n\\reference\nBoksenberg, A., Sargent, W. L. W., \\& Rauch, M. 1998, preprint\n(astro-ph/9810502)\n\\reference\nBryan, G. L., \\& Machacek, M. E. 2000, ApJ, submitted (astro-ph/9906459)\n\\reference\nGiroux, M. L., \\& Shull, J. M. 1997, AJ, 113, 1505\n\\reference\nHeap, S. R., Williger, G. M., Smette, A., Hubeny, I., Sahu, M., Jenkins,\nE. B., Tripp, T. M. \\& Winkler, J. N. 2000, \\apj, in press\n(astro-ph/9812429)\n\\reference\nHaardt, F., \\& Madau, P. 1996, \\apj, 461, 20\n\\reference\nHui, L. \\& Gnedin, N. Y. 1997, \\mnras, 292, 27\n\\reference\nMiralda-Escud\\'e, J., \\& Rees, M. J. 1994, \\mnras, 266, 343\n\\reference\nRicotti, M., Gnedin, N. Y., \\& Shull, J. M. 2000, \\apj, in press\n(astro-ph/9906413)\n\\reference\nSchaye, J., Theuns, T., Leonard, A., \\& Efstathiou, G. 1999, \\mnras, 310, 57\n\\reference\nSchaye, J., Theuns, T., Rauch, M., Efstathiou, G., \\& Sargent, W. L. W. 2000,\n\\mnras, submitted (astro-ph/9912432)\n\\reference\nSongaila, A. 1998, AJ, 115, 2184\n\\reference\nWebb, J. K. 1987, Ph.D. thesis, Univ.~Cambridge\n\\end{references}\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002248
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Big Bang Nucleosynthesis updated with the NACRE Compilation
|
[
{
"author": "Elisabeth Vangioni-Flam\\inst{1}"
},
{
"author": "Alain Coc\\inst{2} and Michel Cass\\'e\\inst{1, 3}"
}
] |
We update the Big Bang Nucleosynthesis calculations on the basis of the recent NACRE compilation of reaction rates. The average values of the calculated abundances of light nuclei do not differ significantly from those obtained using the previous Fowler's compilation. However, ${^7}Li$ is slightly depressed at high baryon to photon ratio $\eta$. Concerning ${^{10}}B$, its abundance is significantly lower than the one calculated with the Caughlan and Fowler (1988) rates as anticipated by Rauscher and Raimann (1997). We estimate the uncertainties related to the nuclear reaction rates on the abundances of $D$, ${^3}He$, ${^4}He$, ${^6}Li$, ${^7}Li$, ${^9}Be$, ${^{10}}B$ and ${^{11}}B$ of cosmological and astrophysical interest. The main uncertainty concerns the $D(p,\gamma){^3}He$ reaction rate affecting the synthesis of ${^7}Li$ at rather high baryonic density and also the ${^3}He(\alpha,\gamma){^7}Be$ and ${^7}Li(p,\alpha){^4}He$ reactions. On the left part of the lithium valley the uncertainty is reduced due to the improvement of the measurement of the $T(\alpha,\gamma)^{7}Li$ reaction rate. The observed abundances of the nuclei of interest are compared to the predictions of the BBN model, taking into account both observational and theoretical uncertainties. Indeed, the ${^7}Li$ abundance observed in halo stars (Spite plateau) is now determined with high precision since the thickness of this plateau appears, in the light of recent observations, exceptionnaly small ($<$ 0.05 dex). The potential destruction/dilution of ${^7}Li$ in the outer layers of halo stars which could mask the true value of the primordial abundance is in full debate, but the present trend is towards a drastic reduction of the depletion factor (about 0.10 dex). It is why we use this isotope as a preferred baryometer. Even though much efforts have been devoted to the determination of deuterium in absorbing clouds in the line of sight of remote quasars, the statistics is very poor compared to the long series of lithium measurements. Taking into account these lithium constraints, two possible baryonic density ranges emerge, $\eta_{10}= 1.5 - 1.9$ and $\eta_{10} = 3.3 - 5.1$. In the first case, $Li$ is in concordance with $D$ from Webb et al (1997) and ${^4}He$ from Fields and Olive (1998) and Peimbert and Peimbert (2000). In the second case, agreement is achieved with $D$ from Tytler et al (2000) and ${^4}He$ from Izotov and Thuan (1998). Concerning the less abundant light isotopes, the theoretical BBN abundance of ${^6}Li$ is affected by a large uncertainty due to the poor knowledge of the $D(\alpha,\gamma){^6}Li$ reaction rate. However, at high $\eta$, its abundance is so low that there is little chance to determine observationally the true BBN ${^6}Li$ abundance. But, at low $\eta$, its abundance being one thousandth of that of primordial ${^7}Li$, 6/7 ratio measurements at very low metallicity are not totally hopeless in the future. Nevertheless, in the present situation, ${^6}Li$ is cosmologically relevant, though indirectly, since its mere presence in a few halo stars, corroborates the fact that it is essentially intact in these stars together with $^{7}Li$ and thus the Spite plateau can be used as such to infer the primordial ${^7}Li$ abundance. The $Be$ and $B$ abundances produced in the Big Bang are orders of magnitudes lower, and spallation of fast carbon and oxygen is probably their unique source, in the early Galaxy.
|
[
{
"name": "bigbang.tex",
"string": "\n\n% Version du 23 mars 2000\n%\\documentclass[referee]{aa}\n\\documentclass{aa}\n%\\usepackage{times}\n\\usepackage{epsfig}\n%\\usepackage{latexsym}\n\n\n\\def\\power#1{\\mbox{$\\times10^{#1}\\ $}}\n\\newcommand{\\gap}{\\mathrel{ \\rlap{\\raise.5ex\\hbox{$>$}}\n {\\lower.5ex\\hbox{$\\sim$}} } }\n\\newcommand{\\lap}{\\mathrel{ \\rlap{\\raise.5ex\\hbox{$<$}}\n\t\t {\\lower.5ex\\hbox{$\\sim$}} } }\n\n\\begin{document}\n\n\\thesaurus{99 % \n (99.999)} % Big Bang Nucleosynthesis, cosmology.\n%\n\\title{Big Bang Nucleosynthesis updated with the NACRE Compilation}\n\n\\author{Elisabeth Vangioni-Flam\\inst{1}, Alain Coc\\inst{2} and \nMichel Cass\\'e\\inst{1, 3}}\n \n\\institute{\nInstitut d'Astrophysique de Paris, 98 bis Bd Arago 75014 Paris, France e-mail:flam@iap.fr\n\\and\nCentre de Spectrom\\'etrie Nucl\\'eaire et de Spectrom\\'etrie\nde Masse, IN2P3-CNRS and Universit\\'e Paris Sud, B\\^atiment 104,\\\\ \n91405 Orsay Campus, France\n\\and\nService d'Astrophysique, DAPNIA, DSM, CEA, Orme des Merisiers,\n91191 Gif sur Yvette CEDEX France\n}\n\n\\date{Received ....; Accepted ....}\n\n\n\\maketitle\n\n\\begin{abstract}\nWe update the Big Bang Nucleosynthesis calculations on the basis of the recent\nNACRE compilation of reaction rates. The average values of the calculated\nabundances of light nuclei do not differ significantly from those obtained\nusing the previous Fowler's compilation.\nHowever, ${^7}Li$ is slightly depressed at high baryon to photon ratio $\\eta$.\nConcerning ${^{10}}B$, its abundance is significantly lower than the one\ncalculated with the Caughlan and Fowler (1988) rates as anticipated by\nRauscher and Raimann (1997).\nWe estimate the uncertainties related to the nuclear reaction\nrates on the abundances of $D$, ${^3}He$, ${^4}He$, ${^6}Li$, ${^7}Li$,\n${^9}Be$, ${^{10}}B$ and ${^{11}}B$ of cosmological and astrophysical interest.\nThe main uncertainty concerns the $D(p,\\gamma){^3}He$ reaction rate affecting\nthe synthesis of ${^7}Li$ \nat rather high baryonic density and also \n the ${^3}He(\\alpha,\\gamma){^7}Be$ and ${^7}Li(p,\\alpha){^4}He$\n reactions.\nOn the left part of the lithium valley the uncertainty is reduced\ndue to the improvement of the measurement of the $T(\\alpha,\\gamma)^{7}Li$\nreaction rate.\nThe observed abundances of the nuclei of interest are compared to the\npredictions of the BBN model, taking into account both observational\nand theoretical uncertainties.\nIndeed, the ${^7}Li$ abundance observed in halo stars (Spite\nplateau) is now determined with high precision since the thickness of\nthis plateau appears, in the light of recent observations,\nexceptionnaly small ($<$ 0.05 dex). The potential destruction/dilution of\n${^7}Li$ in the outer layers of halo stars\nwhich could mask the true value of the primordial abundance is in full debate,\nbut the present trend is towards a drastic reduction of the depletion factor\n(about 0.10 dex).\nIt is why we use this isotope as a preferred baryometer. Even though much\nefforts have been devoted to the determination of deuterium in absorbing\nclouds in the line of sight of remote quasars, the statistics is very poor\ncompared to the long series of lithium measurements.\nTaking into account these lithium constraints, two possible baryonic density\nranges emerge, $\\eta_{10}= 1.5 - 1.9$ and $\\eta_{10} = 3.3 - 5.1$.\nIn the first case, $Li$ is in concordance with $D$ from Webb et al (1997) and\n${^4}He$ from Fields and Olive (1998) and Peimbert and Peimbert (2000).\nIn the second case, agreement is achieved with $D$ from Tytler et al (2000)\nand ${^4}He$ from Izotov and Thuan (1998). \n\nConcerning the less abundant light isotopes, the theoretical BBN abundance\nof ${^6}Li$ is affected by a large uncertainty due to the poor knowledge\nof the $D(\\alpha,\\gamma){^6}Li$ reaction rate. However, at high $\\eta$,\nits abundance is so low that there is little chance to determine\nobservationally the true BBN ${^6}Li$ abundance.\nBut, at low $\\eta$, its abundance being one thousandth of that of primordial\n${^7}Li$, 6/7 ratio measurements at very low metallicity are not totally\nhopeless in the future.\nNevertheless, in the present situation, ${^6}Li$ is cosmologically relevant,\nthough indirectly, since its mere presence in a few halo stars, corroborates\nthe fact that it is essentially intact in these stars together with $^{7}Li$\nand thus the Spite plateau can be used as such to infer the primordial\n${^7}Li$ abundance.\nThe $Be$ and $B$ abundances produced in the Big Bang are orders of magnitudes\nlower, and spallation of fast carbon and oxygen is probably their unique\nsource, in the early Galaxy. \n\\end{abstract}\n\n\n\\section{Introduction}\nBesides the expansion of the Universe and the ubiquitous presence of the\nfossil cosmological radiation, the Big Bang Nucleosynthesis (BBN) is one\npilar of modern cosmology.\nIt allows, in principle, the derivation of the baryonic density of the\nuniverse (see for reviews Schramm and Turner 1998, Sarkar 1996, 1999 and\nOlive et al 2000).\nThe determination of light element abundances has improved dramatically in\nthe recent past and the planned observations of $D$, ${^4}He$, ${^6}Li$\nand ${^7}Li$ should allow a precise determination (10\\% is a\nreachable goal) of the universal baryonic density, provided the\nprecision of the model is made compatible with this objective.\nTaking advantage of the release of a new compilation of thermonuclear\nreation rates, called NACRE (Nuclear Astrophysics Compilation\nof REaction rates) (Angulo et al 1999), we have updated the standard\nBBN model developed at the Institut d'Astrophysique de Paris, including\nthe analysis of the $Be$ and $B$ production in the Big Bang.\n\nOn the other hand, observations of light isotopes have florished:\ni) $D/H$ has been observed in absorbing clouds on the sightline of remote \nquasars, ii) refined observations of $^{4}He$ have been performed in \nextragalactic very metal poor HII regions and in the Small Magellanic Cloud \n(Peimbert and Peimbert 2000), iii) the $^{6}Li$ abundance has been determined\nin two halo stars, iv) high quality $^{7}Li$ observations in the halo stars\nhave been accumulated.\nA review of the present data can be found in Olive et al (2000) and \nTytler et al (2000).\nThus, it is timely to reassess the determination of the baryonic density of \nthe Universe in the light of advances in nuclear physics and astronomical \nobservations.\n\nIn section II, we present the new compilation of the reaction rates\nand compare it with the classical Caughlan-Fowler (1988) ones; we evaluate\nthe sensitivity of the different light element abundances\nto the change of each relevant reaction rate;\nBBN calculations are performed using i) recommended values of the reaction \nrates and ii) extreme values obtained from the low and high rate limits.\nIn section III, we discuss the astrophysical status of each isotope, both\nobservationally and theoretically in order to confront it to the BBN\ncalculation; we deduce the baryonic density of the Universe.\nFinally, we draw conclusion in section IV and stress the importance of\nprecise measurements of a few key nuclear cross sections and refined\nabundance determinations of $D$ and $^{6}Li$.\n\n\n\n\\section{Nuclear Physics and Big Bang nucleosynthesis }\n\nThe new compilation of Angulo et al (1999) of thermonuclear reaction rates\nfor astrophysics, includes 86 charged-particle induced reactions\ncorresponding to the proton capture reactions involved in the cold\npp-chain, CNO cycle, NeNa and MgAl chains.\nThe BBN network is constituted by about 60\nreactions which participate to primordial nucleosynthesis up\nto $^{11}B$. 22 of these reactions are covered by the NACRE compilation.\nThe main innovative features of NACRE with respect to the former\ncompilation Caughlan and Fowler (1988) are the following: (1) detailed references\nare provided to the source of original data; (2) uncertainties\nare analyzed in detail, realistic lower and\nupper bounds of the rates are provided; (3) the rates are given in tabular\nform, available also electronically on the World--Wide--Web.\nFor these reasons, we can adopt the NACRE recommended rates for the calculation\nof the yields and use the upper and lower limits of the rates to test\nthe sensitivity of the abundances to the nuclear uncertainties. As the origins\nfor these uncertainties are documented in Angulo et al (1999), we do not\ndiscuss them here unless they show a significant effect on yields.\nWe calculated the isotopic abundances as a function of\n$\\eta_{10}$ between 1 and 10, changing one single reaction at a time.\nFor each reaction we made a calculation with the high and low NACRE limits\nwhile the remaining reaction rates were set to their recommended NACRE value.\nThen we calculated, the maximum of the quantity\n${\\Delta}N/N{\\equiv}N_{high}/N_{low}-1$ within the range of $\\eta_{10}$\nvariations for each of the 8 isotopes. Positive (resp. negative) values\ncorrespond to higher (resp. lower) isotope production when the high rate is\nused instead of the low one. Note however that following the ${\\Delta}N/N$\ndefinition, the positive values are not bound while the negative values are\nbound by -1. Hence, for instance (see Table 1), ${\\Delta}N/N=+10$ (resp.\n-0.78) means that the isotope yield is 11 times higher (resp. 4.5 times lower)\nwith the high rate than with the low one. \nThe corresponding results are shown in Table 1. \n\n\n\\begin{table}\n\\caption{Influencial reactions and their sensitivity to nuclear uncertainties}\n\\tiny\n\\begin{flushleft}\n\\begin{tabular}{|l|c|c|c|c|c|c|c|c|}\n\\hline\nReaction~${\\backslash}$~${\\Delta}N/N$\n& $^4$He&D&$^3$He&$^7$Li&$^6$Li&$^9$Be&$^{10}$B&$^{11}$B\\\\\n\\hline\n$^1$H(p,$e^+\\nu)^2$H&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.&\nn.s.&n.s.\\\\\n\\hline\n$^2$H(p,$\\gamma)^3$He&n.s.&-0.19&0.19&0.26&-0.19&-0.27&-0.18&0.20\\\\\n\\hline\n$^2$H(d,$\\gamma)^4$He&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.&\nn.s.&n.s.\\\\\n\\hline\n$^2$H(d,n)$^3$He&n.s.&-0.09&0.06&0.12&-0.09&-0.09&-0.08&0.19\\\\\n\\hline\n$^2$H(d,p)$^3$H&n.s.&-0.03&-0.04&0.01&-0.03&0.04&-0.03&0.03\\\\\n\\hline\n$^2$H($\\alpha,\\gamma)^6$Li&n.s.&n.s.&n.s.&n.s.&21.&n.s.\n&10.&n.s.\\\\\n\\hline\n$^3$H(d,n)$^4$He&n.s.&n.s.&n.s.&-0.07&n.s.&-0.13&-0.04&-0.07\\\\\n\\hline\n$^3$H($\\alpha,\\gamma)^7$Li&n.s.&n.s.&n.s.&0.24&n.s.&0.24\n&0.06&0.24\\\\\n\\hline\n$^3$He($^3$He,2p)$^4$He&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.\n&n.s.&n.s.\\\\\n\\hline\n$^3$He($\\alpha,\\gamma)^7$Be&n.s.&n.s.&n.s.&0.39&n.s.&0.21\n&n.s.&0.40\\\\\n\\hline\n2$^{4}$He($\\alpha,\\gamma)^{12}$C&n.s.&n.s.&n.s.&n.s.&n.s.&\nn.s.&n.s.&0.01\\\\\n\\hline\n2$^{4}$He(n,$\\gamma)^{9}$Be&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.\n&n.s.&n.s.\\\\\n\\hline\n$^6$Li(p,$\\gamma)^7$Be&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.\n&n.s.&n.s.\\\\\n\\hline\n$^6$Li(p,$\\alpha)^3$He&n.s.&n.s.&n.s.&n.s.&\n-0.18&n.s.&-0.18&n.s.\\\\\n\\hline\n$^7$Li(p,$\\gamma)^8$Be&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.\n&n.s.&n.s.\\\\\n\\hline\n$^7$Li(p,$\\alpha)^4$He&n.s.&n.s.&n.s.&-0.25&n.s.&-0.25&\n-0.07&-0.24\\\\\n\\hline\n$^7$Li($\\alpha,\\gamma)^{11}$B&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.\n&n.s.&0.39\\\\\n\\hline\n%$^{7}$Li($\\alpha$,n)$^{10}$B&?&?&?&?&?&?&?&? \\\\\n%\\hline\n$^{7}$Li($\\alpha$,n)$^{10}$B&\\multicolumn{8}{c|}{Q$<0$}\\\\\n\\hline\n$^7$Be(p,$\\gamma)^8$B&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.&\nn.s.&0.01\\\\\n\\hline\n$^7$Be($\\alpha,\\gamma)^8$B&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.&\nn.s.&0.81\\\\\n\\hline\n$^9$Be(p,$\\gamma)^{10}$B&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.&\n0.04&n.s.\\\\\n\\hline\n$^9$Be(p,pn)2$^4$He&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.\n&n.s.&n.s.\\\\\n\\hline\n$^9$Be(p,d)2$^4$He&n.s.&n.s.&n.s.&n.s.&n.s.&-0.13\n&-0.02&-0.01\\\\\n\\hline\n$^9$Be(p,$\\alpha)^6$Li&n.s.&n.s.&n.s.&n.s.&n.s.&-0.13\n&-0.02&n.s.\\\\\n\\hline\n$^9$Be($\\alpha$,n)$^{12}$C&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.\n&n.s.&-0.01\\\\\n\\hline\n$^{10}$B(p,$\\gamma)^{11}$C&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.\n&n.s.&-0.01\\\\\n\\hline\n$^{10}$B(p,$\\alpha)^7$Be&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.\n&-0.38&n.s.\\\\\n\\hline\n$^{11}$B(p,$\\gamma)^{12}$C&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.&\nn.s.&n.s.\\\\\n\\hline\n$^{11}$B(p,n)$^{11}$C&\\multicolumn{8}{c|}{Q$<0$} \\\\\n\\hline\n$^{11}$B(p,$\\alpha)2^4$He&n.s.&n.s.&n.s.&n.s.&n.s.&n.s.\n&n.s.&-0.78\\\\\n\\hline\n$^{14}$N(p,$\\alpha)^{11}$C&\\multicolumn{8}{c|}{Q$<0$}\\\\\n\\hline\n%$^{15}$N(p,$\\alpha)^{12}$C&n.s.&n.s.&n.s.&n.s.&n.s.\n%&n.s.&n.s.&-0.01\\\\\n%\\hline\n\\end{tabular}\n\\newline\n${\\Delta}N/N{\\equiv}N_h/N_l-1$\n\\newline\nn.s. : not significant ($|{\\Delta}N/N|<0.01$)\n\\newline\nQ$<0$ : no tabulated reverse rates available for endoenergic reactions.\n\\end{flushleft}\n%\\end{table}\n\\normalsize\n\\end{table}\n\n\n\\begin{figure} % fig 1\n\\epsfig{file=fig1.ps,width=8.cm}\n\\vspace{10pt}\n\\caption{ Two particularly uncertain reaction rates: $D(p,\\gamma){^3}He$\nand $D(\\alpha,\\gamma){^6}Li$ (NACRE/Caughlan-Fowler 1988- CF88) solid line:\nmean ratio and dashed line: NACRE upper limit/CF88 and NACRE lower limit/CF88.\nThe dotted line ($D(p,\\gamma){^3}He$ reaction) represent the small effect of\nthe Schmidt et al. (1996) correction not included in the NACRE compilation.}\n%\\label{f:hcno}\n\\end{figure}\n\nFor three of these reactions, the test has not been made because the NACRE\ncompilation does not provide high and low limits for the reverse rate of\nendoenergic reactions ($^{7}Li(\\alpha,n)^{10}B$ , \n$^{11}B(p,n)^{11}C$ and $^{14}B(p,\\alpha)^{11}C$).\nThe reverse recommended rate can be calculated from\nthe formulas. However, the low and high rates are only tabulated and limited\ndown to temperatures chosen in order that the reaction rate remains above\nthe lower limit of\n$N_{\\rm A}\\langle\\sigma v\\rangle \\leq 10^{-25}$ cm$^3$ mol$^{-1}$ s$^{-1}$.\nFor $Q<0$ reactions, the reverse rate is higher than the direct tabulated\none but limited by $N_{\\rm A}\\langle\\sigma v\\rangle \\leq 10^{-25}$ cm$^3$\nmol$^{-1}$ s$^{-1}$ times the {\\em reverse ratio}.\n\n\n\n\n\nIn the analysis of yield uncertainties, one should keep in mind that\nthe guidelines for the NACRE compilation favoured conservative\nupper and lower limits for the rates in order that the actual rate be\nwithin these limits with a high degree of confidence.\nFor instance, when incompatible data set were present, and if the differences\ncould not be resolved by analysing the publications alone the high and low\nlimits were set in order to incorporate all data sets.\nIn some case (e.g. $D(\\alpha,\\gamma)^6Li$) the incompatibility is between\nexperimental data and theoretical results making very problematic\n the interpretation of the\nrate uncertainty in term of gaussian distributions. When only an upper\nlimit is available experimentally, as in previous compilations, its\ncontribution is weighted by a 0., 0.1 and 1. factor respectively.\nThis again makes difficult the probabilistic interpretation of rate \nuncertainties. \nNevertheless, few NACRE reaction rates are at the origin of a significant \nuncertainty (Table 1).\n\nThe $D(p,\\gamma)^3He$ NACRE reaction rate is responsible for a 20--30\\%\nuncertainty on most isotopes. It comes from the dispersion of experimental\nresults.\nNote that the incompatibility of the two data set at low energy reported in\nAngulo et al. (1999) has been removed after a correction factor \n(Schmidt et al. 1996) has been applied to Schmidt et al. (1995) data to \naccount for an unsuspected experimental bias.\nTo check the effect of this rate update, we reiterate the NACRE calculation by \nfitting the experimental data points up to 2~MeV but with the corrected \nSchmidt et al. (1995,1996) data. Since it affects only the lowest energies,\nit has a negligible effect in the domain of BBN (see Fig. 1). \n\nThe most dramatic effect comes from the $D(\\alpha,\\gamma)^6Li$ reaction\nwhich induces uncertainties of a factor 22 and 11 on the $^6Li$ and $^{10}$B\nyields. This rate uncertainty originates from the discrepancy between\ntheoretical low energy dependance of the S--factor and experimental data\n(Kiener et al. 1991) obtained with the coulomb break--up technique\n(see Kharbach and Descouvemont (1998) for a recent comparison between \ntheories and experiment).\nThis reaction clearly deserves further experimental effort.\nThe reactions $^3He(\\alpha,\\gamma)^7Be$\nand $^7Li(p,\\alpha)^4He$ induce a significant (25--40\\% each) uncertainty \non $^7Li$ production. For these reactions, the rate uncertainties comes \nfrom the dispersion (systematic errors) of non resonant experimental \ndata at low energy. \n\n\n\n\nUncertainties on $BeB$ isotope yields remain negligible when compared\nwith the gap between calculated values and observational limitations.\nAt maximum, a factor of $\\approx4$ uncertainty on $^{11}B$ at\nlow $\\eta$ arises from the influence of the $^{11}B(p,\\alpha)^8Be$ reaction.\nHowever, the NACRE compilation covers only 22 of the 60 reactions\ninvolved in Big Bang Nucleosynthesis. In particular, $BeB$ yield \nuncertainties are most likely dominated by uncertainties in reaction \nrates not included in the NACRE compilation. \n\n\n\n\nIn front of the large systematic uncertainties on the observational abundance\ndata (section 3.1), it seems premature to elaborate complex \nstatistical procedures to get very precise theoretical uncertainties on the\nprimordial abundances.\n\nIndeed, extensive studies have used Monte-Carlo techniques to estimate the\ntheoretical uncertainties studies have used Monte-Carlo techniques \n(Krauss et al 1990, Smith et al 1993, Fiorentini et al 1998, Olive et al 2000,\nNollet and Burles 2000). \n These powerfull methods have proven their\n efficiency in various domains (e.g. simulations of high energy physics\n experiment) provided that the probability distribution involved are known.\n Concerning our approach, since the values given by the NACRE compilation\n do not represent statistical confidence level, but upper and lower limits,\n they are not directly appropriate to Monte-Carlo calculations, but they include\n both statistical and systematic errors (see above).\n\n We estimate the uncertainties performing to global calculations, one with\n all the reaction rates set to their lower limits, and the second\n one with all the reaction rates set to their higher limits\n (dashed lines in figures 4 and 5). This method could lead to compensation (according to\n the signs of individual uncertainties displayed in table 1) \n between production and destruction and therefore to\n underestimate the global uncertainties in some cases. \nThe advantage of this technique is simplicity and transparency. \nBut the disadvantage is that it does not allow to derive a confidence level, \nin the statistical sense.\n\n\nThe primordial abundances of the light elements $D$, $^{3,4}He$ \nand $^{7}Li$ are governed by the expansion rate of the Universe and the \ncooling it induces.\nUnder the classical assumptions, (homogeneity and the isotropy of the Universe\nand standard particle physics: three light neutrino species, neutron lifetime \nequal to 887 seconds) the abundances depend only on the baryon to photon ratio\n$\\eta$, related to the baryonic parameter by $\\eta_{10} = 273\\Omega_{B}.h^{2}$\nwith $h=H/100 kms^{-1}Mpc^{-1}$ (see e.g. for details Olive et al 2000).\n \nWe do not include the small corrections on the $^{4}He$ mass fraction due to\nCoulomb, radiative and finite temperature effects, finite nucleon\nmass effects and differential neutrino heating (Sarkar 1999, Lopez and \nTurner 1999) since these corrections lead to effects much less than the \nuncertainties on the observational data.\n\nThe network extends up to $^{11}C$ (decaying into $^{11}B$), the leakage is\ntaken into account through the reaction $^{11}C(n,2\\alpha)^{4}He$.\n\nIn figures 2 and 3, we compare the results obtained with i) the NACRE\nrecommended reaction rates (solid lines) and ii) the CF88 ones (dashed lines).\nThere is no significant difference except for $^{7}Li$ at high $\\eta$.\nIn this range, ${^7}Li$ comes from $D(p,\\gamma){^3}He(\\alpha,\\gamma){^7}Be$\nfollowed by electron capture. \nSo changes in the first rate result directly in changes of the final ${^7}Li$ \nyield.\n$^{10}B$ presents the largest difference due to the $^{10}B(p,\\alpha)^{7}Be$ \ndestruction reaction rate. The NACRE rate is several orders of magnitude\nhigher due to the inclusion (Rauscher and Raimann 1997) of a 10~keV, \n5/2$^+$ resonance.\nHowever, there is no astrophysical and cosmological consequences since $^{10}B$\nis essentially of spallative origin (Vangioni-Flam et al 2000).\n\nFigures 4 and 5 present the updated theoretical primordial abundances from $D$ to\n$^{11}B$ using the NACRE compilation (mean values and extreme ones).\nD and $^{3,4}He$ are almost not affected.\nDue to the uncertainty of the $D(p,\\gamma)^{3}He$, the $^{7}Li$ abundance\nat $\\eta > 3$ is affected by a significant error (about 30\\% to be\ncompared to the 42\\% one mentionned by Olive et al 2000 deduced from\nthe Smith et al 1993 analysis).\nAt $\\eta < 3$, the $^{7}Li$ uncertainty is reduced due to improvements in the\nderivation of the S factor of the $T(\\alpha,\\gamma)^{7}Li$ reaction\n(Angulo et al 1999). This is the result of the high precision data provided by\nBrune et al (1994) and spanning the entire energy range of interest to BBN\nnucleosynthesis. Considering only the precise Brune et al. (1994) data would\neven reduce the rate uncertainty.\n However, in this\n specific case, with our method, error compensation occurs between the \n $^{7}Li(p,\\alpha) ^{4}He$ and $T(\\alpha,\\gamma) ^{7}Li$ reaction rates \nas shown\n in table 1. From the same table, one sees that the maximized uncertainties\n are $\\pm$25\\%. Consequently on figure 4, the uncertainty is somewhat\n underestimated which does not affect significantly the general conclusions.\n On the contrary, for $\\eta > 3$ region, the errors on the reaction rates\n $D(p,\\gamma)^{3}He$,\n $^{3}He(\\alpha,\\gamma)^{7}Li$ add up and therefore the uncertainties are\n not underestimated.\n\n$^{6}Li$ has a particularly large error bar due to the poor knowledge of\n$D(\\alpha,\\gamma)^{6}Li$. The maximum value of the primordial $^{6}Li/H$\n(at low $\\eta$) which is of the order of 5.\\power{-13} may not be out\nof reach of future measurements in halo stars; it represents a factor 10 below\nthe 6/7 value measured at present in old stars ([Fe/H] = -2.3).\nThe results presented here are in fair agreement with previous calculations\n(Thomas et al 1993, Schramm 1993, Delbourgo-Salvador and Vangioni-Flam 1993,\nVangioni-Flam et al 1999).\nWe confirm that primordial abundances of $BeB$ are negligible even in the most \nfavorable case, and spallation remains the main mechanism to produce them in\nthe course of the galactic evolution.\n \n\n\\begin{figure} % fig 2\n\\epsfig{file=fig2.ps,width=8.cm}\n\\vspace{10pt}\n\\caption{\nTheoretical primordial abundances of ${^4}He$ (by mass), $D$, ${^3}He$ and \n${^7}Li$ (by number) vs the baryon/photon ratio, using the reaction rates \nfrom NACRE (full lines) and GF88 (dashed lines).}\n%\\label{f:hcno}\n\\end{figure}\n\n\n\\begin{figure} % fig 3\n\\epsfig{file=fig3.ps,width=8.cm}\n\\vspace{10pt}\n\\caption{Theoretical primordial abundances of ${^6}Li$, ${^9}Be$, ${^{10}}B$ \nand ${^{11}}B$ (by number) vs the baryon/photon ratio, $\\eta$, using the \nreaction rates from NACRE compilation (full lines) and CF88 (dashed lines).\nThe long-dashed line associated to $^{10}B$ correponds to the Rauscher and\nRaimann 1997 evaluation.}\n%\\label{f:hcno}\n\\end{figure}\n\n\n\n\\section{Astrophysical and cosmological discussion}\n\n\\subsection{Astrophysical aspects}\nIn the following, we decline the astrophysical observational and theoretical\nstatus of each isotope of interest and their possible evolution since the\nBig Bang in order to define reasonable error boxes to prepare the \nconfrontation to the theoretical calculations.\n\n\\subsubsection{Deuterium}\n\n$D$ is particularly sensitive to the baryon/photon ratio, $\\eta$, and has\nbeen considered up to now as the best baryometer (e.g. Reeves 1994). However,\ndue to a certain confusion on $D/H$ abundance evaluations, both at high \nredshifts and in the local Galaxy, some care has to be taken in the \ncosmological use of Deuterium.\nLet us present a brief overview of the observations. \n\n$D$ is measured in three astrophysical and/or cosmological sites i) the local\ninterstellar medium, ISM ($D_{ISM}$), ii) the protosolar nebula ($D_{ps}$),\niii) the cosmological clouds ($D_{cc}$). \nThese three values serve as signposts to follow the evolution of $D$ in the \nUniverse and in the Galaxy.\nDeuterium, due to its fragility is completely burnt in stars. \nThus, if no production mechanism is at work, we must have \n$D_{cc}>D_{ps}>D_{ISM}$.\n\nThe local $D$ abundance, inferred from UV observations of the nearby ISM,\nestimated to $(1.6\\pm0.1)$\\power{-5} (Linsky et al 1995), is probably not\nunique, ranging from 5.\\power{-6} to about 2.\\power{-5}\n(Vidal-Madjar et al 1998, Lemoine et al 1999, Vidal-Madjar 2000).\nThese variations are lacking explanations.\nThus, there is an ambiguity on the true local $D/H$ value which, by the way, \nserves as a normalisation for the chemical evolutionary models. \nThese discrepancies weaken the predictive ability of the evolutionary \nmodels to derive the primordial $D$ abundance.\n\n$D/H$ ratios are measured in the solar system (Jupiter, Saturn, Uranus, Neptun,\ncomets). This allows to derive a precise protosolar value of \n$(3\\pm0.3)$\\power{-5} (Drouart et al 1999), somewhat higher than the estimate\nof Geiss and Gloeckler (1998) $(2.1\\pm0.5)$\\power{-5}.\n\n$D/H$ has also been determined in absorbing clouds on the sightlines of \nquasars.\nOn one side, Tytler et al (2000) (and reference therein) have found three\nabsorption systems in which $D/H$ are i) $(3.24 \\pm 0.3)$\\power{-5},\nii) $4^{+0.8}_{-0.6}$\\power{-5}, iii) $<6.7$\\power{-5}.\nAs a fair representation of these data, we adopt the following range : 3.\nto 4.\\power{-5}. This estimate, if identified with the primordial one,\nis unconfortably close to the protosolar one, since it implies a very small\n$D$ destruction all along the galactic evolution corresponding to a small\nvariation of the star formation rate from the birth of the galaxy up to now,\nin contradiction with the general trend indicated by the strong increase of\nthe cosmic star formation rate vs redshift ($0<z<2$) (Blain et al 2000,\nMadau 2000).\nOn the other side, high values of $D/H$ have been reported concerning the \nquasar QSO 1718+4807 ($z$ = 0.701) namely, $D/H = (2.5 \\pm 0.5)$\\power{-4}\naccording to Webb et al (1997) and 8.\\power{-5}$< D/H <$5.7\\power{-4}\naccording to Tytler et al (2000).\nNote that the analysis of Levshakov et al (1999) allowing non gaussian \nvelocity distributions leads to lower values.\nConsequently, we adopt a second data box bounded by \n8.\\power{-5}$<D/H<$ 3.\\power{-4}.\n \n\n\\subsubsection{Helium-3}\n\nThis isotope is produced in comparable amount to that of deuterium, but at the\nopposite, its stellar and galactic story is not simple. Its production and \ndestruction are model dependent (Vassiliadis and Woods 1993, Charbonnel 2000).\nIn spite of great effort directed to its abundance determination in HII \nregions and planetary nebula (Balser et al 1999, Bania and Rood 2000) \n$^{3}He$ cannot be used, at the moment, as a reliable cosmic baryometer \n(Olive et al 1995, Galli et al 1997) since it is very difficult to extrapolate\nits abundance back to its primordial value. \n\n\\subsubsection{Helium-4}\n\nThe primordial abundance of $^{4}He$ by mass, $Y_{p}$, is measured in low\nmetallicity extragalactic HII regions (for a review see Kunth and Ostlin 2000).\nIn addition to the primordial component, $^{4}He$ is also produced in stars\ntogether with oxygen and nitrogen through global stellar nucleosynthesis.\nTherefore, in order to extract the primordial component from the observational\ndata, it is necessary to extrapolate back the observed $^{4}He$ value down to\nzero metallicity.\nOlive, Skillman and Steigman (1997) selected 62 blue compact galaxies and\nobtained $Y_{p}$ $\\sim$ 0.234. Izotov and Thuan (1998) pointed out that the\neffect of the HeI stellar absorption has more importance that previously\nthought and they reported $Y_{p} = 0.245\\pm0.004$.\nRecently, Fields and Olive (1998) reanalyzed the observational data and\nreported $Y_{p} = 0.238\\;\\pm\\;(0.002)$ stat, $\\pm\\;(0.005)$ syst where the\nerrors are 1 $\\sigma$ values.\nThe new determination $Y_{p} = 0.2345\\pm0.0030$ by Peimbert and \nPeimbert (2000) on the basis of observations of HII regions in the Small \nMagellanic Cloud points towards the lowest helium value proposed by Fields\nand Olive (1998). In this context, two data boxes emerge: \ni) $Y_p = 0.245\\pm0.004$ and ii) $Y_p = 0.238\\pm0.005$.\n\n\\subsubsection{Lithium-6,7}\n\nRecent advances on the determination of $Li$ in halo stars (Spite et al 1996,\nBonifacio and Molaro 1997, Molaro 1999, Smith et al 1998, Ryan et al 1999a)\nindicate that the Spite plateau is exceptionally thin ($<$ 0.05 dex).\nThis small dispersion, together with the presence of $^{6}Li$ in two halo \nstars (Smith et al 1993, 1998, Hobbs and Thorburn 1994, 1997, Cayrel et \nal 1999) indicate that the stellar destruction of ${^7}Li$ if any, is very \nlimited (less than $\\sim$ 0.1 dex, see Ryan et al 1999a).\n$^{6}Li$ is however of cosmological interest since, being more fragile \nthan $^{7}Li$, its mere presence in the atmosphere of halo stars \nconfirms that ${^7}Li$ is essentially intact in these stars (Vangioni-Flam \net al 1999, Fields and Olive 1999). This, combined with the very small \ndispersion around the average of the Spite plateau add confidence in \ninterpreting it as indicative of the primordial $Li$ abundance (especially \nat the lowest metallicities, where the contamination by spallation is \nexpected to be negligible (Ryan et al 1999b).\nStellar modelisation should adapt to this constraint. Indeed, simple models of \nlithium evolution predict little or no depletion (Deliyannis et al 1990),\nthus conforting the primordial nature of lithium in metal poor halo stars. \nHowever, three different mechanisms of alteration of lithium in halo stars\nhave been suggested i) diffusion/gravitational settling (Michaud 2000 and\nreferences therein), ii) rotational mixing (Chaboyer 1998, Pinsonneault \net al 1999) and iii) stellar winds (Vauclair and Charbonnel 1995).\nSome combinations of these three mechanisms have to be envisioned. \nThere is a paradox between the absence of dispersion and the number of the \nprocesses which could produce a potential dispersion.\nThis implies either a curious statistical compensation or more radically,\nthat these physical mechanisms are intrinsically irrelevant. \nHowever, metallicity independent depletion mechanisms for instance (mixing\ninduced by gravity waves) cannot be totally excluded (Cayrel, private \ncommunication).\n\nConsequently, we take the observed value of the Spite plateau including\nthe observational dispersion ( $A(Li)= 2.2\\pm0.04$) to which we add\n0.1 dex to account the maximum $Li$ stellar depletion. This corresponds\nfor the primordial lithium to the following range\n1.4\\power{-10}$<^7Li/H<$2.2\\power{-10}.\nThis evaluation is in fair agreement with that of Olive et al (2000) but\nit is narrower than that of Tytler et al (2000) who have enlarged the limit\nof depletion to allow agreement with their low $D/H$ measurement. \n \nIn the following, due to the high observational quality and the large sample\nanalyzed (more than 70 objects), $^{7}Li$ is used as a baryometer, keeping\nin mind that this isotope has the pecularity to allow to possible solutions\ndepending on the side of the lithium valley.\n\n\\subsubsection{Beryllium and Boron}\n\nAbundance observations of elemental $Be$ and $B$ in very metal poor stars \nin the halo have made great progresses in the recent years (Gilmore et al 1992,\nDuncan et al 1992, Boesgaard and King 1993, Ryan et al 1994, Duncan et \nal 1997, Garcia-Lopez et al 1998, Primas et al 1999, Primas 2000).\nThese observations concern indeed galactic evolution; the lowest observed \nvalues (of the order of $10^{-13}$) are much higher than the BBN calculated\nabundances.\nWe confirm that BBN calculated abundances of $^{9}Be$, $^{10}B$ and $^{11}B$\nare negligible with respect the measured ones in the more metal poor stars.\nThe origin of these elements can be explained in term of spallation of fast\ncarbon and oxygen in the early Galaxy (Vangioni-Flam et al 2000).\n\n\\begin{figure} % fig 4\n\\epsfig{file=fig4.ps,width=8.cm}\n\\vspace{10pt}\n\\caption{\nTheoretical primordial abundances of ${^4}He$ (by mass), $D$, ${^3}He$ and\n${^7}Li$ (by number) vs the baryon/photon ratio,$\\eta$, using the reaction\nrates from the NACRE compilation. \nFull lines: mean values of the reaction rates. Dashed lines: extreme value\nof the reaction rates (for details see section 2).\n Horizontal dotted lines indicate the error boxes \nrelated to different observations, $^{4}He$ left: Fields and Olive 1998, \n$^{4}He$ right: Izotov and Thuan 1998. $D$ left: Webb et al 1997, $D$ right: \nTytler et al 2000. \n$^{7}Li$: Molaro 1999 and Ryan et al 1999a. Vertical full lines are deduced \nfrom the error box of $^{7}Li$.}\n\\end{figure}\n\n\n\\subsection{Baryonic density of the universe}\n\nOnce the different error boxes corresponding to the observed isotopes\nabundances corrected for evolutionary effects are established, we can \ncompare them to the predictions of the BBN calculations.\nAs different $D$ and $^{4}He$ measurements are dichotomic, contrary to \n$^{7}Li$, we put emphasis on this last isotope to determine a possible\nrange of baryonic densities. As shown in figure 4, considering $^{7}Li$ \nalone, two possible ranges emerge: i) $1.5<\\eta_{10} < 1.9$, \nii) $3.3< \\eta_{10} < 5.1$. For h = 0.65, we get \ni) $0.013 <\\Omega{_B} < 0.019$ and ii) $0.029 <\\Omega{_B} < 0.045$.\n\nThe first range is in good concordance with the error boxes related to high\n$D$ and low $^{4}He$.\nHowever, the largest measured value of $D/H$ seems excluded\n($D/H<$ 3.\\power{-4}).\nThe second one, on the right side of the diagram, is in fair agreement with\na lower $D/H$ (except the lowest measured value, $D/H$ = 3.\\power{-5}) and \na higher $^{4}He$ (except also the highest value 0.25).\nAt this stage of the analysis, we have to admit that two ranges of baryonic\ndensity have to be into account, only future observations will help to \nremove the ambiguity.\n\nIt is worth comparing the baryonic density to that of the luminous matter\n($\\Omega_{L}$) in the Universe to infer the amount of the baryonic dark matter.\nRecent estimates of $\\Omega_{L}$ ranges between 0.002 and 0.004 (Salucci and\nPersic 1999), which is lower than both $\\Omega{_B}$ obtained.\nThe difference makes necessary baryonic dark matter.\nFocusing on spiral galaxies the amount of luminous matter is estimated\nto $\\Omega_{LS}$ = $1.44^{+1.55}_{-0.2}$\\power{-3} ( Sallucci and Persic\n1999). Considering that the dynamical mass of the halo of spiral galaxies is about ten\ntimes higher than that of the disk, the corresponding $\\Omega_{HS}$ is about\n0.015.\nIn both cases ( $\\Omega_B\\approx$0.015 or $\\Omega_B\\approx$0.04) all the dark\nmatter in the halo of our Galaxy could in principle be baryonic.\nNote that since eight years of searches for microlensing events by the\nMACHO and EROS collaborations toward the Magellanic clouds have revealed\nonly a few events.\nThe fraction of the halo in the form of dark massive compact objects,\nusing a typical model, is estimated to only 20\\% by Alcock et al (1999) in\nagreement with the limits given by Lasserre et al (2000).\nOn the other hand, the observations of the Lyman alpha forest clouds between\nthe redshifts 0 and 5, lead to a corresponding $\\Omega_B$ of about 0.03 ($\\pm 0.01$), taking \n into account the uncertainty related to ionised hydrogen (Riediger, Petitjean and Mucket 1998).\nThis value is thought to reflect the bulk of the baryons at large scale.\nIt is more consistent with our high $\\Omega_B$ range. \n \n \n\n\\begin{figure} % fig 5\n\\epsfig{file=fig5.ps,width=8.cm}\n\\vspace{10pt}\n\\caption{Theoretical primordial abundances of ${^6}Li$, ${^9}Be$, ${^{10}}B$ \nand ${^{11}}B$ (by number) vs the baryon/photon ratio, $\\eta$, using\nthe reaction rates from NACRE. Full lines: mean values of the reaction rates.\nDashed lines: extreme limits of the reaction rates.}\n\\end{figure}\n\n\n\\section{Conclusion}\n\nBig bang nucleosynthesis has been studied since a long time, but it deserves \npermanent care since it gives access to the baryon density which is a key \ncosmological parameter. This work has been aimed at integrating the last \ndevelopment in both fields of nuclear physics and observational abundance \ndetermination of light elements.\n\n\n1. The update of the reaction rates of the BBN using the NACRE compilation\ndoes not lead to crucial modifications of the general conclusions \nconcerning the baryonic content of the Universe. The average values of the \nabundances of isotopes of cosmological interest are in general similar to \nthat calculated on the basis of the Caughlan-Fowler (1988) compilation.\n\n2. However, the modification of the $D(p,\\gamma)^{3}He$ reaction rate leads to\na $^{7}Li$ abundance slightly lower at $\\eta > 3$. But the uncertainty on this \nreaction rate remains high ($\\pm$30\\%). At $\\eta< 3$, the revision\nof the $T(\\alpha,\\gamma)^{7}Li$ reaction rate leads to a very neat reduction \nof the uncertainty of the calculated $^{7}Li$ abundance. However this reaction, together\n with the $^{7}Li(p,\\alpha)^{4}He$, remain the main sources of the $^{7}Li$ \n uncertainty at low $\\eta$.\n\n3. The abundance of $^{10}B$ is modified by the new $^{10}B(p,\\alpha)^{7}Li$\nreaction rate, but there is no cosmological consequences.\n\n4. $^{6}Li$ is affected by the large uncertainty of the \n$D(\\alpha,\\gamma)^{6}Li$ reaction. \nHowever, $^{6}Li$ is essentially of spallative origin.\n\n5. Owing to the high observational reliability of the $^{7}Li$ abundance data\nwith respect to the $D$ data avalaible both rare and debated, we choose it as \nthe leading baryometer, since it appears that the primitive $^{7}Li$ is almost\nintact in halo stars.\nDue to the competition between $T(\\alpha,\\gamma)^{7}Li$ and\n$D(p,\\gamma)^{3}He(\\alpha,\\gamma)^{7}Be$ (e $\\nu$) $^{7}Li$, the curve of \n$^{7}Li$ vs $\\eta$ presents a valley shape. Consequently, the observational\nerror box of $^{7}Li$ leads to two ranges of $\\eta$ : $1.5<\\eta<1.9$ and \n$3.3<\\eta<5.1$ (corresponding to $0.013<\\Omega_B<0.019$ and \n$0.029<\\Omega_B<0.045$ for h=0.65). \nIn both cases, all the dark matter in the halo of our Galaxy could be baryonic.\nHowever, only a fraction of 20\\% is detected through microlensing events in \nthe direction of the Magellanic clouds.\n\n6. These two $\\eta$ ranges are confronted to the other available \ncosmologically relevant isotopes, namely $D$ and $^{4}He$. The first $\\eta$\nrange agrees with a high $D$ and low $^{4}He$ values, the second range is \nin concordance with a low $D$ and high $^{4}He$ values. At present, none of \nthese solutions can be excluded.\n\n7. In the future, on the nuclear physics front, it would be important to\n(re-)measure the $D(\\alpha,\\gamma)^{6}Li$ reaction to reduce the\nuncertainty on the calculated $^{6}Li$ abundance. High precision\nmeasurements over the full energy range of interest to BBN of the $D(p,\\gamma)^3He$,\n$^3He(\\alpha,\\gamma)^7Be$ and $^7Li(p,\\alpha)^4He$ reactions would also\nreduce the uncertainty on $^7Li$ abundance calculations.\nOn the astronomical front, more data on $D$ in absorbing clouds on the \nsightlines of quasars at different redshifts are mandatory to remove the \nambiguity. However, if the large scale $D$ dichotomy remains, it will be\ntime to invoke specific mechanisms of $D$ production and destruction like\nphotodisintegration of $D$ and $^{4}He$ by $\\gamma$ ray quasars (blazars)\n(Cass\\'e and Vangioni-Flam 1997) and/or nuclear spallation. \nThe observations of $^{6}Li$ in two halo stars has been a great progress and \na determination of its abundance in very metal poor stars should be pursued.\nIt will help to constrain even more stringently the possible lithium depletion\nin these stars and confort definitively the primordial status of the Spite \nplateau. Together with nuclear improvements, refined $^{6}Li$ measurements\nin very metal poor stars (possibly via the VLT) could perhaps lead us towards\nthe primordial $^{6}Li$ abundance.\n \nWe warmly thank Roger Cayrel for illuminating discussions, Jurgen Kiener,\nGilles Bogaert and Carmen Angulo for their comments on nuclear data.\n\n\\begin{thebibliography}{99}\n\\bibitem{Al00} Alcock, C. (MACHO), 2000, preprint, astro-ph/0001272\n\\bibitem{AN99} Angulo~C., Arnould~M., Rayet~M., et al., (The NACRE\ncollaboration) 1999, Nucl. Phys. A656, 3 and http://pntpm.ulb.ac.be/nacre.htm\n\\bibitem{Bal00} Balser, D.S., Bania, T.M., Rood, R.T. and Wilson, T.L. 1999, \nApJ, 510, 759\n\\bibitem{Ban00} Bania, T. and Rood, R. 2000, in\n'The light Elements and their Evolution', IAU Symp. 198, ASP Conf. Series. \nEdts L. da Silva, R. de Meideros and M. Spite, in press\n\\bibitem{Bla00} Blain, D. et al 2000, astro-ph/9906311\n\\bibitem{Bo93} Boesgaard, A.M. and King, J.R. 1993, AJ, 106, 2309\n\\bibitem{Bo97} Bonifacio P. and Molaro, P. 1997, MNRAS, 285, 847\n\\bibitem{Br94} Brune, C.R., Kavanagh, R.W. and Rolfs, C. 1994, \nPhys. Rev., C50, 2205\n\\bibitem{Ca97} Cass\\'e, M. and Vangioni-Flam, E. 1997, in \n'Structure and evolution of the Intergalactic medium from QSO absorption \nline systems', Edts P. Petitjean and S. Charlot, Edts Frontieres, p. 331\n\\bibitem{Ca99} Cayrel, R., Spite, M., Spite, F. Vangioni-Flam, E., Cass\\'e, M\n\\& Audouze, J. 1999, A\\&A. 343, 923\n\\bibitem{CA88} Caughlan G.R. and Fowler W.A. 1988 At. Data Nucl. Data Tables\n 40, 283 \n\\bibitem{Ch98} Chaboyer, B. 1998, UAI 185, p. 25\n\\bibitem{Ch00} Charbonnel, C. 2000, in \n'The light Elements and their Evolution', IAU Symp. 198, ASP Conf. Series. \nEdts L. da Silva, R. de Meideros and M. Spite, in press\n\\bibitem{De90} Deliyannis, C.P., Demarque, P. and Kawaler, S.D. 1990, ApJS,\n73, 21\n\\bibitem{De93} Delbourgo-Salvador, P. and Vangioni-Flam, E. 1993,\n in 'Origin and evolution of the elements', Cambridge University Press, \n edts, N. Prantzos, E. Vangioni-Flam, M. Cass\\'e, p. 132\n\\bibitem{Dr99} Drouart, A., Dubrulle, B., Gautier, D. and Robert, F. 1999,\nIcarus, 140, 129\n\\bibitem{Du92} Duncan, D., Lambert, D.L. and Lemke, M. 1992, ApJ, 401, 584\n\\bibitem{Du97} Duncan, D. et al 1997, ApJ, 488, 338\n\\bibitem{Fi98} Fields, B. and Olive, K.A. 1998, ApJ, 506, 177\n\\bibitem{Fi99} Fields, B. and Olive, K.A. 1999, New Astron. 4, 255\n\\bibitem{Fi98} Fiorentini, G., Lisi, E., Sarkar, S. and Villante, F.L. 1998,\nPhys. Rev. D58, 063506\n\\bibitem{Ga97} Galli, D. Stanghellini, L., Tosi, M. and Palla, F. 1997, ApJ,\n477, 218\n\\bibitem{Ga98} Garcia-Lopez, R.J et al 1998, ApJ, 500, 241\n\\bibitem{Ge98} Geiss, J. and Gloeckler, G. 1998, Space Sci. Rev., 84, 239\n\\bibitem{Gi92} Gilmore, J. et al 1992, Nature, 357, 379\n\\bibitem{Ho94} Hobbs, L.M. and Thorburn, J.A. 1994, ApJ. 428, 25\n\\bibitem{Ho97} Hobbs, L.M. and Thorburn, J.A. 1997, ApJ, 491, 772\n\\bibitem{Iz98} Izotov, Y.I. \\& Thuan, T.X. 1998, ApJ. 500, 1888\n\\bibitem{Kha98} Kharbach, A. and Descouvemont, P., 1998,\nPhys. Rev. C58, 1066\n\\bibitem{Kie91} Kiener, J., Gils, H.J., Rebel, H. et al., 1991,\nPhys. Rev. C44, 2195\n\\bibitem{Ku00} Kunth, D. and Ostlin, G. 2000, to appear in Astro. and \nAstroph. Rev.\n\\bibitem{Kr90} Krauss, L.M. and Romanelli, P. 1990, ApJ, 358, 47\n\\bibitem{La00} Lasserre, T. et al (EROS) 2000, preprint astro-ph/0002253\n\\bibitem{Lem99} Lemoine M. et al, 1999, New Astronomy, 4, 23\n\\bibitem{Lev99} Levshakov, S.A., Kegel, W.H. and Takahara, F. 1999, MNRAS,\n302, 707\n\\bibitem{Li95} Linsky, J. et al 1995, ApJ, 451, 335\n\\bibitem{Lo99} Lopez, R.E. \\& Turner, M.S. 1999, Phys. Rev. D, 59, 103502\n\\bibitem{Ma00} Madau, P. 2000, in 'VLT opening Symp.', in press \nastro-ph/9907268\n\\bibitem{Mi00} Michaud, G. 2000, in\n 'The light Elements and their Evolution', IAU Symp. 198, ASP Conf. Series. \n Edts L. da Silva, R. de Meideros and M. Spite \n\\bibitem{Mo99} Molaro, P. 1999, in \n'LiBeB, Cosmic Rays, and Related X and Gamma-Rays', \nEdts R. Ramaty, E. Vangioni-Flam, M. Cass\\'e and K. Olive, K., \nASP Conf. Series, vol 171, p. 6\n\\bibitem{No00} Nollet, K. M. \\& Burles, S. 2000, astro-ph/0001440\n\\bibitem{Ol95} Olive, K., Rood, R.T., Schramm, D.N., Truran, J. and \nVangioni-Flam, E. 1995,\n ApJ, 444, 680\n\\bibitem{Ol00} Olive, K.A, Steigman, G. and Walker, T.P., 2000, \nin press in Phys. Rep. Astro-ph/9905320\n\\bibitem{Ol97} Olive, K.A., Skillman, E.D. \\& Steigman, G.1997, ApJ 489, 1006\n\\bibitem{Pe00} Peimbert, M. and Peimbert, A. 2000, in\n 'The light Elements and their Evolution', IAU Symp. 198, ASP Conf. Series. \n Edts L. da Silva, R. de Meideros and M. Spite, \n \\bibitem{Pi99} Pinsonneault, M.H., Walker, T.P., Steigman, \nG. and Narayanan, V.K. 1999, ApJ 527, 180\n\\bibitem{Pr99} Primas, F. et al 1999, AA 313, 545\n\\bibitem{Pr00} Primas, F. 2000, in 'The light Elements and their Evolution', \nIAU Symp. 198, ASP Conf. Series. \n Edts L. da Silva, R. de Meideros and M. Spite, \n\\bibitem{Ra97} Rauscher, T. and Raimann, G. 1997, nucl-th/9602029\n\\bibitem{Re94} Reeves, H. 1994, Rev. Mod. Phys. 66, 193\n\\bibitem{Ried} Riediger, R., Petitjean, P. and Mucket, J.P. 1998, A\\&A, 329, 30\n\\bibitem{Ry94} Ryan, S.G., Norris, I., Bessel, M. and Deliyannis, C. 1994,\nApJ, 388, 184\n\\bibitem{Ry99a} Ryan, S.G., Norris, J.E. and Beers, T.C. 1999a, \nastro-ph/9903059\n\\bibitem{Ry99b} Ryan, S.G., Beers, T.C., Olive, K.A., Fields, R.D. \\& \nNorris, J.E., 1999b, astro-ph/9905211\n\\bibitem{Sa99} Salucci, P. and Persic M. 1999, MNRAS, 309, 923 \n\\bibitem{Sa96} Sarkar, S. 1996 Rep. Prog. Phys., 59, 1493,\n\\bibitem{Sar99} Sarkar, S. 1999 astro-ph/9903183\n\\bibitem{Sc98} Schramm, D.N. \\& Turner, M.S. 1998, Rev. Mod. Phys. 70, 303\n\\bibitem{Sc93} Schramm, D. 1993, in 'Origin and evolution of the elements',\nCambridge University Press, edts, N. Prantzos, E. Vangioni-Flam, M. Cass\\'e, \np. 112\n\\bibitem{Sch95} Schmidt, G.J., Chasteler, R.M., Laymon, C.M., et al., 1995,\nPhys. Rev. C52, R1732\n\\bibitem{Sch96} Schmidt, G.J., Chasteler, R.M., Laymon, C.M., et al., 1996,\nNucl. Phys. A607, 139 \n%\\bibitem{Sch97} Schmidt, G.J., Rice, B.J., Chasteler, R.M., et al., 1997,\n%Phys. Rev. C56, 2565\n\\bibitem{Sm93a} Smith, M., Kawano, L., Lawrence, H. and Malaney, R.A. 1993, ApJS, 85, 219 \n\\bibitem{Sm93b} Smith, V.V., Lambert, D.L. and Nissen, P.E, 1993, ApJ, 408, 262\n\\bibitem{Sm98} Smith, V.V., Lambert, D.L. and Nissen, P.E. 1998, ApJ, 506, 405\n\\bibitem{Sp96} Spite, M., Francois, P., Nissen, P.E. and Spite, F. 1996, \nAA 307, 172\n\\bibitem{Th93} Thomas, D. Schramm, D.N., Olive, K.A. \\& Fields, B.D. 1993, \nApJ. 406, 563\n\\bibitem{Ty00} Tytler, D. et al 2000, astro-ph/0001318\n\\bibitem{Va99} Vangioni-Flam et al 1999, New Ast. 4, 245\n\\bibitem{Va00} Vangioni-Flam, E., Cass\\'e, M. \\& Audouze,J. 2000, \nPhys. Rep. In press\n\\bibitem{Va93} Vassiliadis, E. and Wood, P.R. 1993, ApJ, 413, 641\n\\bibitem{Va95} Vauclair, S. and Charbonnel, C. 1995, AA, 295, 715\n\\bibitem{Vi98} Vidal-Madjar, A. et al 1998, AA, 338, 694\n\\bibitem{Vi00} Vidal-Madjar, A. 2000, in \n'The light Elements and their Evolution', IAU Symp. 198, ASP Conf. Series.,\nEdts L. da Silva, R. de Meideros and M. Spite, in press\n\\bibitem{We97} Webb, J.K. et al 1997, Nature, 383, 250\n\n\n\\end{thebibliography}\n\n\n\\end{document}\n\n\n-- \n Alain COC | Phone: (33)-1-69.15.52.37\nMail: C.S.N.S.M., Bat. 104 | Fax: (33)-1-69.15.50.08\n 91405 Orsay Campus | E-Mail: coc@csnsm.in2p3.fr\n\tFRANCE | http://www-csnsm.in2p3.fr\n\n\n"
}
] |
[
{
"name": "astro-ph0002248.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{Al00} Alcock, C. (MACHO), 2000, preprint, astro-ph/0001272\n\\bibitem{AN99} Angulo~C., Arnould~M., Rayet~M., et al., (The NACRE\ncollaboration) 1999, Nucl. Phys. A656, 3 and http://pntpm.ulb.ac.be/nacre.htm\n\\bibitem{Bal00} Balser, D.S., Bania, T.M., Rood, R.T. and Wilson, T.L. 1999, \nApJ, 510, 759\n\\bibitem{Ban00} Bania, T. and Rood, R. 2000, in\n'The light Elements and their Evolution', IAU Symp. 198, ASP Conf. Series. \nEdts L. da Silva, R. de Meideros and M. Spite, in press\n\\bibitem{Bla00} Blain, D. et al 2000, astro-ph/9906311\n\\bibitem{Bo93} Boesgaard, A.M. and King, J.R. 1993, AJ, 106, 2309\n\\bibitem{Bo97} Bonifacio P. and Molaro, P. 1997, MNRAS, 285, 847\n\\bibitem{Br94} Brune, C.R., Kavanagh, R.W. and Rolfs, C. 1994, \nPhys. Rev., C50, 2205\n\\bibitem{Ca97} Cass\\'e, M. and Vangioni-Flam, E. 1997, in \n'Structure and evolution of the Intergalactic medium from QSO absorption \nline systems', Edts P. Petitjean and S. Charlot, Edts Frontieres, p. 331\n\\bibitem{Ca99} Cayrel, R., Spite, M., Spite, F. Vangioni-Flam, E., Cass\\'e, M\n\\& Audouze, J. 1999, A\\&A. 343, 923\n\\bibitem{CA88} Caughlan G.R. and Fowler W.A. 1988 At. Data Nucl. Data Tables\n 40, 283 \n\\bibitem{Ch98} Chaboyer, B. 1998, UAI 185, p. 25\n\\bibitem{Ch00} Charbonnel, C. 2000, in \n'The light Elements and their Evolution', IAU Symp. 198, ASP Conf. Series. \nEdts L. da Silva, R. de Meideros and M. Spite, in press\n\\bibitem{De90} Deliyannis, C.P., Demarque, P. and Kawaler, S.D. 1990, ApJS,\n73, 21\n\\bibitem{De93} Delbourgo-Salvador, P. and Vangioni-Flam, E. 1993,\n in 'Origin and evolution of the elements', Cambridge University Press, \n edts, N. Prantzos, E. Vangioni-Flam, M. Cass\\'e, p. 132\n\\bibitem{Dr99} Drouart, A., Dubrulle, B., Gautier, D. and Robert, F. 1999,\nIcarus, 140, 129\n\\bibitem{Du92} Duncan, D., Lambert, D.L. and Lemke, M. 1992, ApJ, 401, 584\n\\bibitem{Du97} Duncan, D. et al 1997, ApJ, 488, 338\n\\bibitem{Fi98} Fields, B. and Olive, K.A. 1998, ApJ, 506, 177\n\\bibitem{Fi99} Fields, B. and Olive, K.A. 1999, New Astron. 4, 255\n\\bibitem{Fi98} Fiorentini, G., Lisi, E., Sarkar, S. and Villante, F.L. 1998,\nPhys. Rev. D58, 063506\n\\bibitem{Ga97} Galli, D. Stanghellini, L., Tosi, M. and Palla, F. 1997, ApJ,\n477, 218\n\\bibitem{Ga98} Garcia-Lopez, R.J et al 1998, ApJ, 500, 241\n\\bibitem{Ge98} Geiss, J. and Gloeckler, G. 1998, Space Sci. Rev., 84, 239\n\\bibitem{Gi92} Gilmore, J. et al 1992, Nature, 357, 379\n\\bibitem{Ho94} Hobbs, L.M. and Thorburn, J.A. 1994, ApJ. 428, 25\n\\bibitem{Ho97} Hobbs, L.M. and Thorburn, J.A. 1997, ApJ, 491, 772\n\\bibitem{Iz98} Izotov, Y.I. \\& Thuan, T.X. 1998, ApJ. 500, 1888\n\\bibitem{Kha98} Kharbach, A. and Descouvemont, P., 1998,\nPhys. Rev. C58, 1066\n\\bibitem{Kie91} Kiener, J., Gils, H.J., Rebel, H. et al., 1991,\nPhys. Rev. C44, 2195\n\\bibitem{Ku00} Kunth, D. and Ostlin, G. 2000, to appear in Astro. and \nAstroph. Rev.\n\\bibitem{Kr90} Krauss, L.M. and Romanelli, P. 1990, ApJ, 358, 47\n\\bibitem{La00} Lasserre, T. et al (EROS) 2000, preprint astro-ph/0002253\n\\bibitem{Lem99} Lemoine M. et al, 1999, New Astronomy, 4, 23\n\\bibitem{Lev99} Levshakov, S.A., Kegel, W.H. and Takahara, F. 1999, MNRAS,\n302, 707\n\\bibitem{Li95} Linsky, J. et al 1995, ApJ, 451, 335\n\\bibitem{Lo99} Lopez, R.E. \\& Turner, M.S. 1999, Phys. Rev. D, 59, 103502\n\\bibitem{Ma00} Madau, P. 2000, in 'VLT opening Symp.', in press \nastro-ph/9907268\n\\bibitem{Mi00} Michaud, G. 2000, in\n 'The light Elements and their Evolution', IAU Symp. 198, ASP Conf. Series. \n Edts L. da Silva, R. de Meideros and M. Spite \n\\bibitem{Mo99} Molaro, P. 1999, in \n'LiBeB, Cosmic Rays, and Related X and Gamma-Rays', \nEdts R. Ramaty, E. Vangioni-Flam, M. Cass\\'e and K. Olive, K., \nASP Conf. Series, vol 171, p. 6\n\\bibitem{No00} Nollet, K. M. \\& Burles, S. 2000, astro-ph/0001440\n\\bibitem{Ol95} Olive, K., Rood, R.T., Schramm, D.N., Truran, J. and \nVangioni-Flam, E. 1995,\n ApJ, 444, 680\n\\bibitem{Ol00} Olive, K.A, Steigman, G. and Walker, T.P., 2000, \nin press in Phys. Rep. Astro-ph/9905320\n\\bibitem{Ol97} Olive, K.A., Skillman, E.D. \\& Steigman, G.1997, ApJ 489, 1006\n\\bibitem{Pe00} Peimbert, M. and Peimbert, A. 2000, in\n 'The light Elements and their Evolution', IAU Symp. 198, ASP Conf. Series. \n Edts L. da Silva, R. de Meideros and M. Spite, \n \\bibitem{Pi99} Pinsonneault, M.H., Walker, T.P., Steigman, \nG. and Narayanan, V.K. 1999, ApJ 527, 180\n\\bibitem{Pr99} Primas, F. et al 1999, AA 313, 545\n\\bibitem{Pr00} Primas, F. 2000, in 'The light Elements and their Evolution', \nIAU Symp. 198, ASP Conf. Series. \n Edts L. da Silva, R. de Meideros and M. Spite, \n\\bibitem{Ra97} Rauscher, T. and Raimann, G. 1997, nucl-th/9602029\n\\bibitem{Re94} Reeves, H. 1994, Rev. Mod. Phys. 66, 193\n\\bibitem{Ried} Riediger, R., Petitjean, P. and Mucket, J.P. 1998, A\\&A, 329, 30\n\\bibitem{Ry94} Ryan, S.G., Norris, I., Bessel, M. and Deliyannis, C. 1994,\nApJ, 388, 184\n\\bibitem{Ry99a} Ryan, S.G., Norris, J.E. and Beers, T.C. 1999a, \nastro-ph/9903059\n\\bibitem{Ry99b} Ryan, S.G., Beers, T.C., Olive, K.A., Fields, R.D. \\& \nNorris, J.E., 1999b, astro-ph/9905211\n\\bibitem{Sa99} Salucci, P. and Persic M. 1999, MNRAS, 309, 923 \n\\bibitem{Sa96} Sarkar, S. 1996 Rep. Prog. Phys., 59, 1493,\n\\bibitem{Sar99} Sarkar, S. 1999 astro-ph/9903183\n\\bibitem{Sc98} Schramm, D.N. \\& Turner, M.S. 1998, Rev. Mod. Phys. 70, 303\n\\bibitem{Sc93} Schramm, D. 1993, in 'Origin and evolution of the elements',\nCambridge University Press, edts, N. Prantzos, E. Vangioni-Flam, M. Cass\\'e, \np. 112\n\\bibitem{Sch95} Schmidt, G.J., Chasteler, R.M., Laymon, C.M., et al., 1995,\nPhys. Rev. C52, R1732\n\\bibitem{Sch96} Schmidt, G.J., Chasteler, R.M., Laymon, C.M., et al., 1996,\nNucl. Phys. A607, 139 \n%\\bibitem{Sch97} Schmidt, G.J., Rice, B.J., Chasteler, R.M., et al., 1997,\n%Phys. Rev. C56, 2565\n\\bibitem{Sm93a} Smith, M., Kawano, L., Lawrence, H. and Malaney, R.A. 1993, ApJS, 85, 219 \n\\bibitem{Sm93b} Smith, V.V., Lambert, D.L. and Nissen, P.E, 1993, ApJ, 408, 262\n\\bibitem{Sm98} Smith, V.V., Lambert, D.L. and Nissen, P.E. 1998, ApJ, 506, 405\n\\bibitem{Sp96} Spite, M., Francois, P., Nissen, P.E. and Spite, F. 1996, \nAA 307, 172\n\\bibitem{Th93} Thomas, D. Schramm, D.N., Olive, K.A. \\& Fields, B.D. 1993, \nApJ. 406, 563\n\\bibitem{Ty00} Tytler, D. et al 2000, astro-ph/0001318\n\\bibitem{Va99} Vangioni-Flam et al 1999, New Ast. 4, 245\n\\bibitem{Va00} Vangioni-Flam, E., Cass\\'e, M. \\& Audouze,J. 2000, \nPhys. Rep. In press\n\\bibitem{Va93} Vassiliadis, E. and Wood, P.R. 1993, ApJ, 413, 641\n\\bibitem{Va95} Vauclair, S. and Charbonnel, C. 1995, AA, 295, 715\n\\bibitem{Vi98} Vidal-Madjar, A. et al 1998, AA, 338, 694\n\\bibitem{Vi00} Vidal-Madjar, A. 2000, in \n'The light Elements and their Evolution', IAU Symp. 198, ASP Conf. Series.,\nEdts L. da Silva, R. de Meideros and M. Spite, in press\n\\bibitem{We97} Webb, J.K. et al 1997, Nature, 383, 250\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002249
|
CMB ANISOTROPIES AND THE DETERMINATION\protect\\ OF COSMOLOGICAL PARAMETERS
|
[
{
"author": "G EFSTATHIOU"
}
] |
[
{
"name": "nato.tex",
"string": "% The CRCKAPB.STY should be in your LaTeX directory.\n\n% Begin your text file with:\n\n\\documentstyle[NATO]{crckapb} \n\n\\def\\etal{{\\it et al. }\\rm}\n\\def\\simlt{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}\\hbox{$<$}}}}\n\\def\\simgt{\\mathrel{\\hbox{\\rlap{\\hbox{\\lower4pt\\hbox{$\\sim$}}}\\hbox{$>$}}}}\n\\newcounter{parentequation}\\setcounter{parentequation}{0}\n\\def\\beglet{\n \\addtocounter{equation}{1}%\n \\setcounter{parentequation}{\\value{equation}}%\n \\setcounter{equation}{0}%\n \\def\\theequation{\\arabic{parentequation}\\alph{equation}}%\n \\ignorespaces\n}\n\\def\\endlet{\n \\setcounter{equation}{\\value{parentequation}}%\n \\def\\theequation{\\arabic{equation}}%\n}\n\n\n% Alternatives:\n% \\documentstyle[proceedings]{crckapb} \n% \\documentstyle[monograph]{crckapb} \n% \\documentstyle[nato]{crckapb} \n\n\\newcommand{\\stt}{\\small\\tt}\n\n% This document needs the CRCKAPB.STY file to create a \n% document with font size 12pts. \n% The title, subtitle, author's name(s) and institute(s) \n% are handled by the `opening' environment.\n\n\\begin{opening}\n\\title{CMB ANISOTROPIES AND THE DETERMINATION\\protect\\\\\n OF COSMOLOGICAL PARAMETERS}\n\n\n\\subtitle{ }\n\n% You can split the title and subtitle by putting \n% two backslashes at the appropriate place. \n\n\\author{G EFSTATHIOU}\n\\institute{Institute of Astronomy\\\\\n Madingley Road\\\\\n Cambridge CB3 OHA}\n% If there are more authors at one institute, you should first\n% use \\author{...} for each author followed by \\institute{...}.\n\n\\end{opening}\n\n\\runningtitle{CMB Anisotropies}\n\n\\begin{document}\n\n\n\n\\section{Abstract}\nI review the basic theory of the cosmic microwave\nbackground (CMB) anisotropies in adiabatic cold dark matter (CDM)\ncosmologies. The latest observational results on the CMB power\nspectrum are consistent with the simplest inflationary models and\nindicate that the Universe is close to spatially flat with a nearly\nscale invariant fluctuation spectrum. We are also beginning to see\ninteresting constraints on the density of CDM, with a best fit value\nof $\\omega_c \\equiv \\Omega_c h^2 \\sim 0.1$. The CMB constraints, when\ncombined with observations of distant Type Ia supernovae, are\nconverging on a $\\Lambda$-dominated Universe with $\\Omega_m \\approx\n0.3$ and $\\Omega_\\Lambda \\approx 0.7$.\\footnote{To appear in Proceedings of NATO\nASI: Structure formation in the Universe, eds. N. Turok, R. Crittenden.}\n\n\\section{Introduction}\n\nThe discovery of temperature anisotropies in the CMB by the COBE team\n(Smoot \\etal 1992) heralded a new era in cosmology. For the first\ntime COBE provided a clear detection of the primordial fluctuations\nresponsible for the formation of structure in the Universe at a time\nwhen they were still in the linear growth regime. Since then, a large\nnumber of ground based and balloon borne experiments have been\nperformed which have succeeded in defining the shape of the power\nspectrum of temperature anisotropies $C_\\ell$\\footnote{The power\nspectrum is defined as $C_\\ell = \\langle \\vert a_{\\ell m}\\vert^2\n\\rangle$, where the $a_{\\ell m}$ are determined from a spherical\nharmonic expansion of the temperature anisotropies on the sky, $\\Delta\nT/T = \\sum a_{\\ell m} Y_{\\ell m}(\\theta, \\phi)$.} up to multipoles of\n$\\ell \\sim 300$ clearly defining the first acoustic peak in the\nspectrum. Figure 1 shows a compilation of band power anisotropy\nmeasurements\n\\begin{equation}\n {\\Delta T_\\ell \\over T} = \\sqrt{ {1 \\over 2 \\pi} \\ell (\\ell + 1) C_\\ell}\n\\end{equation}\nthat is almost up to date at the time of writing. The horizontal error\nbars show the multipole range probed by each experiment. The recent\nresults from the VIPER experiment (Peterson \\etal 1999) and the\nBoomerang test flight (Mauskopf \\etal 1999) are not plotted because\nthe exact window functions are not yet publically available. Neither\nare the published results from the Python V experiment (Coble \\etal\n1999) which seem to be discrepant with the other experiments particularly in\nthe multipole range $\\ell \\simlt 100$. The points plotted in figure 1\nare generally consistent with each other and provide strong evidence\nfor a peak in the power spectrum at $\\ell \\sim 200$.\n\n\\begin{figure}\n\\vspace{9cm} \n\\special{psfile=pgconf1.ps hscale=65 vscale=65 angle=-90 hoffset= -20\nvoffset=340}\n\\caption{Current constraints on the power spectrum of CMB temperature\nanisotropies. The error bars in the vertical direction show\n$1\\sigma$ errors in the band power estimates and the error bars\nin the horizontal direction indicate the width of the band.\nThe solid line shows the best fit adiabatic CDM model\nwith parameters $\\omega_b = 0.019$, $\\omega_c = 0.10$, $n_s = 1.08$,\n$Q_{10} = 0.98$, $\\Omega_m=0.225$, $\\Omega_\\Lambda = 0.775$.}\n\\end{figure}\n\nIn this introductory article, I will review briefly the theory of CMB\nanisotropies in adiabatic models of structure formation and then\ndiscuss the implications of Figure 1 for values of cosmological\nparameters. The literature on the CMB anisotropies has grown\nenormously over the last few years and it is impossible to do the\nsubject justice in a short article. General reviews of the CMB\nanisotropies are given by Bond (1996) and Kamionkowski and Kosowsky\n(1999). A recent review on constraining cosmological parameters from\nthe CMB is given by Rocha (1999).\n\n\\section{Basic Theory}\n\nMost of the key features of figure 1 can be understood using a simplified\nset of equations. The background universe is assumed to be spatially flat\ntogether with small perturbations $h_{ij}$ so that the metric is \n\\begin{eqnarray}\nds^2 = a^2(\\tau)\\left (\\eta_{ij} + h_{ij} \\right ) dx^i dx^j, \\\\\n\\qquad \\qquad \\eta_{ij} = (1,\\ -1,\\ -1,\\ -1), \\qquad \\tau = \\int dt/a. \\nonumber\n\\end{eqnarray}\nWe adopt the synchronous gauge, $h_{00} = h_{0i} = 0$, and ignore the\nanisotropy of Thomson scattering and perturbations in the relativistic\nneutrino component. With these assumptions, the equations governing\nthe evolution of scalar plane wave perturbations of wavenumber $k$ are\n\\beglet\n\\begin{eqnarray}\n\\dot \\Delta + ik\\mu \\Delta +\\Phi = \\sigma_T n_e a \\left\n[\\Delta_0 + 4 \\mu v_b - \\Delta \\right ] \\\\\n\\Phi = - (3 \\mu^2 -1)\\dot h_{33}-(1 - \\mu^2)\\dot h \\\\\n\\dot v_b + {\\dot a \\over a} v_b = \\sigma_T n_e a {\\bar \\rho_\\gamma \\over \\bar \n\\rho_b} \\left\n( \\Delta_1 - {4 \\over 3} v_b \\right ), \\\\\n\\dot \\delta_b = {1 \\over 2} \\dot h - ikv_b, \\qquad\n\\dot \\delta_C = {1 \\over 2} \\dot h \\qquad\\\\\n\\ddot h + {\\dot a \\over a}\\dot h = 8\\pi G a^2 (\\bar \\rho_b \\delta_b\n+ \\bar \\rho_{c} \\delta_{c} + 2 \\bar \\rho_\\gamma \\Delta_0) \\\\\nik(\\dot h_{33} - \\dot h) = 16 \\pi G a^2 (\\bar \\rho_b v_b + \\bar\n\\rho_\\gamma \\Delta_1).\n\\end{eqnarray}\n\\endlet \nHere, $\\Delta$ is the perturbation to the photon radiation brightness\nand $\\Delta_0$ and $\\Delta_1$ are its zeroth and\nfirst angular moments, $\\delta_b$ and $\\delta_c$ are the density\nperturbations in the baryonic and CDM components, $v_b$ is the baryon\nvelocity and $h = {\\rm Tr}(h_{ij})$. Dots denote differentiation with\nrespect to the conformal time variable $\\tau$. It is instructive to\nlook at the solutions to these equations in the limits of large ($k\n\\tau_R \\ll 1$) and small ($k \\tau_R \\gg 1$) perturbations, where\n$\\tau_R$ is the conformal time at recombination:\n\n\n\\subsection{Large angle anisotropies}\n\n In the limit ${k} \\tau_R \\ll 1$, Thomson scattering is unimportant and so the term in square\nbrackets in the Boltzmann equation for the photons can be ignored. In the\nmatter dominated era $h_{33} = h \\propto \\tau^2$ and so equation (3a) becomes\n\\begin{equation}\n\\dot \\Delta + ik\\mu\\Delta = 2\\mu^2\\dot h \\label{LA1}\n\\end{equation}\nwith approximate solution \n\\begin{equation}\n\\Delta (k,\\mu,\\tau) \\approx - {2 \\ddot h (\\tau_R) \\over k^2} \\exp \\left\n(ik\\mu (\\tau_s - \\tau) \\right ). \\label{LA2}\n\\end{equation}\nThis solution is the Sachs-Wolfe (1967) effect. Any deviation from the\nevolution $\\ddot h ={\\rm constant}$, caused for example by a non-zero\ncosmological constant, will lead to additional terms in equation\n(\\ref{LA2}) increasing the large-angle anisotropies (sometimes\nreferred to as the late-time Sachs-Wolfe effect, see {\\it e.g.} Bond\n1996). The CMB power spectrum is given by\n\\begin{equation}\nC_\\ell = {1 \\over 8\\pi} \\int^\\infty_0 \\vert \\triangle_\\ell \\vert^2\nk^2dk, \\label{LA3}\n\\end{equation} \nwhere the perturbation $\\Delta$ has been expanded in Legendre \npolynomials,\n\\begin{equation}\n\\Delta = {\\displaystyle \\sum_{\\ell}} (2\\ell+1)\\Delta_\\ell P_\\ell (\\mu). \\label{LA4}\n\\end{equation}\nInserting the solution of equation (\\ref{LA2}) into equation (\\ref{LA3}) gives\n\\begin{equation}\nC_\\ell = {1 \\over 2 \\pi}\\int^\\infty_0 {\\vert \\ddot h \\vert^2 \\over\nk^4} j_l^2 (k \\tau_0)k^2\\; dk, \\label{LA5}\n\\end{equation}\nand so for a power-law spectrum of scalar perturbations, $\\vert h \\vert^2 \\propto k^{n_s}$,\nthe CMB power spectrum is\n\\begin{equation}\nC_\\ell = C_2 { \\Gamma \\left ( \\ell + {(n_s - 1) \\over 2} \\right ) \\over \\Gamma \n\\left ( \\ell + {(5 - n_s) \\over 2} \\right ) } { \\Gamma \\left ( { 9 - n_s \\over 2} \\right ) \n\\over \\Gamma \\left ( {3 + n_s \\over 2} \\right ) } \n\\end{equation}\ngiving the characteristic power-law like form, $C_\\ell \\propto \\ell^{(n_s -3)}$ at low\nmultipoles ($\\ell \\simlt 30$).\n\n\\subsection{Small angle anisotropies and Acoustic peaks}\n \n\nIn the matter dominated era, equation (3a) becomes\n\\begin{equation}\n\\dot\\Delta + ik\\mu \\triangle = \\sigma_Tn_e a \\left [ \\Delta_0\n+ 4\\mu v_b -\\Delta \\right ] + 2\\mu^2\\dot h, \\label{SA1}\n\\end{equation}\nand taking the zeroth and first angular moments gives\n\\beglet\n\\begin{eqnarray}\n\\dot\\Delta_0 + ik \\Delta_1 = {2 \\over 3} \\dot h \\qquad \\qquad\\\\\n\\dot\\Delta_1 + ik \\left ({\\Delta_0 + 2 \\Delta_2 \\over 3 }\\right ) = \n\\sigma_Tn_e a \\left [{4 \\over 3} v_b - \\Delta_1 \\right ].\n\\end{eqnarray}\n\\endlet\nPrior to recombination, $\\tau/\\tau_c \\gg 1$\nwhere $\\tau_c = 1/(\\sigma_T n_e a)$ is the mean collision time, and so\nthe matter is tightly coupled to the radiation. In this limit\n $\\Delta_1 \\approx 4/3v_b$ from equation (3c) and \n$\\Delta_2$ in equation (11b) can be ignored. With these approximations, equation (11b)\nbecomes\n\\begin{eqnarray}\n\\dot\\Delta_1 + {ik\\Delta_0 \\over 3} = -{\\bar \\rho_b \\over \\bar \n\\rho_\\gamma}\\left [{3 \\over 4}\n \\dot\\Delta_1 + {\\dot a \\over a} \\Delta_1 \\right ].\n\\end{eqnarray}\nNeglecting the expansion of the universe, equations (11a) and (12) can be combined to\ngive a forced oscillator equation\n\\begin{eqnarray}\n\\ddot\\Delta_0 = -{k^2 \\over 3R} \\Delta_0 + {2 \\over 3}\\ddot h, \\qquad \\ \\ \\\nR \\equiv 1+{3 \\bar \\rho_b \\over 4 \\bar \\rho_\\gamma },\n\\end{eqnarray}\nwith solution\n\\begin{eqnarray}\n\\Delta_0(\\tau)=\\left (\\Delta_0 (0) - {2R\\ddot h \\over k^2}\\right ) \\cos {k\\tau \\over \\sqrt {3R}} + {\\sqrt {3R} \\over k} \\dot\\Delta_0 (0)\\sin {k\\tau \\over \\sqrt {3R}} + {2R \\ddot h \\over k^2},\n\\end{eqnarray}\nwhere $\\Delta_0(0)$ and $\\dot \\Delta_0(0)$ are evaluated when the wave first crosses the Hubble\nradius, $k \\tau \\sim 1$. For adiabatic perturbations the first term dominates over the second\nbecause the perturbation breaks at $k \\tau \\sim 1$ with $\\dot \\Delta_0 \\approx 0$. It is useful\nto define (gauge-invariant) radiation perturbation variables\n\\begin{eqnarray}\n\\tilde\\Delta_0 = \\Delta_0 - { 2\\ddot h \\over k^2}, \\qquad\n\\tilde\\Delta_1 = \\Delta_1+i{ 2 \\dot h \\over 3k}, \\nonumber \n\\end{eqnarray}\nthen the solution of equation (10) is\n\\begin{eqnarray}\n\\tilde\\Delta (k, \\mu, \\tau ) = \\int^\\tau_0 \\sigma_Tn_ea \\left [\\tilde\n\\Delta_0 + 4\\mu \\left (v_b + { i\\dot h \\over 2 k} \\right ) \\right ]\ne^{ik\\mu(\\tau^\\prime-\\tau)-\\int_{\\tau^\\prime}^\\tau [\\sigma_T n_e\na]d\\tau^{\\prime\\prime}}d\\tau^\\prime. \\label{SA2}\n\\end{eqnarray}\nIf $k \\tau \\gg 1$, the second term in the square brackets is smaller\nthan the first by a factor of $k\\tau$, and the solution of equation\n(\\ref{SA2}) gives a power spectrum with a series of modulated acoustic\npeaks spaced at regular intervals of $k_m r_s(a_r) = m \\pi$, where\n$r_s$ is the sound horizon at recombination\n\\begin{eqnarray}\nr_s = {c \\over {\\sqrt 3}H_0\\Omega_m^{1/2}}\\int^{a_r}_0 {\nda \\over \\left (a + a_{equ}\\right )^{1/2}} {1 \\over R^{1/2}}, \\label{SA3}\n\\end{eqnarray}\n(Hu and Sugiyama 1995). Here $a_{equ}$ is the scale factor when matter\nand radiation have equal densities and $a_r$ is the scale factor at\nrecombination.\n\n\nThe multipole locations of the acoustic peaks in the angular power spectrum are given \nby\n\\begin{eqnarray}\n{\\ell}_m = \\alpha m\\pi {d_A (z_r)\\over r_s}\n\\end{eqnarray}\nwhere $\\alpha$ is a number of order unity and \n$d_A$ is the angular diameter distance to last scattering \n\\beglet\n\\begin{eqnarray}\nd_A = {c \\over H_0\\vert \\Omega_k \\vert ^{1/2}} {\\rm sin}_k( \\vert \\Omega_k \\vert \n^{1/2} x)\\\\\nx \\approx \\int^1_{a_r} {da \\over [\\Omega_ma + \\Omega_ka^2 + \\Omega_\\Lambda a^4]^{1/2}}\n\\end{eqnarray}\n\\endlet\nwhere $\\Omega_k = 1-\\Omega_\\Lambda - \\Omega_m$ and ${\\rm sin}_k \\equiv {\\rm sinh}$ if\n$\\Omega_k > 0$ and ${\\rm sin}_k = {\\rm sin}$ if $\\Omega_k < 0$.\n\nThe general dependence of the CMB power spectrum on cosmological\nparameters is therefore clear. The positions of the acoustic peaks\ndepend on the geometry of the Universe via the angular diameter\ndistance of equation (18) and on the value of the sound horizon\n$r_s$. The relative amplitudes of the peaks depend on the physical\ndensities of the various constituents $\\omega_b \\equiv \\Omega_b h^2$,\n$\\omega_c \\equiv \\Omega_c h^2$, $\\omega_\\nu \\equiv \\Omega_\\nu h^2$,\n{\\it etc.} and on the scalar fluctuation spectrum (parameterized here\nby a constant spectral index $n_s$). Clearly, models with the same\ninitial fluctuation spectra and identical physical matter densities\n$\\omega_i$ will have identical CMB power spectra at high multipoles if\nthey have the same angular diameter distance to the last scattering\nsurface. This leads to a strong {\\it geometrical degeneracy} between\n$\\Omega_m$ and $\\Omega_\\Lambda$ ({\\it e.g.} Efstathiou and Bond 1999\nand references therein). The power spectrum on large angular scales\n(equation 9) is sensitive to the spectral index and amplitude of the\npower spectrum, geometry of the Universe and, for extreme values of\n$\\Omega_k$ can break the geometrical degeneracy via the late-time\nSachs-Wolfe effect. We will discuss briefly some of the constraints\non cosmological parameters from the current CMB data in the next\nsection. Before moving on to this topic, I mention some important\npoints that cannot be covered in detail because of space limitations:\n\n\\noindent\n$\\bullet$ Inflationary models can give rise to tensor perturbations\nwith a characteristic spectrum that declines sharply at $\\ell \\simgt\n100$ (see {\\it e.g.} Bond 1996 and references therein). In power-law\nlike inflation, the tensor spectral index $n_t$ is closely linked to\nthe scalar spectral index, $n_t \\approx n_s -1$, and to the relative\namplitude of the tensor and scalar perturbations.\n\n\\noindent\n$\\bullet$ The anisotropy of Thomson scattering causes the CMB\nanisotropies to be linearly polarized at the level of a few\npercent (see Bond 1996, Hu and White 1997, and references\ntherein). Measurements of the linear polarization can distinguish\nbetween tensor and scalar perturbations and can constrain the epoch of\nreionization of the intergalactic medium (Zaldarriaga, Spergel and\nSeljak 1997).\n\n\\noindent\n$\\bullet$ The main effect of reionization is to depress the amplitude\nof the power spectrum at high multipoles by a factor of ${\\rm\nexp}(-2\\tau_{opt})$ where $\\tau_{opt}$ is the optical depth to Thomson\nscattering. In the `best fit' CDM universe described in the next\nsection ($\\omega_b = 0.019$, $h = 0.65$, $\\Omega_m = \\Omega_c +\n\\Omega_b \\approx 0.3$ and $\\Omega_\\Lambda \\approx 0.7$) and a\nreionization redshift of $z_{reion} \\approx 20$ (a plausible value)\n$\\tau_{opt} \\approx 0.2$ which is significant. There is a reasonable chance\nthat we might learn something about the `dark ages' of cosmic history from\nprecision measurements of the CMB.\n\n\n\\begin{figure}\n\\vspace{5.0cm} \n\\special{psfile=pgconf4.ps hscale=63 vscale=63 angle=-90 hoffset= -30\n\nvoffset=316}\n\\caption{Marginalized likelihoods ($1$, $2$ and $3\\sigma$ contours) in\nthe $Q_{10}$--$\\gamma_D$ and $n_s$--$\\gamma_D$ planes, where\n$\\gamma_D$ is the acoustic peak location parameter defined in\nequation 18.}\n\n\\end{figure}\n\n\\begin{figure}\n\\vspace{5.0cm} \n\\special{psfile=pgconf3.ps hscale=63 vscale=63 angle=-90 hoffset= -30\nvoffset=316}\n\\caption{Marginalized likelihoods ($1$, $2$ and $3\\sigma$ contours) in\nthe $Q_{10}$--$n_s$ and $\\omega_c$--$n_s$ planes. The crosses show where the\nlikelihood function peaks.}\n\\end{figure}\n\n\n\\section{Cosmological Parameters from the CMB}\n\n\nIn this section, we review some of the constraints on cosmological\nparameters from the CMB data plotted in figure 1. The analysis is\nsimilar to that presented in Efstathiou \\etal (1999, hereafter E99),\nin which we map the full likelihood function in $5$ parameters\n$\\Omega_\\Lambda$, $\\Omega_m$, $\\omega_c$, $n_s$ and $Q_{10}$ (the\namplitude of $\\sqrt{C_\\ell}$ at $\\ell = 10$ relative to that inferred\nfrom COBE). The baryon density is constrained to $\\omega_b = 0.019$,\nas determined from primordial nucleosynthesis and deuterium abundances\nmeasurements from quasar spectra (Burles and Tytler 1998). The results\npresented below are insensitive to modest variations ($\\sim 25 \\%$) of\n$\\omega_b$ and illustrate the main features of cosmological parameter\nestimation from the CMB. Recently, Tegmark and Zaldarriaga (2000) have\nperformed a heroic $10$ parameter fit to the CMB data, including a\ntensor contribution and finite optical depth from reionization. I will\ndiscuss the effects of widening the parameter space briefly below but\nrefer the reader to Tegmark and Zaldarriaga for a detailed analysis.\n\n\n\n\n\nThe best fit model in this five parameter space is plotted as the\nsolid line in figure 1. It is encouraging that the best fitting model\nhas perfectly reasonable parameters, a spatially flat universe with a\nnearly scale invariant fluctuation spectrum and a low CDM density\n$\\omega_c \\sim 0.1$. Marginalised likelihood functions are plotted\nin various projections in the parameter space in figures 2, 3 and 5\n(uniform priors are assumed in computing the marginalized likelihoods,\nas described in E99). Figure 2 shows constraints on the position of\nthe first acoustic peak measured by the `location' parameter\n\\begin{eqnarray}\n\\gamma_D = {\\ell_D (\\Omega_\\Lambda, \\Omega_m) \\over\n\\ell_D(\\Omega_\\Lambda = 0, \\Omega_m = 1)},\n\\end{eqnarray}\n{\\it i.e.} the parameter $\\gamma_D$ measures the location of the\nacoustic peak relative to that in a spatially flat model with zero\ncosmological constant. The geometrical degeneracy between $\\Omega_m$\nand $\\Omega_\\Lambda$ described in the previous section is expressed by\n$\\gamma_D = {\\rm constant}$. Figure 2 shows that the best fitting\nvalue is $\\gamma_D = 1$ with a $2\\sigma$ range of about $\\pm 0.3$. The\nposition of the first acoustic peak in the CMB data thus provides\npowerful evidence that the Universe is close to spatially flat.\n\n\\begin{figure}\n\\vspace{7cm} \n\\special{psfile=pgconf2.ps hscale=53 vscale=53 angle=-90 hoffset= 30\nvoffset=275}\n\\caption{The crosses show maximum likelihood bandpower averages of the\nobservations shown in figure 1 together with $1\\sigma$ errors. The solid line\nshows the best fit adiabatic CDM model as plotted in figure 1 which\nhas $\\omega_c = 0.1$. The dashed lines show the effects of varying\n$\\omega_c$ keeping the other parameters fixed. The upper dotted line\nshows $\\omega_c = 0.05$ and the lower dashed line shows $\\omega_c = 0.25$.}\n\\end{figure}\n\nFigure $3$ shows the marginalized likelihoods in the $Q_{10}- n_s$ and\n$\\omega_c - n_s$ planes. The constraints on $Q_{10}$ and $n_s$ are not\nvery different to those from the analysis of COBE alone (see {\\it\ne.g.} Bond 1996). The experiments at higher multipoles are so\ndegenerate with variations in other cosmological parameters that they\ndo not help tighten the constraints on $Q_{10}$ and $n_s$. The\nconstraints on $\\omega_c$ and $n_s$ show an interesting result; if\n$n_s \\approx 1$, then the best fit value of $\\omega_c$ is about $0.1$\nwith a $2\\sigma$ upper limit of about $0.3$. This constraint on\n$\\omega_c$ comes from the height of the first acoustic peak, as shown\nin figure 4. In this diagram, the CMB data points have been averaged\nin $10$ band-power estimates as described by Bond, Knox and Jaffe\n(1998). The solid curve shows the best-fit model as plotted in figure\n1, which has $\\omega_c = 0.1$. The dashed lines show models with\n$\\omega_c = 0.25$ and $\\omega_c = 0.05$ with the other parameters held\nfixed. Raising $\\omega_c$ lowers the height of the peak and\nvice-versa. This result is not very sensitive to variations of\n$\\omega_b$ in the neighbourhood of $\\omega_b \\sim 0.02$. Reionization\nand the addition of a tensor component can lower the height of\nthe first peak relative to the anisotropies at lower multipoles\nand so the upper limits on $\\omega_c$ are robust to the addition\nof these parameters. The CMB data have now reached the point where\nwe have good constraints on the height of the first peak, as well\nas its location, and this is beginning to set interesting constraints\non $\\omega_c$. The best fit value of $\\Omega_m \\approx 0.3$, derived\nfrom combining the CMB data with results from distant Type Ia\nsupernovae (see figure 5) implies $\\omega_c \\approx 0.11$ for a Hubble constant\nof $h = 0.65$, consistent with the low values of $\\omega_c$ favoured by the\nheight of the first acoustic peak. \n\nThe left hand panel of figure 5 shows the marginalized likelihood for\nthe CMB data in the $\\Omega_\\Lambda$--$\\Omega_m$ plane. The likelihood\npeaks along the line for spatially flat universes $\\Omega_k=0$ and it\nis interesting to compare with the equivalent figure in E99 to see how\nthe new experimental results of the last year have caused the likelihood\ncontours to narrow down around $\\Omega_k =0$. (See also Dodelson and\nKnox 1999 for a similar analysis using the latest CMB data). As is\nwell known, the magnitude-redshift relation for distant Type Ia\nsupernovae results in nearly orthogonal constraints in the\n$\\Omega_\\Lambda$--$\\Omega_m$ plane, so combining the supernovae and\nCMB data can break the geometrical degeneracy. The right hand panel in\nFigure 5 combines the CMB likelihood function derived here with the\nlikelihood function of the supernovae sample of Perlmutter \\etal\n(1999) as analysed in E99. The combined likelihood function is peaked\nat $\\Omega_m \\approx 0.3$ and $\\Omega_\\Lambda \\approx 0.7$. \n\n\\begin{figure}\n\\vspace{6.5cm} \n\n\\special{psfile=pgconf5.ps hscale=40 vscale=40 angle=-90 hoffset= -60\nvoffset=220}\n\n\\special{psfile=pgconf6.ps hscale=40 vscale=40 angle=-90 hoffset= 125\nvoffset=220}\n\n\\caption{The figure to the left shows the $1$, $2$ and $3\\sigma$\nlikelihood contours marginalized in the $\\Omega_\\Lambda$ and\n$\\Omega_m$ plane from the observations plotted in figure 1. The figure\nto the right shows the CMB likelihood combined with the likelihood\nfunction for Type Ia supernovae of Permutter {\\it et al.} (1999) as\nanalyzed by E99. The dotted contours in both figures extend the\nCMBFAST (Seljak and Zaldarriaga 1996)\ncomputations into the closed universe domain using the\napproximate method described in E99.}\n\\end{figure}\n\n\nIt is remarkable how the CMB data and the supernovae data are homing\nin on a consistent set of cosmological parameters that are compatible\nwith the simplest inflationary models and also with parameters inferred\nfrom a number of other observations ({\\it e.g.} galaxy clustering, \nbaryon content of clusters and dynamical estimates of the mean mass density,\nsee Bahcall \\etal 1999 for a review). It is also remarkable\nthat the `best fit' model requires a non-zero cosmological constant, a result that\nfew cosmologists would have thought likely a few years ago.\n\nThe next few years will see a revolutionary increase in the volume and\nquality of CMB data. The results of the Boomerang Antarctic flight are\nawaited with great interest and should be of sufficient quality to\nrender all previous analyses of cosmological parameters from the CMB\nobsolete. The polarization of the CMB has not yet been discovered, but\na number of ground based and balloon borne experiments designed to\ndetect polarization are under construction (Staggs, Gundersen and\nChurch 1999). The MAP satellite, scheduled for launch in late 2000, will\nhave polarization sensitivity and should determine the power spectrum\n$C_\\ell$ accurately to about $\\ell \\sim 800$, defining the first three\nacoustic peaks. Further into the future, the Planck satellite,\nscheduled for launch in 2007, should determine the power spectrum to\n$\\ell \\simgt 2500$, provide sensitive polarization measurements and\nextremely accurate subtraction of foregrounds. Evidently, the era of\nprecision cosmology is upon us and the next decade should see a\ndramatic improvement in our knowledge of fundamental cosmological\nparameters and in our understanding of the origin of fluctuations in\nthe early Universe.\n\n\n\n\n\n\\begin{thebibliography}{}\n\\bibitem[\\protect\\citeauthoryear{Bahcall}{1999}]{Bahcall99} Bahcall\nN., Ostriker J.P., Perlmutter S., Steinhardt P.J., (1999) The cosmic\ntriangle: revealing the state of the Universe, {\\it Science}, {\\bf\n284}, 1481-1488.\n\\bibitem[\\protect\\citeauthoryear{Bond1}{1996}]{Bond96} Bond J.R.,\n(1996) Theory and Observations of the Cosmic Microwave Background Radiation,\nin Cosmology and large scale structure, eds Schaeffer R., Silk\nJ., Spiro M., Zinn-Justin J., Elsevier Science, Amsterdam, 469-666.\n\\bibitem[\\protect\\citeauthoryear{Bond2}{1998}]{Bond98} Bond J.R.,\nJaffe A.H., Knox L., \n(1998) Estimating the power spectrum of the cosmic\nmicrowave background, {\\it Phys. Rev. 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(1998) The deuterium abundance towards QSO 1009+2956,\n{\\it ApJ}, {\\bf 507}, 732-744.\n\\bibitem[\\protect\\citeauthoryear{Coble}{1999}]{Coble99} Coble K.,\n\\etal (1999) Anisotropy in the cosmic microwave background at degree\nangular scales, {\\it ApJ}, {\\bf 519}, L5-L8.\n\\bibitem[\\protect\\citeauthoryear{Dodelson}{1999}]{Dodelson99} Dodelson\nS., Knox S., (1999) Dark energy and the CMB. astro-ph/9909454.\n\\bibitem[\\protect\\citeauthoryear{Efstathiou}{1999}]{Efstathiou99} \nEfstathiou G., Bond J.R.,\n(1999) Cosmic confusion: degeneracies among cosmological\nparameters derived from measurements of microwave background\nanisotropies, {\\it MNRAS}, {\\bf 304}, 75-97.\n\\bibitem[\\protect\\citeauthoryear{Efstathiou}{1999}]{E99} Efstathiou G.,\nBridle S.L., Lasenby A.N., Hobson M.P., Ellis R.S., (1999) Constraints\non $\\Omega_\\Lambda$ and $\\Omega_m$ from distant Type Ia supernovae and\ncosmic microwave background anisotropies, {\\it MNRAS}, {\\bf 303},\nL47-52.\n\\bibitem[\\protect\\citeauthoryear{Hu}{1995}]{Hu95} Hu W.,\nSugiyama N., (1995) Towards understanding CMB anisotropies and\ntheir implications, {\\it Phys. Rev. D}, {\\bf 51}, 2599-2630.\n\\bibitem[\\protect\\citeauthoryear{Kamionkowski}{1999}]{Kamionkowski99}\nKamionkowski M, Kosowsky A., (1999) The cosmic microwave background\nand particle physics, {\\it Ann. Rev. Nucl. Part. Sci.}, in press.\nastro-ph/9904108.\n\\bibitem[\\protect\\citeauthoryear{Hu}{1997}]{Hu} Hu W., White M.,\n(1997) A CMB polarization primer,\n{\\it New Astronomy}, {\\bf 2}, 323-344.\n\\bibitem[\\protect\\citeauthoryear{Mauskopf}{1999}]{Mauskopf99} Mauskopf\nP.D., \\etal (1999) Measurement of a peak in the cosmic microwave\nbackground power spectrum from the North American test flight of\nBoomerang, {\\it ApJ}, submitted. astro-ph/9911444.\n\\bibitem[\\protect\\citeauthoryear{Perlmutter}{1999}]{Perlmutter99} \nPerlmutter S. \\etal (1999) Measurement of omega and lambda from 42\nhigh-redshift supernovae, {\\it ApJ}, {\\bf 517}, 565-586.\n\\bibitem[\\protect\\citeauthoryear{Peterson}{1999}]{Peterson99} \nPeterson J.B. \\etal (1999) First results from VIPER:\ndetection of small-scale anisotropy at 40 GHz.\n{\\it ApJ}, in press. astro-ph/9910503.\n\\bibitem[\\protect\\citeauthoryear{Rocha}{1999}]{Rocha99} Rocha G.,\n(1999) Constraints on the cosmological parameters using CMB\nobservations, to appear in the proceedings of the `Early\nUniverse and Dark Matter Conference', DARK98,\nHeidelberg. astro-ph/9907312.\n\\bibitem[\\protect\\citeauthoryear{Sachs}{1967}]{Sachs67} Sachs R.K.,\nWolfe A.M., \n(1967) Perturbations of a cosmological model and angular variations\nof the microwave background, {\\it ApJ}, {\\bf 147}, 73-90.\n\\bibitem[\\protect\\citeauthoryear{Seljak}{1996}]{Seljak96} Seljak U.,\nZaldarriaga M., (1996) A line-of-sight integration approach\nto cosmic microwave background anisotropies, {\\it ApJ}, {\\bf 469}, 437-444.\n\\bibitem[\\protect\\citeauthoryear{Smoot}{1992}]{Smoot92} Smoot G.F.,\n(1992) Structure in the COBE differential microwave radiometer\nfirst-year maps, {\\it ApJ}, {\\bf 396}, L1-L5.\n\\bibitem[\\protect\\citeauthoryear{Staggs}{1999}]{Staggs99} Staggs S.T.,\nGundersen J.O., Church S.E.,\n(1999) CMB polarization experiments. astro-ph/9904062.\n\\bibitem[\\protect\\citeauthoryear{Tegmark}{2000}]{Tegmark00} Tegmark\nM., Zaldarriaga M., (2000) Current cosmological constraints from a\n10 parameter CMB analysis\n{\\it ApJ}, submitted. astro-ph/0002091.\n\\bibitem[\\protect\\citeauthoryear{Zaldarriaga}{1997}]{Zaldarriaga97} \nZaldarriaga M., Spergel D.N., Seljak U., \n(1997) Microwave background constraints on cosmological\nparameters, {\\it ApJ}, {\\bf 488}, 1-13.\n\\end{thebibliography}\n\n\\end{document}\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002249.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[\\protect\\citeauthoryear{Bahcall}{1999}]{Bahcall99} Bahcall\nN., Ostriker J.P., Perlmutter S., Steinhardt P.J., (1999) The cosmic\ntriangle: revealing the state of the Universe, {\\it Science}, {\\bf\n284}, 1481-1488.\n\\bibitem[\\protect\\citeauthoryear{Bond1}{1996}]{Bond96} Bond J.R.,\n(1996) Theory and Observations of the Cosmic Microwave Background Radiation,\nin Cosmology and large scale structure, eds Schaeffer R., Silk\nJ., Spiro M., Zinn-Justin J., Elsevier Science, Amsterdam, 469-666.\n\\bibitem[\\protect\\citeauthoryear{Bond2}{1998}]{Bond98} Bond J.R.,\nJaffe A.H., Knox L., \n(1998) Estimating the power spectrum of the cosmic\nmicrowave background, {\\it Phys. Rev. D},{\\bf 57}, 2117-2137.\n\\bibitem[\\protect\\citeauthoryear{Burles}{1998}]{Burles98} Burles S.,\nTytler D. (1998) The deuterium abundance towards QSO 1009+2956,\n{\\it ApJ}, {\\bf 507}, 732-744.\n\\bibitem[\\protect\\citeauthoryear{Coble}{1999}]{Coble99} Coble K.,\n\\etal (1999) Anisotropy in the cosmic microwave background at degree\nangular scales, {\\it ApJ}, {\\bf 519}, L5-L8.\n\\bibitem[\\protect\\citeauthoryear{Dodelson}{1999}]{Dodelson99} Dodelson\nS., Knox S., (1999) Dark energy and the CMB. astro-ph/9909454.\n\\bibitem[\\protect\\citeauthoryear{Efstathiou}{1999}]{Efstathiou99} \nEfstathiou G., Bond J.R.,\n(1999) Cosmic confusion: degeneracies among cosmological\nparameters derived from measurements of microwave background\nanisotropies, {\\it MNRAS}, {\\bf 304}, 75-97.\n\\bibitem[\\protect\\citeauthoryear{Efstathiou}{1999}]{E99} Efstathiou G.,\nBridle S.L., Lasenby A.N., Hobson M.P., Ellis R.S., (1999) Constraints\non $\\Omega_\\Lambda$ and $\\Omega_m$ from distant Type Ia supernovae and\ncosmic microwave background anisotropies, {\\it MNRAS}, {\\bf 303},\nL47-52.\n\\bibitem[\\protect\\citeauthoryear{Hu}{1995}]{Hu95} Hu W.,\nSugiyama N., (1995) Towards understanding CMB anisotropies and\ntheir implications, {\\it Phys. Rev. D}, {\\bf 51}, 2599-2630.\n\\bibitem[\\protect\\citeauthoryear{Kamionkowski}{1999}]{Kamionkowski99}\nKamionkowski M, Kosowsky A., (1999) The cosmic microwave background\nand particle physics, {\\it Ann. Rev. Nucl. Part. Sci.}, in press.\nastro-ph/9904108.\n\\bibitem[\\protect\\citeauthoryear{Hu}{1997}]{Hu} Hu W., White M.,\n(1997) A CMB polarization primer,\n{\\it New Astronomy}, {\\bf 2}, 323-344.\n\\bibitem[\\protect\\citeauthoryear{Mauskopf}{1999}]{Mauskopf99} Mauskopf\nP.D., \\etal (1999) Measurement of a peak in the cosmic microwave\nbackground power spectrum from the North American test flight of\nBoomerang, {\\it ApJ}, submitted. astro-ph/9911444.\n\\bibitem[\\protect\\citeauthoryear{Perlmutter}{1999}]{Perlmutter99} \nPerlmutter S. \\etal (1999) Measurement of omega and lambda from 42\nhigh-redshift supernovae, {\\it ApJ}, {\\bf 517}, 565-586.\n\\bibitem[\\protect\\citeauthoryear{Peterson}{1999}]{Peterson99} \nPeterson J.B. \\etal (1999) First results from VIPER:\ndetection of small-scale anisotropy at 40 GHz.\n{\\it ApJ}, in press. astro-ph/9910503.\n\\bibitem[\\protect\\citeauthoryear{Rocha}{1999}]{Rocha99} Rocha G.,\n(1999) Constraints on the cosmological parameters using CMB\nobservations, to appear in the proceedings of the `Early\nUniverse and Dark Matter Conference', DARK98,\nHeidelberg. astro-ph/9907312.\n\\bibitem[\\protect\\citeauthoryear{Sachs}{1967}]{Sachs67} Sachs R.K.,\nWolfe A.M., \n(1967) Perturbations of a cosmological model and angular variations\nof the microwave background, {\\it ApJ}, {\\bf 147}, 73-90.\n\\bibitem[\\protect\\citeauthoryear{Seljak}{1996}]{Seljak96} Seljak U.,\nZaldarriaga M., (1996) A line-of-sight integration approach\nto cosmic microwave background anisotropies, {\\it ApJ}, {\\bf 469}, 437-444.\n\\bibitem[\\protect\\citeauthoryear{Smoot}{1992}]{Smoot92} Smoot G.F.,\n(1992) Structure in the COBE differential microwave radiometer\nfirst-year maps, {\\it ApJ}, {\\bf 396}, L1-L5.\n\\bibitem[\\protect\\citeauthoryear{Staggs}{1999}]{Staggs99} Staggs S.T.,\nGundersen J.O., Church S.E.,\n(1999) CMB polarization experiments. astro-ph/9904062.\n\\bibitem[\\protect\\citeauthoryear{Tegmark}{2000}]{Tegmark00} Tegmark\nM., Zaldarriaga M., (2000) Current cosmological constraints from a\n10 parameter CMB analysis\n{\\it ApJ}, submitted. astro-ph/0002091.\n\\bibitem[\\protect\\citeauthoryear{Zaldarriaga}{1997}]{Zaldarriaga97} \nZaldarriaga M., Spergel D.N., Seljak U., \n(1997) Microwave background constraints on cosmological\nparameters, {\\it ApJ}, {\\bf 488}, 1-13.\n\\end{thebibliography}"
}
] |
|
astro-ph0002250
|
Modelling galaxy clustering at high redshift
|
[
{
"author": "Eelco van Kampen"
}
] |
Most phenomenological galaxy formation models show a discrepancy between the predicted Tully-Fisher relation and the luminosity function. We show that this is mainly due to overmerging of galaxy haloes, which is inherent in both the Press-Schechter formalism and dissipationless N-body simulations. This overmerging problem be circumvented by including a specific galaxy halo formation recipe into an otherwise standard N-body code. Resolving the overmerging also allows us to include models for chemical evolution and starbursts, which improves the match to observational data {and} renders the modelling more realistic. We use high-redshift clustering data to try and distinguish models which predict similar results at low redshifts for different sets of parameters.
|
[
{
"name": "eelco.tex",
"string": "% Contribution to the proceedings of the meeting in Marseille\n% on 'CLustering at high redshift'\n%\n% Contribution by Eelco van Kampen, evk@roe.ac.uk\n\n\\documentstyle[11pt,newpasp,twoside]{article}\n\n\\begin{document}\n\n\\title{Modelling galaxy clustering at high redshift}\n\\author{Eelco van Kampen}\n\\affil{Institute for Astronomy, University of Edinburgh, Royal Observatory,\nBlackford Hill, Edinburgh EH9 3HJ, United Kingdom}\n\n\\begin{abstract}\nMost phenomenological galaxy formation models show a discrepancy\nbetween the predicted Tully-Fisher relation and the luminosity\nfunction. We show that this is mainly due to overmerging of galaxy haloes,\nwhich is inherent in both the Press-Schechter formalism and dissipationless\nN-body simulations. This overmerging problem be circumvented\nby including a specific galaxy halo formation recipe into an\notherwise standard N-body code. Resolving the overmerging\nalso allows us to include models for chemical evolution and\nstarbursts, which improves the match to observational data {\\it and}\nrenders the modelling more realistic.\nWe use high-redshift clustering data to try and distinguish models\nwhich predict similar results at low redshifts for different sets\nof parameters. \n\\end{abstract}\n\n\\keywords{cosmology: theory - dark matter - large-scale structure of Universe\n- galaxy formation}\n\n\\section{Introduction}\n\nThere has been significant recent progress in the study of galaxy\nformation within a cosmological context, mainly due to a phenomenological\napproach to this problem. The idea is to start with\na structure formation model that describes where and when galactic\ndark haloes form. A simple description of gas dynamics and star formation\nprovides a means to calculate the amount of stars forming in these haloes.\nStellar population synthesis models then provide the spectral evolution,\ni.e.\\ luminosities and colours, of these galaxies.\n\nMany physical processes are modelled as simple functions of the circular\nvelocity of the galaxy halo. Therefore, the Tully-Fisher relation is\nthe most obvious observational relation to try and predict, as it\nrelates the total luminosity of a galaxy to its halo circular\nvelocity. However, most phenomenological galaxy formation models do\nnot simultaneously fit the I-band Tully-Fisher relation and the\nB or K band luminosity function. When one sets the model parameters\nsuch that the Tully-Fisher relation has the right normalization, the\nluminosity functions generally overshoot (e.g.\\ Kauffmann, White \\&\nGuiderdoni 1993; Kauffmann, Colberg, Diaferio \\& White 1999), certainly\nfor the $\\Omega=1$, $H_0=50$ km s$^{-1}$ Mpc$^{-1}$\nstandard CDM cosmology (in the form given by Davis et al.\\ 1985) that\nwe consider in this paper. Alternatively, when making sure that the\nluminosity functions matches by changing some of the model parameters,\nthe Tully-Fisher relation ends up significantly shifted with respect to\nthe observed relation (e.g.\\ Cole et al.\\ 1994; Heyl et al.\\ 1995).\n\nIn order to keep the modelling as analytical as possible, an extension\nto the Press \\& Schechter (1974) prescription for the evolution of galaxy\nhaloes (e.g.\\ Bond et al. 1991; Bower 1991; Lacey \\& Cole 1993; Kauffmann\n\\& White 1993) has been a popular ingredient for implementations of a\nphenomenological theory of galaxy formation. \nHowever, the EPS formalism is designed to identify collapsed\nsystems, irrespective of whether these contain surviving subsystems.\nThis `overmerging' of subhaloes into larger embedding haloes is\nrelevant to the problem of matching both the galaxy luminosity\nfunction and the Tully-Fisher relation, as the central galaxy in an\novermerged halo is the focus of a much larger cooling gas reservoir\nthan the reservoir that galaxy is to focus of in case its parent\nsubhalo survives.\nTraditional N-body simulations suffer from a similar overmerging\nproblem (e.g.\\ White 1976), which is of a purely numerical nature,\ncaused by two-body heating in dense environments when the mass\nresolution is too low (Carlberg 1994; van Kampen 1995).\n\nIn order to circumvent these problems,\nwe use an N-body simulation technique that includes a built-in\nrecipe for galaxy halo formation, designed to prevent overmerging\n(van Kampen 1995, 1997), to generate the halo population and its\nformation and merger history. This resolves most of the discrepancy\nsketched above, {\\it and}\\ allows us to make the modelling more\nrealistic by adding chemical evolution and a merger-driven bursting\nmode of star formation to the modelling.\nOnce stars are formed, we apply the stellar population synthesis models\nof Jimenez et al.\\ (1998) to follow their evolution. We have enhanced\nthese models with a model for the evolution of the average metallicity\nof the population, which depends on the starting metallicity.\nFeedback to the surrounding material means that cooling properties of\nthat material will change with time, affecting the star formation rate,\nand thus various other properties of the parent galaxy.\n\n\\section{Overview of the phenomenological model}\n\nThe key ingredients of the model are described below. We refer\nto van Kampen et al.\\ (1999) for a much more detailed description\nand discussion of the model, and a list of the choices for the various\nparameters involved.\n\n\\subsubsection\n{\\it The merging history of dark-matter haloes.}\nThis is often treated by Monte-Carlo realizations of the\nanalytic `extended Press-Schechter' formalism, which ignores\nsubstructure. We use a special N-body technique \nto prevent galaxy-scale haloes undergoing `overmerging'\nowing to inadequate numerical resolution.\n\n\\subsubsection\n{\\it The merging of galaxies within dark-matter haloes.}\nEach halo contains a single galaxy at formation. When haloes \nmerge, a criterion based on dynamical friction is used to decide how\nmany galaxies exist in the newly merged halo. The most massive\nof those galaxies becomes the single central galaxy to which\ngas can cool, while the others become its satellites. \n\n\\subsubsection\n{\\it The history of gas within dark-matter haloes.}\nWhen a halo first forms, it is assumed to have\nan isothermal-sphere density profile. A fraction\n$\\Omega_b/\\Omega$ of this is in the form of gas\nat the virial temperature, which can cool to form\nstars within a single galaxy at the centre of the halo.\nApplication of the standard radiative cooling\ncurve shows the rate at which this hot gas cools\nbelow $10^4$~K, and is able to form stars.\nEnergy output from supernovae reheats some of the\ncooled gas back to the hot phase. When haloes\nmerge, all hot gas is stripped and ends up in the new halo.\n\n\\subsubsection\n{\\it Quiescent star formation.}\nThe star formation rate is equal the ratio of the amount of\ncold gas available and the star-formation timescale.\nThe amount of cold gas available depends on the merger\nhistory of the halo, the star formation history, and\nthe how much cold gas has been reheated by feedback\nprocesses.\n\n\\subsubsection\n{\\it Starbursts.}\nWe also model star bursts, i.e.\\ the star-formation rate may\nsuffer a sharp spike following a major merger event. \n\n\\subsubsection\n{\\it Feedback from star-formation.}\nThe energy released from young stars heats cold\ngas in proportion to the amount of star-formation,\nreturning it to the reservoir of hot gas.\n\n\\subsubsection\n{\\it Stellar evolution and populations.}\nOur work assumes the spectral models of Jimenez et al.\\ (1998);\nfor solar metallicity, the results are not greatly\ndifferent from those of other workers.\nThe IMF is generally taken to be Salpeter, but any choice is possible.\nUnlike other workers, we take it as established that the\npopulation of brown dwarfs makes a negligible contribution\nto the total stellar mass density, and we do not\nallow an adjustable $M/L$ ratio, $\\Upsilon$, for the stellar\npopulation.\n\n\\subsubsection\n{\\it Chemical evolution.}\nThe evolution of the metals must be followed, for two reasons:\n(i) the cooling of the hot gas depends on metal content;\n(ii) for a given age, a stellar population of high metallicity will\nbe much redder. The models of Jimenez et al.\\ (1998) allow\nsynthetic stellar populations of any metallicity to be\nconstructed. \n\n\\section{Low-redshift results}\n\nWith the set-up described above we match both the B and K band\nluminosity function and the I-band Tully-Fisher relation, for an\n$\\Omega=1$ standard CDM structure formation scenario. Resolving the\novermerging problem is the major contributor to this result,\nbut the inclusion of chemical evolution and starbursts are also\nimportant ingredients.\n\nThe new ingredients we have added to the modelling of galaxy formation\nare needed in order to make the models more realistic, and are not\nintroduced simply in order to give yet more free parameters. Nevertheless,\nour resolution to the Tully-Fisher / luminosity function discrepancy\nmay well not be unique, and various other changes to the ingredients of the\nphenomenological galaxy formation recipe might produce similar\nresults. For example, we have not studied the influence cosmological\nparameters have on the model galaxy populations, where $\\Omega$,\n$\\Lambda$, and $\\sigma_8$ are likely to be the important parameters.\nOther types of ingredients are possible as well:\nSomerville \\& Primack (1998) resolve some of the discrepancy using\na dust extinction model plus a halo-disk approach to feedback.\n\n\\section{High-redshift clustering}\n\nOne way of resolving the worries about degeneracies in the\ncosmological/physical parameter space will be to include data at\nintermediate and high redshifts, which is being gathered with\nincreasing speed and ease, and at increasingly higher redshifts.\nIn this contribution we show a preliminary comparison of the\ncorrelation properties of galaxies at redshift $z=3$. Recently,\nGiavalisco et al.\\ (1998) gave an estimate for the galaxy-galaxy\ncorrelation function $\\xi(r)=(r_0/r)^\\gamma$ for a sample of\nLyman-break galaxies at this redshift. They found $r_0=2.1 h^{-1}$Mpc\nand $\\gamma=2.0$. \n\nWe selected our model galaxies in exactly the same way as Giavalisco\net al.\\ (1998) did, and compared two of the models produced by van Kampen\net al.\\ (1999), models $n$ and $b$, to the observational data.\nThe first model ($n$), which is as close as possible to the model\nby Cole et al.\\ (1994), but with the mass-to-light parameter $\\Upsilon=1$,\ngives $r_0=3.5 h^{-1}$Mpc and $\\gamma=1.72$. \nThe second model ($b$), which includes starbursts and chemical evolution,\ngives $r_0=4.4 h^{-1}$Mpc and $\\gamma=2.1$. Both models fit the\ncorrelation function at $z=0$ very well, and cannot be distinguished\nfrom each other.\n\nAs the observed correlation data are still relatively uncertain at this\nmoment in time, it is premature to rule out models on the basis of this\ndata. The two models discussed above have similar predictions\nfor low redshifts, but predict different clustering properties at\nhigh-redshift. However, the differences are not large, so one needs\neither really good data, or a much larger variety of observational\ncharacteristics of the high-redshift galaxy population.\n\n\\acknowledgments\nMany thanks for the loud vocal support from outside the conference\nbuilding during my presentation. I like to think that the people of Marseille\njust wanted to show how much they supported everything I said ...\n\n\\begin{references} \n\\reference Bond J.R., Cole S., Efstathiou G., Kaiser N., 1991, ApJ, 379, 440\n\\reference Bower R.J., 1991, MNRAS, 248, 332\n\\reference Carlberg R.G., 1994, ApJ, 433, 468\n\\reference Cole S., Arag\\'on-Salamanca A., Frenk C.S., Navarro J.F., Zepf S.E.,\n1994, MNRAS, 271, 781\n\\reference Davis M., Efstathiou G., Frenk C.S., White S.D.M., 1985, ApJ, 292, 371\n\\reference Heyl J.S., Cole S., Frenk C.S., Navarro J.F., 1995, MNRAS, 274, 755\n\\reference Giavalisco, M., Steidel C.C., Adelberger, K.L., Dickinson, M.E.,\nPettini, M., Kellogg, M., 1998, ApJ, 503, 543 \n\\reference Jimenez R., Padoan P., Matteucci F., Heavens A., 1998, MNRAS, 299, 123\n\\reference Kauffman G., White S.D.M., 1993, MNRAS, 261, 921\n\\reference Kauffmann G., Colberg J.M., Diaferio A., White S.D.M., 1999,\nMNRAS, 303, 188\n\\reference Kauffmann G., White S.D.M., Guiderdoni, 1993, MNRAS, 264, 201\n\\reference Lacey C.G., Cole S., 1993, MNRAS, 262, 627\n\\reference Press W.H., Schechter P., 1974, ApJ, 187, 425\n\\reference Somerville R.S., Primack J.R., 1998, astro-ph/9802268\n\\reference van Kampen E., 1995, MNRAS, 273, 295\n\\reference van Kampen E., 1997, in Clarke D.A., West M.J., eds., Proc. 12th\n`Kingston meeting' on Theoretical Astrophysics: Computational Astrophysics,\nASP Conf. Ser. Vol. 123. Astron. Soc. Pac., San Francisco, p. 231,\nastro-ph/9904270\n\\reference van Kampen E., Jimenez R., Peacock J.A, 1999, MNRAS, in press,\nastro-ph/9904274\n\\reference White S.D.M., 1976, MNRAS, 177, 717\n \n\\end{references}\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002251
|
Ionizing radiation in Smoothed Particle Hydrodynamics
|
[
{
"author": "O.~Kessel-Deynet"
},
{
"author": "A.~Burkert"
},
{
"author": "Max-Planck-Institut f\\\"ur Astronomie"
},
{
"author": "K\\\"onigstuhl 17"
},
{
"author": "D-69117 Heidelberg"
},
{
"author": "Germany"
}
] |
A new method for the inclusion of ionizing radiation from uniform radiation fields into 3D Smoothed Particle Hydrodynamics ({\sc sphi}) simulations is presented. We calculate the optical depth for the Lyman continuum radiation from the source towards the {\sc sphi} particles by ray-tracing integration. The time-dependent ionization rate equation is then solved locally for the particles within the ionizing radiation field. Using test calculations, we explore the numerical behaviour of the code with respect to the implementation of the time-dependent ionization rate equation. We also test the coupling of the heating caused by the ionization to the hydrodynamical part of the {\sc sphi} code.
|
[
{
"name": "mz242.tex",
"string": "\n%% Version 0.9 (7.1.99)\n%% Version 1.0 (25.11.99)\n\n\\documentstyle[epsfig]{mn}\n\n\\title[Ionizing radiation in {\\sc sph}]{Ionizing radiation in Smoothed\nParticle Hydrodynamics}\n\n\\author[O.~Kessel-Deynet, A.~Burkert]{O.~Kessel-Deynet, A.~Burkert\\\\\n\tMax-Planck-Institut f\\\"ur Astronomie, K\\\"onigstuhl 17, D-69117\n\tHeidelberg, Germany}\n\n\\begin{document}\n\n\\maketitle\n\\begin{abstract}\nA new method for the inclusion of ionizing radiation\nfrom uniform radiation fields into 3D Smoothed Particle Hydrodynamics\n({\\sc sphi})\nsimulations is presented. We calculate the optical depth for the Lyman continuum\nradiation from the source towards the {\\sc sphi} particles by ray-tracing\nintegration. The time-dependent ionization rate equation is then solved locally for the\nparticles within the ionizing radiation field. Using test calculations, we explore\nthe numerical behaviour of the code with respect to the implementation\nof the time-dependent ionization rate equation. We also test the\ncoupling of the heating caused by the ionization to the hydrodynamical\npart of the {\\sc sphi} code. \n\\end{abstract}\n\\begin{keywords}\nMethods: numerical -- hydrodynamics -- radiative transfer -- H{\\sc ii}\nregions\n\\end{keywords}\n\n\\section{Introduction}\n\nSmoothed Particle Hydrodynamics ({\\sc sph}) has become a numerical method\nwidely used for addressing problems related to fluid flows in\nastrophysics. Due to its Lagrangian nature it is especially well suited\nfor applications involving variations by many orders of magnitude in density. Examples for this type of applications are simulations of the collapse\nof molecular clouds and the formation of a stellar cluster, as\nperformed by Klessen, Burkert \\& Bate~\\shortcite{klebuba}. A comparison between grid based methods\nand {\\sc sph} was performed by Burkert, Bate \\& Bodenheimer~\\shortcite{bbb} and Bate \\&\nBurkert~\\shortcite{bateburk}. They applied both\nmethods to the numerically demanding problem of gravitational collapse and\nfragmentation of a slightly perturbed rotating cloud core with an\n$r^{-2}$ density profile. Both methods yielded the same qualitative\nresults.\n%% Other comparisons between different numerical methods,\n%%a tree sph code~\\cite{HernKatz}, a P$^3$M sph scheme~\\cite{Evrard} and\n%%several Eulerian schemes~\\cite{Ryu,Brian,Cen}, was carried out by Kang et\n%%al.~\\shortcite{Kang}. They found satisfactory convergence of all\n%%methods to the same results with increasing resolution. \nBate~\\shortcite{bate2} performed the first\ncalculation which followed the collapse of a molecular cloud core in\n3 dimensions down to a protostellar object in hydrodynamical equilibrium, thus spanning\n17 (!) orders of magnitude in density. Other applications include\naccretion processes in massive circumbinary disks \\cite{boba1,babo1},\nthe collapse of cloud cores induced by shock waves \\cite{vanhala} or\ncolliding clumps \\cite{bhattal}, the precession of accretion disks in binary systems\n\\cite{larwood}, the dynamical behaviour of massive protostellar disks\n\\cite{nelson} or the formation of large scale structure and galaxies in\nthe early universe \\cite{steinmetz}.\n \nA variety of physical processes are at work in the interstellar medium, like magnetic\nfields, radiation or thermal conductivity, necessitating their\ninclusion into numerical codes. This has already\nbeen achieved to a large extent in grid based methods like the magneto-hydrodynamics\ncodes {\\sc zeus} \\cite{stono} or {\\sc nirvana} \\cite{ziegler},\nor codes including effects of IR and UV radiation \\cite{yorka,sonnha,richling}.\n\nIn contrast, the addition of physical processes to {\\sc sph} codes is just\nat its beginnings. Extensions\nachieved so far are sophisticated equations of state (e.g. Vanhala\net al.~1998) and self-gravity. Some efforts were made to make {\\sc sph} faster and\nmore accurate. The introduction of {\\sc tree} algorithms \\cite{barnes,press,benz} and the use of GRAvity PipE\n({\\sc grape}), a hardware device for fast computation of the gravitational N-body\nforces \\cite{umemura,steinmetz}, helped reducing the\nnumerical effort for the gravitational force calculation and the\ndetermination of the nearest neighbours for each\nparticle. Inutsuka~\\shortcite{inutsuka} presented a Godunov-like solver for\nthe Eulerian equations in {\\sc sph} thus enhancing the numerical treatment of\nshocks. The introduction of gravitational periodic boundaries~\\cite{hernqu,klessen} allows the treatment of fragmentation and\nturbulence in molecular clouds without global collapse. The timestep\nproblem which arises during isothermal collapse calculations at high\ndensities is circumvented by the formation of sink particles, which\nsubstitute the innermost parts of the collapsing clump by one particle\nand accumulate the infalling mass and momenta \\cite{babopri}.\n\nThe strength of {\\sc sph} lies in its Lagrangian\nnature, which makes it especially attractive for problems involving\ngravitational collapse and star formation. Applications like e.g. by Klessen\net al.~\\shortcite{klessen}, which deal with the collapse\nand fragmentation of molecular clouds, neglect the feedback processes\nof newly born stars which act on their parental cloud through stellar\nwinds, outflows and ionization. This simplification may be justified\nas long as the simulations deal with collapse on timescales smaller\nthan $\\approx$ 1 Myr, on which single and binary stars or T Tau-like\nclusters are formed~\\cite{efremov}. The case is different for larger\ntimescales, on which OB subgroups and associations are\nformed. Neglecting feedback in these cases can lead to\nunphysical results, like a star formation efficiency of 100 per cent,\nsince in the purely isothermal case all material will sooner or later\nbe accreted onto the evolving protostellar cores. This is in strong\ncontradiction to observations, which estimate a global star formation\nefficiency for ordinary molecular clouds of order 10 per cent\n\\cite{pppII}. Another possible effect of feedback is the induction of\nstar formation due to the compression of cloud material by shock waves\nand ionization fronts. \n\nIn this paper we discuss the implementation of the effects of\nionizing UV radiation by massive stars into {\\sc sph} calculations as a first\nstep in order to perform collapse calculations on scales where\nOB-stars are formed in a more realistic\nway. This will in future applications allow us to assess questions\nlike: How does the process of ionization by massive stars change the\nstellar initial mass function? What are the implications for the star formation\nefficiency? Can star formation be induced by\nionization, and if yes, what are the time scales and the parameter\nspace, for which induced star formation can be expected? These\nquestions will be discussed in subsequent papers.\n\n%%Some of the questions above were already adressed in the\n%%past. Bertoldi~\\shortcite{bertoldi2} and Bertoldi \\&\n%%McKee~\\shortcite{bertoldi1} developed an analytic theory for \n \n\n\\section{Physical problem}\n\nWe incorporate the effects of ionizing radiation from hot stellar\nphotospheres into {\\sc sph} by dividing the problem into three major substeps:\n\\begin{enumerate}\n\\item calculation of the UV radiation field by solving the time-independent, non-relativistic equation of radiative transfer,\n\\item determination of the ionization and recombination rates from the\nlocal radiation field, density and ionization fraction,\n\\item advancing the ionization state of the particles in time by\nsolving the time-dependent ionization rate equation.\n\\end{enumerate}\n\n\\subsection{Calculation of the UV radiation field}\n\n%%The exact determination of the UV radiation field would require the\n%%solution of the radiation transfer equation, an integro-partial-differential equation in six\n%%phase-space variables and time:\n%%\\begin{eqnarray} \\label{eq:radtrans}\n%% \\frac{1}{c} \\frac{\\partial I_{\\nu}}{\\partial t} + \\hat{\\bf k} \\cdot \\nabla\n%% I_{\\nu} = \\rho \\frac{\\epsilon_{\\nu}}{4 \\pi} -\n%% \\rho \\kappa_{\\nu}^{\\rm abs} I_{\\nu} \n%% - \\rho \\kappa_{\\nu}^{\\rm sca} I_{\\nu} \\nonumber \\\\\n%% + \\rho \\kappa_{\\nu}^{\\rm sca}\n%% \\oint \\Phi_{\\nu} \\left( \\hat{\\bf k},\\hat{\\bf k}' \\right) I_{\\nu}\n%% \\left( \\hat{\\bf k}' \\right) {\\rm d} \\Omega',\n%%\\end{eqnarray}\n%%where $c$ denotes the speed of light, $\\rho$ the density,\n%%$\\epsilon_{\\nu}$ the emissivity, $\\kappa_{\\nu}^{\\rm abs/sca}$ the\n%%absorption/scattering coefficients, $\\Phi(\\hat{\\rm k},\\hat{\\rm k}')$ the\n%%scattering probability density from direction $\\hat{\\rm k}'$ to direction\n%%$\\hat{\\rm k}$, $\\Omega$ , and $I_{\\nu}$ the intensity of the radiation field,\n%%depending on position $\\rm r$, direction $\\hat{\\rm k}$ and frequency $\\nu$ .\n%%\n%%Looking for the exact solution of equation~(\\ref{eq:radtrans}) is too time\n%%consuming for even the fastest computers. In order to find an\n%%approximate answer to the problem we made the following simplifying\n%%assumptions: quasi-static radiation field, neglection of scattering processes, usage of the\n%%on-the-spot approximation and integration of equation\n%%(\\ref{eq:radtrans}) over frequency with introduction of ``effective''\n%%physical constants: $p = \\int \\Psi_{\\nu}^{p} p_{\\nu} {\\rm d} \\nu$.\n%%\n%%\\subsubsection{Quasi-static radiation field}\n%%\n%%In the astrophysical problems we would like to adress with our method,\n%%the source and sink terms on the right hand side of\n%%equation~(\\ref{eq:radtrans}) lead to relaxation time scales for the\n%%radiation field which are\n%%many orders of magnitude smaller than the dynamical timescales $t_{\\rm\n%%dyn}$. We then can assume a quasi-static radiation field and drop\n%%the time dependent term on the left-hand side.\n%%\n%%\\subsubsection{Neglection of scattering processes}\n\n%%Given a point source of ionizing radiation, which emits $S_{\\rm tot}$ Lyman continuum\n%%photons per second, the surface density of ionizing photons at distance\n%%$r$ along a line of sight (LOS) leaving the source i is given by\n%%\\begin{equation}\n%% J^{(\\rm i)}(r) = \\frac{S_{\\rm tot}^{({\\rm i})}}{4 \\pi \\left({\\bf r} - {\\bf\n%% r}^{({\\rm i})}\\right)^{2}} \\cdot \\exp\n%% \\left(- \\tau^{({\\rm i})} \\right),\n%%\\end{equation}\n\nGiven a planar infall of ionizing photons from a distant source onto\nthe border of the volume of interest with a flux $J_0$ Lyman\ncontinuum photons per time and square area, the resulting\nphoton flux inside this volume is given by\n\\[\n J(s)=J_0 \\cdot \\exp \\left( - \\tau \\left( s \\right) \\right),\n\\]\nwhere $\\tau(s)$ is the optical depth for the ionizing photons along\nthe line of sight parallel to the infall direction of the photons, and\n$s$ is the distance from the border of the integration volume along\nthe line of sight: \n\n\\begin{equation} \\label{eq:LOS}\n \\tau(s) = \\int_{0}^{s} \\left[ \\bar{\\kappa} \\left( s^{\\prime} \\right) +\n \\kappa_{\\rm d} \\left( s \\right) \\right] {\\rm d} s^{\\prime}.\n\\end{equation}\n \n%%where $\\tau$ is the optical depth for the ionizing photons along the\n%%LOS:\n%%\\begin{equation} \\label{eq:LOS}\n%% \\tau^{({\\rm i})} = \\int_{{\\bf r}^{({\\rm i})}}^{\\bf r} \\bar{\\kappa}\n%% \\left( s \\right) {\\rm d}s.\n%%\\end{equation} \nWe neglect the effect of `photon hardening', i.e. the stronger\nabsorption of weaker photons, and use an `effective' absorption\ncoefficient $\\bar{\\kappa}$,\nthe mean of $\\kappa_{\\nu}$ over frequency, weighted by the spectrum of\nthe source $S_{\\nu}$:\n\\begin{equation} \\label{eq:crossect}\n \\bar{\\kappa} = n_{\\rm H} \\cdot \\bar{\\sigma} = n_{\\rm H} \\cdot\n \\frac{\\int S_{\\nu}^{({\\rm i})} \\sigma_{\\nu} {\\rm\n d} \\nu}{S_{\\rm tot}^{({\\rm i})}},\n\\end{equation}\nwhere $\\sigma_{\\nu}$ denotes the ionization cross section of hydrogen\nin the ground state and $n_{\\rm H}$ the particle density of the H atoms.\n\nThe role of dust in H{\\sc ii} regions and its effect on ionizing\nradiation is still very uncertain~\\cite{necklace}. If dust is present,\nit will partially absorb UV photons, heat up and reemit the energy in\nthe IR regime. Its first order effect can be included easily under the\nassumption of a homogeneous distribution of the dust in the H{\\sc ii}\nregion. The corresponding contribution to the optical depth can be\nincorporated by adding the dust absorption coefficient at the Lyman\nborder $\\kappa_{\\rm d}$ to the absorption coefficient in\nEq.~\\ref{eq:LOS}. $\\kappa_{\\rm d}$ depends on the dust model used and\nis regularily determined using Mie theory for grains with given\ndistributions in size and shape. In this paper, we set $\\kappa_{\\rm\nd}$ to zero throughout. \n\n%%The flux of ionizing photons in the case of point sources as the only\n%%emitters is given by the superposition:\n%%\\begin{equation}\n%% {\\bf J} = \\sum \\frac{J^{({\\rm i})}}{|{\\bf r}^{({\\rm i})}|} \\cdot {\\bf r}^{({\\rm\n%% i})}.\n%%\\end{equation}\nWe also neglect the diffuse field of Lyman continuum photons, which\nare being produced by recombinations of electrons into the ground\nlevel and which themselves possess sufficient energy for ionizing\nother H atoms. A thorough treatment of this radiation can only be\nachieved by detailed radiation transfer calculations as proposed\ne.g. by Yorke \\& Kaisig~\\shortcite{yorka}. Instead we use the\nassumption of the validity of the `on the spot' approximation as\nfollows: due to the fact that the spectrum of the Lyman\nrecombination photons as well as the the ionization cross section is\nstrongly peaked at the Lyman border, a small\namount of H atoms in the ionized region is sufficient to make the\nmedium optically thick for the Lyman recombination photons. This leads\nto the absorption of these photons in the ultimate vicinity of their\ncreation sites. As the creation of one photon is related to\nthe creation of one H atom, its absorption leads to the\ndestruction of one H atom. Thus the net effect of these photons on the\nlocal ionization structure is zero.\n\nThis assumption breaks down in regions next to OB stars, where due to\nthe high UV flux the density of H atoms is not sufficient to make the\nmedium optically thick to Lyman continuum photons. Next to ionization\nfronts, where the density of H atoms is much higher, the `on the spot'\nassumption is nevertheless a good approximation. On further details\nrefer to Yorke~\\shortcite{yorkebook}.\n\n\\subsection{Ionization and recombination rates}\n\nThe ionization rate in the medium is given by the sinks of the UV\nradiation field, since every ionization leads to the absorption of one\nUV photon:\n\\begin{equation} \\label{eq:ionrate}\n {\\cal I} = n_{\\rm H} \\bar{\\sigma} J = -\\nabla \\cdot {\\bf J},\n\\end{equation}\nwhere ${\\bf J} = J \\hat{{\\bf e}}_s$ is the flux vector in the\ndirection $\\hat{{\\bf e}}_s$ of the line of sight.\n\nThe recombination rate can be estimated as :\n\\begin{equation} \\label{eq:recomb}\n {\\cal R}=n_{\\rm e}^2 \\alpha_{\\rm B}=n^2x^2 \\alpha_{\\rm B},\n\\end{equation}\nwith $n$ being the particle density of H atoms and protons together,\n$n_{\\rm e}$ the particle density of free electrons, $x=n_{\\rm e}/n$\nthe ionization fraction and $\\alpha_{\\rm B}$ the effective\nrecombination coefficient under assumption of validity of the `on the spot'\napproximation. The recombination coefficient $\\alpha$ is given as the\nsum over the individual recombination coefficients $\\alpha_n$, where\nthe electron ends up in the atomic level $n$:\n\\begin{equation} \\label{eq:alpha}\n \\alpha = \\sum_{n} \\alpha_n.\n\\end{equation}\nUnder the assumption of the `on the spot' approximation recombinations\ninto the ground level do not lead to any net effect and thus\n$\\alpha_1$ can be neglected in Eq.~\\ref{eq:alpha}. The resulting net\nrecombination rate which is used in Eq.~\\ref{eq:recomb} is commonly\ncalled $\\alpha_{\\rm B}$ after the nomenclature introduced by Baker \\&\nMenzel~\\shortcite{baker}:\n\\[\n \\alpha_{\\rm B} = \\sum_{n=2}^\\infty \\alpha_n.\n\\]\n\n\\subsection{Ionization rate equation}\n\nKnowing the ionization and recombination rates, ${\\cal I}$ and ${\\cal\nR}$, the ionization fraction can be calculated from the ionization rate\nequation. The time dependency of the ionization fraction in the frame\ncomoving with the corresponding particle, i.e. its Lagrangian\nformulation, is given by:\n\\begin{equation} \\label{eq:ioniztime}\n \\frac{{\\rm d} n_{\\rm e}}{{\\rm d} t} = {\\cal I}-{\\cal R}.\n\\end{equation}\n\n\\subsection{Modeling the source}\n\nSince the spectral distribution of the UV radiation emitted by\nthe photospheres of intermediate to high mass stars is very uncertain,\nwe assume a black radiator with an effective temperature $T_{\\star}$.\n\n\\section{Numerical treatment}\n\nWe developed two different methods for the numerical treatment of time\ndependent ionization in the {\\sc sph} calculations. Both have in common the\nmethod of finding paths from the ionizing source to the particles,\nalong which the optical depth for the Lyman continuum photons can be\ncalculated. They differ in the way the ionization rate is determined\ngiven the radiation field. Method A uses the {\\sc sph} formalism to calculate\nthe divergence of the radiation field in Eq.~\\ref{eq:ionrate}. In method B\nwe adopt a different approach also used in grid methods, where we\nderive the ionization rate from the difference in the numbers of\nphotons entering and leaving a particle.\n\\begin{figure*}\n \\epsfig{file=path.eps}\n \\caption{Illustration of the path finding procedure. Each plus sign\n represents a particle. The circle\n segments symbolize the radius of the volume filled with particles in the nearest\n neighbour list of the corresponding particle. The particle with the smallest angle $\\Theta$\n between the line of sight from S0 to S5 and the line connecting them with the target are\n used for the determination of the evaluation points for the\n integration along the line of sight (small circles).} \\label{fig:construct}\n\\end{figure*}\n\n\\subsection{Finding the evaluation points on the path towards the\n source} \\label{sect:path}\n\n\nFirst, we specify the position, the rate of ionizing photons $S_{\\rm\ntot}$ and $\\bar{\\sigma}$ (from Eq.~\\ref{eq:crossect}) of the source.\n\nFor each particle~i we now proceed in the following way (see Fig.~\\ref{fig:construct}):\nGiven the list of nearest neighbours of particle i, which has to be\ndetermined anyway for the {\\sc sph} formalism, we look for the particle j in\nthe list, closest to the line of sight defined by the smallest angle $\\Theta$\nbetween the line connecting the particles i and j and the line of\nsight. We choose the angle between, not the distance from, the line of\nsight, since we are interested in controlling the error in the\ndirection towards the source. This is not garanteed by the latter\ncriterion.\n\n%%\\begin{figure}\n%% \\epsfig{file=crit.eps,width=8cm}\n%% \\caption{Illustration of the tolerance angle criterion. Although\n%% d$_1$ is smaller than d$_2$, $\\Theta_1$ is larger than\n%% $\\Theta_2$. We are interested in controlling the error in direction,\n%% thus we choose $\\Theta$ as our tolerance criterion.}\n%%\t\\label{fig:criterion}\n%%\\end{figure}\n\nWe store this particle in a list and determine the evaluation point\nS$_{\\rm j}$ as the projected particle position on the line of sight. To\ndetermine the next evaluation point S$_{\\rm k}$ even closer to the\nsource we now repeat this method using the neighbor list of particle j\n and so forth until we reach the source.\n\n%%First, the path from the particle~i to the source has to be\n%%found. Helpful is here the list of nearest neighbours, which must be\n%%determined for the {\\sc sph} algorithm. We now look for the particle j in this\n%%list, for which the LOS and the line connecting it and the particle~i\n%%include the smallest angle $\\theta$. We memorize the number of this\n%%particle and the position of the crossing point of the LOS and the\n%%vertical to it through particle j (see\n%%Fig.~\\ref{fig:construct}). We repeat this method with the particles\n%%in the neighbour list of particle j etc, until at last we reach the source.\n\n\\subsection{Calculating the optical depth and ionization rate for the particles}\n\n\\subsubsection{Method A: {\\sc sph} formalism method}\n\nNow the path from the source to particle~i is known, and the integration of Eq.~(\\ref{eq:LOS}) can be discretized by\nusing the evaluation points $S_{\\rm i}$. The value for\n$n_{\\rm H}$ can be estimated by using the {\\sc sph} smoothing formalism:\n\\begin{equation}\\label{eq:densest}\n n_{\\rm H}\\left( {\\bf r} \\right) = \\sum n_{\\rm H,i} W \\left({\\bf r}-{\\bf\n r}_{\\rm i} \\right),\n\\end{equation}\nwhere the sum runs over the particle corresponding to the evaluation\npoint and its nearest neighbours. $W$ is the weight factor for each\nneighboring particle provided by the smoothing kernel. We calculate the optical depth\nalong the line of sight by applying the Trapezian Formula, until we reach\nparticle~i:\n\\[\n \\tau_{{\\rm k}+1} = \\tau_{\\rm k} + \\frac{1}{2} \\bar{\\sigma} \\left( s_{{\\rm k}+1} -\n s_{\\rm k}\\right) \\left( n_{{\\rm H},{\\rm k}+1} + n_{{\\rm H},{\\rm k}} \\right),\n\\]\nwith $s_{\\rm k}$ being the position of the evaluation point on the line of sight.\nNote that this treatment neglects the effects of scattering of the\nionizing photons by recombination or dust.\n\nThe distance between two successive evaluation points is smaller\nor equal to the local smoothing length, which determines the largest\ndistance of the particles included in the nearest neighbour list as\nwell as the spatial resolution.\nThis guarantees that the line of sight integration of\nEq.~(\\ref{eq:LOS}) is discretized into a reasonable amount of\nsubsteps, consistent with the resolution given by the underlying\nparticle distribution.\n\nThe flux of ionizing photons at the position of particle~i into the\ndirection of photon propagation $\\hat{\\bf e}_s$ is then\ngiven by:\n\\[\n {\\bf J}_{\\rm i} = J_0 \\cdot\n \\hat{\\bf e}_s \\cdot \\exp \\left( - \\tau \\left( s \\right) \\right).\n\\]\n\nWith the ionizing flux known at the particle positions, the\nnabla operator in Eq.~(\\ref{eq:ionrate}) can be calculated by the\n{\\sc sph} formalism. It is given for each particle i as the sum over its\nneighbours:\n\\begin{equation}\\label{eq:nabla}\n {\\cal I}_{\\rm i} = - \\sum \\frac{m_{\\rm\n j}}{\\rho_{\\rm j}} {\\bf J}_{\\rm j} \\cdot \\nabla_{\\rm i} W_{\\rm j,i}.\n\\end{equation}\nNow we are able to solve Eq.~\\ref{eq:ioniztime}, which we write as:\n\\begin{equation} \\label{eq:diffgl}\n \\frac{{\\rm d}x_{\\rm i}}{{\\rm d}t} = {\\cal I}_{\\rm i}-n_{\\rm i}x_{\\rm i}^2\\alpha_{\\rm B}.\n\\end{equation}\nThe time scale for the establishment of ionization equilibrium is\ngiven by $1/(n \\alpha_{\\rm B})$, which is regularly much shorter than the\ndynamical and gravitational timescales we are interested in. In order\nto avoid small timesteps arising from the usage of explicit methods,\nwe use an implicit scheme. \nThe first order discretization of Eq.~\\ref{eq:diffgl} over a time interval $\\Delta t$ is given by:\n\\begin{equation} \\label{eq:firstorder}\nx_{\\rm i}^{{\\rm n}+1} = x_{\\rm i}^{\\rm n}+\\Delta t \\cdot \\left({\\cal\nI}_{\\rm i}^{{\\rm n}+1} - n_{\\rm i}^{{\\rm n}+1} x_{\\rm i}^{{\\rm n}+1} \\alpha_{\\rm B} \\right),\n\\end{equation}\nwhere the indices n and n$+1$ denote the values at the beginning and the\nend of the actual timestep $\\Delta t$, respectively. We already know\nall the values on the right hand side from advancing the particles by\nthe {\\sc sph} formalism, except the value for ${\\cal I}_{\\rm i}^{\\rm n+1}$. Therefore a fully consistent implicit treatment is not feasible. We use the following guess for this value:\n\\begin{equation} \\label{eq:implicit}\n {\\cal I}_{\\rm i}^{{\\rm n}+1} = {\\cal I}_{\\rm i}^{\\rm n} \\cdot \\frac{ 1-\\exp \\left(\n -n_{\\rm i}^{{\\rm n}+1} \\bar{\\sigma} a_{\\rm i}^{{\\rm n}+1} \\left( 1-x_{\\rm\n i}^{{\\rm n}+1} \\right) \\right)\n }{ 1 - \\exp \\left( -n_{\\rm i}^{{\\rm n}+1} \\bar{\\sigma} a_{\\rm i}^{{\\rm\n n}+1} \\left( 1-x_{\\rm i}^{\\rm n} \\right) \\right) }.\n\\end{equation}\nIn this equation, we assign an effective radius $a_{\\rm i}$ to each\nparticle i proportional to the mean particle separation, given by\n$a_{\\rm i}=(M_{\\rm i}/\\rho_{\\rm i})^{1/3}$. This is the estimate of\nthe size of a region with the particle mass $M_{\\rm i}$ and density\n$\\rho_{\\rm i}$. The factor with the exponentials on the right hand\nside accounts for the effect of higher absorption and hence ionization\nrate with decreasing ionization fraction. \n\nWe must use the effective radius $a_{\\rm i}$ in Eq.~\\ref{eq:implicit}\ninstead of the smoothing length $h$, since the method works analogous\nto implementations in grid codes. In contrast to the {\\sc sph}\nformalism, each particle now represents a volume of total mass $M_{\\rm\ni}$ and density $\\rho_{\\rm i}$, in which ionizing radiation enters on\none side and leaves on the opposite side. The size of this volume is\ngiven by $a_{\\rm i}$ as defined above. It is proportional to the\nparticle spacing.\n \nIn contrast, $h_i$ differs from the mean particle separation as it is\ndefined by the condition that there is a fixed number of neighbors\n$N_{\\rm neigh}$ of mass $M$\nin the sphere with radius $2\\, h_i$ and is thus given as\n\\[\n h_i = \\left( \\frac{3 N_{\\rm neigh} M}{32 \\pi \\rho}\n \\right)^{1/3}.\n\\]\nIt depends on $N_{\\rm neigh}$ and can therefore not be used instead of\n$a_{\\rm i}$ in Eq.~\\ref{eq:implicit}.\n\n%%This shows that $h$ depends on the number of neighbours chosen and is\n%%no measure for the size of a spherical volume filled with constant density\n%%$\\rho$ and containing mass $M_{\\rm P}$. Instead $a_i$ as defined above\n%%is the right measure we need in Eq.~\\ref{eq:implicit}. For commonly\n%%used values for $N_{\\rm neigh} \\simeq 50$, both quantities differ by the\n%%factor\n%%\\[\n%% \\frac{a_i}{h_i} = \\left( \\frac{32\\,\\pi}{3\\, N_{\\rm neigh}}\n%% \\right)^{1/3},\n%%\\]\n%%which is of order unity. \n\nOne consequence of the discretization of the ionization rate\nequation is that the solution in ionized regions tends to oscillate\naround the equilibrium value. \nIn order to avoid small timesteps arising from this, we set the\nionization fraction $x$ of particles with an\n$x > 0.95$ to the equilibrium value $x_{\\rm E}$, which is defined by\n${\\rm d}n_{\\rm e}/{\\rm d}t=0$ in Eq.~\\ref{eq:ioniztime}:\n\\[\n \\frac{{\\rm d}x}{{\\rm d}t} = \\frac{1}{n} \\frac{{\\rm d}n_{\\rm e}}{{\\rm\n d}t} = \\bar{\\sigma} (1-x_{\\rm E}) J - n x_{\\rm E}^2 \\alpha_{\\rm B} = 0.\n\\]\nWith $k=\\bar{\\sigma} J / (n \\alpha_{\\rm B})$ follows that\n\\[\n x_{\\rm E} = \\frac{1}{2} \\left[ \\left( k^2+4k \\right)^{1/2}-k\n \\right].\n\\]\n\nThis method works well in absolutely smooth, noise free particle distributions. However, if\none wishes to initially distribute the particles randomly in space,\none runs into problems. The sum in Eq.~\\ref{eq:nabla} is very\nsensitive to noisy particle distributions. Eventually the noise can be\nso high, that the error of the sum introduced by noise reaches the order of the sum\nitself. The ionization rate then locally drops below zero for some\nparticles, which can only be avoided by smoothing\nthe ionization rate spatially over several smoothing lengths. The\nresult is poor resolution. We circumvent this problem in method B.\n \n\\subsubsection{Method B: grid based method}\n\nIn this case, a different method is used to discretize the calculation\nof the optical depth. We determine the positions of the evaluation\npoints i along the line of sight as described in Sect.~\\ref{sect:path}\nand calculate the hydrogen density $n_{\\rm H,i}$ at these positions\nusing Eq.~\\ref{eq:densest}. The path is then divided into pieces with\nlength $\\Delta s_{\\rm i} = (s_{\\rm i+1}-s_{\\rm i-1})/2$, assuming a constant\nhydrogen density $n_{\\rm H,i}$ along each interval. The optical\ndepth for one piece can then be approximated by\n\\[\n \\Delta \\tau_{\\rm i} = \\bar{\\sigma} n_{\\rm H,i} \\Delta s_{\\rm i}.\n\\]\nThese contributions to the optical depth are summed up until we reach\nthe position located one effective radius $a_{\\rm i}$ before the\nposition of particle k. A first order approximation for the\nionization rate is now given by\n\\[\n {\\cal I}_{\\rm k} = \\frac{J_{0}}{2 a_{\\rm k} n_{\\rm\n k}} \\exp \\left(\n \\tau_{\\rm k-a} \\right) \\left( 1 - \\exp \\left(-\\Delta \\tau_{\\rm k}\n \\right) \\right),\n\\]\nwhere $\\tau_{\\rm k-a} = \\sum \\Delta \\tau_{\\rm i}$ denotes the optical\ndepth one effective radius before the particle's position and $\\Delta\n\\tau_{\\rm k} = 2 a_{\\rm k} n_{\\rm H,k} \\bar{\\sigma}$ the optical depth\nacross the particle.\n\nWith the ionization rate derived above we solve the ionization rate\nequation as described for case A. One can\neasily show that Eqs. (\\ref{eq:firstorder}) and (\\ref{eq:implicit})\nnow give the exact implicit first order discretization for\nEq.~(\\ref{eq:diffgl}). The solution now approaches the equilibrium\nvalue $x_{\\rm E}$ in the ionized regions without the instabilities mentioned in\nmethod A. It is not necessary to set $x$ artificially to $x_{\\rm E}$.\n\nMethod A seems to be the more consistent method since it uses\nthe {\\sc sph} formalism for the calculation of ${\\cal I}$. This is the\nreason why it is also discussed in this paper. Nevertheless we prefer\nmethod B due to its robustness against noisy particle distributions and higher\nconsistency concerning the integration scheme and have applied it to a\ncouple of test cases. \n\n\\subsection{Computational effort}\n\n\\begin{figure}[h]\n \\epsfig{file=agang.eps,width=8.2cm}\n \\epsfig{file=agdlog.eps,width=8.2cm}\n \\caption{Mean number of evaluation steps $I$ per path depending on\n tolerance angle $\\Theta_{\\rm tol}$ and number of particles\n $N$. Upper panel: $I$ depending on $\\Theta_{\\rm tol}$ for different\n $N$. Note how $I$ drops with increasing $\\Theta_{\\rm tol}$. Lower\n panel: log-log-plot \n of $I$ depending on $N$ for different $\\Theta_{\\rm tol}$ with\n the scaling law $I \\propto N^{1/3}$ overplotted as a solid\n line. For $\\Theta_{\\rm tol} > 0^\\circ$, $I$ becomes \n independent of $N$ for large~$N$.}\n \\label{fig:angdims}\n\\end{figure}\n\nIf the procedure explained above is used, the computational effort for\nthe line of sight integration scales approximately as $N^{4/3}$, since the\nintegration has to be done for each of the $N$ particles, and the\naverage number of evaluation points on each line of sight scales as\n$N^{1/3}$. \n\nWe can reduce the exponent from $4/3$ to 1 by introducing a\n`tolerance angle' $\\Theta_{\\rm tol}$. Suppose we determine the particles along the line of sight as expalined . As soon as\n$\\Theta$ for a particle j along the line of sight towards the source is smaller\nthan $\\Theta_{\\rm tol}$ we stop our search here. The optical\ndepth of this particle $\\tau_j$ is then used as an estimate of the\noptical depth along the remaining part of the line of sight from the\nsource to S$_{\\rm j}$. Thus no integration is needed for this part of\nthe path. One only has to make sure that $\\tau_j$ is\nalready known, i.e. that the line of sight integration for particle j\nhas been performed earlier. In this case, the average number of\nevaluation points $I$ per line of sight only depends on $\\Theta_{\\rm\ntol}$ for large $N$. As shown in Fig.~\\ref{fig:angdims}, $I$ becomes\nconstant for large $N$ and decreases with increasing $\\Theta_{\\rm\ntol}$. As soon as $I$ becomes independent of $N$ the total\ncomputational effort for all lines of sight together scales $\\propto N$.\n\n%%This is illustrated in Fig.~\\ref{fig:angdims}. The upper panel shows\n%%that, using the \"tolerance angle\", the mean number of evaluation steps\n%%$N_{\\rm mean}$ depends only on $\\Theta_{\\rm tol}$ and is decreasing with\n%%increasing $\\Theta_{\\rm tol}$. As long as the mean number of\n%%integration steps along the {\\it whole} lines of sight is less or of\n%%the same order as $N_{\\rm mean}(\\Theta_{\\rm tol})$, \n%%tol})$ The lower panel shows that with increasing\n%%particle numbers this mean value is approached faster for increasing\n%%$\\Theta_{\\rm tol}$.\n\nWe demonstrate the effects of using the tolerance angle on the\naccuracy of the ionization rate calculation in\nFig.~\\ref{fig:raterrs}. Histograms are plotted for the errors in ${\\cal I}$\nand $\\tau$ for calculations with\n$\\Theta_{\\rm tol}=0.5^\\circ$, $1^\\circ$, $2^\\circ$ and $90^\\circ$\ncompared to $\\Theta_{\\rm tol}=0^\\circ$. As the particle distribution we chose\nthe evolved state of a numerical simulation which studies the compression\nand collapse of a dense clump within the UV field of an OB association\nusing 200\\,000 particles. The results of this calculation will be\npresented elsewhere \\cite{kebu99}. Note that $\\Theta_{\\rm tol}=90^\\circ$\nrepresents the worst case, since the tolerance angle criterion now is\nfulfilled for every particle with minimal $\\Theta$ per search through the\nnearest neighbour list. \n\nThe particles which are most affected by the tolerance angle criterion lie\nnext to\nthe borders of shadows cast by optically thick regions, since here the path\nfor the integration along the line of sight may be bent through the optically\nthick region, thus decreasing the ionizing flux artificially. In the\nopposite case, the path may lead around the opaque region, increasing the ionizing flux\nat the position of a particle in the shadow. These extreme cases lead to the\ntail in the error histograms in Fig.~\\ref{fig:raterrs}. Applying the\ntolerance angle criterion thus numerically blurs shadows. \n\nThe mean errors in $\\tau$ are $1.3$ per cent for $\\Theta_{\\rm\ntol}=0.5^\\circ$, $2.2$ per cent for\n$\\Theta_{\\rm tol}=1.0^\\circ$, $3.4$ per cent for $\\Theta_{\\rm tol}=2.0^\\circ$\nand $11.2$ per cent for $\\Theta_{\\rm tol}=90^\\circ$. The correspnding\nmean errors in ${\\cal I}$ are $2.8$, $4.1$, $5.7$ and $13.3$ per\ncent, respectively. For the remaining test cases presented in this paper the choice\nof $\\Theta_{\\rm tol}$ has no effect, since they deal with\none-dimensional problems, in which the optical depth is only a\nfunction of distance from the source. Applying the tolerance angle\ncriterion only shifts the evaluation points from the lines of sight\nin directions perpendicular to these, along which there is no change in\nthe optical depth. Indeed even the choice $\\Theta_{\\rm tol} = 90^\\circ$\ngives the same results in the one-dimensional test cases as for\n$\\Theta_{\\rm tol}=0^\\circ$. Thus the errors introduced by the angle\ncriterion must be checked with problems in which this symmetry is\nbroken and shadows are present, as the one mentioned above.\n\n\\begin{figure}\n \\epsfig{file=rerrs.eps,width=8.2cm}\n \\epsfig{file=terrs.eps,width=8.2cm}\n \\caption{Histograms of the relative errors in $\\tau$ and ${\\cal I}$\n for different $\\Theta_{\\rm tol}$ in a three-dimensional test\n case.}\n \\label{fig:raterrs}\n\\end{figure}\n \n \n\\subsection{Smoothing the ionization front}\n\nFor reasons of noise reduction we smooth the ionization front,\nwhich is not resolvable by the {\\sc sph} representation, over a distance of\nthe order of one local smoothing length. Nature provides a simple way for doing\nthis. The width of the ionization zone is of the order of one photon mean\nfree path length,\n\\begin{equation}\\label{eq:width}\n d = (\\bar{\\sigma} \\cdot n_{\\rm H}) ^{-1},\n\\end{equation}\nwhere $\\bar{\\sigma}$ is the net absorption cross section for ionizing\nphotons as defined in Eq.~\\ref{eq:crossect}.\n\nSince we cannot resolve the ionization region anyway, we are free to adjust $\\sigma$ in a way that the width of the ionization\nregion given by Eq.~\\ref{eq:width} is equal to a constant factor\n$C \\leq 1$ times\nthe local smoothing length $h$, but never larger than the value\n$\\bar{\\sigma}$ given by Eq.~\\ref{eq:crossect}:\n\\[\n \\sigma = {\\rm min}\\left[\\bar{\\sigma},\\left(n_{\\rm H} \\cdot C\n \\cdot h\\right)^{-1}\\right].\n\\]\nTest calculations have shown that a good value is $C=0.1$. It has\nproven to sufficiently reduce numerical noise introduced into the\nionization structure by noise in the particle distribution and at the\nsame time to keep the resolution of ionization fronts better than the\nresolution of the {\\sc sph} formalism in order not to worsen the\noverall resolution. Note that, when ``smoothing'' the ionization front over\n$0.1$ times the smoothing length, the noise reducing effect is not\ncaused by the spatial smoothing, since it is ten times smaller than the {\\sc\nsph} smoothing. It rather results from a larger number of time steps\nneeded to ionize a particle in the front from an ionization fraction\nof $x=0$ to $x \\simeq 1$. This gives the neighbouring particles the\nopportunity to react to the changed state in a smoother way.\n \n\\subsection{Heating effect}\n\nWe assume that heating and cooling effects lead to an equilibrium\ntemperature of 10\\,000 K in the ionized gas penetrated by ionizing\nradiation. The cross sections for elastic\nelectron--electron and electron--proton scattering are of the order\n$10^{-13} {\\rm cm}^2$. Together with a mean velocity of the electrons of\nthe order of $600 \\rm{\\,km\\, s}^{-1}$ the thermalization timescale for the\nenergies of the ejected electrons is far less than a year for\ndensities of 1 particle cm$^{-3}$, which is many orders of magnitude\nsmaller than the dynamical timescale. Thermalization thus occurs\nquasi instantaneously. This process runs even more rapidly\nfor higher densities. Thus we are allowed to treat the gas behind the\nionization front as thermalized. We set the internal energy to:\n\\[\n e = x \\cdot e_{10000} + (1-x) \\cdot e_{\\rm cold},\n\\]\nwith $e_{10000}$ being the internal energy corresponding to a\ntemperature of 10\\,000 K for ionized hydrogen, and $e_{\\rm cold}$ to the internal energy\nfor the 10 K cold, neutral gas. Note that this\nmethod does not properly treat recombination zones,\nsince in this case one needs the correct inclusion of the heating and cooling\nprocesses in order to achieve the correct gas temperatures, sound\nvelocities and\npressures. Also, the equilibrium temperature in H{\\sc ii}-regions can\nvary by 20 per cent from this value. These deviations can also only be taken\ninto account by proper treatment of heating and cooling.\n\n\\section{Tests of the numerical treatment}\n\nAlthough being of one-dimensional nature, the following test\nproblems were performed fully in three dimensions.\n\n%%\\subsubsection{Test 1: Ionization of a Str\\\"omgren Sphere without\n%%hydrodynamics}\n\n%%Our first test case is the time dependent ionization of a Str\\\"omgren\n%%sphere with hydrodynamics switched off, i.e. we pin the particles in\n%%space. We place a star with ionizing flux $S_{\\star}$ into a medium with\n%%constant hydrogen density $n$. The star starts ionizing its vicinity by running a weak R\n%%type ionization front into it (for an overview of the different types\n%%of ionization fronts and the following theory of expanding H{\\sc ii}\n%%regions see e.g. Shu~1992). The radius of the ionized region\n%%approaches the classical Str\\\"omgren Radius,\n%%\\begin{equation}\n%%R_{\\rm i}=\\left( \\frac{3 S_{\\star}}{4 \\pi n^2 \\alpha_{\\rm B}} \\right) ^{1/3}.\n%%\\end{equation}\n%%The time dependence of this process is described by the exponential\n%%law:\n%%\\begin{equation}\n%%z=1-\\exp (-t/t_{\\rm R}),\n%%\\end{equation}\n%%where z is the fraction between the volume of the ionized medium and the\n%%Str\\\"omgren Sphere, and $t_{\\rm R}=1/n \\alpha_{\\rm B}$\n%%is the recombination time scale.\n%%\n%%This problem is a test case for the time-dependent treatment\n%%of the ionization rate equation. \n%%The evolution of\n%%\\begin{equation}\n%%\\log \\left( \\frac{1}{1-z} \\right) = \\frac{t}{t_{\\rm R}} = n\n%%\\alpha_{\\rm B} t\n%%\\end{equation}\n%%is compared with the analytical prediction in Fig. \\ref{fig:masstestB} for different numbers of particles,\n%%with $z = M_{\\rm ion}/(C \\cdot M_{0})$. $M_{0}$ is the analytically\n%%derived total mass of\n%%the ionized Str\\\"omgren sphere in the initial Str\\\"omgren radius\n%%$R_{\\rm i}$. The correction factor C accounts for the limited\n%%resolution of the sph representation. $M_{\\rm 0}$ is only determined\n%%within a range given by the mass of the particles which lie in the border of the\n%%ionized region. \n%%\\begin{figure}\n%% \\epsfig{file=ionmass.eps,width=8.2cm}\n%% \\caption{Time evolution of $\\log (1/(1-z))$ for different particle\n%% numbers, using method B}\n%% \\label{fig:masstestB}\n%%\\end{figure}\n%%\\begin{figure}\n%% \\epsfig{file=velo.eps,width=8.2cm}\n%% \\caption{Time evolution of the ionization front velocity for\n%% differen particle numbers, using method B}\n%% \\label{fig:veltestB}\n%%\\end{figure}\n%%The solid line shows the theoretical behaviour. The recombination time\n%%scale $t_{\\rm R}$ is overestimated by ca. 15 per cent, independent of the resolution.\n\n%%In order to calculate the ionizing radiation field, we \n%%We solve the time independent, non-relativistic equation of radiation\n%%transfer along lines of sight through the integration volume:\n%%\\begin{equation} \\label{eq:radtrans}\n%% \\frac{{\\rm d} I_{\\nu}}{{\\rm d} s} = - \\kappa_{\\nu} I_{\\nu},\n%%\\end{equation}\n%%where $I_{\\nu}$ is the intensity along the line of sight, $s$ is the\n%%path length and $\\kappa_{\\nu}$ the absorption coefficient for ionizing\n%%radiation. It is given by:\n%%\\begin{equation}\n%% \\kappa_{\\nu} = \\sigma_{\\nu} \\cdot n \\cdot (1-x).\n%%\\end{equation}\n%%$n \\cdot (1-x)$ is the abundance of hydrogen atoms capable of being\n%%ionized. $n$ itself is the sum of the abundances of neutral hydrogen,\n%%$n_{\\rm H}$,\n%%and protons, $n_{\\rm p}$, and x is the ionization fraction, $x=n_{\\rm\n%%p}/n = n_{\\rm e}/n$. $\\sigma_{\\nu}$ is the ionization cross section\n%%for hydrogen.\n%%\n%%We neglect the effect of ``photon hardening'' and use the equations\n%%and variables integrated over frequency:\n%%\\begin{equation}\n%% \\frac{{\n\\subsection{Test 1: Ionization of a slab with constant density}\n\nWith this problem we test the implementation of the time-dependent\nionization rate equation by ionizing a slab of H{\\sc i} gas of\nconstant density $n$ with ionizing radiation falling perpendicular onto one of the boundary\nsurfaces. With hydrodynamics switched off, we let the ionization front\ntraverse the slab with a constant velocity $v_{\\rm f}$.\nTo achieve this, we have to vary the infalling photon flux with\ntime. It is given by\n\\[\n J(t) = J_{\\rm f} + J_{\\rm t} = n v_{\\rm f} + n^2 \\alpha_{\\rm B} v_{\\rm f} t,\n\\]\nwhere the first term on the right hand side is the flux which\nprovides the photons being absorbed in the ionization front.\nThe second, time-dependent term equals the loss of photons on\ntheir way through the slab until they reach the front.\n\nFor the initial setup we place a number $N$ of\nparticles randomly into a slab with length-to-height and\nlength-to-width ratios of~10. Subsequently we let the particle distribution relax by evolving\nit isothermally within the slab, adding a damping term to the force\nlaw. This is necessary to diminish the numerical noise which was\nintroduced by the random distribution. We now have an ensemble of\nthe particles which does not possess any privileged directions and\nwhich represents a gas of constant density and temperature. We\nuse this distribution as our starting configuration. From now on we\nkeep the particles fixed in space and switch off hydrodynamics.\n\n%%\\begin{figure}\n%% \\epsfig{file=parms.eps,height=6cm}\n%% \\caption{Ionized mass vs. time for test 1. Solid line: theoretical\n%% solution. Results of calculations: Plus signs: 2000\n%% particles, stars: 16000 particles, diamonds: 128000 particles.\n%% Mass in unit of\n%% total mass $M_{\\rm slab}$ in the slab. Time in units of time needed for the\n%% ionization front to cross the\n%% slab of length $L_{\\rm slab}$ with a propagation velocity $v_{\\rm f}$.}\n%% \\label{fig:test1}\n%%\\end{figure}\n\n\\begin{figure}\n \\epsfig{file=errors.eps,height=6cm}\n \\caption{Relative error in ionized mass vs. time between\n calculations and theoretical result for test 1. Plus signs: 2000 particles,\n stars: 16000 particles, diamonds: 128000 particles. Time in units of\n time needed for the ionization front to cross the\n slab of length $L_{\\rm slab}$ with a propagation velocity $v_{\\rm f}$.}\n \\label{fig:errors1}\n\\end{figure}\n \nThe test was performed for a total number of $N=2\\,000, 16\\,000$ and\n$128\\,000$ particles. Since the spatial\nresolution for {\\sc sph} calculations scales as $N^{-1/3}$ (with number of\nneighbours $N_{\\rm neigh}$ per particle fixed), this yields an increase\nof linear resolution of a factor of two from one simulation to the\nsimulation with next higher resolution.\nThe results of these tests are shown in Fig.~\\ref{fig:errors1}.\n\nThe mean relative errors between the theoretical result and the\ncalculations decrease linearly with increasing resolution, consistent\nwith our first order discretization of both the line of sight\nintegration and the time dependent ionization equation. The error also\ndecreases with time as the representation of the ionization front gets thinner and\nthinner compared to the already ionized region. The spread in the errors for $N=16000$ and\n$N=128000$ results from the fact that in these cases the numerical\nsolution oscillates around the theoretical solution, sometimes being\nlarger than the latter, sometimes smaller.\n\n\\subsection{Test 2: Ionization of a slab with density gradient}\n\nWe proceed as in test 1, with the difference that we choose a slab\nwith a constant density gradient in the direction of photon\npropagation. We choose the time dependence of $J$ such that the\nionization front should travel through the gas with constant\n$v_{\\rm f}$. $J$ is given by:\n\\begin{eqnarray*}\nJ(t) = n_0 v_{\\rm f} + \\left(\\alpha_{\\rm B} n_0^2 + \\frac{{\\rm\nd}n}{{\\rm d} x} v_{\\rm f} \\right) v_{\\rm f} t + \\alpha_{\\rm B} n_0 \\frac{{\\rm\nd}n}{{\\rm d} x} v_{\\rm f}^2 t^2 + \\\\\n\\alpha_{\\rm B} \\left( \\frac{{\\rm\nd}n}{{\\rm d} x} \\right)^2 v_{\\rm f}^3 t^3,\n\\end{eqnarray*}\nwhere $n_0$ denotes the density at the surface where the radiation\npenetrates the slab and $\\frac{{\\rm d}n}{{\\rm d} x}$ is the density gradient.\n\n%%\\begin{table}\n%%\\caption{Input parameters for test case 2.}\n%%\\label{tbl:test0}\n%%\\begin{tabular}{@{}lcl}\n%%$n_0$ & : & 10 cm$^{-3}$ \\\\\n%%$\\frac{{\\rm d} n}{{\\rm d}x}$ & : & 495 cm$^{-3}$ pc$^{-1}$ \\\\\n%%$v_{\\rm f}$ & : & 1 pc Myr$^{-1}$ \\\\\n%%$\\alpha_{\\rm B}$ & : & 2.59e-13 cm$^3$s$^{-1}$ \\\\\n%%\\end{tabular}\n%%\\end{table}\n\nIn Fig.~\\ref{fig:test0} we plot the ionized mass for the theoretical\nsolution and the numerical simulations against time. The numerical\nresults converge against the theoretical solution with increasing\nresolution. The deviations at $t>0.9$ are caused by the\nionization front reaching the rear boundary of the slab.\n\nNote that the version of {\\sc sphi} used in this paper is not able to follow\nionization fronts exactly which travel faster than one local smoothing\nlength per time step. This must be taken into account during the\ntimestep determination. In applications with fast ionization fronts\n(typically R-type fronts in the early phases of the evolution of\nH{\\sc ii}-regions) this criterion can lead to very small timesteps and thus to\na high amount of CPU time needed. A version which circumvents this\nproblem is being developed.\n\n\\begin{figure}\n \\epsfig{file=pgrad.eps,height=6cm}\n \\caption{Ionized mass vs. time for test 2. Solid line: theoretical\n solution. Plus signs: N=2\\,000. Stars: N=16\\,000. Diamonds: N=128\\,000.}\n \\label{fig:test0}\n\\end{figure}\n\n%%\\begin{figure}\n%% \\epsfig{file=errorsgrad.eps,height=6cm}\n%% \\caption{Errors in ionized mass vs. time for test 2. Solid line: theoretical\n%% solution. Plus signs: N=2,000. Stars: N=16,000. Diamonds: N=128,000.}\n%% \\label{fig:errors0}\n%%\\end{figure}\n\n\n\\subsection{Test 3: Coupling of ionization and hydrodynamics}\n\\label{sect:test1}\n\n\\begin{figure}\n \\epsfig{file=leflt1.ps,height=6cm}\n \\caption{Density profile for test case 3 and different resolutions\n of the {\\sc sphi} calculation. Unit of the x-axis normalized to the\n position of the shock front. Ionizing radiation infall from the\n left. A shock wave traveling to the right into the undisturbed\n medium with $n_0=10$ cm$^{-3}$ and $T_{\\rm cold}=100$K sweeps up a dense shell of post-shock\n material, which is separated from the thin, hot, ionized material by\n an ionization front. Solid line: analytical result. Ratio of the\n thickness of the swept-up layer to the current local smoothing length for\n different resolutions: dotted 6,dashed 12, dash-dot 20. Corresponding\n times in code units: 0.34, 0.70, 1.0.}\n \\label{fig:test2dens}\t\n\\end{figure}\n\n\\begin{figure}\n \\epsfig{file=leflt3.ps,height=6cm}\n \\caption{Velocity profile for test case 3 and different\n resolutions. Unit of the x-axis normalized to the\n position of the shock front. Ionizing radiation infall from the\n left. Solid line: analytical result. Ratio of the\n thickness of the swept-up layer to the current local smoothing length for\n different resolutions: dotted 6,dashed 12, dash-dot\n 20. Corresponding times in code units: 0.34, 0.70, 0.93, 1.0.} \n \\label{fig:test2vel}\n\\end{figure}\n\nFor this test we adopt the problem mentioned by Lefloch \\&\nLazareff~\\shortcite{lefloch1}. A box filled with atomic hydrogen of\nparticle density $n_0=10$ cm$^{-3}$ and temperature $T_{\\rm cold}=100$\\,K is exposed to ionizing\nradiation, with the photon flux increasing from zero linearly with\ntime with a rate ${\\rm d}\\Phi/{\\rm d}t=5.07 \\cdot 10^{-2}$\ncm$^{-2}$\\,s$^{-2}$. There exists an analytical solution to this\nproblem, which is\nself similar in the sense that physical values at position $x$ measured\nin the direction of the photon flow at time $t$ are only functions of\n$x/t$. This means: the structure is stretched with time. The\nconvergence of the code towards the correct solution with increasing resolution can be tested in\none calculation, since for all appearing structures the ratio between\nstructure sizes and smoothing lengths increases linearly with time.\n\nThe resulting structure is the following: an isothermal shock is\ndriven into the neutral medium, sweeping up a dense layer of\nmaterial. This is followed by an ionization front which leaves the\nionized material in quasi-static equilibrium (see Figs. \\ref{fig:test2dens},\\ref{fig:test2vel}). Using the parameter\n$\\Lambda=\\alpha^{-1}({\\rm d}\\Phi/{\\rm d}t)$, Lefloch \\&\nLazareff~\\shortcite{lefloch1} find the following analytical solution:\n\\begin{eqnarray*}\n\\Lambda=n_{\\rm i}^2V_{\\rm i} \\\\\nn_{\\rm i}=\\left(\\frac{n_0 \\Lambda^2}{c_{\\rm i}^2} \\right)^\\frac{1}{5} && V_{\\rm i}=\\left(\\frac{\\Lambda c_{\\rm i}^4}{n_0^2} \\right)^\\frac{1}{5} \\\\\nn_{\\rm c}=n_0 \\left(\\frac{\\Lambda}{n_{\\rm i}^2 c_{\\rm n}} \\right)^2 && V_{\\rm s}=c_{\\rm n} \\left(\\frac{n_{\\rm c}}{n_0} \\right)^\\frac{1}{2},\n\\end{eqnarray*}\nwhere $n_{\\rm i}$, $n_{\\rm 0}$ and $n_{\\rm c}$ denote the particle\ndensities of the ionized gas, the undisturbed neutral gas and the gas\nin the compressed layer, respectively, and $V_{\\rm i}$ and $V_{\\rm s}$ the\nvelocities of the ionization front and the shock front, respectively.\n\nWe adopt $\\alpha_{\\rm B}=2.7 \\cdot 10^{-13}$\\,cm$^3$\\,s$^{-1}$ from Lefloch \\&\nLazareff~\\shortcite{lefloch1} in order to directly compare the results of the\n{\\sc sphi} code to those of their grid-based method using a piecewise linear\nscheme for the advection terms proposed by Van\nLeer~\\shortcite{VanLeer}. The resolution of 192 grid cells along\nthe slab of their calculations,\nfrom which they derived their results, is comparable with the one used\nin our high resolution case. We use the same method as described in\nSect.~\\ref{sect:test1} to produce the initial conditions. No gas is\nallowed to enter or leave the surface.\n\n\\begin{table}\n\\caption{Comparison of analytical and numerical results for test case 3.}\n\\label{tbl:result}\n\\begin{tabular}{@{}llll}\n & analytical & {\\sc sphi} & Lefloch e.a. \\shortcite{lefloch1}\\\\\n\\hline\n$n_{\\rm i}$ (cm$^{-3}$) & $0.756$ & $0.75\\pm0.05$ & $0.748$ \\\\\n$n_{\\rm c}$ (cm$^{-3}$) & $1.59 \\cdot 10^2$ & $(1.55\\pm0.05) \\cdot 10^2$ &\n$1.69 \\cdot 10^2$ \\\\\n$V_{\\rm s}$ (km s$^{-1}$) & $3.71$ & $3.67\\pm0.05$ & $3.51$ \\\\\n$V_{\\rm i}$ (km s$^{-1}$) & $3.48$ & $3.43\\pm0.05$ & $3.36$ \\\\ \\hline\n\\end{tabular}\n\\end{table}\n\nTable \\ref{tbl:result} lists the result of this comparison. The {\\sc sphi}\ncalculation slightly underestimates $V_{\\rm s}$ and $V_{\\rm i}$, as is\nalso observed for the grid code. The errors of order 5 per cent are\ncomparable to those achieved by Lefloch \\&\nLazareff~\\shortcite{lefloch1}.\n\nIn the early phases, i.e. low resolution, the\npoor treatment of the ionization front leads to irregularities in the\nionized region and thus produces sound waves travelling back and forth\nbetween the boundary to the left and the ionization front\n(Figs.~\\ref{fig:test2dens}, \\ref{fig:test2vel}), which decrease in\npower as time increases, i.e. at higher resolution.\nWith increasing resolution, i.e. increasing ratio of layer thickness\nto smoothing length, the representation of the dense layer and the\nshock front improves (Figs.~\\ref{fig:blow1},\n\\ref{fig:blow3}).\n\n\\begin{figure}\n \\epsfig{file=blow1.ps,height=6cm}\n \\caption{Density of the layer for test case 3. Unit of the\n x-axis normalized to the position of the shock front. Ionizing\n radiation infall from the left. Solid line: analytical\n result. Ratio of the thickness of the swept-up layer to the current local\n smoothing length for different resolutions: dotted 6,dashed 12,\n dash-dot 18, dash-dot-dot-dot 20. Corresponding times in code units:\n 0.34, 0.70, 0.93, 1.0.}\n \\label{fig:blow1}\t\n\\end{figure}\n\n\\begin{figure}\n \\epsfig{file=blow3.ps,height=6cm}\n \\caption{Velocity profile for test case 3. Unit of the\n x-axis normalized to the position of the shock front. Ionizing\n radiation infall from the left. Solid line: analytical\n result. Ratio of the thickness of the swept-up layer to the current local\n smoothing length for different resolutions: dotted 6,dashed 12,\n dash-dot 18, dash-dot-dot-dot 20. Corresponding times in code units:\n 0.34, 0.70, 0.93, 1.0.} \n \\label{fig:blow3}\n\\end{figure}\n\n\\section{Summary}\n\nThe method presented in this paper allows the treatment of the\ndynamical effects of ionizing radiation in {\\sc sph}\ncalculations. Thus the study of astrophysical problems arising from\nionization, like the\nimpact of ionizing radiation from newly born stars onto the evolution of\ntheir parental molecular clouds or the more consistent treatment of\nheating by OB associations in galaxy dynamics calculations are now\nfeasible for the first time with {\\sc sphi} in 3 dimensions. We demonstrate that the\ncode is able to treat time-dependent ionization, the related heating\neffects and hydrodynamics correctly. Our first applications, \ndetailed calculations of photoionization induced collapse in\nmolecular clouds and results obtained from them, will be presented in\na subsequent paper.\n\nTo allow the correct treatment of\nrecombination zones, one has to include the effects of time dependent\nheating and cooling processes by ionization and recombination,\nemission of forbidden lines and thermal radiation from dust. Another\nimportant aspect which was neglected here is the effect of the diffuse\nLyman continuum recombination field. It can lead to the penetration of regions\nshielded from the direct ionizing radiation by the ionization front,\nwhich is e.g. seen in calculations of photoevaporating protostellar\ndisks \\cite{yowe,richling}. An implementation\nof these processes into our {\\sc sphi} code is planned in the future.\n\n\\section*{Acknowledgments}\nThis work was supported by the Deutsche Forschungsgemeinschaft (DFG),\ngrant Bu 842/4. We'd also like to kindly thank Matthew\nBate and Ralf Klessen for the useful discussions concerning the\ncapabilities and implementation of the {\\sc sph} method.\n\n\\begin{thebibliography}{}\n\\bibitem[\\protect\\citename{Baker \\& Menzel~}1962]{baker}\nBaker J., Menzel D., 1962, in Menzel D., ed., Selected Papers on\nPhysical Processes in Ionized Plasmas. Dover Publications Inc., 180 Varick\nStreet, p. 58\n\\bibitem[\\protect\\citename{Barnes \\& Hut~}1989]{barnes}\nBarnes J. E., Hut P., 1989, ApJS, 70, 389\n\\bibitem[\\protect\\citename{Bate~}1998]{bate2}\nBate M. R., 1998, ApJL, 508, 95\n\\bibitem[\\protect\\citename{Bate \\& Bonnell~}1997]{babo1}\nBate M. R., Bonnell I. A., 1997, MNRAS, 285, 33\n\\bibitem[\\protect\\citename{Bate, Bonnell \\& Price~}1995]{babopri}\nBate M. R., Bonnell I. A., Price N. M., 1995, MNRAS, 277, 362\n\\bibitem[\\protect\\citename{Bate \\& Burkert~}1997]{bateburk}\nBate M. R., Burkert A., 1997, MNRAS, 288, 1060\n\\bibitem[\\protect\\citename{Benz et al.~}1990]{benz}\nBenz W., Bowers R. L., Cameron A. G. W., Press W. H., 1990, ApJ, 348, 647\n%%\\bibitem[\\protect\\citename{Bertoldi~}1989]{bertoldi2}\n%%Bertoldi F., 1989, Ph.D. thesis, University of California at Berkeley\n%%\\bibitem[\\protect\\citename{Bertoldi \\& NcKee~}1990]{bertoldi1}\n%%Bertoldi F., McKee C.F., 1990, ApJ, 354, 529\n\\bibitem[\\protect\\citename{Bhattal et al.~}1998]{bhattal}\nBhattal A. S., Francis N., Watkins S. J., Whitworth A. P., 1998, MNRAS,\n297, 435\n\\bibitem[\\protect\\citename{Bonnell \\& Bate~}1994]{boba1}\nBonnell I. A., Bate M. R., 1994, MNRAS, 269, L45\n%%\\bibitem[\\protect\\citename{Bryan et al.~}1994]{Bryan}\n%%Bryan G.L., Norman M.L., Stone J.M., Cen R., Ostriker J.P., 1994,\n%%Comp. Phys. Comm., \n\\bibitem[\\protect\\citename{Burkert et al.~}1996]{bbb}\nBurkert A., Bate M. R., Bodenheimer P., 1996, MNRAS, 289, 497 \n%%\\bibitem[\\protect\\citename{Cen~}1992]{Cen}\n%%Cen R., 1992, ApJS 78,341\n%%\\bibitem[\\protect\\citename{Evrard~}1988]{Evrard}\n%%Evrard A.E., 1988, MNRAS 235,911\n%%\\bibitem[\\protect\\citename{Hernquist \\& Katz~}1989]{HernKatz}\n%%Hernquist L., Katz N.S., 1989, ApJS 64,715\n\\bibitem[\\protect\\citename{Efremov \\& Elmegreen~}1998]{efremov}\nEfremov Y. N., Elmegreen B. G., 1998, MNRAS, 299, 588\n\\bibitem[\\protect\\citename{Feldt et al.~}1998]{necklace}\nFeldt M., Stecklum B., Henning Th., Hayward T. L., Lehmann Th., Klein\nR., 1998, A\\&A, 339, 759\n\\bibitem[\\protect\\citename{Hernquist, Bouchet \\& Suto~}1991]{hernqu}\nHernquist L., Bouchet F. R., Suto, Y., 1991, ApJS, 75, 231\n\\bibitem[\\protect\\citename{Inutsuka~}1995]{inutsuka}\nInutsuka S.-I., 1995, IAUS, 174, 373\n\\bibitem[\\protect\\citename{Kessel \\& Burkert~}1999]{kebu99}\nKessel, O., Burkert, A., 1999, in preparation\n\\bibitem[\\protect\\citename{Klessen~}1997]{klessen}\nKlessen R. S., 1997, MNRAS, 292, 11\n\\bibitem[\\protect\\citename{Klessen et al.~}1998]{klebuba}\nKlessen R. S., Burkert A., Bate M. R., 1998, ApJL, 501, 205\n\\bibitem[\\protect\\citename{Larwood \\& Papaloizou~}1997]{larwood}\nLarwood J. D., Papaloizou J. C. B., 1997, MNRAS, 285, 288\n\\bibitem[\\protect\\citename{Lefloch \\& Lazareff~}1994]{lefloch1}\nLefloch B., Lazareff B., 1994, A\\&A, 289, 559\n\\bibitem[\\protect\\citename{Nelson et al.~}1998]{nelson}\nNelson A. F., Benz W., Adams F. C., Arnett D., 1998, ApJ, 502, 342\n\\bibitem[\\protect\\citename{Press~}1986]{press}\nPress W. H., 1986, in Springer Lecture Notes in Physics Vol. 267, The\nUse of Supercomputers in Stellar Dynamics, Springer, Berlin\n\\bibitem[\\protect\\citename{Richling \\& Yorke~}1998]{richling}\nRichling S., Yorke H. W., 1998, A\\&A, 340, 508\n%%\\bibitem[\\protect\\citename{Ryu et al.~}1993]{Ryu}\n%%Ryu D., Ostriker J.P., Kang H., Cen R., 1993, ApJ, 414, 1\n%%\\bibitem[\\protect\\citename{Shu~}1992]{shu}\n%%Shu F. H., 1992, The Physics of Astrophysics Vol. 2: Gas Dynamics,\n%%University Science Books, 20 Edgehill Road, Mill Valley, CA 94941\n\\bibitem[\\protect\\citename{Sonnhalter, Preibisch \\& Yorke~}1995]{sonnha}\nSonnhalter C., Preibisch T., Yorke H. W., 1995, A\\&A, 299, 545\n\\bibitem[\\protect\\citename{Steinmetz~}1996]{steinmetz}\nSteinmetz M., 1996, MNRAS, 278, 1005\n\\bibitem[\\protect\\citename{Stone \\& Norman~}1992]{stono}\nStone J. M., Norman M. L., 1992, ApJS, 80, 791\n\\bibitem[\\protect\\citename{Umemura et al.~}1993]{umemura}\nUmemura M., Fukushige T., Makino J., Ebisuzaki T., Sugimoto D., Turner\nE. L., Loeb A., 1993, PASJ, 45, 311\n\\bibitem[\\protect\\citename{Vanhala \\& Cameron~}1998]{vanhala}\nVanhala, H. A. T., Cameron, A. G. W., 1998, ApJ, 508, 291\n\\bibitem[\\protect\\citename{Van Leer~}1979]{VanLeer}\nVan Leer, B., 1979, J. Comp. Phys., 32, 101\n\\bibitem[\\protect\\citename{Wilking \\& Lada~}1985]{pppII}\nWilking, B. A., Lada, C. J., 1985, in Black D. C., Matthews M. S., eds.,\nProtostars \\& Planets II, The University of Arizona Press, p. 297\n\\bibitem[\\protect\\citename{Yorke~}1988]{yorkebook}\n{Yorke}, H.~W., 1988, in {Chmielewski}~Y., {Lanz}~T., eds., Radiation\nin Moving Gaseous Media, Advanced Course of the Swiss Society of\n Astrophysics and Astronomy vol.~18, pp. 242--246. Geneva Observatory, CH-1290\n Sauverny-Versoix, Switzerland.\n\\bibitem[\\protect\\citename{Yorke \\& Kaisig~}1995]{yorka}\nYorke H. W., Kaisig M., 1995, Comp. Phys. Comm., 89, 29\n\\bibitem[\\protect\\citename{Yorke \\& Welz~}1996]{yowe}\nYorke H. W., Welz A., 1996, A\\&A, 315, 555\n\\bibitem[\\protect\\citename{Ziegler, Yorke \\& Kaisig~}1996]{ziegler}\nZiegler U., Yorke H. W., Kaisig M., 1996, A\\&A, 305, 114\n\\end{thebibliography}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002251.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[\\protect\\citename{Baker \\& Menzel~}1962]{baker}\nBaker J., Menzel D., 1962, in Menzel D., ed., Selected Papers on\nPhysical Processes in Ionized Plasmas. Dover Publications Inc., 180 Varick\nStreet, p. 58\n\\bibitem[\\protect\\citename{Barnes \\& Hut~}1989]{barnes}\nBarnes J. E., Hut P., 1989, ApJS, 70, 389\n\\bibitem[\\protect\\citename{Bate~}1998]{bate2}\nBate M. R., 1998, ApJL, 508, 95\n\\bibitem[\\protect\\citename{Bate \\& Bonnell~}1997]{babo1}\nBate M. R., Bonnell I. A., 1997, MNRAS, 285, 33\n\\bibitem[\\protect\\citename{Bate, Bonnell \\& Price~}1995]{babopri}\nBate M. R., Bonnell I. A., Price N. M., 1995, MNRAS, 277, 362\n\\bibitem[\\protect\\citename{Bate \\& Burkert~}1997]{bateburk}\nBate M. R., Burkert A., 1997, MNRAS, 288, 1060\n\\bibitem[\\protect\\citename{Benz et al.~}1990]{benz}\nBenz W., Bowers R. L., Cameron A. G. W., Press W. H., 1990, ApJ, 348, 647\n%%\\bibitem[\\protect\\citename{Bertoldi~}1989]{bertoldi2}\n%%Bertoldi F., 1989, Ph.D. thesis, University of California at Berkeley\n%%\\bibitem[\\protect\\citename{Bertoldi \\& NcKee~}1990]{bertoldi1}\n%%Bertoldi F., McKee C.F., 1990, ApJ, 354, 529\n\\bibitem[\\protect\\citename{Bhattal et al.~}1998]{bhattal}\nBhattal A. S., Francis N., Watkins S. J., Whitworth A. P., 1998, MNRAS,\n297, 435\n\\bibitem[\\protect\\citename{Bonnell \\& Bate~}1994]{boba1}\nBonnell I. A., Bate M. R., 1994, MNRAS, 269, L45\n%%\\bibitem[\\protect\\citename{Bryan et al.~}1994]{Bryan}\n%%Bryan G.L., Norman M.L., Stone J.M., Cen R., Ostriker J.P., 1994,\n%%Comp. Phys. Comm., \n\\bibitem[\\protect\\citename{Burkert et al.~}1996]{bbb}\nBurkert A., Bate M. R., Bodenheimer P., 1996, MNRAS, 289, 497 \n%%\\bibitem[\\protect\\citename{Cen~}1992]{Cen}\n%%Cen R., 1992, ApJS 78,341\n%%\\bibitem[\\protect\\citename{Evrard~}1988]{Evrard}\n%%Evrard A.E., 1988, MNRAS 235,911\n%%\\bibitem[\\protect\\citename{Hernquist \\& Katz~}1989]{HernKatz}\n%%Hernquist L., Katz N.S., 1989, ApJS 64,715\n\\bibitem[\\protect\\citename{Efremov \\& Elmegreen~}1998]{efremov}\nEfremov Y. N., Elmegreen B. G., 1998, MNRAS, 299, 588\n\\bibitem[\\protect\\citename{Feldt et al.~}1998]{necklace}\nFeldt M., Stecklum B., Henning Th., Hayward T. L., Lehmann Th., Klein\nR., 1998, A\\&A, 339, 759\n\\bibitem[\\protect\\citename{Hernquist, Bouchet \\& Suto~}1991]{hernqu}\nHernquist L., Bouchet F. R., Suto, Y., 1991, ApJS, 75, 231\n\\bibitem[\\protect\\citename{Inutsuka~}1995]{inutsuka}\nInutsuka S.-I., 1995, IAUS, 174, 373\n\\bibitem[\\protect\\citename{Kessel \\& Burkert~}1999]{kebu99}\nKessel, O., Burkert, A., 1999, in preparation\n\\bibitem[\\protect\\citename{Klessen~}1997]{klessen}\nKlessen R. S., 1997, MNRAS, 292, 11\n\\bibitem[\\protect\\citename{Klessen et al.~}1998]{klebuba}\nKlessen R. S., Burkert A., Bate M. R., 1998, ApJL, 501, 205\n\\bibitem[\\protect\\citename{Larwood \\& Papaloizou~}1997]{larwood}\nLarwood J. D., Papaloizou J. C. B., 1997, MNRAS, 285, 288\n\\bibitem[\\protect\\citename{Lefloch \\& Lazareff~}1994]{lefloch1}\nLefloch B., Lazareff B., 1994, A\\&A, 289, 559\n\\bibitem[\\protect\\citename{Nelson et al.~}1998]{nelson}\nNelson A. F., Benz W., Adams F. C., Arnett D., 1998, ApJ, 502, 342\n\\bibitem[\\protect\\citename{Press~}1986]{press}\nPress W. H., 1986, in Springer Lecture Notes in Physics Vol. 267, The\nUse of Supercomputers in Stellar Dynamics, Springer, Berlin\n\\bibitem[\\protect\\citename{Richling \\& Yorke~}1998]{richling}\nRichling S., Yorke H. W., 1998, A\\&A, 340, 508\n%%\\bibitem[\\protect\\citename{Ryu et al.~}1993]{Ryu}\n%%Ryu D., Ostriker J.P., Kang H., Cen R., 1993, ApJ, 414, 1\n%%\\bibitem[\\protect\\citename{Shu~}1992]{shu}\n%%Shu F. H., 1992, The Physics of Astrophysics Vol. 2: Gas Dynamics,\n%%University Science Books, 20 Edgehill Road, Mill Valley, CA 94941\n\\bibitem[\\protect\\citename{Sonnhalter, Preibisch \\& Yorke~}1995]{sonnha}\nSonnhalter C., Preibisch T., Yorke H. W., 1995, A\\&A, 299, 545\n\\bibitem[\\protect\\citename{Steinmetz~}1996]{steinmetz}\nSteinmetz M., 1996, MNRAS, 278, 1005\n\\bibitem[\\protect\\citename{Stone \\& Norman~}1992]{stono}\nStone J. M., Norman M. L., 1992, ApJS, 80, 791\n\\bibitem[\\protect\\citename{Umemura et al.~}1993]{umemura}\nUmemura M., Fukushige T., Makino J., Ebisuzaki T., Sugimoto D., Turner\nE. L., Loeb A., 1993, PASJ, 45, 311\n\\bibitem[\\protect\\citename{Vanhala \\& Cameron~}1998]{vanhala}\nVanhala, H. A. T., Cameron, A. G. W., 1998, ApJ, 508, 291\n\\bibitem[\\protect\\citename{Van Leer~}1979]{VanLeer}\nVan Leer, B., 1979, J. Comp. Phys., 32, 101\n\\bibitem[\\protect\\citename{Wilking \\& Lada~}1985]{pppII}\nWilking, B. A., Lada, C. J., 1985, in Black D. C., Matthews M. S., eds.,\nProtostars \\& Planets II, The University of Arizona Press, p. 297\n\\bibitem[\\protect\\citename{Yorke~}1988]{yorkebook}\n{Yorke}, H.~W., 1988, in {Chmielewski}~Y., {Lanz}~T., eds., Radiation\nin Moving Gaseous Media, Advanced Course of the Swiss Society of\n Astrophysics and Astronomy vol.~18, pp. 242--246. Geneva Observatory, CH-1290\n Sauverny-Versoix, Switzerland.\n\\bibitem[\\protect\\citename{Yorke \\& Kaisig~}1995]{yorka}\nYorke H. W., Kaisig M., 1995, Comp. Phys. Comm., 89, 29\n\\bibitem[\\protect\\citename{Yorke \\& Welz~}1996]{yowe}\nYorke H. W., Welz A., 1996, A\\&A, 315, 555\n\\bibitem[\\protect\\citename{Ziegler, Yorke \\& Kaisig~}1996]{ziegler}\nZiegler U., Yorke H. W., Kaisig M., 1996, A\\&A, 305, 114\n\\end{thebibliography}"
}
] |
astro-ph0002252
|
Very High-Energy Gamma-Ray Observations of PSR B1509$-$58 with the CANGAROO 3.8m Telescope
|
[
{
"author": "T. Sako \\altaffilmark{1,14}"
},
{
"author": "Y. Matsubara \\altaffilmark{1}"
},
{
"author": "Y. Muraki \\altaffilmark{1}"
},
{
"author": "P. V. Ramanamurthy \\altaffilmark{1}"
},
{
"author": "S. A. Dazeley \\altaffilmark{2}"
},
{
"author": "P. G. Edwards \\altaffilmark{3}"
},
{
"author": "S. Gunji \\altaffilmark{4}"
},
{
"author": "T. Hara \\altaffilmark{5}"
},
{
"author": "S. Hara \\altaffilmark{6}"
},
{
"author": "J. Holder \\altaffilmark{7, 15}"
},
{
"author": "S. Kamei \\altaffilmark{6}"
},
{
"author": "A. Kawachi \\altaffilmark{7}"
},
{
"author": "T. Kifune \\altaffilmark{7}"
},
{
"author": "R. Kita \\altaffilmark{8}"
},
{
"author": "A. Masaike \\altaffilmark{9}"
},
{
"author": "Y. Mizumoto \\altaffilmark{10}"
},
{
"author": "M. Mori \\altaffilmark{7}"
},
{
"author": "M. Moriya \\altaffilmark{6}"
},
{
"author": "H. Muraishi \\altaffilmark{8}"
},
{
"author": "T. Naito \\altaffilmark{10}"
},
{
"author": "K. Nishijima \\altaffilmark{11}"
},
{
"author": "S. Ogio \\altaffilmark{6}"
},
{
"author": "J. R. Patterson \\altaffilmark{2}"
},
{
"author": "G. P. Rowell \\altaffilmark{7}"
},
{
"author": "K. Sakurazawa \\altaffilmark{6}"
},
{
"author": "Y. Sato \\altaffilmark{7}"
},
{
"author": "R. Susukita \\altaffilmark{12}"
},
{
"author": "R. Suzuki \\altaffilmark{6}"
},
{
"author": "T. Tamura \\altaffilmark{13}"
},
{
"author": "T. Tanimori \\altaffilmark{6}"
},
{
"author": "G. J. Thornton \\altaffilmark{2}"
},
{
"author": "S. Yanagita \\altaffilmark{8}"
},
{
"author": "T. Yoshida \\altaffilmark{8} and T. Yoshikoshi \\altaffilmark{7}"
}
] |
The gamma-ray pulsar PSR B1509$-$58 and its surrounding nebulae have been observed with the CANGAROO 3.8m imaging atmospheric \v{C}erenkov telescope. The observations were performed from 1996 to 1998 in Woomera, South Australia, under different instrumental conditions with estimated threshold energies of 4.5 TeV (1996), 1.9 TeV (1997) and 2.5 TeV (1998) at zenith angles of $\sim$ 30$^{\circ}$. Although no strong evidence of the gamma-ray emission was found, the lowest energy threshold data of 1997 showed a marginal excess of gamma-ray--like events at the 4.1 $\sigma$ significance level. The corresponding gamma-ray flux is calculated to be $(2.9\,\pm\,0.7) \times 10^{-12}\,cm^{-2}s^{-1}$ above 1.9 TeV. The observations of 1996 and 1998 yielded only upper limits (99.5\% confidence level) of $1.9 \times 10^{-12}\,cm^{-2}s^{-1}$ above 4.5 TeV and $2.0 \times 10^{-12}\,cm^{-2}s^{-1}$ above 2.5 TeV, respectively. Assuming that the 1997 excess is due to Very High-Energy (VHE) gamma-ray emission from the pulsar nebula, our result, when combined with the X-ray observations, leads to a value of the magnetic field strength $\simeq$ 5 $\mu$G. This is consistent with the equipartition value previously estimated in the X-ray nebula surrounding the pulsar. No significant periodicity at the 150\,ms pulsar period has been found in any of the three years' data. The flux upper limits set from our observations are one order of magnitude below previously reported detections of pulsed TeV emission.
|
[
{
"name": "psr1509.tex",
"string": "\\documentstyle[12pt,aasms4]{article}\n\n\\lefthead{Sako et al.}\n\\righthead{Very High-Energy Gamma-rays from PSR B1509$-$58}\n\n\\begin{document}\n\n\\title{Very High-Energy Gamma-Ray Observations of PSR B1509$-$58\nwith the CANGAROO 3.8m Telescope}\n\n\\author{T. Sako \\altaffilmark{1,14},\n Y. Matsubara \\altaffilmark{1},\n Y. Muraki \\altaffilmark{1},\n P. V. Ramanamurthy \\altaffilmark{1},\n S. A. Dazeley \\altaffilmark{2},\\\\\n P. G. Edwards \\altaffilmark{3},\n S. Gunji \\altaffilmark{4},\n T. Hara \\altaffilmark{5},\n S. Hara \\altaffilmark{6},\n J. Holder \\altaffilmark{7, 15},\n S. Kamei \\altaffilmark{6},\n A. Kawachi \\altaffilmark{7},\\\\\n T. Kifune \\altaffilmark{7},\n R. Kita \\altaffilmark{8},\n A. Masaike \\altaffilmark{9},\n Y. Mizumoto \\altaffilmark{10},\n M. Mori \\altaffilmark{7},\n M. Moriya \\altaffilmark{6},\\\\\n H. Muraishi \\altaffilmark{8},\n T. Naito \\altaffilmark{10},\n K. Nishijima \\altaffilmark{11},\n S. Ogio \\altaffilmark{6},\n J. R. Patterson \\altaffilmark{2},\n G. P. Rowell \\altaffilmark{7},\\\\\n K. Sakurazawa \\altaffilmark{6},\n Y. Sato \\altaffilmark{7},\n R. Susukita \\altaffilmark{12},\n R. Suzuki \\altaffilmark{6},\n T. Tamura \\altaffilmark{13},\\\\\n T. Tanimori \\altaffilmark{6},\n G. J. Thornton \\altaffilmark{2},\n S. Yanagita \\altaffilmark{8},\n T. Yoshida \\altaffilmark{8} \n and T. Yoshikoshi \\altaffilmark{7}}\n\n\\altaffiltext{1}{Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya 464-8601, Japan}\n\\altaffiltext{2}{Department of Physics and Mathematical Physics, University of Adelaide, South Australia 5005, Australia}\n\\altaffiltext{3}{Institute of Space and Astronautical Science, Sagamihara 229-8510, Japan}\n\\altaffiltext{4}{Department of Physics, Yamagata University, Yamagata, Yamagata 990-8560, Japan}\n\\altaffiltext{5}{Faculty of Management Information, Yamanashi Gakuin University, Kofu 400-8575, Japan}\n\\altaffiltext{6}{Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan}\n\\altaffiltext{7}{Institute for Cosmic Ray Research, University of Tokyo, Tokyo 188-8502, Japan}\n\\altaffiltext{8}{Faculty of Science, Ibaraki University, Mito 310-8521, Japan}\n\\altaffiltext{9}{Department of Physics, Kyoto University, Kyoto 606-8502, Japan}\n\\altaffiltext{10}{National Astronomical Observatory of Japan, Tokyo 181-8588, Japan}\n\\altaffiltext{11}{Department of Physics, Tokai University, Hiratsuka 259-1292, Japan}\n\\altaffiltext{12}{Institute of Physical and Chemical Research, Wako 351-0198, Japan}\n\\altaffiltext{13}{Faculty of Engineering, Kanagawa University, Yokohama 221-8686, Japan}\n\\altaffiltext{14}{present address; LPNHE, Ecole Polytechnique, Palaiseau CEDEX 91128, France; sako@poly.in2p3.fr}\n\\altaffiltext{15}{present address; LAL, Universite de Paris-Sud, BP 34, ORSAY CEDEX 91898, France}\n\n\n\\begin{abstract}\nThe gamma-ray pulsar PSR B1509$-$58 and its surrounding nebulae have been\nobserved with the CANGAROO 3.8m imaging atmospheric \\v{C}erenkov telescope.\nThe observations were performed from 1996 to 1998 in Woomera, \nSouth Australia, under different instrumental conditions with\nestimated threshold energies of 4.5 TeV (1996), 1.9 TeV (1997) \nand 2.5 TeV (1998) at zenith angles of $\\sim$ 30$^{\\circ}$.\nAlthough no strong evidence of the gamma-ray emission was found,\nthe lowest energy threshold data of 1997 showed a marginal excess of \ngamma-ray--like events at the 4.1 $\\sigma$ significance level.\nThe corresponding gamma-ray flux is calculated to be\n$\\rm (2.9\\,\\pm\\,0.7) \\times 10^{-12}\\,cm^{-2}s^{-1}$ \nabove 1.9 TeV.\nThe observations of 1996 and 1998 yielded only upper limits (99.5\\% \nconfidence level) of\n$\\rm 1.9 \\times 10^{-12}\\,cm^{-2}s^{-1}$ above 4.5 TeV\nand\n$\\rm 2.0 \\times 10^{-12}\\,cm^{-2}s^{-1}$ above 2.5 TeV, respectively.\nAssuming that the 1997 excess is due to Very High-Energy (VHE)\ngamma-ray emission from the pulsar nebula,\nour result, when combined with the X-ray observations, leads to a value of the\nmagnetic field strength $\\simeq$ 5 $\\mu$G.\nThis is consistent with the equipartition value previously estimated in the\nX-ray nebula surrounding the pulsar.\nNo significant periodicity at the 150\\,ms pulsar period has been \nfound in any of the three years' data.\nThe flux upper limits set from our observations are one order of magnitude\nbelow previously reported detections of pulsed TeV emission.\n\\end{abstract}\n\n\\keywords{gamma-rays: observations --- pulsars: individual (PSR B1509$-$58)\n--- supernova remnants}\n\n\\section{Introduction} \\label{INTRO}\nPulsar nebulae have been suggested as a possible acceleration site of \nhigh-energy particles in the galaxy (\\cite{har90}).\nThe first order Fermi acceleration mechanism is expected to occur in a\nshock between the pulsar wind and supernova ejecta, or interstellar matter.\nEvidence of such energetic phenomena has been obtained through observation of\nsynchrotron emission by accelerated electrons and positrons at radio to \ngamma-ray ($\\leq$ 10 GeV) energies.\nHowever, more direct evidence has become obtainable through Very \nHigh-Energy (VHE) gamma-ray ($\\geq$ 300 GeV) observations over the last decade\nusing the Imaging Atmospheric \\v{C}erenkov Technique (IACT).\n\nVHE gamma-ray emissions from the directions of three energetic pulsars,\nthe Crab (\\cite{wee89}; \\cite{vac91}; \\cite{tan94});\nthe Vela pulsar (\\cite{yos97}) and PSR B1706$-$44 (\\cite{kif95}, \\cite{cha97}),\nhave been detected by ground-based telescopes using the IACT.\nAlthough all three pulsars show pulsed emission in the {\\it EGRET} energy\nrange (100MeV--10GeV), none of the VHE gamma-ray detections have shown any\nperiodicity at the radio pulsar period.\nThis steady VHE gamma-ray emission is usually explained to be a result of the \ninverse Compton scattering in the pulsar nebula, and not from the pulsar\nmagnetosphere.\nWhile the mechanism of the emission from the Crab nebula is well studied\n(see, for example, \\cite{jag96}), information on other pulsars is still\nsparse.\nIn order to study pulsars and their surrounding environment\nas possible acceleration sites of the cosmic rays, more examples in the VHE\ngamma-ray range are required.\n\nPSR B1509$-$58 was discovered as an X-ray pulsar by Seward and Harnden (1982)\nusing the {\\it Einstein X-ray Observatory}.\nIt is near the center of the supernova remnant MSH15$-$52 (G320.4$-$1.2).\nSoon after this discovery, pulsed radio emission was found by \nManchester, Tuohy and D'Amico (1982).\nThe pulsar has a period of 150 msec and a period derivative of \n1.5 $\\times$10$^{-12}$ ss$^{-1}$, the largest known today. \nThe characteristic age of the pulsar is \nestimated to be $\\sim$1700 years (\\cite{man98}), which makes it the second \nyoungest pulsar after the Crab.\n\\altaffilmark{1}\n\\altaffiltext{1}\n{ Torii et al.\\ (1997) have reported the discovery of a pulsar 1600 years\nold.\nThis age is somewhat speculative however as the period derivative of the \npulsar has not yet been measured and\nan association with a historical supernova was assumed to estimate\nthe pulsar age.}\nFrom the period and the large period derivative, a very strong\nsurface magnetic field of 1.5 $\\times$ 10$^{13}$ G and a large spin down\nenergy loss rate of 1.8 $\\times$ 10 $^{37}$ ergs s$^{-1}$ are implied.\nWhile the distance to the pulsar is relatively large (4.4 kpc, \\cite{tay95}),\nthe expected energy flux received at the Earth is the fifth largest among the\nknown pulsars.\n\nA compact ($\\rm\\sim\\,10^{\\prime}\\,\\times\\,6^{\\prime}$) synchrotron X-ray nebula\nhas been found to exist around PSR B1509$-$58 (\\cite{sew84}).\nThe synchrotron emission suggests the existence of non-thermal electrons\n(positrons) in the nebula, which will also emit VHE gamma-rays \nvia inverse Compton scattering. \nA detectable VHE gamma-ray flux from this synchrotron nebula was predicted\nby du Plessis et al.\\ (1995) as a function of the magnetic field strength in\nthe nebula.\nThe expected gamma-ray flux above 1 TeV of 10$^{-11}$ to \n10$^{-12}\\,cm^{-2}s^{-1}$ for nebula magnetic fields 4 to 10 $\\mu$G is within\nthe sensitivity of the CANGAROO 3.8m telescope.\nThus, VHE observations should give a good measurement of the magnetic field\nstrength of this nebula.\nDu Plessis et al.\\ (1995) also predicted a very hard differential spectral \nindex of $\\sim$1.8 based on the X-ray observations.\nThis prediction provides us with an extreme example of the utility of\nmultiwavelength studies of synchrotron---inverse- Compton emitting objects.\nBesides the compact nebula, recent X-ray satellite observations suggest\nvarious non-thermal phenomena in this remnant.\n{\\it ROSAT} observations indicate a non-thermal X-ray component from the\ncentral diffuse nebula (CDN) extending to a diameter of 50$^{\\prime}$ \n($\\sim$ 60pc) centered on the pulsar (\\cite{tru96}).\n{\\it ASCA} observations revealed a non-thermal jet structure between the \npulsar and the center of a thermal nebula about 10$^{\\prime}$ north from the\npulsar (\\cite{tam96}).\nIn order to explain the effective thermalization process of the thermal nebula,\nTamura et al.\\ (1996) indicate the existence of accelerated ions as well as\nelectrons in the jet.\nFurthermore, Gaensler et al.\\ (1998) found synchrotron emission from compact \nknots in this thermal nebula from 20cm imaging observations with the\nAustralia Telescope Compact Array.\n\nThe surface magnetic field strength of the pulsar PSR B1509$-$58 is estimated \nto be one of the largest among known pulsars.\nDue to the photon splitting process caused by this strong surface magnetic \nfield, a cut-off in the pulsed emission around MeV energies is predicted\nby Harding, Baring and Gonthier (1997).\nIn fact, Kuiper et al.\\ (1999) have suggested that a cut-off around 10 MeV\nexists in the {\\it COMPTEL} data.\n{\\it EGRET} observations have resulted in only an upper limit for the pulsed \nemission from PSR B1509$-$58 (\\cite{tho94}).\nIn contrast, Nel et al.\\ (1992) have reported the detection of transient \npulsed VHE gamma-rays from the observations between 1985 and 1988\nbased on ground--based (non-imaging) \\v{C}erenkov telescope observations.\nHowever they could not detect any significant pulsed emission in the\nsuccessive years.\nThey tried to explain their observations with the framework of the outer gap\nmodel (\\cite{chr86}).\n(Bowden et al.\\ (1993) reported a upper limit of the pulsed emission above\n0.35 TeV from their observations in 1987 and 1989.\nCombining with the detection by Nel et al.\\ (1992) in 1987 above 1.5 TeV,\npower law index of the integral energy spectrum is limited to be harder than\n$\\sim$ 1.)\nInterestingly, Kuiper et al.\\ (1999) also indicate a marginal detection of the\npulsed emission above 10 MeV, where the origin may\ndiffer from that at lower energies.\nConsequently, we have examined our data for the presence of periodicity as \nwell.\nOur observations are the first results on this pulsar with using the\nIACT, which is one order of magnitude more sensitive than \nnon-imaging observations.\n\nFor the reasons given above, we believed that PSR B1509$-$58 would be an\ninteresting object to study above 1 TeV energies with the CANGAROO 3.8m\nIACT telescope in both the steady nebula emission and the pulsed emission.\nDetails of those observations are given in Section-\\ref{OBS}.\nThe methods of the analysis and results are shown in Section-\\ref{ANA}. \nIn Section-\\ref{DIS}, we summarize our results and discuss their\nimplications.\n\n\\section{Observations} \\label{OBS}\nThe CANGAROO (Collaboration between Australia and Nippon (Japan) for a\nGAmma-Ray Observatory in the Outback) 3.8m telescope is located at Woomera,\nSouth Australia\n(136$^{\\circ}$47$^{\\prime}$E, 31$^{\\circ}$6$^{\\prime}$S and 160m a.s.l.).\n\\v{C}erenkov photons emitted from extensive air showers originated by\nprimary gamma-rays and cosmic rays are collected with a parabolic mirror of\n3.8m diameter and detected with an imaging camera at the focal plane.\nThe camera consists of 256 photomultiplier tubes (PMTs) of 10mm$\\times$10mm\nsize (Hamamatsu R2248).\nThe PMTs are located in a 16$\\times$16 square grid and the field of view\namounts to 3$^{\\circ} \\times$ 3$^{\\circ}$.\nWhen signals from more than 5 tubes exceed 3 photoelectrons each within a \ngate, a trigger is generated.\nThe amplitude and relative time of each PMT signal, the event time,\nand the counting rate of each tube are recorded for each event.\nThe absolute time can be obtained with a precision of 200 nsec using a GPS\nclock.\nIn addition to the GPS clock, the time of a crystal clock with a precision of\n100$\\mu$sec is also recorded.\nThe GPS clock was not available in the 1997 observations due to the\ninstallation work of our new data acquisition system.\nHowever, because the time indicated by the crystal clock shows a stable drift\nfrom that of the GPS clock, we can obtain accurate {\\it relative} arrival \ntimes for events even without the GPS clock.\nThe crystal clock is reset every observation (new moon) period.\nTherefore, a periodicity analysis based on this clock is valid on a \nmonth by month basis.\nGPS timing was restored in July 1997.\nDetails of the camera and the telescope are described in Hara et al.\n(1993).\n\nThe telescope was pointed in the direction of the pulsar PSR B1509$-$58\n(right ascension 15$^{h}$13$^{m}$55$^{s}$.62 and declination\n--59$^{\\circ}$ 08$^{\\prime}$ 08$^{\\prime\\prime}$.9 (J2000), \\cite{tay95})\nin May and June in 1996, from March to May in 1997 and from March to May in\n1998.\nThe pulsar (ON source) and an offset region (OFF source), having the same \ndeclination as the pulsar but different right ascension, were observed for\nequal amounts of time each night under moonless and usually clear sky \nconditions.\nTypically, the ON source region is observed only once in a night around \ntransit for a few hours.\nTwo OFF source runs are carried out before and after the ON source run.\nThe former one covers the first half of the ON source track and\nthe latter covers the second half.\nIn the off-line analysis, those data obtained when a small patch of cloud was\nobscuring the source are omitted.\nAt the same time, the corresponding ON (or OFF) source data \nwere also rejected from the analysis.\nIn addition to the weather selection, the data taken when the electronics\nnoise produced an anomalously large trigger rate were not used in the analysis.\nThis happened in the 1996 observations.\nIn the 1998 data, there are many nights which have a large difference of the \nevent rate between the ON and OFF source regions, which is thought to be due to the \npresence of thin dew on the reflecting mirror.\nData taken under these conditions were also omitted. \nThe durations of selected observations after these procedures are\n$\\rm 26^{h}30^{m}$ , $\\rm 32^{h}08^{m}$ and $\\rm 21^{h}14^{m}$\nfor the 1996, 1997 and 1998 (both ON and OFF) data, respectively.\nThese data are used for the analysis in this paper.\n\nObservations were carried out under different instrumental conditions in each\nyear.\nDuring the 1996 observations, the reflectivity of the mirror was estimated to\nbe $\\simeq$ 45\\%.\nWe recoated the mirror in October 1996 by vacuum evaporation of aluminium at\nthe Anglo Australian Observatory.\nAs a result, the reflectivity of the mirror increased to about 90\\%.\nAs the reflectivity was improved, the threshold energy of our telescope \nwas lowered.\nFor the 1997 observations, the threshold energy,\ndefined here as the energy at which a\ndifferential photon flux with an assumed differential spectral index of 2.5\nis maximized \nin the Monte Carlo calculations, was estimated to be 1.9 TeV,\ncompared to 4.5 TeV before the recoating.\nBy the 1998 observations, the reflectivity had decreased to $\\simeq$ 70\\%, \ncorresponding to a threshold energy of 2.5 TeV.\nIn these estimations, the selection effect of the analysis described\nin the next section is also taken into account.\nIn the Monte Carlo calculation, we assumed that the observations were made at \na zenith angle of 30$^{\\circ}$, which was close to the average value for our \nobservations on PSR B1509$-$58.\n\nThe observation times and threshold energies are summarized in \nTable~\\ref{obssum}, and as well, the analysis results are shown.\n\n\\placetable{obssum}\n\n\\section{Analysis and Results} \\label{ANA}\n\\subsection{Analysis method}\nAt the beginning of each run, the ADC pedestal and gain for each PMT were\nmeasured.\nTo calibrate the gain, a blue LED located at the center of the mirror is used\nto illuminate the PMTs uniformly.\nThe pedestal value is subtracted from the ADC value and any\nvariations in the PMT gains were normalized using the LED calibration data.\nPMTs whose TDC value corresponded to a pulse arrival time within \n$\\pm$ 30 nsec of the shower plane were regarded as \\lq hit \\rq ~tubes and used \nto calculate image parameters.\nAfter omitting some hit tubes which were isolated or which had ADC values\nless than one standard deviation above the pedestal value, the conventional\nimage parameters (\\cite{hil85}) were calculated.\n(In the 1996 data, a fifth of the PMTs at the bottom in the camera were\nomitted from analysis to avoid the effect of electronics noise.\nThis makes the threshold energy higher and the effective area smaller.\nThis effect is included in calculating the threshold energy and the flux \nupper limit.)\n\nThe parameter ranges determined from Monte Carlo simulations to optimize\nthe gamma-ray signals are $\\colon$\n$0^{\\circ}.60<$ {\\it distance} $\\leq1^{\\circ}.30$,\n$0^{\\circ}.04<$ {\\it width} $\\leq 0^{\\circ}.09$,\n$0^{\\circ}.10<$ {\\it length} $\\leq0^{\\circ}.40$, \n$0.35<$ {\\it concentration} $\\leq0.70$ \nand $\\alpha\\,\\leq10^{\\circ}$.\nThese ranges are slightly narrower than those used in case of the Vela\nanalysis (\\cite{yos97}).\nThe upper limit of $\\alpha$, $10^{\\circ}$, is adopted assuming the source is\na point-like.\nTwo orientation parameters, $\\alpha$ and {\\it distance}, are defined with\nrespect to the assumed source position in the field of view.\nIn this paper, this is fixed at the pulsar position except in the spatial \nanalysis discussed in Section-\\ref{MAP}.\nTo avoid the effect of incomplete images near the edge of the camera,\nimages with centroids located at greater than $1^{\\circ}.05$ from the center\nof the camera were also rejected.\nWe also required that the number of hit tubes ($N_{hit}$) must be $\\geq$\n5 and the total number of photo-electrons contained in an image ($N_{p.e.}$)\nmust be $\\geq 40$ to be able to obtain good image parameters and select\nonly air shower induced events.\nThe upper limit of $N_{p.e.}$ is large enough to accept all real\nevents with large numbers of photo-electrons.\nIn Table~\\ref{obssum}, the numbers of events in the raw data and selected\nare presented.\nWe can find a large difference between ON and OFF in the raw data.\nThe main reasons of the difference in number are the electronics noise \nin the 1996 data and the existence of the optically bright stars \n(M$_{V}$ = 4.1 and 4.5) in the field of view in the 1997 data,\nwhere the reflectivity of the mirror was the largest.\nHowever, the numbers match well after the selection of air shower events. \nFor all the three years' data analyses we applied the same criteria as\ndescribed above.\n\n\\subsection{Results of the image analysis}\nThe distributions of the orientation angle ($\\alpha$) after all other cuts\nwere applied are shown in Figure~\\ref{Fig1}.\n\n\\placefigure{Fig1}\n\nAlthough there was no statistically significant excess of the ON source counts\nover the OFF source seen in the 1996 data, the 1997 data shows an excess at \n$\\alpha\\leq10^{\\circ}$ with a statistical significance of 4.1$\\sigma$.\nThis excess may indicate the presence of a VHE gamma-ray signal from the \nsource.\nThe additional use of the {\\it asymmetry} parameter showed an\nexcess in the positive (gamma-ray--like) domain, though not at a level\nwhich would have increased the overall significance of the excess.\nMore careful study would be necessary in use of this third-moment\nparameter for the source near the Galactic Center, where the night-sky\nbackground level is high.\nIn the 1998 data, we find a small excess in the ON source counts, however,\nthe statistical significance is only 1.4$\\sigma$ at $\\alpha\\leq10^{\\circ}$.\nHereafter, we regard the 1996 and 1998 results as non-detections of the VHE\ngamma-ray signal and treat the 1997 result as a marginal detection.\nThe corresponding upper limits and flux are calculated as,\n\n$\\rm F_{99.5\\%}(E\\,\\geq\\,4.5\\,TeV)\\,\\leq\\,1.9 \\times 10^{-12}~cm^{-2}~s^{-1}$\n\n$\\rm F(E\\,\\geq\\,1.9\\,TeV)=(2.9\\,\\pm\\,0.7) \\times 10^{-12}~cm^{-2}~s^{-1}$\n\n$\\rm F_{99.5\\%}(E\\,\\geq\\,2.5\\,TeV)\\,\\leq\\,2.0 \\times 10^{-12}~cm^{-2}~s^{-1}$\n\n\n\\noindent\nfor 1996, 1997 and 1998 results, respectively.\nHere, a differential energy spectral index of 2.5 is assumed.\nThe upper limits and the errors in the flux are estimated based on the numbers\nof the observed counts.\nWe note that in our calculation of the upper limits the difference of\nthe counts between ON and OFF are also taken into account following the\nformula introduced by Helene (1983).\nSo the 1998 flux upper limit becomes higher than that from completely\nnull result.\nIf we change the assumption of the differential energy spectral index over\nthe range \n$2.5~\\pm~1.0$, the corresponding threshold energies are estimated to change\nby $\\sim\\mp$30\\%.\nInstrumental uncertainties also affect the estimation of the threshold\nenergies.\nWe estimate the systematic error in determining the absolute threshold \nenergies to be about 40$\\sim$50\\%.\nHowever, because almost all of the systematic errors behave in the same way \nfor the three years' observations, the uncertainty of the relative threshold\nenergy is smaller than this value.\n\n\\subsection{Consistency and Stability}\nThe positive indication is obtained only from the lowest threshold energy \nobservation.\nBut the derived flux and two flux upper limits require neither variability \nof the source nor a very soft spectral index, that is, the results from the\nthree years are consistent with each other assuming stable emission with a \nCrab-like spectral index ($\\sim 2.5$) or the harder index (1.8) expected\nby du Plessis et al.\\ (1995). \nWe also divided the 1997 data into separate new moon periods to check on\nconsistency.\nThe results are shown in Table~\\ref{obssum}.\nEach month's result has a marginal positive effect on the final result.\nThe excess counting rate is stable during the three observation seasons\nwithin the statistical errors.\n\n\\subsection{Spatial analysis} \\label{MAP}\nPSR B1509$-$58 and its surrounding environment are complex and there are\nindications from X-ray data that non-thermal phenomena possibly occur \nover an extended area of this remnant.\nSo it is possible that the gamma-ray--like signal in the 1997 data is not from\na point source at\nthe pulsar position but from some other region near the pulsar.\nTherefore we have carried out a source search in the $2^{\\circ}\\times2^{\\circ}$\nfield of view centered on the pulsar position.\nTo do this, we shifted the position of the assumed source over a grid of points\naround the pulsar and repeated the analysis at each point to obtain the excess\ncounts in the $\\alpha$ distribution.\nThe resultant map of the significance is shown in Figure~\\ref{Fig4}.\n\n\\placefigure{Fig4}\n\nThe peak of the excess is found at $0^{\\circ}.1$ south-west from the pulsar.\nBut when we consider the degrees of freedom of the search, the significance\nat this maximum should be reduced. \nAnd also, from a Monte Carlo calculation, where the observed counts of signal\nand background are taken into account, we estimated that the precision to \ndetermine the source position is $0^{\\circ}.10$ at the 1$\\sigma$ level.\nWe conclude, therefore, that the position of the excess is consistent with \nthe pulsar position within the statistics of our observations.\n\n\\subsection{Periodicity analysis}\nThe recorded arrival times of the gamma-ray--like signals ($\\alpha \\le\n10^{\\circ}$ after all the image cuts) were converted to the Solar System\nBarycenter arrival times using the solar system ephemeris based on\nepoch 2000 (DE200) (Standish, 1982).\nWe then carried out a phase analysis with the phase parameters summarized \nin Table~\\ref{tbl-eph} (\\cite{man98}).\nBecause Nel et al.\\ (1990) pointed out a possibility of a light curve with \ntriple peaks in the TeV energy range, we applied the H-test (\\cite{jag89})\nto obtain the statistical significance.\nThe virtue of the H-test lies in the fact that it \nrequires no assumptions about bin size and bin location and is \nalso independent of the shape of the\nlight curve.\nThe results are summarized in Table~\\ref{tbl-1}.\n\n\\placetable{tbl-1}\n\nThe results of 1997 are divided into separate observational periods (months), \nbecause GPS timing information was not available in 1997 as mentioned in \nSection-\\ref{OBS}. \nThe relative arrival time of the events is calculated for the 1997 data from \nthe time of the crystal clock, having a constant drift rate \nrelative to the GPS clock.\nThe H-statistics and the corresponding probabilities against a uniform\ndistribution are shown in Table~\\ref{tbl-1}.\nNo evidence for the 150\\,ms periodicity is found in any of the observation \nseasons. \nTo calculate the flux upper limit for the pulsed emission, we used the formula\ngiven by de Jager (1994).\nThis formula combines the observed counts (N) and pulsed fraction (p) through\na parameter, $\\chi$, as, $\\chi = p \\sqrt{N}$.\nWhen the H-statistic is considered as a non-detection of periodicity, $\\chi$\ngiving 3 $\\sigma$ upper limit of p is expressed as,\n\n\\[ \\chi_{3\\sigma} = ( 1.5 + 10.7 \\delta ) ( 0.174 H ) ^{0.17+0.14\\delta} \n exp \\left[ ( 0.08 + 0.15\\delta ) \\left\\{ log_{10}(0.174H) \\right\\}^{2} \n \\right]\n\\]\n\nHere, H is the value of the H-test as shown in Table~\\ref{tbl-1}.\n(For H$<$0.3 we should take H=0.3 in calculating $\\chi_{3\\sigma}$.)\n$\\delta$ is the duty cycle of the pulse profile.\nIn case of PSR B1509$-$58, we assumed $\\delta$ to be 0.3 using the X-ray\nobservation by Kawai et al.\\ (1991).\nThe 3$\\sigma$ upper limits for the pulsed VHE gamma-ray emission are also shown\nin Table~\\ref{tbl-1}.\n\n\\section{Discussion} \\label{DIS}\nOur observations can be summarized as follows $\\colon$ \n(1) In the observations with the lowest detection threshold energy, \na 4.1$\\sigma$ excess of gamma-ray--like events is found.\nNull results in the observations of the other years (when the detection\nthreshold energies were higher) are not in conflict with\nthis marginal positive result $\\colon$\nneither variability of the source nor an especially soft energy spectrum\nneeds to be invoked.\n(2) From the result in the 1997 observations, there is no evidence\nof a variability on a monthly time-scale during three observation seasons.\n(3) In the 1997 data, the peak emission source position is shifted slightly \nto the south-west direction from the pulsar position.\nHowever, considering the statistical error including the real event numbers\nobserved, this is consistent with the pulsar position.\n(4) The periodicity of the events modulated with the radio pulsar period \nis studied.\nWe found no evidence of the 150~ms pulsar periodicity using the H-test \nin any of the observations for three years.\n\nThe statistical significance of the 1997 excess, 4.1$\\sigma$, is too small\nto claim as the detection of a VHE gamma-ray source, however, \nit is sufficiently suggestive to allow discussion supposing \nthe excess was due to a VHE gamma-ray signal.\nWith this scheme\nthe simplest and most straightforward explanation can be made assuming \nthat the emission is found from the pulsar nebula surrounding the pulsar.\nVHE gamma-ray emission from a pulsar nebula is usually considered as a result\nof inverse Compton scattering by relativistic electrons.\nFrom the emission processes of synchrotron and inverse Compton radiations, a \nsimple equation, \n$\\rm \\frac{\\dot{E}_{synch}}{\\dot{E}_{iC}}=\\frac{\\epsilon_{B}}{\\epsilon_{ph}}$,\ncan be obtained.\nHere $\\rm \\dot{E}_{synch}$ and $\\rm \\dot{E}_{iC}$ are the luminosities through\nsynchrotron radiation (mainly resulting in quanta in the X-ray energy range)\nand inverse Compton scattering (mainly producing VHE gamma-rays), respectively,\nand $\\rm\\epsilon_{B}$ and $\\rm\\epsilon_{ph}$ are the energy densities of the \nmagnetic field and the target photons for inverse Compton scattering at the\nemission region.\nAssuming isotropic emission of both X-rays and gamma-rays,\n$\\rm \\frac{\\dot{E}_{synch}}{\\dot{E}_{iC}}$ can be equated to\n$\\rm \\frac{F_{synch}}{F_{iC}}$.\nHere $\\rm F_{synch}=7.2\\times10^{-11}~ergs~cm^{-2}\\,s^{-1}~(0.1-2.4\\,keV)$\nas given by Trussoni et al.\\ (1996) and \n$\\rm F_{iC}=2.7\\times10^{-11}~ergs~cm^{-2}\\,s^{-1}$, \nobtained by integrating the 1997 flux\nabove 1.9\\,TeV assuming a \ndifferential spectral index of 2.5.\n(The corresponding luminosity at the pulsar, $L_{iC}$, is \n$\\rm 6.2\\times10^{34}~ergs~s^{-1}$ assuming the pulsar distance of 4.4 kpc.\nThat is 0.34\\% of the pulsar rotating energy loss.)\nIf the 3\\,K Microwave Background Radiation (MBR) is the only target of the \ninverse Compton radiation, {\\it i.e.},\n$\\rm \\epsilon_{ph}=\\epsilon_{3K}=3.8\\times10^{-13}~ergs~cm^{-3}$, \none obtains\n$\\rm \\epsilon_{B}= 1.0\\times10^{-12}~ergs~cm^{-3}$.\nThis, then, leads to a value for the magnetic field strength\n$\\rm B\\,\\simeq\\,5\\,\\mu G$.\nConsidering the large uncertainties in the arguments above, this value agrees\nwell with the previously estimated value of $\\rm B\\,\\simeq\\,7\\,\\mu G$,\nfrom the equipartition of energy between the particles and the magnetic\nfield (\\cite{sew84}).\nAccording to the prediction of du Plessis et al.\\ (1995), our result \ncorresponds to a magnetic field strength of $\\rm B~\\simeq~5~\\mu G$.\nThese three estimated values of the magnetic field agree very well with each\nother.\n\nAn alternative source of the target photons is the IR source IRAS 15099$-$5856,\nknown to be positionally coincident with the pulsar (\\cite{are91}).\nDu Plessis et al.\\ (1995) estimated that the contribution from the IR photons\nto the VHE gamma-ray flux would be at the same level as that from the 3\\,K MBR.\nHowever the association between IRAS 15099$-$5856 and the pulsar is uncertain.\nIn case that the IRAS source found at 25$\\mu$m supplies the target photon for \nthe inverse Compton process, the resultant VHE gamma-ray spectrum is expected\nto be softer than that made from the 3\\,K MBR.\nThis is because the critical energy of the parent electrons in the \nKlein-Nishina cross section is $\\sim~6~\\times~10^{12}$ eV against 25$\\mu$m\nIR radiation while it is $\\sim~10^{15}$ eV for the 3\\,K MBR.\nTherefore, the VHE gamma-ray spectrum should have a rapid softening over the \nTeV energy range.\nTo understand the association of this IRAS source, detailed spectral\nmeasurements with future observations are required as well as the X-ray \nobservations discussed below.\n\nWhile our observations do not place any interesting limit on the spectral\nindex, the very hard spectrum predicted by du Plessis et al.\\ (1995)\nshould be discussed.\nTheir prediction was based on the observational\nresults of the X-ray spectrum which showed a hardening of the index in the\nenergy range below a few keV (photon index 1.4$^{+0.4}_{-0.2}$ below 4\\,keV \nwhile 2.15$\\pm$0.02 between 2 keV and 60 keV).\nHowever, recent X-ray observations do not confirm this hardening.\nThe photon indices obtained in the wide X-ray energy band are consistent with \na value around 2.2 (\\cite{tru96}; \\cite{tam97}; \\cite{mar97}) though\nthe error of the ROSAT result is large.\nTo discuss the synchrotron spectrum in detail, we need information from \nradio observations. \nBut, even with the recent high resolution observations, a radio pulsar wind \nnebula has not been discovered (\\cite{gae98}).\n \nThe upper limits set to the periodic signal in this paper are one order of\nmagnitude below the previously reported flux in the same energy band \n(\\cite{nel92}).\nAlthough Nel et al.\\ reported upper limits from observations after 1988,\nour results should provide a far stricter limit on models.\nThe VHE pulsed emission is in conflict with the observed cut-off around 10\nMeV as predicted by the polar-cap model.\nTo explain the VHE pulsed emission, an additional hard component,\nprobably outer-gap emission, is required.\nFuture observations by GLAST may reveal the existence of this component and\nstudies of its flux and spectral variability may hint at \nlarge variability in the VHE range.\nThe flux of the transient VHE pulsed emission reported in 1985,\n$\\rm F(E\\,\\geq\\,1.5\\,TeV)=(3.9\\,\\pm\\,0.9) \\times 10^{-11}~cm^{-2}~s^{-1}$,\nwould make this source the brightest known VHE gamma-ray source in the \nsouthern hemisphere.\nWe could detect this kind of activity even with short duration monitoring.\nSemi-simultaneous monitoring of this pulsar with the future large IACT \narrays in the southern hemisphere (CANGAROO-III, HESS) and GLAST\nwould be of great interest if the pulsar were to display such an\nactive phase in the future.\n\nFinally, it is notable that, unlike the other pulsar nebulae detected at\nVHE energies, PSR B1509$-$58 is not firmly detected by \n{\\it EGRET} onboard the {\\it CGRO} satellite.\nIn contrast, this pulsar and its surroundings show a variety of the\nnon-thermal phenomena as introduced in Section-\\ref{INTRO}.\nA comparison of nonthermal X-ray emission with VHE gamma-ray emission is\nbecoming very useful in the search for VHE gamma-ray sources and study of \ntheir environment.\nCombined with the recent studies of pulsar nebulae (\\cite{kaw96}), \nthe new generation of the Imaging Atmospheric \\v{C}erenkov Telescopes\n(e.g.\\ \\cite{mat97}) will result in an improved understanding of pulsar \nnebulae and particle acceleration.\nThe CANGAROO~II 7m telescope started observations at Woomera in mid-1999.\nFrom new observations with a lower energy threshold, we will be able to \nmeasure the\ngamma-ray spectrum precisely and obtain a better estimation of the \nphysical parameters, especially the magnetic field strength, \nin pulsar nebulae. \n\n\\acknowledgments\nThis work is supported by a Grant-in-Aid in Scientific Research from the Japan\nMinistry of Education, Science, Sports and Culture, and also by the Australian\nResearch Council.\nWe would like to thank to Dr. R. N. Manchester who provided us the latest \nradio ephemeris data on the pulsar.\nWe are grateful to the AAO staffs in the recoating work of the 3.8m mirror.\nThe receipt of JSPS Research Fellowships (JH, AK, TN, GPR, KS, GJT and \nTY) is also acknowledged.\nFinally, we thank the anonymous referee whose comments helped us improve\nthe manuscript.\n\n\\clearpage\n\\begin{deluxetable}{ccccccc}\n\\footnotesize\n\\tablecaption{\nSummary of the observations and the analysis results.\nThe number of events in the ` After noise reduction' column are those\nremaining after the \n$N_{hit}$ and $N_{p.e.}$ cuts are applied to obtain the\nnumber of air shower events.\nFlux upper limits for the 1996 and 1998 data are calculated as a\n99.5$\\%$ confidence level.\nFor the 1997 data, the results in each newmoon season are also presented\nwith the excess counts per minute. \n\\label{obssum}}\n\\tablewidth{0pt}\n\\tablehead{ \n & & Threshold \n & \\multicolumn{3}{c}{Number of Events} \n & Flux or Upper Limit \\\\ \n Observation & Time & Energy & & After noise & After image \n & ($\\times 10^{-12} cm^{-2} s^{-1}$) \\\\\n Period & (min) & (TeV) & Recorded & reduction & selection &\n} \n\\startdata\n1996 ON & 1590 & 4.5 & 91622 & 16111 & 170 & $<$1.9 \\nl\n$~~~~~~~~$OFF & 1590 & & 99948 & 17297 & 169 & \\nl\n1997 ON & 1928 & 1.9 & 367689 & 106624 & 1388 & 2.9 \\nl\n$~~~~~~~~$OFF & 1928 & & 282156 & 106772 & 1180 & \\nl\n1998 ON & 1274 & 2.5 & 89752 & 26543 & 345 & $<$2.0 \\nl\n$~~~~~~~~$OFF & 1274 & & 90002 & 26705 & 309 & \\nl\n & & & & & & (excess/min) \\nl\nMarch 1997 ON & 345 & & 73742 & 19440 & 261 & 0.10$\\pm$0.06 \\nl\n$~~~~~~~~~~~~~~~$OFF & 345 & & 62193 & 19610 & 227 & \\nl\nApril 1997 ON & 598 & & 101909 & 33504 & 426 & 0.12$\\pm$0.05 \\nl\n$~~~~~~~~~~~~~~~$OFF & 598 & & 82334 & 33610 & 381 & \\nl\nMay 1997 ON & 985 & & 192038 & 53680 & 701 & 0.13$\\pm$0.04 \\nl\n$~~~~~~~~~~~~~~~$OFF & 985 & & 137629 & 53552 & 572 & \\nl\n \n\\enddata\n\\end{deluxetable}\n\\clearpage\n\n\n\\begin{deluxetable}{ll}\n\\footnotesize\n\\tablecaption{Pulsar timing data (from radio observation) used in the \nperiodicity analysis (\\cite{man98}).\n\\label{tbl-eph}}\n\\tablewidth{0pt}\n\\tablehead{ \n Parameter & Value\n} \n\\startdata\nValidity range (MJD) & 50114 -- 51094 \\nl\n$\\nu_{0}$ (s$^{-1}$) & 6.6244525661182 \\nl\n$\\dot{\\nu}_{0}$ (s$^{-2}$) & -6.73155 $\\times$ 10$^{-11}$ \\nl\n$\\dot{\\nu}_{0}$ (s$^{-3}$) & 1.95 $\\times$ 10$^{-21}$ \\nl\nt$_{0}^{geo}$ (MJD) & 50604.000000816 \\nl\n\\enddata\n\\end{deluxetable}\n\\clearpage\n\n\n\\begin{deluxetable}{cccc}\n%\\begin{center}\n\\footnotesize\n\\tablecaption{Results of the periodicity analysis. \nThe H-test statistics for each year are shown.\nBecause of the GPS clock problem (see text), the 1997 data are divided into\nthree observation seasons.\nChance probabilities P($>$H) are calculated against a uniform light curve \n(no periodicity).\nThe corresponding 3$\\sigma$ flux upper limits are also shown. \\label{tbl-1}}\n\\tablewidth{0pt}\n\\tablehead{ \n Observation & \\multicolumn{2}{c}{H-test} & flux upper limit\\\\ \n Period & H & P($>$H) & ($\\times 10^{-12} cm^{-2} s^{-1}$) \n} \n\\startdata\n1996 & 3.55 & 0.24 & 1.7 \\nl\nMarch 1997 & 6.37 & 0.08 & 5.2 \\nl\nApril 1997 & 0.61 & 0.78 & 2.6 \\nl\nMay 1997 & 0.84 & 0.71 & 2.1 \\nl\n1998 & 3.85 & 0.21 & 1.5 \\nl\n \n\\enddata\n%\\end{center}\n\\end{deluxetable}\n\\clearpage\n\n\n\\begin{thebibliography}{}\n\\bibitem[Arendt \\ 1991]{are91} Arendt, R. G., 1991, \\aj, 101(6), 2160\n\\bibitem[Bowden \\ 1993]{bow93} Bowden, C. C. G. et al., 1993, Proc. 23rd Internat. Cosmic Ray Conf., Calgary, 1, 294\n\\bibitem[Cheng, Ho and Ruderman \\ 1986]{chr86} Cheng, K. S., Ho, C. and Ruderman, M., 1986, \\apj, 300, 500\n\\bibitem[Chadwick et al.\\ 1997]{cha97} Chadwick, P. M. et al., 1997, Proc. 25th Internat. Cosmic Ray Conf., Durban, 3, 189\n\\bibitem[de Jager, Swanepoel and Raubenheimer \\ 1989]{jag89} de Jager, O. C., Swanepoel, J. W. H. and Raubenheimer, B. C., 1989, \\aap, 221, 180\n\\bibitem[de Jager \\ 1994]{jag94} de Jager, O. C., 1994, \\apj, 436, 239\n\\bibitem[de Jager et al.\\ 1996]{jag96} de Jager, O. C. et al., 1996, \\apj, 457, 253\n\\bibitem[du Plessis et al.\\ 1995]{ple95} du Plessis, I. et al. 1995, \\apj, 453, 746\n\\bibitem[Gaensler et al. \\ 1998]{gae98} Gaensler, B. M. et al., 1998, MNRAS, 305, 724\n\\bibitem[Hara et al.\\ 1993]{har93} Hara, T. et al., 1993, Nucl. Inst. \nMeth. Phys. Res. A, 332, 300\n\\bibitem[Harding \\ 1990]{har90} Harding, A. K., 1990, Nucl. Phys. B, 14A, 3\n\\bibitem[Harding, Baring and Gonthier \\ 1997]{hbg97} Harding, A. K., Baring, \nM. G. and Gonthier, P. L., 1997, \\apj, 476, 246\n\\bibitem[Helene \\ 1983]{hel83} Helene, O., 1983, Nucl. Inst. Meth. Phys. Res., 212, 319 \n\\bibitem[Hillas \\ 1985]{hil85} Hillas, A. M., 1985, Proc. 19th Internat.\nCosmic Ray Conf., La Jolla, 3, 445\n\\bibitem[Kawai et al.\\ 1991]{kaw91} Kawai, N. et al., 1991, \\apjl, 383, L65\n\\bibitem[Kawai and Tamura \\ 1996]{kaw96} Kawai, N. and Tamura. K., 1996, in `Pulsars$\\colon$ Problems and Progress', ASP Conference series Vol.\\ 105, eds. S. Johnston, M. A. Walker and M. Bailes, 367\n\\bibitem[Kifune et al.\\ 1995]{kif95} Kifune, T. et al., 1995, \\apjl, 438, L91\n\\bibitem[Kuiper et al.\\ 1999]{kui99} Kuiper, L. et al., 1999, A\\&A, 351, 119\n\\bibitem[Manchester, Tuohy and D'Amico\\ 1982]{man82} Manchester, R. N., Tuohy, I. R. and D'Amico, N. 1982, \\apjl, 262, L31\n\\bibitem[Manchester et al. \\ 1998]{man98} Manchester, R. N. et al., 1998, the Australian Pulsar Timing Archive, http://www.atnf.csiro.au/Research/pulsar/psr/archive/ \n\\bibitem[Marsden et al. \\ 1997]{mar97} Marsden, D. et al., 1997, \\apjl, 491, L39\n\\bibitem[Matsubara et al. \\ 1997]{mat97} Matsubara, Y. et al., 1997, in `Towards a Major Atmospheric \\v{C}erenkov Detector - V', Kruger, ed. de Jager, O. C., 447\n\\bibitem[Nel et al. \\ 1990]{nel90} Nel, H. I. et al., 1990, \\apj, 361, 181\n\\bibitem[Nel et al. \\ 1992]{nel92} Nel, H. I. et al., 1992, \\apj, 398, 602\n\\bibitem[Seward and Harnden\\ 1982]{sew82} Seward, F. D. and Harnden, F. R. 1982, \\apjl, 256, L45\n\\bibitem[Seward et al.\\ 1984]{sew84} Seward, F. D. et al. 1984, \\apj, 281, 650\n\\bibitem[Standish \\ 1982]{sta82} Standish, E. M., 1982, A\\&A, 114, 297\n\\bibitem[Tamura et al.\\ 1996]{tam96} Tamura, K. et al. 1996, PASJ, 48, L33\n\\bibitem[Tamura \\ 1997]{tam97} Tamura, K., 1997, private communication\n\\bibitem[Tanimori et al.\\ 1994]{tan94} Tanimori, T. et al., 1994, \\apjl, 429, L61\n\\bibitem[Taylor et al.\\ 1995]{tay95} Taylor, J. H. et al. 1995, Princeton\nftp service; http://pulsar.princeton.edu/pulsar/\n\\bibitem[Thompson et al.\\ 1994]{tho94} Thompson, D. J. et al. 1994, \\apj, 436, 229\n\\bibitem[Torii et al. \\ 1997]{tor97} Torii. K. et al. 1997, \\apjl, 489, L145\n\\bibitem[Trussoni et al.\\ 1996]{tru96} Trussoni, E. et al. 1996, \\aap, 306, 581\n\\bibitem[Vacanti et al.\\ 1991]{vac91} Vacanti, G. et al., 1991, \\apj, 377, 467\n\\bibitem[Weekes et al.\\ 1989]{wee89} Weekes, T. C. et al., 1989, \\apj, 342, 379\n\\bibitem[Yoshikoshi et al.\\ 1997]{yos97} Yoshikoshi, T. et al., 1997, \\apjl, 487, L65\n\n\n\\end{thebibliography}\n\n\n\\clearpage\n\n\\figcaption[alpha5.eps]{\nDistributions of the $\\alpha$ parameter after all other image cuts. \nThe solid and dashed lines in upper figures show the ON source and OFF source\nresults, respectively.\nThe bottom figures represent the ON--OFF counts of the upper figures.\n\\label{Fig1}}\n\n\\figcaption[map97.eps]{\nThe contour map of the significance around the pulsar position in the 1997\ndata.\nNorth is to the top of the figure, and west is to the right.\nThe field of view is $2^{\\circ}\\times2^{\\circ}$ and the pulsar position is \nindicated by the cross.\nThe distance from the pulsar position to the peak of the excess (SW from the \npulsar) is $0^{\\circ}.1$ and is consistent with the pulsar position within\nthe source localization error, which is indicated by the circle.\n\\label{Fig4}}\n\n\\clearpage\n\n\\plotone{alpha5.eps}\n\n\\clearpage\n\n\\plotone{map97.eps}\n\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002252.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[Arendt \\ 1991]{are91} Arendt, R. G., 1991, \\aj, 101(6), 2160\n\\bibitem[Bowden \\ 1993]{bow93} Bowden, C. C. G. et al., 1993, Proc. 23rd Internat. Cosmic Ray Conf., Calgary, 1, 294\n\\bibitem[Cheng, Ho and Ruderman \\ 1986]{chr86} Cheng, K. S., Ho, C. and Ruderman, M., 1986, \\apj, 300, 500\n\\bibitem[Chadwick et al.\\ 1997]{cha97} Chadwick, P. M. et al., 1997, Proc. 25th Internat. Cosmic Ray Conf., Durban, 3, 189\n\\bibitem[de Jager, Swanepoel and Raubenheimer \\ 1989]{jag89} de Jager, O. C., Swanepoel, J. W. H. and Raubenheimer, B. C., 1989, \\aap, 221, 180\n\\bibitem[de Jager \\ 1994]{jag94} de Jager, O. C., 1994, \\apj, 436, 239\n\\bibitem[de Jager et al.\\ 1996]{jag96} de Jager, O. C. et al., 1996, \\apj, 457, 253\n\\bibitem[du Plessis et al.\\ 1995]{ple95} du Plessis, I. et al. 1995, \\apj, 453, 746\n\\bibitem[Gaensler et al. \\ 1998]{gae98} Gaensler, B. M. et al., 1998, MNRAS, 305, 724\n\\bibitem[Hara et al.\\ 1993]{har93} Hara, T. et al., 1993, Nucl. Inst. \nMeth. Phys. Res. A, 332, 300\n\\bibitem[Harding \\ 1990]{har90} Harding, A. K., 1990, Nucl. Phys. B, 14A, 3\n\\bibitem[Harding, Baring and Gonthier \\ 1997]{hbg97} Harding, A. K., Baring, \nM. G. and Gonthier, P. L., 1997, \\apj, 476, 246\n\\bibitem[Helene \\ 1983]{hel83} Helene, O., 1983, Nucl. Inst. Meth. Phys. Res., 212, 319 \n\\bibitem[Hillas \\ 1985]{hil85} Hillas, A. M., 1985, Proc. 19th Internat.\nCosmic Ray Conf., La Jolla, 3, 445\n\\bibitem[Kawai et al.\\ 1991]{kaw91} Kawai, N. et al., 1991, \\apjl, 383, L65\n\\bibitem[Kawai and Tamura \\ 1996]{kaw96} Kawai, N. and Tamura. K., 1996, in `Pulsars$\\colon$ Problems and Progress', ASP Conference series Vol.\\ 105, eds. S. Johnston, M. A. Walker and M. Bailes, 367\n\\bibitem[Kifune et al.\\ 1995]{kif95} Kifune, T. et al., 1995, \\apjl, 438, L91\n\\bibitem[Kuiper et al.\\ 1999]{kui99} Kuiper, L. et al., 1999, A\\&A, 351, 119\n\\bibitem[Manchester, Tuohy and D'Amico\\ 1982]{man82} Manchester, R. N., Tuohy, I. R. and D'Amico, N. 1982, \\apjl, 262, L31\n\\bibitem[Manchester et al. \\ 1998]{man98} Manchester, R. N. et al., 1998, the Australian Pulsar Timing Archive, http://www.atnf.csiro.au/Research/pulsar/psr/archive/ \n\\bibitem[Marsden et al. \\ 1997]{mar97} Marsden, D. et al., 1997, \\apjl, 491, L39\n\\bibitem[Matsubara et al. \\ 1997]{mat97} Matsubara, Y. et al., 1997, in `Towards a Major Atmospheric \\v{C}erenkov Detector - V', Kruger, ed. de Jager, O. C., 447\n\\bibitem[Nel et al. \\ 1990]{nel90} Nel, H. I. et al., 1990, \\apj, 361, 181\n\\bibitem[Nel et al. \\ 1992]{nel92} Nel, H. I. et al., 1992, \\apj, 398, 602\n\\bibitem[Seward and Harnden\\ 1982]{sew82} Seward, F. D. and Harnden, F. R. 1982, \\apjl, 256, L45\n\\bibitem[Seward et al.\\ 1984]{sew84} Seward, F. D. et al. 1984, \\apj, 281, 650\n\\bibitem[Standish \\ 1982]{sta82} Standish, E. M., 1982, A\\&A, 114, 297\n\\bibitem[Tamura et al.\\ 1996]{tam96} Tamura, K. et al. 1996, PASJ, 48, L33\n\\bibitem[Tamura \\ 1997]{tam97} Tamura, K., 1997, private communication\n\\bibitem[Tanimori et al.\\ 1994]{tan94} Tanimori, T. et al., 1994, \\apjl, 429, L61\n\\bibitem[Taylor et al.\\ 1995]{tay95} Taylor, J. H. et al. 1995, Princeton\nftp service; http://pulsar.princeton.edu/pulsar/\n\\bibitem[Thompson et al.\\ 1994]{tho94} Thompson, D. J. et al. 1994, \\apj, 436, 229\n\\bibitem[Torii et al. \\ 1997]{tor97} Torii. K. et al. 1997, \\apjl, 489, L145\n\\bibitem[Trussoni et al.\\ 1996]{tru96} Trussoni, E. et al. 1996, \\aap, 306, 581\n\\bibitem[Vacanti et al.\\ 1991]{vac91} Vacanti, G. et al., 1991, \\apj, 377, 467\n\\bibitem[Weekes et al.\\ 1989]{wee89} Weekes, T. C. et al., 1989, \\apj, 342, 379\n\\bibitem[Yoshikoshi et al.\\ 1997]{yos97} Yoshikoshi, T. et al., 1997, \\apjl, 487, L65\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002253
|
Not enough stellar Mass Machos in the Galactic Halo \thanks{Based on observations made at the European Southern Observatory, La Silla, Chile.}
|
[
{
"author": "T.~Lasserre\\inst{1}"
},
{
"author": "C.~Afonso\\inst{1}"
},
{
"author": "% C.~Alard\\inst{9}"
},
{
"author": "J.N.~Albert\\inst{2}"
},
{
"author": "J.~Andersen\\inst{6}"
},
{
"author": "R.~Ansari\\inst{2}"
},
{
"author": "\\'E.~Aubourg\\inst{1}"
},
{
"author": "P.~Bareyre\\inst{1,4}"
},
{
"author": "F.~Bauer\\inst{1}"
},
{
"author": "J.P.~Beaulieu\\inst{3}"
},
{
"author": "G.~Blanc\\inst{1}"
},
{
"author": "A.~Bouquet\\inst{4}"
},
{
"author": "S.~Char$^{\\dag}$\\inst{7}"
},
{
"author": "X.~Charlot\\inst{1}"
},
{
"author": "F.~Couchot\\inst{2}"
},
{
"author": "C.~Coutures\\inst{1}"
},
{
"author": "F.~Derue\\inst{2}"
},
{
"author": "R.~Ferlet\\inst{3}"
},
{
"author": "J.F.~Glicenstein\\inst{1}"
},
{
"author": "B.~Goldman\\inst{1}"
},
{
"author": "A.~Gould\\inst{8,1\\,}\\thanks{Alfred P.\\ Sloan Foundation Fellow}"
},
{
"author": "D.~Graff\\"
},
{
"author": "\\inst{8,1}"
},
{
"author": "M.~Gros\\inst{1}"
},
{
"author": "J.~Ha\\\"{\\i}ssinski\\inst{2}"
},
{
"author": "J.C.~Hamilton\\inst{4}"
},
{
"author": "D.~Hardin\\inst{1}"
},
{
"author": "J.~de Kat\\inst{1}"
},
{
"author": "A.~Kim\\inst{4}"
},
{
"author": "\\'E.~Lesquoy\\inst{1,3}"
},
{
"author": "C.~Loup\\inst{3}"
},
{
"author": "C.~Magneville \\inst{1}"
},
{
"author": "B.~Mansoux\\inst{2}"
},
{
"author": "J.B.~Marquette\\inst{3}"
},
{
"author": "\\'E.~Maurice\\inst{5}"
},
{
"author": "A.~Milsztajn \\inst{1}"
},
{
"author": "M.~Moniez\\inst{2}"
},
{
"author": "N.~Palanque-Delabrouille\\inst{1}"
},
{
"author": "O.~Perdereau\\inst{2}"
},
{
"author": "L.~Pr\\'evot\\inst{5}"
},
{
"author": "N.~Regnault\\inst{2}"
},
{
"author": "J.~Rich\\inst{1}"
},
{
"author": "M.~Spiro\\inst{1}"
},
{
"author": "A.~Vidal-Madjar\\inst{3}"
},
{
"author": "L.~Vigroux\\inst{1}"
},
{
"author": "S.~Zylberajch\\inst{1}"
},
{
"author": "\\indent \\indent The EROS collaboration"
}
] |
We combine new results from the search for microlensing towards the Large Magellanic Cloud (\lmc) by \eros2 (Exp\'erience de Recherche d'Objets Sombres) with limits previously reported by \eros1 and \eros2 towards both Magellanic Clouds. The derived upper limit on the abundance of stellar mass \macho s rules out such objects as an important component of the Galactic halo if their mass is smaller than $1 {M}_{\odot}$. % \keywords {Galaxy: halo -- Galaxy: kinematics and dynamics -- Galaxy: stellar content -- Magellanic Clouds -- dark matter -- gravitational lensing } %
|
[
{
"name": "enough.tex",
"string": "\\documentclass{aa}\n% \\documentclass[referee]{aa}\n\\usepackage{epsfig,amsfonts,amssymb}\n\\topmargin=-0.5in\n\n\\def\\kms{{\\rm km}\\,{\\rm s}^{-1}}\n\\def\\kpc{{\\rm kpc}}\n\\def\\lsim{{\\lesssim}}\n\\def\\au{{\\rm AU}}\n\\def\\etal{{et al.}}\n\\def\\eros{{\\sc eros}}\n\\def\\macho{{\\sc macho}}\n\\def\\ogle{{\\sc ogle}}\n\\def\\lmc{{\\sc lmc}}\n\\def\\smc{{\\sc smc}}\n\\def\\ie{{\\em i.e.}}\n\n\\begin{document}\n\n\\thesaurus{10.08.1, 10.11.1, 10.19.2, 11.13.1, 12.04.1, 12.07.1}\n\n\\title{Not enough stellar Mass Machos in the Galactic Halo\n\\thanks{Based on observations made at the European Southern Observatory,\nLa Silla, Chile.}}\n%\n\\author{\nT.~Lasserre\\inst{1},\nC.~Afonso\\inst{1},\n% C.~Alard\\inst{9},\nJ.N.~Albert\\inst{2},\nJ.~Andersen\\inst{6},\nR.~Ansari\\inst{2}, \n\\'E.~Aubourg\\inst{1}, \nP.~Bareyre\\inst{1,4}, \nF.~Bauer\\inst{1},\nJ.P.~Beaulieu\\inst{3},\nG.~Blanc\\inst{1},\nA.~Bouquet\\inst{4},\nS.~Char$^{\\dag}$\\inst{7},\nX.~Charlot\\inst{1},\nF.~Couchot\\inst{2}, \nC.~Coutures\\inst{1}, \nF.~Derue\\inst{2}, \nR.~Ferlet\\inst{3},\nJ.F.~Glicenstein\\inst{1},\nB.~Goldman\\inst{1},\nA.~Gould\\inst{8,1\\,}\\thanks{Alfred P.\\ Sloan Foundation Fellow},\nD.~Graff\\,\\inst{8,1},\nM.~Gros\\inst{1}, \nJ.~Ha\\\"{\\i}ssinski\\inst{2}, \nJ.C.~Hamilton\\inst{4},\nD.~Hardin\\inst{1},\nJ.~de Kat\\inst{1}, \nA.~Kim\\inst{4},\n\\'E.~Lesquoy\\inst{1,3},\nC.~Loup\\inst{3},\nC.~Magneville \\inst{1}, \nB.~Mansoux\\inst{2}, \nJ.B.~Marquette\\inst{3},\n\\'E.~Maurice\\inst{5}, \nA.~Milsztajn \\inst{1}, \nM.~Moniez\\inst{2},\nN.~Palanque-Delabrouille\\inst{1}, \nO.~Perdereau\\inst{2},\nL.~Pr\\'evot\\inst{5}, \nN.~Regnault\\inst{2},\nJ.~Rich\\inst{1}, \nM.~Spiro\\inst{1},\nA.~Vidal-Madjar\\inst{3},\nL.~Vigroux\\inst{1},\nS.~Zylberajch\\inst{1}\n\\\\ \\indent \\indent\nThe EROS collaboration\n}\n%% 1 Saclay, 2 LAL, 3 IAP, 4 CdF, 5 Marseille, 6 Copenhague, 7 La Serena,\n%% 8 Ohio, 9 Alard,\n% \n\\institute{\nCEA, DSM, DAPNIA,\nCentre d'\\'Etudes de Saclay, F-91191 Gif-sur-Yvette Cedex, France\n\\and\nLaboratoire de l'Acc\\'{e}l\\'{e}rateur Lin\\'{e}aire,\nIN2P3 CNRS, Universit\\'e de Paris-Sud, F-91405 Orsay Cedex, France\n\\and\nInstitut d'Astrophysique de Paris, INSU CNRS,\n98~bis Boulevard Arago, F-75014 Paris, France\n\\and\nColl\\`ege de France, Physique Corpusculaire et Cosmologie, IN2P3 CNRS, \n11 pl. M. Berthelot, F-75231 Paris Cedex, France\n\\and\nObservatoire de Marseille,\n2 pl. Le Verrier, F-13248 Marseille Cedex 04, France\n\\and\nAstronomical Observatory, Copenhagen University, Juliane Maries Vej 30, \nDK-2100 Copenhagen, Denmark\n\\and\nUniversidad de la Serena, Facultad de Ciencias, Departamento de Fisica,\nCasilla 554, La Serena, Chile\n\\and\nDepartments of Astronomy and Physics, Ohio State University, Columbus, \nOH 43210, U.S.A.\n% \\and\n% DASGAL, 77 avenue de l'Observatoire, F-75014 Paris, France\n}\n\\offprints{Thierry.Lasserre@cea.fr}\n\n\\date{Received 11 February 2000 / Accepted 23 February 2000}\n\n\\authorrunning{T. Lasserre et al.}\n\\titlerunning{Not enough stellar Mass \\macho s in the Galactic Halo }\n\n\\maketitle\n\n\\begin{abstract}\n\nWe combine new results from the search for microlensing\ntowards the Large Magellanic Cloud (\\lmc) by \\eros2 \n(Exp\\'erience de Recherche d'Objets Sombres)\nwith limits previously reported by \\eros1 and \\eros2 \ntowards both Magellanic Clouds. The derived upper limit on the \nabundance of stellar mass \\macho s rules out such objects \nas an important component of the Galactic\nhalo if their mass is \nsmaller than $1 {\\rm M}_{\\odot}$. \n%\n\\keywords {Galaxy: halo -- Galaxy: kinematics and dynamics -- \nGalaxy: stellar content -- Magellanic Clouds -- dark matter -- \ngravitational lensing\n}\n%\n\\end{abstract}\n\n\\section{Research context}\n%\n The search for gravitational microlensing in our Galaxy\nhas been going on for a decade, following the \nproposal to use this effect as a tool to probe the dark matter content\nof the Galactic halo (\\cite{pac86}). The first microlensing \ncandidates were reported in 1993, towards the \\lmc\\\n(\\cite{aub93}; Alcock et al. 1993) and the Galactic Centre (\\cite{uda93})\nby the \\eros , \\macho\\ and \\ogle\\ collaborations.\n\nBecause they observed no microlensing candidate with a duration\nshorter than 10~days,\nthe \\eros1 and \\macho\\ groups were able to exclude \nthe possibility that a substantial \nfraction of the Galactic dark matter resides in planet-sized objects\n(\\cite{aub95}; \\cite{alc96}; Renault et al. 1997; \n\\cite{ren98}; \\cite{alc98}). \n\nHowever a few events were\ndetected with longer time\\-scales. From 6-8 candidate events\ntowards the \\lmc , the \\macho\\ group estimated an optical depth of\norder half that required to account for the dynamical mass of the \nstandard spherical dark halo; \nthe typical Einstein radius crossing time of the events, $t_E$, \nimplied an average mass of about 0.5~M$_\\odot$ for the lenses \n(Alcock et al. 1997a).\nBased on two candidates, \\eros1 set an upper limit on the \nhalo mass fraction in objects of similar masses\n(Ansari et al. 1996), that is below that required to \nexplain the rotation curve of our Galaxy\\footnote{\nAssuming the \\eros1 candidates are microlensing events, \nthey would correspond to an optical depth six times lower than that\nexpected from a halo fully comprised of \\macho s.}.\n\nThe second phase of the \\eros\\ programme was started in 1996, with a \nten-fold increase in\nthe number of monitored stars in the Magellanic Clouds.\nThe analysis of the first two years of data towards the \nSmall Magellanic Cloud (\\smc)\nallowed the detection of one microlensing event \n(Palanque-Delabrouille et al. 1998; see also Alcock et al., 1997b).\nThis single event, out of 5.3 million stars, allowed \\eros2 \nto further constrain the halo composition, excluding in \nparticular that more than 50~\\% of the standard dark halo\nis made up of $0.01 - 0.5 \\:{\\rm M}_\\odot$ objects \n(Afonso et al. 1999). \nIn contrast, an optical detection of a halo\nwhite dwarf population was reported (Ibata et al. 1999).\n\nIn this letter, we describe the analysis of the two-year light curves\nfrom 17.5 million \\lmc\\ stars. We then \ncombine these results with our previous limits, and derive the\nstrongest limit obtained thus far on the amount of stellar mass\nobjects in the Galactic halo.\n\n\\section{Experimental setup and LMC observations}\n%\n\tThe telescope, camera, telescope operation and data reduction\nare as described in Bauer et al. (1997) and \nPa\\-lan\\-que-Delabrouille et al. (1998). \nSince August 1996, we have been monitoring\n66 one square-degree fields in the \\lmc , \nsimultaneously in two wide passbands. \nOf these, data prior to May 1998 from 25~square-degrees \nspread over 43~fields have been analysed. In this period, about\n70-110~images of each field were taken, with exposure times ranging from \n3~min in the \\lmc\\ center to 12~min on the periphery; \nthe average sampling is once every 6~days. \n\n\\section{LMC data analysis}\n%\n The analysis of the \\lmc\\ data set was done using a program\nindependent from that used in the \\smc\\ study, with largely\ndifferent selection criteria.\nThe aim is to cross-validate both programs \n(as was already done in the analysis\nof \\eros1 Schmidt photographic plates, \\cite{ans96})\nand avoid losing rare microlensing events.\nPreliminary results of the present analysis were reported in \nLasserre (1999).\nWe only give here a list of the various steps, as well as a\nshort description of the principal new features; \ndetails will be provided in Lasserre et al. (2000).\n\nWe first select the 8\\% ``most variable'' light curves, a sample\nmuch larger than the number of detectable variable stars.\nWorking from this ``enriched'' subset, we apply a first \nset of cuts to select, in each colour separately, \nthe light curves that exhibit significant variations.\nWe first identify the baseline flux in the light curve - basically\nthe most probable flux. \nWe then search for {\\it runs} along the light curve,\n\\ie\\ groups of consecutive measurements that are all on the same side \nof the baseline flux.\nWe select light curves that either\nhave an abnormally low\nnumber of runs over the whole light curve, or\nshow one long run (at least \n5 valid measurements) that is very \nunlikely to be a statistical fluctuation. \nWe then ask for a minimum signal-to-noise ratio by requiring that\nthe group of 5 most luminous\nconsecutive measurements be significantly further\nfrom the baseline than the average spread of the measurements.\nWe also check that the measurements inside the most significant run\nshow a smooth time variation.\n\nThe second set of cuts compares the measurements with the best fit\npoint-lens point-source constant speed microlensing light curve\n(hereafter ``simple microlensing''). They\nallow us to reject variable stars whose light curve differs too much\nfrom simple microlensing, and are sufficiently loose not to reject \nlight curves affected by blending, parallax \nor the finite size of the source, \nand most cases of multiple lenses or sources. \n\nAfter this second set of cuts, stars selected \nin at least one passband represent\nabout 0.01\\% of the initial sample; almost all of them\nare found in two thinly populated zones of the colour-magnitude \ndiagram. The third set of cuts deals with this physical background.\nThe first zone\ncontains stars brighter and much redder than those of the red clump;\nvariable stars in this zone are rejected if they vary by less than\na factor two or have a very poor fit to simple microlensing. \nThe second zone is the top of the main sequence. Here we find that\nselected stars, known as blue bumpers (\\cite{alc97a}), \ndisplay variations that are\nalways smaller than 60\\% and lower in the visible passband \nthan in the red one. These cannot correspond to simple microlensing,\nwhich is achromatic; they cannot correspond to microlensing\nplus blending with another unmagnified star either, \nas it would imply blending by even bluer stars,\nwhich is very unlikely. \nWe thus reject all candidates from the second zone\nexhibiting these two features.\n\nThe fourth set of cuts tests for compatibility between the\nlight curves in both passbands.\nWe retain candidates selected in only one passband\nif they have no conflicting data in the other passband.\nFor candidates selected independently in the two passbands,\nwe require that their largest variations coincide in time.\n\nThe tuning of each cut and the calculation of the microlensing \ndetection efficiency are done with \nsimulated simple microlensing light curves, as described in \nPa\\-lanque-Dela\\-brouille et al. (1998). \nFor the efficiency calculation, \nmicrolensing parameters are drawn uniformly in the following\nintervals: time of maximum magnification $t_0$ \nwithin the observing period $\\pm 150$~days,\n% \\in [t_{\\rm first}-150, t_{\\rm last}+150]$ days, \nimpact parameter normalised to the Einstein\nradius $u_0 \\in [0,2]$ and timescale \n$t_E \\in [5,300]$ days. \nAll cuts on the data were also applied to the simulated\nlight curves.\n\n%\n% -------------- FIGURE 1 ------------------------------\n%\n\\begin{figure} [ht] \n \\begin{center} \\epsfig{file=canderos2lmc9698.eps,width=7.8cm} \n% \\vspace{-.1cm}\n \\caption{Light curves of candidates EROS-LMC-3 and 4. \n The plain curves show the best point-lens point-source fits;\n time is in days since Jan. 1, 1990 (JD 2,447,892.5).} \n \\label{cdl_evts}\n \\end{center} \n%\\vspace{-0.7cm}\n\\end{figure}\n%\n% -------------- FIGURE 1 ------------------------------\n%\n\nOnly two candidates remain after all cuts. \nTheir light curves are shown\nin Fig.~\\ref{cdl_evts}; microlensing fit parameters\nare given in Table~\\ref{eventparm}. \nAlthough the candidates pass all cuts, agreement with simple \nmicrolensing is not excellent.\n\n%\n% -------------- TABLE 1 ------------------------------\n%\n\\begin{table}[ht]\n\\begin{center} \\vspace{-0.0cm} \n\\begin{tabular}{|l||c|c|c|c|c|c|c|}\n\\hline\n &$u_0$&$t_E$&$c_{\\rm \\,bl}^R$&$c_{\\rm \\,bl}^V$&$\\chi^2/{\\rm dof}$& \n$V_J$&$R_C$ \\\\\n\\hline\n \\lmc-3 & $0.23$&$41$&$0.76$& 1 &208/145&22.4&21.8\\\\\n\\hline\n \\lmc-4 & $0.20$&$106$& 1 & 1 &406/150&19.7&19.4\\\\\n\\hline\n\n\\end{tabular}\n\\caption{Results of microlensing fits to the two new \\lmc\\ candidates;\n $t_E$ is the Einstein radius crossing time in days, \n$u_{0}$ the impact parameter, and $c_{\\rm \\,bl}^{R(V)}$ the \n$R(V)$ blending coefficients.\n% in both colours.\n}\n\\label{eventparm}\n\\end{center} \\vspace{-0.5cm}\n\\end{table}\n%\n% -------------- TABLE 1 ------------------------------\n%\n\nThe efficiency of the analysis, normalised to events with an impact \nparameter $u_0<1$ and to an observing period $T_{\\rm obs}$ of two\nyears, is summarised in Table~\\ref{eff}.\nThe main source of systematic error is the uncertainty in the \ninfluence of blending. Blending lowers the observed magnifications\nand timescales. While this decreases the efficiency for a given star, \nthe effective number of monitored stars is increased so that there\nis partial compensation.\nThis effect was studied with synthetic images using measured magnitude\ndistributions (\\cite{pal97}). \nOur final efficiency is within 10\\% of the naive efficiency.\n%\n% -------------- TABLE 2 ------------------------------\n%\n\\begin{table}[ht]\n\\vspace{-0.3cm}\n \\begin{tabular}{|c||c|c|c|c|c|c|c|c|c|c|} \\hline\n$t_E$ & 5 & 11& 18& 28& 45& 71& 112& 180& 225& 280\\\\ \\hline\n$\\epsilon$ & 2 & 5& 11& 15& 19& 23& 26& 25& 18& 2.5\\\\ \\hline\n\\end{tabular}\n\\caption{Detection efficiency in \\% as a function of the\nEinstein radius crossing time $t_E$ in days, \nnormalised to events generated with $u_0<1$, and\nto $T_{\\rm obs}=2{\\rm \\: yrs}$. \n% We analysed $N_{*} = 17.5\\times 10^6$ stars.\n}\n\\label{eff} \n\\vspace{-0.6cm}\n\\end{table}\n%\n% -------------- TABLE 2 ------------------------------\n%\n\n\\section{EROS1 results revisited}\n%\n The two \\eros1 microlensing candidates have been monitored by \n\\eros2. \nThe source star in event \\eros -\\lmc -2 had been found to be variable \n(\\cite{ans95}), but microlensing fits taking into account \nthe observed periodicity\ngave a good description of the measurements. Its follow-up by \\eros2\nrevealed a new bump in March 1999, eight years after the first \none\\footnote{We thank the \\macho\\ group for communication about \ntheir data on this star.}.\nThis new variation, of about a factor two, was not well sampled \nbut is significant.\nTherefore, \\eros -\\lmc -2 is no longer a candidate\nand we do not include it in the limit computation.\n\n\\section{Limits on Galactic halo MACHOs}\n%\n \\eros\\ has observed four microlensing candidates towards the\nMagellanic Clouds, one from \\eros1 and two from \\eros2 towards\nthe \\lmc , and one towards the \\smc .\nAs discussed in Palanque-Dela\\-brouille et al. (1998),\nwe consider that the long duration\nof the \\smc\\ candidate together with the absence of any detectable\nparallax, in our data as well as in that of the \\macho\\ group\n(\\cite{alc97b}), indicates that it is most likely\ndue to a lens in the \\smc . For that reason, the limit\nderived below uses the three \\lmc\\ candidates; for completeness,\nwe also give the limit corresponding to all four candidates.\n \nThe limits on the contribution of dark compact objects\nto the Galactic halo are obtained by comparing the number \nand durations of \nmicrolensing candidates with those expected from Galactic\nhalo models. \nWe use here the so-called ``standard'' halo model described in\nPalanque-Delabrouille et al. (1998) as model 1.\nThe model predictions are computed for each \\eros\\\ndata set in turn, taking into account the corresponding detection \nefficiencies\n(\\cite{ans96}; Renault et al. 1998; \nAfonso et al. 1999; Table~\\ref{eff} above),\nand the four predictions are then summed.\nIn this model, all dark objects have the same mass $M$; we have\ncomputed the model predictions for many trial masses $M$ in turn,\nin the range [$10^{-8}\\:{\\rm M}_\\odot$, $10^2\\:{\\rm M}_{\\odot}$].\n\nThe method used to compute the limit is as \nin Ansari et al. (1996). We consider two ranges of\ntimescale $t_E$, smaller or larger than \n$t_E^{\\rm lim} = 10$~days. (All candidates have \n$t_E > t_E^{\\rm lim}$.)\nWe can then compute, for each mass\n$M$ and any halo fraction $f$,\nthe combined Poisson probability for obtaining,\nin the four different \\eros\\ data sets taken as a whole, \nzero candidate with $t_E < t_E^{\\rm lim}$ and \nthree or less (alt.~four or less)\nwith $t_E > t_E^{\\rm lim}$. For any value of $M$,\nthe limit $f_{\\rm max}$ is the value of $f$ for which this probability\nis 5\\%. Whereas the actual limit depends somewhat on the precise\nchoice of $t_E^{\\rm lim}$, the difference ($ \\lsim 5\\%$) is noticeable \nonly for masses around $0.02\\:{\\rm M}_{\\odot}$. \nFurthermore, we consider 10~days to be a conservative choice.\n%\n% -------------- FIGURE 2 ------------------------------\n%\n\\begin{figure} [ht] \n \\begin{center} \\epsfig{file=excl_eros12.eps,width=8.7cm}\n \\vspace{-.1cm} \\caption{ 95\\% C.L. exclusion diagram on the halo mass\n fraction in the form of compact objects of mass $M$, for the\n standard halo model ($4 \\times 10^{11}\\:{\\rm M}_\\odot$ inside\n 50~kpc), from all \\lmc\\ and \\smc\\ \\eros\\ data 1990-98. \n The solid line is the limit inferred from the three \\lmc\\ microlensing \n candidates; the dashed line includes in addition the \\smc\\\n candidate. The {\\sc macho} 95\\%\n C.L. accepted region is the hatched area, with the preferred value\n indicated by the cross (Alcock et al. 1997a).} \n \\label{excl}\n \\end{center} \\vspace{-0.5cm}\n\\end{figure}\n%\n% -------------- FIGURE 2 ------------------------------\n%\n\nFigure \\ref{excl} shows the 95\\% C.L. exclusion limit derived \nfrom this analysis on the halo mass fraction, $f$,\nfor any given dark object mass, $M$. \nThe solid line corresponds to the three \\lmc\\ candidates;\n% ---> our favoured number of halo lens candidates\nit is the main result of this letter. \n(The dashed line includes the \\smc\\ candidate in addition.)\nThis limit rules out a standard spherical halo model fully comprised of \nobjects with any mass function inside the range \n$[10^{-7}-4] \\; M_{\\odot}$.\nIn the region of stellar mass objects, where this result\nimproves most on previous ones, the new \\lmc\\ data contribute\nabout 60\\% to our total sensitivity (the \\smc\\ and \\eros1 \n\\lmc\\ data contribute 15\\% and 25\\% respectively). \nThe total sensitivity, that is proportional to the sum of \n$N_* \\, T_{\\rm obs} \\, \\epsilon (t_E)$\nover the four \\eros\\ data sets,\nis 2.4 times larger than that of Alcock et al. (1997a).\n% \\cite{alc97a}.\nWe observe that a large fraction of the domain previously allowed by \nAlcock et al. (1997a)\nis excluded by the limit in Fig.~\\ref{excl}.\n\n\\section{Discussion and conclusion}\n%\n After eight years of monitoring the Magellanic Clouds, \n\\eros\\ has a meager crop of three microlensing candidates towards \nthe \\lmc\\ and one towards the \\smc , whereas 27 events are expected\nfor a spherical halo fully comprised of $0.5 \\:{\\rm M}_\\odot$ objects.\nThese were\nobtained from four different data sets analysed by four independent,\ncross-validated programs. \nSo, the small number of observed events is unlikely\nto be due to bad detection efficiencies.\n\nThis allows us to put strong constraints on the fraction\nof the halo made of objects in the range [$10^{-7}\\:{\\rm M}_\\odot$,\n$4\\:{\\rm M}_{\\odot}$], excluding in particular at the 95~\\% C.L. that more\nthan 40~\\% of the standard halo be made of objects with up to\n$1 \\:{\\rm M}_\\odot$. The preferred value quoted in Alcock et al. (1997a),\n% \\cite{alc97a}\n$f = 0.5$ and $0.5\\:{\\rm M}_\\odot$,\nis incompatible with the limits in Fig.~\\ref{excl} at the 99.7\\% C.L.\n(but see the note added below).\n\nWhat are possible reasons for such a difference?\nApart from a potential bias in the detection efficiencies,\n% (see the note added below), \nseveral differences \nshould be kept in mind while comparing the two experiments.\nFirst, \\eros\\ uses less crowded fields than \\macho\\ with the result\nthat blending is relatively unimportant for \\eros .\nSecond, \\eros\\ covers a larger solid angle (43~deg$^2$ in the \\lmc\\\nand 10~deg$^2$ in the \\smc ) than \\macho , which monitors primarily\nthe central 11~deg$^2$ of the \\lmc .\nThe \\eros\\ rate should thus be less contaminated by self-lensing\nthat is more common in the central regions~-\nthe importance of\nself-lensing was first stressed \nby Wu (1994) and Sahu (1994).\nThird, the \\macho\\ data have a more frequent time sampling.\nFinally, while the \\eros\\ limit uses both Clouds, the \\macho\\\nresult is based only on the \\lmc .\nFor halo lensing, the timescales towards the two Clouds should\nbe nearly identical and the optical depths comparable.\nIn this regard, we remark that the \\smc\\ event\nis longer than all \\lmc\\ candidates from \\macho\\ and \\eros .\n\nFinally,\ngiven the scarcity of our candidates \nand the possibility that some observed microlenses\nactually lie in the Magellanic Clouds, \n\\eros\\ is not willing to quote at present a non zero \n{\\it lower} limit on the fraction of the Galactic halo comprised of\ndark compact objects with masses up to a few solar masses.\n\n\\smallskip\n{\\bf Note added.} While the writing of\nthis letter was being finalised, the analysis\nof 5.7 yrs of \\lmc\\ observations by the \\macho\\ group was made\npublic (\\cite{alc00}). The new favoured estimate of the \nhalo mass fraction in the form of compact objects, $f = 0.20$,\nis 2.5 times lower than that of Alcock et al. (1997a)\nand is compatible with the limit presented here. \nNone of the conclusions in this article have to be reconsidered.\nA detailed comparison of our results with those of\nAlcock et al. (2000) will be available \nin our forthcoming publication (\\cite{las00a}).\n\n\\begin{acknowledgements}\nWe are grateful to D. Lacroix and the staff at the Observatoire de\nHaute Provence and to A. Baranne for their help with the MARLY\ntelescope. \n% We are also grateful for the support\n% given to our project by the technical staff at ESO, La Silla.\nThe support by the technical staff at ESO, La Silla, \nis essential to our project.\nWe thank J.F. Lecointe for assistance with the online computing.\n\\end{acknowledgements}\n\n\n\\begin{thebibliography}{}\n%\n\\bibitem[Afonso et al. 1999]{afo99}\n Afonso C. et al. (\\eros ), 1999, A\\&A 344, L63\n%\n\\bibitem[Alcock et al. 1993] {alc93} \n Alcock C. et al. (\\macho ), 1993, {Nat} {365}, 621\n%\n\\bibitem[Alcock et al. 1996]{alc96} \n Alcock C. et al. (\\macho ), 1996, {ApJ} 471, 774\n%\n\\bibitem[Alcock et al. 1997a]{alc97a} \n Alcock C. et al. (\\macho ), 1997a, {ApJ} 486, 697\n%\n \\bibitem[Alcock et al. 1997b]{alc97b} \n Alcock C. et al. (\\macho ), 1997b, {ApJ} 491, L11\n%\n\\bibitem[Alcock et al. 1998]{alc98} \n Alcock C. et al. (\\macho ), 1998, {ApJ} 499, L9\n%\n\\bibitem[Alcock et al. 2000]{alc00} \n Alcock C. et al. (\\macho ), 2000, preprint astro-ph/0001272\n%\n\\bibitem[Ansari et al. 1995]{ans95} \n Ansari R. et al. (\\eros ), 1995, {A\\&A} {299}, L21\n%\n\\bibitem[Ansari et al. 1996]{ans96} \n Ansari R. et al. (\\eros ), 1996, {A\\&A} {314}, 94\n%\n\\bibitem[Aubourg et al. 1993]{aub93} \n Aubourg \\'E. et al. (\\eros ), 1993, {Nat} {365}, 623\n%\n\\bibitem[Aubourg et al. 1995]{aub95} \n Aubourg \\'E. et al. (\\eros ), 1995, {A\\&A} {301}, 1\n%\n\\bibitem[Bauer et al. 1997]{bau97} \n Bauer F. et al. (\\eros ), 1997, in Proceedings of the ``Optical \nDetectors for Astronomy'' workshop (ESO, Garching)\n%\n\\bibitem[Ibata et al. 1999]{iba99} \n Ibata R. et al., 1999, {ApJ} 524, L95\n%\n\\bibitem[Lasserre et al. 1999]{las99}\n Lasserre T. (\\eros ), 1999, in Proceedings of ``Gravitational lensing :\nRecent Progress and Future Goals'', Boston (preprint astro-ph/9909505)\n%\n\\bibitem[Lasserre et al. 2000]{las00a}\n Lasserre T. et al. (\\eros ), 2000, in preparation\n%\n\\bibitem[Paczy\\'{n}ski 1986]{pac86} \n Paczy\\'{n}ski B., 1986, {ApJ} {304}, 1\n%\n\\bibitem[Pa\\-lan\\-que-De\\-la\\-brouille 1997]{pal97} \n Palanque-Delabrouille N., 1997, PhD thesis, University of Chicago and\nUniversit\\'e de Paris 7\n%\n\\bibitem[Palanque-Delabrouille et al. 1998]{pal98} \n Palanque-Delabrouille N. et al. (\\eros ), 1998, {A\\&A} 332, 1\n%\n\\bibitem[Renault et al. 1997]{ren97}\n Renault C. et al. (\\eros ), 1997, A\\&A 324, L69\n%\n\\bibitem[Renault et al. 1998]{ren98}\n Renault C. et al. (\\eros ), 1998, A\\&A 329, 522\n%\n\\bibitem[Sahu 1994]{sahu94} \n Sahu K. C., 1994, Nat 370, 275\n%\n\\bibitem[Udalski et al. 1993]{uda93}\n Udalski A. et al. (\\ogle ), 1993, Acta Astron. 43, 289\n%\n\\bibitem[Wu 1994]{wu94} \n Wu X.-P., 1994, {ApJ} 435, 66\n%\n\\end{thebibliography}\n\n\\end{document}\n\n"
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{
"name": "astro-ph0002253.extracted_bib",
"string": "\\begin{thebibliography}{}\n%\n\\bibitem[Afonso et al. 1999]{afo99}\n Afonso C. et al. (\\eros ), 1999, A\\&A 344, L63\n%\n\\bibitem[Alcock et al. 1993] {alc93} \n Alcock C. et al. (\\macho ), 1993, {Nat} {365}, 621\n%\n\\bibitem[Alcock et al. 1996]{alc96} \n Alcock C. et al. (\\macho ), 1996, {ApJ} 471, 774\n%\n\\bibitem[Alcock et al. 1997a]{alc97a} \n Alcock C. et al. (\\macho ), 1997a, {ApJ} 486, 697\n%\n \\bibitem[Alcock et al. 1997b]{alc97b} \n Alcock C. et al. (\\macho ), 1997b, {ApJ} 491, L11\n%\n\\bibitem[Alcock et al. 1998]{alc98} \n Alcock C. et al. (\\macho ), 1998, {ApJ} 499, L9\n%\n\\bibitem[Alcock et al. 2000]{alc00} \n Alcock C. et al. (\\macho ), 2000, preprint astro-ph/0001272\n%\n\\bibitem[Ansari et al. 1995]{ans95} \n Ansari R. et al. (\\eros ), 1995, {A\\&A} {299}, L21\n%\n\\bibitem[Ansari et al. 1996]{ans96} \n Ansari R. et al. (\\eros ), 1996, {A\\&A} {314}, 94\n%\n\\bibitem[Aubourg et al. 1993]{aub93} \n Aubourg \\'E. et al. (\\eros ), 1993, {Nat} {365}, 623\n%\n\\bibitem[Aubourg et al. 1995]{aub95} \n Aubourg \\'E. et al. (\\eros ), 1995, {A\\&A} {301}, 1\n%\n\\bibitem[Bauer et al. 1997]{bau97} \n Bauer F. et al. (\\eros ), 1997, in Proceedings of the ``Optical \nDetectors for Astronomy'' workshop (ESO, Garching)\n%\n\\bibitem[Ibata et al. 1999]{iba99} \n Ibata R. et al., 1999, {ApJ} 524, L95\n%\n\\bibitem[Lasserre et al. 1999]{las99}\n Lasserre T. (\\eros ), 1999, in Proceedings of ``Gravitational lensing :\nRecent Progress and Future Goals'', Boston (preprint astro-ph/9909505)\n%\n\\bibitem[Lasserre et al. 2000]{las00a}\n Lasserre T. et al. (\\eros ), 2000, in preparation\n%\n\\bibitem[Paczy\\'{n}ski 1986]{pac86} \n Paczy\\'{n}ski B., 1986, {ApJ} {304}, 1\n%\n\\bibitem[Pa\\-lan\\-que-De\\-la\\-brouille 1997]{pal97} \n Palanque-Delabrouille N., 1997, PhD thesis, University of Chicago and\nUniversit\\'e de Paris 7\n%\n\\bibitem[Palanque-Delabrouille et al. 1998]{pal98} \n Palanque-Delabrouille N. et al. (\\eros ), 1998, {A\\&A} 332, 1\n%\n\\bibitem[Renault et al. 1997]{ren97}\n Renault C. et al. (\\eros ), 1997, A\\&A 324, L69\n%\n\\bibitem[Renault et al. 1998]{ren98}\n Renault C. et al. (\\eros ), 1998, A\\&A 329, 522\n%\n\\bibitem[Sahu 1994]{sahu94} \n Sahu K. C., 1994, Nat 370, 275\n%\n\\bibitem[Udalski et al. 1993]{uda93}\n Udalski A. et al. (\\ogle ), 1993, Acta Astron. 43, 289\n%\n\\bibitem[Wu 1994]{wu94} \n Wu X.-P., 1994, {ApJ} 435, 66\n%\n\\end{thebibliography}"
}
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astro-ph0002254
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[] |
It is considered gravitational interaction within the framework of the Newton theory and the quantum field theory. It is introduced the Planck neutrino $\nu_{Pl}$. Gravitational interaction of the fields $\psi\psi$ includes short-range interaction $\psi\nu_{Pl}$ and long-range interaction $\nu_{Pl}\nu_{Pl}$. Gravitational radiation can be identified with the Planck neutrino. The theory predicts the decay of proton into Planck neutrino. It is assumed that the Planck mass built from three fundamental constants $\hbar$, $c$ and $G$ is fixed in all the inertial frames. This leads to that the lifetime of proton relative to the decay into Planck neutrino decreases with the Lorentz factor as $\sim \gamma^{-5}$. Such a dependence of the lifetime of proton on the Lorentz factor yields a cut-off in the EHECRs spectrum. It is shown that the first "knee" in the EHECRs spectrum $E\sim 3\times 10^{15}\ {eV}$ corresponds to the lifetime of proton equal to the lifetime of the universe, the second "knee" $E\sim 10^{17}-10^{18}\ {eV}$ corresponds to the lifetime of proton equal to the thickness of our galactic disc. The EHECRs with the energies $E>3 \times 10^{18}\ {eV}$ can be identified with the Planck neutrinos.
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[
{
"name": "astro-ph0002254.tex",
"string": "\\documentstyle[12pt]{article}\n\\bibliographystyle{unsrt}\n\\oddsidemargin 0in\n\\evensidemargin 0in\n\\textwidth 6.5in \\columnsep 10pt \\columnseprule 0pt\n\\textheight = 44\\baselineskip\n\\voffset=-1.0truein\n\\hoffset=0truein\n\\begin{document}\n\\begin{center}\n{\\Large \\bf\nDecay of proton into Planck neutrino in the theory of gravity}\n\\bigskip\n\n{\\large D.L.~Khokhlov}\n\\smallskip\n\n{\\it Sumy State University, R.-Korsakov St. 2\\\\\nSumy 40007 Ukraine\\\\\ne-mail: khokhlov@cafe.sumy.ua}\n\\end{center}\n\n\\begin{abstract}\nIt is considered gravitational interaction within the framework\nof the Newton theory and the quantum field theory.\nIt is introduced the Planck neutrino $\\nu_{Pl}$.\nGravitational interaction of the fields $\\psi\\psi$ includes\nshort-range interaction $\\psi\\nu_{Pl}$ and\nlong-range interaction $\\nu_{Pl}\\nu_{Pl}$.\nGravitational radiation can be identified with\nthe Planck neutrino.\nThe theory predicts the decay of proton into Planck neutrino.\nIt is assumed\nthat the Planck mass built from three fundamental constants\n$\\hbar$, $c$ and $G$ is fixed in all the inertial frames.\nThis leads to that the lifetime of proton relative to\nthe decay into Planck neutrino\ndecreases with the Lorentz factor as $\\sim \\gamma^{-5}$.\nSuch a dependence of the lifetime of proton\non the Lorentz factor yields a cut-off in the EHECRs spectrum.\nIt is shown that the first \"knee\" in the EHECRs spectrum\n$E\\sim 3\\times 10^{15}\\ {\\rm eV}$\ncorresponds to the lifetime of proton equal to the lifetime\nof the universe,\nthe second \"knee\" $E\\sim 10^{17}-10^{18}\\ {\\rm eV}$\ncorresponds to the lifetime of proton equal to the\nthickness of our galactic disc. The EHECRs with the energies\n$E>3 \\times 10^{18}\\ {\\rm eV}$ can be identified with\nthe Planck neutrinos.\n\\end{abstract}\n\n\\section{Introduction}\n\nThe principle of equivalence of inertial and gravitational masses\nunderlines the theory of gravity.\nIn the Einstein theory of gravity~\\cite{M},\nthis leads to that the free gravitational field is nonlocalized.\nUnder the presence of the matter, the gravity is described by\nthe Einstein equations\n\\begin{equation}\nG_{ik}=T_{ik}\n\\label{eq:GT}\n\\end{equation}\nwhere $G_{ik}$ is the Einstein tenzor,\n$T_{ik}$ is the tenzor of momentum-energy of the matter.\nFree gravitational field defined by the absence of the matter\n$T_{ik}=0$ is described by the equations\n\\begin{equation}\nR_{ik}=0\n\\label{eq:R}\n\\end{equation}\nwhere $R_{ik}$ is the Ricci tenzor.\nThe localized field must be described by the tenzor of momentum-energy.\nEinstein characterized the momentum-energy of the\ngravitational field by the pseudo-tenzor defined as\n\\begin{equation}\nt^{ik}=H^{ilkm}_{\\ \\ \\quad ,lm} -G^{ik}\n\\label{eq:tik}\n\\end{equation}\nwhere $H^{ilkm}_{\\ \\ \\quad ,lm}$ is the linearized part of $G_{ik}$.\nThus in the Einstein theory gravitational field is nonlocalized.\n\nThe natural way\nproposed by Lorentz and Levi-Civita~\\cite{Pau} is to take\n$G_{ik}$ as the momentum-energy of the gravitational field. \nHowever in this\ncase $G_{ik}$ is equal to zero for the free gravitational field\n$G_{ik}=R_{ik}=0$. Such a situation may be interpreted as that\nthe gravitational interaction occurs without gravitational field.\nThen the problem arises as to how to introduce gravitational\nradiation. The possible resolution of the problem is to introduce\nsome material field as a radiation.\n\n\\section{Theory}\n\nConsider gravitational interaction within the framework of the Newton\ntheory and the quantum field theory.\nThe Lagrangian of the Newton gravity is given by\n\\begin{equation}\nL=G\\frac{m^2}{r},\n\\label{eq:L1}\n\\end{equation}\nwith the mass m being the gravitational charge.\nWhile expressing the Newton constant $G$\nvia the charge $g=(\\hbar c)^{1/2}$\nand via the Planck mass $m_{Pl}=(\\hbar c/G)^{1/2}$,\nthe Lagrangian (\\ref{eq:L1}) can be rewritten in the form\n\\begin{equation}\nL=G\\frac{m^2}{r}=\\frac{g^2}{m_{Pl}^2}\\frac{m^2}{r}.\n\\label{eq:L2}\n\\end{equation}\nThe Lagrangian of the Newton gravity in the form (\\ref{eq:L2})\ndescribes gravitational interaction by means of the charge $g$.\nIn this way gravity may be implemented into\nthe quantum field theory.\n\nRewrite the Lagrangian (\\ref{eq:L2}) in the form of the effective\nLagrangian of interaction of the spinor fields~\\cite{B}\n\\begin{equation}\nL=\\frac{g^2}{m_{Pl}^2}J_{\\mu}(x)J^{\\mu}(x).\n\\label{eq:L5}\n\\end{equation}\nThe term $1/m_{Pl}^2$ in the Lagrangian (\\ref{eq:L5}) reads that\ngravitational interaction takes place at the Planck scale.\nAt the same time gravity is characterized by the infinite radius\nof interaction.\nTo resolve the problem consider the scheme\nof gravitational interaction which includes both the\nshort-range interaction and the long-range interaction\n\\begin{equation}\nL=L_{short}+L_{long}.\n\\label{eq:L3}\n\\end{equation}\nLet us introduce the Planck neutrino $\\nu_{Pl}$.\nLet the Planck neutrino is the massless particle of the spin 1/2.\nSuppose that\nthe Planck neutrino interacts with the other fields at the Planck scale\n\\begin{equation}\n\\psi\\rightarrow \\nu_{Pl}\n\\label{eq:psnu}\n\\end{equation}\nwhere $\\psi$ denotes all the fields of the spin 1/2.\nThis interaction is of short-range and is governed\nby the Lagrangian (\\ref{eq:L5})\n\\begin{equation}\nL_{short}=\\frac{g^2}{m_{Pl}^2}J_{\\mu}(x)J^{\\mu}(x)\n\\label{eq:L6}\n\\end{equation}\nwhere the current\n$J_{\\mu}$ transforms the field $\\psi$ into the field $\\nu_{Pl}$.\nLet the interaction of the Planck neutrinos $\\nu_{Pl}\\nu_{Pl}$\nis of long-range and\nis governed by the Lagrangian identically equal to zero\n\\begin{equation}\nL_{long}\\equiv 0.\n\\label{eq:L4}\n\\end{equation}\nThe considered scheme allows one to decribe both the classical\ngravity and the decay of the field $\\psi$ into the Planck neutrino.\nIn this scheme gravitational radiation can be identified with\nthe Planck neutrino.\n\nWithin the framework of the standard quantum field theory,\nthe above scheme of gravitational interaction should include\ntwo intermediate fields $\\psi\\nu_{Pl}$ and $\\nu_{Pl}\\nu_{Pl}$.\nSince the Lagrangian of the interaction $\\nu_{Pl}\\nu_{Pl}$ is\nidentically equal to zero,\nthe energy of the field $\\nu_{Pl}\\nu_{Pl}$\nis identically equal to zero.\nThe field $\\psi\\nu_{Pl}$ is defined by the Planck mass.\nIn the theory of gravity there is\nthe limit of ability to measure the length equal to\nthe Planck length~\\cite{Tr}\n$\\Delta l\\geq 2(\\hbar G/c^3)^{1/2}=2l_{Pl}$.\nFrom this it follows that there is no possibility to measure the\nfield $\\psi\\nu_{Pl}$ in the physical experiment.\nThus both intermediate fields\n$\\psi\\nu_{Pl}$ and $\\nu_{Pl}\\nu_{Pl}$ cannot be measured.\nThis means that the intermediate fields $\\psi\\nu_{Pl}$\nand $\\nu_{Pl}\\nu_{Pl}$ do not exist.\nWe arrive at the conclusion that gravitational interaction\noccurs without intermediate fields.\n\n\\section{The lifetime of proton relative to the decay\ninto Planck neutrino}\n\nIn view of eq.~(\\ref{eq:psnu}),\nthe decay of proton into Planck neutrino occurs at the Planck scale\n\\begin{equation}\np\\rightarrow \\nu_{Pl}.\n\\label{eq:pnu}\n\\end{equation}\nThe lifetime of proton relative to the decay\ninto Planck neutrino is defined by the Lagrangian (\\ref{eq:L5})\n\\begin{equation}\nt_p=t_{Pl}\\left(\\frac{m_{Pl}}{2m_p}\\right)^5\n\\label{eq:tp1}\n\\end{equation}\nwhere the factor 2 takes into account the transition from\nthe massive particle to the massless one.\nThis lifetime corresponds to the rest frame.\nConsider the lifetime of proton in the moving frame with the\nLorentz factor\n\\begin{equation}\n\\gamma=\\left(1-\\frac{v^2}{c^2}\\right)^{-1/2}.\n\\label{eq:gam}\n\\end{equation}\nIn the moving frame the rest mass and time are multiplied by the\nLorentz factor\n\\begin{equation}\nm'=\\gamma m\n\\label{eq:gm}\n\\end{equation}\n\\begin{equation}\nt'=\\gamma t.\n\\label{eq:gt}\n\\end{equation}\nThe Planck mass $m_{Pl}=(\\hbar c/G)^{1/2}$ and the Planck time\n$t_{Pl}=(\\hbar G/c^5)^{1/2}$ are built from three fundamental\nconstants $\\hbar$, $c$ and $G$.\nAccording to the special relativity~\\cite{Pau}, the speed of light\nis fixed in all the inertial frames.\nExtend the special relativity principle and suppose\nthat the three constants $\\hbar$, $c$ and $G$ are fixed in all the\ninertial frames\n\\begin{equation}\n\\hbar'=\\hbar \\qquad c'=c \\qquad G'=G.\n\\label{eq:thr}\n\\end{equation}\nHence the Planck mass and time are fixed in all the\ninertial frames.\nThen the lifetime of proton in the moving frame\nis given by\n\\begin{equation}\nt_p '=t_{Pl}\\left(\\frac{m_{Pl}}{2\\gamma m_p}\\right)^5.\n\\label{eq:tp2}\n\\end{equation}\n\nFor comparison consider the decay of muon which is governed by\nthe Lagrangian of electroweak interaction~\\cite{B}\n\\begin{equation}\nL=\\frac{g^2}{m_{W}^2}J_{\\mu}(x)J^{\\mu}(x)\n\\label{eq:Lmu}\n\\end{equation}\nwhere $m_{W}$ is the mass of W-boson.\nIn the rest frame the lifetime of muon\nis given by\n\\begin{equation}\nt_{\\mu}=t_{W}\\left(\\frac{m_{W}}{m_{\\mu}}\\right)^5.\n\\label{eq:tmu1}\n\\end{equation}\nIn the moving frame the lifetime of muon\nis given by\n\\begin{equation}\nt_{\\mu}'=\\gamma t_{W}\\left(\\frac{m_{W}}{m_{\\mu}}\\right)^5.\n\\label{eq:tmu2}\n\\end{equation}\n\nThus unlike the usual situation when the lifetime of the particle,\ne. g. muon, grows with the Lorentz factor\nas $\\sim \\gamma$,\nthe lifetime of proton relative to the decay into Planck neutrino\ndecreases with the Lorentz factor\nas $\\sim \\gamma^{-5}$. State once again that such a behaviour\nis due to that the Planck mass built from three fundamental constants\n$\\hbar$, $c$ and $G$ is fixed in all the inertial frames.\n\n\\section{Extra high energy cosmic rays spectrum\nin view of the decay of proton into Planck neutrino}\n\nIn view of eq.~(\\ref{eq:tp2}),\nthe lifetime of proton relative to the decay into Planck neutrino\ndecreases with the increase of the kinetic energy of proton.\nThen the decay of proton can be observed for the extra high energy\nprotons. In particular the decay of proton can be observed as a cut-off\nin the energy spectrum of extra high energy cosmic rays (EHECRs).\n\nThe EHECRs spectrum above $10^{10}\\ {\\rm eV}$ can be\ndivided into three regions: two \"knees\" and one \"ankle\"~\\cite{Yo}.\nThe first \"knee\" appears around $3\\times 10^{15}\\ {\\rm eV}$\nwhere the spectral power law index changes from $-2.7$ to $-3.0$.\nThe second \"knee\" is somewhere between $10^{17}\\ {\\rm eV}$ and\n$10^{18}\\ {\\rm eV}$ where the spectral slope steepens from\n$-3.0$ to around $-3.3$. The \"ankle\" is seen in the region of\n$3 \\times 10^{18}\\ {\\rm eV}$ above which the spectral slope\nflattens out to about $-2.7$.\n\nConsider the EHECRs spectrum\nin view of the decay of proton into Planck neutrino.\nLet the earth be the rest frame.\nFor protons arrived at the earth,\nthe travel time meets the condition\n\\begin{equation}\nt\\leq t_p.\n\\label{eq:t}\n\\end{equation}\nFrom this the time required for proton travel from the source to the\nearth defines the limiting energy of proton\n\\begin{equation}\nE_{lim}=\\frac{m_{Pl}}{2}\\left(\\frac{t_{Pl}}{t}\\right)^{1/5}.\n\\label{eq:E}\n\\end{equation}\nWithin the time $t$, protons\nwith the energies $E>E_{lim}$ decay and\ndo not give contribution in the EHECRs spectrum.\nThus the energy $E_{lim}$ defines a cut-off in the\nEHE proton spectrum. Planck neutrinos appeared due to the\ndecay of the EHE protons may give \na contribution in the EHECRs spectrum. \nIf the contribution of Planck neutrinos\nin the EHECRs spectrum is less compared with the contribution\nof protons one can observe the cut-off at the energy $E_{lim}$\nin the EHECRs spectrum.\n\nDetermine\nthe range of the limiting energies of proton\ndepending on the range of distances to the EHECRs sources.\nTake the maximum and minimum distances to the source as\nthe size of the universe and the thickness\nof our galactic disc respectively.\nFor the lifetime of the universe\n$\\tau_0=14 \\pm 2 \\ {\\rm Gyr}$~\\cite{age},\nthe limiting energy is equal to $E_1=3.9 \\times 10^{15}\\ {\\rm eV}$.\nThis corresponds to the first \"knee\" in the EHECRs spectrum.\nFor the thickness of our galactic disc $\\simeq 300\\ {\\rm pc}$,\nthe limiting energy is equal to $E_2=5.5 \\times 10^{17}\\ {\\rm eV}$.\nThis corresponds to the second \"knee\" in the EHECRs spectrum.\nThus\nthe range of the limiting energies of proton\ndue to the decay of proton into Planck neutrino\nlies between\nthe first \"knee\" $E\\sim 3\\times 10^{15}\\ {\\rm eV}$ and\nthe second \"knee\" $E\\sim 10^{17}-10^{18}\\ {\\rm eV}$.\n\nFrom the above consideration it follows that\nthe decrease of the spectral power law index from $-2.7$ to $-3.0$\nat the first \"knee\" $E\\sim 3\\times 10^{15}\\ {\\rm eV}$ and\nfrom $-3.0$ to around $-3.3$\nat the second \"knee\" $E\\sim 10^{17}-10^{18}\\ {\\rm eV}$\ncan be explained as a result of\nthe decay of proton into Planck neutrino.\nFrom this it seems natural that, below\nthe \"ankle\" $E<3 \\times 10^{18}\\ {\\rm eV}$,\nthe EHECRs events are mainly caused by the protons.\nAbove the \"ankle\" $E>3 \\times 10^{18}\\ {\\rm eV}$,\nthe EHECRs events are caused by the particles other than protons.\n\nIf Planck neutrinos take part in the strong interactions,\nthey must give some contribution in the EHECRs events.\nTo explain the observed EHECRs spectrum\nit is necessary to assume that the contribution of Planck neutrinos\nin the EHECRs spectrum is less compared with the contribution\nof protons.\nSuppose that proton decays into 5 Planck neutrinos.\nThen the energy of the Planck neutrino is $1/5$ of the energy of\nthe decayed proton.\nFor the spectral power law index equal to $-2.7$,\nthe ratio of the proton flux to the Planck neutrino flux\nis given by\n$J_p/J_{\\nu}=5^{1.7}=15.4$.\n\nFrom the above consideration it is natural to identify EHE\nparticles with the energies $E>3 \\times 10^{18}\\ {\\rm eV}$\nwith the Planck neutrinos.\nContinue the curve with the spectral power law index $-2.7$\nfrom the \"ankle\" $E\\sim 3 \\times 10^{18}\\ {\\rm eV}$ to\nthe first \"knee\" $E\\sim 3\\times 10^{15}\\ {\\rm eV}$ and\ncompare the continued curve with the observational curve.\nComparison gives\nthe ratio of the proton flux to the Planck neutrino flux\n$J_p/J_{\\nu}\\approx 15$.\n\n\n\\begin{thebibliography}{99}\n\n\\bibitem{M}\nC.W. Misner, K.S. Thorne, J.A. Wheeler, {\\it Gravitation}\n(Freeman, San Francisco, 1973)\n\n\\bibitem{Pau}\nW. Pauli, {\\it Theory of relativity}\n(Pergamon, New York, 1958)\n\n\\bibitem{B}\nN.N. Bogoliubov and D.V. Shirkov, {\\it Quantum fields}, 2nd Ed.\n(Nauka, Moscow, 1993)\n\n\\bibitem{Tr}\nH.-J. Treder {\\it in: Astrofisica e Cosmologia Gravitazione Quanti e\nRelativita} (Giunti Barbera, Firenze, 1979)\n\n\\bibitem{Yo}\nS. Yoshida, H. Dai, J.Phys. {\\bf G24} (1998) 905\n\n\\bibitem{age}\nF. Pont, M. Mayor, C. Turon, and D. A. VandenBerg, A\\&A\n{\\bf 329} (1998) 87\n\n\\end{thebibliography}\n\n\\end{document}\n\n"
}
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[
{
"name": "astro-ph0002254.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{M}\nC.W. Misner, K.S. Thorne, J.A. Wheeler, {\\it Gravitation}\n(Freeman, San Francisco, 1973)\n\n\\bibitem{Pau}\nW. Pauli, {\\it Theory of relativity}\n(Pergamon, New York, 1958)\n\n\\bibitem{B}\nN.N. Bogoliubov and D.V. Shirkov, {\\it Quantum fields}, 2nd Ed.\n(Nauka, Moscow, 1993)\n\n\\bibitem{Tr}\nH.-J. Treder {\\it in: Astrofisica e Cosmologia Gravitazione Quanti e\nRelativita} (Giunti Barbera, Firenze, 1979)\n\n\\bibitem{Yo}\nS. Yoshida, H. Dai, J.Phys. {\\bf G24} (1998) 905\n\n\\bibitem{age}\nF. Pont, M. Mayor, C. Turon, and D. A. VandenBerg, A\\&A\n{\\bf 329} (1998) 87\n\n\\end{thebibliography}"
}
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astro-ph0002255
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Multiwavelength observations of Mkn 501 during the 1997 high state
|
[
{
"author": "D. Petry\\altaffilmark{1}"
},
{
"author": "M. B\\\"ottcher\\altaffilmark{2,3}"
},
{
"author": "V. Connaughton\\altaffilmark{4}"
},
{
"author": "A. Lahteenmaki\\altaffilmark{5}"
},
{
"author": "T. Pursimo\\altaffilmark{5}"
},
{
"author": "C.M. Raiteri \\altaffilmark{6}"
},
{
"author": "F. Schr\\\"oder\\altaffilmark{7}"
},
{
"author": "A. Sillanp\\\"a\\\"a\\altaffilmark{5}"
},
{
"author": "G. Sobrito\\altaffilmark{6}"
},
{
"author": "L. Takalo\\altaffilmark{5}"
},
{
"author": "H. Ter\\\"asranta\\altaffilmark{8}"
},
{
"author": "G. Tosti\\altaffilmark{9}"
},
{
"author": "and M. Villata\\altaffilmark{6}"
}
] |
During the observation period 1997, the nearby Blazar Mkn~501 showed extremely strong emission and high variability. We examine multiwavelength aspects of this event using radio, optical, soft and hard X-ray and TeV data. We concentrate on the medium-timescale variability of the broadband spectra, averaged over weekly intervals. We confirm the previously found correlation between soft and hard X-ray emission and the emission at TeV energies, while the source shows only minor variability at radio and optical wavelengths. The non-linear correlation between hard X-ray and TeV fluxes is consistent with a simple analytic estimate based on an SSC model in which Klein-Nishina effects are important for the highest-energy electrons in the jet, and flux variations are caused by variations of the electron density and/or the spectral index of the electron injection spectrum. The time-averaged spectra are fitted with a Synchrotron Self-Compton (SSC) dominated leptonic jet model, using the full Klein-Nishina cross section and following the self-consistent evolution of relativistic particles along the jet, accounting for $\gamma\gamma$ absorption and pair production within the source as well as due to the intergalactic infrared background radiation. The contribution from external inverse-Compton scattering is tightly constrained by the low maximum EGRET flux and found to be negligible at TeV energies. We find that high levels of the X-ray and TeV fluxes can be explained by a hardening of the energy spectra of electrons injected at the base of the jet, in remarkable contrast to the trend found for $\gamma$-ray flares of the flat-spectrum radio quasar PKS~0528+134. \keywords{BL Lacertae objects: individual: Mkn 501 --- radiation mechanisms: non-thermal}
|
[
{
"name": "paper.tex",
"string": "\\documentstyle[aaspp4,epsf,graphicx]{article}\n\n\n\\begin{document}\n\n\n\\title{Multiwavelength observations of Mkn 501 during the 1997 high state}\n\n\\author{ D. Petry\\altaffilmark{1}, M. B\\\"ottcher\\altaffilmark{2,3},\nV. Connaughton\\altaffilmark{4}, A. Lahteenmaki\\altaffilmark{5},\nT. Pursimo\\altaffilmark{5}, C.M. Raiteri \\altaffilmark{6},\nF. Schr\\\"oder\\altaffilmark{7}, A. Sillanp\\\"a\\\"a\\altaffilmark{5},\nG. Sobrito\\altaffilmark{6}, L. Takalo\\altaffilmark{5},\nH. Ter\\\"asranta\\altaffilmark{8}, G. Tosti\\altaffilmark{9},\nand M. Villata\\altaffilmark{6} \n}\n\\altaffiltext{1}{Institut de F\\'{\\i}sica d'Altes Energies, \nUniversitat Autonoma de Barcelona, 08193 Bellaterra, Spain}\n\\altaffiltext{2}{Space Physics and Astronomy Department, \nRice University, MS 108, 6100 S. Main Street, Houston, TX 77005 - 1892, USA}\n\\altaffiltext{3}{Chandra Fellow}\n\\altaffiltext{4}{Marshall Space Flight Center, Alabama, USA (National Research Council Fellow)}\n\\altaffiltext{5}{Tuorla Observatory, 21500 Piikki\\\"o, Finland}\n\\altaffiltext{6}{Osservatorio Astronomico di Torino, \nStrada Osservatorio 20, 10025 Pino Torinese, Italy}\n\\altaffiltext{7}{Universit\\\"at Wuppertal, Fachbereich Physik, \nGau\\ss{}-Str.20, 42119 Wuppertal, Germany}\n\\altaffiltext{8}{Mets\\\"ahovi Radio Observatory, Mets\\\"ahovintie 114, \n 02540 Kylm\\\"al\\\"a, Finland}\n\\altaffiltext{9}{Osservatorio Astronomico di Perugia, Via Bonfigli, 06123 Perugia, Italy}\n\n\n\\bigskip\n\\centerline{\\it Submitted to The Astrophysical Journal}\n\\bigskip\n\n\\begin{abstract}\n\nDuring the observation period 1997, the nearby\nBlazar Mkn~501 showed extremely strong emission\nand high variability. We examine multiwavelength\naspects of this event using radio, optical, soft \nand hard X-ray and TeV data. We concentrate on the \nmedium-timescale variability of the broadband \nspectra, averaged over weekly intervals. \n\nWe confirm the previously found correlation between\nsoft and hard X-ray emission and the emission at\nTeV energies, while the source shows only minor\nvariability at radio and optical wavelengths. The\nnon-linear correlation between hard X-ray and TeV \nfluxes is consistent with a simple analytic estimate \nbased on an SSC model in which Klein-Nishina effects \nare important for the highest-energy electrons in the\njet, and flux variations are caused by variations of\nthe electron density and/or the spectral index of the\nelectron injection spectrum.\n\nThe time-averaged spectra are fitted with a \nSynchrotron Self-Compton (SSC) dominated\nleptonic jet model, using the full Klein-Nishina cross\nsection and following the self-consistent evolution of\nrelativistic particles along the jet, accounting for \n$\\gamma\\gamma$ absorption and pair production within \nthe source as well as due to the intergalactic infrared \nbackground radiation. The contribution from external\ninverse-Compton scattering is tightly constrained by\nthe low maximum EGRET flux and found to be negligible\nat TeV energies. \nWe find that high levels of the X-ray and TeV fluxes \ncan be explained by a hardening of the energy spectra \nof electrons injected at the base of the jet, in \nremarkable contrast to the trend found for \n$\\gamma$-ray flares of the flat-spectrum radio \nquasar PKS~0528+134. \n\n\\keywords{BL Lacertae objects: individual: Mkn 501 ---\nradiation mechanisms: non-thermal}\n\n\\end{abstract}\n\n\\section{Introduction}\n\nThe BL Lac object Mkn 501 is very close ($z = 0.0337$, Ulrich \net al. \\cite{ulrich}) and has been studied extensively \nat all wavelengths. Together with its sister object Mkn 421, \nit was among the two first BL~Lac objects with known radio \n(Colla et al. \\cite{colla}), X-ray (Schwartz et al. \n\\cite{schwartz}) and TeV gamma-ray (Quinn et al. \\cite{quinn}, \nBradbury et al. \\cite{bradbury}) counterparts. Recently, it was\nalso marginally detected at photon energies $> 100$~MeV by the \nEGRET instrument on board CGRO (Kataoka et al. \\cite{kataoka}).\n\nDuring 1997, the object was found to be in an\nextreme high state with a TeV flux on average 20 times higher than\nin 1996 (Breslin et al. \\cite{breslin}). The source exhibited strong \nvariability on timescales of days with a possible quasi-periodically \nvarying component with a timescale of about 25 days (Kranich et al. \\cite{kranich}). \nTo complete the list of reasons for excitement for the observers, \nMkn~501 reached in some of its flares fluxes of more than \n10$^{-10}$~cm$^{-2}$s$^{-1}$ (above 1.5~TeV) - the most intense \nTeV emission ever measured so far from any astronomical object. \nHowever, the shortest observed variability timescale (5 hours, \nAharonian et al. \\cite{hegraparti}) was significantly longer \nthan that observed for Mkn~421 (Gaidos et al. \\cite{gaidos}).\n\nAll available TeV observatories monitored the event for several \nmonths (Samuelson et al. \\cite{whipple}, Aharonian et al. \n\\cite{hegraparti},\\cite{hegrapartii}, Hayashida \net al. \\cite{telarray}, Djannati-Ata\\\"{\\i} et al. \\cite{cat}). The most complete dataset \nwas produced by the HEGRA Cherenkov Telescope ``1'' (CT1) \n(Aharonian et al., \\cite{hegrapartii}) which was even able to \nobserve Mkn~501 under the presence of moonlight, however with \nreduced sensitivity, thereby filling many gaps in the lightcurve. \nThis telescope also obtained the confirmatory observations in 1996.\n\nAlso from HEGRA come probably the most accurate spectral measurements\nin the TeV regime. They were carried out by the HEGRA system of (at \nthe time 4) Cherenkov telescopes (CTS) and are largely concurrent with\nthe CT1 measurements, however with less time coverage (Aharonian et al. \n\\cite{hegraparti}).\n\nThe origin of the TeV $\\gamma$-ray emission and the reasons for its \nvariability are still essentially unknown. The most popular models \nexplain the TeV emission as near-infrared to UV photons which have \nbeen upscattered via the inverse Compton effect by very high energy \nelectrons which are known from radio, optical and X-ray observations \nto be present in the jets of BL Lac objects. Possible sources of the \nseed photons for Compton scattering are the synchrotron radiation produced \nwithin the jet by the same population of relativistic electrons (synchrotron \nself-Compton model, SSC; Marscher \\& Gear \\cite{marscher}; Maraschi, \nCelotti \\& Ghisellini \\cite{maraschi}; Bloom \\& Marscher \\cite{bloom}), \nor radiation from outside the jet (external inverse Compton model, EIC). \nThis external radiation could be the quasi-thermal radiation field of \nan accretion disk surrounding a supermassive black hole which is \ngenerally believed to power the relativistic jets. The accretion \ndisk radiation can enter the jet either directly (Dermer, Schlickeiser \n\\& Mastichiadis \\cite{dermer92}, Dermer \\& Schlickeiser \\cite{dermer93}) \nor after being rescattered by circumnuclear material (Sikora, Begelman \n\\& Rees \\cite{sikora}, Blandford \\& Levinson \\cite{blandford}, Dermer, \nSturner \\& Schlickeiser \\cite{dermer97}). It is also possible that \nsynchrotron radiation produced within the jet and reflected by \ncircumnuclear debris is the dominant source of soft photons during \nflares (Ghisellini \\& Madau \\cite{ghisellini96}, Bednarek \n\\cite{bednarek}), although it has been shown that this process \nis unlikely to be efficient in the case of BL~Lac objects \n(B\\\"ottcher \\& Dermer \\cite{boettcher98}).\n\nAs an alternative, Mannheim (\\cite{mannheim93}) has \nsuggested a hadronic model in which protons are the \nprimarily accelerated particles in the jet and the \n$\\gamma$-ray emission is produced by secondary pions \nand electron-positron pairs produced in photopion and \nphotopair production interactions of the ultrarelativistic \nprotons in the jet with external radiation. The time-averaged\nbroadband spectrum of Mkn~501 has been fitted using this model\nby Mannheim et al. (\\cite{mannheim96}, \\cite{mannheim98}). \nHowever, the attempts to explain the short and intermediate-term \nvariability of blazars with hadronic jet models have only just started\n(Rachen \\& Mannheim \\cite{rachen99}). \nFor this reason, we concentrate on leptonic jet models in this paper \nsince the variability time scales predicted by these models \nare in good agreement with the observed intraday variability \nof blazars.\n\nRecently, Fossati et al. (\\cite{fossati}) have compared the \nbroadband spectra of different types of $\\gamma$-ray emitting \nAGN and suggested a continuous sequence FSRQs (flat spectrum \nradio quasars) $\\to$ LBLs (low-frequency peaked BL~Lac objects) \n$\\to$ HBLs (high-frequency peaked BL~Lac objects), characterized \nby decreasing bolometric luminosity, decreasing dominance of the \ntotal energy output in $\\gamma$-rays compared to the emission at \nlower frequencies and a shift of the peak frequencies of the \nsynchrotron and the $\\gamma$-ray component towards higher \nfrequencies. Recent modelling efforts of various blazar-type \nAGN have revealed that this sequence is consistent with a \ndecreasing importance of external radiation as a source of \nsoft photons for Compton scattering in the jet (Ghisellini \net al. \\cite{ghisellini98}). This suggests that the extreme \nHBLs like Mkn~501 or Mkn~421 can be well fitted with strongly \nSSC-dominated jet models, as was shown, e. g., by Mastichiadis \n\\& Kirk (\\cite{mastichiadis97}) and Pian et al. (\\cite{pian}).\n\nFrom the SSC model one expects a strong correlation between \nthe X-ray and the TeV emission. And indeed, by comparing the \ndaily TeV measurements with daily averages from the All Sky \nMonitor (ASM) on board the Rossi X-Ray Timing Explorer (RXTE), \na significant correlation with a most probable time-lag of 0 \ndays (no time-lag) was found (Aharonian et al. \n\\cite{hegraparti,hegrapartii}). Furthermore, a clear overall \nX-ray high state was visible in the 1997 ASM measurements which \ncoincided with the TeV high state (see also figure \\ref{fig-lightcurve}). \nAnd, as discovered by BeppoSAX, \nthe X-ray peak of the spectral energy distibution (SED) had shifted \nfrom 10-20 keV in 1996 to 100-200 keV in 1997 (Pian et al. \\cite{pian}), \nconsistent with the assumption that the X-ray and TeV-$\\gamma$-ray \nflares are produced by a more powerful electron acceleration, shifting \nthe high-energy cutoff of the electron distribution to higher energies and\nhardening the X-ray spectrum.\nThis observation was, however, only made during one flare in 1997.\nIn this paper we give evidence that the hardening took place during\nall flares in 1997.\nAn alternative explanation for the synchrotron spectral changes, in\nterms of a steadily-emitting helical-jet model, has been presented by Villata\n\\& Raiteri (\\cite{villata99}). \n\nApart from the short-term variability on timescales of hours to days, \nthere is also a longer-term variability in Blazars which has so far\nbeen investigated mainly in the optical regime (see e.g. Katajainen et al. (\\cite{katajainen}) \nand references therein) and recently also in X-rays (e.g. Mc Hardy \\cite{mchardy}).\nThis variability shows remarkable amplitudes (e.g. 4.7 mag for Mkn 421\nin the optical) and in the case of OJ 287 there is even evidence for\nperiodicity. \n\nIn this respect Mkn 501 is not yet very well explored. \nMkn 501 has been observed in the TeV regime since its discovery\nin 1995. The source showed low emission close to the sensitivity\nlimits until the onset of the 1997 high state.\nSince the duty cycle of the TeV observatories is only about 10 \\%,\nthis does not prove the absence of strong short flares prior to this \nhigh state, but the\nincreased average intensity of the source can be described as\nan increase in flaring probability from 1996 to 1997\nby at least an order of magnitude. This description is especially\nappropriate since\neven during the high state, the source returns to quiescent\n(comparable with 1996) levels of emission for periods of up to a few\ndays. These transitions are seen irrespective of the presence of short,\nstrong flares on time-scales of a day.\n\nThe last observations in 1996 were made in August and found Mkn 501 still\nquiescent while the first observations in 1997 were made in February \nand found the source already flaring. \nThe transition from low to high flaring probability obviously\ntook place on timescales shorter than half a year. \nThe correlated X-ray data from the RXTE ASM \nconfirm this and show in addition that the change\nhas been a smooth process over several months (see e.g. figure 8 in\nAharonian et al. \\cite{hegrapartii}).\n\nIn this article we explore the multi-wavelength variability \nof Mkn 501 over medium timescales, and try to relate its \nbehaviour to the physical parameters of a leptonic jet model. \nFor this purpose we construct weekly SEDs using the HEGRA CT1 \nflux data and HEGRA CT System spectral data together with data \nfrom longer wavelengths, namely radio, optical, soft X-ray and \nhard X-rays. See table \\ref{tab-instruments} for an enumeration \nof the instruments and energy ranges.\n\nThis paper may represent an important step toward understanding the \norigin of strong changes in the flaring probability of Mkn 501 \nand Blazars in general, but our data is clearly not sufficient \nto give a final answer to this question.\n\nAll data except that from HEGRA and the RXTE ASM are published \nhere for the first time. The BATSE data are especially valuable \nsince they confine the intensity at the X-ray peak of the SED.\n\n\\section{Observations and Data Analysis}\n\\label{sec-observations}\n\nThe observations used to fit the multi-wavelength spectrum cover\nmostly the synchrotron part of the SED. Only the TeV data explore what\nis believed to be the Inverse Compton emission, although OSSE and EGRET\nobservations cover a few days in 1996 and 1997. As a guide line for our\nfitting procedure we take into account the highest ever observed EGRET \nflux from Mkn~501, $F(> 100 \\, {\\rm MeV}) = (32 \\pm 13) \\cdot \n10^{-8}$~photons~cm$^{-2}$~s$^{-1}$ with a photon spectral index\n$\\alpha = 1.6 \\pm 0.5$, measured during 1996 Mar 25 \\-- 28 (Kataoka\net al. \\cite{kataoka}), as an upper limit.\n\nIn the definition of time-bins for the multi-wavelength dataset, \nwe start by subdividing the HEGRA CT1 lightcurve and bin all other \ndata accordingly. \n\nThe data from HEGRA are binned in time from March through\nOctober 1997 (MJD 50514 - MJD 50708) resulting in 28 equidistant time\nbins. This weekly temporal resolution is an order of magnitude larger\nthat the longest observed TeV intraday variability timescale of 15 h \n(Aharonian et al. \\cite{hegraparti}) and is\nbelieved appropriate, given the nature of the available data and the\nmedium scale variability timescale which we have chosen to explore.\n\nHowever, the HEGRA points are not spread as uniformly over time as\nare the BATSE and RXTE data. The ``center of gravity in observation time'' \n(defined as the weighted mean of the observation time of the daily points \neach weighted by the duration of the individual observation)\nfrom HEGRA would therefore in general not coincide with that from BATSE \nand RXTE.\nIn order to compensate for this, we calculate the center of gravity\nin observation-time for each weekly HEGRA timebin and use these as\ntime-bin-{\\it centers} for the other data. The edges of these bins\nare then defined by the average of two adjacent bin-centers. \n\nFigure \\ref{fig-lightcurve} shows the lightcurves \nfrom each instrument which went into this analysis.\nThe weekly points after the binning are given in \ntable \\ref{tab-data}. The first column in the table gives the\nbin-centers as described above.\nThe following subsections describe the data used to compile the table.\n\n\\subsection{Optical and Radio Observations}\n\nThe optical observations were performed using the telescopes and \nfilters listed in table~\\ref{tab-instruments}. All the observations \nwere made with CCD-cameras. All CCD-images were treated the normal way \nwith flat field and bias corrections. The magnitudes were measured \nusing either DAOPHOT in IRAF (NOT and Tuorla data; for more details \nsee Katajainen et al. \\cite{katajainen}), or with the ROBIN-procedure \ndeveloped in Torino (e.g. Villata et al. \\cite{villata97}), or using\nthe automated reduction routine developed in Perugia (e.g. Tosti et al. \n\\cite{tosti}). All magnitudes were measured using 10 arcsecond aperture. \nThe use of the same aperture is important because Mkn~501 has a large \nhost galaxy (e.g. Nilsson et al. \\cite{nilsson}). For the calibration \nwe used the calibration sequence given by Fiorucci \\& Tosti \n(\\cite{fiorucci}) and Villata et al. (\\cite{villata98}). \n\nFor some of the weekly observing periods, no optical data were \navailable. However, the optical flux is extremely important for \nconstraining the spectral index of the synchrotron spectra in \nthe optical -- X-ray range, which, in turn, is essential for \nconstraining the spectral index of the electron spectrum. As \ncan be seen in table \\ref{tab-data}, the optical flux exhibits \nonly moderate variability on the time scales considered here. \nThus, for fitting purposes we assume that the optical flux \nduring those viewing periods for which no optical observations \nwere available, was within the range of optical fluxes observed \nduring the whole campaign which yields $\\nu F_{\\nu} (opt.) = \n(7.485 \\pm 0.774) \\cdot 10^{-11}$~erg~cm$^{-2}$~s$^{-1}$.\n\nThe radio observations were made with the Mets\\\"ahovi Radio Telescope at 22 GHz\nas part of the ongoing quasar monitoring program, which started in 1980.\nCurrently about 85 sources, mainly Northern flat spectrum quasars, should \nbe observed monthly at 22 and 37 GHz. The total number of observations is \nnow over 40000. For details of the observing strategy and reductions, as \nwell as the data until 1995.5 see Ter\\\"asranta et al. (\\cite{terasranta}).\n\nThe integration time of each point was essentially the same, so single points\nwere formed from the data points in the individual timebins\nby simple averaging. \n\n\n\\subsection{Soft X-Ray Data}\n\nSince the beginning of 1996, the all-sky monitor (ASM) of the\nRossi X-ray Timing Explorer (RXTE) satellite has been observing\nMkn 501 in the 2-12 keV energy band. The data used in this\nanalysis are taken from the publicly available ASM data products\nprovided by the ASM/RXTE teams at MIT and at the RXTE SOF and GOF \nat NASA's GSFC. These measurements are given by the authors (see \ne.g. Levine et al. \\cite{levine}) as rates $R_1, R_2, R_3$ in units \nof counts per second in three energy bins: 1.3-3.0 keV, 3.0-5.0 keV, \nand 5.0-12.1 keV. From these we calculate the total rate $R$ by \nsumming the three bins.\n\nFor Mkn 501 we obtain by averaging over the period MJD 50510 - 50710\n\\begin{equation}\n R_{mkn501} = 1.3 \\pm 0.4\n\\end{equation}\n\nIn order to assess the X-ray spectrum and flux of Mkn 501, we use the \nASM data for the Crab Nebula which is publicly available from the same \nsource. The average rate of the Crab Nebula during the period MJD 50510 \n-- 50710 is\n\\begin{equation}\n R_{crab} = 75.7 \\pm 0.5\\\\\n\\end{equation}\nHence, in soft X-rays, Mkn 501 is even during this high state a significantly weaker \nsource than the Crab Nebula.\n\nIn the energy range 2 keV to 60 keV, the spectrum of the Crab Nebula is a stable \npower law. The spectral index of the differential photon spectrum \nis known with an accuracy of 1\\% to be\n$\\alpha_{crab} = 2.1$ (e.g. Toor \\& Seward \\cite{toor}, Pravdo \\& Serlemitsos \\cite{pravdo}\nor Pravdo, Angelini \\& Harding \\cite{pravdo-b}).\nThe emission measured by the RXTE ASM is the sum of the steady Nebula and the pulsed\nCrab Pulsar emission. The latter has on average a harder spectrum than the nebula.\nBelow 12.1 keV, however, the pulsed fraction of this emission is $< 8$~\\%. \nWe can therefore use the knowledge of the Crab Nebula spectrum to derive an approximate \nrelative calibration factor $k$ for the rates $R_{2}$ and $R_{3}$ using\n\\begin{equation}\n\\frac{k R_{2,crab}}{R_{3,crab}} = \\frac{E_3^{1-\\alpha_{crab}} - E_2^{1-\\alpha_{crab}}}\n {E_4^{1-\\alpha_{crab}} - E_3^{1-\\alpha_{crab}}} = 1.213 \n\\end{equation}\nwhere $E_2 = 3.0$~keV, $E_3 = 5.0$~keV, and $E_4 = 12.1$~keV are the energy bin\nedges of the second and third energy bin. We ignore the first energy bin since it\nis strongly influenced by interstellar X-ray absorption which is dependent on the\ncolumn density and hence varies between sources (Remillard \\cite{remillard}).\n\nAveraging over the available Crab data from the observation period \nunder discussion (MJD 50510 - 50710) we obtain $k = 1.318 \\pm 0.0024$.\nThere is no indication of a variability of the value of $k$ (see figure \\ref{fig-k}).\nHence we can assume that it is also valid for the Mkn 501 observations of the\nsame detector.\nIn order take into account that there is a pulsed component with a harder spectrum,\nwe add an additional error of 8 \\% to the error of $R_3$ and obtain thus\n\\begin{equation}\n k = 1.32 \\pm 0.023\n\\end{equation}\n\nFor Mkn 501 we calculate the spectral index $\\alpha$ of the differential photon spectrum \nusing the equation\n\\begin{equation}\n\\frac{k R_{2,mkn501}}{R_{3,mkn501}} = \\frac{E_3^{1-\\alpha} - E_2^{1-\\alpha}}{E_4^{1-\\alpha} - E_3^{1-\\alpha}} \n\\end{equation}\nand varying $\\alpha$ until the two sides of the equation are equal to an accuracy better\nthan 0.1~\\%.\nThe error $\\delta\\alpha$ of this index, we estimate from the approximate formula\n\\begin{equation}\n\\alpha = -\\frac{\\log(k \\cdot R_2/(5.0 - 3.0)) - \\log(R_3/(12.1 - 5.0))}{\\log((3.0 + 5.0)/(5.0 + 12.1))}\n\\end{equation}\nwhich leads to\n\\begin{equation}\n\\delta\\alpha = \\sqrt{ 1.733 \\cdot ( (\\frac{\\delta k}{k})^2 + (\\frac{\\delta R_2}{R_2})^2 + (\\frac{\\delta R_3}{R_3})^2 ) }\n\\end{equation}\nwhere $\\delta k$, $\\delta R_2$, and $\\delta R_3$ are the errors of the corresponding quantities.\nThe time resolved values for $\\alpha_{mkn501}$ are shown in figure \\ref{fig-alphas}.\nThe same method applied to the Crab Nebula data (however with $\\delta k = 0.0024$) yields, \nas expected, on average the spectral index we have put in. Also this is shown in figure \\ref{fig-alphas}.\nFrom a constant fit to the values in this figure, we obtain\n\\begin{equation}\n \\alpha_{mkn501} = 1.76 \\pm 0.04\n\\end{equation}\nand\n\\begin{equation}\n \\alpha_{crab} = 2.10 \\pm 0.02\n\\end{equation}\nThus we find that during the 1997 high state, Mkn 501 had on average a significantly harder \nsoft X-ray spectrum than the Crab Nebula. \nThe spectral variability of Mkn 501 is below the ASM's sensitivity.\nThe distribution of the weekly values is consistent with a constant value\n(reduced $\\chi^2$ = 0.93) and so is that for the Crab Nebula (reduced $\\chi^2$ = 0.95). \n\nIn order to calculate the $\\nu F_{\\nu}$ values in erg cm$^{-2}$ s$^{-1}$, \nwe use the knowledge of the flux of the Crab Nebula. Here we face the problem that\nthere is still a disagreement of up to 25 \\% between the measured normalization constants of the\nCrab Spectrum from different experiments although there is perfect agreement in the spectral index. \nThe discrepancy seems to stem from not very well understood \nsystematic differences between the detectors (see the discussion in \nPravdo, Angelini \\& Harding \\cite{pravdo-b}). \nWe use the two most extreme recent measurements of the differential photon flux of the Crab Nebula together \nwith the Crab Pulsar (pulse-averaged) and take their average as our normalization and their difference\nas the systematic error of this quantity. From Pravdo \\& Serlemitsos (\\cite{pravdo})\nwe get at 5.2 keV a flux of (0.236 $\\pm$ 0.006) photons~cm$^{-2}$s$^{-1}$keV$^{-1}$, while from\nPravdo, Angelini \\& Harding (\\cite{pravdo-b}) we get (0.302 $\\pm$ 0.001) photons~cm$^{-2}$s$^{-1}$keV$^{-1}$.\nThe average of these values corresponds to a differential energy flux of \n\\begin{equation}\nF_{crab}(5.2 \\mathrm{keV}) = (2.24 \\pm 0.27_{syst}) \\times 10^{-9} \\mathrm{erg}\\,\\mathrm{cm}^{-2}\\mathrm{s}^{-1}\\mathrm{keV}^{-1}\n\\end{equation}\nwhere the systematic error is the difference between the averaged values divided by 2.\nThe statistical errors of the two measurements are negligible. \nThe energy flux of any other source with ASM rates $R_2$ and $R_3$ and differential photon spectral index\n$\\alpha$ is then calculated by\n\\begin{equation}\n\\begin{array}{rcl}\n \\nu F_{\\nu} [\\mathrm{erg\\,cm}^{-2} \\mathrm{s}^{-1}] \n& = & (R_2 + R_3)[\\mathrm{s}^{-1}] \\cdot \n \\frac{\\displaystyle F_{crab}(5.2 \\mathrm{keV})[\\mathrm{erg}\\,\\mathrm{cm}^{-2}\\mathrm{s}^{-1}\\mathrm{keV}^{-1}]}\n {\\displaystyle (R_{2,crab}+R_{3,crab})[\\mathrm{s}^{-1}]} \\\\\n& & \\cdot 5.2^{1 + \\alpha_{crab} - \\alpha} \n \\cdot \\frac{\\displaystyle 1 - \\alpha}{\\displaystyle 1 - \\alpha_{crab}}\n \\cdot \\frac{\\displaystyle E_4^{1 - \\alpha_{crab}} - E_2^{1 - \\alpha_{crab}}}\n {\\displaystyle E_4^{1 - \\alpha} - E_2^{2 - \\alpha}} \\\\\n& = & R[\\mathrm{s}^{-1}] \\cdot \\frac{\\displaystyle 5.2^{1 - \\alpha} \\cdot (1 - \\alpha)}\n {\\displaystyle 12.1^{1 - \\alpha} - 3.0^{1 -\\alpha}} \\cdot 3.13 \\times 10^{-10} \\\\\n\\end{array}\n\\end{equation}\nwhere we correct for the difference in the spectra of Crab Nebula and the source in question\nby making the Ansatz that the measured differential rates have the same ratio\nas the differential fluxes. Furthermore we have used the result $R_{2,crab}+R_{3,crab} = 48.5 \\pm 0.7$ s$^{-1}$\nobtained from the dataset under discussion. \nInserting the spectral index of Mkn 501 gives:\n\\begin{equation}\n \\nu F_{\\nu}(\\mathrm{Mkn 501}, 5.2 \\mathrm{keV}) = \n (R_2 + R_3)[\\mathrm{s}^{-1}] \\cdot 2.40 \\times 10^{-10} \\mathrm{erg\\,cm}^{-2} \\mathrm{s}^{-1}\n\\end{equation} \nThe error of this flux value is determined by propagating all errors of the quantities\ninvolved which gives\n\\begin{equation}\n\\begin{array}{lr}\n \\delta(\\nu F_\\nu)(\\mathrm{Mkn 501}, 5.2 \\mathrm{keV}) = \\\\\n (\\sqrt{5.76 \\times 10^{-20} \\cdot ((\\delta R_2)^2 + (\\delta R_3)^2) + \n 1.21 \\times 10^{-23} \\cdot (R_2 + R_3)^2}\\,+\\,0.12 \\cdot \\nu F_\\nu)\\, \\mathrm{erg\\,cm}^{-2} \\mathrm{s}^{-1}\n\\end{array}\n\\end{equation}\nwhere the term outside the square-root stems from the systematic error of the Crab flux normalization.\n\n\\subsection{Hard X-Ray Data}\n\\label{batse}\n\nThe Hard X-ray fluxes were measured using the Burst and Transient\nSource Experiment (BATSE) onboard the CGRO satellite.\nAlthough BATSE is an uncollimated\ndetector, accurate point source fluxes can be measured using the\nEarth Occultation method described in \nHarmon et al. (\\cite{batsemethod}). Daily sensitivities are 100\nmCrab and over integrations of years, sources as weak as 3 mCrab can be\ndetected. Several months are usually needed to obtain a statistically\nsignificant flux from Mkn 501 with BATSE, but intense daily flares\ncan be seen, and the overall high state of 1997 allowed useful\nmeasurements in each weekly interval even outside the flares.\n\nThe source is measured only when it sets and rises from\nbehind the Earth.\nSince two such occultations occur per spacecraft orbit \n(roughly every 90 minutes), up\nto 32 independent flux measurements can be made per day.\nThere exists, however,\na wide variation in this number\nbecause of passage of the spacecraft through the South\nAtlantic Anomaly, telemetry gaps from loss of TDRSS contact, and other\nevents, which occur randomly relative to the Mkn 501 steps.\nFor the data shown here between 61 and 211 measurements went into\nan individual weekly point. Each measurement lasts about 8\nseconds giving a duty cycle of about 0.2\\%.\nIn a 7 day time bin during the period discussed in this paper, BATSE\nobserves of the order of $10^5$ photons from the \nsource (more during the flares).\n\nThe fluxes are integrated between 20 and 200 keV, and are\ncalculated by folding the measured counts through the BATSE detector response\nassuming a differential source powerlaw spectrum of index -2.0.\nThe -2.0 spectrum is the best fit to the flare\n measured on MJD 50550-51 (between 20 and 1000 keV).\nSpectra for other time intervals were also calculated and were\nconsistent with -2.0. Uncertainties of 10~\\% in the spectral index during \nflare times, larger\noutside, make spectral variability difficult to assess for this source,\nso that the index of -2.0 was used for each weekly interval. Fluxes\nwere calculated for smaller\nenergy bands but the single 20-200 keV (median energy 36.4 keV) point \nfor each interval is the most useful outside intense flares. \n\nSeven of the weekly averages are not statistically significant, and one period\nshows a $1.8 \\sigma$ deficit. These eight points are inconsistent with \na zero-level flux at the 99 \\% confidence level.\nThe seven low but positive points are inconsistent with a zero-flux \nlevel at the 98-99 \\% confidence level and are well fit by \na constant flux of $1.1 \\pm 0.3 \\times\n10^{-10}$ erg cm$^{-2}$ s$^{-1}$, implying that \na flux is present which is below the sensitivity of the BATSE instrument in\nweekly integrations.\nAn analysis of 30 blank fields on the sky shows that with 100\nweekly integrations\nfor each field one can not distinguish (using an F-test) \nbetween a zero-flux level and the weighted mean of the weekly averages for\nany of the 30 fields. This implies that systematic effects are not \nresponsible for the excess seen in the low points and that a flux is indeed\npresent. For this reason these low but positive\nvalues have been included as detections \nin the multiwavelength fits. \n\n\\subsection{TeV data}\n\nAs described above, we use the data from the CT1 lightcurve of \nMkn~501 (integral flux above 1.5 TeV) published by Aharonian et \nal. (\\cite{hegrapartii}). These data are available in daily points \nbased on observations of between 0.5~h and 5~h duration each. We \ngroup these points according to our weekly time-bins and calculate\nan average flux from the up to seven values weighting each daily point \nby its observation time.\n\nApart from giving daily flux measurements, the HEGRA papers\nAharonian et al. (\\cite{hegraparti}), (\\cite{hegrapartii}), and (\\cite{hegraspec}) \nalso determine the average spectral shape in the range between 0.5 and $\\approx$ 25 TeV\nwith high accuracy. They find\n\\begin{equation}\n\\label{equ-spec}\ndF/dE = N_0 E^{-\\alpha} \\exp(-E/E_0)\n\\end{equation}\nwhere $N_0 = (10.8 \\pm 0.2 \\pm 2.1) \\times\n10^{-11}$~cm$^{-2}$~s$^{-1}$~TeV$^{-1}$, $\\alpha = 1.92 \n\\pm 0.03 \\pm 0.20$, and $E_0 = (6.2 \\pm 0.4 \\pm 2.2)$~TeV. \nThe first error given is the statistical, the second the \nsystematic error. Furthermore, they find that there is no \nspectral variability up to their sensitivity of $\\delta\\alpha \n\\le 0.1$ on all relevant timescales. \n\nIn order to include this important spectral information in our model fit,\nwe make the assumption that there is indeed no spectral variability and\nextrapolate the points measured at 1.5 TeV by CT1 up to 10~TeV and down \nto 0.8~TeV. From the average integral flux values $F_{1.5}$ in units of \nphotons cm$^{-2}$s$^{-1}$ we obtain the $\\nu F_{\\nu}$ values at photon \nenergy $E$ in TeV using\n\\begin{equation}\n\\nu F_{\\nu}(E) [\\mathrm{erg \\> cm}^{-2}\\mathrm{s}^{-1}] = 1.6022 \\cdot \nF_{1.5} \\, {E^{(2 - \\alpha)} \\cdot \\exp(-E/E_0) \\over\n\\int\\limits_{1.5}^{\\infty} d\\epsilon \\> \\epsilon^{-\\alpha} \\, \n\\exp(-\\epsilon/E_0)}.\n\\end{equation}\nThe extrapolation uses the measured spectral shape (equation \n\\ref{equ-spec}) and fully propagates all statistical errors (error of the \nCT1 point, error of the spectral index $\\alpha$ and the error of the \ncut-off energy $E_0$) to form the error of the extrapolated point.\nThe systematic errors of the spectral shape are expected to influence\nall measured TeV spectra in the same way since they are caused by the 15~\\%\nuncertainty in the absolute energy calibration of the Cherenkov telescopes. \nThus, for the purpose of a\nspectral variability study, the statistical errors are those which\nactually determine the uncertainty in the differences of the spectral\nshape between different measurements. For this reason we propagate\nonly the statistical errors in the extrapolation. In this way, the \ncolumns 6 and 8 of table \\ref{tab-data} are obtained. In the model fit \n(section \\ref{sec-fitting}) we take into account the uncertainty in the \nenergy scale by introducing errors of $\\pm 15$~\\% along the energy axis.\n\nThe energies to which we extrapolate are chosen as a compromise of maximum\ndistance to 1.5 TeV and minimum systematic errors. The latter are\nincreasing up to several 10\\,\\% towards both ends of the range for \nwhich the spectrum has been measured (see Aharonian et al. \n\\cite{hegraspec}, figure 9) but are still small at 0.8 and 10 TeV.\n\nThe correlation between the three TeV points which we introduce into\nthe model fit by performing the described extrapolation is not problematic\nsince we do not plan to calculate absolute $\\chi^2$ values in the fits for\nproving that the model describes the data better than another.\nInstead, the fits serve the aim to study the time-dependent behaviour of \nthe model parameters.\nThe extrapolated points are only a means to take into account the available\nspectral information.\n\n\\subsection{Fitting the model to the SEDs}\n\\label{sec-fitting}\n\nTo each weekly SED we fit the Blazar jet model described in detail\nby B\\\"ottcher et al. (\\cite{boettcher97}). The model assumes that\nisolated components (blobs) of relativistic pair plasma, which\nare assumed to be spherical in the co-moving frame, are \ninjected instantaneously into the jet, and follows the \nself-consistent evolution of the particle and radiation spectra \nas the blob moves outward along the jet, taking into account\nall relevant radiation, cooling, and absorption mechanisms: \nsynchrotron radiation, synchrotron self-absorption, synchrotron\nself-Compton scattering, external Compton scattering of direct \naccretion disk radiation, $\\gamma$-$\\gamma$ absorption and pair \nproduction intrinsic to the source. The magnetic field is\nassumed to decay along the jet as $B \\propto r^{-1}$, \nwhere $r$ is the distance from the center of the AGN. \nThe emerging, time-averaged spectra are corrected for \n$\\gamma\\gamma$ absorption by the intergalactic infrared \nbackground radiation using the lower model spectrum given \nby Malkan \\& Stecker (\\cite{malkan98}). \n\nSince we are interested in weekly averages, the emission from \nsingle blobs is time-integrated over the jet evolution and\nsubsequently re-converted into a flux by dividing the fluence\nby an average repetition time $\\Delta t_{\\rm rep}$ of blob \nejection events. We assume that a fraction $f < 1$ of the jet \nis filled with relativistic pair plasma. The filling factor \nis given by $f \\sim R'_B / (\\Gamma \\, c \\, \\Delta t_{\\rm rep})$,\nwhere $R'_B$ is the blob radius in the co-moving frame and\n$\\Gamma$ is the bulk Lorentz factor of the blobs. Even if \nthe filling factor is close to unity, it is a reasonable \napproximation to assume that the blobs do not interact \nwith each other because the synchrotron and SSC radiation \nproduced within the jet are isotropic in the comoving \nframe so that most of the radiation escapes to the sides \nwithout interaction with the rest of the jet.\n\nAs mentioned in the introduction, extreme HBLs like Mkn~501 \nor Mkn~421 are generally well described by a pure SSC model. \nA simple analytic estimate shows that the observed TeV \n$\\gamma$-ray spectrum can not plausibly be produced by \nComptonization of radiation from an accretion disk around \nthe putative supermassive black hole in the center of \nMrk~501: The spectrum emitted by an optically thick, \ngeometrically thin accretion disk is reasonably well\napproximated by a blackbody spectrum whose temperature, for\na black hole mass of $\\gtrsim 10^8 \\, M_{\\odot}$, yields an\naverage photon energy of the disk radiation of $\\epsilon_D\n\\equiv h \\nu_D / (m_e c^2) \\sim 10^{-5}$. If external Comptonization\nis to be efficient in competition with the synchrotron self-Compton\nprocess, the blob has to be rather close to the accretion disk,\nor a significant fraction of the disk photons has to be rescattered \ninto the jet by surrounding material, so that the bulk of disk \nphotons enters the blob from the side and is blue shifted \nby a factor of $\\sim \\Gamma$ into the blob rest frame. \nThus, due to the strong reduction of the Klein-Nishina cross \nsection for $\\gamma_e \\epsilon' \\gtrsim 1$ (where $\\epsilon'$\nis the photon energy in the comoving frame), no significant \nradiative output at (observer's frame) energies $\\epsilon_{obs} \n\\gtrsim D / (\\epsilon_D \\Gamma) \\sim 10^5$ (where $D$ is the \nDoppler factor), corresponding to $E_{obs} \\gtrsim 100$~GeV, \nwill be produced by external Comptonization, ruling out this \nprocess to explain the observed high-energy spectrum extending \nto TeV energies. If the high-energy spectrum in the $\\gtrsim \n100$~GeV regime is produced by the SSC process, then the level \nof SSC radiation at 1~GeV may be estimated by\n\\begin{equation}\n\\nu F_{\\nu}^{SSC} (1 \\, {\\rm GeV}) \\approx \\nu F_{\\nu}^{SSC}\n(E_{pk}) \\, \\left( {E_{pk} \\over 1 \\, {\\rm GeV}} \\right)^{p - 3\n\\over 2}\n\\label{GeV_estimate}\n\\end{equation}\nwhere $E_{pk} \\gtrsim 0.1$~TeV is the energy of the $\\nu F_{\\nu}$ \npeak in the high-energy part of the spectrum and $p$ is the spectral \nindex of the injected electron spectrum. Inserting a typical value \nof $\\nu F_{\\nu} (E_{pk}) \\gtrsim 10^{13} \\> {\\rm Jy \\, Hz}$ and \n$p \\sim 2.5$, this yields $\\nu F_{\\nu}^{SSC} (1 \\, {\\rm GeV})\n\\gtrsim 3 \\cdot 10^{12} \\> {\\rm Jy \\, Hz}$, which is already close\nto the maximum ever observed of $\\sim 10^{13} \\> {\\rm Jy \\, Hz}$.\nIn reality, the SSC spectrum is not a straight power-law below\n$E_{pk}$, but shows a gradual turnover so that the actual SSC\nflux at 1~GeV is substantially higher than the above estimate, \nleaving little room for an additional EIC contribution. For our\nfitting procedure, we are thus using a simplified version of\nour jet simulation code, in which the photon output (but not\nthe electron cooling) from Comptonization of accretion disk\nradiation is neglected. These simulations properly account for \nthe self-consistent cooling of the electron population and \n$\\gamma\\gamma$ absorption and pair production in the blob. \nIn the simulations, the exact, angle-averaged synchrotron \nspectrum of an isotropic electron population as given by \nCrusius \\& Schlickeiser (\\cite{crusius86}) is used.\n\nFig. \\ref{ssc_fits} shows two examples of fits to low \nand high flux levels of Mkn~501. The respective fit \nparameters are given in the figure captions. Inverse-Compton \ncooling on accretion-disk photons may be important close to \nthe base of the jet even if the resulting photon spectra do\nnot contribute significantly to the time-averaged emission\nand is thus still included in our simulations.\n\nDue to the non-linear nature of the model system, the fit results\ncannot be described in a simple, linear way as a function of the\nmodel parameters. We therefore construct a three-dimensional mesh\nof simulations in parameter space, with the electron density $n_e$, \nthe high-energy cutoff $\\gamma_2$ and the spectral index $p$ of the \ninjected electron spectrum as parameters which are free to vary on \nthe grid points. \n\nWe calculate our parameter grid varying $p$ in steps of 0.025 between\n1.6 and 2.8, the total electron number density $n_e$ in steps\nof 5~cm$^{-3}$ between 10 and 120~cm$^{-3}$, and $\\gamma_2$\nfor values of $2 \\cdot 10^6$, $3 \\cdot 10^6$, $5 \\cdot 10^6$,\n$7.5 \\cdot 10^6$, $10^7$, $1.5 \\cdot 10^7$, $2 \\cdot 10^7$, \n$2.5 \\cdot 10^7$, and $3 \\cdot 10^7$. We constrain the range \nof $\\gamma_2$ values to $\\gamma_2 \\le 3 \\cdot 10^7$ because of \nthe kinematic limit and because around this energy, electron \ncooling due to triplet pair production on the highest-energy \nsynchrotron photons, which is ignored in our simulations, becomes \ndominant over Compton scattering (Mastichiadis et al. \n\\cite{mastichiadis94}, Anguelov et al. \\cite{ang99}). \nWe find that our simulated spectra are only very weakly \ndependent on the actual value of $\\gamma_2$. A change of \n$\\gamma_2$ by a factor 3 typically results in an increase \nof the reduced $\\chi^2$ of only 0.3 such that the \nabove-mentioned restriction of $\\gamma_2$ values has\nonly minor impact on our results. In fact $\\gamma_2$ can\nbe regarded as constant and of the order of $10^7$. \nWe point out that the instantaneous synchrotron spectra of\nindividual blobs at the time of injection, which might\ncorrespond to short-term X-ray and TeV flares, have \ntheir synchrotron peak at $\\nu_{sy, inst.} \\sim 2.8 \\cdot\n10^6 \\> (B/{\\rm G}) \\, D \\, \\gamma_2^2$~Hz if $p < 3$, in \nagreement with the shift of the synchrotron peak into the \nhard X-ray regime during extreme flaring activity (e. g., \nPian et al. \\cite{pian}).\n\nAll other parameters (in particular, the magnetic field at\nthe particle injection site, $B_0 = 0.05$~G, the low-energy\ncutoff of the electron spectrum $\\gamma_1 = 300$, and the \nDoppler factor, $D = 30$) are fixed to values allowing good \nfits to the observed weekly averaged SEDs using our simulation \ncode. An estimate for the required parameters can be found\non the basis of the location of the synchrotron and SSC peaks\nof the observed broadband spectra as described below.\n\nAlthough we are assuming the injection of a single power-law\ndistribution of ultrarelativistic electrons into the jet, the \ntime-averaged radiation spectrum will be reasonably well \napproximated by the one produced by a broken power-law \ndistribution of electrons with spectral index $p$ below \nthe break energy $\\gamma_b$, and $p + 1$ above the break \nenergy. $\\gamma_b$ may be computed by setting the synchrotron \ncooling time scale equal to the dynamical time scale of jet \nevolution (magnetic field decay), which yields\n\\begin{equation}\n\\gamma_b \\approx 6.4 \\cdot 10^5 \\> {\\Gamma_{25} \\over\nz_{0.03} \\, B_{-1}^2}\n\\label{gamma_b}\n\\end{equation}\nwhere $\\Gamma_{25} \\equiv \\Gamma / 25$, the height of the\ninjection/acceleration site above the accretion disk is \n$z_i = 0.03 \\, z_{0.03}$~pc, and $B_{-1} = B_0 / (0.1 \\, \n{\\rm G})$. Thus, our model calculations will produce a \ntime-averaged synchrotron break at\n\\begin{equation}\n\\nu_{sy} \\sim 3.4 \\cdot 10^{18} \\> \\overline B_{-1} \\, D_{30}\n\\, {\\Gamma_{25}^2 \\over z_{0.03}^2 \\, B_{-1}^4} \\> {\\rm Hz}\n\\label{nu_sy}\n\\end{equation}\nwhere $\\overline B_{-1}$ is an appropriate average of the \nmagnetic field (in units of $0.1$~G) over the jet evolution. \nFor the purpose of these estimates, we neglect factors of\n$(1 + z) \\sim 1$ for Mkn~501. The location of the peak of \nthe SSC component will be strongly influenced by Klein-Nishina \neffects and will thus depend on the actual shape of the \nsynchrotron spectrum, which, in turn, depends on the electron \nspectral index $p$. Considering these effects, Tavecchio et \nal. (\\cite{tav98}) find\n\\begin{equation}\n\\epsilon_{SSC} \\sim \\gamma_b \\, D \\, g(\\alpha_1, \\alpha_2)\n\\label{epsilon_ssc}\n\\end{equation}\nwhere $\\alpha_1 = (p - 1)/2$, $\\alpha_2 = p/2$, and\n\\begin{equation}\ng(\\alpha_1, \\alpha_2) = \\exp\\left[ {1 \\over \\alpha_1 - 1}\n+ {1 \\over 2 \\, (\\alpha_2 - \\alpha_1)} \\right].\n\\label{g_alpha}\n\\end{equation}\nFor $p = 2.5$, this yields $\\epsilon_{SSC} \\sim 9.4 \\cdot 10^5\n\\> D_{30} \\, \\Gamma_{25} / (z_{0.03} \\, B_{-1}^2)$, corresponding\nto\n\\begin{equation}\nE_{SSC} \\sim 490 \\> { D_{30} \\, \\Gamma_{25} \\over z_{0.03} \\,\nB_{-1}^2} \\> {\\rm GeV}.\n\\label{E_ssc}\n\\end{equation}\nCombining Eqs. \\ref{nu_sy} and \\ref{E_ssc} and using the average\nobserved $\\epsilon_{sy} \\sim 10^{-2}$ and $\\epsilon_{SSC} \\sim 10^6$,\nwe find\n\\begin{equation}\n{\\overline B_{-1} \\over D_{30}} \\sim 300 {\\epsilon_{sy} \\over \n\\epsilon_{ssc}^2} \\, g^2 (\\alpha_1, \\alpha_2) \\sim 0.34\n\\label{BD_1}\n\\end{equation}\nfor $p = 2.5$ (see also Tavecchio et al. \\cite{tav98}). Similarly,\nwe may use Eq. (22) of Tavecchio et al. (\\cite{tav98}) to estimate\n\\begin{equation}\n\\overline B \\, D^{2 + \\alpha_1} \\gtrsim \\left[ g(\\alpha_1, \\alpha_2)\n\\, \\epsilon_{SSC} \\, \\epsilon_{sy} \\right]^{(1 - \\alpha_1)/2} \\, \\sqrt{\n2 f(\\alpha_1, \\alpha_2) \\over c^3} \\> {\\left( \\nu L_{\\nu} \\right)_{sy}\n\\over t_{var} \\, \\sqrt{ \\left( \\nu L_{\\nu} \\right)_{SSC}}}\n\\end{equation}\nwhere $f(\\alpha_1, \\alpha_2) = 1/(1 - \\alpha_1) + 1/(\\alpha_2 - 1)$.\nUsing $p = 2.5$, $\\left(\\nu L_{\\nu} \\right)_{sy} \\sim 6 \\cdot 10^{43}$~erg/s,\n$\\left(\\nu L_{\\nu} \\right)_{SSC} \\sim 2 \\cdot 10^{44}$~erg/s, and\n$t_{var} \\sim 5$~h (Aharonian et al. \\cite{hegraparti}), we find\n\\begin{equation}\n\\overline B_{-1} \\, D_{30}^{11/4} \\gtrsim 0.34.\n\\label{BD_2}\n\\end{equation}\nCombining this with Eq. \\ref{BD_1}, we have $D_{30} \\gtrsim 1$ and\n$\\overline B_{-1} \\gtrsim 0.34$. These numbers are consistent with\nthe limits found by Bednarek \\& Protheroe \\cite{bednarek99}, but\nare slightly outside the allowed region of parameter space as found\nby Tavecchio et al. (\\cite{tav98}) and Kataoka et al. (\\cite{kataoka}).\nThis is because in those papers the broadband spectrum is either\ncharacterized by quantities pertaining to individual outbursts or\nto a long-term quiescent state. Those parameters are not representative\nof the weekly averages investigated in this paper. \n\nHaving constructed the three-dimensional mesh of simulations,\nwe compare all weekly SEDs with the simulated spectra and find\nthe simulation with the smallest $\\chi^2$. Results of this\nprocedure are described in the next section.\n\n\\section{Results}\n\n\\subsection{Correlation TeV-X-Ray}\n\nThe SSC model for Mkn~501 predicts a very strong correlation \nbetween the emission at the synchrotron peak (in soft -- hard \nX-rays) and at the inverse-Compton peak (close to TeV \n$\\gamma$-ray energies). We have derived an analytic estimate\nfor the expected correlation, for variations of several input\nparameters. In the following discussion, unprimed quantities are\nmeasured in the co-moving frame, while a superscript $\\ast$ refers\nto quantities measured in the observer's frame. We assume that \nthe time-averaged (cooling) electron spectrum can be described \nby a broken power-law, \n\n\\begin{equation}\nn_e (\\gamma) = n_0 \\cases{ (\\gamma / \\gamma_b)^{-p} & \nfor $\\gamma_1 \\le \\gamma \\le \\gamma_b$ \\cr\n(\\gamma / \\gamma_b)^{-(1 + p)} \n& for $\\gamma_b \\le \\gamma \\le \\gamma_2$ \\cr}\n\\end{equation}\nwhere the injection spectral index $2 < p < 3$, and $\\gamma_b$ \nis the break energy of the spectrum, determined by Eq. \\ref{gamma_b}. \nThe normalization is given by $n_0 \\approx n_e \\, \\gamma_b^{-p}\n\\, \\gamma_1^{p-1} / (p - 1)$. We are using a $\\delta$ approximation \nfor the synchrotron spectrum:\n\\begin{equation}\nL_{sy} (\\epsilon) = L_0 \\cdot \\cases{ (\\epsilon / \\epsilon_b)^{1 - p \n\\over 2} & for $\\epsilon_1 \\le \\epsilon \\le \\epsilon_b$ \\cr\n(\\epsilon / \\epsilon_b)^{-{p \\over 2}} \n& for $\\epsilon_b \\le \\epsilon \\le \\epsilon_2$, \\cr}\n\\end{equation}\nwhere $\\epsilon = h \\nu / (m_e c^2)$ is the dimensionless photon energy\nand $\\epsilon_i = 2.3 \\cdot 10^{-14} \\, (B/ {\\rm G}) \\, \\gamma_i^2$ \nis the characteristic synchrotron energy radiated by an electron of \nLorentz factor $\\gamma_i$. Normalizing the synchrotron luminosity to\n\n\\begin{equation}\nL_{sy} \\propto B^2 \\int\\limits_{\\gamma_1}^{\\gamma_2} d\\gamma \\>\nn_e (\\gamma) \\, \\gamma^2,\n\\label{Lsy}\n\\end{equation}\nwe have \n\\begin{equation}\nL_0 \\propto {B \\, n_e \\over p - 1} \\, \\left( {\\gamma_1 \\over\n\\gamma_b} \\right)^{p-1}.\n\\label{norm_L}\n\\end{equation}\n\nNeglecting Compton scattering events in the Klein-Nishina\nregime, $\\epsilon\\gamma > 3/4$, we may approximate the SSC \nspectrum by\n\n\\begin{equation}\nL_{SSC} (\\epsilon_s) \\propto \\int\\limits_{\\epsilon_1}^{\\epsilon_2} \nd\\epsilon \\> {L_{sy} (\\epsilon) \\over \\epsilon} \\, \\sqrt{\\epsilon_s \n\\over \\epsilon} \\, n_e \\left( \\sqrt{3 \\, \\epsilon_s \\over 4 \\, \n\\epsilon} \\right) \\, \\Theta\\left( {3/4} - \\sqrt{\\epsilon_s \\, \n\\epsilon} \\right),\n\\label{LSSC}\n\\end{equation}\nwhere $\\Theta$ is the Heaviside function. The evaluation of this\nexpressions is straightforward. Observed fluxes in the ASM, BATSE,\nand HEGRA energy ranges are calculated integrating the Doppler\nboosted synchrotron and SSC spectra, $L^{\\ast} (\\epsilon^{\\ast})\n= D^3 \\, L (\\epsilon^{\\ast}/D)$, over the energy ranges \n$4 \\cdot 10^{-3} \\le \\epsilon^{\\ast}_{ASM} \\le 2 \\cdot 10^{-2}$,\n$4 \\cdot 10^{-2} \\le \\epsilon^{\\ast}_{BATSE} \\le 0.4$, and\n$3 \\cdot 10^6 \\le \\epsilon^{\\ast}_{HEGRA} \\le 6 \\cdot 10^7$.\n\nIn Fig. \\ref{fig_ssc_var}, we plot trajectories in the $(F_{BATSE}, \nF_{HEGRA})$ and $(F_{ASM}, F_{HEGRA})$ planes of these solutions, \nvarying individual model parameter separately while all others are \nheld constant at values representative of states of moderate X-ray\nand high-energy $\\gamma$-ray fluxes.\n\nA variation of the electron density obviously yields a\nrelation $F_{SSC} \\propto F_{sy}^2$ since the synchrotron flux\ndepends linearly, the SSC flux quadratically on $n_e$. Note that\nthis dependence may be altered due to an increasing $\\gamma\\gamma$\nabsorption opacity intrinsic to the source, which is not included \nin the analytical estimate (\\ref{LSSC}) used to compute the HEGRA \nflux. A variation of the electron injection spectral index $p$ \nresults in a relation which may be approximated by $F_{HEGRA} \n\\propto F_{BATSE}^{1.4}$ and $F_{HEGRA} \\propto F_{ASM}^{1.6}$, \ni. e. the dependence is weaker than quadratic. \n\nA variation of the magnetic field strength leads to more complex \nflux variations due to the back-reaction on the break Lorentz\nfactor $\\gamma_b$ as a result of radiative cooling. For relatively\nstrong magnetic fields ($B \\gtrsim 0.3$~G), the X-ray and TeV\n$\\gamma$-ray fluxes become anti-correlated.\n\nFinally, if the variability of this source were dominated by a\nvariation of the bulk Lorentz factor $\\Gamma$, the X-ray and\nhigh-energy $\\gamma$-ray fluxes would be expected to be approximately\nlinearly correlated (the back-reaction on $\\gamma_b$ leads to a\nslight deviation from a strictly linear correlation), as long as\nthe observer is located within the $1/\\Gamma$ beaming cone of\nthe jet. If $\\Gamma$ increases beyond $\\sim 1/\\theta_{obs}$,\nboth the X-ray and TeV $\\gamma$-ray fluxes start to decrease\nwith increasing $\\Gamma$. The same quasi-linear correlation\nwould be expected if the variability were due to a bending\njet, i. e. a variation of $\\theta_{obs}$.\n\nThe empirical correlation of the TeV and the X-ray emission of \nMkn~501 in 1997 has already been studied extensively using the \nCT1/CT2 and the CTS data from HEGRA and the soft X-ray data from \nRXTE ASM: Aharonian et al. (\\cite{hegrapartii}) find the correlation \ncoefficient for the daily averages to be $0.61 \\pm 0.057$. This \nmaximum correlation is found for zero time-lag. We examine \nthe correlation between the weekly RXTE, BATSE \nand HEGRA points from table \\ref{tab-data}. Fig. \\ref{sy_ssc_corr}\nshows the observed correlation between the HEGRA and BATSE\nmeasurements, fitted with a second-order\npolynomial as well as with a power-law with\nindex 1.4, which is the theoretical prediction if the variability is \ncaused solely by variations of the electron\ninjection spectral index $p$. Both fits give acceptable values for\nthe reduced $\\chi^2$ (1.1 and 1.65 respectively). Still, due to \nthe large error bars, we can not confidently distinguish between \nthese and similar correlations on the basis of the currently \navailable data. In any case, there is no indication for a \nsuper-quadratic dependence between the X-ray and TeV fluxes, \nwhich would be inconsistent with a pure SSC model, unless\nthere is a persistent quiescent level of emission above\nwhich the observed flaring behaviour is superimposed.\n\nFigure \\ref{fig-hegra-rxte} shows the correlation between the weekly\nTeV and Soft-X-ray points. The linear correlation coefficient\nis $0.59$, nearly the same as found by Aharonian et al. (\\cite{hegrapartii})\nwho compare the same data on a daily basis.\nThe constant term of the linear fit is still consistent with zero.\nHowever, the reduced $\\chi^2$ of 4.7 is too large for a good fit. \nThis is also the case for a fitted power-law with index 1.6 which\ngives $\\chi^2 = 4.9$. The systematic differences in \ntime-coverage which are not taken into account in the determination\nof the error bars may be responsible for this.\nStill, the large linear correlation coefficient suggests that the\ncorrelation is nearly linear. \n\nFigure \\ref{fig-batse-rxte} shows the correlation between the weekly\nHard-X-ray and Soft-X-ray points. In this case, the time coverage is\nthe same for both instruments, only the duty cycles are different.\nThe correlation coefficient is 0.53 corresponding to a 0.5~\\%\nchance probability for a linear correlation. The constant term\nof the linear fit is very well consistent with zero.\nThis figure also illustrates the difference in the dynamical ranges\nof the variability in the soft and the hard X-ray band. At BATSE\nenergies, which are believed to be near the high-energy end of\nthe synchrotron spectrum, the variability amplitude is about 50 \\% \nlarger than at RXTE energies. This fits nicely into the scheme\nthat the strongest variability takes place at the high-energy\nends of both spectral components.\n\n\\subsection{Model fit results}\n\nEach weekly SED is compared to a three-dimensional mesh of \n$48 \\times 22 \\times 9 = 9504$ simulations (48 different \nvalues of $p$, 22 values of $n_e$, and 9 values of $\\gamma_2$), \nselecting the simulated broadband spectrum with the \nsmallest $\\chi^2$. The resulting best-fit parameters\nare listed in table \\ref{fit_parameters}, along with the\nresulting $\\chi^2$ divided by the number of data points. \nSince we do not have a continuous sequence in parameter \nspace, the actual number of degrees of freedom is \nquestionable so that we use the above quantity to\nassess the quality of the fit. \n\nOur best-fit parameters for each individual weekly averaged\nbroadband spectrum are listed in Tab. \\ref{fit_parameters}. \nWith few exceptions (MJD~50549.0, 50576.9, 50618.8,\n50696.1), all fits resulted in acceptable $\\chi^2$ values.\n\nWe find a correlation between the electron injection spectral\nindex $p$ and the X-ray and high-energy $\\gamma$-ray fluxes, while \nthere is no obvious correlation with the total electron density \nand/or the high-energy cut-off $\\gamma_2$ of the injected electron \nspectrum. There also appears to be a weak anti-correlation between \nthe jet filling factor $f \\propto (\\Delta t_{rep})^{-1}$ and the \nX-ray and HEGRA fluxes. This could indicate that during states of \nrelatively low activity, the fluxes are dominated by a quasi-steady \ncomponent from a continuous jet, while in high-activity state the \nemission is dominated by more isolated, eruptive events. However, \nthis latter correlation is much less pronounced than the correlation \nwith the electron spectral index and will need to be tested on \nthe basis of future, more sensitive observations.\n\nIn Fig. \\ref{par_corr} the temporal variation of the best-fit \nvalues of $p$ and $\\Delta t_{rep}$ are compared to the variations of \nthe soft and hard X-ray fluxes and the 1.5 TeV flux. The correlation \nbetween the hard X-ray and TeV $\\gamma$-ray fluxes with the \ninjection spectral index is illustrated in figure \n\\ref{fig-p}.\n\nFurthermore, we show in figure \\ref{fig-peakpos} the correlation between $p$ \nand the positions of the peaks in the\nsynchrotron and the inverse Compton component of the SED.\nThe peak positions are not fit parameters but were determined by finding the\nlocal maxima in the weekly SEDs. We find that, in our model, there is a \nstrong correlation between the peak positions and $p$ such that these\nparameters can be regarded as nearly identical. However, while the \npeak positions \nare directly observable, the electron spectral index is the more fundamental\nquantity.\n\nOur results indicate that medium-timescale high activity states in \nX-rays and high-energy $\\gamma$-rays are consistent with a hardening \nof the electron spectrum injected at the base of the jet. As pointed \nout in the previous subsection, a pure SSC model in which the TeV\n$\\gamma$-ray flux is strongly influenced by Klein-Nishina effects,\npredicts that the HEGRA and both the soft and hard X-ray fluxes should\nroughly be correlated by power-laws $F_{HEGRA} \\propto F_X^{\\delta}$\nwith $1.4 \\lesssim \\delta \\lesssim 1.6$ in high flux-level states, in\nwhich the contribution of a possible quasi-stationary radiation component\nis small. The data available for this study are consistent with this but \ndo not allow a clear distinction between different variability mechanisms, \nand future observations with increased sensitivity, in particular at multi-GeV\nto TeV energies, are needed in order to test this prediction.\n\n\\section{Summary and Conclusions}\n\nWe have presented broadband spectra of the extreme HBL Mkn~501\nduring its high state in 1997, including radio, optical,\nsoft and hard X-ray, and TeV $\\gamma$-ray observations. In this\nstudy we concentrated on the medium-timescale variability, using\nweekly averaged SEDs. We confirmed the strong correlation\nbetween the TeV $\\gamma$-ray flux and the hard X-ray flux. This\ncorrelation was found to be non-linear and could be fitted with \na second-order polynomial, in agreement with the expectation of \nan SSC dominated leptonic jet model, if the flux variations are \nrelated to fluctuations of the electron density in the jet and/or \nthe spectral index of the electron spectrum at the time of injection \ninto the jet.\n\nThe weekly averaged SEDs were fitted with a leptonic jet model,\nstrongly dominated by the SSC process. With a few exceptions,\nthis model yielded acceptable fits to the observed broadband\nspectra. The observed spectral variability of Mkn~501 could be \nexplained mainly by variations of the electron spectral index.\nNo clear correlation between the maximum electron energy\nand the hard X-ray and TeV $\\gamma$-ray fluxes on the 1-week\ntimescale was found, in contrast to the short-term variability \nof Mkn~501. Pian et al. (\\cite{pian}) have shown that the\nintraday variability of this object is most probably related\nto an increase of $\\gamma_2$, leading to pronounced flares in\nhard X-rays, most probably on the synchrotron cooling timescale \nwhich is most likely $\\sim$~a few hours and thus much shorter \nthan the 1-week timescale considered in this paper. Our result\nindicates that such synchrotron flares are isolated events and\nare at most weakly correlated to the activity of the source\non the 1-week timescale.\n\nOur result that the flaring behaviour on intermediate timescales\nis consistent with a hardening of the electron spectrum is in\ncontrast to the flaring characteristics observed in quasars.\nRecently, Mukherjee et al. (\\cite{mukherjee99}) have investigated\nall available broadband data on the very luminous flat-spectrum\nradio quasar (FSRQ) PKS~0528+134, and found that its flaring \nbehaviour is consistent with an increasing contribution of the \nexternal inverse-Compton component during flares, possibly related \nto an increase in the bulk Lorentz factor. The fits to the SEDs\nof PKS~0528+134 required that the average energy of relativistic\nelectrons in the jet shifts towards lower values during flares, \nin contrast to the results found for Mkn~501. As pointed out by\nB\\\"ottcher (\\cite{boettcher99}), this implies that the synchrotron\npeak is expected to shift towards lower frequencies during flares\nof FSRQs, while Mkn~501 and Mkn~421 show clear evidence for a\nshift of the synchrotron peak to higher frequencies. \n\nWe point out that in the present study the magnetic \nfield along the jet and the bulk Lorentz factor of\nindividual blobs were fixed, so that we cannot \nconfidently rule out variations of the Doppler \nfactor, accompanied by appropriate changes of the \nelectron injection spectrum, as the flaring mechanism \nfor Mkn 501. However, the very moderate variability\nat optical frequencies, as observed in Mkn 501, leads\nus to consider this flaring mechanism less likely in\nthis object since it would require a peculiar conspiracy \nbetween the Doppler factor and the electron spectrum to\nkeep the optical flux at an approximately constant level.\n\n\n\\section*{Acknowledgements}\n\nThe work of DP is supported by the Spanish CICYT grant SB97-B12601316. \nThe work of MB was supported by NASA grant NAG 5-4055 (until Aug. 1999) \nand by Chandra Postdoctoral Fellowship grant number PF~9-10007, awarded \nby the Chandra X-ray Center, which is operated by the Smithsonian \nAstrophysical Observatory for NASA under contract NAS~8-39073.\nThe RXTE ASM data has been obtained through the High Energy Astrophysics\nScience Archive Research Center Online Service provided by the\nNASA/Goddard Space Flight Center. We thank C.D. Dermer for valuable \ncomments on the manuscript and J.M. 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(1999b) \\\\\n\\rule[-1mm]{0cm}{0.4cm}HEGRA CT System & $1.9\\times 10^{26}$ \\-- \n $\\approx 1.2 \\times 10^{28}$ & $8\\times 10^{11}$ \\-- $\\approx \n5\\times 10^{13} $ &\n Aharonian et al. (1999a)\\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\n\n\\begin{table}\n\\small\n\\caption{\\label{tab-data} The weekly $\\nu F_{\\nu}$ datapoints from \nobservations of Mkn 501 used for the model fits presented in this\npaper. All entries are in units of $10^{-11}$ erg cm$^{-2}$ s$^{-1}$. \nEntries exactly equal to 0 are those where no data are available. \nThis is mainly radio data. Upper limits are indicated by a ``$<$'' \nsymbol and are calculated with 90\\% confidence level. The fluxes\nat 0.8~TeV and 10~TeV are extrapolated from the flux measurement \nat 1.5~TeV.}\n\\begin{tabular}{llllrrrrr}\n\\hline\nMJD & Radio & Optical & Soft X-ray & Hard X-ray & (0.8 TeV) & 1.5 TeV & (10 TeV) \\\\\n\\hline\n50517.199 & $ 0.02244 \\pm 0.00104 $ & $ 7.068 \\pm 0.124 $ & $ 11.1 \\pm 3.1 $ & $ 26.73 \\pm 8.5 $ & $ 8.7 \\pm 1.9 $ & $ 8.2 \\pm 1.9 $ & $ 2.41 \\pm 0.65 $ \\\\ \n50521.906 & $ 0.02387 \\pm 0.00156 $ & $ 7.148 \\pm 0.069 $ & $ 10.0 \\pm 3.1 $ & $ 1.67 \\pm 9.5 $ & $ 10.6 \\pm 1.5 $ & $ 9.9 \\pm 1.5 $ & $ 2.94 \\pm 0.61 $ \\\\ \n50526.34 & $ 0.02200 \\pm 0.0011 $ & $ 7.275 \\pm 0.047 $ & $ 15.8 \\pm 3.3 $ & $ 14.33 \\pm 6.2 $ & $ 7.4 \\pm 1.4 $ & $ 6.9 \\pm 1.3 $ & $ 2.05 \\pm 0.49 $ \\\\ \n50536.715 & $ 0.02420 \\pm 0.0011 $ & $ 7.394 \\pm 0.120 $ & $ 17.4 \\pm 3.5 $ & $ 8.38 \\pm 8.4 $ & $ 5.6 \\pm 1.9 $ & $ 5.3 \\pm 1.9 $ & $ 1.57 \\pm 0.59 $ \\\\ \n50541.262 & $ 0.02237 \\pm 0.00064 $ & $ 7.607 \\pm 0.077 $ & $ 11.9 \\pm 3.0 $ & $< 8.4 $ & $ 7.8 \\pm 1.7 $ & $ 7.3 \\pm 1.7 $ & $ 2.17 \\pm 0.58 $ \\\\ \n50549.012 & $ 0 $ & $ 7.769 \\pm 0.063 $ & $ 15.3 \\pm 3.8 $ & $ 45.7 \\pm 7.4 $ & $ 13.4 \\pm 1.4 $ & $ 12.6 \\pm 1.5 $ & $ 3.72 \\pm 0.69 $ \\\\ \n50556.32 & $ 0.02508 \\pm 0.00198 $ & $ 7.708 \\pm 0.109 $ & $ 20.9 \\pm 3.9 $ & $ 36.38 \\pm 6.9 $ & $ 17.6 \\pm 2.4 $ & $ 16.5 \\pm 2.4 $ & $ 4.88 \\pm 0.99 $ \\\\ \n50564.566 & $ 0.02382 \\pm 0.00052 $ & $ 7.948 \\pm 0.093 $ & $ 21.9 \\pm 3.8 $ & $ 16.79 \\pm 8.6 $ & $ 7.9 \\pm 1.2 $ & $ 7.4 \\pm 1.2 $ & $ 2.18 \\pm 0.47 $ \\\\ \n50570.254 & $ 0.02420 \\pm 0.00095 $ & $ 7.941 \\pm 0.075 $ & $ 20.1 \\pm 4.3 $ & $ 16.34 \\pm 5.8 $ & $ 6.8 \\pm 0.8 $ & $ 6.4 \\pm 0.8 $ & $ 1.90 \\pm 0.36 $ \\\\ \n50576.934 & $ 0.02409 \\pm 0.00104 $ & $ 8.071 \\pm 0.188 $ & $ 20.6 \\pm 3.9 $ & $ 49.87 \\pm 8.2 $ & $ 16.2 \\pm 1.5 $ & $ 15.2 \\pm 1.7 $ & $ 4.49 \\pm 0.80 $ \\\\ \n50583.305 & $ 0 $ & $ 7.921 \\pm 0.317 $ & $ 18.1 \\pm 3.2 $ & $ 37.24 \\pm 6.6 $ & $ 16.9 \\pm 1.9 $ & $ 15.8 \\pm 2.0 $ & $ 4.68 \\pm 0.89 $ \\\\ \n50592.621 & $ 0 $ & $ 7.829 \\pm 0.153 $ & $ 16.9 \\pm 3.2 $ & $ 13.03 \\pm 7.7 $ & $ 5.7 \\pm 1.8 $ & $ 5.3 \\pm 1.7 $ & $ 1.58 \\pm 0.55 $ \\\\ \n50600.797 & $ 0 $ & $ 7.393 \\pm 0.188 $ & $ 28.3 \\pm 4.7 $ & $ 29.0 \\pm 10.3 $ & $ 6.9 \\pm 1.3 $ & $ 6.5 \\pm 1.2 $ & $ 1.92 \\pm 0.46 $ \\\\ \n50604.852 & $ 0.02574 \\pm 0.00132 $ & $ 0 $ & $ 35.7 \\pm 5.6 $ & $ 43.89 \\pm 9.0 $ & $ 17.2 \\pm 1.8 $ & $ 16.2 \\pm 1.9 $ & $ 4.78 \\pm 0.88 $ \\\\ \n50611.523 & $ 0 $ & $ 7.029 \\pm 0.317 $ & $ 26.0 \\pm 5.4 $ & $ 37.29 \\pm 11 $ & $ 13.3 \\pm 1.5 $ & $ 12.5 \\pm 1.6 $ & $ 3.68 \\pm 0.69 $ \\\\ \n50618.848 & $ 0 $ & $ 0 $ & $ 35.5 \\pm 5.4 $ & $ 52.0 \\pm 7.4 $ & $ 3.0 \\pm 2.0 $ & $ 2.8 \\pm 1.8 $ & $ 0.83 \\pm 0.56 $ \\\\ \n50626.785 & $ 0.02420 \\pm 0.00154 $ & $ 0 $ & $ 37.2 \\pm 6.2 $ & $ 39.19 \\pm 6.1 $ & $ 20.7 \\pm 2.1 $ & $ 20.0 \\pm 2.3 $ & $ 5.90 \\pm 1.07 $ \\\\ \n50634.707 & $ 0.02189 \\pm 0.00148 $ & $ 7.327 \\pm 0.070 $ & $ 16.1 \\pm 3.7 $ & $ 10.61 \\pm 7.4 $ & $ 3.3 \\pm 0.6 $ & $ 3.1 \\pm 0.5 $ & $ 0.92 \\pm 0.21 $ \\\\ \n50640.742 & $ 0 $ & $ 7.271 \\pm 0.138 $ & $ 28.8 \\pm 4.7 $ & $ 36.5 \\pm 8.6 $ & $ 18.2 \\pm 1.8 $ & $ 17.1 \\pm 2.0 $ & $ 5.06 \\pm 0.92 $ \\\\ \n50650.969 & $ 0 $ & $ 7.859 \\pm 0.142 $ & $ 26.0 \\pm 4.5 $ & $ 45.82 \\pm 7.9 $ & $ 9.4 \\pm 1.8 $ & $ 8.8 \\pm 1.7 $ & $ 2.60 \\pm 0.63 $ \\\\ \n50654.59 & $ 0 $ & $ 0 $ & $ 19.4 \\pm 3.7 $ & $ 28.48 \\pm 9.7 $ & $ 8.5 \\pm 1.3 $ & $ 8.0 \\pm 1.3 $ & $ 2.36 \\pm 0.52 $ \\\\ \n50661.887 & $ 0.01672 \\pm 0.00132 $ & $ 7.226 \\pm 0.317 $ & $ 10.4 \\pm 4.6 $ & $ 24.66 \\pm 7.7 $ & $ 9.2 \\pm 1.0 $ & $ 8.7 \\pm 1.1 $ & $ 2.57 \\pm 0.48 $ \\\\ \n50669.164 & $ 0.02706 \\pm 0.00154 $ & $ 7.567 \\pm 0.217 $ & $ 14.0 \\pm 4.8 $ & $ 36.78 \\pm 15 $ & $ 11.3 \\pm 1.5 $ & $ 10.6 \\pm 1.5 $ & $ 3.12 \\pm 0.63 $ \\\\ \n50672.938 & $ 0 $ & $ 7.244 \\pm 0.160 $ & $ 20.4 \\pm 4.7 $ & $ 30.82 \\pm 6.8 $ & $ 4.7 \\pm 1.9 $ & $ 4.5 \\pm 1.8 $ & $ 1.32 \\pm 0.57 $ \\\\ \n50684.598 & $ 0 $ & $ 7.484 \\pm 0.177 $ & $ 24.2 \\pm 5.8 $ & $ 38.19 \\pm 5.8 $ & $ 14.6 \\pm 1.7 $ & $ 13.7 \\pm 1.8 $ & $ 4.04 \\pm 0.77 $ \\\\ \n50689.281 & $ 0 $ & $ 7.162 \\pm 0.094 $ & $ 16.6 \\pm 3.4 $ & $ 12.31 \\pm 7.9 $ & $ 6.6 \\pm 1.1 $ & $ 6.2 \\pm 1.2 $ & $ 1.84 \\pm 0.42 $ \\\\ \n50696.059 & $ 0 $ & $ 0 $ & $ 13.5 \\pm 3.3 $ & $ 45.06 \\pm 8.9 $ & $ 7.1 \\pm 1.1 $ & $ 6.7 \\pm 1.1 $ & $ 1.98 \\pm 0.43 $ \\\\ \n50703.445 & $ 0 $ & $ 0 $ & $ 20.6 \\pm 3.7 $ & $ 13.63 \\pm 8.8 $ & $ 9.4 \\pm 2.8 $ & $ 8.8 \\pm 2.7 $ & $ 2.61 \\pm 0.87 $ \\\\\n\\hline\n\\end{tabular}\n\\end{table} \n\n\\newpage\n\n\\begin{table}\n\\small\n\\caption{\\label{fit_parameters} Best-fit parameters of a\npure SSC jet model to the weekly SEDs, and the quality of\nthe fit, indicated by $\\chi^2$ / (no. of data points).\nThe $\\chi^2$ is calculated without taking into account\nthe radio point. Periods marked with a ``*'' have less than 3\nHEGRA points. $\\nu_s$ and $\\nu_{ic}$ are respectively the \npositions of the peak in the synchrotron and inverse compton component\nof the SED. They were determined by finding the two local maxima\nin each fitted SED. \n}\n\\begin{tabular}{lcccccccc}\n\\hline\nMJD-50000 & $\\gamma_2$/10$^7$ & $p$ & $n_e$ & $\\Delta t$ [10$^3$ s] & $\\log(\\nu_{s}/\\mathrm{Hz})$ & $\\log(\\nu_{ic}/\\mathrm{Hz})$ & red. $\\chi^2$ & no. data points \\\\\n\\hline\n517.199 & 3.0 & 2.425 & 30 & 3.443 & 17.23 & 25.04 & 0.821 & 7 \\\\\n521.906 & 3.0 & 2.450 & 65 & 6.189 & 16.34 & 24.74 & 0.395 & 7 \\\\\n526.340 & 3.0 & 2.425 & 20 & 2.308 & 17.51 & 25.26 & 0.291 & 7 \\\\\n536.715 * & 3.0 & 2.450 & 15 & 1.605 & 17.54 & 25.11 & 0.254 & 7 \\\\\n541.262 & 3.0 & 2.500 & 50 & 4.071 & 16.51 & 24.77 & 0.539 & 7 \\\\\n549.012 & 3.0 & 2.350 & 25 & 3.285 & 18.00 & 25.30 & 3.264 & 6 \\\\\n556.320 & 3.0 & 2.300 & 25 & 3.798 & 18.53 & 25.40 & 0.806 & 7 \\\\\n564.566 & 3.0 & 2.400 & 15 & 1.737 & 17.76 & 25.30 & 0.326 & 7 \\\\\n570.254 & 3.0 & 2.425 & 15 & 1.614 & 17.62 & 25.28 & 0.495 & 7 \\\\\n576.934 & 3.0 & 2.300 & 20 & 2.991 & 18.53 & 25.49 & 2.039 & 7 \\\\\n583.305 & 3.0 & 2.325 & 30 & 4.048 & 18.18 & 25.32 & 1.760 & 6 \\\\\n592.621 * & 3.0 & 2.475 & 20 & 1.849 & 17.34 & 25.08 & 0.241 & 6 \\\\\n600.797 & 3.0 & 2.375 & 10 & 1.363 & 18.00 & 25.49 & 0.412 & 6 \\\\\n604.582 & 2.5 & 2.200 & 10 & 2.476 & 19.00 & 25.74 & 0.309 & 6 \\\\\n611.523 & 3.0 & 2.300 & 15 & 2.609 & 18.42 & 25.52 & 0.483 & 6 \\\\\n618.848 * & 2.0 & 2.400 & 10 & 1.146 & 17.81 & 25.40 & 5.177 & 5 \\\\\n626.785 & 3.0 & 2.225 & 15 & 2.989 & 19.04 & 25.58 & 0.140 & 6 \\\\\n634.707 & 3.0 & 2.500 & 10 & 0.940 & 17.51 & 25.08 & 0.522 & 7 \\\\\n640.742 & 3.0 & 2.250 & 15 & 2.941 & 18.90 & 25.54 & 0.354 & 6 \\\\\n650.969 * & 3.0 & 2.325 & 10 & 1.500 & 18.23 & 25.53 & 1.326 & 6 \\\\\n654.590 & 3.0 & 2.375 & 15 & 2.039 & 17.78 & 25.40 & 0.560 & 5 \\\\\n661.887 & 3.0 & 2.425 & 30 & 3.361 & 17.26 & 25.15 & 0.959 & 7 \\\\\n669.164 & 3.0 & 2.375 & 25 & 3.151 & 17.72 & 25.28 & 0.698 & 7 \\\\\n672.938 * & 3.0 & 2.400 & 10 & 1.291 & 17.78 & 25.38 & 0.706 & 6 \\\\\n684.598 & 3.0 & 2.275 & 15 & 2.676 & 18.64 & 25.53 & 0.849 & 6 \\\\\n689.281 & 3.0 & 2.450 & 20 & 2.175 & 17.36 & 25.08 & 0.378 & 7 \\\\\n696.059 & 3.0 & 2.425 & 20 & 2.319 & 17.51 & 25.15 & 2.996 & 5 \\\\\n703.445 & 3.0 & 2.375 & 20 & 2.629 & 17.76 & 25.30 & 0.197 & 5 \\\\\n\\hline\n\\end{tabular}\n\\begin{tabular}{rcl}\n\\multicolumn{3}{l}{Fit parameters:}\\\\\n $\\gamma_2$ & = & electron spectrum high-energy cutoff \\\\\n $p$ & = & electron spectral index, $n(\\gamma) \\propto \\gamma^{-p}$ \\\\\n $n_e$ [cm$^{-3}$] & = & electron density \\\\\n $\\Delta t$ [s] & = & blob ejection events repetition time scale (normalization) \\\\\n\\multicolumn{3}{l}{Fixed parameters:}\\\\\n $z_i$ & = & 0.03 pc \\ \\ (injection height of blob) \\\\\n $M_{BH}$ & = & $10^8 M_0$ \\ \\ (mass of central black hole) \\\\\n $L_D$ & = & $5 \\times 10^{43}$ erg\\,s$^{-1}$ \\ \\ (isotropic accretion disk luminosity)\\\\\n $R_B$ & = & $3 \\times 10^{15}$ cm \\ \\ (blob radius in the comoving frame) \\\\\n $\\gamma_1$ & = & 200 \\ \\ (low-energy cutoff of electron sp.) \\\\\n $\\Gamma$ & = & 25 \\ \\ (bulk Lorentz factor) \\\\\n $D$ & = & 30 \\ \\ (Doppler factor) \\\\\n $\\delta t_{min}$ & = & 3336 s \\ \\ (contracted blob crossing time) \\\\\n $B$ & = & 0.05 G \\ \\ (magnetic field) \\\\\n $H_0$ & = & 75 km\\,s$^{-1}$Mpc$^{-1}$ \\ \\ (Hubble constant) \\\\\n $q_0$ & = & 0.5 \\ \\ (deceleration parameter) \\\\\n $z$ & = & 0.034 \\ \\ (cosmological redshift) \\\\\n $d_L$ & = & 133 Mpc \\ \\ (luminosity distance) \\\\\n\\end{tabular}\n\\end{table}\n\n\\clearpage\n\n\n\\begin{figure}\n\\epsfysize=21cm\n\\epsffile{f1.eps}\n\\figcaption{\\label{fig-lightcurve} \nThe lightcurve data which were used in this paper to construct\nweekly spectral energy distributions. \nSee section \\protect\\ref{sec-observations} for references.}\n\\end{figure}\n\n\\clearpage\n\n\n\\begin{figure}\n\\epsfxsize=14.5cm\n\\epsffile{f2.eps}\n\\figcaption{\\label{fig-k} \nThe correction factor $k$ for the second RXTE ASM energy bin\nderived from the publicly available Crab Nebula data\ntaken by the detector between MJD 50510 and 50710. See text.}\n\\end{figure}\n\n\\clearpage\n\n\n\\begin{figure}\n\\epsfxsize=14.5cm\n\\epsffile{f3.eps}\n\\figcaption{\\label{fig-alphas} \nThe index $\\alpha$ of the differential photon spectrum in the\nenergy range 3.0 - 12.1 keV derived from the publicly available\nRXTE ASM data for Mkn 501 and the Crab Nebula in weekly time bins. \nThe lines represent\nfits of constant functions. For Mkn 501, the reduced $\\chi^2$ of the fit is\n0.93, for the Crab it is 0.95 . \n}\n\\end{figure}\n\n\n\n\\clearpage\n\n\\begin{figure}\n\\epsfysize=15cm\n\\rotatebox{270}{\\epsffile{f4.eps}}\n\\figcaption{\\label{ssc_fits}\nModel fits to the weekly averaged broadband\nspectra of Mkn~501 for the periods centered on \nMJD~50564.566 (low flux state; filled triangles\nand dot-dashed curve) and MJD~50626.785 (high \nflux state; filled circles and solid curve). Model \nparameters for MJD50564.566: $\\gamma_1 = 500$, \n$\\gamma_2 = 3 \\cdot 10^7$, $p = 2.400$, $n_e = \n15$~cm$^{-3}$, $\\Delta t_{rep} = 1.74 \\cdot 10^3$~s, \n$B = 0.05$~G, $\\Gamma = 25$, $R'_B = 3 \\cdot 10^{15}$~cm, \n$D = 30$. Model parameters for MJD~50626.785: Same as \nfor the low state, except $p = 2.225$, $\\Delta t_{rep} \n= 3.0 \\cdot 10^3$~s.} \n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\\centering\n\\epsfysize=12cm\n\\rotatebox{270}{\\epsffile{f5a.eps}}\n\\vskip 1cm\n\\epsfysize=12cm\n\\rotatebox{270}{\\epsffile{f5b.eps}}\n\\figcaption{\\label{fig_ssc_var}\nCorrelation between the ASM and HEGRA fluxes (a) and between\nthe BATSE and HEGRA fluxes (b) according to our analytical \napproximation. Standard model parameters are $\\gamma_1 = 300$, \n$B = 0.1$~G, $n_e = 100$~cm$^{-3}$, $p = 2.5$, $\\gamma_2 \n= 10^7$. For each curve, one parameter is varied, while\nthe others are fixed to the above values. The curves are\nlabelled by a few representative values of the varying\nparameter.} \n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\centering\n\\epsfxsize=14.5cm\n\\epsffile{f6.eps}\n\\figcaption{\\label{sy_ssc_corr}\nThe correlation between HEGRA TeV and the BATSE X-ray \nflux from Mkn~501. In order to avoid effects from\npoor time-coverage, points obtained from less than three\nindependent HEGRA measurements were excluded. The excluded\npoints are shown as open circles. The fit of a second-order\npolynomial to the remaining points (filled circles) yields \n$y = (5.4 \\pm 0.6) + (- 0.29 \\pm 0.08) x + (0.017 \\pm 0.0035) x^2$ (solid line), \nwhere $y = $~HEGRA flux at 1.5 TeV in units of $10^{-11}$~erg~cm$^{-2}$~s$^{-1}$,\nand $x = $~BATSE flux at 36.4 keV in the same units, and results in a reduced\n$\\chi^2$ of $1.14$. With the open circle points included the reduced \n$\\chi^2$ increases to 1.54. The dashed line is a linear fit to the\nfilled circle points: $y = (-0.3 \\pm 1.7) + (0.40 \\pm 0.06) x$,\nreduced $\\chi^2 = 1.42$ (2.6 with the open circle points).\nThe dot-dashed line is a fit of the function $y = a x^{1.4} + b$. It results\nin $a = 0.063 \\pm 0.0084$, $b = 4.2 \\pm 0.72$, and a reduced $\\chi^2$ of 1.65 \n(2.7 with the open circle points).}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\centering\n\\epsfxsize=14.5cm\n\\epsffile{f7.eps}\n\\figcaption{\\label{fig-hegra-rxte}\nThe correlation between the HEGRA TeV and the RXTE ASM X-ray \nflux from Mkn~501. In order to reduce effects from\npoor time-coverage, points obtained from less than three\nindependent HEGRA measurements were excluded. The excluded\npoints are shown as open circles. \nThe fit of a linear function to the remaining points (filled circles) yields \n$y = (-2.6 \\pm 1.40) + (0.62 \\pm 0.07) x$, where\n$y = $~HEGRA flux at 1.5 TeV in units of $10^{-11}$~erg~cm$^{-2}$~s$^{-1}$,\nand $x = $~RXTE flux at 5.2 keV in the same units, and results in a reduced\n$\\chi^2$ of $4.7$. Only statistical errors were taken into account.\nThe linear correlation coefficient is $0.59$. \nThe dot-dashed line is a fit of the function $y = a x^{1.6} + b$ which results\nin $a = 0.062 \\pm 0.0075$, $b = 2.28 \\pm 0.80$, and a reduced $\\chi^2$ of 4.9 .}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\centering\n\\epsfxsize=14.5cm\n\\epsffile{f8.eps}\n\\figcaption{\\label{fig-batse-rxte}\nThe correlation between the BATSE hard X-ray and the RXTE ASM soft X-ray \nflux from Mkn~501. Here the time coverage is not systematically different,\nonly the BATSE duty cycle is much lower than that of the RXTE ASM. \nSo all points are used in the linear fit. \nThe points where HEGRA had bad time\ncoverage are are still marked as open circles for comparison with the\nother figures. \nThe fit of a linear function yields \n$y = (-0.1 \\pm 5.3) + (1.36 \\pm 0.24) x$, where\n$y = $~BATSE flux at 36.4 keV in units of $10^{-11}$~erg~cm$^{-2}$~s$^{-1}$,\nand $x = $~RXTE flux at 5.2 keV in the same units, and results in a reduced\n$\\chi^2$ of $2.3$. Only statistical errors were taken into account.\nThe linear correlation coefficient is $0.53$.}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\centering\n\\epsfysize=15cm\n\\rotatebox{270}{\\epsffile{f9.eps}}\n\\figcaption{\\label{par_corr}\nBest-fit values of the blob ejection repetition time $\\Delta t_{rep}$ \nand the electron injection spectral index $p$ for the pure SSC model \ncompared to the RXTE ASM, BATSE and HEGRA 1.5 TeV light curves.} \n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\centering\n\\epsfxsize=14.5cm\n\\epsffile{f10.eps}\n\\figcaption{\\label{fig-p}\nThe correlation between the fit parameter spectral index, $p$, \nand the HEGRA TeV (filled circles) and BATSE hard X-ray (stars) \nflux from Mkn~501. \nThe fit of a linear function yields for HEGRA\n$p = (2.57 \\pm 0.018) + (-0.019 \\pm 0.0018) x$, where\n$x = $~HEGRA flux at 1.5 TeV in $10^{-11}$~erg~cm$^{-2}$~s$^{-1}$; \nreduced $\\chi^2 = 1.18$; the linear correlation coefficient is $-0.89$.\nFor BATSE: $p = (2.56 \\pm 0.034) + (-0.0072 \\pm 0.0011) x$, where\n$x = $~BATSE flux at 36.4 keV \nin $10^{-11}$~erg~cm$^{-2}$~s$^{-1}$; reduced $\\chi^2 = 1.2$; \nthe linear correlation coefficient is $-0.76$.\n}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\centering\n\\epsfxsize=14.5cm\n\\epsffile{f11.eps}\n\\figcaption{\\label{fig-peakpos}\nThe correlation between the fit parameter spectral index, $p$, \nand the positions of the peak in the synchrotron (bottom plot) and \ninverse Compton (top plot) component of the weekly SEDs. \nThe fit of a linear function yields \n$\\log(\\nu_{s}/\\mathrm{Hz}) = (39.11 \\pm 0.68) + (-8.97 \\pm 0.29) p$ (linear \ncorrelation coefficient $-0.93$) and\n$\\log(\\nu_{ic}/\\mathrm{Hz}) = (31.84 \\pm 0.38) + (-2.77 \\pm 0.16) p$\n(linear correlation coefficient $-0.88$).\n}\n\\end{figure}\n\n\n\\end{document}\n\n"
}
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[
{
"name": "astro-ph0002255.extracted_bib",
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}
] |
astro-ph0002256
|
Theory of pixel lensing towards M31 I: the density contribution and mass of MACHOs
|
[
{
"author": "E.~Kerins$^1$"
},
{
"author": "B.J.~Carr$^2$"
},
{
"author": "N.W.~Evans$^1$"
},
{
"author": "P.~Hewett$^3$"
},
{
"author": "E.~Lastennet$^2$"
},
{
"author": "\\newauthor Y.~Le~Du$^4$"
},
{
"author": "A.-L.~Melchior$^{2,5}$"
},
{
"author": "S.J.~Smartt$^3$ and D.~Valls-Gabaud$^6$ \\newauthor (The POINT--AGAPE Collaboration)"
},
{
"author": "$^1$Theoretical Physics"
},
{
"author": "1 Keble Road"
},
{
"author": "Oxford OX1 3NP"
},
{
"author": "UK"
},
{
"author": "$^2$Astronomy Unit"
},
{
"author": "School of Mathematical Sciences"
},
{
"author": "Mile End Road"
},
{
"author": "London E1 4NS"
},
{
"author": "Madingley Road"
},
{
"author": "Cambridge CB3 0HA"
},
{
"author": "$^4$Laboratoire de Physique Corpusculaire et Cosmologie"
},
{
"author": "Coll\\`ege de France"
},
{
"author": "11 Place Marcelin Berthelot"
},
{
"author": "F-75231 Paris"
},
{
"author": "France"
},
{
"author": "$^5$DEMIRM UMR~8540"
},
{
"author": "Observatoire de Paris"
},
{
"author": "61 Avenue Denfert-Rochereau"
},
{
"author": "F-75014 Paris"
},
{
"author": "$^6$Laboratoire d'Astrophysique UMR~CNRS~5572"
},
{
"author": "Observatoire Midi-Pyr\\'en\\'ees"
},
{
"author": "14 Avenue Edouard Belin"
},
{
"author": "F-31400 Toulouse"
}
] |
POINT-AGAPE is an Anglo-French collaboration which is employing the Isaac Newton Telescope (INT) to conduct a pixel-lensing survey towards M31. Pixel lensing is a technique which permits the detection of microlensing against unresolved stellar fields. The survey aims to constrain the stellar population in M31 and the distribution and nature of massive compact halo objects (MACHOs) in both M31 and the Galaxy. In this paper we investigate what we can learn from pixel-lensing observables about the MACHO mass and fractional contribution in M31 and the Galaxy for the case of spherically-symmetric near-isothermal haloes. We employ detailed pixel-lensing simulations which include many of the factors which affect the observables, such as non-uniform sampling and signal-to-noise ratio degradation due to changing observing conditions. For a maximum MACHO halo we predict an event rate in $V$ of up to 100 per season for M31 and 40 per season for the Galaxy. However, the Einstein radius crossing time is generally not measurable and the observed full-width half-maximum duration provides only a weak tracer of lens mass. Nonetheless, we find that the near-far asymmetry in the spatial distribution of M31 MACHOs provides significant information on their mass and density contribution. We present a likelihood estimator for measuring the fractional contribution and mass of both M31 and Galaxy MACHOs which permits an unbiased determination to be made of MACHO parameters, even from data-sets strongly contaminated by variable stars. If M31 does not have a significant population of MACHOs in the mass range $10^{-3}~\sm - 1~\sm$ strong limits will result from the first season of INT observations. Simulations based on currently favoured density and mass values indicate that, after three seasons, the M31 MACHO parameters should be constrained to within a factor four uncertainty in halo fraction and an order of magnitude uncertainty in mass ($90\%$ confidence). Interesting constraints on Galaxy MACHOs may also be possible. For a campaign lasting ten years, comparable to the lifetime of current LMC surveys, reliable estimates of MACHO parameters in both galaxies should be possible.
|
[
{
"name": "paper.tex",
"string": "\\documentstyle[epsfig]{mn}\n \n\\begin{document} \n \n\\newcommand{\\sm}{\\mbox{M}_{\\sun}} \n\\newcommand{\\den}{$\\mbox{M}_{\\sun}$pc$^{-3}$} \n\\newcommand{\\kms}{km~s$^{-1}$} \n\\newcommand{\\tst}{\\textstyle} \n\\newcommand{\\be}{\\begin{equation}} \n\\newcommand{\\ee}{\\end{equation}} \n\n\\newcommand{\\nsp}{N_{\\rm pix}}\n\\newcommand{\\nbl}{N_{\\rm bl}}\n\\newcommand{\\nsrc}{N_{\\rm s}}\n\\newcommand{\\ngal}{N_{\\rm gal}}\n\\newcommand{\\nsky}{N_{\\rm sky}}\n\\newcommand{\\sigi}{\\sigma_i}\n\\newcommand{\\fsee}{f_{\\rm see}}\n\\newcommand{\\asp}{A_{\\rm pix}}\n\\newcommand{\\aspt}{A_{\\rm pix,T}}\n\\newcommand{\\amin}{A_{\\rm min}}\n\\newcommand{\\amax}{A_{\\rm max}}\n\\newcommand{\\at}{A_{\\rm T}}\n\\newcommand{\\umax}{u_{\\rm max}}\n\\newcommand{\\ut}{u_{\\rm T}}\n\\newcommand{\\lsrc}{L_{\\rm s}}\n\\newcommand{\\texp}{T_{\\rm exp}}\n\\newcommand{\\te}{t_{\\rm e}}\n\\newcommand{\\tfw}{t_{\\rm FWHM}}\n\\newcommand{\\gp}{\\Gamma_{\\rm p}}\n\\newcommand{\\gpo}{\\Gamma_{\\rm p}^{\\rm obs}}\n\\newcommand{\\gpoj}{\\Gamma_{{\\rm p},j}^{\\rm obs}}\n\\newcommand{\\gpj}{\\Gamma_{{\\rm p},j}}\n\\newcommand{\\gc}{\\Gamma_{\\rm c}}\n\\newcommand{\\dd}{D_{\\rm l}}\n\\newcommand{\\ds}{D_{\\rm s}}\n\\newcommand{\\vt}{V_{\\rm t}}\n\\newcommand{\\re}{R_{\\rm e}}\n\\newcommand{\\bvl}{\\mbox{\\boldmath $V_{\\rm l}$}}\n\\newcommand{\\bvs}{\\mbox{\\boldmath $V_{\\rm s}$}}\n\\newcommand{\\rhoh}{\\rho_{\\rm h}}\n\\newcommand{\\rhod}{\\rho_{\\rm d}}\n\\newcommand{\\rhob}{\\rho_{\\rm b}}\n\\newcommand{\\rhol}{\\rho_{\\rm l}}\n\\newcommand{\\rhos}{\\rho_{\\rm s}}\n\\newcommand{\\lbump}{L_{\\rm bump}}\n\\newcommand{\\massb}{M_{\\rm b}}\n\\newcommand{\\rmax}{R_{\\rm max}}\n\\newcommand{\\mh}{m_{\\rm h}}\n\\newcommand{\\ms}{m_{\\rm s}}\n\\newcommand{\\mlo}{m_{\\rm l}}\n\\newcommand{\\mup}{m_{\\rm u}}\n\\newcommand{\\mtl}{M/L_B}\n\n\\title[Theory of pixel lensing towards M31 I]{Theory of pixel lensing\ntowards M31 I: the density contribution and mass of MACHOs}\n\n\\author[E.~Kerins et al.]{E.~Kerins$^1$, B.J.~Carr$^2$, N.W.~Evans$^1$,\nP.~Hewett$^3$, E.~Lastennet$^2$,\n\\newauthor \nY.~Le~Du$^4$, A.-L.~Melchior$^{2,5}$, S.J.~Smartt$^3$ and D.~Valls-Gabaud$^6$\n\\newauthor\n(The POINT--AGAPE Collaboration)\\\\\n$^1$Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UK\\\\\n$^2$Astronomy Unit, School of Mathematical Sciences, Mile End Road,\n London E1 4NS, UK\\\\\n$^3$Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UK\\\\\n$^4$Laboratoire de Physique Corpusculaire et Cosmologie, Coll\\`ege de France,\n 11 Place Marcelin Berthelot, F-75231 Paris, France\\\\\n$^5$DEMIRM UMR~8540, Observatoire de Paris, 61 Avenue\n Denfert-Rochereau, F-75014 Paris, France\\\\\n$^6$Laboratoire d'Astrophysique UMR~CNRS~5572, Observatoire\n Midi-Pyr\\'en\\'ees, 14 Avenue Edouard Belin, F-31400 Toulouse, France\n}\n\n\\maketitle\n\n\\begin{abstract} \nPOINT-AGAPE is an Anglo-French collaboration which is employing the\nIsaac Newton Telescope (INT) to conduct a pixel-lensing survey towards\nM31. Pixel lensing is a technique which permits the detection of\nmicrolensing against unresolved stellar fields. The survey aims to\nconstrain the stellar population in M31 and the distribution and\nnature of massive compact halo objects (MACHOs) in both M31 and the\nGalaxy.\n\nIn this paper we investigate what we can learn from pixel-lensing\nobservables about the MACHO mass and fractional contribution in M31\nand the Galaxy for the case of spherically-symmetric near-isothermal\nhaloes. We employ detailed pixel-lensing simulations which include\nmany of the factors which affect the observables, such as non-uniform\nsampling and signal-to-noise ratio degradation due to changing\nobserving conditions. For a maximum MACHO halo we predict an event\nrate in $V$ of up to 100 per season for M31 and 40 per season for the\nGalaxy. However, the Einstein radius crossing time is generally not\nmeasurable and the observed full-width half-maximum duration provides\nonly a weak tracer of lens mass. Nonetheless, we find that the\nnear-far asymmetry in the spatial distribution of M31 MACHOs provides\nsignificant information on their mass and density contribution. We\npresent a likelihood estimator for measuring the fractional\ncontribution and mass of both M31 and Galaxy MACHOs which permits an\nunbiased determination to be made of MACHO parameters, even from\ndata-sets strongly contaminated by variable stars. If M31 does not\nhave a significant population of MACHOs in the mass range $10^{-3}~\\sm\n- 1~\\sm$ strong limits will result from the first season of INT\nobservations. Simulations based on currently favoured density and mass\nvalues indicate that, after three seasons, the M31 MACHO parameters\nshould be constrained to within a factor four uncertainty in halo\nfraction and an order of magnitude uncertainty in mass ($90\\%$\nconfidence). Interesting constraints on Galaxy MACHOs may also be\npossible. For a campaign lasting ten years, comparable to the lifetime\nof current LMC surveys, reliable estimates of MACHO parameters in both\ngalaxies should be possible.\n\\end{abstract} \n\n\n\\begin{keywords}\ndark matter --- galaxies: haloes --- galaxies: individual\n(M31) --- Galaxy: halo --- gravitational lensing.\n\\end{keywords}\n\n\\section{Introduction} \\label{s1}\n\n\\subsection{Conventional microlensing: landmarks and limitations}\n\nThe detection of the gravitational microlensing effect due to compact\nobjects in the Galaxy is undoubtedly one of the great success stories\nin astrophysics over the past decade. Surveys have discovered\naround 20 candidates towards the Magellanic clouds and several hundred\ntowards the Galactic Bulge \\cite{uda94,alc97,ala97,lass99,alc00}. \nAmongst these candidates a number of exotic lensing phenomena have been\ncatalogued, such as parallax effects, binary lensing (including\nspectacular examples of caustic-crossing events), and finite\nsource-size effects. These discoveries are facilitated by coordinated\nfollow-up campaigns such as PLANET \\cite{alb98} and MPS \\cite{rhie99}\nwhich act on microlensing alerts broadcast by the survey\nteams. The absence of certain microlensing signals has also yielded a\nclearer insight into the nature of halo dark matter. The null detection\nof short duration events towards the Large Magellanic Cloud (LMC) by\nthe EROS and MACHO surveys indicates that, for a range of plausible\nhalo models, massive compact halo objects (MACHOs) within the mass\ninterval $10^{-7} - 10^{-3}~\\sm$ provide less than a quarter of the\ndark matter \\cite{alc98}. This is an important result when set against\nthe current insensitivity of other techniques to this mass range.\n\nDespite these successes a number of unsolved problems remain. The\noptical depth measured towards the Galactic Bulge is at least a factor\ntwo larger than can be accommodated by theoretical models\n(e.g. Bissantz et al. 1997; Sevenster et al. 1999). Towards the LMC\nthe rate of detected events is consistent with the discovery of a\nsignificant fraction of the halo dark matter. However, the implied\nlens mass range ($0.1 - 1~\\sm$) is not easily reconciled with existing\nconstraints on baryonic dark matter candidates \\cite{carr94}, though\nthe MACHOs need not necessarily be baryonic. Furthermore, the\ndiscovery of two possible binary caustic-crossing events towards the\nLMC and the Small Magellanic Cloud (SMC) has thrown into question the\nvery existence of MACHOs. Their caustic-crossing timescales, which\nprovide an indicator of their line-of-sight position, seem to exclude\neither as being of halo origin, a statistically unlikely occurrence if\nthe halo comprises a significant MACHO component \\cite{ker99}. As a\nresult, there is a growing body of opinion that all events observed so\nfar towards the LMC and SMC may reside in the clouds\nthemselves. However, this explanation is itself problematic because it\nrequires that the clouds must either have a higher MACHO fraction than\nthe Galaxy or comprise substantial but diffuse stellar components not\nin hydrodynamical equilibrium (Evans \\& Kerins 2000, and references\ntherein).\n\nThese problems highlight two principal constraints on the ability of\nconventional microlensing experiments to determine the nature and\ndistribution of MACHOs in the halo. The first limitation is their\ninefficiency in differentiating between lensing by MACHOs and\nself-lensing by the source population, since for most events one\nobserves only a duration and a position on the sky. These observables\nare only weakly correlated with the location of the events along the\nline of sight. The second constraint is the limited number of suitable\nlines of sight through the halo. Conventional microlensing surveys\nrequire rich yet resolved stellar fields and are thus limited to just\ntwo lines of sight, the LMC and SMC, with which to probe MACHOs. The\nline of sight to the Galactic Bulge is dominated by bulge and disc\nlensing. The paucity of halo lines of sight, together with the rather\nweak dynamical and kinematical constraints on Galactic halo structure,\nalso diminishes the prospect of being able to decouple information on\nthe Galactic distribution function and MACHO mass function.\n\n\\subsection{Beyond the Galaxy: a new target, a new technique}\n\nThe possibility of detecting MACHOs in an external galaxy,\nspecifically M31, was initially explored by Crotts (1992) and by\nBaillon et al. (1993). Crotts (1992) pointed out that the high\ninclination of the disc of M31 would result in an asymmetry in the\nobserved rate of microlensing if the disc is surrounded by a MACHO halo, as\nillustrated in Figure~\\ref{f1}. The fact that the M31 MACHO\nmicrolensing rate should be lower towards the near side of the disc\nthan the far side, which lies behind a larger halo column\ndensity, means that the presence of MACHOs in M31 can be established\nunambiguously. In particular, neither variable stars nor stellar\nself-lensing events in the disc of M31 should exhibit near-far\nasymmetry. Additionally, the external vantage point serves to reduce\nsystematic model uncertainties in two ways. Firstly, it permits a\nmore accurate determination of the rotation curve and surface\nbrightness profile than is possible for the Galaxy, which reduces\nthe prior parameter space of viable galactic models. Secondly, it\nprovides many independent lines of sight through the halo of M31,\nallowing the MACHO distribution across the face of the disc to be\nmapped and thus the halo distribution function to be constrained more\nor less directly.\n\n\\begin{figure}\n\\begin{center}\n\\epsfig{file=fig01.ps,width=5cm,angle=270}\n\\end{center}\n\\caption{The principle of near-far asymmetry. The optical depth\nthrough the halo towards the far disc is larger than towards the near\ndisc owing to the tilt of the disc confined within the spheroidal\ndistribution of MACHOs. The distribution of Galaxy MACHOs, disc\nself-lensing events and variable stars does not exhibit asymmetry.}\n\\label{f1}\n\\end{figure}\n\nAs pointed out by Baillon et al. (1993), another appeal of directing\nobservations towards more distant large galaxies like M31 is the\nincrease in the number of potential source stars, more than a factor\nof one thousand over the number available in the LMC and SMC, and all\nconfined to within a few square degrees. However, this also presents\na fundamental problem in that the source stars are resolved only\nwhilst they are lensed (and even then only if the magnification is\nsufficiently large). The presence of many stars per detector pixel\nmeans it is often impossible to identify which is being\nlensed. Furthermore, the flux contribution of the unlensed stars\ndilutes the observed flux variation due to microlensing. Nonetheless,\nBaillon et al. (1993) determined from numerical simulations that the\nnumber of observable events, due to either the lensing of bright stars\nor high magnification events, is expected to be large. As a result of\nthese studies, the Andromeda Galaxy Amplified Pixel Experiment (AGAPE)\nand another group, Columbia-VATT, commenced observing programs towards\nM31 \\cite{ans97,cro97}.\n\nOne of the biggest technical difficulties facing surveys which look\nfor variable sources against unresolved stellar fields is how to\ndistinguish between flux variations due to changing observing\nconditions and intrinsic variations due to microlensing or stellar\nvariability. For example, changes in seeing induce variations in\nthe detected flux within a pixel. One must also deal with the\nconsequences of positional misalignment between exposures, spatial and\ntemporal variations in the point spread function (PSF) and\nphotometric variations due to atmospheric transparency and variable \nsky background.\n\nAGAPE has employed the Pixel Method to cope with the changing\nobserving conditions \\cite{ans97}. AGAPE thoroughly tested\nthis technique with a three-year campaign using the 2m Bernard Lyot\ntelescope at Pic du Midi from 1994 to 1996 \\cite{ans97,ans99,ledu00}. Six\nfields covering about 100 arcmin$^2$ centred on the bulge of M31 were\nmonitored. Whilst the field of view was insufficient to conclude much\nabout the nature of MACHOs, 19 candidate events were detected, though\nit is still premature to rule out many of them being intrinsically\nvariable sources, such as Miras or novae. One event, AGAPE~Z1, appears\nto be a convincing lensing candidate as its flux increase and colour\nare inconsistent with that of a Mira or nova \\cite{ans99}. A longer\nbaseline is needed to determine how many of the other candidates are\ndue to microlensing.\n\nA major observing programme began on the 2.5m Isaac Newton Telescope\n(INT) in La~Palma in the Autumn of 1999, with a run of one hour per\nnight for almost sixty nights over six months. The POINT-AGAPE\ncollaboration is a joint venture between UK-based astronomers and\nAGAPE (where POINT is an acronym for ``Pixel-lensing Observations with\nINT''). We are exploiting the 0.3~deg$^2$ field of view of the INT\nWide-field Camera (WFC) to map the distribution of microlensing\nevents across a large region of the M31 disc. Our initial\nobservations of M31 with the INT employed a $V$ filter and the\nsimulations reported here have been undertaken with parameters\nappropriate to V-band observations. The strategy\nemployed for the actual M31 monitoring campaign involves observations\nin three bands, $g$, $r$, and $i$ [very similar to the bands employed\nby SLOAN \\cite{fuk96}]. The multi-colour observations will improve our\nability to discriminate against variable stars and the $gri$-filter\nplus CCD combination offers a significant improvement in sensitivity\n(the $g$-band zero-point is some 0.4 magnitudes fainter than that for\n$V$). The simulation parameters are thus somewhat conservative in this\nregard. The programme is being conducted in consort with the\nMicrolensing Exploration of the Galaxy and Andromeda (MEGA) survey\n\\cite{cro99}, the successor program to Columbia-VATT. Whilst\nPOINT-AGAPE and MEGA are sharing the data, different techniques are\nbeing employed to search for microlensing events. Henceforth we\nuse the term {\\em pixel lensing}\\/ \\cite{gou96} to describe\nmicrolensing against unresolved stellar fields, regardless of the\ndetection technique.\n\nWhilst the technical viability of pixel lensing is now clearly\nestablished, a number of important theoretical issues are still\noutstanding. The principal concern is that the main observable in\nclassical microlensing, the Einstein crossing time, is generally not\naccessible in pixel lensing. The Einstein crossing time is directly\nrelated to the lens mass, its transverse velocity and the\nobserver--lens--source geometry. In pixel lensing the observed\ntimescale depends upon additional factors, such as the local surface\nbrightness and the source luminosity and magnification, so the\ndependence on lens parameters is much weaker than for classical\nmicrolensing.\n\nThe first detailed study of pixel lensing was undertaken by Gould\n(1996). He defined two regimes: a semi-classical regime in\nwhich the source star dominates the pixel flux and the observable\ntimescale provides a fair tracer of the Einstein crossing time; and\nthe ``spike'' regime where only high-magnification events are\nidentified, and the timescales are only weakly correlated with the\nunderlying Einstein crossing duration. Remarkably, Gould showed that,\ndespite the loss of timescale information, in the spike regime one can\nstill measure the microlensing optical depth. Using Gould's formalism,\nHan (1996) provided the first pixel event rate estimates\nfor the M31 line of sight. However, Gould's formalism assumes a fixed\nsampling rate and unchanging observing conditions. As such it is of\nlimited applicability to a ground-based observing program. Gondolo\n(1999) has proposed an optical depth estimator based on the\nobserved pixel event timescale. Whilst this estimator can be readily\nemployed by a ground-based campaign, it is somewhat sensitive to\nthe shape of the source luminosity function and is valid only to the\nextent that this can be taken to be the same for\nall source components. More recently, Baltz \\& Silk (1999)\nderived expressions for the pixel rate and timescale distribution in\nterms of the observable timescale, rather than the Einstein crossing\ntime. Again, their study assumes constant sampling and observing\nconditions, as would be the case for space-borne programmes.\n\nWhilst these studies provide a solid foundation for predictions of\npixel-lensing quantities (i.e. timescales, rates and optical depth),\nnone of them address to what extent one can constrain galactic and\nlens parameters, in particular the MACHO mass, from pixel lens\nobservables. Gyuk \\& Crotts (2000) have shown that a reliable measure\nof the optical depth from pixel lensing can be used to probe the core\nradius and flattening of the M31 MACHO halo. \n\nIn this paper we quantitatively assess the degree to which the\nPOINT-AGAPE campaign directed towards M31 will constrain the\nfractional contribution and mass of the MACHOs. Since the answer\ninevitably depends upon the assumed galactic distribution function, we\nfocus attention here on the simple case of spherically-symmetric\nnear-isothermal halo models. The line of sight towards M31 is\nsensitive to two MACHO populations, our own and that\nin M31 itself, so we investigate the extent to which they can be\ndistinguished and probed independently. We also model the expected\nbackground due to variable stars and lenses residing in the disc\nand bulge of M31.\n\nThe plan of the paper is as follows. In Section~\\ref{s2} we summarize\nthe basic principles of pixel lensing, with emphasis on the\ndifferences between pixel lensing and classical microlensing. We\ndescribe our Monte-Carlo pixel-lensing simulations in\nSection~\\ref{s3}, including our event selection criteria and the\nincorporation of realistic sampling and observing conditions. In\nSection~\\ref{s4} we construct a reference model for the lens and\nsource populations in the halo of the Galaxy and the halo, disc and\nbulge of M31, seeking consistency with the observed M31 rotation curve\nand surface brightness profiles. In Section~\\ref{s5} we present\npredictions for the POINT-AGAPE survey based on our simulations. In\nSection~\\ref{s6} we use the simulations to generate artificial\ndata-sets and we investigate to what extent the MACHO mass and\nfractional contribution in the two galaxies can be recovered from the\ndata. The results are summarized and discussed in Section~\\ref{s7}.\n\n\\section{Principles of pixel lensing} \\label{s2}\n\nWe review here some of the main aspects of pixel lensing\nand its differences with classical microlensing. A more detailed\noverview can be found in Gould (1996).\n\n\\subsection{Detecting pixel events}\n\nWhilst in classical microlensing one monitors individual sources, in\npixel lensing the sources are resolved only whilst they are lensed. We\ncan therefore only monitor the flux in each detector element rather\nthan the flux from individual sources. If a star is magnified\nsufficiently due to a lens passing close to its line of sight, then\nthe total flux in the detector element containing the source star (due\nto the lensed star, other nearby unlensed stars and the sky\nbackground) will rise significantly above the noise level and be\nrecorded as an event.\n\nBefore treating seeing variations the sequence of images must be\ngeometrically and photometrically aligned with respect to some\nreference image, ${\\cal R}$, as described in Ansari et al. (1997). The\nvariations remaining after alignment are primarily due to changes in\nseeing and source flux, including microlensing events. To minimize\nthe effects of seeing we define our base detector element to be a\nsuperpixel: a square array of pixels. A superpixel is defined for\neach pixel, with that pixel lying at the centre, so that neighbouring\nsuperpixels overlap with an offset of one pixel. The optimal size for\nthe superpixel array is set by the ratio of the size of the seeing\ndisc on images obtained in poor seeing to the individual pixel\nsize. The INT Wide-field Camera (WFC) has a pixel scale corresponding\nto $0\\farcs 33$ on the sky, whilst poor seeing at La~Palma is $\\sim\n2\\arcsec$. Adopting a very conservative value of $2\\farcs 4$ for the\nworst seeing leads to an optimized choice of $7 \\times 7$ pixels for\nthe superpixel array. A larger array would overly dilute source\nvariations, whilst a smaller array would be overly sensitive to\nchanging observing conditions.\n\nWhilst seeing variations are reduced by binning the photon count into\nsuperpixels, this by itself is not enough to make them\nnegligible. Residual variations are minimized by the Pixel Method, in\nwhich a simple, empirically-derived statistical correction is applied\nto each image to match it to the characteristics of the reference\nimage ${\\cal R}$. The Pixel Method is discussed in Ansari et al. (1997) and\ndescribed in detail by Le~Du (2000). The method strikes a good balance\nbetween computational efficiency and optimal signal-to-noise ratio,\nwith the resulting noise level approaching the photon noise limit.\n\nAfter alignment and seeing corrections the excess superpixel photon\ncount $\\Delta \\nsp$ on an image $i$ obtained at epoch $t_i$ due to an\nongoing microlensing event is\n \\be\n \\Delta \\nsp(t_i) \\equiv \\nbl [\\asp(t_i) -1 ] = \\fsee \\nsrc [A(t_i)-1].\n \\label{spix}\n \\ee\nHere $\\nsrc$ and $\\nbl$ are the source and baseline photon counts in\nthe absence of lensing, $A$ is the source magnification factor due to\nlensing and $\\fsee$ is the fraction of the seeing disc contained\nwithin the superpixel. The baseline photon count, $\\nbl = \\ngal ({\\cal\nR}) + \\nsky ({\\cal R})$, is the sum of the local M31 surface brightness\n(including $\\nsrc$) and sky background contributions on the reference\nimage. Whilst the quantities $\\nbl$ and $\\fsee \\nsrc (A-1)$ can be\ndetermined independently, $\\nsrc$ and $A$ cannot in\ngeneral be inferred separately. It is therefore convenient to define\n$\\asp$ as the superpixel count variation factor, which acts as the\nobservable analogue of $A$.\n\nThe superpixel noise on image $i$ is \n \\be\n \\sigi = \\max [ \\sigma_{\\rm T}(t_i), \\alpha_i \n \\nsp (t_i) ^{1/2} ], \\label{err}\n \\ee\nwhere\n \\be\n \\nsp (t_i) = \\Delta \\nsp (t_i) + \\nsky (t_i) + \\ngal\n \\label{supf}\n \\ee\nrefers to the superpixel photon count on image $i$ {\\em prior}\\/ to\ncorrection and, similarly, $\\nsky$ and $\\ngal$ are the uncorrected sky\nbackground and galaxy surface brightness contributions. The threshold\nnoise level $\\sigma_{\\rm T}$ is determined by the superpixel flux\nstability, and the scaling factor $\\alpha_i$ takes account of the fact\nthat the Pixel Method is not photon-noise limited. A preliminary\nanalysis of a sequence of INT WFC images taken in 1998 demonstrated a\nflux stability level of $0.1-0.3\\%$ \\cite{mel99}. We therefore adopt a\nconservative minimum noise level of $\\sigma_{\\rm T} = 2.5 \\times\n10^{-3} \\nbl$ for our simulations. We also apply a constant scaling\nfactor $\\alpha_i = 1.2$, which is a little larger than typical for the\nAGAPE Pic du Midi data\n\\cite{ledu00}. In reality $\\alpha_i$ varies slightly between images\nthough we neglect this variation in our simulations.\n\nNote that $\\ngal$ in equation~(\\ref{supf}) is constant, despite the\nchanging observing conditions. Though some variable fraction of the\nlocal patch of surface brightness is dispersed over neighbouring\nsuperpixels, the same amount of surface brightness leaks into the\nsuperpixel from neighbouring patches, so there is no net\nvariation. The variation in $\\nsky$ results from changing moonlight\nand atmospheric transparency.\n\nWe regard a signal as being statistically significant if it occurs at\na level $3 \\, \\sigi$ above the baseline count $\\nbl$. Our estimate of\n$\\nbl$ must be obtained from a sequence of images and operationally is\ndefined to be the minimum of a sliding average of superpixel photon\ncounts over ten consecutive epochs. In order for a signal to be\ndetected on image $i$ we therefore require a superpixel count\nvariation factor $\\asp (t_i) \\ge 1+ 3 \\, \\sigi/\\nbl$. From\nequation~(\\ref{spix}), a microlensed source satisfies this inequality\nprovided that it is magnified by a factor exceeding\n \\be\n \\amin(t_i) = 1+ \\frac{3 \\, \\sigi}{\\fsee \\nsrc}. \\label{ampt}\n \\ee\nA special case of equation~(\\ref{ampt}) occurs when $\\sigi = \\sigma_{\\rm\nT}$, giving a threshold magnification of\n \\be\n \\at = 1+ 0.0075 \\frac{\\nbl}{\\fsee \\nsrc}. \\label{aspt}\n \\ee\nThe extent to which residual temporal variations in $\\fsee$ and $\\nbl$\nremain after image processing determines the factor by which $\\sigi$\nexceeds the photon noise limit, so this excess noise\nis explicitly accounted for in equation~(\\ref{ampt}).\n\nEquation~(\\ref{ampt}) illustrates some important characteristics of\npixel lensing. Firstly, pixel lensing does not depend directly on the\nlocal surface brightness or sky background, but it does depend on\ntheir contribution to the noise $\\sigi$. Secondly, if the exposure\ntime $\\texp$ is short, or the source star constitutes only a small\nfraction of the superpixel flux, so that $\\nsrc \\ll \\sigi$, only rare\nhigh-magnification events are detected. The relationship between lens\nmagnification and lens--source impact distance (measured in the lens\nplane) is as for the classical case:\n \\be\n A = \\frac{u^2 + 2}{u\\sqrt{u^2 + 4}} \\label{ampu}\n \\ee\nwhere $u$ is the impact distance in units of the Einstein radius. The\nmaximum value for the impact distance can be obtained by inverting\nequation~(\\ref{ampu}) for $A = \\amin$:\n \\be\n \\umax = 2^{1/2} \\left[ \\frac{\\amin}{\\sqrt{\\amin^2 -1}} -1\n \\right]^{1/2} \\simeq \\amin ^{-1} \\quad (\\amin \\ga 10).\n \\label{imp}\n \\ee\nFor pixel lensing in M31 we are often in the regime where $\\nsrc \\ll\n\\sigi$ because the source flux is much less than that of the galaxy\nand background, so it is not unusual to require $\\amin \\ga 10$. In this\ncase equations~(\\ref{ampt}) and (\\ref{imp}) imply\n \\be\n \\umax \\simeq \\frac{\\fsee \\nsrc}{3 \\, \\sigi } < \\frac{\\fsee\n \\nsrc}{3 \\nsp^{1/2} } \\quad \\quad (\\amin \\ga 10), \\label{ueq}\n \\ee\nSince $\\umax \\ll 1$ [typically $\\umax \\sim {\\cal O}(10^{-2} -\n10^{-3})$] only a small fraction of classical ($u \\leq 1$)\nmicrolensing events are detectable.\n\nThe dependence of $\\umax$ on $\\nsrc$ means that the pixel event rate\ndepends on the source luminosity function $\\phi(M)$, the number\ndensity of sources in the absolute magnitude interval $(M,M+dM)$. We\ncan compute a theoretical upper limit, $\\gp$, for the pixel-lensing\nrate at sky coordinate $(x,y)$ by taking $\\amin = \\at$ so that $\\umax\n = u(\\at) = \\ut$. In this case\n \\be\n \\gp (x,y) = \\langle \\ut(x,y) \\rangle_{\\phi} \\gc (x,y),\n \\label{prate}\n \\ee\nwhere $x$ and $y$ are Cartesian coordinates centred on M31 and aligned\nrespectively along the major and minor axes of the projected light\nprofile. We define $y$ to be positive towards the near side of the\ndisc. The quantity $\\gc$ is the classical ($u \\leq 1$) event rate\nintegrated over lens and source populations \\cite{grie91,kir94}, and\n \\be\n \\langle \\ut (x,y) \\rangle_{\\phi} \\equiv \\frac{\\int \\ut(M,x,y)\n \\phi(M) \\, dM}{\\int \\phi(M) \\, dM} \\label{ulf}\n \\ee\nis the mean threshold impact parameter at $(x,y)$ averaged over\n$\\phi$.\n\nWhilst useful in providing a rough order of magnitude estimate, $\\gp$\ncannot be compared directly with observations because it assumes\nperfect sensitivity to all event durations and it also assumes that\nobserving conditions are unchanging. Since one usually has $\\amin >\n\\at$, equation~(\\ref{ulf}) also tends to overestimate the true mean\npixel-lensing cross-section. One can regard $\\gp$, evaluated under the\nbest observing conditions, as providing a strict theoretical upper\nlimit to the observed event rate, in much the same way as $\\gc$\nprovides an upper limit to the observed rate in classical lensing. In\nSection~\\ref{s3} we set about obtaining a more realistic estimate of\nthe observed pixel lensing rate.\n\n\\subsection{Degenerate and non-degenerate regimes} \\label{snon-deg}\n\nIn classical microlensing the most important observable is the\nEinstein radius crossing time, since this is directly related to the\nposition, motion and mass of the lens. Can we obtain similar\ninformation from the duration of pixel events?\n\nFor a lens moving at constant velocity across the line of sight, $u$\nevolves with time $t$ as in the classical case:\n \\be\n u(t)^2 = u(t_0)^2 + \\left( \\frac{t - t_0}{\\te} \\right)^2,\n \\label{utime}\n \\ee\nwhere $t_0$ is the epoch of minimum impact distance and $\\te$ is the\nEinstein radius crossing time. From equations~(\\ref{ampu}) and\n(\\ref{utime}), $\\te$ gives the timescale over which the source\nmagnification $A$ varies significantly. For large magnifications $u\n\\simeq A^{-1}$ from equation~(\\ref{imp}), and inserting\nequation~(\\ref{utime}) into equation~(\\ref{spix}) gives\n \\be\n \\Delta \\nsp(t) \\simeq \\frac{ \\fsee \\amax \\nsrc }{ \\sqrt{1 + \\left(\n \\frac{ {\\tst t-t_0} }{ {\\tst \\te \\amax^{-1} } } \\right)^2} } \\quad\n \\quad [A(t) \\ga 10], \\label{lcurve}\n \\ee\nwhere $\\amax \\equiv A(t_0)$ is the maximum magnification. We infer\nthat in pixel lensing the timescale over which the signal varies\nsignificantly is $\\te \\amax^{-1}$ rather than $\\te$. This means that,\nin the high-magnification regime, the pixel-lensing timescale bears\nlittle relation to $\\te$. We also see that the light-curve is\ndegenerate under transformations $\\amax \\rightarrow \\alpha \\amax$, $\\nsrc\n\\rightarrow \\nsrc/ \\alpha$ and $\\te \\rightarrow \\alpha \\te$\n\\cite{woz97}. So neither $\\te$, $\\amax$ nor $\\nsrc$ can be determined\nindependently. It may sometimes be possible to break this degeneracy\nby looking at the wings of the light-curve \\cite{bal99}, where\ndifferences between the true magnification and its degenerate form can\nbecome apparent. From equation~(\\ref{ampu}), the difference between\nthe exact expression for $A(u)-1$ appearing in equation~(\\ref{spix})\nand its degenerate approximation, $u^{-1}$, is \n \\be\n \\Delta (A-1) = \\frac{u^2 + 2}{u\\sqrt{u^2 + 4}} - 1 - \\frac{1}{u}\n \\simeq \\frac{3u}{8} - 1 \\quad \\quad (u \\la 1).\n \\label{difa}\n \\ee\nTo discriminate reliably (say at the $3 \\, \\sigma$ level) between the\ndegenerate and non-degenerate cases requires $\\fsee \\nsrc |\\Delta\n(A-1)| > 3\\, \\sigi$, so for the high-magnification regime we can\nwrite the condition for non-degeneracy as\n \\be\n \\sigi \\la \\frac{\\fsee \\nsrc}{3}\n \\quad \\quad (u \\ll 1). \\label{uint}\n \\ee\nEquation~(\\ref{uint}) demands that the superpixel noise be no greater\nthan the contribution of the unlensed source to the superpixel flux.\nIn general this will not be the case, so observations will not be able\nto break the light-curve degeneracy and thus will not directly probe\nthe Einstein crossing time.\n\nSince the underlying duration $\\te$ is not generally measurable we use\nthe observed full-width half-maximum (FWHM) event duration:\n \\be\n \\tfw = 2 \\sqrt2 \\, \\te \\, \\left[ \\frac{a+2}{\\sqrt{a^2+4a}} -\n \\frac{a+1}{\\sqrt{a^2+2a}} \\right]^{1/2}, \\label{tfw}\n \\ee\nwhere $a = \\amax-1$. Since $\\amax$ for detected events is typically\nlarger in regions of higher surface brightness, and for fainter stars,\n$\\tfw$ is correlated both with the disc surface brightness and the\nsource luminosity function. This means that it is less strongly\ncorrelated than $\\te$ with the lens mass and velocity and the lens and\nsource distances.\n\nThe observed duration, $\\tfw$, does not afford us with as direct a\nprobe of lens parameters as $\\te$. We are therefore forced to rely on\nother observables, such as spatial distribution, in order to probe the\nunderlying MACHO properties. For M31 MACHOs one can test for near-far\nasymmetry in the event rate \\cite{cro92}. For Galaxy MACHOs there is\nno comparable signature. Looking from the centre of the Galaxy towards\nM31 the halo density distribution in the two galaxies is highly\nsymmetric about the observer--source midpoint. Since the microlensing\ngeometry is also symmetric about the midpoint the timescale\ndistributions for Galaxy and M31 MACHOs are similar for the same mass\nfunction. Since our displacement from the Galactic centre is only\n8~kpc (small compared to the scale of the haloes and the Galaxy--M31\nseparation) this geometrical symmetry is largely preserved at our\nlocation. However, the Galaxy MACHO distribution ought to be less\nconcentrated than that of stellar lenses. One might hope to see this\nas an excess of events at faint isophotes which remains the same\ntowards both the near and far disc. If MACHOs exist, the overall\npixel-lens distribution will be superposition of several lens\npopulations (Galaxy halo, M31 halo, disc and bulge) together with\nvariable stars which, at least in the short term, appear\nindistinguishable from microlensing. The task of disentangling each is\ntherefore potentially tricky.\n\n\\section{Simulating pixel events} \\label{s3}\n\nA straightforward method for probing the lens populations is to\nconstruct simulations of the expected distribution of events for a\nparticular telescope configuration, set of observing conditions and\nselection criteria and then compare these predictions to\nobservations. To this end we have constructed a detailed simulation of\na realistic pixel-lensing experiment.\n\nOur simulation works by first computing a theoretical upper limit to\nthe pixel rate for assumed M31 and Galaxy models. This estimate\nprovides the basis for generating trial pixel microlensing events for\nwhich light-curves are constructed and selection criteria applied. The\nprecise details of our input galaxy models are discussed in\nSection~\\ref{s4}; in this section we lay down the general framework\nfor the simulation. For each generated trial event, a pixel\nlight-curve is constructed using a realistic distribution of observing\nepochs interrupted by poor weather and scheduling constraints. The\neffects of the sky background and seeing are explicitly taken into\naccount in computing flux realizations and errors for each\n``observation''. The observing sequence is then examined to see\nwhether the event passes the detection criteria --- if it does, then\nthe trial counts as a detected event. The simulation is terminated\nonce $10^4$ events are detected or $10^6$ trials generated, whichever\nis reached first. The fraction of trial events which are detected is\nused to compute the observed pixel rate. The statistical error on the\nrate determination is typically about $3\\%$.\n\n\\subsection{Generating trial events} \\label{s3.1}\n\nAs the starting point for our simulation we use the theoretical pixel\nevent rate as a function of position, $\\gp (x,y)$, defined by\nequation~(\\ref{prate}). This quantity, evaluated for the best seeing\nconditions, always provides an upper limit to the detection rate at a\ngiven location and is therefore convenient to use to generate trial\nevents. We compute $\\gpj$ over a grid of locations $(x,y)$ for each\ncombination $j$ of lens and source population. Near the centre of M31,\n$j = 1 \\ldots 8$ since there are two source populations (M31 disc and\nbulge) and four lens populations (Galaxy halo, M31 halo, M31 disc and\nM31 bulge). Beyond 8~kpc the M31 bulge is not in evidence, so $j = 1\n\\ldots 3$.\n\nGiven the grid of $\\gpj (x,y)$, one can write the probability of\nobserving an event at location $(x,y)$ as\n \\be\n P(x,y) \\propto \\Delta x \\Delta y \\sum_j S_j (x,y) \\gpj(x,y),\n \\label{pxy}\n \\ee\nwhere $S_j$ is the source surface density at $(x,y)$ for lens--source\nconfiguration $j$, and $\\Delta x$ and $\\Delta y$ are the local $x$ and\n$y$ grid spacings (required only for non-uniform grids). $P(x,y)$\ntherefore reflects the total event rate in a box of area $\\Delta x\n\\Delta y$ centred on $(x,y)$. The box should be sufficiently small\nthat $S_j (x,y)$ and $\\gpj (x,y)$ provide good estimates of the source\ndensity and theoretical rate anywhere within it. Having fixed the\nevent location, $\\gpj$ is then used to select the lens and source\ncomponents from the probability distribution\n \\be\n P(j) = \\frac{S_j (x,y) \\gpj (x,y)}{\\sum_j S_j (x,y) \\gpj (x,y)}.\n \\label{pi}\n \\ee\n\nOnce the event location and lens and source populations have been\ndecided, the next choice is the line-of-sight distances to the lens,\n$\\dd$, and source, $\\ds$:\n \\begin{eqnarray}\n P(\\ds) & \\propto & \\rhos (\\ds) \\ds ^{3/2} \\int_0^{\\ds} P( \\dd)\n \\, d \\dd \\nonumber \\\\\n P(\\dd) & \\propto & \\rhol (\\dd) \\sqrt{\\dd ( \\ds - \\dd)},\n \\label{posn}\n \\end{eqnarray}\nwhere $\\rhol$ and $\\rhos$ are respectively the lens and source mass\ndensities. These distributions reflect the dependency of the\nmicrolensing rate $\\gpj$ on $\\ds$, integrated over all possible $\\dd$,\nand on $\\dd$, for a given $\\ds$. Next we require the lens mass $m$\nand relative transverse speed $\\vt$. The lens mass realization is\ngenerated from the distribution\n \\be\n P(m) \\propto m^{1/2} \\psi (m) \\label{mfreal},\n \\ee\nsince, in the absence of finite source-size effects, $\\gp \\propto \\re\n\\psi \\propto m^{1/2} \\psi$, where $\\psi$ is the lens mass function\n(i.e. the number density of lenses per unit mass interval) and $\\re$\nis the Einstein radius. The transverse speed $\\vt (\\bvl,\\bvs)$ is\ndrawn from the assumed velocity distributions $P_{\\rm l}(\\bvl)$ and\n$P_{\\rm s}(\\bvs)$ (see section~\\ref{s4}), with $\\bvl$ and $\\bvs$ the\nlens and source three-dimensional velocity vectors. Since the\nmicrolensing rate $\\gp$ is proportional to $\\vt P_{\\rm l} P_{\\rm s}$\nrather than just $P_{\\rm l} P_{\\rm s}$, each of our realizations must\nbe weighted by $\\vt$ in computing the final detection rate. Finally,\nwe also need to generate the source absolute magnitude $M$ (defined\nfor some photometric band). The dependency of $\\gp$ on $M$ derives\nfrom the luminosity function $\\phi$ and the threshold impact parameter\n$\\ut$, so we have\n \\be\n P(M) \\propto \\ut (M,x,y) \\phi(M). \\label{mreal}\n \\ee\n\n\\subsection{Generating light-curves} \\label{s3.2}\n\nAt this point we have only simulated events according to the\nunderlying distributions which govern $\\gp$; we have yet to take into\naccount the distribution of observing epochs, variations in observing\nconditions, or candidate selection criteria.\n\nThe observing season runs from the beginning of August to the end of\nJanuary, so we adopt the duration of an observing season to be $\\Delta\nT = 180$~days. We assume 60 scheduled observing epochs per season ---\napproximately the number of nights awarded for our 1999/2000\nseason. To construct a realistic sequence of observing epochs we\nassume that the WFC is mounted on the telescope and available for\ntwo-week periods every four weeks and that, on average, $25\\%$ of\nscheduled observations are precluded by bad weather. Periods of poor\nweather are superposed on our initial observing sequence to obtain a\nfinal sequence which typically comprises 40--50 epochs per season. In\npractice we expect to obtain observations on more epochs than this,\nbut for the purposes of these simulations we assume 40--50 as a\nconservative lower limit. For example during the 1999/2000 season we\nhave had observations on 56 nights.\n\nThe epoch of maximum magnification $t_0$ and the minimum impact\nparameter $u(t_0)$ are both chosen at random. $u(t_0)$ is selected\nfrom the interval $[0,\\ut]$, where the threshold impact parameter\n$\\ut$ is computed from equations~(\\ref{aspt}) and (\\ref{imp}) taking\n$\\amin = \\at$. This is all that is required to generate\nthe underlying microlensing light-curve. \n\nTo compute the pixel light-curve, we must also model the galaxy\nsurface brightness and sky background. The simulations presented here\nare performed in the $V$ band and we use the radially-averaged surface\nbrightness profile in Table~VI of Walterbos\n\\& Kennicutt (1987) to estimate the contribution to the pixel flux of\nthe galaxy background at the event location. The assumed sky\nbackground corresponding to a dark sky is listed in Table~\\ref{t1},\nalong with other INT detector and site characteristics. The sky\nbackground varies over lunar phase and we adopt a contribution to the\nsky background from the full moon equivalent to $10^3$ tenth magnitude\nstars per deg$^2$ (c.f. Krisciunas \\& Schaefer 1991). The contribution\nis modulated according to the lunar phase. The lunar contribution to\nthe sky background also depends upon whether the moon is above the\nhorizon and on its angular distance from M31. Our assumed value is\ntaken to be an average over the positional dependence, so the true\nvariation in the sky background will be somewhat larger than we\nconsider. We also simplify the computation of the seeing fraction\n$\\fsee$ by adopting a Gaussian PSF with a FWHM equal to the seeing of\nthe reference image. The position of the PSF maximum for the reference\nimage is selected at random within the central pixel of the superpixel\narray.\n\\begin{table}\n\\begin{center}\n\\caption{Adopted characteristics of the INT observing site and\nWide-field Camera (WFC). The sky background is given in\nmag~arcsec$^{-2}$ and the superpixel dimension is quoted in\npixels. The zero-point is given in terms of the apparent magnitude of\na source which results in a 1~photon~sec$^{-1}$ detection rate. All\nmagnitudes are for the $V$ band. Our survey is now observing in $g$,\n$r$ and $i$ filters. For comparison, the sky background and zero-point\nin $g$ are 22.2 and 26.0, respectively.}\n\\label{t1}\n\\begin{tabular}{@{}lc}\nCharacteristic & INT WFC \\\\\n\\hline\nBest seeing & $0 \\farcs 8$ \\\\\nWorst seeing & $2 \\farcs 4$ \\\\\nReference image seeing & $1 \\arcsec$ \\\\\nSky background & 21.9 \\\\\nScheduled epochs per season & 60 \\\\\nField dimensions & $32\\arcmin \\times 32\\arcmin$ \\\\\nPixel field of view & $0\\farcs 33$ \\\\\nSuperpixel dimensions & $7 \\times 7$ \\\\\nZero-point & 25.6 \\\\\nExposure time per field & 760~secs \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\nUsing our computed values for $\\fsee$, the INT\ndetector and site characteristics summarized in Table~\\ref{t1}, and the\nmicrolensing parameters generated for each event, we construct\nsuperpixel light-curves via equation~(\\ref{spix}). The error at each epoch\n$i$ is given by equation~(\\ref{err}). Poisson realizations for the\nsuperpixel flux at each epoch are generated from $\\nsp (t_i)$ and\n$\\sigi$.\n\n\\subsection{Selection criteria and the observed rate} \\label{s3.3}\n\n\\begin{figure*}\n\\centering\n\\begin{minipage}{170mm}\n\\begin{center}\n\\epsfig{file=fig02a.ps,width=7cm,angle=270}\n\\epsfig{file=fig02b.ps,width=7cm,angle=270}\n\\epsfig{file=fig02c.ps,width=7cm,angle=270}\n\\end{center}\n\\caption{Simulated pixel-lensing light-curves. ({\\it Top panel}\\/) A\nlight-curve with a signal-to-noise ratio typical of many of the events;\n({\\it middle panel}\\/) a low signal-to-noise ratio event; ({\\it bottom\npanel}\\/) a high signal-to-noise ratio light-curve.}\n\\label{f3}\n\\end{minipage}\n\\end{figure*}\n\\begin{table*}\n\\centering\n\\begin{minipage}{170mm}\n\\caption{Parameters adopted for the density and velocity distributions\nfor components of the Galaxy and M31. The bulge model is adopted from\nKent (1989).}\n\\label{t2}\n\\begin{center}\n\\begin{tabular}{@{}lllll}\n\\null & \\null & \\null & Rotation & Velocity \\\\\nComponent & Mass normalization & Scale lengths & speed & dispersion \\\\\n\\hline\nM31 bulge & $\\massb = 4 \\times 10^{10}~\\sm$ & --- & 30~\\kms & 100~\\kms \\\\\n\\null & $\\mtl$ = 9 & \\null & \\null & \\null \\\\\nM31 disc & $\\rhod (0) = 0.2$~\\den & $H = 0.3$~kpc, & 235~\\kms & 30~\\kms \\\\\n\\null & $\\mtl$ = 4 & $h = 6.4$~kpc & \\null & \\null \\\\\nM31 halo & $\\rhoh (0) = 0.23$~\\den & $a = 2$~kpc, & 0 & 166~\\kms \\\\\n\\null & \\null & $\\rmax = 200$~kpc & \\null & \\null \\\\\nGalaxy halo & $\\rhoh (0) = 0.036$~\\den & $a = 5$~kpc, & 0 & 156~\\kms \\\\\n\\null & \\null & $\\rmax = 100$~kpc & \\null & \\null\n\\end{tabular}\n\\end{center}\n\\end{minipage}\n\\end{table*}\nThe adoption of selection criteria inevitably reduces the number of\ndetected events, but they are necessary to minimize the number of\ncontaminating non-microlensing signals. As in all microlensing\nexperiments the selection criteria must be based upon the quality of\nthe data and the characteristics of non-microlensing\nvariations. Ultimately the criteria must be derived from the data\nthemselves, so they are inevitably experiment-specific and evolve as\nthe experiment progresses. For our simulations we impose criteria\nbased loosely on the previous AGAPE pixel-lensing at Pic du Midi\n\\cite{ans97,ledu00}.\n\nThe principal criterion for the selection of microlensing events in\nour simulation is that one and only one significant bump be identified\non the light-curve. The bump must comprise at least three consecutive\nmeasurements lying at least $3 \\sigma$ above the baseline superpixel\nflux. Quantitatively, the significance of a bump is defined by its\nlikelihood\n \\be\n \\lbump = \\prod_{i = j}^{i = j+n, n \\geq 3} P(\\Theta > \\Theta_i |\n \\Theta_i \\geq 3), \\label{bumplike}\n \\ee\nwhere $\\Theta_i = [\\nsp (t_i) - \\nbl]/\\sigi$ and $P(\\Theta)$ is the\nprobability of observing a deviation at least as large as $\\Theta$ by\nchance. For a Gaussian error distribution, $P = \\frac{1}{2}\n\\mbox{erfc} (\\Theta / \\sqrt{2} )$. Equation~(\\ref{bumplike})\nindicates that we evaluate $P(\\Theta_i)$ only when $\\Theta_i \\geq\n3$. For our simulations we demand that a candidate have one bump with\n$- \\ln \\lbump > 100$ and no other bump with $- \\ln \\lbump > 20$. We\nfurther demand that the epoch of maximum magnification $t_0$ lies\nwithin an observing season; we reject candidates which attain their\nmaximum brightness between seasons, even if they last long enough for\nthe tails of the light-curve to be evident. This helps to ensure a\nreliable estimate of the peak flux, and in turn the FWHM timescale\n$\\tfw$.\n\nThe bump criterion is both a signal-to-noise ratio condition and a\ntest for non-periodicity. It is crucial for distinguishing\nmicrolensing events from periodic variables, though long-period\nvariables, such as Miras, may pass this test in the short term. In\naddition to the bump test, one can also test the goodness of fit of\nthe light-curve to microlensing, which helps to distinguish microlensing\nfrom typical novae light-curves. Though the presence of the background\nmeans that pixel events will not in general be achromatic, the ratio\nof the flux increase to baseline flux in different colours should\nnonetheless be independent of time, so this provides another test for\nmicrolensing. Colour information may also help to exclude some\nlong-period variables in the absence of a sufficient baseline of\nobservations. In Section~\\ref{s6} we also exploit differences in\nspatial distribution to separate statistically lensing events from\nvariable stars.\n\nFor real data-sets we would require more criteria in order to avoid\nexcessive contamination from variable stars. For now we are\nsimulating only microlensing events, so we are assured of no\ncontamination in our selection. However, the cuts adopted above would\nbe responsible for many of the rejected candidates in a real\nexperiment, so the absence of further criteria should not lead to a\ngross overestimate of the rate. In any case, we have been deliberately\nconservative with our choices of sky background level, worst seeing\nscale, the number of epochs per season and the pixel stability level\n$\\sigma_{\\rm T}$. We therefore feel our predictions are more likely to\nbe underestimates of the actual detection rate.\n\nThe observed rate can be now readily computed from $\\gp$, the number\nof generated trials and the fraction of these which pass the detection\ncriteria. As mentioned in Section~\\ref{s3.1}, the way in which\nvelocities are generated in the simulations means that the correct\nrate is obtained by weighting each event by its transverse speed\n$\\vt$. Thus, the observed rate for lens component $j$ is\n \\be\n \\gpoj = \\langle \\gpj \\rangle_{x,y} \\frac{\\sum_{l = 1}^{N_{\\rm det}(j)}\n V_{{\\rm t},l} }{ \\sum_{k = 1}^{N_{\\rm trial}(j)} V_{{\\rm t},k} },\n \\label{robs}\n \\ee\nwhere $\\langle \\gpj \\rangle_{x,y}$ is the spatial average of $\\gpj$\n(summed over source populations), the lower summation is over all\n$N_{\\rm trial}$ trial events generated for lens component $j$ and the\nupper summation is over the $N_{\\rm det}$ detected events which pass\nthe selection criteria. The total number of events after $n$ observing\nseasons is\n \\be\n N = n \\, \\Delta T \\, 10^{0.4(\\langle M\n \\rangle - M_{\\rm gal})} \\sum_j \\gpoj, \\label{nexp}\n \\ee\nwhere $\\langle M \\rangle$ is the average absolute magnitude of the\nsources (integrated over the luminosity function) and $M_{\\rm gal}$ is\nthe absolute magnitude of M31 ($M_V = -21.2$).\n\n\\subsection{Simulated light-curves} \\label{s5.1}\n\nThree light-curves generated for a first-season simulation involving\n$0.1~\\sm$ MACHOs are shown in Figure~\\ref{f3}. The galactic models\nrequired for the simulation are discussed in Section~\\ref{s4}. The\nlight-curves illustrate the range in signal-to-noise ratio. The\ndown-time for the WFC is evidenced by the way in which the epochs are\nclumped into two-week periods. The variation in the size of the error\nbars reflects the simulated variation in observing conditions.\n\nFigure~\\ref{f3}a shows an M31 halo lens magnifying a bulge star ($M_V\n= -0.4$) and is a typical example. The underlying maximum\nmagnification for this event is $\\amax = 18$, whilst the maximum\nenhancement in superpixel flux is $\\asp (t_0) = 1.06$, indicating that\nthe unlensed source is contributing less than $0.4\\%$ of the\nsuperpixel flux. For this event $\\tfw = 5$~days and $\\te = 28$~days.\nFigure~\\ref{f3}b, which illustrates a poor candidate with a low\nsignal-to-noise ratio, involves a Galaxy MACHO and $M_V = 1.8$ bulge\nsource contributing only $0.1\\%$ of the superpixel flux ($\\amax = 42$,\n$\\asp (t_0) = 1.05$). In this example $\\tfw = 5$~days and $\\te =\n68$~days. Though there appears to be evidence of a second bump after\nthe main peak these points are all within $3\\, \\sigma$ of the baseline\nand so do not count as a bump. Figure~\\ref{f3}c shows a high\nsignal-to-noise ratio ``gold-plated'' event in which a very luminous\n($M_V = -4$) disc source is lensed by an M31 MACHO ($\\amax = 5$, $\\asp\n(t_0) = 2.1$) with an observed duration $\\tfw = 19$~days and\nunderlying timescale $\\te = 33$~days. Here the bright unlensed source\naccounts for $27\\%$ of the superpixel flux.\n\n\\section{Lens and source models} \\label{s4}\n\n\\begin{figure*}\n\\centering\n\\begin{minipage}{170mm}\n\\begin{center}\n\\epsfig{file=fig03.ps,width=10cm,angle=270}\n\\end{center}\n\\caption{(a) The overall surface brightness profile (solid line) as a\nfunction of semi-major axis $a$ for our M31 model produced by the\ncombined bulge (dashed line) and disc (dot-dashed line) light. The\ncrosses are radially-averaged measurements from Table~VI of Walterbos\n\\& Kennicutt (1987). (b) The overall rotation curve (solid line) for\nthe same M31 model summed over bulge (dashed line), disc (dot-dashed\nline) and halo (dotted line) contributions. The crosses are from\nFigure~2 of Kent (1989) and are based on emission line measurements.\nFor conversion to distance $1~\\mbox{kpc} = 4.5$~arcmin.}\n\\label{f2}\n\\end{minipage}\n\\end{figure*}\nIn order to make quantitative estimates for pixel-lensing observables, we\nmust specify models for the principal Galaxy and M31 lens and\nsource components. For M31 the main populations are the bulge,\nthe disc and the dark MACHO halo. For the Galaxy only the MACHO\nhalo is important since the disc does not contribute\nsignificantly. Our complete model therefore consists of these four\npopulations. Two populations, the M31 disc and bulge, also provide the\nsources, so in total we have eight different lens--source\nconfigurations. For each population we must specify distributions for\nthe density and velocity. Additionally, we must specify the lens mass\nand a luminosity function for the source populations. Throughout we\nassume a disc inclination of $77\\degr$ and a distance to M31 of\n770~kpc, consistent with recent determinations (e.g. Stanek \\&\nGarnavich 1998).\n\nWhilst the present paper is concerned only with quantities\nrelating to M31 and Galaxy MACHOs, we must nonetheless include other\nsignificant lens components in our modeling in order to properly\ncharacterize the complexity of extracting physical information from\nobservations. For the observations, unlike the simulations, we do not\nknow in which population a particular lens resides.\n\nThe haloes are modeled as simple near-isothermal spheres with cores, having\ndensity profiles\n \\be\n \\rhoh = \\left\\{ \\begin{array}{ll} \n \\rhoh (0) \\frac{\\tst a^2}{\\tst a^2 + r^2} & (r \\leq \\rmax) \\\\\n 0 & (r > \\rmax)\n \\end{array} \\right., \\label{halod}\n \\ee\nwhere $\\rhoh (0)$ is the central density, $a$ is the core radius,\n$\\rmax$ is the cutoff radius and $r$ is the radial distance measured\nfrom the centre of either M31 or the Galaxy. The assumed values for\n$\\rhoh (0)$, $a$ and $\\rmax$ are given in Table~\\ref{t2}. The halo\nfraction determinations in Section~\\ref{s6} are made with respect to\nthese density normalizations. In our model the M31 halo has about twice the\nmass of the Galactic halo, though this mass ratio is controversial and\nhas been challenged recently by Evans \\& Wilkinson (2000) who have\nstudied the kinematics of several satellite galaxies around M31.\n\nThe M31 disc is modeled by the sech-square law:\n \\be\n \\rhod = \\rhod (0) \\exp \\left( - \\frac{\\sigma}{h} \\right) {\\rm\nsech}^2\n \\left( \\frac{z}{H} \\right), \\label{discd}\n \\ee\nwhere $\\sigma$ is the radial distance measured in the disc plane and\n$z$ is the height above the plane. The normalization $\\rhod (0)$,\nscale-height $H$ and scale-length $h$ are given in Table~\\ref{t2}.\n\nThe bulge distribution is based on the work of Kent (1989). Kent\nmodels the bulge as a set of concentric oblate-spheroidal shells with\naxis ratios which vary as a function of semi-major axis. We use the\ntabulated spatial luminosity density values in Table~1 of Kent (1989)\nand normalize the bulge mass under the assumption that the light\ntraces the mass (constant bulge mass-to-light ratio). The mass\nnormalization $\\massb$ is listed in Table~\\ref{t2}. The assumption of\naxisymmetry may be over-simplistic since the misalignment between the\ndisc and bulge position angles probably implies a triaxial structure\nfor the bulge. However, we are only indirectly concerned with bulge\nlensing in so much as it contaminates halo lensing statistics, so\ndeviations from axisymmetry are not crucial.\n\nThe rotation curve and surface brightness profile for the adopted M31\ncomponents are shown in Figure~\\ref{f2}. In constructing the surface\nbrightness profile, we have assumed $B$-band mass-to-light ratios $\\mtl\n= 4$ for the disc and $\\mtl = 9$ for the bulge, consistent with that\nexpected for typical disc and bulge populations. The overall surface\nbrightness profile is shown by the solid line in Figure~\\ref{f2}a,\nwith the disc and bulge contributions indicated by the dashed and\ndot-dashed lines, respectively. The crosses are the radially averaged\nmeasurements from Table~VI of Walterbos \\& Kennicutt (1987). In\nFigure~\\ref{f2}b the solid, dashed and dot-dashed lines show the\noverall, disc and bulge contributions to the rotation curve, with the\ndotted line giving the halo contribution. The crosses are from Figure~2\nof Kent (1989) and are based on the emission-line curves of Brinks \\&\nShane (1984) and Roberts, Whitehurst \\& Cram (1978). The fit to both\nthe surface brightness and rotation profiles is good, given the\nsimplicity of the models.\n\nThe lens and source velocities are described by rotational and random\ncomponents. The rotation velocity for each component is given in the\n4th column of Table~\\ref{t2}. The random motions are modeled by an\nisotropic Gaussian distribution with a one-dimensional velocity\ndispersion given by the 5th column. When calculating the relative\ntransverse lens speed $\\vt$, we take account of both the motion of the\nsource and the observer. The observer is assumed to move in a circular\norbit about the centre of the Galaxy with a speed of 220~\\kms. We do\nnot assume any relative transverse bulk motion between the Galaxy and\nM31. In practice, only the observer's motion is of consequence for\nGalaxy lenses, and only the source motion for M31 lenses.\n\nSince one of the questions we wish to address is how well\npixel-lensing observables can characterize the MACHO mass, we shall\nsimply model the Galaxy and M31 MACHO mass distributions by a Dirac\n$\\delta$-function:\n \\be\n \\psi (\\mh) \\propto \\frac{1}{\\mh} \\delta (m - \\mh), \\label{halomf}\n \\ee\nThe stellar lens mass distribution in the disc and bulge is described\nby a broken power law:\n \\be\n \\psi (\\ms) \\propto \\left\\{ \\begin{array}{ll}\n \\ms^{-0.75} & (\\mlo < \\ms < 0.5~\\sm) \\\\\n \\ms^{-2.2} & (0.5~\\sm < \\ms < \\mup)\n \\end{array}. \\right. \\label{starmf}\n \\ee\nThe mass function is normalized to yield the same value for $\\psi\n(0.5~\\sm)$ for either slope. We take a lower mass cut-off $\\mlo =\n0.08~\\sm$ and an upper cut-off $\\mup = 10~\\sm$, corresponding closely\nto the local Solar neighbourhood mass function \\cite{gou97}. Whilst\nthis is a reasonable assumption for stars in the M31 disc, the mass\nfunction will overestimate the contribution of massive stars in the\nolder bulge. The higher $\\mtl$ assumed for the bulge also requires\nthat the disc and bulge mass functions be different. However, the\nslope at high masses is steep, so the contribution of high mass stars\nto the lensing rate is in any case small. Furthermore, as already\nmentioned, we are only interested in the bulge population as a\ncontaminant of the halo lensing statistics. The choice of upper mass\ncut-off for the bulge is therefore not critical for the present study,\nso we simply adopt the same mass function for the disc and bulge.\n\nThe stellar components provide both lenses and sources. We assume that\nthe lens and source populations are the same and so described by the\nsame density, velocity and mass distributions. For the disc and bulge\nsources, we use the $V$-band luminosity function of Wielen, Jahreiss\n\\& Kr\\\"uger (1983) for stars with $M_V > 5$ and that of Bahcall \\&\nSoneira (1980) for $M_V \\leq 5$. The two functions are normalized to\nthe same value at $M_V = 5$. A more detailed study of the M31\nluminosity function is underway \\cite{last00}.\n\n\\section{Predictions and trends for pixel lensing} \\label{s5}\n\nThe simulations for the POINT-AGAPE survey are performed over 1, 3 and\n10 observing seasons for 9 MACHO masses spanning the range $10^{-3} -\n10~\\sm$. Each simulation produces an estimate of the number of events\nacross the whole M31 disc for each lens component, together with a\nlibrary of typically $10^4$ candidates containing information such as\nthe lens position, duration and transverse velocity. Since $\\te$\ncannot generally be measured from the light-curve, we output both\n$\\te$ and $\\tfw$. The event libraries can be filtered to provide an\nestimate of the pixel-lensing rate for any field placement.\n\n\\subsection{Number of events} \\label{s5.2}\n\n\\begin{figure}\n\\begin{center}\n\\epsfig{file=fig04.ps,width=6cm,angle=270}\n\\end{center}\n\\caption{The expected event rate as a function of MACHO mass for full\nMACHO haloes. The rates are averages over the M31 disc for M31 (solid\nline) and Galaxy (dashed line) MACHOs and are computed from ten seasons\nof data comprising 460 epochs.}\n\\label{nev}\n\\end{figure}\nWhilst the factor $10^3$ gain over LMC/SMC searches in the number of\nsources certainly boosts the rate of events, the fact that M31\npixel-lensing searches can typically detect only high-magnification\nevents means that the gain in the rate is not of the same\norder. Nonetheless, as Figure~\\ref{nev} indicates, the expected\npixel-lensing rate is almost an order of magnitude larger than for\ncurrent LMC/SMC experiments for same lens mass and halo fraction. In\nthe figure we have plotted the expected number of events for M31\nMACHOs (solid line) and Galaxy MACHOs (dashed line) per season per\ndeg$^2$, assuming MACHOs comprise all the halo dark matter of both\ngalaxies. The rates are averages over the whole M31 disc (rather than\nfor a specific field placement) determined from simulations spanning\nten seasons and 460 observing epochs. Within the first season the\nsensitivity to very massive MACHOs will be a little less than\nindicated in Figure~\\ref{nev}.\n\nThe rate of events occurring within the two INT WFC fields for their\nfirst season (1999/2000) positions are displayed in\nTable~\\ref{t3}. This excludes events occurring within 5~arcmin of the\ncentre of M31 because this region is dominated by stellar self-lensing\n(see Section~\\ref{sdis}). Only a couple of self-lensing events per\nseason are expected outside the exclusion zone. The Monte-Carlo\nerror in the values in Table~\\ref{t3} is small, only about $3\\%$,\nbut one should expect a larger variation when comparing different\nseasons with different numbers of epochs (in addition to Poisson\nvariations).\n\nFrom Figure~\\ref{nev} and Table~\\ref{t3} we see that the sensitivity\nto MACHOs peaks at a mass around $0.003-0.01~\\sm$, when around 140\nMACHO events can be expected within the INT WFC fields for full\nhaloes. Below $10^{-3}~\\sm$ finite-source size effects become\nimportant, so the expected number of events will drop off rapidly. At\nthe high mass end, even haloes comprising MACHOs as massive as\n$10~\\sm$ provide a rate of several events per season. The number of\nM31 MACHOs is about twice as large as the number of Galaxy MACHOs for\nthe same mass and fractional contribution, which is a direct\nconsequence of the mass ratio of the halo models we adopt.\n\n\\begin{table}\n\\begin{center}\n\\caption{The expected number of M31 and Galaxy MACHO detections per\nseason (averaged over ten seasons comprising 460 epochs) for a range\nof MACHO masses based on the placement of the two INT WFC fields in\nthe 1999/2000 observing season. The numbers assume the haloes of both\ngalaxies completely comprise MACHOs, though we exclude events occurring\nwithin 5~arcmin of the centre of M31. For comparison, the expected\nnumber of bulge and disc self-lensing events occurring outside the\nexclusion zone is 2.2 per season. The Monte-Carlo error for a\ngiven sequence of observing epochs is about $3\\%$.}\n\\label{t3}\n\\begin{tabular}{@{}lcc}\nMass/$\\sm$ & $N$(M31)/yr & $N$(Galaxy)/yr \\\\\n\\hline\n0.001 & 87 & 38 \\\\\n0.003 & 98 & 39 \\\\\n0.01 & 97 & 37 \\\\\n0.03 & 95 & 35 \\\\\n0.1 & 76 & 28 \\\\\n0.3 & 52 & 17 \\\\\n1 & 32 & 12 \\\\\n3 & 19 & 7.7 \\\\\n10 & 10 & 3.1\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{figure}\n\\begin{center}\n\\epsfig{file=fig05.ps,width=6cm,angle=270}\n\\end{center}\n\\caption{Observed MACHO timescale distributions for a range of MACHO\nmasses. The curves represent the combined M31 and Galaxy MACHO\nnormalized timescale distributions, shown in terms of the measured\nFWHM timescale $\\tfw$. From the lightest to the darkest curve the\nMACHO mass is $0.001~\\sm$, $0.003~\\sm$, $0.01~\\sm$, $0.03~\\sm$,\n$0.1~\\sm$, $0.3~\\sm$, $1~\\sm$, $3~\\sm$ and $10~\\sm$.}\n\\label{t-dis}\n\\end{figure}\n\n\\subsection{Timescale distributions} \\label{s5.2b}\n\nIn Figure~\\ref{t-dis} we plot the timescale distributions for the\ndetected MACHOs for a range of masses in terms of $\\tfw$.\nThe distributions for nine MACHO masses, spanning\nfour orders of magnitude, are plotted. The masses are as listed in\nTable~\\ref{t3}, with darker lines corresponding to more massive\nMACHOs. Since the timescale distributions for Galaxy and M31 MACHOs\nare practically indistinguishable for a given mass, in\nFigure~\\ref{t-dis} we have combined their timescale distributions, so\nthe normalization of each curve is determined by the combined\npixel-lensing rate shown in Figure~\\ref{nev} for each halo.\n\n\\begin{table}\n\\begin{center}\n\\caption{Average timescales for M31 and Galaxy MACHO populations for a\nrange of masses. $\\langle \\tfw \\rangle$ is the mean FWHM duration, as\nmeasured from the light-curve, whereas $\\langle \\te \\rangle_{\\rm det}$\nand $\\langle \\te \\rangle_{\\rm pop}$ are the mean Einstein radius\ncrossing durations of detected events and of the underlying\npopulation, respectively.}\n\\label{t4}\n\\begin{tabular}{@{}lrcc}\nMass/$\\sm$ & \\null & M31 & Galaxy \\\\\n\\hline\n0.001 & $\\langle \\tfw \\rangle$: & 3.8 & 4.0 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm det}$: & 6.2 & 6.3 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm pop}$: & 2.3 & 3.1 \\\\\n\\null & \\null & \\null & \\null \\\\\n0.003 & $\\langle \\tfw \\rangle$: & 5.1 & 5.1 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm det}$: & 9.1 & 9.2 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm pop}$: & 4.0 & 5.3 \\\\\n\\null & \\null & \\null & \\null \\\\\n0.01 & $\\langle \\tfw \\rangle$: & 7.2 & 7.8 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm det}$: & 14 & 15 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm pop}$: & 7.3 & 9.7 \\\\\n\\null & \\null & \\null & \\null \\\\\n0.03 & $\\langle \\tfw \\rangle$: & 9.7 & 9.4 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm det}$: & 21 & 22 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm pop}$: & 13 & 17 \\\\\n\\null & \\null & \\null & \\null \\\\\n0.1 & $\\langle \\tfw \\rangle$: & 13 & 13 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm det}$: & 34 & 37 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm pop}$: & 23 & 31 \\\\\n\\null & \\null & \\null & \\null \\\\\n0.3 & $\\langle \\tfw \\rangle$: & 16 & 17 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm det}$: & 52 & 57 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm pop}$: & 40 & 53 \\\\\n\\null & \\null & \\null & \\null \\\\\n1 & $\\langle \\tfw \\rangle$: & 21 & 23 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm det}$: & 82 & 98 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm pop}$: & 73 & 97 \\\\\n\\null & \\null & \\null & \\null \\\\\n3 & $\\langle \\tfw \\rangle$: & 26 & 28 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm det}$: & 130 & 160 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm pop}$: & 130 & 170 \\\\\n\\null & \\null & \\null & \\null \\\\\n10 & $\\langle \\tfw \\rangle$: & 41 & 32 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm det}$: & 220 & 300 \\\\\n\\null & $\\langle \\te \\rangle_{\\rm pop}$: & 230 & 310\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{figure}\n\\begin{center}\n\\epsfig{file=fig06.ps,width=6cm,angle=270}\n\\end{center}\n\\caption{The mean FWHM duration, $\\langle \\tfw \\rangle$, as a function\nof MACHO mass. Line coding is as for Figure~\\ref{nev}.}\n\\label{tfwav}\n\\end{figure}\n\\begin{figure}\n\\begin{center}\n\\epsfig{file=fig07.ps,width=6cm,angle=270}\n\\end{center}\n\\caption{The mean ratio of FWHM duration to Einstein radius crossing\nduration, $\\langle \\tfw / \\te \\rangle$, as a function of MACHO\nmass. Line coding is as for Figure~\\ref{nev}.}\n\\label{tfw-te}\n\\end{figure}\nWhilst there is a clear trend of increasing $\\tfw$ with increasing\nMACHO mass, the correlation is much weaker than for $\\te$. For example,\na duration $\\tfw = 10-20$~days is typical of a $0.1~\\sm$ lens, but it\nis also not unusual for a lens as light as $10^{-3}~\\sm$ or as heavy\nas $10~\\sm$. Figure~\\ref{tfwav} shows how the average duration\n$\\langle \\tfw \\rangle$ varies with mass separately for M31 (solid\nline) and Galaxy (dashed line) MACHOs. Over four orders of magnitude\nin mass $\\langle \\tfw \\rangle$ varies by about one order of magnitude,\nincreasing from 4~days for $10^{-3}~\\sm$ MACHOs to 35 days for\n$10~\\sm$ MACHOs (see also Table~\\ref{t4}). For our sampling strategy\nwe find empirically that $\\langle \\tfw \\rangle \\propto m_{\\rm\nh}^{1/4}$, whereas the average Einstein radius crossing timescale for\nthe {\\em underlying}\\/ population of microlensing events (with $u\n\\leq 1$) scales as $\\langle \\te \\rangle_{\\rm pop} \\propto m_{\\rm\nh}^{1/2}$.\n\nThe mean ratio $\\langle \\tfw / \\te \\rangle$ is displayed in\nFigure~\\ref{tfw-te} for detected events. It is clear that the ratio is\nnot fixed but steadily decreases with MACHO mass. For low MACHO masses\nwith short durations, sampling imposes a lower limit on $\\tfw$ and a\nloose lower limit on $\\te$ as well. Whilst most events\ninvolving $\\sim 10^{-3}~\\sm$ lenses are too short to be detected,\nthose that are either have an unusually long $\\te$ or occur in\nregions of low surface brightness (which maximizes $\\tfw$ for a given\nmagnification). Thus $\\langle \\tfw / \\te \\rangle$ is typically larger\nfor the observed events. At the other end of the mass scale the\nconverse is true. The total observation baseline imposes a maximum\ncutoff in $\\tfw$ and a loose upper limit in $\\te$. Those events which\nare detected either have an unusually short $\\te$ or else tend to\noccur in regions of high surface brightness where $\\tfw$ is minimized\nfor a given magnification. So $\\langle \\tfw / \\te\n\\rangle$ tends to be smaller for observed events. From\nTable~\\ref{t4} we see that the average duration of {\\em detected}\\/\nevents $\\langle \\te \\rangle_{\\rm det}$ does not trace the population\naverage $\\langle \\te \\rangle_{\\rm pop}$. This is a consequence of\nsampling bias.\n\n\\subsection{Spatial distributions} \\label{sdis}\n\n\\begin{figure*}\n\\centering\n\\begin{minipage}{170mm}\n\\begin{center}\n\\epsfig{file=fig08.ps,width=10cm,angle=90}\n\\end{center}\n\\caption{A realization for the spatial distribution of pixel-lensing\nevents after three seasons of observing, assuming MACHOs have a mass\nof $0.3~\\sm$ and provide all the halo dark matter in the Galaxy and\nM31. The axis labelling is in arcmins. (a) The distribution of all\nevents. The green dots represent the foreground Galaxy MACHO\ndistribution, the red dots represent stellar lens events and\nthe blue dots depict the M31 MACHO distribution. The circle centred\non the origin demarcates the exclusion zone for the MACHO analysis,\ninside which the rate is dominated by stellar self-lensing. The\ndashed-line templates show the positions of the two INT fields for the\n1999/2000 observing season. (b) The distribution of M31 MACHOs\nonly. The near-far asymmetry can be seen by comparing event number\ndensities at $\\pm(10-20)$~arcmins along the minor axis.}\n\\label{f4}\n\\end{minipage}\n\\end{figure*}\n\\begin{figure*}\n\\centering\n\\begin{minipage}{170mm}\n\\begin{center}\n\\epsfig{file=fig09a.ps,width=5cm,angle=90}\n\\epsfig{file=fig09b.ps,width=5cm,angle=90}\n\\epsfig{file=fig09c.ps,width=5cm,angle=90}\n\\end{center}\n\\caption{Realizations for the spatial distribution of pixel-lensing\nevents after three seasons of observing, assuming the MACHOs\nin M31 and the Galaxy have the same mass and provide all the halo dark\nmatter. (a) The distribution for $0.1~\\sm$ MACHOs; (b) $1~\\sm$ MACHOs;\n(c) $10~\\sm$ MACHOs. The lines and symbols are as for Figure~\\ref{f4}.}\n\\label{f5}\n\\end{minipage}\n\\end{figure*}\nSince event timescales give only limited information in pixel lensing,\nthe location of each event on the sky is a crucial observable. A\nrobust measurement of near-far asymmetry in the event distribution\nwould indicate the existence of an extended spheroidal population of\nlenses within which the visible M31 disc and bulge are embedded. Thus it\nwould represent very firm evidence for the existence of MACHOs.\n\nIn Figure~\\ref{f4} we display the distribution of events across the\nface of the M31 disc after three observing seasons for the case where\nthe haloes of both M31 and the Galaxy are full of $0.3~\\sm$\nMACHOs. The axes are labeled in arcmins and are aligned along the\nmajor and minor axes of the disc light profile. The dashed-line\ntemplates indicate the positions of the two INT WFC fields for the\n1999/2000 observing season. \n\nIn Figure~\\ref{f4}a the positions of all detectable events are\nshown. MACHOs from the Galaxy halo are shown in green whilst M31\nMACHOs are shown in blue. We find that within the central 5 arcmins\n(denoted by the circle) most events are produced by ordinary stellar\nlenses in the disc and bulge (shown in red). In Section~\\ref{s6},\nwhere we try to estimate MACHO parameters from simulated data-sets, we\ndisregard events occurring within this region so as to minimize\ncontamination from stellar lenses.\n\nFigure~\\ref{f4}b shows only the M31 MACHO distribution. The excess of\nevents between $y = -10$ and $-20$~arcmins (along the minor axis\ntowards the far side of the disc) compared to the number between $y =\n+10$ and $+20$~arcmins is a consequence of near-far asymmetry in the\npixel-lensing rate. The strength of this asymmetry depends upon the\nnumber of M31 MACHOs which, in turn, depends upon their mass and density\ncontribution, as well as the span of the\nobservation baseline. The presence of Galaxy MACHOs makes the\nasymmetry harder to detect, so the ratio of M31 to Galaxy MACHOs is\nanother factor which determines whether or not the asymmetry is measurable.\nIt is evident from the figure that there are very few events at $|y| \\ga\n25$~arcmin. This is due to the decrease in both the number of sources\nand the signal-to-noise ratio (because the sky background provides a\nlarger fraction of the total superpixel flux). The presence of the sky \nbackground effectively imposes a cut-off in the spatial distribution.\n\nFigure~\\ref{f5} shows the spatial distribution for a range of MACHO\nmasses expected after three seasons. We again assume that the MACHO\nmass is the same in both galaxies and that MACHOs provide all the dark\nmatter in the two haloes. Figure~\\ref{f5}a is for a MACHO mass of\n$0.1~\\sm$. In Figures~\\ref{f5}b and \\ref{f5}c the MACHO mass is\n$1~\\sm$ and $10~\\sm$ respectively. The most obvious trend in the MACHO\ndistributions is the decrease in the number of detectable events for\nmodels with more massive MACHOs. However, even for a mass as large as\n$10~\\sm$ we still expect to detect $30-40$ MACHOs within the INT\nfields if they make up all the dark matter. After three seasons even\nthese massive MACHOs out-number the disc and bulge lenses lying\noutside of our exclusion zone. This highlights one of the benefits of\npixel lensing: the reduction in $\\tfw$ due to the presence of many\nneighbouring unresolved sources means that more events with relatively\nlarge $\\te$ can be detected and characterized within a given observing\nperiod. In this respect, pixel lensing is relatively more sensitive to\nmassive MACHOs than conventional microlensing experiments, which\nrequire resolved sources.\n\nAnother noticeable trend in Figure~\\ref{f5} is that more massive\nMACHOs are concentrated towards the central regions of the M31\ndisc. The main reason is that the MACHO and source surface densities\nare largest in this region, so the probability of an event occurring\nthere is larger. However, another factor is that it is in the regions\nof highest surface brightness that the ratio $\\tfw / \\te$ is minimized\nfor a given magnification. For the $10~\\sm$ MACHO model, where many\nevents may have a duration $\\te$ exceeding the survey lifetime, this\nmeans more light-curves can be fully characterized, enabling these\nevents to be flagged as microlensing candidates within the observing\nperiod. The converse is true for low-mass MACHOs with short\n$\\te$. Their distribution is biased towards regions of lower surface\nbrightness where $\\tfw / \\te$ is maximized. This effect provides a\nfurther degree of discrimination for different lens masses and means\nthat, for example, a halo with a modest contribution of low mass\nMACHOs may be distinguished from one with a substantial fraction of\nmore massive lenses, even if the number of events for the two models\nis comparable. This in part makes up for the fact that $\\tfw$ is a\nless powerful discriminant than $\\te$.\n\n\\section{Estimating MACHO parameters} \\label{s6}\n\nIn the previous section we found that, whilst the timescale\ninformation in pixel-lensing studies is somewhat more restricted than\nin conventional microlensing we do, at least for M31, have important\ninformation from the spatial distribution of lenses. We now address to\nwhat extent pixel-lensing observables permit a reconstruction of the\nMACHO mass and halo fraction in the Galaxy and M31. \n\n\\subsection{Maximum-likelihood estimation} \\label{s6.1}\n\nAlcock et al. (1996) presented a Bayesian maximum likelihood technique to\nestimate the Galaxy MACHO mass and halo fraction from the observed\nevent timescales towards the LMC. Evans \\& Kerins (2000) extended this\nto exploit the spatial distribution of observed events, and also to\nallow for more than one significant lens population. For pixel\nlensing towards M31 we must also consider the effect of contamination\nby variable stars. This is likely to be a significant problem in the\nshort term. A baseline of more than three years should be sufficient\nto exclude periodic variables, such as Miras, but there still remains\nthe possibility that, occasionally, the signal-to-noise ratio may be\ninsufficient to distinguish between novae and microlensing events. By\ntaking account of variable stars in our likelihood estimator we\nallow ourselves to make an estimate of the MACHO mass and lens\nfraction which, even in the short term, is robust and unbiased.\n\nIn order to allow for different MACHO parameters in the two galaxies\nwe propose an estimator which is sensitive to five parameters: the\nMACHO mass and halo fraction in both the Galaxy and M31, and\nthe degree of contamination by variable stars. We define our model\nlikelihood $L$ by\n \\begin{eqnarray}\n \\ln L(f_{\\rm var},f_j,\\psi_j) = & - & \\left[ f_{\\rm var} N_{\\rm\n var} + \\sum_{j=1}^{n_{\\rm c}} f_j N(\\psi_j) \\right] \\nonumber \\\\\n & + & \\sum_{i = 1}^{N_{\\rm obs}} \\ln\n \\left[ f_{\\rm var} \\frac{d^3 N_{\\rm var}}{d{\\tfw}_i dx_i dy_i}\n \\right. \\nonumber \\\\\n & + & \\left. \\sum_{j = 1}^{n_{\\rm c}} f_j \\frac{d^3\n N(\\psi_j)}{d{\\tfw}_i dx_i dy_i} \\right], \\label{like}\n \\end{eqnarray}\nwhere $f_{\\rm var}$ is the fraction of variable stars relative to some\nfiducial model expectation number $N_{\\rm var}$, $f_j$ and $\\psi_j$ are the\nlens fraction and mass function for component $j$, $n_{\\rm c}$ is\nthe number of lens components and $N_{\\rm obs}$ the number of observed\nevents. For the disc and bulge components $f_j$ and $\\psi_j$ are both\nfixed, with $f_j = 1$ and $\\psi_j$ given by equation~(\\ref{starmf}),\nwhilst for the Galaxy and M31 haloes $\\psi_j \\propto m_j^{-1} \\delta(m\n- m_j)$, as in equation~(\\ref{halomf}), and $f_j$ and $m_j$ are free\nparameters. We define $f_j$ with respect to the halo density\nnormalizations in Table~\\ref{t2}.\n\nThe resolution of our simulation is insufficient to evaluate reliably\nthe third derivatives in equation~(\\ref{like}), so we decouple the\ntimescale and spatial distributions by computing $(dN/d\\tfw) (d^2 N/dx\ndy)$ instead of $d^3N/d\\tfw dx dy$ within our fields. By averaging\nover spatial variations in the timescale distribution we are ignoring\ncorrelations which could provide us with further discriminatory\ninformation. However, in the limit of infinite data and perfect\nmeasurements we are still able to recover precisely the underlying\nparameters because the average event duration is known with infinite\nprecision.\n\nWe assume that the distribution of variable stars traces the\nM31 surface brightness. In reality variable stars will be harder to\ndetect in regions of higher surface brightness, so our idealized\ndistribution is somewhat more concentrated than we should expect for a\nreal experiment. We assume the timescale distribution of detectable\nvariables is log-normal, with a mean and dispersion $\\langle \\ln \\tfw\n\\rangle = 2$ and $\\sigma(\\ln \\tfw) = 0.5$ (where $\\tfw$ is expressed\nin days). Their timescales are therefore assumed to be typical of a\nwide range of lens masses (see Figure~\\ref{t-dis}) and are thus least\nhelpful as regards discrimination between lensing events and variable\nstars.\n\nTo test the likelihood estimator we generate data-set realizations and\ncompute their likelihood over a five-dimensional grid of models\nspanning a range of MACHO masses and variable star and MACHO\nfractions. For the grid sampling we assume uniform priors in the\nvariable star and MACHO fractions and logarithmic priors for the MACHO\nmasses. Since the events in the inner 5~arcmin of the M31 disc are\npredominately due to stellar lenses (mostly bulge self-lensing) we\ncount only events occurring outside of this region.\n\n\\subsection{First-season expectations}\n\n\\begin{figure*}\n\\centering\n\\begin{minipage}{170mm}\n\\begin{center}\n\\epsfig{file=fig10.ps,width=10cm,angle=270}\n\\end{center}\n\\caption{Maximum likelihood recovery of MACHO parameters for a\nsimulated data-set after one season. The input parameters for\nboth Galaxy and M31 MACHO populations are $0.5~\\sm$ for the lens mass\nand 0.25 for their fractional contribution. Here we assume there is no\ncontamination to the data-set from variable stars. The four panels are\ntwo-dimensional projections of the five-dimensional likelihood\nspace. The contours in each plane enclose $34\\%$ (solid line), $68\\%$\n(dashed line), $90\\%$ (dot-dashed line), $95\\%$ (dotted line) and\n$99\\%$ (triple dot-dashed line) of the total likelihood assuming a\nlinear prior in the MACHO and variable star fractions and a\nlogarithmic prior in the MACHO masses. The stars denote the input\nparameters. The four panels represent the likelihood in the planes of\nM31 MACHO fraction and mass ({\\it top left}\\/); Galaxy MACHO fraction\nand mass ({\\it top right}\\/); M31 and Galaxy MACHO fractions ({\\it\nbottom left}\\/); and M31 MACHO and variable star fractions ({\\it bottom\nright}\\/). The variable star fraction is measured relative to a rate\nof 100 events per year in the two INT fields.}\n\\label{f10}\n\\end{minipage}\n\\end{figure*}\n\nFigure~\\ref{f10} shows the degree to which the MACHO parameters can be\nrecovered after one season in the optimal case where the data-set\ncontains no variable stars. For the realization we have adopted a\nMACHO fraction of 0.25 and mass of $0.5~\\sm$ for both the Galaxy and\nM31 haloes, and have set $f_{\\rm var} = 0$. The MACHO parameters\ncorrespond to those preferred by the most recent analyses of the EROS\nand MACHO teams \\cite{lass99,alc00}. Each panel in Figure~\\ref{f10}\nrepresents a two-dimensional projection of the five-dimensional\nlikelihood, in which each point on the two-dimensional plane is a\nsummation of likelihoods over the remaining three dimensions. Contours\nare constructed about the two-dimensional maximum likelihood solution\nwhich enclose a given fraction of the total likelihood over the\nplane. The contours shown enclose $34\\%$ (solid line), $68\\%$ (dashed\nline), $90\\%$ (dot--dashed line), $95\\%$ (dotted line) and $99\\%$\n(triple dot--dashed line) of the total likelihood. The star in each\nplane shows the input values for the realization.\n\n\\begin{figure*}\n\\centering\n\\begin{minipage}{170mm}\n\\begin{center}\n\\epsfig{file=fig11.ps,width=10cm,angle=270}\n\\end{center}\n\\caption{As for Figure~\\ref{f10} but this time there are no\nMACHOs, only variable stars. The input model has a variable star\nfraction of unity.}\n\\label{f11}\n\\end{minipage}\n\\end{figure*}\n\n\\begin{figure*}\n\\centering\n\\begin{minipage}{170mm}\n\\begin{center}\n\\epsfig{file=fig12.ps,width=10cm,angle=270}\n\\end{center}\n\\caption{As for Figure~\\ref{f10}, with the same input parameters, except\nthat we now adopt a variable star fraction of unity rather than\nzero.}\n\\label{f12}\n\\end{minipage}\n\\end{figure*}\n\nThe four panels in Figure~\\ref{f10} depict the likelihood planes for\nM31 MACHO fraction and mass (top left), Galaxy MACHO fraction and mass\n(top right), M31 and Galaxy MACHO fractions (bottom left) and M31\nMACHO and variable star fractions (bottom right). From the top-left\npanel we see that, after just one season, useful constraints are\nalready possible for M31 parameters. In this realization the $90\\%$\nconfidence level spans around two orders of magnitude in MACHO mass\n($\\sim 0.05 - 10~\\sm$) and an order of magnitude in halo fraction\n($\\sim 0.1 - 1.1$). The brown-dwarf regime is mostly excluded. In the\nupper-right panel we see that the Galaxy MACHO parameters are\nill-defined after one season. This is unsurprising since Galaxy MACHOs\nare out-numbered two to one by M31 MACHOs and they have no signature\ncomparable to the near-far asymmetry of their M31 counterparts. The\npanel shows a suggestive spike in the likelihood contours occurring at\nabout the right mass range, though the contours marginally prefer a\nGalaxy halo with no MACHO component. The one firm conclusion that can\nbe drawn is that a substantial contribution of low-mass lenses is\nstrongly disfavoured by the data. The strongest constraints occur at\n$\\sim 0.003~\\sm$, where the expected number of events peaks for a\ngiven fractional contribution. The likelihood estimator indicates that\n$0.003~\\sm$ lenses contribute no more than $\\sim 5\\%$ of the Galactic\ndark matter with $90\\%$ confidence. In the lower-left and lower-right\npanels of Figure~\\ref{f10} we see the trade-off between M31 and Galaxy\nMACHO fractions and between M31 MACHO and variable star fractions,\nrespectively. The lower-left panel indicates that a scenario in which\nthere are no MACHOs is excluded with very high confidence, despite the\nlarge uncertainty in the halo fraction determinations. In the\nlower-right panel we see that the likelihood estimator has correctly\ndetermined that there is little, if any, contamination due to variable\nstars, with a $90\\%$ confidence upper limit of $f_{\\rm var} < 0.03$.\n\nIn Figure~\\ref{f11} we show the results for a simulation over one\nseason in which there are no microlensing events, only variable\nstars. We adopt $N_{\\rm var} = 100$ and $f_{\\rm var} = 1$ within the\nINT WFC fields. It is important to establish whether, in the event of\nthere being no MACHOs, our likelihood estimator is able to correctly\ndetermine a null result even if a significant number of variable stars\npass the microlensing selection criteria. The four panels in\nFigure~\\ref{f11} indicate that our estimator has been very successful\nas regards the M31 MACHO contribution. The M31 MACHO fraction is\nconstrained with $90\\%$ confidence to be below 0.2 for lenses in the\nmass range $0.001 - 0.1~\\sm$ and below $0.4$ for MACHOs up to a few\nSolar masses. This despite a rate in variable stars comparable to full\nhaloes of MACHOs. In the upper-right panel we see that there is\nconsiderable uncertainty in the Galaxy MACHO parameters, though\ninteresting upper limits on the halo fraction are obtained for lenses\nin the mass range $0.03 - 0.1~\\sm$. In the lower-left panel we see\nthat a non-zero MACHO contribution is preferred though the contours\nare consistent with the input model at about the $70\\%$ confidence\nlevel. In the lower-right panel we see that the estimator is able to\nconstrain the number of variables to within $\\pm 30\\%$ of the input\nvalue. Thus our likelihood estimator has provided us with not just an\nestimate of the MACHO parameters but also an estimate of the level of\ncontamination in the data-set. This estimate is completely independent\nof (and thus does not rely upon) additional information one might\nobtain from colour changes or asymmetry in the light-curves of\nindividual events, or from follow-up observations.\n\n\\subsection{Evolution of parameter estimation}\n\n\\begin{figure*}\n\\centering\n\\begin{minipage}{170mm}\n\\begin{center}\n\\epsfig{file=fig13.ps,width=10cm,angle=270}\n\\end{center}\n\\caption{As for Figure~\\ref{f12} but for three seasons of data and a\nvariable stars fraction of 0.3.}\n\\label{f13}\n\\end{minipage}\n\\end{figure*}\n\n\\begin{figure*}\n\\centering\n\\begin{minipage}{170mm}\n\\begin{center}\n\\epsfig{file=fig14.ps,width=10cm,angle=270}\n\\end{center}\n\\caption{As for Figure~\\ref{f12} but for ten seasons of data,\ncomparable to the lifetime of current LMC surveys, and a variable\nstars fraction of 0.1.}\n\\label{f14}\n\\end{minipage}\n\\end{figure*}\n\nFigure~\\ref{f12} shows another first-season simulation in which we\nadopt the same MACHO parameters as in Figure~\\ref{f10} but this time\nwe also take $N_{\\rm var} = 100$ and $f_{\\rm var} = 1$. The contours\nin the plane of M31 MACHO mass and fraction appear largely unaffected\nby the presence of significant variable star contamination, and\nqualitatively resemble those in Figure~\\ref{f10}. There is no\nevidence of estimator bias due to the presence of variables, which for\nour realization out-number the MACHOs from both haloes\ncombined. However the Galaxy MACHO parameter estimation is clearly led\nastray by the presence of variables, with upper limits on halo\nfraction possible for only a narrow range of lens masses. The\nestimator nonetheless strongly excludes a no-MACHO hypothesis\n(lower-left panel) and provides a good estimate of variable star\ncontamination levels.\n\nFigure~\\ref{f13} shows the constraints after three seasons assuming\nthe same parameters as for Figure~\\ref{f12}, except that we have\nreduced the contamination level to $f_{\\rm var} = 0.3$. A significant\ndecrease in contamination would be expected as the increase in\nobservation baseline permits the exclusion of a larger number of\nperiodic variables. The constraints for M31 MACHO parameters have\ntightened up considerably, with a $90\\%$ confidence uncertainty of a\nfactor four in halo fraction and an order of magnitude in MACHO\nmass. The constraints on Galaxy MACHO parameters have also sharpened\nconsiderably, allowing strong upper limits on the halo fraction to be\nmade over a wide mass range, though the data in this case is\nconsistent with a complete absence of Galaxy MACHOs. However, in the\nlower-left panel we see that the joint constraint on M31 and Galaxy\nMACHO fraction advocates a significant overall MACHO contribution. The\nlower-right panel also shows an accurate determination of\ncontamination levels.\n\nIn Figure~\\ref{f14} we depict constraints for ten seasons of data,\ncomparable to the lifetime of current LMC surveys, with the variable\nstar contamination level reduced further to $f_{\\rm var} = 0.1$. The\nM31 MACHO fraction is now essentially specified to within about a\nfactor of three, whilst the MACHO mass uncertainty is\nwithin an order of magnitude. We now also have a positive estimation\nof the Galaxy MACHO contribution and mass. The constraints on Galaxy\nparameters are only a little worse than those for M31 after three\nseasons. The variable star contamination level is once again robustly\ndetermined.\n\nFigures~\\ref{f12} to \\ref{f14} show that the likelihood\nestimator is able to distinguish clearly between microlensing events\nand our naive model for the variable star population. They also show\nthat, given a lifetime comparable to the current LMC surveys, a\nsustained campaign on the INT should determine M31 MACHO parameters\nrather precisely and should also provide a useful estimate of Galaxy\nMACHO parameters. A more modest campaign lasting three seasons would\nprovide a robust estimate of M31 MACHO parameters and useful\nconstraints on the Galaxy MACHO fraction.\n\nSince all the above simulations assume the same halo fraction and\nMACHO mass for both galaxies, we decided to test whether our\nlikelihood estimator was sensitive to Galaxy MACHO parameters\nindependently of M31 MACHO values. We therefore ran a simulation\nover three seasons in which $30\\%$ of the M31 halo comprises $0.5~\\sm$\nlenses and $60\\%$ of the Galaxy halo comprises $0.03~\\sm$ lenses. The\nGalaxy MACHOs actually out-number the M31 MACHOs in this model. Whilst\nthe model is somewhat contrived, and is already ruled out with high\nconfidence \\cite{lass99,alc00}, it provides a useful test case for\nour estimator. We find that the estimator successfully resolves the\nmass scales of the two populations within $90\\%$ confidence, though\nwith a slight tendency to overestimate the Galaxy MACHO mass and\nunderestimate the M31 MACHO mass. Whilst we find a large overlap in\npreferred halo fraction, this is consistent with the sensitivity\ntypically achieved after three seasons when the MACHO masses in the\ntwo galaxies are the same. The Galaxy MACHO parameters are much better\ndefined than in Figure~\\ref{f13}, though for this case the variable\nstar contamination level was set to zero.\n\nThere is one aspect, however, in which our simulation presents an\nover-optimistic picture. The success of the estimator in\ndiscriminating between variable stars and microlensing events is\nmostly due to the fact that our adopted variable star distribution is\nsignificantly more concentrated than the microlensing distribution of\neither M31 or Galaxy MACHOs. The assumption we have made, that their\nobserved distribution traces the M31 surface brightness, is reasonable\nonly for very bright variable phenomena which would be detected\nregardless of where it occurred in M31. For less prominent variables\nthere will be a bias against their detection in the central regions of\nM31, where the surface brightness is high and so their contribution to\nthe superpixel flux relatively small. We might well expect a realistic\ndistribution of variable stars to resemble that of Galaxy MACHOs\nbecause the surface density of Galaxy MACHOs does not vary\nsignificantly over the M31 disc, so their distribution would also\ntrace the M31 surface brightness if there was no detection bias\naway from regions of high surface brightness. However, in the absence\nof a conspiracy between the flux distribution of variable stars at\npeak luminosity and the flux distribution of microlensed sources at\npeak magnification, there should be some distinction between the\nspatial distributions of Galaxy MACHOs and M31 variable stars, though\nthis may be only mild. In any case, even if the two distributions are\nindistinguishable this should not significantly affect the\ndetermination of M31 MACHO parameters because the likelihood relies\nheavily on evidence of near-far asymmetry (which is why the likelihood\ncontours are much better defined for M31 MACHOs than for Galaxy\nMACHOs). This cannot be replicated by variable stars. Only if several\nhundred variable stars passed the selection criteria every season would\nthe signature of asymmetry be washed out and the constraints on M31 MACHO\nparameters severely degraded. Such an occurrence would warrant\ncritical re-examination of the selection criteria!\n\n\\section{Conclusions} \\label{s7}\n\nPixel lensing is a relatively new and powerful method to allow\nmicrolensing searches to be extended to targets where the sources are\nunresolved. It heralds the possibility of detecting or\nconstraining MACHO populations in external galaxies. Though pixel\nlensing is hampered by changes in observing conditions, which\nintroduce spurious variations in detected pixel flux, techniques have\nbeen developed which minimize these variations to a level where genuine \nmicrolensing signals can be detected.\n\nPOINT-AGAPE and another team (MEGA) have embarked on a major joint\nobserving programme using the Isaac Newton Telescope (INT) to monitor\nunresolved stars in M31 for evidence of pixel lensing due to MACHOs\neither in the Galaxy or M31 itself. Two techniques, the Pixel Method\nand difference imaging, are available to minimize flux variations\ninduced by the changing observing conditions. In this paper we have\nassessed the extent to which the Pixel Method allows us to determine\nthe mass and fractional contribution of MACHOs in both M31 and the\nGalaxy from pixel-lensing observables. Our assessment takes account\nof realistic variations in observing conditions, due to changes in\nseeing and sky background, together with irregular sampling.\n\nPixel lensing observables differ from those in classical microlensing,\nwhere one targets resolved stellar fields, in that one is generally\nunable to measure the Einstein radius crossing time, $\\te$, of an\nevent. The fact that the source stars are resolved only whilst they\nare lensed means that one is unable to determine their baseline\nluminosity, so neither the magnification nor the total duration of the\nevent can be measured. As an alternative to $\\te$ one may measure the\nfull-width half-maximum timescale, $\\tfw$, directly from the\nlight-curve. However, this provides only a lower limit to the\nunderlying event duration. Fortunately, M31 provides a signature which\npermits an unambiguous determination of whether or not MACHOs reside\nin its halo: near-far asymmetry \\cite{cro92}. If M31 is embedded in a\ndark spheroidal halo of MACHOs the high disc inclination should\nprovide a measurable gradient in the observed pixel lensing rate. The\nstrength of this signature depends both on the mass and fractional\ncontribution of MACHOs in M31, as well as the level of\n``contamination'' by variable stars, M31 stellar lensing events and\nforeground Galaxy MACHOs.\n\nWe have employed detailed Monte-Carlo simulations to\nestimate the timescale and spatial distributions of MACHOs in both our \nGalaxy and M31 for spherically-symmetric near-isothermal\nhalo models. We also model the lensing contribution due to disc and \nbulge self-lensing. The expected number of M31 MACHOs for our two INT\nfields peaks at about 100 events for $\\sim 0.01~\\sm$ MACHOs, the\nGalaxy MACHO contribution being about half as large. For a given mass\nand halo fraction we expect to detect about an order of magnitude more \nevents than current conventional surveys targeting the LMC.\n\nThe timescale distributions for Galaxy and M31 MACHOs are practically\nidentical because of the symmetry of the microlensing geometry. Our\nsimulations also confirm that $\\tfw$ is less strongly correlated with lens\nmass than $\\te$. For our sampling we find that, empirically, $\\langle \\tfw\n\\rangle \\propto \\langle \\te \\rangle^{1/2} \\propto m^{1/4}$ for lens\nmass $m$. Sampling introduces a significant bias in the duration of\ndetected events with respect to the underlying average for very\nmassive and very light MACHOs.\n\nOur simulations clearly show the near-far asymmetry in the M31 MACHO\nspatial distribution. However, the presence of the foreground Galaxy\nMACHOs makes its measurement more difficult. We also find that the\ndistribution of very massive MACHOs is noticeably more centrally\nconcentrated than that of less massive lenses. Stellar self-lensing\nevents are found to be mostly confined to within the inner 5~arcmin of\nthe M31 disc, and are mostly due to bulge self-lensing. Their tight\nspatial concentration means that they do not pose a serious\ncontamination problem for analysis of the Galaxy and M31 MACHO populations.\n\nWe have constructed a maximum likelihood estimator which uses\ntimescale and position observables to simultaneously constrain the\nMACHO mass and halo fraction of both M31 and the Galaxy. The statistic\nis devised to be robust to data-set contamination by variable\nstars. We find that M31 MACHO parameters can be reliably constrained\nby pixel lensing. For simulated INT data-sets we find pixel-lensing\nconstraints on the M31 halo to be comparable to those obtained for the\nGalaxy halo by the conventional microlensing surveys. Even with severe\ncontamination from variable stars the M31 MACHO parameters are well\ndetermined within three years. In particular, if there are few MACHOs\nin M31 this should become apparent after just one season of data\ncollection, even if as many as a hundred variable stars pass the\nmicrolensing selection criteria, because of the absence of near-far\nasymmetry. Pixel lensing is less sensitive to Galaxy MACHO\nparameters. Our simulations indicate that we require at least three\ntimes as much observing time in order to produce comparable\nconstraints on Galaxy MACHO parameters. If the spatial distribution of\nvariable stars closely follows that of Galaxy MACHOs, then it may\nbecome very difficult to reliably constrain Galaxy MACHO parameters.\n\nThe work presented here clearly demonstrates that a vigorous\nmonitoring campaign on a 2m class telescope with a wide-field camera\ncan identify and characterize MACHOs in M31. We now have the\nopportunity to unambiguously establish the existence or absence of\nMACHOs in an external galaxy. The advantage of targeting M31 over our\nown Galaxy is that we have many lines of sight through the halo of M31\nand a clear signature with which to distinguish M31 MACHOs from\nstellar self-lensing, the primary source of systematic\nuncertainty for Galaxy halo microlensing surveys. M31 therefore\nrepresents one of the most promising lines of sight for MACHO studies.\n\n\\section*{acknowledgments}\nEK, EL and SJS are supported by PPARC postdoctoral fellowships. NWE is\nsupported by the Royal Society. EK would like to thank Yannick\nGiraud-H\\'eraud and Jean Kaplan for many helpful discussions.\n\n\\begin{thebibliography}{} \n \n%\\bibitem[]{}\n\n\\bibitem[Alard \\& Guibert 1997]{ala97}\nAlard, C., Guibert, J., 1997, A\\&A, 326, 1\n\n\\bibitem[Albrow et al. 1998]{alb98}\nAlbrow, M., et al, 1998, ApJ, 509, 687\n\n\\bibitem[Alcock et al. 1996]{alc96}\nAlcock, C., et al., 1996, ApJ, 461, 84\n\n\\bibitem[Alcock et al. 1997]{alc97}\nAlcock, C., et al., 1997, ApJ, 479, 119\n\n\\bibitem[Alcock et al. 1998]{alc98}\nAlcock, C., et al., 1998, ApJ, 499, L9\n\n\\bibitem[Alcock et al. 2000]{alc00}\nAlcock, C., et al., 2000, ApJ, submitted (astro-ph/0001272)\n\n\\bibitem[Ansari et al. 1997]{ans97}\nAnsari, R., et al., 1997, A\\&A, 324, 843\n\n\\bibitem[Ansari et al. 1999]{ans99}\nAnsari, R., et al., 1999, A\\&A, 344, L49\n\n\\bibitem{bah80}\nBahcall J., Soneira R., 1980, ApJS, 44, 73\n\n\\bibitem[Baillon et al. 1993]{bai93}\nBaillon, P., Bouquet, A., Giraud-H\\'eraud, Y., Kaplan, J., 1993, A\\&A,\n277, 1\n\n\\bibitem[Baltz \\& Silk 1999]{bal99}\nBaltz, E., Silk, J., 1999, ApJ, submitted (astro-ph/9901408)\n\n\\bibitem[Bissantz et al. 1997]{bis97}\nBissantz, N., Englmaier, P., Binney, J., Gerhard, O., 1997, MNRAS, 289, 651\n\n\\bibitem[Brinks \\& Shane 1984]{brink84}\nBrinks, E., Shane, W., 1984, A\\&AS, 55, 179\n\n\\bibitem[Carr 1994]{carr94}\nCarr, B.J., 1994, ARA\\&A, 32, 531\n\n\\bibitem[Crotts 1992]{cro92}\nCrotts, A.P.S., 1992, ApJ, 399, L43\n\n\\bibitem[Crotts \\& Tomaney 1997]{cro97}\nCrotts, A.P.S., Tomaney A.B., 1997, ApJ, 473, L87\n\n\\bibitem[Crotts, Uglesich \\& Gyuk 1999]{cro99}\nCrotts, A.P.S., Uglesich, R., Gyuk, G., 1999, in proceedings of\nGravitational Lensing: Recent Progress and Future Goals, eds Brainerd,\nT., Kochanek, C., Astronomical Society of the Pacific Conference\nSeries (astro-ph/9910552)\n\n\\bibitem[Evans \\& Kerins 2000]{evan00}\nEvans, N.W., Kerins, E.J., 2000, ApJ, 529, in press (astro-ph/9909254)\n\n\\bibitem[Evans \\& Wilkinson 2000]{wilk00}\nEvans, N.W., Wilkinson, M., 2000, MNRAS, submitted\n\n\\bibitem[Fukugita et al. 1996]{fuk96}\nFukugita, M., Ichikawa, T., Gunn, J.E., Doi, M., Shimasaku, K.,\nSchneider, D.P., 1996, PASP, 111, 1748\n\n\\bibitem[Gondolo 1999]{gon99}\nGondolo, P., 1999, ApJ, 510, L29\n\n\\bibitem[Gould 1996]{gou96}\nGould, A., 1996, ApJ, 470, 201\n\n\\bibitem[Gould, Bahcall \\& Flynn 1997]{gou97} \nGould, A., Bahcall, J., Flynn, C., 1997, ApJ, 482, 913\n\n\\bibitem[Griest 1991]{grie91}\nGriest, K., 1991, ApJ, 366, 412\n\n\\bibitem[Gyuk \\& Crotts 1999]{gyuk99}\nGyuk, G., Crotts, A., 1999, ApJ, submitted (astro-ph/9904314)\n\n\\bibitem[Han 1996]{han96}\nHan, C., 1996, ApJ, 472, 108\n\n\\bibitem[Kent 1989]{kent89}\nKent, S.M., 1989, AJ, 97, 1614\n\n\\bibitem[Kerins \\& Evans 1999]{ker99}\nKerins, E.J., Evans, N.W., 1999, ApJ, 517, 734\n\n\\bibitem[Kiraga \\& Paczy\\'nski 1994]{kir94}\nKiraga, M., Paczy\\'nski, B., 1994, ApJ, 430, L101\n\n\\bibitem[Krisciunas \\& Schaefer 1991]{kris91}\nKrisciunas, K., Schaefer, B.E., 1991, PASP, 103, 1033\n\n\\bibitem[Lasserre et al. 1999]{lass99}\nLasserre, T., et al., 1999, in proceedings of Gravitational Lensing:\nRecent Progress and Future Goals, eds Brainerd, T., Kochanek, C.,\nAstronomical Society of the Pacific Conference Series (astro-ph/9909505)\n\n\\bibitem[Lastennet et al. 2000]{last00}\nLastennet, E., et al., 2000, in preparation\n\n\\bibitem[Le~Du 2000]{ledu00}\nLe~Du, Y., 2000, Ph.D thesis, University Paris VI, College de France\n\n\\bibitem[Melchior 1999]{mel99}\nMelchior, A.-L., 1999, presentation at the March~12th meeting of the\nRoyal Astronomical Society, London\n\n\\bibitem[Rhie et al. 1999]{rhie99}\nRhie, S.H., et al., 1999, ApJ, 522, 1037\n\n\\bibitem[Roberts, Whitehurst \\& Cram 1978]{rob78}\nRoberts, M., Whitehurst, R., Cram, T., 1978, in Structure and\nProperties of Nearby Galaxies, eds Berkhuijsen, E., Wielebinski,\nR. (Reidel, Dordrecht), p169\n\n\\bibitem[Sevenster et al. 1999]{seven99}\nSevenster, M., et al., 1999, MNRAS, 307, 584\n\n\\bibitem[Stanek \\& Garnavich 1998]{stan98}\nStanek, K.Z., Garnavich, P.M., 1998, ApJ, 503, L131\n\n\\bibitem[Udalski et al. 1994]{uda94}\nUdalski, A., et al., 1994, Acta Astronom., 44, 165\n\n\\bibitem[Walterbos \\& Kennicutt 1987]{wal87}\nWalterbos, R., Kennicutt, R., 1987, A\\&AS, 69, 311\n\n\\bibitem[Wielen, Jahreiss \\& Kr\\\"uger Jahreiss 1983]{wie83}\nWielen, R., Jahreiss, H., Kr\\\"uger, R., 1983, IAU Colloquium 76, p163\n\n\\bibitem[Wo\\`zniak \\& Paczy\\`nski 1997]{woz97}\nWo\\`zniak, P., Paczy\\`nski, B., 1997, ApJ, 487, 55\n\n\\end{thebibliography}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002256.extracted_bib",
"string": "\\begin{thebibliography}{} \n \n%\\bibitem[]{}\n\n\\bibitem[Alard \\& Guibert 1997]{ala97}\nAlard, C., Guibert, J., 1997, A\\&A, 326, 1\n\n\\bibitem[Albrow et al. 1998]{alb98}\nAlbrow, M., et al, 1998, ApJ, 509, 687\n\n\\bibitem[Alcock et al. 1996]{alc96}\nAlcock, C., et al., 1996, ApJ, 461, 84\n\n\\bibitem[Alcock et al. 1997]{alc97}\nAlcock, C., et al., 1997, ApJ, 479, 119\n\n\\bibitem[Alcock et al. 1998]{alc98}\nAlcock, C., et al., 1998, ApJ, 499, L9\n\n\\bibitem[Alcock et al. 2000]{alc00}\nAlcock, C., et al., 2000, ApJ, submitted (astro-ph/0001272)\n\n\\bibitem[Ansari et al. 1997]{ans97}\nAnsari, R., et al., 1997, A\\&A, 324, 843\n\n\\bibitem[Ansari et al. 1999]{ans99}\nAnsari, R., et al., 1999, A\\&A, 344, L49\n\n\\bibitem{bah80}\nBahcall J., Soneira R., 1980, ApJS, 44, 73\n\n\\bibitem[Baillon et al. 1993]{bai93}\nBaillon, P., Bouquet, A., Giraud-H\\'eraud, Y., Kaplan, J., 1993, A\\&A,\n277, 1\n\n\\bibitem[Baltz \\& Silk 1999]{bal99}\nBaltz, E., Silk, J., 1999, ApJ, submitted (astro-ph/9901408)\n\n\\bibitem[Bissantz et al. 1997]{bis97}\nBissantz, N., Englmaier, P., Binney, J., Gerhard, O., 1997, MNRAS, 289, 651\n\n\\bibitem[Brinks \\& Shane 1984]{brink84}\nBrinks, E., Shane, W., 1984, A\\&AS, 55, 179\n\n\\bibitem[Carr 1994]{carr94}\nCarr, B.J., 1994, ARA\\&A, 32, 531\n\n\\bibitem[Crotts 1992]{cro92}\nCrotts, A.P.S., 1992, ApJ, 399, L43\n\n\\bibitem[Crotts \\& Tomaney 1997]{cro97}\nCrotts, A.P.S., Tomaney A.B., 1997, ApJ, 473, L87\n\n\\bibitem[Crotts, Uglesich \\& Gyuk 1999]{cro99}\nCrotts, A.P.S., Uglesich, R., Gyuk, G., 1999, in proceedings of\nGravitational Lensing: Recent Progress and Future Goals, eds Brainerd,\nT., Kochanek, C., Astronomical Society of the Pacific Conference\nSeries (astro-ph/9910552)\n\n\\bibitem[Evans \\& Kerins 2000]{evan00}\nEvans, N.W., Kerins, E.J., 2000, ApJ, 529, in press (astro-ph/9909254)\n\n\\bibitem[Evans \\& Wilkinson 2000]{wilk00}\nEvans, N.W., Wilkinson, M., 2000, MNRAS, submitted\n\n\\bibitem[Fukugita et al. 1996]{fuk96}\nFukugita, M., Ichikawa, T., Gunn, J.E., Doi, M., Shimasaku, K.,\nSchneider, D.P., 1996, PASP, 111, 1748\n\n\\bibitem[Gondolo 1999]{gon99}\nGondolo, P., 1999, ApJ, 510, L29\n\n\\bibitem[Gould 1996]{gou96}\nGould, A., 1996, ApJ, 470, 201\n\n\\bibitem[Gould, Bahcall \\& Flynn 1997]{gou97} \nGould, A., Bahcall, J., Flynn, C., 1997, ApJ, 482, 913\n\n\\bibitem[Griest 1991]{grie91}\nGriest, K., 1991, ApJ, 366, 412\n\n\\bibitem[Gyuk \\& Crotts 1999]{gyuk99}\nGyuk, G., Crotts, A., 1999, ApJ, submitted (astro-ph/9904314)\n\n\\bibitem[Han 1996]{han96}\nHan, C., 1996, ApJ, 472, 108\n\n\\bibitem[Kent 1989]{kent89}\nKent, S.M., 1989, AJ, 97, 1614\n\n\\bibitem[Kerins \\& Evans 1999]{ker99}\nKerins, E.J., Evans, N.W., 1999, ApJ, 517, 734\n\n\\bibitem[Kiraga \\& Paczy\\'nski 1994]{kir94}\nKiraga, M., Paczy\\'nski, B., 1994, ApJ, 430, L101\n\n\\bibitem[Krisciunas \\& Schaefer 1991]{kris91}\nKrisciunas, K., Schaefer, B.E., 1991, PASP, 103, 1033\n\n\\bibitem[Lasserre et al. 1999]{lass99}\nLasserre, T., et al., 1999, in proceedings of Gravitational Lensing:\nRecent Progress and Future Goals, eds Brainerd, T., Kochanek, C.,\nAstronomical Society of the Pacific Conference Series (astro-ph/9909505)\n\n\\bibitem[Lastennet et al. 2000]{last00}\nLastennet, E., et al., 2000, in preparation\n\n\\bibitem[Le~Du 2000]{ledu00}\nLe~Du, Y., 2000, Ph.D thesis, University Paris VI, College de France\n\n\\bibitem[Melchior 1999]{mel99}\nMelchior, A.-L., 1999, presentation at the March~12th meeting of the\nRoyal Astronomical Society, London\n\n\\bibitem[Rhie et al. 1999]{rhie99}\nRhie, S.H., et al., 1999, ApJ, 522, 1037\n\n\\bibitem[Roberts, Whitehurst \\& Cram 1978]{rob78}\nRoberts, M., Whitehurst, R., Cram, T., 1978, in Structure and\nProperties of Nearby Galaxies, eds Berkhuijsen, E., Wielebinski,\nR. (Reidel, Dordrecht), p169\n\n\\bibitem[Sevenster et al. 1999]{seven99}\nSevenster, M., et al., 1999, MNRAS, 307, 584\n\n\\bibitem[Stanek \\& Garnavich 1998]{stan98}\nStanek, K.Z., Garnavich, P.M., 1998, ApJ, 503, L131\n\n\\bibitem[Udalski et al. 1994]{uda94}\nUdalski, A., et al., 1994, Acta Astronom., 44, 165\n\n\\bibitem[Walterbos \\& Kennicutt 1987]{wal87}\nWalterbos, R., Kennicutt, R., 1987, A\\&AS, 69, 311\n\n\\bibitem[Wielen, Jahreiss \\& Kr\\\"uger Jahreiss 1983]{wie83}\nWielen, R., Jahreiss, H., Kr\\\"uger, R., 1983, IAU Colloquium 76, p163\n\n\\bibitem[Wo\\`zniak \\& Paczy\\`nski 1997]{woz97}\nWo\\`zniak, P., Paczy\\`nski, B., 1997, ApJ, 487, 55\n\n\\end{thebibliography}"
}
] |
astro-ph0002257
|
Neural networks and separation of Cosmic Microwave Background and astrophysical signals in sky maps
|
[
{
"author": "C. Baccigalupi$^1$"
},
{
"author": "L. Bedini$^2$"
},
{
"author": "C. Burigana$^3$"
},
{
"author": "G. De Zotti$^4$"
},
{
"author": "A. Farusi$^2$"
},
{
"author": "D. Maino$^5$"
},
{
"author": "M. Maris$^5$"
},
{
"author": "F. Perrotta$^1$"
},
{
"author": "E. Salerno$^2$"
},
{
"author": "L. Toffolatti$^{6}$"
},
{
"author": "A. Tonazzini$^2$"
},
{
"author": "$^1$SISSA/ISAS"
},
{
"author": "Astrophysics Sector"
},
{
"author": "Via Beirut"
},
{
"author": "4"
},
{
"author": "I-34014 Trieste"
},
{
"author": "$^2$IEI-CNR"
},
{
"author": "Via Alfieri"
},
{
"author": "1"
},
{
"author": "I-56010 Ghezzano"
},
{
"author": "Pisa"
},
{
"author": "$^3$ITeSRE-CNR"
},
{
"author": "Via Gobetti"
},
{
"author": "101"
},
{
"author": "I-40129 Bologna"
},
{
"author": "$^4$Oss. Astr. Padova"
},
{
"author": "Vicolo dell'Osservatorio 5"
},
{
"author": "35122 Padova"
},
{
"author": "$^5$Oss. Astr. Trieste"
},
{
"author": "Via G.B. Tiepolo"
},
{
"author": "11"
},
{
"author": "I-34131 Trieste"
},
{
"author": "$^{6}$Dpto. de F\\'\\i{sica}"
},
{
"author": "c. Calvo Sotelo s/n"
},
{
"author": "33007 Oviedo"
}
] |
We implement an Independent Component Analysis (ICA) algorithm to separate signals of different origin in sky maps at several frequencies. Due to its self-organizing capability, it works without prior assumptions either on the frequency dependence or on the angular power spectrum of the various signals; rather, it learns directly from the input data how to identify the statistically independent components, on the assumption that all but, at most, one of them have non-Gaussian distributions. We have applied the ICA algorithm to simulated patches of the sky at the four frequencies (30, 44, 70 and 100 GHz) of the Low Frequency Instrument (LFI) of ESA's {\sc Planck} satellite. Simulations include the Cosmic Microwave Background (CMB), the synchrotron and thermal dust emissions and extragalactic radio sources. The effects of detectors angular response functions and of instrumental noise have been ignored in this first exploratory study. The ICA algorithm reconstructs the spatial distribution of each component with rms errors of about 1\% for the CMB and of about $10\%$ for the, much weaker, Galactic components. Radio sources are almost completely recovered down to a flux limit corresponding to $\simeq 0.7\sigma_{CMB}$, where $\sigma_{CMB}$ is the rms level of CMB fluctuations. The signal recovered has equal quality on all scales larger then the pixel size. In addition, we show that for the strongest components (CMB and radio sources) the frequency scaling is recevered with percent precision. Thus, algorithms of the type presented here appear to be very promising tools for component separation. On the other hand, we have been dealing here with an highly idealized situation. Work to include instrumental noise, the effect of different resolving powers at different frequencies and a more complete and realistic characterization of astrophysical foregrounds is in progress.
|
[
{
"name": "neural.tex",
"string": "\\documentstyle[epsfig]{mn}\n%\\documentstyle[epsfig]{macros/mn}\n%\\documentstyle[onecolumn,referee,epsfig]{macros/mn}\n\n\\begin{document}\n\n%\\textheight 8.8in\n%\\textwidth 6.in\n%\\topmargin -.25in\n%\\oddsidemargin .1in\n%\\evensidemargin 0in\n%\\baselineskip 20pt\n\n\\title[Neural networks and component separation in sky maps]\n{Neural networks and separation of Cosmic Microwave Background and \nastrophysical signals in sky maps}\n\n\\author[Baccigalupi et al.]\n{C. Baccigalupi$^1$, L. Bedini$^2$,\nC. Burigana$^3$, G. De Zotti$^4$, A. Farusi$^2$,\nD. Maino$^5$,\n\\and\nM. Maris$^5$, F. Perrotta$^1$,\nE. Salerno$^2$, L. Toffolatti$^{6}$, A. Tonazzini$^2$\\\\\n$^1$SISSA/ISAS, Astrophysics Sector, Via Beirut, 4,\nI-34014 Trieste, Italy. Email {\\tt bacci@sissa.it,perrotta@sissa.it}\\\\\n$^2$IEI-CNR, Via Alfieri, 1, I-56010 Ghezzano, Pisa, Italy.\nEmail {\\tt $<$name$>$@iei.pi.cnr.it}\\\\\n$^3$ITeSRE-CNR, Via Gobetti, 101, I-40129 Bologna,\nItaly. Email {\\tt burigana@tesre.bo.cnr.it}\\\\\n$^4$Oss. Astr. Padova, Vicolo dell'Osservatorio 5, 35122 Padova, Italy.\nEmail {\\tt dezotti@pd.astro.it}\\\\\n$^5$Oss. Astr. Trieste, Via G.B. Tiepolo, 11, I-34131\nTrieste, Italy. Email {\\tt <name>@ts.astro.it}\\\\\n$^{6}$Dpto. de F\\'\\i{sica}, c. Calvo Sotelo s/n, 33007 Oviedo, Spain\nEmail {\\tt toffol@pinon.ccu.uniovi.es}}\n\n\\maketitle\n\n\\begin{abstract}\nWe implement an Independent Component Analysis (ICA) \nalgorithm to separate signals of different origin in sky maps \nat several frequencies. Due to its \nself-organizing capability, it works without prior assumptions\neither on the frequency dependence or on the angular power spectrum of \nthe various signals; rather, it learns directly from the\ninput data how to identify the statistically independent components, on \nthe assumption that all but, at most, one of them have non-Gaussian \ndistributions.\n\nWe have applied the ICA algorithm to simulated patches of the sky \nat the four frequencies (30, 44, 70 and 100 GHz) of the Low Frequency \nInstrument (LFI) of ESA's {\\sc Planck} satellite. Simulations include \nthe Cosmic Microwave Background (CMB), the synchrotron and thermal dust \nemissions and extragalactic radio sources. The effects of detectors angular \nresponse functions and of instrumental noise have been ignored in this \nfirst exploratory study. The ICA algorithm reconstructs the spatial \ndistribution of each component with rms errors of about 1\\% for the CMB and \nof about $10\\%$ for the, much weaker, Galactic components. \nRadio sources are almost completely recovered down to a flux limit \ncorresponding to $\\simeq 0.7\\sigma_{CMB}$, where \n$\\sigma_{CMB}$ is the rms level of CMB fluctuations. \nThe signal recovered has equal quality on all scales\nlarger then the pixel size. In addition, we show that \nfor the strongest components (CMB and radio sources) \nthe frequency scaling is recevered with percent precision. \nThus, algorithms of the type presented here appear to be very promising \ntools for component separation. On the other hand, we have been dealing \nhere with an highly idealized situation. Work to include instrumental \nnoise, the effect of different resolving powers at different frequencies \nand a more complete and realistic characterization of astrophysical \nforegrounds is in progress.\n\\end{abstract}\n\n\\section{Introduction}\n\\label{introduction}\n\nMaps produced by large area surveys aimed at imaging primordial \nfluctuations of the Cosmic Microwave Background (CMB) contain \na linear mixture of signals by several astrophysical \nand cosmological sources (Galactic synchrotron, free-free and dust emissions, \nboth from compact and diffuse sources, extragalactic sources, \nSunyaev-Zeldovich effect in clusters of galaxies or by inhomogeneous \nre-ionization, in addition to primary and secondary CMB anisotropies) \nconvolved with the spatial and spectral responses of the antenna and of the \ndetectors. In order to exploit the unique cosmological information encoded in \nthe CMB anisotropy patterns as well as the extremely interesting astrophysical \ninformation carried by the foregound signals, we need to accurately separate \nthe different components. \n\nA great deal of work has been carried out in recent years in this area \n(see de Oliveira-Costa \\& Tegmark 1999, and references therein; \nTegmark et al. 2000). \nThe problem of map denoising has been tackled with the\nwavelets analysis on the whole sphere \\cite{TENORIO} and on\nsky patches \\cite{SANZb}. Algorithms to single out the CMB and the \nvarious foregrounds have been developed \\cite{WF,HOBSON,TE}. \nIn these works, Wiener filtering (WF) and the maximum entropy method (MEM) \nhave been applied to simulated data from the {\\sc Planck} satellite,\ntaking into account the expected performances of the instruments. \nAssuming a perfect knowledge of the frequency dependence \nof all the components, as well as priors for the\nstatistical properties of their spatial pattern,\nthese algorithms are able to recover the \nthe strongest components, at the best {\\sc Planck} resolution. \n\nWe adopt a rather different approach, considering denoising and \ndeconvolution of the signals on one side and component separation on the other \nas separate steps in the data analysis process, and focus here on the latter \nstep only, presenting a 'blind separation' method, based on 'Independent \nComponent Analysis' (ICA) techniques. The method does not require any a priori \nassumption \non spectral properties and on the spatial distribution of the various \ncomponents, but only that they are statistically independent \nand all but at most one have a non-Gaussian distribution.\nIt is important to note that this is in fact the physical \nsystem we have to deal with: surely all the foregrounds are non-Gaussian, \nwhile the CMB is expected to be a nearly Gaussian fluctuation \nfield for most of the candidate theories of the early \nuniverse. \n\nThe paper is organized as follows. In Section 2 we introduce the relevant \nformalism and briefly review methods applied in previous works. \nIn Section 3 we outline the ICA algorithm in a rather general \nframework, since it may be useful for a variety of astrophysical \napplications. In Section 4 we describe our simulated maps. In \nSection 5 we give some details on our analysis and present the results. \nIn Section 6 we draw our conclusions and list some\nfuture developments.\n\n\\section{Formalism and previous approaches}\n\\label{formalism}\n\nWe assume that the frequency spectrum of radiation components \n(referred to as sources) is independent \nof the position in the sky. Since we deal here with relatively small patches \nof the sky, we adopt Cartesian coordinates, $(\\xi , \\eta )$. \nThe function describing the i-th source then writes\n%\n\\begin{equation}\n\\label{sorg}\n\t\\tilde{s}_{i}(\\xi , \\eta , \\nu ) = s_{i}(\\xi , \\eta )\\cdot\n\t{\\cal F}_{i}(\\nu ) \\hspace{10mm}i = 1, \\ldots , N\n\\end{equation}\n%\nwhere $N$ is the number of independent sources and ${\\cal F}_{i}(\\nu )$ \nis the emission spectrum. \n\nThe signal received from the point $(\\xi,\\eta)$ in the sky is\n%\n\\begin{equation}\n\\label{freq}\n\t\\tilde{x}(\\xi,\\eta , \\nu ) = \\sum_{i=1}^{N}s_{i}(\\xi , \\eta\n)\\cdot\n\t{\\cal F}_{i}(\\nu )\n\\end{equation}\n%\nSuppose that the instrument has $M$ channels,\nwith spectral response functions $t_{j}(\\nu)$, $j=1,\\ldots M$\ncentered at different frequencies, and that the beam patterns\nare independent of frequency within each passband.\nLet beam patterns be described by the space-invariant\nPSF's $\\ h_{j}(\\xi,\\eta)$, so that the maps are produced by a\nlinear convolutional mechanism. (Note that this is an additional \nsimplifying assumption since in real experiments a position dependent \ndefocussing related to the chosen scanning strategy may occur.) \nThen, the map yielded by j$^{th}$ channel is:\n$$\nx_{j}(\\xi,\\eta) = \\int_{}^{} h_{j}(\\xi - x, \\eta - y)t_{j}(\\nu)\\cdot\n$$\n$$\n\\cdot\\sum_{i=1}^{N}s_{i}(x,y)\n\t{\\cal F}_{i}(\\nu) dx dy d\\nu +\\epsilon_{j}(\\xi ,\\eta) =\n$$\n\\begin{equation}\n\t\\label{chan}\n\t= \\tilde{x}_{j}(\\xi,\\eta) * h_{j}(\\xi,\\eta) +\n\t\\epsilon_{j}(\\xi ,\\eta)\\ ,\n\\hspace{10mm}j=1,\\ldots,M\\ ,\n\\end{equation}\nwhere:\n\\begin{equation}\n\t\\label{freq2}\n\t\\tilde{x}_{j}(\\xi,\\eta) = \\sum_{i=1}^{N}a_{ji}\n\t\\cdot s_{i}(xi ,\\eta )\\ ,\n\t\\hspace{10mm}j=1,\\ldots,M\\ ,\n\\end{equation}\n\\begin{equation}\n\t\\label{aentries}\n\ta_{ji} = \\int_{}^{}{\\cal F}_{i}(\\nu)\n\tt_{j}(\\nu) d\\nu \\ ,\\ \\\n\tj=1,\\ldots,M;\\ i=1,\\ldots,N\\ ,\n\\end{equation}\n$*$ denotes linear convolution and\n$\\epsilon_{j}(\\xi ,\\eta)$ represents the instrumental noise.\nEq.~(\\ref{freq2}) can also be written in matrix form:\n\\begin{equation}\n\\label{freqmat}\n\t\\tilde{\\textbf{x}} (\\xi,\\eta) = A \\textbf{s}(\\xi , \\eta )\n\\end{equation}\nwhere the entries of the $M\\times N$ matrix $A$ are given by \nEq.~(\\ref{aentries}).\n\nThe unknowns of our problem are the $N$ functions $s_{i}(\\xi , \\eta )$,\nand the data set is made of the $M$ maps $x_{j}(\\xi,\\eta)$ in\nEq.~(\\ref{chan}). Besides the measured data, we also know \nthe instrument beam-patterns $h_{j}(\\xi,\\eta)$, and, more or less\napproximately (depending on the specific source), the coefficients\n$a_{ji}$ in Eq.~(\\ref{freq2}).\n%In Figure \\ref{scheme}, the data model described above is schematized.\n\nEq.~(\\ref{chan}) can be easily rewritten in the Fourier space:\n\\begin{equation}\n\\label{fourierdata}\n\tX_{j}(\\omega_{\\xi},\\omega_{\\eta}) \n\t=\\sum_{i=1}^{N}R_{ji}(\\omega_{\\xi},\\omega_{\\eta})\n\tS_{i}(\\omega_{\\xi},\\omega_{\\eta}) +\n\t{\\cal E}_{j}(\\omega_{\\xi},\\omega_{\\eta})\\ ,\n\\end{equation}\nwhere the capital letters denote the Fourier transforms of the\ncorresponding lowercase functions, and\n\\begin{equation}\nR_{ji}(\\omega_{\\xi},\\omega_{\\eta})={\\cal H}_j(\\omega_{\\xi},\\omega_{\\eta})\na_{j i } \\ \\ ,\n\\end{equation}\n${\\cal H}_j $ being the Fourier transform of the beam profile $h_j$. \\\\\nEq.~(\\ref{fourierdata}) can thus be rewritten in matrix form:\n\\begin{equation}\n\\label{eqnbase}\n\t{\\bf X} = R {\\bf S} + {\\bf {\\cal E}}\\ .\n\\end{equation}\nThe above equation must be satisfied by each Fourier mode\n$(\\omega_{\\xi},\\omega_{\\eta})$, independently.\nThe aim is to recover the true signals\n$S_{i}(\\omega_{\\xi},\\omega_{\\eta})$ constituting\nthe column vector ${\\bf S}$. If the matrix $A$ in Eq.~(\\ref{freqmat})\nis known exactly then, in the absence of noise, the problem \nreduces to a linear inversion of Eq.~(\\ref{eqnbase}) for \neach Fourier mode.\n\nIn practice, however, ${\\cal H}_{j}$ vanishes for some Fourier mode. \nFor these modes the entire j-th row of the matrix $R$ also \nvanishes, and $R$ may become a non-full-rank matrix.\nAn inversion based on statistical approaches built on {\\it a priori} \nknowledge is thus needed.\n\nIn the following two subsections we briefly describe two such\napproaches, and in the third one we briefly recall a technique \nso far mostly exploited for the denoising problem and for extraction \nof extragalactic sources. \n\n\\subsection{The maximum entropy approach}\n\\label{the}\n\nThe Maximum Entropy Method (MEM) for the reconstruction of images is \nbased on a Bayesian approach to the problem (Skilling 1988, 1989; \nGull 1988). Let \n${\\bf X}$ be a vector of $M$ observations\nwhose probability distribution $P({\\bf X}|{\\bf S})$ depends on the\nvalues of $N$ quantities ${\\bf S}={S_1,...,S_N}$. \n\nLet us $P({\\bf S})$ be the {\\it prior} probability\ndistribution of ${\\bf S}$, telling us what is known about ${\\bf S}$\nwithout knowledge of the data. Given the data ${\\bf X }$, \nBayes' theorem states that the\nconditional distribution of ${\\bf S}$ (the {\\it posterior} distribution of\n${\\bf S}$) is given by the product of the likelihood of the data,\n$P({\\bf X} | {\\bf S})$, with the prior:\n\\begin{equation}\n\\label{Bayes}\nP( {\\bf S }| {\\bf X} )= z \\cdot P({\\bf X}|{\\bf S}) P({\\bf S})\\ ,\n\\end{equation}\nwhere $z$ is a normalization constant. \n\nAn estimator ${\\hat {\\bf S}}$ of the true signal vector can be constructed \nby maximizing the posterior probability\n$ P( {\\bf S }| {\\bf X} ) \\propto P({\\bf X}|{\\bf S}) P({\\bf S})$.\nHowever, while the likelihood in Eq.~(\\ref{Bayes}) is easily \ndetermined once the noise and signal covariance matrices are known,\nthe appropriate choice of the prior distribution for the model considered \nis a major problem in the Bayesian approach: \nsince Bayes' theorem is simply a rule for manipulating probabilities,\nit cannot by itself help us to assign them in the first place, so one has\nto look elsewhere. The MEM is a consistent\nvariational method for the assignment of probabilities under certain\ntypes of constraints that must refer to the probability distribution\ndirectly. \n\nThe Maximum Entropy principle states that if one has some\ninformation $I$ on which the probability distribution is based, one can\nassign a probability distribution to a proposition $i$ such that $P(i|I)$\ncontains only the information $I$ that one actually possesses. This\nassignment is done by maximizing the Entropy\n\\begin{equation}\nH \\equiv - \\sum_{i=1}^{N} P(i|I)logP(i|I)\n\\end{equation}\nIt can be seen that when nothing is known except that the probability\ndistribution should be normalized, the Maximum Entropy principle yields \nthe uniform prior. In our case the proposition $i$ represents\n{\\bf S}, and the information $I$ is the assumption of signal\nstatistical independence. The standard application of the method \nconsidered strictly positive signals (Skilling 1988, 1989; \nGull 1988); the extension to \nthe case of CMB temperature fluctuations, which can be both positive and \nnegative, was worked out by Hobson et al. (1998).\n\nThe construction\nof the entropic prior requires, in general, the\nknowledge of the frequency dependence of the components\nto be recovered as well as of the signal covariance matrix\n${\\bf C }({\\bf k}) =< {\\bf S}({\\bf k}) {\\bf S}^{\\dagger}({\\bf k})>$, \n%c%\nwith the average taken on all the possible realizations.\n%c%\n\n\\subsection{The multifrequency Wiener filtering}\n\nIf a Gaussian prior is adopted, the Bayesian approach gives the \nmultifrequency Wiener filtering (WF) solution \\cite{WF}. In \nin this case too an estimator of the signal vector is obtained by maximizing \nthe posterior probability in Eq.~(\\ref{Bayes}), \n%${\\bf N }(k) =< {\\bf \\epsilon}(k) {\\bf \\epsilon}^{\\dagger} (k)> $\ngiven the signal covariance matrix ${\\bf C}({\\bf k})$.\n\nThe Gaussian prior probability distribution for the signal has the form\n\\begin{equation}\nP( {\\bf S}) \\propto \\exp (-{\\bf S}^{\\dagger} {\\bf C}^{-1}{\\bf S}) \\ \\ .\n\\end{equation}\nThe estimator ${\\bf{\\hat{\\rm S}}}$ is linearly related to the data vector\n${\\bf{\\hat{\\rm X}}}$ through the Wiener matrix\n${\\bf W} \\equiv ( {\\bf C}^{-1}+{\\bf R}^{\\dagger} {\\bf N}^{-1}{\\bf\nR})^{-1}$, where ${\\bf R}$ corresponds to the matrix in\n(\\ref{eqnbase}) and ${\\bf N}({\\bf k})=<{\\bf \\epsilon}({\\bf k})\n{\\bf \\epsilon}^{\\dagger}({\\bf k})>$ is the noise covariance\nmatrix:\n\\begin{equation}\n{\\hat {\\bf S}} = {\\bf W}{\\bf X} \\ \\ .\n\\label{Wiener}\n\\end{equation}\nThe ${\\bf W}$ matrix has the role of a linear filter;\nagain, its construction requires an {\\it a\npriori} knowledge of the spectral behavior of the signals.\n\nThis method is endangered by the clear non-Gaussianity of foregrounds. \n\n\\subsection{Wavelet methods }\n\nThe development of wavelet techniques for signal processing\nhas been very fast in the last ten years \\cite{JAWERTH}. \nThe wavelet approach is conceptually very simple: \nwhereas the Fourier transform is highly inefficient in dealing with \nthe local behavior, the wavelet transform is able to \nintroduce a good space-frequency localization, \nthus providing information on the contributions coming from different\npositions and scales. \n\n\\noindent\nIn one dimension, we can define the {\\it analyzing} wavelet as\n$\\Psi (x; R, b) \\equiv R^{-1/2}\\psi[(x - b)/R]$, dependent on two\nparameters, dilation ($R$) and translation ($b$); \n$\\psi (x)$ is a one-dimensional function satisfying the following\nconditions: a) $\\int_{-\\infty}^{\\infty}dx\\,\\psi (x) = 0$, b)\n$\\int_{-\\infty}^{\\infty}dx\\,{\\psi}^2 (x) = 1$ and\nc) $\\int_{-\\infty}^{\\infty}dk\\,|k|^{-1}\\psi^2 (k) < \\infty $,\nwhere $\\psi (k)$ is the Fourier transform of $\\psi (x)$.\nThe wavelet $\\Psi$ operates as a mathematical\nmicroscope of magnification $R^{-1}$ at the space point $b$.\nThe wavelet coefficients associated to a one-dimensional\nfunction $f(x)$ are:\n\n\\begin{equation}\nw(R, b) = \\int dx\\, f(x)\\Psi (x; R, b)\\; .\n\\end{equation}\n\n\\noindent\nThe computationally faster algorithms for the wavelet analysis of \n2-dimensional images are those based on\nMultiresolution analysis \\cite{MALLAT} or on 2D wavelet analysis\n\\cite{LEMARIE}, using tensor products of one-dimensional wavelets.\nThe discrete Multiresolution analysis entails the definition of a\none-dimensional {\\it scaling} function $\\phi$, normalized as\n$\\int_{-\\infty}^{\\infty}dx\\,\\phi (x) = 1$ \\cite{OGDEN}.\nScaling functions act as low-pass filters whereas wavelet functions\nsingle out one scale. \nThe 2D wavelet method \\cite{SANZb} is based on two scales,\nproviding therefore more information on different resolutions (defined\nby the product of the two scales) than the Multiresolution one.\n\n\\medskip\\noindent\nRecently, wavelet techniques\nhave been introduced in the analysis of CMB data.\nDenoising of CMB maps has been performed on patches of the sky of\n$12^{\\circ}.8\\times 12^{\\circ}.8$\nusing either multiresolution techniques \\cite{SANZa}\nand 2D wavelets \\cite{SANZb}, as well as on the whole celestial\nsphere \\cite{TENORIO}. As a first step, \nmaps with the cosmological signal plus a Gaussian instrumental \nnoise have been considered. \n\nDenoising of CMB maps has been carried out by using a \nsignal--independent prescription, the SURE thresholding method\n\\cite{DONOHO}. The results are model independent\nand only a good knowledge of the noise affecting\nthe observed CMB maps is required, whereas nothing has to be assumed\non the nature of the underlying field(s).\nMoreover, wavelet techniques are highly efficient in localizing noise \nvariations and features in the maps. \n\nThe wavelet method is able to improve the signal-to-noise ratio by a \nfactor of 3 to 5; correspondingly, the error on $C_{\\ell}$'s \nderived from denoised maps is about 2 times lower than that obtained \nwith the WF method.\n\nWavelets were also successfully applied to the detection of \npoint sources in CMB maps in the presence of the cosmological signal \nand of instrumental noise \\cite{TENORIO}; \nmore recently, successfull results on source\ndetection have also been obtained in presence of diffuse galactic\nforegrounds \\cite{CAYON}.\nThe results are comparable to those obtained \nwith the filtering method presented by \\cite{TEGMARKCOSTA} which, \nhowever, relies on the assumption that all the underlying fields are\nGaussian.\n\n\\section{The ICA approach}\n\\label{the ICA}\n\nWe present here a rather different approach, characterized by the capability\nof working `blindly' i.e. without prior knowledge of spectral \nand spatial properties of the signals to be separated. The method is of \ninterest for a broad variety of signal and image processing applications, \ni.e. whenever a number of\nsource signals are detected by multiple transducers, and the\ntransmission channels for the sources are unknown, so that each\ntransducer receives a mixture of the source signals with unknown\nscaling coefficients and channel distortion.\n\nIn this exploratory study we confine ourselves to the case of \nsimple linear combinations of unconvolved source signals \n\\cite{AMARI,BELL}. The problem can be stated as follows: a set of $N$\nsignals is input to an unknown frequency\ndependent multiple-input-multiple-output linear instantaneous system,\nwhose $M$ outputs are our observed signals. We use the term\n{\\it instantaneous} to denote a system whose output at a given point\nonly depends on the input signals at the same point.\nOur objective is to find a stable {\\it reconstruction system} to estimate \nthe original input signals with no\nprior assumptions either on the signal distributions\nor on their frequency scalings. The problem in its general form is\nnormally unsolvable, and a ``working hypothesis\" must be made. The \nhypothesis we make is the mutual {\\it statistical independence} \nof our source signals, whatever their actual distributions are.\n%spostato:\nSeveral solutions have been proposed for this problem, each based on\nmore or less sound principles, not all of which are typical of\nclassical signal processing. Indeed, information theory, neural\nnetworks, statistics and probability have played an important part in\nthe development of these techniques.\n\n%The necessary new concept with respect to previous approaches\n%that we introduce here is the self-learning capability of the\n%algorithm; indeed, in this blind approach it is necessary for\n%the algorithm to learn directly from the data, by using\n%the hypothesis of mutual independence of the\n%signal components.\n%A self-learning algorithm like this is commonly known as neural\n%network and we will describe it below.\n\nWe do not consider here specific instrumental\nfeatures like beam convolution and noise contamination,\nleaving the specialization of the ICA method to \nspecific experiments to future work; this allows us to\nhighlight the capabilities of this approach, able to work\nin conditions where other algorithms would not be viable.\nTherefore, we adopt Eq.~(\\ref{freqmat}) as our data model, just dropping the\ntilde accent on vector ${\\bf x}$. Also, the instrumental noise term in \nEq.~(\\ref{fourierdata}) will be neglected. \n\nIt can be proved that, to solve the problem described above, the\nfollowing hypotheses should be verified \\cite{AMARI,COMON}:\n\\begin{itemize}\n\\item All the source signals are statistically independent;\n\\item At most one of them has a Gaussian distribution;\n\\item $M \\geq N$;\n\\item Low noise.\n\\end{itemize}\n\nThe last two assumptions can be somewhat relaxed by choosing suitable\nseparation strategies. As far as independence is concerned, roughly\nspeaking, we may say that the search for an ICA model from non-ICA data (i.e.\ndata not coming from independent sources) should give the most\n`interesting' (namely, the most structured) projections of the data\n\\cite{HYVARINEN,FRIEDMAN}.\nThis is not equivalent to say that separation is achieved; however, we\nhave seen from our experiments that a good separation can be obtained\neven for sources that are not totally independent. The second\nassumption above tells us that Gaussian sources cannot be separated.\nMore specifically, they can only be separated up to an orthogonal\ntransformation. In fact, it can be shown that the joint probability of \na mixture of Gaussian signals is invariant to orthogonal \ntransformations. This means that if independent components are found\nfrom Gaussian mixtures, then any orthogonal transformation of them \ngives mutually independent components.\n\nMany strategies have been adopted to solve the separation problem on\nthe basis of the above hypotheses, all based on looking for a\nset of independent signals, which can be shown to be the original\nsources. A formal criterion to test independence, from which all the\nseparating strategies can be derived, is described later in this section.\n\nIn order to recover the original source signals from the observed\nmixtures, we use a separating scheme in the form of a feed-forward\nneural network. The observed signals are \ninput to an $N\\times M$ matrix $W$, referred to as the {\\it the synaptic\nweight\nmatrix}, whose adjustable entries, $w_{ij}, i=1, \\ldots N, j=1,\n\\ldots M$, are updated\nfor every sample of the input vector $\\textbf{x}(\\xi , \\eta )$ (at\nstep $\\tau$)\nfollowing a suitable {\\it learning algorithm}.\nThe output of matrix $W$ at step $\\tau$ will be:\n\\begin{equation}\n\\label{weight}\n\t\\textbf{u}(\\xi ,\\eta ,\\tau ) = W(\\tau )\n\t\\textbf{x}(\\xi ,\\eta )\\ .\n\\end{equation}\n$W(\\tau )$ is expected to converge\nto a true separating matrix, that is, a matrix whose output is a {\\it\ncopy} of the inputs, for every point $(\\xi , \\eta )$. Ideally,\nthis final matrix $W$ should be such that $WA = I$,\nwhere $I$ is the $N\\times N$\nidentity. As an example, if $M = N$, we should have $W = A^{-1}$.\nThere are, however, two basic indeterminacies in our problem:\nordering and scaling. Even if we are able to extract $N$ independent\nsources from $M$ linear mixtures, we cannot know {\\it a\npriori} the order in which they will be arranged, since this corresponds\nto unobservable permutations of the columns of matrix $A$. Moreover,\nthe scales of the extracted signals are unknown, because when a\nsignal is multiplied by some scalar constant, the effect is the same\nas of multiplying by the same constant the corresponding column of the\nmixing matrix. This means that $W(\\tau )$ will converge, at best, to a\nmatrix $W$ such that:\n\\begin{equation}\n\\label{converg}\n\tWA = PD\\ ,\n\\end{equation}\nwhere $P$ is any $N\\times N$ permutation matrix, and $D$ is a\nnonsingular diagonal scaling\nmatrix. From Eqs.~(\\ref{freqmat}), (\\ref{weight}) and\n(\\ref{converg}) we thus have:\n\\begin{equation}\n\\label{invert}\n\t{\\bf u} = W{\\bf x} = WA{\\bf s} = PD{\\bf s}\\ .\n\\end{equation}\nThat is, as anticipated, each component of $\\bf u$ is a scaled version\nof a component of $\\bf s$, not necessarily in the same order.\nThis is not a serious inconvenience in our application, since we should\nbe able to recover the proper scales for the separated sources from\nother pieces of information, for example matching with independent\nlower resolution observations like those of COBE on the \ncase of MAP and {\\sc Planck}.\nIf $A$ was known, the performance of the separation algorithm could\nbe evaluated by means of the \nmatrix $WA$. If the separation is perfect, this matrix has only one\nnonzero element for each row and each column.\nIn any non-ideal situation each row and column of $WA$ should contain only \none dominant element.\n\nIn all the cases treated\nhere we assume $M \\geq N$, but we consider\nthe case where $N$, although smaller than $M$, is not known.\n\nThe mutual statistical independence of the source signals can be\nexpressed in terms of a separable joint probability density function\n$q({\\bf s})$:\n\\begin{equation}\n\\label{separable}\n\tq({\\bf s}) = \\prod_{j=1}^{N}q_{j}(s_{j})\n\\end{equation}\nwhere $q_{j}(s_{j})$ is the marginal probability density of the\n$j^{th}$ source.\n\nVarious algorithms can be used to learn the \nmatrix $W$. All these algorithms can be derived from a unified principle\nbased on the Kullback--Leibler (KL) divergence between the joint\nprobability\ndensity of the output vector $\\bf u$, $p_{U}(\\bf u)$, and a\nfunction $q({\\bf u})$, which should\nbe suitably chosen among the ones of the type of Eq.~(\\ref{separable}).\nThe KL divergence between the two functions mentioned\nabove may be written as a function of the matrix $W$, and can be\nconsidered as a cost function in the sense of Bayesian statistics:\n\\begin{equation}\n\\label{kullei}\n\tR(W) = \\int_{}^{}p_{U}({\\bf u}) {\\rm log} \\frac{p_{U}({\\bf\nu})}{q({\\bf u})} d {\\bf u}\\ .\n\\end{equation}\nIt can be proved that, under mild\nconditions on $q({\\bf u})$, $R(W)$ has a global minimum\nwhere $W$ is such that $WA = PD$.\nThe different possible choices for $q({\\bf s})$ lead to the\ndifferent particular learning strategies proposed in the\nliterature \\cite{AMARI,AMARI2,BELL}.\n\nThe {\\it uniform gradient} search\nmethod, which is a gradient-type algorithm, takes into account\nthe Riemannian metric structure of our objective parameter space,\nwhich is the set of all nonsingular matrices $W$ \\cite{AMARI}.\nIn a general case, where the number $N$ of sources is only known to\nbe smaller than the number of observations, the following formula is derived:\n$$\n\tW(\\tau +1)=W(\\tau ) +\n$$\n\\begin{equation}\n\\label{alg2}\n+\\alpha(\\tau )\\cdot[\\Lambda - {\\bf u}(\\tau ){\\bf u}^{T}(\\tau )\n\t-{\\bf f}({\\bf u}(\\tau )) {\\bf u}^{T}(\\tau )]W(\\tau )\\ ,\n\\end{equation}\nwhere $\\Lambda$ is a $M\\times M$ diagonal matrix:\n\\begin{equation}\n\t\\Lambda ={\\rm diag} { [ (u_{1} + f_{1}(u_{1}))u_{1}]\n\t\\ldots [(u_{M} + f_{M}(u_{M}))u_{M} ] }\\ .\n\\end{equation}\nPixel by pixel,\nthe $M\\times M$ matrix $W$ is multiplied by the M--vector {\\bf x}, and\ngives vector ${\\bf u}$ as its output. This output is transformed through\nthe nonlinear vector function ${\\bf f}({\\bf u})$, and the result is\ncombined with $\\bf u$ itself to build the update to matrix $W$,\nthrough Eq.~(\\ref{alg2}). The process has to be iterated by\nreading the data maps several times. If $N$ is strictly smaller than\n$M$, then $M-N$ outputs can be shown to rapidly converge to zero, or\nto pure noise functions.\n\nThe convergence properties of this iterative formula are shown to be\nindependent\nof the particular matrix $A$, so that, even a strongly ill-conditioned\nsystem does not affect the convergence of the learning algorithm. In\nother words, even when the contributions from some components are very small,\nthere is no problem to recover them. This property is\ncalled the {\\it equivariant property} since the asymptotic properties\nof the algorithm are independent of the mixing matrix.\nThe $\\tau$-dependent parameter $\\alpha$\nis the {\\it learning rate}; its value is normally\ndecreased during the iteration. As far as the choice of $\\alpha\n(\\tau)$ is concerned, a strategy to\nlearn it and its annealing scheme\nis given in Amari et al. (1998);\nwe have chosen $\\alpha (\\tau )$ decreasing from $10^{-3}$ to\n$10^{-4}$ linearly with the number of iterations.\n\nThe final problem is how to choose the function ${\\bf f}({\\bf u})$. If we\nknow the true source distributions\n$q_{j}(u_{j})$, the best choice is to make $f'_{j}(u_{j}) =\nq_{j}(u_{j})$,\nsince this gives the maximum likelihood estimator. However, the point\nis that when $q_{j}(u_{j})$ are specified incorrectly, the algorithm\ngives the correct answer under certain conditions. In any case, the\nchoice of ${\\bf f}({\\bf u})$ should be made to ensure the existence\nof an equilibrium point for the cost function and the stability of the\noptimization algorithm. These requirements can be satisfied even\nthough the nonlinearities chosen are not optimal. A suboptimal choice\nfor sub-Gaussian source signals (negative kurtosis), is:\n\\begin{equation}\n\\label{subgauss}\n\tf_{i}(u_{i}) = \\beta u_{i} + u_{i}|u_{i}|^{2}\\ ,\n\\end{equation}\nand, for super-Gaussian source signals (positive kurtosis):\n\\begin{equation}\n\\label{supergauss}\nf_{i}(u_{i}) = \\beta u_{i} + {\\rm tanh}(\\gamma u_{i})\\ ,\n\\end{equation}\nwhere $\\beta \\geq 0$ and $\\gamma \\geq 2$; if one source is \nGaussian, the above choices remain viable as well. \nIn our case, we verified that all the source functions \nexcept CMB are super-Gaussian,\nand thus we implemented the learning algorithm following Eq.(\\ref{alg2}),\nwith the nonlinearities in Eq.~(\\ref{supergauss}), and $\\beta =0$,\n$\\gamma = 2$. As already stated, the mean of\nthe input signal at each frequency is subtracted.\nIn previous works \\cite{AMARI2} the initial matrix was chosen as\n$W\\propto I$; in that analysis, the image data consisted of a set of\ncomponents with nearly the same amplitude.\nThe initial guess for $W$ affects the computation\ntime, as well as the scaling of the reconstructed signals\nand their order.\nInterestingly, we found that adjusting the diagonal elements so that \nthey roughly reflect the different weights of the\ncomponents in the mixture can speed-up the convergence. For the\nproblem at hand, the results shown in \\S~\\ref{blind} have\nbeen obtained starting from $W=$diag[1,3,30,10], for the case of\na $4\\times 4 \\ W$-matrix, and using only 20 learning steps:\nthe time needed was about 1 minute on a UltraSparc machine,\nequipped with an 300 MHz UltraSparc processor, 256 MBytes RAM,\nrunning down SUN Solaris 7 Operating System, compiling the\n{\\tt FORTRAN 90} code using SUN Fortran Workshop 5.0\n\n\\section{Simulated maps}\n\\label{database}\n\nWe produced simulated maps of the antenna temperature distribution \nwith 3'.5 pixel size of a $15^{\\circ}\\times \n15^{\\circ}$ region centered at $l=90^{\\circ}$, $b=45^{\\circ}$, \nat the four central frequencies of \nthe {\\sc Planck}/LFI channels \\cite{MANDOLESI},\nnamely 30, 44, 70 and 100 GHz (Fig.~\\ref{icasissain}).\nThe HEALPix pixelization scheme \\cite{Heal} was adopted. \nThe maps include CMB anisotropies, Galactic synchrotron and dust emissions, \nand extragalactic radio sources.\n \nCMB fluctuations correspond to a flat Cold Dark Matter (CDM) model \n($\\Omega_{CDM}=.95$, $\\Omega_{b}=.05$, three massless neutrino species), \nnormalized to the COBE data \\cite{SZ}. As it is well known, the CMB\nspectrum, in terms of antenna temperature, writes:\n\\begin{equation}\n\\label{nucmb}\ns^{antenna}_{CMB}(\\xi ,\\eta ,\\nu)=s^{thermod.}_{CMB}(\\xi ,\\eta ) \\cdot\n{ \\tilde{\\nu}^2 e^{\\tilde{\\nu}} \\over (e^{\\tilde{\\nu}} -1 )^2 }\\ ,\n\\end{equation}\nwhere $\\tilde{\\nu}={\\nu/ 56.8}$ and $\\nu$ is the frequency in GHz;\n$s^{thermod.}_{CMB}(\\xi ,\\eta )$ is frequency independent \\cite{FIXSEN}. \n\nAs for Galactic synchrotron emission, we have extrapolated the \n408 MHz map with about 1 degree resolution \\cite{H}, assuming \na power law spectrum, in terms of antenna temperature:\n\\begin{equation}\n{\\cal F}_{syn} \\propto \\tilde{\\nu}^{-n_s}\\ ,\n\\end{equation}\nwith spectral index $n_s=2.9$.\n\nThe dust emission maps with about 6' resolution constructed by Schlegel et \nal. (1998) combining IRAS and DIRBE data have been used as templates for \nGalactic dust emission. The extrapolation to {\\sc Planck}/LFI frequencies \nwas done assuming a grey-body spectrum:\n\\begin{equation}\n{\\cal F}_{dust} \\propto {\\tilde{\\nu}^{m+1} \\over\ne^{\\tilde{\\nu}} -1}\\ ,\n\\end{equation}\nwith $m=2$, $\\tilde{\\nu}=h \\nu / kT_{dust}$, $T_{dust}$ being the dust \ntemperature. Although, in general, $T_{dust}$ varies across the sky, \nit turns out to be approximately constant at about $18\\,$K in the region \nconsidered here; we have therefore adopted this value in the above equation.\n \nBecause of the lack of a suitable template, we have ignored here free-free \nemission, which may be important particularly at 70 and 100 GHz. This \ncomponent needs to be included in future work.\n\nThe model by Toffolatti et al. (1998) was adopted for extragalactic radio \nsources, assumed to have a Poisson distribution. An antenna temperaure \nspectral index $n_{\\rm rs}=1.9$ was adopted \n$({\\cal F}_{\\rm rs} \\propto \\tilde{\\nu}^{-n_{\\rm rs}})$.\n\n\\begin{table*}\n\\caption{Input and output frequency scalings of the various components.}\n\\begin{tabular}{r c c c c c c c c }\n\\hline\n\\multicolumn{1}{c}{Frequency} & \\multicolumn{2}{c}{Radio sources} & \n\\multicolumn{2}{c}{CMB} & \\multicolumn{2}{c}{synchrotron} & \n\\multicolumn{2}{c}{dust} \\\\\n\\multicolumn{1}{c}{(GHz)} & input & output\\qquad & input & output\\qquad & \ninput & output\\qquad & input & output \\\\ \n\\hline\n100\\quad\\quad & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00\\\\\n70\\quad\\quad & 1.97 & 1.95 & 1.14 & 1.14 & 2.81 & 1.36 & 0.68 & 0.93\\\\\n44\\quad\\quad & 4.76 & 4.70 & 1.22 & 1.23 & 10.8 & 1.72 & 0.35 & 1.93\\\\\n30\\quad\\quad & 9.86 & 9.70 & 1.26 & 1.26 & 32.8 & -12. & 0.19 & 3.77\\\\\n & & & & & & &\n\\label{frequencyin}\n\\end{tabular}\n\\end{table*}\n\n\\section{Blind analysis and results}\n\\label{blind}\n\nAs it is well known, the strongest signals at the {\\sc Planck}/LFI \nfrequencies come from the CMB and from radio sources\n(although the latter show up essentially as a few high peaks),\nwhereas synchrotron emission and thermal dust are roughly\n1 or 2 orders of magnitude lower, depending on frequency.\nThus we are testing the performances of the ICA algorithm \nwith four signals exhibiting very different\nspatial patterns, frequency dependences and amplitudes.\n\nSince we are interested in the fluctuation pattern, the mean of the total \nsignal (sum of the four components) is set to zero at each frequency. \nWe adopt a ``blind'' approach: no information on either the spatial \ndistribution or the frequency dependence of the signals is provided to the \nalgorithm.\n\nThe reconstructed maps of the the four components are shown in \nFig.~\\ref{icasissaout}. Several interesting features may be noticed.\nThe order of the plotted maps is permuted with respect to the input maps in \nFig.~\\ref{icasissain}, reflecting the order of the ICA outputs:\nthe first output is synchrotron, the second represents radio\nsources, the third is CMB and the fourth is dust. \nAll the output maps look very similar to the true ones; even\nsynchrotron lower resolution pixels have been reproduced.\nIn Figs.~\\ref{icacmb}, \\ref{icadust}, \\ref{icasyn} and\n\\ref{icaradio} we analyze the goodness of the separation by\ncomparing power spectra and showing scatter plots between\nthe inputs and the outputs.\n%following criteria adopted previous works \\cite{HOBSON,WF}.\n\n\\subsection{Signal reconstruction}\n\nFor each map, we have computed the angular power spectrum,\ndefined by the expansion coefficients $C_{\\ell}$ of the two\npoint correlation function in Legendre polynomials.\nAs is well known, it can conveniently be expressed\nin terms of the coefficients of the expansion of the signal\n$S$ into spherical harmonics, $S (\\theta ,\\phi )=\n\\sum_{\\ell m}a_{\\ell m}Y_{\\ell m}(\\theta ,\\phi )$:\n\\begin{equation}\n\\label{cl}\nC_{\\ell}={1\\over 2\\ell +1}\\sum_{m}|a_{\\ell m}|^{2}\\ .\n\\end{equation}\nSuch coefficients are useful because\nfrom elementary properties of the Legendre polynomials\nit can be seen that the coefficient $C_{\\ell}$ quantifies the\namount of perturbation on the angular scale $\\theta$ given by\n$\\theta\\simeq 180/ \\ell$ degrees. \n\nThe panels on the top of Figs.~\\ref{icacmb}, \\ref{icasyn},\n\\ref{icadust}, \\ref{icaradio} show the power spectra \nof the input (left) and output (right) signals. The CMB exhibits the \ncharacteristic peaks on sub-degree angular scales due to acoustic\noscillations of the photon-baryon fluid at decoupling;\nthe dashed line represents the theoretical model from which\nthe map was generated, while the solid line is the power\nspectrum of our simulated patch: the difference between\nthe two curves is due to the sample variance corresponding to the CMB Gaussian\nstatistics. Radio sources are completely different, having all the\npower on small scales with the typical shot noise spatial\npattern; dust and synchrotron emissions have power decreasing\non small scales roughly as a power law, as expected \\cite{MANDOLESI,PUGET}.\nThe left-hand side panels on the bottom show the quality factor, defined\nas the ratio between true and reconstructed power spectrum\ncoefficients, for each multipole $\\ell$. Due to the limited size of the \nanalyzed region, the power spectrum can be defined on scales\nbelow roughly $2^\\circ$. The bottom right-hand side panels are scatter plots \nof the ICA results: for each pixel of the maps, we plotted the value of the\nreconstructed image vs. the corresponding input value. \n\nThe reconstructed signals have zero mean and are in unit of the\nconstant $d$ multiplying each output map, produced during the\nseparation phase, as mentioned in \\S$\\,3$: the scale of each\nsignal is unreproducible for a blind separation algorithm\nlike ICA. Nevertheless, a lot of information is encoded\ninto the spatial pattern of each signals, and ultimately\nits overall normalization could be recovered exploiting data \nfrom other experiments.\nTherefore, the relation between each true signal and\nits reconstruction is\n\\begin{equation}\n\\label{relation}\ns_{i}^{in}=d\\cdot s_{i}^{out}+b\\ \\ ,\\ \\ i=1,...,N_{pixels}\\ ,\n\\end{equation}\nwhere $b$ represents merely the mean of the input signal,\nthat is zero for the CMB and some positive value for the foregrounds. \n\nTo quantify the quality of the reconstruction, we have recovered $d$ and $b$ by\nperforming a linear fit of output to \ninput maps ({\\bf s}$^{in}$,{\\bf s}$^{out}$) for each signal:\n\\begin{equation}\n\\label{alpha}\nd={\\sum_{i}s^{in}_{i}s^{out}_{i}-\n\\bar{s}^{in}\\cdot\\sum_{i}s_{i}^{out}\\over\n\\sum_{i}(s_{i}^{out})^{2}-\\bar{s}^{out}\\cdot\\sum_{i}s_{i}^{out}}\n\\ \\ ,\\ \\ b=\\bar{s}^{in}-d\\cdot\\bar{s}^{out}\\ ,\n\\end{equation}\nwhere the sums run over all the pixels, and the bar indicates the\naverage value over the patch; the values of $d$ and $b$, as well\nas the linear fits (dashed lines), are indicated\nfor all the signals in the scatter plot panels.\nAlso, in the same panels we show the standard deviation of the\nfit, that is\n\\begin{equation}\n\\label{sigma}\n\\sigma =\\left[{1\\over N_{pixels}}\n\\sum_{i}(s^{in}_{i}-d\\cdot s^{out}_{i}-b)^{2}\\right]^{1/2}\\ .\n\\end{equation}\nA comparison of such quantity with the input signals\n(bottom right-hand side panels) gives an estimate of\nthe goodness of the reconstruction. CMB and radio sources are\nrecovered with percent and $0.1\\%$ precision, respectively, while \nthe accuracy drops roughly to $10\\%$ for the (much weaker) Galactic \ncomponents, synchrotron and dust. Also, the latter \nappear to be slightly mixed; this is likely due to the fact that \nthey are somewhat correlated \nso that the hypothesis of statistical independence\nis not properly satisfied.\n\nWe have also tested to what extent the counts of radio sources are recovered. \nThis was done in terms of the relative flux \n\\begin{equation}\n\\label{fracflux}\n\\Delta s=s/s_{\\rm max}\\ ,\n\\end{equation}\n$s_{\\rm max}$ being the flux of the brightest source. \n\nIn Fig.~\\ref{numbercounts} we show the cumulative number of input (dashed) \nand output (solid line) pixels exceeding a given value of $\\Delta s$.\nThe algorithm correctly recovers essentially all sources\nwith $\\Delta s\\ge 2\\times 10^{-2}$, corresponding to a \nsignal of $T_s\\simeq 50\\,\\mu$K, or to a flux density \n$S=(2k_{B}T_s/\\lambda^{2})\\Delta\\Omega\\simeq 15\\,$mJy, where \n$k_{B}$ the Boltzmann constant,\n$\\lambda$ the wavelength and $\\Delta\\Omega$ the solid angle\ncovered by a pixel, that is $3.5'\\times 3.5'\\simeq 10^{-6}\\,$sr. \nAt fainter fluxes the counts are overestimated;\nthis is probably due to the contamination from the other signals. \nIn any case, the flux limit for source detection is surprisingly\nlow, even lower of the rms CMB fluctuations ($\\sigma_{CMB}\\simeq 70\\mu$K \nat the resolution limit of our maps), \nsubstantially lower or at least comparable to that\nachieved with other methods which require stronger assumptions \n\\cite{CAYON,HOBSONII}. \nThis high efficiency in detecting point sources illustrates\nthe ability of the method in taking the maximum advantage\nof the differences in frequency and spatial properties of the various \ncomponents. \n\nOn the other hand, we stress that our approach is idealized\nin a number of aspects: beam convolution and \ninstrumental noise have not been taken into account, \nand the same frequency scaling has been\nassumed for all radio sources. \nTherefore more detailed investigations \nare needed to estimate a realistic source detection limit.\n\nFinally note that the quality of the\nseparation is similar on all scales, as shown by the bottom left-hand side \npanels of Figs.~\\ref{icacmb}, \\ref{icasyn}, \\ref{icadust}, \\ref{icaradio}. \nThe exception are radio sources, whose true power spectrum goes to zero at \nlow $\\ell$'s more rapidly than the reconstructed one. \n\n\\subsection{Reconstruction of the frequency dependence}\n\nAnother asset of this technique is the possibility of recovering \nthe frequency dependence of individual components. \nThe outputs can be written as ${\\bf u}=W{\\bf x}$, \nwhere ${\\bf x}=A{\\bf s}$. As previously mentioned, in the ideal case\n$WA$ would be a diagonal matrix containing\nthe constants $d$ for all the signals, multiplied by a permutation\nmatrix. It can be easily seen that, if this is true, the frequency scalings \nof all the components can be obtained by inverting\nthe matrix $W$ and performing the ratio, column by column, of\neach element with the one corresponding to the row corresponding to \na given frequency. However, as pointed out in \\S$\\,3$, \nif some signals are much smaller than others the above \nreasoning is only approximately valid. This is precisely what is \nhappening in our case: we are able\nto accurately recover the frequency scaling of the strongest signals,\nCMB and radio sources, while the others are lost (see \nTable \\ref{frequencyin}).\n\n\\section{Concluding remarks and future developments}\n\nWe have developed a neural network suitable to implement the \nIndependent Component Analysis technique for separating different \nemission components in maps of the sky at microwave wavelengths. \nThe algorithm was applied to simulated maps of a \n$15^{\\circ}\\times 15^{\\circ}$ region of sky at 30, 44, 70, 100 GHz,\ncorresponding to the frequency channels of {\\sc Planck}'s \nLow Frequency Instrument (LFI).\n\nSimulations include the Cosmic Microwave Background, \nextragalactic radio sources and Galactic synchrotron and thermal dust \nemission. The various components have markedly\ndifferent angular patterns, frequency dependences and amplitudes. \n\nThe technique exploits the statistical independence of the different signals \nto recover each individual component with no prior assumption either on \ntheir spatial pattern or on their frequency dependence. \nThe great virtue of this approach is the\ncapability of the algorithm to {\\it learn} how to recover\nthe independent components in the input maps. \nThe price of the lack of {\\it a priori} information\nis that each signal can be recovered\nmultiplied by an unknown constant produced during the\nlearning process itself. However this is not a substantial\nlimitation, since a lot of physics is encoded in the spatial\npatterns of the signals, and ultimately\nthe right normalization of each \ncomponent can be obtained by resorting to independent observations.\n\nThe results are very promising. The CMB map is recovered with an accuracy \nat the 1\\% level. The algorithm is remarkably efficient also in the\ndetection of extragalactic radio sources: almost all \nsources brighter then 15 mJy at 100 GHz (corresponding to $\\simeq 0.7\n\\sigma_{CMB}$, $\\sigma_{CMB}$ being the rms level of CMB fluctuations on \nthe pixel scale) are recovered; on the other hand, it must be stressed \nthat is not directly indicative of what can be achieved in the analysis \nof Planck/LFI data because the adopted resolution ($3'.5\\times 3'.5$) is \nmuch better than that of the real experiment, \ninstrumental noise has been neglected and the \nsame spectral slope was assumed for all sources. \n\nAlso the frequency dependences of the strongest components are \ncorrectly recovered (error on the spectral index of 1\\% for the CMB \nand extragalactic sources).\n\nMaps of subdominant signals (Galactic synchrotron and dust emissions) \nare recovered with rms errors of about 10\\%; their spectral properties \ncannot be retrieved by our technique. \n\nThe reconstruction has equal quality on\nall the scales of the input maps, down to the pixel size.\n\nAll this indicates that this technique is suitable for a variety of \nastrophysical applications, i.e. whenever we want to separate \nindependent signals from different astrophysical processes occurring \nalong the line of sight.\n\nOf course, much work has to be done to better explore the potential \nof the ICA technique. It has to be tested under more realistic \nassumptions, \ntaking into account instrumental noise and the effect \nof angular response functions as well as including a more \ncomplete and accurate characterization of foregrounds.\n\nIn particular, the assumption that the spectral properties of each \nforeground component is independent of position will have to be relaxed \nto allow for spectral variations across the sky. Also, it will be \nnecessary to deal with the fact that Galactic emissions are correlated. \n\nThe technique is flexible enough to offer good prospects in this respect. \nIn the learning stage, the ICA algorithm makes use\nof non-linear functions that, case by case, are chosen to\nminimize the mutual information between the outputs; \nimprovements could be obtained by specializing\nthe ICA inner non-linearities to our specific needs.\nAlso, it is possible to take properly into account \nour prior knowledge on some of the signals to recover, still \ntaking advantage as far as possible of the ability of \nthis neural network approach to carry out a ``blind\" separation.\nWork in this direction is in progress.\n\n\\vskip .1in\nWe warmly thank Luigi Danese for original suggestions.\nWe also thank Krzysztof M. G\\'orski and all the people who\ncollaborated to build the HEALPix pixelization scheme\nextensively used in this work. Work supported in part by ASI and \nMURST. 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(eds), 1999, Microwave Foregrounds, ASP Conf. \nSer. 181\n\\bibitem[Donoho \\& Johnstone 1995]{DONOHO}\nDonoho D.L., Johnstone I. M., 1995, J. Am. Statis. Assoc., 90, 1200.\n\\bibitem[Fixsen et al. 1996]{FIXSEN}\nFixsen D.J., Cheng E.S., Gales J.M., Mather J.C., Shafer R.A.,\nWright E.L., 1996, ApJ, 473, 576\n\\bibitem[Friedman 1987]{FRIEDMAN}\nFriedman J. H., 1987, J. Am. Stat. Ass., 82, 249\n\\bibitem[see G\\'orski et al. 1999]{Heal}\nG\\'orski M., Wandelt B.D., Hansen F.K., Hivon E., \nBanday A.J., 1999, astro-ph/9905275; see also the HEALPix\nweb page at http://www.tac.dk:80/~healpix/\n\\bibitem[]{}\nGull S.F., 1988, in Maximum Entropy and Bayesian Methods in Science\nand Enginereeng, G.J. Erickson, C.R. Smith eds., Kluwer, Dordrech, p. 53\n\\bibitem[Haslam et al. 1982]{H} Haslam C.G.T., et al., 1982,\nA\\&AS, 47, 1\n\\bibitem[Hobson et al. 1998]{HOBSONII} Hobson M.P.,\nBarreiro R.B., Toffolatti L., Lasenby A.N., Sanz J.L.,\nJones A.W., Bouchet F.R., 1999, MNRAS 306, 232\n\\bibitem[Hobson et al. 1998]{HOBSON} Hobson M.P., Jones A.W.,\nLasenby A.N., Bouchet F.R., 1998, MNRAS, 300, 1 \n\\bibitem[Hyv\\\"{a}rinen \\& Oja 1999]{HYVARINEN}\nHyv\\\"{a}rinen A., Oja, E., 1999, Independent Component Analysis:\nA Tutorial,\nhttp://www.cis.hut.fi/~aapo/papers/IJCNN99\\_tutorialweb/ \n\\bibitem[see, e.g., Jawerth et al. 1994]{JAWERTH}\nJawerth B., Sweldens W., 1994, SIAM review, 36 (3), 377\n\\bibitem[Lemari\\'e \\& Meyer 1986]{LEMARIE}\nLemari\\'e P.G., Meyer Y., 1986, Rev. Mat. Ib., 2, 1\n\\bibitem[Mallat 1989]{MALLAT}\nMallat S.G., 1989, IEEE Trans. Pat. Anal. \\& Mach. Int., 11, 674\n\\bibitem[Mandolesi et al. 1998]{MANDOLESI}\nMandolesi N., et al., 1998, {\\sc Planck} Low Frequency Instrument,\nA Proposal Submitted to the ESA for\nthe FIRST/{\\sc Planck} Programme\n%\\bibitem[Mather et al. 1999]{MATHER}\n%Mather, J.C., Fixsen, D.J., Shafer, R.A., Mosier, C., Wilkinson, D.T.,\n%1999, ApJ, 512, 511\n\\bibitem[Ogden et al. 1997]{OGDEN}\nOgden R.T., 1997, Essential Wavelets for Statistical Applications\nand Data Analysis, Birkhauser, Boston\n\\bibitem[Puget et al. 1998]{PUGET}\nPuget J.~L., et~al., 1998, High Frequency Instrument for\nthe {\\sc Planck} Mission, A Proposal Submitted to the ESA for\nthe FIRST/{\\sc Planck} Programme\n\\bibitem[Sanz et al. 1999a]{SANZa}\nSanz J.L., Arg\\\"ueso F., Cay\\'on L., Mart\\'\\i nez-Gonz\\'alez \nE., Barreiro R.B., Toffolatti L., 1999a, MNRAS, 309, 672\n\\bibitem[Sanz et al. 1999b]{SANZb}\nSanz J.L., Barreiro R.B., Cay\\'on L., Mart\\'\\i nez-Gonz\\'alez \nE., Ruiz G.A., D\\'\\i az F.J., Arg\\\"ueso F., Silk J., Toffolatti L.,\n1999b, A\\&A, 140, 99\n\\bibitem[Schlegel et al. 1998]{SFD} Schlegel D.J., Finkbeiner D.P.\n\\& Davies M., 1998, ApJ, 500, 525\n\\bibitem[see Seljak \\& Zaldarriaga 1996]{SZ} Seljak U., Zaldarriaga M.,\n1996, ApJ, 469, 437\n\\bibitem[]{} \nSkilling J., 1988, in Maximum Entropy and Bayesian Methods in Science\nand Enginereeng, G.J. Erickson, C.R. Smith eds., Kluwer, Dordrech, p. 173\n\\bibitem[]{} \nSkilling J., 1989, in Maximum Entropy and Bayesian Methods, Skilling\nJ. ed., Kluwer, Dordrech, p. 53\n%\\bibitem[Smoot et al. 1992]{COBE} Smoot G.F. et al., 1992,\n%ApJL L1\n\\bibitem[Tegmark \\& de Oliveira-Costa (1998)]{TEGMARKCOSTA}\nTegmark M., de Oliveira-Costa A., 1998, ApJ, 500, L83\n\\bibitem[]{}\nTegmark M., Eisenstein D.J.,\nHu W., de Oliveira-Costa A., 2000, ApJ, 530, 133\n\\bibitem[Tenorio et al. 1999]{TENORIO}\nTenorio L., Jaffe A.H., Hanany S., Lineweaver C.H., 1999, MNRAS, 310, 823\n\\bibitem[Toffolatti et al. 1998]{TOFFOLATTI}\nToffolatti L., Arg\\\"ueso F., De Zotti G.,\nMazzei P., Franceschini A., Danese L., Burigana C.,\n1998, MNRAS, 297, 117\n%\\bibitem[see Turner \\& Tyson 1999 for reviews]{TURNER}\n%Turner M.S., Tyson J.A., 1999, astro-ph/9901113,\n%Rev.Mod.Phys. 71 S145\n\\bibitem[Yang \\& Amari 1997]{AMARI2}\nYang H.H., Amari S., 1997, Neural Comp. 9, 1457\n\\end{thebibliography}\n\n\\newpage\n\n\\onecolumn\n\n\\begin{figure}\n%\\psfig{file=isin.ps} %%%,height=2.in,width=3.in}\n\\vskip 3.in\n\\caption{Inputs maps used in the ICA\nseparation algorithm: from top left, in a clockwise sense, \nsimulations of CMB, synchrotron, radio sources and dust\nemission are shown. Radio sources and dust grey scale are is \nnon-linear to better show the signal features. \n}\n\\label{icasissain}\n\\end{figure}\n\\begin{figure}\n%\\psfig{file=isout.ps} %%%,height=2.in,width=3.in}\n\\vskip 3.in\n\\caption{Reconstructed maps produced by the\nICA method; the initial ordering has not been conserved in the outputs.\nFrom top left, in a clockwise sense, we can recognize synchrotron, radio\nsources, dust and CMB. Radio sources and dust grey scale is \nnon-linear as in Fig.1.}\n\\label{icasissaout}\n\\end{figure}\n\\begin{figure}\n%\\psfig{file=icmbw2.ps} %%%,height=4.in,width=4.in}\n\\caption{Top left: input angular power spectra,\nsimulated (solid line) and theoretical (dashed line, see text). Top\nright: the angular power spectrum of the reconstructed CMB patch. Bottom\nleft: quality factor relative to the input/output angular spectra.\nBottom right: scatter plot and linear fit (dashed line)\nfor the CMB input/output maps.\n}\n\\label{icacmb}\n\\end{figure}\n\\begin{figure}\n%\\psfig{file=isynw2.ps} %%%,height=4.in,width=4.in}\n\\caption{Top panels: angular power spectra for the\nsimulated input (left) and reconstructed (right) synchrotron map.\nBottom left: quality factor relative to the input/output angular spectra.\nBottom right: scatter plot and linear fit (dashed line)\nfor the synchrotron input/output maps.\n}\n\\label{icasyn}\n\\end{figure}\n\\begin{figure}\n%\\psfig{file=idustw2.ps} %%%,height=4.in,width=4.in}\n\\caption{Top panels: angular power spectra for the simulated input \n(left) and reconstructed (right) dust emission map.\nBottom left: quality factor relative to the input/output angular spectra.\nBottom right: scatter plot and linear fit (dashed line) for\nthe dust input/output maps.\n}\n\\label{icadust}\n\\end{figure}\n\\begin{figure}\n%\\psfig{file=iradiow2.ps} %%%,height=4.in,width=4.in}\n\\caption{Top panels: angular power spectra for the\nsimulated (left) and reconstructed (right) radio source map.\nBottom left: quality factor relative to the input/output angular spectra.\nBottom right: scatter plot and linear fit (dashed line)\nfor the radio source emission input/output maps.}\n\\label{icaradio}\n\\end{figure}\n\\begin{figure}\n%\\psfig{file=radioc.ps} %%%,height=4.in,width=4.in}\n\\caption{Cumulative number of pixels as a function of the\nthreshold $\\Delta s$ (see text for more details):\ninput (dashed line) versus output (solid line).}\n\\label{numbercounts}\n\\end{figure}\n\n\\end{document}\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002257.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[Amari \\& Chichocki 1998]{AMARI}\nAmari S., Chichocki A., 1998, Proc. IEEE, 86, 2026\n\\bibitem[Bell \\& Sejnowski 1995]{BELL}\nBell A.J., Sejnowski T.J., 1995, Neural Comp. 7, 1129\n%\\bibitem[Bennet et al. 1996]{BENNET}\n%Bennet, C. et al., 1996, Amer. Astro. Soc. Meet., 88.05\n\\bibitem[Bouchet et al. 1999]{WF}\nBouchet F.R., Prunet S., Sethi S.K., 1999, MNRAS, 302, 663 \n\\bibitem[]{TE}\nTegmark M., Efstathiou G., 1996, MNRAS 281, 1297\n\\bibitem[Cay\\'on et al. 2000]{CAYON}\nCay\\'on L., Sanz J.L., Barreiro R.B., Mart\\'\\i nez-Gonz\\'alez\nE., Vielva P., Toffolatti L., Silk J., Diego J.M., Arg\\\"ueso F.,\n2000, MNRAS, in press, astro-ph/9912471\n\\bibitem[Comon 1994]{COMON}\nComon P., 1994, Signal Processing, 36, 287.\n\\bibitem[]{}\nde Oliveira-Costa A., Tegmark M. (eds), 1999, Microwave Foregrounds, ASP Conf. \nSer. 181\n\\bibitem[Donoho \\& Johnstone 1995]{DONOHO}\nDonoho D.L., Johnstone I. M., 1995, J. Am. Statis. Assoc., 90, 1200.\n\\bibitem[Fixsen et al. 1996]{FIXSEN}\nFixsen D.J., Cheng E.S., Gales J.M., Mather J.C., Shafer R.A.,\nWright E.L., 1996, ApJ, 473, 576\n\\bibitem[Friedman 1987]{FRIEDMAN}\nFriedman J. H., 1987, J. Am. Stat. Ass., 82, 249\n\\bibitem[see G\\'orski et al. 1999]{Heal}\nG\\'orski M., Wandelt B.D., Hansen F.K., Hivon E., \nBanday A.J., 1999, astro-ph/9905275; see also the HEALPix\nweb page at http://www.tac.dk:80/~healpix/\n\\bibitem[]{}\nGull S.F., 1988, in Maximum Entropy and Bayesian Methods in Science\nand Enginereeng, G.J. Erickson, C.R. Smith eds., Kluwer, Dordrech, p. 53\n\\bibitem[Haslam et al. 1982]{H} Haslam C.G.T., et al., 1982,\nA\\&AS, 47, 1\n\\bibitem[Hobson et al. 1998]{HOBSONII} Hobson M.P.,\nBarreiro R.B., Toffolatti L., Lasenby A.N., Sanz J.L.,\nJones A.W., Bouchet F.R., 1999, MNRAS 306, 232\n\\bibitem[Hobson et al. 1998]{HOBSON} Hobson M.P., Jones A.W.,\nLasenby A.N., Bouchet F.R., 1998, MNRAS, 300, 1 \n\\bibitem[Hyv\\\"{a}rinen \\& Oja 1999]{HYVARINEN}\nHyv\\\"{a}rinen A., Oja, E., 1999, Independent Component Analysis:\nA Tutorial,\nhttp://www.cis.hut.fi/~aapo/papers/IJCNN99\\_tutorialweb/ \n\\bibitem[see, e.g., Jawerth et al. 1994]{JAWERTH}\nJawerth B., Sweldens W., 1994, SIAM review, 36 (3), 377\n\\bibitem[Lemari\\'e \\& Meyer 1986]{LEMARIE}\nLemari\\'e P.G., Meyer Y., 1986, Rev. Mat. Ib., 2, 1\n\\bibitem[Mallat 1989]{MALLAT}\nMallat S.G., 1989, IEEE Trans. Pat. Anal. \\& Mach. Int., 11, 674\n\\bibitem[Mandolesi et al. 1998]{MANDOLESI}\nMandolesi N., et al., 1998, {\\sc Planck} Low Frequency Instrument,\nA Proposal Submitted to the ESA for\nthe FIRST/{\\sc Planck} Programme\n%\\bibitem[Mather et al. 1999]{MATHER}\n%Mather, J.C., Fixsen, D.J., Shafer, R.A., Mosier, C., Wilkinson, D.T.,\n%1999, ApJ, 512, 511\n\\bibitem[Ogden et al. 1997]{OGDEN}\nOgden R.T., 1997, Essential Wavelets for Statistical Applications\nand Data Analysis, Birkhauser, Boston\n\\bibitem[Puget et al. 1998]{PUGET}\nPuget J.~L., et~al., 1998, High Frequency Instrument for\nthe {\\sc Planck} Mission, A Proposal Submitted to the ESA for\nthe FIRST/{\\sc Planck} Programme\n\\bibitem[Sanz et al. 1999a]{SANZa}\nSanz J.L., Arg\\\"ueso F., Cay\\'on L., Mart\\'\\i nez-Gonz\\'alez \nE., Barreiro R.B., Toffolatti L., 1999a, MNRAS, 309, 672\n\\bibitem[Sanz et al. 1999b]{SANZb}\nSanz J.L., Barreiro R.B., Cay\\'on L., Mart\\'\\i nez-Gonz\\'alez \nE., Ruiz G.A., D\\'\\i az F.J., Arg\\\"ueso F., Silk J., Toffolatti L.,\n1999b, A\\&A, 140, 99\n\\bibitem[Schlegel et al. 1998]{SFD} Schlegel D.J., Finkbeiner D.P.\n\\& Davies M., 1998, ApJ, 500, 525\n\\bibitem[see Seljak \\& Zaldarriaga 1996]{SZ} Seljak U., Zaldarriaga M.,\n1996, ApJ, 469, 437\n\\bibitem[]{} \nSkilling J., 1988, in Maximum Entropy and Bayesian Methods in Science\nand Enginereeng, G.J. Erickson, C.R. Smith eds., Kluwer, Dordrech, p. 173\n\\bibitem[]{} \nSkilling J., 1989, in Maximum Entropy and Bayesian Methods, Skilling\nJ. ed., Kluwer, Dordrech, p. 53\n%\\bibitem[Smoot et al. 1992]{COBE} Smoot G.F. et al., 1992,\n%ApJL L1\n\\bibitem[Tegmark \\& de Oliveira-Costa (1998)]{TEGMARKCOSTA}\nTegmark M., de Oliveira-Costa A., 1998, ApJ, 500, L83\n\\bibitem[]{}\nTegmark M., Eisenstein D.J.,\nHu W., de Oliveira-Costa A., 2000, ApJ, 530, 133\n\\bibitem[Tenorio et al. 1999]{TENORIO}\nTenorio L., Jaffe A.H., Hanany S., Lineweaver C.H., 1999, MNRAS, 310, 823\n\\bibitem[Toffolatti et al. 1998]{TOFFOLATTI}\nToffolatti L., Arg\\\"ueso F., De Zotti G.,\nMazzei P., Franceschini A., Danese L., Burigana C.,\n1998, MNRAS, 297, 117\n%\\bibitem[see Turner \\& Tyson 1999 for reviews]{TURNER}\n%Turner M.S., Tyson J.A., 1999, astro-ph/9901113,\n%Rev.Mod.Phys. 71 S145\n\\bibitem[Yang \\& Amari 1997]{AMARI2}\nYang H.H., Amari S., 1997, Neural Comp. 9, 1457\n\\end{thebibliography}"
}
] |
astro-ph0002258
|
Dithering Strategies for Efficient Self-Calibration of Imaging Arrays
|
[
{
"author": "Richard G. Arendt\\altaffilmark{1}"
},
{
"author": "D. J. Fixsen\\altaffilmark{1}"
},
{
"author": "\\& S. Harvey Moseley"
}
] |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% With high sensitivity imaging arrays, accurate calibration is essential to achieve the limits of detection of space observatories. One can simultaneously extract information about the scene being observed and the calibration properties of the detector and imaging system from redundant dithered images of a scene. There are large differences in the effectiveness of dithering strategies for allowing the separation of detector properties from sky brightness measurements. In this paper, we quantify these differences by developing a figure of merit (FOM) for dithering procedures based on their usefulness for allowing calibration on all spatial scales. The figure of merit measures how well the gain characteristics of the detector are encoded in the measurements, and is independent of the techniques used to analyze the data. Patterns similar to the antenna arrangements of radio interferometers with good $u-v$ plane coverage, are found to have good figures of merit. We present patterns for both deep surveys of limited sky areas and for shallow surveys. By choosing a strategy that encodes the calibration in the observations in an easily extractable way, we enhance our ability to calibrate our detector systems and to reach the ultimate limits of sensitivity which are required to achieve the promise of many missions.
|
[
{
"name": "dither.tex",
"string": "%\\documentclass[preprint]{aastex} %aastex v5.0\n\\documentstyle[aaspp4]{article} %aastex v4.0\n\\begin{document}\n\\slugcomment{Scheduled for ApJ, v536n1, Jun 10, 2000}\n\\title{Dithering Strategies for Efficient Self-Calibration of Imaging Arrays}\n\\author{Richard G. Arendt\\altaffilmark{1}, D. J. Fixsen\\altaffilmark{1},\n\\& S. Harvey Moseley}\n\\affil{Laboratory for Astronomy and Solar Physics,\\\\\nCode 685, NASA GSFC, Greenbelt, MD 20771;\\\\\narendt, fixsen, moseley@stars.gsfc.nasa.gov}\n\\altaffiltext{1}{Raytheon ITSS}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{abstract}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nWith high sensitivity imaging arrays,\naccurate calibration is essential to achieve the limits of\ndetection of space observatories. One can simultaneously\nextract information about the scene being observed and the\ncalibration properties of the detector and imaging system\nfrom redundant dithered images of a scene.\nThere are large differences in the\neffectiveness of dithering strategies for\nallowing the separation of detector properties from sky\nbrightness measurements. In this paper, we quantify these\ndifferences by developing a figure of merit (FOM) for dithering \nprocedures based on their usefulness for allowing calibration on \nall spatial scales. \nThe figure of merit measures how well the \ngain characteristics of the detector are encoded in the \nmeasurements, and is independent of the \ntechniques used to analyze the data.\nPatterns similar to the antenna arrangements \nof radio interferometers with good $u-v$ plane coverage, are found\nto have good figures of merit. We present\npatterns for both deep surveys of limited sky areas and for\nshallow surveys. \nBy choosing a strategy that encodes the calibration in the\nobservations in an easily extractable way, we enhance our\nability to calibrate our detector systems and to reach the\nultimate limits of sensitivity which are required to\nachieve the promise of many missions.\n\\end{abstract}\n\\keywords{instrumentation: detectors --- methods: data analysis ---\ntechniques: photometric}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Introduction}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nIn order to achieve their required performance, many\nobserving systems must observe with sensitivities near\ntheir confusion limits. \nMany instruments are capable of reaching these limits in crowded \nstellar fields such as the Galactic center. Future instruments\nsuch as the Infrared Array Camera (IRAC) and the \nMultiband Imaging Photometer (MIPS) on the\n{\\it Space Infrared Telescope Facility} ({\\it SIRTF}) and those\nplanned for the Next Generation Space Telescope (NGST) will\nbe able to reach limits in which the confusion of extragalactic\nsources becomes significant.\nIn general, the measurement noise is determined by both the statistical\nfluctuations of the photon flux and\nuncertainties in detector gain and offset. Any successful\ncalibration procedure must determine these detector\nparameters sufficiently accurately so that their uncertainties\nmake small contributions to the measurements errors\ncompared to those of the background fluctuations.\nIf the science done with the instrument requires\nsubstantial spatial or temporal modeling,\ncalibration requirements become more demanding, ultimately\nrequiring similar integration time for observation and\ncalibration as in the case of the {\\it COBE} FIRAS instrument\n(Mather et al. 1994; Fixsen et al. 1994). Additionally, in such cases\nrobust error estimators are often needed. A common\nmethod to determine the instrument calibration is to look at known\ncalibration scenes (e.g. a dark shutter, an illuminated screen, \nor a blank region of sky) \nof different brightnesses to deduce gain\nand offset of each detector pixel. This requires a well\ncharacterized calibration source and often a change in instrument\nmode to carry out the measurement.\nThis procedure may introduce systematic errors relating to the\nextrapolations from the time and conditions of the calibration observations\nto the time and conditions of the sky observations and \nfrom the intensity (and assumed\nflatness) of the calibration source to the intensity of the observed\nsky. A different approach is to use the measurements of the sky alone to\nextract the calibration data for the system. \nBy using the sky observations for calibration, the systematic\nerrors introduced by applying a calibration derived from a distinctly\ndifferent data set are eliminated. Such methods\nrequire a set of dithered images, where a single sky location is\nimaged on many different detector pixels. \n\nTypical CCD and IR array data reduction procedures for a set of dithered \nimages make use of a known or measured dark frame\n($F^p$) and derive the flat field ($G^p$) through taking the weighted average\nor median value of all data ($D^i$) observed by each detector pixel $p$ \n($i \\in p$) in a stack of dithered images (e.g.\nTyson 1986, Tyson \\& Seitzer 1988, Joyce 1992, Gardner 1995). \nThe least squares solution of \n\\begin{equation}\n{\\cal D}^i = G^p S^0\n\\end{equation}\nwhere ${\\cal D}^i = D^i - F^p$ ($i \\in p$) and $S^0$ is the perfectly flat \nsky intensity, for $G^p$, the flat field, is\n\\begin{equation}\nG^p = \\frac{\\sum_{i \\in p}{\\cal D}^i W_i}{\\sum_{i \\in p}W_i} \\frac{1}{S^0}\n\\end{equation}\nwhich is simply the weighted average of the data collected by each detector \npixel normalized by the constant sky intensity (to be determined later though\nthe absolute calibration of the data). \nThe weights, $W_i$, are normally determined by the inverse variance of the\ndata, but may also be set to zero to exclude sources above the background \nlevel.\nThe use of the median, instead \nof the weighted average, also rejects the outliers arising from \nthe observations of real sources instead of the flat background, $S^0$, \nand formally corresponds to a minimization of the mean absolute deviation\nrather than a least squares procedure. \nIn either form, this method requires \nobservations of relatively empty fields where variations in the background \nsky level are not larger than the faintest signal that is sought. \nThus, throughout this paper we refer to such procedures as\n``flat sky'' techniques.\nAs instrumentation improves and telescope sensitivity increases, \nthis condition is becoming harder to fulfill. \nIn fields at low Galactic latitude, stellar and nebular confusion \ncan be unavoidable, and at high latitude deep imaging (particularly in \nthe infrared) is expected to reach the extragalactic confusion limit.\nIn such cases, because of the complex background, and in other \ncases where external influences (e.g. moonlight, zodiacal light) create\na sky background with a gradient, the flat sky\napproach does not work and a more comprehensive approach must be used.\n\nSuch an approach has been presented by Fixsen et al. (2000) who \ndescribe the general least squares solution for deriving \nthe sky intensity $S^{\\alpha}$ at each pixel $\\alpha$, in addition to the \ndetector gain (or flat field) $G^p$ and offset (or dark current + bias) $F^p$\nat each detector pixel $p$, where each measurement, $D^i$, is represented by\n\\begin{equation}\nD^i = G^p S^{\\alpha} + F^p.\n\\end{equation}\n(Throughout this paper we refer to the procedure described by Fixsen et al. \n(2000) as the ``least squares'' procedure.)\nThey show how the problem of inverting large matrices can be \ncircumvented, and how the formulation of the problem allows for explicit \ntracking of the uncertainties and correlations in the derived $G^p$, $F^p$, \nand $S^{\\alpha}$. Fixsen et al. also show that although the formal size of the \nmatrices used in the least squares solution increases as $P^2$, where $P$ is \nthe number of pixels in the detector array, the number of non-zero elements \nin these matrices increases only as $M\\times P$, where $M$ is the number of \nimages in the data set. In practice, the portion of the least squares solution \nfor the detector gains and offsets is calculated first, and then the data \nare corrected to produce images of the sky ($S^{\\alpha}$) that are \nregistered and mapped into a final single image.\nBecause this approach explicitly assumes a different sky\nintensity at each pixel, the crowded or confused fields that can cause the \nflat sky technique to fail are an aid to finding the least\nsquares solution. Thus, the need for chopping away from a complex source \nin order to observe a blank sky region is eliminated.\nThe simultaneous solution for both the detector gain and offset also \neliminates the need for dark frame measurements, although if dark frame\nmeasurements are available then they can be used with the other data to \nreduce the uncertainty of the procedure. \nWe note that this general least squares approach may also be applied in \nnon-astronomical situations (e.g. terrestrial observing) where complex images\nare the norm.\n\nThe flat sky technique works well in situations where \nall detector pixels \nspend most of the time observing the same celestial calibration source,\nnamely the flat sky background. For this technique, dithering is required \nonly to ensure that all pixels usually do see the background.\nBecause all pixels have observed the same\nsource, the relative calibrations of any two pixels in the detector are\ntightly constrained, regardless of the separation between the pixels, i.e.\n\\begin{equation}\n\\frac{G^1}{G^2} = \\frac{G^1 S^0}{G^2 S^0} = \\frac{{\\cal D}^1}{{\\cal D}^2}.\n\\end{equation}\nHowever, in the more general least squares solution of Fixsen et al. (2000), \neach sky pixel ($S^{\\alpha}$) \nrepresents a different celestial calibration source. The only pixels\nfor which the relative calibrations are tightly constrained are \nthose that through dithering have observed common sky pixels. Pixels \nthat do not observe a common sky pixel are still constrained, though \nless directly, by intermediate detector pixels that do observe \ncommon sky pixels. For example, the relative calibration of detector\npixels 1 and 3 which observe sky pixels $\\alpha$ and $\\beta$ respectively,\nbut no common sky pixels, may be established if an intermediate detector\npixel 2 does observe both sky pixels $\\alpha$ and $\\beta$, i.e.\n\\begin{equation}\n\\frac{G^1}{G^3} = \n\\frac{G^1 S^{\\alpha}}{G^2 S^{\\alpha}} \\frac{G^2 S^{\\beta}}{G^3 S^{\\beta}} = \n\\frac{{\\cal D}^{1\\alpha}}{{\\cal D}^{2\\alpha}} \\frac{{\\cal D}^{2\\beta}}{{\\cal D}^{3\\beta}}.\n\\end{equation}\nOther detector pixels might require multiple intermediate pixels to \nestablish a relative calibrations. As the chain of intermediate\npixels grows longer, the uncertainty of the relative calibration of the\ntwo pixels also grows. Therefore, when applying the least squares solution, \nthe exact dither pattern becomes much more important than in the \nflat sky technique. For the least squares solution to \nproduce the smallest uncertainty, \nthe dither pattern should be one that establishes the tightest \ncorrelations between all pairs of detector pixels using a small\nnumber of dithered images. Even if one is only interested \nin small scale structure on the sky (e.g. point sources), it is still \nimportant to have the detector properly calibrated on {\\it all} spatial \nscales to prevent large scale detector variations from biasing results \nderived for both sources and backgrounds imaged in different parts of \nthe array.\n\nWhether obtained by flat sky, least squares, or other techniques, \nthe quality of the calibration is ultimately determined by its\nuncertainties. For the least squares solution of Fixsen et al. (2000), \nunderstanding the uncertainties is relatively straight forward, because it\nis a linear process, i.e. $P^{\\alpha} = L^{\\alpha}_i D^i$ where $P^{\\alpha}$\nis the set of fitted parameters, $D^i$ is the data, and $L^{\\alpha}_i$ is \na linear operator. Then, given a covariance matrix of the data, $\\Sigma^{ij}$,\nthe solution covariance matrix is \n$V^{\\alpha\\beta} = L^{\\alpha}_i L^{\\beta}_j \\Sigma^{ij}$. \nFor a nonlinear process such as a median filter the uncertainties are \nharder to calculate. The diagonal terms of the covariance matrix of the \nsolution might be\nsufficiently well approximated by Monte Carlo methods, but the off-diagonal\ncomponents are far more numerous and often more pernicious as the effects\ncan be more subtle than the simple uncertainty implied by the diagonal\ncomponents. For this reason the off-diagonal components are often ignored. \nCreating final images at subpixel resolution (e.g. ``drizzle'', Fruchter\n\\& Hook 1998) may introduce additional correlations beyond those\ndescribed by the covariance matrix, and disproportionately \nincrease the effects of the off-diagonal elements of the correlation matrix. \nAccurate knowledge of all these \nuncertainties is especially important for studies that seek spatial \ncorrelations within large samples, such as deep galaxy surveys\nor studies of cosmic backgrounds, so that any detected correlations are \ncertifiably real and not artifacts caused by the calibration errors\nand unrecognized because of incomplete or faulty knowledge of the \nuncertainties.\n\nTable 1 itemizes some of the features of each data analysis technique.\nThe remainder of this paper is concerned with characterizing what makes a\ndither pattern good for self-calibration purposes using the least squares \nsolution. We present a ``figure of merit'' (FOM) which can be used as a\nquantitative means of ranking\nthe suitability of different dither patterns (\\S2). We then present\nseveral examples of good, fair and poor dither patterns (\\S3), and investigate\nhow changes to the patterns affect their FOM. In \\S4, we show how dithered\ndata can be collected in the context of both\ndeep and shallow surveys. We also\ninvestigate the combined effects of dithering and the survey grid geometry on\nthe completeness of coverage provided by the survey. Section 5 discusses\nmiscellaneous details of the application and implementation of dithering.\nSection 6 summarizes the results.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Evaluation of Dithering Strategies}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Dithering}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nTo be specific, we define the process of ``dithering'' as obtaining\nmultiple mostly overlapping images of a single field. \nNormally, each of the dithered \nimages has a different spatial offset from the center of the field, and none\nof the offsets of the dither pattern is larger than about half of the size \nof the detector array.\nGenerally, the set of dithered images is averaged in some manner into a \nsingle high-quality image for scientific analysis.\nThis is distinct from the processes of ``surveying'' or ``mapping'', in which\na field much larger than the size of the array is observed, using images that\nare only partially overlapping. If survey data is combined into a \nsingle image for analysis, then the process required is one of \nmosaicking more than averaging.\nA region may be surveyed or mapped using dithered images at each of the survey\ngrid points. \n\nThere are several reasons why an observer might wish to collect dithered data.\nOne is simply to make sure that no point in the \nfield remains unobserved \nbecause it happened to be targeted by a defective pixel in the detector array.\nTo meet this objective, two dither images would suffice, provided their \noffsets are selected to prevent two different bad pixels from targeting the \nsame sky location. A second reason to dither is so that point\nsources sample many different subpixel locations or phases. Such a data set \nallows recovery of higher resolution in the event that the detector pixel \nscale undersamples the instrumental point spread function. Several procedures\nhave been developed for this type of analysis, which is commonly applied to \nHST imaging data and 2MASS data (e.g. Fruchter \\& Hook 1998; Williams \net al. 1996; Lauer 1999; Cutri et al. 1999). \nA third reason to dither is to obtain a data set which contains sufficient \ninformation to derive the detector calibration and the sky intensities from \nthe dithered data alone. As discussed in the introduction, \nfor the flat sky approach, the flatness of the background is a \nmore important concern than the particular dither pattern. However, \nthis is reversed when the least squares solution to the calibration is \nderived (Fixsen et al. 2000). The structure of the sky is less important \nthan the dither pattern which needs to be chosen carefully so that the \nsolution is well-constrained. \n\nIn an attempt to cover as wide a field as possible, the detector array\noften undersamples the instrument point spread function. This undersampling \ncan lead to increased noise in the least squares calibration procedure. \nThere are several ways this extra noise can be alleviated. One way is\nto use strictly integer-pixel offsets in the dither pattern. However, \nthis requires very precise instrument control, and eliminates the possibility \nof reconstruction of the image at subpixel resolution (i.e. resolution \ncloser to that of the point spread function). A second way to reduce noise is\nto assign lower weights to data where steep intensity gradients are present.\nA third way of dealing with the effects of undersampled data is to use\nsubpixel interlacing of the sky pixels within the least squares solution \nprocedure. This technique may require additional dithering over the region \nsince the interlaced sky subpixels are covered less densely than full \nsize pixels. A fourth means is that the least squares procedure of \nFixsen et al. (2000) could be modified to account for each datum ($D^i$) \narising from a combination of several pixel (or subpixel) sky intensities \n($S^{\\alpha}$). This is a significant complication of the procedure. \n\nAfter the least squares method is used to derived the detector \ncalibration, users can always apply the method of their choice (e.g. \n``drizzle'' described by Fruchter \\& Hook 1998) \nfor mapping the set of calibrated images into a single subpixelized image. \nSuch methods may or may not allow continued tracking of the uncertainties and\ntheir correlations that the least squares procedure provides.\n\nDithering involves repointing the telescope or instrument, \nand thus may require additional\ntime compared to simply taking multiple exposures of the same field. \nMultiple exposures of the same field without dithering would \nallow rejection of data affected\nby transient effects (e.g. cosmic rays), and improved sensitivity \nthrough averaging exposures, but of course lack the benefits described above.\nWhether the time gained by not dithering outweighs the benefits lost, \nwill depend on the instrument and the observer's scientific goals.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{A Figure of Merit}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nThe accuracy of the calibration of an array detector cannot be fully specified\nby a single number or even a single number per detector pixel. The\nfull covariance matrix is necessary to provide a complete description \nof the uncertainties. The magnitude of the diagonal elements \nof the covariance matrix (i.e. $\\sigma^2_p$) is determined primarily by\nthe noise characteristics of the instrument and the sky, and is sensitive\nto the number of images collected in a set of dithered data, but not to\nthe dither pattern. The off-diagonal elements of the covariance matrix \nare sensitive to the dither pattern, and through the correlations they \nrepresent, any measurements made from the calibrated data will contain\nsome imprint of the dither pattern. \n(In general these correlations degrade the signal quality although they\ncan improve the results of some types of measurements depending on\nwhether the correlations are positive or negative and whether the two\ndata elements are used with the same or opposite sign in the measurement.)\nIn order to obtain the best calibration,\none would like to use a dither pattern that minimizes the correlations \nit leaves in the calibrated data. Since comparison of the entire \ncovariance matrices for different dither patterns is awkward, we adopt\na single number, a ``figure of merit'', that is intended to provide a generic\nmeasure of the relative size of the off diagonal terms of the covariance \nmatrix. \nThe figure of merit (FOM) is designed only to compare different dither \npatterns rather than investigating all of the details of a full \nobserving system (i.e. particular telescope/instrument combinations). \nThe instrumental details matter of course, and in practice they may \nplace additional constraints in choosing the dither pattern. \n\nHere we make several simplifying assumptions to ease the \ncalculations and comparisons. First we assume that all of the \ndetector pixels have approximately the same noise and gain.\nNext we assume that the noise is independent of sky position, either because\nthe Poisson counting statistics are not important or the observed field\nis so uniform that the photon counting statistics do not vary appreciably\nacross the field.\nWith these assumptions we can simultaneously solve for both the \ngain and/or offset for each detector pixel and the sky brightness of \neach sky pixel (Fixsen et al. 2000). The\nsolution necessarily introduces correlations into the uncertainties.\n\nFor the figure of merit we choose only a single pixel at the center \nof the array and look at its correlations. This\nis done to reduce the calculational burden which includes 4 billion \ncorrelations for a modest $256\\times 256$ detector. Since all of the pixels are\nlocked to the same dither pattern the correlations are similar for the other\npixels (discussed below).\nWe sum the absolute value of the correlations between the \ncentral pixel and all of the other pixels. \nThis is compared with the variance of the central pixel, \n$\\sigma^2_{p_0}$,\nas this is the irreducible uncertainty due to detector noise alone. \nThus, we define the figure of merit ($FOM$) as:\n\\begin{equation}\nFOM = \\frac{\\sigma^2_{p_0}}{\\sum_{i\\in {\\rm\\ all\\ pixels}} |V_{ip_0}|}\n\\end{equation}\nwhere $V$ is the covariance matrix of the detector parameters. \nThe absolute value is used here to ensure that the sum will be small\nonly if all of the terms are small, not because some of the frequent\nnegative correlations happen to cancel the positive correlations.\nIn detail,\nthe FOM is a function ($f(x) \\approx 1/(1+x)$) of the mean absolute value\nof the normalized off-diagonal elements of the covariance matrix.\nWith this definition, the FOM is bounded on the range [0,1], and can \nbe thought of as an efficiency of encoding correlations in the dither \npattern, i.e. a high FOM is desired in a dither pattern. \n\nEquation 6 is not unique. A wide variety of possible quantitative\nfigures of merit could be calculated. Ideally one would choose the FOM that \ngives the lowest uncertainties in the final answer. This can be done if the \nquestion, i.e. quantity to be measured or scientific goal, \nis well determined. In that case the question can be posed as a vector\n(or if there is a set of questions, a corresponding \nset of vectors in the form of a\nmatrix). The vector (or matrix) can then be dotted on either side of the\ncovariance matrix and the resulting uncertainty minimized. There are several\nproblems in this approach. One is that the matrix is too large to \npractically fit in most computers. A second problem is that the question may \nnot be known before the data are collected. A third problem is that the same \ndata may be used to answer several\nquestions. To deal with the first issue we use only a single row or column\nof the symmetric covariance matrix. As shown below, the rows of the matrix\nhave a similar structure over most of the array. To deal with the other two\nissues, the FOM uses the sum the absolute value of all of the terms. This may \nnot be the ideal FOM for a specific measurement, but it should be a good\nFOM for a wide variety of measurements to be made from the data. \n\nThroughout this paper, we calculate the FOM based on calibration \nwhich only seeks to determine the detector gains or offsets, but not both.\nWhen both gains and offsets are sought, the solution for the covariance\nmatrix contains degeneracies that are only broken by the presence \nof a non-uniform sky brightness (Fixsen et al. 2000). The FOM when solving\nfor one detector parameter is similar to that which would \napply when solving for both gains and offsets.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Dither Patterns and Radio Interferometers}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nIn order to compute relative gain and/or offset, two detector pixels must\nobserve the same sky pixel or have a connection through other detector\npixels that mutually observe one or more sky pixels. A shorter path of \nintermediate detectors implies a tighter connection and lower uncertainties.\nOne goal of dithering is to tighten the connections between\ndetectors and thus lower the uncertainties. This combinatorial problem happens\nto share geometrical similarities with another problem that has \nbeen dealt with previously,\nnamely covering the $u-v$ plane with a limited number of antennas in a radio \ninterferometer. \n\nFigure 1 shows the $u-v$ coverage of the VLA for a snapshot of a source at \nthe zenith. Each antenna pair leads to a single sample marked with a dot \nin the $u-v$ plane. Also shown is the map of $|V_{ip_0}|$ generated by using\na 27-position dither pattern with the same geometry as the \nVLA array (\\S3.2). The strongest correlations are found at locations \nof the direct dither steps corresponding to the VLA baselines.\nHowever, the non-zero correlations (and anti-correlations) found elsewhere in \nthe map make a significant contribution to the total FOM.\n\\begin{figure}[t]\n\\plotone{fig1.eps}\n\\caption{On the left is the $u-v$ baseline coverage of the VLA for\na snapshot of a source at the zenith. In the center and on the right is\nthe map of $|V_{ip_0}|$ for a ``VLA'' dither pattern, stretched to emphasize\nthe similarity to the VLA $u-v$ plane coverage, and the weaker correlations\nrespectively.}\n\\end{figure}\n\nFigure 2 shows maps of $|V_{ip_0}|$ generated using different choices of\n$p_0$. These maps illustrate that the correlations of all pixels are similar \nin structure to those of the central pixel, but the finite size of the \ndetector limits the correlations available to pixels near the detector edges.\nThe dither pattern used in this demonstration is the VLA pattern\ndescribed in \\S3.2.\n\\begin{figure}[t]\n\\plotone{fig2.eps}\n\\caption[]{The panels show the $|V_{ip_0}|$ correlations for detectors at \nthe locations (128,128), (64,128), (32,128), (0,128), (64,64), \nand (0,0) in a $256\\times256$ array \n(left to right and top to bottom). Dark spots represent \nstrong correlations. The dither pattern used to calculate\nthese correlations is a 27-point VLA pattern.}\n\\end{figure}\n\nDespite the similar geometries of radio interferometer $u-v$ coverage and \ndither pattern maps of $|V_{ip_0}|$, several important differences should be\nnoted. \nFirst, with radio telescopes only direct pairs of antennas\n(although all pairs) can be used to generate interference patterns, whereas\nwith dither patterns a path involving several \nintermediate detector pixels can be \nused to generate an indirect correlation. However, the greater the number of \nintermediate steps that must be used to establish a correlation, the noisier \nit will be. \nSecond, the $u-v$ coverage is derived instantly. Observing over a \nperiod of time fills in more of the $u-v$ plane as the earth's rotation \nchanges the interferometer baselines relative to the target source. In \ncontrast, the $|V_{ip_0}|$ coverage shown in Figs. 1 and 2 is only achieved\nafter collecting dozens of dithered images. To fill in additional coverage,\nthe dither pattern must be altered directly because there is no equivalent\nof the earth rotation that alters the geometry of the instrument with \nrespect to the sky. Another important difference is that the short\ninterferometer baselines (found near the center of the $u-v$ plane) are\nsensitive to the large-scale emission. For dither patterns the inverse \nrelation holds. Direct correlations between nearby detector pixels are \nsensitive to small-scale structure in the detector properties and sky\nintensities. Thus the outer edge of the interferometer's $u-v$ coverage\nrepresents a limit on the smallest-scale structure that can be resolved,\nwhile the outer edge of strong $|V_{ip_0}|$ correlations represents a \nlimit on the largest-scale variations that can be reliably distinguished.\n\nOverall, the geometrical similarities suggest that patterns used and \nproposed for radio interferometers may prove to be a useful basis set for\nconstructing dither patterns. In the following section, we calculate the FOM\nfor several patterns inspired by radio interferometers in addition to \nother designs.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Various Dither Patterns}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nSeveral general algorithms for generating dither patterns have been examined. \nIn many cases, we have also explored variants of the basic algorithms by\nchanging functional forms, adding random perturbations, or applying overall\nscale factors. We have also tested several specific examples of dither patterns\nfrom various sources. Examples of the patterns described below are shown in \nFigure 3. All tests reported here assumed detector dimensions \nof $256\\times 256$ pixels unless otherwise noted.\n\\begin{figure}[t]\n\\plotone{fig3.eps}\n\\caption[]{Examples of some of the tested dither patterns. The dots\nmark the center of the array for each of the $M$ positions for each pattern.}\n\\end{figure}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Reuleaux Triangle}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nTake an equilateral triangle and draw three 60\\arcdeg\\ arcs connecting each pair\nof vertexes, while centered on the opposite vertex. The resulting fat triangle \nis a Reuleaux triangle. This basic shape has been used to set the geometry of\nthe Sub-Millimeter Array (SMA) on Mauna Kea (Keto 1997). \n\nThis shape can be used as a dither pattern by taking equally spaced steps\nalong each side of the Reuleaux triangle. The length of the steps is set\nby the overall size of the triangle (a free parameter) and the number of\nframes to be used in the pattern. For an interferometer, Keto (1997) shows \nthat the $u-v$ coverage can be improved by displacing the antennas from \ntheir equally spaced positions around the triangle. \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{VLA}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nThe ``Y''-shaped array configurations of the Very Large Array (VLA) radio \ninterferometer are designed such that the antenna positions from the center\nof the array are proportional to $i^{1.716}$ (Thompson, et al. 1980).\nThe three arms of the array are separated from each other by \n$\\sim 120$\\arcdeg. We have adopted this geometry to provide a dither pattern\nwith positions chosen along each of the three arms at \n\\begin{equation}\ndr = \\sqrt{dx^2+dy^2} = i^p {\\rm \\ \\ where\\ \\ } i = 1,2,3,...,M/3.\n\\end{equation}\n\\noindent and $p$ is an arbitrary power which can be used to scale \nthe overall size \nof the pattern. The first step along each of the 3 arms is always at \n$dr = 1.0$. The azimuths of the arms were chosen to match those of the VLA, \nat 355\\arcdeg, 115\\arcdeg, and 236\\arcdeg. \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Random}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nRandom dither patterns were tested using $dx$ and $dy$ steps generated \nindependently from\nnormal (Gaussian) or from uniform (flat) distributions. The widths of the \nnormal distribution or the symmetric minimum and maximum of the uniform \ndistribution are free parameters. \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Geometric Progression}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nWe have generated a geometric progression pattern, stepping in $x$ in \nsteps of $(-f)^n$, where\n$n=0,1,...N-1$ and $f^N=256$. The same steps are also used in the $y$ direction.\nThis pattern separates the $x$ and $y$ dimensions. \nIn each dimension the pattern is\nquite economical in generating correlations up to the point where $f=2$. \nBeyond this\nthere is little to be gained in adding more dither steps in the $x$ or $y$\ndirection. However, there is some benefit expected in adding steps combining\n$x$ and $y$ offsets. Hence, for a $256\\times256$ array, we should expect the \ngeometric pattern to be good for $M\\leq 2\\ log_2(256)=16$ positions \nand not show much improvement by adding more positions.\n\nThe geometric progression patterns used here contain two additional steps \nchosen at $(dx,dy) = (0,0)$ and at a position \nsuch that $\\sum dx = \\sum dy = 0.0$.\nThis is a cross-shaped pattern, with one diagonal pointing,\nfrom which any desired pixel-to-pixel correlation can be made \nwith a small number of intermediate steps. The alternating sign of the steps \nbuilds up longer separations quickly. \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Other Patterns}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nSeveral other patterns were also tested with little or no modifications. \nThe patterns that were planned for the WIRE moderate and deep \nsurveys were examined with both the nominal dither steps, and with steps\nscaled by a factor of 2 to account for the difference between the \n$128\\times128$ pixel WIRE detectors and a larger $256\\times256$ pixel \ndetector. The pattern used for NICMOS observations of the HDF-S was tested.\nThe configuration of the 13 antennas of the Degree Angular Scale \nInterferometry (DASI; Halverson, et al. 1998) was used as a scalable \npattern. The declination scanning employed by 2MASS yields a linear dither \npattern. \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Figures of Merit for the Patterns}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nIn the simplest form, a specific pattern, $M$ images deep, would be used to \ncollect data at a single target. The FOM for all patterns tested, with various\n$M$ and other modifications, are listed in Table 2. \nFor all patterns, the FOM increases (improves) as $M$ increases. For $M < 20$\nthe change is quite rapid. The variations of FOM as a function of $M$ for the \ntabulated versions of each of the patterns are shown in Figure 4. \n\\begin{figure}[t]\n\\plotone{fig4.eps}\n\\caption[]{The FOM as a function $M$ the number of positions in each pattern.\n``+'' = geometric progression, inverted ``Y'' = VLA, \n``{\\small $\\bigcirc$}'' = random (normal), \n``$\\bigtriangleup$'' = Reuleaux triangle, ``W'' = WIRE moderate and\ndeep surveys, ``D'' = DASI, and ``N'' = NICMOS coverage of the HDF-S.\nThe right panel shows the same data on an enlarged scale.}\n\\end{figure}\n\nTable 2 also lists results for a Reuleaux triangle pattern applied to a \n$32 \\times 32$ detector, and for two large grid dither patterns applied\nto the same array. The grid dither patterns are square grids with 1 pixel \nspacings between dithers, such that for the $M = 1024$ pattern\na single sky pixel is observed with each detector, and for the $M = 4096$ \npattern a $32 \\times 32$ pixel region of sky is observed with each detector\npixel. These results demonstrate that in the extreme limit where all \ncorrelations are directly measured, the $FOM \\rightarrow 1.0$. The FOM \ndoes not reach 1.0 because of the finite detector and dither pattern sizes.\n\nFor the $256 \\times 256$ arrays, the Reuleaux and random \n(normal) patterns have the best FOM for $M > 20$.\nThe VLA pattern is only a little worse, but other patterns have distinctly \nsmaller FOM than these patterns. For the scalable VLA, random, Reuleaux, and\nDASI patterns, the best FOM for a fixed $M$ usually occurs when \nthe maximum $|dx|$ or $|dy| \\approx 128$ pixels. For patterns with \nsmall $M$ the optimum scale factor is usually smaller, to avoid too many large \nspacings between widely scattered dither positions.\nFor values of $M<20$ no pattern seems to produce a good FOM, however, \nthe geometric pattern usually does best in this regime. \nRotating the patterns with respect to the detector array generally produces\nonly modest changes in the FOM. For $M \\lesssim 30$, \nthe FOM of a Reuleaux pattern is improved by adding small random perturbations\nto the dither positions. No optimization of the perturbations was performed\n(as Keto 1997), but apparently any perturbation is better than none for small\n$M$ patterns. Deep Reuleaux triangle patterns are neither improved nor \nworsened by small perturbations.\n\nThe results presented in Fig. 4 and Table 2 indicate that a good\nFOM is dependent on patterns that sample a large number and \nwide range of spatial scales. \nA variety of patterns with different geometries can yield satisfactory \nresults, as demonstrated by the rather different Reuleaux triangle\nand random patterns. Therefore, attempts to find the single ``optimum'' \npattern may not be very useful, and selection of a dither pattern needs\nto carefully avoid patterns that contain obvious or hidden redundancies\nthat lead to a poor FOM. An example of this sort of pitfall is the $M = 18$\ngeometric pattern, for which all dither steps are integer powers of 2, \nleading to a FOM that is worse than geometric patterns with depths of $M = 14$ \nor 16. \n\nThe coverage of the VLA, random, and Reuleaux triangle dither patterns when \nused for observation of a single target is shown as maps in Figure 5, and \nhistograms in Figure 6. The Reuleaux triangle dither pattern provides the\nlargest region covered at maximum depth, but if a depth less than the \nmaximum is still useful then the VLA dither pattern may provide the \nlargest area covered.\n\\begin{figure}[t]\n\\plotone{fig5.eps}\n\\caption[]{Coverage maps for $M=39$ single target dither patterns\n(left) VLA: $FOM = 0.282$, (center) Random Gaussian: $FOM = 0.302$, \n(right) Reuleaux triangle: $FOM = 0.307$.}\n\\end{figure}\n\\begin{figure}[t]\n\\plotone{fig6.eps}\n\\caption[]{Cumulative histograms of the coverage as a function\nof minimum depth for $M=39$ VLA (thin), random Gaussian (dotted), and \nReuleaux triangle (thick) dither patterns. Coverage for a single target is \nshown at left; coverage for a deep $3\\times 3$ survey with a $256\\times 256$ \npixel grid spacing is shown at right.}\n\\end{figure}\n\nThe importance of the largest dither steps in a pattern is demonstrated \nthrough analysis of simulated WIRE data. A synthetic sky was sampled using \nboth geometric progression and random dither patterns. The maximum dither\noffset was 38 pixels for the geometric progression pattern and 17 pixels\nfor the random pattern. The FOM for this geometric pattern is 0.127, and for \nthis random pattern it is 0.099. WIRE's detectors were $128\\time 128$ arrays. \nThe gain response map used in the simulations contained large scale \ngradients with amplitudes of $\\sim 10\\%$. Figure 7 shows comparisons\nbetween the actual gains and the gains derived when the self-calibration \nprocedure described by Fixsen, et al. (2000) is employed. \nThe random dither pattern \nwithout the larger dither offsets was less effective at identifying the\nlarge scale gain gradient. The undetected structure in the gain winds up \nappearing as a sky gradient that affects the photometry of both the \npoint sources and the background in the images.\n\\begin{figure}[t]\n\\plotone{fig7.eps}\n\\caption[]{The median fractional gain errors are plotted as a \nfunction of detector row\nfor detector gains derived from two simulated WIRE data sets. \nEach simulation contains 10 dithered images. Only one simulation includes \nrelatively large dither steps. \nWhen applying a self-calibration algorithm, a lack of large dither steps \nleads to large-scale gain errors.}\n\\end{figure}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Surveys}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Deep Surveys}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nFor obtaining a standard deep survey, we have assumed that the same dither \npattern is repeated at each location of a grid. The survey grid is assumed to \nbe aligned with the detector array and square, with a spacing \nno larger than the size of the array. The FOM for surveys using several \ndifferent dither patterns and grid spacings are listed in Table 3.\nThe FOM derived for the entire survey as a single data set is basically \ndetermined by the FOM of the dither pattern used. \nThe overlap between dithers from\nadjacent points in the survey grid, effectively adds additional \nsteps to the dither pattern, which slightly improves the FOM over that of the \npattern when used for a single target. Smaller survey grid spacings lead\nto increased overlap and increased FOM, but also lead to a smaller area of\nsky covered in a fixed number of frames. \nThe improvement in the FOM when used in surveys rather than singly is most \nsignificant for relatively shallow dither patterns, however, even in a survey,\nthe FOM of a shallow pattern is still not very good. The FOM improves only\nslightly as the survey grid grows larger than the basic $2\\times 2$ unit cell.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Shallow Surveys}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nFor shallow surveys in which as few as 2 images per grid location are \ndesired, using \nthe same small $M$ dither pattern at each location yields a very poor FOM.\nAn alternate method of performing a shallow survey is to choose a larger $M$\ndither pattern and apply successive steps of the dither pattern at successive\nlocations in the survey grid (Figure 8). If the survey is large enough, \nit can contain \nall the direct correlations of the large $M$ dither pattern, though spread out\namong many survey grid points rather than at a single location. The FOM of the \nshallow survey can thus approach the FOM of the single deeper dither pattern.\nThe advantage of altering the dither pattern at each survey grid point is \nstill present, though less significant, as the survey depth increases. \nThe FOM derived from various surveys using this shallow survey strategy are \nshown in Table 4. \n\\begin{figure}[t]\n\\epsscale{0.5}\n\\plotone{fig8.eps}\n\\caption[]{An example of a $4\\times 4$ $M=3$ shallow survey \non a $181\\times 181$ pixel grid using an $M=33$ Reuleaux triangle \ndither pattern. The dots show the repetition of the full dither pattern, \nwhile the crosses mark the dither points that were actually used at \neach survey grid point.}\n\\end{figure}\n\nA random dither pattern is a natural choice for use in this shallow survey\nstrategy. One can proceed by simply generating a new random set of dithers\nat each survey grid point. If a more structured dither pattern \nis used as the basis for the shallow survey (e.g. the Reuleaux \ntriangle in Fig. 8), then one must address the\ncombinatorial problem of selecting the appropriate subsets of the larger \ndither pattern at each survey grid point. The example shown in Fig. 8 is\n{\\it not} an optimized solution to the combinatorial problem.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{Survey Coverage \\& Grids}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nWhen a large area is to be observed, the most efficient way to cover the \nregion is to use a square survey grid aligned with the detector array and\nwith a grid spacing equal to the size of the array, or slightly less to\nguard against bad edges or pointing errors. In this mode a deep survey \nusing the same $M$ position dither pattern at each survey grid point\nwill cover the desired region at a depth of $M$ or greater. There will\nbe no holes in the coverage, though the edges of the surveyed region will\nfade from coverage of $M$ to 0 with a profile determined by the dither \npattern used (Fig. 6). A shallow survey, using a different dither pattern at\neach grid point, may or may not have coverage holes depending on the \nmaximum size of the dither steps and the grid spacing of the survey. The \nconstraint for avoiding coverage holes is that the overlap of the \nsurvey grid must be more than the maximum range of dither step offsets \n(independently in the $x$ and $y$ coordinates), e.g.\n\\begin{equation}\nX - \\Delta X > {\\rm max}(dx_i) - {\\rm min}(dx_i)\n\\end{equation}\nwhere $X$ is the size of the array, $\\Delta X$ is the survey grid spacing, and\n$dx_i$ are the dither steps ($i=1...M$). This constraint places the survey grid\npoints close enough together that coverage holes are avoided even if dithers\nat adjacent grid point are offset in the maximum possible opposite directions. \nIf the shallow survey observing program can be arranged to avoid this worst \ncase, then the grid spacing may be increased without developing coverage holes.\nCoverage holes may be undesirable when mapping \nan extended object, but may be irrelevant if one is simply seeking \na random selection of point sources to count.\nNote that some minor coverage holes are inevitable, where data are lost to \nbad pixels or cosmic rays. Additionally, a coverage hole where a depth of $M=1$\nis achieved instead of $M=3$ might be more serious than one where $M=18$ is\nachieved instead of $M=20$.\n\nFor this shallow survey strategy there is an inherent tradeoff between \nthe area covered (without holes) and the FOM. Using a dither pattern \ncontaining large dither steps as the basis for the survey will lead to \na good FOM, but require a relatively large overlap in the survey grid\nspacing and a consequent loss of area covered by the survey. Decreasing\nthe scale of the dither pattern leads to a lower FOM, but permits an \nincrease in the survey grid spacing and total area covered. The ideal \nbalance between these will depend on the instrumental characteristics \nand the scientific objectives.\n\nIn many instances, an observer may want to survey or map a region of fixed\ncelestial coordinates. In some cases, instrumental constraints (i.e. the \nability to rotate the telescope or detector array relative to the optical \nboresight)\nmay not allow alignment between the detector array and the desired survey\ngrid. This will result in coverage holes in the surveyed region, unless \nthe grid spacing is reduced enough to prevent holes regardless of the \narray orientation. If a square grid with a spacing of $\\Delta X = X/\\sqrt{2}$\nis used then coverage holes are prevented for any possible orientation\nof the arrays. This is illustrated by plots in the first two rows of \nFigure 9, which shows the array positions for $4\\times 4$ $M=1$ survey\n(without dithering). With a deep survey strategy, avoidance of holes in the \n$M=1$ case will prevent holes at any depth $M$, but for the shallow survey \nstrategy additional overlap may need to be built into the survey grid\nto prevent holes as discussed above. Decreasing the survey grid by a \nfactor of $\\sqrt{2}$ in each dimension results in a grid that covers only\nhalf the area that could be covered if the detectors and grid are aligned.\nThis efficiency can be increased if the survey is set up on a triangular grid \nrather than a square grid. If alternate rows of the survey grid are \nstaggered by $X/2$ (middle row of Fig. 9) and the vertical spacing \nof the grid is reduced by a factor of $\\sqrt{3}/2$, then holes are prevented\nas long as the array orientation remains fixed throughout the survey (4th \nrow of Fig. 9). The area covered by this triangular grid will be $\\sim~87\\%$\nof the maximum possible area, rather than $50\\%$ for the square grid required\nto prevent holes. If the array orientation is not fixed throughout the survey \n(last column of Fig. 9) then the triangular grid must be reduced by an \nadditional factor of $\\sqrt{3}/2$ in both dimensions. This results in a \n$\\sim65\\%$ efficiency for the triangular grid versus $50\\%$ for the square\ngrid, which requires no further reduction. The FOM of a survey on a triangular\ngrid is similar to that of a survey on a square grid with an equivalent amount \nof overlap.\n\\begin{figure}[t]\n\\epsscale{0.75}\n\\plotone{fig9.eps}\n\\caption[]{Examples of $4\\times 4$ $M=1$ surveys on square \n(1st and 2nd rows), staggered (middle row), and triangular grids (4th and 5th\nrows) for various angles between the detector array and the grid orientation.\nIn the last column the array orientation was rotated by $34\\arcdeg$ at each\nsuccessive survey grid point. The squares indicate the outline of the entire \narray as pointed at each survey grid point.}\n\\end{figure}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Other Miscellaneous Details}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nThe most flexible implementation of the dithering strategies presented here\nwould be to have the dither steps be determined algorithmically from \na small set of user-supplied parameters. For example, an observer could\nselect: a type of dither pattern (e.g. Reuleaux triangle or random),\na pattern depth $M_{pattern}$, and a scaling factor to control the overall size\nof the pattern. From this information, the telescope control software could\ncalculate and execute the desired dither pattern. For the shallow survey \nstrategy presented above, the observer would also need to supply:\nthe survey depth, $M_{survey} < M_{pattern}$, and perhaps an index to track \nwhich grid point of the survey is being considered (software might handle \nthis automatically). \n\nSometimes design or operational constraints require that the \ndither patterns reside in\na set of pre-calculated look-up tables. In this case (which has applied\nto both WIRE and IRAC) the observer's ability to set the dither pattern is \nmore limited. However, some of the limitations of using dither tables can be \nmitigated if the observer is not forced to use dither steps from \nthe tables in a strictly sequential fashion. \nFor example, one dither table might contain an $M=72$ \nReuleaux triangle dither pattern calculated on a scale to produce the\noptimum FOM. If the observer is allowed to set the increment, $\\Delta i$, \nused in stepping through this dither table, then by selecting \n$\\Delta i = 3$ or $\\Delta i = 4$, then dither patterns of $M=24$ or $M=18$ \ncan be generated. Allowing non-integer increments (subsequently rounded) \nwould enable the selection of a dither pattern of any depth $M\\leq 72$. \nThis adjustment of the \nincrement is most clearly useful for very symmetric dither patterns such as\nthe Reuleaux triangle pattern. For a dither table containing a \nrandom pattern, non-sequential access to the table can have other uses.\nFirst, in applying the shallow survey strategy, a random dither table\nof length $M_{pattern}$ could be used to sequentially generate \n$M_{survey} < M_{pattern}$ dithers at each successive survey grid point. \nSelection of dither steps would wrap around to the beginning of the table\nonce the end of the table is reached. For example a dither table of\n$M_{pattern} = 100$ could be used sequentially to generate 20 different \npatterns for an $M=5$ shallow survey. Even better would be to have a\ntable with $M_{pattern}$ a prime number, e.g. 101. Then, wrapping the \ntable allows the sequential generation of $M_{pattern}$ different dither\npatterns for any $M_{survey}$, though some of these dither patterns \nwill differ from others by only one step. Additional random patterns can\nbe generated by setting different increments for stepping through the table. \nEnabling specification of the starting point in the dither table would\nadditionally allow the observer to pick up the random dither pattern sequence\nat various (or the same) positions as desired. These capabilities would\nenable an observer to exploit the large number of {\\it combinations} of dither\nsteps available in a finite length dither table, in efforts to maximize \nthe FOM. \nUse of a fixed dither table can also be made less restrictive if a scaling \nfactor can be applied to the dither pattern size.\nA free scaling factor provides an additional means of adjusting the \npattern size as desired to meet coverage or FOM goals. \n\nFor the cases presented in this paper, we have assumed that the orientation\nof the detector array remains fixed throughout the execution of the dither\npattern and any larger survey (except for the last column of Fig. 9).\nHowever, rotation of the detector array relative to the dither pattern,\neither within a single pointing, or at different pointings in a deep survey,\nis an effective way of establishing combinations of direct pixel-to-pixel \ncorrelations that cannot be obtained using purely translational dither steps.\nInclusion of rotation of the detector can lead to further improvements\nin the FOM of a given dither pattern or survey. In the extreme, a dither\npattern could even be made entirely out of rotational rather than \ntranslational dither steps. However, without an orthogonal ``radial'' dither\nstep, rotation alone is similar to dithering with steps in the $x$-direction \nbut not the $y$-direction. The ability to implement rotations of the \ndetector will be allowed or limited by the design and operating \nconstraints of the telescope and instruments being used.\n\nBright sources can often saturate detectors and cause residual time-dependent \nvariations in detector properties. For observations of a field containing \na bright source, use of a random dither pattern may lead to \nstreaking as the source is trailed back and forth across the detector \narray between dithers. In contrast the use of a basically hollow or \ncircular dither pattern such as the Reuleaux triangle pattern, will only \ntrail the source through a short well-defined pattern, which will lie \ntoward the outer edge of the detector if the source position is centered\nin the dither pattern. If the pattern scale of the dither pattern is increased,\nthe trail of the source can be pushed to or off the edges of the detector,\nthough the $FOM$ will suffer if the pattern scale is greatly increased.\nIn other words, a hollow dither pattern with a large scale could be used to \nobtain a series of images looking around but not at a bright source.\n\nDithering may be performed by repointing the telescope, or by repositioning\nthe instrument in the focal plane, for example through the use of a \ntilting optics as in the 2MASS (Kleinmann 1992) or \n{\\it SIRTF} MIPS (Heim, et al. 1998) instruments.\nCalculation of the $FOM$ of the dither pattern will be independent of the \ntechnique used. The self-calibration procedure, however, may be affected by\neffective instrumental changes if it is repositioned in the focal plane.\nThe alternative repointing of the telescope can be much more time consuming \nand may limit the use of large $M$ dither patterns.\n\nThe combined use of two or more non-contiguous fields is transparent to the\nself-calibration procedure. If the same dither pattern is used on each of\nthe separate fields, the resulting $FOM$ will be the same as that for a single\nfield. The $FOM$ would be improved for the combined data set if the dither\npattern is different for each of the subset. The $FOM$ for data set \nof non-contiguous regions is thus similar to that obtained using the same\ndither strategy in a contiguous survey, except there is a small loss in the\n$FOM$ because of the lack of overlap between adjacent regions.\n\nAnother means of minimizing coverage holes when using a shallow survey strategy\nis to oversample the depth of the survey. For example, performing the \nshallow survey at a depth of $M=4$ when $M=3$ is the intended goal \nwill result in fewer holes at a depth of 3 for a fixed grid spacing, and in \na better FOM for the overall survey. However, the cost in time of the \nadditional exposures may be prohibitive.\n\nThe FOM as calculated here only depends upon the offsets of the dither pattern\nrounded to the nearest whole pixel. This means that any desired combination\nof fractional pixel offsets to facilitate subpixel image reconstruction may\nbe added to the dither patterns without affecting the various aspects discussed \nin this paper. If using dither tables, one could have separate tables for the \nlarge scale and the fractional pixel dithers, with the actual dithers made \nby adding selected entries from the two tables. This could allow \nsimultaneous and independent implementation of large-scale and subpixel \ndithering strategies.\nOnly subpixel image reconstruction that demands exclusively\nsmall ($\\sim1$ pixel) dithering would be incompatible with the dithering\nstrategies presented here.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{Conclusion}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nWe have shown that proper selection of observing strategies can \ndramatically improve the quality of self-calibration of imaging detectors.\nWe have established a figure of merit (Eq. 6) for quantitatively ranking \ndifferent dither patterns, and have identified several patterns\nthat enable good self-calibration of a detector on\nall spatial scales. The layouts of radio interferometers \ncorrespond to good dither patterns. Both the highly ordered Reuleaux triangle \npattern and the unstructured random pattern provide good FOM with moderate\nor deep observations. This indicates that good patterns must sample a range \nof spatial scales without redundancy, and if this condition is met, \nthen secondary characteristics of the patterns or instrument constraints\nmay determine the actual choice of the dither pattern. Any dither pattern \nmust contain steps as large as half the size of the detector array if large \nscale correlations are to be effectively encoded in the dithered data set.\nDeep surveys can take advantage of the use of a single good dither pattern.\nShallow surveys can obtain good FOM by altering the dithers used at each of \nthe survey grid points. Using a fixed pattern \nthroughout a shallow survey makes it\ndifficult or impossible to apply a self-calibration procedure to the \nresulting data sets. The use of triangular instead of square survey grids\ncan be more efficient in executing complete-coverage surveys when the array \norientation cannot be set to match the survey grid. Good dither patterns \nand survey strategies can be devised even in some seemingly restricted \nsituations. The ultimate importance of dithering and a good FOM will depend\non the nature of the instrument and the data and on the scientific goals.\nFor many goals, obtaining a larger quantity of data may not be an adequate\nsubstitute for obtaining data with a good FOM. \n\n\\acknowledgements\nWe thank D. Shupe and the WIRE team for supplying simulated data using several\ndifferent dither patterns. W. Reach and members of the SSC and \nIRAC instrument teams were helpful in providing useful ideas and criticism \nthroughout the development of this work. J. Gardner, J. Mather, and the \nanonymous referee provided very helpful criticism of the manuscript.\n\n\\begin{references}\n\n\\reference{}{Cutri, R., Van Dyck, S. \\& the 2MASS Team, 1999, Explanatory\nSupplement to the 2MASS Spring 1999 Incremental Data Release,\nhttp://www.ipac.caltech.edu/2mass/releases/spr99/doc/explsup.html}\n\n\\reference{}{Fixsen, D. J., et al. 1994, \\apj, 420, 457}\n\n\\reference{}{Fixsen, D. J., Moseley, S. H., \\& Arendt, R. G. 2000, \n\\apjs, 128, in press}\n\n\\reference{}{Fruchter, A. S. \\& Hook, R. N. 1998, \\pasp, submitted, \n(astro-ph/9808087)}\n\n\\reference{}{Gardner, J. P. 1995, \\apjs, 98, 441}\n\n\\reference{}{Halverson, N. W., Carlstrom, J. E., Dragovan, M., \nHolzapfel, W. L., \\& Kovac, J. 1998, in\nAdvanced Technology MMW, Radio, and Tetrahertz Telescopes, Proc. SPIE 3357, \ned. T. G. Phillips (Bellingham, WA: SPIE), 416}\n\n\\reference{}{Heim, G. B., et al. 1998, in Space Telescopes and Instruments V, \nProc. SPIE 3356, ed. P. Y. Bely, \\& J. B. Breckinridge, (Bellingham, WA: SPIE), \n985}\n\n\\reference{}{Joyce, R. R. 1992, in ASP Conf. Ser. 23, Astronomical CCD \nObserving and Reduction Techniques, ed. S. B. Howell, (San Francisco: ASP), 258}\n\n\\reference{}{Keto, E. 1997, \\apj, 475, 843}\n\n\\reference{}{Kleinmann, S. G. 1992, in Robotic Telescopes in the 1990s, ed. \nA. V. Filippenko, (San Francisco: ASP), 203}\n\n\\reference{}{Lauer, T. R. 1999, \\pasp, 111, 227}\n\n\\reference{}{Mather, J. C., et al. 1994, \\apj, 420, 439}\n\n\\reference{}{Thompson, A. R., Clark, B. G., Wade, C. M., \\& Napier, P. J. \n1980, \\apjs, 44, 151}\n\n\\reference{}{Tyson, J. A. 1986, J. Opt. Soc. Am. A, 3, 2131}\n\n\\reference{}{Tyson, J. A. \\& Seitzer, P. 1988, \\apj, 335, 552}\n\n\\reference{}{Williams, R. E., et al. 1996, \\aj, 112, 1335}\n\n\\end{references}\n\n\\begin{deluxetable}{ll}\n\\footnotesize\n\\tablewidth{0pt}\n\\tablecaption{Comparison of Data Reduction Procedures}\n\\tablehead{\n\\colhead{Flat Sky Technique} &\n\\colhead{Least Squares Solution} \n}\n\\startdata\nassumes sky is flat ($S^0$) & \nsolves for real sky ($S^{\\alpha}$); will find $S^0$ if warranted\\\\\n & \\\\\nrequires dark frames &\nno dark frames needed, but they are useful if available\\\\\n & \\\\\nmay take time for chopping to nearby &\nno chopping needed\\\\\nflat field region (if such exists) &\n\\\\\n & \\\\\nconfused fields can ruin the solution & \nconfused fields can improve the solution\\\\\n & \\\\\nmay remove flat emission components of the astronomical sky &\npreserves full sky intensity\\\\\n(e.g. zodiacal emission, nebular emission, cosmic backgrounds) &\n\\\\\n & \\\\\nrequires Monte Carlo or ad hoc assessment of uncertainties & \ncan accurately and analytically track\\\\\nor unbiased source removal & \nuncertainties and correlations\\\\\n & \\\\\nobservations of $S^0$ by all pixels automatically tightly & \ndithering must establish tight correlations between \\\\\ncorrelate all detector pixels on all spatial scales &\nall detector pixels\\\\ \n & \\\\\ncomputationally simple & \ncan be simplified to produce the flat sky result\\\\\n & \\\\\n & can be used in non-astronomical applications\\\\\n\\enddata\n\\end{deluxetable}\n\n\\begin{deluxetable}{cccccccccccc}\n%\\scriptsize\n\\tiny\n\\tablewidth{0pt}\n\\tablecaption{Figures of Merit for Single Pointings}\n\\tablehead{\n & \\multicolumn{8}{c}{$256\\times 256$ arrays} & & \\multicolumn{2}{c}{$32\\times 32$ arrays} \\\\\n\\cline{2-9}\\cline{11-12}\n\\colhead{$M_{pattern}$} &\n\\colhead{Reuleaux} &\n\\colhead{Random} & \n\\colhead{VLA} &\n\\colhead{Geometric} &\n\\colhead{DASI} &\n\\colhead{WIRE} &\n\\colhead{NICMOS HDF-S} &\n\\colhead{2MASS} &\n\\colhead{} &\n\\colhead{Reuleaux} &\n\\colhead{Grid} \n}\n\\startdata\n 6 & 0.002 & \\nodata & 0.020\\tablenotemark{e} & 0.016 & \\nodata & \\nodata & \\nodata & 0.002 & & \\nodata & \\nodata \\\\\n 8 & \\nodata & \\nodata & \\nodata & 0.058 & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 9 & 0.003\\tablenotemark{a} & \\nodata & 0.059\\tablenotemark{f} & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & & 0.217\\tablenotemark{k} & \\nodata \\\\\n 10 & \\nodata & \\nodata & \\nodata & 0.094 & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 12 & \\nodata & \\nodata & \\nodata & 0.112 & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 13 & \\nodata & \\nodata & \\nodata & \\nodata & 0.100 & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 14 & \\nodata & \\nodata & \\nodata & 0.139 & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 15 & 0.117\\tablenotemark{b} & \\nodata & 0.128\\tablenotemark{g} & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 16 & \\nodata & 0.162 & \\nodata & 0.152 & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 18 & 0.153\\tablenotemark{c} & 0.181 & 0.166 & 0.133 & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 24 & \\nodata & \\nodata & \\nodata & 0.168 & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 27 & 0.265 & \\nodata & 0.240\\tablenotemark{h} & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 32 & \\nodata & 0.286 & \\nodata & 0.193 & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 39 & 0.307 & \\nodata & 0.282 & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 40 & \\nodata & \\nodata & \\nodata & 0.193 & \\nodata & 0.228\\tablenotemark{i} & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 60 & 0.323 & 0.318 & 0.303 & 0.204 & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 90 & 0.341 & 0.335 & 0.316 & 0.208 & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 120 & 0.361 & 0.351 & 0.329 & 0.208 & \\nodata & 0.225\\tablenotemark{j} & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 142 & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & 0.131 & \\nodata & & \\nodata & \\nodata \\\\\n 150 & 0.387 & 0.365 & 0.347 & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 180 & 0.416 & 0.378 & 0.366 & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 210 & 0.448 & 0.415 & 0.392 & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 240 & 0.485\\tablenotemark{d} & 0.437 & 0.419 & 0.212 & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n 300 & 0.526 & 0.439 & 0.469 & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & \\nodata \\\\\n1024 & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & 0.783 \\\\\n4096 & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & \\nodata & & \\nodata & 0.889 \\\\\n\\enddata\n\\tablecomments{Standard pattern sizes are: Reuleaux width = 128 pixel, Random 3 \n$\\sigma$ = 128 pixel, VLA $r_{max}$ = 125.7 pixel, Geometric is scaled to the \n256 pixel array size, DASI $r_{max}$ = 82.5 pixel, WIRE medium and deep surveys\nscaled by a factor of 2, NICMOS HDF-S all camera 3 F110W data, $32 \\times 32$\nReuleaux width = 12 pixel, Grid spacing = 1 pixel}\n\\tablenotetext{a}{0.037 if 3\\% random variations added}\n\\tablenotetext{b}{0.146 if 3\\% random variations added}\n\\tablenotetext{c}{0.171 if 3\\% random variations added}\n\\tablenotetext{d}{0.396 for width = 110 pixel, 0.513 for width = 144 pixel}\n\\tablenotetext{e}{$r_{max}$ = 16 pixel}\n\\tablenotetext{f}{$r_{max}$ = 32 pixel}\n\\tablenotetext{g}{$r_{max}$ = 125 pixel}\n\\tablenotetext{h}{0.176 for $r_{max}$ = 16 pixel, 0.199 for \n$r_{max}$ = 16 pixel}\n\\tablenotetext{i}{0.065 for the unscaled pattern}\n\\tablenotetext{j}{0.062 for the unscaled pattern}\n\\tablenotetext{k}{0.162 for width = 8 pixel}\n\\end{deluxetable}\n\n\\newpage\n\\begin{deluxetable}{ccccccccccccccccc}\n%\\scriptsize\n\\tiny\n\\tablewidth{0pt}\n\\tablecaption{Figures of Merit for Deep Surveys}\n\\tablehead{\n\\colhead{Survey} &\n\\colhead{Spacing} &\n\\colhead{} &\n\\multicolumn{2}{c}{Reuleaux} &\n\\colhead{} &\n\\multicolumn{3}{c}{Random} &\n\\colhead{} &\n\\multicolumn{3}{c}{VLA} &\n\\colhead{} &\n\\multicolumn{3}{c}{Geometric} \\\\\n\\cline{4-5}\\cline{7-9}\\cline{11-13}\\cline{15-17}\n\\colhead{Size} &\n\\colhead{(pixels)} &\n\\colhead{} & \n\\colhead{$M = 15$} &\n\\colhead{39} &\n\\colhead{} &\n\\colhead{$M = 6$} &\n\\colhead{16} &\n\\colhead{40} &\n\\colhead{} &\n\\colhead{$M = 6$} &\n\\colhead{15} &\n\\colhead{39} &\n\\colhead{} &\n\\colhead{$M = 6$} &\n\\colhead{16} &\n\\colhead{40}\n}\n\\startdata\n$2\\times 2$ & 181 & & 0.194 & 0.318 & & 0.028 & 0.209 & 0.318 & &\n 0.028 & 0.156 & 0.310 & & 0.027 & 0.183 & 0.221 \\\\\n$2\\times 2$ & 218 & & 0.173 & 0.314 & & 0.016 & 0.191 & 0.313 & &\n 0.022 & 0.168 & 0.303 & & 0.022 & 0.174 & 0.216 \\\\\n$2\\times 2$ & 256 & & 0.166 & 0.311 & & 0.012 & 0.172 & 0.309 & &\n 0.020 & 0.153 & 0.298 & & 0.020 & 0.165 & 0.211 \\\\\n$3\\times 3$ & 181 & & 0.198 & \\nodata & & 0.020 & 0.213 & \\nodata & &\n 0.028 & 0.160 & \\nodata & & 0.027 & 0.187 & \\nodata \\\\\n$3\\times 3$ & 218 & & 0.182 & \\nodata & & 0.017 & 0.194 & \\nodata & &\n 0.022 & 0.172 & \\nodata & & 0.022 & 0.177 & \\nodata \\\\\n$3\\times 3$ & 256 & & 0.170 & \\nodata & & 0.016 & 0.178 & \\nodata & &\n 0.020 & 0.158 & \\nodata & & 0.020 & 0.168 & \\nodata \\\\\n$4\\times 4$ & 181 & & \\nodata & \\nodata & & 0.022 & \\nodata & \\nodata & &\n 0.028 & \\nodata & \\nodata & & 0.027 & \\nodata & \\nodata \\\\\n\\enddata\n\\end{deluxetable}\n\n\\begin{deluxetable}{cccccccccccccccc}\n\\scriptsize\n\\tablewidth{0pt}\n\\tablecaption{Figures of Merit for $4\\times 4$ Shallow Surveys}\n\\tablehead{\n\\colhead{Survey} &\n\\colhead{} &\n\\multicolumn{2}{c}{Reuleaux} &\n\\colhead{} &\n\\multicolumn{2}{c}{Random} &\n\\colhead{} &\n\\multicolumn{2}{c}{VLA} &\n\\colhead{} &\n\\multicolumn{2}{c}{Geometric} &\n\\colhead{} &\n\\multicolumn{2}{c}{Grid} \\\\\n\\cline{3-4}\\cline{6-7}\\cline{9-10}\\cline{12-13}\\cline{15-16}\n\\colhead{Depth} &\n\\colhead{} & \n\\colhead{$M = 16$} &\n\\colhead{32} &\n\\colhead{} &\n\\colhead{$M = 16$} &\n\\colhead{32} &\n\\colhead{} &\n\\colhead{$M = 16$} &\n\\colhead{32} &\n\\colhead{} &\n\\colhead{$M = 16$} &\n\\colhead{32} &\n\\colhead{} &\n\\colhead{$M = 2$} &\n\\colhead{3}\n}\n\\startdata\n2 & & 0.088 & 0.117 & & 0.086 & 0.120 & & 0.090 & 0.120 & & \n 0.079 & 0.077 & & 0.001 & \\nodata \\\\\n3 & & 0.113 & 0.175 & & 0.115 & 0.177 & & 0.109 & 0.168 & & \n 0.110 & 0.135 & & \\nodata & 0.002 \\\\\n3\\tablenotemark{a} & & 0.182 & \\nodata & & 0.165 & \\nodata & & 0.167 & \\nodata & & \n 0.136 & \\nodata & & \\nodata & \\nodata \\\\\n\\enddata\n\\tablecomments{All surveys used 181 pixel grid spacing.}\n\\tablenotetext{a}{Random rather than sequential selections \nfrom the dither patterns.}\n\\end{deluxetable}\n\n\\end{document}\n"
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astro-ph0002259
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The elusive structure of the diffuse molecular gas: shocks or vortices in compressible turbulence?
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[
{
"author": "J. Pety and {\\'E}. Falgarone"
}
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The cold diffuse interstellar medium must harbor pockets of hot gas to produce the large observed abundances of molecular species, the formation of which require much more energy than available in the bulk of its volume. These hot spots have so far escaped direct detection but observations and modeling severely constrain their phase-space structure \ie{} they must have a small volume filling factor (a few \%), surface filling factors larger than unity with large fluctuations about average and comparable velocity structure in ``pencil beams'' and ``large beams''. The dissipation of the non-thermal energy of supersonic turbulence occurs in bursts, either in shocks or in the regions of large shear at the boundary of coherent vortices. These two processes are susceptible to generate localized hot regions in the cold medium. Yet, it is of interest to determine which of them, if any, dominates the dissipation of turbulence in the cold interstellar medium. In this paper, we analyze the spatial and kinematic properties of two subsets of hydrodynamical compressible turbulence: the regions of largest negative divergence and those of largest vorticity and confront them with the observational constraints. We find that these two subsets fulfill the constraints equally well. A similar analysis should be conducted in the future on simulations of MHD turbulence. \keywords{ISM: evolution - ISM: kinematics and dynamics - ISM: molecules - ISM: structure - Turbulence}
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[
{
"name": "ms9327.tex",
"string": "\n\\documentclass{aa}\n\n\\usepackage{times}\n\\usepackage{graphics}\n\\usepackage{aabib99}\n\n\\def\\ie{{\\rm i.e.}}\n\n\\def\\cc{\\ifmmode{\\,{\\rm cm}^{-3}}\\else{$\\,{\\rm cm}^{-3}$}\\fi}\n\\def\\cq{\\ifmmode{\\,{\\rm cm}^{-2}}\\else{$\\,{\\rm cm}^{-2}$}\\fi}\n\\def\\kms{\\ifmmode{\\,{\\rm km}\\,{\\rm s}^{-1}}\\else{km~s$^{-1}$}\\fi} \n\n\\def\\HH{\\ifmmode{\\rm H_2}\\else{$\\rm H_2$}\\fi}\n\\def\\twCO{\\ifmmode{\\rm^{12}CO}\\else{$\\rm^{12}CO$}\\fi} \n\\def\\thCO{\\ifmmode{\\rm^{13}CO}\\else{$\\rm^{13}CO$}\\fi} \n\\def\\Cp{\\ifmmode{\\rm C^+}\\else{$\\rm C^+$}\\fi} \n\\def\\CHp{\\ifmmode{\\rm CH^+}\\else{$\\rm CH^+$}\\fi}\n\\def\\CHthp{\\ifmmode{\\rm CH_3^+}\\else{$\\rm CH_3^+$}\\fi} \n\\def\\HCOp{\\ifmmode{\\rm HCO^+}\\else{$\\rm HCO^+$}\\fi} \n\n\\newcommand{\\emm}[1]{\\ensuremath{#1}} % Ensures math mode.\n\\newcommand{\\emr}[1]{\\emm{\\mathrm{#1}}} % Uses math roman fonts.\n\n\\newcommand{\\Ntot}{\\emm{N_\\emr{tot}}}\n\\newcommand{\\Tac}{\\emm{\\tau_\\emr{ac}}}\n\\newcommand{\\Dvtot}{\\emm{\\Delta v_\\emr{tot}}}\n\\newcommand{\\Dvpdf}{\\emm{\\Delta v_\\emr{PDF}}}\n\\newcommand{\\Dvmp} {\\emm{\\Delta v_\\emr{mp}}}\n\\newcommand{\\Dvem}{\\emm{\\Delta v_\\emr{em}}}\n\\newcommand{\\Dvabs}{\\emm{\\Delta v_\\emr{abs}}}\n\\newcommand{\\fvol}{\\emm{f_\\emr{v}}}\n\\newcommand{\\fsur}[1][\\mbox{}]{\\emm{f_\\emr{s#1}}}\n\n\\begin{document}\n\n\\thesaurus{09(09.05.1; 09.11.1; 09.13.2; 09.19.1; 02.20.1)}\n\n\\title{The elusive structure of the diffuse molecular gas: shocks or\n vortices in compressible turbulence?}\n\n\\author{J. Pety and {\\'E}. Falgarone}\n\n\\offprints{J. Pety} \\mail{pety@lra.ens.fr}\n\n\\institute{Radioastronomie, CNRS, UMR 8540, {\\'E}cole Normale\n Sup{\\'e}rieure, 24 rue Lhomond, F-75005 Paris, France}\n\n\\date{Received xxxx / Accepted xxxx}\n\n\\titlerunning{Structure of diffuse molecular gas}\n\n\\authorrunning{Pety \\& Falgarone}\n\n\\maketitle %\n\n\\begin{abstract}\n \n The cold diffuse interstellar medium must harbor pockets of hot gas to\n produce the large observed abundances of molecular species, the formation\n of which require much more energy than available in the bulk of its\n volume. These hot spots have so far escaped direct detection but\n observations and modeling severely constrain their phase-space structure\n \\ie{} they must have a small volume filling factor (a few \\%), surface\n filling factors larger than unity with large fluctuations about average\n and comparable velocity structure in ``pencil beams'' and ``large\n beams''.\n \n The dissipation of the non-thermal energy of supersonic turbulence occurs\n in bursts, either in shocks or in the regions of large shear at the\n boundary of coherent vortices. These two processes are susceptible to\n generate localized hot regions in the cold medium. Yet, it is of\n interest to determine which of them, if any, dominates the dissipation of\n turbulence in the cold interstellar medium.\n \n In this paper, we analyze the spatial and kinematic properties of two\n subsets of hydrodynamical compressible turbulence: the regions of largest\n negative divergence and those of largest vorticity and confront them with\n the observational constraints. We find that these two subsets fulfill the\n constraints equally well. A similar analysis should be conducted in the\n future on simulations of MHD turbulence.\n \n \\keywords{ISM: evolution - ISM: kinematics and dynamics - ISM: molecules\n - ISM: structure - Turbulence}\n\n\\end{abstract}\n\n\\section{Introduction}\n\nFor several decades now, molecules have been detected in the diffuse\ncomponent of the cold neutral medium and these observations raise several\nintriguing questions. Firstly, the large observed abundances of \\CHp{}\n\\cite{crane95:hrsiCH,gredel97:iCHsOBa} and \\HCOp{} and OH\n\\cite{lucas96:pbsgHCOatecs} in the cold diffuse medium imply that\nactivation barriers and endothermicities of several thousands Kelvin be\novercome. The formation of \\CHp{} proceeds through the endothermic\nreaction of \\Cp{} with \\HH{} ($\\Delta E/k$=4640 K) and that of OH via the\nreaction of O with \\HH{} which has an activation energy $\\Delta E/k$ =2980\nK. In the diffuse gas, \\HCOp{} forms from \\CHthp, a daughter molecule of\n\\CHp. None of the large observed abundances can be explained by standard\nsteady-state chemistry in cold diffuse gas. Pockets of hot gas must\ntherefore exist in the cold diffuse medium.\n\nSecondly, many other molecules like CO, CS, SO, CN, HCN, HNC, H$_2$S,\nC$_2$H have now been detected in absorption in front of extragalactic\ncontinuum sources in local or redshifted gas (Lucas \\& Liszt 1993, 1994,\n1997; Liszt \\& Lucas 1994, 1995, 1996; Wiklind \\& Combes 1997, 1998).\n\\nocite{lucas93:pbommwmaBLL,lucas94:pbommwma,lucas97:mwodc}\n\\nocite{liszt94:mHCOedctdo,liszt95:mwmeaca,liszt95:mwmeaca}\n\\nocite{wiklind97:malhr,wiklind98:cmals} The lines of sight sample the\nedges of molecular clouds or the diffuse medium, which corresponds to gas\npoorly shielded from the ambient UV radiation field. This derives from the\nlow excitation temperatures (often close to the temperature of the cosmic\nbackground) measured in these transitions. Yet, the molecular abundances\nderived are close to those of dark clouds.\n\nThirdly, the spatial and velocity distribution of these molecules is highly\nelusive. Observations of CO emission and absorption lines toward\nextragalactic sources by Liszt \\& Lucas \\cite*{liszt98:COaecercs} show\nthat: {\\it (i)} absorption and emission line profiles have comparable\nlinewidths whereas the projected size of the sampled volumes of gas differ\nby more than four orders of magnitude (60 vs. 10$^{-3}$ arcsec), {\\it (ii)}\nthe excitation temperature of the CO molecules changes only weakly across\nthe profiles and {\\it (iii)} there are very few lines of sight with no\nabsorption line detected. The phase-space distribution of the CO--rich gas\nin diffuse clouds must therefore have a surface filling factor close to\nunity, and its velocity field must be as adequately sampled by a pencil\nbeam than by a large beam. As mentioned by the authors, these observations\nsuggest a one-dimensional structure for the molecular component, which\ncontrasts with the profuse small scale structure observed in emission.\n\nTwo mechanisms, operating at very different size scales, can trigger a {\\it\n hot chemistry} in the cold diffuse medium and produce the observed\nmolecular abundances: magneto-hydrodynamical (MHD)\nshocks~\\cite{elitzur78,draine86:mhdsdc:ps,draine86:mhdsdc:lstro,pineau86:tsisms:fdc,flower98:ctsim:pal}\nand intense coherent vortices, responsible for a non-negligible fraction of\nthe viscous dissipation of supersonic turbulence\n\\cite{falgarone95:iticigktdhpfgm,falgarone95:csitldic,joulain98:necdsit}.\nThis is so because the dissipation of the non-thermal energy of supersonic\nturbulence is concentrated in shocks and in the regions of large shear at\nthe boundary of coherent vortices. In both cases, only a few \\% of hot gas\non any line of sight across the cold medium is sufficient to reproduce the\nobserved column densities of molecules. This small fraction of hot gas\ncorresponds to about 6 MHD shocks of 10 \\kms{} or 1000 vortices with\nrotation velocity of 3.5~\\kms{} per magnitude of gas (or $\\Ntot=1.8\\times\n10^{21}$ \\cq) of density $n \\approx 30$ \\cc{}\n\\cite{verstraete99:hcdm:ssHHrl}.\n\nThe main problem met with the models of individual C shocks or vortices is\nthat the predicted shift between neutral and ionized species is larger than\nobserved. In this paper, we simply address the issue of the impact of the\nline of sight averaging upon the resulting line profiles in a turbulent\nvelocity field. We investigate the spatial and velocity distribution of the\nregions of high vorticity or high negative divergence (shocks) in a\nsimulation of compressible turbulence to test whether or not the\nspace-velocity characteristics of any of these subsets fulfill the\nobservational requirements. We carry our analysis on the numerical\nsimulations of compressible turbulence of Porter, Pouquet \\& Woodward\n\\cite*{porter94:ksdtdsf}. They are $512^3$ simulations of midly\ncompressible turbulence (initial rms Mach number=1). The time step analysed\nhere is $t=1.2 \\Tac$ where \\Tac{} is the acoustic crossing time. At that\nepoch in the simulation, many shocks have survived producing density\ncontrasts as large as 40, but the bulk of the energy at small scales is\ncontained in the vortical modes.\n\nThese simulations are hydrodynamical and do not include magnetic field.\nThe impact of magnetic field upon the statistical properties of turbulence\nmay be less important than foreseen. Recent simulations of MHD\ncompressible turbulence \\cite{ostriker99:ksesgmc:ddt} show that the\ndissipation timescale of MHD turbulence is closer than previously thought\nto that of hydrodynamical turbulence. Descriptions of the energy cascade\nin models of MHD turbulence also predict that vortices must play an\nimportant role~\\cite{goldreich95:tist.II:sat,lazarian99:rwsf}. Magnetic\nfield does not prevent either the intermittency of the velocity field to\ndevelop\n\\cite{brandenburg96,galtier98:imhdf,politano98:khemhdctolscf,politano98:dlstmf,politano95:mimhdt}.\nIn MHD as in hydrodynamic turbulence, shocks interact and generate vortex\nlayers, which are Kelvin-Helmholtz unstable and eventually form vorticity\nfilaments.\n \nAnother limitation of our study lies in the fact that the Reynolds number\nof the simulations is small compared to that of interstellar turbulence.\nRecent studies of high Reynolds number turbulence in Helium bring the\nunexpected result that the statistical properties of the velocity field\nhave little dependence with the Reynolds number, at large Reynolds\nnumbers~\\cite{tabeling96:pdfsflrnt}. We therefore believe that the analysis\npresented here on hydrodynamical simulations has some relevance to the\nunderstanding of interstellar turbulence.\n\nWe discuss the velocity structure of the two subsets (regions of high\nvorticity or of high negative divergence) and compare in each case the\nvelocity samplings provided by pencil beams versus large beams\n(Sect.~\\ref{sec:vssivsct}). In Sect.~\\ref{sec:sdhvds}, we discuss the\nspatial distributions of the two subsets. In Sect.~\\ref{sec:co}, we compare\nthe results derived from the numerical simulations with the observations.\n\n\\section{Velocity structure of subsets of intense vortices and shocks in\n compressible turbulence.}\n\\label{sec:vssivsct}\n\n\\subsection{Integrated profiles}\n\nWe first compare the velocity distributions obtained with all the data\npoints in the simulation with those obtained by selecting only 3\\% (or $4\n\\times 10^6$) of these data points. These subsamples are of three kinds: a\nsubset of randomly selected positions in space and the upper tails of the\ndistributions of the negative divergence and vorticity (see\nFigs.~\\ref{fig:pdfs:ngv}a and~\\ref{fig:pdfs:ngv}b). In the following, for\nthe sake of simplicity, we will call them shocks and vortices.\n\n\\begin{figure}\n \\resizebox{\\hsize}{!}{%\n \\includegraphics*[1.6cm,19.5cm][10.3cm,26.5cm]{ms9327.f1}}\n \\caption{PDFs of the values of {\\it (a)} the positive and negative\n divergence and {\\it (b)} the vorticity in the whole cube. The\n integrated numbers of points below (case {\\it a}) above (case {\\it b})\n each threshold indicated by a vertical bar are 3\\%.}\n \\label{fig:pdfs:ngv}\n\\end{figure}\n\nThe choice of 3\\% of the points is a compromise between the value of\n$\\approx$ 1\\% dictated by the chemical models and their confrontation to\nthe observations and a number large enough so that the statistical analysis\ndescribed below be meaningful. The actual values of the thresholds in the\nvorticity or in the divergence correspond to this choice. As said above,\nmany of the molecular species observed in the cold diffuse medium, require\nlarge temperatures for their formation. Below gas temperatures of the order\nof 10$^3$ K, there is an exponential cut-off of the speed or the\nprobability of these chemical reactions. Since the heating sources are\neither the viscous dissipation enhanced in the layers of large velocity\nshear at the boundary of coherent vortices \\cite{joulain98:necdsit}, or the\nion-neutral streaming in the magnetic precursor of the shocks\n\\cite{flower95:ntsigmhds}, the thresholds in vorticity and in negative\ndivergence correspond to temperature thresholds. It is only above such\nthresholds in negative divergence (shock velocity) or vorticity (shear),\nthat the {\\it hot chemistry} required by the observations can be triggered\nin the cold diffuse medium. As seen on Fig.~\\ref{fig:pdfs:ngv}, the\nselected thresholds for the vorticity and the divergence fall in the\nnon-Maxwellian (non-Gaussian) tails of each distribution. The sets of\nstructures that we describe therefore belong to the non-Maxwellian\n(non-Gaussian) tails of the corresponding distributions.\n \nThe velocity distributions of each subset (normalized to their peak value)\nis shown in Fig.~\\ref{fig:vd} together with that of the whole cube. They\nare remarkably similar. The only subset which provides a slightly (10\\%)\nbroader spectrum is that built on the shocks. A tracer passively advected\nin a turbulent flow (subset of spatially random positions) would therefore\ncarry the characteristics of the turbulent field of the bulk of the volume,\neven though its volume filling factor is as small as a few \\%.\n\n\\begin{figure}\n \\resizebox{\\hsize}{!}{%\n \\includegraphics*[1.5cm,20.0cm][10.3cm,26.65cm]{ms9327.f2}}\n \\caption{Velocity distributions obtained with the full velocity field and\n all the points in the simulation (solid), with 3\\% of the data points\n randomly selected in space (dashed), with the 3\\% of the points which\n have the largest vorticity (dotted) and with the 3\\% of the points\n which have the largest negative divergence (dot-dashed). The intensity\n scale corresponds to the number of points in each of the 218 velocity\n bins. The velocity scale is the bin number.}\n \\label{fig:vd}\n\\end{figure}\n\n\\subsection{Velocity widths of pencil beam and large beam line profiles.} \n\n\\begin{figure}\n \\resizebox{\\hsize}{!}{%\n \\includegraphics*[5.0cm,4.1cm][15.1cm,21.9cm]{ms9327.f3}}\n \\caption{PDFs of the velocity widths of the $1.6 \\times 10^4$ individual\n spectra, each sampling $4 \\times 4 \\times 512$ pixels, and therefore\n mimicking spectra obtained with a beam 128 times narrower than that\n obtained by integrating the emission of the whole cube. The spectra are\n built on {\\it (a)} the complete velocity field, and on only 3\\% of the\n data points selected {\\it (b)} as the most intense vortices and {\\it\n (c)} as the most intense shocks. The vertical bar, in each panel\n indicates the width, at the same level, of the integrated spectrum over\n the whole cube.}\n \\label{fig:pdfs:sw}\n\\end{figure}\n\n\\newcommand{\\e}[1]{\\ensuremath{\\times 10^{#1}}}\n\\newcommand{\\DivV}{\\ensuremath{|\\nabla .v|}}\n\\begin{table*}\n \\begin{flushleft}\n \\caption{Comparison of integrated and individual spectra.}\n \\label{tab:ciis}\n \\begin{tabular}{lrcccccc}\n \\hline\n \\noalign{\\smallskip}\n & &\n \\multicolumn{2}{c}{Integrated spectrum} &\n \\multicolumn{4}{c}{Individual spectra} \\\\\n% \\cline{3-4}\n \\cline{5-8}\n Sample & level &\n \\fvol{} & \\Dvtot{} & $\\fvol'$ & \\Dvmp{} \n & ${\\Dvtot - \\Dvmp \\over \\Dvtot }$ & \n \\Dvpdf{} \\\\\n \\noalign{\\smallskip}\n \\hline\\noalign{\\smallskip}\n full field & 8\\% & 1 & 114 & 6\\e{-5} & 85 & 0.25 & 43 \\\\\n & 16\\% & & 97 & & 73 & 0.25 & 43 \\\\\n \\\\\n large $\\omega$ & 8\\% & 3\\e{-2} & 113 & 2\\e{-6} & 70 & 0.38 & 61 \\\\\n & 16\\% & & 96 & & 64 & 0.33 & 62 \\\\\n \\\\\n large \\DivV{} & 8\\% & 3\\e{-2} & 130 & 2\\e{-6} & 70 & 0.46 & 61 \\\\\n & 16\\% & & 110 & & 62 & 0.44 & 62 \\\\\n \\noalign{\\smallskip}\n \\hline\n \\end{tabular}\n \\end{flushleft}\n\\end{table*}\n\nWe now compare the velocity width of synthetic spectra obtained with a\nlarge beam (\\ie{} profiles observed in emission) to those obtained in a\npencil beam (\\ie{} profiles observed in absorption). To do so we have\ncomputed the velocity distribution in $4\\times 4\\times 512$ subsamples of\nthe whole cube and of the two subsets of largest vorticity and largest\ndivergence. Under the approximation that the line radiation is optically\nthin \\cite{falgarone94:sstc}, we consider that these velocity distributions\ncapture the main characteristics of the line profiles. The velocity\ndistributions will therefore be called profiles (or spectra) for simplicity\nin what follows. A total number of $1.6 \\times 10^4$ individual spectra are\ntherefore obtained across the face of the cube, for each set. To achieve\nthe comparison of these individual spectra (surrogates of pencil beam\nspectra) with the total spectrum (surrogate of the large beam spectrum), we\nuse a width computed at levels 1\\%, 8\\%, 16\\% and 32\\% of the local peak of\nthe velocity distribution (spectrum). Radiative transfer affects more\nseverely the velocity domains where the crowding is the largest (the peaks\nof the velocity distributions) and this is the reason why we analyze the\nvelocity coverage of each distribution at levels low enough for radiation\nto be reasonably assumed optically thin.\n\nWe have computed the probability distribution functions (PDF) of the widths\nof the individual profiles at the four levels quoted above. They are shown\non Fig.~\\ref{fig:pdfs:sw} at the 8\\% level for the whole velocity field and\nthe large vorticity and divergence subsets. The dotted curve shows the\nGaussian distributions with the same mean and dispersion. On each panel,\nthe vertical bar indicates the width of the large beam profile at the same\nlevel (\\Dvtot{} in Table~\\ref{tab:ciis}). The width (\\Dvpdf{}) and peak\n(\\ie{} most probable value, \\Dvmp{}) of the PDFs are given in\nTable~\\ref{tab:ciis} for the 8\\% and 16\\% levels and differ by less than\n20\\% with the level selected. The volume filling factors \\fvol{} and\n$\\fvol'$ represent the fraction of points included in each sample.\n\nIn all cases, the pencil beam spectra are narrower than the large beam\nspectrum but by only 25 to 45\\% (column 7 of Table~\\ref{tab:ciis}) while\nthe projected sizes of the sampled volumes differ by a factor 128. This is\ndue to the fact that although the projected size of the volumes sampled by\nthe pencil beams are small, the depth along the line of sight has remained\nunchanged (512). Along one dimension at least, the pencil beam samples the\nvelocity over large scales. We have made similar computations for $8\\times\n8\\times 512$ and $32\\times 32\\times 512$ pencil beams and the widths of the\ncorresponding velocity distributions remain almost the same. For this\nreason we believe that the results for a pencil beam as small as those of\nactual observations compared to the large beam (\\ie{} 60\"/0.001\"=6$\\times\n10^4$, a ratio which cannot be achieved by any direct numerical simulation)\nwould not be significatively different. As long as the depth of the medium\nsampled by the line of sight is large, the velocity signature of the pencil\nbeam profile remains close to that of these large scales.\n\nThen it is interesting to note that the differences between the subsets of\nstrong shocks and intense vortices are not marked. On average, vortices\nproduce pencil beam profiles closer to the large beam profile than do the\nshocks, but the effect in the present simulation is small.\n\n\\subsection{PDFs of line centroid increments}\n\nWe have computed the line centroid of each spectrum across the face of the\ncube according to the method described in Lis et\nal.~\\cite*{lis96:splcvcvict}. Fig.~\\ref{fig:pdfs:ci} displays the\nprobability distribution functions of the transverse increments of these\ncentroids for several lags. These PDFs are normalized to the rms\ndispersion of the increments. The comparison of the PDFs obtained for the\nfull velocity field (Fig.~\\ref{fig:pdfs:ci}a) with those obtained with the\n3\\% most intense vortices (Fig.~\\ref{fig:pdfs:ci}b) and shocks\n(Fig.~\\ref{fig:pdfs:ci}c) shows that, at the smallest lag, the non-Gaussian\ntails of the PDFs extend much further for the latter subsets that for the\nformer. Non-Gaussian tails disappear at $\\Delta=9$ for the full velocity\nfield while they persist up to $\\Delta=15$ for the regions of large\ndivergence and large vorticity. The non-Gaussian tails of the PDFs of line\ncentroid increments have been shown to be associated with regions of\nenhanced vorticity in turbulence~\\cite{lis96:splcvcvict}. This result shows\nthat both the subsets of shocks and vortices exhibit pronounced\nnon-Gaussian behaviour in those PDFs.\n \n\\begin{figure*}\n \\resizebox{12.0cm}{!}{%\n \\includegraphics*[3.0cm,3.0cm][15.1cm,26.7cm]{ms9327.f4}} \\hfill\n \\parbox[b]{55mm}{%\n \\caption{PDFs of the line centroid increments for different lags\n $\\Delta$ and {\\it (a)} the full velocity field, {\\it (b)} the subset\n of most intense vortices and {\\it (c)} the subset of positions of\n largest negative divergence.}}\n \\label{fig:pdfs:ci}\n\\end{figure*}\n\n\\begin{figure*}\n \\resizebox{\\hsize}{!}{%\n \\includegraphics*[1.0cm,3.0cm][20.0cm,26.5cm]{ms9327.f5}}\n \\caption{Channel maps of the surface filling factor on each line of sight\n in {\\it (a)} the complete velocity field, {\\it (b)} the subset of the\n most intense vortices and {\\it (c)} the subset of the largest negative\n divergence. The color scales are different for each velocity range and\n do not cover the whole dynamic range for the vortices and the shocks.\n From top to bottom panel, the values of the actual maxima are (52, 326,\n 512, 457, 135) for the complete velocity field, (23, 46, 90, 79, 24)\n for the vortices and (36, 83, 116, 73, 30) for the shocks.}\n \\label{fig:cmsff}\n\\end{figure*}\n\n\\begin{figure*}\n \\resizebox{\\hsize}{!}{%\n \\includegraphics*[1.5cm,7.5cm][19.5cm,22.5cm]{ms9327.f6}}\n% \\vspace*{-1.0cm}\n \\caption{Maps of the surface filling factors of {\\it (a)} the \n most intense vortices {\\it (b)} the regions of largest negative\n divergence. Maps of line--of--sight average of {\\it (c)} the vorticity\n modulus and {\\it (d)} the negative divergence.}\n \\label{fig:msff}\n\\end{figure*}\n\n\\section{Spatial distribution of the high vorticity/divergence\n subsets}\n\\label{sec:sdhvds}\n\n\\subsection{Channel maps}\n\nThe three channel maps of Fig.~\\ref{fig:cmsff} display the surface filling\nfactor of the data points in five adjacent velocity intervals for the whole\ncube and the two subsets of vortices and shocks. To optimize the visibility\nof the weakly populated regions, the color scale does not span the whole\ndynamic range and is not the same in each velocity interval. At almost all\nvelocities, the surface filling factors reach larger values for the shocks\nthan for the vortices (see caption of Fig.~\\ref{fig:cmsff}). Thus the\nshocks are more clustered in space than the vortices. Shocks also appear as\nthicker (or more extended) projected structures than vortices. Both subsets\nhave a much more pronounced filamentary texture than the whole velocity\nfield. Many small scale filaments are visible with lengths reaching a\nsignificant fraction of the integral scale. This result has been already\nrecognized for the regions of large vorticity by Vincent \\& Meneguzzi\n\\cite*{vincent91,vincent94} or She, Jackson \\& Orszag \\cite*{she90} in\nincompressible turbulence and by Porter, Woodward \\& Pouquet\n\\cite*{porter98:irsdctf} in compressible turbulence.\n\nFor the bulk of the structures, there is no coincidence between the\npatterns delineated by the shocks and the vortices. There are exceptions,\nthough, like the structures seen in the extreme velocity channels. The\nsmall scale patterns delineated in these channels by the regions of large\nvorticity or large divergence closely follow each other, although the\ndetails do not exactly coincide. It is remarkable that all the small scale\npatterns seen in the extreme velocity channels in the maps of large\nvorticity and divergence are also those of the full velocity field\n(Fig.~\\ref{fig:cmsff}a): in the first channel (top left), the data points\nof the full velocity field are either shocks or vortices or both.\n\nThese maps also show that shocks and vortices are not randomly distributed\nbut are clustered in space and in velocity. There are large voids with only\na few vortex or shocks on the line of sight. The contrasts are large as\nindicated by the peak values given in the caption of Fig.~\\ref{fig:cmsff}.\n\n\\subsection{Integrated maps and surface filling factors}\n\nWe now turn to the spatial distribution across the face of the cube of the\ntwo subsets of shocks and vortices. The set of randomly selected positions\ndoes not have any significant spatial structure. It is therefore not shown.\nThe spatial distribution of the surface filling factor \\fsur{} is shown in\nFig.~\\ref{fig:msff} for the vortices and the shocks.\n\nFig.~\\ref{fig:msff} shows that the contrasts are large ($\\approx 100:1$) in\nthe two subsets for which the average surface filling factor per pixel is\nonly 15.3 (\\ie{} 3\\% of the data points over 512$^2$ pixels). There are\nonly 5\\% and 2\\% empty lines of sight for the vortices and the shocks\nrespectively, \\ie{} the surface filling factors of the regions of large\nvorticity or large divergence are almost everywhere larger than unity,\nalthough they fill only 3\\% of the whole volume. These numbers depend on\nthe thresholds selected for the vorticity and divergence.\n\nThe maps of the filling factors (Figs.~\\ref{fig:msff}a and~\\ref{fig:msff}b)\nare very similar to the maps of the vorticity and of the negative\ndivergence (Figs.~\\ref{fig:msff}c and~\\ref{fig:msff}d) computed with the\nwhole data cube. In particular the maxima in vorticity and in negative\ndivergence are those of the surface filling factors of the upper tails of\nthe corresponding distribution. It means than for the vortices and for the\nshocks, the origin of the maxima observed in projection is the crowding of\nrare events populating the upper tails of the distributions.\n\nWe have computed the fractional area covered by structures with surface\nfilling factors larger than a threshold \\fsur[0]. The dependence of this\nfractional area on \\fsur[0] is shown in Fig.~\\ref{fig:fa}. Unlike randomly\nselected positions (dotted curve), the high vorticity/divergence\ndistributions exhibit structures with large filling factors which cover\nonly a tiny fraction of the total area. The large crowdings of shocks are\nmore numerous than those of vortices, but the bulk of the ensemble of\nvortices (those which fill most of the surface, $\\fsur[0]<50$) cover a\nfractional area slightly larger that the bulk of the shocks.\n\n\\begin{figure}\n \\resizebox{\\hsize}{!}{%\n \\includegraphics*[1.5cm,20.0cm][10.3cm,26.6cm]{ms9327.f7}}\n \\caption{Fractional area covered by the structures with a surface\n filling factor above a threshold \\fsur[0] in the high vorticity (solid)\n and high negative divergence (dashed) subsets. The same curve for the\n randomly selected positions is the dotted curve.}\n \\label{fig:fa}\n\\end{figure}\n\n\\section{Comparison with observations}\n\\label{sec:co}\n\nStatistics on molecular absorption lines in the cold diffuse medium are\nstill sparse. We have used the data set of Liszt \\& Lucas\n\\cite*{liszt98:COaecercs} to compare the velocity widths of 9 pairs of\n\\thCO(1-0) and \\thCO(2-1) absorption and emission lines toward\nextragalactic sources. In 5 cases (B1730, B2013, B2200 and B2251), the\n\\twCO{} lines are simple enough that a comparison between the emission and\nabsorption profiles is meaningful. Out of the 14 pairs, two exhibit\nemission and absorption profiles of equal widths, three have absorption\nprofiles larger than the emission profiles (this is a possible\nconfiguration according to the simulations, see Fig.~\\ref{fig:pdfs:sw}) and\nnine have absorption narrower than emission profiles. The differences are\nnot large and the average value of the 9 relative width differences\n($\\Dvem-\\Dvabs/\\Dvem$) is only 0.34. This number is very close to the\nvalues listed in Column 7 of Table~\\ref{tab:ciis} for the subset of large\nvortices (although the difference with that of large divergence is not\nsignificant).\n\nAnother interesting property of the molecular line absorption measurements\nis the large scatter of column densities detected for a given amount of gas\nsampled by the line of sight, \\Ntot{}. On average, the observed column\ndensity of \\CHp{} for instance increases almost linearly with \\Ntot{} (see\nreferences in Joulain et al. \\cite*{joulain98:necdsit}), but the scatter of\nthe values at a given value of \\Ntot{} is large. Scatters of about a factor\n10 are found in merging the samples of Crane et al. \\cite*{crane95:hrsiCH}\nand Gredel \\cite*{gredel97:iCHsOBa}. It means that the spatial distribution\nof the structures bearing these molecules is highly heterogeneous, although\n{\\it on average}, the larger the total column density of gas sampled, the\nlarger the column density of molecules. This characteristic may be brought\ntogether with the fact that the surface filling factor of the most intense\nvortices and shocks have large fluctuations (a factor $\\sim$ 10) about\ntheir average value (15) (Figs.~\\ref{fig:msff}a and~\\ref{fig:msff}b).\n\n\\section{Conclusion}\n\nThe regions of largest vorticity or largest divergence in compressible\nturbulence are small subsets of a whole turbulent velocity field but we\nhave shown that, despite their small volume filling factor (here\n$\\fvol=0.03$):\n\n(i) they sample the whole velocity field,\n\n(ii) pencil beam samplings across these subsets have velocity coverages\nalmost as broad as those obtained with large beams. The values (35\\% to\n45\\%) and the signs of these differences are consistent with the\nobservations.\n\n(iii) the PDFs of centroid velocity increments built on these subsets have\nmore extended non-Gaussian wings than those of the full velocity field.\nTheir intermittent characteristics subsist at larger lags than for the full\nvelocity field.\n\n(iv) copious small scale structure with large contrasts is seen in the maps\nof the surface filling factor of the regions of large vorticity and large\ndivergence. These contrasts are of the same order of magnitude as those\nobserved in the column densities of \\CHp{} for instance for a given column\ndensity of sampled gas.\n\n(v) the surface filling factor of the subsets of high vorticity/divergence\nare almost everywhere larger than unity even though their volume filling\nfactor is as small as 3\\% in the subsets studied here. Vortices are\nslightly more efficient than shocks at covering the sky: they tend to be\nmore numerous, and to form smaller structures which are less clustered in\nspace.\n\nIn summary our study confirms that mild shocks as well as intense vortices\ncould be the subsets of the cold diffuse medium enriched in molecules and\nresponsible for the molecular absorption lines detected in the direction of\nextragalactic sources.\n\nNumerical simulations of hydrodynamical turbulence are not ideally suited\nto test the properties of such subsets, but one-fluid simulations of MHD\nturbulence are not ideal either because of the importance of the\nion-neutral streaming in the triggering of hot chemistry, whether in MHD\nshocks or in magnetized vortices. More detailed predictions of the\nphase-space structures of the subsets of turbulence where hot chemistry is\nactivated in the cold diffuse medium require calculations of MHD\ncompressible turbulence which take ion-neutral drift into account.\n\n\\begin{acknowledgements}\n We thank D. H. Porter, A. Pouquet, and P. R. Woodward for providing us\n with the result of their hydrodynamic simulation and our referee, A.\n Lazarian, for his helpful comments.\n\\end{acknowledgements}\n\n\\bibliography{ms9327}\n\\bibliographystyle{aabib99}\n\n\\end{document}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%% Local Variables: \n%%% mode: latex\n%%% TeX-master: t\n%%% End: \n"
}
] |
[
{
"name": "ms9327.bbl",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[\\protect\\astroncite{Brandenburg et~al.}{1996}]{brandenburg96}\nBrandenburg, A., Jennings, R.~L., Nordlund, A.~K., Rieutord, M., Stein, R.~F.,\n and Tuominen, I., 1996,\n\\newblock {J. Fluid Mech.} {306}, 325\n\n\\bibitem[\\protect\\astroncite{Crane et~al.}{1995}]{crane95:hrsiCH}\nCrane, P., Lambert, D.~L., and Sheffer, Y., 1995,\n\\newblock {ApJS} {99(1)}, 107\n\n\\bibitem[\\protect\\astroncite{Draine}{1986}]{draine86:mhdsdc:lstro}\nDraine, B.~T., 1986,\n\\newblock {ApJ} {310(1)}, 408\n\n\\bibitem[\\protect\\astroncite{Draine and Katz}{1986}]{draine86:mhdsdc:ps}\nDraine, B.~T. and Katz, N., 1986,\n\\newblock {ApJ} {310(1)}, 392\n\n\\bibitem[\\protect\\astroncite{Elitzur and Watson}{1978}]{elitzur78}\nElitzur, M. and Watson, W.~D., 1978,\n\\newblock {ApJ Lett.} {222}, L141\n\n\\bibitem[\\protect\\astroncite{Falgarone et~al.}{1994}]{falgarone94:sstc}\nFalgarone, E., Lis, D.~C., Phillips, T.~G., Pouquet, A., Porter, D.~H., and\n Woodward, P.~R., 1994,\n\\newblock {ApJ} {436(1)}, 728\n\n\\bibitem[\\protect\\astroncite{Falgarone et~al.}{1995}]{falgarone95:csitldic}\nFalgarone, E., Pineau Des~For�ts, G., and Roueff, E., 1995,\n\\newblock {A\\&A} {300(3)}, 870\n\n\\bibitem[\\protect\\astroncite{Falgarone and\n Puget}{1995}]{falgarone95:iticigktdhpfgm}\nFalgarone, E. and Puget, J.-L., 1995,\n\\newblock {A\\&A} {293(3)}, 840\n\n\\bibitem[\\protect\\astroncite{Flower and Pineau~des\n For�ts}{1995}]{flower95:ntsigmhds}\nFlower, D.~R. and Pineau~des For�ts, G., 1995,\n\\newblock {MNRAS} {275(4)}, 1049\n\n\\bibitem[\\protect\\astroncite{Flower and Pineau~des\n For�ts}{1998}]{flower98:ctsim:pal}\nFlower, D.~R. and Pineau~des For�ts, G., 1998,\n\\newblock {MNRAS} {297(4)}, 1182\n\n\\bibitem[\\protect\\astroncite{Galtier et~al.}{1998}]{galtier98:imhdf}\nGaltier, S., Gomez, T., Politano, H., and Pouquet, A., 1998,\n\\newblock in U. Frisch (ed.), {Advances in Turbulence {VII}}, pp 453--456,\n Kluwer Academic Publishing\n\n\\bibitem[\\protect\\astroncite{Goldreich and\n Sridhar}{1995}]{goldreich95:tist.II:sat}\nGoldreich, P. and Sridhar, S., 1995,\n\\newblock {ApJ} {438(2)}, 763\n\n\\bibitem[\\protect\\astroncite{Gredel}{1997}]{gredel97:iCHsOBa}\nGredel, R., 1997,\n\\newblock {A\\&A} {320(3)}, 929\n\n\\bibitem[\\protect\\astroncite{Joulain et~al.}{1998}]{joulain98:necdsit}\nJoulain, K., Falgarone, E., Pineau~des For�ts, G., and Flower, D., 1998,\n\\newblock {A\\&A} {340(1)}, 241\n\n\\bibitem[\\protect\\astroncite{Lazarian and Vishniac}{1999}]{lazarian99:rwsf}\nLazarian, A. and Vishniac, E.~T., 1999,\n\\newblock {ApJ} {517(2)}, 700\n\n\\bibitem[\\protect\\astroncite{Lis et~al.}{1996}]{lis96:splcvcvict}\nLis, D.~C., Pety, J., Phillips, T.~G., and Falgarone, E., 1996,\n\\newblock {ApJ} {463(1)}, 623\n\n\\bibitem[\\protect\\astroncite{Liszt and Lucas}{1994}]{liszt94:mHCOedctdo}\nLiszt, H.~S. and Lucas, R., 1994,\n\\newblock {ApJ Lett.} {431(2)}, L131\n\n\\bibitem[\\protect\\astroncite{Liszt and Lucas}{1995}]{liszt95:mwmeaca}\nLiszt, H.~S. and Lucas, R., 1995,\n\\newblock {A\\&A} {294(3)}, 811\n\n\\bibitem[\\protect\\astroncite{Liszt and Lucas}{1998}]{liszt98:COaecercs}\nLiszt, H.~S. and Lucas, R., 1998,\n\\newblock {A\\&A} {339(2)}, 561\n\n\\bibitem[\\protect\\astroncite{Lucas and Liszt}{1993}]{lucas93:pbommwmaBLL}\nLucas, R. and Liszt, H.~S., 1993,\n\\newblock {A\\&A} {276(1)}, L33\n\n\\bibitem[\\protect\\astroncite{Lucas and Liszt}{1994}]{lucas94:pbommwma}\nLucas, R. and Liszt, H.~S., 1994,\n\\newblock {A\\&A} {282(1)}, L5\n\n\\bibitem[\\protect\\astroncite{Lucas and Liszt}{1996}]{lucas96:pbsgHCOatecs}\nLucas, R. and Liszt, H.~S., 1996,\n\\newblock {A\\&A} {307(1)}, 237\n\n\\bibitem[\\protect\\astroncite{Lucas and Liszt}{1997}]{lucas97:mwodc}\nLucas, R. and Liszt, H.~S., 1997,\n\\newblock in E.~F. Van~Dishoeck (ed.), {Molecules in Astrophysics: Probes and\n Processes}, Vol. 178 of {IAU Symposium}, pp 421--430, Kluwer Academic\n Publisher, Leiden\n\n\\bibitem[\\protect\\astroncite{Ostriker et~al.}{1999}]{ostriker99:ksesgmc:ddt}\nOstriker, E.~C., Gammie, C.~F., and Stone, J.~M., 1999,\n\\newblock {ApJ} {513(1)}, 259\n\n\\bibitem[\\protect\\astroncite{Pineau~des For�ts\n et~al.}{1986}]{pineau86:tsisms:fdc}\nPineau~des For�ts, G., Flower, D.~R., Hartquist, T.~W., and Dalgarno, A., 1986,\n\\newblock {MNRAS} {220(4)}, 801\n\n\\bibitem[\\protect\\astroncite{Politano and Pouquet}{1995}]{politano95:mimhdt}\nPolitano, H. and Pouquet, A., 1995,\n\\newblock {Phys. Rev. E} {52(1)}, 636\n\n\\bibitem[\\protect\\astroncite{Politano and Pouquet}{1998a}]{politano98:dlstmf}\nPolitano, H. and Pouquet, A., 1998a,\n\\newblock {Geophys. Res. Lett.} {25(3)}, 273\n\n\\bibitem[\\protect\\astroncite{Politano and\n Pouquet}{1998b}]{politano98:khemhdctolscf}\nPolitano, H. and Pouquet, A., 1998b,\n\\newblock {Phys. Rev. E} {57(1)}, R21\n\n\\bibitem[\\protect\\astroncite{Porter et~al.}{1994}]{porter94:ksdtdsf}\nPorter, D.~H., Pouquet, A., and Woodward, P.~R., 1994,\n\\newblock {Phys. Fluids} {6(6)}, 2133\n\n\\bibitem[\\protect\\astroncite{Porter et~al.}{1998}]{porter98:irsdctf}\nPorter, D.~H., Woodward, P.~R., and Pouquet, A., 1998,\n\\newblock {Phys. Fluids} {10(1)}, 237\n\n\\bibitem[\\protect\\astroncite{She et~al.}{1990}]{she90}\nShe, Z.~S., Jackson, E., and Orszag, S.~A., 1990,\n\\newblock {Nat} {334}, 226\n\n\\bibitem[\\protect\\astroncite{Tabeling et~al.}{1996}]{tabeling96:pdfsflrnt}\nTabeling, P., Zocchi, G., Belin, F., Maurer, J., and Willaime, H., 1996,\n\\newblock {Phys. Rev. E} {53(2)}, 1613\n\n\\bibitem[\\protect\\astroncite{Verstraete\n et~al.}{1999}]{verstraete99:hcdm:ssHHrl}\nVerstraete, L., Falgarone, E., Pineau~des For�ts, G., Flower, D., and Puget,\n J.-L., 1999,\n\\newblock in P. Cox and M.~F. Kessler (eds.), {The Universe as Seen by {ISO}},\n Vol.~2, pp 779--782, ESA, UNESCO, Paris\n\n\\bibitem[\\protect\\astroncite{Vincent and Meneguzzi}{1991}]{vincent91}\nVincent, A. and Meneguzzi, M., 1991,\n\\newblock {J. Fluid Mech.} {225}, 1\n\n\\bibitem[\\protect\\astroncite{Vincent and Meneguzzi}{1994}]{vincent94}\nVincent, A. and Meneguzzi, M., 1994,\n\\newblock {J. Fluid Mech.} {258}, 245\n\n\\bibitem[\\protect\\astroncite{Wiklind and Combes}{1997}]{wiklind97:malhr}\nWiklind, T. and Combes, F., 1997,\n\\newblock {A\\&A} {328(1)}, 48\n\n\\bibitem[\\protect\\astroncite{Wiklind and Combes}{1998}]{wiklind98:cmals}\nWiklind, T. and Combes, F., 1998,\n\\newblock {ApJ} {500(1)}, 129\n\n\\end{thebibliography}\n"
}
] |
astro-ph0002260
|
Calibrating Array Detectors
|
[
{
"author": "D.~J.~Fixsen\\altaffilmark{1}$^"
},
{
"author": "$\\altaffilmark{3}"
},
{
"author": "S.~H.~Moseley\\altaffilmark{2}"
},
{
"author": "and R.~G.~Arendt\\altaffilmark{1}"
}
] |
The development of sensitive large format imaging arrays for the infrared promises to provide revolutionary capabilities for space astronomy. For example, the Infrared Array Camera (IRAC) on SIRTF will use four $256\times 256$ arrays to provide background limited high spatial resolution images of the sky in the 3 to 8 $\mu$m spectral region. In order to reach the performance limits possible with this generation of sensitive detectors, calibration procedures must be developed so that uncertainties in detector calibration will always be dominated by photon statistics from the dark sky as a major system noise source. In the near infrared, where the faint extragalactic sky is observed through the scattered and reemitted zodiacal light from our solar system, calibration is particularly important. Faint sources must be detected on this brighter local foreground. We present a procedure for calibrating imaging systems and analyzing such data. In our approach, by proper choice of observing strategy, information about detector parameters is encoded in the sky measurements. Proper analysis allows us to simultaneously solve for sky brightness and detector parameters, and provides accurate formal error estimates. This approach allows us to extract the calibration from the observations themselves; little or no additional information is necessary to allow full interpretation of the data. Further, this approach allows refinement and verification of detector parameters during the mission, and thus does not depend on {a priori} knowledge of the system or ground calibration for interpretation of images.
|
[
{
"name": "calibration.tex",
"string": "\\documentstyle[11pt,aaspp4]{article}\n\\def\\um\t\t{$\\mu$m\\ }\n\\def\\etal\t{{et al.}}\n\n\\begin{document}\n\\slugcomment{Scheduled for ApJS, Jun 2000}\n\n\\title{Calibrating Array Detectors}\n\\author{\nD.~J.~Fixsen\\altaffilmark{1}$^,$\\altaffilmark{3}, \nS.~H.~Moseley\\altaffilmark{2}, and \nR.~G.~Arendt\\altaffilmark{1}}\n\n\\altaffiltext{1}{Raytheon-ITSS Corp., Code 685, NASA/GSFC, Greenbelt, MD 20771}\n\\altaffiltext{2}{Code 685, Infrared Astrophysics Branch, Goddard Space Flight \nCenter, Greenbelt, MD 20771}\n\\altaffiltext{3}{email address fixsen@stars.gsfc.nasa.gov}\n\n\\begin{abstract}\nThe development of sensitive large format imaging arrays for the\ninfrared promises to provide revolutionary capabilities for space\nastronomy. For example, the Infrared Array Camera (IRAC) on SIRTF will\nuse four $256\\times 256$ arrays to provide background limited high spatial\nresolution images of the sky in the 3 to 8 $\\mu$m spectral region. In order to\nreach the performance limits possible with this generation of sensitive\ndetectors, calibration procedures must be developed so that uncertainties\nin detector calibration will always be dominated by photon statistics\nfrom the dark sky as a major system noise source. In the near infrared,\nwhere the faint extragalactic sky is observed through the scattered and\nreemitted zodiacal light from our solar system, calibration is particularly\nimportant. Faint sources must be detected on this brighter local\nforeground.\n\nWe present a procedure for calibrating imaging systems and\nanalyzing such data. In our approach, by proper choice of observing\nstrategy, information about detector parameters is encoded in the sky\nmeasurements. Proper analysis allows us to simultaneously solve for sky\nbrightness and detector parameters, and provides accurate formal error\nestimates.\n\nThis approach allows us to extract the calibration from the observations \nthemselves; little\nor no additional information is necessary to allow full interpretation of\nthe data. Further, this approach allows refinement and verification of\ndetector parameters during the mission, and thus does not depend on \n{\\it a priori} knowledge of the system or ground calibration for \ninterpretation of images.\n\n\\end{abstract}\n\\section{Introduction}\n\nThe Infrared Array Camera (IRAC) (Fazio \\etal\\ 1998) will employ four \n$256\\times256$ \nimaging infrared arrays and the cooled telescope of the SIRTF to produce \nimages of the sky which are limited by the photon statistics from the natural \nbackground, which, in this spectral region (8-25 $\\mu$m), is dominated by \nscattered and emitted light from the zodiacal dust particles. This will be \ntypical of future applications of infrared detectors in space. \nIn order to produce high quality images in the\npresence of this strong background, the relative response of the different\npixels in the detector array must be known to high precision. A technique\nmust be developed that allows the detector properties to be determined in\noperation, so that the requisite stability can be experimentally verified,\nand changes in response can be measured and included in the analysis of\nthe data. We present a technique by which the detector properties\nare determined simultaneously with the estimates of sky brightness, and\nformal errors developed for both instrument and sky parameters. \n\nWe observe the same area of the sky with the detector array \nat a number of spatially offset positions. These observations are used to \nset up a system of linear equations involving both sky brightness and detector\nproperties. In solving this system of equations, we can deduce the sky\nbrightness and detector gain and offset parameters. By appropriate\nchoices of offset spacings and sky brightness distributions, this\ntechnique allows us to continuously improve our knowledge of the detector\nproperties or detect changes. This approach embeds the\nrelative calibration of the detector array into the survey process; all\ninformation required to produce an internally consistent survey\ncan deduced from the survey itself. Since the data on which the calibration\nis based is the survey itself, it is the way to calibrate the data which is, \nin some sense, least susceptible to systematic errors. In the case that an \n{\\it a priori} calibration is used, this technique offers a method to test\ninternal consistency.\n\nIn this paper, we describe this least squares solution for sky and\ndetector properties, and suggest implementations of the technique for the\nIRAC instrument. We present the analysis of synthetic Wide-Field\nInfrared Explorer (WIRE) data and real Hubble NICMOS data, in\nwhich we derive the sky brightness, detector gain and detector offset. \n(We had planned a demonstration of the technique on the Wide-field\nInfrared Explorer, but its unfortunate demise renders the point moot.)\nThe results are encouraging, and form the basis of our plans for the\nanalysis of the IRAC imaging data. Optimization of the observational strategy \nto produce the best encoding of the detector parameters in the survey\nobservations is treated in a separate paper (Arendt, Fixsen \\& Moseley 2000).\nThis approach can offer significant insurance to the observer, in that\nregardless of the availability or applicability of independent relative\ncalibration data for the instrument, sufficient information is present in\nthe observations themselves to allow the relative calibration of the\ndata. This provides the capability for the observer to validate the\nstatistical properties of the data or to calibrate it as required.\n\nLeast squares techniques are an important staple of model fitting.\nIn this paper, we use a least squares technique, combined\nwith sampling over a wide range of spatial scales, to produce an intensity\ncalibration for the imaging system. Investigators have long used \"sky flats\" \nto produce estimates of system response (e.g. Joyce, 1992). In this process, \nimages are taken at a variety of positions around the object of interest.\nThese images are often processed using median filtering to produce estimates\nof detector response. In this paper , we derive the full algorithm for\noptimal use of the sampled data for intensity calibration of an imaging\ndetector. This algorithm then allows us to ask more sophisticated\nquestions important for planning observations, such as comparing the\nrelative goodness of different sampling procedures (Arendt et al. 1999).\nThis algorithm provides the optimal tool for calibrating imaging detectors;\nif the algorithm does not produce reliable results, it is indicative of\nincompleteness in the sampling of the sky. The algorithm provides an\noptimal detector calibration based on the data provided it. If a priori\ninformation about the detector is known, the algorithm can be adjusted to\ninclude it.\n\nOther algorithms have been described in the literature for\nanalyzing dithered image data. The drizzle method (Fruchter and Hook, 1998)\nis an approach for combining undersampled dithered images to produce a\nsingle combined image with improved resolution and signal-to-noise ratio.\nHowever, this technique is a means of a producing final image from calibrated\ndata, and is not intended as a method of deriving the detector calibration.\n\nFuture observatories will generate survey data. The accuracy of analysis of\nthese data will depend on a\nclear understanding of the statistical properties of the uncertainties in\nthe data, their level, and spatial and temporal correlations. We present\nan approach for the analysis of such data, with specific application to the\nimaging data from the SIRTF IRAC instrument.\n\nThis comprehensive least squares approach has been successfully applied to\nthe analysis of the data from the FIRAS instrument on COBE, in which a \ncomplex instrument model was required (Fixsen \\etal 1994).\n\n\\section{Overview}\nThe following equations show the derivation of the simultaneous extraction \nof sky brightness and instrument parameters to the data. The advantages of \nthis system are: 1) It uses the\nsame data for calibration and observation which saves separate observation\ntime for\ncalibration and uses the same time and exactly the same conditions for\ncalibration and observation. 2) It uses a well understood process for\ncalibration allowing for complete error analysis and flexible response\nin the case that unexpected errors arise. 3) It {\\it explicitly} includes\nthe uncertainties and correlations introduced in the calibration process\nin the uncertainties of the resulting data. We\nfocus on an imaging array observing sections of the sky, but the derivation\nis either directly applicable or easily generalized to other problems.\n\nThe underlying process is a simple linear fit which is easily understood,\nalthough the matrices involved are unwieldy. The inverses\nof the matrices are assumed to exist. If there are problems inverting\nthese matrices, it is an indication that \ninformation is missing in the calibration process. We do not go into\ndetail about the convergence or singularities of the process, but these need\nto be addressed as they show key weaknesses in the\ncalibration process and can generally be corrected by improving the \nmeasurement strategy (Arendt et al. 2000).\n\nSince the details of the calibration process leave their impact on the noise\ncharacteristics of the final data set, the procedure for taking data must\nbe be carefully designed. This is not unique to this particular process for \ncalibration, but this procedure\nmakes the costs of poor measurement strategies obvious.\n\n\\section{Derivation of the Algorithm}\nWe follow the Einstein summation convention\nand use different indices for the different vector \nspaces. Latin indices are used for the raw data and instrument pixels while \ngreek indices are used for the derived solution and the sky pixels. We use \nthe same variable names for the contravariant and covariant cases even though \nthe numerical values are different, because the underlying information is \nthe same (see Table 1).\n\nConsider the general solution, where we have a model of the data, \n$H^i(\\theta^\\mu)$, where $\\theta^\\mu$ is a vector of parameters which \nincludes both detector and sky parameters.\nFirst we linearize the equation, about a point $\\Theta^\\mu$ at or near the \nsolution yielding:\n\\begin{equation}\nH^i(\\theta^\\mu)\\approx H^i(\\Theta^\\mu)+H^i_\\mu \\delta^\\mu,\n\\end{equation}\nwhere $H^i_\\mu=\\partial H^i/\\partial\\theta^\\mu$. The derivatives are performed \nat $\\Theta^\\mu$ and $\\delta^\\mu$ are perturbations from $\\Theta^\\mu$\n($\\delta^\\mu=\\theta^\\mu-\\Theta^\\mu$).\n\nGiven a data set $D^i$ we define $\\Delta^i=D^i-H^i(\\Theta^\\mu)$.\nWith a symmetric weight matrix, $W_{ij}$, $\\chi^2$ is calculated as\n\\begin{equation}\n\\chi^2 = (\\Delta^i-H^i_\\mu\\delta^{\\mu})W_{ij}(\\Delta^j-H^j_\\nu\\delta^\\nu)\n\\end{equation}\nand its minimum is determined by\n\\begin{eqnarray}\n\\frac{\\partial\\chi^2}{\\partial\\delta^\\omega} &=& -H^i_\\omega W_{ij}\n(\\Delta^j-H^j_\\nu\\delta^\\nu)-(\\Delta^i-H^i_\\mu\\delta^\\mu)W_{ij}H^j_\\omega\n\\nonumber \\\\\n&=& -2 H^i_\\omega W_{ij}\\Delta^j+ 2 H^i_\\omega W_{ij}H^i_\\nu\\delta^\\nu=0.\n\\end{eqnarray}\nThus the solution for $\\delta^\\mu$ can be expressed as\n\\begin{equation}\n\\delta^\\mu=(H^i_\\mu W_{ij} H^j_\\nu)^{-1} H_\\nu ^k W_{kl} \\Delta^l=(H^i_\\mu\nH_{i\\nu})^{-1}H^k_\\nu\\Delta_k.\n\\end{equation}\n\nThere are several potential pitfalls here particularly if the second derivative,\n$H^i_{\\mu\\nu}=\\partial H^i_\\mu/\\partial\\theta^\\nu$, is ill-behaved in the region of \ninterest. If $H^i_{\\mu\\nu}\\delta^\\mu\\delta^\\nu>1$ the expansion point $\\Theta^\\mu$\nis too far from the solution. A new $\\Theta^\\mu$ closer to the solution should be \nused. If $H^i_{\\mu\\nu}(H^i_\\mu H_{i\\nu})^{-1}$ is close to 1 or larger \na full differential geometric treatment is in order which is beyond the\nscope of this paper.\n\nThe inversion of the matrix $H^i_\\mu H_{i\\nu}$ is the hard part of \nthe problem. In what follows we show how properties of this matrix \nthat frequently exist can reduce the problem to one that can be computed on a\nmodest computer. The inverse of the matrix is also the covariance matrix\nof the parameters including the sky parameters.\n\nIt is also interesting that:\n\\begin{equation}\n\\delta_\\mu = H^i_\\mu \\Delta_i.\n\\end{equation}\nThis is a simple mnemonic to remember the solution. It also shows that the \ncovariant form of the solution on the left is like the covariant form of the \ndata on the right. This is the weighted form of the solution needed if one \ndesires to fit this solution to some higher level theory. This can be\ndone even if the matrix cannot be inverted.\n\nTo develop a more tractable form of equation (4),\nwe separate the detector parameters from the sky parameters. \n\\begin{equation}\n\\delta^\\mu=(X^1 \\dots X^{\\cal P},\\delta S^1 \\dots \\delta S^\\Gamma).\n\\end{equation}\nThe parameters are not required to have the same units; the weight\nmatrix has all of the appropriate inverse units. \nAnalogously the parameter weight matrix is separated into 3 parts,\n\\begin{equation}\nH^i_\\mu W_{ij}H^j_\\nu=\\left(\n\\begin{array}{ll}\n A & B \\\\\n B^T & C\n\\end{array}\n\\right).\n\\end{equation}\n\nThe part dealing with the instrument is $A=H^i_q W_{ij}H^j_r$. The part \ndealing with the resulting sky map is $C=H^i_\\alpha W_{ij}H^j_\\beta$. And \nthe connections between them are $B=H^i_\\alpha W_{ij}H^j_q$. The \ncovariance matrix (inverse of the weight matrix) is broken into\nthe same sorts of parts. Often, each detector observes only one sky pixel at \na time and the weight matrix is simple enough that the large submatrix, \n$C=H^i_\\alpha W_{ij} H^j_\\beta$ can be easily stored and inverted. \nLet us then consider \n\\begin{equation}\n(H^i_\\mu W_{ij}H^j_\\nu)^{-1}=(H^i_\\mu~H_{i\\nu})^{-1}=\\left(\n\\begin{array}{ll}\n Q & R \\\\\n R^T & \\Psi\n\\end{array}\n\\right).\n\\end{equation}\n\nThe inverse or covariance can be calculated by:\n\\begin{equation}\nQ=(A-B C^{-1} B^T)^{-1}\n\\end{equation}\n\\begin{equation}\nR = -Q B C^{-1}\n\\end{equation}\nand\n\\begin{equation}\n\\Psi= C^{-1} +C^{-1}B^TQBC^{-1}.\n\\end{equation}\n\nWhen the only interest is in the uncertainties in the array parameters,\n(e.g. when the calibration is used for other data) only $Q$ is needed.\nSimilarly, if only the sky uncertainties are required, only $\\Psi$ is needed.\n\nThe covariance of the derived sky, $\\Psi$, is composed of two parts. The \n$C^{-1}$ is the direct propagation of the measurement errors to the sky. The\nother part $C^{-1}B^TQBC^{-1}$ shows the additional uncertainty due to \nthe calibration. For a well chosen set of observations this part can\napproach $({\\cal P}/PM)C^{-1}$, the limit set by the number statistics.\n\nThe matrix, $Q$, is much smaller than $H^i_\\mu H_{i\\nu}$, but still may be\ninconveniently large.\nEquation (4) is really a system of linear equations. By substituting \nequation (8) into equation (4) and retaining only the first ${\\cal P}$ equations \nwe have:\n\\begin{equation}\nX= (Q H^i_q + R H^i_\\alpha)\\Delta_i = Q Y\n\\end{equation}\nwhere\n\\begin{equation}\nY = H^i_q\\Delta_i- B C^{-1} H^i_\\alpha\\Delta_i.\n\\end{equation}\n\nThe matrix $A$ relates the detector parameters to each other. With care these \ncan be chosen so that the matrix can be inverted. With the size and speed\nof modern computers this is can even be accomplished with brute force\ntechniques. In many cases $A$ will be a multiple of a kernel which is the\nresult of a single observation.\n\nNow to get a form of equation (12) suitable for computing, let\n\\begin{equation}\nT=A^{-1/2}BC^{-1/2}=(H^i_q H_{ir})^{-1/2}H^j_r H_{j\\alpha}(H^k_\\alpha \nH_{k\\beta})^{-1/2}.\n\\end{equation}\nThen\n\\begin{equation}\nX = (A-BC^{-1}B^T)^{-1}Y\n =A^{-T/2}(I-A^{-1/2}BC^{-1}B^TA^{-T/2})^{-1}A^{-1/2}Y\n =A^{-T/2}(I-TT^T)^{-1}A^{-1/2}Y.\n\\end{equation}\nLike $B$, the size of $T$ is ${\\cal P} \\times \\Gamma$, but it is sparse.\n\nFinally, we use $(I-TT^T)^{-1}=\\sum^\\infty_{n=0} (TT^T)^n $ to get a form\nthat is tractable with a modest computer. Although formally the sum\nmust be carried to infinity the sum converges in tens to hundreds of\niterations for well chosen observations. Then,\n\\begin{equation}\nX= QY=A^{-T/2} \\left[ \\sum^\\infty_{n=0} (TT^T)^n \\right] A^{-1/2} Y.\n\\end{equation}\n\nThe matrix, $TT^T$, is avoided by defining $Z_0=A^{-1/2}Y$, and iterating\n\\begin{equation}\nZ_{n+1}=Z_0+T(T^TZ_n)\n\\end{equation}\nuntil $Z$ is stable.\nIt is trivial then to get the solution $X=A^{-T/2}Z$. This is only the solution \nfor the detector, but the solution for the sky is then straight forward.\n\n\\begin{deluxetable}{rl}\n\\tablewidth{0pt}\n\\tablecaption{Variable Definitions}\n\\tablehead{\n\\colhead{Variable} & \n\\colhead{Definition}\n}\n\\startdata\n$P$ & number of Array pixels, e.g. $256\\times256 = 65536$\\\\\n${\\cal P}$ & number of detector parameters, e.g. $2P = 131072$\\\\\n$M$ & number of images in the data set, e.g. 100\\\\\n$i,j,k$ & are indices to data $\\in(1 \\dots P\\times M)$\\\\\n$D^i$ & data\\\\ \n$\\Delta^i$ & model error\\\\\n$V^i$ & data variance (assumed to be diagonal)\\\\\n$\\Gamma$ & number of observed sky locations, e.g. 500000\\\\\n$\\alpha,\\beta$ & indices to sky locations $ \\in (1 \\dots\n \\Gamma ) ,\\Gamma < P \\times M)$\\\\\n$S^\\alpha$ & set of sky parameters\\\\\n$p$ & index to pixels $ \\in (1 \\dots P)$\\\\\n$G^p$ & set of gain parameters\\\\\n$F^p$ & set of offset parameters\\\\\n$q,r$ & indices to detector parameters $\\in (1 \\dots {\\cal P})$\\\\\n$X^q$ & set of detector parameters $ (\\delta F^p,\\delta G^p)$\\\\\n$\\mu ,\\nu,\\omega$ & indices to all parameters $\\in(1 \\dots {\\cal P}+\\Gamma)$\\\\\n\\enddata\n\\end{deluxetable}\n\n\\section{Example}\nNext we show how the algorithm is used in a practical program.\nSome of the key details are given in the appendix, here we outline the steps\nof the program and relate them to the previous derivation.\n\nWe adopt a simple model for the data, but more complex models\nare as easily handled as long as they are relatively linear in the\nrange of interest, do not require large numbers of parameters to be determined,\nand are not undetermined. A formal derivative must be calculated for each \nof the extra parameters and coded into the algorithm, while this may be messy \nand clutter the program, small numbers of parameters (e.g. temperature effects)\nthat affect the entire array make only small changes to the required time\nor the final accuracy of the algorithm. If some part \nof the parameter space is undetermined the program may not converge.\n\nOur example has a separate gain, $G$, and offset, $F$, for each detector\nthat modify the sky intensity, $S$, as it is detected. The model, $H^i$ for \nthe data is given by\n\\begin{equation}\nH^i(G^p,S^\\alpha,F^p)= G^p S^\\alpha + F^p.\n\\end{equation}\n\\begin{equation}\nX=(\\delta G^1\\dots \\delta G^P,\\delta F^1\\dots \\delta F^P)\n\\end{equation}\nThe example is obviously nonlinear and we must be careful to chose an initial \npoint close enough to the solution for the algorithm to converge to the \nsolution. For a particular detector array one would use the algorithm\nmany times so one can use the last solution as the starting point and\neither add more data to improve the solution or find a new solution with new\ndata. Either way, only once, do we need to start without a previous solution.\nIn that case we can let $G^p=1$, $F^p=0$, and $V^p=\\sum_{i\\in p} (D^i-F^p)^2/M$.\nThen with the assumption that the uncertainties are a function of pixel\nonly, we have an estimate for $V^i$. We will return to this estimation in\nsection 6.\n\nWe assume a diagonal weight matrix $W_{ii}=(V^i)^{-1}$ to keep the\nexample simple. However, we emphasize that this is {\\it not} required. The \nderivation is completely general and can accommodate a nondiagonal weight\nmatrix. Note that this assumption does not\nmean that the data are uncorrelated. Indeed, the data are correlated as\nsome of the data are derived from the same pixel or are observations of the \nsame part of the sky with different detectors. If there are other sources of \ncorrelation (such as detector temperature) they need to be explicitly included \nin the model. The assumption here is that the residual errors are uncorrelated.\n\nThe first step of the program is to calculate\n\\begin{equation}\n\\Delta_i=W_i(D^i-G^pS^\\alpha-F^p).\n\\end{equation}\n\nAs there are two types of parameters we divide the matrix $A$ into its four\nquadrants for discussion.\n\\begin{equation}\nA=\\left(\n\\begin{array}{ll}\n A_G & A_{GF} \\\\\n A^T_{GF} & A_F\n\\end{array}\n\\right).\n\\end{equation}\nEach of the submatrices of $A$ is diagonal, including the part relating the \ngain and offset of each pixel. The whole matrix is treated as $P$ $2\\times2$ \nmatrices. There is not a unique $A^{-1/2}$, mathematically the choice is \narbitrary, but the symmetric choice and the \nchoice where the lower left are zero are easier to program. We have used both\nand found the nonsymmetric version is less susceptible to numerical instability.\n\nAlthough the size of $H^i_\\mu$ is $PM\\times({\\cal P}+\\Gamma)$ it can be treated as a set of\ndelta functions. With care in the processing, the parts of $H$ that are zero \nneed never be accessed (appendix). There are 3$P\\times M$ nonzero parts. \nThat is each datum appears 3 times, once associated with $G$, $F$ and $S$.\n\nThe second step makes use of the following relations:\n\\begin{tabular}{l}\n$\\partial_{G^p}H^i = S^\\alpha\\delta_{pi}$ \\\\\n$\\partial_{F^p}H^i = \\delta_{pi}$\\\\\n$\\partial_{S^\\alpha}H^i = G^p \\delta_{\\alpha i}$\\\\\n\\end{tabular}\nto construct\n\n\\begin{equation}\n{\\rm diag}~~A_G = \\sum_{i\\in p,i\\in \\alpha} S^\\alpha W_i S^\\alpha,\n~~~~~{\\rm diag}~~A_F =\\sum_{i\\in p} W_i\n\\end{equation}\n\n\\begin{equation}\n{\\rm diag}~~A_{FG} =\\sum_{i\\in p,i\\in \\alpha} S^\\alpha W_i\n\\end{equation}\nand\n\\begin{equation}\n{\\rm diag}~~C=\\sum_{i\\in \\alpha,i\\in p} G^p W_i G^p.\n\\end{equation}\n$C$ is diagonal as well.\n\nThe matrix $B$ is divided into two parts similar to $A$:\n\\begin{equation}\nB_G=\\sum_{i \\in p,i \\in \\alpha} S^\\alpha W_i G^p,\n~~~B_F=\\sum_{i\\in p,i\\in\\alpha} W_i G^p.\n\\end{equation}\n\nFinally $Y$ has two parts\n\\begin{equation}\nY_G= \\sum_{i\\in \\alpha,i\\in p} S^\\alpha \\Delta_i\n-B_GC^{-1}\\sum_{i\\in p,i\\in \\alpha} G^p\\Delta_i,\n~~~Y_F=\\sum_{i\\in p} \\Delta_i-B_FC^{-1}\\sum_{i\\in p,i\\in \\alpha} G^p\\Delta_i.\n\\end{equation}\n\nNote that $B$ is $2P\\times\\Gamma$ but it is sparse. We then calculate \n$T=A^{-1/2}BC^{-1/2}$. With the elements of equation (16), the program iterates \nequation (17) until $Z$ is stable. Then the solution \n$X=A^{-T/2}Z$. This is only the solution \nfor the detector, but the solution for the sky is then:\n\\begin{equation}\nS^\\alpha=\\sum_{i\\in\\alpha, i\\in p} [(D^i-F^p)G^pW_i]\n /\\sum_{i\\in\\alpha, i\\in p}(G^p)^2W_i.\n\\end{equation}\n\nThis then is a form which can be handled by a modest computer. The vectors\n$X$ and $Y$ are each only $2P=131072$ long. The matrix $A$ is stored as\nthree $P$ long diagonal parts of its submatrices. The matrix $T$ is nominally\nlarge ($2P\\times \\Gamma$) but is sparse and has at most $2P\\times M$ nonzero\ncomponents.\n\nAt this point there are two obvious singularities.\nThese correspond to the uniform change in the sky brightness and a cancelling \nchange in the offset, and to a multiplication of the sky by an arbitrary \namount and a cancelling effect in the gain term. These two singularities \npoint out what we already know; in order to get an {\\it absolute} calibration \nwe need an {\\it absolute} standard. There are several ways to deal with this \nissue: 1) An absolute calibration could be done in the laboratory. 2) Certain \nplaces on the sky could be determined in some other way and used to impose a \ncondition that would break the singularity.\n3) A map could be produced with an arbitrary gain and offset.\n\nThe three methods are not mutually exclusive. A map with arbitrary gain and \noffset can be produced which is subsequently calibrated by laboratory \nmeasurements or sky measurements or a combination of sky and laboratory\nmeasurements. The absolute calibration can be included in the fit or applied \nlater. We choose to apply it separately as this maintains the uniformity of the\nalgorithm whether viewing a calibration object or not.\n\nWithout treating the singularity, the sum in equation (16) does not converge.\nIf there are no dark frames to determine the offset, after each iteration we \nimpose the condition that $\\sum_p \\sqrt{\\sum_{i\\in p}W_i}~\\delta F^p =0$.\nThe weight applied to the $\\delta F^p$ is only for computational convenience\n(it is the form of $F^p$ in $Z$). The key is that the net offset is not allowed \nto change.\nIf dark frames are present we can use them to determine the offset and do\nnot impose this condition. Similarly, a weighted mean gain is held fixed, \n$\\sum_p \\sqrt{\\sum_{i\\in p, i\\in\\alpha}S^\\alpha W_i S^\\alpha}~\\delta G^p=0$.\n\nThis completes the solution for the detector and the sky. The calculation\nof a single uncertainty vector is completely analogous. However the full\ncovariance matrix $\\Psi$ is $\\sim500000\\times500000$. This matrix is symmetric\nbut it is not sparse. In fact it is likely that all of the\nelements are nonzero. The $2.5\\times10^{11}$ components of $\\Psi$ are awkward \nto carry around but they contain all of the information about the\ncorrelations imposed by the calibration process. It can be stored more\ncompactly by keeping $T$, and noting that\n\\begin{equation}\n\\Psi= C^{-1/2}(I-T^TT)^{-1}C^{-1/2}\n\\end{equation}\nsince $T$ is sparse and $C^{-1/2}$ is diagonal.\n\nNow we return to the issue of variance (weight) estimation. Without a\nmodel for the noise we have a hopeless task. However with a simple model\nwe can estimate the variance. An unbiased, but poor,\nestimation only increases the noise (and the estimate of the uncertainty).\n\nIn the model program we assume three sources of error: 1)Poisson statistics, \n2)A pixel dependent readout noise, 3)A cosmic ray induced error. The Poisson\nnoise is easily calculated if the approximate gain of the system is known. \nThe readout noise is best\nestimated by using the RMS of all of the data from that pixel (except the \ncosmic ray contaminated data). Cosmic rays are identified by seeking\nlarge discrepancies. These should not be used in either the sky or variance\nestimation. Obviously as data are collected a more detailed model\ncan be developed.\n\nAfter a solution is found, the model program recalculates $\\Delta^i$. \nData with errors greater than $2.5~\\sigma$\nare assumed to be cosmic particle hits or other glitches. These data\nare marked and not used in the next iteration. The remaining $\\Delta^i$s\nare squared and summed to estimate the noise. The model program noise is \ntreated separately for each pixel. If hundreds or thousands of pictures\nare available this process could potentially identify subtle problems with\nparticular pixels. If fewer data are available a smooth\napproximation over entire detector array is more appropriate.\n\n\\section{Practical Matters}\n\nThe algorithm described in the preceding sections can produce mosaics \nof large regions provided that at least some parts of the region\n(preferably all parts) contain repeated (dithered) observations. \nThe algorithm can be applied to a data set containing spatially \nseparate regions. There is no constraint on the size or geometry of the\nregion(s) in the data set. It is only required that the detector gain and\noffset and the sky intensity ($G^p$, $F^p$, and $S^{\\alpha}$) are constant\nfor the entire data set. These restrictions can be relaxed by explicitly\nparameterizing known or suspected variations.\n\nIf dark frames are available, they are added to the data set as if\nthey are observations of a region of sky that is separate from the \nrest of the data and that has an intensity $S^{\\alpha} \\equiv 0$.\nThe addition of dark frames to the data set allows the algorithm \nto determine the offset components.\n\nThe algorithm can be implemented in a general manner, such that the detector \ndimensions and number of frames processed are adjustable. A general code can\nbe applied to different data sets from different instruments if a new\n``front end'' is written for each type of data to ingest the data and\nprovide the necessary initial estimates and control parameters.\n\nThe selection of the weights ($W_{ii}$) to use in the algorithm can be \nimportant. Poor weighting of the data may cause spurious features to\npropagate through the solutions for $G^p$, $F^p$, and $S^{\\alpha}$.\nCosmic ray hits on the detector also cause spurious features\nin the results, if not properly handled. Data affected by cosmic rays\ncan be given very low weights or flagged. It is best if the effects of\ncosmic rays are removed from the data before processing, though this\nis not always possible. The algorithm can recognize \ncosmic rays as outliers provided that they are not so numerous that they\nseverly bias the results.\n\nIn most cases, the algorithm will be used iteratively for \n2 - 5 cycles. Subsequent iterations use the previously derived gain and \noffset values as inputs, and make use of successively improved weights \nand exclusions of cosmic rays as well. \n\nAn IDL implementation of this algorithm requires free memory $\\sim$15 times \nlarger than the size of the data set to be processed. For a data set of\n27 256$\\times$256 images the algorithm takes $\\sim$450 seconds of CPU time on\na 300 MHz Pentium II machine running Red Hat Linux 5.2 and IDL 5.0.3.\nAbout 270 seconds of that CPU time is spent in the calculation of the \nsummation of equation (16), using the iterative step of equation (17) for 100 \nterms. The key data arangements of the program are discussed in the appendix.\nThe time for the procedure is linear with the number of input data \nelements as long as more iterations are not needed. The number of iterations\nrequired is strongly related to the connection map which is determined\nby the dither pattern of the input data.\n\nSolving only for detector gains in cases where the detector offsets are\nnegligible is a minor simplification of the algorithm and is a more\nrobust procedure. Figure 1 illustrates the results of using this procedure to \nsolve for only the detector gains and sky intensities. The data used is \nfrom Wide-Field Infrared Explorer (WIRE) simulations. The model for the sky\nincludes point sources, cirrus and a zodiacal background. The model for the \n$128\\times128$ detector array included gain variations, bad pixels, and \ncosmic ray hits. The data\nset consists of 10 dithered images, one of which is shown in the upper left \nof Figure 1. The detector gain variations dominate the qualitative appearance\nof the data. The derived gain compares favorably with the true gain, with the\nexception of $\\sim0.2\\%$ of the pixels with remaining artifacts from bad \ndetectors and cosmic\nrays. There is a small ($\\sim1.0025$) scale factor between the derived and \ntrue gains, which reflects the lack of absolute calibration in the \nprocedure. The derived sky is a good representation of the real sky, with the \nadditional noise component indicated by the second term of equation (11). \n\nFigure 2 illustrates the application of the algorithm to real data, namely\nthe HST NICMOS observations of the Hubble Deep Field - South. The raw data used\nhere were 59 good 1152 and 1472 s integrations. The worst effects of cosmic \nrays were eliminated by calculating linear fits to the multiaccum readouts \nfrom each pixel. Fits with poor correlation coefficients were refit using\na combination of linear and step functions. Additional pre-processing involved\nsubtracting the median value of each quadrant of each frame from that frame\nquadrant. This helped compensate for a variable ``pedestal'' effect which is not \nmodelled by our current algorithm. (The bottom 16 rows of each frame were\nignored in the processing to avoid vignetting effects.) The initial gain map \nwas assumed to be flat and unity. The initial offset map was assumed to be flat \nand zero. A dark file from the NICMOS reference files was used for a simulated \ndark frame that was processed simultaneously with the sky data.\nThe derived sky after 2 iterations of the algorithm and truncation of the series\nexpansion after 100 terms, is not as clean as the publicly released \nprocessed data. Spurious large scale structure is present at low levels.\nA faint stripe along the detector columns is visible through the brightest\nstar in the field. The gain and offset maps are similar to calibration flat \nand dark reference files. In our derived gain and offset maps there are \nresidual defects in pixels where the bright sources in the map were observed. \nThe gain and offset maps also contain visible quadrant errors and vertical\nbars from ``shading\" because of instrumental effects that are not adequately\ndescribed by the simple method used here.\nClearly there is room for improvement, but the algorithm \nworked well. The process allowed the simultaneous determination of sky and\ndetector parameters using only sky measurements and dark frames.\nBy inspecting the residuals there are indications that the offsets are\nnot constant from observation to observation. This suggests an improved \nmodel for the data could be constructed by parameterizing and fitting\nthese offsets.\n\nIn the case of IRAC, such an algorithm is essential. With it, we can continuously\nderive detector parameters from the normal observations and improve the \nmodel of the detectors as well as the model of the sky. Just such a procedure\nwas used on the FIRAS data to improve the sensitivity by a factor of\n$\\sim100$ over the initial publication.\n\n\\section{Uncertainties and Correlations}\n\nThe algorithm produces a formal estimate of the uncertainties, $\\Psi$, based on the \nderivation and the estimated uncertainties of the input data, $V$. The resulting\nuncertainties are only as good as the uncertainty estimates of the original\ndata. Those uncertainties, $V$, are checked against the actual deviations from \nthe model to either give an improved estimate of the input data uncertainty or \nan indication of short comings of the model.\n\nIdentifying the weight matrix (or metric) as the inverse of the covariance\nmatrix, only defers the question to how to determine the covariance matrix.\nThere are two sorts of ways to attack this problem. The theoretical approach\nuses {\\it a priori} knowledge about the system to estimate what the noise should be.\nThis includes such things as the Poisson arrival of photons, the Johnson\nnoise of the resistors and other known sources of noise. The empirical\napproach uses the residuals in the data itself to make an estimate of the \nnoise. Each approach has its strengths and weaknesses. The theoretical \napproach often underestimates the noise because there are unmodeled noise sources\npresent. The empirical approach often overestimates the noise, as\nit treats parts of the signal that are not properly modeled as noise. If\nboth approaches lead to the same estimate one has reasonable assurance that\nthe model and estimate are correct. If the approaches differ significantly\nthere are either noise sources that are included in the estimate or signal \nthat is not included in the model. In this example, we \nassume that the noise variance $V$ is known.\n\nThe calibration process introduces correlations into the resulting map,\n$C^{-1}B^TQBC^{-1}$. The correlations for a single detector are easily \ngenerated by using a unit vector in place of the $Y$ in equation (12) and \ncarrying out the \ncalculations as with the data. The process is slightly shorter than for the \ndata (checking for convergence is omitted). Obviously this could be repeated for each \nof the detectors and then equation (11) could be used to generate the full \ncovariance matrix.\n\nThere are two problems with this approach. First, the time required is \nproportional to the number of detectors (65536 for IRAC or NICMOS data). \nSecond, the space for the final result is $\\Gamma^2$, which is $\\sim10^{11}$,\nfor even the modest WIRE example shown here. Storing and using such a large\ndata set is problematical.\n\nFortunately the correlations for different detectors are nearly identical\n(see figure 3). This should not be a surprise since the detectors are locked\ninto their relative positions and all move together in each dither move.\nBad detectors in the array, cosmic rays, and rotations will obviously\nbreak this symmetry but except for the rotations the effects are minor\nand rather localized. So the correlations can be calculated for typical\ndetectors and the results can be used for the entire data set.\n\n\\section{Summary}\n\nAs demonstrated with the simulated WIRE data the program can calculate the \ngains and offsets to the theoretical limit on the accuracy if it is given\na good model of the data. As shown with the NICMOS data the program works\nreasonably well on real data as well even with he normal complexities of\nreal errors and uncertainties. The uncertainties are calculated, and the \ncorrelations can be calculated with minor changes to the program. These allow\nthe user to interpret the result without ad hoc assumptions or guesses about\nhow the errors are related. The speed of the program allows modest data\nsets to be processed in a few minutes and with the availability of machines\nwith large memories will allow the large data sets of the future to be processed\nin reasonable times.\n\n\\section{Acknowledgements}\nWe thank D. Shupe and the WIRE team for supplying simulated WIRE observations\nfor testing the algorithm.\n\n\\section{References}\n\\frenchspacing\n\\setlength{\\leftmargini}{0cm}\n\\begin{verse}\n\n\\bibitem[arendt 00]{dither}{Arendt, R.~G., Fixsen, D.~J. \\& Moseley, S.~H. \n2000 ApJ submitted}\n\n\\bibitem[Fazio 98]{irac}{Fazio, G.~G. \\etal 1998, Proc. SPIE, 3354, 1024}\n\n\\bibitem[Fixsen 94]{Calib}{Fixsen, D.~J. \\etal 1994 ApJ 420,427}\n\n\\bibitem[Fruc]{}{Fruchter, A.S. \\& Hook R. N. 1998, \npreprint (astro-ph/9808087)}\n\n\\bibitem[Joyce]{}{Joyce, R. R., 1992 ASP Conference Series, Vol. 23, Astronomical CCD\nObserving and Reduction Techniques, ed. S. B. Howell (San Fransisco: ASP)}\n\n\\bibitem[NumR]{Num}{Press, W. H., Teukolsky, S. A., Vetterling, W. T., \n\\& Flannery, B. P. 1992, Numerical Recipes in C: The Art of Scientific \nComputing, Second Edition, Cambridge: Cambridge University Press}\n\n\\end{verse}\n\\nonfrenchspacing\n\n\\appendix{}\n\\section{Code Considerations}\n\nThis appendix points out several details of implementing this\nleast squares calibration procedure in a computer code.\nThe first detail is that a sparse matrix storage and multiplication\nsystem must be applied.\nAs presented here, the solution (eq. 16) requires construction\nof the matrix $T$ which has dimensions $\\Gamma\\times{\\cal P}$.\nFor a $256\\times 256$ detector array, $T$ contains at least $256^4 =\n17\\times 10^9$ elements, making it difficult to store in memory\nHowever most of the elements of $T$ are 0.0, because a single detector,\n$p$, observes no more than $M$ of the $\\Gamma$ sky pixels.\nFollowing the example presented in \\S4, we note that $T$ contains\nthe same non-zero elements as $B$. Furthermore, each datum\nleads to one element in $B_G$ and one element in $B_F$ (eq. [25]).\nThus $B$ or $T$ can be stored in an array corresponding to the $P\\times M$\ndata, and replicated for each of the detector parameters (gain, offset, etc.)\nto be determined. The position within the array indicates the\n$p \\in [1,{\\cal P}]$ index of the element, while the $\\alpha \\in [1,\\Gamma]$\nindex is stored in a separately constructed array. In this way, the\nstorage requirements are reduced by a factor of $\\sim({\\cal P}/P)M/\\Gamma$\nwhich is generally very large as $M\\ll\\Gamma$ for most datasets.\n\nThe second detail is to note that equation (17) is can be implemented as\na pair of matrix $\\times$ vector multiplications: $T^TZ_n$, followed by\n$T(T^TZ_n)$. This pair of multiplications is much faster and requires\nnegligible storage compared to calculating the matrix multiplication\n$TT^T$ first, and then $(TT^T)Z_n$. The $TT^T$ matrix is not nearly\nas compact as the $T$ matrix. Furthermore, with the appropriate juggling of\nindices both matrix $\\times$ vector multiplications are performed using\nthe stored format of $T$ without explicitly calculating the transpose of $T$.\nAn example of this is found in Press et al. (Chapter 2, 1992).\n\n\\clearpage\n\\figcaption[wire]{The top left image shows one of ten frames of simulated WIRE data.\nThe top center image shows the detector gains derived from the data, while the \ntop right image shows the actual gains used to generate the simulated data.\nThe lower left graph shows the histogram of the differences between the derived \nand actual gains. The bottom middle and right images show the derived sky \nintensities and the true sky used to generate the simulated data.}\n\n\\figcaption[nicmos]{The raw data is one of the NICMOS multiaccum frames after \nfitting linear fits to the readouts from each pixel and removing the worst\nof the cosmic rays. The other pairs of derived and reference images are \neach shown on equivalent scales. The derived gain and offset maps only cover\nthe upper $256\\times240$ detectors in the $256\\times256$ array.}\n\n\\figcaption[cor]{The panels show six columns of the $2P\\times 2P$ matrix \n$A^{T/2}QA^{1/2}$ for a $256\\times 256$ detector array and an idealized data \nset collected using a dither pattern consisting of 36 pointings evenly spaced \nalong the sides of a Reuleaux triangle. The columns are reformated into \n$256\\times (256*2)$ arrays. From left to right and top to bottom the columns \ncorrespond to those containing the correlations for $G^p$ $(p = [128,128],\n[16,128],[16,16])$ and $F^p$ $(p = [128,128],[16,128],[16,16])$. Correlations \nagainst $G^p$ and $F^p$ map into the bottom and top half, respectively, of \neach panel. Black indicates strong positive correlations. Displayed ranges for \n$G^pG^p$, $F^pF^p$, and $G^pF^p\\ =\\ F^pG^p$ correlations are \n[$1.5\\ 10^{-3}$, $1.55\\ 10^{-3}$], [$1.2\\ \n10^{-3}$, $2.0\\ 10^{-3}$], and [$-8\\ 10^{-5}$, $8\\ 10^{-5}$] respectively.}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002260.extracted_bib",
"string": "\\bibitem[arendt 00]{dither}{Arendt, R.~G., Fixsen, D.~J. \\& Moseley, S.~H. \n2000 ApJ submitted}\n\n\n\\bibitem[Fazio 98]{irac}{Fazio, G.~G. \\etal 1998, Proc. SPIE, 3354, 1024}\n\n\n\\bibitem[Fixsen 94]{Calib}{Fixsen, D.~J. \\etal 1994 ApJ 420,427}\n\n\n\\bibitem[Fruc]{}{Fruchter, A.S. \\& Hook R. N. 1998, \npreprint (astro-ph/9808087)}\n\n\n\\bibitem[Joyce]{}{Joyce, R. R., 1992 ASP Conference Series, Vol. 23, Astronomical CCD\nObserving and Reduction Techniques, ed. S. B. Howell (San Fransisco: ASP)}\n\n\n\\bibitem[NumR]{Num}{Press, W. H., Teukolsky, S. A., Vetterling, W. T., \n\\& Flannery, B. P. 1992, Numerical Recipes in C: The Art of Scientific \nComputing, Second Edition, Cambridge: Cambridge University Press}\n\n"
}
] |
astro-ph0002261
|
Cooling curves and initial models for low--mass white dwarfs ($< 0.25 ~M_\odot$) with helium core
|
[
{
"author": "Marek J. Sarna$^1$"
},
{
"author": "Ene Ergma$^2$ and Jelena Antipova$^2$"
},
{
"author": "$^1~$ N. Copernicus Astronomical Center"
},
{
"author": "Polish Academy of Sciences"
},
{
"author": "ul. Bartycka 18"
},
{
"author": "00--716 Warsaw"
},
{
"author": "Poland."
},
{
"author": "$^2~$ Physics Department"
},
{
"author": "\\\"Ulikooli 18"
},
{
"author": "EE2400 Tartu"
},
{
"author": "Estonia."
}
] |
We present a detailed calculation of the evolution of low--mass ($< 0.25~M_\odot $) helium white dwarfs. These white dwarfs (the optical companions to binary millisecond pulsars) are formed via long--term, low--mass binary evolution. After detachment from the Roche lobe, the hot helium cores have a rather thick hydrogen layer with mass between 0.01 to 0.06$~M_\odot $. Due to mixing between the core and outer envelope, the surface hydrogen content is 0.5 to 0.35, depending on the initial value of the heavy element (Z) and the initial secondary mass. We found that the majority of our computed models experience one or two hydrogen shell flashes. We found that the mass of the helium dwarf in which the hydrogen shell flash occurs depends on the chemical composition. The minimum helium white dwarf mass in which a hydrogen flash takes place is 0.213$~M_\odot $ (Z=0.003), 0.198$~M_\odot $ (Z=0.01), 0.192$~M_\odot $ (Z=0.02) or 0.183$~M_\odot $ (Z=0.03). The duration of the flashes (independent of chemical composition) is between few $\times 10^6 $ years to few $\times 10^7 $ years. In several flashes the white dwarf radius will increase so much that it forces the model to fill its Roche lobe again. Our calculations show that cooling history of the helium white dwarf depends dramatically on the thickness of the hydrogen layer. We show that the transition from a cooling white dwarf with a temporary stable hydrogen--burning shell to a cooling white dwarf in which almost all residual hydrogen is lost in a few thermal flashes (via Roche--lobe overflow) occurs between 0.183--0.213$~M_\odot $ (depending on the heavy element value).
|
[
{
"name": "paper35.tex",
"string": "%%%%%%%%%%%%%%%%%%%%%%%%%% beginning %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%\\documentstyle[12pt]{l-aa}\n\\scrollmode\n\\documentstyle[draft]{mn}\n\\renewcommand{\\baselinestretch}{1.0}\n\n%\\begin{document}\n\\input epsf\n\n\\voffset -0.5in\n\n\\title[Cooling curves]{Cooling curves and initial models for low--mass \nwhite dwarfs ($< 0.25 ~M_\\odot$) with helium core}\n\n\\author[Marek J. Sarna et al.]{Marek J. Sarna$\\rm ^1$, Ene \nErgma$\\rm ^2$ and Jelena Antipova$\\rm ^2$ \\\\\n$\\rm ^1~$ N. Copernicus Astronomical Center, \n Polish Academy of Sciences,\n ul. Bartycka 18, 00--716 Warsaw, Poland. \\\\\n$\\rm ^2~$ Physics Department, Tartu University, \\\"Ulikooli 18, EE2400 \n Tartu, Estonia. \\\\}\n\n\\date{\\small Accepted . Received ; in original \nform 1999 }\n\n\\begin{document}\n\n\\maketitle\n\n\\begin{abstract}\n\nWe present a detailed calculation of the evolution of low--mass\n($< 0.25~M_\\odot $) helium white dwarfs. These white dwarfs (the \noptical companions\nto binary millisecond pulsars) are formed via long--term, low--mass\nbinary evolution. After detachment from the Roche lobe, the hot helium \ncores have a rather thick hydrogen layer with mass between 0.01 to \n0.06$~M_\\odot $. Due to mixing between the core and outer envelope, \nthe surface \nhydrogen content is 0.5 to 0.35, depending on the initial value of the \nheavy element (Z) and the initial secondary mass. We found that the majority \nof our computed models experience one or two hydrogen shell flashes. \nWe found that the mass of the helium dwarf in which the hydrogen shell \nflash occurs depends on the chemical composition. \nThe minimum helium white dwarf mass in which a hydrogen flash takes \nplace is 0.213$~M_\\odot $ (Z=0.003), 0.198$~M_\\odot $ (Z=0.01), \n0.192$~M_\\odot $ (Z=0.02) or 0.183$~M_\\odot $ (Z=0.03).\nThe duration of the flashes (independent of chemical composition) is between\nfew $\\times 10^6 $ years to few $\\times 10^7 $ years. In several flashes \nthe white dwarf radius will increase so much that it forces the model to fill\nits Roche lobe again.\nOur calculations show that cooling history of the helium white dwarf depends\ndramatically on the thickness of the hydrogen layer. We show that the\ntransition from a cooling white dwarf with a temporary stable\nhydrogen--burning shell to a cooling white dwarf in which almost all residual\nhydrogen is lost in a few thermal flashes (via Roche--lobe overflow) occurs\nbetween 0.183--0.213$~M_\\odot $ (depending on the heavy element value). \n\n\\end{abstract}\n\n\\begin{keywords}\n\\quad binaries: close \\quad --- \\quad binaries: general \\quad --- \\quad\nstars: mass loss\nevolution \\quad --- \\quad stars: millisecond binary pulsars\n\\quad --- \\quad pulsars: individual: PSR J0437 + 4715 \\quad ---\n\\quad pulsars: individual: PSR J1012 + 5307\n\\end{keywords}\n\n\\section{Introduction}\n\nKippenhahn, Kohl \\& Weigert (1967) were the first who followed the formation\nof helium white dwarfs (WD) of low mass in a binary system. The\nevolution of a helium WD of 0.26$~M_\\odot$ (remnant) was\ninvestigated by Kippenhahn, Thomas \\& Weigert (1968) who found that a\nhydrogen flash can be initiated near the base of the hydrogen rich\nenvelope. The energy of the flash is sufficient to cause the envelope\nto expand to giant dimensions and hence it may be possible that another\nshort term Roche lobe filling can occur.\n\nIn Webbink (1975), models of a helium white dwarf were constructed\nby formally evolving a model from the homogeneous zero--age main sequence \nwith the reduction of the mass of the hydrogen--rich envelope. When the \nmass of the envelope is less than some critical value, the model contracts\nadopting white dwarf dimensions. Webbink found that thermal flashes do not\noccur for WDs less massive than 0.2$~M_\\odot$.\nAlberts et al. (1996) have confirmed Webbink's finding that \nlow--mass white dwarfs do not show thermal flashes and the\ncooling age for WDs of mass\n$M_{wd}$$\\leq$0.20$M_\\odot$ can be considerably underestimated if\nusing the traditional WD cooling curves which were constructed for $\nM_{wd}$$>$0.3$M_\\odot$ (Iben \\& Tutukov 1986, IT 86).\n \nRecently, Hansen \\& Phinney (1998a -- HP98) and Benvenuto \\& \nAlthaus (1998 -- BA98) investigated the effect of different mass of\nthe hydrogen layer \n($\\rm 10^{-8} \\le M_{env}/M_\\odot \\le 4 \\times 10^{-3} $) on the \ncooling evolution of $\\rm 0.15 \\le M_{He}/M_\\odot \\le 0.5 $ helium WDs. In both calculations (BA98 and HP98) the mass of the hydrogen\nenvelope left on the top of white dwarf has been taken as free parameter.\nBA98 found that thick envelopes appreciably modify the radii\nand surface gravities of no--H models, especially in the case of low--mass \nhelium white dwarfs. \n\nDriebe et al. (1998 -- DSBH98) present a grid of evolutionary tracks \nfor low-mass white dwarfs with helium cores in the mass range from 0.179 to\n0.414$~M_\\odot$. The tracks are based on a 1$~M_\\odot$ model sequence \nextending\nfrom the pre--main sequence stage up to the tip of red giant branch.\nApplying large mass loss rates forced the models to move off the giant \nbranch and evolve across the Hertzsprung--Russell diagram and down\nthe cooling branch. They found that hydrogen flashes take place only\nfor two model sequences, 0.234$~M_\\odot$ and 0.259$~M\\odot$, and for \nvery low--mass WDs \nthe hydrogen shell burning remains dominant even down to\neffective temperatures well below 10 000 K.\nAccording to our previous calculations (Ergma, Sarna \\& Antipova, 1998)\nwe find that for a low--mass white dwarf with a helium core, which was formed during low--mass binary evolution (after detachment from the\nRoche lobe), the hydrogen layer left on the top of the helium core is much \nthicker ($\\rm \\sim 1-6 \n\\times 10^{-2} M_\\odot $ with $\\rm X_{surf} $ ranging from 0.3 to 0.52) \nthan used in cooling calculation by HP98 and BA98. \nAlso in DSBH98 (see their Table 1), for the two lowest total remnant \nmasses the envelope mass value is smaller that obtained in our calculations. \n\n%(There is \n%mistake in DSBH98 Table 1. For M/$M_\\odot$ =0.179 and 0.195, $M_{env}$ is \n%equal 10.211$\\times10^{-3} ~M_\\odot$ and 9.598$\\times10^{-3} ~M_\\odot$ \n%correspondingly (Sch\\\"oenberner, private communication)). \n\n\\section{The main aim}\n\nLow--mass helium white dwarfs are present in millisecond binary \npulsars and double degenerate systems. This gives a unique \nopportunity to test the cooling age of the WD in a binary and, \nespecially in the case of millisecond binary pulsars, allows for \nage determinations for neutron stars that are independent of \ntheir rotational history. \n\n\\begin{figure}\n\\epsfverbosetrue\n\\begin{center}\n\\leavevmode\n\\epsfxsize=7cm\n\\epsfbox{fig1.ps}\n%\\plottwo{fig1.ps}{fig2.ps}\n\\end{center}\n\\caption{Hertzsprung--Russell diagram with evolutionary tracks. Evolutionary \nsequence (model 20) which undergoes long term stable hydrogen burning is \nshown by the solid line. \nDashed line, the same for model 22 which shows one weak (without RLOF) and \none strong (with RLOF) hydrogen flash. Circles and triangles mark \ncooling ages of 1 and 3 Gyr, respectively.} \n\\end{figure}\n\n\\begin{figure}\n\\epsfverbosetrue\\begin{center}\n\\leavevmode\n\\epsfxsize=7cm\n\\epsfbox{fig2.ps}\n%\\plottwo{fig1.ps}{fig2.ps}\n\\end{center}\n\\caption{The surface effective temperature ({\\it upper panel}), the nuclear \nenergy production ({\\it middle panel}) and the surface luminosity \n({\\it lower panel}) plotted as a function of the cooling time $t_{cool}$\nwhich is the time elapsed from $t_{0}$.\nModel 20 with stationary hydrogen shell burning -- thick \nline $t_{0}$=7.9$\\times 10^{9}$yrs, model 22 with unstable hydrogen shell \nburning -- dashed line $t_{0}$=7.8$\\times 10^{9}~$yrs. First\nflash is without RLOF and second flash is accompanied by RLOF. For all \nfigures with cooling time $t_{cool}$ is time elapsed from $t_{0}$. } \n\\end{figure}\n\n\\section{The evolutionary code}\n\nThe evolutionary sequences we have calculated are comprised of \nthree main phases: \n\n\\noindent$\\bullet$ detached evolution lasting until the companion \nfills its Roche lobe on the time--scale $t_{d}$; \n\n\\noindent\n$\\bullet $ semi--detached evolution (non--conservative in our\ncalculations) on the time--scale $t_{sd}$; $t_{0}$=$t_{d}+t_{sd}$;\n\n\\noindent\n$\\bullet $ a cooling phase of the WD on the time--scale $t_{cool}$ \n(the final phase during which a\nsystem with a ms pulsar + low--mass helium WD is left behind). \nThe total evolutionary time is $t_{evol}= t_{0}+t_{cool}$. \n\nThe duration of the detached phase is somewhat uncertain; \nit may be determined either by the nuclear time--scale or by the \nmuch shorter time--scale of the orbital angular momentum loss owing \nto the magnetized stellar wind. \n\nIn our calculations we assume that the semi--detached evolution of a binary \nsystem is non--conservative, i.e. the total mass and angular momentum of the \nsystem are not conserved. We can express the total orbital angular \nmomentum (J) of a binary system as\n\n\\begin{equation}\n{{\\dot J} \\over J} = \\left. {{\\dot J} \\over J} \\right|_{SML} + \\left. \n{{\\dot J} \\over J} \\right|_{MSW} + \\left. {{\\dot J} \\over J} \\right|_{GR} ,\n\\end{equation}\n\nwhere the terms on the right hand side are due to: stellar mass angular\nmomentum loss from the system, magnetic stellar wind braking, and \ngravitational wave radiation.\n\n\\subsection{Stellar mass angular momentum loss}\n\nThe formalism which we have adopted is described in \nMuslimov \\& Sarna (1993). We introduce the parameter $f_1$ characterizing \nthe loss of mass from the binary system and defined by the relations,\n\n\\begin{equation}\n\\dot M = \\dot M_2 f_1 ~~~~and~~~~ \\dot M_1 \n= - \\dot M_2 (1 - f_1) , \n\\end{equation}\n\nwhere $\\dot M$ is the mass--loss rate from the system, $\\dot M_2$ is \nthe rate of mass loss from the donor (secondary) star and $\\dot M_1$ is \nthe accretion rate onto the neutron star (primary). The matter leaving the \nsystem will carry off its intrinsic angular momentum in agreement with \nformula\n\n\\begin{equation}\n\\left. {{\\dot J} \\over {J}} \\right|_{SML} = f_1f_2 {{M_1 \\dot M_2} \\over {M_2 M}} \n~~~~~yr^{-1} , \n\\end{equation}\n\nwhere $M_1$ and $M_2$ are the masses of the neutron star and donor star, \nrespectively and M=$M_1$+$M_2$. Here we have introduced the additional \nparameter \n$f_2$, which describes the efficiency of the orbital angular momentum \nloss from the system due to a stellar wind (Tout \\& Hall 1991). In our \ncalculations we have $f_2$=1 and $f_1$=1; we calculate the fully \nnon--conservative case, although additional calculations with $f_1$ \n= 0.9 and 0.5 (with $f_2$=1) give similar results. A similar result to ours \nwas found by Tauris (1996), who showed that the change in orbital \nseparation due to mass transfer in LMXB (low--mass X-ray binaries) as a \nfunction of the fraction of exchanged matter\n$f_1$ which is lost from system is small (for 0.5$\\leq f_1\\leq 1$). \nTo understand whether the system evolution is conservative \nor non--conservative is not easy in the case of a rapidly rotating \nneutron star; no easy solution can be found. We propose as one \npossibility a factor which may help us to distinguish between the two \ncases -- the surface magnetic field of the neutron star and its evolution \nduring the accretion. \n\n\\subsection{Magnetic stellar wind braking}\n\nWe also assume that the donor star, possessing a convective envelope, \nexperiences magnetic braking (Mestel 1968; Mestel \\& Spruit 1987; Muslimov \\& \nSarna 1995), and, as a consequence, the system loses its orbital \nangular momentum. For a magnetic stellar wind we used the formula for \nthe orbital angular momentum loss\n\n\\begin{equation}\n\\left. {{\\dot J} \\over {J}} \\right|_{MSW}= -3\\times 10^{-7}{{M^2R_2^2} \\over \n{M_1M_2 a^5}}~~~~~yr^{-1} ,\n\\end{equation}\n\nwhere $a$ and $R_2$ are the separation of the components and the radius of \nthe donor star in solar units.\n\n\\subsection{Gravitational wave radiation}\n\nFor systems with very short orbital periods, during the \nfinal stages of their evolution we also take into account the loss of \norbital angular momentum due to emission of gravitational radiation \n(Landau \\& Lifshitz 1971):\n\n\\begin{equation}\n\\left. {{\\dot J} \\over J} \\right|_{GR} = 8.5 \\times 10^{-10} {{M_1 M_2 M} \n\\over {a^4}}~~~~~yr^{-1} \n\\end{equation}\n\nThe mass and accompanying orbital angular momentum loss from these system are\npoorly understood problems in the evolution of binary stars. As is well known,\nthe variation of the angular momentum depends critically on the assumed \nmodel (Ergma et al. 1998). In the case of binary systems with ms pulsar\ntypically two different models concerning the mass ejection and\nangular momentum loss can be adopted. The first is that the amount of\nangular momentum lost per 1 gram of ejected matter is equal to the average\norbital angular momentum of 1 gram of the binary. The second is that the \nmatter that flows from\nthe companion star onto the neutron star (after accretion) is ejected \nisotropically with the specific angular momentum of the neutron star. \nIn this paper, for our non--conservative approach we have adopted the \nfirst model. \nThis affects significantly our results on the \nsemi--detached evolution (see fig. 2 in Ergma et al. 1998), but \nvery little changes the cooling time--scale of the helium white dwarf.\n\n\\subsection{Illumination of the donor star}\n\nIn all cases we have included the effect of illumination of the donor \nstar by the millisecond pulsar. In our calculations we assume that \nillumination of the component by the hard (X--ray and $\\gamma$--ray) \nradiation from the millisecond pulsar leads to additional heating of its \nphotosphere (Muslimov \\& Sarna 1993). The effective temperature $T_{eff} $ of the companion during the illumination stage is \ndetermined from the relation \n\n\\begin{equation}\nL_{in} + P_{ill} = 4 \\pi \\sigma R_2^2 T^4_{eff} , \n\\end{equation}\n\nwhere $L_{in} $ is the intrinsic luminosity corresponding to the \nradiation flux coming from the stellar interior and $\\sigma $ is the \nStefan--Boltzmann constant.\n\n$P_{ill} $ \nis the millisecond pulsar radiation that heats the photosphere, which is \ndetermined by \n\n\\begin{equation}\n P_{ill} = f_3 \\left({{R_2} \\over {2a}}\\right)^2 L_{rot}\n\\end{equation}\n\nand $L_{rot}$ is ``rotational luminosity'' of the neutron star due to \nmagneto--dipole radiation (plus a wind of relativistic particles)\n\n\\begin{equation}L_{rot}= {{2} \\over {3 c^3}} B^2 R_{ns}^6 \\left({{2 \\pi} \n\\over {P_p}}\\right)^4 ~~~~,\n\\end{equation}\n\nwhere $R_{ns}$ is the neutron star radius, B is the value of the magnetic \nfield strength at the neutron star and $ P_p $ is the pulsar period.\n$f_3$ is the factor characterizing the efficiency of transformation of \nirradiation flux into thermal energy (in our case we take $f_3 = 2\\times \n10^{-3}$). Note that in our calculations \nthe effect of irradiation is formally treated by means of modification \nof the outer boundary condition, according to relation (6).\n\nIn this paper we do not follow the magnetic field and pulsar period \n($P_p $) evolution, as we did in our earlier papers (Muslimov \\& Sarna 1993,\nErgma \\& Sarna 1996). We were mainly interested in finding initial models for\nlow--mass helium white dwarfs and in investigating the initial cooling phase \nof these low--mass helium white dwarfs. From earlier calculations we know that\nif the magnetic field strength is greater than about $ 10^9 ~$G, the \nneutron star spins--up to tenths and hundreds of milliseconds, rather than \nseveral milliseconds. This\nleads to a situation where the pressure of the magneto--dipole radiation is\ninsufficient to eject matter from the system. Also from our \nprevious calculations (see for example Ergma \\& Sarna 1996) we find that\nafter accretion of a maximum of about 0.2$~M_\\odot $, the neutron star has\nspun--up to millisecond periods if B$< 10^9 ~$G. Therefore in this \npaper we accept that after accretion of 0.2$~M_\\odot $ the neutron star\nspins--up to about 2 ms. After spin--up the pulsar irradiation is strong \nenough to prevent accretion, and at this moment we include non--conservative \nmass loss from the system as described above. \n\nDuring the initial high mass accretion phase ($ \\dot M_2 \\sim 10^{-8} - \n10^{-9} \n~M_\\odot ~yr^{-1}$, $t_{acc} \\sim 10^7 - 10^8 ~$yrs) the system may be\nobserved as a bright low--mass X--ray binary (LMXB). It is necessary to point\nout that majority of LMXBs for which orbital period determinations are \navailable (21 systems out of 24 according to van Paradijs catalogue 1995), \nhave orbital period of less than one day. These systems therefore \ncannot be the progenitors of the majority of low--mass helium white dwarf + \nmillisecond pulsar binary systems. \nA lack of LMXB systems with orbital period between 1 -- 3 days \ndoes not allow us to make a direct comparison between the observational \ndata and the results of our calculations.\n\n\\subsection{The code}\n\nThe models of the stars filling their Roche lobes were computed using a \nstandard stellar evolution code based on the Henyey--type code of Paczy\\'nski \n(1970), which has been adapted to low--mass stars. \nThe Henyey method involves iteratively improving a\ntrail solution for the whole star. During each iteration, corrections to all\nvariables at all mesh points in the star are evaluated using the\nNewton--Raphson method for linearised algebraic equations (see for example\nHansen \\& Kawaler 1994). The Henyey method extended to calculate stellar\nevolution with mass loss, as adopted here, is well explain by Zi\\'o\\l kowski\n(1970). We note here that our code makes use of the stationary envelope \ntechnique, which was developed early on in the life of our code in order to\nsave disc space (Paczy\\'nski 1969). This method makes the assumption that the \nsurface 0.5 -- 5\\% (by mass) of the star is not significantly affected by\nnuclear processes, such that it can be treated to a good approximation as \nhomogeneous region (in composition) throughout the whole evolutionary\ncalculation. During the cooling phase we assume that the static envelope \nis the\nsurface 0.5\\% of the star. This assumption is valid during the flashes \nbecause the time--scale is longer than thermal time--scale of the\nenvelope. We tested the possibility that \nthe algorithm for redistributing meshpoints introduces numerical diffusion \ninto the composition profile. \nWe find that if such numerical diffusion is real, it has only a marginal \ninfluence on the hydrogen profile.\nWe would also like to note that in the heat equation we neglect the \nderivative with respect to molecular weight, since its effect is small. \nConvection is treated with \nthe mixing--length algorithm proposed by Paczy\\'nski (1969). We solve the \nproblem of radiative transport by employing the opacity tables of Iglesias \\&\nRogers (1996). Where the Iglesias \\& Rogers (1996) tables \nare incomplete, we have filled the gaps using the opacity tables of Huebner et\nal. (1977). For temperatures less than 6000 K we use the opacities given by \nAlexander \\& Ferguston (1994) and Alexander (private communication). \nThe contribution from conduction \npresent in the opacity tables of Huebner et al. (1977) has been included by\nus in \nthe other tables, since they don't include it (Haensel, private \ncommunication). \nThe equation of state (EOS) includes radiation and gas pressure, \nwhich is composed of the ion and electron pressure. Contribution to the \nEOS owing to the non--ideal effects of Coulomb interaction and pressure \nionization which influence the EOS, as discussed by Pols et al. (1995), \nhave not been included in our program, and for this reason we stopped our \ncooling calculations before these effects become important.\nDuring the initial phase of cooling, the physical conditions in the hot \nwhite dwarfs are such that these effects are usually small.\n\n\n\\section{Evolutionary calculations}\n\nWe perform our evolutionary calculations \nfor binary systems initially consisting of a 1.4 $\\rm M_{\\odot }$ neutron \nstar (NS) and a slightly evolved companion (subgiant) of two masses, \n1 and 1.5, and four chemical compositions (Z: 0.003, 0.01, 0.02, \n0.03). We have produced (Table 1)\na number of evolutionary tracks corresponding to the different possible \nvalues of the initial orbital period (ranging from 0.7 to 3.0 days) at the \nbeginning of mass transfer phase.\n\n\\section{The Results}\n\nIn Table 1 we list the characteristic of the cooling \nphase of the WD, $\\rm t_{cool}$, and the maximum possible evolution \ntime of a system, $\\rm t_{evol}$, which is a sum of times of detached\n(determined by nuclear evolution), semi--detached, and cooling phases. \nThe cooling is the last phase of evolution of the WD, and in our \ncalculations starts at the end of RLOF. \nThe cooling\ntime, $\\rm t_{cool}$, is limited to an initial cooling stage during which the \nWD cools until its central\ntemperature has decreased by 50 $\\% $ of its maximum value. From Table 1 it \nis clearly seen that to produce short orbital period \nsystems in a time--scale shorter than Hubble time it is necessary either to \nhave low Z or a more massive secondary. \n\nIn our calculations the donor star fills its Roche lobe while it is evolving \nthrough the Hertzsprung gap, and therefore it transfers mass on its companion\nin a thermal time--scale. \n\nFigure 1 show the evolutionary cooling sequences for models 20 and 22 (more \ndetails in Table 1). Model 20 presents the case with stable hydrogen \nburning. Model 22 shows the case when the thermal instability of the \nhydrogen--burning shell occurs. The first flash is not strong enough to allow \nthe star to overflow its Roche lobe, but during the second flash the radius of \nthe secondary increases to fill its Roche lobe and short--time Roche lobe \noverflow (RLOF) occurs. \n\nIn Table 2 we present the mass--radius relationship for WDs from our \ncalculations, DSBH98, the Wood models, and \nthe Hamada \\& Salpeter (1961) zero--temperature helium WD models \ncalculated for a surface temperature of 8500 K (as in van Kerkwijk, \nBergeron \\& Kulkarini 1996 for PSR1012+5307). Comparison of the numbers demonstrate that for WD \nmasses of $<$ 0.25$~M_\\odot $, the results of our calculations \ndiffer significantly from a simple extrapolation obtained from the\ncooling curves (Wood 1990) performed for carbon WDs with the thick \nhydrogen envelopes. In addition comparing the cooling \ntime--scales of HP98 and BA98 with those of Webbink and our models, shows \ndifferences of an order of magnitude (Table 3) for WD masses of $<$ \n0.25$~M_\\odot $. \n\n\\begin{figure}\n\\epsfverbosetrue\n\\begin{center}\n\\leavevmode\n\\epsfxsize=7cm\n\\epsfbox{fig3.ps}\n%\\plottwo{fig3.ps}{fig4.ps}\n\\end{center}\n\\caption{Hydrogen flashes on a helium WD of mass 0.213$~M_\\odot$\n(model 7) which show four flashes without RLOF. The curves present the \neffective temperature ({\\it upper panel}), nuclear energy production in the hydrogen burning shell ({\\it middle panel}) and the luminosity \n({\\it lower panel}) as a function of cooling time, $t_0$=5.2$\\times 10^9$ \nyrs.} \n\\end{figure}\n\n\\begin{figure}\n\\epsfverbosetrue\n\\begin{center}\n\\leavevmode\n\\epsfxsize=7cm\n\\epsfbox{fig4.ps}\n%\\plottwo{fig3.ps}{fig4.ps}\n\\end{center}\n\\caption{Hydrogen flashes on a helium WD of mass 0.213$~M_\\odot$ (model 7). \nThe curves present the white dwarf radius ({\\it upper panel}), \nthe envelope mass ({\\it middle panel}) and the mass of the helium core \n({\\it lower panel}) as a function of the cooling time, $t_0$=5.2$\\times \n10^9$yrs.} \n\\end{figure}\n\n\\begin{figure}\n\\epsfverbosetrue\\begin{center}\n\\leavevmode\n\\epsfxsize=7cm\n\\epsfbox{fig5.ps}\n%\\plottwo{fig3.ps}{fig4.ps}\n\\end{center}\n\\caption{Same as for Fig.3 but for model 17. During first flash the secondary \ndoes not fill its Roche lobe but during the second and third flashes RLOF \noccurs \nand the total mass of white dwarf decreases ($t_0$= 1.4$\\times 10^9$ yrs).} \n\\end{figure}\n\n\\begin{figure}\n\\epsfverbosetrue\n\\begin{center}\n\\leavevmode\n\\epsfxsize=7cm\n\\epsfbox{fig6.ps}\n%\\plottwo{fig3.ps}{fig4.ps}\n\\end{center}\n\\caption{Same as for Fig.4 but for model 17. During the first flash \nthe secondary does not fill its Roche lobe but during the second and third \nflashes RLOF occurs \nand the total mass of white dwarf decreases ($t_0$= 1.4$\\times 10^9$ yrs).} \n\\end{figure}\n\n\\section{Hydrogen flash burning}\n\nThe problem of unstable hydrogen shell burning in low--mass helium WDs \nwas first discussed in the literature more than 30 years ago (Kippenhahn, \nThomas \\& Weigert 1968). Recently, Alberts et al. (1996) have claimed that \nthey do not \nsee any thermal flashes that result from thermally unstable \nshell--burning, as reported in papers IT86 and Kippenhahn, Thomas \\& \nWeigert (1968). Webbink (1975) found that in none of \nhis model sequences, such a severe thermal runaway as described \nby Kippenhahn et al. (1968) was found, although mild flashes for \nM$>$0.2 $M_\\odot$ did take place. Alberts et al. found that even reducing \nthe time step to 50--100 years would not lead to thermally unstable \nshell--burning for $M_{wd}$$<$0.25 $~M_\\odot$. In DSBH98, \nthermal instabilities of the hydrogen--burning shell occurs in their \ntwo models, 0.234$~M_\\odot$ and 0.259$~M_\\odot$. They concluded that \nhydrogen flashes take place only in the mass interval 0.21$\\leq$ $M/M_\\odot \\leq 0.3$.\n\nAccording to our computations, low--mass helium WDs with masses more\nthan 0.183$~M_\\odot$ \n(Z=0.03), 0.192$~M_\\odot$ (Z=0.02), 0.198$~M_\\odot$ (Z=0.01) and \n0.213$~M_\\odot$, (Z=0.003) may experience up to several hydrogen \nflashes before they enter the cooling stage. In Table 4 we present several \ncharacteristics for the computed flashes. We discussion two kinds \nof flashes: in the first case (in Table 4 shown as ``1''), during the\nflash the secondary does not fill its \nRoche lobe i.e. the mass of the white dwarf does not change, and in the \nsecond case \n(``2''), during the unstable hydrogen burning phase the secondary fills its \nRoche lobe and the system again enters into a very short duration \naccretion phase (see Table 4). \nWe introduce four time--scales to describe the flash behaviour: (i) the \nflash rise time--scale $\\Delta t_1$, which is the time for the luminosity to \nincrease from minimum to maximum value (typically this value is between \nfew $ \\times 10^6$ to few $ \\times 10^7$ yrs -- third column in the Table 4);\n(ii) the flash decay time--scale $\\Delta t_2$, which is the time for the \nluminosity to decrease to the initial value (typically from few hundred thousand to few tenth million years); \n(iii) $\\Delta$ T is the recurrence time between two successive flashes (iv) \n$ \\Delta t_{acc}$ is the duration of the accretion phase when the secondary \nfills its Roche lobe during hydrogen shell flash.\n\nFor all sequences with several unstable hydrogen shell burning stages\n(usually for case ``1''), the first flash is the weakest. \nIn the majority of cases when the flash forces \nthe star to fill its Roche lobe, only one flash takes place. For four cases \nwe found two successive flashes with Roche lobe overflow (models 17, 23, \n24, 31), and for another two cases (models 47, 53) to the first flash is not \npowerful enough to force the secondary fill its Roche lobe, but during \nthe second flash it is.\n\nHow does the hydrogen flash burning influence the cooling time--scale? \nIn Fig.2, the luminosity and nuclear energy production rates versus cooling \ntime for models 20 and 22 are shown. Model 20 shows stationary hydrogen \nburning and model 22, hydrogen flash burning.\nAlthough before flash model 22 was more luminous than model 20, \nlater the situation is reversed. After the flash, \nthe burning mass of the \nhydrogen rich envelope in model 22 has decreased to 0.0116$~M_{\\odot}$, \nwhereas the mass of the hydrogen envelope in model 20, \nin which stationary hydrogen burning occurs, is almost twice as large \n(0.0241$~M_{\\odot}$). If we look at how the maximum \nnuclear energy rate behaves with cooling time, we can see that after the \nflash in model 22, the maximum energy production rate is less than in \nmodel 20 (stationary hydrogen burning).\n \nIn Fig. 3 we present the behaviour of log$ ~T_{eff}$, log $\\epsilon_{nuc}$ \nand \nlog L/$L_\\odot$, and in Fig.4 log $R_{wd}$, $M_{env}$ and $M_f/M_{\\odot} $ as \na function of \ncooling time for model 7. Before the helium white dwarf enters the \nfinal cooling phase, four unstable hydrogen flash burnings occur. \nThe same parameters for model 17 (with RLOF) are shown in Figs. 5 and 6. \n\n\\begin{figure}\n\\epsfverbosetrue\n\\begin{center}\n\\leavevmode\n\\epsfxsize=7cm\n\\epsfbox{fig7.ps}\n%\\plottwo{fig3.ps}{fig4.ps}\n\\end{center}\n\\caption{Hydrogen flashes on a helium WD of model 17. \nThe white dwarf radius (solid line) together with Roche lobe radius (dashed\nline) ({\\it upper panel}) the nuclear energy production in the hydrogen \nburning shell ({\\it upper middle panel}) the maximum shell temperature \n(solid line) and central temperature (dashed line) ({\\it lower middle panel})\nand the surface luminosity ({\\it lower panel}) as a function of model \nnumber are shown. The vertical lines define different time--scales \nduring the flashes.} \n\\end{figure}\n\nTo investigate in more detail how the flashes develop, we show in Fig. 7 \nthe evolution of the white dwarf radius (upper panel), nuclear energy \ngeneration rate (upper middle panel), maximum shell\ntemperature and central temperature (lower middle panel) and the surface \nluminosity (lower panel) as a function of computed model number. \nIn Fig. 7, as vertical dashed lines we marked several time--scales which\ncharacterize the flash behaviour (for numbers see Table 4). $\\Delta t_1$ and \n$\\Delta t_2 $ describe the rise and decay times; the first \ncharacterizes the nuclear shell burning time--scale ($ \\tau^{shell}_{nuc}$), \nthe second the Kelvin--Helmholtz (thermal) envelope time--scale \nmodified \nby nuclear shell burning ($\\Delta t_2 = \\sqrt {\\tau^{env}_{K-H}\n\\tau^{shell}_{nuc}} $). The accretion time ($\\Delta t_{acc} $) is described\nby the square of the Kelvin--Helmholtz time--scale. The radiative diffusion \ntime is defined as the Kelvin--Helmholtz time--scale of the extended envelope \nabove the shell ($\\Delta t_{rd} = \\tau^{env}_{K-H} $). \nThe shape of the first flash on Fig. 7 \nshows some characteristic changes which are connected with physical \nprocesses in the stellar interior. At the beginning of the flash \nthe luminosity increases due to the more effective hydrogen burning \nin the shell source. After reaching a local maximum, the luminosity then \ndecreases while the nuclear energy generation rate is still increasing \nrapidly. This decrease of the surface luminosity is due to a temperature \ninversing forming below the hydrogen shell. The energy generated in \nthe hydrogen shell splits into two fluxes; coming outwards and going inwards. \nThe helium core is heated effectively by the shell nuclear source -- the \ncentral temperature increases by 2\\%. On Fig. 8 the evolution of the \nluminosity and temperature profiles during the $\\Delta t_1 $ and \n$\\Delta t_2 $ phases are shown. We clearly see how the inversion profile \nevolves and how the luminosity wave moves into the surface.\n\n\\begin{figure}\n\\epsfverbosetrue\n\\begin{center}\n\\leavevmode\n\\epsfxsize=7cm\n\\epsfbox{prof.ps}\n%\\plottwo{fig3.ps}{fig4.ps}\n\\end{center}\n\\caption{The evolution of temperature inversion layers and luminosity \nprofile during a hydrogen flash. The evolutionary sequences are as follow: \nsolid line -- local luminosity minimum; dashed line -- maximum temperature of\nthe hydrogen shell; short dashed line -- luminosity front moves outwards; \nlong dashed line -- maximum luminosity; dashed doted line -- decline of\nluminosity, heated core cooling effectively.} \n\\end{figure}\n \nThe nuclear energy generation rate in the shell has a maximum value far \naway from maximum surface luminosity. This is because the luminosity front \nis moving towards the stellar surface in a time--scale described by radiative \ndiffusion ($\\Delta t_{rd} $). After reaching a maximum value, the luminosity \nstarts to decrease and the \nenergy generation rate also declines in the hydrogen shell over a time-scale \n$\\Delta t_2 $ (for a contracting envelope) the \nluminosity decreases to the minimum value. During the first flash, \nthe stellar radius does not fill the inner Roche lobe. In the second and \nthird flashes we have short\nepisodes of super--Eddington mass transfer (see Table 4). During the RLOF \nphase, the orbital period slightly increases and the subgiant companion \nevolves quickly from spectral type F0 to A0. \n\n\nAs already pointed out, for several cases the secondary \nfills its Roche lobe and the system enters an accretion phase. \nDuring RLOF, the mass accretion rate is about three orders of magnitude\ngreater than the Eddington limit (Fig. 9). All the accreted matter \nwill be lost from the system ($\\Delta M_{acc} \\sim 0.0001 - 0.001 ~M_\\odot $). \nThe accretion phase is very short, usually less than 1000 years (ranging \nfrom 160 to 2500 yrs -- see Table 4). During the short super--Eddington \naccretion phase the system is a very bright X--ray source, with orbital period\nbetween 2 to 8 days.\n\nWe notice that during the flash the evolutionary time step strongly decreases \nand may be as short as several years.\n\n\\begin{figure}\n\\epsfverbosetrue\n\\begin{center}\n\\leavevmode\n\\epsfxsize=7cm\n\\epsfbox{fig8.ps}\n%\\plottwo{fig3.ps}{fig4.ps}\n\\end{center}\n\\caption{Mass accretion rate (model 42) versus time during a hydrogen shell \nflash with RLOF} \n\\end{figure}\n\n\\section{Role of binarity in the cooling history of the low--mass white dwarf}\n\nDSBH98 modelled single star evolution and produced white dwarfs with various \nmasses by applying large mass loss rates at appropriate positions in the \nred--giant \nbranch to force the models to move off the giant branch. To show how \nbinarity influences the final fate of the white dwarf cooling, \nwe have computed extra \nsequences (1.0+ 1.4 $M_\\odot$, Z=0.02, $P_i$=2.0 days) where we did not \ntake into account that the star is in a binary system e.g. during hydrogen \nshell flash we do not allow RLOF. In complete binary model calculation, \nonly one shell \nflash occurs accompanied with RLOF, whereas for the single star model \ncalculation, four \nhydrogen shell flashes take place. Due to RLOF, the duration \nof the flash phase is 2.7$\\times 10^6 $yrs; if we do not include binarity \nthe duration of the flash phase is 1.8$\\times 10^8 $yrs. However, \nthe cooling time for helium white dwarfs \nless massive than 0.2$~M_\\odot $ is not significantly changed. \nThis is because the duration of flash phase \nis very short in comparison to the normal cooling phase \n(towards the white dwarf region). However, the effect of binarity \nwill be important for the cooling history of more massive helium white\ndwarfs. In Fig. 10 both cases of evolution on the Hertzsprung--Russell \ndiagram are shown -- on the left panel Roche lobe overflow is not allowed, \non right panel RLOF takes place. \n\n\\section{Application to individual systems}\n\nBelow we discuss the observational data for several systems for which \nresults of our calculations may be applied, by taking into account the \norbital parameters of the system, the pulsar spin--down time, and the white \ndwarf cooling timescale. \n\n\\subsection{\\bf PSR J0437--4715}\n\nTiming information for this millisecond binary system: $P_p$=5.757 ms, \n$P_{orb}$=5.741 days, $\\tau$ (intrinsic characteristic age of pulsar) = \n4.4 -- 4.91 Gyrs, mass function f(M)= 1.239$10^{-3}$$M_\\odot$ (Johnston et \nal. 1993; Bell et al. 1995). Hansen \\& Phinney (1998b) have discussed the \nevolutionary stage of this system using their own cooling models described \nin HP98. They found consistent solution for all masses in the range 0.15 -- \n0.375$~M_\\odot$ with thick (in the terminology of HP98) hydrogen envelopes \nof 3$\\times 10^{-4} ~M_\\odot$.\n\n\\begin{figure*}\n\\epsfverbosetrue\n\\begin{center}\n\\leavevmode\n\\epsfxsize=7cm\\epsfbox{hr1.ps}\\quad\n\\epsfxsize=7cm\\epsfbox{hr2.ps}\n\\end{center}\n\\caption{Hertzsprung--Russell diagram with evolutionary tracks. \nEvolutionary sequence 1+1.4 $M_\\odot$, Z=0.02, $P_i$=2.0 days. Left \npanel RLOF is not allowed, right panel with RLOF.} \n\\end{figure*} \n\nTiming measurements by Sandhu et al. (1997) have detected a rate of change \nin the projected orbital separation $\\it a \\sin i$, which they interpret \nas a change in $\\it i$ and they calculate for an upper limit for \n$\\it i$$<$ $43^0$ \nand new lower limit to the mass of the companion of M$\\sim$ 0.22$~M_\\odot$. \nOur calculations also allow us to produce the orbital parameters and \nsecondary mass for the PSR \nJ0437--4715 system and fit its cooling age (2.5--5.3 Gyrs, Hansen \\& Phinney, \n1998b), and we find that the secondary fills its Roche lobe when the orbital period \n$P_i$ is $\\sim$ 2.5 days (Tables 1, 4). From our cooling tracks for \na binary orbital\nperiod of 5.741 days, the mass of the companion is 0.21$\\pm 0.01 ~M_\\odot $ \nand its cooling age 1.26--2.25 Gyrs (for a Population I chemical \ncomposition). These cooling models usually have one strong (with RLOF) \nhydrogen shell flash, after which the helium WD enters the normal cooling \nphase. \n\n\\subsection{\\bf{PSR J1012+5307}}\n\nLorimer et al. (1995) determined a characteristic age of the radio pulsar to \nbe 7 Gyr, which could be even larger if the pulsar has a significant \ntransverse velocity (Hansen \\& Phinney 1998b). Using the IT86 cooling \nsequences, they estimated the companion to be at most 0.3 Gyr old. HP98 \nmodels yield the following results for this system: the companion mass \nlies in the range 0.13--0.21$~M_\\odot$ and the WD age is $<$ 0.6 Gyr, \nthe neutron star mass in the range 1.3--2.1$~M_\\odot$.\n\nAlberts et al. (1996) were the first to show that the cooling timescale of a \nlow--mass \nWD can be substantially larger if there are no thermal flashes which \nlead to RLOF and a reduction of the hydrogen envelope mass. Our and DSBH98 \ncalculations confirmed their results that for low--mass helium WDs ($<$ 0.2 \n$M_\\odot$), indeed stationary hydrogen burning plays important role. To \nproduce short (less that one day) orbital period systems with a low--mass \nhelium WD and a millisecond pulsar it is necessary that the secondary fills \nits \nRoche lobe between $P_{bif}$ and $P_b$ (Ergma, Sarna \\& Antipova, 1998). \nIf the initial orbital period $P_{i}$ (at RLOF) is less than $P_{bif}$, \nthe binary system evolves towards short orbital periods. $P_b$ is another \ncritical orbital period value. If $P_b$ $<$ $P_{i}(RLOF)$ $<$ $P_{bif}$, then \na short orbital period ($<$ 1 day) millisecond binary pulsar with \nlow--mass helium white dwarf may form. \nSo the initial conditions of the formation of \nsuch systems are rather important. We calculated one extra sequence to \nproduce a binary system with orbital parameters similar to PSR J1012+5307. \nInitial system: 1 + 1.4 $M_\\odot$, $P_{i}$(RLOF) = 1.35 days, Z=0.01. \nFinal system : $M_s$=0.168$~M_\\odot$, $P_f$=0.605 days, \n$M_{env}$=0.041$~M_\\odot$. \nIn Fig. 11 in the effective temperature and gravity diagram we \nshow the cooling history of this white dwarf after \ndetachment of the Roche lobe. The two horizontal regions are the gravity \nvalues inferred by van Kerkwijk et al. (1996) (lower) and Callanan et al. \n(1998) (upper). Our results are consistent with the Callanan et al. (1998) \nestimates. It is necessary to mention that after detachment from its \nRoche lobe, the outer envelope is rather helium--rich. Bergeron et al. (1991)\nhave shown that a small amount of helium in a hydrogen--dominated envelope \ncan mimic the effect of a larger gravity.\n\n\\section{Discussion}\n\nThe results of our evolutionary calculations differ \nfrom those of Iben \\& Tutukov (1986) and Driebe et al. (1998) because \nof the different formation scenarios for \nlow--mass helium WDs. In IT86's calculations a donor star \nfills its Roche lobe while it is on the red giant branch (i.e. has a thick\nconvective envelope) with a well developed helium core and a thin hydrogen \nburning \nlayer. They proposed that the mass transfer time scale is so short that the \ncompanion will not be able to accrete the transferred matter and will itself \nexpand and overflow its Roche lobe. The final output is the formation of a \ncommon envelope and\nthe result of this evolution is a close binary with a helium WD\nof mass $\\rm 0.298~M_{\\odot }$ having a rather thin ($\\rm 1.4 \\times \n10^{-3}~M_{\\odot }$) hydrogen--rich (X=0.5) envelope.\n\nDSBH98 did not calculate the mass exchange phases during the red giant \nbranch evolution in detail but they also simulated the mass--exchange \nepisode by subjecting a red giant branch model to a sufficiently large mass \nloss rate. In both cases (IT86 and DSBH98) mass loss starts when the star \n(with a well developed helium core) is on the red giant branch.\n\nIn our calculations the Roche lobe overflow starts when the secondary \nhas either almost exhausted hydrogen in the center of the star or \nhas a very small helium core with a thick hydrogen burning layer. During \nthe semi--detached evolution the mass of the helium core increases from almost \nnothing to final value (for more detail about evolution of such systems, see \nErgma, Sarna \\& Antipova, 1998). \nThis is the reason that a much thicker ($\\rm \\sim [1.5-6] \\times \n10^{-2}~M_{\\odot }$, with X ranging from 0.30 to 0.52) hydrogen--rich\nenvelope is left on the donor star at the moment it shrinks \nwithin the Roche lobe.\n\nThe second important point where our results differ from that of DSBH98 is \nthat in our calculations we can produce (after the secondary detaches \nfrom its \nRoche lobe) final millisecond binary pulsar parameters which we \ncompare with observational data (orbital period, \nspin period of ms pulsar, mass of the companion). It was shown by \nJoss, Rappaport \\& Lewis (1987) and more recently by \nRappaport et al. (1995) that the evolution of a binary system initially \ncomprising of a neutron star and a low--mass giant will end up as a wide binary \ncontaining a radio pulsar and a white dwarf in a nearly circular orbit. The \nrelation between the white dwarf mass and orbital period (see eq. (6) in \nRappaport et al. 1995) shows that if the secondary fills its Roche lobe \nwhile on the red giant branch, then for $M_{wd} \\approx 0.19M_\\odot$ \nthe final orbital period would \nbe $\\sim$ 5 days, which is far from observed orbital period of the binary \npulsar PSR J 1012+ 5307 ($P_{orb}$=0.6 days).\n\nAlberts et al. (1996), DSBH98, and the results of our calculations \ndemonstrate \nclearly that especially for low--mass helium WDs ($<$ 0.2$~M_\\odot$) \nstationary hydrogen burning remains an important, if not the main, \nenergy source. HP98 and BA98 did consider nuclear \nburning but found it to be of little importance since their artificially chosen \nhydrogen envelope mass was less than some critical value, disallowing \nsignificant hydrogen burning. If we compare now the cooling curves of \nHP98, DSH98 with ours then there is one very important difference; \nthey did not model the evolution of the helium WD progenitor and all their \ncooling models (see for example Figs. 11, 12 in HP98) start with a high \n$T_{eff}$. In \nour models, cooling of the helium WD starts after detachment of the secondary \nfrom its Roche lobe (DSBH98 mimic this situation with mass loss from the \nstar). This time, the secondary (proto--white dwarf) has rather low effective \ntemperature (see for example Fig.1). During the evolution with L approximately \nconstant, the effective temperature increases to a maximum value, after which \nit decreases while still having a active hydrogen shell burning source. \nThe evolutionary time needed for the proto--white dwarf to travel from the \nminimum $T_{eff}$ (after detachment from Roche lobe) to maximum $T_{eff}$ \ndepends strongly on mass of the WD (for a smaller mass a longer evolutionary \ntime--scale).\n\nSo for low--mass helium WDs the evolutionary prehistory plays a very \nimportant role in cooling history of the white dwarf.\n\n\\begin{figure}\n\\epsfverbosetrue\n\\begin{center}\n\\leavevmode\n\\epsfxsize=7cm\n\\epsfbox{fig11.ps}\n%\\plottwo{fig3.ps}{fig4.ps}\n\\end{center}\n\\caption{log g -- log $T_{eff}$ diagram with $M_{wd}$= 0.168$~M_\\odot$. \nThe arrow marks the position of the PSR J1012+5307 white dwarf. Two horizontal\nregions are the gravity values inferred by Callanan et al. (1998) (upper) \nand van Kerkwijk et al. (1996) (lower). The vertical lines show effective \ntemperature constraints of Callanan et al. (1998)}\n\\end{figure} \n\n\\section{Conclusion}\n\nWe have performed comprehensive evolutionary calculations to\nproduce a close binary system consisting of a NS and a low--mass helium\nWD. \n\nWe argue that the presence of a thick hydrogen layer changes \ndramatically the cooling\ntime--scale of the helium white dwarf ($\\rm < 0.25 ~M_\\odot $), compared to\nthe previous calculations (HP98, BA98) where the mass of the hydrogen \nenvelope \nwas chosen as free parameter and was usually one order of magnitude\nless than that obtained from real binary evolution computations. \n\nAlso, we have demonstrated that using new cooling tracks \nwe can consistently explain the evolutionary status of the binary pulsar PSR \nJ1012+53. \n\nTables with cooling curves are available on {\\bf \nhttp://www.camk.edu.pl/~sarna/}.\n\n\\section*{\\sc Acknowledgments}\n\nWe would like to thank Dr. Katrina M. Exter for help in improving the form\nand text of the paper. We would like to thank our referee Dr. Peter Eggleton \nfor \nvery useful referee opinion. At Warsaw, this work is supported through \ngrants 2--P03D--014--07 and 2--P03D--005--16 of the \nPolish National Committee for Scientific Research. Also, J.A. and E.E. \nacknowledges support through Estonian SF grant 2446.\n\n\n\n\\begin{thebibliography}{}\n\n\\bibitem{}Alberts F., Savonije G. J., van den Heuvel E. P. J., Pols \nO. R., 1996, {\\it Nature}, 380, 676\n\n\\bibitem{}Alexander D. R., Ferguson J. W., 1994, ApJ, 437, 879\n\n\\bibitem{}Benvenuto O. G., Althaus L. 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A., 1990, PhD thesis, The University of Texas at Austin\n\n\\bibitem{}Zi\\'o\\l kowski J., 1970, Acta Astron., 20, 59\n\n\\end{thebibliography}\n\n\\begin{table*}\n\\begin{center}\n\\begin{tabular}{clrrrrrlrrcc}\n%\\footnotesize\n\\multicolumn{12}{c}{Table 1a Cooling track characteristics} \\\\\n\\multicolumn{12}{c}{} \\\\\n%\\tablewidth{0pt}\n%\\tablehead{\n\\hline\n\\multicolumn{12}{c}{} \\\\\nmodel & {$ P_{i}$} & \\multicolumn{1}{c}{$M_{i}$} & {$\\lg t_{cool}$}\n& \\multicolumn{1}{c}{$\\lg t_{evol}$} & {$X_{surf}^{f}$} & \n\\multicolumn{1}{c}{$P_{f}$} & \\multicolumn{1}{c}{$M_{f}$} & {$M_{2,He}(RLOF)$} \n& {$M_{2,He}(COOL)$} & {$\\lg L_{f}$} & {$\\lg T_{eff,f}$} \\\\\n& {[days]} & [{$M_\\odot$}] & \\multicolumn{1}{c}{[yrs]} \n& \\multicolumn{1}{c}{[yrs]} & & {[days]} & [{$M_\\odot$}] \n& \\multicolumn{1}{c}{[$M_\\odot$]} & \n\\multicolumn{1}{c}{[$M_\\odot$]} & [{$L_\\odot$}] & \\\\\n\\multicolumn{12}{c}{} \\\\\n\\hline\n\\multicolumn{12}{c}{} \\\\\n\\multicolumn{12}{c}{Z=0.003} \\\\\n\\multicolumn{12}{c}{} \\\\\n\n1 & 1.02 & 1.0 & 10.004 & 10.197 & 0.38 & 0.421 & 0.172 & 0.112 & 0.150 \n& -2.299 & 3.920 \\\\\n2 & 1.05 & 1.0 & 9.948 & 10.159 & 0.39 & 0.554 & 0.175 & 0.115 & 0.152 \n& -2.232 & 3.936 \\\\\n3 & 1.10 & 1.0 & 9.867 & 10.108 & 0.39 & 0.708 & 0.178 & 0.119 & 0.158 \n& -2.139 & 3.959 \\\\\n4 & 1.30 & 1.0 & 9.685 & 10.008 & 0.40 & 1.180 & 0.187 & 0.134 & 0.169 \n& -1.944 & 4.008 \\\\\n5 & 1.50 & 1.0 & 9.582 & 9.958 & 0.40 & 1.584 & 0.192 & 0.143 & 0.177 \n& -1.843 & 4.035 \\\\\n6 & 2.00 & 1.0 & 9.399 & 9.885 & 0.41 & 2.614 & 0.203 & 0.160 & 0.189 \n& -1.673 & 4.080 \\\\ \n7 & 2.50~~H & 1.0 & 9.211 & 9.831 & 0.43 & 4.275 & 0.213 & 0.176 & 0.201 \n& -1.499 & 4.125 \\\\\n8 & 3.00~~H & 1.0 & 9.107 & 9.809 & 0.44 & 5.498 & 0.219 & 0.185 & 0.207 \n& -1.403 & 4.142 \\\\\n\\multicolumn{12}{c}{} \\\\\n\n9 & 0.70 & 1.5 & 9.479 & 9.645 & 0.43 & 1.591 & 0.191 & 0.137 & 0.175 & -1.659\n& 4.066 \\\\\n10 & 0.80 & 1.5 & 9.122 & 9.474 & 0.44 & 2.092 & 0.199 & 0.146 & 0.184 & -1.364\n& 4.129 \\\\\n11 & 0.90 & 1.5 & 9.061 & 9.392 & 0.44 & 2.450 & 0.204 & 0.154 & 0.190 \n& -1.201 & 4.165 \\\\\n12 & 1.20~~H* & 1.5 & 8.845 & 9.304 & 0.46 & 3.409 & 0.213/ & 0.169 & 0.200 \n& -0.986 & 4.210 \\\\\n& & & & & & & 0.212 & & & & \\\\\n13 & 1.50~~H* & 1.5 & 8.788 & 9.286 & 0.48 & 4.280 & 0.217/ & 0.178 & 0.206 \n& -0.929 & 4.224 \\\\\n& & & & & & & 0.217 & & & & \\\\\n14 & 1.80~~H* & 1.5 & 8.753 & 9.277 & 0.49 & 5.105 & 0.221/ & 0.185 & 0.210 \n& -0.925 & 4.230 \\\\\n& & & & & & & 0.221 & & & & \\\\\n15 & 2.10~~H* & 1.5 & 8.766 & 9.283 & 0.49 & 5.866 & 0.225/ & 0.192 & 0.214 \n& -0.957 & 4.229 \\\\\n& & & & & & & 0.224 & & & & \\\\\n16 & 2.50~~H* & 1.5 & 8.742 & 9.278 & 0.48 & 6.831 & 0.229/ & 0.197 & 0.219 \n& -0.976 & 4.232 \\\\\n& & & & & & & 0.228 & & & & \\\\\n17 & 3.00~~H* & 1.5 & 8.665 & 9.259 & 0.49 & 7.888 & 0.232/ & 0.203 & 0.223 \n& -1.010 & 4.231 \\\\\n& & & & & & & 0.231 & & & & \\\\\n\\multicolumn{12}{c}{} \\\\\n\\hline\n\\multicolumn{12}{c}{} \\\\\n\\multicolumn{12}{c}{Z=0.01} \\\\\n\\multicolumn{12}{c}{} \\\\\n18 & 1.30 & 1.0 & 10.212 & 10.388 & 0.38 & 0.366 & 0.163 & 0.120 & 0.143 \n& -2.601 & 3.847 \\\\\n19 & 1.35 & 1.0 & 9.907 & 10.316 & 0.39 & 0.605 & 0.168 & 0.127 & 0.150 \n& -2.477 & 3.877 \\\\\n20 & 1.45 & 1.0 & 9.886 & 10.193 & 0.40 & 1.092 & 0.177 & 0.139 & 0.161 \n& -2.231 & 3.934 \\\\\n21 & 1.65 & 1.0 & 9.661 & 10.094 & 0.42 & 1.945 & 0.188 & 0.154 & 0.175 \n& -1.995 & 3.993 \\\\\n22 & 2.00~~H* & 1.0 & 9.490 & 10.037 & 0.43 & 2.936 & 0.197/ & 0.166 & 0.185 \n& -1.829 & 4.035 \\\\\n& & & & & & & 0.196 & & & & \\\\\n23 & 2.50~~H* & 1.0 & 9.165 & 9.967 & 0.45 & 4.272 & 0.205/ & 0.173 & 0.194 \n& -1.606 & 4.085 \\\\\n& & & & & & & 0.203 & & & & \\\\\n24 & 3.00~~H* & 1.0 & 9.152 & 9.965 & 0.45 & 5.546 & 0.211/ & 0.184 & 0.201 \n& -1.546 & 4.104 \\\\\n& & & & & & & 0.209 & & & & \\\\\n\\multicolumn{12}{c}{} \\\\\n\n25 & 0.90 & 1.5 & 9.902 & 10.007 & 0.44 & 1.075 & 0.174 & 0.132 & 0.156 \n& -2.168 & 3.937 \\\\\n26 & 1.05 & 1.5 & 9.650 & 9.810 & 0.47 & 1.855 & 0.186 & 0.148 & 0.172 \n& -1.872 & 4.008 \\\\\n27 & 1.10 & 1.5 & 9.596 & 9.772 & 0.46 & 2.032 & 0.188 & 0.152 & 0.175 \n& -1.832 & 4.020 \\\\\n28 & 1.20 & 1.5 & 9.504 & 9.710 & 0.47 & 2.378 & 0.192 & 0.157 & 0.180 \n& -1.741 & 4.042 \\\\\n29 & 1.50~~H* & 1.5 & 9.368 & 9.629 & 0.47 & 3.152 & 0.200/ & 0.169 & 0.188 \n& -1.645 & 4.069 \\\\\n& & & & & & & 0.199 & & & & \\\\\n30 & 2.00~~H* & 1.5 & 9.273 & 9.578 & 0.48 & 4.153 & 0.206/ & 0.178 & 0.195 \n& -1.572 & 4.091 \\\\\n& & & & & & & 0.205 & & & & \\\\\n31 & 2.50~~H* & 1.5 & 9.111 & 9.505 & 0.49 & 5.091 & 0.211/ & 0.185 & 0.201 \n& -1.475 & 4.114 \\\\\n& & & & & & & 0.209 & & & & \\\\\n32 & 3.00~~H* & 1.5 & 9.091 & 9.501 & 0.50 & 7.896 & 0.221/ & 0.197 & 0.213 \n& -1.455 & 4.130 \\\\\n& & & & & & & 0.221 & & & & \\\\\n\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\begin{table*}\n\\begin{center}\n\\begin{tabular}{clrrrrrlrrcc}\n%\\footnotesize\n\\multicolumn{12}{c}{Table 1b Cooling track characteristics} \\\\\n\\multicolumn{12}{c}{} \\\\\n%\\tablewidth{0pt}\n%\\tablehead{\n\\hline\n\\multicolumn{12}{c}{} \\\\\nmodel & {$ P_{i}$} & \\multicolumn{1}{c}{$M_{i}$} & {$\\lg t_{cool}$}\n& \\multicolumn{1}{c}{$\\lg t_{evol}$} & {$X_{surf}^{f}$} & \n\\multicolumn{1}{c}{$P_{f}$} & \\multicolumn{1}{c}{$M_{f}$} & {$M_{2,He}(RLOF)$} \n& {$M_{2,He}(COOL)$} & {$\\lg L_{f}$} & {$\\lg T_{eff,f}$} \\\\\n& {[days]} & [{$M_\\odot$}] & \\multicolumn{1}{c}{[yrs]} \n& \\multicolumn{1}{c}{[yrs]}& & {[days]} & [{$M_\\odot$}] \n& \\multicolumn{1}{c}{[$M_\\odot$]} & \n\\multicolumn{1}{c}{[$M_\\odot$]} & [{$L_\\odot$}] & \\\\\n\\multicolumn{12}{c}{} \\\\\n\\hline\n\\multicolumn{12}{c}{} \\\\\n\\multicolumn{12}{c}{Z=0.02} \\\\\n\\multicolumn{12}{c}{} \\\\\n\n33 & 1.20 & 1.0 & 10.237 & 10.467 & 0.37 & 0.416 & 0.162 & 0.128 & 0.145 \n& -2.673 & 3.830 \\\\\n34 & 1.50 & 1.0 & 9.850 & 10.277 & 0.41 & 1.489 & 0.179 & 0.149 & 0.166 \n& -2.245 & 3.929 \\\\\n35 & 2.00~~H* & 1.0 & 9.582 & 10.193 & 0.43 & 2.912 & 0.192/ & 0.164 & 0.181\n& -1.978 & 3.995 \\\\\n& & & & & & & 0.191 & & & & \\\\\n36 & 2.50~~H* & 1.0 & 9.420 & 10.159 & 0.45 & 4.242 & 0.200/ & 0.175 & 0.190\n& -1.819 & 4.033 \\\\\n& & & & & & & 0.199 & & & & \\\\\n37 & 3.00~~H* & 1.0 & 9.299 & 10.139 & 0.47 & 5.551 & 0.206/ & 0.182 & 0.196\n& -1.698 & 4.062 \\\\\n& & & & & & & 0.205 & & & & \\\\\n\\multicolumn{12}{c}{} \\\\\n\n38 & 1.20 & 1.5 & 10.168 & 10.255 & 0.44 & 0.736 & 0.170 & 0.141 & 0.155 \n& -2.570 & 3.854 \\\\\n39 & 1.50 & 1.5 & 9.835 & 9.987 & 0.44 & 1.737 & 0.183 & 0.154 & 0.171 \n& -2.198 & 3.939 \\\\\n40 & 2.00~~H* & 1.5 & 9.448 & 9.747 & 0.48 & 4.230 & 0.203/ & 0.179 & 0.193 \n& -1.831 & 4.032 \\\\\n& & & & & & & 0.202 & & & & \\\\\n41 & 2.50~~H* & 1.5 & 9.295 & 9.677 & 0.49 & 5.910 & 0.210/ & 0.188 & 0.202 \n& -1.690 & 4.067 \\\\\n& & & & & & & 0.209 & & & & \\\\\n42 & 3.00~~H* & 1.5 & 9.074 & 9.599 & 0.52 & 7.686 & 0.216/ & 0.196 & 0.209 \n& -1.537 & 4.100 \\\\\n& & & & & & & 0.215 & & & & \\\\\n\\multicolumn{12}{c}{} \\\\\n\\hline\n\\multicolumn{12}{c}{} \\\\\n\\multicolumn{12}{c}{Z=0.03} \\\\\n\\multicolumn{12}{c}{} \\\\\n43 & 1.15 & 1.0 & 10.287 & 10.553 & 0.37 & 0.305 & 0.160 & 0.130 & 0.143 \n& -2.753 & 3.809 \\\\\n44 & 1.30 & 1.0 & 10.104 & 10.462 & 0.38 & 0.882 & 0.169 & 0.140 & 0.156 \n& -2.562 & 3.856 \\\\\n45 & 1.50 & 1.0 & 9.909 & 10.384 & 0.40 & 1.488 & 0.177 & 0.149 & 0.166 \n& -2.343 & 3.906 \\\\\n46 & 1.65 & 1.0 & 9.809 & 10.353 & 0.41 & 1.884 & 0.182 & 0.156 & 0.171\n& -2.242 & 3.930 \\\\\n47 & 1.80~~H* & 1.0 & 9.693 & 10.323 & 0.41 & 2.303 & 0.185/ & 0.160 & 0.175\n& -2.149 & 3.950 \\\\\n& & & & & & & 0.184 & & & & \\\\\n48 & 2.50~~H* & 1.0 & 9.474 & 10.281 & 0.45 & 4.222 & 0.197/ & 0.175 & 0.188\n& -1.912 & 4.008 \\\\\n& & & & & & & 0.196 & & & & \\\\\n49 & 3.00~~H* & 1.0 & 9.366 & 10.265 & 0.47 & 5.541 & 0.203/ & 0.181 & 0.195\n& -1.798 & 4.035 \\\\\n& & & & & & & 0.202 & & & & \\\\\n\\multicolumn{12}{c}{} \\\\\n50 & 1.35 & 1.5 & 10.264 & 10.353 & 0.42 & 0.497 & 0.165 & 0.137 & 0.150 \n& -2.694 & 3.822 \\\\\n51 & 1.50 & 1.5 & 10.045 & 10.173 & 0.42 & 1.190 & 0.174 & 0.146 & 0.161 \n& -2.464 & 3.876 \\\\\n52 & 1.70 & 1.5 & 9.829 & 10.015 & 0.42 & 1.968 & 0.184 & 0.156 & 0.173 \n& -2.246 & 3.929 \\\\\n53 & 1.80~~H* & 1.5 & 9.580 & 9.873 & 0.46 & 3.380 & 0.196/ & 0.174 & 0.187\n& -2.020 & 3.984 \\\\\n& & & & & & & 0.194 & & & & \\\\\n54 & 2.50~~H* & 1.5 & 9.353 & 9.772 & 0.49 & 5.850 & 0.208/ & 0.188 & 0.200\n& -1.801 & 4.039 \\\\\n& & & & & & & 0.207 & & & & \\\\\n55 & 3.00~~H* & 1.5 & 9.151 & 9.705 & 0.51 & 7.671 & 0.214/ & 0.195 & 0.207\n& -1.651 & 4.073 \\\\\n& & & & & & & 0.213 & & & & \\\\\n\\end{tabular}\n\\end{center}\n%\\tablenote{}\n\\begin{flushleft}\n{Listed are:\\\\\n$\\rm P_i$ is initial orbital period of the system (at the beginning of mass transfer)\\\\\n $\\rm M_i$ is the mass of the progenitor of white dwarf \\\\\n$\\rm t_{cool}$ is duration of the cooling phase of a white dwarf starting at the end of\nRLOF\\\\\n$\\rm t_{evol} $ is total evolution time \\\\\n $\\rm X_{surf}^{f} $ is the final surface hydrogen content\\\\\n$\\rm P_f$ is final orbital period at the moment of shrinking of the donor within its Roche lobe\\\\\n$\\rm M_f$ is final WD mass \\\\ \n$\\rm M_{2,He}(RLOF)$ is the mass of the helium core at the moment \nof shrinking of the donor within its Roche lobe\\\\\n $\\rm M_{2,He}(COOL)$ is\nthe final mass of helium core after the central temperature has decreased \nby 50\\% of its maximum value\\\\\n$L_f$ is the final luminosity\\\\\n $T_{eff,f}$ is the final effective temperature.\\\\ }\n%\\tablenote\n{H}{~- hydrogen flashes without RLOF}\\\\\n%\\tablenote\n{H*}{~- hydrogen flashes with RLOF}\\\\\n\\end{flushleft}\n\\end{table*}\n\n\\begin{table*}\n\\begin{center}\n\\begin{tabular}{lcccccc}\n\\multicolumn{7}{c}{Table 2 M-R relation for a cooling low--mass WD with a \nhelium core} \\\\\n\\hline\n\\multicolumn{7}{c}{} \\\\\n$\\rm M_{wd}/M_\\odot $ & $\\rm R_0/R_\\odot $ & $\\rm R_{8500}/R_0 $ & \n$\\rm R_{8500}/R_0 $ & log $\\rm g_1 $ & $\\rm R_{8500}/R_0 $ & log $\\rm g_2 $ \\\\\n\\multicolumn{6}{c}{} \\\\\n\\hline\n0.155 & 0.0218 & 2.100 & - & 6.31 & 1.351 & 6.69 \\\\\n0.180 & 0.0208 & 1.594 & 1.687 & 6.65 & 1.300 & 6.82 \\\\\n0.206 & 0.0198 & 1.469 & 1.476 & 6.83 & 1.236 & 7.00 \\\\\n0.296$^*$ & 0.0173 & 1.224 & 1.220 & 7.26 & 1.111 & 7.36 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n%\\tablenotetext{}\n{The first two columns present the zero--temperature\nM--R relation for a helium WD obtained by Hamada \\& Salpeter (1961). \nThe third and fifth columns display our calculations of the \nstellar radius and gravity, while fourth and fifth the DSBH98 calculations, \nrespectively. The last two columns \nillustrate the same quantities taken from the cooling tracks \nproduced by Wood (1990) for carbon WDs with thick hydrogen envelopes. \nThe stellar radius is calculated at T = 8500 K and is normalized by \nthe zero--temperature radius.}\\\\\n\n%\\tablenotetext\n{*}{the last two values in this row are taken from IT86.} \n\\end{table*}\n\n\\begin{table*}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\multicolumn{4}{c}{Table 3 Comparison of the cooling time-scales of} \\\\\n\\multicolumn{4}{c}{HP98, BA98 and Webbink, ours models} \\\\\n\\hline\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{} & \\multicolumn{1}{c}{} \\\\\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{HP98 and BA98} & \n\\multicolumn{1}{c}{Webbink and ours} \\\\\n\\multicolumn{2}{c}{} & \\multicolumn{1}{c}{} & \\multicolumn{1}{c}{} \\\\\n\\hline\n& & & \\\\\n{$\\rm M_{He}/M_\\odot$} & $\\rm \\log L/L_\\odot $ & {$\\rm t_{cool}$ (Gyrs)} & \n{$\\rm t_{cool}$} (Gyrs) \\\\\n& & & \\\\\n\\hline\n0.15 & -3.1 & 1.0 & {36.4} \\\\\n0.25 & -2.9 & 1.0 & {6.1} \\\\\n0.30 & -2.9 & 1.0 & {4.2} \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\begin{table*}\n\\begin{center}\n\\begin{tabular}{ccrrrrccrrr}\n%\\footnotesize\n\\multicolumn{11}{c}{Table 4a Flash characteristics} \\\\\n\\multicolumn{11}{c}{} \\\\\n%\\tablewidth{0pt}\n%\\tablehead{\n\\hline\n\\multicolumn{11}{c}{} \\\\\nmodel & case & \\multicolumn{1}{c}{$\\lg \\Delta t_1$} \n& \\multicolumn{1}{c}{$\\lg \\Delta t_{acc}$} \n& \\multicolumn{1}{c}{$\\lg \\Delta t_2$} & \\multicolumn{1}{c}{$\\lg \\Delta T$} \n& $\\lg L_{max}/L_\\odot$ & $\\lg T_{eff}$ & $M_{b,env}$ & $M_{a,env}$\n& \\multicolumn{1}{c}{$\\Delta M_{acc}$} \\\\\n& & [yrs] & [yrs] & [yrs] & [yrs] & & [L=$L_{max}$] \n& \\multicolumn{1}{c}{[$M_\\odot$]} & \\multicolumn{1}{c}{[$M_\\odot$]} \n& \\multicolumn{1}{c}{[$\\times 10^{-4}M_\\odot$]} \\\\ \n\\multicolumn{11}{c}{} \\\\\n\\hline\n\\multicolumn{11}{c}{} \\\\\n7 & 1 & 6.377 & & 6.349 & 6.595 & 0.526 & 4.349 & & & \\\\\n& 1 & 6.852 & & 6.599 & 6.450 & 1.525 & 4.117 & & & \\\\\n& 1 & 7.095 & & 6.609 & 6.584 & 1.603 & 4.073 & & & \\\\\n& 1 & 7.346 & & 6.598 & & 1.693 & 4.011 & & & \\\\\n\\multicolumn{11}{c}{} \\\\\n8 & 1 & 6.453 & & 6.509 & 6.520 & 1.571 & 4.147 & & & \\\\\n& 1 & 6.906 & & 6.580 & 6.553 & 1.658 & 4.084 & & & \\\\\n& 1 & 7.183 & & 6.596 & & 1.740 & 4.037 & & & \\\\\n\\multicolumn{11}{c}{} \\\\\n12 & 1 & 6.634 & & 6.551 & 6.484 & 0.912 & 4.330 & & & \\\\\n& 1 & 6.907 & & 6.608 & 6.449 & 1.548 & 4.084 & & & \\\\\n& 1 & 7.139 & & 6.601 & 6.649 & 1.619 & 4.044 & & & \\\\\n& 2 & 7.367 & 2.673 & 6.456 & & 1.703 & 4.015 & 0.0129 & 0.0123 & 1.7 \\\\\n\\multicolumn{11}{c}{} \\\\\n13 & 1 & 6.717 & & 6.590 & 6.474 & 1.577 & 4.099 & & & \\\\\n& 1 & 6.971 & & 6.612 & 6.574 & 1.646 & 4.053 & & & \\\\\n& 2 & 7.215 & 2.192 & 6.571 & & 1.727 & 3.979 & 0.0119 & 0.0118 & 0.2 \\\\\n\\multicolumn{11}{c}{} \\\\\n14 & 1 & 6.372 & & 6.519 & 6.473 & 1.588 & 4.119 & & & \\\\\n& 1 & 6.861 & & 6.585 & 6.475 & 1.670 & 4.078 & & & \\\\\n& 1 & 7.141 & & 6.588 & 7.603 & 1.751 & 3.994 & & & \\\\\n& 2 & 6.435 & 2.593 & 6.258 & & 1.843 & 3.982 & 0.0113 & 0.0105 & 3.5 \\\\\n\\multicolumn{11}{c}{} \\\\\n15 & 1 & 6.538 & & 6.558 & 6.443 & 1.669 & 4.099 & & & \\\\\n& 1 & 6.975 & & 6.567 & 6.516 & 1.748 & 4.038 & & & \\\\\n& 2 & 7.283 & 2.433 & 6.450 & & 1.842 & 3.963 & 0.0108 & 0.0103 & 1.2 \\\\\n\\multicolumn{11}{c}{} \\\\\n16 & 1 & 6.643 & & 6.551 & 6.462 & 1.757 & 4.082 & & & \\\\\n& 1 & 7.091 & & 6.553 & 6.622 & 1.846 & 4.016 & & & \\\\\n& 2 & 7.501 & 2.513 & 6.172 & & 1.965 & 3.983 & 0.0100 & 0.0095 & 4.4 \\\\\n\\multicolumn{11}{c}{} \\\\\n17 & 1 & 5.774 & & 6.646 & 6.510 & 1.829 & 4.047 & & & \\\\\n& 2 & 7.202 & 2.272 & 6.477 & 6.723 & 1.933 & 3.940 & 0.0120 & 0.0094 & 0.6 \\\\\n& 2 & 7.688 & 2.389 & 5.931 & & 2.094 & 3.983 & 0.0094 & 0.0082 & 8.2 \\\\\n\\multicolumn{11}{c}{} \\\\\n22 & 1 & 6.495 & & 6.513 & 6.674 & 0.312 & 4.253 & & & \\\\\n& 2 & 7.029 & 3.154 & 6.113 & & 1.311 & 3.938 & 0.0121 & 0.0116 & 4.7 \\\\\n\\multicolumn{11}{c}{} \\\\\n23 & 2 & 6.998 & 2.994 & 6.124 & 6.884 & 1.459 & 3.922 & 0.0115 & 0.0105 \n& 4.9 \\\\\n& 2 & 7.902 & 2.806 & 5.915 & & 1.679 & 3.975 & 0.0105 & 0.0088 & 14.1 \\\\\n\\multicolumn{11}{c}{} \\\\\n24 & 2 & 6.823 & 2.914 & 6.171 & 6.801 & 1.546 & 3.914 & 0.0103 & 0.0097 \n& 3.9 \\\\\n& 2 & 7.623 & 2.769 & 5.966 & & 1.695 & 3.939 & 0.0097 & 0.0086 & 10.4 \\\\\n\\multicolumn{11}{c}{} \\\\\n29 & 1 & 6.662 & & 6.583 & 6.634 & 0.371 & 4.246 & & & \\\\\n& 2 & 6.971 & 3.177 & 5.984 & & 1.307 & 3.293 & 0.0120 & 0.0108 & 6.2 \\\\\n\\multicolumn{11}{c}{} \\\\\n30 & 2 & 6.880 & 3.066 & 5.967 & & 1.412 & 3.918 & 0.0112 \n& 0.0100 & 5.7 \\\\\n\\multicolumn{11}{c}{} \\\\\n31 & 2 & 6.652 & 2.994 & 6.011 & 6.793 & 1.470 & 3.906 & 0.0103 \n& 0.0095 & 4.3 \\\\\n& 2 & 7.666 & 2.843 & 5.899 & & 1.641 & 3.955 & 0.0095 & 0.0083 & 11.6 \\\\\n\\multicolumn{11}{c}{} \\\\\n32 & 2 & 7.005 & 2.779 & 5.825 & & 1.682 & 3.900 & 0.0090 & 0.0078 & 7.9 \\\\\n\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\n\\begin{table*}\n\\begin{center}\n\\begin{tabular}{ccrrrrccrrr}\n%\\footnotesize\n\\multicolumn{11}{c}{Table 4b Flash characteristics} \\\\\n\\multicolumn{11}{c}{} \\\\\n%\\tablewidth{0pt}\n%\\tablehead{\n\\hline\n\\multicolumn{11}{c}{} \\\\\nmodel & case & \\multicolumn{1}{c}{$\\lg \\Delta t_1$} \n& \\multicolumn{1}{c}{$\\lg \\Delta t_{acc}$} \n& \\multicolumn{1}{c}{$\\lg \\Delta t_2$} & \\multicolumn{1}{c}{$\\lg \\Delta T$} \n& $\\lg L_{max}/L_\\odot$ & $\\lg T_{eff}$ & $M_{b,env}$ & $M_{a,env}$\n& \\multicolumn{1}{c}{$\\Delta M_{acc}$} \\\\\n& & [yrs] & [yrs] & [yrs] & [yrs] & & [L=$L_{max}$] \n& \\multicolumn{1}{c}{[$M_\\odot$]} & \\multicolumn{1}{c}{[$M_\\odot$]} \n& \\multicolumn{1}{c}{[$\\times 10^{-4}M_\\odot$]} \\\\ \n\\multicolumn{11}{c}{} \\\\\n\\hline\n\\multicolumn{11}{c}{} \\\\\n35 & 1 & 6.510 & & 6.425 & 6.799 & -0.068 & 4.205 & & & \\\\\n& 2 & 6.864 & 3.290 & 5.969 & & 1.173 & 3.911 & 0.0111 & 0.0102 & 7.4 \\\\\n\\multicolumn{11}{c}{} \\\\\n36 & 2 & 6.720 & 3.158 & 5.850 & & 1.313 & 3.897 & 0.0102 & 0.0089 \n& 8.6 \\\\\n\\multicolumn{11}{c}{} \\\\\n37 & 2 & 6.885 & 2.999 & 5.810 & & 1.419 & 3.877 & 0.0097 \n& 0.0082 & 10.5 \\\\\n\\multicolumn{11}{c}{} \\\\\n40 & 2 & 6.622 & 3.168 & 5.549 & & 1.275 & 3.883 & 0.0098 & 0.0084 & 9.2 \\\\\n\\multicolumn{11}{c}{} \\\\\n41 & 2 & 6.876 & 2.981 & 5.719 & & 1.427 & 3.875 & 0.0087 & 0.0076 & 10.2 \\\\\n\\multicolumn{11}{c}{} \\\\\n42 & 2 & 7.362 & 2.744 & 5.737 & & 1.615 & 3.876 & 0.0079 & 0.0063 & 11.6 \\\\\n\\multicolumn{11}{c}{} \\\\\n47 & 1 & 7.373 & & 6.594 & 6.966 & 0.208 & 4.151 & & & \\\\\n& 2 & 6.095 & 3.388 & 5.938 & & 1.072 & 3.926 & 0.0109 & 0.0095 & 12.7 \\\\\n\\multicolumn{11}{c}{} \\\\\n48 & 2 & 6.809 & 3.200 & 5.820 & & 1.239 & 3.864 & 0.0094 \n& 0.0080 & 11.1 \\\\\n\\multicolumn{11}{c}{} \\\\\n49 & 2 & 6.871 & 3.081 & 5.836 & & 1.317 & 3.863 & 0.0089 & 0.0074 & 9.9 \\\\\n\\multicolumn{11}{c}{} \\\\\n53 & 1 & 6.471 & & 6.690 & 6.819 & 0.190 & 4.170 & & & \\\\\n& 2 & 6.920 & 3.239 & 6.785 & & 1.160 & 3.889 & 0.0094 & 0.0078 & 12.4 \\\\\n\\multicolumn{11}{c}{} \\\\\n54 & 2 & 6.927 & 2.962 & 5.722 & & 1.355 & 3.855 & 0.0081 & 0.0066 & 11.1 \\\\\n\\multicolumn{11}{c}{} \\\\\n55 & 2 & 7.180 & 2.785 & 5.734 & & 1.521 & 3.849 & 0.0074 & 0.0058 & 11.8 \\\\\n\n\\end{tabular}\n\\end{center}\n%\\tablenote{}\n\\begin{flushleft}\n{Listed are:\\\\\n number of model (Table 1)\\\\\n number of case (1 or 2)\\\\ \n$\\Delta t_1$ and $\\Delta t_2$ are the rise and decay times responsively\\\\ \n$\\Delta T$ and $\\Delta t_{acc}$ are recurrence time between two successful \nflashes and duration of accretion phase during the flash \\\\\n $T_{eff}$ is effective temperature when the luminosity has its maximum value $L_{max} $\\\\ \n$M_{b,env}$ and \n$M_{a,env}$ are the envelope masses before and after flash \\\\\n $\\Delta M_{acc}$ is accreted mass\\\\ \n $M_{b,env}$-$M_{a,env}$=\n$\\Delta M_{He,c}$+$\\Delta M_{acc}$ where $\\Delta M_{He,c}$ is the increase \nof the helium core mass during the flash.\\\\}\n\\end{flushleft}\n\\end{table*}\n\n\n\\end{document} \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n"
}
] |
[
{
"name": "astro-ph0002261.extracted_bib",
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astro-ph0002262
|
Structural and Photometric Classification of Galaxies -- I. Calibration Based on a Nearby Galaxy Sample
|
[
{
"author": "Matthew A. Bershady"
}
] |
In this paper we define an observationally robust, multi-parameter space for the classification of nearby and distant galaxies. The parameters include luminosity, color, and the image-structure parameters: size, image concentration, asymmetry, and surface brightness. Based on an initial calibration of this parameter space using the ``normal'' Hubble-types surveyed by Frei \etal (1996), we find that only a subset of the parameters provide useful classification boundaries for this sample. Interestingly, this subset does not include distance-dependent scale parameters, such as size or luminosity. The essential ingredient is the combination of a spectral index (e.g., color) with parameters of image structure and scale: concentration, asymmetry, and surface-brightness. We refer to the image structure parameters (concentration and asymmetry) as indices of ``form.'' We define a preliminary classification based on spectral index, form, and surface-brightness (a scale) that successfully separates normal galaxies into three classes. We intentionally identify these classes with the familiar labels of Early, Intermediate, and Late. This classification, or others based on the above four parameters can be used reliably to define comparable samples over a broad range in redshift. The size and luminosity distribution of such samples will not be biased by this selection process except through astrophysical correlations between spectral index, form, and surface-brightness.
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[
{
"name": "bershady.tex",
"string": "\\documentstyle[emulateaj]{article}\n% \\documentstyle[12pt,aasms4]{article}\n% \\documentstyle[11pt,aaspp4]{article}\n% \\documentstyle[11pt,aas2pp4]{article}\n\n\\newcommand\\etal{{\\it et~al.\\ }}\n\n\\begin{document}\n\n\\submitted{To Appear in AJ, June 2000}\n\n\\title{Structural and Photometric Classification of Galaxies -- \nI. Calibration Based on a Nearby Galaxy Sample}\n\n\\author{Matthew A. Bershady}\n\n\\affil{Department of Astronomy, University of Wisconsin, 475 N Charter\nStreet, Madison, WI 53706; mab@astro.wisc.edu}\n\n\\author{Anna Jangren}\n\n\\affil{Department of Astronomy and Astrophysics, Pennsylvania State\nUniversity, 525 Davey Lab, University Park, PA 16802;\njangren@astro.psu.edu}\n\n\\author{Christopher J. Conselice}\n\n\\affil{Department of Astronomy, University of Wisconsin, 475 N Charter\nStreet, Madison, WI 53706; chris@astro.wisc.edu}\n\n% \\author{David C. Koo}\n% \n% \\affil{University of California Observatories / Lick\n% Observatory, Department of Astronomy and Astrophysics,\n% University of California, Santa Cruz, CA 95064; koo@ucolick.org}\n% \n% \\author{Rafael Guzm\\'an\\altaffilmark{1}}\n% \n%\\affil{Department of Astronomy, Yale University, P.O. Box\n% 208101, New Haven, CT 06520-8101; rguzman@astro.yale.edu}\n\n% \\altaffiltext{1}{Hubble Fellow.} \n\n\\begin{abstract}\n\nIn this paper we define an observationally robust, multi-parameter\nspace for the classification of nearby and distant galaxies. The\nparameters include luminosity, color, and the image-structure\nparameters: size, image concentration, asymmetry, and surface\nbrightness. Based on an initial calibration of this parameter space\nusing the ``normal'' Hubble-types surveyed by Frei \\etal (1996), we\nfind that only a subset of the parameters provide useful\nclassification boundaries for this sample. Interestingly, this subset\ndoes not include distance-dependent scale parameters, such as size or\nluminosity. The essential ingredient is the combination of a spectral\nindex (e.g., color) with parameters of image structure and scale:\nconcentration, asymmetry, and surface-brightness. We refer to the\nimage structure parameters (concentration and asymmetry) as indices of\n``form.'' We define a preliminary classification based on spectral\nindex, form, and surface-brightness (a scale) that successfully\nseparates normal galaxies into three classes. We intentionally\nidentify these classes with the familiar labels of Early,\nIntermediate, and Late. This classification, or others based on the\nabove four parameters can be used reliably to define comparable\nsamples over a broad range in redshift. The size and luminosity\ndistribution of such samples will not be biased by this selection\nprocess except through astrophysical correlations between spectral\nindex, form, and surface-brightness.\n\n\\end{abstract}\n\n\\keywords{galaxies: classification --- galaxies: morphology ---\ngalaxies: colors}\n \n\\section{Introduction}\n\nIt is now well-established that a large fraction of galaxies\ndiscovered at intermediate and high redshift have unusual\nmorphologies, and thus cannot be classified in terms of the nominal\nHubble-Sandage system (Driver \\etal 1995, 1998; Abraham \\etal 1996a,\n1996b). The Hubble classification scheme is also difficult to apply\nto many local galaxies, dubbed `peculiar,' or any galaxies\nimaged at low signal-to-noise ($S/N$), or apparently small size\n(relative to the point-spread function). The Hubble-Sandage\nclassification system was predicated on the study of nearby,\n``normal'' galaxies -- luminous and relatively quiescent\nobjects(\\cite{san61}, \\cite{san87}, \\cite{san93}). While the\nclassification system developed by de~Vaucouleurs \\etal (1976) makes\nan attempt to push the framework to ``later'' types, it still suffers\nfrom the above shortcomings. Fundamentally, these traditional\nclassification schemes are based on the concept of `pigeon-holing'\ngalaxies based on a reference-set, or archetypes. These archetypes are\nselected from samples in the local universe, and are preferentially\naxisymmetric systems. Since our local census is undoubtedly\nincomplete, and, since galaxies evolve, such reference sets by their\nvery definition are incomplete. Thus it is not surprising that these\nsystems are of marginal utility in the study of dwarf galaxies,\ninteracting galaxies, or galaxies at high redshift.\n\nAn alternative classification scheme could be based on quantitative\nindices, the inter-relation of which is not predetermined by a finite\nreference set. This would permit galaxies to be classified, for\nexample, in different stages of their evolution; albeit the\nclassification would be different but the basis set of indices would\nbe the same. The goal of this paper is to define such a set of\nindices that can be used as quantitative, objective classifiers of\ngalaxies (i) over a wide range in redshift, and (ii) for wide range of\ngalaxy types. In particular, we desire classifiers that are well\nsuited to typing both ``normal'' galaxies and the compact galaxies\nthat are the focus of a companion study (Jangren \\etal 2000;\nhereafter, paper II). We anticipate that such a classification scheme\nis both necessary and enabling for the exploration of the physical\nmechanisms driving galaxy evolution (Bershady 1999).\n\nWhat are the desired characteristics of classification parameters?\nThey should be physically interesting (closely related to underlying\nphysical properties of galaxies), model-independent, and measurable\nfor all galaxy types. It also should be possible to accurately\ndetermine the parameters chosen for a wide range of image resolution \nand signal-to-noise ratios.\n\nFrom Hubble's classification {\\it a posteriori} we have learned that a\nstrong correlation exists between galaxy spectral type and apparent\nmorphological features -- at least for the galaxy types which fit well\nwithin his scheme. This correlation -- noted by Hubble as early\nas 1936 (Hubble 1936) -- can loosely be termed a `color-morphology'\nrelation, although the correlation is not necessarily limited to\nbroad-band color. This is a triumph of Hubble's classification\nexplicitly because it is not part {\\it of} the classification.\nFurthermore, the correlation yields clues about the physical\nconnection of the present matter distribution and the star-formation\nhistories in galaxies. But while morphology (or `form') and spectral\ntype are correlated, there is also significant dispersion in this\ncorrelation. Some of the more notable deviations from the nominal\ncolor-morphology relation are found in the plethora of forms for\nspectrally `late' type galaxies, the presence of `E+A' galaxies\n(Dressler \\& Gunn 1993), and the compact, luminous, blue, emission-line\ngalaxies studied in paper II (as we shall show). This points to the\nimportance of form and spectral type as key, yet independent axes of a\nrevised classification system.\n\nHowever, the only example of such a revised classification system is\nthat of Morgan (1958, 1959), where central light concentration is used\nas the primary classification parameter. Morgan was motivated by the\nfact that (i) a salient criterion used in classifying galaxies in the\nHubble-Sandage system is the degree of central concentration of light;\n(ii) there was a significant dispersion in spectral type and Hubble\ntype (\\cite{hum56}); and (iii) spectral type appeared to correlate\nmore strongly with light concentration. In this way, Morgan hoped to\nwed the classification of stellar populations to the classification of\ngalaxies. Nonetheless, he was compelled to introduce a secondary\nparameter, i.e. the `Form Family,' because there was still a\ndispersion of morphological forms within each of his spectral types.\nToday, one should be able to improve upon Morgan's scheme by\nintroducing quantitative measures of image concentration and other\nindices of form, and by independently assessing the spectral type via\ncolors or spectra.\n\nA number of subsequent attempts have been made to construct\nquantitative classification system that could replace or modify the\ncurrent Hubble scheme. Yet these schemes are generally based purely\neither on photometric form (e.g. \\cite{elm82}; \\cite{oka84};\n\\cite{wat85}; \\cite{doi93}; \\cite{abr94}; \\cite{ode95}; \\cite{han95})\nor spectral type (e.g. \\cite{ber95}; \\cite{conn95}; \\cite{zar95};\n\\cite{fol96}; \\cite{bro98}; \\cite{ron99}). In essence, they have\nrelied implicitly on an assumed correlation between galaxy spectral\ntype and apparent morphology. Related attempts have been made to use\nartificial neural networks to reproduce the Hubble scheme in an\nobjective way (e.g. \\cite{bur92}; \\cite{sto92}; \\cite{spie92};\n\\cite{ser93}; \\cite{nai95}; \\cite{ode95}; \\cite{ode96}). Yet these go\nno further in differentiating between spectral type and form. Only in\nWhitmore's (1984) scheme are spectral and structural parameters\ncombined, i.e., $B-H$ color, size, and bulge-to-total ratio are used\nto define two principal classification axes of {\\it scale} and {\\it\nform}. But again, the correlation(s) between galaxy spectral type,\nscale and form are not explicit.\n\nHere we attempt to expand on Morgan's program by fully quantifying the\nclassification of form via image concentration and several other\nstructural parameters, and explicitly using color as an indicator of\nspectral type. In this study we choose to use only a single color\n($B-V$), but we anticipate that a more desirable, future development\nwould be to include broad-wavelength coverage, multi-color data and\nspectroscopic line-indices. Spectroscopic line-indices would be\nrequired, for example, to identify E+A galaxies. While such galaxies\nare not the focus of the present work, a comprehensive classification\nscheme should be able to isolate these systems and determine the range\nof their morphology ({\\it cf.} Dressler \\& Gunn 1992, Couch \\etal\n1994, and Wirth \\etal 1994). Nonetheless, broad-band colors are a\ncost-effective way to characterize the spectral continuum ({\\it cf.}\nBershady, 1995, and Connolly \\etal 1995). Of more direct relevance to\nthe study at hand, a future elaboration of including $U-V$ and $V-K$\nwould enhance the ability to distinguish between spectral types\nparticularly for galaxies with extremely blue, optical colors\n(e.g. Aaronson 1978, Bershady 1995).\n\nWe have also chosen to quantify form and scale via non-parametric\nmeasures, such as luminosity, half-light size and surface-brightness,\nasymmetry, and image concentration. An alternative, model-dependent\napproach is to decompose a galaxy's light profile into a disk and\nbulge. The traditional one-dimensional decompositions are fraught with\ntechnical problems such that decompositions can only be achieved\nreliably for about half of all disk galaxies (\\cite{ken85}). The newer\ntwo-dimensional decomposition techniques are superior (e.g.\n\\cite{jong96b}), and have been shown to successfully reproduce\nobserved light profiles for faint galaxies (e.g. \\cite{sim99}).\nIndeed, one can argue that two-dimensional model fitting to imaging\ndata is optimum in terms of using the available information, and for\nminimizing random error. At high $S/N$ and high angular resolution,\nhowever, even the most ``normal'' galaxies exhibit peculiarities (as\ndiscussed in more detail in \\S 3.3.2) such that simple bulge-plus-disk\nmodels cannot reproduce these frequently observed peculiarities in\nlight distributions with high fidelity. The situation worsens for\n``peculiar'' galaxies. For this reason we have some concerns about the\nuniqueness of the observationally derived model parameters, and hence\ntheir interpretation. We anticipate future developments which use the\nmodels and non-parametric measurements in a hybrid scheme optimal for\ncharacterizing galaxy light distributions both in terms of random and\nsystematic errors.\n\nIt is worth noting again that bright galaxy samples are notorious for\nmissing or under-representing certain galaxy types -- particularly\ndwarfs and low-surface-brightness galaxies. The samples used here are\nno exception. While this was one of our complaints about the classical\nHubble scheme, there are two key differences with our approach: (i)\nthe classification parameters we develop are objective; and (ii) these\nparameters do not assume the presence of basic axi-symmetry,\ndisk-plus-bulge structure, or spiral patterns which underly the Hubble\nscheme. As we will show, the galaxies examined here are sufficiently\ndiverse to establish the {\\it parameter space} for a comprehensive\nclassification scheme, although not the comprehensive classification\nitself. By developing an initial classification of these galaxies,\nhowever, we intend to use it as a foil against which we can begin to\ncompare the classification of more distant samples: How are the\nclassifications different? Do the nearby and distant samples occupy\nthe same regions of parameter space? If not, do the differences\nrepresent continuous extensions of these parameters, or are they\nphysically disjoint? These are the types of questions one can address\ngiven the limitations of current local samples. Note that we must\nstop short of identifying differences as ``new,'' epoch-specific\nclasses of galaxies. Without a complete census of both the nearby and\ndistant universe, it is not possible to establish whether there are\ndifferent ``classes'' of galaxies at different redshifts; apparent\ndifferences could simply be artifacts of the presently limited\nsamples. With such a complete census, in the future we may hope to\naddress deeper issue of how the comoving space-densities of different\nclasses evolve.\n\nTowards the goal of establishing a comprehensive classification scheme\nof utility to distant galaxy studies, in this paper we assemble a\nrobust set of non-parametric, photometric and structural properties\nfor a range of nearby, lumimous galaxies. We define a multivariate,\nphotometric parameter space that forms an initial classification\nscheme for these galaxies. This classification can be used reliably to\nidentify comparable samples in other surveys and at higher redshift.\nIn the accompanying paper (II) we measure these properties for\ncompact, luminous emission-line galaxies at intermediate redshift,\ncompare them to the ``normal,'' nearby galaxies studied here, and\ndemonstrate that our classification parameter space distinguishes\nbetween these two samples. We discuss the implications for the\nevolution of this intermediate-redshift sample therein. In future\npapers in this series we intend to extend our analysis (a) to more\nrepresentative samples of the local volume that include dwarf and\nemission-line galaxies (e.g., the University of Michigan Objective\nPrism Survey (\\cite{sal89}); (b) to more comprehensive samples of\ndistant galaxies, e.g magnitude-limited samples from the Hubble Deep\nField; and (c) to studies of the morphological evolution of these\ndistant samples. The classification scheme which we propose here is\nintended as a framework for these future studies.\n\nThe data sets are presented in \\S 2; the analysis is described in \\S\n3. The results are presented in \\S 4, and summarized in \\S\n5. Throughout this paper we adopt $H_0$ = 50 km s$^{-1}$ Mpc$^{-1}$,\n$q_0 = 0.1$, $\\Lambda = 0$.\n\n\\section{Nearby galaxy samples} \n\nAs a primary reference sample, 101 of the 113 local Hubble-type\ngalaxies from the catalog of Frei \\etal (1996) were analyzed. This\nsample will define what we mean by ``normal'' galaxies in this paper.\nThis catalog is the only digital, multi-band, sample publicly\navailable that is reasonably comprehensive; it consists of\nground-based CCD images of bright galaxies, all apparently large (most\nhave diameters of 4\\arcmin~-~6\\arcmin) and well resolved. As a result,\nthe sample contains mostly luminous and physically large galaxies: out\nof the 101 objects we used in our analysis, only seven have $L <\n0.1\\,L^*$. We excluded 12 objects whose apparent sizes were larger\nthan the CCD field of view (thus their image structure parameters\ncould not be well estimated). Two of the excluded objects are\nearly-type galaxies (E--S0), seven are intermediate (Sa--Sb), and\nthree are late-type (Sc--Irr).\\footnote{The excluded objects are: NGC\n2403, 2683, 3031, 3079, 3351, 3623, 4406, 4472, 4594, 4826, 5746, and\n6503.} The majority of the remaining sample are spirals and S0\ngalaxies. Frei \\etal have removed foreground stars from the images of\nthe nearby galaxies, in a few cases leaving visible ``scars;'' except\nin the case of NGC 5792, these residuals did not cause noticeable\nproblems when determining the structural parameters (\\S 3.3).\n\nIn several instances in the present analysis we reference the sample\nof Kent (1984, 1985), which is composed of 53 nearby, luminous and\nphysically large galaxies similar to the Frei \\etal sample. We find\nKent's sample useful for comparison of both photometric and structural\nparameters. We also reference the sample of 196 normal (non-active)\nMarkarian galaxies studied by Huchra (1977a). Relevant characteristics\nof the above three samples are summarized in Table 1, including an\nenumeration of the effective filter systems used in each\nstudy. Further details on these photometric systems are found in the\nstudies listed in the Table and references therein.\n\n\\subsection{Comparison of reference samples to emission-line galaxy samples}\n\nBoth the Frei \\etal and Kent samples are under-representative of dwarf\ngalaxies, and contain neither HII galaxies nor low surface-brightness\ngalaxies. The latter objects have been shown to make up a significant\nfraction of the local galaxy population (de Jong 1995, 1996a). Clearly\nour reference samples do not constitute a representative template of\nthe local population. Here we estimate where these samples may be\nparticularly un-representative with an eye towards the study of faint\ngalaxy samples in future papers. In Figures 1 and 2 we compare the\nFrei \\etal samples photometric properties of color and luminosity to\n(i) the normal Markarian galaxies (Huchra 1977a), (ii) dwarf\nspheroidals (as described in the following section), and (iii) the\nintermediate redshift samples presented in paper II.\n\nSince the Markarian galaxies were selected from objective prism plates\nbased on their strong UV continua, the sample is biased toward bluer\ncolors than the Frei \\etal galaxies and is thus likely more\nrepresentative of star-forming galaxies. Huchra's sample contains\nfainter galaxies that extend the magnitude range down to $M_B \\sim\n-14$ and the color-color locus blue-ward of $B-V = 0.4$.\n\nThe intermediate-redshift galaxies, also selected in part due to their\nblue color (see paper II), have blue luminosities comparable to the\nbrighter half of the Frei \\etal sample, but with bluer colors. This\nplaces most of them in a distinct region of the color-luminosity plot\nfrom the Frei \\etal sample. In contrast, the distribution of the\nMarkarian galaxies extends into the region occupied by the\nintermediate-redshift objects. In the color-color diagram, again the\nintermediate-redshift galaxies largely overlap with the Markarian\nsample in the region corresponding to extreme blue colors {\\it not}\noccupied by the Frei \\etal or Kent samples.\n\nIn short, the Frei \\etal sample is spectro-photometrically disjoint\nfrom extreme samples of blue, star-forming galaxies at\nintermediate-redshift (e.g., paper II), even though both contain\nintrinsically luminous and moderate-to-high surface-brightness\nsystems. Yet clearly there ar local examples (e.g., from Markarian)\nwhich are as blue and luminous as these intermediate-redshift,\nstar-forming galaxies. These sources are simply missing from the Frei\n\\etal sample. The comparison of the global properties of the\nintermediate-redshift, compact, star-forming galaxies in paper II to\nthose of local galaxies from Frei \\etal (here) is then an initial step\nin mapping the range of galaxy types at any redshift. Further\ninvestigation of the nature and evolution of these types of extreme,\nstar-forming systems will be greatly facilitated by future work\nquantifying the image structure of local counterparts \\bv $< 0.4$ and\n$M_B<-19$.\n\n\\subsection{Comparison of reference samples to dwarf spheroidals}\n\nWe have made some attempt, where possible, to access the photometric\nand structural properties of other key dwarf populations. We\nschematically indicate the locus of dwarf ellipticals/spheroidals in\nFigures 1 and 2 using data from \\cite{cald83}, \\cite{bing91}, and\n\\cite{bing98}. The dwarf spheroidals occupy a virtually unpopulated\nregion of the color-luminosity diagram at relatively red colors and\nlow luminosity. The absence of such objects from most surveys is\nattributed typically to a selection bias since these sources are at\nlow surface-brightness. It is interesting to note that in the\ncolor-color diagram the dwarf spheroidals occupy a region over-lapping\nwith the early-to-intermediate type spirals. Hence the integrated\nbroad-band light of these systems are unusual compared to our\nreference samples only with respect to their luminosity. We refer to\nthe dwarf spheroidal properties extensively in future papers where we\nalso explore their image structural properties.\n\n\\section{Analysis}\n\nAs noted in the Introduction, many galaxies are sufficiently unusual\nthat they cannot be classified in terms of the normal Hubble\nscheme. This becomes increasingly true at intermediate redshifts. The\ncompact, luminous emission-line galaxies in paper II are such an\nexample. This is not due to poor spatial resolution, but to truly\nunusual morphological properties, e.g., off-centered nuclei, tails,\nasymmetric envelopes, etc. To compare such objects morphologically to\n``normal'' galaxies, we define here six fundamental parameters of\ngalaxy type that are quantitative, can be reliably determined over a\nrange in redshift, and are physically meaningful.\n\nTwo of these parameters are photometric, derived from existing\nground-based imaging and estimated $k$-corrections: rest-frame color\n\\bv, and absolute blue luminosity $M_B$. Two are image structure\nparameters, derived from multi-aperture photometric analysis presented\nbelow: physical half-light radius $R_e$, and image concentration\n$C$. One is a combined photometric-structural parameter: average\nrest-frame surface brightness $SB_e$ within $R_e$. Of the three\nparameters luminosity, half-light radius, and surface brightness, any\none can obviously be derived from the other two. (We consider all\nthree since in any given range of, e.g., luminosity, there is\nsignificant dispersion in both $SB_e$ and $R_e$.) The sixth parameter,\na 180$^{\\circ}$-rotational asymmetry index ($A$), utilizes the\nmulti-aperture photometry indirectly through definition of the\nextraction radius for rotation; we refer to $A$ as a structural\nparameter. Table 2 contains all individual measurements for\nthe Frei \\etal sources. Luminosities and all image-structure\nparameters are measured in the rest-frame $B$ band.\n\n\\subsection{Photometric parameters: restframe color and luminosity}\n\nWhile the Frei \\etal (1995) data set contains $B_J$ images for 75\\% of\nthe sample and $g$ band images for the remaining objects, there is no\nblue bandpass in which observations are available for all galaxies\n(see Table 1). We have made a comparison of the apparent (uncorrected)\n$B$ magnitudes listed in the {\\it Third Reference Catalogue of Bright\nGalaxies} (\\cite{vau91}, RC3) to those derived from our photometry of\nthe Frei \\etal images, appropriately transformed to the $B$-band using\nthe tabulated corrections of Frei and Gunn (1994). This comparison\nshows that while the two magnitude estimates do not differ in the\nmean, there is a 0.25 mag (rms) scatter. To avoid the uncertainty\nassociated with SED-dependent color transformations (see also \\S A.3)\nwe use the RC3 uncorrected $B$ magnitudes and \\bv \\ colors instead of\nthe values from our own photometry.\n\nWe apply $k$-corrections and corrections for galactic extinction to\nthe \\bv \\ colors and apparent $B$ band magnitudes of the nearby galaxy\nsample in the manner described in RC3. The heliocentric velocities\n$v_{hc}$ of the galaxies are small (no greater than 3000 km s$^{-1}$\nfor any object); the average velocity is $\\langle v_{hc} \\rangle \\sim\n1000$ km s$^{-1}$. Hence the associated $k$-corrections are $<0.05$\nmag. We use the distances given in the {\\it Nearby Galaxies\nCatalogue} (\\cite{tul88}), recalculated to $H_0$=50 km s$^{-1}$\nMpc$^{-1}$, to derive absolute magnitudes $M_B$ from the corrected\napparent magnitudes. Note we do not correct for internal extinction\nsince the suitability and procedure for applying such corrections\nmay be ill-defined for higher-redshift galaxies.\n\n\\subsection{Multi-aperture photometry}\n\nTo characterize the light distributions of the galaxies, we performed\nmulti-aperture photometry on all images. The apertures are centered\nat the intensity-weighted centroid of each object. Since much of the\nprofile shape information is contained in the central parts of the\nimage, logarithmically spaced apertures are used. For the photometry\nof the Hubble Space Telescope ($HST$) images in paper II, the smallest\naperture corresponds to 0.\\arcsec05, the largest to 15\\arcsec; for the\nnearby galaxy photometry here, the aperture radii are scaled to\ncorrespond to similar linear sizes. The apertures are circular to\naccommodate the irregular morphology of the intermediate redshift\ngalaxies in paper II that would be difficult to fit with another\ngeometrical figure. The efficacy of this approach is addressed in more\ndetail below and in the Appendix (\\S A.3).\n\n\\subsection{Structural parameters}\n\nImage structure is most commonly quantified via bulge--disk\ndecomposition, yielding a bulge-to-total ratio, $B/T$. We refrain from\nthis approach here, for reasons which we alluded to in the\nIntroduction. For example, $B/T$ parameter may be poorly defined for\nasymmetric and compact galaxies. Irregularities in the surface\nbrightness profiles, which can be caused by asymmetric structure,\nrings, or lenses, also cause problems for bulge--disk decompositions.\nWhile Kent showed that the concentration parameter correlates well\nwith the bulge-to-total ratio, this holds only for objects with $B/T <\n0.63$. At larger values of $B/T$, bulge-disk decomposition fails for\nseveral objects in Kent's sample, resulting in galaxies of type S0 --\nSa being given extremely high values of $B/T$. Bulge--disk\ndecomposition also becomes unreliable when galaxy disks are fainter\nthan the bulges.\n\nIt is worth noting again that these problems mainly arise from older,\none-dimensional methods of decomposition. The newer two-dimensional\ndecomposition techniques are clearly successful at reproducing the\nobserved light profiles, with remarkably small residuals (Schade \\etal\n1995, 1996; \\cite{sim98}; \\cite{mar98}). Still, there are physical\nsituations where bulge--disk decomposition techniques in general\nbecome problematic, namely where the astrophysical reality is more\ncomplex than simple bulge--disk models. Some galaxies have central\ncondensations better described by an exponential profile rather than\nan $r^{1/4}$-law (\\cite{wyse97}); many galaxies have strong\nbi-symmetries, such as bars; virtually all galaxies have varying\ndegrees of asymmetry due to star formation, dust, or large-scale\ngravitational perturbations and lopsidedness. All of these features\nrepresent details that decomposition into bulge and disk components do\nnot address correctly. Simple disk and bulge decomposition is also\ninadequate for disk galaxies where the luminosity profile deviates\nfrom a pure exponential (\\cite{fre70}), e.g. type I and type II\ndisks. (Type I disk profiles have an added component which contributes\nto the light just outside the bulge region; the surface brightness of\na type II profile shows the opposite behavior (an inner truncation),\nand drops below the level of an exponential profile in the region near\nthe center.)\n\nGiven the astrophysical complexity of real galaxies, the physical\ninterpretation of the derived model parameters of disk-bulge fits\nremains uncertain. Nonetheless, such profile-fitting methods should be\nuseful for estimating non-parametric structural and photometric\nparameters (e.g. characteristic sizes, surface brightness, image\nconcentration, and ellipticity) in a way that uses the data in an\noptimal manner. In the current effort, however, we have taken a\ncompletely non-parametric approach of measuring sizes,\nsurface-brightness, image concentration and asymmetry using\nmulti-aperture photometry rather than deriving a model-dependent $B/T$\nparameter.\n\n\\subsubsection{Half-light radii and surface-brightness}\n\nWe define first our working definition of a total magnitude since it\nrepresents the critical zeropoint for measurement of the half-light\nradius and surface-brightness. We use the dimensionless parameter\n$\\eta$ to define the total aperture of the galaxies -- a limiting\nradius which is {\\it not} based on isophotes.\\footnote{Isophotal radii\nintroduce redshift-dependent biases unless careful consideration and\ncorrections are made for dimming due to the expansion ($\\propto\n(1+z)^{-3}$ in broad-band photon counts) and $k$-corrections. While\nsuch redshift-dependent biases are not an issue for the samples\nstudied in this paper, in future papers in the series this would be an\nissue were we not to avoid isophotes.} The concept of defining the size\nof a galaxy based on the rate of change in the enclosed light as a\nfunction of radius was first introduced by Petrosian (1976). In terms\nof intensity, $\\eta$ can be defined as the ratio of the average\nsurface brightness within radius $r$ to the local surface brightness\nat $r$ (\\cite{djo81}; \\cite{san90}). Like Wirth \\etal (1994), we\nfollow Kron's (1995) suggestion to use the inverted form, $\\eta (r)\n\\equiv I(r)/\\langle I(r)\\rangle$, which equals one at the center of\nthe galaxy and approaches zero at large galactic radii. The radius\n$r(\\eta=0.5)$ corresponds roughly to the half-light radius $r_e$.\n\nSince $\\eta$ is defined as an intensity {\\it ratio}, it is not\naffected by the surface brightness dimming effect that makes the use\nof isophotes problematic. Moreover, $\\eta$ is only dependent on the\nsurface brightness within a given radius and not on any prior\nknowledge of total luminosity or the shape of the light profile. These\nproperties make it advantageous for faint object photometry. We\ndefined the ``total'' aperture of the intermediate-redshift objects as\ntwice the radius $r(\\eta=0.2)$. The apparent total magnitudes are then\ndefined within this aperture. For ideal Gaussian or exponential\nprofiles, the magnitude $m_{0.2}$ within the radius $2r(\\eta=0.2)$ is\napproximately equal to the true total magnitude $m_{tot}$; more than\n99$\\%$ of the light is included with the radius $r(\\eta=0.2)$. For an\n$r^{1/4}$-law profile, there is a difference $m_{0.2} - m_{tot} \\sim\n0.13$ mag; this is due to the slow decline in luminosity at large\nradii that characterizes this profile. The radius $r(\\eta = 0.2)$ was\nchosen based on visual inspection of the curves of growth, derived\nfrom the aperture photometry, out to large radii.\n\nFor reference, the theoretical value for the ratio of $r(\\eta=0.2)$ to\nhalf-light radius is 2.16, 1.95, and 1.82 for three standard profiles:\nExponential, Gaussian, and $r^{1/4}$-law, respectively. The observed\nratio is 2.3 $\\pm$ 0.3 for \\bv $< 0.85$ (with little trend with\ncolor), but rises slightly (2.6 $\\pm$ 0.25) for the reddest galaxies\nwith \\bv $> 0.85$. A contributing cause to this rise is that for\nabout half of the reddest objects, $r_{1/2}$ has been underestimated\nby $\\sim 20\\%$ because of their higher ellipticity. As we show in the\nAppendix (\\S~A.3.2), the half-light radii of early-type galaxies with\naxis ratio $a/b > 2$ are systematically underestimated by up to\n30$\\%$. This effect will also cause small changes to the measured\nimage concentration (\\S~3.3.2) of these galaxies.\n\nA weak downward trend can be seen from blue towards red colors; \nthis is what we expect since bluer objects tend to have exponential \nluminosity profiles, and redder objects are better described by \n$r^{1/4}$-law profiles. However, this trend is broken by the reddest \nobjects ($\\bv > 0.87$), which have higher values of $r(\\eta=0.2)/r_{1/2}$ \nthan what is expected for an $r^{1/4}$-law profile. \n\n\nFinally, the angular half-light radii $r_e$ were determined from the\nnormalized curves of growth. Based on $M_B$ and (corrected) $R_e$ we\ncalculated the photometric-structural parameter $SB_e$, the average\nblue surface brightness within the half-light radius, for all objects.\nFor the nearby galaxy sample, the Tully catalog distances (as\ndescribed in \\S~3.1) were used to determine $R_e$ (kpc).\n\n\\subsubsection{Image concentration} \n\nWe use the image concentration parameter $C$ as defined by Kent\n(1985), which is based on the curve of growth. This parameter was\nshown to be closely correlated with Hubble type for ``normal''\ngalaxies: \\begin {eqnarray*} C \\equiv 5\\,log(r_{o}/r_{i}) \\end\n{eqnarray*} In the above equation, $r_o$ and $r_i$ are the outer and\ninner radii, enclosing some fraction of the total flux. In contrast,\nthe concentration parameter defined by Abraham \\etal (1994) is not\nbased on curve of growth radii, but on a flux ratio within two\nisophotal radii.\n\nHowever, in practice Kent also uses isophotes: He replaces the outer\nradius $r_o$, which encloses 80$\\%$ of the total light, by the radius\nof the 24th mag/arcsec$^2$ isophote. He has demonstrated that this\nradius encloses $\\sim 79\\%$ of the total light for all galaxy types in\nthe restrictive confines of his sample (\\cite{ken84}). Because of the\nsurface brightness dimming effect that becomes important for non-local\ngalaxies, we instead use a method that is independent of isophotes.\nThe total aperture of the galaxy, which determines the curve of\ngrowth, is defined based on the $\\eta$-radius as described in\n\\S~3.3.1.\n\nWe have also explored the possibility of using $\\eta$-radii to define\na concentration parameter. However, a concentration parameter based on\nthe curve of growth was ultimately found to be the more robust\nmeasure: the curve of growth increases monotonically with galactic\nradius for all objects, while the $\\eta(r)$-function will be\nnon-monotonic for a ``bumpy'' light profile (like that of a\nwell-resolved spiral galaxy). As a consequence, image concentration\ndefined by the curve of growth rather than $\\eta$ exhibits less\nscatter when plotted against other correlated observables (e.g. color,\nsurface-brightness) than an image concentration parameter based on the\n$\\eta$-function.\n\nAnticipating our need to measure image concentration for small\ngalaxies in paper II and future papers in this series, we have studied\nthe effects of spatial resolution and $S/N$ on $C$. Here we focus\nprimarily on resolution, as this was the dominant effect. The\nimportance of resolution is demonstrated by the comparison of Schade\n\\etal (1996) of decompositions of compact objects in ground-based and\n$HST$ images: the cores of the blue nucleated galaxies are not\nresolved in ground-based imaging, and hence they are frequently\nmisclassified as having much lower $B/T$-ratios than what is revealed\nby $HST$-imaging. In paper II we analyze this sample of galaxies, and\nhence this illustration is of particular relevance.\n\nResolution effects on image concentration were estimated by\nblock-averaging the images of nearby galaxy sample over a range of\nvalues until the spatial sampling (as measured in pixels per\nhalf-light radius) was comparable to that of the compact galaxies at\nintermediate redshift observed with the WFPC2. The details of these\nsimulations are presented in the Appendix (\\S A.1). In short, as the\nobjects' half-light radii get smaller, the scatter in the measured\nconcentration indices increases. While larger inner radii or a\nsmaller outer radii decrease this scatter (due to improved resolution\nand $S/N$, respectively), such choices decrease the dynamic range of\nthe concentration index.\n\nBased on these simulations, we chose a definition of $C$ that is, to\nfirst order, sufficiently robust to allow a direct comparison of the\nimage concentration of the local and the higher-redshift samples\nstudied here and in paper II, and furthermore gives a large dynamic\nrange: $C = 5\\,log(r(80\\%)/r(20\\%))$. This concentration index is\nremarkably stable: The mean concentration does not deviate from that\nmeasured in the original image by more than 0.2, or $\\sim 8\\%$ of the\ndynamic range in $C$, down to resolution of five pixels per half-light\nradius.\n\nOur definition is sufficiently close to that of Kent's (1985) so that\nit is meaningful to compare our values directly to those he determined\nfrom photometric analysis of a sample of nearby galaxies. With this\nchoice of radii, a theoretical $r^{1/4}$-law profile has $C=5.2$, an\nexponential profile has $C=2.7$, and a Gaussian has $C=2.1$. These\nvalues agree well with the results of Kent's analysis: he finds that\nelliptical galaxies have $C \\sim 5.2$, and late-type spirals have $C\n\\sim 3.3$.\n\nLastly, since we use circular apertures, the measured image\nconcentration may be affected by the ellipticity of the galaxy. Based\non the comparison between our results for the Frei \\etal sample and\nthose of Kent's elliptical aperture photometry, we believe this to be\na negligible effect in all cases but the earliest, must elliptic\ngalaxies. Wirth, Koo and Kron (1994) found that for an $r^{1/4}$ law\nprofile with axis ratio $b/a=0.2$, the change in $C$ is less than\n5$\\%$. The effect appears to be larger in our study. A more detailed\ndescription of this possible systematic is given in the Appendix.\n\n\\subsubsection{Image asymmetry} \n\nThe last image structure parameter is rotational asymmetry, $A$, as\ndefined by Conselice, Bershady \\& Jangren (2000). This definition\ndiffers from earlier methods in that the asymmetry is determined\nwithin a constant $\\eta$-radius of $\\eta=0.2$, a noise correction is\napplied, and an iterative procedure which minimizes $A$ is used to\ndefine the center of rotation. This algorithm was tested to be robust\nto changes in spatial resolution and signal-to-noise by Conselice\n\\etal (1999) using simulations similar to those described here for the\nconcentration parameter $C$; the systematics with resolution are below\n10$\\%$ of the original value for galaxies in paper I and II here.\n\n\\subsubsection{Morphological $k-$corrections}\n\nTo obviate the issue of `morphological' k-corrections, image\nstructural parameters should ideally be measured at the same\nrest-frame wavelength for all objects. Anticipating our needs to\nderive the structural parameters for intermediate-redshift objects in\npaper II (and future papers in this series), we have adopted the\nfollowing protocol: (i) For the nearby galaxy sample we use the images\nin the $B_J$ and $g$ bands to derive the primary local image structure\nparameters. (The rest-frame wavelengths sampled by the $R,r$ band\nimages correspond to bands redshifted into the near-infrared for the\nintermediate-redshift galaxies.) (ii) We use the multi-band\nimages of the Frei \\etal sample to determine corrections to compensate\nfor the wavelength dependence of asymmetry, concentration, and\nhalf-light radius -- as described in the Appendix (\\S~A.2). For\nexample, $HST$ Wide Field Planetary Camera-2 (WFPC-2) images in the\n$I_{814}$ band of objects between $0.3<z<0.8$ correspond to first\norder to the rest-wavelength range of the $B_J$ and $g$\nbands. Nonetheless, the effective rest-wavelength for such\nintermediate-redshift galaxies is typically slightly redward of\nrest-frame $B_J$ and $g$ bands. The corrections in \\S~A.2 are suitable\nfor such samples, as well as higher redshift samples imaged in redder\nbands.\n\n\\section{Results}\n\n\\subsection{Mean Properties, Distributions and Correlations}\n\nThe mean properties for our six parameters (M$_B$, $B-V$,\n$R_e$, $SB_e$, $C$, and $A$) are listed in Table 3, as a function of\nHubble Type. While we would like to move away from using `Hubble\nTypes,' they are so ingrained in the astronomical culture that they\nare a useful point of departure. For clarity in the following\ndiscussion, we group these types together into ``Early'' (E-S0),\n``Intermediate'' (Sa-Sb), and ``Late'' (Sc-Irr). These names are\npotentially misleading, of course, and so we encourage the reader to\ntreat them as labels which evoke, at best, a well-conceived galaxy\ntype, but not necessarily an evolutionary state. Clearly further\nsub-division could be made, but our current purposes are illustrative,\nnot definitive.\n\nA typical approach to exploring the correlations in (and\ndimensionality of) a multivariate parameter space is principal\ncomponent analysis. While this is valuable, it is not particularly\ninstructive for a first understanding of the distribution of different\ntypes of objects in the parameter space. We are interested both in\ncorrelations between observables and in trends as a function of the\nqualitative Hubble-type. These correlations and trends need not be one\nand the same. For example, two observables can be uncorrelated but\nstill exhibit a distribution segregated by Hubble type. To develop\nsuch an understanding, we therefore inspected the 15 possible\n2-dimensional projections of our 6-dimensional parameter space.\n\n% A summary of the parameter pairs is given in Table~4.\n\nTo distill this information further, we considered that there are in\nfact three types of physically-distinct parameters:\n\\begin{enumerate}\n\n\\item spectral index (color): this parameter is purely photometric, by\nwhich we mean there is no information about the shape of the light\nprofile. There is also no scale information, i.e. the amplitude and\nsize of the light profile is also unimportant. In the balance of this\npaper we will use ``color'' and ``spectral index''\ninterchangeably.\n\n\\item form ($A$, $C$): these parameters are purely structural, by\nwhich we mean that they do not depend -- to first order -- on the\namplitude or the shape of the spectral energy distribution, nor on the\nphysical scale of the light distribution; they reflect only the {\\it\nshape} of the light profile.\\footnote{We consider image concentration\nto be a form, in contrast to Morgan who used it as a surrogate for\nspectral index.}\n\n\\item scale ($R_e$, $L$, and $SB_e$): these parameters are physically\ndistinct. Luminosity is purely photometric (by our above\ndefinition). Size, which we also refer to as a structural parameter,\nis influenced by image shape, i.e., depending on the definition of\nsize, two galaxies with different light profile {\\it shapes} can have\nrelatively different {\\it sizes} (see \\S3.3.1, for example).\nSurface-brightness is a hybrid, photometric {\\it and} structural\nparameter; it is a function of size and luminosity. While\nsurface-brightness is a ratio of luminosity to surface area, it is still\na measure of ``scale'' -- in this case, the luminosity surface-density.\n\\footnote{A fourth scale parameter which we do not consider here is\nline-width, or some measure of the amplitude of the internal\ndynamics.}\n\n\\end{enumerate}\nThis reduces the types of combinations (by parameter-type) to 6,\ni.e. between color, form, and scale.\n\n% For referece:\n%\tcolor vs color\n% \tcolor vs form\n% \tcolor vs scale\n% \tscale vs form\n% \tscale vs scale\n%\tform vs form\n\nWe find the strongest and physically most interesting correlations are\nbetween color, form, and the one scale parameter, $SB_e$ (Figures\n3-5). We focus on these for the remainder of the paper. Before\nturning to them, for completeness we first summarize our observations\nof the other types of correlations:\n\nColor-color correlations are strong and well known (e.g. Figure\n2). Effectively they add higher-order information about spectral\ntype. Here we consider only $B-V$ as a simple spectral index which\neffectively represents the first-order information of spectral type.\nIn general, one might adopt several spectral indices, e.g. $U-V$ and\n$V-K$, or a single index based on multi-colors.\n\nColor-scale correlations also have been explored in detail elsewhere,\ne.g. color-luminosity relationships, known to exist for all galaxy\ntypes in both the optical and near-infrared (Huchra, 1977b; Mobasher\n\\etal 1986; Bershady 1995). The limited dynamic range of the Frei\n\\etal sample in size and luminosity (they are mostly large and\nluminous systems) preclude useful results being drawn here in this\nregard. For example, the correlation of color with size in this sample\nis subtle and depends in detail on how size is defined, as noted\nabove. Form-scale correlations including size and luminosity are also\ndifficult to assess for this sample for the same reasons of limited\ndynamic range in scale. However, scale versus scale {\\it is} an\ninteresting diagnostic because, for example, size and luminosity allow\none to probe the range of surface-brightness in the sample. We explore\nthis in paper II.\n\n\\subsubsection{Spectral index versus form and scale}\n\nStrong correlations exist in all three plots of color versus form\nparameters $C$ and $A$ and scale parameter $SB_e$ (Figure\n3). Early-type galaxies are redder, more concentrated,\nhigh-surface-brightness, and more symmetric than Intermediate- and\nLate-type systems. The best correlation is between color and\nconcentration in the sense that there is a smooth change in both\nquantities with Hubble Type. This is expected from a simple\ninterpretation of the Hubble Sequence as a sequence parameterized by\nthe relative dominance of a red, concentrated bulge (or spheroid)\nversus a bluer, more diffuse disk.\\footnote{A few of the local\ngalaxies have values of $C$ that are lower than the theoretical\nconcentration for an exponential disk (the errors in $C$ are $\\lesssim\n0.02$ for all of them). The majority of these objects are late-type\nspiral galaxies with prominent, bright regions of star formation in\nthe spiral arms. The star-forming regions cause the image profiles to\nbecome less centrally concentrated than a simple disk profile.} In\ncontrast, the distinction between Hubble Types in $SB_e$ and $A$ is\nmost pronounced between Early-types and the remainder; Intermediate-\nand Late-types galaxies are not well distinguished by either of these\nparameters.\n\nA more complete local sample will likely include a larger\nfraction of objects that do not follow these trends. For example,\namorphous galaxies have surface brightnesses comparable to elliptical\ngalaxies but are generally quite blue in color (\\cite{gal87};\n\\cite{mar97}). Nonetheless, what is physically compelling about these\ncolor-form correlations is that each axis carries distinct\ninformation, respectively, on the integrated stellar population and\nits spatial distribution. \n\n\\subsubsection{Form versus form and scale}\n\nThere are clear trends present in the two plots of form versus $SB_e$\n(scale) in Figure 4 as well as the plot of form parameters along in\nFigure 5. More centrally concentrated galaxies have higher average\nsurface-brightnesses and lower asymmetry; more symmetric objects have\nhigher surface-brightness. In general, the concentrated, high\nsurface-brightness galaxies are Early-type, while the Late-type\ngalaxies are less-concentrated, have lower surface-brightness, and are\nmore asymmetric. While there is substantial scatter in the form and\nscale parameters for Early and Late types, these two extreme groups\nstill are well-separated in the above three plots. The\nIntermediate-type galaxies, however, are {\\it not} well separated from\nthese extremes, and tend to overlap substantially with the Late-type\ngalaxies, consistent with what is found in plots of color versus form\nand scale: Intermediate- and late-type galaxies have comparable\ndegrees of asymmetry, and similar surface-brightness.\n\nOne should be cautious in concluding the relative merits of form-scale\nand form-form and versus color-form and color-scale correlations based\non the relative separation of Hubble Types. Using Hubble Types may be\nunfair if, for example, they were designed to correlate well with\ncolor but not necessarily with the quantitative form and scale\nparameters explored here. Since the form-form and form-scale\ncorrelations themselves are comparable, and nearly as strong as for\ncolor-form and color-scale, we are inclined to consider both as part\nof a general classification scheme. Certainly the form and scale\nparameters will each have different sensitivity to stellar evolution\nthan color and so are advantageous to consider in isolation.\n\n\\subsubsection{Comparisons to previous work}\n\nThe correlation between image concentration and mean\nsurface-brightness within the effective radius (Figure 4) has been\nexplored by several groups in the context of galaxy classification\n(\\cite{oka84}; \\cite{wat85}; \\cite{doi93}; \\cite{abr94}). We focus\nhere, however, on Kent's (1985) $r$-band study since his definition of\nimage concentration and effective surface-brightness are the most\nsimilar to our own. While similar, nonetheless the slope of the\ncorrelation is steeper for our sample, albeit with much larger\nscatter, as illustrated in the top panel of Figure 6. As the middle\nand bottom panels reveal, the cause of the steeper slope in our sample\nis due to a smaller dynamic range in image concentration. This is\nlikely due to the fact that we use circular apertures when performing\nsurface photometry, whereas Kent used elliptical apertures. We attempt\nto quantify the systematics due to differences in aperture shape in \\S\nA.3. While the dynamic range in image concentration is reduced using\ncircular apertures for the Frei \\etal sample, there does appear to be\na somewhat smaller scatter in $C$ as a function of $B-V$.\n\nThe nature of the large scatter in the top two panels of Figure 6 for\nthe Frei \\etal sample is also discussed further in \\S A.3. In short,\nwe believe much of this scatter is due to uncertainties in the $R$- and\n$r$-band zeropoints of the Frei \\etal sample. These uncertainties\nadversely affect only the surface-brightness values in Figure\n6. Robust estimators of the scatter about a mean regression (i.e.,\niterative, sigma-clipping of outlying points) eliminate the outlying\npoints, but still yield 50\\% larger scatter in $R$-band $SB_e$ for\nthe Frei \\etal sample as a function of either image concentration or\n$B-V$. A plausible additional source contributing to this larger\nscatter is that Kent's observed surface brightnesses were converted to\nface-on values, while ours were not ``corrected'' in this way. We\nconclude that if accurate and appropriate inclination corrections are\npossible to apply to all galaxies in a given study, this would be\ndesirable. Since such corrections cannot be performed for the\nintermediate-redshift objects in paper II (and in general, if such\ncorrections are not possible for a critical subset of the data), we\nbelieve it is best not make such corrections at {\\it any} redshift.\n\nThe asymmetry--concentration plane has also been explored for galaxy\nclassification purposes by, e.g., Abraham \\etal (1994, 1996a) and\nBrinchmann \\etal (1998). Our methods of measuring these parameters\ndiffer from theirs, and thus our quantitative results cannot be\ndirectly compared. However, a qualitative comparison to the $A-C$ plot\nof Brinchmann \\etal shows that both methods yield very similar\nresults: the distribution of galaxies can be subdivided into sectors\nwhere early-type, intermediate-type, and late-type objects dominate.\nBrinchmann \\etal also use the local sample from the Frei catalog to\ndefine these bins, but note however that the points they plot\nrepresent a sample of intermediate-redshift galaxies. The $A-C$\ncorrelation in the Brinchmann \\etal diagram is not as clear as that\nseen here for the local sample in Figure 5; the scatter in\ntheir diagram is comparable to the dynamic range of the parameters.\nThis is probably due to the different properties of the samples,\nrather than to the differences in how we determine the parameters. For\na more direct comparison, we plot $B$ band asymmetry and concentration\nversus rest-frame \\bv \\ color for 70 galaxies from the Frei \\etal\nsample (Figure 7), using both the $A$, $C$ values from this\nstudy and those found by Brinchmann \\etal \\ It can be seen that the\ndistributions are overall quite similar; however, the separation in\nasymmetry of the different Hubble types is more apparent in this\nstudy, and the scatter in concentration is somewhat smaller. The\nconclusion here, then, is that our methodology offers typically\nmodest, but sometimes significant improvements over previous work.\n\n\\subsection{Classification}\n\nThe above results point to how we can most effectively define a\nparameter demarcation to isolate, identify, and classify normal\ngalaxies. In the four-dimensional parameter space of ($B-V$, $A$,\n$SB_e$, $C$), we define boundaries (``cuts'') in the 6 two-dimensional\nprojections between galaxies classified in the Hubble Sequence as\nEarly/Intermediate and Intermediate/Late. These boundaries, selected\nby eye on the basis of the distribution of Hubble types, are listed in\nTable 4 and illustrated in Figures 3-5. Segregation by\nhigher-dimensional hyper-surfaces are likely to be more effective\n(galaxies appear to be distributed on a `fundamental' hyper-surface --\nthe subject of a future paper), but the projected boundaries here are\nmeant as illustrative, and practical for application when all of the\nparameters are not available. We stress that these boundaries\nare not definitive in some deeper physical sense. For example, in\nterms of formal Hubble Types cuts involving color are clearly ``best;''\nhowever, as noted above, this may not be physically significant.\n\nIt would be uninteresting if all of the cuts provided the same\nclassification. Moreover, one expects there will be discrepancies for\nobjects near boundaries. We find that 49\\% of the sample matches in\nall cuts, while 64\\%, 87\\%, and 99\\% of the sample matches in at least\n5, 4, or 3 cuts, respectively. (Hereafter, we refer to cases where 5\nout of 6 cuts match as ``5/6,'' etc.) This degree of consistency seems\nreasonable so we have not tried to fine-tune the boundaries (such\nfine-tuning would not be sensible anyway since the details of the\nclassification self-consistency are likely to be sample-dependent):\nThe preponderance of objects are classifiable by a simple majority of\nthe classifications based on the 6 cuts; 13\\% of the objects have a\nmore ambiguous classification.\n\nOf interest are the discrepancies within and between cuts in different\ncombinations of color, form, and scale. We found that it is useful to\ngroup the six cuts into two groups of three. The first consists of the\ncuts in Figure 3 between color, form and scale, which we refer to as\ncolor-form/scale. The second consists of the cuts in Figures 4 and 5\nbetween form and scale, which we refer to as scale/form-form. For\nexample, 64\\% of the variance in the 5/6 cases comes from cuts in\n$C$--$SB_e$, whereas cuts in $C$--$(B-V)$ and $A$--$C$ are always\nconsistent with the majority classification. More generally,\nscale/form-form cuts are internally mis-matched 40\\% of the time,\nwhile color-form/scale cuts are internally mis-matched only 21\\% of\nthe time (and two-thirds of these color-form/scale mis-matches are\nalso present in scale/form-form mis-matches). In other words, the\ncolor-form/scale cuts tend to be more consistent; much of the variance\nin the scale/form-form cuts again comes from $C$--$SB_e$.\n\nOnly two galaxies pose a substantial problem for classification: NGC\n4013 and NGC 4216. They are classified by various cuts to be in all\ncategories (Early, Intermediate, and Late), and have no majority\nclassification. However, both are highly inclined (4013 is edge on),\nwhich appears to give them unusual observed properties. Indeed, they\nare extreme outliers in several of the projections in Figures 3 and 4\n(see also A.3.2 and figures therein). Hence such problem cases are\nlikely to be easy to identify. Three other sources classified in all\nthree categories (NGC 4414, 4651, and 5033) are not a problem: They\nhave 4/6 consistent classifications. Two of these (NGC 4651 and 5033)\nhave Seyfert nuclei, and are outliers only in plots with image\nconcentration; they are highly concentrated for their color. NGC 4414\nis not an outlier in any of the plots.\n\nFinally, it is interesting to note that 23\\% of the sample has\ninconsistent majority classifications in color-form/scale versus\nscale/form-form cuts. This is true for 100\\% of the 3/6 cases, and\n55\\% of the 4/6 cases. However, we believe this is for different\nreasons. In the latter cases (only) we find that the galaxies are\npredominantly at high inclination ($\\sim$50\\% excess in the top half\nand top quartile of the sample distribution in inclination). Moreover,\nthe color-form/scale classifications in these cases are all {\\it\nearlier} than the majority scale/form-form classifications. We surmise\nthis is due to the effects of reddening on $B-V$.\\footnote{Inclination\nwill also cause changes in other measured parameters. Changes in $C$,\nhowever, appear to be small (see \\S A.3.2). Surface-brightness will\ntend to increase at modest inclinations, and then decrease at high\ninclinations if a prominent dust lane obscures the bulge. Likewise,\n$A$ may increase due to a dust lane until the galaxy is directly\nedge-on. As a consequence of these changes and the distributions and\ncuts, $C$--$SB_e$ tends to mimic the color-form cuts in the\nhigh-inclination cases, while $A$--$SB_e$ and $A$--$C$ do not.} While\nthe color-form/scale classifications tend to be earlier for the 3/6\ncases, because there is no apparent inclination dependence, these\ndifferences are due likely to other physical effects. Two\npossibilities include low star-formation rates or high metallicity for\ngalaxies of their form. Both of these conjectures are testable via\nspectroscopic observation.\n\nWe suggest then, as a practical, {\\it simple} prescription, that the\nmajority classification for all 6 cuts be taken as the classifier,\nexcept in the situation where the galaxy in question is highly\ninclined. In the latter case, the majority classification of the\nscale/form-form cuts should be adopted. When galaxies have only 3/3\nconsistent classifications, (13\\% of the Frei \\etal sample), the\nadopted classifier should be intermediate between the two most common\nclassifications. It also may be of interest to note if the\ncolor-form/scale and scale/form-form majority classifications\ndiffer. However, further elaboration based on these two-dimensional\nprojections of a higher-dimensional distribution is not likely to be\nwarranted.\n\n\\subsubsection{Discussion}\n\nWe note that there are no distance-dependent scale parameters in our\nclassification. By this we mean specifically that the classification\nparameters do not depend on knowledge of the distance modulus. Hence\nthis classification is both quantitative and independent of the\ncosmological distance-scale and its change with cosmological epoch\n(i.e. no {\\it a priori} knowledge is needed about H$_0$ or q$_0$).\nThe effects of the expansion do change the {\\it observed}\nclassification parameters. However, with knowledge of galaxy redshifts\nand judicious choice of ``redshifted'' photometric bands,\nsurface-brightness dimming can be corrected and band-shifting either\neliminated or corrected via the protocol described in the\nAppendix. Galaxy evolution, of course, will also modify the values of\nthe parameters, but this is precisely the utility of the\nclassification systems as applied to such a study: In what way do the\nparameters and their correlations evolve? How do the scale parameters\nchange for a fixed range in classification parameters? These are\nissues which we intend to explore in subsequent papers in this series.\n\nWe also comment on the efficacy of using the four-dimensional\nparameter space of color, concentration, surface-brightness, and\nasymmetry for the classification of distant galaxies. As noted\nearlier, Abraham \\etal (1996a) and Brinchmann \\etal (1998) have\nexplored the use of the asymmetry--concentration plane as a tool for\ndistant galaxy classification. The use of the additional parameters of\ncolor and surface-brightness are clearly advantageous; they offer\nsubstantially more information, particularly as a diagnostic of the\nstellar population age and surface-density. The reasoning behind using\n$A$ and $C$ alone has been that to first order, they can be estimated\nwithout redshift information. Yet the wavelength dependence of both\nparameters (i.e., what is referred to as `morphological\nk-corrections') can lead to measurement systematics. These\nsystematics, if not corrected, in turn result in objects over a range\nin redshift to be systematically misclassified. For example,\nBrinchmann estimates that at $z = 0.9$, $25\\%$ of spiral galaxies are\n{\\it mis}-classified as peculiar objects in the $A - C$ plane. This\nfraction is expected to increase at larger redshifts. Hence, for\nhigh-$z$ studies of galaxy morphology, redshift information is crucial\neven when using asymmetry and concentration. Therefore, since\nredshift information is crucial no matter what, there is no reason\n{\\it not} to use the four-dimensional classification we have outlined\nin future studies. The recent refinements and calibration of the\ntechnique of estimating redshifts photometrically make this all the\nmore tractable.\n\nFinally, we note that while the classification we have proposed here\nis practical and useful, there are five areas where we anticipate it\ncan be improved or elaborated: (i) As we have mentioned before, the\nspectral-index parameter could have much greater leverage at\ndistinguishing between different stellar populations by adding\npass-bands that expand the wavelength baseline (e.g. the $U$ and $K$\nbands in the near-UV and near-IR, respectively), or by increasing the\nspectral resolution (e.g. line-strengths and ratios). A further step\nof elaboration would be to explore spatially resolved spectral indices\n(gradients) and determine their correlation with form parameters.\n(ii) Internal kinematics should be considered. Ideally, the kinematic\ninformation would include estimates of both the random and ordered\nmotion (rotation) so that the dynamical temperature could be assessed,\nin addition to the overall scale. Kinematics are relatively expensive\nto obtain (compared to images), but with modern spectrographs on large\ntelescopes, the absolute cost is minimal at least for nearby\ngalaxies. (iii) Higher-dimensional correlations are worthy of\nexploration to determine, for example, whether ``fundamental''\nhyper-planes can adequately describe the entirety of the galaxy\ndistribution. (iv) It is worth considering whether there are\nadditional form parameters of value for classification that have not\nbeen included here. (v) The classification scheme needs to be tested\nagainst much larger, and more volume-representative samples of\ngalaxies.\n\n\\section{Summary and Conclusions}\n\nWe have presented results from a study of the photometric and\nimage-structural characteristics and correlations of a sample of\nlocal, bright galaxies (Frei \\etal 1996). We find it illuminating to\ndistinguish between parameters which characterize spectral-index\n(color), form (image concentration and asymmetry), and scale (size,\nluminosity, and surface-brightness). In this context, we arrive at the\nfollowing main results and conclusions.\n\n\\begin{itemize}\n\n\\item We find that a combination of spectral-index, form and scale\nparameters has the greatest discriminatory power in separating normal\nHubble-types. The strongest correlation is found between color and\nimage concentration. However, there are equally strong correlations\nbetween form parameters (e.g. $A$ and $C$), but here the Hubble-types\nare not as well distinguished. As an indicator of classification\nutility, we suggest that the strength of the correlation between\nparameters is likely more important than the separation of Hubble\nTypes within the correlation.\n\n\\item It is possible to define a quantitative classification system\nfor normal galaxies based on a four-parameter sub-set of\nspectral-index, form and scale: rest-frame \\bv \\ color, image\nconcentration, asymmetry, and average surface brightness within the\nhalf-light radius. We propose a specific classification that\ndistinguishes between ``normal'' galaxies as Early, Intermediate, and\nLate based on cuts in these four parameters. The classification is\nsuccessful for 99\\% of the Frei \\etal sample. Nonetheless, we\ndesignate this as ``preliminary'' until larger, more comprehensive\nsamples of galaxies are needed than analyzed in the present study.\n\n\\item Distance-dependent scale parameters are {\\it not} part of this\npreliminary classification.\n\n\\item These classification parameters can be measured reliably over a\nbroad range in $S/N$ and image resolution, and hence should be\napplicable to reliably distinguishing between a wide variety of\ngalaxies over a large range in redshift.\n\n\\item Redshift information {\\it is} needed to estimate reliably both\nthe photometric properties (rest-frame color and surface brightness)\nas well as the structural parameters asymmetry and concentration at a\nfixed ($B$-band) rest-frame wavelength. In terms of redshift\nindependence, asymmetry and concentration alone thus offer no\nadvantages over the additional parameters classifiers proposed\nhere. Indeed, incorporating the full suite of parameters defined here\nis advantageous for the purposes of classification.\n\n\\end{itemize}\n\n\\acknowledgements\n\nThe authors wish to thank Greg Wirth for his highly-refined algorithm\nfor calculating $\\eta$-radii user here and in paper II; our\ncollaborators David Koo and Rafael Guzm\\'an for their comments on the\nmanuscript and input on assembling dwarf galaxy samples; and Jarle\nBrinchmann for providing us with his measurements of structural\nparameters for the local galaxy sample. We also gratefully acknowledge\nJay Gallagher and Jane Charlton for a critical reading of the original\nversion of this paper (I and II), and for useful discussions on this\nwork. Most importantly, we thank Zolt Frei, Puragra Guhathakurta,\nJames Gunn, and Anthony Tyson for making their fine set of digital\nimages publicly available. Funding for this work was provided by NASA\ngrants AR-07519.01 and GO-7875 from STScI, which is operated by AURA\nunder contract NAS5-26555. Additional support came from NASA/LTSA\ngrant NAG5-6032.\n\n\\begin{appendix}\n\n\\section{A. Corrections for Measurement Systematics}\n\nHere we establish the measurement systematics due to changes in image\nresolution for half-light radius and image concentration, and for\nband-shifting effects on half-light radius and image concentration,\nand asymmetry. Systematic effects of images resolution and noise on\nasymmetry are quantified in Conselice \\etal (1999).\n\n\\subsection{A.1. Resolution dependence of observed size and image concentration}\n\nTo maximize the dynamic range of the measured concentration index,\n$C$, the inner radius should be small, and the outer radius large\nrelative to the half-light radius. In this way, one samples the light\nprofile gradients in both the central and outer regions of a galaxy\nwhere the bulge and disk contribute quite differently. This strategy\nmaximizes the leverage for discriminating between different profiles,\ne.g. exponential and $r^{1/4}$-law. In the presence of noise and\nlimited spatial resolution, however, the choice of radii determines\nthe robustness of the concentration index: As noted by Kent (1985),\nthe inner radius should be large enough to be relatively insensitive\nto seeing effects, and the outer radius should not be so large that it\nis affected by uncertainties in the sky background and $S/N$. In the\ncurrent study, the sources are resolved, and the images are at\nmoderately high signal-to-noise: within the half-light radius, the\nsample of local galaxies have $600 \\lesssim S/N \\lesssim 3000$. The\nintermediate redshift galaxies in paper II have $S/N$ in the range 40\nto 90, with a mean of $\\sim 55$. This is sufficiently high that we\nfocus our attention here on the effects of spatial sampling and\nresolution.\n\nEven in the absence of significant image aberrations, an additional\nlimiting factor is the number of resolution elements sampling the\ninner radius. This is likely to become a limiting factor when the\nhalf-light radii is only sampled by a few pixels. To understand this\npotential systematic, we have calculated six concentration indices $C\n= 5\\,log(r_{o}/r_{i})$ for several different choices of inner and\nouter radii. We use $r_i$ enclosing 20 and 30$\\%$ of the light, and\n$r_o$ enclosing 50, 70, an 80$\\%$ of the light. The radii were\nmeasured for nearby galaxies that were block-averaged by factors 2, 4,\nand 6 to simulate coarser spatial sampling, as shown in Figure\n8. The six different concentration indices are plotted as a\nfunction of sampling in Figure 9. These simulations span\nsufficient dynamic range in size to cover most galaxies observed, for\nexample, in the Hubble Deep Field. With factors of 4 and 6, we\nmeasure radii with pixel sampling similar to that observed in the\nHST/WFPC-2 images of the intermediate-redshift objects of paper\nII. Typically, these galaxies have half-light radii of 0.3 --\n0.7\\arcsec. For the Planetary Camera, the scale is 0.046\\arcsec/pixel,\nand for the Wide Field, 0.10\\arcsec/pixel; hence the half-light radii\nare of order 3 to 15 pixels.\n\nThe half-light radius $r(50\\%)$ is remarkably stable, even with poor\nsampling. Unfortunately, the dynamic range given by concentration\nindices with $r_o = r(50\\%)$ is too small to be useful. As expected,\nthe 30$\\%$ radius was more stable than the 20$\\%$ radius to \ndecreased spatial resolution. However, the concentration indices using\n$r(30\\%)$ were less sensitive to the differences between galaxy types,\nand gave a smaller dynamic range than indices using $r(20\\%)$. The\ninner radius dominated the effect on the amplitude of the systematics;\nchanging the outer radius from $70\\%$ to 80$\\%$ decreased the scatter\nonly marginally. With a block-averaging factor of 6, where the\nhalf-light radii are typically only $\\sim 5$ pixels, the scatter\nbecomes large for all choices of concentration indices.\n\nBased on these simulations, we decided to use the radii enclosing\n80$\\%$ and 20$\\%$ of the total light (as did Kent, 1985), even though\n$r_o = r(70\\%)$ gives concentration indices with slightly smaller\nscatter at poor resolution. For objects with half-light radii of only\n7 pixels, the mean differences in concentration (relative to the\noriginal image) are $\\Delta C_{80:20} = -0.10_{-0.60}^{+0.20}$ and\n$\\Delta C_{70:20} = -0.10_{-0.50}^{+0.15}$. Even at a resolution of\nonly five pixels per half-light radius, the concentration index only\ndeviates by 0.2 relative to the original image; this is $\\sim 8\\%$ of\nthe dynamic range in $C_{80:20}$. Thus we consider this parameter to\nbe robust enough to useful in the comparison of local and\nintermediate-redshift samples.\n\n\\subsection{A.2. Systematics with wavelength} \n\nObservations at different wavelengths sample preferentially different\nstellar populations in a galaxy. Since these populations are not\nalways spatially homogeneous, the image-structural characteristics\n(concentration, asymmetry, and half-light radius) will will have some\nwavelength dependence [e.g., see de Jong's (1995) study of disk\nscale-lengths]. Hence, when comparing one of these parameters for\ndifferent galaxies, the parameter ideally should be measured at the\nsame rest-frame wavelength for all objects. This is not possible in\ngeneral for studies over a wide range in redshifts employing a finite\nnumber of observed bands. To determine the amplitude of the\nwavelength-dependence for the measured structural parameters, we\ntherefore compare the $B_J$ and $R$ structural parameters for 72 of\nthe Frei \\etal galaxies. The differences between the red and blue\nstructural parameters versus the rest-frame color, \\bv, are shown in\nFigure 10. For comparison, all intermediate-redshift objects in\npaper II, except two, fall in the bluest bin ($\\bv < 0.62$).\n\nThe plot of $\\Delta C = C_B - C_R$ shows that in most cases, the\nvalues are slightly negative, i.e. the majority of objects are more\nhighly concentrated in the red band than in the blue, as expected\nbecause of the redness of the central bulge. Only the bluest galaxies\nhave comparable image concentration in both bands. There is a weak\ntrend towards more negative values for the redder (early-type)\nobjects, which also show a larger scatter than the bluer objects.\n\nIn the plot of $\\Delta A = A_B - A_R$ it is clear that most galaxies\nhave at positive values, i.e. their image structures are more\nasymmetric in the blue band than in the red, as shown by Conselice\n(1997). The difference in asymmetry is only seen for late- and\nintermediate-type objects; red objects are generally very symmetric in\nboth bands, and have $A_B-A_R \\sim 0$. This trend was also noted by\nBrinchmann \\etal (1998).\n\nThe plot of half-light radii ($\\Delta R_e = R_{e,B} - R_{e,R}$) shows\nthat most values are slightly positive, with a larger scatter for\nredder objects. No other trend with color is seen. The fact that the\ngalaxies have slightly larger half-light radii in the blue band is\nconsistent with their image concentration being higher in the red\nband, as a bulge profile generally has a much smaller scale length\nthan an exponential profile.\n\nIn summary, the average differences ($\\pm1\\sigma$) between parameters\nfor galaxies with $\\bv<0.62$, determined from the $B_J$ and $R$ bands,\nare: $\\Delta C=-0.15 \\pm 0.30$, $\\Delta A = 0.013 \\pm 0.044$, and\n$\\Delta R_e=0.21 \\pm 0.80$ kpc. \n\n\\subsubsection{A.2.1. Corrections for wavelength systematics}\n\nBased on the mean values above, we correct the measured structural\nparameters for galaxies at non-zero redshift to the rest-frame $B$\nband values as follows, where for clarity we use the intermediate\nredshift galaxies in paper II as an example. The structural parameters\nof these intermediate-redshift objects generally were measured at\nrest-frame wavelengths between $B_J$ and $R$, i.e., in the observed\nWFPC2 $I_{814}$ band for $z\\sim0.6$. For ``normal'' galaxies, this\nwould cause us to overestimate $C$, and underestimate $A$ and\n$R_e$. Hence we use the differences listed above and the redshift of\nthe objects to linearly interpolate the correction to the measured\nvalues. Specifically, for a given parameter and color bin, we use the\nmean difference between values measured in the $B_J$ and $R$ bands,\nand the position of the rest-frame wavelength relative to the $B_J$\nband, to make corrections to the measured parameters. (Note that the\ncorrection made to $R_e$ also affects the value of $SB_e$ in general.)\nFor some objects, the combination of observed band-pass and redshift\ncorresponds to rest-frame wavelengths slightly blueward of $B_J$. When\ncomputing the corrections for these objects, we assumed that the\nwavelength trends continue outside the $B_J$ -- $R$ wavelength\nrange. Overall, these corrections are small for objects in paper II,\nwhile for higher-redshift objects we expect band-shifting effects to\nbecome increasingly important.\n\nWe add a final, cautionary note that it is not certain the corrections\nfor intermediate-redshift objects should be made based on the\ncorrelations we see for the nearby sample. When comparing the\nobservations in the bluer bands ($B_{450}$ or $V_{606}$) to those in,\ne.g. the $I_{814}$ used in paper II, we find that most objects are\nmore concentrated in the blue band, and slightly larger in the red\nband -- this is the opposite of what we see for the Frei \\etal\nsample.\\footnote{Indeed, Huchra noted that the Markarian galaxies get\nbluer toward their centers, reminiscent of the blue ``bulges'' seen in\nthe blue nucleated galaxies of paper II, yet in contrast to the color\ngradients found for ``normal'' galaxies. This type of color-aperture\nrelation was also noted by de~Vaucouleurs (1960, 1961) for the latest\nHubble-type galaxies (Sm, Im).} For asymmetry, the trend is the same\nfor both samples (higher $A$ in bluer bands). The trends are not\ndirectly comparable, however, to what we see in the local sample, as\nthe observations in the bluer bands correspond to rest-frame\nwavelengths in the UV region for most intermediate-redshift\ngalaxies. For this reason, and since the small sample of\nintermediate-$z$ objects poorly defines the variation in image\nstructure with wavelength, we adopt the more well-determined trends\nseen for the Frei \\etal sample to calculate the band-shifting\ncorrections. These corrections based on local galaxy trends tend to\nmake the intermediate-redshift objects somewhat less ``extreme'';\ntheir half-light radii become larger, their surface brightnesses\nfainter, and their image concentrations lower. If instead we had based\nour corrections on the trends seen within the intermediate-$z$ sample\nof paper II, then this sample would be even more extreme relative to\nthe local galaxy sample. The corrections would then tend to shift the\npositions of the intermediate-$z$ objects even farther from the nearby\ngalaxies in diagrams that include any of the parameters $R_e$, $SB_e$,\nand $C$.\n\n\\subsection{A.3. Systematics with aperture shape}\n\n\\subsubsection{A.3.1. Comparison to elliptical aperture photometry}\n\nCircular-aperture surface-photometry will yield systematic differences\nin the measured structural parameters when compared to those derived\nfrom elliptical-aperture surface-photometry. To assess this, we\ncompared our results for the Frei \\etal catalog in $R$ and $r$ bands\nto the results of Kent (1985) for a sample of local, Hubble-type\ngalaxies (Figure 6). Kent used elliptical apertures tailored to fit the\naxis ratio and position angle of each isophote in galaxy images to\ndetermine $r$ band image concentration and average surface brightness\nwithin the half-light radius. \n\nAs we detail in the figure caption, we have attempted to transform all\nof the surface-brightness values to the Cousins $R$ band ($R_c$). For\neach of the relations in Figure 6 we have characterized the slopes and\nscatter about a mean regression using a simple linear, least-squares\nalgorithm with an iterative, sigma-clipping routine to remove outlying\npoints. Given the nature of the data, such an algorithm is not\nstatistically correct (see, e.g., Akritas and Bershady,\n1996). However, given the potential photometric uncertainties\n(discussed below) and the need for robust estimation, it is not\npossible to formally implement more appropriate\nalgorithms. Nonetheless, the relative characterization of the slopes\nand scatter between Frei \\etal and Kent samples is useful.\n\nAs discussed in \\S 4.1.3, the slope of the correlation between average\nsurface-brightness and image concentration is steeper for our study\nthan for Kent's because of a decreased range in image concentration in\nour study. The effect (bottom panel of Figure 6) is such that the\nbluest galaxies have comparable image concentration values in both\nstudies while the image concentration of the reddest galaxies differ\nby as much as 1 unit in the mean (Kent's values are larger). We\ninterpret this as likely to be the effect of different aperture\nshapes. The results of our study of systematics with axis ratio\n(below) support this conclusion. Surprisingly, there is no indication\nthat elliptical apertures give significantly different results than\ncircular apertures for intermediate- and late-type (disk dominated)\ngalaxies.\n\nThe larger scatter in the Frei \\etal (1996) sample in the top two\npanels of Figure 6 might lead one to conclude that the elliptical\napertures provide a superior measurement of effective\nsurface-brightness. However, much of the scatter is due to the subset\nof the Frei \\etal sample observed at Palomar Observatory. We believe\nthat zeropoint problems are the cause of much of this scatter,\nconsistent with discussion in Frei \\etal concerning the difficulty of\nphotometric calibration. The bulk of the objects observed at Lowell\nObservatory are consistent with independent $R_c$-band photometry from\nButa and Williams (1996), although there are some points that are very\ndiscrepant. In general, the overlap is excellent in $SB_e$ and $B-V$\nbetween the Kent sample, the Lowell subset of the Frei \\etal sample,\nand the subset of the Frei \\etal sample with Buta and Williams'\nphotometry.\n\n\\subsubsection{A.3.2. Systematics with axis ratio}\n\nA second approach to determine the systematic effects of aperture\nshape on measured structural parameters was also used: we quantify the\ndegree to which ``normal'' galaxies with the same intrinsic morphology\nbut with different axial ratios $a/b$ will have different $C$ when\nmeasured with circular apertures. The galaxies in the Frei \\etal\ncatalog were divided into early-, intermediate- and late-type objects\n(using the same bins as elsewhere in the paper), and we plot\nconcentration and half-light radius versus the logarithm of the axis\nratio (taken from the RC3 catalog).\n\nIn the image concentration plots (Figure 11), a weak trend can be seen\nfor the late-type galaxies (top panel), with slightly higher values of\n$C$ for the more inclined objects. This effect, if caused by the shape\nof the apertures, will lead us to overestimate the image concentration\nby at most $\\sim 0.1$ ($3\\%$) for the nearly edge-on galaxies. We do\nnot expect this to be a problem for our analysis. The two labeled\nobjects have unusually high values of $C$ for their morphological\ntype. One of them, NGC 5033, is known to be a Seyfert 1 galaxy; the\nother, NGC 4651, is a suspected ``dwarf-Seyfert'' galaxy (Ho \\etal,\n1997). For intermediate-type objects (middle panel), no trend is\nobserved. The lowest $C$-value, which belongs to NGC 4013, could be\ncaused by the prominent dust lane in this object: the central light\ndistribution is divided into two parts, making it difficult to\ndetermine the position of the center. Effects like these will likely\nbe more problematic for objects with high values of $a/b$. The highest\n$C$-value in this plot is that of NGC 4216, which also is highly\ninclined and has spiral arm dust lanes superimposed on the bulge. In\nthe bottom panel, a trend is observed for the early-type galaxies: the\nconcentration is lower for objects with higher $a/b-$ratio. This\neffect will cause us to underestimate the image concentration of these\nobjects by $\\sim 0.5$, or 10--15$\\%$. This result agrees well with\nwhat was seen in the comparison of the Frei \\etal sample to Kent's\nimage concentration measurements, as described above. This leads us to\nconclude that our circular aperture photometry will underestimate the\nimage concentration somewhat for elliptical/S0 galaxies. Again, there\nis no indication that the aperture shapes lead to different results\nfor intermediate- and late-type galaxies.\n\nIn the plots of half-light radius $R_e$ versus $a/b$ (Figure 12), no\ntrends are seen for the intermediate- and late-type objects. For the\nearly-type objects, however, the measured half-light radii become\nprogressively smaller for increasing values of $a/b$. The trend is\nweak; it will cause us to underestimate the half-light radii by at\nmost 30 $\\%$ for objects with $a/b \\sim 4$. 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Ser. 145, \nAstronomical Data Analysis Software Systems VII, ed. R. Albrecht, \nR.~N. Hook, \\& H.~A. Bushouse (ASP, San Francisco), 108\n\n\\bibitem[Simard \\etal 1999]{sim99} Simard, L., Koo, D.~C., Faber, S.~M., \nSarajedini, V.~L., Vogt, N.~.P., Phillips, A.~C., Gebhardt, K., \nIllingworth, G.~D., \\& Wu, K.~L. 1999, \\apj, 519, 563\n\n% \\bibitem[Smail \\etal 1998]{sma98} Smail, I., Ivison, R.~J., \n% Blain, A.~W., \\& Kneib, J.-P. 1998, \\apj, 507, L21\n\n\\bibitem[Spiekermann 1992]{spie92} Spiekermann, G. 1992, \\aj, 103, 2102\n\n\\bibitem[Stein 1988]{ste88} Stein, W.~A. 1988, \\aj, 96, 1861\n\n\\bibitem[Storrie-Lombardi \\etal 1992]{sto92} Storrie-Lombardi, M.~C., \nLahav, O., Sodre, L.,~Jr., \\& Storrie-Lombardi, L.~J. 1992, \\mnras, 259, 8\n\n% \\bibitem[Telles \\etal 1997]{tel97} Telles, E., Melnick, J., \n% \\& Terlevich, R. 1997, \\mnras, 288, 78\n\n% \\bibitem[Thuan \\& Martin 1981]{thu81} Thuan, T.~X., \\& Martin, G.~E. \n% 1981, \\apj, 247, 283 \n\n\\bibitem[Tully 1988]{tul88} Tully, R.~B. 1988, Nearby Galaxies\nCatalogue (Cambridge University Press, Cambridge)\n\n\\bibitem[Watanabe \\etal 1985]{wat85} Watanabe, M., Kodaira, K.,\n\\& Okamura, S., 1985, \\apj, 292, 72\n\n% \\bibitem[Weedman \\etal 1998]{wee98} Weedman, D.~W., Wolovitz, J.~B., \n% Bershady, M.~A., \\& Schneider, D.~P. 1998, \\apj, 116, 1643\n\n\\bibitem[Whitmore 1984]{whi84} Whitmore, B.~C., 1984, \\apj, 278, 61\n\n\\bibitem[Wirth \\etal 1994]{wir94} Wirth, G.~D., Koo, D.~C., \n\\& Kron, R.~G. 1994, \\apj, 435, 105\n\n% \\bibitem[Worthey 1994]{wor94} Worthey, G. 1994, \\apjs, 95, 107\n\n\\bibitem[Wyse \\etal 1997]{wyse97} Wyse, R.~F.~G., Gilmore, G., \n\\& Franx, M. 1997, \\araa, 35, 637\n\n% \\bibitem[Zamorano \\etal 1994]{zam94} Zamorano, J., Rego, M., \n% Gallego, J., Vitores, A.~G., Gonz\\'alez-Riestra, R., \n% \\& Rodriguez-Caderot, G. 1994, \\apjs, 95, 387\n\n\\bibitem[Zaritsky \\etal 1995]{zar95} Zaritsky, D., Zabludoff, A.~I., \n\\& Willick, J.~A. 1995, \\aj, 110, 1602\n\n% \\bibitem[Zwicky 1964]{zwi64} Zwicky, F. 1964, \\apj, 140, 1467\n\n\\end{thebibliography}\n\n\\input bershady_tables.tex\n\n\\centerline{\\bf Figure captions}\n\n\\bigskip\n\n\\noindent Fig. 1.--- Rest-frame \\bv \\ versus $M_B$ for the nearby\ngalaxy sample of Frei \\etal (E-S0, Sa-Sb, and Sc-Irr) and Huchra's\n(1977a) sample of normal Markarian galaxies (pluses). The dotted\noutline indicates the approximate locus of dE/dSph galaxies. The\nintermediate redshift samples from paper II are also plotted for\ncomparison: blue nucleated galaxies (BNGs) compact, narrow\nemssion-line galaxies (CNELGs), and small, blue galaxies (SBGs). (The\ntwo SBGs and the BNG that we ultimately determine not to be ``Luminous\nBlue Compact Galaxies'' in paper II are shown as hatched symbols.)\nOnly a few Markarian galaxies and late-type galaxies from the Frei\n\\etal catalog share the extreme color--magnitude properties of the\nintermediate-redshift objects. In this plot, and in Figures 2-6,\nthe vigorously star-forming galaxy NGC 4449 is labeled.\nCharacteristic random errors are indicated separately for the Frei\n\\etal sample and the intermediate-$z$ objects.\n\n\\bigskip\n\n\\noindent Fig. 2.--- Rest-frame \\ub \\ versus \\bv \\ for the sample\nsamples as in Figure 1. The intermediate-redshift samples of paper II\nlargely overlap with the bluest Markarian galaxies, which extend\nblueward the color-color relation seen for the ``normal'' galaxies\nfrom Kent.\n\n\\bigskip\n \n\\noindent Fig. 3.--- Rest-frame $B$-band form and scale parameters\nversus spectral index for the Frei \\etal sample. Top panel: Average\nsurface-brightness within the half-light radius ($SB_e$) versus\nrest-frame \\bv. Middle panel: Image concentration ($C$) versus\n\\bv. Bottom panel: 180-degree rotational image asymmetry ($A$) versus\n\\bv. Characteristic errors are given in the top-left corner of each\npanel. Outlying objects are labeled and discussed in the text. Dashed\nlines demark Early, Intermediate, and Late types in our classification\nscheme. Symbols are by Hubble type, as defined in the key. Different\nHubble types are well distinguished, particularly in\ncolor. Morphological types are also well separated in $C$, but only\nthe earliest types are well separated in $SB_e$ and $A$.\n\n\\bigskip\n\n\\noindent Fig. 4.--- Rest-frame $B$-band parameters of form versus\nscale for the Frei \\etal sample. Top panel: Image asymmetry ($A$)\nversus average surface-brightness ($SB_e$). Bottom panel: image\nconcentration ($C$) versus $SB_e$. Outlying objects are labeled and\ndiscussed in the text. Dashed lines demark Early, Intermediate, and\nLate types in our classification scheme. The separation of\nmorphological types is less clear than in Figure 3, but the different\nHubble types are reasonably segregated.\n\n\\bigskip\n\n\\noindent Fig. 5.--- Form versus form parameters for the Frei \\etal\nsample: Rest-frame $B$-band image asymmetry ($A$) versus image\nconcentration ($C$). Outlying objects are labeled and discussed in the\ntext. Dashed lines demark Early, Intermediate, and Late types in our\nclassification scheme. The separation of morphological types is less\nclear than in Figure 3, but is comparable to figure 5 where the\ndifferent Hubble types are reasonably segregated.\n\n\\bigskip\n\n\\noindent Fig. 6.--- Comparison of form, scale, and spectral index\ncorrelations between Frei \\etal and Kent samples. {\\it Top panel:}\naverage $R$ band (Kron-Cousins) surface brightness within the\nhalf-light radius, $SB_e(R_c)$, versus $R$- or $r$-band image\nconcentration, $C(R)$. {\\it Middle panel:} $SB_e(R_c)$ versus\nrest-frame \\bv. {\\it Bottom panel:} $C(R)$ versus rest-frame \\bv. {\\it\nStructural parameters:} We measured half-light radius and image\nconcentration for the Frei \\etal sample using their $R$ or $r$-band\nCCD images and circular photometry apertures. Kent measured these\nstructural parameters using elliptical apertures on $F$-band CCD\nimages. {\\it Photometric parameters:} The Frei \\etal sample is\nsubdivided between objects observed at (a) Lowell Observatory (filled\nsquares), (b) Palomar Observatory (dotted-circles), and (c) an\noverlapping subset of the Frei \\etal sample with existing $R_c$-band\nphotometry from Buta and Williams (1996; outlined-triangles). For (a)\nand (b) we used the zeropoints from the Frei \\etal image headers\n(DNATO\\_BV), and transformations from Thuan-Gunn $r$ and Gullixson\n\\etal $R$ to Cousins $R_c$ from Frei \\& Gunn (1994). We have\ntransformed Kent's photometry reported in the Thuan-Gunn $r$-band to\n$R_c$ again based on transformations in Frei \\& Gunn (1994); Kent\ncorrected surface brightnesses to ``face-on'' values. {\\it\nRegressions:} Lines indicate $\\pm1\\sigma$ about linear least-squares\nfits to the correlations (dotted, Kent; dashed, Frei \\etal) using an\niterative clipping method ($\\pm2.5\\sigma$ clip; 10 iterations). In the\ntop and middle panels only the Lowell subset of the Frei \\etal sample\nwas used in the regressions. The substantial scatter in the Frei \\etal\n$SB_e(R_c)$ values we infer is due primarily to zeropoint\ndifficulties; we detect no noticeable systematics effects with\ninclination in $SB_e(R_c)$. The difference in the correlation between\n$SB_e(R_c)$ and $C(R)$ is largely due to the shallower trend in $C(R)$\nwith \\bv \\ for the Frei \\etal sample. This may be due to differences\nbetween circular versus elliptical apertures. While elliptical\naperture photometry provides greater dynamic range in $C(R)$, the\ncorrelation of $C(R)$ with \\bv \\ has larger scatter.\n\n\\bigskip\n\n\\noindent Fig. 7.--- Form parameters and spectral index for 70\ngalaxies from the Frei \\etal sample as determined by Brinchmann\n\\etal Top panel: $B$ band image concentration versus rest-frame \\bv.\nMiddle panel: $B$ band asymmetry versus rest-frame \\bv. Bottom panel:\n$B$ band asymmetry versus concentration. The asymmetry parameter was\ndetermined in a very similar manner as our own and thus should have\ncomparable dynamic range. Since our $C$ parameter is logarithmic, we\nplot the logarithm of the Brinchmann \\etal $C$ values. These\nplots are displayed so that they may be directly comparable to Figures\n3 and 5. The trend in asymmetry for the different Hubble types is more\napparent in Figure 3 and 5. In the concentration--color plane, the\ndistributions are similar for both studies, although we find a smaller\nscatter among the late-type galaxies, and a larger scatter among the\nearly-type objects.\n\n\\bigskip\n\n\\noindent Fig. 8.--- A representative subset of galaxy images from the\nFrei \\etal catalog, block-averaged by factors 1, 2, 4, and 6 (top to\nbottom). While the apparent change in qualitative (visually-assessed)\nmorphology is small, the effects on the quantitative parameters $C$\nand $A$ can be substantial. Half-light radius and surface-brightness\nare only weakly affected.\n\n\\bigskip\n\n\\noindent Fig. 9.--- Resolution dependence of image concentration,\n$C$, for the galaxies in the Frei \\etal catalog: $\\Delta C$ versus the\nhalf-light radius $R_e$ (in pixel units of the block-averaged images).\n$\\Delta C$ is the difference between the concentration index for a\ngiven simulated value of $R_e$ relative to the original concentration\nvalue (i.e. that value measured on the observed image). Measurements\nfor six definitions of the concentration index are plotted (two types\nper panel, labeled by line-type). The central line (bold) is the\nmedian value of this difference, and the bounding lines are the 25$\\%$\nand 75$\\%$ values, i.e. 50$\\%$ of the simulations are contained\nbetween the upper and lower lines for each index.\n\n\\bigskip\n\n\\noindent Fig. 10.--- Wavelength dependence of structural parameters\nfor galaxies in the Frei \\etal sample, plotted versus galaxy\nrest-frame color. Dashed lines show the mean\ndifferences between blue and red bands and the error bars show the\n1$\\sigma$ dispersions for three bins in color: $\\bv < 0.62$\n(late-type), $0.62<\\bv<0.87$ (intermediate-type), and $\\bv>0.87$\n(early-type). Top panel: Image concentration $C_B-C_R$. Nearly all\ngalaxies are more highly concentrated in the red band than in the\nblue, and thus fall below the dotted line at $C_B-C_R=0$. This\ndifference is slightly larger for galaxies with intermediate-type\nmorphology. Middle panel: Image asymmetry $A_B-A_R$. Late- and\nintermediate-type galaxies are more asymmetric in the blue band than\nin the red band. Red objects are generally very symmetric in both\nbands, and have $A_B-A_R \\sim 0$. This panel can be compared to Figure\n2 in Conselice \\etal (1999) where $A_B-A_R$ is plotted versus $A_R$.\nSince asymmetry and color are strongly correlated for the Frei \\etal\nsample (as seen in Figure 3), the trend in Conselice's plot is\nsimilar to what is shown here. Bottom panel: Half-light radius\n$R_{e,B} - R_{e,R}$. Although the scatter in this diagram is\nrelatively large, it is clear that the half-light radius shows little\nwavelength dependence over this wavelength range (cf. de Jong\n1995). Objects of intermediate \\bv \\ color tend to be slightly larger\nin the blue band than in the red, but this trend is not seen for\neither the bluest or the reddest objects.\n \n\\bigskip\n\n\\noindent Fig. 11.--- Axis ratio dependence of image concentration $C$\nfor galaxies of different morphological types in the Frei \\etal\nsample. The dotted line separates the sample into two bins at\nlog$_{10} [a/b]=0.3$, corresponding to an inclination of\n60\\arcdeg. The dashed lines and error bars show the mean and 1$\\sigma$\ndispersion for each morphological type and bin. Labeled objects are\ndiscussed in the text. Top panel: Late-type objects with high\ninclination have slightly higher measured $C$ than more face-on\nobjects. Middle panel: For intermediate-type galaxies the measured\nconcentration indices show no correlation with the axial ratio\n$[a/b]$. Bottom panel: For early-type galaxies, a tendency can be seen\nwhere objects with larger axial ratio $[a/b]$ are measured to have\nlower image concentration.\n\n\\bigskip\n\n\\noindent Fig. 12.--- Axis ratio dependence of half-light radius $R_e$\nfor galaxies of different morphological types in the Frei \\etal\nsample. The dotted line separates the sample into two bins at\nlog$_{10} [a/b]=0.3$, corresponding to an inclination of\n60\\arcdeg. The dashed lines and error bars show the mean and 1$\\sigma$\ndispersion for each morphological type and bin. Top panel: The\nmeasured $R_e$ are slightly larger for late-type objects with high\naxial ratios. Middle panel: Intermediate-type objects have somewhat\nsmaller $R_e$ for high values of $[a/b]$. In both of these panels the\nscatter is large and the differences between the bins are small.\nBottom panel: Early-type galaxies with larger axial ratio $[a/b]$ are\nmeasured to have $\\lesssim 30\\%$ smaller half-light radii.\n\n\\input bershady_figures.tex\n\n\\end{document}\n"
},
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}
] |
astro-ph0002263
|
Interactions as a driver of \\ galaxy evolution
|
[
{
"author": "Fran\\c cois Schweizer"
}
] |
{Galaxy interactions, mergers, elliptical formation, bulge formation, starbursts, quasars} Gravitational interactions and mergers are shaping and reshaping galaxies throughout the observable universe. While observations of interacting galaxies at low redshifts yield detailed information about the processes at work, observations at high redshifts suggest that interactions and mergers were much more frequent in the past. Major mergers of nearby disk galaxies form remnants that share many properties with ellipticals and are, in essence, present-day protoellipticals. There is also tantalizing evidence that minor mergers of companions may help build bulges in disk galaxies. Gas plays a crucial role in such interactions. Because of its dissipative nature, it tends to get crunched into molecular form, turning into fuel for starbursts and active nuclei. Besides the evidence for ongoing interactions, signatures of past interactions and mergers in galaxies abound: tidal tails and ripples, counterrotating disks and bulges, polar rings, systems of young globular clusters, and aging starbursts. Galaxy formation and transformation clearly is a prolonged process occurring to the present time. Overall, the currently available observational evidence points towards Hubble's morphological sequence being mainly a sequence of decreasing merger damage.
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"name": "schweizer.tex",
"string": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%% RoySoc Discussion Meeting, `The Formation of Galaxies', Nov 3-4, 1999 %%%\n%%% Contribution by Francois Schweizer (OCIW): `Interactions as a driver %%%\n%%% of galaxy evolution', submitted to Philosophical Transactions %%%\n%%% This contribution includes 5 figures in PostScript format. %%%\n%%% Version for `astro-ph': Figs. 1, 3, & 5 are compressed\t\t %%%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\documentclass{rspublic}\n\\usepackage{psfig}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DEFINITIONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\newcommand{\\etal}{{\\it et al.}}\t\t% Present RoySoc style\n\\newcommand{\\hi}{H\\;I}\t\t\t\t% Neutral hydrogen (HI)\n\\newcommand{\\msun}{\\mbox{${\\cal M}_{\\odot}$}}\t% Solar mass\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\begin{document}\n\n\\title[Interactions driving galaxy evolution]{Interactions as a driver of \\\\\ngalaxy evolution}\n\n\\author[F. Schweizer]{Fran\\c cois Schweizer}\n\\affiliation{The Observatories of the Carnegie Institution of Washington \\\\\n813 Santa Barbara Street, Pasadena, CA 91101, USA}\n\n\\label{firstpage}\n\n\\maketitle\n\n\\begin{abstract}{Galaxy interactions, mergers, elliptical formation, bulge\nformation, starbursts, quasars}\nGravitational interactions and mergers are shaping and reshaping galaxies\nthroughout the observable universe. While observations of interacting\ngalaxies at low redshifts yield detailed information about the processes\nat work, observations at high redshifts suggest that interactions and\nmergers were much more frequent in the past. Major mergers of nearby\ndisk galaxies form remnants that share many properties with ellipticals\nand are, in essence, present-day protoellipticals. There is also\ntantalizing evidence that minor mergers of companions may help build\nbulges in disk galaxies. Gas plays a crucial role in such interactions.\nBecause of its dissipative nature, it tends to get crunched into molecular\nform, turning into fuel for starbursts and active nuclei. Besides the\nevidence for ongoing interactions, signatures of past interactions and\nmergers in galaxies abound: tidal tails and ripples, counterrotating disks\nand bulges, polar rings, systems of young globular clusters, and aging\nstarbursts. Galaxy formation and transformation clearly is a prolonged\nprocess occurring to the present time. Overall, the currently available\nobservational evidence points towards Hubble's morphological sequence\nbeing mainly a sequence of decreasing merger damage. \n\\end{abstract}\n\n\n\\section{Introduction}\n\nEver since Hubble (1936) published his famous `Sequence of Nebular Types'\n(a.k.a.\\ tuning-fork diagram) the question has been: What determines the\nposition of a galaxy along this sequence? And why are galaxies at one end\nof the sequence disk-shaped and at the other end ellipsoidal? Was this\nshape dichotomy imprinted during an early collapse phase of galaxies, or\ndid it arise through subsequent evolution?\n\nWork begun several decades ago by Zwicky (1956), Arp (1966), Alladin (1965),\nand Toomre \\& Toomre (1972, hereafter `TT'), among others, has led to growing\nevidence that gravitational interactions between neighbor galaxies do not\nonly explain some of the most striking `bridges' and `tails' observed in\ndisturbed galaxy pairs, but also tend to lead to galactic mergers that\noften trigger bursts of star formation and clearly represent important\nphases of galaxy building (Larson 1990; Barnes \\& Hernquist 1992;\nKennicutt \\etal\\ 1998).\n\nBefore reviewing some of the evidence for interactions and mergers being\na significant driver of galaxy evolution, it seems wise to agree on\nsome terminology and point out biases.\n\nTo be called a `merger', a galaxy pair or single galaxy should show\nat least clear morphological signatures of an advanced tidal interaction,\nsuch as significant distortions, major tails, and ripples or `shells'\n(for a review, see Schweizer 1998). A stronger case for merging can\nusually be made when {\\it kinematic\\,} signatures are available as well,\nsuch as opposite tail motions, counter-rotating parts, or tail material\nfalling back onto a remnant. As figure~\\ref{fig:n4038kin} illustrates,\nmuch recent progress in this area is due to the upgraded {\\it Very Large\nArray}'s ability to map the line-of-sight motions of neutral hydrogen\n(\\hi ) in tidal features in great detail (Hibbard 1999).\n\n\\begin{figure}\n\\centerline{\\psfig{file=schweizer_fig1.ps,height=7.0cm,angle=-90}}\n\\caption{Neutral hydrogen distribution and kinematics of NGC\\,4038/4039.\nLeft: \\hi\\ contour lines ({\\it white}) superposed on an optical photograph;\nright: \\hi\\ position--velocity plot, with declination along $y$-axis and\nline-of-sight velocity along $x$-axis (from Hibbard 1999).}\n\\label{fig:n4038kin}\n\\end{figure}\n\nThe main bias in studies of gravitational interactions has been toward\nmajor mergers, which involve two galaxies of nearly equal mass. Such\nmergers are highly destructive and tend to lead to spectacular\nmorphologies, whence they can be observed from the local universe\nout to redshifts of $z\\approx 2$ and beyond. Minor mergers\ninvolving galaxies with mass ratios of, say, $m/M = 0.1$--0.5 are less\nspectacular and often require verification via some kinematic signature\n(esp.\\ in the remnant phase). Hence, such interactions and mergers have\nbeen studied mainly in nearby galaxies and out to $z\\lesssim 0.5$.\nFinally, although satellite accretions leading to mass increases of a few\npercent or less may be relatively frequent, they are the most difficult to\ndetect and have been studied only in the Local Group, and even there nearly\nexclusively in our Milky-Way galaxy. Thus, our knowledge of growth through\naccretions and minor mergers is severely limited.\n\nBecause of its dissipative nature gas plays a disproportionately large\nrole in galaxy interactions. Even at the present epoch, the vast majority\nof galaxies contain significant amounts of cold gas (Roberts \\& Haynes\n1994). During tidal interactions and mergers this gas tends to be driven\ntoward the centers of galaxies through gravitational torques exerted on it by\ntidally induced {\\it stellar\\,} bars (e.g. Barnes \\& Hernquist 1996).\nThe ensuing shocks and energy dissipation allow the gas to get compressed,\nleading to intense bursts of star formation, globular-cluster formation,\nand the feeding of nuclear activity. Starbursts and active galactic\nnuclei in turn drive galactic winds and jets, which can have profound\neffects on the chemical evolution of galaxies (Heckman 2000).\n\nSome of these processes can now be reproduced by modern $N$-body\nsimulations that include gas hydrodynamics. Barnes (1999) shows a\nbeautiful sequence of two gas-rich disk galaxies merging. Whereas\ntheir stars end up in a three-dimensional pile not unlike an elliptical\ngalaxy with considerable fine structure, more than half of the cold\ngas from the input disks gets funneled to the center of the remnant\ninto a region only about 0.5\\3kpc in diameter, while the initially warm\ngas ($T\\approx 10^4$\\3K) gets heated to X-ray temperatures\n($\\sim$10$^6$\\3K) and forms a pressure-supported atmosphere of\nsimilar dimensions as the stellar pile.\nThe time scale for this transformation from two disk galaxies to one\nmerged remnant is remarkably short: about 1.5 rotation periods\nof the input disks or, when scaled to component galaxies of Milky-Way\nsize, about 400\\3Myr.\n\nThe rapidity of this equal-mass merger is due to strong dynamical friction.\nWe should keep this in mind when trying to understand the formation of\nelliptical galaxies in dense environments. Claims have been made\nthat cluster ellipticals formed in a rapid monolithic collapse because\ntheir present-day colors are rather uniform. Yet, experts\nagree that age differences of $\\lesssim$3\\3Gyr cannot be discerned\nfrom broad-band colors of galaxies 10--15\\3Gyr old. A time interval of\n3\\3Gyr may seem short when we struggle with logarithmic age estimates,\nyet it is long when compared to the merger time scale. About eight major\nmergers of the kind simulated by Barnes could take place one after\nanother during this time interval, and 12\\3Gyr later all their remnants\nwould look nearly the same color and age. Hence, claims about\nmonolithic collapses and a single epoch of elliptical formation are to\nbe taken with a grain of salt. There was time for many major mergers\nof juvenile disks during the first few Gyr after the big bang, and most\ncluster ellipticals could have formed through such mergers without us\nknowing it from their present-day colors.\n\nThe following review of evidence for interactions being a driver\nof galaxy evolution begins with accretions in the Local Group, continues\nwith minor mergers and the damage they inflict on disk galaxies,\nmoves on to major mergers forming ellipticals from wrecked disks,\nand ends with a brief description of what we have learned from first\nglimpses of high-redshift mergers.\n\n\n\\section{Interactions in the Local Group}\n\nThere are many signs of recent or ongoing gravitational interactions in\nthe Local Group, including the warped disks of the Milky Way, M\\,31, and\nM\\,33, the Magellanic Stream, and the integral-sign distortion of NGC\\,205,\ncompanion to M\\,31. However, the details of these interactions are often\ndifficult to establish, and the cumulative effect of interactions not\ndirectly leading to mergers remains largely unknown.\n\nFortunately, there is now---in the Milky Way---some good, detailed evidence\nfor interactions leading to accretions. Three pieces of evidence stand out\nas particularly reliable among the many that have been claimed.\n\nFirst and most impressive is the Sagittarius dwarf galaxy, hidden from us\n% because of its position\nbehind the Milky-Way bulge until its recent discovery\nby Ibata \\etal\\ (1994). Located at a distance of 16\\3kpc from the\ngalactic center, this dwarf appears very elongated in a direction\napproximately perpendicular to the galactic plane and is thought\nto move in a nearly polar orbit with current peri- and apogalactic\ndistances of $\\sim$20\\3kpc and $\\sim$60\\3kpc, respectively (Ibata \\& Lewis\n1998). Although it may have started out with a mass of as much as\n10$^{11}$\\3\\msun\\ or as little as $\\sim$10$^9$\\3\\msun\\ (Jiang \\& Binney\n2000), the dwarf is estimated to currently have a mass of\n$2\\times 10^8$--$10^9$\\3\\msun\\ and an orbital period of about 0.7--1\\3Gyr.\nIt will probably disrupt completely over the next few orbits and will\nthen deliver its four globular clusters, one of which appears to be its\nnucleus (e.g. Da Costa \\& Armandroff 1995), to the halo of the Milky Way.\n\nAs Searle \\& Zinn (1978) conjectured already, similar accretions of\ngas fragments and dwarfs may have built this halo over a prolonged period.\nA second piece of evidence strongly supporting this view is the observed\nretrograde mean motion of certain subsystems of globular clusters\n(Rodgers \\& Paltoglou 1984; Zinn 1993). How could a monolithic collapse\npossibly have led to a 15\\% minority of slightly younger halo globulars\norbiting in the opposite sense from the majority of old globulars and\nthe disk itself? Accretions from different directions provide a natural\nexplanation.\n\nMost accretions into the halo must have occurred in the first 25\\%--30\\%\nof the age of our Galaxy. Colors and inferred minimum ages of halo stars\nsuggest that by 10\\3Gyr ago such accretions had diminished to a trickle\nand since then $\\lesssim$6~Sagittarius-like dwarfs can have been accreted\n(Unavane \\etal\\ 1996). Hence, the ongoing accretion of Sgr Dwarf is\nby now a relatively rare event.\n\nHowever, a much more massive accretion may still lie in the future. This\nis suggested by the Magellanic Stream, the third piece of good evidence\nfor a relatively strong interaction involving the Milky Way. This stream\nof \\hi\\ extends over 120$^\\circ$ in the sky, arching from the Magellanic\nClouds through the south galactic pole to declination $-$30$^\\circ$, where\nit was first discovered (Dieter 1965; Mathewson \\etal\\ 1974). After a long\nand tortuous history of interpretations, modern models based on a past\ngravitational interaction between the LMC--SMC system and the Milky Way \nare now reasonably successful at explaining the observed morphology of\nthe stream, the high approach velocities near its end, and the existence\nof a counter-stream on the other side of the Clouds (e.g. Gardiner\n\\& Noguchi 1996). According to such models, the stream and counter-stream\nrepresent a tidal tail and bridge drawn from the outer gas disk of the\nSMC during a close passage to the Milky Way about 1--1.5\\3Gyr ago. The\nprediction is that the LMC--SMC binary will soon break up and the more\nmassive LMC will be the first to merge with the Milky Way in about\n7--8\\3Gyr (Lin \\etal\\ 1995).\n\nThe LMC's mass is about 4\\% of that of the Milky Way, and its visual\nluminosity twice that of the entire halo. Hence, this future accretion\nwill be a major event, at least an order of magnitude more massive and \nspectacular than the ongoing Sgr~Dwarf accretion. Our descendants can\nexpect significant halo growth, induced star formation, and probably also\na thickening of the present thin disk of the Milky Way.\n\nThe main message from the above evidence is that---even though most\naccretions in galaxies outside the Local Group are difficult to\ndetect---they must have occurred primarily early ($z\\gtrsim 2$) and\nmust have contributed significantly to the growth and perhaps even\nmorphology of many disk galaxies similar to ours and M\\,31.\n\n\n\\section{Damaged disks}\n\nBetween small accretions that barely affect disk galaxies and major mergers\nthat wreck disks there must be intermediate-strength interactions and\nminor mergers that significantly affect disks yet do not destroy them.\nThis immediately suggests three questions: (1) How fragile are galaxy disks? \n(2) Can bulges form through minor mergers? And (3) if so, what fraction of\nbulges formed in this manner?\n\nEarly theoretical worries that accretions of even only a few percent in mass\nmight disrupt disks (T\\'oth \\& Ostriker 1992) have been dispelled by $N$-body\nsimulations showing that model disk galaxies do survive minor mergers with\nmass ratios of up to $m/M\\approx 0.3$, albeit tilted, warped, slightly\nthickened, and often with an increased bulge (Walker \\etal\\ 1996;\nHuang \\& Carlberg 1997; Vel\\'azquez \\& White 1999). Hence, galaxy disks\nare apparently less fragile than once thought, a fact also suggested\nby observations.\n\nFirst, note that optical images are not always a reliable indicator of\ntidal interactions, as the case of M\\,81 illustrates. Even when displayed\nat high contrast such images of M\\,81 paint a rather serene scene of a\nsymmetric grand-design spiral. Yet, the \\hi\\ distribution is highly\nasymmetric and dominated by long tidal features whose kinks reveal\na strong triple interaction between M\\,81, NGC\\,3077, and M\\,82 (Yun\n\\etal\\ 1994). M\\,81 has not only survived this interaction, but probably\nowes its beautiful spiral structure to it (TT).\n\n\\begin{figure}\n\\centerline{\\psfig{file=schweizer_fig2.ps,height=6.0cm,angle=90}}\n\\caption{Neutral hydrogen distribution of NGC\\,4650A, a S0 galaxy with\na `polar ring'. The \\hi\\ contours are superposed on an optical image of\nthe galaxy (from Arnaboldi \\etal\\ 1997).}\n\\label{fig:n4650ahi}\n\\end{figure}\n\nSecond, S0 galaxies with polar rings of gas, dust, and young stars\nincreasingly suggest that especially gas-rich disks may well survive\nminor mergers occurring from near-polar orbits. Such S0 galaxies were\nlong thought to have accreted their ring gas during a flyby or minor\nmerger (e.g. Toomre 1977; Schweizer \\etal\\ 1983). Yet, many of the\nS0 bodies feature poststarburst spectra, and \\hi\\ observations show that\nthe gas contents of the polar rings tend to be large and typical of\nfull-grown late-type spirals (Richter \\etal\\ 1994; Reshetnikov \\&\nCombes 1994; Arnaboldi \\etal\\ 1997), as illustrated in\nfigure~\\ref{fig:n4650ahi}. Thus it appears that the central\nS0 galaxies may be remnants of disk companions having fallen into spiral\ngalaxies---now polar rings---nearly over their poles (Bekki 1998).\nIf so, these central S0 bodies represent failed bulges. The crucial point\nis that two disk systems of not too dissimilar mass apparently {\\it can\\,}\nsurvive a merger and---helped by gaseous dissipation---retain their disk\nidentity.\n\nDisk galaxies survive even non-polar minor mergers, as\nevidenced by a multitude of kinematic signatures. For example, the\nSab galaxy NGC\\,4826 has a gas disk consisting of two nested\ncounterrotating parts, each of nearly equal mass (Braun \\etal\\ 1994).\nThe inner component rotates like the stellar disk and bulge, while the\nouter component counterrotates (Rubin 1994). The two comparable\ngas masses suggest that the intruder galaxy was not a mere dwarf a few\npercent in mass, but a more massive companion leading to a minor merger.\n\nWhereas similar kinematic signatures are rare among Sb galaxies, they\nare more frequent among Sa galaxies and nearly the norm among\nS0 galaxies. From the statistics of counterrotating, skewedly rotating,\nand corotating ionized-gas disks one can conclude that at least 40\\%--70\\%\nof all S0 galaxies experienced minor mergers (Bertola \\etal\\ 1992).\nThe fact that the frequency of kinematic signatures of past mergers\nincreases with bulge size strongly suggests that at least major bulges\nformed through mergers.\n\nAnother powerful merger signature correlating with morphological\ntype is the subpopulations of stars counterrotating in disk galaxies of\ntypes S0 to Sb. A well known example is the E/S0 galaxy NGC\\,4550, in\nwhich half of the disk {\\it stars\\,} rotate one way and the other half the\nopposite way (Rubin \\etal\\ 1992). In several Sa and Sb galaxies the\nsplit between normal- and counterrotating disk stars is of the order\nof 70/30\\%. Finally, a bulge rotating at right angles to the stellar\ndisk has been observed in the Sa galaxy NGC\\,4698 (Bertola \\etal\\ 1999),\nand bulges counterrotating to the disks are seen in the Sb galaxies\nNGC\\,7331 and NGC\\,2841 (Prada \\etal\\ 1996, and private commun.; but see\nBottema 1999). $N$-body simulations suggest that minor and not-so-minor\nmergers can indeed produce such odd rotations (Thakar \\& Ryden 1998;\nBalcells \\& Gonz\\'alez 1998).\n\nIn short, galactic disks---especially those rich in gas---appear not nearly\nas fragile as thought only a few years ago. Both observations and\nnumerical simulations suggest that minor mergers do occur in disk galaxies\nand contribute to bulge building. However, we do not know the exact fraction\nof bulges that were built in this manner. Also unclear is how unique\nor varied the possible paths to, say, a present-day Sb galaxy are. Which\nformed first: the disk or the bulge? And did disks and bulges grow\nepisodically, perhaps even by turns?\n\n\n\\section{Ellipticals from wrecked disks}\n\nThe notion that galaxy collisions are highly inelastic (Alladin 1965) and\nlead---via dynamical friction and orbital decay---to mergers (TT) is now\nwell supported by both $N$-body simulations and observations (e.g. Barnes\n1998). Major mergers clearly do wreck disks and can form giant ellipticals,\nas first proposed by TT. What remains controversial is whether {\\it most\\,}\nellipticals formed in this manner, and whether those in clusters formed\nin a systematically different way from those in the field. As described\nbelow, there is growing evidence that most giant ellipticals did indeed\nform through major mergers, and that this occurred earlier on average in\nclusters than in the field.\n\n\\begin{figure}\n\\centerline{\\psfig{file=schweizer_fig3.ps,width=12.2cm}}\n\\caption{Two recent merger remnants NGC\\,3921 ({\\it left}) and NGC\\,7252\n({\\it right}) with properties marking them as present-day protoellipticals\n(from Schweizer 1996, 1982).}\n\\label{fig:twoproto}\n\\end{figure}\n\nFirst, the evidence is strong that remnants of {\\it recent\\,} equal-disk\nmergers are present-day protoellipticals. The main theoretical advance\nhas been the inclusion of dark-matter halos and gas in the\n$N$-body simulations, leading to efficient mechanisms for outward\nangular-momentum transport and central density increases (Barnes 1988;\nBarnes \\& Hernquist 1996). The model remnants are generally triaxial,\nviolently but incompletely relaxed, and lack rotational support.\nTheir projected isophotes---determined mainly by the inclinations of\nthe progenitor disks and the viewing geometry---can range\nfrom boxy through boxy-and-disky to rather strongly disky, as\nobserved in real E and E/S0 galaxies (Barnes 1992; Heyl \\etal\\ 1994).\nObservationally, recent merger remnants such as NGC\\,3921 and NGC\\,7252\n(fig.~\\ref{fig:twoproto})\nfeature pairs of tidal tails but single main bodies with relaxed,\n$r^{1/4}$-type light distributions (Schweizer 1982, 1996; Stanford \\&\nBushouse 1991). Their power-law cores, central luminosity densities,\nvelocity dispersions, and radial color gradients are typical of giant\nellipticals (Lake \\& Dressler 1986; Doyon \\etal\\ 1994). Major starbursts,\nreflected in the integrated-light spectra and in major populations of\nyoung star clusters, seem to have converted 10\\%--30\\% of the visible\nmass into stars and have nearly doubled the number of globular clusters.\nTherefore, in all their observed properties such remnants appear to be\n$\\lesssim$1\\3Gyr old protoellipticals.\n\nSecond, recent remnants of disk--disk mergers display several phenomena\nthat connect them also to much older ellipticals. Foremost among these\nphenomena is the return of tidally ejected material. Model simulations\nincluding the effects of massive dark halos predict that most of the\nmatter ejected by two merging disks into tails remains bound and must\neventually fall back onto the merger remnant (Barnes 1988). This infall\nis observed in the \\hi\\ gas near the base of the tails of NGC\\,7252 and\nNGC\\,3921 (Hibbard \\etal\\ 1994; Hibbard \\& van Gorkom 1996) and is\npresumably shared by the stars. Interestingly, \\hi\\ absorption in\nradio ellipticals invariably indicates gas infall (van Gorkom \\etal\\\n1989). Infalling stars also yield a natural explanation for many of\nthe faint ripples (`shells') and plumes observed in elliptical\ngalaxies. As dynamically cold streams of stars fall back into the\nremnants, they wrap around the center and form sharp-edged features at\ntheir turnaround points (Hernquist \\& Spergel 1992; Hibbard \\& Mihos 1995). \nThe high percentage ($\\sim$70\\%) of field ellipticals featuring such fine\nstructure (Schweizer \\& Seitzer 1992) and the considerable amounts of\nmaterial indicated by integrated photometry (Prieur 1990) suggest that\nmost of the observed fine structure cannot be due to mere dwarf galaxies\nfalling in. Instead, such structure is much more likely the signature\nof past major mergers that formed most, or even all, ellipticals.\n\n\\begin{figure}\n\\centerline{\\psfig{file=schweizer_fig4.ps,height=7.0cm}}\n\\caption{Oddly rotating cores in two elliptical galaxies. Mean stellar\nvelocities are shown as function of position along major axes. Note\ncounterrotating core of NGC\\,3608 and corotating, but kinematically\ndistinct core of NGC\\,4494 (Jedrzejewski \\& Schechter 1988).}\n\\label{fig:oddcores}\n\\end{figure}\n\nThird, various unexpected kinematic signatures in giant ellipticals\nalso point toward past mergers of gas-rich disks. About a quarter of\nall ellipticals show oddly rotating cores, some rotating in the opposite\nsense of the main body, others at right angles, and still others in the\nsame sense but much faster (fig.~\\ref{fig:oddcores}). When studied in\ndetail, such cores appear to\nbe small disks ($r\\approx 0.2$--3\\3kpc) indicative of gaseous dissipation\n(e.g. Bender 1996; Mehlert \\etal\\ 1998). A similar central disk violently\nforming stars and probably fed by gas returning from the tails is observed\nin the merger remnant NGC\\,7252 (Wang \\etal\\ 1992; Whitmore \\etal\\ 1993).\nModel simulations of disk mergers reproduce such odd core rotations\nquite naturally (Hernquist \\& Barnes 1991). The existence of distinct\nkinematic subsystems then argues against ellipticals having assembled from\nmany gaseous fragments and in favor of {\\it two\\,} input disks. Exactly the\nsame message is conveyed by the growing number of ellipticals that---like\ne.g. NGC\\,5128 (Schiminovich \\etal\\ 1994)---possess {\\it two}, often nearly\northogonally rotating, \\hi\\ disks. Nearly three dozen ellipticals are\nnow known to feature often fragmentary outer gas disks or rings whose\nkinematics appears decoupled from that of the main body (van Gorkom,\nprivate comm.). Given that the gaseous tails of the remnant NGC\\,7252\nlie in mutually inclined planes, there is strong reason to suspect that\nthese much older ellipticals acquired their outer gas through disk--disk\nmergers as well.\n\nFourth, yet another connection between disk mergers and elliptical\ngalaxies is provided by globular star clusters. Although in nearby\ngalaxies most such clusters appear to be very old and seem to have\noriginated in the earliest days of galaxy formation, young globulars have\nrecently been found to form by the hundreds in the vehement starbursts\ninduced by major mergers. Mergers like `The Antennae', NGC\\,3921, and\nNGC\\,7252 can apparently produce nearly as many young globular clusters\nas the combined number of old globulars in the component disks, thus\napproximately doubling the number of clusters in the process (Miller \\etal\\\n1997; Ashman \\& Zepf 1998). First spectroscopic evidence shows that,\nas one would expect, the young globulars have much higher heavy-element\nabundances than the old ones, being of solar `metallicity' in the case of\nNGC\\,7252 (Schweizer \\& Seitzer 1998). If major mergers formed most\nellipticals, one would therefore expect to find bimodal abundance\ndistributions among their globular-cluster populations (Ashman \\& Zepf\n1992). This is exactly what has been discovered during the past few years.\n{\\it Hubble Space Telescope\\,} observations show that at least half\nof all giant ellipticals feature bimodal cluster distributions (Gebhardt \\&\nKissler-Patig 1999; Kundu 1999). The ratio of second- to\nfirst-generation clusters seems to typically range between 0.5 and 1, and\nthe second-generation, metal-rich clusters tend to be more concentrated\ntoward the centers of their host galaxies, as the merger hypothesis\npredicted. \n\nBimodal globular-cluster systems, oddly rotating cores, ripples and plumes,\nand fast outer-halo rotation (Bridges 1999) occur not only in field\nellipticals, but also in cluster ellipticals, indicating that giant\nellipticals formed via major disk--disk mergers both in the field\n{\\it and\\,} in clusters.\n\nMerging galaxies and recent remnants show that disk wrecking is an ongoing\nprocess. If the wrecks are mainly ellipticals, the latters' ages should\nvary widely.\nMeasured $U\\!BV$ colors and spectral line-strength indices suggest that\nthis is indeed the case, with ages of field ellipticals ranging between\nabout 2\\3Gyr and 12\\,Gyr (Schweizer \\& Seitzer 1992; Gonz\\'alez 1993; Faber\n\\etal\\ 1995; Davies 1996; Trager \\etal\\ 2000). In cluster ellipticals, the\ncolors and line strengths vary less and the inferred ages are more uniformly\nold (de Carvalho \\& Djorgovski 1992), especially near the cluster centers\n(Guzm\\'an \\etal\\ 1992). These observations all agree with the notion\nthat---on average---major mergers occurred earliest in high-density regions\nnow at the centers of rich clusters, significantly later in cluster\noutskirts where galaxies are still falling in, and at the slowest rate in\nthe field.\n\n\n\\section{High-redshift interactions}\n\nObservational evidence that interactions and mergers were more frequent\nin the past has trickled in since the late 1970s and has grown more rapidly\nsince the late-1993 repair of the {\\it Hubble Space Telescope}. In\ngeneral this evidence agrees with expectations based on numerical simulations\nof hierarchical clustering in an expanding universe dominated by\ndissipationless dark matter. However, quantitative observations of high-$z$\ninteractions remain difficult to obtain. As we study objects from\n$z\\approx 0.3$ to $\\sim$1.2 morphological details and kinematic\nsignatures fade, and we are reduced to judging gross morphologies from a\nfew pixels or simply counting galaxy pairs.\n\nQuasars yielded some of the earliest evidence for\ninteractions at higher redshifts ($z\\gtrsim 0.2$). When near enough for\ndetails to be visible, they are seen to often occur in host galaxies that\neither have close companions or are involved in major mergers (Stockton 1990;\nBahcall \\etal\\ 1997). The quasar OX\\,169, for example, features at least one\ntidal tail (probably a pair) and shows a variable H$\\beta$ emission-line\nprofile indicative of {\\it two\\,} active nuclei (Stockton \\& Farnham 1991).\n\nOf special interest is the emerging connection between quasars and\ninfrared-luminous galaxies. At bolometric luminosities above\n10$^{12}$\\,$L_{\\odot}$ the so-called ultraluminous infrared galaxies (ULIG)\nbecome the dominant population in the local universe and are 1.5--2\ntimes as numerous as optically selected quasars. When ordered by\nincreasing far-infrared color temperature, ULIGs and quasars seem to form\nan evolutionary sequence: ULIGs with low color temperature are starbursting\ndisk mergers with well separated components, warm ULIGs appear to be just\ncompleting their merging into one object, and the `hot', optically visible\nquasars shine in peculiar ellipticals that resemble nearby merger remnants\n(Sanders \\etal\\ 1988, 1999). Nuclear separations and merger velocities\nindicate that the ULIG phase lasts about 200--400\\3Myr. Hence, extreme\nstarbursts occurring while the nuclei merge and nuclear feeding frenzies\nclimaxing in a quasar phase appear to be natural byproducts of elliptical\nformation through mergers. The peak quasar activity observed around\n$z\\approx 2$ may, then, mark the culmination of major mergers and\nelliptical formation.\n\nBeyond $z\\approx 2$ we have precious little {\\it direct\\,} evidence of\ninteractions and merging. The radio galaxy MCR 0406$-$244 at $z=2.44$\nmay be one of the highest redshift mergers for which there is some\ndetailed structural information. Deep optical {\\it Hubble Space Telescope\\,}\nimages show a double nucleus and a\n30\\3kpc-size pair of continuum-emitting `tails' suggestive of a tidal\norigin, while infrared images show two emission-line bubbles indicative\nof a strong bipolar wind (Rush \\etal\\ 1997; McCarthy 1999). Hence, at\nleast some mergers at this high redshift may have been similar to local\nones and involved pairs of already sizeable disks.\n\nThe important role played by interactions and mergers is also becoming\napparent in galaxy {\\it clusters\\,} of increasingly high redshifts. Despite\na widely held prejudice that mergers cannot happen in clusters because of\nhigh galaxy-velocity dispersions, both theory and observations show\nunmistakably that strong interactions and mergers do occur there. In some\nlocal clusters ongoing interactions and mergers are obvious. In Hercules at\nleast five major interactions and mergers are visible in the central region\nalone (fig.~\\ref{fig:hercules}), and even in relaxed-looking Coma `The Mice'\n(NGC\\,4676) provide an example of a major merger occurring on the outskirts.\nIn $z\\approx 0.2$--0.5 clusters a fair fraction of the blue galaxies\ncausing the Butcher--Oemler effect (Butcher \\& Oemler 1978, 1984) have been\nfound to be interacting or merging (Lavery \\& Henry 1994), while a majority\nappear to be disturbed gas-rich disks shaken either by high-velocity\nencounters or minor mergers (Dressler \\etal\\ 1994; Barger \\etal\\ 1996;\nOemler \\etal\\ 1997). Most impressive are new {\\it Hubble Space Telescope\\,}\nimages of the rich cluster\nMS 1054$-$03 at $z=0.83$. Fully 17\\% of its 81 spectroscopically confirmed\nmembers are ongoing mergers, all with luminosities similar to, or higher\nthan, that of a $L^*$ galaxy (van Dokkum \\etal\\ 1999). These mergers\noccur preferentially in the cluster outskirts, probably in small infalling\nclumps, and present `direct evidence against the formation of ellipticals\nin a single monolithic collapse at high redshift'.\n\nIn order to quantitatively assess the impact of mergers on galaxy\nevolution, one needs to determine the merger rate (i.e. the number of\nmergers per unit time and comoving unit volume) as a function of redshift.\nWe can only hope to do this for major mergers, since minor mergers\nare undetectable at $z\\gtrsim0.5$ and accretions are known only in the\nLocal Group. There are many estimates of the merger rate based on\ncounts of binary galaxies as a function of redshift, and on the assumption\nthat most such binaries will merge in a short time. This\nassumption is a bit unrealistic, given that even for a much studied\ninteracting pair like M\\,51 we do not know whether\nthe presumed merger will occur within 2, 5, or 10\\3Gyr. Nevertheless,\ntaken at face value several recent estimates based on binary counts\nsuggest a merger rate approximately proportional to $(1+z)^{3\\pm 1}$\n(e.g. Abraham 1999), implying an order-of-magnitude increase in\nmergers at $z\\approx 1$ compared to the local rate.\n\n\\begin{figure}\n\\centerline{\\psfig{file=schweizer_fig5.ps,width=12.2cm,angle=180}}\n\\caption{Galaxy interactions and mergers in Hercules cluster. Strongly\ninteracting pair near lower left corner shows giant diffuse tails.\nPhotograph courtesy of Alan Dressler.}\n\\label{fig:hercules}\n\\end{figure}\n\nTwo estimates of numbers of mergers are relatively reliable and bracket\nthe range of likely rates. First, given that there are $\\sim$11\nongoing disk mergers among the 4000$^+$ galaxies of the New General\nCatalog (NGC) and their median `age' is $\\sim$0.5\\3Gyr, there should be\nabout 250 remnants of similar mergers among NGC galaxies {\\it if\\,} the\nrate has remained constant since high redshifts, and about 750 remnants\nif---more realistically---the rate declined with time like $t^{-5/3}$\n(Toomre 1977). Thus, nearly 20\\% of all NGC galaxies may be remnants of\nmajor mergers, a fraction that agrees remarkably well with the observed\nnumber of elliptical and S0 galaxies. Second, if all gas collapsed into\ndisks and all spheroids are due to mergers, then the fractional amount of\nmass in spheroids---about 50\\% when estimated from bulge-to-disk ratios\nof a complete sample of nearby galaxies---provides an upper limit to the\nintegrated effect of all mergers (Schechter \\& Dressler 1987). This\nupper limit emphasizes that at least major mergers cannot have been too\nfrequent, or else they would have destroyed all disks. Especially\nin late-type, nearly pure-disk galaxies (e.g. M\\,33 and M\\,101) most of\nthe assembly must have been gaseous, dissipative, and---after perhaps\nsome initial collapse phase---involving mere accretions.\n\n\n\\section{Conclusions}\n\nThis review has high-lighted the role that interactions and mergers\nplay in driving galaxy evolution. At present we remain challenged to\nunderstand the relative importance of weak and strong interactions, the\ndetails of bulge formation, the existence of nearly pure-disk galaxies,\nand the merger rate as a function of redshift. Yet, some firm conclusions\nhave been reached and are as follows:\n\n\\begin{itemize}\n\\item Gravitational interactions and mergers are forming and transforming\ngalaxies throughout the observable universe. The vast majority involve\ngas, dissipation, and enhanced star formation.\n\n\\item The close link between mergers, ultra-luminous infrared galaxies,\nand quasars suggests that---like quasar activity---major merging may have\npeaked around $z\\approx 2$.\n\n\\item Major disk--disk mergers form elliptical galaxies with kinematic\nsubsystems, bimodal globular-cluster populations, and remnant fine structure.\nSuch mergers occurred relatively early near the centers of rich clusters,\nbut continue to the present time in rich-cluster outskirts, poorer clusters,\nand the field.\n\n\\item Minor mergers tend to move disk galaxies toward earlier morphological\ntypes, creating kinematic subsystems and some bulges (fraction remains\nunknown).\n\n\\item In short, the currently available evidence strongly suggests that\nHubble's morphological sequence is mainly a sequence of decreasing merger\ndamage.\n\n\\end{itemize}\n\n\\begin{acknowledgements}\nI gratefully acknowledge research support from the Carnegie Institution of\nWashington and from the National Science Foundation under Grant AST--99\\,00742.\n\\end{acknowledgements}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%% REFERENCES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{thebibliography}{}\t\t\t% Note the empty braces!\n\\item\nAbraham, R. 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}
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{
"name": "astro-ph0002263.extracted_bib",
"string": "\\begin{thebibliography}{}\t\t\t% Note the empty braces!\n\\item\nAbraham, R. G., \\etal\\ 1996, \\textit{MNRAS}, {\\bf 279}, L47.\n\\item\nAlladin, S. M. 1965, \\textit{ApJ}, {\\bf 141}, 768.\n\\item\nArnaboldi, M., \\etal\\ 1997, \\textit{AJ}, {\\bf 113}, 585.\n\\item\nArp, H. C. 1966, \\textit{Atlas of Peculiar Galaxies}. Pasadena: California\n Inst.\\ of Technology.\n\\item\nAshman, K. M. \\& Zepf, S. E. 1992, \\textit{ApJ}, {\\bf 384}, 50.\n\\item\nAshman, K. M. \\& Zepf, S. E. 1998, \\textit{Globular Cluster Systems}.\n Cambridge: Cambridge Univ.\\ Press.\n\\item\nBahcall, J. N., Kirhakos, S., Saxe, D. H. \\& Schneider, D. P. 1997,\n \\textit{ApJ}, {\\bf 479}, 642.\n\\item\nBalcells, M. \\& Gonz\\'alez, A. C. 1998, \\textit{ApJ}, {\\bf 505}, L109.\n\\item\nBarger, A. J., \\etal\\ 1996, \\textit{MNRAS}, {\\bf 279}, 1.\n\\item\nBarnes, J. E. 1988, \\textit{ApJ}, {\\bf 331}, 699.\n\\item\nBarnes, J. E. 1992, \\textit{ApJ}, {\\bf 393}, 484.\n\\item\nBarnes, J. E. 1998, in \\textit{Galaxies: Interactions and Induced Star\n Formation} (eds. D.\\ Friedli \\etal), pp.\\ 275--394. Berlin: Springer.\n\\item\nBarnes, J. E. 1999, in \\textit{Galaxy Interactions at Low and High Redshift}\n (eds.\\ J.\\ E.\\ Barnes \\& D.\\ B.\\ Sanders), pp.\\ 137--144, esp.\\ plate 4.\n Dordrecht: Kluwer.\n\\item\nBarnes, J. E. \\& Hernquist, L. E. 1992, \\textit{ARA\\&A}, {\\bf 30}, 705.\n\\item\nBarnes, J. E. \\& Hernquist, L. E. 1996, \\textit{ApJ}, {\\bf 471}, 115.\n\\item\nBekki, K. 1998, \\textit{ApJ}, {\\bf 499}, 635.\n\\item\nBender, R. 1996, in {\\it New Light on Galaxy Evolution} (eds.\\ R.\\ Bender \\&\n R.\\ L.\\ Davies), pp.\\ 181--190. Dordrecht: Kluwer.\n\\item\nBertola, F., Buson, L. M. \\& Zeilinger, W. W. 1992, \\textit{ApJ}, {\\bf 401},\n L79.\n\\item\nBertola, F., \\etal\\ 1999, \\textit{ApJ}, {\\bf 519}, L127.\n\\item\nBottema, R. 1999, \\textit{A\\&A}, {\\bf 348}, 77.\n\\item\nBraun, R., Walterbos, R. A. M., Kennicutt, R. C. \\& Tacconi, L. 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astro-ph0002264
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Optical Observations of Type II Supernovae
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"author": "Alexei V. Filippenko"
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I present an overview of optical observations (mostly spectra) of Type II supernovae. SNe~II are defined by the presence of hydrogen, and exhibit a very wide variety of properties. SNe~II-L tend to show evidence of late-time interaction with circumstellar material. SNe~IIn are distinguished by relatively narrow emission lines with little or no P-Cygni absorption component and (quite often) slowly declining light curves; they probably have unusually dense circumstellar gas with which the ejecta interact. Some SNe~IIn, however, might not be genuine SNe, but rather are super-outbursts of luminous blue variables. The progenitors of SNe~IIb contain only a low-mass skin of hydrogen; their spectra gradually evolve to resemble those of SNe~Ib. Limited spectropolarimetry thus far indicates large asymmetries in the ejecta of SNe~IIn, but much smaller ones in SNe~II-P. There is intriguing, but still inconclusive, evidence that some peculiar SNe~IIn might be associated with gamma-ray bursts. SNe~II-P are useful for cosmological distance determinations with the Expanding Photosphere Method, which is independent of the Cepheid distance scale.
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"name": "snIIreview.tex",
"string": "%\\documentstyle[epsfig,longtable]{aipproc}\n\\documentstyle[epsfig]{aipproc}\n\\pagestyle{empty}\n\n\\begin{document}\n\\input psfig.tex\n\\title{Optical Observations of Type II Supernovae}\n\n\\author{Alexei V. Filippenko}\n\\address{Department of Astronomy, University of California,\nBerkeley, CA 94720-3411}\n\\maketitle\n\n\n\\begin{abstract} \nI present an overview of optical observations (mostly spectra)\nof Type II supernovae. SNe~II are defined by the presence of hydrogen, and\nexhibit a very wide variety of properties. SNe~II-L tend to show evidence of\nlate-time interaction with circumstellar material. SNe~IIn are distinguished\nby relatively narrow emission lines with little or no P-Cygni absorption\ncomponent and (quite often) slowly declining light curves; they probably have\nunusually dense circumstellar gas with which the ejecta interact. Some SNe~IIn,\nhowever, might not be genuine SNe, but rather are super-outbursts of luminous\nblue variables. The progenitors of SNe~IIb contain only a low-mass skin of\nhydrogen; their spectra gradually evolve to resemble those of SNe~Ib. Limited\nspectropolarimetry thus far indicates large asymmetries in the ejecta of\nSNe~IIn, but much smaller ones in SNe~II-P. There is intriguing, but still\ninconclusive, evidence that some peculiar SNe~IIn might be associated with\ngamma-ray bursts. SNe~II-P are useful for cosmological distance determinations\nwith the Expanding Photosphere Method, which is independent of the \nCepheid distance scale.\n\\end{abstract}\n\n\n\\section*{ INTRODUCTION}\n\n Supernovae (SNe) occur in several spectroscopically distinct varieties; see\nreference \\cite{avf97}, for example. Type I SNe are defined by the absence of\nobvious hydrogen in their optical spectra, except for possible contamination\nfrom superposed H~II regions. SNe~II all prominently exhibit hydrogen in their\nspectra, yet the strength and profile of the H$\\alpha$ line vary widely among\nthese objects.\n\n The early-time ($t \\approx 1$ week past maximum brightness) spectra of SNe\nare illustrated in Figure 1. [Unless otherwise noted, the optical spectra\nillustrated here were obtained by my group, primarily with the 3-m Shane\nreflector at Lick Observatory. When referring to phase of evolution, the\nvariables $t$ and $\\tau$ denote time since {\\it maximum brightness} (usually in\nthe $B$ passband) and time since {\\it explosion}, respectively.] The lines are\nbroad due to the high velocities of the ejecta, and most of them have P-Cygni\nprofiles formed by resonant scattering above the photosphere. SNe~Ia are\ncharacterized by a deep absorption trough around 6150~\\AA\\ produced by\nblueshifted Si~II $\\lambda$6355. Members of the Ib and Ic subclasses do not\nshow this line. The presence of moderately strong optical He~I lines,\nespecially He~I $\\lambda$5876, distinguishes SNe~Ib from SNe~Ic.\n\n\\bigskip\n\n\\hbox{\n\\hskip +.7truein\n\\psfig{figure=figure1.ps,height=4.5truein,width=4.5truein,angle=0}\n}\n%\\bigskip\n\\noindent\n{\\it Figure 1:} Early-time spectra of SNe, showing the main subtypes.\\\\\n\\medskip\n\n The late-time ($t \\gtrsim 4$ months) optical spectra of SNe provide\nadditional constraints on the classification scheme (Figure 2). SNe~Ia show\nblends of dozens of Fe emission lines, mixed with some Co lines. SNe~Ib and\nIc, on the other hand, have relatively unblended emission lines of\nintermediate-mass elements such as O and Ca. At this phase, SNe~II are\ndominated by the strong H$\\alpha$ emission line; in other respects, most of\nthem spectroscopically resemble SNe~Ib and Ic, but with narrower emission\nlines. The late-time spectra of SNe~II show substantial heterogeneity, as do\nthe early-time spectra.\n\n To a first approximation, the light curves of SNe~I are all broadly similar\n\\cite{lei91a}, while those of SNe~II exhibit much dispersion \\cite{pat93}. It\nis useful to subdivide the majority of early-time light curves of SNe~II into\ntwo relatively distinct subclasses \\cite{bar79,dog85}. The light curves of\nSNe~II-L (``linear'') generally resemble those of SNe~I, with a steep decline\nafter maximum brightness followed by a slower exponential tail. In contrast,\nSNe~II-P (``plateau\") remain within $\\sim 1$ mag of maximum brightness for an\nextended period. The peak absolute magnitudes of SNe~II-P show a very wide\ndispersion \\cite{you89}, almost certainly due to differences in the radii of\nthe progenitor stars. The light curve of SN 1987A, albeit unusual, was\ngenerically related to those of SNe~II-P; the initial peak was very low because\nthe progenitor was a blue supergiant, much smaller than a red supergiant\n\\cite{arn89}. The remainder of this review concentrates on SNe~II. \n\n\\bigskip\n\n\\hbox{\n\\hskip +.7truein\n\\psfig{figure=figure2.ps,height=4.5truein,width=4.5truein,angle=0}\n}\n\n\\noindent\n{\\it Figure 2:} Late-time spectra of SNe. At even later phases, SN\n1987A was dominated by strong emission lines of H$\\alpha$, [O~I], [Ca~II], and\nthe Ca~II near-infrared triplet.\n\\medskip\n\n\\section*{ SUBCLASSES OF TYPE II SUPERNOVAE}\n\n Most SNe~II-P seem to have a relatively well-defined spectral development, as\nshown in Figure 3 for SN 1992H (see also reference \\cite{clo96}). At early\ntimes the spectrum is nearly featureless and very blue, indicating a high color\ntemperature ($\\gtrsim$ 10,000~K). He~I $\\lambda$5876 with a P-Cygni profile\nis sometimes visible. The temperature rapidly decreases with time, reaching\n$\\sim 5000$~K after a few weeks, as expected from the adiabatic expansion and\nassociated cooling of the ejecta. It remains roughly constant at this value\nduring the plateau (the photospheric phase), while the hydrogen recombination\nwave moves through the massive ($\\sim 10~M_\\odot$) hydrogen ejecta and releases\nthe energy deposited by the shock. At this stage strong Balmer lines and Ca~II\nH\\&K with well-developed P-Cygni profiles appear, as do weaker lines of Fe~II,\nSc~II, and other iron-group elements. The spectrum gradually takes on a nebular\nappearance as the light curve drops to the late-time tail; the continuum fades,\nbut H$\\alpha$ becomes very strong, and prominent emission lines of [O~I],\n[Ca~II], and Ca~II also appear.\n\n\\bigskip\n\n\\hbox{\n\\hskip +1truein\n\\psfig{figure=figure3.ps,height=5truein,width=4truein,angle=0}\n}\n\n\\noindent\n{\\it Figure 3:} Montage of spectra of SN 1992H in NGC 5377. Epochs\n(days) are given relative to the estimated time of explosion,\nFebruary 8, 1992.\n\\medskip\n\n Few SNe~II-L have been observed in as much detail as SNe~II-P. Figure 4\nshows the spectral development of SN 1979C \\cite{bra81}, an unusually luminous\nmember of this subclass. Near maximum brightness the spectrum is very blue and\nalmost featureless, with a slight hint of H$\\alpha$ emission. A week later,\nH$\\alpha$ emission is more easily discernible, and low-contrast P-Cygni\nprofiles of Na~I, H$\\beta$, and Fe~II have appeared. By $t \\approx 1$ month,\nthe H$\\alpha$ emission line is very strong but still devoid of an absorption\ncomponent, while the other features clearly have P-Cygni profiles. Strong,\nbroad H$\\alpha$ emission dominates the spectrum at $t \\approx 7$ months, and\n[O~I] $\\lambda\\lambda$6300, 6364 emission is also present. Several authors\n\\cite{whe90,avf91a,sch96} have speculated that the absence of H$\\alpha$\nabsorption spectroscopically differentiates SNe~II-L from SNe~II-P, but the\nsmall size of the sample of well-observed objects precluded definitive\nconclusions.\n\n\\bigskip\n\n\\hbox{\n\\hskip +1truein\n\\psfig{figure=figure4.ps,height=5truein,width=4truein,angle=0}\n}\n\n\\noindent\n{\\it Figure 4:} Montage of spectra of SN 1979C in NGC 4321, from\nreference \\cite{bra81}; reproduced with permission. Epochs\n(days) are given relative to the date of maximum brightness,\nApril 15, 1979.\n\\medskip\n\n The progenitors of SNe~II-L are generally believed to have relatively\nlow-mass hydrogen envelopes (a few $M_\\odot$); otherwise, they would exhibit\ndistinct plateaus, as do SNe~II-P. On the other hand, they may have more\ncircumstellar gas than do SNe~II-P, and this could give rise to the\nemission-line dominated spectra. They are often radio sources \\cite{sra90};\nmoreover, the ultraviolet excess (at $\\lambda \\lesssim 1600$~\\AA) seen in SNe\n1979C and 1980K may be produced by inverse Compton scattering of photospheric\nradiation by high-speed electrons in shock-heated ($T \\approx 10^9$~K)\ncircumstellar material \\cite{fra82,fra84}. Finally, the light curves of some\nSNe~II-L reveal an extra source of energy: after declining exponentially for\nseveral years, the H$\\alpha$ flux of SN 1980K reached a steady level, showing\nlittle if any decline thereafter \\cite{uom86,lei91b}. The excess almost\ncertainly comes from the kinetic energy of the ejecta being thermalized and\nradiated due to an interaction with circumstellar matter \\cite{che90,lei94}.\n\n The very late-time optical recovery of SNe 1979C and 1980K\n\\cite{lei91b,fes95,fes99} and other SNe~II-L supports the idea of ejecta\ninteracting with circumstellar material. The spectra consist of a few strong,\nbroad emission lines such as H$\\alpha$, [O~I] $\\lambda\\lambda$6300, 6364, and\n[O~III] $\\lambda\\lambda$4959, 5007. A {\\it Hubble Space Telescope (HST)}\nultraviolet spectrum of SN 1979C reveals some prominent, double-peaked emission\nlines with the blue peak substantially stronger than the red, suggesting dust\nextinction within the expanding ejecta \\cite{fes99}. The data show general\nagreement with the emission lines expected from circumstellar interaction\n\\cite{che94}, but the specific models that are available show several\ndifferences with the observations. For example, we find higher electron\ndensities ($10^5$ to $10^7$ cm$^{-3}$), resulting in stronger collisional\nde-excitation than assumed in the models. These differences can be used to\nfurther constrain the nature of the progenitor star. Note that based on\nphotometry of the stellar populations in the environment of SN 1979C (from {\\it\nHST} images), the progenitor of the SN was at most 10 million years years old,\nso its initial mass was probably 17--18~$M_\\odot$ \\cite{van99a}.\n\n During the past decade, there has been the gradual emergence of a new,\ndistinct subclass of SNe~II \\cite{avf91a,avf91b,sch90,lei94} whose ejecta are\nbelieved to be {\\it strongly} interacting with dense circumstellar gas, even at\nearly times (unlike SNe~II-L). The derived mass-loss rates for the progenitors\ncan exceed $10^{-4} M_\\odot$ yr$^{-1}$ \\cite{chu94}. In these objects, the\nbroad absorption components of all lines are weak or absent throughout their\nevolution. Instead, their spectra are dominated by strong emission lines, most\nnotably H$\\alpha$, having a complex but relatively narrow profile. Although the\ndetails differ among objects, H$\\alpha$ typically exhibits a very narrow\ncomponent (FWHM $\\lesssim 200$ km s$^{-1}$) superposed on a base of\nintermediate width (FWHM $\\approx$ 1000--2000 km s$^{-1}$; sometimes a very\nbroad component (FWHM $\\approx$ 5000--10,000 km s$^{-1}$) is also present. This\nsubclass was christened ``Type IIn\" \\cite{sch90}, the ``n\" denoting ``narrow\"\nto emphasize the presence of the intermediate-width or very narrow emission\ncomponents. Representative spectra of five SNe~IIn are shown in Figure 5, with\ntwo epochs for SN 1994Y.\n\n The early-time continua of SNe~IIn tend to be bluer than normal.\nOccasionally He~I emission lines are present in the first few spectra (e.g., SN\n1994Y in Figure 5). Very narrow Balmer absorption lines are visible in the\nearly-time spectra of some of these objects, often with corresponding Fe~II,\nCa~II, O~I, or Na~I absorption as well (e.g., SNe 1994W and 1994ak in Figure\n5). Some of them are unusually luminous at maximum brightness, and they\ngenerally fade quite slowly, at least at early times. The equivalent width of\nthe intermediate H$\\alpha$ component can grow to astoundingly high values at\nlate times. The great diversity in the observed characteristics of SNe~IIn\nprovides clues to the various degrees and forms of mass loss late in the lives\nof massive stars.\n\n\\bigskip\n\n\\hbox{\n\\hskip +0.6truein\n\\psfig{figure=figure5.ps,height=5.5truein,width=4.5truein,angle=0}\n}\n\\bigskip\n\\noindent\n{\\it Figure 5:} Montage of spectra of SNe~IIn. Epochs are given relative \nto the estimated dates of explosion.\\\\\n\n\\bigskip\n\n\\section*{ TYPE II SUPERNOVA IMPOSTORS?}\n\n The peculiar SN~IIn 1961V (``Type V\" according to Zwicky \\cite{zwi65}) had\nprobably the most bizarre light curve ever recorded. (SN 1954J, also known as\n``Variable 12\" in NGC 2403, was similar \\cite{hum94}.) Its progenitor was a\nvery luminous star, visible in many photographs of the host galaxy (NGC 1058)\nprior to the explosion. Perhaps SN 1961V was not a genuine supernova (defined\nto be the violent destruction of a star at the end of its life), but rather the\nsuper-outburst of a luminous blue variable such as $\\eta$ Carinae\n\\cite{goo89,avf95}.\n\n A related object may have been SN~IIn 1997bs, the first SN discovered in the\nLick Observatory Supernova Search (LOSS) that we are conducting with the 0.75-m\nKatzman Automatic Imaging Telescope (KAIT) at Lick Observatory \\cite{wli00}.\nIts spectrum was peculiar (Figure 6), consisting of narrow Balmer and Fe~II\nemission lines superposed on a featureless continuum. Its progenitor was\ndiscovered in an {\\it HST} archival image of the host galaxy \\cite{van99b}. It\nis a very luminous star ($M_V \\approx -7.4$ mag), and it didn't brighten as\nmuch as expected for a SN explosion ($M_V \\approx -13$ at maximum). These data\nsuggest that SN 1997bs may have been like SN 1961V --- that is, a supernova\nimpostor. The real test will be whether the star is still visible in future\n{\\it HST} images obtained years after the outburst.\n\n\\bigskip\n\n\\hbox{\n\\hskip +0.3truein\n\\psfig{figure=figure6.ps,height=5truein,width=3truein,angle=90}\n}\n\\bigskip\n\\noindent\n{\\it Figure 6:} Spectrum of SN 1997bs, obtained on April 16, 1997 UT.\\\\\n\n\\bigskip\n\n\\section*{ LINKS BETWEEN TYPE II AND TYPE Ib/Ic SUPERNOVAE}\n\n Filippenko \\cite{avf88} discussed the case of SN 1987K, which appeared to be\na link between SNe~II and SNe~Ib. Near maximum brightness, it was undoubtedly a\nSN~II, but with rather weak photospheric Balmer and Ca~II lines. Many months\nafter maximum brightness, its spectrum was essentially that of a SN~Ib. The\nsimplest interpretation is that SN 1987K had a meager hydrogen atmosphere at\nthe time it exploded; it would naturally masquerade as a SN~II for a while, and\nas the expanding ejecta thinned out the spectrum would become dominated by\nemission from deeper and denser layers. The progenitor was probably a star\nthat, prior to exploding via iron core collapse, lost almost all of its\nhydrogen envelope either through mass transfer onto a companion or as a result\nof stellar winds. Such SNe were dubbed ``SNe~IIb\" by Woosley et\nal. \\cite{woo87}, who had proposed a similar preliminary model for SN 1987A\nbefore it was known to have a massive hydrogen envelope.\n\n\\bigskip\n\n\\hbox{\n\\hskip +0.3truein\n\\psfig{figure=figure7.ps,height=5truein,width=5truein,angle=0}\n}\n\\bigskip\n\\noindent\n{\\it Figure 7:} Early-time spectral evolution of SN 1993J. A comparison\nwith the Type Ib SN 1984L is shown at bottom, demonstrating the\npresence of He~I lines in SN 1993J. The explosion date was\nMarch 27.5, 1993.\\\\\n\n\\bigskip\n\n The data for SN 1987K (especially its light curve) were rather sparse,\nmaking it difficult to model in detail. Fortunately, the Type II SN 1993J in\nNGC 3031 (M81) came to the rescue, and was studied in greater detail than any\nsupernova since SN 1987A \\cite{whe96}. Its light curves \\cite{ric96} and\nspectra \\cite{avf93,avf94,mat00} amply supported the hypothesis that the\nprogenitor of SN 1993J probably had a low-mass (0.1--0.6~$M_\\odot$) hydrogen\nenvelope above a $\\sim 4~M_\\odot$ He core \\cite{nom93,pod93,woo94}. Figure 7\nshows several early-time spectra of SN 1993J, showing the emergence of He~I\nfeatures typical of SNe~Ib. Considerably later (Figure 8), the H$\\alpha$\nemission nearly disappeared, and the spectral resemblance to SNe~Ib was\nstrong. The general consensus is that its initial mass was $\\sim\n15~M_\\odot$. A star of such low mass cannot shed nearly its entire hydrogen\nenvelope without the assistance of a companion star. Thus, the progenitor of SN\n1993J probably lost most of its hydrogen through mass transfer to a bound\ncompanion 3--20~AU away. In addition, part of the gas may have been lost from\nthe system. Had the progenitor lost essentially {\\it all} of its hydrogen\nprior to exploding, it would have had the optical characteristics of\nSNe~Ib. There is now little doubt that most SNe~Ib, and probably\nSNe~Ic as well, result from core collapse in stripped, massive stars, rather\nthan from the thermonuclear runaway of white dwarfs.\n\n\n SN 1993J held several more surprises. Observations at radio \\cite{van94} and\nX-ray \\cite{suz95} wavelengths revealed that the ejecta are interacting with\nrelatively dense circumstellar material \\cite{fra96}, probably ejected from the\nsystem during the course of its pre-SN evolution. Optical evidence for this\ninteraction also began emerging at $\\tau \\gtrsim 10$ months: the H$\\alpha$\nemission line grew in relative prominence, and by $\\tau \\approx 14$ months it\nhad become the dominant line in the spectrum \\cite{avf94,pat95,fin95},\nconsistent with models \\cite{che94}. Its profile was very broad (FWHM\n$\\approx$ 17,000 km s$^{-1}$; Figure 8) and had a relatively flat top, but with\nprominent peaks and valleys whose likely origin is Rayleigh-Taylor\ninstabilities in the cool, dense shell of gas behind the reverse shock\n\\cite{che92}. Radio VLBI measurements show that the ejecta are circularly\nsymmetric, but with significant emission asymmetries \\cite{mar95}, possibly\nconsistent with the asymmetric H$\\alpha$ profile seen in some of the spectra\n\\cite{avf94}.\n\n\\bigskip\n\n\\hbox{\n\\hskip +0.3truein\n\\psfig{figure=figure8.ps,height=5truein,width=3truein,angle=90}\n}\n\\bigskip\n\\noindent\n{\\it Figure 8:} In the {\\it top} spectrum, which shows SN 1993J about 7\nmonths after the explosion, H$\\alpha$ emission is very weak; the\nresemblance to spectra of SNe~Ib is striking. A year later ({\\it bottom}), \nhowever, H$\\alpha$ was once again the dominant feature\nin the spectrum (which was scaled for display purposes).\\\\\n\n\\bigskip\n\n\\section*{ SPECTROPOLARIMETRY OF TYPE II SUPERNOVAE}\n\n Spectropolarimetry of SNe can be used to probe their geometry\n\\cite{leo00a}. The basic question is whether SNe are round. Such work is\nimportant for a full understanding of the physics of SN explosions and can\nprovide information on the circumstellar environment of SNe. We have obtained\nspectropolarimetry of one object from each of the major SN types and subtypes,\ngenerally with the Keck-II 10-m telescope.\n\n\\bigskip\n\n\\hbox{\n\\hskip +1truein\n\\psfig{figure=figure9.ps,height=5truein,width=4truein,angle=0}\n}\n\\bigskip\n\\noindent\n{\\it Figure 9:} Polarization data for SN 1998S, obtained with Keck-II on \nMarch 7, 1998. {\\it (a)} Total flux, in units of $10^{-15}$ ergs s$^{-1}$\ncm$^{-2}$ \\AA$^{-1}$. {\\it (b)} Observed degree of polarization. {\\it (c,d)} The\nnormalized $q$ and $u$ Stokes parameters, with prominent narrow-line\nfeatures indicated. {\\it (e)} Average of the (nearby identical) $1\\sigma$\nstatistical uncertainties in the Stokes $q$ and $u$ parameters. See\nreference \\cite{leo00b} for details.\\\\\n\n\\bigskip\n \n We have completed our analysis of the peculiar Type IIn SN 1998S\n\\cite{leo00b}. The data consist of one epoch of spectropolarimetry (5 days\nafter discovery) and total flux spectra spanning the first 494 days after\ndiscovery. The SN is found to exhibit a high degree of linear polarization\n(Figure 9), implying significant asphericity for its continuum-scattering\nenvironment. Prior to removal of the interstellar polarization, the\npolarization spectrum is characterized by a flat continuum (at $p \\approx 2\\%$)\nwith distinct changes in polarization associated with both the broad\n(symmetric, half width near-zero intensity $\\gtrsim 10,000$ km s$^{-1}$) and\nnarrow (unresolved, FWHM $< 300$ km s$^{-1}$) line emission seen in the total\nflux spectrum. When analyzed in terms of a polarized continuum with\nunpolarized broad-line recombination emission, however, an intrinsic continuum\npolarization of $p \\approx 3\\%$ results, suggesting a global asphericity of\n$\\gtrsim 45\\%$ from the oblate, electron-scattering dominated models of\nH\\\"{o}flich \\cite{hof91}. The smooth, blue continuum evident at early times is\ninconsistent with a reddened, single-temperature blackbody, instead having a\ncolor temperature that increases with decreasing wavelength. Broad\nemission-line profiles with distinct blue and red peaks are seen in the total\nflux spectra at later times, suggesting a disk-like or ring-like morphology for\nthe dense ($n_e \\approx 10^7 {\\rm\\ cm^{-3}}$) circumstellar medium, generically\nsimilar to what is seen directly in SN 1987A, although much denser and closer\nto the progenitor in SN 1998S.\n\n The Type IIn SN 1997eg also exhibits considerable polarization \\cite{leo00a};\nthere are sharp polarization changes across its strong, multi-component\nemission lines, suggesting distinct scattering origins for the different\ncomponents. Based on our rather small sample, it appears as though SNe~II-P are\nconsiderably less polarized than SNe~IIn, at least within the first month or\ntwo after the explosion. Leonard et al. \\cite{leo00a} show some\nspectropolarimetric evidence of asphericity in the ejecta of SN II-P 1997ds,\nbut it does not match the degree of polarization of SNe~IIn 1998S and 1997eg.\nMoreover, SN II-P 1999em does not reveal significant polarization variation\nacross the strong Balmer lines shortly after its explosion \\cite{leo99}.\n\n\\section*{ SUPERNOVAE ASSOCIATED WITH GAMMA-RAY BURSTS?}\n\n At least a small fraction of gamma-ray bursts (GRBs) may be associated with\nnearby SNe. Probably the most compelling example thus far is that of SN 1998bw\nand GRB 980425 \\cite{gal98,iwa98,woo99}, which were temporally and spatially\ncoincident. SN 1998bw was, in many ways, an extraordinary SN; it was very\nluminous at optical and radio wavelengths, and it showed evidence for\nrelativistic outflow. Its bizarre optical spectrum is often classified as that\nof a SN~Ic, but the object should be called a ``peculiar SN~Ic\" if not a\nsubclass of its own; the spectrum was distinctly different from that of a\nnormal SN~Ic.\n\n As discussed by several speakers at this meeting, models suggest that SNe\nassociated with GRBs are highly asymmetric. Thus, spectropolarimetry should\nprovide some useful tests. In particular, perhaps objects such as SN 1998S,\ndiscussed above, would have been seen as GRBs had their rotation axis been\npointed in our direction. That of SN 1998S was almost certainly {\\it not}\naligned with us \\cite{leo00b}; both the spectropolarimetry and the appearance\nof double-peaked H$\\alpha$ emission suggest an inclined view, rather than\npole-on.\n\n\\bigskip\n\n\\hbox{\n\\hskip +0.3truein\n\\psfig{figure=figure10.ps,height=5truein,width=4.5truein,angle=0}\n\\hskip +.3truein\n}\n\\noindent\n{\\it Figure 10:} Spectral evolution of SN 1999E, which may have been\nassociated with GRB 980910.\n\\medskip\n\n The case of GRB 970514 and the very luminous SN IIn 1997cy is also\ninteresting \\cite{ger00,tur00}; there is a reasonable possibility that the two\nobjects were associated. The optical spectrum of SN 1997cy was highly unusual,\nand bore some resemblance to that of SN 1998bw, though there were some\ndifferences as well. SN 1999E, which might be linked with GRB 980910 but with\nlarge uncertainties \\cite{tho99}, also had an optical spectrum similar to that\nof SN 1997cy \\cite{avf99,cap99}; see Figure 10. The undulations are very\nbroad, indicating high ejection velocities. Besides H$\\alpha$, secure line\nidentifications are difficult, though some of the emission features seem to be\nassociated with oxygen and calcium. Perhaps SN 1999E was produced by the highly\nasymmetric collapse of a carbon-oxygen core.\n\n Shortly before this meeting, SN~IIn 1999eb was discovered with KAIT\n\\cite{mod99}, and Terlevich et al. \\cite{ter99} pointed out that it might be\nassociated with GRB 991002. However, KAIT data show that the optical SN was\nvisible at least 10 days {\\it before} the GRB occurred, making it very unlikely\nthat the two were linked. If SN 1999eb ends up showing double-peaked H$\\alpha$\nemission at late times, as did SN 1998S, it will be another argument against\nthe SN/GRB association in this particular case, since our view will not have\nbeen pole-on.\n\n\\section*{ THE EXPANDING PHOTOSPHERE METHOD}\n\n Despite {\\it not} being anything like ``standard candles,\" SNe~II-P (and\nsome SNe~II-L) are very good distance indicators. They are, in fact, ``custom\nyardsticks\" when calibrated with the ``Expanding Photosphere Method\" (EPM); see\n\\cite{eas96}. A variant of the famous Baade-Wesselink method for determining\nthe distances of pulsating variable stars, this technique relies on an accurate\nmeasurement of the photosphere's effective temperature and velocity during the\nplateau phase of SNe~II-P.\n\n Briefly, here is how EPM works. The radius ($R$) of the photosphere can be\ndetermined from its velocity ($v$) and time since explosion ($t - t_0$) if the\nejecta are freely expanding: $R = v(t - t_0) + R_0 \\approx v(t - t_0)$,\nwhere we have assumed that the initial radius of the star ($R_0$ at $t =\nt_0$) is negligible relative to $R$ after a few days. The velocity of\nthe photosphere is determined from measurements of the wavelengths of the\nabsorption minima in P-Cygni profiles of weak lines such as those of Fe~II\nor, better yet, Sc~II. (The absorption minima of strong lines like\nH$\\alpha$ form far above the photosphere.) The angular size ($\\theta$) of\nthe photosphere, on the other hand, is found from the measured, dereddened\nflux density ($f_\\nu$) at a given frequency. We have $4 \\pi D^2 f_\\nu = \n4 \\pi R^2 \\zeta^2 \\pi B_\\nu (T)$, so\n\n\\[ \\theta = {R\\over D} = \\left[{f_\\nu \\over {\\zeta^2 \\pi \nB_\\nu (T)}}\\right]^{1/2}, \\]\n \n\\noindent\nwhere $D$ is the distance to the supernova, $B_\\nu (T)$ is the value \nof the Planck function at color temperature $T$ (derived from broadband\nmeasurements of the supernova's brightness in at least two passbands),\nand $\\zeta^2$ is the flux dilution correction factor (basically a measure\nof how much the spectrum deviates from that of a blackbody, due primarily\nto the electron-scattering opacity). \n\n The above two equations imply that $t = D(\\theta/v) + t_0.$ Thus, for a\nseries of measurements of $\\theta$ and $v$ at various times $t$, a plot of\n$\\theta/v$ versus $t$ should yield a straight line of slope $D$ and intercept\n$t_0$. This determination of the distance is independent of the various\nuncertain rungs in the cosmological distance ladder; it does not even depend on\nthe calibration of the Cepheids. It is equally valid for nearby and distant\nSNe~II-P.\n\n An important check of EPM is that the derived distance be {\\it constant}\nwhile the SN is on the plateau (before it has started to enter the nebular\nphase). This has been verified with SN 1987A \\cite{eas89} and a number of\nother SNe~II-P \\cite{schmidt92,schmidt94a}. Moreover, the EPM distance to SN\n1987A agrees with that determined geometrically through measurements of the\nbrightening and fading of emission lines from the inner circumstellar ring\n\\cite{pan91}. It\nis also noteworthy that EPM is relatively insensitive to reddening: an\nunderestimate of the reddening leads to an underestimate of the color\ntemperature $T$ [and hence of $B_\\nu (T)$ as well], but this is compensated by\nan underestimate of $f_\\nu$, yielding a nearly unchanged value of\n$\\theta$. Indeed, for errors in $A_V$ [the visual extinction, or\n$\\sim 3.1 E(B-V)$] of 0--1 mag, one incurs an error in $D$ of only\n$\\sim 0$--20\\% \\cite{schmidt92}.\n\n Of course, EPM has some caveats or potential limitations. A critical\nassumption is spherical symmetry for the expanding ejecta, yet polarimetry\nshows that SN 1987A was not spherical \\cite{jef91}, as do direct {\\it HST}\nmeasurements of the shape of the ejecta. As discussed above, the few other\nSNe~II-P that have been studied don't show very much polarization, though it is\npossible that deviations from spherical symmetry could be a severe problem for\nsome SNe~II-P. On the other hand, the {\\it average} distance derived with EPM\nfor many SNe~II-P might be almost unaffected, given random orientations to the\nline of sight. (Sometimes the cross-sectional area will be too large, and other\ntimes too small, relative to spherical ejecta.) Indeed, comparison of EPM and\nCepheid distances to the same galaxies shows agreement to within the expected\nuncertainties for a sample of 6 objects ($D_{\\rm Cepheids}/D_{\\rm EPM} = 0.98\n\\pm 0.08$; \\cite{eas96}).\n\n Another limitation of EPM is that one needs a well-observed SN~II-P in a\ngiven galaxy in order to measure its distance; thus, the technique is most\nuseful for aggregate studies of galaxies, rather than for distances of specific\ngalaxies in a random sample. Finally, knowledge of the flux dilution correction\nfactor, $\\zeta^2$, is critical to the success of EPM. Fortunately, an\nextensive grid of models \\cite{eas96} shows that the value of $\\zeta^2$ is\nmainly a function of $T$ during the plateau phase of SNe~II-P; it is relatively\ninsensitive to other variables such as helium abundance, metallicity, density\nstructure, and expansion rate. Also, it does not differ too greatly from unity\nduring the plateau. There are, however, some differences of opinion regarding\nthe treatment of radiative transfer and thermalization in expanding supernova\natmospheres \\cite{bar96}. The calculations are difficult and various\nassumptions are made, possibly leading to significant systematic errors.\n\n The most distant SN~II-P to which EPM has successfully been applied is SN\n1992am at $z = 0.0487$ \\cite{schmidt94b}. The derived distance is $D =\n180^{+30}_{-25}$ Mpc. This object, together with 15 other SNe~II-P at smaller\nredshifts, yields a best fit value of $H_0 = 73 \\pm 7$ km s$^{-1}$ Mpc$^{-1}$,\nwhere the quoted uncertainty is purely statistical \\cite{schmidt94a,eas96}. A\nsystematic uncertainty of $\\sim \\pm 6$ km s$^{-1}$ Mpc$^{-1}$ should also be\nassociated with the above result. The main source of statistical uncertainty\nis the relatively small number of SNe~II-P in the EPM sample, and the low\nredshift of most of the objects (whose radial velocities are substantially\naffected by peculiar motions). My group is currently trying to remedy the\nsituation with EPM measurements of additional nearby SNe~II-P (at Lick\nObservatory), as well as with Keck spectra of SNe~II-P in the redshift range\n0.1--0.3.\n\n\\section*{ ACKNOWLEDGMENTS}\n\n My recent research on SNe has been financed by NSF grant AST--9417213, as\nwell as by NASA grants GO-6584, GO-7434, AR-6371, and AR-8006 from the Space\nTelescope Science Institute, which is operated by AURA, Inc., under NASA\nContract NAS5-26555. The Committee on Research (U.C. Berkeley) provided partial\ntravel support to attend this meeting. I am grateful to the students and\npostdocs who have worked with me on SNe over the past 14 years for their\nassistance and discussions. Tom Matheson and Doug Leonard were especially\nhelpful with the figures for this review.\n\n\\begin{references}\n\n\\bibitem{avf97}Filippenko, A. V., {\\it ARAA}, {\\bf 35}, 309 (1997).\n\\bibitem{lei91a}Leibundgut, B., Tammann, G. 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P., {\\it ApJ}, {\\bf 347}, \n 771 (1989).\n\\bibitem{schmidt92}Schmidt, B. P., Kirshner, R. P., Eastman, R. G., {\\it ApJ}, \n {\\bf 395}, 366 (1992).\n\\bibitem{schmidt94a}Schmidt, B. P., {\\it et al.}, {\\it ApJ}, {\\bf 432}, 42 \n (1994a).\n\\bibitem{pan91}Panagia, N., {\\it et al.}, {\\it ApJ}, {\\bf 380}, L23 \n (1991).\n\\bibitem{jef91}Jeffery, D. J., {\\it ApJ}, {\\bf 375}, 264 (1991).\n\\bibitem{bar96}Baron, E., Hauschildt, P. H., \\& Mezzacappa, A., \n {\\it MNRAS}, {\\bf 278}, 763 (1996).\n\\bibitem{schmidt94b}Schmidt, B. P., {\\it et al.}, {\\it AJ}, {\\bf 107}, \n 1444 (1994b).\n\n\\end{references}\n\n\\end{document}\n"
}
] |
[
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"name": "astro-ph0002264.extracted_bib",
"string": "\\bibitem{avf97}Filippenko, A. V., {\\it ARAA}, {\\bf 35}, 309 (1997).\n\n\\bibitem{lei91a}Leibundgut, B., Tammann, G. A., Cadonau, R., \\& Cerrito, D., \n {\\it A\\&AS}, {\\bf 89}, 537 (1991a).\n\n\\bibitem{pat93}Patat, F., Barbon, R., Cappellaro, E., \\& Turatto, M., \n {\\it A\\&AS}, {\\bf 98}, 443 (1993).\n\n\\bibitem{bar79}Barbon, R., Ciatti, F., \\& Rosino, L. {\\it A\\&A}, {\\bf 72},\n 287 (1979).\n\n\\bibitem{dog85}Doggett, J. B., \\& Branch, D., {\\it AJ}, {\\bf 90}, 2303 (1985).\n\n\\bibitem{you89}Young, T. R., \\& Branch, D., {\\it ApJ}, {\\bf 342}, L79 (1989).\n\n\\bibitem{arn89}Arnett, W. D., Bahcall, J. N., Kirshner, R. P., \\& Woosley, \n S. E., {\\it ARAA}, {\\bf 27}, 629 (1989).\n\n\\bibitem{clo96}Clocchiatti, A., et al., {\\it AJ}, {\\bf 111}, 1286 (1996). \n\n\\bibitem{bra81}Branch, D., Falk, S. W., McCall, M. L., Rybski, P., Uomoto, \n A. K., \\& Wills, B. J., {\\it ApJ}, {\\bf 224}, 780 (1981).\n\n\\bibitem{whe90}Wheeler, J. C., \\& Harkness, R. 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McLaughlin, pp. 367. Chicago: Univ. Chicago Press \n (1965).\n\n\\bibitem{hum94}Humphreys, R. M., \\& Davidson, K., {\\it PASP}, {\\bf 106}, \n 1025 (1994).\n\n\\bibitem{goo89}Goodrich, R. W., Stringfellow, G. S., Penrod, G. D., \\& \n Filippenko, A. V., {\\it ApJ}, {\\bf 342}, 908 (1989).\n\n\\bibitem{avf95}Filippenko, A. V., et al., {\\it AJ}, {\\bf 110}, 2261 (1995) \n [Erratum: {\\bf 112}, 806].\n\n\\bibitem{wli00}Li, W. D., et al., {\\it These Proceedings} (2000).\n\n\\bibitem{van99b}Van Dyk, S. D., Peng, C. Y., Barth, A. J., \\& Filippenko, \n A. V., {\\it AJ}, {\\bf 118}, 2331 (1999b).\n\n\\bibitem{avf88}Filippenko, A. V., {\\it AJ}, {\\bf 96}, 1941 (1988).\n\n\\bibitem{woo87}Woosley, S. E., Pinto, P. A., Martin, P. G., \\& Weaver, T. A., \n {\\it ApJ}, {\\bf 318}, 664 (1987).\n\n\\bibitem{whe96}Wheeler, J. C., \\& Filippenko, A. V., in {\\it Supernovae and \n Supernova Remnants}, eds. R. McCray \\& Z. 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J., \\& Matheson, \n T., {\\it ApJ}, in press, astro-ph/9908040 (2000b).\n\n\\bibitem{hof91}H\\\"{o}flich, P., {\\it A\\&A}, {\\bf 246}, 481 (1991).\n\n\\bibitem{leo99}Leonard, D. C., Filippenko, A. V., \\& Chornock, R. T., {\\it IAU \n Circ.} 7305 (1999).\n\n\\bibitem{gal98}Galama, T. J., et al., {\\it Nature}, {\\bf 395}, 670 (1998).\n\n\\bibitem{iwa98}Iwamoto, K., et al., {\\it Nature}, {\\bf 395}, 672 (1998).\n\n\\bibitem{woo99}Woosley, S. E., Eastman, R. G., \\& Schmidt, B. P., {\\it ApJ}, \n {\\bf 516}, 788 (1999).\n\n\\bibitem{ger00}Germany, L. M., et al., {\\it ApJ}, in press, astro-ph/9906096 \n (2000).\n\n\\bibitem{tur00}Turatto, M., et al., astro-ph/9910324 (2000).\n\n\\bibitem{tho99}Thorsett, S. E., \\& Hogg, D. W., {\\it GCN Circ.} 197 (1999).\n\n\\bibitem{avf99}Filippenko, A. V., Leonard, D. C., \\& Riess, A. G., {\\it IAU \n Circ.} 7091 (1999).\n\n\\bibitem{cap99}Cappellaro, E., Turatto, M., \\& Mazzali, P., {\\it IAU Circ.} \n 7091 (1999).\n\n\\bibitem{mod99}Modjaz, M., et al., {\\it IAU Circ.} 7268 (1999).\n\n\\bibitem{ter99}Terlevich, R., Fabian, A., \\& Turatto, M., {\\it IAU Circ.} \n 7269 (1999).\n\n\\bibitem{eas96}Eastman, R. G., Schmidt, B. P., \\& Kirshner, R. P., {\\it ApJ}, \n {\\bf 466}, 911 (1996).\n\n\\bibitem{eas89}Eastman, R. G., \\& Kirshner, R. P., {\\it ApJ}, {\\bf 347}, \n 771 (1989).\n\n\\bibitem{schmidt92}Schmidt, B. P., Kirshner, R. P., Eastman, R. G., {\\it ApJ}, \n {\\bf 395}, 366 (1992).\n\n\\bibitem{schmidt94a}Schmidt, B. P., {\\it et al.}, {\\it ApJ}, {\\bf 432}, 42 \n (1994a).\n\n\\bibitem{pan91}Panagia, N., {\\it et al.}, {\\it ApJ}, {\\bf 380}, L23 \n (1991).\n\n\\bibitem{jef91}Jeffery, D. J., {\\it ApJ}, {\\bf 375}, 264 (1991).\n\n\\bibitem{bar96}Baron, E., Hauschildt, P. H., \\& Mezzacappa, A., \n {\\it MNRAS}, {\\bf 278}, 763 (1996).\n\n\\bibitem{schmidt94b}Schmidt, B. P., {\\it et al.}, {\\it AJ}, {\\bf 107}, \n 1444 (1994b).\n\n"
}
] |
astro-ph0002265
|
Hard X-Ray Spectra of Broad-Line Radio Galaxies from the Rossi X-Ray Timing Explorer
|
[
{
"author": "Michael Eracleous \\& Rita Sambruna"
}
] |
%======== Added by Mike to justify the text on the right side \rightskip 0pt \pretolerance=100 \noindent We present the results of hard-X-ray observations of four broad-line radio galaxies (BLRGs) with the {Rossi X-Ray Timing Explorer} ({RXTE}). The original motivation behind the observations was to search for systematic differences between the BLRGs and their radio-quiet counterparts, the Seyfert galaxies. We do, indeed, find that the Fe~K$\alpha$ lines and Compton ``reflection'' components, which are hallmarks of the X-ray spectra of Seyferts galaxies, are weaker in BLRGs by about a factor of 2. This observational result is in agreement with the conclusions of other recent studies of these objects. We examine several possible explanations for this systematic difference, including beaming of the primary X-rays away from the accretion disk, a low iron abundance, a small solid angle subtended by the disk to the primary X-ray source, and dilution of the observed spectrum by beamed X-rays from the jet. We find that a small solid angle subtended by the disk to the primary X-ray source is a viable and appealing explanation, while all others suffer from drawbacks. We interpret this as an indication of a difference in the inner accretion disk structure between Seyfert galaxies and BLRGs, namely that the inner accretion disks of BLRGs have the form of an ion-supported torus or an advection-dominated accretion flow, which irradiates the geometrically thin outer disk.
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[
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Daniel Smith, 9 October 1990.\n%\n\\newread\\ps@stream\n\\newif\\ifnot@eof % continue looking for the bounding box?\n\\newif\\if@noisy % report what you're making?\n\\newif\\if@atend % %%BoundingBox: has (at end) specification\n\\newif\\if@psfile % does this look like a PostScript file?\n%\n% PostScript files should start with `%!'\n%\n{\\catcode`\\%=12\\global\\gdef\\epsf@start{%!}}\n\\def\\epsf@PS{PS}\n%\n\\def\\epsf@getbb#1{%\n%\n% The first thing we need to do is to open the\n% PostScript file, if possible.\n%\n\\openin\\ps@stream=#1\n\\ifeof\\ps@stream\\ps@typeout{Error, File #1 not found}\\else\n%\n% Okay, we got it. Now we'll scan lines until we find one that doesn't\n% start with %. We're looking for the bounding box comment.\n%\n {\\not@eoftrue \\chardef\\other=12\n \\def\\do##1{\\catcode`##1=\\other}\\dospecials \\catcode`\\ =10\n \\loop\n \\if@psfile\n\t \\read\\ps@stream to \\epsf@fileline\n \\else{\n\t \\obeyspaces\n \\read\\ps@stream to \\epsf@tmp\\global\\let\\epsf@fileline\\epsf@tmp}\n \\fi\n \\ifeof\\ps@stream\\not@eoffalse\\else\n%\n% Check the first line for `%!'. Issue a warning message if its not\n% there, since the file might not be a PostScript file.\n%\n \\if@psfile\\else\n \\expandafter\\epsf@test\\epsf@fileline:. \\\\%\n \\fi\n%\n% We check to see if the first character is a % sign;\n% if so, we look further and stop only if the line begins with\n% `%%BoundingBox:' and the `(atend)' specification was not found.\n% That is, the only way to stop is when the end of file is reached,\n% or a `%%BoundingBox: llx lly urx ury' line is found.\n%\n \\expandafter\\epsf@aux\\epsf@fileline:. \\\\%\n \\fi\n \\ifnot@eof\\repeat\n }\\closein\\ps@stream\\fi}%\n%\n% This tests if the file we are reading looks like a PostScript file.\n%\n\\long\\def\\epsf@test#1#2#3:#4\\\\{\\def\\epsf@testit{#1#2}\n\t\t\t\\ifx\\epsf@testit\\epsf@start\\else\n\\ps@typeout{Warning! File does not start with `\\epsf@start'. It may not be a PostScript file.}\n\t\t\t\\fi\n\t\t\t\\@psfiletrue} % don't test after 1st line\n%\n% We still need to define the tricky \\epsf@aux macro. This requires\n% a couple of magic constants for comparison purposes.\n%\n{\\catcode`\\%=12\\global\\let\\epsf@percent=%\\global\\def\\epsf@bblit{%BoundingBox}}\n%\n%\n% So we're ready to check for `%BoundingBox:' and to grab the\n% values if they are found. We continue searching if `(at end)'\n% was found after the `%BoundingBox:'.\n%\n\\long\\def\\epsf@aux#1#2:#3\\\\{\\ifx#1\\epsf@percent\n \\def\\epsf@testit{#2}\\ifx\\epsf@testit\\epsf@bblit\n\t\\@atendfalse\n \\epsf@atend #3 . \\\\%\n\t\\if@atend\t\n\t \\if@verbose{\n\t\t\\ps@typeout{psfig: found `(atend)'; continuing search}\n\t }\\fi\n \\else\n \\epsf@grab #3 . . . \\\\%\n \\not@eoffalse\n \\global\\no@bbfalse\n \\fi\n \\fi\\fi}%\n%\n% Here we grab the values and stuff them in the appropriate definitions.\n%\n\\def\\epsf@grab #1 #2 #3 #4 #5\\\\{%\n \\global\\def\\epsf@llx{#1}\\ifx\\epsf@llx\\empty\n \\epsf@grab #2 #3 #4 #5 .\\\\\\else\n \\global\\def\\epsf@lly{#2}%\n \\global\\def\\epsf@urx{#3}\\global\\def\\epsf@ury{#4}\\fi}%\n%\n% Determine if the stuff following the %%BoundingBox is `(atend)'\n% J. Daniel Smith. Copied from \\epsf@grab above.\n%\n\\def\\epsf@atendlit{(atend)} \n\\def\\epsf@atend #1 #2 #3\\\\{%\n \\def\\epsf@tmp{#1}\\ifx\\epsf@tmp\\empty\n \\epsf@atend #2 #3 .\\\\\\else\n \\ifx\\epsf@tmp\\epsf@atendlit\\@atendtrue\\fi\\fi}\n\n\n% End of file reading stuff from epsf.tex\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% trigonometry stuff from \"trig.tex\"\n\\chardef\\psletter = 11 % won't conflict with \\begin{letter} now...\n\\chardef\\other = 12\n\n\\newif \\ifdebug %%% turn me on to see TeX hard at work ...\n\\newif\\ifc@mpute %%% don't need to compute some values\n\\c@mputetrue % but assume that we do\n\n\\let\\then = \\relax\n\\def\\r@dian{pt }\n\\let\\r@dians = \\r@dian\n\\let\\dimensionless@nit = \\r@dian\n\\let\\dimensionless@nits = \\dimensionless@nit\n\\def\\internal@nit{sp }\n\\let\\internal@nits = \\internal@nit\n\\newif\\ifstillc@nverging\n\\def \\Mess@ge #1{\\ifdebug \\then \\message {#1} \\fi}\n\n{ %%% Things that need abnormal catcodes %%%\n\t\\catcode `\\@ = \\psletter\n\t\\gdef \\nodimen {\\expandafter \\n@dimen \\the \\dimen}\n\t\\gdef \\term #1 #2 #3%\n\t {\\edef \\t@ {\\the #1}%%% freeze parameter 1 (count, by value)\n\t\t\\edef \\t@@ {\\expandafter \\n@dimen \\the #2\\r@dian}%\n\t\t\t\t %%% freeze parameter 2 (dimen, by value)\n\t\t\\t@rm {\\t@} {\\t@@} {#3}%\n\t }\n\t\\gdef \\t@rm #1 #2 #3%\n\t {{%\n\t\t\\count 0 = 0\n\t\t\\dimen 0 = 1 \\dimensionless@nit\n\t\t\\dimen 2 = #2\\relax\n\t\t\\Mess@ge {Calculating term #1 of \\nodimen 2}%\n\t\t\\loop\n\t\t\\ifnum\t\\count 0 < #1\n\t\t\\then\t\\advance \\count 0 by 1\n\t\t\t\\Mess@ge {Iteration \\the \\count 0 \\space}%\n\t\t\t\\Multiply \\dimen 0 by {\\dimen 2}%\n\t\t\t\\Mess@ge {After multiplication, term = \\nodimen 0}%\n\t\t\t\\Divide \\dimen 0 by {\\count 0}%\n\t\t\t\\Mess@ge {After division, term = \\nodimen 0}%\n\t\t\\repeat\n\t\t\\Mess@ge {Final value for term #1 of \n\t\t\t\t\\nodimen 2 \\space is \\nodimen 0}%\n\t\t\\xdef \\Term {#3 = \\nodimen 0 \\r@dians}%\n\t\t\\aftergroup \\Term\n\t }}\n\t\\catcode `\\p = \\other\n\t\\catcode `\\t = \\other\n\t\\gdef \\n@dimen #1pt{#1} %%% throw away the ``pt''\n}\n\n\\def \\Divide #1by #2{\\divide #1 by #2} %%% just a synonym\n\n\\def \\Multiply #1by #2%%% allows division of a dimen by a dimen\n {{%%% should really freeze parameter 2 (dimen, passed by value)\n\t\\count 0 = #1\\relax\n\t\\count 2 = #2\\relax\n\t\\count 4 = 65536\n\t\\Mess@ge {Before scaling, count 0 = \\the \\count 0 \\space and\n\t\t\tcount 2 = \\the \\count 2}%\n\t\\ifnum\t\\count 0 > 32767 %%% do our best to avoid overflow\n\t\\then\t\\divide \\count 0 by 4\n\t\t\\divide \\count 4 by 4\n\t\\else\t\\ifnum\t\\count 0 < -32767\n\t\t\\then\t\\divide \\count 0 by 4\n\t\t\t\\divide \\count 4 by 4\n\t\t\\else\n\t\t\\fi\n\t\\fi\n\t\\ifnum\t\\count 2 > 32767 %%% while retaining reasonable accuracy\n\t\\then\t\\divide \\count 2 by 4\n\t\t\\divide \\count 4 by 4\n\t\\else\t\\ifnum\t\\count 2 < -32767\n\t\t\\then\t\\divide \\count 2 by 4\n\t\t\t\\divide \\count 4 by 4\n\t\t\\else\n\t\t\\fi\n\t\\fi\n\t\\multiply \\count 0 by \\count 2\n\t\\divide \\count 0 by \\count 4\n\t\\xdef \\product {#1 = \\the \\count 0 \\internal@nits}%\n\t\\aftergroup \\product\n }}\n\n\\def\\r@duce{\\ifdim\\dimen0 > 90\\r@dian \\then % sin(x+90) = sin(180-x)\n\t\t\\multiply\\dimen0 by -1\n\t\t\\advance\\dimen0 by 180\\r@dian\n\t\t\\r@duce\n\t \\else \\ifdim\\dimen0 < -90\\r@dian \\then % sin(-x) = sin(360+x)\n\t\t\\advance\\dimen0 by 360\\r@dian\n\t\t\\r@duce\n\t\t\\fi\n\t \\fi}\n\n\\def\\Sine#1%\n {{%\n\t\\dimen 0 = #1 \\r@dian\n\t\\r@duce\n\t\\ifdim\\dimen0 = -90\\r@dian \\then\n\t \\dimen4 = -1\\r@dian\n\t \\c@mputefalse\n\t\\fi\n\t\\ifdim\\dimen0 = 90\\r@dian \\then\n\t \\dimen4 = 1\\r@dian\n\t \\c@mputefalse\n\t\\fi\n\t\\ifdim\\dimen0 = 0\\r@dian \\then\n\t \\dimen4 = 0\\r@dian\n\t \\c@mputefalse\n\t\\fi\n%\n\t\\ifc@mpute \\then\n \t% convert degrees to radians\n\t\t\\divide\\dimen0 by 180\n\t\t\\dimen0=3.141592654\\dimen0\n%\n\t\t\\dimen 2 = 3.1415926535897963\\r@dian %%% a well-known constant\n\t\t\\divide\\dimen 2 by 2 %%% we only deal with -pi/2 : pi/2\n\t\t\\Mess@ge {Sin: calculating Sin of \\nodimen 0}%\n\t\t\\count 0 = 1 %%% see power-series expansion for sine\n\t\t\\dimen 2 = 1 \\r@dian %%% ditto\n\t\t\\dimen 4 = 0 \\r@dian %%% ditto\n\t\t\\loop\n\t\t\t\\ifnum\t\\dimen 2 = 0 %%% then we've done\n\t\t\t\\then\t\\stillc@nvergingfalse \n\t\t\t\\else\t\\stillc@nvergingtrue\n\t\t\t\\fi\n\t\t\t\\ifstillc@nverging %%% then calculate next term\n\t\t\t\\then\t\\term {\\count 0} {\\dimen 0} {\\dimen 2}%\n\t\t\t\t\\advance \\count 0 by 2\n\t\t\t\t\\count 2 = \\count 0\n\t\t\t\t\\divide \\count 2 by 2\n\t\t\t\t\\ifodd\t\\count 2 %%% signs alternate\n\t\t\t\t\\then\t\\advance \\dimen 4 by \\dimen 2\n\t\t\t\t\\else\t\\advance \\dimen 4 by -\\dimen 2\n\t\t\t\t\\fi\n\t\t\\repeat\n\t\\fi\t\t\n\t\t\t\\xdef \\sine {\\nodimen 4}%\n }}\n\n% Now the Cosine can be calculated easily by calling \\Sine\n\\def\\Cosine#1{\\ifx\\sine\\UnDefined\\edef\\Savesine{\\relax}\\else\n\t\t \\edef\\Savesine{\\sine}\\fi\n\t{\\dimen0=#1\\r@dian\\advance\\dimen0 by 90\\r@dian\n\t \\Sine{\\nodimen 0}\n\t \\xdef\\cosine{\\sine}\n\t \\xdef\\sine{\\Savesine}}}\t \n% end of trig stuff\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\def\\psdraft{\n\t\\def\\@psdraft{0}\n\t%\\ps@typeout{draft level now is \\@psdraft \\space . }\n}\n\\def\\psfull{\n\t\\def\\@psdraft{100}\n\t%\\ps@typeout{draft level now is \\@psdraft \\space . }\n}\n\n\\psfull\n\n\\newif\\if@scalefirst\n\\def\\psscalefirst{\\@scalefirsttrue}\n\\def\\psrotatefirst{\\@scalefirstfalse}\n\\psrotatefirst\n\n\\newif\\if@draftbox\n\\def\\psnodraftbox{\n\t\\@draftboxfalse\n}\n\\def\\psdraftbox{\n\t\\@draftboxtrue\n}\n\\@draftboxtrue\n\n\\newif\\if@prologfile\n\\newif\\if@postlogfile\n\\def\\pssilent{\n\t\\@noisyfalse\n}\n\\def\\psnoisy{\n\t\\@noisytrue\n}\n\\psnoisy\n%%% These are for the option list.\n%%% A specification of the form a = b maps to calling \\@p@@sa{b}\n\\newif\\if@bbllx\n\\newif\\if@bblly\n\\newif\\if@bburx\n\\newif\\if@bbury\n\\newif\\if@height\n\\newif\\if@width\n\\newif\\if@rheight\n\\newif\\if@rwidth\n\\newif\\if@angle\n\\newif\\if@clip\n\\newif\\if@verbose\n\\def\\@p@@sclip#1{\\@cliptrue}\n\n\n\\newif\\if@decmpr\n\n%%% GDH 7/26/87 -- changed so that it first looks in the local directory,\n%%% then in a specified global directory for the ps file.\n%%% RPR 6/25/91 -- changed so that it defaults to user-supplied name if\n%%% boundingbox info is specified, assuming graphic will be created by\n%%% print time.\n%%% TJD 10/19/91 -- added bbfile vs. file distinction, and @decmpr flag\n\n\\def\\@p@@sfigure#1{\\def\\@p@sfile{null}\\def\\@p@sbbfile{null}\n\t \\openin1=#1.bb\n\t\t\\ifeof1\\closein1\n\t \t\\openin1=\\figurepath#1.bb\n\t\t\t\\ifeof1\\closein1\n\t\t\t \\openin1=#1\n\t\t\t\t\\ifeof1\\closein1%\n\t\t\t\t \\openin1=\\figurepath#1\n\t\t\t\t\t\\ifeof1\n\t\t\t\t\t \\ps@typeout{Error, File #1 not found}\n\t\t\t\t\t\t\\if@bbllx\\if@bblly\n\t\t\t\t \t\t\\if@bburx\\if@bbury\n\t\t\t \t\t\t\t\\def\\@p@sfile{#1}%\n\t\t\t \t\t\t\t\\def\\@p@sbbfile{#1}%\n\t\t\t\t\t\t\t\\@decmprfalse\n\t\t\t\t \t \t\\fi\\fi\\fi\\fi\n\t\t\t\t\t\\else\\closein1\n\t\t\t\t \t\t\\def\\@p@sfile{\\figurepath#1}%\n\t\t\t\t \t\t\\def\\@p@sbbfile{\\figurepath#1}%\n\t\t\t\t\t\t\\@decmprfalse\n\t \t\t\\fi%\n\t\t\t \t\\else\\closein1%\n\t\t\t\t\t\\def\\@p@sfile{#1}\n\t\t\t\t\t\\def\\@p@sbbfile{#1}\n\t\t\t\t\t\\@decmprfalse\n\t\t\t \t\\fi\n\t\t\t\\else\n\t\t\t\t\\def\\@p@sfile{\\figurepath#1}\n\t\t\t\t\\def\\@p@sbbfile{\\figurepath#1.bb}\n\t\t\t\t\\@decmprtrue\n\t\t\t\\fi\n\t\t\\else\n\t\t\t\\def\\@p@sfile{#1}\n\t\t\t\\def\\@p@sbbfile{#1.bb}\n\t\t\t\\@decmprtrue\n\t\t\\fi}\n\n\\def\\@p@@sfile#1{\\@p@@sfigure{#1}}\n\n\\def\\@p@@sbbllx#1{\n\t\t%\\ps@typeout{bbllx is #1}\n\t\t\\@bbllxtrue\n\t\t\\dimen100=#1\n\t\t\\edef\\@p@sbbllx{\\number\\dimen100}\n}\n\\def\\@p@@sbblly#1{\n\t\t%\\ps@typeout{bblly is #1}\n\t\t\\@bbllytrue\n\t\t\\dimen100=#1\n\t\t\\edef\\@p@sbblly{\\number\\dimen100}\n}\n\\def\\@p@@sbburx#1{\n\t\t%\\ps@typeout{bburx is #1}\n\t\t\\@bburxtrue\n\t\t\\dimen100=#1\n\t\t\\edef\\@p@sbburx{\\number\\dimen100}\n}\n\\def\\@p@@sbbury#1{\n\t\t%\\ps@typeout{bbury is #1}\n\t\t\\@bburytrue\n\t\t\\dimen100=#1\n\t\t\\edef\\@p@sbbury{\\number\\dimen100}\n}\n\\def\\@p@@sheight#1{\n\t\t\\@heighttrue\n\t\t\\dimen100=#1\n \t\t\\edef\\@p@sheight{\\number\\dimen100}\n\t\t%\\ps@typeout{Height is \\@p@sheight}\n}\n\\def\\@p@@swidth#1{\n\t\t%\\ps@typeout{Width is #1}\n\t\t\\@widthtrue\n\t\t\\dimen100=#1\n\t\t\\edef\\@p@swidth{\\number\\dimen100}\n}\n\\def\\@p@@srheight#1{\n\t\t%\\ps@typeout{Reserved height is #1}\n\t\t\\@rheighttrue\n\t\t\\dimen100=#1\n\t\t\\edef\\@p@srheight{\\number\\dimen100}\n}\n\\def\\@p@@srwidth#1{\n\t\t%\\ps@typeout{Reserved width is #1}\n\t\t\\@rwidthtrue\n\t\t\\dimen100=#1\n\t\t\\edef\\@p@srwidth{\\number\\dimen100}\n}\n\\def\\@p@@sangle#1{\n\t\t%\\ps@typeout{Rotation is #1}\n\t\t\\@angletrue\n%\t\t\\dimen100=#1\n\t\t\\edef\\@p@sangle{#1} %\\number\\dimen100}\n}\n\\def\\@p@@ssilent#1{ \n\t\t\\@verbosefalse\n}\n\\def\\@p@@sprolog#1{\\@prologfiletrue\\def\\@prologfileval{#1}}\n\\def\\@p@@spostlog#1{\\@postlogfiletrue\\def\\@postlogfileval{#1}}\n\\def\\@cs@name#1{\\csname #1\\endcsname}\n\\def\\@setparms#1=#2,{\\@cs@name{@p@@s#1}{#2}}\n%\n% initialize the defaults (size the size of the figure)\n%\n\\def\\ps@init@parms{\n\t\t\\@bbllxfalse \\@bbllyfalse\n\t\t\\@bburxfalse \\@bburyfalse\n\t\t\\@heightfalse \\@widthfalse\n\t\t\\@rheightfalse \\@rwidthfalse\n\t\t\\def\\@p@sbbllx{}\\def\\@p@sbblly{}\n\t\t\\def\\@p@sbburx{}\\def\\@p@sbbury{}\n\t\t\\def\\@p@sheight{}\\def\\@p@swidth{}\n\t\t\\def\\@p@srheight{}\\def\\@p@srwidth{}\n\t\t\\def\\@p@sangle{0}\n\t\t\\def\\@p@sfile{} \\def\\@p@sbbfile{}\n\t\t\\def\\@p@scost{10}\n\t\t\\def\\@sc{}\n\t\t\\@prologfilefalse\n\t\t\\@postlogfilefalse\n\t\t\\@clipfalse\n\t\t\\if@noisy\n\t\t\t\\@verbosetrue\n\t\t\\else\n\t\t\t\\@verbosefalse\n\t\t\\fi\n}\n%\n% Go through the options setting things up.\n%\n\\def\\parse@ps@parms#1{\n\t \t\\@psdo\\@psfiga:=#1\\do\n\t\t {\\expandafter\\@setparms\\@psfiga,}}\n%\n% Compute bb height and width\n%\n\\newif\\ifno@bb\n\\def\\bb@missing{\n\t\\if@verbose{\n\t\t\\ps@typeout{psfig: searching \\@p@sbbfile \\space for bounding box}\n\t}\\fi\n\t\\no@bbtrue\n\t\\epsf@getbb{\\@p@sbbfile}\n \\ifno@bb \\else \\bb@cull\\epsf@llx\\epsf@lly\\epsf@urx\\epsf@ury\\fi\n}\t\n\\def\\bb@cull#1#2#3#4{\n\t\\dimen100=#1 bp\\edef\\@p@sbbllx{\\number\\dimen100}\n\t\\dimen100=#2 bp\\edef\\@p@sbblly{\\number\\dimen100}\n\t\\dimen100=#3 bp\\edef\\@p@sbburx{\\number\\dimen100}\n\t\\dimen100=#4 bp\\edef\\@p@sbbury{\\number\\dimen100}\n\t\\no@bbfalse\n}\n% rotate point (#1,#2) about (0,0).\n% The sine and cosine of the angle are already stored in \\sine and\n% \\cosine. The result is placed in (\\p@intvaluex, \\p@intvaluey).\n\\newdimen\\p@intvaluex\n\\newdimen\\p@intvaluey\n\\def\\rotate@#1#2{{\\dimen0=#1 sp\\dimen1=#2 sp\n% \tcalculate x' = x \\cos\\theta - y \\sin\\theta\n\t\t \\global\\p@intvaluex=\\cosine\\dimen0\n\t\t \\dimen3=\\sine\\dimen1\n\t\t \\global\\advance\\p@intvaluex by -\\dimen3\n% \t\tcalculate y' = x \\sin\\theta + y \\cos\\theta\n\t\t \\global\\p@intvaluey=\\sine\\dimen0\n\t\t \\dimen3=\\cosine\\dimen1\n\t\t \\global\\advance\\p@intvaluey by \\dimen3\n\t\t }}\n\\def\\compute@bb{\n\t\t\\no@bbfalse\n\t\t\\if@bbllx \\else \\no@bbtrue \\fi\n\t\t\\if@bblly \\else \\no@bbtrue \\fi\n\t\t\\if@bburx \\else \\no@bbtrue \\fi\n\t\t\\if@bbury \\else \\no@bbtrue \\fi\n\t\t\\ifno@bb \\bb@missing \\fi\n\t\t\\ifno@bb \\ps@typeout{FATAL ERROR: no bb supplied or found}\n\t\t\t\\no-bb-error\n\t\t\\fi\n\t\t%\n%\\ps@typeout{BB: \\@p@sbbllx, \\@p@sbblly, \\@p@sbburx, \\@p@sbbury} \n%\n% store height/width of original (unrotated) bounding box\n\t\t\\count203=\\@p@sbburx\n\t\t\\count204=\\@p@sbbury\n\t\t\\advance\\count203 by -\\@p@sbbllx\n\t\t\\advance\\count204 by -\\@p@sbblly\n\t\t\\edef\\ps@bbw{\\number\\count203}\n\t\t\\edef\\ps@bbh{\\number\\count204}\n\t\t%\\ps@typeout{ psbbh = \\ps@bbh, psbbw = \\ps@bbw }\n\t\t\\if@angle \n\t\t\t\\Sine{\\@p@sangle}\\Cosine{\\@p@sangle}\n\t \t{\\dimen100=\\maxdimen\\xdef\\r@p@sbbllx{\\number\\dimen100}\n\t\t\t\t\t \\xdef\\r@p@sbblly{\\number\\dimen100}\n\t\t\t \\xdef\\r@p@sbburx{-\\number\\dimen100}\n\t\t\t\t\t \\xdef\\r@p@sbbury{-\\number\\dimen100}}\n%\n% Need to rotate all four points and take the X-Y extremes of the new\n% points as the new bounding box.\n \\def\\minmaxtest{\n\t\t\t \\ifnum\\number\\p@intvaluex<\\r@p@sbbllx\n\t\t\t \\xdef\\r@p@sbbllx{\\number\\p@intvaluex}\\fi\n\t\t\t \\ifnum\\number\\p@intvaluex>\\r@p@sbburx\n\t\t\t \\xdef\\r@p@sbburx{\\number\\p@intvaluex}\\fi\n\t\t\t \\ifnum\\number\\p@intvaluey<\\r@p@sbblly\n\t\t\t \\xdef\\r@p@sbblly{\\number\\p@intvaluey}\\fi\n\t\t\t \\ifnum\\number\\p@intvaluey>\\r@p@sbbury\n\t\t\t \\xdef\\r@p@sbbury{\\number\\p@intvaluey}\\fi\n\t\t\t }\n%\t\t\tlower left\n\t\t\t\\rotate@{\\@p@sbbllx}{\\@p@sbblly}\n\t\t\t\\minmaxtest\n%\t\t\tupper left\n\t\t\t\\rotate@{\\@p@sbbllx}{\\@p@sbbury}\n\t\t\t\\minmaxtest\n%\t\t\tlower right\n\t\t\t\\rotate@{\\@p@sbburx}{\\@p@sbblly}\n\t\t\t\\minmaxtest\n%\t\t\tupper right\n\t\t\t\\rotate@{\\@p@sbburx}{\\@p@sbbury}\n\t\t\t\\minmaxtest\n\t\t\t\\edef\\@p@sbbllx{\\r@p@sbbllx}\\edef\\@p@sbblly{\\r@p@sbblly}\n\t\t\t\\edef\\@p@sbburx{\\r@p@sbburx}\\edef\\@p@sbbury{\\r@p@sbbury}\n%\\ps@typeout{rotated BB: \\r@p@sbbllx, \\r@p@sbblly, \\r@p@sbburx, \\r@p@sbbury}\n\t\t\\fi\n\t\t\\count203=\\@p@sbburx\n\t\t\\count204=\\@p@sbbury\n\t\t\\advance\\count203 by -\\@p@sbbllx\n\t\t\\advance\\count204 by -\\@p@sbblly\n\t\t\\edef\\@bbw{\\number\\count203}\n\t\t\\edef\\@bbh{\\number\\count204}\n\t\t%\\ps@typeout{ bbh = \\@bbh, bbw = \\@bbw }\n}\n%\n% \\in@hundreds performs #1 * (#2 / #3) correct to the hundreds,\n%\tthen leaves the result in @result\n%\n\\def\\in@hundreds#1#2#3{\\count240=#2 \\count241=#3\n\t\t \\count100=\\count240\t% 100 is first digit #2/#3\n\t\t \\divide\\count100 by \\count241\n\t\t \\count101=\\count100\n\t\t \\multiply\\count101 by \\count241\n\t\t \\advance\\count240 by -\\count101\n\t\t \\multiply\\count240 by 10\n\t\t \\count101=\\count240\t%101 is second digit of #2/#3\n\t\t \\divide\\count101 by \\count241\n\t\t \\count102=\\count101\n\t\t \\multiply\\count102 by \\count241\n\t\t \\advance\\count240 by -\\count102\n\t\t \\multiply\\count240 by 10\n\t\t \\count102=\\count240\t% 102 is the third digit\n\t\t \\divide\\count102 by \\count241\n\t\t \\count200=#1\\count205=0\n\t\t \\count201=\\count200\n\t\t\t\\multiply\\count201 by \\count100\n\t\t \t\\advance\\count205 by \\count201\n\t\t \\count201=\\count200\n\t\t\t\\divide\\count201 by 10\n\t\t\t\\multiply\\count201 by \\count101\n\t\t\t\\advance\\count205 by \\count201\n\t\t\t%\n\t\t \\count201=\\count200\n\t\t\t\\divide\\count201 by 100\n\t\t\t\\multiply\\count201 by \\count102\n\t\t\t\\advance\\count205 by \\count201\n\t\t\t%\n\t\t \\edef\\@result{\\number\\count205}\n}\n\\def\\compute@wfromh{\n\t\t% computing : width = height * (bbw / bbh)\n\t\t\\in@hundreds{\\@p@sheight}{\\@bbw}{\\@bbh}\n\t\t%\\ps@typeout{ \\@p@sheight * \\@bbw / \\@bbh, = \\@result }\n\t\t\\edef\\@p@swidth{\\@result}\n\t\t%\\ps@typeout{w from h: width is \\@p@swidth}\n}\n\\def\\compute@hfromw{\n\t\t% computing : height = width * (bbh / bbw)\n\t \\in@hundreds{\\@p@swidth}{\\@bbh}{\\@bbw}\n\t\t%\\ps@typeout{ \\@p@swidth * \\@bbh / \\@bbw = \\@result }\n\t\t\\edef\\@p@sheight{\\@result}\n\t\t%\\ps@typeout{h from w : height is \\@p@sheight}\n}\n\\def\\compute@handw{\n\t\t\\if@height \n\t\t\t\\if@width\n\t\t\t\\else\n\t\t\t\t\\compute@wfromh\n\t\t\t\\fi\n\t\t\\else \n\t\t\t\\if@width\n\t\t\t\t\\compute@hfromw\n\t\t\t\\else\n\t\t\t\t\\edef\\@p@sheight{\\@bbh}\n\t\t\t\t\\edef\\@p@swidth{\\@bbw}\n\t\t\t\\fi\n\t\t\\fi\n}\n\\def\\compute@resv{\n\t\t\\if@rheight \\else \\edef\\@p@srheight{\\@p@sheight} \\fi\n\t\t\\if@rwidth \\else \\edef\\@p@srwidth{\\@p@swidth} \\fi\n\t\t%\\ps@typeout{rheight = \\@p@srheight, rwidth = \\@p@srwidth}\n}\n%\t\t\n% Compute any missing values\n\\def\\compute@sizes{\n\t\\compute@bb\n\t\\if@scalefirst\\if@angle\n% at this point the bounding box has been adjsuted correctly for\n% rotation. PSFIG does all of its scaling using \\@bbh and \\@bbw. If\n% a width= or height= was specified along with \\psscalefirst, then the\n% width=/height= value needs to be adjusted to match the new (rotated)\n% bounding box size (specifed in \\@bbw and \\@bbh).\n% \\ps@bbw width=\n% ------- = ---------- \n% \\@bbw new width=\n% so `new width=' = (width= * \\@bbw) / \\ps@bbw; where \\ps@bbw is the\n% width of the original (unrotated) bounding box.\n\t\\if@width\n\t \\in@hundreds{\\@p@swidth}{\\@bbw}{\\ps@bbw}\n\t \\edef\\@p@swidth{\\@result}\n\t\\fi\n\t\\if@height\n\t \\in@hundreds{\\@p@sheight}{\\@bbh}{\\ps@bbh}\n\t \\edef\\@p@sheight{\\@result}\n\t\\fi\n\t\\fi\\fi\n\t\\compute@handw\n\t\\compute@resv}\n\n%\n% \\psfig\n% usage : \\psfig{file=, height=, width=, bbllx=, bblly=, bburx=, bbury=,\n%\t\t\trheight=, rwidth=, clip=}\n%\n% \"clip=\" is a switch and takes no value, but the `=' must be present.\n\\def\\psfig#1{\\vbox {\n\t% do a zero width hard space so that a single\n\t% \\psfig in a centering enviornment will behave nicely\n\t%{\\setbox0=\\hbox{\\ }\\ \\hskip-\\wd0}\n\t%\n\t\\ps@init@parms\n\t\\parse@ps@parms{#1}\n\t\\compute@sizes\n\t%\n\t\\ifnum\\@p@scost<\\@psdraft{\n\t\t%\n\t\t\\special{ps::[begin] \t\\@p@swidth \\space \\@p@sheight \\space\n\t\t\t\t\\@p@sbbllx \\space \\@p@sbblly \\space\n\t\t\t\t\\@p@sbburx \\space \\@p@sbbury \\space\n\t\t\t\tstartTexFig \\space }\n\t\t\\if@angle\n\t\t\t\\special {ps:: \\@p@sangle \\space rotate \\space} \n\t\t\\fi\n\t\t\\if@clip{\n\t\t\t\\if@verbose{\n\t\t\t\t\\ps@typeout{(clip)}\n\t\t\t}\\fi\n\t\t\t\\special{ps:: doclip \\space }\n\t\t}\\fi\n\t\t\\if@prologfile\n\t\t \\special{ps: plotfile \\@prologfileval \\space } \\fi\n\t\t\\if@decmpr{\n\t\t\t\\if@verbose{\n\t\t\t\t\\ps@typeout{psfig: including \\@p@sfile.Z \\space }\n\t\t\t}\\fi\n\t\t\t\\special{ps: plotfile \"`zcat \\@p@sfile.Z\" \\space }\n\t\t}\\else{\n\t\t\t\\if@verbose{\n\t\t\t\t\\ps@typeout{psfig: including \\@p@sfile \\space }\n\t\t\t}\\fi\n\t\t\t\\special{ps: plotfile \\@p@sfile \\space }\n\t\t}\\fi\n\t\t\\if@postlogfile\n\t\t \\special{ps: plotfile \\@postlogfileval \\space } \\fi\n\t\t\\special{ps::[end] endTexFig \\space }\n\t\t% Create the vbox to reserve the space for the figure.\n\t\t\\vbox to \\@p@srheight sp{\n\t\t% 1/92 TJD Changed from \"true sp\" to \"sp\" for magnification.\n\t\t\t\\hbox to \\@p@srwidth sp{\n\t\t\t\t\\hss\n\t\t\t}\n\t\t\\vss\n\t\t}\n\t}\\else{\n\t\t% draft figure, just reserve the space and print the\n\t\t% path name.\n\t\t\\if@draftbox{\t\t\n\t\t\t% Verbose draft: print file name in box\n\t\t\t\\hbox{\\frame{\\vbox to \\@p@srheight sp{\n\t\t\t\\vss\n\t\t\t\\hbox to \\@p@srwidth sp{ \\hss \\@p@sfile \\hss }\n\t\t\t\\vss\n\t\t\t}}}\n\t\t}\\else{\n\t\t\t% Non-verbose draft\n\t\t\t\\vbox to \\@p@srheight sp{\n\t\t\t\\vss\n\t\t\t\\hbox to \\@p@srwidth sp{\\hss}\n\t\t\t\\vss\n\t\t\t}\n\t\t}\\fi\t\n\n\n\n\t}\\fi\n}}\n\\psfigRestoreAt\n\\let\\@=\\LaTeXAtSign\n"
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"string": "\\def\\xte{{\\it RXTE}}\n\n%==========================================================================\n\n%\\documentstyle[12pt,aasms4,psfig]{article}\n\\documentstyle[11pt,aaspp4,psfig]{article}\n%\\documentstyle[11pt,aaspp4,psfig]{article}\n%\\documentstyle[11pt,aaspp4]{article}\n%\\documentstyle[aas2pp4,10pt]{article}\n\n\\received{1999 Dec. 1}\n\\accepted{2000 Feb. 11}\n\\journalid{}{}\n\\articleid{}{}\n\n%\\slugcomment{To appear in {\\it The Astrophysical Journal}, vol.537, July 10, 2000}\n\n\n\\lefthead{Eracleous, Sambruna, \\& Mushotzky}\n\\righthead{BLRGs With {\\it RXTE}}\n\n\\begin{document}\n\n%\\topfraction 0.9\n%\\textfraction 0.1\n\n%======== Added by Mike to justify the text on the right side\n\\rightskip 0pt \\pretolerance=100\n\n\\input psu_prep_logo.tex\n\n\\title{Hard X-Ray Spectra of Broad-Line Radio Galaxies from the \nRossi X-Ray Timing Explorer}\n\n\\author{Michael Eracleous \\& Rita Sambruna}\n\\affil{Department of Astronomy and Astrophysics, The Pennsylvania State\nUniversity, \\\\525 Davey Laboratory, University Park, PA 16802\n\\\\e-mail: {\\tt mce@astro.psu.edu, sambruna@astro.psu.edu}}\n\n\\and\n\n\\author{Richard F. Mushotzky}\n\\affil{NASA/GSFC, Code 662, Greenbelt, MD 20771\n\\\\ e-mail: {\\tt richard@xray-5.gsfc.nasa.gov}}\n\n\\medskip\n\\centerline\n{To appear in {\\it The Astrophysical Journal}, vol. 537, July 10, 2000}\n\n\\begin{abstract}\n%======== Added by Mike to justify the text on the right side\n\\rightskip 0pt \\pretolerance=100 \\noindent\nWe present the results of hard-X-ray observations of four\nbroad-line radio galaxies (BLRGs) with the {\\it Rossi X-Ray Timing\nExplorer} ({\\it RXTE}). The original motivation behind the observations\nwas to search for systematic differences between the BLRGs and their\nradio-quiet counterparts, the Seyfert galaxies. We do, indeed, find that\nthe Fe~K$\\alpha$ lines and Compton ``reflection'' components, which are\nhallmarks of the X-ray spectra of Seyferts galaxies, are weaker in BLRGs\nby about a factor of 2. This observational result is in agreement with the\nconclusions of other recent studies of these objects. We examine several\npossible explanations for this systematic difference, including beaming of\nthe primary X-rays away from the accretion disk, a low iron abundance, a\nsmall solid angle subtended by the disk to the primary X-ray source, and\ndilution of the observed spectrum by beamed X-rays from the jet. We find\nthat a small solid angle subtended by the disk to the primary X-ray source\nis a viable and appealing explanation, while all others suffer from\ndrawbacks. We interpret this as an indication of a difference in the\ninner accretion disk structure between Seyfert galaxies and BLRGs, namely\nthat the inner accretion disks of BLRGs have the form of an ion-supported\ntorus or an advection-dominated accretion flow, which irradiates the\ngeometrically thin outer disk.\n\\end{abstract}\n%\\keywords{Galaxies: active -- X-rays: galaxies -- Radio galaxies: \n%individual (3C 111, 3C 120, Pictor A, 3C 382)}\n\n\\clearpage\n\n\\section{Introduction}\n\nAn important issue in our study of active galactic nuclei (hereafter\nAGNs) is the as yet unexplained difference between radio loud and\nradio-quiet objects. All AGNs are thought to be powered by accretion of\nmatter onto a supermassive black hole, presumably via an equatorial\naccretion disk. From a theoretical perspective, the accretion disk is an\nessential ingredient for the formation of radio jets, although the exact\nmechanism is not well known (see the review by Livio 1996). The\nobservational evidence\\footnote{The most direct observational evidence\nfor the presence of accretion disks in AGNs takes the form of\nFe~K$\\alpha$ lines with disk-like profiles in the X-ray spectra of\nSeyfert galaxies (e.g., Tanaka et al. 1995; Nandra et al. 1997b) and\ndouble-peaked H$\\alpha$ lines in the optical spectra of BLRGs (Eracleous\n\\& Halpern 1994).} suggests that both radio-loud and radio-quiet AGNs\nharbor accretion disks, but it is a mystery why well-collimated,\npowerful, relativistic radio jets only exist in the former class of\nobject. The origin of the difference could lie in the nature of the host\ngalaxy. At low redshifts ($z<0.5$) radio-loud AGNs are found only in\nelliptical galaxies, whereas radio-quiet AGNs can have either elliptical\nor spiral hosts (Smith et al. 1986; Hutchings, Janson, \\& Neff 1989;\nV\\'eron-Cetty \\& Woltjer 1990; Dunlop et al. 1993; Bahcall et al. 1997;\nBoyce et al. 1998). This observational trend has led to the suggestion\nthat the interstellar medium of the host galaxy may play an important\nrole in the propagation and collimation of the radio jets on large scales\n(e.g., Blandford \\& Levinson 1995; Fabian \\& Rees 1995). Alternatively,\none may seek the fundamental cause of the difference between radio-loud\nand radio-quiet AGNs in the properties of their accretion flows or the\nproperties of their central black holes. One possibility is that\nradio-loud AGNs may harbor rapidly spinning black holes, whose energy is\nextracted electromagnetically via the Blandford \\& Znajek (1977)\nmechanism and used to power the radio jets. Rapidly spinning black holes\ncould be associated with elliptical galaxies if both the black hole and\nthe host galaxy result from the merger of two parent galaxies, each with\nits own nuclear black hole (see Wilson \\& Colbert 1995). Another\npossibility is that the inner accretion disks of radio-quiet AGNs are\ngeometrically thin and optically thick throughout (Shakura \\& Sunyaev\n1973) while the inner accretion disks of radio-loud AGNs are\nion-supported tori (Rees et al. 1982; known today as advection-dominated\naccretion flows, or ADAFs, after the work of Narayan \\& Yi 1994, 1995).\nBecause ADAFs are nearly spherical and parts of the flow are unbound,\nthey can lead to the formation of outflows (e.g., Blandford \\& Begelman\n1999). In either of the above pictures, an additional mechanism may be\nnecessary to {\\it collimate} the radio jets (see for example, Blandford\n\\& Payne 1982; Meier 1999).\n\nIf the difference between radio-loud and radio-quiet AGNs is related to \ndifferences in their central engines, it would lead to observable\ndifferences in their respective X-ray spectra, in particular in the\nproperties (profiles and equivalent width) of the Fe~K$\\alpha$ lines and\nin the shape of the continuum. This is because the Fe~K$\\alpha$ lines are\nthought to result from fluorescence of the dense gas in the geometrically\nthin and optically thick regions of the disk (e.g., George \\& Fabian\n1991; Matt et al 1992). Similarly, the continuum above 10~keV is thought\nto include a significant contribution from X-ray photons from the\n``primary'' X-ray source, near the center of the disk, which undergo \nCompton scattering (``reflection'') in the same regions of the disk where\nthe Fe~K$\\alpha$ line is produced (e.g., Lightman \\& White 1988; George\n\\& Fabian 1991; Matt, Perola, \\& Piro 1991). It is, therefore, extremely\ninteresting that studies of the X-ray spectra of broad-line radio\ngalaxies (BLRGs) by Zdziarski et al. (1995) and Wo\\'zniak et al. (1998)\nfound them to be systematically different from those of (radio-quiet)\nSeyfert galaxies. In particular, these authors found that the signature\nof Compton reflection, which is very prominent in the spectra of Seyfert\ngalaxies above 10~keV (Pounds et al. 1989; Nandra \\& Pounds 1994), is\nweak of absent in the spectra of BLRGs. Moreover, Wo\\'zniak et al. (1997)\nfound that the Fe~K$\\alpha$ lines of BLRGs are narrower and weaker than\nthose of Seyfert galaxies.\n\nMotivated by the above theoretical considerations and observational\nresults, we have undertaken a systematic study of the X-ray spectra of\nradio-loud AGNs with {\\it ASCA} and {\\it RXTE} in order to characterize\ntheir properties. Our main goal is to compare their spectroscopic\nproperties with those of Seyfert galaxies and test the above ideas for\nthe origin of the difference between the two classes. In our re-analysis\nof archival {\\it ASCA} spectra of BLRGs and radio-loud quasars (Sambruna,\nEracleous, \\& Mushotzky 1999) we found that the Fe~K$\\alpha$ lines of\nsome objects are indeed weaker and narrower than those of Seyferts, in\nagreement with the findings of Wo\\'zniak et al. (1997). In other \nobjects, however, the uncertainties are large enough that we cannot reach\nfirm conclusions, thus we have not been able to confirm this result in\ngeneral. In this paper we present the results of new observations of four\nBLRGs with {\\it RXTE}, aimed at measuring the shape of their hard X-ray\ncontinuum and the equivalent width of their Fe~K$\\alpha$ lines. As such,\nthese observations complement our study of the {\\it ASCA} spectra of\nthese objects. In \\S2 we describe the observations and data screening. In\n\\S3 we present and discuss the light curves and in \\S4 we compare the\nobserved spectra with models. In \\S5 we discuss the implications of the\nresults, while in \\S6 we summarize our conclusions. Throughout this\npaper we assume a Hubble constant of $H_0=50~{\\rm km~s^{-1}~Mpc^{-1}}$ and\na deceleration parameter of $q_0=0.5$.\n\n%==========================================================================\n\n\\begin{deluxetable}{lcrcccc}\n\\tablenum{1}\n\\tablewidth{6.5in}\n\\tablecolumns{6}\n\\tablecaption{Target Objects, Basic Properties, and Observation Log}\n\\tablehead{\n & & & \\multicolumn{2}{c}{$N_{\\rm H}$ (cm$^{-2}$)} & \\nl\n & & & \\multicolumn{2}{l}{\\hrulefill} & \\colhead{Observation} & Duration \\nl\n\\colhead{Object} & \n\\colhead{$z$} &\n\\colhead{$i$\\tablenotemark{\\;a}} & \n\\colhead{Galactic\\tablenotemark{\\;b}} & \n\\colhead{{\\it ASCA}\\tablenotemark{\\;c}} &\n\\colhead{Start Time (UT)} &\n\\colhead{(hours)}\n}\n\\startdata\n3C 111 & 0.048 & $37^{\\circ}>i>24^{\\circ}$ & $1.2\\times 10^{22}$ & $9.63\\times 10^{21}$ & 1997/3/22 01:23 & 62 \\nl\n3C 120 & 0.033 & $14^{\\circ}>i>1^{\\circ}\\phantom{4}$ & $1.2\\times 10^{21}$ & $1.65\\times 10^{21}$ & 1998/2/13 04:53 & 58 \\nl\nPictor A & 0.035 & $i>24^{\\circ}$ & $4.2\\times 10^{20}$ & $8.30\\times 10^{20}$ & 1997/5/08 02:21 & 82 \\nl\n3C 382 & 0.057 & $i>15^{\\circ}$ & $6.7\\times 10^{20}$ & $6.70\\times 10^{20}$ & 1997/3/28 23:26 & 47 \\nl\n\\tablenotetext{a\\;} {The inclination angle of the radio jet (see Eracleous \\&\n Halpern 1998, and references therein).}\n\\tablenotetext{b\\;} {The Galactic equivalent H{\\sc\\, i} column density.\n {\\it References}: \n 3C~111: Bania, Marscher, \\& Barvainis (1991);\n 3C~120: Elvis et al. (1989);\n Pictor~A: Heiles \\& Cleary (1979);\n 3C 382: Murphy et al. (1996).\n }\n\\tablenotetext{c\\;} {The Galactic equivalent H{\\sc\\, i} column density \n as measured by the {\\it ASCA} SIS (taken from \n Sambruna et al. 1999).}\n\\enddata\n\\end{deluxetable}\n\n%==============================================================================\n\n\\begin{deluxetable}{lcccccc}\n\\tablenum{2}\n\\tablewidth{6.5in}\n\\tablecolumns{7}\n\\tablecaption{Exposure Times and Count Rates}\n\\tablehead{\n & \\multicolumn{3}{c}{PCA (2.5--30 keV)} & \n\\multicolumn{3}{c}{HEXTE cluster 0 (20-100 keV)}\\nl\n & \\multicolumn{3}{c}{\\hrulefill} & \\multicolumn{3}{c}{\\hrulefill}\\nl\n\\colhead{} &\n\\colhead{Exp.} &\n\\colhead{Source} &\n\\colhead{Backg.} &\n\\colhead{Exp.} &\n\\colhead{Source} &\n\\colhead{Backg.} \\nl\n\\colhead{} &\n\\colhead{Time} &\n\\colhead{Count Rate} &\n\\colhead{Count Rate} &\n\\colhead{Time} &\n\\colhead{Count Rate} &\n\\colhead{Count Rate} \\nl\n\\colhead{Object} &\n\\colhead{(s)} &\n\\colhead{(s$^{-1}$ PCU$^{-1}$)} &\n\\colhead{(s$^{-1}$ PCU$^{-1}$)} &\n\\colhead{(s)} &\n\\colhead{(s$^{-1}$)} &\n\\colhead{(s$^{-1}$)} \n}\n\\startdata\n3C 111 & 33,440 & 22.9 & 39.1 & 12,748 & 7.5 & 158.4 \\nl\n3C 120 & 55,904\\tablenotemark{\\;a} & 25.2 & 39.9 & 17,572 & 3.7 & 187.5 \\nl\nPictor A & 30,240\\tablenotemark{\\;a} & 9.6 & 38.7 & 12,461 & 9.4 & 166.9 \\nl\n3C 382 & 28,192 & 13.9 & 22.0 & 10,606 & 3.0 & 114.9 \\nl\n\\tablenotetext{a\\;} {The PCA exposure time refers to PCUs 0, 1, and 2.\n PCUs 3 and 4 were off during part of the observation.}\n\\enddata\n\\end{deluxetable}\n\n%==========================================================================\n\n\n\\section{Targets, Observations, and Data Screening}\n\nOur targets were selected to be among the X-ray brightest BLRGs, since\nthe background in the {\\it RXTE} instruments is rather high. They are\nlisted in Table~1 along with their basic properties, namely the redshift,\nthe inferred inclination of the radio jet (see Eracleous \\& Halpern 1998a\nand references therein), and two different estimates of the column\ndensity in the Galactic interstellar medium. The 2--10~keV fluxes are\nabout a few $\\times 10^{-11}~{\\rm erg~s^{-1}~cm^{-2}}$, which makes the\ntargets readily detectable by the {\\it RXTE} instruments. The\nobservations were carried out with the Proportional Counter Array (PCA;\nJahoda et al. 1996) and the High-Energy X-Ray Timing Experiment (HEXTE;\nRothschild et al. 1998) on {\\it RXTE}. Three out of the four objects in\nour collection (3C~111, Pictor~A, and 3C~382) were observed in the spring\nof 1997 as part of our own guest-observer programs. The fourth object\n(3C~120) was observed in 1998 February as part of a different program and\nthe data were made public immediately. Although a fair number of\nobservations of 3C~120 exist in the {\\it RXTE} archive, only the above\nobservation was a long, continuous observation suitable for our purposes.\nAll other observations were intended to monitor the variability of this\nobject; they consist of short snapshots spanning a long temporal\nbaseline. Similarly, the only observations of 3C~390.3 available in the\narchive are also monitoring observations of this type. Therefore we have\nnot included 3C~390.3 in our sample. A log of the observations is\nincluded in Table~2. All of the observations fall within PCA gain epoch~3.\n\nThe PCA data were screened to exclude events recorded when the pointing\noffset was greater than 0\\fdg02, when the Earth elevation angle was less\nthan 10\\arcdeg, or when the electron rate was greater than 0.1. Events\nrecorded within 30 minutes of passage though the South-Atlantic Anomaly\nwere also excluded. After screening, time-averaged spectra were extracted\nby accumulating events recorded in the top layer of each Proportional\nCounter Unit (PCU) since these include about 90\\% of the source photons\nand only about 50\\% of the internal instrument background. In the case\nof 3C~111 and 3C~382 we extracted light curves and spectra from all five\nPCUs. In the case of 3C~120 and Pictor~A, PCUs 3 and 4 were turned off\npart of the time, therefore the spectra from these two PCUs and PCUs 0,\n1, and 2 were accumulated separately and then added together. Light\ncurves corresponding to the energy range 3.6--11.6~keV (PCA channels\n6--27), were also extracted for all objects and rectified over the time\nintervals when one or more of the PCUs were not turned on. The PCA\nbackground spectrum and light curve were determined using the\n\\verb+L7_240+ model developed at the {\\it RXTE} Guest-Observer Facility\n(GOF) and implemented by the program \\verb+pcabackest v.2.1b+. This\nmodel is appropriate for ``faint'' sources, i.e., those producing count\nrates less than 40~s$^{-1}$~PCU$^{-1}$. All of the above tasks were\ncarried out using the \\verb+FTOOLS v.4.2+ software package and with the\nhelp of the \\verb+rex+ script provided by the {\\it RXTE}~GOF, which also\nproduces response matrices and effective area curves appropriate for the\ntime of the observation. The net exposure times after data screening, as\nwell as the total source and background count rates, are given in\nTable~2. \n\nThe HEXTE data were also screened to exclude events recorded when the\npointing offset was greater than 0\\fdg02, when the Earth elevation angle\nwas less than 10\\arcdeg. The background in the two HEXTE clusters is\nmeasured during each observation by rocking the instrument slowly on and\noff source. Therefore, source and background photons are included in the\nsame data set and are separated into source and background spectra\naccording to the time they were recorded. After screening we extracted\nsource and background spectra from each of the two HEXTE clusters and\ncorrected them for the dead-time effect, which can be significant because\nof the high background rate. As with the PCA data, the HEXTE data were\nscreened and reduced using the \\verb+FTOOLS v.4.2+ software package. The\nexposure times and count rates in HEXTE/cluster~0 are given in Table~2\nfor reference. In Figure~1 we show the on-source and background spectra\nfrom the PCA and HEXTE/cluster~0, using 3C~111 as an example. This figure\nillustrates that the background makes the dominant contribution to the\nHEXTE count rate. In the case of the PCA, the background contributes\napproximately the same count rate as the source, and its relative\ncontribution increases with energy. At energies above 30~keV the\nbackground dominates the count rate in the PCA.\n\n%-----------\n% FIGURE 1\n%-----------\n\\begin{figure}[t]\n\\centerline{\\psfig{file=fig1.ps,height=3in,angle=-90}}\n\\caption{\\footnotesize \nThe PCA and HEXTE count rate spectra of 3C~111 as examples of typical\ndata obtained from the {\\it RXTE} instruments. The on-source spectrum, shown as\nlarge dots, is compared to the background spectrum. In the case of the PCA, the\nbackground spectrum was computed using the {\\tt L7\\_240} model, while in the\ncase of the HEXTE the background spectrum was measured during the observation\nby rocking the instrument on and off source. Notice that the contribution of \nthe background to the total count rate in the PCA increases with energy so\nthat above 30~keV the observed count rate is dominated by the background.\nIn the case of HEXTE, the background dominates the total count rate at all\nenergies.}\n\\end{figure}\n\n\\section{Light Curves and Time Variability}\n\nIn Figure~2 we show the light curves of the four targets. For each\nobject we plot the net count rate (after background subtraction) as well\nas the the background count rate {\\it vs} time, for reference. The {\\it\nmean} background count rate is generally comparable to the net source\ncount rate, although the background level varies dramatically over the\ncourse of an observation. A visual inspection of the object light curves\nshows no obviously significant variability. To quantify this result we\nsearched the light curves for variability using two complementary methods:\n\n%-----------\n% FIGURE 2\n%-----------\n\\begin{figure}\n\\centerline{\\psfig{file=fig2.ps,width=7.5in,rheight=5.5in,angle=90}}\n\\caption{\\footnotesize\nLight curves showing the 4--10~keV count rate per PCU of the\ntarget BLRGs as a function of time over the course of the {\\it RXTE}\nobservation. For each object we plot the net source light curve and the\nbackground light curve computed from the {\\tt L7\\_240} model for reference}\n\\end{figure}\n\n\\begin{enumerate}\n%======== Added by Mike to justify the text on the right side\n\\rightskip 0pt \\pretolerance=100 \n\n\\item\nWe compared the variance (i.e., the r.m.s. dispersion about the mean)\nwith the average uncertainty of points in the light curve. This method\nis sensitive to fluctuations in the count rate that exceed the noise\nlevel on time scales comparable to the width of the bins in the light\ncurve (the bin width in the light curves of Figure~2 is 640~s). We\nfound no large fluctuations in any of the light curves, save for two\ninstances of poor background subtraction (in Pictor~A and 3C~382). We\nhave also computed the ``excess variance'', $\\sigma^2_{\\rm rms}$,\nfollowing Nandra et al. (1997a), with the following results:\n$(3.1\\pm0.1)\\times 10^{-4}~{\\rm s}^{-2}$ for 3C~111,\n$(1.23\\pm0.01)\\times 10^{-3}~{\\rm s}^{-2}$ for 3C~120,\n$(-8.3\\pm0.6)\\times 10^{-4}~{\\rm s}^{-2}$ for Pictor~A, and\n$(6.1\\pm0.4)\\times 10^{-4}~{\\rm s}^{-2}$ for 3C~382. Since their\nluminosities are $L_{\\rm x}$(2--10~keV)$\\sim 10^{44}~{\\rm erg~s^{-1}}$,\nthese objects fall on the extrapolation of the $\\sigma^2_{\\rm\nrms}$--$L_{\\rm x}$ trend for Seyfert galaxies, found by Nandra et\nal. (1997a). It is noteworthy, however, that the excess variance is\nsmall enough at this luminosity that it is comparable to that of LINERs\nand other very low-luminosity AGNs (Ptak et al. 1998).\n\n\\item\nWe fitted each light curve with a polynomial to find the lowest order\nthat gives an acceptable fit. This method detects small, relatively\nslow variations in the light curve on time scales somewhat shorter\nthan the length of the observations. We found that 3C~111, Pictor~A,\nand 3C~382 show small secular variations on the order of a few percent\nrelative to the mean while 3C~120 shows relatively slow variations\nwith excursions of $\\pm6$\\% from the mean. For reference, we note that\nprevious observations of 3C~120 with {\\it ASCA} have shown it to be\nvariable at the 20\\% level (Grandi et al. 1997).\n\n\\end{enumerate}\n\n\\noindent\nThe above results are not surprising since BLRGs are generally known\nnot to be highly variable on short time scales, although they can vary\nsubstantially on time scales of several days (see for example the soft\nX-ray light curve of 3C~390.3 presented by Leighly \\& O'Brien 1997).\nWe will return to the issue of variability in our later discussion of\nour overall findings.\n\n\n\n\\section{Model Fits to the Observed Spectra}\n\n\\subsection{The Continuum Shape}\n\nThe shape of the continuum was determined by fitting models to the\nobserved spectra with the help of the \\verb+XSPEC v.10.0+ software\npackage (Arnaud 1996). We used PCA response matrices and effective\narea curves created specifically for the individual observations by\nthe program \\verb+pcarsp v.2.37+, taking into account the evolution of\nthe detector properties. All the spectra from individual PCUs were\nadded together and the individual response matrices and effective area\nwere combined accordingly. In fitting the HEXTE spectra we used the\nresponse matrices and effective area curves created on 1997 March 20.\nThe spectra from the two HEXTE clusters were not combined. All spectra\nwere rebinned so that each bin contained enough counts for the $\\chi^2$\ntest to be valid. The PCA spectra were truncated at low energies at\n4~keV and at high energies at either 20 or 30~keV depending on the\nsignal-to-noise ratio. In the case of the HEXTE spectra we retained the\nenergy channels between 20 and 100~keV. \n\nWe compared the spectra with models consisting of a continuum component\nand a Gaussian line, modified by interstellar photoelectric absorption.\nWe adopted the absorbing column densities measured by {\\it ASCA}\n(listed in Table~1), which we held fixed throughout the fitting\nprocess. These column densities are comparable to or greater than the\nGalactic column densities inferred from \\ion{H}{1}~21~cm observations\n(see Table~1). The photoelectric absorption cross-sections used were\nthose of Morrison \\& McCammon (1983). We tried three different models\nfor the continuum shape: a simple power law, a broken power law, and a\npower law plus its Compton reflection from dense, neutral matter. The\nCompton reflection model is meant to describe the effects of Compton\nscattering of photons from an X-ray source associated with the inner\nparts of the accretion disk in the gas that makes up the disk proper\n(e.g., Lightman \\& White 1988; George \\& Fabian 1991). The spectrum of\nreflected X-rays was computed as a function of disk inclination using\nthe transfer functions of Magdziarz \\& Zdziarski (1995)\\footnote{The\nCompton reflection calculation is carried out by the \\verb+pexrav+\nmodel routine in \\verb+XSPEC+}. The free parameters of this model, in\naddition to the spectral index of the primary power law and the\ninclination angle of the disk, are the folding (i.e., upper cut-off)\nenergy of the primary X-ray spectrum, the solid angle subtended by the\ndisk to the central X-ray source, and the abundances of iron and other\nheavy elements. In our fits the inclination angles were constrained to\nlie within the limits inferred from the radio properties of each object\n(see Table~1), and the folding energy of the primary X-ray spectrum was\nconstrained to be greater than 100~keV since all objects are detected\nby HEXTE up to that energy. The broken power law model is effectively a\nparameterization of the Compton reflection model: we included it in\nour suite of continuum models because it serves as an additional\nverification of the possible departure of the continuum shape from a\nsimple power law. Although the broken power law and Compton reflection\nmodels have different shapes in detail, the difference is not\ndiscernible at the signal-to-noise ratio of the available HEXTE\nspectra.\n\n\nThe results of fitting the above models to the observed spectra are\nsummarized in Table~3. The fits yield 2--10~keV unabsorbed fluxes for\nthe target objects in the range\n2--6$\\times 10^{-11}$~erg~cm$^{-2}$~s$^{-1}$ and corresponding\nluminosities in the range 1--5$\\times 10^{44}$~erg~s$^{-1}$, as listed\nin Table~3. Spectra with models superposed, are shown in Figures~3 and\n4. We find that the spectra of two objects, 3C~111 and Pictor~A, are\ndescribed quite well by a simple power law throughout the observed\nenergy range (4--100~keV), as shown in Figure~3. A broken power law\nmodel produces a slightly better fit but the improvement is not\nstatistically significant in view of the additional free parameters\n(the F-test gives chance improvement probabilities of 0.35 and 0.29\nrespectively). Similarly, the Compton reflection model does not produce\na significantly improved fit either.\\footnote{In fact, the Compton\nreflection fit results in a higher value of $\\chi^2$ than the broken\npower law, even though it has more free parameters.} In the case of the\nother two objects, 3C~120 and 3C~382, we find that a simple power law\ndoes not provide an adequate description of the continuum shape (see\nFigure~3); a broken power law or a Compton reflection model is required\nby the data (the F-test gives chance improvement probabilities for the\nCompton reflection model of $5\\times 10^{-5}$ and $5\\times 10^{-3}$,\nrespectively). Fits of power-law plus Compton reflection models to the\nspectra of these two objects are shown in Figure~4. Finally, we note\nthat all of the BLRGs in our collection were also observed with {\\it\nSAX} and detected at high energies up to 50~keV (Padovani et al. 1999;\nGrandi et al. 1999a,b). The {\\it SAX} spectra yield very similar results\nto what we obtain here, namely very similar spectral indices and\nCompton reflection strengths.\n\n\\clearpage \n\n\\begin{deluxetable}{lllll}\n\\tablenum{3}\n\\tablewidth{6.5in}\n\\tablecolumns{5}\n\\tablecaption{Results of Model Fits\\tablenotemark{\\;a}}\n\\tablehead{\n\\colhead{Model and Parameters} &\n\\colhead{3C 111} &\n\\colhead{3C 120} &\n\\colhead{Pictor A} &\n\\colhead{3C 382}\n}\n\\baselineskip 23pt\n\\startdata\n\\cutinhead{\\sc Continuum Models}\n\\sidehead{\\it Simple Power Law}\nSpectral Index, $\\Gamma$ & $1.76\\pm0.01$ & $1.82\\pm0.01$ & $1.80\\pm0.03$ & $1.81\\pm0.02$ \\nl\nFlux density at 1 keV ($\\mu$Jy)\\tablenotemark{\\;b} & 8.9$\\pm0.2$ & 10.6$\\pm0.2$ & 3.9$\\pm0.3$ & 5.6$\\pm0.2$ \\nl\nTotal and Reduced $\\chi^2$ & 52.30, 0.84 & 125.5, 2.02 & 38.51, 0.79 & 68.83, 1.41 \\nl\n\\sidehead{\\it Broken Power Law}\nLow-Energy Spectral Index, $\\Gamma_1$ & $1.77\\pm0.02$ & $1.87^{+0.05}_{-0.02}$ & $1.77^{+0.04}_{-0.05}$ & $1.86^{+0.03}_{-0.04}$ \\nl\nHigh-Energy Spectral Index, $\\Gamma_2$ & $1.7\\pm0.1$ & $1.7\\pm0.1$ & $2\\pm1$ & $1.5^{+0.1}_{-0.2}$\\nl\nBreak Energy (keV) & $11\\pm5$ & $9\\pm1$ & $11\\pm3$ & $10\\pm2$ \\nl\nFlux density at 1 keV ($\\mu$Jy)\\tablenotemark{\\;b} & 9.0$\\pm0.2$ & 11.5$\\pm0.2$ & 3.8$\\pm0.3$ & 6.1$\\pm0.2$ \\nl\nTotal and Reduced $\\chi^2$ & 47.79, 0.80 & 58.55, 0.98 & 33.53, 0.71 & 40.81, 0.73 \\nl\n\\sidehead{\\it Power Law + Compton Reflection\\tablenotemark{\\;c}}\nSpectral Index, $\\Gamma$ & $1.78^{+0.03}_{-0.05}$ & $1.90\\pm0.03$ & $1.72^{+0.04}_{-0.03}$ & $1.92^{+0.07}_{-0.09}$ \\nl \nFolding Energy (keV)\\tablenotemark{\\;d} & 1000 ($>100$) & 15,700 ($>300$) & $>100$ & 300 ($>100$) \\nl \nReflector Solid Angle, $\\Omega/2\\pi$ & $0.1^{+0.4}_{-0.1}$ & $0.4^{+0.4}_{-0.1}$ & $<0.3$ & $0.5^{+0.8}_{-0.2}$ \\nl \nInclination Angle, $i$\\tablenotemark{\\;e} & 24\\arcdeg & 10\\arcdeg & 60\\arcdeg & 16\\arcdeg \\nl \nFlux density at 1 keV ($\\mu$Jy)\\tablenotemark{\\;b} & 9.1$\\pm0.2$ & 11.8$\\pm0.2$ & 3.3$\\pm0.2$ & 6.5$\\pm0.2$ \\nl\nTotal and Reduced $\\chi^2$ & 47.75, 0.81 & 64.37, 1.09 & 35.61, 0.76 & 40.46, 0.88 \\nl\n\\sidehead{}\n2--10 keV Flux (${\\rm erg~s^{-1}~cm^{-2}}$)\\tablenotemark{\\;f} & $5.6\\times 10^{-11}$ & $6.1\\times 10^{-11}$ & $2.3\\times 10^{-11}$ & $3.3\\times 10^{-11}$ \\nl\n2--10 keV Luminosity (${\\rm erg~s^{-1}}$)\\tablenotemark{\\;f} & $5.5\\times 10^{44}$ & $2.9\\times 10^{44}$ & $1.2\\times 10^{44}$ & $4.6\\times 10^{44}$ \\nl\n\\cutinhead{\\sc Gaussian Emission-Line Model}\nRest Energy Dispersion, $\\sigma_{\\rm rest}$ (keV) & $<0.9$ & $<1.2$ & $<1.5$ & $<1.2$ \\nl\nFWHM (km s$^{-1}$) & $<44,000$ & $<55,000$ & $<70,000$ & $<56,000$ \\nl\nLine Flux ($10^{-5}~{\\rm photons~s^{-1}~cm^{-2}}$)& $3.2^{+1.1}_{-0.5}$ & $4.9^{+1.6}_{-1.1}$ & $1.8\\pm0.8$ & $3.1\\pm0.9$ \\nl\nRest Equivalent Width (eV) & $60^{+20}_{-10}$ & $90^{+30}_{-20}$ & $80\\pm40$ & $90\\pm30$ \\nl\n\\tablenotetext{a\\;} \n{All error bars and limits correspond to the 90\\% confidence level.}\n\\tablenotetext{b\\;}\n{The flux density at 1 keV was derived from the normalization of the PCA \nspectrum. It is related to the monochromatic photon flux at 1keV\nvia $f_{\\nu}=h\\,E\\,N_{\\rm E}$, where $h$ is Planck's constant. If \n$N_{\\rm E}$ is measured in ${\\rm photons~s^{-1}~cm^{-2}~keV^{-1}}$,\nthen $f_{\\nu}(1\\;{\\rm keV})=663\\;N_{\\rm E}~\\mu{\\rm Jy}$.}\n\\tablenotetext{c\\;}\n{The results reported here were obtained by keeping the\nabundances of iron and other heavy elements fixed at the solar \nvalue.}\n\\tablenotetext{d\\;}\n{Best-fitting value and lower limit to the folding energy.}\n\\tablenotetext{e\\;}\n{The inclination angles were restricted to lie in the range given in \nTable~1. In the case of Pictor~A and 3C~382, \nwe assumed conservatively that $i<60\\arcdeg$.}\n\\tablenotetext{f\\;}\n{The observed 2--10~keV fluxes and luminosities turn out to be the same \nfor all models. The luminosities reported here have been corrected for\nabsorption.}\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\n%-----------\n% FIGURE 3\n%-----------\n\\begin{figure}\n\\centerline{\\psfig{file=fig3.ps,rheight=6.5in,height=8in}}\n\\caption{\\footnotesize\nThe 4--100~keV spectra of the target objects with the best\nfitting simple power-law continuum model superposed. The model continuum is\nalso modified by interstellar photoelectric absorption. The PCA\nspectra cover the range 4--30~keV or 4--20~keV (finely binned) while\nthe HEXTE spectra cover the range 20--100~keV (coarsely binned). The\nlower panel in each set shows the residual spectrum after subtraction\nof the continuum model, in which the Fe~K$\\alpha$ line is\nobvious. The residual count rate at each point has been scaled by the error\nbar. In the case of 3C~111 and Pictor~A, the simple power-law model\nprovides a good description of the continuum. In the case of 3C~120\nand 3C~382 however, this model does not provide an adequate description\nof the continuum: there are substantial negative residuals at energies\njust below 10~keV and substantial positive residuals at energies between\n10 and 20~keV.}\n\\end{figure}\n\n\\clearpage\n\n%-----------\n% FIGURE 4\n%-----------\n\\begin{figure}[t]\n\\centerline{\\psfig{file=fig4.ps,rheight=3.5in,height=8in}}\n\\caption{\\footnotesize\nThe 4--100~keV spectra of 3C~120 and 3C~382 with the best fitting\npower-law plus Compton reflection model superposed. The model\ncontinuum is also modified by interstellar photoelectric\nabsorption. The PCA spectra cover the range 4--30~keV or 4--20~keV\n(finely binned) while the HEXTE spectra cover the range 20--100~keV\n(coarsely binned). The lower panel in each set shows the residual\nspectrum after subtraction of the continuum model, in which\nthe Fe~K$\\alpha$ line is obvious. The residual count rate at each\npoint has been scaled by the error bar. This model provide a good\ndescription of the continuum in these two objects, unlike the simple\npower-law model shown in Figure~3.}\n\\end{figure}\n\n\n%-----------\n% FIGURE 5\n%-----------\n\\begin{figure}\n\\centerline{\\psfig{file=fig5.ps,width=7.5in,rheight=5.5in,angle=-90}}\n\\caption{90\\% confidence contours model in the $\\cos i$--$\\Omega/2\\pi$\nplane for the Compton reflection. The range of $\\cos i$ plotted on the\nvertical axis corresponds to the allowed values listed in Table~1. In the\ncases of Pictor~A and 3C~382 we have assumed conservatively that\n$i<60\\arcdeg$. The region of acceptable fits is bounded by two lines of the\nsame style except for Pictor~A, where the lines represent upper limits on\n$\\Omega/2\\pi$. Different line styles represent different assumed values of\nthe folding energy of the primary power-law spectrum as follows: solid: \n$E_{\\rm fold}=100$~keV, dashed: $E_{\\rm fold}=300$~keV, and dotted:\n$E_{\\rm fold}=600$~keV. In the case of 3C~120 the data imply that\n$E_{\\rm fold}>300$~keV, therefore the $E_{\\rm fold}=100$~keV contour is\nnot plotted.}\n\\end{figure}\n\n%-----------\n% FIGURE 6\n%-----------\n\\begin{figure}[t]\n\\centerline{\\psfig{file=fig6.ps,height=3in,angle=-90}}\n\\caption{An illustration of the negligible effect of the Fe abundance on\nthe confidence contours in the $\\cos i$--$\\Omega/2\\pi$ plane, using 3C~111\nas an example. The solid lines correspond to a Solar iron abundance, the\ndashed lines to half Solar, the dash-dot lines to a quarter of Solar, and\nthe dotted lines to twice Solar. The results are nearly identical,\nindependently of the Fe abundance.}\n\\end{figure}\n\n\nWe have explored the multidimensional space defined by the free\nparameters of the Compton reflection model to find the range of\nacceptable parameter values. We found that the folding energy of the\nprimary X-ray spectrum is not constrained very well by the observed\nspectra. Thus our initial physical restriction of $E_{\\rm\nfold}>100$~keV is the only constraint on the folding energy of the\nprimary power-law spectrum. Only in the case of 3C~120 (the brightest\nobject, with the longest exposure time) are we able to derive a\nsomewhat better constraint from the data of $E_{\\rm fold}>300$~keV. We\nare particularly interested in the solid angle subtended by the\nreflector to the primary X-ray source, which is a diagnostic of the\ngeometry and structure of the accretion flow. This parameter\ndetermines the {\\it absolute} strength of the reflected component. In\npractice, however, it is not straightforward to constrain the reflector\nsolid angle because the inclination angle of the disk and the iron\nabundance affect the {\\it observed} strength of this component, through\nprojection and photoelectric absorption above the Fe K edge at 7.1~keV\n(see, for example, George \\& Fabian 1991; Reynolds, Fabian, \\& Inoue\n1995), respectively. Moreover, the folding energy of the primary X-ray\nspectrum also affects the determination of the reflector solid angle\nbecause it controls the number of energetic photons available for\nCompton downscattering. We have, therefore, examined the effect of\neach of the above parameters on our derived values of the reflector\nsolid angle by searching the inclination angle - solid angle ($\\cos\ni$--$\\Omega/2\\pi$) plane for regions with acceptable fits for different\nassumed values of the folding energy and iron abundance. In other\nwords, we have taken 2-dimensional slices of the 4-dimensional\nparameter space defined by the solid angle, inclination angle, folding\nenergy, and iron abundance. In Figure~5 we show the 90\\% confidence\ncontours in the $\\cos i$--$\\Omega/2\\pi$ plane for a Solar iron\nabundance and three different assumed values of the folding energy \n($E_{\\rm fold}=100$, 300, and 600~keV). The same results are also\nsummarized in Table~3. The strength of the Compton reflection\ncomponent, as parameterized by $\\Omega/2\\pi$ is systematically lower\nthan what is found in Seyferts observed with either {\\it Ginga} or\n{\\it RXTE}. In particular, we find that $\\Omega/2\\pi\\lesssim 0.5$,\nwhile in Seyferts $\\Omega/2\\pi\\approx 0.8$, with a dispersion of 0.2\n(Nandra \\& Pounds 1994; see also Weaver, Krolik, \\& Pier 1998 and Lee\net al. 1998, 1999 for results from {\\it RXTE} observations). 3C~382 is\nthe only case where the measured value of $\\Omega/2\\pi$ is consistent,\nwithin uncertainties, with what is found in Seyferts. Pictor~A\nrepresents the opposite extreme where only an upper limit of\n$\\Omega/2\\pi<0.3$ can be obtained. In the case of 3C~111, the \ndetection of a Compton reflection hump should be regarded as only\nmarginal since (a) it is only detected at the 90\\% confidence level and\nis consistent with zero at the 99\\% confidence level for $E_{\\rm\nfold}=300,\\,600$~keV, and (b) the probability of chance improvement of\nusing the Compton-reflection model compared to the power-law model is\n0.39 according to the F-test. In the case of 3C~111 and 3C~382 our\nresults are consistent with what Nandra \\& Pounds (1994) and Wo\\'zniak\net al. (1998) report based on {\\it Ginga} observations. The iron\nabundance does not affect the above conclusions at all. We find that \nthe confidence contours in the $\\cos i$--$\\Omega/2\\pi$ plane are\nnearly identical for iron abundances ranging from one quarter to twice\nthe Solar value. We illustrate this result in Figure~6 using 3C~111 as\nan example. This issue is relevant to the strength of the Fe~K$\\alpha$\nlines whose measurements we report in the next section.\n\n%-----------\n% FIGURE 7\n%-----------\n\\begin{figure}[t]\n\\vskip -0.5truein\n\\centerline{\\psfig{file=fig7.ps,width=6.5in,rheight=4.8in,angle=-90}}\n\\caption{\\footnotesize\n68\\%, 90\\%, and 99\\% confidence contours in the $EW$--$FWHM$\nplane for the Fe~K$\\alpha$ lines. The dashed lines in the case of 3C~111\nand Pictor~A are the 68\\%, 90\\%, and 99\\% upper limits obtained from {\\it\nASCA} spectra by Eracleous \\& Halpern (1998a,b). The error bar in the\n3C~111 plot is the measurement of the line by Reynolds et al. (1998) using\n{\\it ASCA}, while the upper limit in Pictor~A comes from the {\\it SAX}\nspectrum of Padovani et al. (1999).}\n\\end{figure}\n\n\\subsection{The Fe~K$\\alpha$ Line}\n\nTo study the properties of the Fe~K$\\alpha$ line we modeled its\nprofile as a Gaussian of energy dispersion, $\\sigma$, and intensity,\n$I_{\\rm Fe\\,K\\alpha}$. Because of the low energy resolution of the PCA,\nmore sophisticated models for the line profile are not warranted. For\neach object we used the best-fitting continuum model and we ignored the\nHEXTE spectra since they do not extend to energies below 20~keV. After\nchecking that the line centroid energies were consistent with the value\nfor ``cold'' Fe, we fixed them to the nominal value based on the\nredshift of each object. We scanned the $I_{\\rm Fe\\,K\\alpha}$--$\\sigma$\nplane for regions where the fit was acceptable, allowing the continuum\nparameters to vary freely. We found that variations in the continuum\nparameters were negligible throughout this plane, which we attribute to\nthe fact that the continuum is well constrained over a wide range of\nenergies. As a result the intensity of the line can be converted to an\nequivalent width ($EW$) via a simple scaling. We, therefore, present\nthe outcome of the parameter search in the form of confidence contours\nin the $EW$--$FWHM$\\footnote{$FWHM$ is the full {\\it velocity} width of\nthe line at half maximum.} plane, which we display in Figure~7. These\nresults are also summarized in Table~3. The lines are unresolved in all\ncases, with upper limits on the $FWHM$ ranging from 44,000 to\n70,000~km~s$^{-1}$ (at 90\\% confidence). The $EW$s range from 60 to\n90~eV with uncertainties around 30--50\\% (at 90\\% confidence). \n\nIn the case of 3C~111 and Pictor~A, the results obtained here are\nconsistent with the results of {\\it ASCA} and {\\it SAX} observations in\nwhich the Fe~K$\\alpha$ line was either marginally detected (3C~111;\nReynolds et al. 1998; Eracleous \\& Halpern 1998b) or not detected at\nall (Pictor~A; Eracleous \\& Halpern 1998a; Padovani et al. 1999). In\nFigure~7 we overlay the {\\it ASCA} upper limits on the {\\it RXTE}\nconfidence contours for reference. In the case of 3C~120 and 3C~382\nthere is a significant discrepancy between the parameters determined\nfrom the {\\it ASCA} spectra and those we determine here: the lines\nappear to be much broader and much stronger in the {\\it ASCA} spectra\nthan in the {\\it RXTE} spectra. In particular, Grandi et al. (1997)\nfind that the Fe~K$\\alpha$ line of 3C~120 has $FWHM=91,000~{\\rm\nkm~s^{-1}}$ and $EW=380$~eV while Reynolds (1997) finds that the\nFe~K$\\alpha$ line of 3C~382 has $FWHM=197,000~{\\rm km~s^{-1}}$ and\n$EW=950$~eV. These velocity widths seem uncomfortably large, as pointed\nout by the authors themselves. In view of the jet inclination angles\nthe line widths imply that some of the line-emitting gas moves faster\nthan light. We suspect that the discrepancy is due to incorrect\ndetermination of the continuum in the {\\it ASCA} spectra (see Wo\\'zniak et\nal. 1998 and the discussion by Sambruna et al. 1999). This may be related\nto the fact that the sensitivity of the {\\it ASCA} SIS, the instrument\nmost commonly used to measure the lines, is extremely low at $E>8$~keV.\nAnother possible cause for this discrepancy is calibration uncertainties\nin the {\\it ASCA} SIS below 1~keV, which affect the detection of a soft\nexcess, hence the determination of the spectral index. In fact, Wo\\'zniak \net al. (1998) find that if the continuum in the {\\it ASCA} spectra of\n3C~120 and 3C~382 is modeled as a broken power law (to account for a\nsoft soft excess) the measured $FWHM$ and $EW$ of the Fe~K$\\alpha$ line \nbecome considerably smaller and consistent with our findings. It also\nnoteworthy, however, that Wo\\'zniak et al. (1998) have almost certainly\nunderestimated the $EW$ of the Fe~K$\\alpha$ line of 3C~120 since they\nassumed the line to be unresolved. We have also been investigating the\ncause of this discrepancy through simultaneous {\\it ASCA} and {\\it RXTE}\nobservations of 3C~382, the results of which we will report in a\nforthcoming paper. \n\n\\section{Discussion}\n\n%-----------\n% FIGURE 8\n%-----------\n\\begin{figure}[t]\n\\centerline{\\psfig{file=fig8.ps,height=3.5in,angle=-90}}\n\\caption{\\footnotesize\nThe distribution of spectral parameters of Seyfert~1 galaxies\nobserved by {\\it Ginga} (Nandra \\& Pounds 1994) with the BLRGs observed\nby {\\it RXTE} marked for comparison. The distribution of $EW$s of Seyfert~1\ngalaxies observed {\\it ASCA} (Nandra et al. 1997b) is also shown. Seyfert~1\ngalaxies are represented by hollow bins and BLRGs are represented by filled\nbins.}\n\\end{figure}\n\n\\subsection{Comparison With Seyfert 1 Galaxies}\n\nTo search for systematic differences between BLRGs and Seyfert~1\ngalaxies, we compare the X-ray spectral properties of the two classes\nof objects using the results of our observations. In particular we\ncompare the photon indices, the strength of the Compton reflection\nhump (parameterized by $\\Omega/2\\pi$), and the $EW$ of the Fe~K$\\alpha$\nline. We use the collection of Seyfert galaxies observed with {\\it\nGinga} (Nandra \\& Pounds 1994) as a comparison sample since the {\\it\nGinga} LAC has a broad enough bandpass to allow a measurement of the\nCompton reflection hump. We also use the collection of Seyfert galaxies\nobserved by {\\it ASCA} (Nandra et al. 1997b) as an additional comparison\nsample for the $EW$ of the Fe~K$\\alpha$ line since the uncertainties in\nthe determination of the $EW$ from the {\\it Ginga} spectra are relatively\nlarge. In Figure~8 we show the distribution of the above parameters\n(spectral index, $\\Omega/2\\pi$, and Fe~K$\\alpha$ $EW$) among Seyfert~1\ngalaxies with the values for the 4 BLRGs observed by {\\it RXTE} superposed\nas filled bins for comparison. A visual inspection of the histograms shows\nthat the spectral indices of BLRGs and Seyfert~1s are fairly similar\nbut the Compton reflection humps and Fe~K$\\alpha$ lines of BLRGs are\nconsiderably weaker than those of Seyfert~1s. Application of the\nKolmogorov-Smirnov (KS) test shows that the distributions of\nCompton-reflection strengths and Fe~K$\\alpha$ $EW$s are indeed\nsignificantly different between Seyferts and BLRGs (chance\nprobabilities of 2\\% for the former and 4\\% for the latter; if the {\\it\nASCA} $EW$ measurements are used instead of the {\\it Ginga}\nmeasurements, the chance probability is 3\\%). In the case of the\nspectral indices the KS test gives a 41\\% probability that the spectral\nindices of Seyferts and BLRGs were drawn from the same parent\npopulation. Sambruna et al. (1999) reach a similar conclusion based\non the larger sample of BLRGs observed by {\\it ASCA}.\nTo investigate whether the weakness of the Fe~K$\\alpha$\nlines of BLRGs is a consequence of the X-ray Baldwin effect (Nandra et\nal. 1997c) we also plot the BLRGs observed by {\\it RXTE} in the\n$EW$-$L_{\\rm X}$ diagram shown in Figure~9. This figure shows clearly\nthat the BLRGs have weaker lines than Seyfert~1s of comparable X-ray\nluminosity, supporting the outcome of the KS test presented above.\nThese results are in agreement with the conclusions of Wo\\'zniak et al.\n(1998) and Sambruna et al. (1999), who found that radio-loud AGNs in\ngeneral, and BLRGs in particular have weaker Fe~K$\\alpha$ lines and\nCompton reflection humps than their radio-quiet counterparts. They are\nalso supported by the results of {\\it SAX} observations by Padovani et\nal. (1999) and Grandi et al. (1998,1999). This raises the question of\nthe origin of the observed differences, which we discuss below.\n\n%-----------\n% FIGURE 9\n%-----------\n\\begin{figure}[t]\n\\centerline{\\psfig{file=fig9.ps,height=3in,angle=-90}}\n\\caption{\\footnotesize\nThe location of the BLRGs observed by {\\it RXTE} in the\n$EW$--$L_{\\rm X}$ plane. The shaded band shows the region occupied by\nSeyfert~1 galaxies in this plane, according to Nandra et al. (1997c); the\nwidth of the band indicates the r.m.s. dispersion above and below the mean\n$EW$ in that luminosity bin.}\n\\end{figure}\n\n\\subsection{Interpretation}\n\nPossible causes of the systematic differences between radio-loud and\nradio-quiet AGNs were discussed by Wo\\'zniak et al. (1998) and by\nEracleous \\& Halpern (1998a). Wo\\'zniak et al. (1998) favored a\nscenario in which the Fe~K$\\alpha$ is produced in the obscuring torus\ninvoked in the unification schemes for type~1 and type~2 AGNs. A\ncolumn density in the reprocessing medium of $N_{\\rm H}\\sim\n10^{23}~{\\rm cm^{-2}}$ was found to reproduce the equivalent width of\nthe Fe~K$\\alpha$ line. In this picture the reflection hump is still\ndue to Compton scattering in the accretion disk. However the continuum\nis postulated to to be beamed away from the disk so that the\nillumination of the disk is ineffective with the result that Compton\nreflection and line emission from the disk made a relatively small\ncontribution to the observed spectrum of BLRGs. Eracleous \\& Halpern\n(1998a) concluded that there were two equally viable explanations for\nthe weakness of the Fe~K$\\alpha$ line in the {\\it ASCA} spectra of\nPictor~A and 3C~111: either the iron abundance in BLRGs is low (it\nneed only be lower by a factor of 2 compared to Seyferts), or the\nsolid angle subtended by the reprocessor to the primary X-ray source\nis about a factor of 2 smaller in BLRGs than in Seyferts. Another\npossibility worth examining is that the disks of BLRGs are in a higher\nionization state than those of Seyfert galaxies. In such a case,\nphotons emerging from the disk will be Compton scattered by electrons\nin the ionized skin of the disk, with the result that both the\nFe~K$\\alpha$ line and the Fe~K edge are smeared out (Ross, Fabian, \\&\nBrandt 1996; Ross, Fabian, \\& Young 1999) and appear weaker. Finally,\nwe mention one more possible explanation: X-rays with a featureless\nspectrum from the jets of BLRGs ``dilute'' the X-ray spectrum from the\ncentral engine, which is otherwise similar to that of Seyferts. This\npossibility was dismissed by both Wo\\'zniak et al. (1998) and by\nEracleous \\& Halpern (1998a), but we re-examine it here in the light\nof the latest observational results. We evaluate the merits and\napplicability of these scenarios below.\n\n\\begin{enumerate}\n%======== Added by Mike to justify the text on the right side\n\\rightskip 0pt \\pretolerance=100\n\n\\item {\\it Continuum beamed away from the accretion disk resulting in weak\nFe~K$\\alpha$ emission and Compton reflection from it; additional\nFe~K$\\alpha$ emission from obscuring torus:} This explanation requires\n{\\it mild} beaming by a sub-relativistic outflow, so that the X-ray beam\nhas an opening angle that is just right to illuminate the obscuring torus\neffectively, while it it illuminates the accretion disk only ``mildly'' so\nthat the strength of the Compton reflection hump from the disk is\nsuppressed. This scenario suffers from the following drawbacks,\nwhich make it untenable:\n\n\\begin{enumerate}\n\\item\nIt is contrary to observational evidence showing that the jets of BLRGs are\nhighly relativistic. In particular, such jets are thought to have bulk\nLorentz factors of $\\gamma=(1-\\beta^2)^{-1/2} \\gtrsim 10$ (Padovani \\& Urry\n1992; Ghisellini et al. 1993, 1998), which implies that their emission is\ntightly focused in a cone of opening angle $\\psi\\approx 1/\\gamma \\lesssim\n6^{\\circ}$. This means that neither the accretion disk nor the obscuring\ntorus can be illuminated by the primary X-ray source, if this is\nassociated with a jet. Postulating that the X-ray continuum is beamed away\nfrom the disk without being associated with the jet is an {\\it ad hoc}\nsolution with no clear physical foundation. In fact, Reynolds \\& Fabian\n(1997) consider beaming of the X-ray continuum produced in a disk corona\nand conclude that the beamed emission is directed in large part towards \nthe disk. The result is that the $EW$ of the Fe~K$\\alpha$ line is {\\it\nenhanced}.\n\\item\nIf the accretion disk is responsible for producing a Compton reflection\nhump, then it should also be producing Fe~K$\\alpha$ emission, which should\nbe added to the emission from the obscuring torus. If this were the case,\nthe Fe~K$\\alpha$ $EW$ should have been disproportionately large compared to\nthe strength of the Compton reflection hump, since it would include\ncontributions from two different sources. The observations, however, show\nthat both the strength of the Compton reflection hump and the $EW$ of the\nFe~K$\\alpha$ line are weaker by about the same factor compared to Seyfert\ngalaxies.\n\\item\nPart of the motivation of Wo\\'zniak et al. (1998) for associating\nthe source of the Fe~K$\\alpha$ line with the obscuring torus was their\nclaimed lack of correlated variations of the continuum and line\nintensities in 3C~390.3. This conclusion is not justified by their data,\nhowever, because of the large uncertainties in the line intensity: a\nfactor of 2 at 68\\% confidence (see their Figure~7). Since the continuum\nvariations span a range of a factor of 2, it is next to impossible to find\ncorrelated variations in the line intensities when the error bars are as\nlarge as they are. \n\\end{enumerate}\n\nIndependently of the above arguments, this interpretation can be tested\nobservationally using the profiles of the Fe~K$\\alpha$ lines. If the lines\nare produced in the accretion disk, their profiles should be considerably\nbroader than if they are produced in the obscuring torus, with very\ndistinct asymmetries caused by Doppler and gravitational redshift.\n\n\\item {\\it Low Iron Abundance:} A low iron abundance would have a very\nclear observational consequence: it would make the Fe~K$\\alpha$ lines\nweaker but at the same time it would make the Compton reflection humps\nstronger by reducing the opacity above the Fe~K edge (George \\& Fabian\n1991; Reynolds, Fabian, \\& Inoue 1995). The {\\it RXTE} spectra\npresented here contradict this interpretation since both the\nFe~K$\\alpha$ lines and the Compton reflection humps are weak. We have\nspecifically tested the hypothesis that the iron abundance is low with\nnegative results (see \\S4.1 and Figure~6). Based on these findings we\nconclude that a low iron abundance is not a viable interpretation. \n\n\\item {\\it Small solid angle subtended by the reprocessor to the\nprimary X-ray source:} The weakness of both the Fe~K$\\alpha$ line and\nthe Compton reflection hump can be explained if the reprocessing medium\nsubtends a relatively small solid angle to the primary X-ray source. In\nthe case of Seyfert galaxies, the primary X-ray source is thought to\nmake up a hot corona overlaying the disk proper, which serves as the\nreprocessor. In such a picture the reprocessor covers half the sky as\nseen from the primary X-ray source, i.e., the solid angle is\n$\\Omega/2\\pi=1$, in reasonable agreement with the observed X-ray\nspectra of Seyfert galaxies. In the case of BLRGs, on the other hand,\nthe {\\it RXTE} spectra indicate that $\\Omega/2\\pi \\lesssim 0.5$. This\ncan be explained in a picture where the primary X-ray source is a\nquasi-spherical ion torus (or ADAF) occupying the inner disk and the\nreprocessor is the geometrically thin, optically thick outer disk. The\nsolid angle subtended by the outer disk to the ion torus is\n$\\Omega/2\\pi < 0.5$ on geometrical grounds (Chen \\& Halpern 1989;\nZdziarski, Lubi\\'nski \\& Smith 1999), in agreement with our findings.\nThis is our preferred interpretation over all the others we consider\nhere and has the following additional attractive features: (a) the\nassociation of ion tori with BLRGs is appealing because these\nstructures offer a way of producing radio jets as we have mentioned in\n\\S1, and (b) such an accretion disk structure also explains the\ndouble-peaked profiles of the Balmer lines in some of these objects\n(Pictor~A, 3C~382, and 3C~390.3; Chen \\& Halpern 1989; Eracleous \\&\nHalpern 1994; Halpern \\& Eracleous 1994). The profiles of the\nFe~K$\\alpha$ lines offer a way of testing this scenario further: if the\nlines do indeed originate in the outer parts of the accretion disk at\nradii $R\\gtrsim 100~R_{\\rm g}$ (where $R_{\\rm g}\\equiv GM/c^2$ is the\ngravitational radius, with $M$ the mass of the black hole), then their\nprofiles should be narrower than those observed in Seyfert galaxies,\nalthough still skewed, asymmetric, and possibly double-peaked.\n\n\\item{\\it Smearing by Compton scattering in an ionized accretion\ndisk:} If the disk is photoionized so that the ionization parameter\nreaches values of $\\xi > 10^4$, photons emerging from the disk will be\nCompton scattered by hot electrons in the disk atmosphere. This\nprocess will smear out of the Fe~K$\\alpha$ line and the Compton\nreflection and make them appear weaker (see Ross et al. 1996, 1999).\nWe consider this an unlikely explanation for our results because the\nobserved spectra lack the distinct signature of this process. Namely,\nat $\\xi > 10^3$, the Fe~K$\\alpha$ lines is considerably broadened by\nCompton scattering while at $\\xi > 10^4$, the line centroid shifts to\nenergies greater than 6.7~keV because most of the iron atoms are\nhighly ionized. Neither of these effects is observed in either the\n{\\it RXTE}~PCA spectra presented here or in published {\\it ASCA}\nspectra.\n\n\\item {\\it Dilution of the X-ray spectrum of the central engine by\nbeamed emission from the jet:} At first glance this is a plausible\ninterpretation since a flux from the jet comparable to the flux from\nthe central engine would provide the necessary dilution. \nThis hypothesis does not withstand close scrutiny, however, for the\nfollowing reasons: (a) as shown by Wo\\'zniak et al. (1998) the spectra of\nBLRGs {\\it cannot} be described as the sum of two power-law components,\nwhich should have been possible if they included comparable contributions\nfrom the jet and the central engine, (b) the light curves of our targets\n(\\S3 and Figure~2) do not show a great deal of variability on time scales\nup to a few days, contrary to what is observed in blazars; 3C~120 shows\nthe largest variability amplitude, consistent with the small inclination\nangle of the jet to the line of sight (Table~1), which make the\ncontribution of the jet to the observed X-ray emission rather\nsignificant, (c) the X-ray spectral indices of BLRGs are systematically\ndifferent from those of blazars, which are typically around 1.4 to 1.5\n(Kubo et al. 1998), and (d) 3C~120 is the object where dilution of the\nobserved spectrum by emission from the jet is expected to be most severe\nbecause of the very small inclination angle; nevertheless both an\nFe~K$\\alpha$ line and a Compton reflection hump are detected, when they\nshould have been undetectable.\n\n\\end{enumerate}\n\n\n\\section{Conclusions and Future Prospects}\n\nOur study of the hard X-ray spectra of 4 BLRGs observed with {\\it RXTE}\nhas shown them to be systematically different from those of Seyfert\ngalaxies. In particular, the Fe~K$\\alpha$ lines and Compton reflection\nhumps in the spectra of BLRGs are at least a factor of 2 weaker than those\nobserved in the spectra of Seyfert galaxies. This result is consistent\nwith the conclusions of previous studies and is supported by the results\nof {\\it SAX} observations of the same targets. After examining several\npossible explanations for this difference, we conclude that the most\nlikely one is that the solid angle subtended by the source of these\nspectral features to the primary X-ray source is a factor of 2 smaller in\nBLRGs than in Seyferts. Since this reprocessing medium is thought to be\nthe accretion disk, we interpret this difference as the result of a\ndifference in the accretion disk structure between BLRGs and Seyferts.\nMore specifically, we argue that if the inner accretion disks of BLRGs\nhave the form of an ion-supported torus (or an ADAF) that irradiates the\nouter disk, then the observed differences can be explained. We find this\nexplanation particularly appealing because ADAFs offer a possible way of\nproducing the radio jets in these objects and because such a disk\nstructure can also account for the double-peaked Balmer line profiles\nobserved in these objects. \n\nThis interpretation, as well as some of the other scenarios we have\nconsidered, can be tested further by studying the profiles of of the\nFe~K$\\alpha$ lines. Unfortunately, such a test has not been possible so\nfar using spectra from {\\it ASCA}, because of their low signal-to-noise\nratio. It will be possible, however, to carry out the test using spectra\nfrom upcoming observatories such as {\\it XMM} and {\\it Astro-E}.\nCorrelated variations of the intensity of the Fe~K$\\alpha$ line and the\nstrength of the X-ray continuum afford an additional observational test of\nthese ideas. The light travel time between the ion torus and the outer\naccretion disk is $\\tau_{\\ell} \\approx 1.7\\,(R/300\\,R_{\\rm\ng})\\,(M/10^8\\,M_{\\odot})$~days, which means that one may expect lags of\nthis order between line and continuum variations. If, on the other hand,\nthe line is produced very close to the center of the disk, the lags should\nbe considerably shorter, while if the line is produced in the obscuring\ntorus, the lags should be on the order of several years. Monitoring\ncampaigns with {\\it RXTE} may provide the data needed for such a test. \n\n\\acknowledgements \n\nWe are grateful to Karen Leighly and Niel Brandt for useful discussions \nand we thank the anonymous referee for thoughtful comments. This work was\nsupported by NASA through grants NAG5--7733 and NAG5--8369. 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}
] |
[] |
astro-ph0002266
|
Spatially resolved Spectro-photometry of M81: \\ Age, Metallicity and Reddening Maps
|
[
{
"author": "Xu Kong\\altaffilmark{1,2}"
},
{
"author": "Xu Zhou\\altaffilmark{1}"
},
{
"author": "Jiansheng Chen\\altaffilmark{1}"
},
{
"author": "Fuzhen Cheng\\altaffilmark{2,1}"
},
{
"author": "Zhaoji Jiang\\altaffilmark{1}"
},
{
"author": "Jin Zhu\\altaffilmark{1}"
},
{
"author": "Zhongyuan Zheng\\altaffilmark{1}"
},
{
"author": "Shude Mao\\altaffilmark{3,10}"
},
{
"author": "Zhaohui Shang\\altaffilmark{1,4}"
},
{
"author": "Xiaohui Fan\\altaffilmark{1,5}"
},
{
"author": "Yong-Ik Byun\\altaffilmark{6,7}"
},
{
"author": "Rui Chen\\altaffilmark{1}"
},
{
"author": "Wen-ping Chen\\altaffilmark{6}"
},
{
"author": "Licai Deng\\altaffilmark{1}"
},
{
"author": "Jeff J. Hester\\altaffilmark{8}"
},
{
"author": "Yong Li\\altaffilmark{8}"
},
{
"author": "Weipeng Lin\\altaffilmark{1}"
},
{
"author": "Hongjun Su\\altaffilmark{1}"
},
{
"author": "Wei-hsin Sun\\altaffilmark{6}"
},
{
"author": "Wean-shun Tsay\\altaffilmark{6}"
},
{
"author": "Rogier A. Windhorst\\altaffilmark{8}"
},
{
"author": "Hong Wu\\altaffilmark{1}"
},
{
"author": "Xiaoyang Xia\\altaffilmark{9,1}"
},
{
"author": "Wen Xu\\altaffilmark{1,8}"
},
{
"author": "Suijian Xue\\altaffilmark{1}"
},
{
"author": "Haojing Yan\\altaffilmark{1,8}"
},
{
"author": "Zheng Zheng\\altaffilmark{1}"
},
{
"author": "and Zhenglong Zou\\altaffilmark{1}"
}
] |
In this paper, we present a multi-color photometric study of the nearby spiral galaxy M81, using images obtained with the Beijing Astronomical Observatory $60/90$ cm Schmidt Telescope in 13 intermediate-band filters from 3800 to 10000{\AA}. The observations cover the whole area of M81 with a total integration of 51 hours from February 1995 to February 1997. This provides a multi-color map of M81 in pixels of $1\arcsec.7 \times 1\arcsec.7$. Using theoretical stellar population synthesis models, we demonstrate that some BATC colors and color indices can be used to disentangle the age and metallicity effect. We compare in detail the observed properties of M81 with the predictions from population synthesis models and quantify the relative chemical abundance, age and reddening distributions for different components of M81. We find that the metallicity of M81 is about $Z=0.03$ with no significant difference over the whole galaxy. In contrast, an age gradient is found between stellar populations of the central regions and of the bulge and disk regions of M81: the stellar population in its central regions is older than 8 Gyr while the disk stars are considerably younger, $\sim 2$ Gyr. We also give the reddening distribution in M81. Some dust lanes are found in the galaxy bulge region and the reddening in the outer disk is higher than that in the central regions.
|
[
{
"name": "kongxu.tex",
"string": "\\documentstyle[aasms4,psfig,flushrt]{article}\n\n\\textheight=9.4in\n\\newcommand\\beq{\\begin{equation}} \n\\newcommand\\eeq{\\end{equation}}\n\\newcommand\\mum{\\mu{m}} \n\\def\\DeltaRA{|\\Delta{\\rm RA|}}\n\\def\\DeltaDec{|\\Delta{\\rm DEC|}}\n\n\\received{27 October 1999} \n\\accepted{31 January 2000} \n\n\\lefthead{Kong et al.} \n\\righthead{Age, Metallicity and Reddening of M81} \n\n\\begin{document}\n\n{ \\title{Spatially resolved Spectro-photometry of M81: \n\\\\ Age, Metallicity and Reddening Maps}\n\n\\author{ \nXu Kong\\altaffilmark{1,2}, \nXu Zhou\\altaffilmark{1},\nJiansheng Chen\\altaffilmark{1}, \nFuzhen Cheng\\altaffilmark{2,1} ,\nZhaoji Jiang\\altaffilmark{1}, \nJin Zhu\\altaffilmark{1}, \nZhongyuan Zheng\\altaffilmark{1}, \nShude Mao\\altaffilmark{3,10}, \nZhaohui Shang\\altaffilmark{1,4},\nXiaohui Fan\\altaffilmark{1,5},\nYong-Ik Byun\\altaffilmark{6,7},\nRui Chen\\altaffilmark{1},\nWen-ping Chen\\altaffilmark{6},\nLicai Deng\\altaffilmark{1},\nJeff J. Hester\\altaffilmark{8},\nYong Li\\altaffilmark{8},\nWeipeng Lin\\altaffilmark{1},\nHongjun Su\\altaffilmark{1},\nWei-hsin Sun\\altaffilmark{6},\nWean-shun Tsay\\altaffilmark{6},\nRogier A. Windhorst\\altaffilmark{8},\nHong Wu\\altaffilmark{1},\nXiaoyang Xia\\altaffilmark{9,1},\nWen Xu\\altaffilmark{1,8},\nSuijian Xue\\altaffilmark{1},\nHaojing Yan\\altaffilmark{1,8},\nZheng Zheng\\altaffilmark{1},\nand\nZhenglong Zou\\altaffilmark{1}\n}\n\n\\altaffiltext{1}{Beijing Astronomical Observatory and Beijing\nAstrophysics Center (BAC), National Astronomical Observational Center, \nChinese Academy of Sciences, Beijing, 100012, P. R. China }\n\n\\altaffiltext{2}{Center for Astrophysics, University of Science and\n Technology of China, Hefei, 230026, P. R. China}\n\\altaffiltext{3}{Max-Planck-Institute for Astrophysics \n Karl-Schwarzschild-Strasse 1, 85740, Garching, Germany }\n\\altaffiltext{4}{Department of Astronomy, University of Texas at Austin,\n Austin, TX 78712}\n\\altaffiltext{5}{Princeton University Observatory, Princeton, New\n Jersey, 08544}\n\\altaffiltext{6}{Institute of Astronomy, National Central University,\n Chung-Li, Taiwan}\n\\altaffiltext{7}{Center for Space Astrophysics and Department of\nAstronomy,\nYonsei University, Seoul, 120--749, Korea}\n\\altaffiltext{8}{Department of Physics and Astronomy, Box 871504, Arizona\n State University, Tempe, AZ 85287--1504}\n\\altaffiltext{9}{Department of Physics, Tianjin Normal University,\nChina}\n\\altaffiltext{10}{Univ. of Manchester,Jodrell Bank Observatory \nMacclesfield, Cheshire SK11 9DL, UK}\n\n\n\\authoremail{xkong@mail.ustc.edu.cn}\n\n\\begin{abstract}\n\nIn this paper, we present a multi-color photometric study of the nearby\nspiral galaxy M81, using images obtained with the Beijing Astronomical\nObservatory $60/90$ cm Schmidt Telescope in 13 intermediate-band filters\nfrom 3800 to 10000{\\AA}. The observations cover the whole area of M81\nwith a total integration of 51 hours from February 1995 to February\n1997. This provides a multi-color map of M81 in pixels of $1\\arcsec.7\n\\times 1\\arcsec.7$. Using theoretical stellar population synthesis\nmodels, we demonstrate that some BATC colors and color indices can be\nused to disentangle the age and metallicity effect. We compare in detail\nthe observed properties of M81 with the predictions from population\nsynthesis models and quantify the relative chemical abundance, age and\nreddening distributions for different components of M81. We find that\nthe metallicity of M81 is about $Z=0.03$ with no significant difference\nover the whole galaxy. In contrast, an age gradient \nis found between stellar populations of the central regions and of the\nbulge and disk regions of M81: the stellar population in its central\nregions is older than 8 Gyr while the disk stars are considerably\nyounger, $\\sim 2$ Gyr. We also give the reddening distribution in M81.\nSome dust lanes are found in the galaxy bulge region and the reddening\nin the outer disk is higher than that in the central regions.\n\n\\end{abstract}\n\n\\keywords{galaxies: abundances -- galaxies: evolution -- galaxies:\nindividual (M81) -- galaxies: stellar content -- (ISM:) dust, reddening}\n\n\\section{INTRODUCTION}\n\nSpatially resolved information about the age, metallicity and interstellar\nmedium reddening of galaxies is a powerful tool to study galaxy\nevolution since it provides essential clues in star formation history,\nchemical composition and enrichment history and environment of galaxies\n(\\cite{Buzzoni89}). To obtain such information, we need to know the\nstellar component and the overall properties of stellar populations\n(\\cite{Leitherer95}). Ideally one would like to study\nresolved individual stars in galaxies. However, given the limited spatial\nresolution of current telescopes, this is only possible for a few very\nnearby galaxies. As a result, the stellar content of even some relatively\nsimple galaxies remain to be unraveled (\\cite{Thuan91}). Information of\nstellar population and star formation history in these galaxies, however,\ncan still be obtained from studying the {\\it integrated} properties of\nthe stars (e.g. \\cite{Schmitt96}, \\cite{Goerdt98}).\n\nSince the pioneering work of Tinsley (1972) and Searle et al. (1973),\nevolutionary population synthesis has become a standard technique to\nstudy the stellar populations of galaxies. This is a result of improvements\nin the theory of the chemical evolution of galaxies, star formation,\nstellar evolution and atmospheres, and the development of synthesis\nalgorithms and the availability of various evolutionary synthesis models.\nA comprehensive compilation of such models was published by Leitherer et\nal. (1996) and Kennicutt (1998). Widely used models include those from\nthe Padova and Geneva group (e.g. \\cite{Schaerer97}, \\cite{Schaerer98},\n\\cite{Bressan96}, and \\cite{Chiosi98}), GISSEL96 (\\cite{Charlot91},\n\\cite{Bruzual93}, \\cite{Bruzual96}), PEGASE (\\cite{Fioc97}) and\nSTARBURST99 (\\cite{Leitherer99}).\n\nMany previous studies of integrated stellar populations use\nspectroscopic data, usually for limited regions in galaxies. In this\npaper, we will, instead, use multi-color photometry to probe the stellar\npopulations. The multi-color photometry provides accurate spectral energy\ndistributions (SEDs) for the {\\it whole} galaxy, although at low spectral\nresolution. We shall demonstrate that it is a powerful tool to study\nthe structure and evolution of the galaxy together with the theoretical\nevolutionary population synthesis methods (for an application of a\nsimilar technique with, but with fewer colors, to moderate redshifts,\nsee Abraham et al. 1999). For this purpose, we pick M81 as the first\napplication of this multi-color approach. \n\nM81 is an excellent candidate\nbecause it is a nearby early-type Sab spiral galaxy at a distance of\n3.6 Mpc and with an angular size of $\\sim 26^{\\prime}$. The angular\nextent is large enough such that the disk and bulge regions are well\nseparated from the ground. \nIt has been the subject of numerous previous studies providing\na wealth of information with which to compare the new metallicity and \ninternal reddening distribution. The internal reddening has been studied\nby Kaufman et al. (1987, 1989), Devereux et al. (1995), Ho et al. (1996) \nand Allen et al. (1997). The metallicity has been studied by Stauffer \\& \nBothun (1984), Garnett \\& Shields (1987), Brodie \\& Huchra (1991) and \nPerelmuter et al. (1995).\nIn this paper,\nwe present a further detailed study of M81 using the unique dataset\nobtained from the BATC \\footnote[1]{The Beijing-Arizona-Taiwan-Connecticut\nMulticolor Sky Survey} multi-color sky survey.\n\nThe outline of the paper is as follows. Details of observations\nand data reduction are given in section 2. In section 3, we provide\na brief description of the model, and analyze the evolution of\nthe integrated colors, color indices with age and metallicity. The\nobserved two-dimensional spectral energy distributions (SEDs) of M81\nwere analyzed using stellar population synthesis models of Bruzual \\&\nCharlot (1996). The distributions of metallicity, age and interstellar\nreddening are given in section 4. In section 5, we discuss how different\nstar formation histories and stellar population synthesis models change\nour results, and compare our results with previous studies.\n. The conclusions are summarized in section 6.\n\n\\section{OBSERVATIONS AND DATA REDUCTION}\n\n\\subsection{CCD Image Observation}\n\nThe large field multi-color observations of the spiral galaxy M81 were\nobtained in the BATC photometric system. The telescope used is the\n60/90 cm f/3 Schmidt Telescope of Beijing Astronomical Observatory (BAO),\nlocated at the Xinglong station. A Ford Aerospace 2048$\\times$2048 CCD\ncamera with 15$\\mu$m pixel size is mounted at the Schmidt focus of the\ntelescope. The field of view of the CCD is $58^{\\prime}$ $\\times $ $\n58^{\\prime}$ with a pixel scale of $1^{\\prime\\prime}.7$. \n\nThe multi-color BATC filter system includes 15 intermediate-band filters,\ncovering the total optical wavelength range from 3000 to 10000{\\AA}\n(see Fan et al, 1996). The filters were specifically designed to avoid\ncontamination from the brightest and most variable night sky emission\nlines. A full description of the BAO Schmidt telescope, CCD, data-taking\nsystem, and definition of the BATC filter systems are detailed elsewhere\n(\\cite{Fan96}, \\cite{Chen00}). To study the age, metallicity and\ninterstellar reddening of M81, the images of M81 covering most part\nof the optical body of M81 were accumulated in 13 intermediate band\nfilters with a total exposure time of about 51 hours from February\n5, 1995 to February 19, 1997. The CCD images are centered at ${\\rm\nRA=09^h55^m35^s.25}$ and DEC=69$^\\circ21^{\\prime}50^{\\prime\\prime}.9$\n(J2000). The dome flat-field images were taken by using a diffuse plate in\nfront of correcting plate of the Schmidt telescope. For flux calibration,\nthe Oke-Gunn primary flux standard stars HD19445, HD84937, BD+262606\nand BD+174708 were observed during photometric nights. The parameters of\nthe filters and the statistics of the observations are given in Table 1.\n\n\n\\begin{table}[ht]\n\\caption[]{Parameters of the BATC filters and statistics of observations}\n\n\\vspace {0.5cm}\n\\begin{tabular}{ccccccrr}\n\\hline\n\\hline\n No. & Name& cw(\\AA)\\tablenotemark{a}& Exp.(h)& N.img\\tablenotemark{b}\n & RMS.\\tablenotemark{c} & Err.\\tablenotemark{d} &\n SM.err. \\tablenotemark{e}\\\\\n\\hline\n1 & BATC02& 3894 & 04:52& 26 &0.021& 7.2& 0.5\\\\\n2 & BATC04& 4546 & 01:00& 10 &0.017& 11.5& 0.7\\\\\n3 & BATC05& 4872 & 03:05& 11 &0.016& 3.5& 0.2\\\\\n4 & BATC06& 5250 & 03:03& 13 &0.016& 5.2& 0.3\\\\\n5 & BATC07& 5785 & 03:12& 16 &0.011& 7.7& 0.5\\\\\n6 & BATC08& 6075 & 02:14& 10 &0.016& 18.3& 1.2\\\\\n7 & BATC09& 6710 & 02:46& 14 &0.018& 5.7& 0.4\\\\\n8 & BATC10& 7010 & 02:19& 11 &0.019& 25.1& 1.6\\\\\n9 & BATC11& 7530 & 03:00& 13 &0.017& 8.2& 0.5\\\\\n10 & BATC12& 8000 & 04:50& 16 &0.014& 16.1& 1.0\\\\\n11 & BATC13& 8510 & 04:45& 15 &0.019& 20.9& 1.4\\\\\n12 & BATC14& 9170 & 05:10& 17 &0.021& 25.7& 1.7\\\\\n13 & BATC15& 9720 & 11:00& 35 &0.019& 25.8& 1.7\\\\\n\\hline\n\\end{tabular}\\\\\n\\tablenotetext{a}{Central wavelength for each BATC filter}\n\\tablenotetext{b}{Image numbers for each BATC filter}\n\\tablenotetext{c}{Zero point error, in magnitude, for each filter\nas obtained from the standard stars}\n\\tablenotetext{d}{Background errors before image smoothing}\n\\tablenotetext{e}{Background errors after image smoothing}\n\\end{table}\n\n\\subsection{ Image data reduction }\n\nThe data were reduced with standard procedures, including bias subtraction\nand flat-fielding of the CCD images, with an automatic data reduction\nsoftware named PIPELINE 1 developed for the BATC multi-color sky survey\n(Fan et al. 1996). The flat-fielded images of each color were combined\nby integer pixel shifting. The cosmic rays and bad pixels were corrected\nby comparison of multiple images during combination. The images were\nre-centered and position calibrated using the HST Guide Star Catalogue.\nThe sky background of the images was obtained by fitting image areas\nfree of stars and galaxies using the method described in Zheng et\nal. (1999). The absolute flux of intermediate-band filter images was\ncalibrated using observations of standard stars. Fluxes as observed\nthrough the BATC filters for the Oke-Gunn stars were derived by convolving\nthe SEDs of these stars with the measured BATC filter transmission\nfunctions (\\cite{Fan96}). {\\it Column} 6 in Table 1 gives the zero point\nerror, in magnitude, for the standard stars in each filter. The formal\nerrors we obtain for these stars in the 13 BATC filters is $\\la 0.02$\nmag. This indicates that we can define the standard BATC system to an\naccuracy of $\\la 0.02$ mag.\n\nAfter background subtraction, the standard deviation of the background\nfor each image is 2.0ADU. Because the signal-to-noise ratio decreases\nfrom the center to the edge of the galaxy, we smoothed the images with a\nboxcar filter. The window sizes of the boxcar were selected depending on\nthe ADU values of the BATC10 band image (7010{\\AA}). If the ADU value\nwas less than 100, the pixel was set to zero; if the value was higher\nthan 100, the pixel was adaptive-smoothed by boxcar filter of $N \\times\nN $ (cell size), where N={\\rm min}($151/\\sqrt {{\\rm ADU}_{\\rm BATC10}},\n15$). By this method, the images were smoothed depending on the S/N of\neach cell. In the central area of M81, the original pixels were used,\nwhereas near the edge of M81 the mean value of multiple pixels (cells)\nwere used, as a result, the spatial resolution decreased from center to\nouter edge. The background errors before and after smoothing are given\nin the last two columns in Table 1.\n\nFinally, the flux derived at each point of M81 is listed in Table 2\n\\footnote[2]{The full Table 2 and color versions of Figs. 1, 4a, 5 and 6\nare available electronically.}\n. The results provide a two-dimensional spectral energy\ndistributions (SED) for M81. The ADU number of each image were converted\ninto units of $10^{-30} {\\rm erg\\,s^{-1}\\,cm^{-2}\\,Hz^{-1}}$. As an\nexample, we present some SEDs for the different areas of M81 in this\npaper. The table gives the following information: {\\it Column 1} and\n{\\it Column 2} give the $(X, Y)$ positions of the photometric center\nof the regions, in units of arcseconds. The coordinate system is\ncentered on the nucleus of the galaxy (${\\rm RA=09^h55^{m}35^s25}$;\n${\\rm DEC=69^{\\circ}21^{\\prime}50^{\\prime\\prime}.9}$, in J2000).\nThe $X$-axis is along the E-W direction with positive values towards the\neast, and the $Y$-axis is along the N-S direction with positive values\ntowards the north. {\\it Column} 3 to {\\it Column} 14 give the fluxes\nrelative to the BATC08 filter (6075{\\AA}). {\\it Column} 15 gives the\nflux in the BATC08 filter in units of ${\\rm 10^{-30} erg s^{-1} cm^{-2}\nHz^{-1}}$. For convenience in later discussions, we define the `central'\nareas as regions with $\\DeltaRA \\leq 1^{\\prime}.0, \\DeltaDec \\leq\n1^{\\prime}.9$, the `bulge' region with $1.0< \\DeltaRA \\leq 3^{\\prime}.4,\n1.9 <\\DeltaDec \\leq 4^{\\prime}.0$ and the `disk' region with $3^{\\prime}.4\n<\\DeltaRA \\le 6^{\\prime}.2, 4^{\\prime}.0 <\\DeltaDec <8^{\\prime}.0$. \n\n%\\hoffset -1.5cm\n\\begin{deluxetable}{llrrrrrrrrrrrrc}\n\\tablewidth{0pc}\n\\tablecaption{Two dimensional spectral energy distributions\nfor the central, bulge and disk areas of M81}\n\\tablehead{ \\colhead{}&\\colhead{}&\n\\multicolumn{12}{c}{Fluxes in different filters relative\nto the $F_{BATC08}$ filter}& \\colhead{Flux of}\\\\\n\\cline{3-14}\n\\colhead{X}&\\colhead{Y}&\\colhead{02}&\\colhead{04}&\n\\colhead{05}&\\colhead{06}&\\colhead{07}&\n\\colhead{09}&\\colhead{10}&\\colhead{11}&\\colhead{12}&\n\\colhead{13}&\\colhead{14}&\\colhead{15}&\\colhead{BATC08} }\n\\startdata\n\n292&330&0.083&0.287&0.368&0.441&0.660&0.726&0.864&1.104&1.227&1.303&1.604&1.717&9232\\nl\n\n291&330&0.084&0.289&0.367&0.440&0.661&0.723&0.862&1.096&1.216&1.287&1.594&1.703&8923\\nl\n\n290&330&0.085&0.294&0.366&0.444&0.665&0.722&0.865&1.094&1.221&1.278&1.585&1.702&8527\\nl\n\n292&331&0.085&0.289&0.366&0.443&0.665&0.720&0.866&1.102&1.221&1.301&1.604&1.727&8695\\nl\n\n291&331&0.086&0.291&0.365&0.444&0.669&0.726&0.872&1.101&1.224&1.304&1.604&1.726&8398\\nl\n\n\\nl\n286&399&0.098&0.309&0.361&0.451&0.660&0.729&0.866&1.073&1.213&1.244&1.571&1.683&1199.\\nl\n\n287&400&0.099&0.307&0.360&0.450&0.656&0.721&0.864&1.068&1.211&1.233&1.568&1.665&1168.\\nl\n\n284&401&0.099&0.313&0.365&0.454&0.659&0.728&0.863&1.065&1.198&1.233&1.556&1.654&1179.\\nl\n\n285&402&0.102&0.315&0.365&0.454&0.660&0.724&0.862&1.063&1.194&1.227&1.547&1.646&1154.\\nl\n\n283&403&0.105&0.320&0.374&0.462&0.671&0.736&0.872&1.068&1.202&1.228&1.546&1.644&1150.\\nl\n\n\\nl\n302&499&0.207&0.415&0.442&0.526&0.712&0.743&0.886&1.009&1.161&1.186&1.445&1.498&266.\\nl\n\n300&499&0.217&0.427&0.457&0.534&0.723&0.751&0.894&1.014&1.150&1.181&1.454&1.489&277.\\nl\n\n299&500&0.218&0.429&0.457&0.533&0.719&0.743&0.891&1.009&1.139&1.173&1.441&1.482&278.\\nl\n\n299&502&0.219&0.431&0.459&0.538&0.723&0.732&0.899&1.018&1.142&1.174&1.438&1.496&268.\\nl\n\n298&502&0.221&0.436&0.463&0.542&0.725&0.736&0.904&1.024&1.146&1.177&1.453&1.511&271.\\nl\n\n\\enddata\n\\tablecomments{Rows 1-5, 6-10, 11-15 are for the central,\nbulge and disk areas respectively. The absolute flux (last column)\nis in units of $10^{-30} {\\rm erg s^{-1} cm^{-2} Hz^{-1}}$. The full\ntable for M81 is available electronically. The pixel values for the\ncenter\nof M81 is (300, 375). }\n\\end{deluxetable}\n\nWe show a black and white image of M81 in Figure 1. To display the\nfeatures clearer, a ``true-color'' image of M81 is available in the\nelectronic version, which is combined with the\n``blue''(3894{\\AA}), ``green''(5785{\\AA}) and ``red''(7010{\\AA}) filters.\nThe filters selected here are free from any strong emission lines. From\nthis image, we can see directly the stellar population difference in\ndifferent areas of the spiral galaxy M81. In the following sections,\nwe will analyze quantitatively the stellar populations in M81 with our\n13 color data.\n\nThe bright HII regions consist of young clusters, and the \nevolutionary population synthesis methods used in this paper\ndo not represent young clusters well. In addition, the central \nnucleus of M81 exhibits some of the same characteristics as classical \nSeyfert galaxies, has no evidence of stellar clusters or a population \nof hot young stars (\\cite{kaufman96}, \\cite{devereux97}, \\cite{davidge99}).\nSo we mask some bright HII regions and the central nucleus of M81 \n(shown as white spots in Fig. 4a, 5, 6, including the foreground stars) \nin this paper. \n\n\\begin{figure}\n\\centerline{\\psfig{file=kongxu.fig1.ps,width=12.0cm,angle=0}}\n\\caption{``True-color\" estimate of the M81 generated by using\nthe BATC02 (3894{\\AA}) filter image for blue, BATC07 (5785{\\AA}) for\ngreen, and BATC10 (7010{\\AA}) for red; the image is balanced by making\nthe background old population orange and hot stars blue. The center\n(origin) of the image is located at $\\rm \\alpha=09^h55^{m}35^s.25, \\delta\n=69^{\\circ}21'50''.9 (J2000.0)$. The image size is about $17^{\\prime}.0$\nby $21^{\\prime}.0$. North is up and east is to the left. We refer to\nthe region with $\\DeltaRA \\leq 1^{\\prime}.0, \\DeltaDec \\leq 1^{\\prime}.9$\nas the central region, the region with $1.0< \\DeltaRA \\leq 3^{\\prime}.4,\n1.9 <\\DeltaDec \\leq 4^{\\prime}.0$ as the bulge, and the region with\n$3^{\\prime}.4 <\\DeltaRA \\le 6^{\\prime}.2, 4^{\\prime}.0 <\\DeltaDec\n<8^{\\prime}.0$ as the disk. A black and white image of Figure 1 be\ndisplayed in paper, the ``true-color'' image of Figure 1 is available\nin the electronic version.}\n\\label{fig1}\n\\end{figure}\n\n\n\\section{DATABASES OF SIMPLE STELLAR POPULATIONS}\n\nA simple stellar populations (SSP) is defined as a single generation\nof coeval stars with fixed parameters such as metallicity, initial\nmass function, etc (\\cite{Buzzoni97}). In evolution synthesis models,\nthey are modeled by a collection of stellar evolutionary tracks with\ndifferent masses and initial chemical compositions, supplemented\nwith a library of stellar spectra for stars at different evolutionary\nstages. Because SSPs are the basic building blocks of synthetic spectra\nof galaxies that can be used to infer the formation and subsequent\nevolution of the parent galaxies (\\cite{Jab96}). In order to study the\nintegrated properties of stellar population in M81, as the first step,\nwe use the SSPs of Galaxy Isochrone Synthesis Spectra Evolution Library\n(Bruzual \\& Charlot 1996 hereafter GSSP). We study the SSPs as the\nfirst step for two reasons. First, they are simple and reasonably well\nunderstood, so it is important to see what one can learn using this\nsimplest assumption, and then check whether more complex star formation\nhistory give qualitatively similar conclusions. This is a common approach\noften taken in the evolutionary population synthesis models for galaxies\n(\\cite{Vazdekis97}, \\cite{mayya95}). Second, although we assume each pixel \nis described by an SSP, we emphasize that the whole galaxy is not SSP; so \nour assumption is not as strong as it may seem. Nevertheless, this is a \nsignificant assumption. Fortunately, it appears the adoption of more \ncomplex star formation history does not change the results \nqualititatively; we return to this issue in \\S 5.1.\n \n\\subsection{Spectral Energy Distribution of GSSPs}\n\nThe Bruzual \\& Charlot (1996) study has extended the Bruzual \\& Charlot\n(1993) evolutionary population synthesis models. The updated version\nprovides the evolution of the spectrophotometric properties for a wide\nrange of stellar metallicity. They are based on the stellar evolution\ntracks computed by Bressan et al. (1993), Fagotto et al. (1994), and\nby Girardi et al. (1996), who use the radiative opacities of Iglesias\net al. (1992). This library includes tracks for stars with metallicities\n$Z=0.0004, 0.004, 0.008, 0.02, 0.05,$ and $0.1$, with the helium abundance\ngiven by $Y=2.5Z+0.23$ (The solar metallicity is $Z_\\odot=0.02$). The\nstellar spectra library are from Lejeune et al. (1997,1998) for all\nthe metallicities listed above, which in turn consist of Kurucz (1995)\nspectra for the hotter stars (O-K), Bessell et al. (1991) and Fluks\net al. (1994) spectra for M giants, and Allard \\& Hauschildt (1995)\nspectra for M dwarfs. The initial mass function is assumed to follow the\nSalpeter's (1955) form, $dN/dM \\propto M^{-2.35}$, with a lower cutoff\n$M_{\\rm l}=0.1M_{\\odot}$ and an upper cutoff $M_{\\rm u}=125M_{\\odot}$\n(\\cite{Sawicki98}).\n\n\\subsection{Integrated Colors of GSSPs}\n\nTo determine the age, metallicity and interstellar medium reddening\ndistribution for M81, we find the best match between the observed colors\nand the predictions of GSSP for each cell of M81. Since the observational\ndata are integrated luminosity, to make comparisons, we first convolve\nthe SED of GSSP with BATC filter profiles to obtain the optical\nand near-infrared integrated luminosity. The integrated luminosity\n$L_{\\lambda_i}(t,Z)$ of the $i$th BATC filter can be calculated with\n%\n\\beq \nL_{\\lambda_i}(t,Z) =\\frac{{\\int_{\\lambda_{\\rm min}(i)}^{\\lambda_{\\rm\nmax}(i)} F_{\\lambda}(t,Z)\\varphi_i(\\lambda)d\\lambda}} {{\\int_{\\lambda_{\\rm\nmin}(i)}^{\\lambda_{\\rm max}(i)} \\varphi_i(\\lambda)d\\lambda}}, \n\\eeq\n%\nwhere the $F_{\\lambda}(t,Z)$ is the spectral energy distribution of\nthe GSSP of metallicity $Z$ at age $t$, $\\varphi_i(\\lambda)$ is the\nresponse functions of the BATC filter system, and $\\lambda_{\\rm min}(i)$\nand $\\lambda_{\\rm max}(i)$ are respectively the maximum and the minimum\neffective wavelength of the $i$th filter ($i=1, 2, \\cdot\\cdot\\cdot, 13$).\n\nThe absolute luminosity can be obtained if we know the distance to a\ngalaxy and the extinction along the line of sight. Since we do not\nknow the exact distance to M81, in this paper, we shall work with\nthe colors that are independent of the distance. We calculate\nthe integrated colors of a GSSP relative to the BATC filter BATC08\n($\\lambda=6075${\\AA}):\n\n\\beq \n\\label{color}\nC_{\\lambda_i}(t,Z)={L_{\\lambda_i}(t,Z)}/{L_{6075}(t,Z)}. \n\\eeq\n\nAs a result, we obtain intermediate-band colors for 6 metallicities from\n$Z=0.0004$ to $Z=0.1$. In the panels of Fig. 2, we plot the colors as\na function of age for GSSP with different metallicities. The following\nremarks can be made. (a) It is apparent that there is a uniform tendency\nfor SSPs to become redder for all colors as the metallicity increases\nfrom $Z=0.0004$ to $Z=0.05$. The near-UV and optical colors show the same\nqualitative behavior as those at longer wavelengths. (b) There is a wide\nrange in age (from 1 to 20 Gyr) in which the colors vary monotonically\nwith time except for the highest metallicity $Z=0.1$. Therefore, once we\nknow the metallicity and interstellar reddening, we can use these colors\nto determine the age distribution of M81, provided that the stellar\npopulation is well modeled by SSPs. (c) For $Z=0.1$, there is only a\nlimited age range for the monotonic behavior in colors. One reason for\nthis behavior is the appearance of AGB-manqu\\'{e} stars at $Z=0.1$.\nThese stars skip the AGB phase and directly go through a long-lived\nhot HB phase (\\cite{Bruzual96}). There are very few, if any, examples\nof galactic stars with such a high metallicity. So our results are not\naffected by this peculiar high-metallicity case.\n\n\\begin{figure}\n\\figurenum{2}\n\\centerline{\\psfig{file=kongxu.fig2.ps,width=16.0cm,angle=-90}}\n\\caption[fig2.ps]{Evolution of eight selected colors $C_{\\lambda_i}$\n(cf. eq. \\ref{color}) for simple stellar population (SSP) models for\ndifferent metallicities as predicted by the GISSEL96 library. Each\nline pattern represents a different metallicity, as indicated inside\nthe frame. All the models shown are computed with a the Salpeter(1955)\ninitial mass function with a lower cutoff of $0.1M_\\odot$ and an upper\ncutoff of $125M_\\odot$.}\n\\label{fig2}\n\\end{figure}\n\n\n\\subsection{Color Indices of GSSPs}\n\nThe observed colors are affected by interstellar reddening, which will of\ncourse complicate our interpretations (\\cite{Ostlin98}). The interstellar\nreddening in the center region of M81 can be measured by its emission\nlines, but for the outer regions, the problem becomes very complex. If\nwe suppose that the extinction law from 3800{\\AA} to 10000{\\AA} has\nno high frequency features, the spectral indices will not be affected\nmuch by the uncertainties in the extinction, so we can use the spectral\nindices to reduce the effect of interstellar extinction.\n\nSpectral indices are (by definition) constructed by means of a\ncentral band pass and two pseudo-continuum band-pass on either side\nof the central band. The continuum flux is interpolated between the\nmiddle-points of the pseudo-continuum band passes (\\cite{Bressan96},\n\\cite{Worthey97}). Since we only observed M81 with intermediate-band\nfilters, not a genuine one-dimensional spectrum, so we must use some\npseudo-color indices to replace the conventional definitions. We define\na color index $I_{\\lambda_j}(t,Z)$ of a SSP by\n\\beq \nI_{\\lambda_j}(t,Z)=L_{\\lambda_j}(t,Z)/L_{\\lambda_{j+1}}(t,Z), \n\\eeq\nwhere $L_{\\lambda_j}(t,Z)$ is the luminosity of a SSP with the metallicity\n$Z$ at age $t$ and wavelength $\\lambda_j$, $L_{\\lambda_{j+1}}(t,Z)$ is\nthe luminosity in the $(j+1)$th filter for the same SSP. The color indices\ncan reduce the effect of reddening, especially in the wavelength region\nlonger than 5000{\\AA}.\n\nAmong all the BATC filter bands, we find that the color index centered\nat 8510{\\AA} ($I_{8510}$) is much more sensitive to the metallicity than\nto the age; the center of this filter band is near the CaII triplets\n($\\lambda=8498, 8542, 8662{\\rm \\AA}$). The strength of CaII triplet\ndepends on the effective temperature, surface gravity and the metallicity\nfor late type stars (\\cite{Zhou91}). \n\nIn an old stellar system, the effect of metallicity on CaII triplet\nbecomes prominent. In fact, we find that there is a very good relation\nbetween the flux ratio of $I_{8510}\\equiv L_{8510}/L_{9170}$ and the\nmetallicity for stellar populations older than 1 Gyr. We plot this\nrelation in Figure 3. Similar relations are also found in many other\nobservation and stellar population synthesis models.\n\nThe relation shown in Figure 3 is crucial for our metallicity\ndetermination and later studies, so it is important to check whether this\nis indeed a reliable method. An early study by Alloin \\& Bica (1989),\nbased on the analysis of stars, star clusters and galaxy nuclei indicated\na strong correlation of CaII triplet with the surface gravity, $\\log\ng$. However, further studies suggested that the CaII triplet strength\ndepends not only on the surface gravity but also on the metallicity.\nA detailed analysis of the behavior of the CaII triplet feature as a\nfunction of stellar parameters was performed by Erdelyi-Mendes \\& Barbuy\n(1991), making use of a large grid of synthetic spectra. They concluded\nthat CaII triplet has a weak dependence on the effective temperature,\na modest dependence on surface gravity, but a quite important dependence\non metallicity. They even suggested that the CaII triplet strength\nmay vary exponentially with the metallicity. Moreover, these lines\nhave been studied by Diaz et al. (1989) , Mallik (1994) and Idiart et\nal. (1997). They have also suggested the CaII triplet strengths depend\non the metallicity (Mayya 1997). So the relation between the $I_{8510}$\nand metallicity seems to be reliable and can be used to determine the\nmetallicities; our own investigation of GSSPs seems to be consistent with\nthese recent studies.\n\n\\begin{figure}\n\\figurenum{3}\n\\centerline{\\psfig{file=kongxu.fig3a.ps,width=12.0cm,angle=-90}}\n\\end{figure}\n\n\\begin{figure}\n\\figurenum{3}\n\\centerline{\\psfig{file=kongxu.fig3b.ps,width=12cm,angle=-90}}\n\\caption[kongxu.fig3.ps]{a) Dependence of the pseudo color-indice $I_{8510}$\nwith metallicity for the GISSEL96 SSP models. The line symbols are the\nsame as in Fig. 2. The metallicities are labeled above each line. b) The\ncorrelation between the pseudo color-index $I_{8510}$ and metallicity,\nfor five different ages ($T=15,10,5,3,1$ Gyr). The solid line shows the\nbest fit through the curves. The lower panel for the PSSPs, the upper\npanel for the GSSPs.\n\\label{fig3}}\n\\end{figure}\n\n\n\\section{DISTRIBUTION OF METALLICITY, AGE AND REDDENING}\n\nIn general, the SED of a stellar system depends on age, metallicity\nand reddening along the line of sight. The effects of age, metallicity\nand reddening are difficult to separate (e.g., \\cite{Calzetti97},\n\\cite{Origlia99},\\cite{Vazdekis97}). Older age, higher metallicity or\nlarger reddening all lead to a redder SEDs of stellar systems in the\noptical (\\cite{Molla97}, \\cite{Bressan96}). In order to separate the\neffects of age, metallicity and interstellar reddening of M81, we first\ndetermine the metallicity by the color index $I_{8510}$, as discussed\nabove, and then obtain the age and reddening by using GSSP model of\nknown metallicity and a extinction law (see \\S 4.2). \n\n\\subsection{Metallicity distribution}\n\nAs discussed in \\S 3.3, there is a good correlation between the color\nindex $I_{8510}$ and the metallicity. We will use the relation obtained\nfrom GSSP; this relation is similar for other stellar population synthesis\nmodels. We find that the correlation can be fit with a simple formula: \n\\beq \nZ=(0.83 - 0.84 \\times I_{8510})^{2}.\n\\eeq\nThis curve is shown in the upper panel of Figure 3. The scatter in Figure\n3 is due to the difference in age. If the ages are younger than 1 Gyr,\nthe scatter becomes larger. Figure 3 shows that for a stellar system of\nages older than 0.5 Gyr, we can estimate the metallicity with an error\nless than the interval of metallicity given by GSSPs. \n\nUsing this method we obtained the metallicities for each part of \nM81 except for the nucleus and the H$\\alpha$ line emission region \n(we have masked them out, see \\S 2.2). Figure 4a shows the resulting \nmetallicity map of M81. \nFigure 4b shows the radial distribution of the metallicity, the\ncurve is derived from the Fig. 4a by averaging over ellipses\nof widths $17\\arcsec$ along the major axis. We used an\ninclination angle of $i=59^{\\circ}$ and a position angle of\n${\\rm PA}=157^{\\circ}$ for the major axis of the galaxy.\n\n\nTo our surprise, we do not find, within our errors, any obvious\nmetallicity gradient from the central region to the bulge and disk\nof M81. In most parts of M81, the mean metallicity is about 0.03 with\nvariation $\\lesssim 0.005$. \nThese results are identical to past suggestions that early-type spirals\nmay have relative high abundances and weak gradients.\nTaking into account of the age scatter,\nthe true value of the metallicity is likely within a range between\n$Z =0.02$ and $Z =0.05$. From the metallicity map of M81, we can also\nclearly see that in some outer regions the metallicities are higher;\nmost of these regions are located in spiral arms and around HII regions,\nwhere a younger stellar population is present.\n\n\\begin{figure}\n\\figurenum{4a}\n\\centerline{\\psfig{file=kongxu.fig4a.eps,width=16.0cm}}\n\\caption[kongxu.fig4a.ps]{A map of the population metallicity in M81.\nLight gray corresponds to the low and dark gray to the high metallicity.\nSome bright HII regions, the central nucleus of M81 and most of\nforeground stars are masked, shown as white spots.\n\\label{fig4a}}\n\\end{figure}\n\n\\begin{figure}\n\\figurenum{4b}\n\\centerline{\\psfig{file=kongxu.fig4b.ps,width=16.0cm,angle=-90}}\n\\caption[kongxu.fig4b.ps]{The radial distribution of metallicity\nfor M81, averaging over ellipses along the major axis (its position\nangle is taken to be $157^{\\circ}$). The line is the regression line\nobtained by a polynomial fit.\nNo obvious metallicity gradient exists from the\ncentral region to the bulge and disk of M81.\n\\label{fig4b}\n}\n\\end{figure}\n\n\\subsection{Age and reddening distribution}\n\nSince we model the stellar populations by SSPs, the observed colors for\neach cell are determined by two parameters: age, $t$, and dust reddening,\n$E(B-V)$. In this section, we will determine these parameters for M81\nsimultaneously by a least square method. The procedure is as follows.\nFor given reddening and age (recall that the metallicity is known, see\nthe previous subsection), we can obtain the predicted integrated colors\nby convolving the dust-free predictions from GSSP with the extinction\ncurve given by Zombeck (1990). The best fit age and reddening values\nare found by minimizing the difference between the observed colors and\nthe predicted values:\n\\beq \nR^2(x,y,t,Z,E)=\\sum_{i=1}^{12}[C_{\\lambda_i}^{\\rm\nobs}(x,y)-C_{\\lambda_i}^ {\\rm ssp}(t, Z, E)]^2, \n\\eeq\nwhere $C_{\\lambda_i}^{\\rm ssp}(t, Z, E)$ represents integrated color in\nthe $i$th filter of a SSP with age $t$, metallicity $Z$ and reddening\ncorrection $E$, and $C_{\\lambda_i}^{\\rm obs}(x,y)$ is the observed\nintegrated color at position $(x,y)$.\n\nFigure 5 shows the age map for M81. It clearly indicates that the\nstellar population in the central regions is much older than that in\nthe outer regions and the youngest components reside in the spiral arms\nof M81. There is a smooth age gradient from the center of the galaxy to\nthe edge of the bulge. The age in the innermost central region (within\n17\\arcsec) is older than $\\ga$ 15 Gyr. The age at the more extended central\nregion is about 9 Gyr. In the bulge edge area, the age is about 4 Gyr. In\ncontrast, the stellar component in the disk area is much younger than\nthat in the bulge region. The mean age in disk area is about 2.0 Gyr. We\ncan see that the age in spiral arms is even younger than the inter-arm areas,\nabout 1 Gyr.\n\nBecause the age obtained in the outer disk region is around 1 Gyr, the\nmetallicity, which is determined by the color indices, might have large\nerrors (see \\S 4.1). The errors in turn will make the age determination\nuncertain. Therefore the age for disk can only be regarded as a rough\nestimation. However, the general trend in the age distribution should\nbe reliable.\n\n\\begin{figure}\n\\figurenum{5}\n\\centerline{\\psfig{file=kongxu.fig5.eps,width=16.0cm}}\n\\caption[kongxu.fig5.ps]{A map of the population ages in M81.\nLight gray corresponds to the young and dark gray to the oldest zones.\nSame as in Fig. 4a, the white spots represent the masked regions,\nsuch as bright HII regions, the central nucleus of M81 and most\nof foreground stars.\n\\label{fig5}}\n\\end{figure}\n\n\nFigure 6 shows the reddening map for M81. From this figure, we find\na large difference in reddening between the bulge and the disk. In the\nbulge, the reddening, E(B-V), is in the range of 0.08 to 0.15. For regions\nwhere E(B-V) is larger than 0.1, we found some spiral like cirrus. There\nis a very obvious high reddening lane around the nucleus with reddening\nequal to or higher than the disk area. The maximum of E(B-V) in the lane\nreaches 0.25. This half-loop lane can be verified in the future with IR\nor CO line observations. In the disk area, the mean reddening of E(B-V)\nis about 0.20. \nIn the central regions, the mean reddening of E(B-V) is very small. These\nresults suggest that dust is largely absent in the central regions\nof M81. The dust seems to be distributed mainly along the inner part\nof spiral arms and around the nucleus. Color versions of Figs. 4-6 are\navailable electronically.\n\n\\begin{figure}\n\\figurenum{6}\n\\centerline{\\psfig{file=kongxu.fig6.eps,width=16.0cm}}\n\\caption[kongxu.fig6.ps]{The interstellar\nreddening map of M81, using the method described in the text.\n\\label{fig6}\n}\n\\end{figure}\n\n\\section{DISCUSSION}\n\nThe results we presented so far are based on the (strong) assumption that\nall stars in a small region form in an instantaneous burst and hence the\nstellar population of each cell can be modeled as SSPs. Unfortunately, the\nstar formation rate history is an essential but very uncertain ingredient\nin the evolutionary population synthesis method since it can vary from\ngalaxy to galaxy and from region to region inside a single galaxy as\nwell. It is only for simplicity that we have adopted an instantaneous star\nformation history, clearly it is important to check whether the results\nare significantly changed if one varies the star formation history; we\naddress this issue in \\S 5.1. While there seems to be general agreement\nbetween the GISSEL96 SSPs models (which we used) with other similar ones\n(\\cite{Charlot96}), there are some fine differences. In \\S 5.2, we study\nhow the results are changed if we adopt a different population synthesis\nmodel from the Padova group. In \\S 5.3, we compare our results with\nearlier works.\n\n\\subsection{Continuous Star Formation}\n\nWe assume that stars are formed from the interstellar gas exponentially\nwith a characteristic time-scale $\\tau$, i.e., $\\Psi(t)=\\Psi_0\n\\exp^{-t/\\tau}$. This model is often used to calculate the integrated\ncolors of galaxies (\\cite{Kennicutt98}) and allows a more diverse star\nformation history. If $\\tau\\rightarrow\\infty$ the model approximates\nconstant star formation rate, while for $\\tau\\rightarrow 0$ it\napproximates an instantaneous burst (\\cite{Abraham99}). It seems that\nspiral galaxies could be well fitted with $\\tau$ of the order of several\nGyr (Fioc et al. 1997).\n\nSince we do not know the appropriate $\\tau$ value for M81, we have\nexplored the values $\\tau = 0.1, 1, 3$ Gyr. We have calculated the\nage, metallicity and interstellar reddening distributions for each\nvalue of $\\tau$. As the value of $\\tau$ increases, the age ($t$)\nincreases throughout M81, while the interstellar reddening decreases\nand the metallicity is little changed. Although the numerical values\nof these quantities do change in each point of M81, the two dimensional\ndistributions of age, metallicity and interstellar reddening of M81 for\ndifferent values of $\\tau$ are similar to the ones shown in Figs. 4-6.\n\n\\subsection{Comparison With Other SSP Models}\n\nThere exist a number of SSP models that are synthesized with different\napproaches. It is important to check the sensitivity of our results\nto the SSP models adopted. The SSP models from the Padova group\n(hereafter, PSSPs) is suitable for the comparison, because they use a\nsimilar technique of ``isochrone synthesis'' to predict the spectral\nevolution of stellar populations. The PSSPs provide the basis for the\npopulation synthesis models (\\cite{Bressan94}, see Bressan et al. 1996\nfor revisions and extensions). The PSSPs use a comprehensive set of\nstellar evolutionary tracks of the Padova group for a wide range of\ninitial chemical compositions from $Z = 0.0004$ to $Z = 0.1$ with ${\\Delta\nY}/{\\Delta Z} = 2.5$. The initial masses of the evolutionary tracks cover\nthe range of $0.6 - 120 M_{\\odot}$, except for the set of metallicity\nZ=0.1, where the masses are from $0.6 - 9 M_{\\odot}$. The initial\nmass function is the Salpeter (1955) law. More details can be found in\nBressan et al. (1994), Silva (1995), and Tantalo et al. (1996). The main\ndifference between GSSPs and PSSPs is the library of stellar spectra:\nthe GSSPs use theoretical stellar spectra from Lejeune et al. (1997)\nwhile the PSSPs use theoretical stellar spectra from Kurucz (1992).\n\nUsing our method, we calculate the colors and color indices for each\nPSSP in the BATC filter system. Using similar procedures as for the GSSP\n(see \\S 4), we obtained the metallicity, age and reddening distributions\nof M81. For PSSP, the metallicity map of M81 again has no obvious\nmetallicity gradient, but the mean metallicity is somewhat higher, about\n0.035. There is a smooth age gradient from the center of M81 to the edge\nof the bulge, except that the mean age in the disk area is lower than 1\nGyr. The interstellar reddening value from PSSP is obvious bigger than\nthat from GSSP. In the bulge, the reddening value is in the range of\n0.18 to 0.35. In the disk area, the mean reddening of E(B-V) is about\n0.40. The reddening value in the central region amount to 0.15. The\ndistributions of metallicity, age and interstellar reddening are very\nsimilar to those found using GSSP.\n\n\n\\subsection{Comparison with previous work}\n\nNumerous determinations of the amount of extinction in M81 have recently\nbeen obtained.\nAllen et al. (1997) compared the detailed distribution of HI, $H\\alpha$,\n150 nm Far-UV continuum emission in the spiral arms of M81. They found every\nreliable bright peak in the $H\\alpha$ has a peak in the Far-UV, and concluded\nthat the effects of extinction on the morphology are small \non the spiral arms. Filippenko \\& Sargent (1988), based on the ratio of the \nnarrow components of $H\\alpha$ and $H\\beta$, concluded that the central \nregions of M81 is reddened by E(B-V)=0.094 mag. These results are very \nsimilar to our results for internal reddening, that the mean reddening in\nthe spiral arms and in the central regions of M81 are small. \nIn addition, Kaufman et al. (1987, 1989), using the $H\\alpha$ and radio \ncontinuum (\\cite{bash86}) \nobservations, have studied the distribution of extinction \nalong the spiral arms in M81, and obtained a mean $A_v = 1.1 \\pm 0.4$ \nmag for 42 giant HII regions with high surface brightness.\nHill et al. (1992) used Near-UV, Far-UV and V-band images of M81 and cluster \nmodels to derive an $A_v =1.5$ mag for the HII regions on the arms.\nThese internal reddening values are larger than ours for\nspiral arms. It can be explained for two reasons. First, the internal\nreddening value of Kaufman et al. are derived from the giant HII \nregions of M81 with high surface brightness, but these bright HII \nregions are excluded in our study. So we have have used different regions\nfor the internal reddening study, it is therefore not clear that they\nmust agree.\nSecond, the continuum regions are affected less by reddening than the \nemission line regions in a galaxy. The internal reddening value of \nKaufman et al. is the reddening for emission line regions, but \nour results are from the continuum regions.\nThe former is significantly larger \nthan the latter; this systematic difference has been seen in \nmany other emission line galaxies (\\cite{kong99}, \\cite{Calzetti97}).\n\nPerelmuter et al. (1995) have obtained spectra for 25 globular cluster\nin M81. Following the method of Brodie \\& Huchra (1990), based on the \nweighted mean of six indices, they measured these clusters' metallicity.\nThe mean metallicity was calculated both from the weighted mean of the \nindividual metallicities, and directly from the cumulative spectrum of \nthe 25 globulars. Both results yielded the same value, \n$\\langle{\\rm Fe/H}\\rangle\n=-1.48 \\pm 0.19$ $(Z=0.033)$, which is identical to that derived by \nBrodie \\& \nHuchra (1991) using 8 clusters ($\\langle{\\rm Fe/H}\\rangle\n=-1.46 \\pm 0.31$). No correlation \nhas been observed between magnitude and metallicity of the globulars in\nthe Milky Way and in M31. Thus the mean metallicity of the 25 globulars \nshould be representative of the M81 system as a whole. These results \nagree with our results for the metallicity of M81 ($Z \\approx 0.03$) very well.\nOn the other hand,\nusing the low-dispersion spectra of 10 HII regions in M81, Stauffer \\& \nBothun (1984) estimated the oxygen abundances for those HII regions from \nthe observed emission lines. They derived a mean abundance near solar \nand a weak abundance gradient in M81. Using the empirical calibration \nmethod and the photoionization models, Garnett \\& Shields (1987) have \nanalyzed the metallicity abundance and abundance gradients for 18 HII \nregions in the galaxy M81. The major result of this study is the \npresence of order-of-magnitude gradient in the oxygen abundance across \nthe disk of M81. These results differ from ours. However, the differences\ncan be readily explained. First, as for the internal reddening, the\nprevious results are derived from the bright HII regions of M81, \nthe abundance gradient is therefore for these\nHII regions. But our result come from the whole \ngalaxy {\\it except} these bright HII regions. So it is not clear that\nthey should have the same behaviors in metallicity. \nAnother caveat to\nthe previous results is that the Pager et al.\n(1980) abundance calibration (which was used in Stauffer \\& Bothun 1984, \nGarnett \\& Shields 1987) is not expected to be exact. \n\nAt last, we must emphasize that although the method we used in this \npaper can be used to constrain the variation of metallicity, population \nage, and reddening across M81 are for the central region, the bulge, and \nthe disk minus the spiral arms, it may not be suited to study the property\nof the spiral arms. There are two main reasons. First, there are hundreds \nof HII regions on the spiral arms, and, the evolutionary population \nsynthesis methods that we used in this paper are not well represented \nvery young clusters. Second, the signal-to-noise ratio decreases from the \ncenter to the edge of the galaxy, we have smoothed the images with a \nboxcar filter (See \\S 2.2). For the outer disk regions, such as the \nspiral arms, the smoothing tends to blend the hundreds of HII regions with \ntheir surroundings. We will study these bright HII regions at the spiral \narms of M81 in more detail in a subsequent paper when we have better data, \nusing the evolutionary population synthesis method, and show how well it \ncan work for young clusters.\n\n\\section{Conclusions}\n\nIn this paper, we have, for the first time, obtained a two-dimensional SED\nof M81 in 13 intermediate colors with the BAO 60/90 cm Schmidt telescope.\nBelow, we summarize our main conclusions.\n\n\\begin{itemize} \n\n\\item Using the new extensive grid of GSSPs covering a wide range of\nmetallicity and age, we calculated the colors and color indices for\n13 colors in BATC intermediate-band filter system. We find that some\nof them can be used to break the age and metallicity degeneracy, which\nenables us to obtain two-dimensional maps of metallicity, interstellar\nreddening and age of M81.\n\n\\item From the two dimensional metallicity distribution of M81, we find\nno obvious metallicity gradient from the central regions to the outer\ndisk. In most part of M81, the mean metallicity is about 0.03 with\nvariation $\\lesssim 0.005$. Some regions in M81, however, have higher\nmetallicity; they are mostly located in the spiral arms and around HII\nregions, where the younger component resides. \n\n\\item From the two dimensional age distribution in M81, we find that the\nmean ages of the stellar populations in the central regions are older\nthan those in the outer regions, which suggests that star formations in\nthe central regions occurred earlier than the outer regions.\n\n\n\\item We find a strong difference in reddening between the bulge region\nand the disk region. In the bulge area, the reddening, E(B-V), is in the\nrange of 0.08 to 0.15. The mean reddening in the disk area is higher,\nabout 0.2. There are some high reddening spiral-like cirrus in the bulge.\n\n\\item In order to understand how sensitive our method is to different\nassumptions about star formation history and different stellar population\nsynthesis models, we have studied an exponential star formation history\nand compared the results obtained with GSSP and PSSP. We find that\nalthough the precise values of age, metallicity and interstellar reddening\nare different, the general trend of in the metallicity, age and reddening\ndistributions is similar.\n\n\\item Finally, we have compared the \ninternal reddening and metallicity maps of M81 with previous studies.\nWe find that the agreements are generally good. In addition, we\nfind that the properties for the bright HII regions and other parts may be\ndifferent.\n\n\\end{itemize}\n\nThe results of M81 presented here illustrate that our method and\nobservational data provide an efficient way to study the distribution of\nmetallicity, age and interstellar reddening for nearby face-on galaxies.\nSimilar data have already been collected for similar galaxies M13,\nNGC589 and NGC5055. The analysis results of these galaxies will be\npublished in a forthcoming paper.\n\n\\acknowledgments\nWe are indebted to Dr. Michele Kaufman for a critical and helpful\nreferee's report that improved the paper.\nWe would like to thank A. Bressan, D. Burstein, and G. Worthey for \nuseful discussion and suggestion.\nWe are grateful to the Padova group for providing us with a set of\ntheoretical isochrones and SSPs. We also thank G. Bruzual and\nS. Charlot for sending us their latest calculations of SSPs and\n for explanations of their code. The BATC Survey is supported by the\nChinese Academy of Sciences (CAS), the Chinese National Natural Science\n Foundation (CNNSF) and the Chinese State Committee of Sciences and\nTechnology (CSCST). Fuzhen Cheng also thanks Chinese National Pandeng\nProject for financial support. The project is also supported in part\nby the U.S. National Science Foundation (NSF Grant INT-93-01805), and\n by Arizona State University, the University of Arizona and Western\n Connecticut State University.\n\n\\begin{thebibliography}{}\n\n\\bibitem[Abraham et al. 1999]{Abraham99} \nAbraham, R. G., Ellis, R. S., Fabian, A. C., et al. 1999, \\mnras, 303, 641\n\n\\bibitem[Allard \\& Hauschildt 1995]{Allard95} \nAllard, F., \\& Hauschildt, P. H. 1995, \\apj, 445, 433\n\n\\bibitem[Allen et al. 1997]{Allen97} \nAllen, R. J., Knapen, J. 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"name": "astro-ph0002266.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Abraham et al. 1999]{Abraham99} \nAbraham, R. G., Ellis, R. S., Fabian, A. C., et al. 1999, \\mnras, 303, 641\n\n\\bibitem[Allard \\& Hauschildt 1995]{Allard95} \nAllard, F., \\& Hauschildt, P. H. 1995, \\apj, 445, 433\n\n\\bibitem[Allen et al. 1997]{Allen97} \nAllen, R. J., Knapen, J. H., Bohlin, R., Stecher, et al. 1997, \\apj, 487, 171\n\n\\bibitem[Alloin \\& Bica 1989]{alloin89} \nAlloin, D., \\& Bica, E. 1989, \\aap, 217, 57\n\n\\bibitem[Bash \\& Kaufman 1986]{bash86}\nBash, F. N., Kaufman, M. 1986, \\apj, 310, 621\n\n\\bibitem[Bessell et al. 1991]{Bessell91} \nBessell, M. S., Brett, J. M., Wood, P. R., et al. 1991, \\aaps, 89, 335\n\n\\bibitem[Bressan et al. 1993]{Bressan93} \nBressan, A., Bertelli, G., Fagotto, F., et al. 1993, \\aaps, 100, 647\n\n\\bibitem[Bressan et al. 1994]{Bressan94} \nBressan, A.,Chiosi, C., \\& Fagotto, F. 1994, \\apjs, 94, 63\n\n\\bibitem[Bressan et al. 1996]{Bressan96} \nBressan, A.,Chiosi, C., Tantalo, R. 1996, \\aap, 311, 425\n\n\\bibitem[Brodie \\& Huchra 1990]{brodie90}\nBrodie, J.P., \\& Huchra, J. P. 1990, \\apj, 362, 503\n\n\\bibitem[Brodie \\& Huchra 1991]{brodie91}\nBrodie, J.P., \\& Huchra, J. P. 1991, \\apj, 379, 157\n\n\\bibitem[Bruzual \\& Charlot 1993]{Bruzual93} \nBruzual, G., \\& Charlot, S. 1993, \\apj, 405, 538\n\n\\bibitem[Bruzual \\& Charlot 1996]{Bruzual96} \nBruzual, G., \\& Charlot, S. 1996, Documentation for GISSEL96 Spectral Synthesis Code.\n\n\\bibitem[Buzzoni 1989]{Buzzoni89} \nBuzzoni, A. 1989, \\apjs, 71,817\n \n\\bibitem[Buzzoni 1997]{Buzzoni97} \nBuzzoni, A. 1997, in IAU Symp. 183, Cosmological Parameters and Evolution of the Universe, ed. K. Sato, 18\n \n\\bibitem[Calzetti 1997]{Calzetti97} \nCalzetti, D. 1997, \\aj, 113, 162\n\n\\bibitem[Charlot \\& Bruzual 1991]{Charlot91} \nCharlot, S., \\& Bruzual, G. 1991, \\apj, 367, 126\n\n\\bibitem[Charlot et al. 1996]{Charlot96} \nCharlot, S., Worthey, G., \\& Bressan, A. 1996, \\apj, 457, 625\n\n\\bibitem[Chen et al. 2000]{Chen00} \nChen, J.-S. et al. 2000, in preparation\n\n\\bibitem[Chiosi et al. 1998]{Chiosi98} \nChiosi, C., Bressan, A., Portinari, L., et al. 1998, \\aap, 339, 355\n\n\\bibitem[Davidge \\& Courteau 1999]{davidge99}\nDavidge, T. J., \\& Courteau, S. 1999, \\aj, 117, 2781\n\n\\bibitem[Devereux et al. 1997]{devereux97} \nDevereux, N. A., Ford, H., Jacoby, G. 1997, \\apj, 481, L71\n\n\\bibitem[Devereux et al. 1995]{devereux95}\nDevereux N. A., Jacoby, G., Ciardullo, R. 1995, \\aj, 110, 1115\n\n\\bibitem[Diaz et al. 1989]{diaz89} \nDiaz, A., Terlevich, E.,\\& Terlevich, R. 1989, \\mnras, 239, 325 \n\n\\bibitem[Erdelyi-Mendes \\& Barbuy 1991]{erdelyi91} \nErdelyi-Mendes, M., \\& Barbuy, B. 1991, \\aap, 241, 176\n\n\\bibitem[Fagotto et al. 1994]{Fagotto94} \nFagotto, F., Bressan, A., Bertelli, G., et al. 1994, \\aaps, 105, 39\n\n\\bibitem[Fan et al. 1996]{Fan96} \nFan, X.-H. et al. 1996, \\aj, 112, 628\n\n\\bibitem[Fioc \\& Rocca-Volmerange 1997]{Fioc97} \nFioc, M., Rocca-Volmerange, B. 1997, \\aap, 326,950\n\n\\bibitem[Fluks et al. 1994]{Fluks94} \nFluks, M. A., Plez, B., Th\\'{e}, P. S., et al. 1994,\\aaps, 105, 311\n\n\\bibitem[Filippenko \\& Sargent 1988]{filippenko88}\nFilippenko, A. V., \\& Sargent,W. L. W. 1988, \\apj, 324, 134\n\n\\bibitem[Garnett \\& Shields 1987]{garnett87}\nGarnett, D. R., \\& Shields, G. A. 1987, \\apj, 327, 82\n\n\\bibitem[Girardiet al. 1996]{Girardiet96} \nGirardi, L., Bressan, A.,Chiosi, C., et al. 1996,\\aaps,117,113\n\n\\bibitem[Goerdt \\& Kollatschny 1998]{Goerdt98} \nGoerdt, A., Kollatschny, W. 1998, \\aap, 337, 699\n\n\\bibitem[Ho et al. 1996]{ho96}\nHo, L.C., Filippenko, A. V., \\& Sargent W.L.W. 1996, \\apj, 462, 183\n\n\\bibitem[Idiart et al. 1997]{idiart97} \nIdiart, T. P., Th\\'{e}venin, F., de Freitas Pacheco, J. A. 1997, \\aj, 113, 1066 \n\\bibitem[Iglesias et al. 1992]{Iglesias92} \nIglesias, C. A., Rogers, F. J., and Wilson, B. G. 1992, \\apj, 397,717\n\n\\bibitem[Jablonka et al. 1996]{Jab96} \nJablonka, P., Bica, E., Pelat, D., Alloin, D. 1996, \\aap, 307, 385\n\n\\bibitem[Kaufman et al. 1996]{kaufman96}\nKaufman, M., Bash, F. N., Crane, P. C., Jacoby, G. H. 1996, \\aj, 112, 1021\n\n\\bibitem[Kaufman et al. 1989]{kaufman89}\nKaufman, M., Bash, F. N., Hine, B. et al. 1989, \\apj, 345, 674\n\n\\bibitem[Kaufman et al. 1987]{kaufman87}\nKaufman, M., Bash, F. N., Kennicutt, JR. R. C., et al. 1987, \\apj, 319, 61\n\n\\bibitem[Kennicutt 1998]{Kennicutt98} \nKennicutt, R. C. 1998, \\aapr, 36, 189\n\n\\bibitem[Kong \\& Cheng 1999]{kong99}\nKong, X., \\& Cheng, F. Z. 1999, \\aap, 351, 477 \n\n\\bibitem[Kurucz 1992]{Kurucz92} \nKurucz, R. L. 1992, in IAU Symp. 149, The Stellar Population of Galaxies, ed. B. Barbuy and A. Renzini (Dordrecht, Kluwer). p. 255\n\n\\bibitem[Kurucz 1995]{Kurucz95} \nKurucz, R. L. 1995 (private communication)\n\n\n\\bibitem[Leitherer et al. 1996]{Leitherer96} \nLeitherer, C., et al. 1996, \\pasp, 108, 996\n\n\\bibitem[Leitherer \\& Heckman 1995]{Leitherer95} \nLeitherer, C., Heckman, T. M. 1995, \\apjs, 96, 9\n\n\\bibitem[Leitherer et al. 1999]{Leitherer99} \nLeitherer, C., Schaerer, D., Goldader, J. D., et al. 1999, \\apjs, 123, 3\n\n\\bibitem[Lejeune et al. 1997]{Lejeune97} \nLejeune, Th., Cuisinier, F., Buser, R. 1997, \\aaps, 125, 229\n\n\\bibitem[Lejeune et al. 1998]{Lejeune98} \nLejeune, Th., Cuisinier, F., Buser, R. 1998, \\aaps, 130, 65\n\n\\bibitem[Mallik 1994]{mallik94} \nMallik, S. V. 1994, \\aaps, 103, 279\n\n\\bibitem[Mayya 1995]{mayya95} \nMayya, Y. D. 1995, \\aj, 109, 2503\n\n\\bibitem[Mayya 1997]{mayya97} \nMayya, Y. D. 1997, \\apj, 482, L149\n\n\\bibitem[Moll\\`{a} et al. 1997]{Molla97} \nMoll\\`{a}, M., Ferrini, F., Diaz, A. I. 1997, \\apj, 475,519\n\n\\bibitem[Origlia et al. 1999]{Origlia99} \nOriglia, L., Goldader, J. D., Leitherer, C., et al. 1999, \\apj, 514, 96\n\n\\bibitem[\\\"{O}stlin et al. 1998]{Ostlin98} \n\\\"{O}stlin, G., Bergvall, N., B\\\"{o}nnback, J. 1998, \\aap, 335, 85\n\n\\bibitem[Pagel et al. 1980]{pagel80}\nPagel, B. E. J., Edmunds, M. G., Smith, G. 1980, \\mnras, 193, 219\n\n\\bibitem[Perelmuter et al. 1995]{perelmuter95}\nPerelmuter, J.-M., Brodie, J. P., Huchra, J.P. 1995, AJ, 110, 620\n\n\\bibitem[Salpeter 1995]{Salpeter95} \nSalpeter, E. E. 1955, \\apj, 121, 161\n\n\\bibitem[Sawicki \\& Yee 1998]{Sawicki98} \nSawicki, M., \\& Yee, H.K.C. 1998, \\aj, 115, 1329\n\n\\bibitem[Schaerer \\& de Koter 1997]{Schaerer97} \nSchaerer, D., \\& de Koter, A. 1997, \\aap, 322, 598\n\n\\bibitem[Schaerer \\& Vacca 1998]{Schaerer98} \nSchaerer, D., \\& Vacca, W. D. 1998, \\apj, 497, 618\n\n\\bibitem[Schmitt et al. 1996]{Schmitt96} Schmitt, H. R., Bica, E.,\nPastoriza, M. G. 1996, \\mnras, 278, 965\n\n\\bibitem[Searle et al. 1973]{Searle73} \nSearle, L., Sargent, W.L.W., Bagnuolo, W. G. 1973, \\apj, 179, 427\n\n\\bibitem[Silva 1995]{Silva95} \nSilva, L. 1995, Master's thesis, University of Padova, Italy\n\n\\bibitem[Stauffer \\& Bothun 1984]{stauffer84}\nStauffer, J. R., \\& Bothun, G. D. 1984, \\aj, 84, 1702\n\n\\bibitem[Tantalo et al. 1996]{Tantalo96} \nTantalo, R., Chiosi, C., Bressan, A., et al. 1996, \\aap, 311, 361\n\n\\bibitem[Thuan 1991]{Thuan91} \nThuan, T. X. 1991, in Massive Stars in Starbursts, ed. C. Leitherer et al. (Cambridge: Cambridge Univ. Press), 183\n\n\\bibitem[Tinsley 1972]{Tinsley71} \nTinsley, B. M. 1972, \\aap, 20, 382\n\n\\bibitem[Vazdekis et al. 1997]{Vazdekis97} \nVazdekis, A., Peletier, R. F., Beckman, J. E., et al. 1997, \\apjs, 111, 203\n\n\\bibitem[Worthey et al. 1997]{Worthey97} \nWorthey, G., Ottaviani, D. L. 1997, \\apjs, 111, 377\n\n\\bibitem[Zheng et al. 1999]{Zheng99} \nZheng, Z. Y., Shang, Z. H., Su, H. J., et al. 1999, \\aj, 117, 2757\n\n\\bibitem[Zhou 1991]{Zhou91} \nZhou, X. 1991, \\aap, 248, 367\n\n\\bibitem[Zombeck 1990]{Zombeck90} \nZombeck, M. V. 1990, Handbook of Space Astronomy and Astrophysics-2'nd edn, \nCambrigde University Press\n\\end{thebibliography}"
}
] |
astro-ph0002268
|
Extended Quintessence: imprints on the cosmic microwave background spectra
|
[
{
"author": "C. Baccigalupi"
},
{
"author": "F. Perrotta"
}
] |
We describe the observable features of the recently proposed Extended Quintessence scenarios on the Cosmic Microwave Background (CMB) anisotropy spectra. In this class of models a scalar field $\phi$, assumed to provide most of the cosmic energy density today, is non-minimally coupled to the Ricci curvature scalar $R$. We implement the linear theory of cosmological perturbations in scalar tensor gravitational theories to compute CMB temperature and polarization spectra. All the interesting spectral features are affected: on sub-degree angular scales, the acoustic peaks change both in amplitude and position; on larger scales the low redshift dynamics enhances the Integrated Sachs Wolfe effect. These results show how the future CMB experiments could give information on the vacuum energy as well as on the structure of the gravitational Lagrangian term.
|
[
{
"name": "NMCcosmo99proc.tex",
"string": "\\documentstyle[sprocl]{article}\n\n\\font\\eightrm=cmr8\n\n\\bibliographystyle{unsrt} %for BibTeX - sorted numerical labels by\n %order of first citation.\n\\arraycolsep1.5pt\n\n\\input{psfig}\n\n\\begin{document}\n\n\\title{Extended Quintessence: imprints on the cosmic microwave background \nspectra}\n\n\\author{C. Baccigalupi, F. Perrotta}\n\n\\address{SISSA/ISAS, Via Beirut 4, 34014 Trieste, Italy, \\\\\nE-mail: bacci@sissa.it, perrotta@sissa.it}\n\n\\author{S. Matarrese}\n\n\\address{Dipartimento di Fisica `Galileo Galilei', Universit\\'a di\nPadova,\\\\ \nand INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy, \\\\\nE-mail: matarrese@pd.infn.it}\n\n\\maketitle\\abstracts{We describe the observable features of \nthe recently proposed Extended Quintessence scenarios \non the Cosmic Microwave Background (CMB) anisotropy \nspectra. In this class of models a scalar field $\\phi$, assumed to provide \nmost of the cosmic energy density today, is non-minimally coupled to the \nRicci curvature scalar $R$. \nWe implement the linear theory of cosmological perturbations \nin scalar tensor gravitational theories to compute CMB \ntemperature and polarization spectra. \nAll the interesting spectral features are affected: \non sub-degree angular scales, \nthe acoustic peaks change both in amplitude and \nposition; on larger scales the low redshift dynamics enhances \nthe Integrated Sachs Wolfe effect. \nThese results show how the future CMB experiments could give \ninformation on the vacuum energy as well as on the structure of \nthe gravitational Lagrangian term.} \n\n\\section{Introduction}\n\nOne of the most interesting novelty in modern cosmology is \nthe observational trend for an\naccelerating Universe, as suggested by distance measurements \nto type Ia Supernovae \\cite{Perlm}. \nThese results astonishingly indicate that almost two thirds \nof the energy density today is {\\it vacuum} energy. \n\nIt has been thought that this vacuum \nenergy could be mimicked by a minimally-coupled scalar field \n\\cite{Stain1}, considered as a \"Quintessence\" (Q). \nThe main features of such a vacuum energy component, that could\nalso allow to distinguish it from a cosmological constant, are \nits time-dependence as well as its capability to develop spatial \nperturbations. \n\nTheoretically, Quintessence models are attractive, since they \noffer a valid alternative explanation of the smallness of the \npresent vacuum energy density instead of the cosmological constant; \nindeed, we must have $| \\rho_{vac}| < 10^{-47}$ GeV$^4$ \\ today, while\nquantum field theories would predict a value for the cosmological\nconstant which�is larger by more than 100 orders \nof magnitude \\cite{Lambda}. Instead, the vacuum \nenergy associated to the Quintessence is dynamically evolving towards\nzero driven by the evolution of the scalar field. \nFurthermore, in the Quintessence scenarios one can select a subclass of\nmodels, which admit \"tracking solutions\" \\cite{Stain1}: here a\ngiven amount of scalar field energy density today can be reached \nstarting from a wide set of initial conditions. \n\nThe effects of possible couplings \nof this new cosmological component with the other species \nhave been explored in recent works, \nboth for what regards matter \\cite{carrollame0} and gravity\n\\cite{ChibaAmeUzan}. \nHere we review some of the results obtained in a recent paper \n\\cite{EQ}, for what concerns the effects on the Cosmic Microwave \nBackground (CMB) anisotropy: this scenario has been named \n`Extended Quintessence' (EQ), by meaning that \nthe scalar field coupled with the Ricci scalar $R$\nhas been proposed as the Quintessence candidate, in analogy with \nExtended Inflation models \\cite{exte}. \n\n\\section{Cosmological dynamics in scalar-tensor theories of gravity}\n\nThe action \n$S=\\int d^4 x \\sqrt{-g} [ F(\\phi)R -\n\\phi^{; \\mu} \\phi_{; \\mu} -2V( \\phi)+ L_{fluid} ]$ \nrepresents scalar-tensor theories of gravity, \nwhere $R$ is the Ricci scalar and $L_{fluid}$ \nincludes matter and radiation. \n\nWe assume a standard Friedman-Robertson-Walker (FRW) form for the\nunperturbed background metric, with signature $(-,+,+,+)$, \nand we restrict ourselves to a spatially \nflat universe. The FRW and Klein Gordon equations are \n\\begin{equation} \n\\label{FriedmannKleinGordon}\n{\\cal H}^2=\n{a^2 {\\rho}_{fluid}\\over 3F} +{\\dot{\\phi}^2\\over 6F} + \n+{a^2 V\\over 3F} - {{\\cal H}\\dot{F}\\over F}\\ ,\\ \n\\ddot{\\phi}+2{\\cal H} \\dot{\\phi}=\n{a^2 F_{, \\phi}R\\over 2} -a^2 V_{,\\phi}\\ ,\n\\end{equation}\nwhere the overdot denotes differentiation with respect to the conformal\ntime $\\tau$ and ${\\cal H } = {\\dot a}/a$.\nFurthermore, the continuity equations for the \nindividual fluid components are \n$\\dot{\\rho}_i = -3 {\\cal H} ({\\rho}_i + p_i)$. \n\nFor what concerns our treatment of the perturbations \\cite{EQ}, \nwe give here only the very basic concepts. \nA scalar-type metric perturbation in the synchronous gauge is\nparameterized as \n\\begin{equation}\nds^2=a^2 [-d\\tau ^2 + (\\delta_{i j }+h_{i j })dx^i dx^j ] \\ \\ ;\n\\end{equation}\nby linearly perturbing the Einstein and Klein Gordon equations \nabove, the equation for the metric perturbing quantities can \nbe derived; these equations are linked to the fluid perturbed \nquantities, from any species including $\\phi$, \nobeying the perturbed continuity equations. \n\nLet us define now the gravitational sector of \nthe Lagrangian. We require that $F$ has the correct physical \ndimensions of $1/G$. Note that all this fixes the link between \nthe value of $F$ today and the Newtonian gravitational constant $G$:\n$F_{0}=F(\\phi_{0})=1/8\\pi G$. Different forms of $F(\\phi )$ can be \nconsidered \\cite{EQ}. \nIn Induced Gravity (IG) models, that we treat here, \nthe gravitational constant is directly \nlinked to the scalar field itself, as originally proposed in the \ncontext of the Brans-Dicke theory: \n\\begin{equation}\nF(\\phi )=\\xi\\phi^{2}\\ ,\n\\label{IG}\n\\end{equation}\nwhere $\\xi$ is the IG coupling constant. \nNote that solar system experiments already offer \nconstraints to the viable values of $\\xi$, that may be easily \nobtained by integrating the background equations \\cite{EQ}. \nThe dynamics of $\\phi$ \nis determined by its coupling with $R$, as well as by its \npotential, that is responsible for the vacuum energy today; \nwe take the simplest inverse power potential, \n$V(\\phi )=M^5/\\phi$, where the mass-scale $M$ is fixed by the \nlevel of energy contribution today from the Quintessence. \nIn our integrations, \nwe adopt adiabatic initial conditions. \nWe require that the present value of $\\Omega_{\\phi}$ is $0.6$, \nwith Cold Dark Matter at \n$\\Omega_{CDM}=0.35$, three families of massless neutrinos, \nbaryon content $\\Omega_{b}=0.05$ and Hubble constant $H_{0}=50$ Km/sec/Mpc; \nthe initial kinetic energy of $\\phi$ is taken equal to the \npotential one at the initial time $\\tau=0$. \n\n\\begin{figure}[t]\n\\centerline{\n\\psfig{file=clpknmc4proc.ps,height=3.in,width=3.in}\n}\n\\vskip -4.cm\n\\caption{Perturbations for IG models for various \nvalues of $\\xi$: \nCMB temperature (left), and polarization (right).\nDotted, dashed, solid lines are for $\\xi=0,.01,.02$ \nrespectively}\n\\label{fig}\n\\end{figure}\n%\\begin{figure}[t]\n%\\rule{5cm}{0.2mm}\\hfill\\rule{5cm}{0.2mm}\n%\\vskip 2.5cm\n%\\rule{5cm}{0.2mm}\\hfill\\rule{5cm}{0.2mm}\n%\\psfig{figure=filename.ps,height=1.5in}\n%\\caption{A generalized cactus tree: the confluent\n%transfer-matrix $S$ transforms the state function $f(x)$ and \n%$f(z)$ into $f(x)$. \\label{fig:radish}}\n%\\end{figure}\n\n\\section{Effects on the CMB} \n\nThe phenomenology of CMB anisotropies in EQ models \nis rich and possesses distinctive features. \nIn Fig.\\ref{fig}, \nthe effect of increasing $\\xi$ on \nthe power spectrum of COBE-normalized CMB anisotropies \nis shown. \nThe rise of $\\xi$ makes substantially three \neffects: the low $\\ell$'s region is enhanced, the oscillating \none attenuated, and the location of the peaks shifted \nto higher multipoles. Let us now explain these effects. \nThe first one is due to the integrated Sachs-Wolfe effect, \narising from the change from matter to Quintessence dominated \nera occurred at low redshifts. This occurs also in ordinary Q models, \nbut in EQ this effect is enhanced. \nIndeed, in ordinary Q models the dynamics of $\\phi$ is governed by \nits potential; in the present model, one more independent \ndynamical source is the coupling between the Q-field and the Ricci\ncurvature $R$. The dynamics of \n$\\phi$ is boosted by $R$ together with its potential $V$. \nAs a consequence, part of the COBE normalization at \n$\\ell=10$ is due to the Integrated Sachs-Wolfe effect; \nthus the actual amplitude of the underlying \nscale-invariant perturbation spectrum \ngets reduced. In addition, it can be seen \n\\cite{EQ} that the Hubble length was smaller in the past \nin EQ than in Q models. This has the immediate \nconsequence that the horizon crossing of a given \ncosmological scale is delayed, making \nthe amplitude the acoustic oscillations slightly \ndecreasing since the matter content at decoupling is \nincreased. \n\nFinally, note how the location of the acoustic peaks \nin term of the multipole $\\ell$ at which the oscillation occurs, \nis shifted to the right. Again, the reason is the time dependence \nof the Hubble length, which at decoupling \nsubtended a smaller angle on the sky. It can indeed \nverified that the ratio of the peak multipoles in \nFig.\\ref{fig} coincides numerically with the \nthe ratio of the values of the Hubble lengths at decoupling \nin EQ and Q models \\cite{EQ}. \n\nWe have used here values of $\\xi$ large in order to clearly \nshow the CMB effects. \nIt can be seen these values do not satisfy the solar system \nexperimental constraints; however, a smaller $\\xi$ produces \nthe same spectral features, reduced but still \ndetectable by the future \ngeneration of CMB experiments, able \nto bring the accuracy on the CMB power spectrum \nat percent level up to $\\ell\\simeq 1000$ \\cite{CMBFUTURE}. \n\n\\section*{References}\n\\begin{thebibliography}{99}\n\\bibitem{Perlm} S. Perlmutter {\\it et al.}, \n{\\it Nature} {\\bf 391}, 51 (1998); \nA.G. Riess {\\it et al.}, {\\it Astron. J.} {\\bf 116}, 1009 (1998). \n\\bibitem{Stain1} \nP.J. Peebles, B. Ratra, {\\it Astrophys.J.} {\\bf 352}, L17 (1988); \nK. Coble, S. Dodelson, J. Friemann, {\\it Phys. Rev. D} {\\bf 55},\n1851 (1997); I. Zlatev, L. Wang, P.J. Steinhardt, \n{\\it Phys. Rev. Lett.} {\\bf 82}, 896 (1999).\n\\bibitem{Lambda} E. I. Guendelman, A. B. Kaganovich, \n{\\it Phys.Rev. D}{\\bf 60} 065004 (1999).\n\\bibitem{carrollame0} S.M.\nCarroll, {\\it Phys. Rev. Lett.} {\\bf 81}, 15, 3097 (1998). \n\\bibitem{ChibaAmeUzan} T. Chiba, {\\it Phys.Rev. D}{\\bf 60} \n083508 (1999); L. Amendola, {\\it Phys.Rev. D}{\\bf 60} 043501 \n(1999); J.P. Uzan, {\\it Phys. Rev. D}{\\bf 59}, 123510 (1999). \n\\bibitem{EQ} F. Perrotta, C. Baccigalupi \\& S. Matarrese, \n{\\it Phys. Rev. D}{\\bf 61}, 023507 (2000). \n\\bibitem{exte} D. La, P.J. Steinhardt, \n{\\it Phys. Rev. Lett.}{\\bf 62}, 376 (1989). \n\\bibitem{HW2} J.C. Hwang, {\\it Class. Quantum Grav.}{\\bf 7}, \n1613 (1990).\n\\bibitem{CMBFUTURE}Microwave Anisotropy Probe home page:\\\\ \nhttp://map.gsfc.nasa.gov/ ;\nPlanck Surveyor home page:\\\\\nhttp://astro.estec.esa.nl/SA-general/Projects/Planck/\n\\end{thebibliography}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002268.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{Perlm} S. Perlmutter {\\it et al.}, \n{\\it Nature} {\\bf 391}, 51 (1998); \nA.G. Riess {\\it et al.}, {\\it Astron. J.} {\\bf 116}, 1009 (1998). \n\\bibitem{Stain1} \nP.J. Peebles, B. Ratra, {\\it Astrophys.J.} {\\bf 352}, L17 (1988); \nK. Coble, S. Dodelson, J. Friemann, {\\it Phys. Rev. D} {\\bf 55},\n1851 (1997); I. Zlatev, L. Wang, P.J. Steinhardt, \n{\\it Phys. Rev. Lett.} {\\bf 82}, 896 (1999).\n\\bibitem{Lambda} E. I. Guendelman, A. B. Kaganovich, \n{\\it Phys.Rev. D}{\\bf 60} 065004 (1999).\n\\bibitem{carrollame0} S.M.\nCarroll, {\\it Phys. Rev. Lett.} {\\bf 81}, 15, 3097 (1998). \n\\bibitem{ChibaAmeUzan} T. Chiba, {\\it Phys.Rev. D}{\\bf 60} \n083508 (1999); L. Amendola, {\\it Phys.Rev. D}{\\bf 60} 043501 \n(1999); J.P. Uzan, {\\it Phys. Rev. D}{\\bf 59}, 123510 (1999). \n\\bibitem{EQ} F. Perrotta, C. Baccigalupi \\& S. Matarrese, \n{\\it Phys. Rev. D}{\\bf 61}, 023507 (2000). \n\\bibitem{exte} D. La, P.J. Steinhardt, \n{\\it Phys. Rev. Lett.}{\\bf 62}, 376 (1989). \n\\bibitem{HW2} J.C. Hwang, {\\it Class. Quantum Grav.}{\\bf 7}, \n1613 (1990).\n\\bibitem{CMBFUTURE}Microwave Anisotropy Probe home page:\\\\ \nhttp://map.gsfc.nasa.gov/ ;\nPlanck Surveyor home page:\\\\\nhttp://astro.estec.esa.nl/SA-general/Projects/Planck/\n\\end{thebibliography}"
}
] |
astro-ph0002269
|
On the universality of the spectrum of cosmic rays accelerated at highly relativistic shocks
|
[
{
"author": "{Mario Vietri}"
}
] |
I consider analytically particle acceleration at relativistic shocks, in the limit of pitch angle diffusion and large shock Lorentz factors. The derived energy spectral index ($k = (1+\sqrt{13})/2 \approx 2.30$), and particle pitch angle distribution at the shock are successfully compared with the results of numerical solutions. This totally analytic derivation is completely independent of the detailed dependence of the diffusion coefficient $D(\mu,p)$ on either parameter, and it is argued on a physical basis that the orientation of the magnetic field is also irrelevant, making $k$ a universal index.
|
[
{
"name": "uni4.tex",
"string": "\\documentclass[preprint]{aastex}\n%\\documentclass[preprint]{/home/astro/vietri/corelli/aastex/aastex}\n\\begin{document}\n%\\tighten\n\\def\\etal{{\\it et al.\\/}}\n\\def\\cf{{\\it cf.\\/}}\n\\def\\ie{{\\it i.e.\\/}}\n\\def\\eg{{\\it e.g.\\/}}\n\n\n\\title{On the universality of the spectrum of cosmic rays accelerated\nat highly relativistic shocks}\n\\author{{\\bf Mario Vietri}}\n\\affil{\nUniversit\\`a di Roma 3, Via della Vasca Navale 84, 00147 Roma, \\\\\nItaly, E-mail: vietri@amaldi.fis.uniroma3.it \\\\\n}\n\n\\begin{abstract}\nI consider analytically particle acceleration at relativistic shocks, in the \nlimit of pitch angle diffusion and large shock Lorentz factors.\nThe derived energy spectral index ($k = (1+\\sqrt{13})/2\n\\approx 2.30$), and particle pitch angle distribution at the shock are \nsuccessfully compared with the results of numerical solutions. This totally \nanalytic derivation is completely independent of the detailed dependence\nof the diffusion coefficient $D(\\mu,p)$ on either parameter, and it is\nargued on a physical basis that the orientation of the magnetic field is also\nirrelevant, making $k$ a universal index.\n\\end{abstract}\n\n\\keywords{acceleration of particles -- shock waves -- gamma rays: bursts}\n\n\\section{Introduction}\n\nThere is currently a growing interest in the acceleration of non--thermal\nparticles at highly relativistic shocks. There are three classes of \n{\\it bona fide} relativistic sources: beyond the well--established \nextra--Galactic (Blazars) and Galactic (superluminal) sources, both of which \nexhibit superluminal motions, \nit is now also well-established that Gamma Ray Bursts (GRBs) display\nhighly relativistic expansions, with Lorentz factors well in excess of \n$100$. Other classes of relativistic sources may include \nSoft Gamma Ray Repeaters (SGRs), whose recurrent explosions are largely \nsuper--Eddington, and special SNe similar to SN 1998bw, which displayed\nmarginally Newtonian expansion ($\\approx 6\\times 10^4\\; km\\; s^{-1}$) when \noptical emission lines became detectable, about a month after the explosion. \n\nWith the discovery of GRBs' afterglows, it has now become feasible to \nderive the energy spectral index $k$ of electrons accelerated at the forward\nshock, as a function of the varying (decreasing) shock Lorentz factor \n$\\gamma$, provided simultaneous wide--band spectral coverage is available. With \nthe launch of the USA/Italy/UK mission SWIFT, these data will become available \nfor a statistically significant number of bursts, testing directly models for\nparticle acceleration at relativistic shocks. Furthermore, since GRBs must also\nclearly accelerate protons, the same index $k$ may determine the spectrum\nof ultra high energy cosmic rays observed at Earth. \n\nHowever, until recently, both the lack of astrophysical motivation and the \ndifficulty inherent in treating highly anisotropic distribution functions have \nstiffened research on this topic. Early work, both semi--analytic\nand outright numerical, has concentrated on barely relativistic flows with\nLorentz factors of a few, well suited to Blazars and Galactic superluminals,\nbut clearly insufficent for GRBs, the only exception being the numerical\nsimulations of Bednarz and Ostrowski (1998). It is the purpose of this {\\it \nLetter} to perform an analytic investigation of the large $\\gamma$ limit, to \nestablish which (if any) of the properties of the particles' distribution \nfunction depend upon the physical conditions of the fluid. \n\n\\section{The analysis}\n\nI deal first with pure pitch angle scattering, and then (Subsection 2.3) I\ndiscuss oblique shocks. In the well--known equation for the particles' \ndistribution function, under the assumption of pure pitch angle scattering,\n\\begin{equation}\n\\label{main}\n\\gamma(u+\\mu)\\frac{\\partial f}{\\partial z} = \\frac{\\partial}{\\partial\n\\mu} \\left(D(\\mu, p) (1-\\mu^2)\\frac{\\partial f}{\\partial \\mu}\\right) \\;,\n\\end{equation}\n$f$ is computed in the shock frame, in which are also defined the \ndistance from the shock $z$, the fluid speed in units of $c$, $u$, and \nfluid Lorentz factor $\\gamma$. Instead, the scattering coefficient $D$, \nparticle momentum $p$ and particle pitch angle cosine, $\\mu$, are all defined\nin the local fluid frame. I make no hypothesis whatsoever about $D$, except\nthat it is positive definite and smooth. We place ourselves in the shock frame,\nand call $z =0$ the shock position; the upstream section is for $z < 0$, so that\nthe fluid speeds are both $> 0$. The above equation admits of an integral: by \nintegrating over $\\mu$ and $z$ we see that\n\\begin{equation}\n\\label{conserved1}\n\\int_{-1}^{1} (u+\\mu) f d\\!\\mu = \\mbox{const.}\\;,\n\\end{equation}\nindependent of $z$. The required boundary condition for $f$, \\ie, that \n$f \\rightarrow 0$ as $z \\rightarrow -\\infty$, implies that the constant, \nupstream, is $0$. Downstream, Eq. \\ref{conserved1} is also a constant, but, \nbecause of Taub's jump conditions, it is not the same constant as upstream. \nSince the required boundary condition for $f$ far downstream ($f_\\infty$)\nis that it becomes isotropic and $f$ is a relativistic invariant, we see that, \nfar downstream, $\\int_{-1}^{1} \\mu f_\\infty d\\!\\mu = 0$. We thus have \n\\begin{equation}\n\\label{conserved2}\n\\int_{-1}^{1} (u+\\mu) f d\\!\\mu = \\left\\{\n\\begin{array}{ll}\n0 & z < 0 \\\\\n\\int_{-1}^{1} u f_\\infty d\\!\\mu > 0 & z > 0\n\\end{array}\n\\right.\n\\end{equation}\nwhere the inequality in Eq. \\ref{conserved2}b (which will become necessary \nlater on) derives from the obvious constraint $f > 0$. \n\n\\subsection{Upstream}\n\nI begin the analysis by considering Eq. \\ref{conserved2}a in the limit of\nvery large shock Lorentz factors, in which case, upstream, $u \\rightarrow 1$.\nFor $u=1$, this reduces to \n\\begin{equation}\n\\int_{-1}^1 (1+\\mu) f d\\!\\mu = 0 \\;.\n\\end{equation}\nSince $1+\\mu > 0$ everywhere in the integration interval except of course at\n$\\mu = -1$, and since $f\\geq 0$ we see that, \nfor $u = 1$ we must have $f \\propto \\delta(\\mu+1)$ where $\\delta(x)$ is \nDirac's delta. Thus, in this limit, the angular dependence factors out. \nFor reasons to be explained in the next Subsection, we shall also need $f$\nfor $ 1-u \\ll 1$, but still $\\neq 0$. To search for such a solution, we let\nourselves be guided by the solution at $u =1$: thus, we let the angular\ndependence factor out, and use the {\\it Ansatz} $f = g(z) w((\\mu+1)/h(u))$. \nHere $h(u)$ is an as yet undetermined function of the pre--shock fluid speed\nsuch that $h(u) \\rightarrow 0$ as $u \\rightarrow 1$. In this way, as the speed \ngrows, the angular dependence becomes more and more concentrated toward \n$\\mu = -1$, as required by the previously found solution for $u = 1$. \nIntroducing our {\\it Ansatz} into Eq. \\ref{main} I find\n\\begin{equation}\n\\frac{\\gamma}{g} \\frac{d g}{d z} = \n\\frac{1}{(1+\\mu)w} \n\\frac{d}{d\\mu} \\left( D(\\mu,p)(1-\\mu^2)\\frac{d w}{d \\mu}\\right)\n= \\frac{2 D_{-1} \\lambda^2}{h^2(u)}\\;,\n\\end{equation}\nwhere I defined $D_{-1} \\equiv D(\\mu = -1, p)$, and I factored the eigenvalue\nfor future convenience. Concentrating on the angular part, and defining \n$(\\mu+1)/h(u) \\equiv y$, and $\\dot{w} \\equiv dw/dy$, $\\ddot{w} \\equiv \nd^2 w/d y^2$, I find\n\\begin{equation}\n\\label{down}\n\\frac{D(\\mu,p)(1-\\mu^2)}{h^2(u)} \\ddot{w} + \n\\frac{\\dot{w}}{h(u)}\\frac{d}{d\\mu} \\left(D(\\mu,p)(1-\\mu^2)\\right) - \n\\frac{2\\lambda^2 D_{-1}(1+\\mu) w}{h^2(u)} = 0\\;.\n\\end{equation}\nWe are interested in a solution of the above equation only in the limit\n$h(u)\\rightarrow 0$, the only one in which our factored {\\it Ansatz} is a good \napproximation to the true $f$. In this case, the term $\\propto \\dot{w}$ is \nclearly subdominant, and can be neglected in a first approximation (this \ntechnique is called dominant balance, Bender and Orszag 1978). Furthermore,\nfor $h(u)\\rightarrow 0$, we expect $w(\\mu)$ to be more and more concentrated \naround $\\mu = -1$, so that in this range we can approximate the term \n$D(\\mu,p)(1-\\mu^2) \\approx 2 D_{-1} (1+\\mu)$, and I obtain $\\ddot{w} \\approx \n\\lambda^2 w$ with obvious solution $w \\approx w_0 \\exp{(-\\lambda \n(\\mu+1)/h(u))}$. The factor $\\lambda/h(u)$\ncan be determined by inserting this approximate expression for $w$ into Eq. \n\\ref{conserved2}a. A trivial computation yields $\\lambda/h(u) = 1/(1-u)$. \n\nNow, going back to the equation for $g$, the spatial part of $f$, we find,\nalso using the above,\n\\begin{equation}\n\\frac{1}{g} \\frac{d g}{d z} \\approx \\frac{2 D_{-1}}{\\gamma (1-u)^2}\n\\approx 8\\gamma^3 D_{-1}\n\\end{equation} \nfrom which, in the end, I find an approximate solution for the distribution\nfunction in the limit $u\\rightarrow 1$:\n\\begin{equation}\n\\label{up}\nf \\approx A \\exp{(8 \\gamma^3 D_{-1} z}) \\exp{\\left(- (\\mu+1)/(1-u)\\right)}\\;.\n\\end{equation}\nIt is thus seen that the detailed shape of the pitch angle scattering \nfunction $D(\\mu, p)$ is irrelevant, and that what is left of it (its value\n$D_{-1}$ at $\\mu = -1$) only enters the spatial part of the distribution\nfunction $f$, not the angular one. \n\n\\subsection{Downstream}\n\nWe make here the usual assumption, that the distribution function depends\nupon the particle momentum $p$ as $f \\propto p^{-s}$ in either frame \n(but see the Discussion for further comments). From the condition\nof continuity of the distribution function at the shock, denoting as $p_a$ and \n$\\mu_a$ the particle's momentum and cosine of the pitch angle in the downstream \nframe, we have\n\\begin{equation}\n\\frac{1}{p_a^{s}} w_a(\\mu_a) \\propto \n\\frac{1}{p^{s}} \\exp{(-(\\mu+1)/(1-u))}\n\\end{equation}\nwhere the irrelevant constant of proportionality does not depend on $p, p_a,\n\\mu, \\mu_a$. Using the Lorentz transformations to relate $p, p_a, \\mu, \\mu_a$\n($\\mu = (\\mu_a - u_r)/(1-u_r\\mu_a)$, $p = p_a \\gamma_r (1-u_r \\mu_a)$, \nwith $u_r$ and $\\gamma_r$ the relative speed and corresponding Lorentz factor\nbetween the upstream and downstream fluids), I find\n\\begin{equation}\nw_a(\\mu_a) = \\frac{1}{(1-u_r \\mu_a)^s} \\exp{\\left(-\n\\frac{(\\mu_a+1)(1-u_r)}{(1-u)(1-u_r \\mu_a)}\\right)}\\;.\n\\end{equation}\nFor $u \\rightarrow 1$, it is easy to derive from Taub's conditions (Landau\nand Lifshitz 1987) that $u_r\\rightarrow 1$, and that $(1-u_r)/(1-u) \\approx \n\\gamma^2/\\gamma_r^2 \\rightarrow 2$. This result does use a post--shock \nequation of state $p = \\rho/3$, which is surely correct in the limit $u\n\\rightarrow 1$. In the end, I obtain\n\\begin{equation}\n\\label{incomplete}\nw_a(\\mu_a) = \\frac{1}{(1-\\mu_a)^s} \\exp{\\left(-2\n\\frac{\\mu_a+1}{1-\\mu_a}\\right)}\\;.\n\\end{equation}\nThis equation shows why we needed to determine the pitch angle distribution,\nin the upstream frame, even for $1-u \\neq 0$: in fact, even though the\nangular distribution in the upstream frame (Eq. \\ref{up}) tends to a \nsingularity, the downstream distribution does not (because the factor \n$(1-u)/(1-u_r)$ has a finite, non--zero limit), and the concrete form to \nwhich it tends depends upon the departures of the upstream distribution from a\nDirac's delta. \n\nFrom now on I will drop the subscript $a$ in $\\mu_a$, since all quantities\nrefer to downstream.\nIn order to determine $s$, we now appeal to a necessary regularity condition \nwhich must be obeyed by the initial (\\ie, for $z = 0$) pitch angle distribution,\nEq. \\ref{incomplete}. Looking at Eq. \\ref{main} specialized to the downstream \ncase, where $u = 1/3$ for very fast shocks, we see that this equation has a \nsingularity at $\\mu = -1/3$. Passing through this singularity will fix the \nindex $s$. \n%We begin by recasting Eq. \\ref{main} by defining a new, more \n%convenient variable $v$:\n%\\begin{equation}\n%\\label{map}\n%d\\!v \\equiv \\frac{d\\!\\mu}{D(\\mu, p)(1-\\mu^2)}\n%\\end{equation}\n%in terms of which Eq. \\ref{main} becomes\n%\\begin{equation}\n%\\label{transformed}\n%\\gamma (1/3 + \\mu) D(\\mu, p) (1-\\mu^2) \\frac{\\partial f}{\\partial z} = \n%\\frac{\\partial^2 f}{\\partial v^2}\\;. \n%\\end{equation}\nIt is not convenient to use $f$ directly; rather, I use its Laplace transform\n\\begin{equation}\n\\label{laplace}\n\\hat{f}(r,\\mu) \\equiv \\int_0^{+\\infty} f(z,\\mu) e^{-rz} d\\!z\\;.\n\\end{equation}\nTaking Laplace transforms of both sides of Eq. \\ref{main} I obtain\n\\begin{equation}\n\\label{transformed2}\n-\\frac{\\gamma (1/3+\\mu)w_a(\\mu)}{r} + \\gamma (1/3+\\mu) \\hat{f} = \n\\frac{1}{r} \\frac{\\partial }{\\partial \n\\mu} \\left(D(\\mu,p)(1-\\mu^2) \\frac{\\partial\\hat{f}}{\\partial\\mu}\\right)\\;.\n\\end{equation}\n\nI am interested in the limit $r \\rightarrow +\\infty$. In fact, here I can use\ntwo results. First, in this limit, it is well--known (Watson's Lemma, Bender\nand Orszag 1978) that Eq. \\ref{laplace} reduces to \n\\begin{equation}\n\\label{watson}\n\\hat{f}(r,\\mu) \\rightarrow \\frac{f(z=0,\\mu)}{r} = \\frac{w_a(\\mu)}{r}\\;.\n\\end{equation}\nDespite this wonderful result in all its generality, I will actually use it\nonly in the neighborhood of $\\mu = -1/3$; here, Eq. \\ref{transformed2} takes \non a simple form: defining $t \\equiv \\mu + 1/3$, \n\\begin{equation}\n\\label{localized}\n\\frac{b t}{r} + a t \\hat{f} = \\frac{1}{r} \\frac{\\partial^2 \\hat{f}}{\\partial \nt^2} + \\frac{c}{r}\\frac{\\partial \\hat{f}}{\\partial t}\n\\end{equation}\nwhere I defined $b \\equiv (\\gamma w_a(\\mu) D(\\mu,p)(1-\\mu^2))|_{\\mu =-1/3}$, \n$a \\equiv (\\gamma D(\\mu,p)(1-\\mu^2))|_{\\mu =-1/3}$, and $c \\equiv \n(\\partial/\\partial\\mu D(\\mu,p)(1-\\mu^2))/D(\\mu,p)(1-\\mu^2)|_{\\mu = -1/3}$. \nNow I make the {\\it Ansatz} (to be checked {\\it a posteriori}) that the term \n$\\propto\\partial\\hat{f}/\\partial t$ is negligible compared to the second order\nderivative in the limit $r\\rightarrow +\\infty$. I am interested only in the\nmost significant term in $r$, since Eq. \\ref{watson} was only obtained to \nthis order. Then, the equation \\ref{localized} becomes\n\\begin{equation}\n\\label{model}\na t \\hat{f} = \\frac{1}{r}\\frac{\\partial^2 \\hat{f}}{\\partial t^2}\\;.\n\\end{equation}\nThe above equation is the prototype of the \none--turning point problem. Its solution, strictly in the neighborhood of the \npoint $t=\\mu+1/3=0$, is (Bender and Orszag 1978, Sect. 10.4, Eq. 10.4.13b):\n\\begin{equation}\n\\label{airy}\n\\hat{f}(t) \\approx r^{1/12} C Ai(r^{1/3} a t)\n\\end{equation}\nwhere $C$ is an arbitrary constant, and $Ai(x)$ is one of Airy's functions. \nFrom this it can easily be checked that our {\\it Ansatz} was justified. \n\nClearly, close to the point $t=\\mu+1/3=0$, Eq. \\ref{watson} and Eq.\n\\ref{airy} must give the same results. Thus I find that, close to $\\mu = -1/3$,\n\\begin{equation}\n\\label{nearly}\nw_a(\\mu) \\propto Ai(r^{1/3} a (\\mu+1/3))\n\\end{equation}\nwhich solves our problem: from this in fact we see that, since $d^2 Ai(x)/d x^2 \n= x Ai(x)$ by definition, and thus $d^2 Ai(x)/d x^2 = 0$ in $x=0$, then we \nmust have\n\\begin{equation}\n\\label{sospirata}\n\\frac{\\partial^2 w_a}{\\partial \\mu^2} |_{\\mu = -1/3} = 0\\;.\n\\end{equation}\nThis is our sought for extra condition for $s$; we have seen that it comes \ndirectly from demanding that the boundary condition of the problem, Eq. \n\\ref{incomplete}, manages to pass through the singular point of Eq. \\ref{main},\nwhich I showed to be a conventional one--turning point problem familiar from\nelementary quantum mechanics. \n\nBy substituting into Eq. \\ref{incomplete} I find\n\\begin{equation}\n\\left(\\frac{\\partial^2 w_a}{\\partial \\mu^2}\\right)_{\\mu = -1/3} = \n2^{-2(2+s)} 3^{2+s} e^{-1} (s^2 -5s + 3) = 0\n\\end{equation}\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{zero.eps}\n\\caption{The integral of Eq. \\ref{conserved2}b with $u=1/3$, for the angular \ndistribution of Eq. \\ref{incomplete}, as a function of the parameter $s$, \nwith arbitrary vertical scale.}\n\\end{figure}\nfrom which we obtain $s = (5 \\pm \\sqrt{13})/2$. The solution with the \nminus sign is unacceptable: in fact, if we plug Eq. \n\\ref{incomplete} into the conservation equation \\ref{conserved1}, we see (Fig. \n1) that for $s \\leq 3$ the integral is $\\leq 0$. We remarked after Eq. \n\\ref{conserved2}b, however, that this integral had necessarily to be $> 0$, so \nthat we may conclude that $3$ is an absolute lower limit to $s$. Thus we discard\nthe solution with the minus sign, and are left with the unique solution\n\\begin{equation}\n\\label{ss}\ns = \\frac{5 + \\sqrt{13}}{2} \\approx 4.30\\;.\n\\end{equation}\n\n\\subsection{Oblique shocks}\n\nLet us call $\\phi$ the angle that the magnetic field makes with the shock \nnormal, in the upstream fluid. Then shocks can be classified as either\nsubluminal or superluminal, depending upon whether, upstream, $u/\\cos\\phi < 1$\nor $u/\\cos\\phi > 1$, respectively (de Hoffmann and Teller 1950). We are \ninterested in the limit $u\\rightarrow 1$, so that most shocks will be of the\nsuperluminal type. In this case, we could (but we won't) move to a frame where \nthe magnetic field is parallel to the shock surface, both upstream and \ndownstream. However, downstream this extremely orderly field configuration \nappears more idealized than warranted by physical \nreality and observations. In fact, behind a relativistic shock, a large number\nof processes (compression, shearing, turbulent dynamo, Parker instability, \ntwo--stream instability) can generate magnetic fields; furthermore, there is\nno obvious reason why these fields should have large coherence lengths. In \nGRBs, a large number of observations of different afterglows supports this \npicture, the most detailed of all being those of GRB 970508, extending from a \nfew hours to $400\\;d$ after the burst (Waxman, Frail and Kulkarni 1998; Frail, \nWaxman and Kulkarni 2000, and references therein). Accurate and successful\nmodeling fixes the \npost--shock ratio of magnetic to non--magnetic energy densities to $\\epsilon_B \n\\approx 0.1$. Notice that here the protons' rest mass is not even the largest\ncontribution to the non--magnetic energy density! Polarization measurements\nalso support, albeit less cogently, the idea of a small coherence length: of \nthe four bursts observed so far, only one has a detected polarization, at the \n$1.7\\%$ level (GRB 990510, Covino \\etal, 1999). \n\nThus the most plausible physical model downstream, is that particles move in a \nlocally generated turbulent, dynamically negligible magnetic field; if then\nwe call $l$ the average post--shock field coherence length, and \nrestrict our attention to particles with sufficiently large energies (\\ie,\nwith gyroradii $r_g > l$), we see there can be no reflection as \nparticles approach the shock from downstream. It follows that we expect the \nsituation downstream to be identical to that of pure pitch angle scattering.\nUpstream, the parallel magnetic field is also irrelevant. In fact, backward\ndeflection of a particle occurs on a length--scale $r_g$, but backward \ndiffusion of the particle by magnetic irregularities only requires the\nsideways deflection by an angle $\\approx \\gamma^{-2}$ ($\\gamma$ being the shock\nLorentz factor), for the shock to overrun the particle. \nThis typically occurs on a length $\\eta r_g/\\gamma^2$, \nwith $\\eta \\approx $ a few. So, as $\\gamma \\rightarrow \\infty$, the \nlength--scale for scattering upstream by the magnetic field increases, while \nthat by magnetic irregularities decreases: the field is irrelevant. In the end,\nthe same analysis as for pure pitch angle scattering applies, and the same\nindex $s$ and pitch angle distributions at the shock follow. \n\nIn the case of subluminal shocks, a similar comment applies. Downstream, we \nexpect on a physical basis the same situation as for superluminal shocks. \nUpstream, Eq. \\ref{main} is replaced by (Kirk and Heavens 1989)\n\\begin{equation}\n\\gamma\\cos\\phi (u+\\mu)\\frac{\\partial f}{\\partial z} = \\frac{\\partial}{\\partial\n\\mu} \\left(D(\\mu, p) (1-\\mu^2)\\frac{\\partial f}{\\partial \\mu}\\right) \\;.\n\\end{equation}\nto which the same analysis as in Subsection 2.1 can be applied. Thus we find\nthe same $s$ and pitch angle distributions at the shock as above. \n\nAs a corollary, it may be noticed that the above argument also implies that\nthe results above are independent of the ratio $\\kappa_\\perp/\\kappa_\\parallel$,\nthe cross--field and parallel diffusion coefficients.\n\n\n\\section{Discussion}\n\nFor ultrarelativistic particles the energy spectral index $k$ is related \nto $s$ by \n\\begin{equation}\n\\label{final}\nk = s-2 = \\frac{1 +\\sqrt{13}}{2} \\approx 2.30\\;,\n\\end{equation}\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{dist.eps}\n\\caption{Pitch angle distribution at the shock in the downstream frame, Eq. \n\\ref{incomplete} with $s$ from Eq. \\ref{ss}, with arbitrary vertical scale.}\n\\end{figure}\nwhich is our final result. Also, now\nthat we know $s$, the final pitch angle distribution at the shock, but \ndownstream, can be determined (Eq. \\ref{incomplete}), and is plotted in Fig. 2.\nNone of these results depends upon the specific form of $D(\\mu, p)$, so that\nwidely differing assumptions should yield precisely the same results. \n\nHow does this compare with numerical work? The near--constancy of the index\n$s$ (or $k$) explains moderately well the results of previous authors: \nKirk and Schneider (1987) find $s= 4.3$ for their computation with the highest \nspeed, which is however a modest Lorentz factor of $\\gamma = 5$, and a single\nfunctional dependence of $D$ on $\\mu$. Heavens and Drury (1988) find again\na result of $s=4.2$ for equally modest Lorentz factors, but for \ntwo different recipes for $D$. Extensive numerical computations using a \nMonteCarlo technique (\\ie, totally independent of the validity of Eq. \n\\ref{main}) were performed by Bednarz and Ostrowski (1998), for a wide variety\nof assumptions about the scattering properties of the fluids. They \nremarked quite explicitly that the energy spectral index $k$ seemed to \nconverge to a constant value, independent of shock Lorentz factor (provided\n$\\gamma \\gg 1$), magnetic field orientation angle $\\phi$, and diffusion\ncoefficient ratio, $\\kappa_\\perp/\\kappa_\\parallel$. They found $k \\approx 2.2$. \nThe present \nwork confirms (for all untried forms for $D(\\mu, p)$) and extends their \nsimulations (by yielding the exact value, and explicit forms for the particle \nangular distributions). The upstream angular distributions also agree well:\nFig.3a of Bednarz and Ostrowski clearly shows that this is (for the highest \ndisplayed value of $\\gamma = 27$) a Dirac's delta, in agreement with the \nlarge--$\\gamma$ limit in Section 2.1. However, the downstream pitch angle\ndistributions (in their Fig. 3b) agree well with mine, but not perfectly. \nGallant, Achterberg and Kirk (1998) have claimed that there is a small error in \nBednarz and Ostrowksi's distributions. As a matter of fact, my distribution\n(Fig. 2) agrees much better with Gallant \\etal's and Kirk and Schneider's\n(1987) than Bednarz and Ostrowski's, despite the very small shock Lorentz\nfactors of these two papers ($\\gamma = 2.3$ and $\\gamma = 5$, respectively). \nPossibly, the small error in question may even explain the (small!) discrepancy \nbetween the two values of $k$.\n\nA limitation applies to the claim of universality of Eqs. \n\\ref{up}, \\ref{incomplete} and \\ref{final}: I\nneglected any process altering the particles' energy during the scattering.\nClearly, the results of this paper only apply in the limit $\\delta\\!p/p \\la \n1$, where $\\delta\\!p$ is the typical momentum transfer in each scattering \nevent. In the large momentum limit considered here, it seems unlikely\nthat this constraint may be violated. \n\nLastly, a comment on the assumed dependence $\\propto p^{-s}$ of the \ndistribution function upon particle momenta is in order. It can be seen from\nEq. \\ref{main} that such a dependence is {\\it not} required by this equation. \nTo see this, let us make the usual assumption that $D$ is homogeneous of\ndegree $-r$ in $p$, \\ie, $D(\\mu, p) = q(\\mu) p^{-r}$. Then by defining a new \nvariable $\\hat{z} \\equiv z/p^r$, we see that the form assumed by Eq. \\ref{main}\nafter this change of variable is identical to the original one, except that now\n$p$ has altogether disappeared. At large $z$ (\\ie, far downstream), $f \n\\rightarrow f_\\infty =$ constant, and there is no $p$--dependence. This \nparadox is solved by noticing that the real problem to be solved involves\nboth scattering (= Fermi acceleration) and injection. In this case, a\ntypical injection momentum $p_0$ arises naturally, and the dimensional problem\ndiscussed above is naturally solved: we must have $f = f(...,p/p_0,...)$\nwhere the dots indicate all other parameters. In the limit of $p_0 \n\\rightarrow 0$, $f$ {\\it does not} tend to a constant independent of $p_0$\nas is always assumed, but tends instead to zero as $f \\rightarrow (p_0/p)^s$.\nProblems of this sort, though rare in astrophysics, are common in hydrodynamics,\nwhere they are called self--similar problems of the second kind (Zel'dovich\n1956). They range from the deceptively simple laminar flow of an ideal fluid\nplast an infinite wedge (Landau and Lifshitz 1987) to the illuminating case of\nthe filtration in an elasto--plastic porous medium (Barenblatt 1996). It is\nremarkable that, in the problem at hand, no such complication is necessary to\nfix the all--important index $s$, yet the powerful methods of intermediate\nasymptotics (Barenblatt 1996) and the renormalization group (Goldenfeld 1992)\ncan be brought to bear on the intermediate $\\gamma$ cases, where no easy \nlimiting solution can be found. \n\nIn short, what I have done in this paper is to show that the spectrum of \nnon--thermal particles accelerated at relativistic shocks is universal, in\nthe sense that the energy spectral index $k$, and the angular distributions\nin both the upstream and downstream frames (Eqs. \\ref{up}, \\ref{incomplete},\n\\ref{final}, and Fig. 2) do not depend upon the scattering function $D(\\mu, p)$,\nthe shock Lorentz factor (provided of course $\\gamma \\gg 1$), the magnetic\nfield geometry, and the ratio of cross--field to parallel diffusion \ncoefficients.Thus we have the result that the cosmic rays' spectra are \nindependent of flow details in both the Newtonian (Bell 1978) and the \nrelativistic regimes. \n\n{}\n\n\\begin{references}\n\\reference{} Barenblatt, G.I., 1996, {\\it Scaling, self--similarity and\nintermediate asymptotics}, Cambridge Univ. Press, Cambridge.\n\\reference{} Bednarz, J., Ostrowski, M., 1998, \\prl, 80, 3911. \n\\reference{} Bender, C.M., Orszag, S.A., 1978, {\\it Advanced mathematical \nmethods for scientists and engineers}, Mc Graw--Hill, New York.\n\\reference{} Bell, A.R., 1978, \\mnras, 182, 147.\n\\reference{} Covino, S., \\etal, 1999, \\aap, 348, L1.\n\\reference{} de Hoffmann, F., Teller, E., 1950, Phys. Rev., 80, 692.\n\\reference{} Frail, D., Waxman, E., Kulkarni, S., 2000, \\apj, in press,\nastro--ph 9910319.\n\\reference{} Gallant, Y.A., Achterberg, A., Kirk, J.G., 1998, in {\\it Rayos\nc\\'osmicos 98}, Proc. 16th. European Cosmic Ray Symposium, Ed. J. Medina,\nUniv., de Alcal\\`a, Madrid, p. 371.\n\\reference{} Goldenfeld, N., 1992, {\\it Lectures on phase transitions and the \nrenormalization group}, Addison--Wesley, New York. \n\\reference{} Heavens, A.F., Drury, L.O'C., 1988, \\mnras, 235, 997. \n\\reference{} Kirk, J.G., Heavens, A.F., 1989, \\mnras, 239, 995.\n\\reference{} Kirk, J.G., Schneider, P., 1987, \\apj, 315, 425. \n\\reference{} Landau, L.D., Lifshitz, 1987, {\\it Fluid Mechanics},\nPergamon Press, Oxford.\n\\reference{} Waxman, E., Frail, D., Kulkarni, S., 1998, \\apj, 497, 288.\n\\reference{} Zel'dovich, Ya.B., 1956, Sov. Phys. Acoustics, 2, 25.\n\\end{references}\n\n\n\\end{document}\n\n\n\n"
}
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astro-ph0002270
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Systematic effects in the interpretations of Cluster X-ray Temperature functions
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[
{
"author": "S.~M.~Molnar $^{1,2}$ and K.~Jahoda $^1$"
}
] |
The formation and evolution of clusters of galaxies are sensitive to the underlying cosmological model. Constraints on cosmological parameters of cold dark matter models have been derived from mass, temperature and luminosity functions of clusters. We study the importance of including cluster formation history and a correction for collapsed fraction of objects in determining the cluster X-ray temperature function. We find that both effects are important. We compare temperature functions obtained by using a power law approximation for the mass variance normalized to X-ray clusters to those obtained by using a COBE normalized full CDM treatment. We conclude that the temperature function could be a powerful test on the average density of the Universe if we could find the correct way of interpreting the data. \keywords{galaxies: clusters: general --- large-scale structure of universe.}
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[
{
"name": "molnar.tex",
"string": "% File: molnar.tex\n\\documentstyle[bo99B,epsfig]{article}\n\n\\def\\nop{\\noindent} \n\\def\\etal{et al.}\n\\def\\ecssr{{\\rm erg}\\,{\\rm s}^{-1}\\,{\\rm cm}^{-2}\\,{\\rm sr}^{-1}}\n\\def\\ecs{{\\rm erg}\\,{\\rm s}^{-1}\\,{\\rm cm}^{-2}}\n\\def\\Kms{$\\rm km\\,s^{-1}$} \n\n\n\\title{Systematic effects in the interpretations of \n Cluster X-ray Temperature functions}\n\n\\author{S.~M.~Molnar $^{1,2}$ and K.~Jahoda $^1$} \n\n\\affil{1) Laboratory for High Energy Astrophysics, Code 662\n Goddard Space Flight Center\n Greenbelt, MD 20771 \\\\\n 2) NAS/NRC Research Associate}\n\n\\begin{document}\n\n\\maketitle\n\n\\begin{abstract}\nThe formation and evolution of clusters of galaxies are sensitive to \nthe underlying cosmological model. Constraints on cosmological \nparameters of cold dark matter models have been derived from mass, \ntemperature and luminosity functions of clusters.\nWe study the importance of including cluster formation history\nand a correction for collapsed fraction of objects\nin determining the cluster X-ray temperature function.\nWe find that both effects are important.\nWe compare temperature functions obtained by using a \npower law approximation for the mass variance normalized to X-ray clusters\nto those obtained by using a COBE normalized full CDM treatment.\nWe conclude that the temperature function could be a powerful test\non the average density of the Universe if we could\nfind the correct way of interpreting the data.\n\n\n\\keywords{galaxies: clusters: general --- large-scale structure of universe.}\n\\end{abstract}\n\n\n\\section{Introduction}\n\nClusters of galaxies are the largest known virialized gravitational\nsystems in the Universe. According to our working hypothesis of structure\nformation, the cold dark matter (CDM) model, clusters form via gravitational \ncollapse of high density peaks of primordial density fluctuations.\nThe distribution and evolution of these peaks strongly depend on the \nCDM model parameters. We use the following parameterization for our CDM models:\n$\\Omega_0$, $\\Omega_b$, $\\Omega_\\Lambda$, $h$ (matter density,\nbaryon density, cosmological constant, all in units of the\ncritical density, all at $z$ = 0, and $h$ is the Hubble constant in units of \n$100 \\, \\rm Km\\,s^{-1}\\,Mpc^{-1}$).\nSemi-analytical methods, like the Press-Schechter approximation, use some version of \na spherical collapse model to predict the distribution of collapsed objects and \ntheir masses as a function of redshift.\nAssuming a physical model for the clusters and their intracluster medium,\none can translate cluster virial masses to X-ray luminosity, or temperature of\nthe intracluster gas, which can be compared to observations.\nWe use the temperature function of clusters in our study.\nThe most popular method is to assume a power law approximation for the\npower spectra of CDM models, use the Press-Schechter mass function (PSMF) to predict\nthe abundance, and then derive the virial temperature to get the intracluster gas temperature,\nor integrate over formation epochs to determine the mass-temperature conversion.\nThis method has the power spectrum normalization and the power law exponent of the\nmass variance on cluster scales as free parameters and determines matter density,\nand has no dependence on the Hubble constant.\nWe use COBE normalized spectra of CDM models to derive the mass variance and the \nPress-Schechter mass function to derive the distribution of cluster masses.\nThis method returns the matter density as a function of the Hubble constant,\nthus one can not derive either parameter separately.\nWe use four different methods to obtain theoretical temperature functions.\nWe integrate over formation epochs in methods A and B but not in methods C and D.\nWe take into account the collapsed fraction of objects in methods A and C and\nnot in B and D. Method A thus take both effects and method D none of them\ninto account. For each method (A, B, C, and D) we use a grid of CDM model\nparameters, $0.2 < \\Omega_m < 0.9$ and $0.2 < h < 0.9$,\nand calculate the temperature functions assuming open and flat CDM cosmologies.\nWe compare these theoretical temperature functions to data and determine the best fit models\nby minimizing the corresponding $\\chi^2$.\n\n\n\n\\section{Outline of the methods}\n\nThe power law approximation for the mass variance \nassumes a power exponent $\\alpha$, and derives the mass variance as\n$\\sigma(M) = \\sigma_8 (M/M_{15})^{-\\alpha}$, \nwhere $M_{15} = M /(10^{15} M_\\odot)$, and $M$ is the mass we will identify \nwith the virial mass in the PSMF.\nIt is commonly assumed that the power spectrum then can be approximated by a power law\nwith an exponent $\\alpha = (n_{PS}+3)/6$, but that is true only \nif the power spectrum could be approximated by one power law\nin all scales (note the integral in equation 1). \nThat is not true for CDM models, therefore we quote the mass variance power exponents \non cluster scale for power law approximations.\nInstead of the approximation we use COBE normalized power spectra of CDM models \n(Hu and Sugiyama 1996) and obtain the mass variance from a numerical integral\n\n\\begin{equation}\n \\sigma^2_{R(M)} = (1 / 2 \\pi^2) \\int P(k) W^2(kR) k^2 dk\n,\n\\end{equation}\nwhere $P(k)$, $W(kR)$, $R(M)$, and $k$ are the power spectrum, filter function\nin Fourier space, the radius of filtering, and the co-moving wavenumber.\nWe use the standard PSMF corrected for collapsed fraction $f_c$, \nwhich gives the fraction of matter in collapsed objects:\n% DEFINE collapsed fraction ???\n$n(z, M)\\, dM = (f_c/f_c^{PS}) \\; n_{PS}(z, M)\\, dM$,\nwhere $f_c^{PS}$ is the Press-Schechter collapsed fraction (Martel and Shapiro 1999).\nIn order to obtain the temperature function, we\nassume that clusters form over a period of time and integrate over formation\n$n_T(z, M) = \\int_z^\\infty F(M, z_f, z) {dM \\over dT}(T, z_f, z) d z_f$, \nwhere $F(M, z_f, z)$ depends on $\\sigma(M)$, $\\delta_c(z)$, and $n(z_f, M)$\n(Kitayama and Suto 1996).\nWe used the spherical collapse model virial temperature (Eke et al. 1998):\n\n\\begin{equation}\n M(T) = M_{15} \\Bigg[ {\\beta k \\,T[keV] \\over 1.38 keV (z+1) } \\;\\; \\Bigg]^{3 \\over 2} \n \\Bigg[ {\\Omega(z) \\over \\Omega(0) \\Delta_c(z) } \\;\\; \\Bigg]^{1 \\over 2}\n.\n\\end{equation}\nWe use $\\beta =1$ as suggested by numerical simulations (Eke et al. 1998).\n\n\n\\section{Results and Conclusions}\n\n\nIn Figure~1a we show the resulting best fit temperature functions using the power \nlaw approximation of Donahue and Voit (1999) and Blanchard et al. (1999) as we \nreconstructed them following their method.\nWe used Horner et al. (1999)'s compilation of data \ntaken from Edge et al. (1990) Henry and Arnaud (1991), and Markevitch (1998) \n(squares, diamonds, and triangles).\nThe solid and dashed dotted lines represent best fit flat model,\n$\\Omega_m = 0.27$, $\\sigma_8 = 0.73$ $\\alpha = 0.13$, of\nDonahue and Voit (they integrated over cluster formation epoch) and their\nbest fit model, but not integrated over cluster formation epoch. \nBlanchard et al.'s best fit flat model, \n$\\Omega_m = 0.735$, $\\sigma_c = 0.623$, $\\alpha = 0.18$, is represented by a long dashed line. \nThe short dashed line represents Blanchard et al.'s best fit temperature function, but\nintegrated over cluster formation epoch. \nOpen model temperature functions (not shown) are very similar to those of the flat models.\nThe difference between temperature functions from methods with and without integration over \ncluster formation epoch is significant even with existing data.\nThe large difference between density parameters derived by Donahue and Voit, and \nBlanchard et al. is due to the different normalizations of the $M(T)$ relation and not \nintegration over cluster formation, which can cause a change less than 0.1 in the \ndensity parameter (cf. next paragraph).\n\nFigure~1b shows temperature functions of the best fit flat CDM model \n(best fit using method A) with $\\Omega_m = 0.39$, $\\Lambda = 0.61$, $h = 0.5$, and this \nbest fit model, but temperature functions with and without taking the collapsed fraction \nand/or integrating over cluster formation epochs (our methods B, C and D). \nThe data are the same as in figure 1a. \nThe solid, long dashed, short dashed and dashed dot lines\nrepresent temperature functions using our methods A, B, C and D.\nOpen models behave similarly so we do not show them here.\nThe smallest effect is the correction for collapsed fraction of objects\nwhich is about the size of the error bars of the data, thus an important effect \n(compare methods A and B).\nA larger difference is caused by integration over formation epoch (methods A and C).\nIf one fits models without integrating and/or taking collapsed fraction into account \n(methods B, C and D), one get matter densities \n$\\Omega_m = 0.36$, $\\Omega_m = 0.34$, and $\\Omega_m = 0.31$ (assuming $h = 0.5$).\nNot taking either effects into account causes about 0.1 change \nin the derived matter density (compare results using methods A and D). \nAs we can see, the temperature function is very sensitive to CDM model parameters \nif one uses a full CDM treatment, and thus a precise determination of the matter density \nis possible if the Hubble constant is known. We should keep in mind, however, that the\nnormalization of the $M(T)$ relation, for example, causes much larger error \nin determining $\\Omega_m$.\nSince this method does not allow us to separate the density parameter from \nthe Hubble constant, the result is a best fit function of the two.\nWe can make use of the results from the power law approximation\nwhich gives the best fit density parameter, and check if the corresponding\nHubble constant is reasonable using our methods.\nWe find that our best fit CDM models yield the same matter density as the \nbest fit models of Donahue and Voit (1999) and Blanchard et al. (1999)\nif we use $h = 0.55$ and $h = 0.35$. Thus Blanchard et al.'s method is \nonly marginally compatible to ours.\n\nFigure 1b shows that systematic errors from interpretation of\nthe temperature function are larger than the error bars on even the existing data.\nWe conclude that, if the Hubble constant is known, a comparison between the\nobservationally derived cluster temperature function and those\nderived from a full CDM treatment may yield an accurate determination\nof the density parameter (with an error less then 0.05), however, this can be done \nonly if we find other ways to derive a correct theoretical model to interpret the data.\n\n\n\n\\begin{figure}\n\\centerline{\\psfig{file=fig1a.eps, width=6cm}\n \\psfig{file=fig1b.eps, width=6cm}}\n\\caption[]{a) left panel: temperature functions using best fit power law approximations;\n b) right panel: temperature functions of the best fit CDM flat model using\n different methods. See text for details.}\n\\end{figure}\n\n\n\n\\begin{acknowledgements}\nWe thank N. Aghanim and R. Mushotzky for valuable \ndiscussions, and Don Horner for providing us his compilation of the temperature data.\nWe thank N. Aghanim for her hospitality at the Institute of Astronomy of Orsay University.\n\\end{acknowledgements}\n\n\n\\begin{references}\n\n\n\\reff Blanchard, A., \\etal 1999, astro-ph/9908037\n\n\\reff Donahue, M., and Voit, G. M., 1999, preprint, astro-ph/9907333\n\n\\reff Edge \\etal 1990, MNRAS, 245, 559\n\n\\reff Eke, V. R., Cole S., Frenk, C. S., and Henry, J. P., 1998, MNRAS, 298, 1145\n\n\\reff Horner, D. \\etal 1999, in prepaparation\n\n\\reff Hu, W, and Sugiyama, N, 1996, ApJ, 471, 542\n\n\\reff Markevitch, M., 1998, ApJ, 504, 27\n\n\\reff Martel, H., and Shapiro, P. R., 1999, astro-ph/9903425\n\n\\reff Henry, J. P., and Arnaud, K. A., 1991, ApJ, 372, 410\n\n\\reff Voges et al., 1999, A\\&A, 349, 389\n\n\n\\end{references} \n\n\\end{document}\n\n\n"
}
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astro-ph0002271
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Contributions to the Power Spectrum of Cosmic Microwave \\ Background from Fluctuations Caused by \\ Clusters of Galaxies
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[
{
"author": "S. M. Molnar\\altaffilmark{1,2}"
}
] |
\nop We estimate the contributions to the cosmic microwave background radiation (CMBR) power spectrum from the static and kinematic Sunyaev-Zel'dovich (SZ) effects, and from the moving cluster of galaxies (MCG) effect. We conclude, in agreement with other studies, that at sufficiently small scales secondary fluctuations caused by clusters provide important contributions to the CMBR. At $\ell \gtrsim 3000$, these secondary fluctuations become important relative to lensed primordial fluctuations. Gravitational lensing at small angular scales has been proposed as a way to break the ``geometric degeneracy'' in determining fundamental cosmological parameters. We show that this method requires the separation of the static SZ effect, but the kinematic SZ effect and the MCG effect are less important. The power spectrum of secondary fluctuations caused by clusters of galaxies, if separated from the spectrum of lensed primordial fluctuations, might provide an independent constraint on several important cosmological parameters.
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[
{
"name": "SMM_MB0001.tex",
"string": "% latex SMM_MB0001\n% S. M. Molnar: email: sandor@pcasrv2.gsfc.nasa.gov\n\\documentstyle[12pt,aaspp4]{article}\n\n\\def\\nop{\\noindent} \n\\def\\etal{et al.}\n\\def\\L{$\\Lambda$}\n\n\n\\begin{document}\n\n\n\n\n\\title{Contributions to the Power Spectrum of Cosmic Microwave \\\\\n Background from Fluctuations Caused by \\\\\n Clusters of Galaxies}\n\n\\author{S. M. Molnar\\altaffilmark{1,2}}\n\\affil{Laboratory for High Energy Astrophysics, Code 662 \\\\\n Goddard Space Flight Center \\\\\n Greenbelt, MD 20771}\n\n\\author{M. Birkinshaw\\altaffilmark{3}}\n\\affil{Department of Physics, University of Bristol, \\\\\n Tyndall Avenue, Bristol, BS8 1TL, UK}\n \n\\altaffiltext{1}{NAS/NRC Research Associate}\n\n\\altaffiltext{2}{previous address: Department of Physics, University of Bristol,\n Tyndall Avenue, Bristol, BS8 1TL, UK}\n\n\\altaffiltext{3}{also: Center for Astrophysics,\n 60 Garden Street, Cambridge, MA 02138, USA}\n\n\n\n\\begin{abstract}\n\n\n\\nop We estimate the contributions to the cosmic microwave background radiation (CMBR)\npower spectrum from the static and kinematic Sunyaev-Zel'dovich (SZ) effects, and from \nthe moving cluster of galaxies (MCG) effect. \nWe conclude, in agreement with other studies, that at sufficiently small scales\nsecondary fluctuations caused by clusters provide important contributions to the CMBR. \nAt $\\ell \\gtrsim 3000$, these secondary fluctuations become important relative to\nlensed primordial fluctuations.\nGravitational lensing at small angular scales has been proposed as a way to break the \n``geometric degeneracy'' in determining fundamental cosmological parameters. \nWe show that this method requires the separation of the static SZ effect, \nbut the kinematic SZ effect and the MCG effect are less important.\nThe power spectrum of secondary fluctuations caused by clusters of galaxies, \nif separated from the spectrum of lensed primordial fluctuations, might provide an\nindependent constraint on several important cosmological parameters. \n\n\n\\end{abstract}\n\n\nSubject headings: \ncosmic microwave background --- \ngalaxies: clusters: general --- \nmethods: numerical --- \n\n\n\n\\section{Introduction}\n\\label{S:INTRO}\n\n\nThe power spectrum of the cosmic microwave radiation (CMBR) carries much cosmological\ninformation about primordial density fluctuations in the early Universe.\nAs photons leave the last scattering surface and travel across the Universe, however, \nthese brightness fluctuations are modified by intervening structures, causing secondary\nfluctuations, which we would expect to become more important on small angular scales. \n\nThe power spectrum of the CMBR alone can be used to determine cosmological parameters.\nRecently it has been shown, however, that a geometrical degeneracy effect\nprevents some combinations of cosmological parameters from being disentangled by \nthe power spectrum alone (\\cite{BondEfTeg97}; \\cite{EfstathBond98}; \\cite{ZaldarrSperSel97}). \nThe primordial density fluctuations and matter content determine the positions\nand magnitudes of the Doppler peaks at the last scattering surface. These fluctuations\nare transferred to apparent angular scales determined by their angular diameter distance. \nAs a result, cold dark matter (CDM) models with the same primordial density fluctuations, \nmatter content, and angular diameter distance can not be distinguished. \nThe models are ``effectively degenerate'' in the sense that their power spectrum is degenerate \nfor parameter determination on intermediate and small scales. \nAlthough the observed power spectrum also depends on the time variation of the metric, via the \nintegrated Sachs-Wolfe effect, this breaks the degeneracy only at large angular scales.\nUnfortunately observations of the power spectrum do not provide strong constraints on models at \nlarge scales, since this is where the statistics of the data are dominated by the cosmic \nvariance due to the fact that we have only one realization of our cosmological model, \nthe Universe itself, and we encounter a sampling problem). \nTherefore we can determine, for example, only combinations such as $\\Omega_0 h^2$ and \n$\\Omega_b h^2$ (where $\\Omega_0$ and $\\Omega_b$ are the $z = 0$ matter and baryon density \nparameters and $h$ is the dimensionless Hubble parameter).\n\nIt has been noticed that gravitational lensing can break the geometric degeneracy at \nsmall angular scales, $\\ell \\gtrsim 2000$, in such a way that the cosmological parameters can be \ndetermined separately (\\cite{MetcalfSilk98}; \\cite{StomporEfstath98}). \nThe effect of gravitational lensing on the CMBR was studied by several authors \n(see for example \\cite{BlanchardSchneider87}; \\cite{MetcalfSilk97}; \\cite{Seljak97}).\nStatic gravitational lenses do not change a smooth CMBR, but the fluctuations get \ndistorted by lensing. As a result, power from the acoustic peaks is transferred \nto small angular scales, conserving the variance of the spectrum. \nThe amount of power transferred depends on the cosmological model, thus, in principle,\nwe can determine separately $\\Omega_0$, $\\Omega_b$, and $h$.\nThis method makes use of the small angular scale part of the power spectrum, \nwhere the amplitude of primordial fluctuations is declining and secondary fluctuations \nare becoming more important. The question naturally arises: \nHow do contributions to the power spectrum from secondary fluctuations influence \nparameter determination based on the small scale CMBR power spectrum?\n\n\nThe most important secondary fluctuations are the thermal static and kinematic Sunyaev-Zel'dovich \n(SSZ and KSZ) effects (\\cite{sz80}), the Rees-Sciama (RS) effect (\\cite{ReesSciama68}), \nthe moving cluster of galaxies (MCG) effect (\\cite{BirkGull83}; \\cite{GurvitsMitrof86}\n; \\cite{PyneBirkinshaw93}), point sources (\\cite{ToffZAB99}), and, \nif the Universe was re-ionized at some early stage, the Ostriker-Vishniac effect\n(\\cite{OstrVish86}; \\cite{Vish87}). \nIn this paper we concentrate on secondary effects caused by clusters of galaxies.\nSince detailed reviews are available on the SZ and the MCG effects \n(\\cite{Reph95}; \\cite{Birk98}), here we just summarize their major features. \nThe thermal SZ effect is a change in the CMBR via inverse Compton scattering \nby electrons in the hot atmosphere of an intervening cluster of galaxies. \nWe use the terms kinematic or static SZ effect depending on whether or not the intracluster gas\npossesses bulk motion. \nTo date only the static thermal SZ effect has been detected (\\cite{Birk98}). \n\nThe MCG effect is a special type of RS effect, due to the time-varying gravitational field of \na cluster of galaxies as it moves relative to the rest frame of the CMBR. \nUnlike the original RS effect, the MCG effect is not caused by \nintrinsic variation of the gravitational field, so that in the rest frame of the \ncluster, the photons fall into and climb out of the same gravitational field. \nHowever, in the rest frame of the cluster the CMBR is not\nisotropic, but has a dipole pattern, being brighter in the direction of the cluster\npeculiar velocity vector. Photons passing the cluster are deflected towards its center.\nThus in the direction of the cluster peculiar velocity vector (ahead of the cluster)\none can see a cooler part of the dipole pattern. Towards the tail of the cluster, one can see a\nbrighter part of the dipole (ahead of the cluster). When transferring back to the\nrest frame of the CMBR, we transfer the dipole out, but the fluctuations remain,\nshowing a bipolar pattern of positive and negative peaks. \nAt cluster center there is no deflection, thus there is no effect.\nThe amplitude of the MCG effect is proportional to the product of the gravitational deflection \nangle and the peculiar velocity of the cluster.\n\nThe most important characteristics of the SSZ, KSZ, and MCG effects in the context of cosmology \nis that their amplitudes do not depend on the redshift of the clusters causing the effect.\nUsing thermodynamic temperature units, their maximum amplitude are about 500 $\\mu$K, 20 $\\mu$K, \nand 10 $\\mu$K, respectively. The SSZ and KSZ effects have the same spatial dependence as the line \nof sight optical depth, the MCG effect has a unique bipolar pattern.\nAssuming a King approximation for the total mass and an isothermal beta model for the intracluster\ngas, the full width at half maximum (FWHM) of the SSZ and KSZ effects\n$\\approx (2 - 4)\\,r_c$, where $r_c$ is the core radius, depending on $\\beta$, \nwhich is typically between 2/3 and 1.\nThe MCG effect has a much larger spatial extent, with FWHM for each part of the bipolar \ndistribution $\\approx 10\\, r_c$. \n\nThe spectra of the effects are also important: the SSZ effect has a unique spectrum which \nchanges sign from negative to positive at about 218 GHz.\nThe KSZ and MCG effects have the same frequency dependence as the primordial\nfluctuations. The most important difference between the SZ effect and the MCG effect is that\nthe SZ effect is caused by intracluster gas, the MCG effect is caused by gravitational lensing\nby the total mass regardless the physical nature of that mass. \nTherefore the SZ effect only arises from clusters with intracluster gas.\nClusters can produce significant MCG effects even if devoid of intracluster gas.\n\n\nThe effects of clusters of galaxies on the CMBR in a given cosmology have been a subject of \nintensive research since the late 1980s. \nThere are several different ways of extracting information from these effects. \nSource counts of the SSZ effect were estimated by using the Press-Schechter mass function (PSMF) \nand scaling relations \n(\\cite{ColeKaiser88}; \\cite{Markevitchet92}; 1994; \\cite{MakiSuto93}; \\cite{BartSilk94}, \nDe Luca, Desert \\& Puget 1995, \\cite{ColaMRV94}; 1997, \\cite{sutoet99}). \nThe importance of the SSZ effect was demonstrated and it was shown that thousands of detections \nare expected with the next generation of satellites. \nContributions to the CMBR from the RS and the KSZ effects were derived by \nTuluie, Laguna \\& Anninos (1996) and Seljak (1996) for CDM models with zero cosmological constant. \nTuluie et al. used N-body simulations and a ray-tracing technique, Seljak used N-body simulations \nand second order perturbation theory. Contributions from the SSZ and KSZ effects originating from \nlarge scale mass concentrations (superclusters) were studied by Persi et al. (1995).\nBersanelli et al. (1996), in their extensive study of the CMBR for the Planck mission, \nestimated the contribution to the power spectrum from the SSZ and KSZ effects. \nAghanim et al. (1998) estimated the effects of the KSZ and MCG effects on the CMBR including\ntheir contributions to the CMBR power spectrum.\nAghanim et al. simulated $12.5^\\circ \\times 12.5^\\circ$ maps with pixel size of \n$1.5^\\prime \\times 1.5^\\prime$. They used the PSMF normalized to X-ray \ndata (assuming an X-ray luminosity-mass relation). The total mass was assumed \nto have a Navarro-Frenk-White profile (\\cite{Navarroet97}), and the intracluster gas\nwas assumed to follow an isothermal beta model distribution. \nThe time evolution of the electron temperature and the core radius were assumed to follow \nmodels of Bartlett \\& Silk (1994), which are based on self-similar models of Kaiser (1986).\nAccording to Aghanim et al. (1998)'s results, the KSZ effect is many orders of magnitude\nstronger than the primordial CMBR on small angular scales, and therefore the effect would prevent\nthe use of the power spectrum to break the geometric degeneracy. \nAtrio-Barandela \\& Mucket (1998) estimated the power spectra of the SSZ effect in \na standard dark matter dominated model with different lower mass cut-offs.\nContributions to the power from the Ostriker-Vishniac effect in CDM models were estimated\nby Jaffe \\& Kamionkowski (1998). \n\n\nIn this paper we estimate the contributions to the CMBR power spectrum from the \nSSZ, KSZ, and MCG effects on small angular scales adopting cold dark matter dominated models. \nIn our models we assumed scale invariant primordial fluctuations with\na processed spectrum having a power law form on cluster scales with a power law index \nof $n_P = -1.4$ (Bahcall \\& Fan 1998). This maybe used as a first approximation as long as\ncontributions from very low and/or very high mass clusters are small\n(cf. our discussion about mass cut offs at section~\\ref{s:PSMF}).\nWe use three representative models in our study:\n{\\it Model 1}, open CDM (OCDM) model: \na low density open model with $\\Omega_0 = 0.2$, $\\Lambda = 0$, $\\sigma_8 = 1.2$;\n{\\it Model 2}, flat lambda CDM (\\L CDM) model: \na low density flat model with $\\Omega_0 = 0.2$, $\\Lambda = 0.8$, $\\sigma_8 = 1.35$;\n{\\it Model 3}, standard CDM (SCDM) model:\na flat model with $\\Omega_0 = 1$, $\\Lambda = 0$, and $\\sigma_8 = 0.65$.\n\nIn Section~\\ref{s:method} we outline our method of estimating the power spectra of\nsecondary fluctuations caused by clusters of galaxies and discuss our normalization\nmethod for the PSMF.\nSections~\\ref{s:PSMF} and ~\\ref{s:physpar} describe how we used the PSMF and the\nscaling relations to obtain masses and other physical parameters of clusters.\nIn section~\\ref{s:PowerSpectr} we present the spherical harmonic expansion of the SSZ, \nKSZ and MCG effects, and our method of estimating their power spectra.\nSection~\\ref{s:Simulation} describes our simulations to evaluate the integrals over clusters.\nSections~\\ref{s:Results} and \\ref{s:Discussion} present our results and discuss\nthe differences from previous work.\n\n\n\\section{Outline of the method}\n\\label{s:method}\n\n\nWe used the Press-Schechter Mass Function (PSMF, \\cite{presschechter74}) as a distribution \nfunction for cluster masses. We used $n=-1.4$ as indicated by \nobservations (Bahcall and Fan 1998, and references therein). \nWe used observationally determined cluster abundances as a constraint on the PSMF. \nWhere necessary, we altered the model parameters resulting from the usual top hat spherical \ncollapse model since that model is only an approximation. \nIn our SCDM model we changed only the overall normalization of the PSMF by multiplying it by 0.23 \n(a similar normalization was used by \\cite{DeLucaet95}). This procedure is inconsistent with the\ninterpretation of the PSMF as a probability distribution (it does not integrate to unity),\nbut we use results for the SCDM model only as a comparison to the other two models. \nIn our Lambda-CDM model we multiplied the critical density threshold, $\\delta_c^0$, \nobtained from the spherical collapse model (equation~[\\ref{E:delta_c}]), by 1.23 \n(which is equivalent to changing the $\\sigma_8$ normalization) and made no other changes. \nOur OCDM model needed no adjustments.\nWith these changes all three models agree well with the present day ($z=0$) observed mass spectrum \n(Figure~\\ref{F:PSMF_OBS}; Bahcall \\& Cen 1993). \nFor high masses, the first two models (OCDM, and \\L CDM) also agree with the observed $z$ dependence \nof the high mass cumulative mass function (Figure~\\ref{F:PSMF_Z_OBS}; Bahcall, Fan \\& Cen 1997).\nThe \\L CDM and the SCDM models agree with CMBR constraints, while \nthe OCDM model is rejected by these constraints (\\cite{LinewBar98}).\nAs a cautionary note, it is useful to keep it in mind that taking {\\it all} data\ninto account none of these models are acceptable. \n\nWe assumed that the total mass distribution follows a truncated King profile \n(\\cite{King62}). For the intra-cluster gas we assumed an isothermal beta model\n(Cavaliere \\& Fusco-Femiano 1976). Isothermal beta model fits to X-ray images of clusters give\n$\\beta \\approx 2/3$ (\\cite{JonesForman84}). Determinations of the $\\beta$ parameter\nbased on spectroscopy suggest $\\beta \\approx 1$ (\\cite{Girardiet96}; \\cite{LubinBahcall93}). \nNumerical simulations imply a range for $\\beta$ from 1 to about 1.3\n($\\beta = 1.05$: \\cite{EvrardMetNav96}); $\\beta \\approx 1.3$: \\cite{BryanNorman98}; \n\\cite{Frenket99} suggest $\\beta = 1.17$). \nWe follow the precepts of \\cite{Ekeet98} and adopt $\\beta = 1$. \nThis choice provides a mass temperature function which is in a good\nagreement with the observed function (\\cite{Horneret99}). The fitted\nX-ray spatial distribution is highly dependent on the X-ray structure\nof the core, and may be expected to be less reliable in the outer\nregions of clusters. The SZ effect is more sensitive to the outer\nregions (the SZ effect is proportional to the electron density as\nopposed to thermal bremsstrahlung, which is proportional to density\nsquared). Choosing the spectroscopically derived $\\beta = 1$ gives a\nsmaller SZ effect, and so our choice of $\\beta$ should provide a\nconservative estimate of the contribution of the SZ effect to the\npower spectrum. A slightly larger $\\beta$ would not change our results\nsignificantly. Although the beta model describes the inner\nintra-cluster gas well, for more accurate SZ work an improved cluster\nmodel, which fits the outer regions better, will be needed.\n\nThe other physical parameters were determined using the virial theorem, a\nspherical collapse model, and models of the intra-cluster gas by Colafrancesco \\& Vittorio (1994).\nWe assumed a Maxwellian distribution for the peculiar velocities, $v_{pec}$, and \nused results of N-body simulations by Gramann et al. (1995) to normalize the distribution.\nWe took velocity bias into account, and assumed that the peculiar velocities \nare isotropically distributed. \n\nWe used analytical approximations to calculate the contributions of the SSZ, KSZ and MCG effects\nto the CMBR power spectrum. \nThese contributions are important only at small angular scales, where we can neglect the overlap \nbetween cluster images and ignore the weak cluster-cluster correlation, \nand therefore we can approximate the resulting power spectrum by summing\nthe contributions from individual clusters (similar methods were used by \n\\cite{ColeKaiser88}; \\cite{BartSilk94}; and \\cite{AtBaMuck99}).\nWe expanded the SSZ, KSZ, and MCG effects as Laplace series (i.e., series of spherical harmonics), \nthen determined the individual cluster contributions and summed over the clusters\n(for a detailed description see \\cite{Molnar98}).\n\nOur approximation breaks down at large angular scales, but at these scales primordial\nfluctuations dominate the CMBR, and the cluster contribution is only a minor perturbation,\nso that only a rough indication of the cluster effect is needed.\n\n\n\n\\section{Total Mass Distribution}\n\\label{s:PSMF}\n\n\nAccording to the Press-Schechter method, the co-moving number density of clusters of \ntotal mass $M$ at redshift $z$ (the PSMF) is given by\n\n\\begin{equation} \\label{E:PSMF}\n { d\\, n_c(M, z) \\over d\\, \\ln M} = \\sqrt{ 2 \\over \\pi } \\, { \\Omega_0 \\rho_c \\over M } \\, \n \\nu(M, z) \\,\n \\Bigl(- { d \\, \\ln \\sigma \\over d\\, \\ln M} \\Bigr) \\, e^{-\\nu(M,z)^2/2}\n,\n\\end{equation}\nwhere $\\Omega_0$ is the matter density today in units of the critical density, \n$\\rho_c = 1.88 \\times 10^{-29} \\, \\rm g\\, cm^{-3}$ is the current critical density of the universe\n(we adopt a dimensionless Hubble parameter $h_{100} = 0.5$ in our work); \n$\\nu(M, z) = \\delta_c^0(\\Omega_0, z) /\\sigma(M)$, \nwhere the present mass variance for a power law power spectrum, $P(k) \\propto k^n$, is\n\n\\begin{equation}\n \\sigma(M) = \\sigma_{8} \\, \\Biggl( { M \\over M_8} \\Biggr)^{-\\alpha}\n,\n\\end{equation}\n$\\alpha = (n + 3)/6$, $M_8 = 6 \\times 10^{14} \\Omega_0\\, h^{-1}M_\\odot$ \nis the mass within an $R_8 = 8 h^{-1}$ Mpc sphere, and $\\sigma_8$ is the normalization\n(Lacey \\& Cole 1993, Press \\& Schechter 1974).\nThe over-density threshold linearly extrapolated to the present may be expressed as\n(\\cite{LaceyCole93}; \\cite{Navarroet97})\n\n\\begin{equation} \\label{E:delta_c}\n \\delta_c^0(\\Omega_0, z) = \\cases{\n { 3 \\over 20} (12 \\pi )^{2/3} ( 1 + z) & $\\Omega_0 = 1$, $\\Lambda = 0$ \\cr\n {3 \\over 2} D(\\Omega_0, 0) \\Bigl[ \n \\bigl( { 2 \\pi \\over \\sinh \\eta - \\eta } \\bigr)^{2/3} + 1 \\Bigr] & \n $\\Omega_0 < 1$, $\\Lambda = 0$ \\cr\n 0.15 (12 \\pi)^{2/3} \\Omega_m^{0.0055}\n D_\\Lambda(\\Omega_0, 0)/D_\\Lambda(\\Omega_0, z) & \n $\\Omega_0 < 1$, $\\Lambda = 1 - \\Omega_0$ \\cr \n } \n,\n\\end{equation}\nwhere the conformal time for open models is\n\n\\begin{equation}\n \\eta = \\cosh^{-1} \n \\Biggl[ {2 \\over \\Omega_m(z) } - 1 \\Biggr]\n.\n\\end{equation}\nFor open models with cosmological constant $\\Lambda = 0$ \nthe linear growth factor is (Peebles 1980)\n\n\\begin{equation} \\label{E:Dz_LAM0}\n D(\\Omega_0, z) = 1 + { 3 \\over w} + { 3 (1 + w)^{1/2} \\over w^{3/2}}\n \\ln \\Bigl( (1 + w)^{1/2} - w^{1/2} \\Bigr)\n, \n\\end{equation}\nwhere $w(\\Omega_0, z) = \\Omega_m^{-1}(z) - 1$, \nand the density parameter $\\Omega_m(z)$ is\n\n\\begin{equation}\n \\Omega_m (z) = \n {\\Omega_0 (1 + z) \\over \\Omega_0 (1 + z) + (1 - \\Omega_0) } \n.\n\\end{equation}\nFor models with a non-zero cosmological constant\nthe integral can not be done analytically, thus we use\nan approximation (Lahav et al 1991; Caroll, Press \\& Turner 1992) to obtain\nthe equivalent expression to (\\ref{E:Dz_LAM0}), \n\n\\begin{equation}\n D_\\Lambda(\\Omega_0, z) = ( 1 + z )^{-1} \n { 5 \\Omega_f(z) \\over 2}\n \\Biggl\\{ \\Omega_f(z)^{4/7} - \\Omega_\\Lambda(z) + \n \\Biggl[ 1 + {\\Omega_f(z) \\over 2} \\Biggr]\n \\Biggl[ 1 + {\\Omega_\\Lambda(z) \\over 70} \\Biggr] \\Biggr\\}^{-1}\n.\n\\end{equation}\nThe density parameters, $\\Omega_f (z)$ and $\\Omega_\\Lambda (z)$, \nfor spatially flat Universes with $\\Lambda = 1 - \\Omega_0$, are \n\n\\begin{eqnarray} \n \\Omega_f (z) & = {\\Omega_0 (1 + z)^3 \\over \\Omega_0 (1 + z)^3 + 1 - \\Omega_0 } \\\\\n \\Omega_\\Lambda (z) & = {1 - \\Omega_0 \\over \\Omega_0 (1 + z)^3 + 1 - \\Omega_0 } \n.\n\\end{eqnarray}\nThe normalization of these growth functions is chosen so that at high redshifts they approximately\nmatch the time variation of density contrast in an Einstein-de Sitter ($\\Omega_0 = 1$) \nUniverse, which is a good approximation to the early Universe whatever its density parameter today.\nThe total number of clusters at redshift $z$ (in a redshift interval of $dz$) is\n\n\\begin{equation}\n N(z) dz = \\int_{M_{low}}^{M_{up}} {d n_c(M, z) \\over d M} \\; { dV \\over dz} \\; d M d z\n,\n\\end{equation}\nwhere $M_{low}$ and $M_{up}$ are the lower and upper mass cut offs for clusters.\nWe used $M_{low} = 10^{13} \\; M_\\odot$ for the SSZ and KSZ effects, \n$M_{low} = 10^{12} \\; M_\\odot$ for the MCG effect, and \n$M_{up} = 1 \\times 10^{16} \\; M_\\odot$ for all effects.\nThe lower cut off, $M_{low}$, for SZ effects signifies the lowest cluster mass for which \nwe expect a well-developed intracluster atmosphere. In the case of the MCG effect, $M_{low}$ \nis the mass limit from which we consider a mass concentration as a cluster (``formation''). \nWe found that low mass clusters do not contribute substantially to the power spectrum, \nthus the lower cut off, $M_{low}$, has little effect on our results. \nThe upper cut off, $M_{up}$, has no effect on our results (as long as it is large enough): \nthe probability of getting such a large cluster is negligible, so that the contribution \nfrom more massive clusters is negligible.\n\n\n\\section{Other physical parameters of clusters of galaxies}\n\\label{s:physpar}\n\nWe assumed a truncated King profile for the total mass distribution\n\n\\begin{equation} \\label{E:King_ro}\n \\rho(r) = \\cases{ \n \\rho_0 \\biggl( 1+ {r^2 \\over r_c^2} \\biggr)^{-{3\\over 2}} & $ r < p r_c$\\cr\n 0 & $ r \\ge p r_c$}\n\\end{equation}\nwhere $\\rm r_c$ is the core radius, $p r_c$ is the cut off, \nand an isothermal $\\beta$ model for the intra-cluster gas\n\n\\begin{equation} \\label{E:n_el}\n n(r) = \\cases{\n n_0 \\biggl(1+{r^2 \\over r_c^2}\\biggr)^{-{3\\beta \\over 2}} & $ r < p r_c$ \\cr\n 0 & $ r \\ge p r_c$ }\n,\n\\end{equation}\nwhere $n(r)$ and $n_0$ are the electron number density at radius $r$ and at the\ncenter of the cluster (Cavaliere \\& Fusco-Femiano 1976).\nAnalytical studies and numerical simulations show that the gas density profile scales\nwith the total density, and that the gas central electron density may be expressed as\n\n\\begin{equation} \\label{E:n_el_0}\n n_0 = f_g { 2 \\rho_0 \\over m_p (1 + X) }\n,\n\\end{equation}\nwhere $X=0.69$ is the average Hydrogen mass fraction, $f_g$ is the intra-cluster gas\nmass fraction. $\\rho_0$, the central mass density, is determined from the total \nmass by integrating equation~(\\ref{E:King_ro}).\nLittle is known about the total mass and redshift dependence of the intra-cluster gas from \nobservations. Here, we adopt Colafrancesco \\& Vittorio (1994)'s model which assumes that changes \nin the intra-cluster gas are driven by entropy variation and/or shock compression and heating.\nAccording to their model, the gas mass fraction may be expressed as\n\n\\begin{equation}\n f_g = f_{g0} \\Biggl( { M \\over 10^{15} h^{-1} M_\\odot } \\Biggr)^\\eta ( 1 + z)^{-s}\n,\n\\end{equation}\nwhere the normalization, $f_{g0} = 0.1$, is based on local rich clusters, and we\nused $\\eta = 0.5$ and $s = 1$, which are consistent with available data.\nUsing the virial radius to express the core radius, $r_c = R_v/p$, and assuming \nspherical collapse, we obtain\n\n\\begin{equation} \\label{E:r_cor}\n r_c(\\Omega_0, M, z) = {1.69 h^{-1} {\\rm Mpc} \\over p} \n \\Biggl[ \\Biggl( {M \\over 10^{15} h^{-1} M_\\odot } \\Biggr)\n { 178 \\over \\Omega_0 \\Delta_c(\\Omega_0, z) } \\Biggr]^{1/3} \n {1 \\over 1 + z } \n,\n\\end{equation}\nwhere $\\Delta_c(z) \\equiv \\rho_v(z) / \\rho_b(z)$ \nis the overdensity of the cluster relative to the background (\\cite{ColaBlasi98}). \nFor $\\Lambda = 0$ models (our OCDM and SCDM models) the over density may be expressed as\n\n\\begin{equation} \\label{E:Delta_c_L0}\n \\Delta_c(\\Omega, z) = 4 \\pi^2 Q^2 \n \\Bigl[ ( Q^2 + 2Q)^{1/2} - \\ln \\bigl(1 + Q + ( Q^2 + 2Q)^{1/2} \\bigr) \\Bigr]\n,\n\\end{equation}\nwhere $Q = 2( 1 - \\Omega_0)/ (\\Omega_0 (1+z))$ (Oukbir \\& Blanchard 1997).\nFor spatially flat models with finite cosmological constant (our \\L CDM model) we have\n\n\\begin{equation} \\label{E:Delta_c_L}\n \\Delta_c(\\Omega, z) = 18 \\pi^2 \\biggl[1 + 0.4093 \n \\bigl( \\Omega_f(z)^{-1} - 1 \\bigr)^{0.9052} \\biggr]\n,\n\\end{equation}\nwhere we used the approximation of Kitayama \\& Suto (1996).\n\nNumerical models of cluster formation show that cluster temperature scales\nwith total mass. Using the virial theorem and assuming spherical collapse with\na recent-formation approximation in a standard CDM model, the electron temperature, \n$T_e$, becomes\n\n\\begin{equation} \\label{E:T_eOM1}\n k T_e = 7.76 \\, \\beta^{-1} \n \\Biggl( { M \\over 10^{15} h^{-1} M_\\odot } \\Biggr)^{2/3} \\, ( 1 +z )\\, {\\rm keV}\n,\n\\end{equation}\nwhere $\\Delta_c$ is the density contrast of a spherical top-hat perturbation \nrelative to the background density just after virialization \n(cf. for example Eke, Cole \\& Frenk 1996).\nThe recent-formation approximation, however is valid only for $\\Omega_0 = 1$.\nFor our low matter density open model ({\\it Model 1}, OCDM), \nwe use a model which takes into account accretion during the evolution of clusters, \nand leads to the following scaling:\n\n\\begin{equation} \\label{E:T_eOPEN}\n k T_e = 2.76 \\, \\beta^{-1} {1 - \\Omega_0 \\over \\Omega_0^{2/3}}\n \\Biggl( { M \\over 10^{15} h^{-1} M_\\odot } \\Biggr)^{2/3}\n \\Biggl[ \\biggl( {2 \\pi \\over \\sinh \\eta - \\eta } \\biggr)^{2/3} + \n {n_P + 3 \\over 5} \\Biggr] \\, {\\rm keV}\n.\n\\end{equation}\nThis was derived for open models with zero cosmological constant (\\cite{VoitDonahue98}), \nbut since structure formation evolves similarly in a low density model with the same matter density \nand a zero cosmological constant, we use it for our {\\it Model 2} (\\L CDM) as an approximation.\n\nWe assumed a Maxwellian for the cluster peculiar velocity distribution, $v_{pec}$, \nas expected from a Gaussian initial density field:\n\n\\begin{equation} \\label{E:P_v_pec}\n P(v_{pec}, z)\\, d v_{pec} \\propto\n v_{pec}^2 \\, \\exp \\bigl\\{ - v_{pec}^2/2 \\sigma_p(z)^2 \\bigr\\} d v_{pec} \n,\n\\end{equation}\nwhere $\\sigma_p(z)$ is the Maxwellian width of the peculiar velocity distribution.\nThe rms peculiar velocity from linear theory, smoothed with a top-hat\nwindow function of radius $R$, $W_R$, is given by \n\n\\begin{equation} \\label{e:pecvel1}\n \\langle v^2 \\rangle _R (z) = H^2(z)\\, a^2(z) \\, f^2(\\Omega_0, \\Lambda) \\, \\sigma_{-1}(R)\n,\n\\end{equation} \nwhere $a(z)$ is the scale factor, and the moments, $\\sigma_j(R)$, are defined as\n\n\\begin{equation}\n \\sigma_j(R) = { 1 \\over 2 \\pi^2 } \\int_0^\\infty k^{2j + 2} P(k) W(kR) dk\n,\n\\end{equation}\nwhere $P(k)$ is the Fourier transform of the power spectrum and \nequation~(\\ref{e:pecvel1}) uses the moment $j = -1$ (\\cite{Peebles80}). \nThe velocity factor, $f(z) \\equiv d \\ln \\delta / d \\ln a$, can be approximated as \n(\\cite{Peebles80}; 1984)\n\n\\begin{equation} \n f(z) \\approx \\cases{\n \\Omega_m^{0.6} (z) & $\\Lambda = 0$ \\cr\n \\Omega_f(z) \\Bigl[ {5 \\over 2 (1+z) D_\\Lambda(\\Omega_0, z) } - { 3 \\over 2} \\Bigr] & \n $\\Lambda = 1 - \\Omega_0$ \\cr\n } \n.\n\\end{equation}\nThe cluster peculiar velocity rms differs from this since we assume that clusters form at the \npeaks of the density distribution, and with this bias may be expressed as\n\n\\begin{equation}\n \\langle v_p^2 \\rangle_R (z) = \\langle v^2 \\rangle_R (z) \n \\biggl[ 1 - { \\sigma_0^4(R) \\over \\sigma_1^2(R) \\sigma_{-1}^2(R) } \\biggr]\n\\end{equation}\n(Bardeen et al 1986). Colberg et al. (1998) calculated the velocity bias in a series of\nCDM models using a top-hat filter and processed CDM power spectra. \nThe correction factor has a weak dependence on $\\Omega_0$: it is about 0.8 for low density \nand flat CDM models. \n\nWe obtain the Maxwellian width in equation~(\\ref{E:P_v_pec}) from the rms peculiar velocity \nfrom averaging a Maxwellian:\n\n\\begin{equation} \\label{E:sigm_v_pec}\n \\langle v_p^2 \\rangle = { \\int_0^\\infty v^4 \\, \\exp\\{ - v_{pec}^2/2 \\sigma_p(z)^2\\} dv\n \\over \n \\int_0^\\infty v^2 \\, \\exp\\{ - v_{pec}^2/2 \\sigma_p(z)^2 \\} dv }\n = 3 \\sigma_p^2\n.\n\\end{equation}\nWe expressed $\\sigma_p$ as \n$\\sigma_p = norm \\times [ H(z) a(z) f(z)) ]/[ H(0) a(0) f(0) ]$.\nThe normalization at $z = 0$ was determined by using results on the peculiar velocity \ndistribution from numerical simulations (\\cite{Gramannet95}). \nThus we obtain the following expression for the Maxwellian width of the peculiar velocities, \n$\\sigma_p(\\Omega_0, \\Lambda, z)$, \nwith velocity bias for models with no cosmological constant (OCDM, SCDM, $\\Lambda = 0$):\n\n\\begin{equation} \\label{E:sigma_p_L0}\n \\sigma_p(\\Omega_0, 0, z) = (410 \\, {\\rm km\\,s^{-1}} )\\, \\Omega_m^{0.6} (z) \n \\bigl( \\Omega_0 ( 1 + z) + 1 - \\Omega_0 \\bigr)^{1/2}\n.\n\\end{equation}\nFor our \\L CDM model ($\\Lambda = 1 - \\Omega_0$) we obtain\n\n\\begin{eqnarray} \\label{E:sigma_p_LAM}\n \\sigma_p(\\Omega_0, 1 - \\Omega_0, z) & = & 410 \\, {\\rm km\\,s^{-1}}\\, {1 + z \\over ( \\Omega_0 (1+z)^2 + 1 - \\Omega_0)^{1/2} } \\, {D_\\Lambda(\\Omega_0, 0) \\over D_\\Lambda(\\Omega_0, z) } \\, \\times \\nonumber \\\\\n & & \\nonumber \\\\\n&\\times & \\Biggl[ {5 - 3 (1+z) D_\\Lambda(\\Omega_0, z) \\over 5 - 3 D_\\Lambda(\\Omega_0, 0) } \\Biggr], \\\\\n & & \\nonumber\n\\end{eqnarray}\nThis normalization is significantly larger than some recent measurements suggest\n(Bahcall \\& Oh 1996), but it is a good match to others (Gramann 1998). \nThis uncertainty should be remembered when interpreting our final results.\n\n\n\\section{Power Spectra of SSZ, KSZ and MCG Effects}\n\\label{s:PowerSpectr}\n\n\nIgnoring the correlation between clusters, the power spectrum becomes\n\n\\begin{equation} \\label{e:c_ell_int}\n C_\\ell^X = \\int dz \\int dM \\; {d n_c(M, z) \\over d M}\\; G_\\ell^X\\; { dV \\over dz}\n,\n\\end{equation}\nwhere $G_\\ell^X$ is the contribution from clusters with total mass $M$ at\nredshift $z$, and $X$ denotes the SSZ, KSZ or MCG effects.\n$dV/dz$ is the differential volume element (assumed isotropy)\n\n\\begin{equation} \\label{E:dV_dz}\n { dV \\over dz} = r(z)^2 { 4 \\pi c \\over H_0} \\biggl[ \\Omega_0 (1 + z)^3 +\n (1 - \\Omega_0 - \\Lambda) (1 + z)^2 + \\Lambda \\biggr]^{-1/2}\n,\n\\end{equation}\nwhere the effective distance $r(z)$ is \n\n\\begin{equation} \\label{E:r_z_dist}\n r(z) = \\cases{ { 2 c \\over H_0 } \\Bigl[{ \\Omega_0 z + (\\Omega_0 -2) \n (\\sqrt {1 + \\Omega_0 z} -1) \\over \\Omega_0^2 (1 + z)} \\Bigr] \n & $\\Lambda = 0$\\cr\n {c \\over H_0 } \\int_0^z dx \\bigl[\\Omega_0 (1 + x)^3 + 1 - \\Omega_0 \n \\bigr]^{-1/2}\n & $\\Lambda = 1 - \\Omega_0$}\n\\end{equation}\n(Peebles 1993). \nIn general, the coefficients $G_\\ell$ may be determined by calculating the spherical \nharmonic expansion of the cluster image by averaging out the azimuthal parameter, $m$, \n\n\\begin{equation}\n G_\\ell = { 1 \\over 2 \\ell +1} \\sum_{m = -\\ell}^\\ell\\, | a_{\\ell m} |^2 \n.\n\\end{equation}\nOur task is to determine the $a_{\\ell m}$ coefficients.\n\n\n\nThe SSZ and KSZ effects are cylindrically symmetric for spherical clusters, \ntherefore we may describe them using only one coordinate, the angular distance from \nthe cluster center. We separate the effects into amplitudes and geometrical form factors which \ncarry their spatial dependence.\nThe SSZ and KSZ effects in thermodynamic temperature units may be\nexpressed as\n\n\\begin{eqnarray}\n \\Biggl( {\\Delta T \\over T } \\Biggr)_S(x, \\theta) \\equiv \\Delta_S & = & \\Delta_S^0(x) \\zeta(\\theta) \\\\\n \\Biggl( {\\Delta T \\over T }\\Biggr)_K(x, \\theta) \\equiv \\Delta_K & = & \\Delta_K^0(x) \\zeta(\\theta) \n,\n\\end{eqnarray}\nwhere the central effects for the SSZ and KSZ effects are\n\n\\begin{equation} \\label{E:Delta_I_S_R}\n \\Delta_S^0(x, \\Theta) = \\bigl[ Y_0(x) + \\Theta Y_1(x) + \\Theta^2 Y_2(x) + \\Theta^3 Y_3(x) +\n \\Theta^4 Y_4(x) \\bigr] \\, \\Theta \\, \\tau_0\n,\n\\end{equation}\nand\n\n\\begin{eqnarray} \\label{E:Delta_I_K_R}\n \\Delta_K^0(x, \\Theta) & = & \\Biggl\\{\n \\Bigl[ {1 \\over 3} Y_0 + \\Theta \\Bigl( {5 \\over 6} Y_0 + {2 \\over 3} Y_1 \\Bigr) \\Bigr] \\, \\beta^2 \n - \\bigl[1 + \\Theta C_1(x) + \\Theta^2 C_2(x) \\bigr]\\, \\beta \\, P_1(\\alpha) \\\\\n & + & \\bigl[ D_0(x) + \\Theta D_1(x) \\bigr] \\, \\beta^2 \\, P_2(\\alpha) \\Biggr\\}\\, \\tau_0 \\nonumber\n.\n\\end{eqnarray}\nIn these expressions $P_k$ is the Legendre polynomial of order of $k$, \n$x = h \\nu / k_B T_{CB}$ is the dimensionless frequency,\n$\\Theta = k_B T_e/(m_e c^2)$ is the dimensionless temperature, \n$\\alpha$ is the angle between the cluster's peculiar velocity vector and its position vector, \n$h$, $\\nu$, $k_B$ and $T_{CB}$ are the Planck constant, frequency, Boltzmann constant,\nand temperature of the CMBR, $T_{CB} = 2.728 \\pm 0.002$ K (\\cite{Fixsenet96}), \nand the lengthy expressions for the spectral functions $Y_i(x)$, $C_i(x)$ and $D_i(x)$\nmay be found in Nozawa, Itoh \\& Kohyama (1998).\nThese functions arise from an expansion of the Boltzmann equation and although they are inaccurate\nfor high temperature clusters, their precision is sufficient \nfor our purposes here (for a discussion see \\cite{MolnarBirkinshaw99} and references therein).\nThe optical depth through the cluster center for gas model (\\ref{E:n_el}) is\n\n\\begin{equation}\n \\tau_0 = 2 \\sigma_T n_0 r_c \\, I_p(3 \\beta/2, p)\n,\n\\end{equation}\nand the geometrical form factor is\n\n\\begin{equation}\n \\zeta(\\theta) = \\int (n_e/n_0) dz = \\bigl( 1 + d_c^2 \\bigr)^{ {1 \\over 2} - {3 \\beta \\over 2} }\n \\,j(\\beta, p, d_c)\n,\n\\end{equation}\nwhere the function $j(\\beta, p, d_c)$ is defined as \n\n\\begin{equation}\n j(\\beta, p, d_c) = { I_p( 3 \\beta/2,\\sqrt{ p^2 - d_c^2}) \\over I_p(3 \\beta/2, p) }\n,\n\\end{equation}\n$d_c = \\theta/\\theta_c$ holds in the small angle approximation, and the integral, \n$I_p(\\alpha, q)$, is \n\n\\begin{equation}\n I_p (\\alpha, q) = {\\sqrt{\\pi} \\over 2} { \\Gamma( \\alpha - { 1 \\over 2} ) \\over \\Gamma( \\alpha )} - \n (q + 1)^{-\\alpha} (q - 1)^{1-\\alpha} \n {\\Gamma( 2 \\alpha- 1 ) \\over \\Gamma( 2 \\alpha ) } F(\\alpha; 1; 2 \\alpha; 2 q)\n,\n\\end{equation}\nwhere $\\Gamma$ is the gamma function, $F(x; y; w; z)$ is Gauss' hyper-geometric function, and \n$\\alpha$ must be greater than 1/2 (\\cite{GradshtRyzh80}).\nThe geometrical form factor is normalized to one at the cluster center ($\\zeta(0) = 1$). \nWe may expand the SSZ and KSZ effects in Legendre series as \n\n\\begin{equation}\n \\Delta_{SZ} = \\Delta_{SZ}^0\\, \\sum_{\\ell=0}^\\infty { 2 \\ell + 1 \\over 4 \\pi } \\zeta_\\ell P_\\ell\n,\n\\end{equation}\nwhere $\\zeta_\\ell$ are Legendre coefficients of $\\zeta$, and \n$SZ$ refers to the SSZ or the KSZ effect.\nWe determine the Legendre coefficients using a small angle approximation, as\n\n\\begin{equation} \\label{E:zeta_ell}\n \\zeta_\\ell = 2 \\pi \\int_0^{p \\theta_c} \\zeta(\\theta) \n J_0[(\\ell + {1\\over 2}) \\, \\theta ] \\, \\theta \\, d \\theta \n,\n\\end{equation}\nwhere we used the approximation\n\n\\begin{equation}\n P_\\ell \\approx J_0[(\\ell + {1\\over 2}) \\, \\theta ]\n,\n\\end{equation}\nwhere $J_0$ is a Bessel function of the first kind and zero order (\\cite{Peebles80}).\nWe can convert Legendre coefficients to Laplace coefficients by expressing the\nLaplace series of such a function as \n\n\\begin{equation}\n \\sum_\\ell a_{\\ell 0} Y_\\ell^0(\\theta, \\varphi) = \n \\sum_\\ell a_{\\ell 0} \\sqrt { 2 \\ell + 1 \\over 4 \\pi} P_\\ell(\\mu) = \n \\sum_\\ell { 2 \\ell + 1 \\over 4 \\pi } \\, b_\\ell P_\\ell(\\mu)\n,\n\\end{equation}\nwhere $\\mu = \\cos \\theta$, and $Y_\\ell^m$ and $P_\\ell$ are the \nspherical harmonics and Legendre polynomials.\nTherefore the conversion can be done as\n\n\\begin{equation}\n a_{\\ell 0} = \\Bigl( { 2 \\ell + 1 \\over 4 \\pi} \\Bigr)^{1/2} b_\\ell \n.\n\\end{equation}\nThus the Laplace series of the SSZ and KSZ effects become\n\n\\begin{equation} \\label{E:Delta_SZ}\n \\Delta_{SZ} (\\theta) = \\Delta_{SZ}^0 \\sum_\\ell \\Bigl( { 2 \\ell + 1 \\over 4 \\pi} \\Bigr)^{1/2} \n \\zeta_\\ell Y_\\ell^0 (\\theta) \n.\n\\end{equation}\n\n\n\nUsing equation~(\\ref{E:Delta_SZ}), the contribution of one cluster to the power spectrum \nof the SSZ and KSZ effects becomes\n\n\\begin{equation}\n G_\\ell^{SZ} = {1 \\over 4 \\pi } (\\Delta_{SZ}^0)^2 \\zeta_\\ell^2\n,\n\\end{equation}\nwhere $\\Delta_{SZ}^0$ and $\\zeta_\\ell$ are given by \nequations~(\\ref{E:Delta_I_S_R}), (\\ref{E:Delta_I_K_R}), and (\\ref{E:zeta_ell}).\n\n \n\nSimilarly, the MCG effect may be expressed as\n\n\\begin{equation} \\label{E:Delta_T_MCG}\n \\Biggl( {\\Delta T \\over T } \\Biggr)_M(x, \\theta, \\varphi ) \\equiv \\Delta_M = \n \\Delta_M^{max} \\xi (\\theta,\\varphi )\n,\n\\end{equation}\nwhere $\\xi (\\theta,\\varphi )$ is the geometrical form factor. $\\theta$ is the angle of the line \nof sight relative to the center of the cluster. The azimuthal angle, $\\varphi$, \nis measured in the plane of the sky\nfrom the direction of the tangential component of the peculiar velocity.\nThe maximum of the MCG effect is \n\n\\begin{equation}\n \\Delta_M^{max} = - (v_p/c) \\sin \\alpha\\, \\delta_{max}\n,\n\\end{equation}\nwhere $\\delta_{max}$ is the maximum deflection angle, $\\alpha$ is the angle between the \ncluster's peculiar velocity vector, $v_p$, and its position vector, \nand $c$ is the speed of light in vacuum.\nFor a spherically symmetric thin lens the deflection angle is given by \n\n\\begin{equation} \\label{E:delta_MCG0}\n \\delta(d) = { 4 G \\over c^2 \\, d } {\\cal M}(d)\n,\n\\end{equation}\nwhere $d$ is the impact parameter at the source, \nand $\\cal M$ is the mass enclosed by a cylindrical volume with axis parallel to the\nline of sight and radius equal to the impact parameter $d$\n(cf. for example Schneider, Ehlers \\& Falco 1992).\nUsing the King approximation for the density distribution (equation~[\\ref{E:King_ro}]),\nthe total mass in cylindrical coordinates, $(R, \\psi, z)$, becomes\n\n\\begin{equation}\n {\\cal M} = \\rho_0 r_c^3 \\, \\int_0^{2 \\pi} d \\psi\n \\int_{-d_c}^{d_c} dz \\int_0^p\\, \n { R dR \\over \\bigl(1 + R^2 + z^2 \\bigr)^{3 \\over 2} }\n,\n\\end{equation}\nwhere $d_c \\equiv d/r_c \\approx \\theta/\\theta_c$ in the small angle approximation.\nA straightforward integration and equation~(\\ref{E:delta_MCG0}) lead to\n\n\\begin{equation}\n \\delta(d_c, p) = { 4 G {\\cal M} \\over c^2 r_c g(p, p) }\\, { g(d_c, p) \\over d_c }\n,\n\\end{equation}\nwhere the function $g(x, p)$ is \n\n\\begin{equation}\n g(x, p) = \\ln ( 1 + x^2) + \n \\ln \\Biggl[ { p + \\sqrt{ 1 + p^2} \\over p + \\sqrt{ 1 + p^2 + x^2 } } \\Biggr]\n.\n\\end{equation}\nThus the geometrical form factor in our case becomes\n\n\\begin{equation} \\label{E:xi_g}\n \\xi(\\theta, \\varphi) = { g(d_c, p) \\over b_m d_c} \\cos \\varphi \n,\n\\end{equation}\nwhere $b_m$ is the maximum value of the function $g(x, p)/x$.\n\nThe MCG effect depends only on $\\cos \\varphi$, therefore we need to determine only the \n$m = \\pm 1$ terms in the spherical harmonic expansion.\nExpressing the spherical harmonics by associated Legendre polynomials, equation~(\\ref{E:xi_g}) \nexpands as\n\n\\begin{equation} \\label{E:xi_thetaphi}\n \\xi(\\theta, \\varphi) = -1 {2 \\ell +1 \\over 4 \\pi} {(\\ell-1)! \\over(\\ell+1) } \n \\sum_\\ell P_\\ell^1 \\biggl[ \\xi_\\ell^1 e^{i \\varphi} - \\xi_\\ell^{-1} e^{-i \\varphi} \\biggr]\n,\n\\end{equation}\nwhere we used the identity\n\n\\begin{equation}\n P_\\ell^{-m} = (-1)^m {(\\ell-m)! \\over(\\ell+m) }\\, P_\\ell^m\n.\n\\end{equation}\nIn order to obtain a real function, the imaginary terms must vanish, therefore we must have \n\n\\begin{equation} \\label{E:xi_ell}\n \\xi_\\ell^{-1} = - \\xi_\\ell^1\n.\n\\end{equation}\nUsing orthogonality, expressing the spherical harmonics in terms of associated Legendre polynomials\nand using equations~(\\ref{E:xi_ell}) and (\\ref{E:xi_thetaphi}), we obtain\n\n\\begin{equation}\n \\xi_\\ell^1 = - {k_\\ell \\over b_{max} } \\, \\int_{\\Omega_{{\\hat x}^\\prime}} \\,\n d \\Omega_{{\\hat x}^\\prime}\n {g(d_c, p) \\over d_c} P_\\ell^1(\\cos \\theta) \\cos^2 \\varphi\n,\n\\end{equation}\nwhere\n\n\\begin{equation}\n k_\\ell = \\sqrt{ 2 \\ell + 1 \\over 4 \\pi} \\sqrt{ ( \\ell - 1 )! \\over ( \\ell + 1 )! } \n.\n\\end{equation}\nThe $\\varphi$ integral can be performed \nsince $g(x, p)$ and $P_\\ell^1$ do not depend on $\\varphi$ giving\n\n\\begin{equation}\n \\xi_\\ell^1 = - {\\pi k_\\ell \\over b_{max} } \\, \n \\int_{-1}^1\\, d \\mu {g(d_c, p) \\over d_c} P_\\ell^1(\\mu) \n,\n\\end{equation}\nfrom which we find\n\n\\begin{equation} \\label{E:xi_ell_1_J1}\n \\xi_\\ell^1 = - {\\pi k_\\ell \\over b_{max} } (\\ell + 1/2) \\,\\theta_c \n \\int_0^{p \\theta_c} g(\\theta, p) J_1[(\\ell + {1 \\over 2}) \\,\\theta ] \\, d \\theta\n.\n\\end{equation}\nHere we used the small angle approximation for the\nassociated Legendre polynomials:\n\n\\begin{equation}\n P_\\ell^1(\\mu) \\approx (\\ell + 1/2)\\, J_1[(\\ell + {1 \\over 2}) \\,\\theta ]\n,\n\\end{equation}\nwhere $J_1$ is the Bessel function of the first kind and order 1 \n(for a derivation see Appendix). Thus the Laplace series of the MCG effect is \n\n\\begin{equation} \\label{E:Delta_MCG_Y}\n \\Delta_M = \\Delta_M^{max} \n \\sum_\\ell \\xi_\\ell^1 \\Bigl( Y_\\ell^1 - Y_\\ell^{-1} \\Bigr)\n,\n\\end{equation}\nwhere $\\xi_\\ell^1$ is given by equation~(\\ref{E:xi_ell_1_J1}).\n\n\nFor the power spectrum of the MCG effect, using equation~(\\ref{E:Delta_MCG_Y}), \nwe obtain\n\n\\begin{equation}\n G_\\ell^M = { 2 \\over 2 \\ell + 1} \\bigl( \\Delta_M^{max} \\bigr)^2 |\\xi_\\ell^1|^2\n.\n\\end{equation}\n\n\n\nThe observed effects are calculated by convolving the theoretical fluctuation pattern\nwith the telescope's point spread function (PSF).\nOne advantage of using the spherical harmonic coefficients is that this convolution is just a \nmultiplication in spherical harmonic space.\nAssuming an axially symmetric PSF, $R$, its Legendre polynomial expansion may be expressed as\n\n\\begin{equation} \\label{E:PSF_r}\n R({\\hat x} \\cdot {\\hat x}^\\prime) = \n \\sum_\\ell \\, {2 \\ell +1 \\over 4 \\pi } R_\\ell P_\\ell ({\\hat x} \\cdot {\\hat x}^\\prime) \n,\n\\end{equation}\nwhere the unit vectors, $\\hat x$ and ${\\hat x}^\\prime$, point to an arbitrary direction\n(where we want to evaluate the expansion) and to the center of the PSF.\nAssuming a non-axially symmetric effect, its spherical harmonic expansion can be written as\n\n\\begin{equation}\n f({\\hat x}) = \\sum_{\\ell , m} f_\\ell^m \\, Y_\\ell^m({\\hat x}) \n,\n\\end{equation}\nwhere $\\ell$ runs from zero to infinity and $m$ runs from -$\\ell$ to $\\ell$. \nUsing the addition theorem for spherical harmonics and their orthogonality, \nthe convolution of these two functions, $M = R \\star f$, becomes\n\n\\begin{equation}\n M({\\hat x}) = \\sum_{\\ell , m} R_\\ell f_\\ell^m Y_\\ell^m ({\\hat x}) \n. \n\\end{equation}\n\n\n\n\\section{Simulation of clusters of galaxies}\n\\label{s:Simulation}\n\n\nWe used Monte Carlo simulations to generate an ensemble of clusters of galaxies with masses\nsampled from the PSMF (equation~\\ref{E:PSMF}) with parameters those of \nour OCDM, \\L CDM and SCDM models. \nWe obtained the central electron number density and temperature, \nand the cluster core radius from scaling relations \n(equations~\\ref{E:n_el_0}, \\ref{E:T_eOM1}, \\ref{E:T_eOPEN}, and \\ref{E:r_cor}).\n\nWe choose to sample the PSMF using a rejection method. \nThe magnitude of the peculiar velocity may be sampled using an inversion method on the \nMaxwellian (\\ref{E:P_v_pec}), and yields\n\n\\begin{equation} \\label{E:v_p_RN}\n v_p = \\sqrt{2} \\sigma_p \\gamma^{-1} (3/2, RN)^{-1}\n,\n\\end{equation}\nwhere $\\gamma^{-1}(order, x)$ is the inverse of the incomplete gamma function and \n$\\sigma_p$ can be determined by using equations~(\\ref{E:sigm_v_pec}), \n(\\ref{E:sigma_p_L0}) and (\\ref{E:sigma_p_LAM}). \n$RN$ is a uniformly distributed random number in (0,1). \nWe assumed an isotropic distribution in space for the directions of the peculiar \nvelocity vectors, and ignored correlations between cluster peculiar velocities. \nThe tangential and radial peculiar velocities are distributed as projections of \nequation~(\\ref{E:v_p_RN}) accordingly.\nAs an illustration, in Figure~\\ref{F:MCG1} we show results from one simulation using our SCDM\nmodel projected on a grid.\n\nThe observational mass function (Figure~\\ref{F:PSMF_OBS}) is specified by $M_{1.5}$, the \nmass contained within co-moving radius of 1.5 Mpc. To convert $M_{1.5}$\nto the virial mass, $M_v$, which we use in the PSMF, we assume that the mass profile near 1.5 Mpc\ncan be approximated with $M_v(R) \\propto R^q$. We obtain\n\n\n\\begin{equation} \n M_v = \\Biggl( { \\Delta_c(0) \\over \\Delta_c \\Omega_m(z) }\n { M_{1.5} \\over \\Delta_c(0) (4 \\pi/3) \\rho_c(0) (1.5 h^{-1} {\\rm Mpc})^3}\n \\Biggr)^{q \\over 3 - q} M_{1.5}\n,\n\\end{equation}\nor, substituting the numerical values, \n\n\\begin{equation} \n M_v = \\Biggl( { 178 \\over \\Delta_c \\Omega_m(z) }\n { M_{1.5} \\over 6.98 \\times 10^{14} h^{-1} M_\\odot }\n \\Biggr)^{q \\over 3 - q} M_{1.5}\n.\n\\end{equation}\nWe used q = 0.64 (\\cite{Carlberget97}) to obtain curves shown in Figure~\\ref{F:PSMF_Z_OBS}.\n\nThe power spectrum for an ensemble of clusters may be determined by summing the individual \ncontributions of the simulated clusters (equation~[\\ref{e:c_ell_int}]).\nWe binned clusters by their apparent core radii, $\\theta_c$, then we summed the amplitudes in each bin. \nThe numerical evaluation of integral (\\ref{e:c_ell_int}), in this case, can be performed as\n\n\\begin{equation}\n C_\\ell^{SZ} = { 1 \\over 4 \\pi} \\sum_i (\\zeta_\\ell)_i^2 \n \\sum_{cl} (\\Delta_{SZ}^0)_{cl}^2\n,\n\\end{equation}\nand \n\n\\begin{equation}\n C_\\ell^M = { 2 \\over 2 \\ell + 1} \\sum_i (\\xi_\\ell^1)_i^2\n \\sum_{cl} (\\Delta_M^{max})_{cl}^2\n,\n\\end{equation}\nwhere the index $cl$ runs over clusters whose core radii fall within the $i^{th}$ bin.\n\n\n\\section{Results}\n\\label{s:Results}\n\n\nOur results for the power spectra\n(more exactly the dimensionless ${\\cal C}(\\ell) \\equiv \\ell(\\ell+1) C_\\ell$)\nfrom our {\\it Model 1} (OCDM) are shown on Figure \\ref{f:PowerSpOCDM}.\nFigures~\\ref{f:PowerSpLCDM} and \\ref{f:PowerSpSCDM} show\nour results for {\\it Model 2}, (\\L CDM) and {\\it Model 3}, (SCDM) respectively.\nAs a comparison, in each figure, we plot the corresponding primordial CMBR \npower spectrum (solid line) with $COBE$ normalization including the effects of gravitational lensing\ncalculated by using a new version of CMBFAST (\\cite{ZaldarriagaSeljak98}; \\cite{ZaldarrSperSel97}).\nOn large angular scales (up to about $\\ell \\approx 10$) the \ncosmic variance dominates (not shown).\nOn small angular scales the shape of the power spectra depends on the apparent angular\nsizes of the clusters and the amplitudes of the effects. \nThe apparent angular size depends on how the core radius and the angular diameter\ndistance change with redshift, while the amplitude is sensitive to the gas content, \ngas temperature and total mass as a function of redshift. \nFigures \\ref{f:PowerSpOCDM}-\\ref{f:PowerSpSCDM} \ndemonstrate that for small angular scales ($\\ell \\gtrsim 3000$) \nthe contribution to the power spectrum from the SSZ effect exceeds that of the primordial CMBR\nin all our models. \nThe contributions of the KSZ and MCG effects become important only on small scales, \nbut, at those scales, they may dominate over the lensed primordial fluctuations.\n\nDue to the early structure formation, there are more clusters at high redshift in our \nOCDM and \\L CDM than in our SCDM simulations. \nTherefore the contribution to the power spectrum from clusters in a low matter density model is \nsubstantially larger than in a SCDM model. \nAlso, most clusters are closer to us in a SCDM model, thus the contribution from clusters to the \npower spectrum peaks at higher angular scales (lower $\\ell$) than in low matter density models. \nThe KSZ and MCG effects have their coherence length (peak contributions) at $\\ell \\gtrsim 10000$.\nThe coherence length of the SSZ effect is about $\\ell \\approx 1000$ for our SCDM model and \nat about $\\ell \\approx 2000$ for our OCDM and \\L CDM models. \nIn general, the contributions to the power spectrum from the SSZ effect are\nabout 2 and 3 orders of magnitude greater than those from the KSZ and MCG effects.\nAt very small angular scales, $\\ell > 10000$, the contribution to the power spectrum from the \nMCG effect might exceed that of the SSZ or KSZ effects, and even the primordial\nfluctuations in the CMBR, but this depends on the details of the evolution of cluster atmospheres.\n\nOur simulations give somewhat different results for the KSZ and MCG effects than those\nof Aghanim et al. (1998).\nIn our simulations the amplitudes of the KSZ and MCG effects for low matter density \nmodels are about an order of magnitude greater than those for our SCDM model, and have a coherence \nlength of about $\\ell = 10000$, while rising monotonically at smaller $\\ell$.\nAccording to Aghanim et al.'s simulations, with similar cut off to ours, \n$M_{low} = 10^{13} M_\\odot$, \ncontributions from the KSZ effect in all models constantly grow and show no signs\nof leveling off, and their amplitude has a very weak dependence on cosmological model.\nContributions from the MCG effect on the other hand show a plateau in all Aghanim et al.'s models \nfor $\\ell > 1000$, and for the SCDM model, the MCG effect is larger than for the other two models.\n\n\nQuantitatively, our models show cluster-related effects that are weaker by \na factor of 10 for the MCG effect in our SCDM model and a factor of 100 \nfor the KSZ effect for all models.\nWe attribute these differences mostly to the different evolution models for the intracluster gas. \nThe ratio between the overall amplitudes of the KSZ and MCG effects in our calculations is\nabout the same as in Aghanim et al. (1998)'s results.\nOur results show that the power spectra of the KSZ and MCG effects do not exceed the \ngravitationally lensed primordial power spectrum up to $\\ell \\approx 10000$, while the power \nspectrum of the SSZ effect becomes dominant at $\\ell \\gtrsim 7000$ in all our models.\nContributions to the power spectrum from the SSZ and KSZ effects \nbased on Aghanim et al.'s model would exceed those from the CMBR at $\\ell \\gtrsim 5000$\neven if one takes gravitational lensing of the primordial CMBR into account.\nOur results are comparable to those obtained by Tuluie et al. (1996) and Seljak (1996).\nPersi et al. (1995)'s results for contributions to the power spectrum from the SSZ (KSZ) \neffect are about the same as (an order of magnitude higher than) our results suggest.\n\n\n\\section{Discussion}\n\\label{s:Discussion}\n\n\nAn observed power spectrum is made up from the sum of all astrophysical effects and noise.\nWe rely on the different frequency and/or power spectra of the secondary effects to separate \nthese foregrounds from the primordial CMBR signal (\\cite{Tegmark98}).\n\nOf the effects discussed here, it should be easy to separate the SSZ effect\nby using multi-frequency measurements of its unique spectrum. \nThe separation of primordial fluctuations in the CMBR and fluctuations caused by \nthe KSZ and MCG effects is more difficult since their frequency spectra are the same. \nOptimal filters have been designed to separate the\nKSZ effect (\\cite{HaehneltTegmark96}; \\cite{Aghanimet97}): here it helps to know the SSZ effect \nfor the same cluster, since that would give us a position and even an estimate for the expected\namplitude of the effect. \nAghanim et al. (1998) discussed methods to separate the MCG effect: this is facilitated by its\nunique dipole pattern with sharp peaks (Figure~\\ref{F:MCG1}). \nPrimordial fluctuations are usually assumed to be gaussian, where the probability of getting such \na strongly peaked bipolar pattern is small, and we would expect the strong small angular scale \ngradient near a known cluster of galaxies to be a definite indication of the presence of the \nMCG effect. \nAlso, knowing the position of clusters helps to find the effect.\nHowever, contributions from other effects, such as early ionization and discrete radio sources\ncauses further confusion, and may be expected to make it difficult to determine\nthe power from the SZ or MCG effects. \n\n\nWe analyzed the contributions to the power spectrum from the SSZ, KSZ and MCG \neffects to check their impact on the determination of cosmological parameters, especially at\nlarge $\\ell$ where gravitational lensing may break the geometric degeneracy.\nIn Figure~\\ref{f:Lens01} we show the small scale lensed primordial fluctuation power spectra \nof our three models (OCDM, SCDM, \\L CDM; solid lines) with power spectra resulting \nfrom the sum of fluctuations due to the lensed primordial CMBR and the SSZ effect (long dashed lines), \nand from the sum of the lensed primordial CMBR, the KSZ and the MCG effects (short dashed lines). \nAccording to our models, if the fluctuations due to the SSZ effect are fully separated, \nthe KSZ and MCG effects do not prevent the use of this part of the power spectrum to\nbreak the geometric degeneracy and distinguish between different CDM models. \nNote that normalization at the first Doppler peak, rather than the usual {\\it COBE} normalization,\nwould lower the contributions to the power spectrum from primordial\nfluctuations in a \\L CDM model relative to those from a SCDM model, and thus\nsecondary effects would become more important relative to the primordial CMBR fluctuations.\n\nOur simulations also show that the power spectrum of the SSZ effect may itself be used to break the \ngeometric degeneracy.\nSince the separation of the SSZ effect from other secondary effects should be straightforward, \nwe should be able to determine the power spectrum of the SSZ effect alone.\nAs can be seen from Figure~\\ref{f:PowerSp3}, this power spectrum depends on \n$\\Omega_0 h^2$ and $\\Omega_b h^2$, providing an additional constraint on these parameters.\nWe note, however, that the amplitude of the SSZ effect is model dependent.\nSince the contributions to the power spectrum from the SZ and MCG effects are model dependent, \nto evaluate fully their power spectra we need a better observationally-supported model for the \nintracluster gas.\nSensitive, high-resolution all-sky, X-ray observations could map the emission from intracluster gas\nup to high redshift providing strong constraints on gas formation and evolution\nand thus a good basis for modeling the SSZ and KSZ effects (\\cite{Jahoda.et97}).\nNumber counts of clusters based on their SSZ effect can also be used to constrain\ncosmological models (\\cite{sutoet99}).\n\nThere are many possibilities of using observations to break the geometric degeneracy.\nFor example measurements of the CMBR polarization, the Hubble constant, or light curves of Type Ia \nsupernovae have been discussed (Zaldarriaga et al. 1997; \\cite{EisensteinHuTeg98}; \\cite{Tegmarket98}).\nAlso, combination of measurements of the SSZ effect and thermal bremsstrahlung (X-ray) emission \nfrom clusters can be used to determine the Hubble constant for a large number of clusters, \nproviding a statistical sample which might enable us to determine the Hubble constant, and\nperhaps the acceleration parameter, to good accuracy (\\cite{Birk98}).\n\n\nSecondary fluctuations introduce non-gaussianity into the primordial spectrum\nat small scales. This non-gaussianity should be taken into account when estimating\nCMBR non-gaussianity at these scales. \nWinitzky (1998) estimated the effect of lensing and concluded that Planck may \nobserve non-gaussianity due to lensing near the angular scale of maximum effect, $\\sim 10^\\prime$.\nOther processes, including the SSZ, KSZ, and especially the MCG effect, \nintroduce a highly non-gaussian signal as is easily seen for the MCG effect on Figure~\\ref{F:MCG1}.\nA similar non-gaussian pattern arises from moving cosmic strings \n(the Kaiser-Stebbins effect, compare our Figure~\\ref{F:MCG1} to Figure 6a of \\cite{MagueijoLewin97}).\nOur results indicate that at $\\ell \\gtrsim 10^4$ the MCG effect might be comparable in strength \nto the primordial fluctuations. \nEvidence for non-gaussianity has been reported by Ferreira, Magueijo \\& Gorski (1998) and \nGaztanaga, Fosalba, \\& Elizalde (1997) at angular scales $\\ell \\approx 16$ and $\\ell \\approx 150$.\nThey do not exclude the possibility that this non-gaussianity has been introduced by\nforegrounds, but our results show that clusters can not introduce detectable non-gaussianity\non such scales (Figure~\\ref{f:PowerSp3}).\n\n\nWe convolved our theoretical results (Figures~\\ref{f:PowerSpOCDM} - \\ref{f:PowerSpSCDM}) with the \nexpected point spread functions (PSFs) of instruments on the MAP and Planck missions to estimate the \nlevel of the secondary fluctuations caused by clusters of galaxies on the observable power spectrum.\nThe observed $C_{\\ell}$ values become\n\n\\begin{equation}\n C_{\\ell}^{obs} = C_{\\ell} W_{\\ell}\n,\n\\end{equation}\nwhere the $W_{\\ell}$ values are the Legendre coefficients of the PSF.\nFor an assumed gaussian response function and in the small angle approximation, the \n$W_{\\ell}$ coefficients are\n\n\\begin{equation}\n W_{\\ell} = e^{- \\sigma^2 (\\ell + 1/2)^2}\n,\n\\end{equation}\nwhere $\\sigma = h / 2 \\sqrt{ \\ln 4}$, and $h$ is the FWHM\nof the beam (for a detailed description of window functions and $W_{\\ell}$ coefficients, \nsee White \\& Srednicki 1995).\nThe observed rms fluctuations then become \n\n\\begin{equation} \\label{E:DT_rms}\n \\langle \\Delta T/ T_0 \\rangle_{rms}^2 = \n \\sum_\\ell { 2 \\ell + 1 \\over 4 \\pi} C_\\ell W_{\\ell} \n.\n\\end{equation}\n\nIn general, contributions from unresolved cluster static effects add to provide a cumulative \ncontribution to the CMBR power spectrum. Contributions from the KSZ and MCG\neffects from unresolved sources tend to cancel. In the case of the MCG effect this is because\neach unresolved source contribution would be zero owing to the dipole spatial\npattern of the effect. For small-scale KSZ effects there are several\nsources in the field of view of the telescope, and different sources have positive or\nnegative contributions depending on the sign of their line of sight peculiar velocity, and\ntherefore they tend to cancel each other.\nThe larger the beam size, the more effective is the cancellation of the MCG and KSZ effects.\nNote that the spatial extension of the MCG effect is much\nlarger than that of the KSZ effect, so many clusters may be unresolved in their KSZ\nand resolved in their MCG effect.\nThe MCG effect might be relatively more important at high redshifts, since it does not require\na well-developed cluster atmosphere.\n\nIn Figures~\\ref{f:MAP94} and \\ref{f:PLANCK353} we show the\ncontributions to the power spectrum from primordial fluctuations, and the SSZ, KSZ and MCG effects, \nconvolved with the PSF of the planned $\\nu = 94$ GHz receiver on MAP, and the planned \n$\\nu = 353$ GHz bolometer on Planck.\nThe amplitude of the fluctuations from the the SSZ effect is negative at $\\nu = 94$ GHz \nand positive at $\\nu = 353$ GHz, but only the the absolute value of the effect contributes to \nthe power spectrum.\nThe different maximum $\\ell$ values for the MAP and Planck systems ($\\ell_{max} \\sim$ 1000 and 2000,\nrespectively) can clearly be seen on Figures~\\ref{f:MAP94} and \\ref{f:PLANCK353}.\nBecause of these cutoffs, the observable power spectrum is dominated by \nprimordial fluctuations at all $\\ell$ for these missions.\nAccording to our results, the SSZ effect may cause a 1\\% \nenhancement in the amplitude of the Doppler peaks, which is at the limit of the sensitivity\nof the MAP and Planck missions.\nFrom the analysis of the power spectrum, this would lead to an overestimation\nof the parameter $\\Omega_0 h^2$ by about 1\\%,.\n% !!!!!! of the parameter $\\Omega_0 h^2$ by about 1\\%.\nThe shift in the position of peaks as a function of $\\ell$ caused by the SSZ effect \nis less important since \nthe spectrum of the SSZ effect has only a weak dependence on $\\ell$.\n\nIn Table~\\ref{T:RMS_ALL} we show the $(\\Delta T/T)_{rms}$ values of the contributions to the CMBR\nfrom the SSZ, KSZ, and MCG effects convolved with the the 94 GHz MAP and 353 GHz Planck\nreceivers for our three models (OCDM; \\L CDM; SCDM).\nAs a comparison, we display the corresponding rms values of the primordial fluctuations.\nThe rms values of all these secondary effects are an order of magnitude\nsmaller than rms values from primordial fluctuations. The most important contribution\nis that of the SSZ effect at these frequencies. The KSZ and MCG effects give similar contributions\nwith the KSZ effect being about a factor of two stronger. \nAghanim et al. (1998)'s results for the rms values of the MCG effect is a factor of 10 (SCDM)\nor a factor of 3 (OCDM and \\L CDM) larger than our results.\nNote, however, that rms values give only a crude estimate of the magnitude of the effects. \nAt large angular scales the primordial fluctuations are about 100 (for the SSZ effect)\nor $10^5 - 10^7$ (KSZ, MCG effects) times stronger than the secondary fluctuations. \n\nAn ideal observation to measure the contribution to the power spectrum from the\nSSZ effect would use high angular resolution ($\\ell \\gtrsim 7000$) and high frequency\n($\\nu \\gtrsim 250$ GHz). \nSuZIE probes the power spectrum at angular scale $\\ell \\approx 7500$ at 140 GHz.\nThe 2$\\sigma$ upper limit on the power at this scale from SuZIE is \n$\\ell (\\ell+1) C_\\ell \\leq 1.4 \\times 10^{-9}$ (\\cite{Gangaet97}). \nUnfortunately our models suggest that at this frequency the primordial contribution \nto the power spectrum is about 10 times stronger than that from the SSZ effect.\nA promising experiment is SCUBA, which probes the anisotropies at \nangular scale $\\ell \\approx 10000$ and frequency 348.4 GHz.\nTheir preliminary 2$\\sigma$ upper limit on the power spectrum at this scale is \n$\\ell (\\ell+1) C_\\ell \\leq 4.7 \\times 10^{-8}$. \nMuch further work is planned, and should lower this limit by a factor of 3-10 (\\cite{BorysCS98}).\n\n\n\\acknowledgments\n\nSMM is grateful to Bristol University for a full scholarship, where most of this work was done. \nThis work was finished while SMM held a National Research Council Research Associateship at \nNASA Goddard Space Flight Center. \nWe thank N. Aghanim for comments on an earlier version of the manuscript, and \nour referee, Dr Bartlett, for his detailed comments and for helping us to clarify some aspects of \nour approximations. We thank U. Seljak and M. Zaldarriaga for making the CMBFAST code available. \n\n\n% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %\n% \n% A P P E N D I X \n% \n% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %\n\n\n\\clearpage\n\n\n\\appendix\n\n\\centerline{ \\bf{Appendix: Small Angle Approximation for $P_\\ell^1$}}\n\nWe derive a small angle approximation for the associated Legendre polynomial\n$P_\\ell^1$. We express the associated Legendre polynomial\n$P_\\ell^1$ in terms of the Legendre polynomial $P_\\ell$\n(see for example \\cite{ArfkenWeber95}) as \n\n\\begin{equation} \n P_\\ell^1(\\mu) = \\sqrt{1 - \\mu^2} { d \\over d \\mu} P_\\ell (\\mu)\n.\n\\end{equation}\nIntroducing a new variable, $x = \\ell(\\ell+1) \\theta$, using the chain rule and a \nsmall angle approximation, we get\n\n\\begin{equation} \n P_\\ell^1(\\mu) = \\sqrt{1 - \\mu^2} { d P_\\ell\\over d x} { d x \\over d \\theta} \n { d \\theta\\over d \\mu} \\approx - \\ell(\\ell+1) { d P_\\ell\\over d x} \n.\n\\end{equation}\nUsing a small angle approximation for $P_\\ell$ (Peebles 1980) we obtain\n\n\\begin{equation} \n - \\ell(\\ell+1) { d P_\\ell\\over d x} \\approx - \\ell(\\ell+1) { d \\over d x} J_0 (x)\n.\n\\end{equation}\nUsing the relation \n\n\\begin{equation} \n J_1(x) = - { d \\over d x} J_0 (x) \n\\end{equation}\nfor Bessel functions, we finally obtain\n\n\\begin{equation} \\label{E:P_ell_1_J1}\n P_\\ell^1(\\mu) \\approx - \\ell(\\ell+1) { d \\over d x} J_0 (x) = \\ell(\\ell+1) J_1(x)\n.\n\\end{equation}\n\n\n\n% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %\n% \n% B I B L I O G R A P H Y \n% \n% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %\n\n\n\\clearpage\n\n\\begin{thebibliography}{plain}\n\n\\bibitem[Aghanim et al. 1997]{Aghanimet97}\n Aghanim, N., De Luca, A., Bouchet, F. 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N., \\& Seljak, U., 1997, \\apj, 488, 1\n\n\n\\end{thebibliography}\n\n\n \n\n% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %\n% \n% F I G U R E S F I G U R E S F I G U R E S \n% \n% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %\n\n\\clearpage\n\n% FIGURE 1\n\\begin{figure} \n\\centerline{\n\\plotone{fig01.eps}\n}\n\\caption{\n The PSMFs, $dN/(dV d \\ln M)(>M)$, at $z = 0$,\n used in our simulations compared to observations. \n The long dashed, dash dot, and short dashed lines\n refer to the PSMFs of our $\\Lambda = 0$, $\\Omega_0 = 1$ (SCDM); \n $\\Lambda = 0$, $\\Omega_0 = 0.2$ (OCDM); \n and $\\Lambda = 0.8$, $\\Omega_0 = 0.2$ (\\L CDM) models respectively. \n The solid line represents the observationally-derived mass function \n of Bahcall and Cen (1993).\n\\label{F:PSMF_OBS} \n} \n\\end{figure} \n\n% FIGURE 2\n\\begin{figure} \n\\centerline{\n\\plotone{fig02.eps}\n}\n\\caption{\n High mass ($M > 1.6 \\times 10^{15} M_\\odot$) PSMFs, \n $d N/ (dV dz)$ in units of number Mpc$^{-3}$, as a function of redshift, $z$, \n used in our simulations compared to observations.\n The long dashed, dash dot, and short dashed lines\n refer to the cumulative PSMFs of our $\\Lambda = 0$, $\\Omega_0 = 1$ (SCDM); \n $\\Lambda = 0$, $\\Omega_0 = 0.2$ (OCDM); and $\\Lambda = 0.8$, $\\Omega_0 = 0.2$ \n (\\L CDM) models respectively.\n The solid line represents the mass function derived from observations \n (Bahcall et al. 1997), which is a close match to our OCDM model.\n\\label{F:PSMF_Z_OBS} \n} \n\\end{figure} \n\n\n% FIGURE 3\n\\begin{figure} \n\\centerline{\n\\plotone{fig03.ps}\n}\n\\caption{\n Fluctuations in the CMBR ($\\rm \\Delta T$ in $\\mu$K) caused by the moving \n clusters effect in our SCDM model (see text for details).\n Primordial fluctuations and other source of secondary fluctuations are not displayed.\n The area covers $30^\\circ \\times 25^\\circ$ of the sky with pixel size \n $2.6^\\prime \\times 2.6^\\prime$. The maxima and minima are about $\\pm 2\\mu$K.\n\\label{F:MCG1}\n} \n\\end{figure}\n\n\n% FIGURE 4\n\\begin{figure} \n\\centerline{\n\\plotone{fig04.eps}\n}\n\\caption{ \n The power spectrum ${\\cal C}(\\ell) \\equiv \\ell(\\ell+1) C_\\ell$ of the \n lensed primordial CMBR (solid line), SSZ (long dashed), \n KSZ (dashed dot), and MCG (short dashed) effects\n for an OCDM model with $\\Omega = 0.2$, $\\Lambda = 0$, $n = -1.4$.\n\\label{f:PowerSpOCDM} \n}\n\\end{figure}\n\n\n% FIGURE 5\n\\begin{figure} \n\\centerline{\n\\plotone{fig05.eps}\n}\n\\caption{\n The power spectrum ${\\cal C}(\\ell) \\equiv \\ell(\\ell+1) C_\\ell$ of the \n lensed primordial CMBR (solid line), SSZ (long dashed), \n KSZ (dashed dot), and MCG (short dashed) effects\n for a \\L CDM model with $\\Omega = 0.2$, $\\Lambda = 0.8$, and $n = -1.4$.\n\\label{f:PowerSpLCDM}\n}\n\\end{figure}\n\n\n% FIGURE 6\n\\begin{figure} \n\\centerline{\n\\plotone{fig06.eps}\n}\n\\caption{\n The power spectrum ${\\cal C}(\\ell) \\equiv \\ell(\\ell+1) C_\\ell$ of the \n lensed primordial CMBR (solid line), SSZ (long dashed), \n KSZ (dashed dot), and MCG (short dashed) effects\n for an OCDM model with$\\Omega = 1$, $\\Lambda = 0$, and $n = -1.4$.\n\\label{f:PowerSpSCDM}\n}\n\\end{figure}\n\n\n% FIGURE 7\n\\begin{figure} \n\\centerline{\n\\plotone{fig07.eps}\n}\n\\caption{\n Power spectra ${\\cal C}(\\ell) \\equiv \\ell(\\ell+1) C_\\ell$: \n lensed primordial CMBR (solid line), SSZ (long dashed), \n KSZ (dashed dot), and MCG (short dashed) effects\n for our three models: OCDM, \\L CDM, and SCDM.\n\\label{f:PowerSp3}\n}\n\\end{figure}\n\n\n% FIGURE 8\n\\begin{figure} \n\\centerline{\n\\plotone{fig08.eps}\n}\n\\caption{\n Small scale power spectrum ${\\cal C}(\\ell) \\equiv \\ell(\\ell+1) C_\\ell$\n of the lensed primordial CMBR, \n the static and kinematic SZ effects, and the MCG effect for our three\n models: OCDM, \\L CDM, SCDM. The long and short \n dashed lines represent the sum of the lensed primordial CMBR and the SSZ effect, and the sum\n of the lensed primordial CMBR, the KSZ and RSC effects respectively. \n The contribution from the static SZ effect is important in all models. \n Contributions from the kinematic SZ and MCG effects are negligible at these $\\ell$ values.\n We may conclude that if fluctuations due to the\n static SZ effect are removed the kinematic and MCG effects do not\n prevent using gravitational lensing to break the geometric degeneracy. \n Note that different normalizations shift the sets of curves.\n For example, normalization to the first Doppler peak makes\n the power spectra of our SCDM and \\L CDM models shift closer.\n\\label{f:Lens01}\n}\n\\end{figure}\n\n\n% FIGURE 9\n\\begin{figure} \n\\centerline{\n\\plotone{fig09.eps}\n}\n\\caption{\n Power spectra ${\\cal C}(\\ell) \\equiv \\ell(\\ell+1) C_\\ell$\n of fluctuations in the CMBR as MAP would\n observe them at $\\nu = 94$ GHz with FWHM = 12.6$^\\prime$.\n Models and line codes are the same as in Figure~\\ref{f:PowerSp3}.\n The contribution from the primordial fluctuations dominates on all scales.\n\\label{f:MAP94}\n}\n\\end{figure}\n\n\n% FIGURE 10\n\\begin{figure} \n\\centerline{\n\\plotone{fig10.eps}\n}\n\\caption{\n Power spectra ${\\cal C}(\\ell) \\equiv \\ell(\\ell+1) C_\\ell$\n of fluctuations in the CMBR as Planck would\n observe them at $\\nu = 353$ GHz with FWHM = 5 arc minute.\n Models and line codes are the same as in Figure~\\ref{f:PowerSp3}.\n The contribution to the power spectrum from the static SZ effect \n at this frequency is 1.2 times that in the Rayleigh-Jeans region, \n and the static SZ effect dominates over the processed primordial fluctuations\n above about $\\ell \\approx 3000$ (except for the SCDM model).\n\\label{f:PLANCK353}\n}\n\\end{figure}\n\n\n\n% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % \n% \n% T A B L E S \n% \n% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % \n\n\\clearpage\n\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{cccccccccc} \n\\hline\n\\hline\n\\noalign{\\vskip 1pt} \\\\\n Model & & MAP & 94 GHz & & & & Planck & 353 GHz & \\\\\n\\noalign{\\vskip 0pt} \\\\\n\\hline\n\\noalign{\\vskip 0pt} \\\\\n & CMBR & SSZ & PKSZ & MCG & & CMBR & SSZ & PKSZ & MCG \\\\\n & $\\mu$K & $\\mu$K & $\\mu$K & $\\mu$K & & $\\mu$K & $\\mu$K & $\\mu$K & $\\mu$K \\\\\n\\noalign{\\vskip 0pt} \\\\\n\\hline\n\\hline \\\\[-2pt]\n1. OCDM & 86 & 7.0 & 0.54 & 0.20 & & 100 & 14 & 0.81 & 0.33 \\\\[-2pt]\n2. LCDM & 119 & 5.9 & 0.49 & 0.20 & & 130 & 11 & 0.71 & 0.32 \\\\[-2pt]\n3. SCDM & 93 & 3.2 & 0.36 & 0.12 & & 101 & 5.7 & 0.50 & 0.17 \\\\[-2pt]\n\\end{tabular} \n\\end{center} \n\\caption{\\label{T:RMS_ALL}\n Root mean square ($\\Delta T_{rms}$) of the SSZ, KSZ, and MCG effects convolved \n with response functions of the 94 GHz MAP (FWHM = $12.6^\\prime$) and \n 353 GHz Planck (FWHM = $5^\\prime$) instruments from our three models \n (OCDM; LCDM; SCDM, see section~\\ref{S:INTRO}). \n As a comparison, we display the rms values of the primordial fluctuations (CMBR).\n }\n\\end{table}\n\n\n\n% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % \n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002271.extracted_bib",
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T., 1986, \\apjl, 306, L51\n\n\\bibitem[Oukbir \\& Blanchard 1997]{OukbirBlanchard97}\n Oukbir, J., \\& Blanchard 1997, A\\&A, 317, 1\n\n\\bibitem[Persi et al. 1995]{Persiet95}\n Persi, F. M., Spergel, D. N., Cen, R., \\& Ostriker, J. P., 1995, \\apj, 442, 1\n\n\\bibitem[Peebles 1980]{Peebles80}\n Peebles, P. J., 1980, ``The Large Scale Structure of the Universe'', \n Princeton: Princeton University Press\n\n\\bibitem[Peebles 1984]{Peebles84}\n Peebles, P. J., 1984, \\apj, 284, 439\n\n\\bibitem[Peebles 1993]{Peebles93}\n Peebles, P. J., 1993, ``Principles of Physical Cosmology'', \n Princeton: Princeton University Press\n\n\\bibitem[Press \\& Schechter 1974]{presschechter74}\n Press W. H., \\& Schechter P., 1974, \\apj, 187, 425\n\n\\bibitem[Pyne \\& Birkinshaw 1993]{PyneBirkinshaw93}\n Pyne, T., Birkinshaw, M., 1993, \\apj, 415, 459\n\n\\bibitem[Rees \\& Sciama 1968]{ReesSciama68}\n Rees, M.J., \\& Sciama, D.W., 1968. \\nat, 217, 511\n\n\\bibitem[Rephaeli 1995]{Reph95} \n Rephaeli, Y., 1995, \\araa, 33, 541\n\n\\bibitem[Schneider, Ehlers \\& Falco 1992]{Schneideret92}\n Schneider, P., Ehlers, J., \\& Falco, E. E., 1992, ``Gravitational Lenses'', Springer: Berlin\n\n\\bibitem[Seljak 1996]{Seljak96}\n Seljak, U., 1996, \\apj, 460, 549\n\n\\bibitem[Seljak 1997]{Seljak97}\n Seljak, U., 1997, preprint, astro-ph/9711124\n\n\\bibitem[Stompor \\& Efstathiou 1998]{StomporEfstath98}\n Stompor, R., \\& Efstathiou, G., 1998, preprint, astro-ph/9806294\n\n\\bibitem[Sunyaev \\& Zel'dovich 1980]{sz80} \n Sunyaev, R. A., \\& Zel'dovich, Y. B., 1980, \\araa, 18, 537\n\n\\bibitem[Suto et al. 1999]{sutoet99}\n Suto et al., 1999, Advances in Space Research, in press\n\n\\bibitem[Tegmark 1998]{Tegmark98} \n Tegmark, M., 1998, \\apj, 502, 1\n\n\\bibitem[Tegmark et al. 1998]{Tegmarket98} \n Tegmark, M., Eisenstein, D. J., Hu, W., \\& Kron, R. G., 1998, preprint, astro-ph/9805117\n\n\\bibitem[Toffolatti et al. 1999]{ToffZAB99}\n Toffolatti, L., De Zotti, G., Argueso, F., \\& Burigana, C., 1999, preprint, astro-ph/9902343\n\n\\bibitem[Tuluie, Laguna \\& Anninos 1996]{TuluiLagA96}\n Tuluie, R., Laguna, P., \\& Anninos, P., 1996, \\apj, 463, 15\n\n\\bibitem[Vishniac 1987]{Vish87}\n Vishniac, E. T., 1987, \\apj, 322, 597 \n\n\\bibitem[Voit \\& Donahue 1998]{VoitDonahue98}\n Voit, G. M., \\& Donahue, M., 1998, preprint, astro-ph/9804306\n\n\\bibitem[White \\& Srednicki 1995]{WhiteSrednicki95} \n White, M., \\& Srednicki, M., 1995, \\apj, 443, 6\n\n\\bibitem[Winitzky 1998]{Winitzky98}\n Winitzky, S., 1998, preprint, astro-ph/9806105\n\n\\bibitem[Zaldarriaga \\& Seljak 1998]{ZaldarriagaSeljak98}\n Zaldarriaga, M., \\& Seljak, U., 1998, preprint, astro-ph/9803150\n\n\\bibitem[Zaldarriaga, Spergel \\& Seljak 1997]{ZaldarrSperSel97}\n Zaldarriaga, M., Spergel, D. N., \\& Seljak, U., 1997, \\apj, 488, 1\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002272
|
Detection of X-ray pulsations from the Be/X-ray transient A\,0535+26 during a disc loss phase of the primary
|
[
{
"author": "I.~Negueruela\\inst{1}"
},
{
"author": "P.~Reig\\inst{2,3}"
},
{
"author": "M.~H.~Finger\\inst{4}"
},
{
"author": "P. Roche\\inst{5}"
}
] |
Using the {\em RossiXTE} experiment, we detect weak X-ray emission from the recurrent Be/X-ray transient A\,0535+26 at a time when the optical counterpart V725 Tau displayed H$\alpha$ in absorption, indicating the absence of a circumstellar disc. The X-ray radiation is strongly modulated at the 103.5-s pulse period of the neutron star, confirming that it originates from A\,0535+26. The source is weaker than in previous quiescence detections by two orders of magnitude and should be in the centrifugal inhibition regime. We show that the X-ray luminosity cannot be due to accretion on to the magnetosphere of the neutron star. Therefore this detection represents a new state of the accreting pulsar. We speculate that the X-ray emission can be due to some matter leaking through the magnetospheric barrier or thermal radiation from the neutron star surface due to crustal heating. The observed luminosity is probably compatible with recent predictions of thermal radiation from X-ray transients in quiescence. The detection of the X-ray source in the inhibition regime implies a reduced density in the outflow from the Be companion during its disc-less phase.
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[
{
"name": "Neg9434.tex",
"string": "\\documentclass{aa}\n\n\\hyphenation{Ne-gue-rue-la}\n\n\\begin{document}\n\n\\thesaurus{07(08.03.4;08.05.2;08.09.2 A\\,0535+26;08.02.1;08.14.1;13.25.5)} \n\n\\title{Detection of X-ray pulsations from the Be/X-ray transient \nA\\,0535+26 during a disc loss phase of the primary}\n\n\n\\author{I.~Negueruela\\inst{1}\n\\and P.~Reig\\inst{2,3} \n\\and M.~H.~Finger\\inst{4}\n\\and P. Roche\\inst{5}} \n \n\\institute{SAX SDC, ASI, c/o Nuova Telespazio, via Corcolle 19, I00131\nRome, Italy\n\\and Foundation for Research and Technology-Hellas, 711 10, Heraklion,\nCrete, Greece\n\\and Physics Department, University of Crete, 710 03, Heraklion, Crete, Greece\n\\and Space Science Laboratory, ES84, NASA/Marshall Space Flight\nCenter, Huntsville, AL 35812, USA\n\\and Department of Physics \\& Astronomy, University of Leicester, Leicester,\nLE1 7RH, U.K.}\n\n\\mail{ignacio@tocai.sdc.asi.it}\n\n\\date{Received / Accepted }\n\n\n\\titlerunning{Pulsations from A\\,0535+26}\n\\authorrunning{Negueruela et al.}\n\\maketitle \n\n\\begin{abstract}\nUsing the {\\em RossiXTE} experiment, we detect weak X-ray emission from the \nrecurrent Be/X-ray transient A\\,0535+26 at a time when the optical counterpart\nV725 Tau displayed H$\\alpha$ in absorption, indicating the absence of a \ncircumstellar disc. The X-ray radiation is strongly modulated at the \n103.5-s pulse\nperiod of the neutron star, confirming that it originates from A\\,0535+26. \nThe source is weaker than in previous quiescence detections by two orders of\nmagnitude and should be in the centrifugal inhibition regime. We show that \nthe X-ray luminosity cannot be due to accretion on to the magnetosphere of\nthe neutron star. Therefore this detection represents a new state of the\naccreting pulsar. We speculate that the X-ray emission can be due to some \nmatter leaking through the magnetospheric barrier or thermal \nradiation from the neutron star surface due to crustal heating. The\nobserved luminosity is probably compatible with recent predictions of\nthermal radiation from X-ray transients in quiescence.\nThe detection of the X-ray source in the inhibition regime implies a \nreduced density in the outflow from the Be companion during its\ndisc-less phase.\n \\end{abstract}\n\n\\keywords{stars: circumstellar matter -- emission-line, Be -- individual: \nA\\,0535+26, -- binaries:close -- neutron -- X-ray: stars}\n\n\n\\section{Introduction}\n\nBe/X-ray binaries are X-ray sources composed of a Be star and a neutron star.\nMost of these systems are transient X-ray pulsars displaying strong\noutbursts in which their X-ray luminosity increases by a factor $\\ga 100$\n(see Negueruela 1998).\nIn addition, those systems in which the neutron star does not rotate fast\nenough for centrifugal inhibition of accretion to be effective (see Stella\net al. 1986) display persistent X-ray luminosity at a level $\\la 10^{35}$ erg\ns$^{-1}$.\nThe high-energy radiation is believed to arise due to accretion of material \nassociated with the Be star by the compact object. It has long been known\nthat accretion from the fast polar wind that is detected in the UV resonance\nlines of the Be primaries cannot provide the observed luminosities, even for \ndetections at the weakest level (see Waters et al. 1988 and references \ntherein; see also the calculations made for X Persei\nby Telting et al. 1998). Therefore it is believed that\nthe material accreted comes from the dense equatorial disc that surrounds \nthe Be star. Waters et al. (1989) modelled the radial outflow as a relatively\nslow ($\\sim 100$ km s$^{-1}$) dense wind. However most modern models for Be\nstars consider much slower outflows, due to strong evidence for rotationally \ndominated motion (quasi-Keplerian discs). This is due not only to the\nline shapes (see Hanuschik et al. 1996), which set an upper limit on \nthe bulk motion at $v \\la 3\\:{\\rm km}\\,{\\rm s}^{-1}$ (Hanuschik 2000), but \nalso to the success of the Global One-Armed Oscillation model (which\ncan only work in quasi-Keplerian discs) at explaining V/R variability\nin Be stars (Hummel \\& Hanuschik 1997; Okazaki 1997ab). \nThe viscous decretion disc model (Okazaki 1997b; Porter 1999; \nNegueruela \\& Okazaki 2000) considers\nmaterial in quasi-Keplerian orbit with an initially very subsonic outflow \nvelocity that is gradually accelerated by gas pressure and\nbecomes supersonic at distances $\\sim 100 R_{*}$, i.e., much further than the\norbits of neutron stars in Be/X-ray transients.\n\n\nThe transient A\\,0535+26 is one of the best studied Be/X-ray binaries \n(Clark et al. 1998 and references therein). It contains a slowly \nrotating ($P_{{\\rm s}} = 103 \\: \n{\\rm s}$) neutron star in a relatively wide ($P_{{\\rm orb}} = \n110.3 \\: {\\rm d}$) and eccentric ($e = 0.47$) \norbit around the B0IIIe star V725 Tau (see Finger et al. 1996; Steele et\nal. 1998). After its last giant outburst in February 1994 (Clark et al. \n1998; Negueruela et al. 1998), the strength of the emission lines in \nthe optical spectrum of V725 Tau has declined steadily. \nThe last normal (periodic) outburst \ntook place in September 1994 and the source has since not been detected \nby the BATSE experiment on board {\\em CGRO}.\n\n\n\\section{Observations}\n\n\\subsection{Optical spectroscopy}\n\nV725 Tau, the optical counterpart to A\\,0535+26, was observed on November 7th\n1998, using the 4.2-m William Herschel Telescope, \nlocated at the Observatorio del Roque de los Muchachos, La Palma, Spain.\nThe telescope was equipped with the Utrecht Echelle Spectrograph using the\n31.6 lines/mm echelle centred at H$\\alpha$ and the SITe1 CCD camera. This\nconfiguration gives a resolution $R \\sim 40000$ over the range $\\sim 4600 \n\\,-\\, 10200$ \\AA. The data have been reduced using the {\\em Starlink} packages\n{\\sc ccdpack} (Draper 1998), {\\sc echomop} (Mills et al. 1997) and {\\sc dipso}\n(Howarth et al. 1997). A detailed analysis of the whole spectrum is left for a \nforthcoming paper. In Figure~\\ref{fig:opt}, we show the shape of H$\\alpha$,\nH$\\beta$ and \\ion{He}{i} $\\lambda$6678\\AA. When in emission, these three\nlines sample most of the radial extent of the circumstellar envelope. However,\nit is apparent that the lines seen in Fig.~\\ref{fig:opt} correspond to \nphotospheric absorption from the underlying star. The emission \ncontribution from circumstellar material, if any, is certainly very small.\nThe asymmetry in the shape of H$\\alpha$ and \\ion{He}{i} $\\lambda$6678\\AA\\\nsuggests that some fast-moving material is present close to the \nstellar surface (see Hanuschik et al. 1993; \nRivinius et al. 1998 for the discussion of low-level activity\nin disc-less Be stars), but \nthe circumstellar disc is basically absent. H$\\beta$, which, when in emission,\nis typically produced at distances of a few $R_{*}$, looks completely \nphotospheric. In Be stars H$\\alpha$ probes a region extending to \n$\\sim 10\\: R_{*}$, as measured from line-peak separation (Hummel \\&\nVrancken 1995) and direct imaging (Quirrenbach et al. 1997). Again, \ncircumstellar material seems to be almost absent from this region. There\nis weak emission emission in-filling at the line centre -- transient emission \ncomponents have been seen in this star during the disc-less state\n(Haigh et al. 2000), a behaviour typical of disc-less Be stars \n(Rivinius et al. 1998 and references therein).\n\n\\begin{figure}\n\\begin{picture}(250,250)\n\\put(0,0){\\special{psfile=fig1.ps angle =0\nhoffset=-40 voffset=-100 hscale=58 vscale=58}}\n\\end{picture}\n\\caption{Spectroscopy of V725 Tau taken on November 7, 1998, with the WHT\nand UES. The lines are, from top to bottom H$\\beta$, H$\\alpha$ and \\ion{He}{i}\n$\\lambda$6678\\AA. The spectra have been divided by a spline fit to the\ncontinuum and arbitrarily offset for display. The sharp lines surrounding\nH$\\alpha$ are atmospheric water vapour features.} \n\\label{fig:opt} \n\\end{figure}\n\n\\subsection{X-ray observations}\n\nObservations of the source were taken using the Proportional Counter Array \n(PCA) on board {\\em RossiXTE} on 1998 August 21 and 1998 November 12 for a \ntotal on-source time of 4170 s and 2250 s, respectively. \n\nIn both observations there is an excess of $\\sim4$ counts/s/(5 PCU) in the\n2.5\\,--15 keV range of the Standard2 data compared to the faint source\nbackground model. Fits to power-law models with interstellar absorption\nresult in flux estimates of $6\\times10^{-12}$ and \n$9\\times10^{-12}\\:{\\rm erg}\\,{\\rm cm}^{-2}\\,{\\rm s}^{-1}$ (2\\,--\\,10 keV) for\nthe two observations respectively. These can only be considered as upper\nlimits on the flux, due to the uncertain contribution of diffuse Galactic \nDisc emission to the count rates (Valinia \\& Marshall 1998).\n\n\\subsubsection{Timing analysis}\n\nThe issue of whether the source of high energy radiation was active or not\nduring the low activity optical phase can be solved by searching for the\npreviously reported X-ray pulsations at $\\approx$103.5-s spin period\n(e.g., Finger et al. 1996). In order to improve the signal-to-noise, \nwe accumulated events from the top anode layer of the detectors. \nWe also used the latest version of \nthe faint background model. \n\nFor the power spectral analysis we selected a stretch of continuous data\nand divided it into intervals of 309 s. A power spectrum was\nobtained for each interval and the results averaged together. \nGiven that the pulse frequency ($\\nu \\approx 0.0097$ Hz)\nlies on a region dominated by red noise, we have to correct for such noise\nif the statistical significance of the pulsations are to be established. \nFirst, we fitted the Poisson level by restricting ourselves to the\nfrequency range 0.2\\,--\\,0.4 Hz, that is far away from the region where the\nred noise component may contribute appreciably. The strongest peak in \nthe power spectrum corresponds to $\\approx 103.5\\:{\\mathrm s}$.\n\nWe also searched\nfor periodicities in the light curves by folding the data over a period\nrange and determining the $\\chi^{2}$ of the folded light-curve (epoch-folding \ntechnique). In this case we used 20 phase bins (19 degrees of\nfreedom) and a range of 100 periods, around the expected period. This\nmethod has the advantage that the result is not affected by the presence\nof gaps in the data, hence a longer baseline can be considered than\nwith Fourier analysis. Times\nin the background subtracted light-curve were converted into times\nat the solar-system barycentre. The result for the 1998 November\nobservation is shown in Fig~\\ref{fig:epoch}. We found that the peak at \n$\\sim 103.5\\:{\\mathrm s}$\nis significant at $> 5 \\sigma$, confirming that the source was active\nduring the observations.\n\n\n\\begin{figure}\n\\begin{picture}(250,280)\n\\put(0,0){\\special{psfile=fig2.ps angle =0\nhoffset=-10 voffset=-30 hscale=42 vscale=42}}\n\\end{picture}\n\\caption{3\\,--\\,20 keV light-curve folded over a range of trial periods \n(epoch folding) for the November 1998 observation. The arrival times \nwere corrected to the\nsolar barycentre. The dashed and dash-dotted lines represent the 3-$\\sigma$\nand 5-$\\sigma$ detection levels considering that all trial periods have the\nsame probability.} \n\\label{fig:epoch} \n\\end{figure}\n\nIt is\nworth mentioning that the detection levels shown in Fig.~\\ref{fig:epoch}\nwere obtained without {\\em a priori} knowledge of the frequency of pulsations. \nIn other words, we searched for pulsations in the frequency/period range\nshown in the figure. If we take into account the fact that we are \ninterested in the pulse period {\\em at} $103.5\\:{\\mathrm s}$, \nthe peak becomes still more significant. \n\nThe analysis of the 1998 August observation provides a much less significant\ndetection. A peak at the expected frequency ($\\nu \\approx \n0.0097$ Hz) is seen in the power spectrum. However, epoch-folding \nanalysis gave a significance of $3\\sigma$ only when we considered one \nsingle period, that is, the number of trials is one. A search for \npulsations in a period range \ndid not yield any maximum above the 3-$\\sigma$ detection level although a peak \nat the 103-s period is present (see Fig. \\ref{fig:epoch2})\n\n\\begin{figure}\n\\begin{picture}(250,280)\n\\put(0,0){\\special{psfile=fig3.ps angle =0\nhoffset=-10 voffset=-30 hscale=42 vscale=42}}\n\\end{picture}\n\\caption{Same as Fig.~\\ref{fig:epoch} but for the August 1998 observation. \nThe dash-dotted line\nrepresents the 3-$\\sigma$ detection level and was obtained by considering\none trial period only (that at which pulsations are expected).} \n\\label{fig:epoch2} \n\\end{figure}\n\n\n\\subsubsection{Pulse shape}\n\nThe pulse shape (see Figure~\\ref{fig:pulse}) is nearly sinusoidal, as \nexpected from the absence of\nsecond or higher harmonics in the power density spectra. The amplitude of\nthe modulation is $\\sim 2$ count s$^{-1}$ in the 3\\,--\\,20 keV energy range,\nwhich implies a pulse fraction of $\\sim 53$\\%. Given the unknown contribution \nfrom Galactic Disc diffuse emission, this represents only a lower limit\nto the pulsed fraction in the signal from the source.\n\nWe have divided the November 1998 observation into two sections, \ncorresponding to the peak of the pulse (phase bins 0.6 to 1.0)\nand the interpulse minimum (phase bin 0.1--0.5). An absorbed power-law fit \nin the energy range 2.7\\,--\\,10 keV to the two spectra gave \n$\\Gamma=2.9\\pm0.4$, $N_{\\mathrm H}=9\\pm4$,\n$\\chi_{\\mathrm r}^{2}=0.8$ (18 dof) for pulse maximum and $\\Gamma=3.3\\pm0.5$,\n$N_{\\mathrm H}=10\\pm5$, $\\chi_{\\mathrm r}^{2}=0.9$ (18 dof) for pulse minimum.\nThe two values are consistent with each other within the error margins. \nThe lack of spectral changes with phase requires any significant \ncomponent of the detected flux due to diffuse emission to have a spectrum \nsimilar to that of the pulsar.\n\n\n\\begin{figure}\n\\begin{picture}(250,280)\n\\put(0,0){\\special{psfile=fig4.ps angle =0\nhoffset=-10 voffset=-30 hscale=42 vscale=42}}\n\\end{picture}\n\\caption{PCA RXTE 3--20 keV background subtracted pulse profile\ncorresponding to the November 1998 observation.}\n\\label{fig:pulse}\n\\end{figure}\n\n\\subsubsection{Spectral fit}\n\nFormally the X-ray spectra are equally \nwell represented by an absorbed power-law,\nblackbody and bremsstrahlung models. Table \\ref{tab:models} shows the spectral\nfit results. All these models gave fits of comparable quality, which means\nthat we are unable to distinguish meaningfully between the different\nspectral models of Table \\ref{tab:models}, even though the blackbody fit\nis unlikely to have any physical meaning, because of very small emitting\narea and the fact that it does not require any absorption (introducing \n$N_{\\mathrm H}$ does not improve the fit) -- see Rutledge\net al. (1999) for a discussion of the physical inadequacy of this model\nfor neutron stars. The value of the hydrogen column density ($N_{\\mathrm H}$),\nwhich is consistent for the power-law and bremsstrahlung fits, is too\nhigh to be purely interstellar. The interstellar reddening to the source\nmust be smaller than the measured $E(B-V) \\approx 0.7$ (Steele et al. 1998),\nwhich is the sum of interstellar and circumstellar contribution\nfrom the disc surrounding the Be star. According to the relation by Bohlin \net al. (1978), $E(B-V) = 0.7$ implies \n$N_{\\mathrm H} =4.1\\times10^{21}\\:{\\rm cm}^{-2}$ and therefore there must be\na substantial contribution of local material to the absorption.\n\nFrom the spectral fits, we estimate the 3\\,--\\,20 keV X-ray\nflux to be $3.5 \\times 10^{33}\\:{\\rm erg}\\,{\\rm s}^{-1}$ and \n $4.5 \\times 10^{33}\\:{\\rm erg}\\,{\\rm s}^{-1}$\nfor the August 1998 and November 1998 observations respectively, \nassuming a distance of 2 kpc (Steele et al. 1998).\nAlthough the values of the spectral parameters are consistent with each\nother within the error margins, they all show the same trend, namely, a\nharder spectral state during the 1998 August observations (lower photon\nindex and higher blackbody and bremsstrahlung temperatures).\n\n\\begin{table}\n\\caption{Results of the spectral fits. Uncertainties are given at \n$90\\%$ confidence for one parameter of interest. All fits correspond to \nthe energy range 3\\,--\\,20 keV}\n\\begin{center}\n\\begin{tabular}{lc}\n\\hline\n\\multicolumn{2}{c}{August 1998 observation} \\\\\n\\hline\n\\multicolumn{2}{l}{{\\bf Power-law}}\\\\\n$\\Gamma$ & 2.6$\\pm$0.2 \\\\\n$N_{\\mathrm H}$ (10$^{22}$ atoms cm$^{-2}$) & 5.6$\\pm$2.2 \\\\\n$\\chi^2_{\\mathrm r}$(dof) & 1.46(43) \\\\\n\\hline\n\\multicolumn{2}{l}{{\\bf Blackbody}}\\\\\nkT$_1$ (keV) & 1.45$\\pm$0.05 \\\\\nR (km) & 0.09$\\pm$0.01 \\\\\n$\\chi^2_{\\mathrm r}$(dof) & 1.73(44) \\\\\n\\hline\n\\multicolumn{2}{l}{{\\bf Bremsstrahlung }}\\\\\n$kT_{\\mathrm brem}$ (keV) & 6.4$\\pm$1.3 \\\\\n$N_{\\mathrm H}$ (10$^{22}$ atoms cm$^{-2}$) & $2.2^{+1.8}_{-1.3}$ \\\\\n$\\chi^2_{\\mathrm r}$(dof) & 1.31(44) \\\\\n\\hline\n\\hline\n\\multicolumn{2}{c}{November 1998 observation} \\\\\n\\hline\n\\multicolumn{2}{l}{{\\bf Power-law}}\\\\\n$\\Gamma$ & 3.2$\\pm$0.3 \\\\\n$N_{\\mathrm H}$ (10$^{22}$ atoms cm$^{-2}$) & 10.3$\\pm$2.6 \\\\\n$\\chi^2_{\\mathrm r}$(dof) & 1.09(43) \\\\\n\\hline\n\\multicolumn{2}{l}{{\\bf Blackbody}}\\\\\n$kT_1$ (keV) & 1.40$\\pm$0.05 \\\\\n$R$ (km) & 0.11$\\pm$0.01 \\\\\n$\\chi^2_{\\mathrm r}$(dof) & 1.01(44) \\\\\n\\hline\n\\multicolumn{2}{l}{{\\bf Bremsstrahlung }}\\\\\n$kT_{\\mathrm brem}$ (keV) & 4.4$\\pm$0.7 \\\\\n$N_{\\mathrm H}$ (10$^{22}$ atoms cm$^{-2}$) & 5.4$\\pm$2.1 \\\\\n$\\chi^2_{\\mathrm r}$(dof) & 0.96(44) \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\label{tab:models}\n\\end{table}\n\n\\begin{figure}\n\\begin{picture}(250,280)\n\\put(0,0){\\special{psfile=fig5.ps angle =0\nhoffset=-10 voffset=-30 hscale=42 vscale=42}}\n\\end{picture}\n\\caption{PCA RXTE source spectrum for the November 1998 observation. \nAlso shown is the best-fit power-law model and the residuals.}\n\\label{fig:spectrum} \n\\end{figure}\n\n\n\\section{Results}\n\nOur November 1998 X-ray observations represent a clear detection of \nA\\,0535+26 at a time when the optical counterpart showed no evidence for \nthe presence of circumstellar material. Moreover, Haigh et al. (2000) \npresent spectroscopy showing that the disc was already absent as early \nas late August 1998, when our first observation was taken.\nThe observed luminosities in the 2\\,--\\,10 keV range \n($2\\times10^{33}\\:{\\rm erg}\\,{\\rm s}^{-1} \\la L_{{\\rm x}} \\la \n4.5\\times10^{33}\\:{\\rm erg}\\,{\\rm s}^{-1}$) are definitely \nsmaller than the quiescence luminosity observed in other occasions when the \nequatorial disc surrounding the Be star was present. For example, Motch \net al. (1991) observed the source on several occasions \nat a level $L_{{\\rm x}} \\simeq 1.5\\times 10^{35}\\:{\\rm erg}\\,{\\rm s}^{-1}$ \nin the 1\\,--\\,20 keV range (correcting \ntheir value to the adopted distance of 2 kpc) using {\\em EXOSAT}.\n\nThe {\\em EXOSAT} observation, as well as several other quiescence \ndetections of Be/X-ray binaries with $P_{\\mathrm s} \\ga 100\\:{\\rm s}$,\nhave always been interpreted in terms of accretion on to the surface\nof the neutron star from the equatorial outflow from the Be star. However, \non this occasion we have observed the source when the disc of the Be\nstar had been absent for several months and at an X-ray luminosity\ntwo orders of magnitude lower. Therefore we cannot consider as an\n{\\em a priori} assumption that the emission mechanism at operation is\nthe same.\n\nIn order to explain the difference in the luminosity by two orders of\nmagnitude, we can invoke accretion from a far less dense outflow or\nassume that some other emission mechanism is at work. We first consider \nthe possibility that the observed \nluminosity is due to accretion on to the surface of the neutron star. \nAssuming an efficiency $\\eta=1$ in the conversion of gravitational \nenergy into X-ray luminosity, \n$L_{{\\rm x}} = 4\\times10^{33}\\:{\\rm erg}\\,{\\rm s}^{-1}$\ntranslates into an accretion rate \n$\\dot{M} = 2.1\\times10^{13}\\:{\\rm g}\\,{\\rm s}^{-1} = 3.3\\times 10^{-13}\n\\:M_{\\sun}\\,{\\rm yr}^{-1}$.\n\nFollowing Stella et al. (1986), we define the corotation radius as that\nat which the pulsar corotation velocity equals Keplerian velocity.\nThe corotation radius is given by\n\\begin{equation}\nr_{{\\rm c}} = \\left( \\frac{GM_{{\\rm x}}P_{{\\rm s}}^{2}}{4\\pi^{2}}\\right)^{\\frac{1}{3}}\n\\end{equation}\nwhere $G$ is the gravitational constant, $M_{{\\rm x}}$ is the mass of \nthe neutron star (assumed to be \n$1.44\\:M_{\\sun}$) and $P_{{\\rm s}}$ is the spin period. For A\\,0535+26, \n$r_{{\\rm c}} = 3.7\\times10^{9}\\:{\\rm cm}$.\n\nThe magnetospheric radius at which the magnetic field begins to dominate\nthe dynamics of the inflow depends on the accretion rate and \ncan be expressed as\n\\begin{equation}\nr_{{\\rm m}} = K \\left(GM_{{\\rm x}}\\right)^{-1/7}\\mu^{4/7}\\dot{M}^{-2/7}\n\\end{equation}\nwhere $\\mu$ is the neutron star magnetic moment and $\\dot{M}$\nis the accretion rate. $K$ is a constant that in the case of A\\,0535+26\nhas been determined to be $K\\simeq1.0$ when an accretion disc is present\n(Finger et al. 1996) and from theoretical calculations is expected to\nhave a similar value for wind accretion. Following\nFinger et al. (1996), we will assume a magnetic dipolar field \n$9.5\\times10^{12}\\:{\\rm G}$, resulting in $\\mu= \n4.75\\times10^{30}\\:{\\rm G}\\,{\\rm cm}^{3}$. \n\nFor the accretion rate $\\dot{M} = 2.1\\times10^{13}\\:{\\rm g}\\,{\\rm s}^{-1}$ \nderived above,\nthe magnetospheric radius would be $r_{{\\rm m}} = 9.3\\times10^{9}\\:{\\rm cm}$.\nTherefore $r_{{\\rm m}} > r_{{\\rm c}}$ and the neutron star must be in the\ncentrifugal inhibition regime. In order to estimate the solidity of this \nresult, we point out that if the 110 keV cyclotron line detected in the\nspectrum of A\\,0535+26 (Kendziorra et al. 1994; Grove et al. 1995) is the\nsecond harmonic instead of the first, as has been suggested, the magnetic\nfield (and magnetic moment) would be smaller by a factor 2. However, this \nwould require a higher value for $K$ in order to fit the observations of a \nQPO in this system (Finger et al. 1996), leaving the value of $r_{{\\rm m}}$\nunaffected. An efficiency in the conversion of gravitational energy into \nradiation as low as $\\eta=0.5$ will translate into a reduction in\n$r_{{\\rm m}}$ by only a factor $\\sim 0.8$. Therefore we conclude \nthat the neutron star is certain to be in the inhibited regime.\n\nAccording to Corbet (1996), when the source is in the inhibition regime,\na luminosity comparable to that observed could be produced by release of\ngravitational energy at the magnetospheric radius (for short, accretion \nonto the magnetosphere. However,\neven assuming that the magnetosphere is \nat the corotation radius and an efficiency $\\eta=1$ (i.e., best case), in\norder to produce $L_{{\\rm x}} = 4\\times10^{33}\\:{\\rm erg}\\,{\\rm s}^{-1}$,\nthe accretion rate needed is\n$\\dot{M}_{\\mathrm m} = 8.2\\times10^{16}\\:{\\rm g}\\,{\\rm s}^{-1}$. With\nsuch an accretion rate, the magnetosphere would be driven in well within\nthe corotation radius, and produce a luminosity of \n$L_{{\\rm x}} \\approx 1.5\\times10^{37}\\:{\\rm erg}\\,{\\rm s}^{-1}$ by accretion\non to the surface of the neutron star. Therefore we conclude that the\nobserved luminosity is not due to accretion on to the magnetosphere.\n\nTherefore we are left with the following possibilities for the origin \nof the X-ray emission:\n\n\\begin{itemize}\n\n\\item Accretion on to the neutron star through some sort of leakage through\nthe magnetospheric barrier. This could adopt two forms. Either directly\nfrom the Be star outflow and only through a fairly limited region near \nthe spin axis or mediated by an accretion torus, supported by the \ncentrifugal barrier, with a small amount of material\nmanaging to penetrate the magnetosphere.\n\n\n\\item Thermal emission from the heated core of the neutron star. Brown\net al. (1998) and Rutledge et al. (1999) have studied thermal emission\nfrom X-ray transients in quiescence. They predict a\nthermal luminosity in quiescence\n\\begin{equation} \nL_{\\mathrm x}= 6\\times10^{32}\\:{\\rm erg}\\,{\\rm s}^{-1}\\times\\frac{\\dot{M}}\n{10^{-11}\\:M_{\\sun}\\,{\\rm yr}^{-1}}\n\\end{equation}\nwhere $\\dot{M}$ here represents the long term average mass accretion rate. \nFrom the number of observed Type II outbursts in A\\,0535+26, we assume\none giant outburst every 5\\,--\\,10 years, which translates into a long-term \naverage of $\\dot{M} = 4-8\\times10^{-11}\\:M_{\\sun}\\,{\\rm yr}^{-1}$. \nThis would imply quiescence thermal emission in the range $L_{\\mathrm x}= \n2-5\\times10^{33}\\:{\\rm erg}\\,{\\rm s}^{-1}$, which is consistent\nwith our observations.\n\\end{itemize}\n\n\\section{Discussion}\n\nIt is very difficult to estimate the fraction of the signal that actually\ncomes from the source, though the pulsed component is evidently a lower limit \nto it. The diffuse emission from the Galactic disc is not well described\nat high Galactic longitudes (for A\\,0535+26, $l=181.5\\degr$), but if the \nassumption by Valinia \\& Marshall (1998) that its latitude distribution\nshould be similar to that in the Galactic Ridge can be held, then it \nshould not be very strong at the position of A\\,0535+26 ($b=-2.6\\degr$).\nIn any case, the total (source + diffuse) flux detected is lower\nthan the average diffuse emission from the Galactic Ridge, which is \n$2.4\\times10^{-11}\\:{\\rm erg}\\,{\\rm cm}^{-2}\\,{\\rm s}^{-1}$ in the\n2\\,--\\,10 keV band (Valinia \\& Marshall 1998).\n\nGiven that the fitted spectra are much softer than the model fits to\nGalactic Ridge diffuse emission by Valinia \\& Marshall (1998), which \nhave photon indexes $\\Gamma \\sim 1.8$, and the similitude between the \npulse-peak and pulse-minimum spectra, it seems likely that most of the\ndetected signal comes actually from the source. The high value of \n$N_{\\mathrm H}$ obtained in all the non-thermal fits argues for the\npresence of large amounts of material in the vicinity of the neutron star.\nThis could be caused by the pile-up of incoming material outside the \nmagnetosphere. The observed spectrum\nis much softer than the spectra of Be/X-ray binaries at low luminosity\nduring quiescence states (Motch et al. 1991 quote a photon index of\n1.7 for their observations of A\\,0535+26) and could favour the\nthermal emission interpretation. \n\nBrown et al. (1998) proposed that thermal reactions deep within the \ncrust of an accreting neutron star would maintain the neutron star \ncore at temperatures of $\\sim 10^{8}\\:{\\mathrm K}$, similar to that in \na young radio pulsar. During the quiescent state of transient accretors, \nthe conduction of thermal energy from the core should result in a \ndetectable thermal spectrum from the neutron star atmosphere. In a \nhigh magnetic field pulsar, this thermal emission should be pulsed \ndue to both the anisotropic surface temperature distribution caused \nby the dependence of the thermal conductivity on the magnetic field \n(Shibanov \\& Yakovlev 1996), and the anisotropic radiation \npattern from the neutron star atmosphere resulting from the magnetic \nfield (Zavlin et al. 1995). \n\nOur blackbody fit to the A0535+26 spectrum resulted in an emission \nradius much smaller than the neutron star. Rutledge at al. (1999) show \nthat fits to Hydrogen atmosphere spectral models result in larger emission \nareas and lower effective temperature than blackbody fits. The spectra may \ntherefore be consistent with thermal emission from the pulsar. However, if \nthis interpretation is correct, most of the emitted luminosity should be\nbelow the energy band that we observe. In that case, the bolometric \nluminosity may well exceed that predicted \nfrom our estimates of the long-term average accretion rates.\n\n\nOur detection of A\\,0535+26 can also be used to set limits on the outflow\nfrom the Be companion. The condition for centrifugal inhibition is\n$r_{{\\rm m}} \\geq r_{{\\rm c}}$. Therefore the minimum accretion rate\nat which there is no inhibition corresponds to that at which \n$r_{{\\rm m}} = r_{{\\rm c}}$. Using the values above, we obtain \nan accretion rate onto the magnetosphere \n$\\dot{M}_{\\mathrm m} = 5.3\\times10^{14}\\:{\\rm g}\\,{\\rm s}^{-1}= \n8\\times10^{-12}\\:M_{\\sun}\\,{\\rm yr}^{-1}$. If the observed\nluminosity is due to accretion on to the surface of the neutron star, the \nrate of mass flow into the vicinity of the neutron star is then \nconstrained to be in the range $3\\times10^{-13}\\:M_{\\sun}\\,{\\rm yr}^{-1}\\la \n\\dot{M} \\la 8\\times10^{-12}\\:M_{\\sun}\\,{\\rm yr}^{-1}$ (of course, if it is\ndue to thermal emission, only the upper limit holds). \nThe lower limit represents a small fraction of the mass lost from the \nBe star (which should be $\\ga 10^{-11}\\:M_{\\sun}\\,{\\rm yr}^{-1}$), but\nthe upper limit is close to the mass-loss values derived in the\ndecretion disc model (Okazaki 1997b; Porter 1999). This value is also close\nto the accretion rate needed to sustain the quiescence luminosity\nobserved by Motch et al. (1991), which is \n$\\dot{M} \\sim 10^{-11}\\:M_{\\sun}\\,{\\rm yr}^{-1}$. Such an accretion\nrate would represent a substantial fraction of the stellar \nmass-loss, though still only a small fraction of the disc mass (estimated\nto be $ 10^{-9}\\,-\\,10^{-10}\\:M_{\\sun}$). As has been calculated above,\nmost of the long-term accretion rate is due to the giant outbursts, where\na substantial fraction of the Be disc mass must be accreted.\n\nFrom all the above, it is clear that the amount of material reaching \nthe vicinity of the neutron\nstar during the disc-less phase of the companion is smaller than during\nprevious quiescence states. This cannot be due to an orbital effect because\nMotch et al. (1991) observed the source at different orbital times and\nalso because our two observations took place close to periastron (orbital\nphases $\\phi \\simeq 0$ for the August observation and $\\phi \\simeq 0.8$ for \nthe November observation, according to the ephemeris of Finger et al. \n1996). \n\nExisting evidence seems to argue against the existence of a persistent \naccretion disc surrounding the neutron star in A\\,0535+26. The statistical \nanalysis of Clark et al. (1999) showed that there is no\nsignificant contribution from an accretion disc to the optical/infrared\nluminosity of A\\,0535+26. This does not rule out the presence of an accretion\ndisc (which could, for example, be too small to radiate a significant \nflux in comparison to the Be circumstellar disc). It is believed that \nA\\,0535+26 does indeed form an accretion disc around\nthe neutron during Type II outbursts, since very fast spin-up and \nquasi-periodic oscillations have been observed (Finger et al. 1996).\nHowever, the lack of spin-up during Type I outbursts led Motch et al. (1991)\nto conclude that no persistent accretion disc was present.\nIn contrast, the Be/X-ray binary 2S\\,1845$-$024 shows large spin-up \nduring every Type I outburst (Finger et al. 1999). If no accretion disc\nis present, the reduced amount\nof material reaching the neutron star must be directly due to a change in the\nparameters of the outflow from the Be star. Within the framework of modern\nmodels for Be star discs, considering very subsonic outflow velocities, \nsuch a change can only be due to a lower outflow density. Unfortunately,\nsince the details of the magnetic inhibition process are poorly understood,\nwe can only constrain the mass rate reaching the neutron star to be\nbelow that corresponding to the transition at which inhibition occurs,\nwhich is very close to the rate deduced from previous quiescence \nobservations in which the source was not in the inhibition regime.\n\n\\section{Conclusions}\n\nA\\,0535+26 was active at a time when the optical counterpart V725 Tau\nshowed no evidence for a circumstellar disc. The luminosity was two\norders of magnitude lower than in previous quiescence detections and\naccretion was centrifugally inhibited. Given that the observed luminosity\ncannot be due to accretion onto the magnetosphere, we are observing\neither some material leaking through the magnetosphere or thermal \nemission from the heated core of the neutron star. In any case, this\ndetection represents a state of an accreting X-ray pulsar that had not\nbeen observed before.\n\nFurther observations of Be/X-ray binaries in a similar state (when their\ncompanions have lost their discs and very little material can reach the\nvicinity of the neutron star) are needed. Observations with {\\em Chandra} \nor {\\em XMM}, which combine much higher sensitivities with more adequate\nenergy ranges, could\ndetermine whether the observed spectrum is compatible with thermal emission\nmodels.\n\n\n\\section*{Acknowledgements}\n\nWe thank Jean Swank and the {\\em RossiXTE} team for granting a Target of\nOpportunity observation and carrying it out on very short notice. Simon\nClark is thanked for his help in preparing the proposal. The WHT is\noperated on the island of La Palma by the Royal Greenwich Observatory in \nthe Spanish Observatorio del Roque de Los Muchachos of the Instituto de\nAstrof\\'{\\i}sica de Canarias. The observations were taken as part of the\nING service observing programme. This research has made use of data \nobtained through the High Energy Astrophysics Science Archive Research \nCenter Online Service, provided by the NASA/Goddard Space Flight Center.\n\nIN is supported by an ESA external fellowship. 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{
"name": "astro-ph0002272.extracted_bib",
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}
] |
astro-ph0002273
|
Jupiter's hydrocarbons observed with ISO-SWS:\\ vertical profiles of $C_2H_6$ and $C_2H_2$, detection of $CH_3C_2H$
|
[
{
"author": "T.\\ Fouchet\\inst{1}"
},
{
"author": "E.\\ Lellouch\\inst{1}"
},
{
"author": "B.\\ B\\'ezard\\inst{1}"
},
{
"author": "H.\\ Feuchtgruber\\inst{2}"
},
{
"author": "P.\\ Drossart\\inst{1}"
},
{
"author": "T.\\ Encrenaz\\inst{1}"
}
] |
We have analysed the ISO-SWS spectrum of Jupiter in the 12--16 $\mu{m}$ range, where several hydrocarbons exhibit rovibrational bands. Using temperature information from the methane and hydrogen emissions, we derive the mixing ratios ($q$) of acetylene and ethane at two independent pressure levels. For acetylene, we find $q=(8.9^{+1.1}_{-0.6})\times10^{-7}$ at 0.3 mbar and $q=(1.1^{+0.2}_{-0.1})\times10^{-7}$ at 4 mbar, giving a slope $-d\ln q / d\ln P=0.8\pm0.1$, while for ethane $q=(1.0\pm0.2)\times10^{-5}$ at 1 mbar and $q=(2.6^{+0.5}_{-0.6})\times10^{-6}$ at 10 mbar, giving $-d\ln q / d\ln P=0.6\pm0.2$. The ethane slope is consistent with the predictions of Gladstone et al.\ (\cite{Gladstone96}), but that predicted for acetylene is larger than we observe. This disagreement is best explained by an overestimation of the acetylene production rate compared to that of ethane in the Gladstone et al.\ (\cite{Gladstone96}) model. At 15.8 $\mu{m}$, methylacetylene is detected for the first time at low jovian latitudes, and a stratospheric column density of $(1.5\pm0.4)\times10^{15}$ molecule\,cm$^{-2}$ is inferred. We also derive an upper limit for the diacetylene column density of $7\times10^{13}$ molecule\,cm$^{-2}$. \keywords{Planets and satellites: Jupiter --Infrared: solar system}
|
[
{
"name": "hydro.tex",
"string": "% hydro.tex\n% AA vers. 4.01, LaTeX class for Astronomy & Astrophysics\n% (c) Springer-Verlag HD\n%-----------------------------------------------------------------------\n%\n%\\documentclass[referee]{aa} % for a referee version\n%\n\\documentclass{aa}\n\\usepackage{graphics}\n%\n\\begin{document}\n\n\\thesaurus{01 % A&A Section 1: Letters\n (07.16.2; % Planets and satellites: Jupiter,\n 13.09.5)} % Infrared: solar system\n\n \\title{Jupiter's hydrocarbons observed with ISO-SWS:\\\\\nvertical profiles of $\\rm C_2H_6$ and $\\rm C_2H_2$, detection of $\\rm CH_3C_2H$}\n\n \\author{T.\\ Fouchet\\inst{1}\n \\and\n E.\\ Lellouch\\inst{1}\n\t \\and\n\t B.\\ B\\'ezard\\inst{1}\n\t \\and\n H.\\ Feuchtgruber\\inst{2}\n\t \\and\n\t P.\\ Drossart\\inst{1}\n\t \\and\n\t T.\\ Encrenaz\\inst{1}\n }\n\n \\institute{DESPA, Observatoire de Paris, 5 Place Jules Janssen,\n 92195 Meudon Cedex, France\\\\\n email: thierry.fouchet@obspm.fr\n \\and\n Max-Planck-Institut f\\\"ur Extraterrestrische Physik,\n 85748 Garching, Germany}\n\n \\offprints{T.\\ Fouchet}\n\n \\date{Received; accepted}\n\n \\titlerunning{Jupiter's hydrocarbons observed with ISO-SWS}\n \\maketitle\n\n\\begin{abstract}\n\nWe have analysed the ISO-SWS spectrum of Jupiter in the 12--16 $\\mu{\\rm m}$\nrange, where several hydrocarbons exhibit rovibrational bands. Using\ntemperature information from the methane and hydrogen emissions, we derive the\nmixing ratios ($q$) of acetylene and ethane at two independent pressure levels.\nFor acetylene, we find $q=(8.9^{+1.1}_{-0.6})\\times10^{-7}$ at 0.3 mbar and\n$q=(1.1^{+0.2}_{-0.1})\\times10^{-7}$ at 4 mbar, giving a slope\n$-d\\ln q / d\\ln P=0.8\\pm0.1$, while for ethane $q=(1.0\\pm0.2)\\times10^{-5}$ at\n1 mbar and $q=(2.6^{+0.5}_{-0.6})\\times10^{-6}$ at 10 mbar, giving\n$-d\\ln q / d\\ln P=0.6\\pm0.2$. The ethane slope is consistent with the\npredictions of Gladstone et al.\\ (\\cite{Gladstone96}), but that predicted for\nacetylene is larger than we observe. This disagreement is best explained by an\noverestimation of the acetylene production rate compared to that of ethane in\nthe Gladstone et al.\\ (\\cite{Gladstone96}) model.\n\nAt 15.8 $\\mu{\\rm m}$, methylacetylene is detected for the first time at low\njovian latitudes, and a stratospheric column density of\n$(1.5\\pm0.4)\\times10^{15}$ molecule\\,cm$^{-2}$ is inferred. We also derive an\nupper limit for the diacetylene column density of $7\\times10^{13}$\nmolecule\\,cm$^{-2}$.\n\n\\keywords{Planets and satellites: Jupiter --Infrared: solar system}\n\n\\end{abstract}\n\n\\section{Introduction}\n\n\\indent\\indent Hydrocarbons in Jupiter are produced in a series of chemical pathways initiated by the photolysis of methane in the upper stratosphere. Vertical transport, mainly turbulent diffusion, redistributes the molecules throughout the stratosphere and down to the troposphere, where they are eventually destroyed. Hydrocarbons, and particularly the most stable of them, are therefore good tracers of the upper atmospheric dynamics. In addition, as they strongly contribute to the atmospheric opacity in the UV and IR, hydrocarbons act as major sources and sinks of heat, thereby participating to the stratospheric dynamics.\n\nAll these reasons have strongly motivated theoretical studies of the jovian stratospheric photochemistry (Strobel \\cite{Strobel69}; Yung \\& Strobel \\cite{Yung80}; and most recently Gladstone et al.\\ \\cite{Gladstone96}). Although nowadays very detailed, these models still need to be constrained by observations of minor species. However, prior to the ISO mission, only two molecules, acetylene (${\\rm C_2H_2}$) and ethane (${\\rm C_2H_6}$), had been detected, except in the auroral zones where several other minor species (${\\rm C_2H_4}$, ${\\rm C_3H_4}$ and ${\\rm C_6H_6}$) have been observed (Kim et al.\\ \\cite{Kim85}). Mean stratospheric mole fractions have been inferred for ${\\rm C_2H_2}$ and ${\\rm C_2H_6}$ by various authors, but no precise information on their vertical variations was made available. In this paper, we analyse the ISO-SWS spectrum of Jupiter between 7 and 17 $\\mu{\\rm m}$, in order to determine the vertical distributions of ${\\rm C_2H_2}$ and ${\\rm C_2H_6}$, and to search for more complex (C$_3$ and C$_4$) molecules. Sect.~2 presents the observations. Our analysis of the spectrum is presented in Sect.~3. The results are compared with previous observations and theoretical predictions in Sect.~4.\n\n%__________________________________________________________________\n\n\\section{Observations}\n\n\\indent\\indent Descriptions of the Infrared Space Observatory (ISO) and of the Short Wavelength Spectrometer (SWS) can be found respectively in Kessler et al.\\ (\\cite{Kessler96}) and de Graauw et al.\\ (\\cite{deGraauw96}). A preliminary analysis of the Jupiter SWS spectrum can be found in Encrenaz et al.\\ (\\cite{Encrenaz96}). New ISO-SWS grating observations of Jupiter were obtained on May 23, 1997 UT using the AOT 01 observing mode. These observations have an average spectral resolution of 1500, and range from 2.4 to 45 $\\mu{\\rm m}$. However, the useful range is limited to 2.4--17 $\\mu{\\rm m}$, due to partial saturation at longer wavelengths. The instrument aperture, $14\\times20$ arcsec$^2$ at $\\lambda<12.5$ $\\mu{\\rm m}$ and $14\\times27$ arcsec$^2$ at $\\lambda>12.5$ $\\mu{\\rm m}$, was centered on the planet with the long axis aligned perpendicular to the ecliptic, thus roughly parallel to the N-S polar axis. It covered latitudes between 30$^{\\circ}$S and 30$^{\\circ}$N, and $\\pm20^{\\circ}$ longitude range from the central meridian. The absolute flux accuracy is $\\sim20\\%$.\n\nInstrumental fringing generates a spurious signal between 12.5 and 17 $\\mu{\\rm m}$, which amounts to $\\sim$10\\%\nof the continuum level. This parasitic signal was for the most part removed by fitting the detector relative response function to the observed spectrum and then dividing it out. Residual fringes were further removed by selective frequency filtering.\n\n%__________________________________________________________________\n\n\\section{Analysis}\n\n%-----------------------------------------------------CH4 et H2\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{hydro_fig1.eps}}\n \\caption{Comparison between ISO-SWS spectra (solid line) and synthetic spectra (dotted line) in the ${\\rm CH_4}$ $\\nu_4$ band (upper panel) and the ${\\rm H_2}$ S(1) line (lower panel)}\n\\label{FigTemp}\n\\end{figure}\n%\n\n\\indent\\indent We analysed the ISO-SWS spectrum using a standard line-by-line radiative transfer code adapted to Jupiter's conditions. We included the molecular absorptions by ${\\rm NH_3}$, ${\\rm CH_4}$, ${\\rm C_2H_2}$, ${\\rm C_2H_6}$, and ${\\rm CH_3C_2H}$ using the spectroscopic parameters of the GEISA97 databank (Jacquinet-Husson et al.\\ \\cite{Husson99}). We also considered ${\\rm C_4H_2}$ absorption, using a linelist provided by E.\\ Ari\\'e (private communication) and band intensities from Koops et al.\\ (\\cite{Koops84}). Spectroscopic parameters for the ${\\rm H_2}$ S(1) line were calculated using molecular constants from Jennings et al.\\ (\\cite{Jennings87}) and Reuter \\& Sirota (\\cite{Reuter94}). The H$_2$-He collision-induced continuum was calculated following the work of Borysow et al.\\ (\\cite{Borysow85}, \\cite{Borysow88}). The ${\\rm NH_3}$ vertical distribution was taken from Fouchet et al. (\\cite{Fouchet99}).\n\n\\subsection{Temperature profile}\n\n\\indent\\indent We first calculated synthetic spectra in the region of the ${\\rm CH_4}$ $\\nu_4$ band. For ${\\rm CH_4}$, we used a deep mixing ratio of $2.1\\times10^{-3}$ (Niemann et al.\\ \\cite{Niemann98}) and the vertical profile derived by Drossart et al.\\ (\\cite{Drossart99}) from the ${\\rm CH_4}$ fluorescence emission at 3.3 $\\mu{\\rm m}$. The $\\nu_4$ band allows one to retrieve 4 independent points on the temperature profile between 35 and 1 mbar. We also generated synthetic spectra of the ${\\rm H_2}$ S(1) rotational line at 17 $\\mu{\\rm m}$. This line probes a broad atmospheric layer at 3--30 mbar. The ortho-to-para ratio of ${\\rm H_2}$ was assumed to follow local thermodynamical equilibrium. The stratospheric temperature profile was adjusted in order to best match the absolute emission in the ${\\rm CH_4}$ band, and the line-to-continuum ratio of the ${\\rm H_2}$ S(1) line.\n\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{hydro_fig2.eps}}\n \\caption{Vertical profiles of ${\\rm C_2H_2}$ (upper panel) and ${\\rm C_2H_6}$ (lower panel) used for the calculation of the synthetic spectra of Fig.~\\ref{FigAce} and Fig.~\\ref{FigEth}. The best-fit profiles are shown as solid lines. The triangles are from the Gladstone et al.\\ (\\cite{Gladstone96}) model.}\n\\label{FigPro}\n\\end{figure}\n\nIn practice, starting with the temperature profile measured in-situ by the Galileo Probe (Seiff et al.\\ \\cite{Seiff98}), it was necessary to cool it by 2 K between 30 and 5 mbar. At pressures lower than 5 mbar, the initial profile was warmed by 4 K up to $165$ K. The $\\nu_4$ band is also somewhat sensitive to the temperature around the 10-$\\mu$bar pressure level. We found that the temperature remains constant within a few degrees between 1 mbar and 1 $\\mu$bar, as already observed by Seiff et al.\\ (\\cite{Seiff98}). At pressures lower than 1 $\\mu$bar, we adopted the measurements of Seiff et al.\\ (\\cite{Seiff98}), vertically smoothed in order to remove oscillations due to gravity waves, noting that our measurements are essentially insensitive to this pressure range. The fit to the ${\\rm CH_4}$ and ${\\rm H_2}$ emissions is presented in Fig.~\\ref{FigTemp}.\n\nThe 20\\%\nuncertainty on the absolute flux calibration directly results in an uncertainty of $\\pm2 $K on the temperature profile inferred from the ${\\rm CH_4}$ emission. This uncertainty partly explains the minor disagreement between the modelled and observed ${\\rm H_2}$ line. Indeed, our model, while giving an optimum fit to the ${\\rm CH_4}$ emission, slightly (5--10\\%) overpredicts the observed line-to-continuum ratio of the S(1) line. We also note that the ${\\rm H_2}$ ortho-to-para ratio could differ from the thermal equilibrium value, as observed in the troposphere by Conrath et al. (\\cite{Conrath98}). For example, a synthetic spectrum calculated with a constant para fraction of 0.34, corresponding to the thermal equilibrium value at 115 K, would fully reconcile the ${\\rm CH_4}$ and ${\\rm H_2}$ measurements.\n\\subsection{Acetylene}\n\n%--------------------------------------------------------acetylene\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{hydro_fig3.eps}}\n \\caption{Comparison near 13.7 $\\mu{\\rm m}$ between the ISO-SWS spectrum (upper panel) and three synthetic spectra (lower panel) calculated with the ${\\rm C_2H_2}$ vertical distributions of Fig.~\\ref{FigPro}. Solid line gives the best fit.}\n \\label{FigAce}\n\\end{figure}\n\n\\indent\\indent The ISO-SWS observations in the vicinity of the ${\\rm C_2H_2}$ emission at 13.7 $\\mu{\\rm m}$ were compared with synthetic spectra obtained with three distinct ${\\rm C_2H_2}$ vertical distributions (Fig.~\\ref{FigPro}). All three profiles reproduce the emissions due to the P-,Q-, and R-branches of the main $\\nu_5$ ${\\rm C_2H_2}$ band (Fig.~\\ref{FigAce}). However, only one profile (Fig.~\\ref{FigPro}, solid line) fits the observed spectrum in the Q-branches of the $\\nu_4+\\nu_5-\\nu_4$ band at 13.68 and 13.96 $\\mu{\\rm m}$. Indeed, while the $\\nu_5$ band probes atmospheric levels between 2 and 5 mbar, the hot band sounds warmer, higher levels around 0.3 mbar, allowing us to determine the slope of the ${\\rm C_2H_2}$ profile between these two regions.\n\nError bars on the ${\\rm C_2H_2}$ mixing ratio were estimated by taking into account instrumental noise and the uncertainty in the relative strengths of the ${\\rm C_2H_2}$ lines. The resulting mixing ratios are $q=(8.9^{+1.1}_{-0.6})\\times10^{-7}$ at 0.3 mbar and $q=(1.1^{+0.2}_{-0.1})\\times10^{-7}$ at 4 mbar, giving a slope $-d\\ln q / d\\ln P=0.8\\pm0.1$. The error on the temperature profile ($\\pm2 $K) introduces an additional uncertainty on the ${\\rm C_2H_2}$ mixing ratios of about 20\\%.\nThis error, however, essentially equally applies to all pressure levels, and thus leaves the retrieved ${\\rm C_2H_2}$ profile slope mostly unaffected.\n\n\\subsection{Ethane}\n\n%--------------------------------------------------------ethane\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{hydro_fig4.eps}}\n \\caption{Same as Fig.~\\ref{FigAce} for ${\\rm C_2H_6}$ at 12 $\\mu{\\rm m}$}\n \\label{FigEth}\n\\end{figure}\n\n\\indent\\indent Similarly to ${\\rm C_2H_2}$, we compare in Fig.~\\ref{FigEth} the ISO-SWS spectrum in the ${\\rm C_2H_6}$ $\\nu_9$ band with synthetic spectra calculated with three distinct ${\\rm C_2H_6}$ vertical profiles (Fig.~\\ref{FigPro}). Each of the profiles was designed to reproduce the observed emission in the ${\\rm ^{R}Q_{0}}$ multiplet at 12.16 $\\mu{\\rm m}$, which probes the 1-mbar pressure level. The rest of the $\\nu_9$ band consists of weaker multiplets, which sound deeper levels extending from 1 to 10 mbar. This combination of strong and weak multiplets makes this band sensitive to the ${\\rm C_2H_6}$ vertical distribution. In addition, the pseudo-continuum level in between the ${\\rm C_2H_6}$ emissions is also sensitive to the ${\\rm C_2H_6}$ abundance in the lower stratosphere.\n\nOur best-fit model (Fig.~\\ref{FigPro}, solid line) has a slope $-d\\ln q / d\\ln P=0.6$, but the steep-slope model (Fig.~\\ref{FigPro}, dotted line) is also marginally compatible with the observations. This results in a relatively large uncertainty on the slope determination: $q=(1.0\\pm0.2)\\times10^{-5}$ at 1 mbar, and $q=(2.6^{+0.5}_{-0.6})\\times10^{-6}$ at 10 mbar, giving $-d\\ln q / d\\ln P=0.6\\pm0.2$. An additional error of 25\\% on $q$ comes from the uncertainty on the temperature. Again, it should not affect the retrieved slope.\n\n\\subsection{Methylacetylene and diacetylene}\n\n\\indent\\indent The ISO-SWS spectrum exhibits a broad emission near 15.8 $\\mu{\\rm m}$, which coincides with the $\\nu_9$ band of ${\\rm CH_3C_2H}$ (Fig.~\\ref{FigMet}). Since the ${\\rm CH_3C_2H}$ lines are optically thin, no information on the vertical profile can be derived. Using a vertical profile similar to that calculated by Gladstone et al.\\ (\\cite{Gladstone96}), we found a column density of $(1.5\\pm0.4)\\times10^{15}$ molecule\\,cm$^{-2}$. The synthetic spectrum exhibits small-scale structures which are not seen in the observations. This mismatch is propably due to an imperfect data reduction. Indeed, the respective frequencies of the fringes and of the ${\\rm CH_3C_2H}$ features lie close to each other. It is therefore very difficult to fully remove the former without altering the latter. On the contrary, the broad emission is a low frequency signal and is therefore left unaffected by the frequency filtering. This explanation is admittedly not entirely satisfactory, but given the wavelength match of the emission with the $\\nu_9$ mode of ${\\rm CH_3C_2H}$, and in the absence of any other plausible candidates, we regard the detection of methylacetylene as unambiguous.\n\n%--------------------------------------------------------C3H4 et C4H2\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{hydro_fig5.eps}}\n \\caption{Comparison between the ISO-SWS spectrum (solid line) and two synthetic spectra; with (dash-dotted line) and without (dotted line) ${\\rm CH_3C_2H}$ and ${\\rm C_4H_2}$ opacities.}\n \\label{FigMet}\n\\end{figure}\n\nThe $\\nu_8$ band of ${\\rm C_4H_2}$ is not detected at 15.92 $\\mu{\\rm m}$. We inferred an upper limit of the ${\\rm C_4H_2}$ column density of $7\\times10^{13}$ molecule\\,cm$^{-2}$, using the Gladstone et al.\\ (\\cite{Gladstone96}) profile.\n\n\\section{Discussion}\n\n\\indent\\indent B\\'ezard et al.\\ (\\cite{Bezard95}) first showed from 13.4-$\\mu{\\rm m}$ high-resolution spectroscopy that the ${\\rm C_2H_2}$ mixing ratio increases with height in the stratosphere, and that most of the acetylene is concentrated above the $\\sim$0.5-mbar level. Their distribution has a mixing ratio of about $7\\times10^{-7}$ at 0.3 mbar, in reasonable agreement with our results. More recently, B\\'etremieux \\& Yelle (\\cite{Betremieux99}), using UV observations, found an average ${\\rm C_2H_2}$ mixing ratio in the 20--60 mbar range of $1.5\\times10^{-8}$, consistent with our value of $1.9\\times10^{-8}$, extrapolated to this pressure range. Using height-dependent mixing ratio profiles to analyse high-resolution infrared observations, Sada et al.\\ (\\cite{Sada98}) derived mixing ratios of $3.9^{+1.9}_{-1.3}\\times10^{-6}$ for ${\\rm C_2H_6}$ at 5 mbar and $2.3\\pm0.5\\times10^{-8}$ for ${\\rm C_2H_2}$ at 8 mbar. While the former value exactly agrees with our results, the latter is almost 3 times less than that extrapolated downwards from our ${\\rm C_2H_2}$ profile. Also from infrared observations, Noll et al.\\ (\\cite{Noll86}), using a slope of $-d\\ln q / d\\ln P=0.3$, found a ${\\rm C_2H_6}$ mixing ratio of $7.5\\times10^{-6}$ at 1 mbar, which compares reasonably well with our measurement at the same pressure level.\n\nWe also compared our retrieved mixing ratios with those calculated in the photochemical model of Gladstone et al.\\ (\\cite{Gladstone96}). For ${\\rm C_2H_6}$, our results are in excellent agreement with their model both at 1 and 10 mbar (Fig.~\\ref{FigPro}). For ${\\rm C_2H_2}$, while the agreement is good at 4 mbar, their mixing ratio at 0.3 mbar is higher than ours by a factor of 4. Our ${\\rm C_2H_2}$ slope is then significantly lower than theirs ($-d\\ln q / d\\ln P=0.8\\pm0.1$ vs.\\ $-d\\ln q / d\\ln P=1.2$). Note that our derived ${\\rm C_2H_2}$ slope is still steeper than that of ${\\rm C_2H_6}$ ($-d\\ln q / d\\ln P=0.6\\pm0.2$), as expected. Indeed, ${\\rm C_2H_6}$, being less subject to photolysis, has a longer lifetime in the jovian stratosphere than ${\\rm C_2H_2}$ (Gladstone et al.\\ \\cite{Gladstone96}, their Fig.~6).\n\nHydrocarbons are formed from the photolysis of ${\\rm CH_4}$ around the homopause. Small-scale turbulence, parameterized in a photochemical model by the eddy diffusion coefficient ($K$), transports them downwards in the stratosphere. This process is approximately modelled for long-lived products by the equation $K(z)n(z){\\rm d}q/{\\rm d}z = P(z)$, where $n(z)$ is the number density at altitude $z$ and $P(z)$ the vertically integrated net production rate above altitude $z$. A first hypothesis would attribute the difference between the observed and calculated ${\\rm C_2H_2}$ abundances to an overestimation of the ${\\rm C_2H_2}$ production rate $P(z)$ in the Gladstone et al.\\ model. Our two abundance measurements at 4 and 0.3 mbar allow us to calculate the mean ${\\rm d}q/{\\rm d}z$ over this pressure range. Comparing with the value of ${\\rm d}q/{\\rm d}z$ predicted by Gladstone et al.\\ at 1 mbar, we found that $P(z)$ should be decreased by a factor of $\\sim$3.\n\nA second explanation would be that Gladstone et al.\\ underestimated the eddy diffusion coefficient $K$ by a factor of $\\sim$3 around 1 mbar. This underestimation at 1 mbar should also apply to the level and eddy diffusion coefficient ($K_H$) at the homopause. However, it is difficult to directly quantify the changes on the homopause parameters, because of the strong coupling between production rates and homopause level. Simply, we note that our analysis could imply an increase in $K_H$. It is consistent with Drossart et al.\\ (\\cite{Drossart99}), who, analysing ${\\rm CH_4}$ fluorescence, found $K_H=(7\\pm1)\\times10^6$ ${\\rm cm^{-2}\\,s^{-1}}$, higher than the value of 1.4$\\times10^6$ assumed in the Gladstone et al.\\ model. In this case, the agreement on the ${\\rm C_2H_6}$ slope would also imply that the ${\\rm C_2H_6}$ production rate has been underestimated by Gladstone et al.\\ (\\cite{Gladstone96}). In fact, the most direct conclusion of our measurements is that Gladstone et al.\\ have overestimated the ${\\rm C_2H_2}$/${\\rm C_2H_6}$ production rate ratio.\n\nThe ISO-SWS spectrum enables the first detection of ${\\rm CH_3C_2H}$ in the equatorial region of Jupiter. We retrieved a column density of $(1.5\\pm0.4)\\times10^{15}$ molecule\\,cm$^{-2}$. Kim et al.\\ (\\cite{Kim85}) had previously detected ${\\rm CH_3C_2H}$ in the north polar auroral zone of Jupiter, and had retrieved a column density of $(2.8^{+2.4}_{-1.1})\\times10^{16}$ molecule\\,cm$^{-2}$. At least a large part of the difference is explained by different modelling assumptions. Kim et al.\\ (\\cite{Kim85}) assumed a uniform vertical distribution throughout the stratosphere and used a temperature profile for the auroral region which is now known to be incorrect (Drossart et al.\\ \\cite{Drossart93}). For ${\\rm C_4H_2}$, we found only an upper limit of $7\\times10^{13}$ molecule\\,cm$^{-2}$, 65 times lower than the stratospheric column density predicted by Gladstone et al.\\ (4.5$\\times$10$^{15}$ molecule\\,cm$^{-2}$). This is consistent with their overestimate of ${\\rm C_2H_2}$ production, since the production of ${\\rm C_4H_2}$ is essentially quadratically dependent on the abundance of ${\\rm C_2H_2}$. As our ${\\rm CH_3C_2H}$ column density is 3.5 times larger than calculated by Gladstone et al., we derived a ${\\rm CH_3C_2H}$/${\\rm C_4H_2}$ ratio larger than 20, while they found a ratio of $\\sim2$. This discrepancy is all the more remarkable as, in the case of Saturn, where both ${\\rm CH_3C_2H}$ and ${\\rm C_4H_2}$ are detected (de Graauw et al.\\ \\cite{deGraauw97}), the photochemical model of Moses et al.\\ (\\cite{Moses99}) gives, as observed, a ${\\rm CH_3C_2H}$/${\\rm C_4H_2}$ ratio of about 10. This stresses that the C$_3$ and C$_4$ chemistry in Jupiter should be reassessed with a complete photochemical model of the jovian stratosphere. \n\n\n\\begin{acknowledgements}\nThis study is based on observations with ISO, an ESA project with instruments funded by ESA Member States (especially the principal investigators countries: France, Germany, the Netherlands and the United Kingdom), and with participation of ISAS and NASA.\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\n \\bibitem[1999]{Betremieux99}B\\'etremieux, Y., and R.\\ V.\\ Yelle, 1999, \n BAAS, 31, 1180.\n\n \\bibitem[1995]{Bezard95}B\\'ezard, B., C.\\ A.\\ Griffith,\n et al., 1995, Icarus, 118, 384.\n\n \\bibitem[1985]{Borysow85}Borysow, A., L.\\ Trafton, et al., 1985, ApJ,\n 296, 644.\n\n \\bibitem[1988]{Borysow88}Borysow, J., L.\\ Frommhold, and G.\\ Birnbaum, 1988,\n ApJ, 326, 509.\n\n \\bibitem[1998]{Conrath98}Conrath, J.\\ B.,\n P.\\ J.\\ Gierasch, and E.\\ A.\\ Ustinov, 1998, Icarus, 135, 501.\n\n \\bibitem[1996]{deGraauw96}de Graauw, T., L.\\ N.\\ Haser,\n et al., 1996, A\\&A, 315, L49.\n\n \\bibitem[1997]{deGraauw97}de Graauw, T., H. Feuchtgruber, et al., 1997,\n A\\&A, 321, L13.\n\n \\bibitem[1993]{Drossart93}Drossart, P., B.\\ B\\'ezard, et al., 1993, JGR, 98,\n 18803.\n\n \\bibitem[1999]{Drossart99}Drossart, P., T.\\ Fouchet, et al.,\n 1999, ESA SP-427, 169.\n\n \\bibitem[1996]{Encrenaz96}Encrenaz, T., T.\\ de Graauw, et al., 1996,\n A\\&A, 315, L397.\n\n \\bibitem[2000]{Fouchet99}Fouchet, T., E.\\ Lellouch, et al.,\n 2000, Icarus, In press.\n\n \\bibitem[1996]{Gladstone96}Gladstone, G.\\ R., M.\\ Allen, and Y.\\ L.\\ Yung,\n 1996, Icarus, 119, 1.\n\n \\bibitem[1999]{Husson99}Jacquinet-Husson, N., E.\\ Ari\\'e,\n et al., 1999, JQSRT, 62, 205.\n\n \\bibitem[1987]{Jennings87}Jennings, D.\\ E., A.\\ Weber, J.\\ W.\\ Brault, 1987,\n JMS, 126, 19.\n\n \\bibitem[1996]{Kessler96}Kessler, M.\\ F., J.\\ A.\\ Steinz,\n et al., 1996, A\\&A, 315, L27.\n\n \\bibitem[1985]{Kim85}Kim, S.\\ J., J.\\ Caldwell, et al.,\n 1985, Icarus, 64, 233.\n\n \\bibitem[1984]{Koops84}Koops, T., T.\\ Visser, and W.\\ M.\\ A.\\ Smit, 1984,\n J.\\ Mol.\\ Struct., 125, 179.\n\n \\bibitem[2000]{Moses99}Moses, J.\\ I., B.\\ B\\'ezard, et al.,\n 2000, Icarus, In Press.\n\n \\bibitem[1998]{Niemann98}Niemann, H.\\ B., S.\\ K.\\ Atreya, et al., 1996,\n JGR, 103, 22831.\n\n \\bibitem[1986]{Noll86}Noll, K.\\ S., R.\\ F.\\ Knacke,\n et al., 1986, Icarus, 65, 257.\n\n \\bibitem[1994]{Reuter94}Reuter, D.\\ C., and J.\\ M.\\ Sirota, 1994, ApJ,\n 428, L77.\n\n \\bibitem[1998]{Sada98}Sada P.\\ V., G.\\ L.\\ Bjoraker, et al., 1998, Icarus,\n 136, 192.\n\n \\bibitem[1998]{Seiff98}Seiff, A., D.\\ B.\\ Kirk, et al.,\n 1998, JGR, 103, 22857.\n\n \\bibitem[1969]{Strobel69}Strobel, D.\\ F., 1969, J.\\ Atmos.\\ Sci., 26, 906.\n\n \\bibitem[1980]{Yung80}Yung, Y.\\ L., and D.\\ F.\\ Strobel, 1980, ApJ, 239,\n 395.\n\n\n\\newpage % if processed with CM fonts, balances the references columns\n\n\\end{thebibliography}\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002273.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n \\bibitem[1999]{Betremieux99}B\\'etremieux, Y., and R.\\ V.\\ Yelle, 1999, \n BAAS, 31, 1180.\n\n \\bibitem[1995]{Bezard95}B\\'ezard, B., C.\\ A.\\ Griffith,\n et al., 1995, Icarus, 118, 384.\n\n \\bibitem[1985]{Borysow85}Borysow, A., L.\\ Trafton, et al., 1985, ApJ,\n 296, 644.\n\n \\bibitem[1988]{Borysow88}Borysow, J., L.\\ Frommhold, and G.\\ Birnbaum, 1988,\n ApJ, 326, 509.\n\n \\bibitem[1998]{Conrath98}Conrath, J.\\ B.,\n P.\\ J.\\ Gierasch, and E.\\ A.\\ Ustinov, 1998, Icarus, 135, 501.\n\n \\bibitem[1996]{deGraauw96}de Graauw, T., L.\\ N.\\ Haser,\n et al., 1996, A\\&A, 315, L49.\n\n \\bibitem[1997]{deGraauw97}de Graauw, T., H. Feuchtgruber, et al., 1997,\n A\\&A, 321, L13.\n\n \\bibitem[1993]{Drossart93}Drossart, P., B.\\ B\\'ezard, et al., 1993, JGR, 98,\n 18803.\n\n \\bibitem[1999]{Drossart99}Drossart, P., T.\\ Fouchet, et al.,\n 1999, ESA SP-427, 169.\n\n \\bibitem[1996]{Encrenaz96}Encrenaz, T., T.\\ de Graauw, et al., 1996,\n A\\&A, 315, L397.\n\n \\bibitem[2000]{Fouchet99}Fouchet, T., E.\\ Lellouch, et al.,\n 2000, Icarus, In press.\n\n \\bibitem[1996]{Gladstone96}Gladstone, G.\\ R., M.\\ Allen, and Y.\\ L.\\ Yung,\n 1996, Icarus, 119, 1.\n\n \\bibitem[1999]{Husson99}Jacquinet-Husson, N., E.\\ Ari\\'e,\n et al., 1999, JQSRT, 62, 205.\n\n \\bibitem[1987]{Jennings87}Jennings, D.\\ E., A.\\ Weber, J.\\ W.\\ Brault, 1987,\n JMS, 126, 19.\n\n \\bibitem[1996]{Kessler96}Kessler, M.\\ F., J.\\ A.\\ Steinz,\n et al., 1996, A\\&A, 315, L27.\n\n \\bibitem[1985]{Kim85}Kim, S.\\ J., J.\\ Caldwell, et al.,\n 1985, Icarus, 64, 233.\n\n \\bibitem[1984]{Koops84}Koops, T., T.\\ Visser, and W.\\ M.\\ A.\\ Smit, 1984,\n J.\\ Mol.\\ Struct., 125, 179.\n\n \\bibitem[2000]{Moses99}Moses, J.\\ I., B.\\ B\\'ezard, et al.,\n 2000, Icarus, In Press.\n\n \\bibitem[1998]{Niemann98}Niemann, H.\\ B., S.\\ K.\\ Atreya, et al., 1996,\n JGR, 103, 22831.\n\n \\bibitem[1986]{Noll86}Noll, K.\\ S., R.\\ F.\\ Knacke,\n et al., 1986, Icarus, 65, 257.\n\n \\bibitem[1994]{Reuter94}Reuter, D.\\ C., and J.\\ M.\\ Sirota, 1994, ApJ,\n 428, L77.\n\n \\bibitem[1998]{Sada98}Sada P.\\ V., G.\\ L.\\ Bjoraker, et al., 1998, Icarus,\n 136, 192.\n\n \\bibitem[1998]{Seiff98}Seiff, A., D.\\ B.\\ Kirk, et al.,\n 1998, JGR, 103, 22857.\n\n \\bibitem[1969]{Strobel69}Strobel, D.\\ F., 1969, J.\\ Atmos.\\ Sci., 26, 906.\n\n \\bibitem[1980]{Yung80}Yung, Y.\\ L., and D.\\ F.\\ Strobel, 1980, ApJ, 239,\n 395.\n\n\n\\newpage % if processed with CM fonts, balances the references columns\n\n\\end{thebibliography}"
}
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astro-ph0002274
|
Hidden Source of High-Energy Neutrinos \\ in Collapsing Galactic Nucleus
|
[
{
"author": "V.~S. Berezinsky$^{a,b}$"
},
{
"author": "V.~I. Dokuchaev$^{b}$"
},
{
"author": "$^{a}${\\emph Laboratori Nazionali del Gran Sasso, INFN, Italy}"
}
] |
We propose the model of a short-lived very powerful source of high energy neutrinos. It is formed as a result of the dynamical evolution of a galactic nucleus prior to its collapse into a massive black hole and formation of high-luminosity AGN. This stage can be referred to as ``pre-AGN''. A dense central stellar cluster in the galactic nucleus on the late stage of evolution consists of compact stars (neutron stars and stellar mass black holes). This cluster is sunk deep into massive gas envelope produced by destructive collisions of a primary stellar population. Frequent collisions of neutron stars in a central stellar cluster are accompanied by the generation of ultrarelativistic fireballs and shock waves. These repeating fireballs result in a formation of the expanding rarefied cavity inside the envelope. The charged particles are effectively accelerated in the cavity and, due to $pp$-collisions in the gas envelope, they produce high energy neutrinos. All high energy particles, except neutrinos, are absorbed in the thick envelope. Duration of this pre-AGN phase is $\sim10$~yr, the number of the sources can be $\sim 10$ per cosmological horizon. High energy neutrino signal can be detected by underground neutrino telescope with effective area $S\sim1$~km$^2$. \medskip \noindent PACS: 95.55.Vj, 95.85.Ry, 98.62.Js, \noindent {\emph Keywords:} galactic nuclei; high-energy neutrino
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[
{
"name": "astro-ph0002274.tex",
"string": "\\documentclass[12pt]{article}\n\\title{Hidden Source of High-Energy Neutrinos \\\\\n in Collapsing Galactic Nucleus}\n\\author{V.~S. Berezinsky$^{a,b}$, V.~I. Dokuchaev$^{b}$ \\\\\n$^{a}${\\small\\emph\nLaboratori Nazionali del Gran Sasso, INFN, Italy} \\\\\n$^{b}${\\small\\emph\nInstitute for Nuclear Research, Russian Academy of Sciences, Moscow}}\n\n\n\\begin{document}\n\n\n\\date{}\n\\maketitle\n\n\\begin{abstract}\n\nWe propose the model of a short-lived very powerful source of high\nenergy neutrinos. It is formed as a result of the dynamical\nevolution of a galactic nucleus prior to its collapse into a\nmassive black hole and formation of high-luminosity AGN. This stage\ncan be referred to as ``pre-AGN''. A dense central stellar cluster\nin the galactic nucleus on the late stage of evolution consists of\ncompact stars (neutron stars and stellar mass black holes). This\ncluster is sunk deep into massive gas envelope produced by\ndestructive collisions of a primary stellar population. Frequent\ncollisions of neutron stars in a central stellar cluster are\naccompanied by the generation of ultrarelativistic fireballs and\nshock waves. These repeating fireballs result in a formation of the\nexpanding rarefied cavity inside the envelope. The charged\nparticles are effectively accelerated in the cavity and, due to\n$pp$-collisions in the gas envelope, they produce high energy\nneutrinos. All high energy particles, except neutrinos, are\nabsorbed in the thick envelope. Duration of this pre-AGN phase is\n$\\sim10$~yr, the number of the sources can be $\\sim 10$ per\ncosmological horizon. High energy neutrino signal can be detected\nby underground neutrino telescope with effective area\n$S\\sim1$~km$^2$.\n\n\\medskip\n\\noindent PACS: 95.55.Vj, 95.85.Ry, 98.62.Js,\n\n\\noindent {\\emph Keywords:} galactic nuclei; high-energy neutrino\n\\end{abstract}\n\n\n\\section{Introduction: Hidden Sources}\n\nHigh energy (HE) neutrino radiation from astrophysical sources is\naccompanied by other types of radiation, most notably by the HE\ngamma-radiation. These HE gamma-radiation can be used to put upper\nlimit on the neutrino flux emitted from a source. For example, if\nneutrinos are produced due to interaction of HE protons with low\nenergy photons in extragalactic space or in the sources transparent\nfor gamma-radiation, the upper limit on diffuse neutrino flux\n$I_{\\nu}(E)$ can be derived from e-m cascade radiation. This\nradiation is produced due to collisions with photons of microwave\nradiation $\\gamma_{bb}$, such as $\\gamma+\\gamma_{bb} \\to e^++e^-,\n\\quad e+\\gamma_{bb} \\to e'+\\gamma'$~etc. These cascade processes\ntransfer the energy density released in high energy photons\n$\\omega_{\\gamma}$ into energy density of the remnant cascade\nphotons $\\omega_{cas}$. These photons get into the observed energy\nrange $100$~MeV$-10$~GeV and their energy density is limited by\nrecent EGRET observations \\cite{EGRET} as\n$\\omega_{cas}\\leq2\\cdot10^{-6}$~eV/cm$^3$. Introducing the energy\ndensity for neutrinos with individual energies higher than E,\n$\\omega_{\\nu}(>E)$, it is easy to obtain the following chain of\ninequalities (reading from left to write)\n\\begin{equation}\n\\omega_{cas}> \\omega_{\\nu}(>E)\n= \\frac{4\\pi}{c}\\int\\limits_E^{\\infty}EI_{\\nu}(E)dE >\n\\frac{4\\pi}{c}E\\int\\limits_E^{\\infty}I_{\\nu}(E)dE\n=\\frac{4\\pi}{c}EI_{\\nu}(>E).\n\\label{cas-lim}\n\\end{equation}\nNow the upper limit on the integral HE neutrino flux can be written\ndown as\n\\begin{equation}\nI_{\\nu}(>E) < \\frac{4\\pi}{c}\\frac{\\omega_{cas}}{E}=\n4.8\\cdot 10^3E_{eV}^{-1}\\mbox{\ncm}^{-2}\\mbox{s}^{-1}\\mbox{sr}^{-1}.\n\\label{u-l}\n\\end{equation}\nHowever, there can be sources, where accompanying electromagnetic\nradiation, such as gamma and X-rays, are absorbed. They are called\n``hidden sources'' \\cite{book}. Several models of hidden sources\nwere discussed in the literature.\n\n\\begin{itemize}\n\n\\item {\\em Young SN Shell} \\cite{BePr} during time\n$t_{\\nu}\\sim10^3-10^4$~s are opaque for all radiation, but\nneutrinos.\n\n\\item {\\em Thorne-Zytkow Star} \\cite{ThZy}, the binary with a pulsar\nsubmerged into a red giant, can emit HE neutrinos while all kinds\nof e-m radiation are absorbed by the red giant component.\n\n\\item {\\em Cocooned Massive Black Hole} (MBH) in AGN \\cite{ber81} is\nan example of AGN as hidden source: e-m radiation is absorbed in a\ncocoon around the massive black hole.\n\n\\item {\\em AGN with Standing Shock} in the vicinity of a MBH\n\\cite{Ste} can produce large flux of HE neutrinos with relatively\nweak X-ray radiation.\n\n\\end{itemize}\n\nIn this paper we propose a new model of the hidden source which can\noperate in a galactic nucleus at pre-AGN phase, i.e. prior to MBH\nformation in it. The MBH in AGN is formed through the dynamical\nevolution of a central stellar cluster resulting in a secular\ncontraction of the cluster and its final collapse\n\\cite{beree78,ree84}. The first stage of this evolution is\naccompanied by collisions and destruction of normal stars in the\nevolving cluster, when virial velocities of constituent stars become\nhigh enough. The compact stars (neutron stars and black holes)\nsurvive this stage and their population continue to contract, being\nsurrounded by the massive envelope composed of the gas from destroyed\nnormal stars. Pre-AGN phase corresponds to a near collapsing\ncentral cluster of compact stars in the galactic nucleus. Repeating\nfireballs after continuous collisions of compact stars in this very\ndense cluster result in the formation of a rarefied cavity in the\nmassive gas envelope. Particles accelerated in this cavity interact\nwith the gas in the envelope and produce HE neutrinos. Accompanying\ngamma-radiation can be fully absorbed in the case of thick envelope\n(matter depth $X_{env}\\sim10^4$~g/cm$^2$). The proposed source is\nshort-lived (lifetime $t_s\\sim10$~years) and very powerful:\nneutrino luminosity exceeds the Eddington limit for e-m radiation.\n\n\\section{The Model}\n\nWe consider in the following the basic features of the formation of\na short-lived extremely powerful hidden source of HE neutrinos in\nthe process of dynamical evolution of the central stellar cluster\nin a typical galactic nucleus.\n\n\\subsection{Dynamical Evolution of Galactic Nucleus}\n\\label{dynamic}\n\nThe dynamical evolution of dense central stellar clusters in the\ngalactic nuclei is accompanied by a secular growth of the\nvelocity dispersion of constituent stars $v$ or, equivalently, by\nthe growth of the central gravitational potential. This process is\nterminated by the formation of the MBH when the velocity dispersion\nof stars grows up to the light speed (see for a review e.g.\n\\cite{ree84} and references therein). On its way to a MBH\nformation the dense galactic nuclei inevitably proceed through the\nstellar collision phase of evolution \\cite{spi66}--\\cite{dok91},\nwhen most normal stars in the cluster are disrupted in\nmutual collisions. The necessary condition for the collisional\ndestruction of normal stars with mass $m_*$ and radius $r_*$ in the\ncluster of identical stars with a velocity dispersion $v$ is\n\\begin{equation}\nv>v_p,\n\\label{disr}\n\\end{equation}\nwhere\n\\begin{equation}\nv_p=\\left(\\frac{2Gm_*}{r_*}\\right)^{1/2}\n\\simeq6.2\\cdot10^2\\left(\\frac{m_*}{\\rm M_{\\odot}}\\right)^{1/2}\n\\left(\\frac{r_*}{R_{\\odot}}\\right)^{-1/2} \\mbox{ km s}^{-1}.\n\\label{vpar}\n\\end{equation}\nis an escape (parabolic) velocity from the surface of a constituent\nnormal star. The kinetic energy of colliding star is greater in\ngeneral than its gravitational bound energy under the inequality\n(\\ref{disr}). If $v>v_p$, the normal stars are eventually disrupted\nin mutual collisions or in collisions with the extremely compact\nstellar remnants, i.e. with neutron stars (NSs) or stellar mass\nblack holes. Only these compact stellar remnants will survive\nthrough the stellar-destruction phase of evolution ($v=v_p$) and\nform the self-gravitating core. We shall refer for simplicity to\nthis core as to the NS cluster. Meanwhile the remnants of disrupted\nnormal stars form a gravitationally bound massive gas envelope in\nwhich the NS cluster is submerged. The virial radius of this\nenvelope is\n\\begin{equation}\nR_{env}=\\frac{GM_{env}}{2v_p^2}\n=\\frac{1}{4}\\frac{M_{env}}{m_*}r_* \\simeq0.56M_8\n\\left(\\frac{m_*}{\\rm M_{\\odot}}\\right)^{-1}\n\\left(\\frac{r_*}{R_{\\odot}}\\right) \\mbox{ pc},\n\\label{Renv}\n\\end{equation}\nwhere $M_{env}=10^8M_8{\\rm M_{\\odot}}$ is a corresponding mass of\nthe envelope. The gas from disrupted normal stars composes the\nmajor part of the progenitor central stellar cluster in the\ngalactic nucleus. So the natural range for the total mass of the\nenvelope is the same as the typical range for the mass of a central\nstellar cluster in the galactic nucleus, $M_{env}=10^7-10^8{\\rm\nM_{\\odot}}$. The envelope radius $R_{env}$ is given by the virial\nradius of a central cluster in the galactic nucleus at the moment\nof evolution corresponding to normal stars destructions, i.~e,\n$v=v_p$. The mean number density of gas in the envelope is\n\\begin{equation}\nn_{env}=\\frac{3}{4\\pi}\\frac{1}{R_{env}^3}\\frac{M_{env}}{m_p}\n\\simeq5.4\\cdot10^{9}M_8^{-2}\n\\left(\\frac{m_*}{\\rm M_{\\odot}}\\right)^{3}\n\\left(\\frac{r_*}{R_{\\odot}}\\right)^{-3} \\mbox{ cm}^{-3},\n\\label{nenv}\n\\end{equation}\nwhere $m_p$ is a proton mass. A column density of the envelope is\n\\begin{equation}\nX_{env}=m_p n_{env} R_{env}\n\\simeq1.6\\cdot10^4M_8^{-1}\n\\left(\\frac{m_*}{\\rm M_{\\odot}}\\right)^{2}\n\\left(\\frac{r_*}{R_{\\odot}}\\right)^{-2} \\mbox{ g cm}^{-2}.\n\\label{depth}\n\\end{equation}\nSuch an envelope completely absorbs electromagnetic radiation and\nHE particles outgoing from the interior, except neutrinos and\ngravitational waves. A column density becomes less for more massive\nenvelopes.\n\nWe assume that energy release due to star collisions supports the\ngas in the cluster in (quasi-)dynamical equilibrium. It implies the\nequilibrium temperature $T_{eq}$ of the gas,\n\\begin{equation}\nT_{eq} \\sim \\frac{m_p}{6k}\\frac{GM_{env}}{R_{env}} \\sim\n1.6\\cdot 10^7\\mbox{ K}.\n\\label{Teq}\n\\end{equation}\nThe thermal velocity of gas particles at the equilibrium\ntemperature is of order of an escape velocity from the surface of a\nnormal star.\n\n\\noindent\nIf $T \\gg T_{eq}$ the gas outflows from the cluster with the sound speed\n\\begin{equation}\nv_s=\\left( 2\\gamma \\frac{kT}{m_p} \\right)^{1/2}\n\\approx 600\\left( \\frac{T}{T_{eq}}\\right)^{1/2}\\mbox{ km/s},\n\\label{vsound}\n\\end{equation}\nwhere $\\gamma$ is adiabatic index ($\\gamma=5/3$ for hydrogen).\\\\\n\\noindent\nIf $T \\ll T_{eq}$ gas collapses to the core.\n\n\\subsection{Dense Cluster of Stellar Remnants}\n\nAs was discussed above, the dense NS cluster survives inside the\nmassive envelope of the post-stellar-destruction galactic nucleus.\nThe total mass of this cluster is $\\sim1-10$~\\% of the total mass\nof a progenitor galactic nucleus \\cite{spi66}--\\cite{spi71} and so\nof the massive envelope, i.~e. $M\\sim0.01 - 0.1M_{env}$. We will\nuse the term `evolved galactic nucleus' for this cluster of NSs\nassuming that (i) $v>v_p$ and (ii) the (two-body) relaxation time\nin the cluster is much less than the age of the host galaxy. Under\nthe last condition the cluster has enough time for an essential\ndynamical evolution. For example the relaxation time of stars\ninside a central parsec of the Milky Way galaxy is\n$t_r\\sim10^7-10^8$~years. A further dynamical evolution of the\nevolved cluster is terminated by the dynamical collapse to a MBH.\n\nWe consider in the following an evolved central cluster of NSs with\nidentical masses $m=1.4{\\rm M_{\\odot}}$. This evolved cluster of\nNSs is sunk deep into the massive gas envelope remaining after the\nprevious evolution epoch of a typical normal galactic nucleus. Let\n$N=M/m=10^6N_6$ is a total number of NSs stars in the cluster. The\nvirial radius of this cluster is:\n\\begin{equation}\nR=\\frac{GNm}{2v^2}=\\frac{1}{4}\\left(\\frac{c}{v}\\right)^2 N r_g\n\\simeq1.0\\cdot10^{13} N_6 (v/0.1c)^{-2} \\mbox{ cm},\n\\label{Radius}\n\\end{equation}\nwhere $r_g=2Gm/c^2$ is a gravitational radius of NS. For\n$N\\sim10^6$ and $v\\sim0.1c$ one has nearly collapsing cluster with\nthe virial size of $\\sim1$~AU. The characteristic times are (i) the\ndynamical time\n$t_{dyn}=R/v=(1/4)N(c/v)^{3}r_g/c\\simeq0.95N_6(v/0.1c)^{-3}$~hour\nand (ii) the evolution (two-body relaxation) time of the NS cluster\n$t_{rel}\\simeq0.1 (N/\\ln\nN)t_{dyn}\\simeq19N_6^2(v/0.1c)^{-3}$~years. In general $t_{rel}\\gg\nt_{dyn}$, if $N\\gg 1$. This evolution time determines the duration\nof an active phase for the considered below hidden source, as\n$t_s\\sim t_{rel}\\sim10$~years.\n\n\\subsection{Fireballs in Cluster}\n\nThe most important feature of our model is a secular growing rate\nof accidental NS collisions in the evolving cluster, accompanied by\nlarge energy release. The corresponding rate of NS collisions in\nthe cluster (with the gravitational radiation losses taken into\naccount) is \\cite{qui87}--\\cite{dok98}\n\\begin{eqnarray}\n\\dot N_c & = & 9\\sqrt2\\left(\\frac{v}{c}\\right)^{17/7}\\frac{c}{R}=\n36\\sqrt2\\left(\\frac{v}{c}\\right)^{31/7}\\frac{1}{N}\\frac{c}{r_g}\n\\nonumber \\\\\n& \\simeq & 4.4\\cdot10^{3}N_6^{-1}(v/0.1c)^{31/7} \\mbox{\nyr}^{-1}.\n\\label{Nrate}\n\\end{eqnarray}\nThe time between two successive NS collisions is\n\\begin{eqnarray}\nt_c & = & \\dot N^{-1}_c\n=\\frac{1}{9\\sqrt2}\\left(\\frac{c}{v}\\right)^{10/7}t_{dyn}\n=\\frac{1}{36\\sqrt2}\\left(\\frac{c}{v}\\right)^{31/7}\nN\\frac{r_g}{c}\\nonumber \\\\ & \\simeq &\n7.3\\cdot10^{3}N_6(v/0.1c)^{-31/7} \\mbox{ s}.\n\\label{tcoll}\n\\end{eqnarray}\nNote that a number of NS collisions, given by $\\dot{N_c}t_s$,\ncomprises only a small fraction, about $1\\%$, of a total number of\nNSs in the cluster to the time of the onset of dynamical collapse\nof the whole cluster into a MBH.\n\nMerging of two NSs in collision is similar to the process of a\ntight binary merging: the NSs are approaching to each other by\nspiralling down due to the gravitational waves radiation and then\ncoalesce by producing an ultrarelativistic photon-lepton fireball\n\\cite{cav78}--\\cite{mes92}, which we assume to be spherically\nsymmetric.\n\nThe energy of one fireball is $E_0=E_{52}10^{52}$~ergs, and the\ntotal energy release in the form of fireballs during lifetime of\nthe hidden source $t_s\\sim10$~yr is\n\\begin{equation}\nE_{tot} \\sim \\dot{N_c} E_0 t_s \\sim 4\\cdot 10^{56}\\mbox{ ergs},\n\\label{Etot}\n\\end{equation}\nwhere $\\dot{N_c}$ is the NS collision rate.\n\nThe physics of fireballs is extensively elaborated especially in\nrecent years for the modeling of cosmological gamma-ray bursts\n(GRBs) (for review see e.~g. \\cite{pir96} and references therein).\nThe newborn fireball expands with relativistic velocity,\ncorresponding to the Lorentz factor $\\Gamma_f\\gg 1$. The relevant\nparameter of a fireball is the total baryonic mass\n\\begin{equation}\nM_0= E_0/\\eta c^2\\simeq5.6\\cdot10^{-6}E_{52}\\eta_3^{-1}M_{\\odot},\n\\label{M0}\n\\end{equation}\nwhere baryon-loading mass parameter $\\eta=10^3\\eta_3$. The maximum\npossible Lorentz factor of expanding fireball is $\\Gamma_f=\\eta+1$\nduring the matter-dominated phase of fireball expansion\n\\cite{cav78,she90}. During the initial phase of expansion, starting\nfrom the radius of the `inner engine' $R_0\\sim10^6 - 10^7$~cm, the\nfireball Lorentz factor increases as $\\Gamma\\propto r$, until it is\nsaturated at the maximum value $\\Gamma_f=\\eta\\gg1$ at the radius\n$R_{\\eta}=R_0\\eta $ (see e.~g. \\cite{pir96}). Internal shocks will\ntake place around $R_{sh}=R_0\\eta^2$, if the fireball is\ninhomogeneous and the velocity is not a monotonic function of\nradius, e.g. due to the considerable emission fluctuations of the\ninner engine \\cite{pac94}--\\cite{kob97}. The fireball expands with\nthe constant Lorentz factor $\\Gamma=\\eta$ at $R>R_{\\eta}$ until it\nsweeps up the mass $M_0/\\eta$ of ambient gas and looses half of its\ninitial momentum. At this moment ($R=R_{\\gamma}$) the deceleration\nstage starts \\cite{mes92}--\\cite{mes93}.\n\nInteraction of the fireball with an ambient gas determines the\nlength of its relativistic expansion. In our case the fireball\npropagates through the massive envelope with a mean gas number\ndensity $n_{env}=\\rho_{env}/m_p=n_9 10^9$~cm$^{-3}$ as it follows\nfrom Eq.~(\\ref{nenv}). Fireball expands with $\\Gamma\\gg1$ up to the\ndistance determined by the Sedov length\n\\begin{equation}\nl_S=\\left(\\frac{3}{4\\pi}\\frac{E_0}{\\rho_{env}c^2}\\right)^{1/3}\n\\simeq1.2\\cdot10^{15}n_9^{-1/3}E_{52}^{1/3} \\mbox{ cm}.\n\\label{Sedov}\n\\end{equation}\nFireball becomes mildly relativistic at radius $r=l_S$ due to\nsweeping up the gas from the envelope with the mass $M_0 \\eta$. The\nradius $r=l_S$ is the end point of the ultrarelativistic fireball\nexpansion phase. Far beyond the Sedov length radius ($r\\gg l_S$)\nthere is the non-relativistic Newtonian shock driven by the\ndecelerated fireball. Its radius $R(t)$ obeys the Sedov--Taylor\nself-similar solution \\cite{lan87}, with\n$R(t)=(E_0t^2/\\rho_{env})^{1/5}$. The corresponding shock expansion\nvelocity is $u=(2/5)[l_S/R(t)]^{3/2}c\\ll c$.\n\n\\subsection{Cavity and Shocks}\n\nWe show here that relativistic fireballs from a dense central\ncluster of NSs produce the dynamically supported rarefied cavity\ndeep inside the massive gaseous envelope.\n\nThe first fireball sweeps out the gas from the envelope producing\nthe cavity with a radius $l_S$. This cavity expands due to the next\nfireballs, which propagate first in a rarefied cavity and then hit\nthe boundary pushing it further. \n\nEach fireball hitting the dense\nenvelope is preceded by a shock. Propagating through the envelope,\nthe shock sweeps up the gas ahead of it and gradually decelerates.\nThe swept out gas forms a thin shell with a density profile given\nby Sedov self-similar solution. The next fireball hits this thin\nshell when it is decelerated down to the non-relativistic velocity.\nMoving in the envelope, the shell accumulates more gas,\nretaining the same density profile, and then it is hit by the next\nfireball again. After a number of collisions the shell becomes massive,\nand the successive hitting fireballs do not change its velocity\nappreciably. In this regime one can consider the propagation of\nmassive non-relativistic thin shell with a shock (density\ndiscontinuity) ahead of it. The shock speed $v_{sh}$ is connected\nwith a velocity $v_g$ of gas behind it as $v_{sh}=(\\gamma+1)v_g/2$,\nwhere $\\gamma$ is an adiabatic index. The density perturbation in\nthe envelope propagates as a shock until $v_{sh}$ remains higher\nthan sound speed $v_s$. In the considered case, the shock\ndissipates in the middle of the envelope. For the Sedov solution the\nshock velocity changes with distance $r$ as\n\\begin{equation}\nv_{sh}(r)=\n\\frac{2}{5}\\alpha_S^{-1}\\left(\\frac{E_{sh}}{\\rho_{env}}\\right)^{1/2}\nr^{-3/2},\n\\label{v-sh}\n\\end{equation}\nwhere $\\alpha_S$ is the constant of self-similar Sedov solution;\nwhen radiative pressure dominates $\\alpha_S=0.894$. The other\nquantities in Eq.~(\\ref{v-sh}) are $E_{sh}= (1/2)E_{tot} = 2\\cdot\n10^{56}$~erg/s is the energy of the shock, which includes kinetic\nand thermal energy (the half of a total energy is transformed to\nparticles accelerated in the cavity), and $\\rho_{env}$ is a density\nof the envelope given by Eq.~(\\ref{nenv}). From Eqs.~(\\ref{v-sh})\nand (\\ref{vsound}) it follows that $v_{sh}>v_s$ holds at distance\n$r<1\\cdot10^{18}\\mbox{ cm}\\sim0.6R_{env}$, i.~e. that shock does\nnot reach the outer surface of the envelope. In fact the latter\nconclusion follows already from energy conservation. The\ngravitational energy of the envelope $V_0$ is\n\\begin{equation}\nV_0=\\kappa \\frac{GM_{env}^2}{R_{env}}>9.2\\cdot 10^{56}\\mbox{ ergs},\n\\label{V_0}\n\\end{equation}\nwhere $\\kappa$ depends on a radial profile of the gas density in\nthe envelope $\\rho(r)$, and changes from 3/5 to 1. This energy is\nhigher than a total injected energy $E_{tot}\\sim 4\\cdot\n10^{56}$~ergs, and thus the system remains gravitationally bound.\nWhen a shock reaches the boundary of the envelope, the gas\ndistribution changes there. It has the form of a thin shell with\ngravitational energy $V_e=GM_{env}^2/2R_{env}$. To provide the exit\nof the shock to the surface of the envelope,\na total energy release must satisfy the relation $E_{tot}> V_0-V_e$, \nwhere the minimum value of $V_0-V_e$ is \n$1.5\\cdot 10^{56}$~ergs for $\\kappa=3/5$. Actually $E_{tot}$ must \nbe higher because (i) part of the\ninjected energy goes to heat, (ii) more realistic value of $\\kappa\n=1$, and (iii) the shell has a non-zero velocity, when the shock\ndisappears, with a gravitational braking taken into account. We\nconclude thus that for $E_{tot}\\sim 4\\cdot 10^{56}$~ergs, shock\ndissipates inside the envelope.\n\nThe cavity radius grows with time. For the stage, when a shell\nmoves non-relativistically, the cavity radius calculated as a\ndistance to the shell in the Sedov solution is\n\\begin{equation}\nR_{cav}(t)=\\left(\\frac{E_{sh}}{\\alpha_S \\rho_{env}}\\right )^{1/5}t^{2/5}.\n\\label{R-cav}\n\\end{equation}\nAt the end of a phase of the hidden source activity,\n$t_s\\sim10$~yr, the radius of the cavity reaches\n$\\sim3\\cdot10^{17}$~cm, remaining thus much less than $R_{env}$.\n\nThe cavity is filled by direct and reverse relativistic shocks from\nfireballs. Reverse shocks are produced by decelerated fireballs,\nmost notably when they hit the boundary of the cavity. \nThe expanding fireballs inside the cavity have a\nshape of thin shells \\cite{MeLaRe} and are separated by distance\n\\begin{equation}\nR_c= ct_c\\simeq2.2\\cdot10^{14}N_6(v/0.1c)^{-31/7}\\mbox{ cm}.\n\\label{Rc}\n\\end{equation}\nThe gas between two fireballs is swept up by the preceding one. A\ntotal number of fireballs existing in the cavity simultaneously is\n$N_f \\sim R_{cav}/R_c\\gg1$, and this number grows with time as\n$t^{2/5}$.\n\nShocks generated by repeating fireballs are ultrarelativistic\ninside the cavity and mildly relativistic in the envelope near the\ninner boundary. Collisions of multiple shocks in the cavity, as\nwell as inside the fireballs, produce strongly turbulized medium\nfavorable for generation of magnetic fields and particle\nacceleration.\n\n\\section{High Energy Particles in Cavity}\n\nThere are three regions where acceleration of particles take place.\n\n(i) NS cluster, where fireballs collide, producing the turbulent\nmedium with large magnetic field. This region has a small size of\norder of virial radius of the cluster $R \\sim 10^{13}$~cm, and we\nneglect its contribution to production of accelerated particles.\n\n(ii) The region at the boundary between the cavity and the\nenvelope. During the active period of a hidden source, $t_s \\sim\n10$~yr, the fireballs hit this region, heating and turbulizing it.\nThe large magnetic equipartition field is created here. This\nboundary region has density $\\rho \\sim \\rho_{env}$, the radius $R\n\\sim R_{cav}$ and the width $\\Delta < 0.1 R_{cav}$.\n\n(iii) Most of the cavity volume is occupied by fireballs, separated\nby distance $R_c$. Due to collisions of internal shocks, the gas in\na fireball is turbulized and equipartition magnetic field is\ngenerated \\cite{pir96,wax}.\n\nIn all three cases the Fermi II acceleration mechanism operates.\nFor all three sites we assume existence of equipartition magnetic\nfield, induced by turbulence and dynamo mechanism:\n\\begin{equation}\n\\frac{H^2}{8\\pi} \\sim \\frac{\\rho u_t^2}{2},\n\\label{equip}\n\\end{equation}\nwhere $\\rho$ and $u_t$ are the gas density and velocity of\nturbulent motions in the gas, respectively. Since turbulence is\ncaused by shocks, the shock spectrum of turbulence $F_k \\sim\nk^{-2}$ is valid, where $k$ is a wave number. Assuming\nequipartition magnetic field on each scale $l \\sim 1/k, \\quad\nH_l^2\\sim kF_k$, one obtains the distribution of magnetic fields\nover the scales as\n\\begin{equation}\nH_l/H_0 = (l/l_0)^{1/2},\n\\end{equation}\nwhere $l_0$ is a maximum scale with the coherent field $H_0$ there.\n\nThe maximum energy of accelerated particles is given by\n\\begin{equation}\nE_{max} \\sim eH_0l_0\n\\label{Emax}\n\\end{equation}\nwith an acceleration time\n\\begin{equation}\nt_{acc} \\sim \\frac{l_0}{c} \\left( \\frac{c}{v}\\right)^2.\n\\label{tac}\n\\end{equation}\nFor the turbulent shell at the boundary between the cavity and\nenvelope, assuming mildly relativistic turbulence $u_t \\sim c$ and\n$\\rho \\sim \\rho_{env}$, we obtain $H_{eq}=4\\cdot10^3$~G. The\nmaximum acceleration energy is $E_{max}= 2\\cdot 10^{21}$~eV, if the\ncoherent length of magnetic field $l_0$ is given by the Sedov\nlength $l_{S}$, and the acceleration time is $t_{acc}= 4\\cdot 10^4\nE_{52}^{1/3}n_9^{-1/3}$~s. The typical time of energy losses,\ndetermined by $pp$-collisions, is much longer than $t_{acc}$, and\ndoes not prevent acceleration to $E_{max}$ given above:\n\\begin{equation}\nt_{pp}=\\left(\\frac{1}{E}\\frac{dE}{dt}\\right)^{-1}\n=\\frac{1}{f_p\\sigma_{pp}n_{env} c}\n\\simeq2\\cdot10^6 n_9^{-1} \\mbox{ s},\n\\label{tpp}\n\\end{equation}\nwhere $f_p \\approx 0.5$ is the fraction of energy lost by HE proton\nin one collision, $\\sigma_{pp}$ is a cross-section of\n$pp$-interaction, and $n_{env}$ is the gas number density in the\nboundary turbulent shell.\n\nThe turbulence in the fireball is produced by collisions of\ninternal shells, and a natural scale for coherence length $l_0$ is\na width of the internal shell in the local frame $\\delta'$. The\nmaximum energy in the laboratory frame $E_{max}\\sim\neH'_{eq}\\delta$, where $\\delta$ is the corresponding width in the\nlaboratory frame. Since $H'\\propto 1/R$ and $\\delta \\propto R$, the\nmaximum energy does not change with time, and can be estimated as\nin Ref.~\\cite{wax}, $E_{max}\\sim 3\\cdot 10^{20}$~eV. Note that in\nour case a fireball propagates in the very low-density medium.\n\nA gas left in the cavity by preceding fireball, as well as high\nenergy particles escaping from it, are accelerated by the next\nfireball by a factor $\\Gamma_f^2$ at each collision. This\n$\\Gamma^2$-mechanism of acceleration works only in pre-hydrodynamic\nregime of fireball expansion, after reaching the hydrodynamic\nstage, $\\Gamma^2$-mechanism ceases \\cite{BBH}.\n\nWe conclude, thus, that both efficiency and maximum acceleration\nenergy are very high. We assume that a fireball transfers half of\nits energy to accelerated particles.\n\n\\section{Neutrino Production and Detection}\n\nParticles accelerated in the cavity interact with the gas in the\nenvelope producing high energy neutrino flux. We assume that about\nhalf of the total power of the source $L_{tot}$ is converted into\nenergy of accelerated particles $L_p \\sim 7\\cdot 10^{47}$~erg/s. As\nestimated in Section 2.1, the column density of the envelope varies\nfrom $X_{env}\\sim10^2$~g/cm$^2$ (for very heavy envelope) up to\n$X_{env}\\sim10^4$~g/cm$^2$ (for the envelope with mass $M \\sim\n10^8M_{\\odot}$. Taking into account the magnetic field, one\nconcludes that accelerated protons loose in the envelope a large\nfraction of their energy. The charged pions, produced in\n$pp$-collisions, with Lorentz factors up to\n$\\Gamma_c\\sim1/(\\sigma_{\\pi N}n_{env}c\\tau_{\\pi})\n\\sim4\\cdot10^{13}n_9^{-1}$ freely decay in the envelope (here\n$\\sigma_{\\pi N}\\sim3\\cdot10^{-26}$~cm$^2$ is $\\pi N$-cross-section,\n$\\tau_{\\pi}$ is the lifetime of charged pion, and $n_{env}=10^9\nn_9$~cm$^{-3}$ is the number density of gas in the envelope). We\nassume $E^{-2}$ spectrum of accelerated protons\n\\begin{equation}\nQ_p(E)= \\frac{L_p}{\\zeta E^2},\n\\end{equation}\nwhere $\\zeta=\\ln (E_{max}/E_{min})\\sim20-30$. About half of its\nenergy protons transfer to high energy neutrinos through decays of\npions, $L_{\\nu} \\sim (2/3)(3/4)L_p$, and thus the production rate\nof $\\nu_{\\mu}+\\bar{\\nu}_{\\mu}$ neutrinos is\n\\begin{equation}\nQ_{\\nu_{\\mu}+\\bar{\\nu}_{\\mu}}(>E) = \\frac{L_p}{4\\zeta E^2}.\n\\label{Qnu}\n\\end{equation}\nCrossing the Earth, these neutrinos create deep underground the\nequilibrium flux of muons, which can be calculated as \\cite{nu90}:\n\\begin{equation}\nF_{\\mu}(>E)=\\frac{\\sigma_0\nN_A}{b_{\\mu}}Y_{\\mu}(E_{\\mu})\\frac{L_p}{4\\xi E_{\\mu}}\n\\frac{1}{4\\pi r^2} , \\label{Fmu}\n\\end{equation}\nwhere the normalization cross-section\n$\\sigma_0=1\\cdot10^{-34}$~cm$^2$, $N_A=6\\cdot10^{23}$ is the\nAvogadro number, $b_{\\mu}=4\\cdot10^{-6}$~cm$^2$/g is the rate of\nmuon energy losses, $Y_{\\mu}(E)$ is the integral muon moment of\n$\\nu_{\\mu}N$ interaction (see e.~g. \\cite{book,nu90}). The most\neffective energy of muon detection is $E_{\\mu}\\geq1$~TeV\n\\cite{nu90}. The rate of muon events in the underground detector\nwith effective area $S$ at distance $r$ from the source is given by\n\\begin{equation}\n\\dot N(\\nu_{\\mu})=F_{\\mu}S\\simeq70\\left(\\frac{L_p}{10^{48}\\mbox{\nerg s}^{-1}}\\right)\n\\left(\\frac{S}{1\\mbox{ km}^{2}}\\right)\n\\left(\\frac{r}{10^3\\mbox{ Mpc}}\\right)^{-2}\n\\quad\\mbox{yr}^{-1}. \\label{Number}\n\\end{equation}\nThus, we expect about 10 muons per year from the source at distance\n$10^3$~Mpc.\n\n\\section{Accompanying Radiation}\n\nWe shall consider below HE gamma-ray radiation produced by\naccelerated particles and thermalized infrared radiation from the\nenvelope. As far as HE gamma-ray radiation is concerned, there will\nbe considered two cases: (i) thin envelope with\n$X_{env}\\sim10^2$~g/cm$^2$ and (ii) thick envelope with\n$X_{env}\\sim10^4$~g/cm$^2$. In the latter case HE gamma-ray\nradiation is absorbed.\n\n\\subsection{Gamma-Ray Radiation}\n\nApart from high energy neutrinos, the discussed source can emit HE\ngamma-radiation through $\\pi^0\\to2\\gamma$ decays and synchrotron\nradiation of the electrons. In case of the thick envelope with\n$X_{env}\\sim10^4$~g/cm$^2$ most of HE photons are absorbed in the\nenvelope (characteristic length of absorption is the radiation\nlength $X_{rad}\\approx60$~g/cm$^2$). In the case of the thin\nenvelope, $X_{env}\\sim100$~g/cm$^2$, HE gamma-radiation emerges\nfrom the source. Production rate of the synchrotron photons can be\nreadily calculated as\n\\begin{equation}\ndQ_{syn}=\\frac{dE_e}{E_{\\gamma}}Q_e(>E_e),\n\\end{equation}\nwhere $E_e$ and $E_{\\gamma}$ are the energies of electron and of\nemitted photon, respectively. Using $Q_e(>E_e)=L_e/(\\eta E_e)$ and\n$E_{\\gamma}=k_{syn}(H)E_e^2$, where $k_{syn}$ is the coefficient of\nthe synchrotron production, one obtains\n\\begin{equation}\nQ_{syn}(E_{\\gamma})= \\frac{1}{12} \\frac{L_p}{\\eta E_{\\gamma}^2}.\n\\label{Qsyn}\n\\end{equation}\nNote, that the production rate given by Eq.~(\\ref{Qsyn}) does not\ndepend on magnetic field. Adding the contribution from $\\pi^0 \\to\n2\\gamma$ decays, one obtains\n\\begin{equation}\nQ_{\\gamma}(E_{\\gamma})= \\frac{5}{12} \\frac{L_p}{\\eta E_{\\gamma}^2},\n\\label{Qgamma}\n\\end{equation}\nand the flux at $E_{\\gamma}\\geq1$~GeV at the distance to the source\n$r=1\\cdot10^3$~Mpc is\n\\begin{eqnarray}\nF_{\\gamma}(>E_{\\gamma}) & = &\n\\frac{5}{12} \\left(\\frac{1}{4\\pi\nr^2}\\right)\\frac{L_p}{\\xi E_{\\gamma}} \\nonumber\\\\\n& \\simeq &\n2.2\\cdot 10^{-8}\\left(\\frac{L_p}{10^{47}\\mbox{ erg s}^{-1}}\\right)\n\\left(\\frac{r}{10^3\\mbox{ Mpc}}\\right)^{-2}\n\\mbox{ cm}^{-2} \\mbox{ s}^{-1},\n\\end{eqnarray}\ni.~e. the source is detectable by EGRET.\n\n\\subsection{Infrared and Optical Radiation}\n\nHitting the envelope, fireballs dissipate part of its kinetic\nenergy in the envelope in the form of low-energy e-m radiation.\nThis radiation is thermalized in the optically thick envelope and\nthen re-emitted in the form of black-body radiation from the\nsurface of the envelope. It appears much more later than HE\nneutrino and gamma-radiation. The thermalized radiation diffuses\nthrough the envelope with a diffusion coefficient $D \\sim c\nl_{dif}$, where a diffusion length is $l_{dif}=1/(\\sigma_T\nn_{env})$ and $\\sigma_T$ is the Thompson cross-section. A mean time\nof the radiation diffusion through the envelope of radius $R_{env}$\nis\n\\begin{equation}\nt_d \\sim \\frac{R_{env}^2}{D} \\sim 1\\cdot 10^4\\mbox{ yr},\n\\label{tdiff}\n\\end{equation}\nindependently of the envelope mass. This diffusion time is to be\ncompared with a duration of an active phase $t_s \\sim 10$~years\nand with a time of flight $R_{env}/c \\sim2$~years.\n\nSince the produced burst is very short, $t_s \\sim 10$~yr, the\narrival times of photons to the surface of the envelope have a\ndistribution with a dispersion $\\sigma \\sim t_d$. An average\nsurface black body luminosity is then\n\\begin{equation}\n\\bar{L}_{bb}\\sim E_{tot}/t_d \\sim 1\\cdot10^{45}\\mbox{ erg/s},\n\\label{Lbb}\n\\end{equation}\nwith a peak luminosity being somewhat higher. The temperature of\nthis radiation corresponds to IR range\n\\begin{equation}\nT_{bb}=\n\\left(\\frac{\\bar{L}_{bb}}{4\\pi R^2_{env}\\sigma_{SB}}\\right)^{1/4}\n\\simeq 8.4\\cdot10^2\\mbox{ K}.\n\\end{equation}\nThus, in $\\sim 10^4$ years after neutrino burst, the hidden source\nwill be seen in the sky as a luminous IR source. Since we consider\na model of production of high-luminosity AGN, the object is\ntypically expected to be at high redshift $z$. Its visible\nmagnitude is\n\\begin{equation}\nm=-2.5\\log \\left(\\frac{L_{bb}H_0^2}{16\\pi(z+1-\\sqrt{1+z})^2f_0}\\right)\n\\label{magn}\n\\end{equation}\nwhere $H_0=100h$~km/s~Mpc is the Hubble constant and the flux\n$f_0=2.48\\cdot 10^{-5}$~erg/cm$^2$s. For $L_{bb}=1\\cdot\n10^{45}$~erg/s, $z=3$ and $h=0.6$, the visible magnitude of the IR\nsource is $m=22.7$. Such a faint source is not easy identify in\ne.g. IRAS catalogue as a powerful source, because for redshift\ndetermination it is necessary to detect the optical lines from the\nhost galaxy, which are very weak at assumed redshift $z=3$. The\nnon-thermal optical radiation can be also produced due to HE\nproton-induced pion decays in the outer part of the envelope, but\nits luminosity is very small. Most probably such source will be\nclassified as one of the numerous non-identified weak IR source.\n\n\\subsection{Duration of activity and the number of sources}\n\nAs was indicated in Section 2.2 the duration of the active phase\n$t_s$ is determined by relaxation time of the NS cluster: $t_s\\sim\nt_{rel}\\sim10-20$~yr. This stage appears only once during the\nlifetime of a galaxy, prior to the MBH formation. If to assume that\na galactic nucleus turns after it into AGN, the total number of\nhidden sources in the Universe can be estimated as\n\\begin{equation}\nN_{HS} \\sim \\frac{4}{3}\\pi (3ct_0)^3 n_{AGN} t_s/t_{AGN},\n\\label{totnum}\n\\end{equation}\nwhere $\\frac{4}{3}\\pi(3ct_0)^3$ is the cosmological volume inside\nthe horizon $ct_0$, $n_{AGN}$ is the number density of AGNs and\n$t_{AGN}$ is the AGN lifetime. The value $t_s/t_{AGN}$ gives a\nprobability for AGN to be observed at the stage of the hidden\nsource, if to include this short stage ($t_s \\sim 10$~yr) in the\nmuch longer ($t_{AGN}$) AGN stage and consider (for the aim of\nestimate) the hidden source stage as the accidental one in the AGN\nhistory. The estimates for $n_{AGN}$ and $t_{AGN}$ taken for\ndifferent populations of AGNs result in $N_{HS} \\sim 10 - 100$.\n\n\\section{Conclusions}\n\nDynamical evolution of the central stellar cluster in the galactic\nnucleus results in the stellar destruction of the constituent\nnormal stars and in the production of massive gas envelope. The\nsurviving subsystem of NSs submerges deep into this envelope. The\nfast repeating fireballs caused by NS collisions in the central\nstellar cluster produce the rarefied cavity inside the massive\nenvelope. Colliding shocks generate the turbulence inside the\nfireballs and in the cavity, and particles are accelerated by Fermi\nII mechanism. These particles are then re-accelerated by\n$\\Gamma^2$-mechanism in collisions with relativistic shocks and\nfireballs.\n\nAll high energy particles, except neutrinos, can be completely\nabsorbed in the thick envelope. In this case the considered source\nis an example of a powerful hidden source of HE neutrinos.\n\nPrediction of high energy gamma-ray flux depends on the thickness\nof envelope. In case of the thick envelope,\n$X_{rad}\\sim10^4$~g/cm$^2$, HE gamma-radiation is absorbed. When an\nenvelope is thin, $X_{rad}\\sim10^2$~g/cm$^2$, gamma-ray radiation\nfrom $\\pi^0\\to2\\gamma$ decays and from synchrotron radiation of the\nsecondary electrons can be observed by EGRET and marginally by\nWhipple detector at $E_{\\gamma}\\geq1$~TeV.\n\nIn all cases the thickness of the envelope is much larger than the\nThompson thickness ($x_T\\sim3$~g/cm$^{2}$), and this condition\nprovides the absorption and X-rays and low energy gamma-rays.\n\nA hidden source is to be seen as a bright IR source but, due to\nslow diffusion through envelope, this radiation appears\n$\\sim10^4$~years after the phase of neutrino activity. During the\nperiod of neutrino activity the IR luminosity is the same as before\nit. A considered source is a precursor of most powerful AGN, and\ntherefore most of these sources are expected to be at the same\nredshifts as AGNs. The luminosity $L_{IR} \\sim 10^{45} -\n10^{46}$~erg/s is not unusual for powerful IR sources from IRAS\ncatalogue. The maximum observed luminosity exceeds\n$1\\cdot10^{48}$~erg/s \\cite{Row}, and there are many sources with\nluminosity $10^{45}-10^{46}$~erg/s \\cite{SaMi}. Moreover, for\nmost of the hidden sources the distance cannot be determined, and\nthus they fall into category of faint non-identified IR sources.\n\nLater these hidden sources turn into usual powerful AGNs, and\nthus the number of hidden sources is restricted by the total\nnumber of these AGNs.\n\nIn our model the shock is fully absorbed in the envelope. Since\nthe total energy release $E_{tot}$ is less than gravitational energy\nof the envelope $E_{grav} \\sim GM_{env}^2/R_{env}$, the system remains\ngravitationally bound, and in the end the envelope will collapse\ninto black hole or accretion disc.\n\nThe expected duration of neutrino activity for a hidden source is\n$\\sim10$~yr, and the total number of hidden sources in the horizon\nvolume ranges from a few up to $\\sim100$, within uncertainties of\nthe estimates.\n\nUnderground neutrino detector with an effective area\n$S\\sim1$~km$^2$ will observe $\\sim10$ muons per year with energies\n$E_{\\mu}\\geq1$~TeV from this hidden source.\n\n%\\noindent\n{\\bf Acknowledgments:} We are grateful to Bohdan Hnatyk for useful\ndiscussions. This work was supported in part by the INTAS through\ngrant No. 99-1065. One of the authors (VID) is grateful to the\nstaff of Laboratori Nazionali del Gran Sasso for hospitality during\nhis visit.\n\n\\begin{thebibliography}{99}\n\\bibitem{EGRET} P. Sreekumar et al., (EGRET collaboration),\n Astrophys. J. 494 (1998) 523.\n\\bibitem{book} V.S. Berezinsky, S.V. Bulanov, V.A. Dogiel, V.L. Ginzburg,\n V.S.~Ptu\\-skin, Astrophysics of Cosmic Rays, (North-Holland,\n Amsterdam, 1990).\n\\bibitem{BePr} V.S. Berezinsky, O.F. Prilutsky, Astron. \\& Astrophys.\n 66 (1987) 325.\n\\bibitem{ThZy} K.S. Thorne, A.N. Zytkow, Astrophys. J. 212 (1977) 832.\n\\bibitem{ber81} V.S. Berezinsky, V.L. Ginzburg, Mon. Not. R. Astron. Soc.\n 194 (1981) 3.\n\\bibitem{Ste} F.W. Stecker, C.Done, M.H. Salamon, P. Sommers,\n Phys. Rev. Lett. 66 (1991) 2697.\n\\bibitem{beree78} M.C. Begelman, M.J. Rees Mon. Not. R. Astron. Soc.\n185 (1978) 847.\n\\bibitem{ree84} M.J. Rees, Ann. Rev. Astron. \\& Astrophys. 22 (1984) 471.\n\\bibitem{spi66} L. Spitzer, W.C. Saslaw, Astrophys. J. 143 (1966) 400.\n\\bibitem{col67} S.A. Colgate, Astrophys. J. 150 (1967) 163.\n\\bibitem{san70} R.H. Sanders, Astrophys. J. 162 (1970) 791.\n\\bibitem{spi71} L. Spitzer, Galactic Nuclei, D.~Q'Connel, ed.\n (North Holland, Amsterdam, 1971), p.~443.\n\\bibitem{dok91} V.I. Dokuchaev, Mon. Not. R. Astron. Soc. 251 (1991) 564.\n\\bibitem{qui87} C.D. Quinlan, S.L. Shapiro, Astrophys. J. 321 (1987) 199.\n\\bibitem{qui90} C.D. Quinlan, S.L. Shapiro, Astrophys. J. 356 (1990) 483.\n\\bibitem{dok98} V.I. Dokuchaev, Yu.N. Eroshenko, L.M. Ozernoy,\n Astrophys. J. 502 (1998) 192.\n\\bibitem{cav78} G. Cavallo, M.J. Rees, Mon. Not. R. Astron. Soc.\n 183 (1978) 359.\n\\bibitem{goo86} J. Goodman, Astrophys. J. 308 (1986) L47.\n\\bibitem{pac86} B. Paczy\\'nski, Astrophys. J. 308 (1986) L51.\n\\bibitem{she90} A. Shemi, T. Piran, Astrophys. J. 365 (1990) L55.\n\\bibitem{mes92} P. M\\'esz\\'aros, M.J. Rees, Mon. Not. R. Astron. Soc.\n 248 (1992) 41P.\n\\bibitem{pir96} T. Piran, Physics Report, 314 (1999) 575.\n\n\\bibitem{pac94} B. Paczy\\'nski, G. Hu, Astrophys. J. 427 (1994) 708.\n\\bibitem{mes94} P. M\\'esz\\'aros, M.J. Rees, Astrophys. J. 430 (1994) L93.\n\\bibitem{kob97} S. Kobayashi, T. Piran, R. Sari, Astrophys. J. 490 (1997)\n92.\n\\bibitem{bla76} R.D. Blandford, C.F. McKee, Phys. Fluids, 19 (1976) 1130.\n\\bibitem{mes93} P. M\\'esz\\'aros, M.J. Rees, Astrophys. J. 405 (1993) 278.\n\\bibitem{lan87} L.D. Landau, E.M. Lifshitz, Fluid Mechanics 2nd ed.\n (Pergamon Press, 1987), Chap.~X.\n\\bibitem{MeLaRe} P.Meszaros, P.Laguna, M.Rees, Astrophys. J. 415 (1993) 181.\n\\bibitem{wax} E. Waxman, Phys. Rev. Lett. 75 (1995) 386.\n\\bibitem{BBH} V. Berezinsky, P. Blasi, B. Hnatyk, in preparation.\n\\bibitem{nu90} V. Berezinsky, Nucl. Phys. B (Proc. Suppl.). 19 (1990) 375.\n\\bibitem{Row} M. Rowan-Robinson, T. Broadhurst, A. Lawrence, R.G. McMahon\net al, Nature, 351 (1991) 719.\n\\bibitem{SaMi} D.B. Sanders, I.F. Mirabel, Ann.~Rev.~Astron.~Astroph.\n34 (1996) 749.\n\\end{thebibliography}\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002274.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{EGRET} P. Sreekumar et al., (EGRET collaboration),\n Astrophys. J. 494 (1998) 523.\n\\bibitem{book} V.S. Berezinsky, S.V. Bulanov, V.A. Dogiel, V.L. Ginzburg,\n V.S.~Ptu\\-skin, Astrophysics of Cosmic Rays, (North-Holland,\n Amsterdam, 1990).\n\\bibitem{BePr} V.S. Berezinsky, O.F. Prilutsky, Astron. \\& Astrophys.\n 66 (1987) 325.\n\\bibitem{ThZy} K.S. Thorne, A.N. Zytkow, Astrophys. J. 212 (1977) 832.\n\\bibitem{ber81} V.S. Berezinsky, V.L. Ginzburg, Mon. Not. R. Astron. Soc.\n 194 (1981) 3.\n\\bibitem{Ste} F.W. Stecker, C.Done, M.H. Salamon, P. Sommers,\n Phys. Rev. Lett. 66 (1991) 2697.\n\\bibitem{beree78} M.C. Begelman, M.J. Rees Mon. Not. R. Astron. Soc.\n185 (1978) 847.\n\\bibitem{ree84} M.J. Rees, Ann. Rev. Astron. \\& Astrophys. 22 (1984) 471.\n\\bibitem{spi66} L. Spitzer, W.C. Saslaw, Astrophys. J. 143 (1966) 400.\n\\bibitem{col67} S.A. Colgate, Astrophys. J. 150 (1967) 163.\n\\bibitem{san70} R.H. Sanders, Astrophys. J. 162 (1970) 791.\n\\bibitem{spi71} L. Spitzer, Galactic Nuclei, D.~Q'Connel, ed.\n (North Holland, Amsterdam, 1971), p.~443.\n\\bibitem{dok91} V.I. Dokuchaev, Mon. Not. R. Astron. Soc. 251 (1991) 564.\n\\bibitem{qui87} C.D. Quinlan, S.L. Shapiro, Astrophys. J. 321 (1987) 199.\n\\bibitem{qui90} C.D. Quinlan, S.L. Shapiro, Astrophys. J. 356 (1990) 483.\n\\bibitem{dok98} V.I. Dokuchaev, Yu.N. Eroshenko, L.M. Ozernoy,\n Astrophys. J. 502 (1998) 192.\n\\bibitem{cav78} G. Cavallo, M.J. Rees, Mon. Not. R. Astron. Soc.\n 183 (1978) 359.\n\\bibitem{goo86} J. Goodman, Astrophys. J. 308 (1986) L47.\n\\bibitem{pac86} B. Paczy\\'nski, Astrophys. J. 308 (1986) L51.\n\\bibitem{she90} A. Shemi, T. Piran, Astrophys. J. 365 (1990) L55.\n\\bibitem{mes92} P. M\\'esz\\'aros, M.J. Rees, Mon. Not. R. Astron. Soc.\n 248 (1992) 41P.\n\\bibitem{pir96} T. Piran, Physics Report, 314 (1999) 575.\n\n\\bibitem{pac94} B. Paczy\\'nski, G. Hu, Astrophys. J. 427 (1994) 708.\n\\bibitem{mes94} P. M\\'esz\\'aros, M.J. Rees, Astrophys. J. 430 (1994) L93.\n\\bibitem{kob97} S. Kobayashi, T. Piran, R. Sari, Astrophys. J. 490 (1997)\n92.\n\\bibitem{bla76} R.D. Blandford, C.F. McKee, Phys. Fluids, 19 (1976) 1130.\n\\bibitem{mes93} P. M\\'esz\\'aros, M.J. Rees, Astrophys. J. 405 (1993) 278.\n\\bibitem{lan87} L.D. Landau, E.M. Lifshitz, Fluid Mechanics 2nd ed.\n (Pergamon Press, 1987), Chap.~X.\n\\bibitem{MeLaRe} P.Meszaros, P.Laguna, M.Rees, Astrophys. J. 415 (1993) 181.\n\\bibitem{wax} E. Waxman, Phys. Rev. Lett. 75 (1995) 386.\n\\bibitem{BBH} V. Berezinsky, P. Blasi, B. Hnatyk, in preparation.\n\\bibitem{nu90} V. Berezinsky, Nucl. Phys. B (Proc. Suppl.). 19 (1990) 375.\n\\bibitem{Row} M. Rowan-Robinson, T. Broadhurst, A. Lawrence, R.G. McMahon\net al, Nature, 351 (1991) 719.\n\\bibitem{SaMi} D.B. Sanders, I.F. Mirabel, Ann.~Rev.~Astron.~Astroph.\n34 (1996) 749.\n\\end{thebibliography}"
}
] |
astro-ph0002275
|
Mining for Metals in the Ly$\alpha$ Forest
|
[
{
"author": "Sara L. Ellison"
}
] |
In order to ascertain the extent of metal enrichment in the Ly$\alpha$ forest, we have analysed a very high S/N spectrum of the $z = 3.625$ QSO Q1422+231. We find that in high column density Ly$\alpha$ clouds, the power law column density distribution function of C~IV continues down to log $N$(C~IV) = 11.7. In addition, by analysing pixel-by-pixel optical depths we show that there are considerably more metals in the Ly$\alpha$ forest than are currently directly detectable.
|
[
{
"name": "ellisons.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\n\\markboth{Ellison et al}{Mining for Metals in the Ly$\\alpha$ Forest}\n\n\\pagestyle{myheadings}\n\n\\begin{document}\n\n\\title{Mining for Metals in the Ly$\\alpha$ Forest}\n\\author{Sara L. Ellison}\n\\affil{Institute of Astronomy, Cambridge, UK}\n\\author{Antoinette Songaila}\n\\affil{Institute for Astronomy, University of Hawaii, USA}\n\\author{Joop Schaye, Max Pettini}\n\\affil{Institute of Astronomy, Cambridge, UK}\n%\\keywords{cosmology: observations -- galaxies: formation --\n%intergalactic medium -- quasars:absorption lines} \n\n\\begin{abstract}\nIn order to ascertain the extent of metal enrichment in the Ly$\\alpha$\nforest, we have analysed a very high S/N spectrum of the $z = 3.625$ QSO\nQ1422+231. We find that in high column density Ly$\\alpha$ clouds, the\npower law column density distribution function of C~IV continues down to log\n$N$(C~IV) = 11.7. In addition, by analysing pixel-by-pixel optical\ndepths we show that there are considerably more metals in the\nLy$\\alpha$ forest than are currently directly detectable.\n\\end{abstract}\n\\vspace{-1cm}\n\\section{Introduction}\n\nOur understanding of the Ly$\\alpha$ forest and its connection with the\nIntergalactic Medium (IGM) have undergone radical revision in recent\nyears. The paradigm in which the IGM consists of discrete, isolated\nclouds has been revolutionised by a generation of hydrodynamical\nsimulations (e.g. Hernquist et al 1996). These simulations show\nthat the `bottom-up' hierarchy of structure formation knits a\ncomplex but smoothly fluctuating cosmic web, consisting of filaments,\nknots and extensive `voids'. Originally thought to\nbe chemically pristine, it is now well-established that a large\nfraction of the strongest Ly$\\alpha$ absorbers exhibit some metal\nenrichment, most notably C~IV (e.g. Cowie et al 1995). \nHere, we address two specific\nquestions. Firstly, are the C~IV absorbers that have thus far been\ndetected just the tip of the iceberg and can more sensitive spectra\nmine ever weaker systems? Secondly, to what H~I column densities does\nthe enrichment extend? This latter point has particularly poignant\nimplications for the origin and transport mechanism of these metals.\nIn-situ formation in a nearby galaxy could be responsible for the\nenrichment of its local IGM, explaining the presence of C~IV\nin the relatively high column density Ly$\\alpha$ clouds. However, \nlow column density Ly$\\alpha$ clouds (log$N$(H~I) $<$ 14.0), which\nare associated with physically less dense regions, are found \nfurther from the sites of\nstar formation. The presence of C~IV in these clouds could be\nindicative of widespread metal enrichment, possibly by an early\nepoch of Population III star formation. This is an overview of work\ndescribed in more detail in Ellison et al (2000).\n\n\\section{C~IV in High Column Density Ly$\\alpha$ clouds}\n\nWith a S/N ratio in excess of 200 redward of Ly$\\alpha$, our Keck/HIRES\nspectrum of Q1422+231 is one of the most sensitive currently\navailable to search for C~IV associated with the Ly$\\alpha$ forest.\nAlthough this target has been extensively studied in the past, our\ndata reveal several C~IV systems that had not been previously detected\nin spectra of lower S/N. We undertake the standard procedure of\nfitting Voigt profiles to determine column densities, $b$-values and\nredshifts of the 34 detected C~IV systems associated mainly\nwith Ly$\\alpha$ clouds with log $N$(H~I) $>$ 14.5. Previous studies\nof C~IV absorbers have established a power law column density\ndistribution of the form $f(N)dN = BN^{-\\alpha} dN$\nand determined $\\alpha \\sim 1.5$, complete down to log $N$(C~IV)\n$\\simeq$ 12.75 for $z > 3$ (Songaila 1997). Below this limit, there is an\napparent departure from the power law which could be due to either\nincompleteness or a real turnover in the number density of C~IV systems.\nWe perform a maximum likelihood fit to our data points and determine a\npower law index $\\alpha = 1.44 \\pm 0.05$, in good agreement with\nprevious estimates (see Figure \\ref{f_N}). \nThe column density limits at which previous studies have\nexhibited a departure from the power law are sketched and clearly our\ndata establish that this was due to incompleteness. The C~IV systems\nfrom this single high quality spectrum are sufficient to show that\nthe power law continues down to at least log $N$(C~IV) $\\sim$\n12.3, below which the data points start to turn-over. Again, this could be due\nto the incompleteness caused, for example, by a bias against weak C~IV\nlines with large \n$b$-values, or evidence of a real turn-over in column density distribution.\nBy simulating C~IV lines for the two lowest column\ndensity intervals in Figure \\ref{f_N} with $b$-values drawn at random\nfrom the observed distribution, we can estimate the incompleteness\ncorrection factor by determining the frequency with which these lines\nare recovered. Once this has been taken into account, there is no\nshortfall compared with the power law, showing that it\ncontinues at least down to log $N$(C~IV) = 11.7, a factor\nof ten more sensitive than previous analyses.\n\n\\begin{figure}\n\\plotfiddle{ellisons1.ps}{6.5cm}{270}{40}{40}{-150}{220} \n\\caption{\\label{f_N} Column density distribution of C~IV absorbers in\nQ1422+231. Points corrected for incompleteness are shown with open\ncircles. The approximate turnovers seen in \nprevious determinations of the $f(N)$ power law are shown as a grey\nsolid line (Petitjean \\& Bergeron 1994) and black dashed line\n(Songaila 1997).} \n\\end{figure}\n\n\\section{Probing the Low Column Density Ly$\\alpha$ Forest}\n\n\\begin{figure}\n\\plotfiddle{ellisons2.ps}{10cm}{0}{48}{48}{-90}{-20} \n\\caption{The results from the optical depth analysis of Q1422+231\n(solid points) are compared with three synthetic spectra. Top panel:\nopen circles show the measured optical depths in a synthetic spectrum\nenriched solely with the detected C~IV systems. \nMiddle panel: In addition to the detected C~IV\nsystems, log $N$(C~IV)= 12.0 is included in all Ly$\\alpha$ clouds with log\n$N$(H~I) $> 14.5$. Bottom panel: Supplementary C~IV is now added in\nall weak (log $N$(H~I)$<14.5$) Ly$\\alpha$ lines with log C~IV/H~I =\n$-2.6$.} \n\\label{testabc}\n\\end{figure}\n\nDirect detection of the C~IV systems associated with low column\ndensity Ly$\\alpha$ clouds (log $N$(H~I) $<$ 14.0) is observationally\nvery challenging due to the extreme weakness of the absorption.\nIn the past, efforts have been made to overcome this problem by\nstacking together the regions where C~IV absorption is expected in\norder to produce a high S/N composite spectrum (e.g Lu et al 1998). In Ellison\net al (1999), we showed how a random redshift offset between the\nLy$\\alpha$ line and its associated C~IV feature could `smear' out the\nstacked feature and consequently underestimate the amount of metals\npresent. Instead, we favour the optical depth method developed by\nCowie \\& Songaila (1998) which we have found is more robust against\nredshift offset (see Ellison et al 2000 for a detailed\ndiscussion of this point). Briefly, the optical depth method consists\nof stepping through the spectrum and measuring the optical depth\n($\\tau$) of each Ly$\\alpha$ pixel and its corresponding C~IV. The\nresults of this analysis are shown by the solid line in Figure\n\\ref{testabc} and are consistent with a constant level of C~IV/H~I\n(as shown by the dashed line) for optical depths down from\n$\\tau$(Ly$\\alpha$) $\\sim 100$ over two orders of magnitude, below\nwhich $\\tau$(C~IV) flattens off to an approximately constant value.\nIn order to interpret these results, simulated spectra were reproduced\nusing the Ly$\\alpha$ forest taken directly from the data, adding C~IV\nwith a given enrichment recipe and then analysing the synthetic\nspectrum with the optical depth technique. A total of 3 simulated\nspectra were created, all of which include a random redshift offset of\n17 kms$^{-1}$ between Ly$\\alpha$ and C~IV and assume $b$(C~IV) = 1/2\n$b$(Ly$\\alpha$). Spectrum `A' includes only the directly detected C~IV \nwith no additional enrichment and the optical\ndepth analysis reveals that it is clearly C~IV deficient in comparison\nwith the data at almost all optical depths. Clearly, there is more\nC~IV in the data than is accounted for in the 34 directly identifiable\nsystems. Adding C~IV to the log\n$N$(C~IV) $>$ 14.5 Ly$\\alpha$ clouds at the detection limit of the\nspectrum (log $N$(C~IV) = 12.0) can reproduce the results obtained for\nthe data for $\\tau$(Ly$\\alpha$) $>$3 but not at lower optical depths\n(spectrum `B'). The data are more consistent with spectrum `C' in\nwhich a constant C~IV/H~I ratio of $-2.6$ was also included in log $N$(H~I)\n$<$ 14.5. \n\nWe investigated the possible limitations of our analysis due to such\neffects as contamination by other metal lines, errors in the continuum\nfit and scatter in the C~IV/H~I ratio. We conclude that overall this\nis a robust technique and that the limiting factor is likely to\nbe the accuracy of the continuum fit in the Ly$\\alpha$ forest\nregions which could mimic the flattening of $\\tau$(C~IV) that we\nobserve in the data at low H~I optical depths. Nevertheless, we find\nthat even in the high optical depth H~I pixels (that will not be\nseriously affected by small continuum errors) the \nidentified C~IV systems are insufficient to account for the all the\nmeasured absorption and that there are clearly more metals in the IGM\nthan we can currently detect.\n\n\\acknowledgements\n\nSLE is very grateful to the LOC for their generous financial\nassistance towards attending this conference.\n\n\\begin{references}\n\\reference{Cowie, L. L. \\& Songaila, A. 1998, Nature, 394, 44}\n\\reference{Cowie, L. L., Songaila, A., Kim, T. -S. \\& Hu, E. M. 1995\n\\aj, 109, 1522} \n\\reference{Ellison, S. L., G. F., Pettini, M., Chaffee, F. H. \\& \nIrwin, M. J. 1999, \\apj, 520, 456} \n\\reference{Ellison, S. L., Songaila, A., Schaye, J. \\& Pettini, M. 2000,\n\\aj, submitted}\n\\reference{Hernquist, L., Katz, N., Weinberg, D. H. \\&\nMiralda-Escud\\'{e}, J. 1996, \\apjl, 457, L51}\n\\reference{Lu, L., Sargent, W. L. W., Barlow, T. A. \\& Rauch, M. 1998,\npreprint, astro--ph/9802189}\n\\reference{Petitjean, P. \\& Bergeron, J. 1994, \\aap, 283, 759}\n\\reference{Songaila, A. 1997, \\apjl, 490, L1}\n\\end{references}\n\\end{document}"
}
] |
[] |
astro-ph0002276
|
New $\gamma$ Doradus Stars from the Hipparcos Mission and Geneva Photometry
|
[
{
"author": "Laurent Eyer"
},
{
"author": "Conny Aerts\\altaffilmark{1}"
}
] |
A search for new $\gamma$ Dor stars was undertaken using the Hipparcos periodic variable star catalogue and the Geneva photometric database, leading to a list of 40 new candidates. We started a monitoring of the candidates which suited the observational window with the CORALIE spectrograph at the Swiss Euler Telescope for establishing a robust list of new $\gamma$ Dor stars and studying line profile variations. We here present our long-term program.
|
[
{
"name": "eyer1.tex",
"string": "\\documentstyle[11pt,newpasp,epsf,twoside]{article}\n\\markboth{Eyer, L. \\& Aerts, C.}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{New $\\gamma$ Doradus Stars from the Hipparcos Mission and Geneva\nPhotometry}\n\\author{Laurent Eyer, Conny Aerts\\altaffilmark{1}}\n\\affil{Instituut voor Sterrenkunde,\n Katholieke Universiteit Leuven,\n Celestijnenlaan 200 B, B-3001 Leuven,\n Belgi\\\"e}\n\\altaffiltext{1}{Postdoctoral Fellow, Fund for Scientific Research, Flanders;\ne-mail: conny@ster.kuleuven.ac.be}\n\n\\begin{abstract}\nA search for new $\\gamma$ Dor stars was undertaken using\nthe Hipparcos periodic variable star catalogue and the Geneva\nphotometric database, leading to a list of 40 new candidates.\nWe started a monitoring of the candidates which\nsuited the observational window with the CORALIE spectrograph\nat the Swiss Euler Telescope for establishing a robust list\nof new $\\gamma$ Dor stars and studying line profile variations.\nWe here present our long-term program.\n\\end{abstract}\n\n\\section{Introduction}\nThe $\\gamma$ Dor stars have amplitude variations up to 0.1 mag\nin Johnson V and periods ranging from 0.4 to 3 days (Kaye, these proceedings).\nWe searched in two databases for finding new members of this class of\nvariable stars.\nThe first one is the Hipparcos main mission photometric database.\nIt contains a mean of 110 measurements for 118\\,204 stars brighter\nthan 12.4 and is magnitude complete up to 7.3-7.9 depending on the\ngalactic latitude $b$.\nAs the sampling is ruled by the scanning law of the satellite,\nit is not affected by the aliasing around\n1/day, which might be a problem for detecting $\\gamma$ Dor stars.\n\nThe second scanned database is the Geneva photometric catalogue\n(Burki \\& Kienzle, these proceedings), it counts 48\\,000 stars and\n345\\,000 measurements in a seven colour system.\nThe content of the Geneva catalogue is the reunion of more than\n200 scientific programmes, including namely the Bright Star\nCatalogue south of $\\delta < +20$.\n\n\n\\section{Hipparcos main mission}\nThousands new variable stars were discovered by the Hipparcos\nsatellite. During the analysis of the Hipparcos photometry,\nstars from the Periodic Catalogue having accurate parallaxes\nand colours were plotted in the HR diagram (Eyer 1998).\nA clump of stars just at the cool lower edge of the $\\delta$\nScuti instability strip was present and gave rise to a\nlist of 15 candidates (excluding redundant cases from\nthe other studies). A clump is also present when plotting\nthe variable stars of the Hipparcos Unsolved Catalogue. \n\n\\section{Hipparcos main mission and Geneva photometry}\nA systematic search for finding new $\\gamma$ Dor stars\nwas undertaken in the Hipparcos periodic variable star\ncatalogue using also Geneva photometry and performing\na multivariate discriminant analysis. This study led to a list\nof 14 new $\\gamma$ Dor stars (Aerts et al. 1998).\nThis method is stricter since information on amplitude,\nperiod, physical parameters and multiperiodic behaviour were taken into\naccount.\n\n\\section{The search in Geneva photometry}\nFinally the Geneva photometric database was scanned to find\nF dwarf stars with high standard deviation. Eleven candidates\nwere then measured with the 70-cm Swiss telescope, resulting in\nabout 1000 photometric measurements, which are under study\n(Eyer \\& Aerts, in preparation). It turns out that about half\nsuspected stars might be constant stars.\n\n\n\\section{Spectroscopic measurements}\nIn order to confirm the pulsational character of these stars,\nnew spectra have been taken with the CORALIE spectrograph on\nthe 1.2-m Swiss telescope at ESO-La Silla\nObservatory. The photometry and spectroscopy are necessary\nsteps since we want to establish a robust list of new $\\gamma$\nDor stars.\nUp to now 22 stars have been measured, the strategy consist of\ntaking at least five spectra of each candidate.\nAmong the stars, some are binaries, some are fast rotators\nand some show clear line profile variations (cf. Fig.~1).\nSome stars are too faint for the telescope size, thus\ncorrelation techniques are used to lower the noise level.\nThe following step is to accumulate photometry and spectra\nfor promising candidates in order to perform mode identification.\n\\begin{figure}[thb]\n \\plotfiddle{eyer1_1.eps}{3.6cm}{-90}{28}{23}{-120}{120}\n \\caption{Line profile variations of the star HD~14940.} \n\\end{figure}\n\n%\n\\begin{references}\n \\reference Aerts, C., Eyer, L., \\& Kestens, E. 1998, \\aap 337, 790\n \\reference Eyer, L. 1998, PhD Thesis, Geneva University\n\\end{references}\n%\n%\n\\end{document}\n\n\n\n"
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astro-ph0002277
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Gas and dust in NGC 7469: sub-mm imaging and CO J=3--2
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[
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"author": "Padeli P. Papadopoulos\\altaffilmark{1}"
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We present sensitive sub-mm imaging of the Seyfert 1 galaxy NGC 7469 at 850 $\mu $m and 450 $\mu $m with the Submillimetre Common User Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope (JCMT) and $ ^{12}$CO J=3--2 line observations of its central starbursting region. The global dust spectrum, as constrained by the new set of sub-mm data and available 1.30~mm and IRAS 100~$\mu $m, 60 $\mu $m data reveals a dominant warm dust component with a temperature of $T_{d} \sim 35$ K and a global molecular gas-to-dust ratio $M(H_2)/M_{d}\sim 600$. Including the atomic gas component yields a total gas-to-dust ratio of $\sim 830$. Such high values are typical for IR-bright spirals and in order to reconcile them with the significantly lower ratio of $\sim 100$ obtained for the Milky Way a cold dust reservoir, inconspicuous at FIR wavelengths, is usually postulated. However, while there is good evidence for the presence of cold gas/dust in NGC~7469 beyond its central region, our 450 $\mu $m map and available interferometric $ ^{12}$CO J=1--0 maps show the bright sub-mm/CO emission confined in the inner $\sim 2.5$~kpc, where a high $ ^{12}$CO (J=3--2)/(J=1--0) ratio ($\sim 0.85-1.0$) is measured. This is consistent with molecular gas at $T_{kin}\ga 30$K, suggesting that the bulk of the ISM in the starburst center of NGC~7469 is warm. Nevertheless the corresponding total gas-to-dust ratio there remains high, of the order of $\sim 500$. We argue that, rather than unaccounted cold dust mass, this high ratio suggests an overestimate of $M(H_2)$ from its associated $ ^{12}$CO J=1--0 line luminosity by a factor of $\sim 5$ when a Milky Way value for this conversion is used. Finally the diffuse cold gas and dust that is the likely source of the observed faint extended 450 $\mu $m and $ ^{12}$CO J=1--0 emission has an estimated total gas-to-dust ratio of $\sim 50-160$, closer to the Galactic value.
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[
{
"name": "ApJ7.tex",
"string": "\\documentstyle[12pt, aasms4]{article}\n\\begin{document}\n\n\\vspace*{2.0in}\n\\title{Gas and dust in NGC 7469: sub-mm imaging and CO J=3--2}\n\n\n\n\\author{Padeli P. Papadopoulos\\altaffilmark{1}}\n\n\\and\n\n\\author{Michael L. Allen \\altaffilmark{2}} \n\n\n\n\\altaffiltext{1}{Sterrewacht Leiden, P. O. Box 9513, 2300 RA Leiden, \nThe Netherlands}\n\\altaffiltext{2}{Department of Astronomy, University of Toronto, 60\nSt. George street, Toronto,\\\\ \\hspace*{0.5cm} ON M5S-3H8, Canada}\n\n\n\\begin{abstract}\n\n\nWe present sensitive sub-mm imaging of the Seyfert 1 galaxy NGC 7469\n at 850 $\\mu $m and 450 $\\mu $m with the Submillimetre Common User\n Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope (JCMT)\n and $ ^{12}$CO J=3--2 line observations of its central starbursting\n region. The global dust spectrum, as constrained by the new set of\n sub-mm data and available 1.30~mm and IRAS 100~$\\mu $m, 60 $\\mu $m\n data reveals a dominant warm dust component with a temperature of\n $\\rm T_{\\rm d} \\sim 35$ K and a global molecular gas-to-dust ratio\n $\\rm M(H_2)/M_{\\rm d}\\sim 600$. Including the atomic gas component\n yields a total gas-to-dust ratio of $\\sim 830$. Such high values\n are typical for IR-bright spirals and in order to reconcile them\n with the significantly lower ratio of $\\sim 100$ obtained for the\n Milky Way a cold dust reservoir, inconspicuous at FIR wavelengths,\n is usually postulated. However, while there is good evidence for\n the presence of cold gas/dust in NGC~7469 beyond its central region,\n our 450 $\\mu $m map and available interferometric $ ^{12}$CO J=1--0\n maps show the bright sub-mm/CO emission confined in the inner $\\sim\n 2.5$~kpc, where a high $ ^{12}$CO (J=3--2)/(J=1--0) ratio ($\\sim\n 0.85-1.0$) is measured. This is consistent with molecular gas at\n $\\rm T_{\\rm kin}\\ga 30$K, suggesting that the bulk of the ISM in the\n starburst center of NGC~7469 is warm. Nevertheless the\n corresponding total gas-to-dust ratio there remains high, of the\n order of $\\sim 500$. We argue that, rather than unaccounted cold\n dust mass, this high ratio suggests an overestimate of $\\rm M(H_2)$\n from its associated $ ^{12}$CO J=1--0 line luminosity by a factor of\n $\\sim 5$ when a Milky Way value for this conversion is used.\n Finally the diffuse cold gas and dust that is the likely source of\n the observed faint extended 450 $\\mu $m and $ ^{12}$CO J=1--0\n emission has an estimated total gas-to-dust ratio of $\\sim 50-160$,\n closer to the Galactic value.\n\n\\end{abstract}\n\n\\keywords{galaxies:\\ individual (NGC 7469)---galaxies:\\\nISM---galaxies:\\ Seyfert---galaxies: starburst}\n\n\n\\section{Introduction}\n\nThe role of molecular gas as the fuel of both starburst activity and\nan Active Galactic Nucleus (AGN) is now well established. In Seyfert\ngalaxies such gas is found on scales ranging from the inner $\\sim 1-2$\nkpc ``feeding'' an intense circumnuclear starburst down to $\\rm L\\la\n$100~pc from the AGN, where in the form of a geometrically thick torus\nobscures the active nucleus along certain viewing angles thus creating\nthe difference between type 2 and type 1 Seyferts (Miller \\& Antonucci\n1983; Krolik 1990 and references therein).\n\n\nEstimates of molecular gas mass in other galaxies from their\n velocity-integrated $ ^{12}$CO J=1--0 luminosity $\\rm L_{\\rm CO}$ (in\n K km s$ ^{-1}$ pc$ ^2$) are based on the so-called conversion factor\n $\\rm X_{\\rm CO}=M(H_2)/L_{\\rm CO}\\approx 5\\ M_{\\odot } (K\\ km\\\n s^{-1}\\ pc^2)^{-1}$ (e.g. Solomon \\& Barrett 1991) whose value is\n derived from studies of molecular gas in the Galactic disk. Numerous\n studies quantify the effects of the various physical conditions on\n this factor (e.g. Bryant \\& Scoville 1996; Israel 1997).\n Particularly in the starburst nuclei of very luminous IR galaxies\n ($\\rm L_{\\rm FIR} > 10^{11}\\ L_{\\odot }$) these conditions are\n significantly different than in the disk environment of quiescent\n spirals like the Milky Way. More specifically in the inner $\\sim\n 1-2$ kpc, where a starburst usually occurs, the gas differentiates\n into two distinct phases (e.g. Aalto et al. 1995) with a warm,\n diffuse and possibly non self-gravitating phase dominating the $\n ^{12}$CO emission. This results in a significant overestimate of\n $\\rm H_2$ mass from $\\rm L_{\\rm CO}$ when a Galactic value of $\\rm\n X_{\\rm CO}$ is used (Solomon et al. 1997; Downes \\& Solomon~1998).\n\n\n\nThe aforementioned conditions are expected in the nuclear region of\nthe SBa Seyfert~1 galaxy NGC~7469 (Arp 298, Mrk 1514), a luminous IR\nsource with $\\rm L_{\\rm FIR}\\approx 3\\times 10^{11}\\ L_{\\odot }$\nemanating from a powerful starburst deeply embedded into its $\\rm\nL\\sim 1$~kpc circumnuclear region (Wilson et al. 1991; Genzel et al.\n1995). High resolution $ ^{12}$CO J=1--0 observations revealed large\namounts of molecular gas within this region (Meixner et al. 1990;\nTacconi \\& Genzel 1996) with mass comparable to the dynamical, and\nthere is significant evidence that application of the standard\nGalactic conversion factor overestimates $\\rm M(H_2)$ in the\ncircumnuclear starburst of this galaxy (Genzel et al. 1995). In this\npaper we present sensitive sub-mm imaging of NGC 7469 at 850~$\\mu $m\nand 450~$\\mu $m and $ ^{12}$CO J=3--2 spectroscopy of its central\nregion. Under the assumption of a canonical gas-to-dust ratio of\n$\\sim 100$, our results confirm the overestimate of H$_2$ gas mass\nwhen a Galactic value for $\\rm X_{\\rm CO}$ is used, and demonstrate\nthe significance of CO spectroscopy and sub-mm imaging in offering a\nbetter assessment of the molecular gas mass and its average physical\nconditions.\n\n\nThroughout this work we adopt $\\rm H_{\\circ } = 75\\ km\\ sec^{-1}\\\nMpc^{-1}$ and $\\rm q_{\\circ } = 0.5$, which for cz=4900 km s$ ^{-1}$\nyields a luminosity distance of $\\rm D_{\\rm L}\\sim 66$ Mpc for NGC\n7469, where 1$''$ corresponds to $\\sim 310$ pc.\n \n\n\\section{Observations}\n\n\nThe sub-mm observations were made on the nights of 1997 December 3 and\n1998 January 15 with the Sub-mm Common User Bolometer Array (SCUBA) at\nthe 15-m James Clerk Maxwell Telescope (JCMT)\\footnote{The JCMT is\noperated by the Joint Astronomy Center in Hilo, Hawaii on behalf of\nthe parent organizations PPARC in the United Kingdom, the National\nResearch Council of Canada and the The Netherlands Organization for\nScientific Research.}. SCUBA is a dual camera system cooled to $\\sim\n0.1$ K allowing sensitive simultaneous observations with two arrays.\nThe short-wavelength array contains 91 pixels and the long-wavelength\narray 37 pixels, with approximately the same field of view, namely\n$\\sim 2.3'$. For a description of the instrument see Holland et\nal. (1998).\n\nWe performed dual wavelength imaging at 450 $\\mu $m and 850 $\\mu $m\nusing the 64-point jiggle mapping mode that allows Nyquist sampling of\nthe field of view. (\\cite{Ho98}). We employed the recommended rapid\nbeam switching at a frequency of $\\sim 8$ Hz and a beam throw of\n$150''$ in azimuth. The pointing and focus were monitored frequently\nusing Uranus and CRL 618, with an expected rms pointing error of $\\sim\n3''$. All maps of NGC 7469 were ``bracketed'' by sky-dips that were\nlater used to correct for atmospheric extinction. Conditions were\ngenerally excellent for sub-mm observations with typical opacities of\n$\\tau _{850}\\sim 0.1-0.2$ and $\\tau _{450}\\sim 0.45-0.55$ throughout\nour runs.\n\nThe beam characteristics and calibration gains (Jy V$ ^{-1}$ beam$\n ^{-1}$) were deduced from an extensive archive of beam maps of Uranus\n and CRL 618 taken during similar periods as our observations and with\n a similar beam-throw ($120''$). High S/N beam maps are particularly\n important for the calibration of 450 $\\mu $m images since the beam\n shape and the gain can change significantly as the dish thermally\n relaxes. All jiggle maps were flat-fielded, corrected for\n atmospheric extinction and edited for bad bolometers/integrations\n using the standard reduction package SURF (Jenness \\& Lightfoot\n 1998). Sky-noise was removed by using the bolometers in the outer\n ring of the two arrays (Jenness, Lightfoot \\& Holland 1998) which\n were assumed ``looking'' only at sky emission. This is a good\n assumption for NGC 7469 where most of its $ ^{12}$CO J=1--0 emission\n (and presumably most of the sub-mm emission from dust) lies within a\n $\\sim 4''$ radius (Tacconi \\& Genzel~1996, Tacconi et al. 2000).\n\n\nThe gain and beam characteristics at 850 $\\mu $m remained essentially\nthe same throughout the runs. This is further corroborated by the\nfact that the ``raw'' peak and integrated intensities of the NGC 7469\nimages at this wavelength agree to within $\\sim 10\\%$, which is the\nexpected calibration uncertainty. Hence we co-added all the\nnoise-weighted frames after subtracting a small gradient from one of\nthem, and then scale the final one with the single gain factor of $\\rm\nG_{850} =290$ Jy Volt$ ^{-1}$ beam$ ^{-1}$. The deduced beam-width is\n$\\Theta _{\\rm HPBW}^{(850)}\\sim 15''$.\n\n\n\n\n\n The 450~$\\mu $m beam maps revealed substantial gain variations ($\\sim\n40\\%$) between observations taken early in the first shift and the\nones taken later on, presumably due to the thermal relaxation of the\ndish. Thus before co-adding the images of NGC~7469 we scaled them by\nthe appropriate gains of $\\rm G_{450} =1170$ Jy Volt$ ^{-1}$ beam$\n^{-1}$ and $\\rm G_{450} =780$~Jy~Volt$ ^{-1}$~beam$ ^{-1}$. This\nscaling brought their peak and integrated intensities in agreement to\nwithin $\\sim 15\\%$, which is comparable to the calibration uncertainty\nexpected at 450 $\\mu $m. The average beam-width deduced for this\nwavelength is $\\Theta _{\\rm HPBW}^{(450)}\\sim 9''$.\n\n \n \n\n\nThe $ ^{12}$CO J=3--2 line at 345.796 GHz was observed towards the\nnucleus of NGC 7469 with receiver B3 on 1999 August 6. We used the\nDAS spectrometer with a bandwidth of 920~MHz ($\\sim 800$ km s$\n^{-1}$), and two independent channels centered on the line. The chop\nscheme employed was rapid beam switching with a 120$''$ azimuthal\nthrow at the recommended frequency of 1 Hz. The HPBW of the telescope\nbeam at this frequency is $\\sim 14''$ with a beam efficiency of $\\eta\n_{\\rm mb}=0.62$ (Matthews 1999). Typical system temperatures were of\nthe order of $\\rm T_{\\rm sys}\\sim 600$ K. After subtracting linear\nbaselines from all spectra their integrated line intensities were\nfound to agree to within $\\sim 10\\%$, the typical calibration\nuncertainty for receiver B3. We then co-added all of them to produce\nthe final spectrum.\n\n\n\\section{RESULTS} \n\n\nThe galaxy is detected as a bright sub-mm source at 850 $\\mu $m where\nit appears marginally resolved, as well as at 450~$\\mu $m where it\nclearly shows faint extended emission. We convolved a high-resolution\nmap of $ ^{12}$CO J=1--0 emission (Tacconi et al. 2000) from its\noriginal resolution of $\\sim 2.5''$ to the resolution of the 450 $\\mu\n$m map ($\\sim 9''$) and show them, together with the 850 $\\mu $m\nmap, in Figure 1.\n\n\\placefigure{fig1}\n\n\nThe correspondence between the bright 450 $\\mu $m and $ ^{12}$CO\nJ=1--0 emission is very good, suggesting that they both trace the same\nISM material. The high-resolution interferometric $ ^{12}$CO J=1--0\nmaps (Tacconi \\& Genzel 1996; Tacconi et al.~2000) show bright\nemission arising from a region with a diameter of $\\rm d\\sim 8''$,\nwhere an intense starburst is embedded (Wilson et al. 1991), hence\nthe presence of warm gas and dust is expected there. Indeed the\ncentral region of NGC 7469, besides hosting an AGN, also harbors\nseveral supergiant star formation regions containing numerous (few\n$\\times 10^4$) OB stars each (Genzel et al. 1995), whose intense UV\nlight and subsequent supernova explosions will warm and disrupt the\nmolecular clouds present. The warm dust of these clouds can easily\ndominate the global FIR and even the mm/sub-mm emission from this\ngalaxy. In principle the new sub-mm measurements allow for a better\nevaluation of the dust mass and temperature. Thus in Table 1 we\ncompile them together with available mm and FIR data and use them to\nmodel the dust emission SED, shown in Figure 2.\n\n\\vspace*{1.0cm}\n\n\n\\centerline{EDITOR: PLACE TABLE 1 HERE}\n\\vspace*{0.3cm}\n\n\n\\placefigure{fig2}\n\nThe reported mm/sub-mm fluxes at 1.3 mm and 850 $\\mu $m have been\ncorrected for non-dust emission from CO lines, which can be rather\nsignificant (see Appendix). The fitted dust temperature and mass are:\n$\\rm T_{\\rm d}\\sim 35$ K and $\\rm M_{\\rm d}=2.5\\times 10^{7}\\ M_{\\odot\n}$. It can be seen that a single dust component fits the data rather\nwell, except for wavelengths shortward of 60~$\\mu $m where the hot\ndust ($\\ga 300$ K) present in the central region (Cutri et al. 1984)\nmakes a significant contribution to the total flux but contains a\nnegligible fraction ($\\leq \\rm few \\times 10^{-4}$) of the total dust\nmass. From the $ ^{12}$CO J=1--0 map obtained by Tacconi et al.\n(2000), we find a total flux of $\\rm S_{\\rm CO}=(275\\pm 30)$~Jy~km~s$\n^{-1}$, which allows an estimate the global molecular mass from\n\n\\begin{equation}\n\\rm M(H_2) = 2.45\\times 10^3\\ X_{\\rm CO}\\ D^2\\ S_{\\rm CO}\n\\end{equation}\n\n\n\\noindent\nwhere D=66 Mpc and $\\rm X_{\\rm CO}\\sim 5\\ M_{\\odot }\\ (km\\ s^{-1}\\\npc^2)^{-1}$. This yields a mass of $\\rm M(H_2)\\approx 1.5\\times\n10^{10}\\ M_{\\odot }$ and $\\rm M(H_2)/M_{\\rm d}\\approx 600$, a typical\nvalue for IRAS galaxies (Young et al. 1986; Young et al. 1989; Stark\net al. 1986). Including the HI gas mass $\\rm M(HI)=5.7\\times 10^{9}\\\nM_{\\odot }$ (Mirabel \\& Wilson 1984) yields a total gas-to-dust ratio\nof~$\\sim 830$.\n\nThe presence of warm and dense molecular gas in the nucleus of NGC\n7469 is responsible for the strong $ ^{12}$CO J=3--2 line observed\ntowards it. The high resolution $ ^{12}$CO J=1--0 interferometer map\nallows for an estimate of the (J=3--2)/(J=1--0) line ratio in the\ninner $\\rm d\\sim 8''$ of this galaxy. This is possible since virtually\nall the bright $ ^{12}$CO J=1--0 emission lies within that region, and\nhence the $ ^{12}$CO J=3--2 emission with its higher excitation\nrequirements will have, at most, a similar size. Hence the observed\nmain-beam brightness of the J=3--2 transition can be expressed as\nfollows\n\n\\begin{equation}\n\\rm T_{\\rm mb} = \\left( \\rm 1-e^{\\rm -x^2} \\right)\\ T^{(\\rm w)}_{\\rm b }\n\\left(1+\\frac{e^{\\rm -x^2}}{1-e^{\\rm -x^2}} \\ \\rm C \\right)\n\\end{equation}\n\n\\noindent\nwhere $\\rm T^{(\\rm w)} _{\\rm b}$ is the brightness temperature of the\nwarm gas in the nucleus, $\\rm x=\\sqrt{ln2}\\ d/\\Theta_{\\rm HPBW}$ (a\ndisk source assumed), and $\\rm C = T^{(\\rm c)} _{\\rm r}/T^{(\\rm w)}\n_{\\rm r}$ is the ratio of radiation temperatures for J=3--2 of the\ncold and warm gas phase. The former dominates at larger\ngalactocentric distances in this galaxy (Papadopoulos \\&\nSeaquist~1998), and fills the rest of the 14$''$ beam.\n\n\nSubstituting $\\rm d=8''$ and $\\Theta _{\\rm HPBW}=14''$ we obtain $ \\rm\nT^{(\\rm w)} _{\\rm b} = 4.94\\left(1+3.94 \\rm C\\right)^{-1} T_{\\rm mb}$,\nwhich we plot in Figure 3 (for $\\rm C=0$) together with the $ ^{12}$CO\nJ=1--0 brightness temperature averaged over the inner diameter of\n$\\sim 8''$.\n\n\\placefigure{fig3}\n\n\nThe excellent agreement between the two spectral line profiles\n demonstrates that they arise from the same region, which the\n high-resolution $ ^{12}$CO J=1--0 maps (e.g. Tacconi \\& Genzel 1996)\n allow us to identify with the inner $8''$. The velocity-averaged\n $\\rm R_{32}=(3-2)/(1-0)$ ratio for that region is $\\rm R_{32}\\sim\n 1.1$ (C=0). If the typical physical characteristics of the cold\n phase, namely $\\rm n(H_2)\\approx 3\\times 10^2$ cm$ ^{-3}$ and $\\rm\n T_{\\rm kin}\\approx 10 $~K (Papadopoulos \\& Seaquist 1998), dominate\n beyond the central $8''$ while warm and dense gas ($\\rm\n n(H_2)>10^3$~cm$ ^{-3}$, $\\rm T_{\\rm kin}>20$ K) is present in the\n central region, then $\\rm C\\sim 0.030-0.045$. This yields a range\n $\\rm R_{32}\\sim 0.95-1.0$, which for a gaussian source brightness\n will be somewhat lower, namely $\\sim 0.80-0.85$.\n\n\nSuch high $\\rm R_{32}$ ratios are characteristic of an optically thick\nand thermalised J=3--2 transition at gas temperatures of $\\rm T_{\\rm\nkin}\\ga 30$ K, consistent with the deduced dust temperature of $\\sim\n35$ K. A simple Large Velocity Gradient (LVG) analysis\n(e.g. Richardson 1985) yields a variety of conditions that can produce\n$\\rm R_{32}\\sim 0.8-1.1$, all of them characterized by $\\rm T_{\\rm\nkin}\\ga 30$ K and with the most typical temperature being $\\sim 50$ K.\nThis suggests that most of the molecular ISM in the starburst nucleus\nof NGC 7469 is indeed warm with its dust emission dominating the\nglobal mm/sub-mm/FIR spectrum (Figure 2).\n\n\\section{Discussion}\n\n\nThe high $\\rm R_{32}$ ratio and gas temperature inferred for the\ncentral region of NGC 7469 are in sharp contrast with the low $\\rm\nR_{21}=(2-1)/(1-0)\\sim 0.5$ and $\\rm T_{\\rm kin}\\approx 10$ K\ncharacterizing the global CO emission from its disk (Papadopoulos \\&\nSeaquist 1998). Such steep excitation gradients in spiral galaxies,\nparticularly the ones with starburst nuclei, are expected and known to\nexist in numerous cases (Knapp et al 1980; Wall \\& Jaffe 1990; Wall et\nal. 1991; Eckart et al 1991; Harris et al. 1991; Wild et al. 1992;\nAalto et al. 1995). This is further corroborated by the new generation\nof mm and sub-mm bolometers that allow sensitive imaging of the dust\nemission out to large galactocentric distances and show large masses\nof cold dust ($\\rm T_{\\rm d}=10-15$~K) residing in spiral disks away\nfrom the nucleus (e.g. Neininger et al. 1996; Dumke et al. 1997;\nAlton et al. 1998; Papadopoulos \\& Seaquist~1999a).\n \n\nIt is often argued that such a cold dust component is responsible for\na systematic underestimate of dust mass when only FIR data are used.\nThis would naturally lead to the large $\\rm M(H_2)/M_{\\rm d}\\sim\n500-600$ ratios ($\\rm M(H_2+HI)\\sim 1000$ when HI is included) found\nfor spiral galaxies in contrast to $\\sim 100-150$ found for the Milky\nWay (e.g. Devereux \\& Young 1990 and references therein). On the\nother hand extragalactic $\\rm M(H_2)$ estimates are thought to be\naccurate to within a factor of $\\sim 2$ (Young \\& Scoville 1991), and\nparticularly for spirals to within $\\pm 30\\%$ (Devereux \\& Young\n1990). However recent sensitive sub-mm imaging at 450 $\\mu $m and 850\n$\\mu $m of IR-bright spirals like NGC 891 (Alton et al. 1998) and NGC\n1068 (Papadopoulos \\& Seaquist 1999a) reveals that the warm and cold\ndust are spatially well separated, with the former being concentrated\nmainly in the inner $\\la 2$ kpc where significant star formation\noccurs and the latter residing at larger galactocentric radii.\n \n\nThe case of NGC 1068 is particularly relevant since its host galaxy\nproperties are remarkably similar to NGC 7469 (Wilson et al. 1991),\nwith both galaxies harboring a central starburst and having similar\nFIR, $ ^{12}$CO J=1--0 and HI luminosities. The relative proximity of\nNGC 1068 allowed extensive multi-line CO and sub-mm imaging of its\ninner 2.5~kpc (Papadopoulos \\& Seaquist 1999a, 1999b) which showed\nthat the bulk of the gas and dust in that region is warm with $\\rm\nM(H_2)/M_{\\rm d}\\sim 330$. The latter is essentially identical to the\ntotal gas-to-dust ratio since most of the gas in the circumnuclear\nstarburst of NGC 1068 is molecular. This ratio is actually $\\sim\n30-40\\%$ higher still if the bright $ ^{12}$CO J=3--2 emission is\nsubtracted from the 850 $\\mu $m flux used to estimate the dust mass.\nIn the regions beyond the starburst nucleus of NGC 1068 emission from\ncold dust ($\\rm T_{\\rm d}\\sim 10-15$~K) dominates the sub-mm bands,\nwhile low-brightness $ ^{12}$CO J=1--0 and bright HI emission reveal\nthe diffuse H$_2$ and HI that make up the gas reservoir (Papadopoulos\n\\& Seaquist 1999a). Interestingly the total gas-to-dust ratio in\nthose regions is $\\sim 70-150$, close to the Galactic value.\n\n\n\n\nThe larger distance of NGC 7469 precludes a similar detailed study,\nhowever the high-resolution $ ^{12}$CO J=1--0 and 450 $\\mu $m maps\n(Figure 1) together with the lower limit of $\\sim 35$~K for the\ndust/gas temperature in its central 8$''$ allow for a firm lower limit\non the gas-to-dust ratio in that region. We measure $\\rm\nS_{450}(r\\leq 4'')= (0.80\\pm 0.08)$~Jy, probably a slight overestimate\nowing to the larger beam area at this wavelength coupling to a region\nsomewhat larger than the inner 8$''$, beyond which only faint sub-mm\nemission from cold dust is expected. The velocity-integrated $\n^{12}$CO J=1--0 line flux is $\\rm S_{\\rm CO}(r\\leq 4'')=(175\\pm\n25)$~Jy~km~s$ ^{-1}$, estimated from the original high resolution map.\nAssuming that H$_2$ dominates the gas phase in the starburst region, a\nGalactic $\\rm X_{\\rm CO}$, and $\\rm T_{\\rm d}=35$ K, yields a total\ngas-to-dust ratio of~$\\sim 500$.\n\n\nHence for both NGC 7469 and NGC 1068 it can be convincingly argued\nthat the high gas-to-dust ratios found for their IR-luminous\nstarbursting central regions are not due to the presence of\nsignificant amounts of cold dust but to an overestimate of the\nmolecular gas mass in such environments. In the case of NGC 7469 this\nconclusion is further supported by a dynamical study of its central\nregion concluding that $\\rm X_{\\rm CO}$ is $\\sim 1/5$ of the\nGalactic value (Genzel et al. 1995). This would bring the gas-to-dust\nratio estimated for that region in good accord with the Milky Way\nvalue with no need for an unaccounted mass of cold~dust.\n\n\n\n\n\\subsection{The systematic overestimate of $\\rm M(H_2)$ in starburst\nenvironments}\n\n\nThere has been mounting evidence that the Galactic value of $\\rm\nX_{\\rm CO}$ overestimates the molecular gas mass in the intense\nstarburst environments of luminous IR galaxies ($\\rm L_{\\rm FIR} >\n10^{11}\\ L_{\\odot }$ by a factor of $\\sim 5$ (Solomon et al. 1997;\nDownes \\& Solomon 1998). This seems to be due to a two-phase\ndifferentiation that the molecular gas undergoes in such environments\n(Aalto et al. 1995; Downes \\& Solomon 1998). The phase that dominates\nthe $ ^{12}$CO emission is diffuse, warm and possibly non\nself-gravitating, the latter being the main reason for the\noverestimate of molecular gas when a Galactic value for $\\rm X_{\\rm\nCO}$ is used.\n\n\n Indeed a standard expression for this conversion factor is (e.g.\nBryant \\& Scoville 1996)\n\n\\begin{equation}\n\\rm X_{\\rm CO}=2.1\\ \\frac{n^{1/2}}{\\rm T_{\\rm\nb}}\\ Q\\ M_{\\odot }\\ (K\\ km\\ s^{-1})^{-1}\n\\end{equation}\n\n\\noindent\nwhere n (cm$ ^{-3}$) is the average gas density and $\\rm T_{\\rm b}$\n(K) is the average brightness temperature of $ ^{12}$CO J=1--0 of the\nmolecular cloud ensemble. The factor $\\rm Q= \\delta V_{vir} /\\delta\nV$ accounts for the non-virial linewidth of the ``average'' cloud, for\nself gravitating clouds it is $\\rm Q=1$.\n\n\nFor typical conditions in the Galaxy, namely $\\rm Q\\approx 1$, $\\rm\nn\\approx 300$ cm$ ^{-3}$ and $\\rm T_{\\rm kin}\\approx 15$~K ($\\rm\nT_{\\rm b} \\approx 8$ K), one obtains $\\rm X_{\\rm CO}\\approx 5\\\nM_{\\odot }\\ (K\\ km\\ s^{-1})^{-1}$, the typical Galactic value. In the\ndiffuse molecular phase that is present in starburst nuclei, it can be\n$\\rm Q<1$ (e.g. Solomon et al. 1997), thus a Galactic $\\rm X_{\\rm\nCO}$ will overestimate the molecular gas mass present. Moreover, even\nin the case of self-gravitating clouds, a diffuse ($\\rm n\\approx 10^3$\ncm$ ^{-3}$) but warm phase ($\\rm T_{\\rm kin}\\sim 60$ K) dominating the\n$ ^{12}$CO J=1--0 emission will have $\\rm T_{\\rm b}=30-40$ K ($\\tau\n_{10}\\sim 2-4$) and thus yield a $\\rm X_{\\rm CO}$ factor that is $\\sim\n2-3$ times smaller than the Galactic value.\n\n\nIf such a gas phase is characteristic of the starburst regions in\n luminous IR galaxies, then a {\\it systematic} overestimate of H$_2$\n mass rather than an underestimate of dust mass is responsible for the\n high $\\rm M(H_2)/M_{\\rm d}$ ratios found for them. Because the\n effect is systematic it can produce both a high total gas-to-dust\n ratio and a small dispersion around its mean. Hence earlier claims\n that such small dispersion ($\\sim \\pm 30\\%$) observed in IR-luminous\n spirals (Devereux \\& Young 1990) argues in favor of a similar\n accuracy in molecular gas mass estimates are not supported by\n this~picture.\n\n\n\\subsection{The cold gas and dust in NGC 7469}\n\n\nThe global excitation of CO in NGC 7469 seems to be dominated by cold\nand diffuse molecular gas out to a scale of $\\rm d\\la 20''$\n(Papadopoulos \\& Seaquist 1998). A gaussian fit of the 850~$\\mu $m\nemission (Figure 1) yields a source size of $\\sim 17.2''\\times 18.5''$\n(FWHM), clearly larger than the beam at this wavelength. Considering\nthe geometric mean of $\\Theta _{\\rm s} \\sim 18''$ to be the observed\ndiameter of the source (assumed to be a disk), and for a gaussian beam\nwith $\\Theta_{\\rm HPBW}=15''$, we obtain an intrinsic source diameter\nof $\\rm d=\\left [2\\ (ln 2) ^{-1}\\ (\\Theta ^2 _{\\rm s}-\\Theta ^2 _{\\rm\nHPBW})\\right]^{1/2}\\sim 17''$. This is $\\sim 2$ times larger than the\nsize of the bright $ ^{12}$CO J=1--0 emission and comparable to the\nsource size seen at 450 $\\mu $m (Figure~1).\n\n\nIn NGC 1068 the warm gas/dust resides in the inner $\\rm d\\sim\n(2.7-3.4)$~kpc, which is comparable to the size of a similar region in\nNGC~7469, both regions containing an embedded starburst. Furthermore,\ngiven the similarities of the disk properties between these two\ngalaxies, it is reasonable to identify the extended faint sub-mm, $\n^{12}$CO J=1--0 emission in NGC~7469 with emission from cold dust/gas.\nIndeed simply scaling the total size of the faint sub-mm emission from\ncold dust in NGC 1068 ($\\sim 6$ kpc) to the distance of NGC~7469\nyields an angular size of $\\sim 20''$, closely matching the one\nobserved for the latter.\n\n\nIt is intriguing that faint $ ^{12}$CO J=1--0 emission is detected out\nto significantly larger radii than the inner radius of $\\rm r=4''$\n(Figure 1). Assuming that, as in NGC 1068, this emission ``marks''\ncold and diffuse H$_2$ coexisting with cold dust ($\\rm T_{\\rm\nd}=10-15$ K) and the bulk of HI, yields a ratio $\\rm\n[M(H_2+HI)]/M_{\\rm d} \\sim 50-160$, close to the Milky Way value.\n\n\n\\subsection{Warm versus cold gas/dust: sub-mm imaging and CO\nspectroscopy}\n\nIt is striking that in the spatially integrated dust emission of this\ngalaxy the cold dust is inconspicuous even after the inclusion of the\nsub-mm data. On the other hand its molecular gas counterpart dominates\nthe global excitation characteristics as revealed by the low $\n^{12}$CO (J=2--1)/(J=1--0) line ratio (Papadopoulos \\& Seaquist 1998).\n\n\nThis could simply be due to the fact that spectral line luminosity is\nsensitive to the local gas density as well as its temperature and\ntotal mass but only the latter two determine the continuum luminosity\nfrom dust (for a fixed gas-to-dust ratio). In other words two\nmolecular clouds with the same mass and gas/dust temperature will emit\nthe same dust continuum (optically thin case) but their CO line fluxes\ncan differ drastically if their average H$_2$ densities are different.\nThis will occur mainly in the density regime of sub-thermal excitation\nof the observed CO line(s).\n\nIn NGC 7469 the relative amounts of warm and cold dust can be\nestimated from the relation\n\n\\begin{equation}\n\\rm m= \\frac{M^{(c)} _{\\rm d}}{M^{(w)} _{\\rm d}} = \\left[ \\frac{\\rm e^{\\rm 32/T_{\\rm c}}-1}{\\rm e^{\\rm 32/T_{\\rm w}}-1}\\right] \\frac{\\rm S^{(\\rm c)} _{450}}{\n\\rm S^{(\\rm w)} _{450}},\n\\end{equation}\n\n\n\\noindent\nwhere (w) and (c) denote the quantities corresponding to the warm and\ncold dust respectively. It is $\\rm S^{(\\rm w)} _{450} = S_{450}(r\\leq\n4'') = 0.8$ Jy and $\\rm S^{(\\rm c)} _{450} = S_{450}(4''\\leq r\\leq\n11'') =0.5$ Jy. Hence for $\\rm T_{\\rm w}\\ga 35$ K and $\\rm T_{\\rm\nc}=10-15$ K we obtain $\\rm m \\ga 3-10$.\n\n\nEven for $\\rm m\\sim 10$, the spatially averaged sub-mm emission will\nnot necessarily reveal the presence of the cold component. Indeed,\nsince the ratio $\\rm r= S_{450}/S_{850}$ is temperature-sensitive when\n$\\rm T_{\\rm d}\\la 30$ K, it is expected to differ if a cold dust\ncomponent is present along with the warm one. Assuming spatial\naveraging of the emission from the two dust components the observed r\ncan be written as follows\n\n\n \n\\begin{equation}\n\\rm r= r_{\\rm w} \\left[ \\frac{\\rm 1+m\\ f_{450} (T_w, T_c)}{\\rm 1 + m\\ f_{850}(T_w, T_c)}\\right],\n\\end{equation}\n\n\\noindent\nwhere $\\rm r_{\\rm w}$ is the ratio corresponding to warm dust alone and, \n\n\\begin{equation}\n\\rm f_{\\lambda}(T_w, T_c) = \\frac{\\rm e^{\\rm T_{\\lambda }/T_{\\rm w}}-1}{\n\\rm e^{\\rm T_{\\lambda }/T_{\\rm c}}-1}, \\ \\ \nT_{\\lambda } = \\frac{\\rm\\ h\\ c}{\\lambda \\ k}.\n\\end{equation}\n\n\n\nFor $\\rm T_{\\rm w}=40$ K, $\\rm T_{\\rm c}=10$ K and $\\rm m= 10$ we\nobtain $\\rm r \\approx 0.70\\times r_{\\rm w}$, which is barely\ndiscernible from $\\rm r_{\\rm w}$ given that the value of r carries a\n$\\sim 20\\%$ uncertainty due to the calibration uncertainties of SCUBA\nat 450 $\\mu $m and 850 $\\mu $m.\n\n\nOn the other hand besides temperature the spectral line ratios are\nalso sensitive to the local gas density. Thus a cold {\\it and\nsub-thermally excited} molecular gas phase may dominate the observed\nglobal line ratio even in the presence of a warm and thermalized\nphase. For example, the global $\\rm R_{21}=(2-1)/(1-0)$ ratio can be\nexpressed as\n\n\n\\begin{equation}\n\\rm R_{21} = R^{(w)} _{21}\\left[ \\frac{\\rm 1+m\\ x\\ (\\rm R^{\\rm (c)} _{21}/R^{\\rm (w)} _{21})}{\\rm 1 + m\\ x}\\right],\n\\end{equation} \n\n\\noindent\nwhere $\\rm x = X^{(\\rm w)}_{\\rm CO}/X^{(\\rm c)} _{\\rm CO}$ is the\nratio of the CO(1--0)-to-H$_2$ conversion factors for the two gas\nphases. Assuming $\\rm x\\sim 1/5$, $\\rm m\\sim 10$ and, $\\rm R^{(\\rm\nw)} _{21} \\sim 1$, we obtain $\\rm R_{21}\\sim 1/3\\ (1+2\\ R^{(\\rm c)}\n_{21})$.\n\n\nIn NGC 7469 it is $\\rm R_{21}\\approx 0.5$ (Papadopoulos \\& Seaquist\n1998), hence the cold-phase ratio will be $\\rm R^{\\rm (c)}\n_{21}\\approx 0.25$, and for $\\rm T_{\\rm kin}=10$ K, the latter\ncorresponds to densities of $\\rm n(H_2)\\approx 10^2$ cm$ ^{-3}$. For\nthe same temperature but thermalized and optically thick $ ^{12}$CO\nJ=2--1 it is $\\rm R^{\\rm (c)} _{21}\\approx 0.8$, yielding $\\rm\nR_{21}\\approx 0.85$ which is significantly larger than observed.\n\n\nThe aforementioned simple analysis demonstrates the significance of\ncombining sub-mm and CO observations in evaluating the physical\nconditions and the mass of molecular gas. The sub-mm measurements\noffer an independent means of estimating gas mass under the assumption\nof a canonical gas-to-dust ratio of $\\sim 100$. For H$_2$-dominated\ngas this mass can then be compared to the one deduced from the $\n^{12}$CO J=1--0 luminosity and the $\\rm X_{\\rm CO}$ conversion factor\nand hence the influence of the physical conditions on $\\rm X_{\\rm CO}$\ncan be assessed. On the other hand, if a cold and diffuse molecular\ngas phase is present along with a warm one but only global averages\nare available, CO line ratios can be more sensitive to the presence of\nthe cold ISM phase than sub-mm intensity ratios.\n\n\n \n\\section{Conclusions} \n \n \nWe presented sensitive 850 $\\mu $m, 450 $\\mu $m maps of the Seyfert 1\ngalaxy NGC 7469 and a measurement of the $ ^{12}$CO J=3--2 line\ntowards its starbursting central region. Our main conclusions can be\nsummarized as follows\n\n1. The FIR/sub-mm/mm spectrum of this source is dominated by a warm\ndust component with a temperature of $\\sim 35$ K and a global\nmolecular gas-to-dust ratio of $\\sim 600$, both typical for IR-luminous \nspirals. Including the atomic gas mass yields a total gas-to-dust ratio\nof $\\sim 800$.\n \n\n\n2. The warm dust and gas lies in the inner 8$''$ ($\\sim $2.5 kpc)\n where a starburst is embedded. In this region we find no evidence\n for a significant mass of cold dust, yet the ratio of the mainly\n molecular gas to the dust mass is $\\sim 500$, still five times larger\n than the Galactic value. We argue that this is the result of a\n systematic overestimate of $\\rm H_2$ mass by a factor of $\\sim 5$\n when a Galactic value for $\\rm X_{\\rm CO}=M(H_2)/L_{\\rm CO}$ is used\n in starburst environments.\n\n\n3. On larger scales (radius $\\ga 1.2$ kpc) the ISM in NGC 7469 is\ndominated by cold, sub-thermally excited gas where the faint 450 $\\mu\n$m and $ ^{12}$CO J=1--0 emission originate. The gas-to-dust ratio for\nthis phase, is $\\sim 50-150$; in better accord with the\nMilky~Way~value.\n \n\n\\subsection{Acknowledgments}\n\nWe would like to thank Linda Tacconi for providing us with data prior\nto publication, Henry Matthews for obtaining the SCUBA maps, and Remo\nTilanus for conducting the CO observations on our\nbehalf. P. P. Papadopoulos is supported by the ``Surveys with the\nInfrared Space Observatory'' network set up by the European Commission\nunder contract FMRX-CT96-0086 of its TMR programme.\n\n\n\\newpage\n \n\n\n\n\n\\appendix\n\n\\section{Spectral line contribution to mm/sub-mm bands}\n\n\nIn mm and sub-mm continuum observations one must correct for non-dust\n emission contributions. The most significant comes from molecular\n spectral lines and can reach up to $\\sim 60\\%$ of the total flux\n observed with a typical bolometer bandwidth (Gordon 1995). In warm\n cores of Orion such line contributions are found to be of the order\n of $\\sim 30\\%$ in 850~$\\mu $m and 450 $\\mu $m bands (Johnstone \\&\n Bally 1999 and references therein). However in the extragalactic\n domain a typical beam of a mm/sub-mm telescope samples areas of\n several hundred parsecs, and the contributions from warm cores ($\\leq\n 1$ pc) in star forming regions are negligible because of the\n resulting spatial dilution. Over such scales only the emission from\n the three lowest rotational transitions of $ ^{12}$CO can be\n ubiquitous and bright, since these transitions can be easily excited\n in the general conditions prevailing in the ISM in quiescent or\n starburst environments.\n\n \n\nIn the case of NGC 7469 we expect that all the significant spectral\nline emission from the $ ^{12}$CO J=2--1 (1.3 mm band) and $ ^{12}$CO\nJ=3--2 (850 $\\mu $m band) lines arises from the region of bright $\n^{12}$CO J=1--0 emission in the central 8$''$ where the starburst\nresides. In the case of the 1.3 mm band only line-free channels were\nused to produce the continuum map (Tacconi, private communication).\nThe 850 $\\mu $m band includes the $ ^{12}$CO J=3--2 line whose\ncontribution can be estimated from our observation of this line\ntowards the nucleus, namely\n\n\\begin{equation}\n\\rm S_{850 } ^{\\rm (dust)} = S_{850 } - \\frac{2\\ k \\ \\nu _{\\circ }\n^3}{c^3\\ \\Delta \\nu _{B}}\\left(\\frac{\\rm x^2}{\\rm 1-e^{\\rm\n-x^2}}\\right) I_{\\rm mb}\\ \\Omega _{\\rm mb}\n\\end{equation}\n\n\n\\noindent\nwhere $\\rm I_{\\rm mb}$ (K km s$ ^{-1}$) is the velocity-integrated\nmain-beam brightness of $ ^{12}$CO J=3--2, $\\nu _{\\circ } = 345.796$\nGHz, and $\\Omega _{\\rm mb}$ is the gaussian beam area at this\nfrequency. The term in the parenthesis corrects for the beam-source\ngeometrical coupling assuming a disk source of diameter d, where $\\rm\nx=\\sqrt{ln2}\\ d/\\Theta _{\\rm HPBW}$, and $\\Delta \\nu _{\\rm B}$ is the\nbolometer bandwidth.\n\n\nFor $ ^{12}$CO J=3---2 in NGC 7469 we measured $\\rm I_{\\rm mb}=(77\\pm\n8)$ K km s$ ^{-1}$ (Figure 3), hence for $\\Theta _{\\rm HPBW}=14''$,\n$\\Delta \\nu _{\\rm B}= 30$ GHz (Holland, private communication) and\n$\\rm d=8''$ we obtain a line contribution of $\\Delta \\rm S= 63$ mJy,\nwhich amounts to $\\sim 40\\%$ of the total flux at 850 $\\mu $m. The $\n^{13}$CO J=3--2 is expected to have $\\la 0.1$ of the $ ^{12}$CO J=3--2\nflux, and hence contribute $\\la 4\\%$ of the total flux in 850 $\\mu $m.\n\n\n In the case of the 450 $\\mu $m band the only CO line that may\ncontribute to the observed flux is $ ^{13}$CO J=6--5 at 661.067\nGHz. 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P. 1997, \\aap, 328, 471\n\n\n%\\bibitem[Krugel et al. 1990]{Kru90} Krugel E., Steppe, H., \\& Chini,\n% R. 1990, \\aap, 229, 17 \n\n\\bibitem[Matthews 1999]{Ma99} Matthews, H. in ``Receiver B3 User Information'',\n1999, (http://www.jach.hawaii.edu/JACpublic/JCMT/)\n\n\n\n\\bibitem[Meixner et al. 1990]{Mei90} Meixner, M., Puchalsky, R., Blitz,\nL., Wright, M., \\& Heckman, T. 1990, \\apj, 354, 158\n\n\n\\bibitem[Miller \\& Antonucci 1983]{Mi83} Miller, J., \\& Antonucci, R.\n1983, \\apj, 271, L7\n\n\n\\bibitem[Mirabel \\& Wilson 1984]{Mi84} Mirabel I. F., \\& Wilson A. S. 1984,\n\\apj, 277, 22\n\n\n\\bibitem[Neininger et al. 1996]{Ne96} Neininger, N., Gu\\'elin, M., Garc\\'ia-Burillo, S., Zylka, R., \\& Wielebinski, R. 1996 \\aap, 310,~725\n\n\n%\\bibitem[Nieten et al. 1999]{Ni99} Nieten, C., Dumke, M., Beck, R., \\&\n%Wielebinski, R. 1999, \\aap, 347, L5\n\n\\bibitem[Papadopoulos \\& Seaquist 1998]{Pa98} Papadopoulos, P. P., \\&\nSeaquist, E. R. 1998, \\apj, 492, 521\n\n\n\\bibitem[Papadopoulos \\& Seaquist 1999]{Pa99} Papadopoulos, P. P., \\&\nSeaquist, E. R. 1999a, \\apj, 514, L95\n\n\n\\bibitem[Papadopoulos \\& Seaquist 1999]{Pa99} Papadopoulos, P. P. \\&\nSeaquist, E. R. 1999b, \\apj, 516, 114\n\n\n\\bibitem[Soifer et al. 1989]{Soi89} Soifer, B. T., Boehmer, L., Neugebauer, G.,\n\\& Sanders, D. B. 1989, \\aj, 98, 766\n\n\n\\bibitem[Sandell 1997]{San97} Sandell, G. 1998, The SCUBA mapping\ncookbook, A first step to proper map reduction.\n\n\\bibitem[Solomon \\& Barrett 1991]{So91} Solomon, P. M., \\& Barrett J. W. 1991, \nin IAU Symp. 146, Dynamics of Galaxies and Molecular Cloud Distribution\n(Dordrecht: Kluwer), 235\n\n\\bibitem[Solomon et al. 1997]{So97} Solomon, P. M., Downes, D.,\nRadford, S. J. E., \\& Barett, J. W. 1997, \\apj, 478, 144\n\n\\bibitem[Stark et al. 1986]{St86} Stark, A. A., Knapp, G. R., Bally, J.,\nWilson, R. W., Penzias, A. A., \\& Rowe, H. E. 1986, \\apj, 310, 660\n\n\n\\bibitem[Tacconi \\& Genzel 1996]{Ta96} Tacconi, L. J., \\& Genzel, R. 1996\nin ``Science with Large Millimetre Arrays'', pg. 125, ESO Astrophysics\nSymposia, Springer (Ed. P. A. Shaver)\n\n\n\\bibitem[Tacconi, Genzel, Gallimore \\& Tacconi-Garman]{Ta99} Tacconi, L. J., \nGenzel, R., Gallimore, J. \\& Tacconi-Garman L. E. 2000, \\apj, \\ (in press)\n\n\n\\bibitem[Richardson 1985]{Ric85} Richardson, K. J. 1985, PhD thesis, \nDepartment of Physics, Queen Mary College, University of London\n\n\n\\bibitem[Wall \\& Jaffe 1990]{WaJa90} Wall, W. F., \\& Jaffe, D. T. 1990 \\apj, 361, L45 \n\n\\bibitem[Wall et al. 1991]{Wal91} Wall, W. F., Jaffe, D. T., Israel, F. P., \n\\& Bash, F. N. 1991 \\apj, 380, 384\n\n\n\\bibitem[Wild et al. 1992]{Wild92} Wild, W., Harris, A. I., Eckart, A., Genzel, R., Graf, U. U., Jackson, J. M., Russell, A. P. G., \\& Stutzki, J. 1992, \\aap, 265, 447 \n\n\\bibitem[Wilson et al. 1991]{Wi91} Wilson, A. S., Helfer, T. T., \nHaniff, C. A., \\& Ward, M. J. 1991, \\apj, 381, 79\n\n\\bibitem[Young et al. 1986]{Yo86} Young, J. S., Schloerb, F. P., Kenney,\nJ. D., \\& Lord, S. D. 1986, \\apj, 304, 443\n\n\\bibitem[Young et al. 1989]{Yo89} Young, J. S., Xie, S., Kenney, J. D.,\n\\& Rice, W. L. 1989, \\apjs, 70, 699\n\n\\bibitem[Young \\& Scoville 1991]{Yo91} Young, J. S., \\& Scoville, N. Z. 1991\n\\araa, 29, 581\n\n\\end{thebibliography}{}\n\n\n\n\\newpage\n\n\n\\figcaption{Top: the 850 $\\mu $m map with a FWHM= 15$''$ beam shown at\nthe lower left, the contours are $(-3, 3, 6, 9, 12, 15, 18, 21, 24,\n27, 30)\\times \\sigma _{850}$, with $\\sigma _{850} = 5$ mJy beam$\n^{-1}$. \\\\ Bottom: the 450 $\\mu $m map (contours) overlaid to the\nintegrated $ ^{12}$CO J=1--0 emission (grey scale) at a common\nresolution of 9$''$ (FWHM beam shown at the bottom left). The contours\nare $(-4, 4, 6, 8, 10, 14, 16, 18)\\times \\sigma_{450 }$, with $\\sigma\n_{450 }= 40$ mJy beam$ ^{-1}$ and the grey scale is I=6--200 Jy beam$\n^{-1}$ km s$ ^{-1}$ ($\\sigma (\\rm I)= 1\\rm \\ Jy\\ beam ^{-1}\\ km\\\ns^{-1}$) \\\\ The map center is at RA: 23$ ^{\\rm h}$ 03$ ^{\\rm m}$ 15$\n^{\\rm s}$.6, Dec: +08$^{\\circ }$ 52$'$ 26$''$ (J2000).\n\\label{fig1}}\n\n\n\\figcaption{A $\\chi ^2$-fitted SED for the mm/sub-mm/FIR data of NGC\n7469 (Table 1). An optically thin isothermal dust reservoir has been\nassumed with an emissivity law of $\\alpha=2$ and emissivity at 200\n$\\mu $m (1196 GHz) of $\\rm k _{\\circ }= 10 $ cm$ ^{2}$ gr$ ^{-1}$\n(Hildebrand 1983). The flux at 25 $\\mu $m is not used in the fit.\n\\label{fig2}}\n\n\n\\figcaption{The $ ^{12}$CO J=1--0 and J=3--2 brightness temperatures\nfor the inner $8''$ of NGC~7469 (see text). The thermal rms\nuncertainty across the band is $\\rm \\delta T_{\\rm rms} (1-0)=30 $ mK, and\n$\\rm \\delta T_{\\rm rms} (3-2)=40$ mK.\n\\label{fig3}}\n\n\n\\newpage\n\n\\centerline{\\large Table 1}\n\\vspace*{0.5cm}\n\\centerline{\\large NGC 7469: The mm, sub-mm and FIR data}\n\\begin{center}\n\\begin{tabular}{ c c c }\\hline\\hline\n\nWavelength & Flux & Reference \\\\ \\hline\n\n1.3 mm & $19\\pm 5$ mJy & Tacconi et al. 1999 $ ^{\\rm a}$ \\\\\n850 $\\mu $m & $91 \\pm 13$ mJy & this work $ ^{\\rm b}$ \\\\\n450 $\\mu $m & $1.30\\pm0.14$ Jy & this work $ ^{\\rm b}$ \\\\\n100 $\\mu $m & $34.9\\pm 0.6$ Jy & Soifer et al. 1989 \\\\\n60 $\\mu $m & $27.7\\pm 0.04$ Jy & `` `` \\\\ \n25 $\\mu $m & $5.84\\pm 0.05$ Jy & `` `` \\\\ \\hline\n\\end{tabular}\n\\end{center}\n\n\\noindent\n$ ^{\\rm a}$ Derived from the 1.3 mm continuum map for a radius of $\\rm\nr=4''$ that contains all the mm emission and corrected\nfor non-thermal emission using the data from Wilson et al. 1991.\n\n\n\\noindent\n$ ^{\\rm b}$ Fluxes are estimated for a radius of $\\rm r= 11''$ and the\n appropriate error-beam corrections (Sandell 1997) are $\\rm f\n _{850}=0.80$, $\\rm f _{450}=1.05-1.10$, derived from Uranus and CRL\n 618 maps. The 850 $\\mu $m flux has also been corrected for\n contribution from the $ ^{12}$CO J=3--2 line (see Appendix). The\n errors reported include (besides the thermal rms errors) a $\\sim\n $10\\% (850 $\\mu $m) and a $\\sim $15\\% (450~$\\mu $m) calibration\n uncertainty.\n\n\n\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002277.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\n\\bibitem[Aalto et al. 1995]{Aa95} Aalto, S., Booth, R. S., Black,\nJ. H., \\& Johansson, L. E. B. 1995, \\aap, 300, 369\n\n\\bibitem[Alton et al. 1998]{A98} Alton, P. B., Bianchi, S., Rand, R. J.,\nXilouris, E. M., Davies, J. I., \\& Trewhella, M. 1998, \\apj, 507, L125\n\n\n\n\\bibitem[Bryant \\& Scoville 1996]{Br96} Bryant, P. M., \\& Scoville, N. Z.\n1996, \\apj, 457, 678\n\n\n\\bibitem[Cutri et al. 1984]{Cu84} Cutri, R. M., Rudy, R. J., Rieke, G. H., \nTokunaga, A. T., \\& Willner, S. P. 1984, \\apj, 280, 521\n\n\n\\bibitem[Devereux \\& Young]{Dv90} Devereux, N. A., \\& Young, J. S. 1990, \n\\apj, 359, 42\n\n\\bibitem[Downes \\& Solomon 1998]{Do98} Downes, D., Solomon, P. M. 1998, \\apj, \n507, 615\n\n\n\\bibitem[Dumke et al. 1997]{Du97} Dumke, M., Braine, J., Krause, M., \nZylka, R., Wielebinski, R., \\& Gu\\'elin M. 1997, \\aap, 325, 124\n\n\n\\bibitem[Eckart et al. 1991]{Eck91} Eckart, A., Cameron, M., Jackson, J. M., Genzel, R., Harris, A. I., Wild, W., \\& Zinnecker, H. 1991 \\apj, 372, 67\n\n\n\\bibitem[Genzel et al. 1995]{Gen95} Genzel, R., Weitzel, L. E., Tacconi-Garman,\nL. E., Blietz, M., Cameron, M., Krabbe, A., \\& Lutz, D. 1995, \\apj, 444, 129\n\n\n\\bibitem[Gordon et al. 1995]{Go95} Gordon, M. A. 1995, \\aap, 301, 853\n\n\n\\bibitem[Harris et al. 1991]{Har91} Harris, A. I., Hills, R. E., Stutzki, J., Graf, U. U., Russel, A. P. G., \\& Genzel, R. 1991, \\apj, 382, L75\n\n\n\\bibitem[Hildebrand, R. H. 1983]{Hi83} Hildebrand, R. H. 1983, \\mnras, 24, 267\n\n\n\\bibitem[Holland et al. 1998]{Ho98} Holland. W. S., Robson, E. I.,\nGear, W. K., Cunningham, C. R., Lightfoot, J. F., Jenness, T., Ivison,\nR. J., Stevens, J. A., Ade, P. A. R., Griffin, M. J., Duncan W. D.,\nMurphy J. A., \\& Naylor, D. A. 1998 \\mnras, 303, 659\n\n\n\\bibitem[Knapp et al. 1980]{Knap80} Knapp, G. R., Phillips, T. G., Huggins, P. J., Leighton, R. B., \\& Wannier, P. G. 1980 \\apj, 240, 60\n\n\n\\bibitem[Jenness~\\&~Lightfoot~1998]{Jen98a} Jenness, T., \\& Lightfoot,\nJ. F. 1998 in SURF-SCUBA User Reduction Facility, User's manual\n\n\n\\bibitem[Jenness, Lightfoot \\& Holland 1998]{Jen98b} Jenness, T.,\nLightfoot, J. F., \\& Holland, W. S. 1998, astro-ph/9809120\n\n\n\n\\bibitem[Johnstone \\& Bally]{Jon99} Johnstone, D., \\& Bally, J. 1999,\n\\apj, 510, L49\n\n\\bibitem[Krolik 1990]{Kr90} Krolik, J. H. in ``The Interstellar Medium\nin Galaxies'', pg 239, Kluwer Academic Publishers, H. A. Thronson Jr.,\n\\& J. M. Shull (Eds)\n\n\\bibitem[Israel 1997]{Is97} Israel, F. P. 1997, \\aap, 328, 471\n\n\n%\\bibitem[Krugel et al. 1990]{Kru90} Krugel E., Steppe, H., \\& Chini,\n% R. 1990, \\aap, 229, 17 \n\n\\bibitem[Matthews 1999]{Ma99} Matthews, H. in ``Receiver B3 User Information'',\n1999, (http://www.jach.hawaii.edu/JACpublic/JCMT/)\n\n\n\n\\bibitem[Meixner et al. 1990]{Mei90} Meixner, M., Puchalsky, R., Blitz,\nL., Wright, M., \\& Heckman, T. 1990, \\apj, 354, 158\n\n\n\\bibitem[Miller \\& Antonucci 1983]{Mi83} Miller, J., \\& Antonucci, R.\n1983, \\apj, 271, L7\n\n\n\\bibitem[Mirabel \\& Wilson 1984]{Mi84} Mirabel I. F., \\& Wilson A. S. 1984,\n\\apj, 277, 22\n\n\n\\bibitem[Neininger et al. 1996]{Ne96} Neininger, N., Gu\\'elin, M., Garc\\'ia-Burillo, S., Zylka, R., \\& Wielebinski, R. 1996 \\aap, 310,~725\n\n\n%\\bibitem[Nieten et al. 1999]{Ni99} Nieten, C., Dumke, M., Beck, R., \\&\n%Wielebinski, R. 1999, \\aap, 347, L5\n\n\\bibitem[Papadopoulos \\& Seaquist 1998]{Pa98} Papadopoulos, P. P., \\&\nSeaquist, E. R. 1998, \\apj, 492, 521\n\n\n\\bibitem[Papadopoulos \\& Seaquist 1999]{Pa99} Papadopoulos, P. P., \\&\nSeaquist, E. R. 1999a, \\apj, 514, L95\n\n\n\\bibitem[Papadopoulos \\& Seaquist 1999]{Pa99} Papadopoulos, P. P. \\&\nSeaquist, E. R. 1999b, \\apj, 516, 114\n\n\n\\bibitem[Soifer et al. 1989]{Soi89} Soifer, B. T., Boehmer, L., Neugebauer, G.,\n\\& Sanders, D. B. 1989, \\aj, 98, 766\n\n\n\\bibitem[Sandell 1997]{San97} Sandell, G. 1998, The SCUBA mapping\ncookbook, A first step to proper map reduction.\n\n\\bibitem[Solomon \\& Barrett 1991]{So91} Solomon, P. M., \\& Barrett J. W. 1991, \nin IAU Symp. 146, Dynamics of Galaxies and Molecular Cloud Distribution\n(Dordrecht: Kluwer), 235\n\n\\bibitem[Solomon et al. 1997]{So97} Solomon, P. M., Downes, D.,\nRadford, S. J. E., \\& Barett, J. W. 1997, \\apj, 478, 144\n\n\\bibitem[Stark et al. 1986]{St86} Stark, A. A., Knapp, G. R., Bally, J.,\nWilson, R. W., Penzias, A. A., \\& Rowe, H. E. 1986, \\apj, 310, 660\n\n\n\\bibitem[Tacconi \\& Genzel 1996]{Ta96} Tacconi, L. J., \\& Genzel, R. 1996\nin ``Science with Large Millimetre Arrays'', pg. 125, ESO Astrophysics\nSymposia, Springer (Ed. P. A. Shaver)\n\n\n\\bibitem[Tacconi, Genzel, Gallimore \\& Tacconi-Garman]{Ta99} Tacconi, L. J., \nGenzel, R., Gallimore, J. \\& Tacconi-Garman L. E. 2000, \\apj, \\ (in press)\n\n\n\\bibitem[Richardson 1985]{Ric85} Richardson, K. J. 1985, PhD thesis, \nDepartment of Physics, Queen Mary College, University of London\n\n\n\\bibitem[Wall \\& Jaffe 1990]{WaJa90} Wall, W. F., \\& Jaffe, D. T. 1990 \\apj, 361, L45 \n\n\\bibitem[Wall et al. 1991]{Wal91} Wall, W. F., Jaffe, D. T., Israel, F. P., \n\\& Bash, F. N. 1991 \\apj, 380, 384\n\n\n\\bibitem[Wild et al. 1992]{Wild92} Wild, W., Harris, A. I., Eckart, A., Genzel, R., Graf, U. U., Jackson, J. M., Russell, A. P. G., \\& Stutzki, J. 1992, \\aap, 265, 447 \n\n\\bibitem[Wilson et al. 1991]{Wi91} Wilson, A. S., Helfer, T. T., \nHaniff, C. A., \\& Ward, M. J. 1991, \\apj, 381, 79\n\n\\bibitem[Young et al. 1986]{Yo86} Young, J. S., Schloerb, F. P., Kenney,\nJ. D., \\& Lord, S. D. 1986, \\apj, 304, 443\n\n\\bibitem[Young et al. 1989]{Yo89} Young, J. S., Xie, S., Kenney, J. D.,\n\\& Rice, W. L. 1989, \\apjs, 70, 699\n\n\\bibitem[Young \\& Scoville 1991]{Yo91} Young, J. S., \\& Scoville, N. Z. 1991\n\\araa, 29, 581\n\n\\end{thebibliography}"
}
] |
astro-ph0002278
|
LOW FREQUENCY RADIO PULSES FROM GAMMA-RAY BURSTS?
|
[
{
"author": "Vladimir V. Usov"
}
] |
Gamma-ray bursts, if they are generated in the process of interaction between relativistic strongly magnetized winds and an ambient medium, may be accompanied by very short pulses of low-frequency radio emission. The bulk of this emission is expected to be at the frequencies of $\sim 0.1-1$ MHz and cannot be observed. However, the high-frequency tail of the low-frequency radio emission may reach a few ten MHz and be detected, especially if the strength of the magnetic field of the wind is extremely high. \keywords{gamma-rays: bursts - radio emission: pulses}
|
[
{
"name": "mypaper.tex",
"string": "\\documentstyle[12pt,aaspp4]{article}\n\n\\received{2000 February 14}\n\n\\begin{document}\n\n\\title{LOW FREQUENCY RADIO PULSES FROM GAMMA-RAY BURSTS?}\n\n\\author{Vladimir V. Usov}\n\n\\affil{Department of Condensed-Matter Physics,\nWeizmann Institute of Science, Rehovot\n76100, Israel}\n\n\\author{Jonathan I. Katz}\n\n\\affil{Department of Physics and McDonnell Center for the Space Sciences,\nWashington University, St. Louis, Mo. 63130}\n\n\\authoremail{fnusov@weizmann.weizmann.ac.il, katz@wuphys.wustl.edu}\n\n\\date{}\n\n\\begin{abstract}\nGamma-ray bursts, if they are generated in the process of interaction\nbetween relativistic strongly magnetized winds and an ambient\nmedium, may be accompanied by very short pulses of low-frequency \nradio emission. The bulk of this emission is expected to be at\nthe frequencies of $\\sim 0.1-1$ MHz and cannot be observed. However,\nthe high-frequency tail of the low-frequency radio emission may reach\na few ten MHz and be detected, especially if the strength of \nthe magnetic field of the wind is extremely high.\n\\keywords{gamma-rays: bursts - radio emission: pulses}\n\n\\end{abstract}\n\n\\newpage\n\n\\section{Introduction}\nThe prompt localization of gamma-ray bursts (GRBs) by\nBeppoSAX led to the discovery of X-ray/optical/radio afterglows and \nassociated host galaxies. Subsequent detections of\nabsorption and emission features at high redshifts ($0.43\\leq z \\leq \n3.42$) in optical afterglows of GRB and their host galaxies \nclearly demonstrate that at least some of the GRB sources lie at \ncosmological distances (for reviews, see \\cite{Piran99}; \\cite{Vietri99}).\n\nA common feature \nof all acceptable models of cosmological $\\gamma$-ray bursters is that a\nrelativistic wind is a source of GRB radiation. The Lorentz factor,\n$\\Gamma_0$, of such a wind is about $10^2-10^3$ or\neven more (e.g., \\cite{Fenimore93}; \\cite{Harding97}).\nA very strong magnetic field may be in the plasma \noutflowing from cosmological $\\gamma$-ray bursters (\\cite{Usov94}; \n\\cite{Blackman96}; \\cite{Vietri96}; \\cite{Katz97}; \\cite{Meszaros97}).\nA relativistic, strongly magnetized wind interacts with an ambient medium \n(e.g. an ordinary interstellar gas) and decelerates.\nIt was pointed out (\\cite{Meszaros92}) that such an interaction, assumed to\nbe shock-like, may be responsible for generation of cosmological GRBs. \n\nThe interaction between a relativistic, strongly magnetized wind and\nan ambient plasma was studied numerically by Smolsky \\& Usov (1996,\n2000) and Usov \\& Smolsky (1998). These studies showed that\nabout 70\\% of the wind energy is transferred to the ambient plasma\nprotons that are reflected \nfrom the wind front. The other $\\sim 30$\\% of the wind energy losses \nis distributed between high-energy electrons and low-frequency \nelectromagnetic waves that are generated at the wind front because of\nnonstationarity of the wind---ambient plasma interaction (see below).\nHigh-energy electrons, accelerated at the wind front \nand injected into the region ahead of the front, generate \nsynchro-Compton radiation in the fields of the low-frequency \nwaves. This radiation closely resembles synchrotron radiation and can \nreproduce the non-thermal radiation of GRBs observed in \nthe Ginga and BATSE ranges (from a few KeV to a few MeV).\n\n\\cite{Ginzburg73} and \\cite{Palmer93} suggested that GRB might be sources of\nradio emission, and that it might be used to determine their distances and,\nthrough the dispersion measure, the density of the intergalactic plasma.\nHere we consider some properties of the low-frequency waves generated at the\nwind front. We argue that coherent emission by the high-frequency tail of\nthese waves may be detected, in addition to the high-frequency (X-ray and\n$\\gamma$-ray) emission of GRBs, as a short pulse of low-frequency radio\nemission (\\cite{Katz94,Katz99}).\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\section{Low-frequency electromagnetic waves generated at the wind front}\n\\par\nOur mechanism for production of short pulses of low-frequency\nradio emission from relativistic, strongly magnetized wind-generated \ncosmological GRBs applies very generally. For the sake of concreteness, we\nconsider wind parameters that are natural in a GRB model that involves a\nfast rotating compact object like a millisecond pulsar or dense transient\naccretion disc with a surface magnetic field $B_s \\sim\n10^{15}-10^{16}$ G (\\cite{Usov92}; \\cite{Blackman96}; \\cite{Katz97};\n\\cite{Kluzniak98}; \\cite{Spruit99}).\n\nIn this model the rotational\nenergy of compact objects is the energy source of cosmological GRBs.\nThe electromagnetic torque transfers this energy on a time scale of \nseconds to the energy of a Poynting flux-dominated wind that flows away \nfrom the object at relativistic speeds, $\\Gamma_0\\simeq 10^2-10^3$\n(e.g., \\cite{Usov94}). The wind structure at a time $t\\gg\\tau_{_\\Omega}$\nis similar to a shell with radius $r\\simeq ct$ and thickness of\n$\\sim c\\tau_{_\\Omega}$, where $\\tau_{_\\Omega}$ is the characteristic\ndeceleration time of the compact object's rotation, or the dissipation time\nof a transient accretion disc.\n\nThe strength of the magnetic field at the front of the wind may be as high as\n\n\\begin{equation}\nB\\simeq B_s \\frac {R^3}{r_{\\rm lc}^2r}\n\\simeq 10^{15}\\frac Rr\\left(\n\\frac{B_{_S}}{ 10^{16}\\,\\rm{G}}\\right) \\left(\\frac\\Omega\n{10^4\\,\\rm{s}^{-1}}\\right)^2\\rm{G},\n\\label{Bobj}\n\\end{equation}\n \n\\noindent\nwhere $R\\simeq 10^6$ cm is the radius of the compact object,\n$\\Omega\\simeq 10^4$ is the angular velocity at the moment of its formation\nand $r_{\\rm lc}=c/\\Omega=3\\times 10^6(\\Omega /10^4\\,$s$^{-1})$~cm\nis the radius of the light cylinder. \n\nThe distance at which deceleration of the wind due to its interaction \nwith an ambient gas becomes important is \n\n\n\\begin{equation}\nr_{\\rm{dec}}\\simeq 10^{17}\\left({\\frac{Q_{\\rm{kin}}}{10^{53}\\,\n\\rm{ergs}}}\\right)^{1/3}\\left({\\frac n{1\\,\\rm{cm}^{-3}}}\\right)^{-1/3}\\left(\n{\\frac{\\Gamma_0}{10^2}}\\right)^{-2/3}\\rm{cm},\n\\label{rdec}\n\\end{equation}\n\n\\noindent \nwhere $n$ is the density of the ambient gas and $Q_{\\rm{kin}}$\nis the initial kinetic energy of the outflowing wind. \nEq. (2) assumes spherical symmetry; for beamed flows $Q_{\\rm{kin}}$ is\n$4\\pi$ times the wind energy per steradian.\nAt $r\\sim r_{\\rm dec}$, the main part of $Q_{\\rm kin}$ is\nlost by the wind in the process of its inelastic interaction with the\nambient medium, and the GRB radiation is generated.\n\nSubstituting $r_{\\rm{dec}}$ for $r$ into equation (\\ref{Bobj}), we\nhave the following estimate for the magnetic field at the wind\nfront at $r\\sim r_{\\rm {dec}}$:\n\n\\begin{equation}\nB_{\\rm{dec}}\\simeq 10^4 \\epsilon_B^{1/2} \\left(\\frac{B_s}{10^{16}\\,\\rm{G}}\n\\right)\\left(\\frac\\Omega{10^4\\,\\rm{s}^{-1}}\\right)^2\\left(\n\\frac{Q_{\\rm{kin}}}{10^{53}\\,\\rm{ergs}}\\right)^{-1/3}\\left(\\frac\nn{1\\,\\rm{cm}^{-3}}\\right)^{1/3}\\left({\\frac{\\Gamma_0}{10^2}}\\right)\n^{2/3}\\rm{G}\\,,\n\\label{Bdec}\n\\end{equation}\n \n\\noindent\nwhere we have introduced a parameter $\\epsilon_B < 1$ which gives the\nfraction of the wind power remaining in the magnetic field at the\ndeceleration radius. For plausible parameters of cosmological $\\gamma$-ray\nbursters, $B_{_S} \\simeq 10^{16}$~G, $\\Omega\\simeq 10^4$~s$^{-1}$,\n$Q_{\\rm{kin}}\\simeq 10^{53}$~ergs, $\\Gamma_0\\simeq 10^2-10^3$ and $n\\sim 1$\ncm$^{-3}$, from equation (\\ref{Bdec}) we have $B_{\\rm{dec}}\\simeq (1-5)\n\\times 10^4 \\epsilon_B^{1/2}$~G. \n\nFor consideration of the interaction between a\nrelativistic magnetized wind and an ambient gas, it is convenient\nto switch to the co-moving frame of the outflowing plasma (the wind frame).\nWhile changing the frame, the magnetic and electric fields in the wind\nare reduced from $B$ and $E=B[1-(1/\\Gamma_0^2)]^{1/2}\n\\simeq B$ in the frame of\nthe $\\gamma$-ray burster to $B_0\\simeq B/\\Gamma_0$ and $E_0=0$\nin the wind frame. This is analogous to the the well-known transformation\nof the Coulomb field of a point charge: purely electrostatic in the frame of\nthe charge, but with $E \\approx B$ in a frame in which the charge moves\nrelativistically. Using this and equation (\\ref{Bdec}), for\ntypical parameters of cosmological $\\gamma$-ray bursters we have \n$B_0\\simeq (0.5-1)\\times 10^2 \\epsilon_B^{1/2}$~G at $r\\simeq r_{\\rm dec}$.\n\n\nIn the wind frame, the ambient gas moves to the wind front with the Lorentz \nfactor $\\Gamma_0$ and interacts with it. The main parameter which describes \nthe wind---ambient gas interaction is the ratio of the energy densities of \nthe ambient gas and the magnetic field, $B_0$, of the wind \n\n\\begin{equation}\n\\alpha = 8\\pi n_0m_pc^2(\\Gamma_0-1)/B^2_0\\,, \n\\label{alpha}\n\\end{equation}\n\n\\noindent \nwhere $n_0=n\\Gamma_0$ is the density of the ambient gas in the wind frame\nand $m_p$ is the proton mass. \n \nAt the initial stage of the wind outflow, $r\\ll r_{\\rm dec}$, $\\alpha \\ll\n1$, but it increases in the process of the wind expansion as $B_0$\ndecreases. When $\\alpha$ is $\\gtrsim \n\\alpha_{\\rm cr}\\simeq 0.4$ (at $r\\sim r_{\\rm dec})$, \nthe interaction between the wind and the ambient gas is strongly\nnonstationary, and effective acceleration of electrons and generation of\nlow-frequency waves at the wind front both begin \n(\\cite{Smolsky96}, 2000; \\cite{Usov98}). For $0.4\\lesssim \\alpha\n\\lesssim 1$, the mean Lorentz factor of outflowing high-energy electrons\n$\\Gamma_e^{\\rm{out}}$ accelerated at the wind front and the mean field of\nlow-frequency waves $\\langle B_w \\rangle$ weakly depend on $\\alpha$ (see\nTable 1) and are approximately given by\n\n\\begin{equation}\n\\langle\\Gamma_e^{\\rm {out}}\\rangle \\simeq 0.2\n(m_p/m_e)\\Gamma_0 \\,\\,\\,\\,{\\rm and}\\,\\,\\,\\,\n\\langle B_w\\rangle =(\\langle B_z\\rangle^2 + \n\\langle E_y\\rangle^2)^{1/2}\\simeq 0.1 B_0\n\\label{Gammamean} \n\\end{equation}\n\n\\noindent \nto within a factor of 2, where $B_z$ and $E_y$ are the magnetic and\nelectric field components of the waves. The mechanism of generation\nof these waves is coherent and consists of the following:\nAt the wind front there is a surface \ncurrent that separates the wind matter with a very strong magnetic \nfield and the ambient gas where the magnetic field strength is\nnegligible. This current varies in time because of nonstationarity of\nthe wind - ambient gas interaction and generates low-frequency waves.\n\n\\section{Possible detection}\n\nAt $\\alpha\\sim 1$, for the bulk of high-energy electrons in the region\nahead of the wind front the characteristic time of their synchrotron energy\nlosses is much less than the GRB duration. In this case, the luminosity\nper unit area of the wind front in $\\gamma$-rays is\n$l_\\gamma\\simeq m_ec^3n\\langle \\Gamma_e^{\\rm {out}}\\rangle$ while the same\nluminosity in low-frequency waves is $l_w\\simeq c\\langle B_w\\rangle^2/4\\pi$.\nUsing these, the ratio of the luminosity in low-frequency waves \nand the $\\gamma$-ray luminosity is \n\n\\begin{equation}\n\\delta ={l_w\\over l_\\gamma}={2\\over \\alpha}{m_p\\over m_e}\n{\\langle B_w\\rangle^2\\over B_0^2}\n{\\Gamma_0\\over \\langle \\Gamma_e^{\\rm {out}}\\rangle}\\,.\n\\label{delta}\n\\end{equation}\n\n\\par\nFrom Table 1, we can see that the GRB light curves in both \n$\\gamma$-rays and low-frequency waves have maximum when $\\alpha$ is \nabout 0.4, and the maximum flux in low-frequency waves is\nabout two times smaller than the maximum flux in $\\gamma$-rays ($\\delta\n\\simeq 0.5$). At $\\alpha > 0.4$ the value of $\\delta$ decreases with\nincreasing $\\alpha$. Therefore, we expect that the undispersed duration\n$\\Delta t_r$ of the low-frequency pulse to be somewhat\nsmaller than the GRB duration, and the energy\nfluence in low-frequency waves to be roughly an order of magnitude smaller\nthan the energy fluence in $\\gamma$-rays.\nThe rise time of the radio pulse is very short because\nthat the value of $\\langle B_w\\rangle^2$ increases very fast when $\\alpha$\nchanges from 0.3 to 0.4 (see Table I). \n\n\nFigure~1 shows a typical spectrum of low-frequency waves generated at\nthe wind front in the wind frame. \nThis spectrum has a maximum at the frequency $\\omega_{\\rm max}'$ \nwhich is about three times higher than the proton\ngyrofrequency $\\omega_{Bp}=eB_0 /m_pc\\Gamma_0$\nin the wind field $B_0$. Taking into account the Doppler effect,\nin the observer's frame the spectral maximum for\nlow-frequency waves is expected to be at the frequency\n\n\\begin{equation}\n\\nu_{\\rm max}\\simeq {2\\Gamma_0\\over {1+z}}{\\omega_{\\rm max}'\\over 2\\pi}\n\\simeq {eB_0 \\over (1+z)m_pc} \\simeq {1\\over {1+z}}\n\\left({B_0\\over 10^2\\,{\\rm G}}\\right)\\,\\,\\,{\\rm MHz}\\,,\n\\label{numax}\n\\end{equation}\n \n\\noindent\nwhere $z$ is the cosmological redshift. For typical parameters of\ncosmological GRBs, $B_0\\simeq (0.5-1)\\times 10^2 \\epsilon_B^{1/2}$ G and\n$z\\simeq 1$, we have $\\nu_{\\rm max}\\simeq (0.2-0.5)\\epsilon_B^{1/2}$ MHz.\nUnfortunately, the bulk of the low-frequency waves is at low frequencies,\nand cannot be observed. However, their high-frequency tail may be detected.\n\n\nAt high frequencies, $\\nu > \\nu_{\\rm max}$,\nthe spectrum of low-frequency waves may be fitted by a power law\n(\\cite{Smolsky00}):\n\n\\begin{equation}\n|B(\\nu )|^2\\propto \n\\nu ^{-\\beta}\\,,\n\\label{Bnu}\n\\end{equation}\n\n\\noindent\nwhere $\\beta\\simeq 1.6$. In the simulations of the wind---ambient\ngas interaction (\\cite{Smolsky96}, 2000; \\cite{Usov98})\nboth the total numbers of particles of the ambient gas and the sizes of \nspatial grid cells are restricted by computational reasons, so that the \nthe spectrum (\\ref{Bnu}) is measured reliably\nonly at $\\nu\\lesssim 10\\nu_{\\rm max}$. The amplitudes of the computed\noscillations with $\\nu > 10\\nu_{\\rm max}$ are so small ($\\lesssim (0.2-0.3)\n\\langle B_w\\rangle$) that they cannot be distinguished from computational\nnoise (\\cite{Smolsky96}). Future calculations with greater computational\nresources may alleviate this problem.\n\nThe value of $\\nu_{\\rm max}$ depends on many parameters of \nboth the GRB bursters and the ambient gas around them, \nand its estimate, $\\nu_{\\rm max}\\simeq (0.2-0.5)\\epsilon_B^{1/2}$ MHz, \nis uncertain within a factor of 2--3 or so. In the most extreme case\nin which $\\nu_{\\rm max}$ is as high as a few~MHz, the high-frequency tail of \nlow-frequency waves may be continued up to $\\sim 30$ MHz where ground-based\nradio observations may be performed. In this case, the energy fluence in a\npulse of radio emission at $\\nu\\sim 30$ MHz may be as high\nas a few percent of the GRB energy fluence in $\\gamma$-rays. \n\nA pulse of low-frequency radio emission is strongly affected by intergalactic \nplasma dispersion in the process of its propagation. At the frequency \n$\\nu$, the radio pulse retardation time with respect to a GRB is\n\n\\begin{equation}\n\\tau(\\nu)={D\\over v} -{D\\over c}={e^2 \\int n_e\\,d\\ell \\over 2\\pi m_ec\\nu^2}\n\\simeq 1.34\\times 10^{-3}{\\int n_e\\,d\\ell \\over \\nu^2}\\,\\,\\,{\\rm s}\\,,\n\\label{taunu}\n\\end{equation}\n\n\\noindent\nwhere $\\int n_e\\,d\\ell$ is the intergalactic dispersion measure in\nelectrons/cm$^2$, $v=cn$ is the group velocity of\nradio emission, $n=1-(e^2 n_e/2\\pi m_e\\nu^2)$ is the refractive index\nand $\\nu$ in Hz. From equation (\\ref{taunu}), for the plausible\nparameters of $n_e \\simeq 10^{-6}$ cm$^{-3}$ and a distance of $10^{28}$ cm,\nat $\\nu = 30$ MHz we have $\\tau(\\nu)\\simeq 10^4$ s. This is time\nenough to steer a radio telescope for the radio pulse detection. In equation\n(\\ref{taunu}), we neglected the radio pulse retardation time in our Galaxy,\nwhich is typically one or two orders of magnitude less than that in the\nintergalactic gas.\n\nThe observed duration of the low-frequency pulse at the frequency $\\nu$\nin the bandwidth $\\Delta \\nu$ is\n\n\\begin{equation}\n\\Delta t_{obs}(\\nu,\\,\\Delta \\nu )= {\\rm max}\\,[\\Delta t_r,\\,2\n(\\Delta \\nu /\\nu)\\tau (\\nu)]\\,.\n\\label{Deltatnu}\n\\end{equation}\n\n\\noindent\nFor plausible parameters, $\\nu \\sim 30$ MHz, $\\Delta\\nu\\sim 1$ MHz,\n$\\tau(\\nu )\\sim 10^4$ s and $\\Delta t_r\\sim 1-10^2$ s, we have\n$\\Delta t_{obs}(\\nu,\\,\\Delta \\nu )\\sim 7\\times 10^2$ s; the observed\nduration of low-frequency radio pulses is determined \nby intergalactic plasma dispersion, except for extremely long GRBs. \n\nIt is now possible to estimate, given assumed values for the magnetic field,\nthe amplitude of the signal produced. We also assume that the plasma field\ncouples efficiently to the free space radiation field. For a radio fluence\n${\\cal E}_R = \\delta {\\cal E}_{GRB}$ and a radio fluence spectral density\n\\begin{equation}\n{\\cal E}_\\nu = \\cases{0 & {\\rm for}\\,\\,\\,\\,\n$\\nu < \\nu_{max}$\n,\\cr {\\beta -1 \\over \\nu_{max}}\n{\\cal E}_R \\left(\n{\\nu \\over \\nu_{max}}\\right)^{-\\beta} & {\\rm for}\\,\\,\\,\\,\n$\\nu \\ge \\nu_{max}$\n,\\cr}\n\\label{Rfluence}\n\\end{equation}\nthe radio spectral flux density is\n\\begin{equation}\nF_\\nu = \\cases{{\\delta (\\beta - 1) \\over \\Delta t_r \\nu_{max}} \\left({\\nu\n\\over \\nu_{max}}\\right)^{-\\beta} {\\cal E}_{GRB} & {\\rm for}\\,\\,\\,\\,\n${2 \\Delta \\nu \\over \\nu}\n\\tau(\\nu) < \\tau_r$\n,\\cr {\\delta (\\beta - 1) \\over 2 \\Delta \\nu \\tau(\\nu)}\n\\left({\\nu \\over \\nu_{max}}\\right)^{1 - \\beta} \n{\\cal E}_{GRB} & {\\rm for}\\,\\,\\,\\,\n${2 \\Delta\n\\nu \\over \\nu} \\tau(\\nu) \\ge \\tau_r$\n.\\cr}\n\\label{Rflux} \n\\end{equation}\nFor the latter (dispersion-limited) case with the parameters ${\\cal E}_{GRB}\n= 10^{-4}$ erg cm$^{-2}$, $\\delta = 0.1\\epsilon_B$, $\\beta = 1.6$,\n$\\nu_{max} = 0.3$ MHz, $\\nu = 30$ MHz, $\\Delta \\nu = 1$ MHz, $\\tau(\\nu) =\n10^4$ s we find $F_\\nu \\approx 2 \\times 10^6 \\epsilon_B^{(\\beta+1)/2}$ Jy.\n\nThe appropriate value of $\\epsilon_B$ is very uncertain. In some models it\nmay be $O(1)$, but for GRB with sharp subpulses its value is limited by the\nrequirement that the magnetic stresses not disrupt the thinness of the\ncolliding shells (\\cite{Katz97}). For subpulses of width $\\zeta$ of the GRB\nwidth this suggests $\\epsilon_B < \\zeta^2$; typical estimates are $\\zeta\n\\sim 0.03$ and $\\epsilon_B < 10^{-3}$, leading to $F_\\nu \\lesssim 10^2$ Jy.\n\nThese large values of $F_\\nu$ may be readily detectable, although the\nassumed values of $\\epsilon_B$ are very uncertain. There are additional\nuncertainties. We have assumed that the radio pulse spectrum (11) is valid\nup to a frequency $\\nu\\simeq 30$ MHz that may be hundreds of times higher\nthan $\\nu_{\\rm max}$. As discussed above, the spectrum (11) of\nlow-frequency waves is calculated directly only at $\\nu\\lesssim 10\n\\nu_{\\rm max}$. At $\\nu > 10 \\nu_{\\rm max}$, the spectrum must be\nextrapolated, with unknown confidence, from the calculations. The radio\nspectral flux density at $\\nu\\simeq 30$ MHz may therefore be less than the\npreceding estimates. However, even in this case the very high sensitivity\nof measurements at radio frequencies may permit the detection of coherent\nlow-frequency radio emission from GRB.\n\n\\section{Discussion} \n\nIn this Letter, we have shown that GRBs may be accompanied by very \npowerful short pulses of low-frequency radio emission. For detection of\nthese radio pulses it may be necessary to perform observations at lower\nfrequencies than are generally used in radio astronomy, which are limited by\nthe problem of transmission through and refraction by the ionosphere. In\nparticular, observations from space are free of ionospheric refraction and\nare shielded by the ionosphere from terrestrial interference. Although even\nharder to predict, detection from the ground at higher frequencies may also\nbe possible.\n\nSpace observations are possible at frequencies down to that at which the\ninterstellar medium becomes optically thick to free-free absorption. This\nfrequency is\n\\begin{equation}\n\\nu_{abs} = 1.0 \\times 10^6 \\left\\langle{n_{0.03}^2 \\over T_3^{3/2}}\n\\right\\rangle^{1/2} \\vert\\csc b^{II}\\vert^{1/2}\\ {\\rm Hz},\n\\label{ISMabs}\n\\end{equation}\nwhere $n_{0.03} \\equiv n_e/(0.03$ cm$^{-3}$) and $T_3 \\equiv\nT/10^{3\\,\\circ}$K (\\cite{Spitzer62}), $n_e$ and $T$ are the interstellar\nelectron density and temperature, respectively, and $b^{II}$ is the Galactic\nlatitude. The expression $\\langle\\rangle$ may be $O(1)$, but could be\nsubstantially larger if the electrons are strongly clumped or cold.\nOn the other hand, although much of the interstellar volume is filled with\nvery hot ($10^{6\\,\\circ}$K) and radio-transparent gas, this probably\ncontains very little of the electron column density. Intergalactic\nabsorption poses a somewhat less restrictive condition if the medium is hot\n($10^{6\\,\\circ}$K), as generally assumed.\n\nAt these low frequencies, and even at\ntens of MHz, interstellar scintillation (\\cite{Goodman97}) will be very\nlarge. Observations of coherent radio emission from GRB would not only\nilluminate the physical conditions in their radiating regions, but would\ndetermine (through the dispersion measure) the mean intergalactic plasma\ndensity and (through the scintillation) its spatial structure.\n\nThe flux density implied by Eq. (\\ref{Rflux}) appears impressively large,\nbut it applies only to the brief period when the dispersed signal is\nsweeping through the bandwidth $\\Delta\\nu$ of observation, so that it is\nunclear if it is, in fact, excluded by the very limited data\n(\\cite{Cortiglioni81}) available. Further, the extrapolation of the\nradiated spectrum to $\\nu \\gg \\nu_{max}$ is very uncertain. Finally, we\nhave also not considered the (difficult to estimate) temporal broadening of\nthis brief transient signal by intergalactic scintillation, which will both\nreduce its amplitude and broaden its time-dependence.\n\nSearches for radio pulses started about 50 years ago, prior to the discovery\nof GRBs. During wide beam studies of ionospheric scintillations, simultaneous\nbursts at 45 MHz of $10-20$ s duration were reported by Smith (1950)\nat sites 160 km apart. These events were detected at night, approximately\nonce a week. The origin of these bursts was never determined. \nThe results of Smith (1950) were not confirmed by subsequent observations\nat frequencies of 150 MHz or higher.\n\nModern observations (\\cite{Dessenne96} at 151 MHz; \\cite{Balsano98} at 74\nMHz; \\cite{Benz98} broadband; see \\cite{Frail98} for a review) set upper\nbounds to the brightnesses of some GRB at comparatively high frequencies.\nThese bounds are not stringent, and do not exclude extrapolations of the\nlower frequency fluxes suggested here. There are few data at lower\nfrequencies.\n\n\\acknowledgments\n\nWe thank D. M. Palmer for discussions.\nV.V.U. acknowledges support from MINERVA Foundation, Munich, Germany.\n\n\\clearpage\n\n\\begin{thebibliography}{}\n\\bibitem[Balsano et al. 1998]{Balsano98} Balsano, R. J., {\\it et al.}\n1998, Gamma-Ray Bursts: 4th Huntsville Symposium, Huntsville, Ala., eds. C.\nA. Meegan, R. D. Preece \\& T. M. Koshut (New York: AIP) p. 585\n\n\\bibitem[Baring and Harding 1997]{Harding97} Baring, M. G., \\&\nHarding, A. K. 1997, \\apj, 491, 663 \n\n\\bibitem[Benz \\& Paesold 1998]{Benz98} Benz, A. O. \\& Paesold, G. 1998,\n\\aap, 329, 61\n\n\\bibitem[Blackman, Yi, \\& Field 1996]{Blackman96} Blackman,~E.~G.,\nYi, I., \\& Field,~G.~B. 1996, \\apj, 473, L79\n\n\\bibitem[Cortiglioni et al. 1981]{Cortiglioni81} Cortiglioni,~S.,\nMandolesi,~N., Morigi,~G., Ciapi,~A., Inzani,~P., \\&\nSironi,~G. 1981, ApSS, 75, 153\n\n\\bibitem[Dessenne et al. 1996]{Dessenne96} Dessenne, C. A.-C., {\\it\net al.} 1996, \\mnras, 281, 977\n\n%\\bibitem[Djorgovski et~al. 1998]{D98} Djorgovski, S. G. 1998,\n%\\apj, 508, L21\n\n\\bibitem[Fenimore, Epstein, \\& Ho 1993]{Fenimore93} \nFenimore,~E.~E., Epstein,~R.~I., \\& Ho,~C. 1992, A\\&AS, 97, 59\n\n%\\bibitem[Frail et~al. 1997]{Frail97} Frail,~D.~A., Kulkarni,~S.~R.,\n%Nicastro,~L., Feroci,~M., \\& Taylor,~G.~B. 1997, \\nat, 389, 261\n\\bibitem[Frail 1998]{Frail98} Frail, D. A. 1998, Gamma-Ray Bursts: 4th\nHuntsville Symposium, Huntsville, Ala., eds. C. A. Meegan, R. D. Preece, T.\nM. Koshut (New York: AIP) p. 563\n\n%\\bibitem[Galama et~al. 1998]{Galama98} Galama,~T.~J., et al. 1998, \\nat,\n%395, 670\n\n\\bibitem[Ginzburg (1973)]{Ginzburg73} Ginzburg, V. L. 1973, \\nat, 246, 415\n\n\\bibitem[Goodman 1997]{Goodman97} Goodman,~J. 1997, New Astr., 2, 449\n\n\\bibitem[Katz 1994]{Katz94} Katz,~J.~I. 1994, \\apj, 422, 248\n\n\\bibitem[Katz 1997]{Katz97} Katz,~J.~I. 1997, \\apj, 490, 633\n\n\\bibitem[Katz 1999]{Katz99} Katz,~J.~I. 1999, The Largest Explosions Since\nthe Big Bang: Supernovae and Gamma-Ray Bursts, eds. M. Livio, K. Sahu \\& N.\nPanagia (Baltimore: STScI) p. 43 (astro-ph/9908217)\n\n\\bibitem[Klu\\'{z}niak \\& Ruderman 1998]{Kluzniak98}\nKlu\\'{z}niak,~W., \\& Ruderman,~M. 1998, \\apj, 505, L113\n\n%\\bibitem[Kouveliotou et~al. 1996]{Kouveliotou96} Kouveliotou, C., et al.\n%1996, AIP Conf. Proc. 384, Gamma-Ray Bursts, eds. C.~Kouveliotou,\n%M.F.~Briggs, \\& G.J.~ Fishman (New York: AIP), 42\n\n%\\bibitem[Kulkarni et~al. 1998b]{Kulkarni98b} Kulkarni,~S.~R., et al.\n%1998b, \\nat, 395, 663\n\n%\\bibitem[Kulkarni et~al. 1999]{Kulkarni99} Kulkarni,~S.~R., et al.\n%1999, \\nat, 398, 389\n\n\\bibitem[M\\'esz\\'aros \\& Rees 1992]{Meszaros92} M\\'esz\\'aros,~P. \\&\nRees,~M.~J. 1992, \\apj, 397, 570\n\n\\bibitem[M\\'esz\\'aros \\& Rees 1997]{Meszaros97} M\\'esz\\'aros,~P. \\&\nRees,~M.~J. 1997, \\apj, 482, L29\n\n%\\bibitem[Niemeyer \\& Woosley 1997]{Niemeyer97}Niemeyer,~J.~C.\n%\\& Woosley,~S.~E. 1997, \\apj, 475, 740\n\n\\bibitem[Palmer (1993)]{Palmer93} Palmer, D. M. 1993, \\apjl, 417, L25\n\n\\bibitem[Piran 1999]{Piran99} Piran,~T. 1999, Phys. Reports, 314, 575\n\n\\bibitem[Smith 1950]{Smith50} Smith, F. G. 1950, \\nat, 165, 422\n\n\\bibitem[Smolsky \\& Usov 1996]{Smolsky96} Smolsky, M. V., \\&\nUsov, V. V. 1996, \\apj, 461, 858\n\n\\bibitem[Smolsky \\& Usov 2000]{Smolsky00} Smolsky, M. V., \\&\nUsov, V. V. 2000, \\apj, in press\n\n\\bibitem[Spitzer 1962]{Spitzer62} Spitzer, L., 1962, Physics of Fully\nIonized Gases (New York: Interscience)\n\n\\bibitem[Spruit 1999]{Spruit99} Spruit, H. C. 1999, A\\&A, 341, L1\n\n\\bibitem[Usov 1992]{Usov92} Usov,~V.~V. 1992, \\nat, 357, 472\n\n\\bibitem[Usov 1994]{Usov94} Usov,~V.~V. 1994, MNRAS, 267, 1035\n\n%\\bibitem[Usov \\& Chibisov 1975]{Usov75} Usov,~V.~V., \\&\n%Chibisov,~G.~V. 1975, Soviet Astron., 19, 115\n\n\\bibitem[Usov \\& Smolsky 1998]{Usov98} Usov, V. V., \\& Smolsky, M. V.\n1998, Phys. Rev. E, 57, 2267\n\n\\bibitem[Vietri 1996]{Vietri96} Vietri, M. 1996, \\apj, 471, L95\n\n\\bibitem[Vietri 1999]{Vietri99} Vietri,~M. 1999, astro-ph/9911523\n\n\\end{thebibliography}\n\n\\clearpage\n\n\\begin{table}\n\\caption{Derived parameters of simulations for both high-energy electron\nLorentz factor $\\Gamma_e^{\\rm{out}}$ and low-frequency electromagnetic wave\namplitudes $B_w$ and their power ratio $\\delta$ in the region ahead of the\nwind front}\n\\label{Results}\n$$\n\\begin{array}{ccccc}\n\\rm{\\alpha} &{\\langle\\Gamma^{\\rm {out}}_e\\rangle\\over\\Gamma_0}&\n\\langle B_w^2\\rangle \\over B_0^2 \n& \\delta\\\\\n\\tableline\n\\rm {0.2} & 9.5 & 10^{-5} & 0.017 \\\\\n\\rm {0.3} & 37 & 1.4\\times 10^{-4} & 0.048 \\\\\n\\rm {0.4} & 396 & 0.021 & 0.49 \\\\\n\\rm {0.5} & 339 & 0.02 & 0.42 \\\\\n\\rm {0.57} & 296 & 0.011 & 0.24 \\\\\n\\rm {0.67} & 276 & 0.008 & 0.16 \\\\\n\\rm {1} & 214 & 0.005 & 0.084 \\\\\n\\rm {1.33} & 137 & 1.6\\times 10^{-3} & 0.032 \\\\\n\\rm {2} & 75 & 4.4\\times 10^{-4} & 0.01 \\\\\n\\rm {4} & 47 & 1.2\\times 10^{-4} & 0.0024 \\\\\n\\end{array}\n$$\n\n\\tablecomments{The accuracy of the derived parameters is $\\sim 20$\\%\nat $0.4\\lesssim \\alpha\\lesssim 2$ and decreases out of this range of\n$\\alpha$.} \n\n\\end{table}\n\n\\clearpage\n\n\\bigskip\n\n\\noindent\nFIGURE CAPTION\n\n\\noindent\nFig. 1. Power spectrum of low-frequency electromagnetic waves generated\nat the front of the wind in the wind frame in a simulation with\n$B_0=300$ G, $\\Gamma_0=300$, and $\\alpha=2/3$. The spectrum is fitted\nby a power law (dashed line).\n\n\\end{document}\n"
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{
"name": "astro-ph0002278.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[Balsano et al. 1998]{Balsano98} Balsano, R. J., {\\it et al.}\n1998, Gamma-Ray Bursts: 4th Huntsville Symposium, Huntsville, Ala., eds. C.\nA. Meegan, R. D. Preece \\& T. M. Koshut (New York: AIP) p. 585\n\n\\bibitem[Baring and Harding 1997]{Harding97} Baring, M. G., \\&\nHarding, A. K. 1997, \\apj, 491, 663 \n\n\\bibitem[Benz \\& Paesold 1998]{Benz98} Benz, A. O. \\& Paesold, G. 1998,\n\\aap, 329, 61\n\n\\bibitem[Blackman, Yi, \\& Field 1996]{Blackman96} Blackman,~E.~G.,\nYi, I., \\& Field,~G.~B. 1996, \\apj, 473, L79\n\n\\bibitem[Cortiglioni et al. 1981]{Cortiglioni81} Cortiglioni,~S.,\nMandolesi,~N., Morigi,~G., Ciapi,~A., Inzani,~P., \\&\nSironi,~G. 1981, ApSS, 75, 153\n\n\\bibitem[Dessenne et al. 1996]{Dessenne96} Dessenne, C. A.-C., {\\it\net al.} 1996, \\mnras, 281, 977\n\n%\\bibitem[Djorgovski et~al. 1998]{D98} Djorgovski, S. G. 1998,\n%\\apj, 508, L21\n\n\\bibitem[Fenimore, Epstein, \\& Ho 1993]{Fenimore93} \nFenimore,~E.~E., Epstein,~R.~I., \\& Ho,~C. 1992, A\\&AS, 97, 59\n\n%\\bibitem[Frail et~al. 1997]{Frail97} Frail,~D.~A., Kulkarni,~S.~R.,\n%Nicastro,~L., Feroci,~M., \\& Taylor,~G.~B. 1997, \\nat, 389, 261\n\\bibitem[Frail 1998]{Frail98} Frail, D. A. 1998, Gamma-Ray Bursts: 4th\nHuntsville Symposium, Huntsville, Ala., eds. C. A. Meegan, R. D. Preece, T.\nM. Koshut (New York: AIP) p. 563\n\n%\\bibitem[Galama et~al. 1998]{Galama98} Galama,~T.~J., et al. 1998, \\nat,\n%395, 670\n\n\\bibitem[Ginzburg (1973)]{Ginzburg73} Ginzburg, V. L. 1973, \\nat, 246, 415\n\n\\bibitem[Goodman 1997]{Goodman97} Goodman,~J. 1997, New Astr., 2, 449\n\n\\bibitem[Katz 1994]{Katz94} Katz,~J.~I. 1994, \\apj, 422, 248\n\n\\bibitem[Katz 1997]{Katz97} Katz,~J.~I. 1997, \\apj, 490, 633\n\n\\bibitem[Katz 1999]{Katz99} Katz,~J.~I. 1999, The Largest Explosions Since\nthe Big Bang: Supernovae and Gamma-Ray Bursts, eds. M. Livio, K. Sahu \\& N.\nPanagia (Baltimore: STScI) p. 43 (astro-ph/9908217)\n\n\\bibitem[Klu\\'{z}niak \\& Ruderman 1998]{Kluzniak98}\nKlu\\'{z}niak,~W., \\& Ruderman,~M. 1998, \\apj, 505, L113\n\n%\\bibitem[Kouveliotou et~al. 1996]{Kouveliotou96} Kouveliotou, C., et al.\n%1996, AIP Conf. Proc. 384, Gamma-Ray Bursts, eds. C.~Kouveliotou,\n%M.F.~Briggs, \\& G.J.~ Fishman (New York: AIP), 42\n\n%\\bibitem[Kulkarni et~al. 1998b]{Kulkarni98b} Kulkarni,~S.~R., et al.\n%1998b, \\nat, 395, 663\n\n%\\bibitem[Kulkarni et~al. 1999]{Kulkarni99} Kulkarni,~S.~R., et al.\n%1999, \\nat, 398, 389\n\n\\bibitem[M\\'esz\\'aros \\& Rees 1992]{Meszaros92} M\\'esz\\'aros,~P. \\&\nRees,~M.~J. 1992, \\apj, 397, 570\n\n\\bibitem[M\\'esz\\'aros \\& Rees 1997]{Meszaros97} M\\'esz\\'aros,~P. \\&\nRees,~M.~J. 1997, \\apj, 482, L29\n\n%\\bibitem[Niemeyer \\& Woosley 1997]{Niemeyer97}Niemeyer,~J.~C.\n%\\& Woosley,~S.~E. 1997, \\apj, 475, 740\n\n\\bibitem[Palmer (1993)]{Palmer93} Palmer, D. M. 1993, \\apjl, 417, L25\n\n\\bibitem[Piran 1999]{Piran99} Piran,~T. 1999, Phys. Reports, 314, 575\n\n\\bibitem[Smith 1950]{Smith50} Smith, F. G. 1950, \\nat, 165, 422\n\n\\bibitem[Smolsky \\& Usov 1996]{Smolsky96} Smolsky, M. V., \\&\nUsov, V. V. 1996, \\apj, 461, 858\n\n\\bibitem[Smolsky \\& Usov 2000]{Smolsky00} Smolsky, M. V., \\&\nUsov, V. V. 2000, \\apj, in press\n\n\\bibitem[Spitzer 1962]{Spitzer62} Spitzer, L., 1962, Physics of Fully\nIonized Gases (New York: Interscience)\n\n\\bibitem[Spruit 1999]{Spruit99} Spruit, H. C. 1999, A\\&A, 341, L1\n\n\\bibitem[Usov 1992]{Usov92} Usov,~V.~V. 1992, \\nat, 357, 472\n\n\\bibitem[Usov 1994]{Usov94} Usov,~V.~V. 1994, MNRAS, 267, 1035\n\n%\\bibitem[Usov \\& Chibisov 1975]{Usov75} Usov,~V.~V., \\&\n%Chibisov,~G.~V. 1975, Soviet Astron., 19, 115\n\n\\bibitem[Usov \\& Smolsky 1998]{Usov98} Usov, V. V., \\& Smolsky, M. V.\n1998, Phys. Rev. E, 57, 2267\n\n\\bibitem[Vietri 1996]{Vietri96} Vietri, M. 1996, \\apj, 471, L95\n\n\\bibitem[Vietri 1999]{Vietri99} Vietri,~M. 1999, astro-ph/9911523\n\n\\end{thebibliography}"
}
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astro-ph0002279
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Optical, near-infrared and hard X--ray observations of SAXJ~1353.9$+$1820: a red quasar \thanks{Based on observations performed with the Italian National Telescope, which is operated on the island of La Palma by the Centro Galileo Galilei/CNAA at the Spanish Observatorio del Roque de Los Muchachos of the Instituto de Astrofisica de Canarias %% %Based on observations collected %at the Italian National Telescope Galileo (TNG), La Palma, Canary Islands, Spain}
|
[
{
"author": "C. Vignali$^{1,2}$"
},
{
"author": "M. Mignoli$^{2}$"
},
{
"author": "A. Comastri$^{2}$"
},
{
"author": "R. Maiolino$^{3}$"
},
{
"author": "F. Fiore$^{4,5,6}$"
},
{
"author": "$^1$ Dipartimento di Astronomia"
},
{
"author": "Universit\\`a di Bologna"
},
{
"author": "Via Ranzani 1"
},
{
"author": "I--40127 Bologna"
},
{
"author": "Italy"
},
{
"author": "$^2$ Osservatorio Astronomico di Bologna"
},
{
"author": "$^3$ Osservatorio Astrofisico di Arcetri"
},
{
"author": "Largo E. Fermi 5"
},
{
"author": "I--50125 Firenze"
},
{
"author": "$^4$ Osservatorio Astronomico di Roma"
},
{
"author": "Via Frascati 33"
},
{
"author": "I--00044 Monteporzio"
},
{
"author": "$^5$ BeppoSAX Science Data Center"
},
{
"author": "Via Corcolle 19"
},
{
"author": "I--00131 Roma"
},
{
"author": "$^6$ Harvard-Smithsonian Center of Astrophysics"
},
{
"author": "60 Garden Street"
},
{
"author": "Cambridge MA 02138 USA"
}
] |
We present the results of a follow--up {ASCA} observation and multicolour optical and near-infrared photometry carried out at the 3.5-m Italian National Telescope Galileo of SAXJ~1353.9$+$1820. This object, serendipitously discovered by {BeppoSAX} in the 5--10 keV band, has been spectroscopically identified as a red quasar at $z$=0.217. The combined X--ray and optical--infrared data reveal the presence of a moderately luminous X--ray source ($\sim$ 10$^{44}$ erg s$^{-1}$) obscured by a column density of the order of 10$^{22}$ cm$^{-2}$ in a otherwise optically passive early-type galaxy. The implications for the nature of red quasars and their possible contribution to the hard X--ray background are briefly outlined.
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[
{
"name": "redqso_mn.tex",
"string": "\\documentstyle[psfig]{mn-1.4}\n\n%\\topmargin=-0.5in\n\n%\\title{The first hard X--ray spectrum of an optically red quasar: SAXJ~1353.9$+$1820}\n\\title[Broad-band study of the red quasar SAXJ~1353.9$+$1820]\n{Optical, near-infrared and hard X--ray observations of SAXJ~1353.9$+$1820: a red quasar\n\\thanks{Based on observations performed with \nthe Italian National Telescope, which is operated on the island of La Palma by the \nCentro Galileo Galilei/CNAA at the Spanish Observatorio del Roque de Los \nMuchachos of the Instituto de Astrofisica de Canarias\n%%\n%Based on observations collected \n%at the Italian National Telescope Galileo (TNG), La Palma, Canary Islands, Spain}}\n}}\n\n\\author[C. Vignali et al.]{\nC. Vignali$^{1,2}$, \nM. Mignoli$^{2}$, \nA. Comastri$^{2}$, \nR. Maiolino$^{3}$, \nF. Fiore$^{4,5,6}$ \\\\ \n$^1$ Dipartimento di Astronomia, Universit\\`a di Bologna, \nVia Ranzani 1, I--40127 Bologna, Italy \\\\\n$^2$ Osservatorio Astronomico di Bologna, \nVia Ranzani 1, I--40127 Bologna, Italy \\\\\n$^3$ Osservatorio Astrofisico di Arcetri, \nLargo E. Fermi 5, I--50125 Firenze, Italy \\\\\n$^4$ Osservatorio Astronomico di Roma, \nVia Frascati 33, I--00044 Monteporzio, Italy \\\\\n$^5$ BeppoSAX Science Data Center, \nVia Corcolle 19, I--00131 Roma, Italy \\\\\n$^6$ Harvard-Smithsonian Center of Astrophysics, \n60 Garden Street, Cambridge MA 02138 USA \\\\\n}\n\\date{Accepted ...\n Received ...;\n in original form ...}\n\n\\pagerange{\\pageref{firstpage}--\\pageref{lastpage}}\n\\pubyear{1999}\n\n\\begin{document}\n\n\\maketitle\n\n\\label{firstpage}\n\n\\begin{abstract}\n\nWe present the results of a follow--up {\\it ASCA} observation \nand multicolour optical and near-infrared photometry carried out\nat the 3.5-m Italian National Telescope Galileo of SAXJ~1353.9$+$1820.\nThis object, serendipitously discovered by {\\it BeppoSAX}\nin the 5--10 keV band, has been spectroscopically identified as a \nred quasar at $z$=0.217.\nThe combined X--ray and optical--infrared data reveal the \npresence of a moderately luminous X--ray source ($\\sim$ 10$^{44}$ erg s$^{-1}$)\nobscured by a column density of the order of 10$^{22}$ cm$^{-2}$ \nin a otherwise optically passive early-type galaxy. \nThe implications for the nature of red quasars and their possible \ncontribution to the hard X--ray background are briefly outlined.\n\n\\end{abstract}\n\n\\begin{keywords}\ngalaxies: active -- \nquasars: individual: SAXJ~1353.9$+$1820 --\nX--rays: galaxies\n\\end{keywords}\n\n\\section{Introduction}\n\nThe {\\it BeppoSAX} High Energy Large Area Survey (HELLAS) has discovered a large \npopulation of hard X--ray sources, \nwhich account for about 20--30 per cent of the cosmic X--ray background (XRB) in \nthe 5--10 keV energy range (Fiore et al. 1999). \nThis band provides an efficient tool to discriminate between accretion-powered sources, \nlike the Active Galactic Nuclei (AGN) are generally thought to be, and sources dominated by the starlight \ncomponent. Moreover, hard X--ray selection \nis less affected by obscuration with respect to other bands, making \npossible the study of the nuclear \ncontinuum without any relevant contamination by reprocessed radiation. \n%(unless the source is Compton-thick or \n%the reflection component is shifted in this energy range). \nIndeed the optical identification process indicates that the large majority\nof the HELLAS sources are AGN (La Franca et al., in preparation). \nAmong these, SAXJ~1353.9$+$1820 can be considered one of the most \nintriguing sources. \nAfter its discovery in the context of the HELLAS survey, it was \nspectroscopically identified as a radio-quiet AGN at a redshift of 0.2166 \n(Fiore et al. 1999). Its optical spectrum \nis dominated by starlight, as the presence of H and K plus\nMg~I absorption lines clearly indicates. \nThe H$\\alpha$ equivalent width (about 90 $\\AA$),\nthe absence of the H$\\beta$ and the {\\it BeppoSAX} hardness ratio \nare suggestive of significant reddening of the nuclear radiation.\n%line provide a lower limit to the extinction, \n%$A_{\\rm V}$ $\\ga$ 4.8,\n%which corresponds to $N_{\\rm H}$ $\\ga$ 9 $\\times$ 10$^{21}$ cm$^{-2}$ assuming the Galactic\n%gas-to-dust ratio (Bohlin, Savage \\& Drake 1978; Whittet 1992).\nThe hard X--ray luminosity, L$_{5-10~keV}$ $\\sim$ 1.4 $\\times$ 10$^{44}$ \nerg s$^{-1}$, the presence of a broad Balmer line and the optical \nspectrum properties allow to classify this object as a fairly low-luminosity, red quasar. \\\\\nThis class of objects, originally discovered in radio--selected samples \n(Smith \\& Spinrad 1980), is characterized by red optical colours \n($B-K$ up to 8, Webster et al. 1995).\nOn the basis of {\\it ROSAT} PSPC observations and optical\nspectroscopy Kim \\& Elvis (1999) pointed out that a significant fraction \n(from a few percent up to 20 per cent) \nof soft X--ray selected radio--quiet quasars belong to this class.\nThe origin of the observed `redness' may be ascribed to dust absorption, \nto intrinsic red colours ($\\ga$ 70 per cent of the red sources of the Parkes sample\nhas $\\la$ 30 per cent of contribution to B--K by their host galaxies, \nMasci et al. 1998) or to an excess of light in K band rather than \na dust-induced deficit in B (Benn et al. 1998).\nWhatever is the origin of the red colours, it is likely \nthat a large fraction of quasars could have been missed by the usual \nselection techniques in the optical band (Webster et al. 1995).\nIf this is the case, red quasars could constitute a sizeable fraction \nof the absorbed AGN population needed to explain the hard X--ray \nbackground spectrum (i.e. Comastri et al. 1995) especially \nif the optical reddening is associated with X--ray absorption. \nHard X--ray observations provide the most efficient way to \nselect these objects;\nindeed already two candidates have been found among the first optical\nidentifications of HELLAS sources (Fiore et al. 1999). \nIn order to better understand the spectral properties of these objects \nwe have started a program of multiwavelength follow--up \nobservations of a sub--sample of HELLAS sources.\nHere we present the first results obtained \nin the X--ray band with {\\it ASCA} and at optical--infrared \nwavelengths with the 3.5-m Italian National Telescope Galileo (TNG) at La Palma \n(OIG and ARNICA photometric cameras). \nThroughout the paper $H_{0}$ = 50 km s$^{-1}$ Mpc$^{-1}$ and $q{_0}$ = 0 are assumed.\n%%%\n\n\\section{ASCA data reduction and spectral analysis}\nSAXJ~1353.9$+$1820 (RA: 13$^{h}$ 53$\\arcmin$ 54$\\arcsec$.4, DEC: 18$^{\\circ}$ 20$\\arcmin$ 16$\\arcsec$) \nwas observed with the {\\it ASCA} satellite (Tanaka, Inoue \\& Holt 1994) in January 1999 \nfor about 60 ks. \nThe observation was performed in FAINT mode and then corrected for dark frame error and echo uncertainties \n(Otani \\& Dotani 1994). \nThe data were screened with the {\\sc XSELECT} package (version 1.4b) with standard criteria. \nSpectral analysis on the resulting cleaned data was \nperformed with {\\sc XSPEC} version 10 (Arnaud et al. 1996). \\\\\nThe background-subtracted count rates are 6.0$\\pm{0.4}$ $\\times$ 10$^{-3}$ counts s$^{-1}$ for \nSIS (Solid-State Spectrometers, Gendreau 1995) \nand 7.4$\\pm{0.4}$ $\\times$ 10$^{-3}$ counts s$^{-1}$ for GIS (Gas-Scintillation Spectrometers, Makishima et. al 1996). \nBoth SIS and GIS spectra were grouped with almost 20 photons \nfor each spectral bin in order to apply $\\chi^{2}$ statistics. \n%binned with almost 20 counts per bin in order to apply $\\chi^{2}$ statistics. \nCalibration uncertainties in the soft X--ray band have been avoided by selecting only data \nat energies higher than 0.9 keV. No discrepancies have been found between SIS and GIS \nspectral analysis, therefore all the data have been fitted together allowing the relative normalizations \nto be free of varying. \nThe uncertainties introduced by background subtraction have been \ncarefully checked using both local and blank--sky background spectra\nand also varying their normalizations by $\\pm$ 10 per cent.\nThe lack of significant variations for the source count rate \nand spectral shape makes us confident on the robustness of\nthe results. \\\\\nA simple power law model plus Galactic absorption ($N_{\\rm H}$ $\\simeq$ 2.05 $\\times$ 10$^{20}$ cm$^{-2}$, Dickey \\& \nLockman 1990) leaves some residuals in the fit ($\\chi^{2}$=174/158) and\n gives a very flat slope ($\\Gamma$ $<$ 0.9).\nThe addition of an extra cold absorber at the \nredshift of the source (model {\\bf (a)} in Table~1) improves the fit \nand the continuum X--ray spectral slope \nis now $\\Gamma$ = 1.28$^{+0.23}_{-0.28}$ (errors are at 90 per cent for one interesting parameter, \nor $\\Delta\\chi^{2}$=2.71, Avni 1976), \nattenuated by a column density $N_{\\rm H}$ = 6.14$^{+2.10}_{-4.56}$ $\\times$ 10$^{21}$ cm$^{-2}$, assuming cosmic abundances \n(Anders \\& Grevesse 1989) and cross sections derived by Balucinska-Church \n\\& McCammon (1992). \nThe best-fitting spectrum and the confidence contours for \nthe absorbed power law model are presented in Fig.~1 and Fig.~2, respectively. \nThe unabsorbed 2--10 keV flux and luminosity are\n$\\sim$ 6.2 $\\times$ 10$^{-13}$ erg cm$^{-2}$ s$^{-1}$\nand $\\sim$ 1.3 $\\times$ 10$^{44}$ erg s$^{-1}$. \nThe 5--10 keV {\\it ASCA} flux is about 40 per cent lower than in {\\it BeppoSAX}. \nX--ray variability and/or cross--calibration uncertainties could provide\na likely explanation. \\\\\n\n% FIGURE 1\n\\begin{figure}\n\\psfig{figure=spectrum.ps,width=0.48\\textwidth,angle=-90}\n\\caption[]{ASCA SIS $+$ GIS spectrum and relative data/model ratio for\nthe absorbed power law model (model {\\bf (a)} in Table~1).}\n\\label{fig1}\n\\end{figure}\n\n\\begin{table}\n\\caption[]{ASCA SIS$+$GIS spectral fits (0.9--10 keV energy range)}\n\\begin{tabular}{lcccc}\n\\noalign{\\smallskip}\n\\hline\n\\noalign{\\smallskip}\n{\\bf Model} & $\\Gamma$ & $N_{\\rm H}$ & CvrFract & $\\chi^{2}$/dof \\\\\n\\noalign{\\smallskip}\n & & (10$^{21}$ cm$^{-2}$) & (\\%) & \\\\\n\\noalign{\\smallskip}\n\\hline \\hline\n\\noalign{\\smallskip}\n{\\bf (a)} & 1.28$^{+0.23}_{-0.28}$ & 6.14$^{+2.10}_{-4.56}$ & \\dots & 168/157 \\\\\n\n{\\bf (b)} & 1.9 (frozen) & 15.4$^{+3.70}_{-3.20}$ & \\dots & 181/158 \\\\\n\n{\\bf (c)} & 1.28$^{+0.43}_{-0.30}$ & 8.55$^{+24.0}_{-6.89}$ & 81$^{+19}_{-44}$ & 168/156 \\\\\n\n{\\bf (d)} & 1.9 (frozen) & 28.7$^{+17.2}_{-5.90}$ & 80$^{+11}_{-8}$ & 171/157 \\\\\n\n\\noalign{\\smallskip}\n\\hline\n\\end{tabular}\n\\end{table}\n\n\\par\\noindent\nSAXJ~1353.9$+$1820 does not show any particular feature or any other indication of \nreprocessed radiation. \nNeither the iron K$\\alpha$ emission line (the 90 per cent upper limit on the equivalent width being \n330 eV) nor the reflection component (which is basically unconstrained \nby the present data)\n%R $<$ 7.3, with $\\Gamma$ = 1.18$^{+0.53}_{-0.23}$) \ndo improve the fit.\nThe $N_{\\rm H}$ value \n(which has been fixed at the quasar redshift but which could lie along the line \nof sight to the QSO) \nis in agreement with the value found by the hardness \nratio analysis of {\\it BeppoSAX} data.\n\n% FIGURE 2\n\\begin{figure}\n\\psfig{figure=contours.ps,width=0.48\\textwidth,angle=-90}\n\\caption[]{ASCA confidence contours in the $\\Gamma$ -- $N_{{\\rm H}_{\\rm int}}$ space parameters.}\n\\label{fig2}\n\\end{figure}\n\nThe best-fitting slope is extremely hard and significantly flatter than the\naverage slope of Seyfert Galaxies and quasars with similar luminosities\nand redshifts (Nandra \\& Pounds 1994; Reeves et al. 1997; George et al. 1999). \nIndeed assuming a `canonical' $\\Gamma$ = 1.9 value\nwe were not able to obtain a good fit as relatively large residuals \nare present at high energies (model {\\bf (b)}). \nThe underlying continuum spectrum could be either intrinsically flat\nor flattened by a complex (multicolumn and/or leaky) absorber (Hayashi et al. 1996; Vignali et al. 1998). \nTo test this last hypothesis we have fitted a partial covering model (models {\\bf (c)} and {\\bf (d)} in Table~1), \nwhere part of the direct component escapes without being absorbed.\nWhile the best-fitting model still requires a flat slope, a steeper continuum\npartially absorbed by a column density of $\\sim$ \n3 $\\times$ 10$^{22}$ cm$^{-2}$ does provide a good fit to the observed \nspectrum.\\\\\n%%%\n%The red quasar appears also in the field of view of the spectroscopic binary \n%HD~121370 (ID number 25041000). The long exposure of this observation (about 120 ks) makes up \n%partially for the large off-axis angle. The slope \n%($\\Gamma$=1.16$^{+0.36}_{-0.23}$), the \n%upper limit for intrinsic absorption ($N_{\\rm H}$ $<$ 3.9 $\\times$ 10$^{21}$ cm$^{-2}$)\n%and the 2--10 keV flux are consistent with the values found from the pointed observation.\n%Given the large uncertainities associated with off--axis observations we\n%have not tried to fit more complicated models.\n%%%\n\n\\section{Optical and NIR photometry}\n%%\n%%The absolute V magnitude (M$_{\\rm V}$ $\\simeq$ $-$ 24.3) and its optical spectrum makes this sources \n%%a border-line objects between the quasars and the Seyfert 1 classes ...\n%%\nSAXJ~1353.9+1820 has been observed at the 3.5-m National Telescope Galileo \nwith the Optical Imager (OIG) during the night of 1999 June 18. \nWe carried out optical broad band imaging in the Johnson--Kron--Cousins \n{\\it U,~B,~V,~R} and~{\\it I} filters. The \nexposure times were respectively 900,~480,~180,~120 and~120 seconds while \nthe seeing ranges from 0.9~arcsec (FWHM) in the reddest band to 1.3 arcsec in \nthe ultraviolet, with a steady increase through the optical bands giving \nevidence that the blurring is mainly due to atmospheric causes. During the same \nnight we observed the standard fields PG~1323$-$086, PG~1633$+$099 and \nSA~110 in order to obtain accurate photometric calibrations and to determine \nthe colour terms of the relatively new OIG system. \nAll the frames were acquired at airmass $\\leq 1.5$. The data \nreduction and analysis has been performed in a standard way using \n{\\sc IRAF}\\footnote{{\\sc IRAF} is distributed by the National Optical Astronomy \nObservatories, which are operated by the Associated Universities for Research \nin Astronomy, Inc. under cooperative agreement with the National Science \nFoundation}\nroutines. Bias exposures taken at the beginning and at the end of the night were \nstacked, checked for consistency with the overscan region of the scientific \nimages and subtracted out. The bias--subtracted frames were then flat--fielded \nusing sky flats. The cosmic rays of the CCD region around the target have \nbeen interactively identified and removed by fitting of the neighbouring pixels. \n% using the IRAF task {\\tt cosmicrays}. \n\n\\noindent\nThe photometry has been performed using {\\tt apphot}, the Aperture Photometry \nPackage available in {\\sc IRAF}. The object is clearly extended, and we used \na quite large aperture radius ($\\sim$ 8~arcsec) for all the bands, \ncorresponding to a projected distance of about 15 $h_{50}^{-1}$~kpc at the redshift \nof SAXJ~1353.9+1820. Measurements in the J and K-short bands were also made with \nthe ARNICA instrument at the same telescope within the framework of a wider \nnear--IR follow-up of the HELLAS sources. The data reduction and analysis \nof the near--IR \ndata will be discussed in detail in Maiolino et al. (in preparation), here we simply report the resulting \nphotometry. \nThe results of the combined aperture photometry are presented in Table~2. \n\n% FIGURE 3\n\\begin{figure}\n\\psfig{figure=prof_redqso.eps,width=0.48\\textwidth,angle=0}\n\\caption[]{The optical surface brightness profiles \nfitted with a de Vaucouleurs r$^{1/4}$ law (dashed line). \nDifferent symbols are referred to different filters.\nThe vertical dotted line represents the adopted aperture radius.}\n\\label{fig3}\n\\end{figure}\n\nThe surface brightness (SB) profiles in the U, B, V, R and \nI filters have been estimated computing a curve of growth for each \npassband with increasing circular apertures (Fig.~3).\nAn effective radius of $\\sim$~1.5 arcsec \nwas indipendently derived from all but one fits (for the I--band we obtained a \nslightly more concentrated profile). \nThe dashed line in figure represents the $r^{1/4}$ law, which fits \nvery well the observed profiles outside of the seeing-dominated region\ndown to the faintest flux levels. \nThe SB profiles are typical for elliptical galaxies suggesting \nthat at optical wavelengths there is no evidence of\nan unresolved nucleus in SAXJ~1353.9$+$1820.\n\n\\begin{table}\n\\caption{Optical and NIR photometry}\n\\label{phot}\n\\begin{center}\n\\begin{tabular}{lccccccc}\n\\hline\nFilter & {\\bf U} & {\\bf B} & {\\bf V} & {\\bf R} & {\\bf I} & {\\bf J} & {\\bf Ks} \\\\\n\nMag. & 19.98 & 19.55 & 18.15 & 17.32 & 16.62 & 15.29 & 13.91 \\\\\n\nErrors & 0.07 & 0.03 & 0.03 & 0.02 & 0.04 & 0.05 & 0.07 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\n\\section{Discussion and Conclusions}\n\nThe {\\it ASCA} observation confirms \nthe presence of a bright and moderately \nabsorbed ($N_{\\rm H}$ $\\sim$ 6 $\\times$ 10$^{21}$ cm$^{-2}$) \nnucleus with a flat hard X--ray spectrum, in agreement with the BeppoSAX hardness ratio analysis. \nAssuming for the underlying continuum slope the average value \nof quasars in the same energy range, the absorption column density\ncould be as high as $N_{\\rm H}$ $\\sim$ 3 $\\times$ 10$^{22}$ cm$^{-2}$\nif some 20 per cent of the nuclear radiation is not absorbed.\nEven if the X--ray data alone does not allow to distinguish \nbetween the two possibilities, we can safely conclude \nthat SAXJ~1353.9$+$1820 harbours a mildly obscured, \nluminous (L$_{\\rm 2-10 keV}$ $\\simeq$ 1.3 $\\times$ 10$^{44}$ erg s$^{-1}$)\nactive nucleus. \n\nNot surprisingly high energy observations of quasars \ncharacterized by similar dust reddened optical continua \ndo reveal the presence of absorption by cold \n(IRAS 23060+0505, Brandt et al. 1997a) \nand/or warm (IRAS 13349+2438, Brandt et al. 1997b) gas. \n\nA basic step forward in understanding the nature of this red quasar\nand of red quasars as a whole, is provided \nby optical plus near--IR studies \n(see Maiolino et al., in preparation, for further details).\nThe surface brightness profiles are consistent with those of an elliptical galaxy, and \nthe optical colours (U$-$B=0.43, B$-$V=1.40, V$-$R=0.83 and R$-$I=0.70) \nagree with the properties of a early-type galaxy at $z$=0.2 (Fukugita et al. 1995).\n\nIn order to obtain a self--consistent description of the optical-IR properties \nwe fitted the photometric points with a two-components model consisting \nof an old stellar population template (10$^{10}$ yr, Bruzual \\& Charlot 1993) \nand a moderately absorbed ($A_{\\rm V} \\simeq$ 2 mag, corresponding\nto $N_{\\rm H} \\simeq$ 4 $\\times$ 10$^{21}$ cm$^{-2}$ for Galactic \ndust--to--gas ratio, {\\rm i.e.} Bohlin, Savage \\& Drake 1978) \nquasar spectrum template (Elvis et al. 1994; Francis et al. 1991). \nAs shown in Fig.~4, \nthe combination of these two spectra provides a good description of \nthe observed data \n(possibly with the exception of the J photometry, which deviates by 1.4 sigma). \nThe quality of the fit is acceptable ($\\chi^2_{\\rm r}$ = 1.3 when \nboth the uncertainties in the photometric data and in the template spectra\nare taken into account) indicating that most \nof the optical and near--IR flux is dominated by star--light. \n\n% FIGURE 4\n\\begin{figure}\n%\\centerline{\n%\\hbox{\n\\psfig{figure=h8final.ps,width=0.48\\textwidth,angle=0}\n%\\newline\n%}}\n\\caption[]{SAXJ~1353.9$+$1820 photometric (optical $+$ NIR) points \nfitted with a synthetic model of an evolved early-type galaxy \n(dashed line) plus the contribution of a moderately absorbed \nquasar (dotted line). The sum is represented by the solid line.}\n\\label{fig4}\n\\end{figure}\n\nThe present results add further evidence on the hypothesis of \nsubstantial gas and dust absorption as an explanation of the \nobserved properties of this red quasar.\nEven more interesting is that the active nucleus peers only\nat X--ray energies and possibly at wavelenghts longward of 2 $\\mu$m (see Fig.~4), \nwhile at optical wavelengths \nSAXJ~1353.9$+$1820 looks like a normal evolved elliptical galaxy.\nIf this behaviour applies also to other objects it may well be \nthat a significant fraction of obscured AGNs resides\nin otherwise normal passive galaxies.\nThese nuclei would have been completely missed in optical quasar surveys\nbecause of their extended morphology and galaxy-like colours. \nIf the column density is of the order of 10$^{22}$ cm$^{-2}$ or higher, \ntheir fraction could be understimated also in soft X--ray surveys. \nIf this is the case, the fraction of red objects \namong radio quiet quasars ($\\sim$ 3--20 per cent, Kim \\& Elvis 1999) \n%and radio-loud ($\\sim$ 15 per cent in the 3CR \n%source sample and $\\sim$ 6--20 per cent of the 1~Jy sample, Carilli et al. 1998) \nshould be considered as a lower limit. \nThis may have strong implications \nfor the XRB synthesis models, which in their \nsimplest version (i.e. Madau, Ghisellini \\& Fabian 1994; Comastri et al. 1995)\npredict a large number of high-luminosity absorbed quasars (called type 2 QSO).\nDespite intensive optical searches, these objects appears to be elusive \nindicating a much lower space density than that of \nlower luminosity Seyfert 2 galaxies (Halpern, Eracleous \\& Forster 1998) and\ncalling for a substantial revision of AGN synthesis models for the\nXRB (Gilli, Risaliti \\& Salvati 1999). \\\\\n \nAn alternative possibility (see Comastri 2000) is that X--ray obscured AGN \nshow a large variety of optical properties including \nthose of SAXJ~1353.9$+$1820. It \nis worth noting that column densities as high as 10$^{23.5}$ cm$^{-2}$ \nhave been detected in Broad Absorption Line QSO (Gallagher et al. 1999), \nin some UV bright soft X--ray weak QSO (Brandt et al. 1999), \nand in a few HELLAS sources optically identified with broad line blue quasars (Fiore et al. 1999).\nIt is thus possible that the sources responsible for a \nlarge fraction of the XRB energy density are characterized by \na large spread in their optical to X--ray properties. \nThe $\\alpha_{ox}$ spectral index, defined as the slope joining \nthe 2500 $\\AA$ and the 2 keV flux densities, is usually employed to measure the optical to X--ray ratio. \nNot surprisingly, absorbed objects are characterized \nby values of $\\alpha_{ox}$ ($>$ 1.8) much steeper than the \naverage value of bright unabsorbed quasars and Seyfert galaxies, \n$\\alpha_{ox}$ $\\simeq$ 1.5 (Laor et al. 1997; Yuan et al. 1998), \nwhile the faint nuclear UV flux density and the relatively bright 2 keV flux \nof SAXJ~1353.9$+$1820 correspond to $\\alpha_{ox}$ $\\simeq$ 1, which is quite \nflat but not unusual for red quasars (Kim \\& Elvis 1999). \n\nA detailed discussion on the quasars contribution \nto the XRB is beyond the purposes of this Letter. \nHere we note that as far as the X--ray spectral properties \nand the bolometric luminosity of $\\simeq$ 10$^{45}$ erg s$^{-1}$ \n(estimated using the average SED of Elvis et al. 1994 \nwith the measured $\\alpha_{ox}$) are concerned, SAXJ~1353$+$1820 \ncan be classified as a high--luminosity absorbed AGN.\n \nFuture sensitive X--ray observations with Chandra and XMM coupled with \noptical spectropolarimetry data would be extremely helpful to \nbetter understand the nature of red quasars and to estimate \ntheir contribution to the XRB. \n\n\n\\section*{Acknowledgments}\nWe thank the {\\it ASCA} team, who operate the satellite and maintain the software and \ndatabase. We are also grateful to {\\it BeppoSAX} Science Data Center and to the staff at the \nNational Telescope Galileo who made possible our observations. \nThe data discussed in this paper have been obtained within the \nTNG experimental phase programme (PI: F. La Franca \\& R. Maiolino).\nWe thank G. Matt and L. Pozzetti for useful comments and an anonymous\nreferee for constructive suggestions. \nFinancial support from Italian Space Agency under the contract ASI--ARS--98--119 \nis acknowledged by C.~V. and A.~C. \nThis work was partly supported by the Italian Ministry \nfor University and Research (MURST) under grant Cofin98-02-32. \\\\\n\n\\begin{thebibliography}{99}\n\n\\bibitem{} Anders E., Grevesse N., 1989, Geochimica et Cosmochimica Acta, 53, 197\n\\bibitem{} Arnaud K.~A., in Jacoby G., Barnes J., eds, Astronomical Data Analysis Software \nand Systems V, Vol.~101, 17, ASP Conf. Ser., San Francisco\n\\bibitem{} Avni Y., 1976, ApJ, 210, 642\n\\bibitem{} Balucinska-Church M., McCammon D., 1992, ApJ, 400, 699\n\\bibitem{} Benn C.~S., Vigotti M., Carballo R., Gonzalez-Serrano J.~I., Sanchez S.~F., 1998, MNRAS, 295, 451\n\\bibitem{} Bohlin R.~C., Savage B.~D., Drake J.~F., 1978, ApJ, 224, 291\n\\bibitem{} Brandt W.~N., Fabian A.~C., Takahashi K., Fujimoto R., Yamashita A., \nInoue H., Ogasaka Y., 1997a, MNRAS, 290, 617\n\\bibitem{} Brandt W.~N., Mathur S., Reynolds C.~S., Elvis M., 1997b, MNRAS, 292, 407\n\\bibitem{} Brandt W.~N., Laor A., Wills B.~J., 1999, ApJ, in press (astroph/9908016)\n\\bibitem{} Bruzual A.~G., Charlot S., 1993, ApJ, 405, 538\n%\\bibitem{} Carilli C.~L., Menten K.~M., Reid M.~J., Rupen M.~P., Yun M.~S., 1998, ApJ, 494, 175\n\\bibitem{} Comastri A., Setti G., Zamorani G., Hasinger G., 1995, A\\&A, 296, 1\n\\bibitem{} Comastri A., 2000, Astroph. Lett. \\& Comm., submitted\n\\bibitem{} Dickey J.~M., Lockman F.~J., 1990, ARA\\&A, 28, 215\n\\bibitem{} Elvis M., et al., 1994, ApJS, 95, 1\n\\bibitem{} Fiore F., La Franca F., Giommi P., Elvis M., Matt G., \nComastri A., Molendi S., Gioia I., 1999, MNRAS, 306, L55\n\\bibitem{} Francis P.~J., Hewett P.~C., Foltz C.~B., Chaffee F.~H., \nWeymann R.~J., Morris S.~L., 1991, ApJ, 373, 465\n\\bibitem{} Fukugita M., Shimasaku K., Ichikawa T., 1995, PASP, 107, 945\n\\bibitem{} Gallagher S.~C., Brandt W.~N., Sambruna R.~M., Mathur S., Yamasaki N., 1999, ApJ, 519, 549\n\\bibitem{} Gendreau K., 1995, Ph.D. Thesis, Massachussets Inst. Tech.\n\\bibitem{} George I.~M., Turner T.~J., Yaqoob T., et al., 1999, ApJ, in press (astroph/9910218)\n\\bibitem{} Gilli R., Risaliti G., Salvati M., 1999, A\\&A, 347, 424\n\\bibitem{} Halpern J.~P., Eracleous M., Forster K., 1998, ApJ, 501, 103\n\\bibitem{} Hayashi I., Koyama K., Awaki H., Ueno S., Yamauchi S., 1996, PASJ, 48, 219\n\\bibitem{} Kim D.-W., Elvis M., 1999, ApJ, 516, 9\n\\bibitem{} Laor A., Fiore F., Elvis M., Wilkes B.~J., McDowell J.~C., 1997, ApJ, 477, 93 \n\\bibitem{} Madau P., Ghisellini G., Fabian A.~C., 1994, MNRAS, 270, L17 \n\\bibitem{} Makishima K., et al., 1996, PASJ, 48, 171\n\\bibitem{} Masci F.~J., Webster R.~L., Francis P.~J., 1998, MNRAS, 301, 975\n\\bibitem{} Nandra K., Pounds K.~A., 1994, MNRAS, 268, 405\n\\bibitem{} Otani C., Dotani T., 1994, ASCA Newslett., 2, 25\n\\bibitem{} Reeves J.~N., Turner M.~J.~L., Ohashi T., Kii T., 1997, MNRAS, 292, 468\n\\bibitem{} Smith H.~E., Spinrad H., 1980, ApJ, 236, 419\n\\bibitem{} Tanaka Y., Inoue H., Holt S.~S., 1994, PASJ, 46, L37\n\\bibitem{} Vignali C., Comastri A., Stirpe G.~M., Cappi M., Palumbo G.~G.~C., Matsuoka M., \nMalaguti G., Bassani L., 1998, A\\&A, 333, 411\n\\bibitem{} Webster R.~L., Francis P.~J., Peterson B.~A., Drinkwater M.~J., \nMasci F.~J., 1995, Nature, 375, 469\n\\bibitem{} Yuan W., Brinkmann W., Siebert J., Voges W., 1998, A\\&A, 330, 108 \n\\end{thebibliography}\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002279.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bibitem{} Anders E., Grevesse N., 1989, Geochimica et Cosmochimica Acta, 53, 197\n\\bibitem{} Arnaud K.~A., in Jacoby G., Barnes J., eds, Astronomical Data Analysis Software \nand Systems V, Vol.~101, 17, ASP Conf. Ser., San Francisco\n\\bibitem{} Avni Y., 1976, ApJ, 210, 642\n\\bibitem{} Balucinska-Church M., McCammon D., 1992, ApJ, 400, 699\n\\bibitem{} Benn C.~S., Vigotti M., Carballo R., Gonzalez-Serrano J.~I., Sanchez S.~F., 1998, MNRAS, 295, 451\n\\bibitem{} Bohlin R.~C., Savage B.~D., Drake J.~F., 1978, ApJ, 224, 291\n\\bibitem{} Brandt W.~N., Fabian A.~C., Takahashi K., Fujimoto R., Yamashita A., \nInoue H., Ogasaka Y., 1997a, MNRAS, 290, 617\n\\bibitem{} Brandt W.~N., Mathur S., Reynolds C.~S., Elvis M., 1997b, MNRAS, 292, 407\n\\bibitem{} Brandt W.~N., Laor A., Wills B.~J., 1999, ApJ, in press (astroph/9908016)\n\\bibitem{} Bruzual A.~G., Charlot S., 1993, ApJ, 405, 538\n%\\bibitem{} Carilli C.~L., Menten K.~M., Reid M.~J., Rupen M.~P., Yun M.~S., 1998, ApJ, 494, 175\n\\bibitem{} Comastri A., Setti G., Zamorani G., Hasinger G., 1995, A\\&A, 296, 1\n\\bibitem{} Comastri A., 2000, Astroph. Lett. \\& Comm., submitted\n\\bibitem{} Dickey J.~M., Lockman F.~J., 1990, ARA\\&A, 28, 215\n\\bibitem{} Elvis M., et al., 1994, ApJS, 95, 1\n\\bibitem{} Fiore F., La Franca F., Giommi P., Elvis M., Matt G., \nComastri A., Molendi S., Gioia I., 1999, MNRAS, 306, L55\n\\bibitem{} Francis P.~J., Hewett P.~C., Foltz C.~B., Chaffee F.~H., \nWeymann R.~J., Morris S.~L., 1991, ApJ, 373, 465\n\\bibitem{} Fukugita M., Shimasaku K., Ichikawa T., 1995, PASP, 107, 945\n\\bibitem{} Gallagher S.~C., Brandt W.~N., Sambruna R.~M., Mathur S., Yamasaki N., 1999, ApJ, 519, 549\n\\bibitem{} Gendreau K., 1995, Ph.D. Thesis, Massachussets Inst. Tech.\n\\bibitem{} George I.~M., Turner T.~J., Yaqoob T., et al., 1999, ApJ, in press (astroph/9910218)\n\\bibitem{} Gilli R., Risaliti G., Salvati M., 1999, A\\&A, 347, 424\n\\bibitem{} Halpern J.~P., Eracleous M., Forster K., 1998, ApJ, 501, 103\n\\bibitem{} Hayashi I., Koyama K., Awaki H., Ueno S., Yamauchi S., 1996, PASJ, 48, 219\n\\bibitem{} Kim D.-W., Elvis M., 1999, ApJ, 516, 9\n\\bibitem{} Laor A., Fiore F., Elvis M., Wilkes B.~J., McDowell J.~C., 1997, ApJ, 477, 93 \n\\bibitem{} Madau P., Ghisellini G., Fabian A.~C., 1994, MNRAS, 270, L17 \n\\bibitem{} Makishima K., et al., 1996, PASJ, 48, 171\n\\bibitem{} Masci F.~J., Webster R.~L., Francis P.~J., 1998, MNRAS, 301, 975\n\\bibitem{} Nandra K., Pounds K.~A., 1994, MNRAS, 268, 405\n\\bibitem{} Otani C., Dotani T., 1994, ASCA Newslett., 2, 25\n\\bibitem{} Reeves J.~N., Turner M.~J.~L., Ohashi T., Kii T., 1997, MNRAS, 292, 468\n\\bibitem{} Smith H.~E., Spinrad H., 1980, ApJ, 236, 419\n\\bibitem{} Tanaka Y., Inoue H., Holt S.~S., 1994, PASJ, 46, L37\n\\bibitem{} Vignali C., Comastri A., Stirpe G.~M., Cappi M., Palumbo G.~G.~C., Matsuoka M., \nMalaguti G., Bassani L., 1998, A\\&A, 333, 411\n\\bibitem{} Webster R.~L., Francis P.~J., Peterson B.~A., Drinkwater M.~J., \nMasci F.~J., 1995, Nature, 375, 469\n\\bibitem{} Yuan W., Brinkmann W., Siebert J., Voges W., 1998, A\\&A, 330, 108 \n\\end{thebibliography}"
}
] |
astro-ph0002280
|
Use of DPOSS data to study globular cluster halos: an application to \object{M~92}
|
[
{
"author": "V. Testa \\inst{1}"
},
{
"author": "S. R. Zaggia \\inst{2,3}"
},
{
"author": "S. Andreon \\inst{2}"
},
{
"author": "G. Longo \\inst{2}"
},
{
"author": "R. Scaramella \\inst{1}"
},
{
"author": "S.G. Djorgovski \\inst{4}"
},
{
"author": "R. de Carvalho \\inst{5}"
}
] |
We exploited the large areal coverage offered by the Digitized Palomar Observatory Sky Survey to analyze the outermost regions of the galactic globular cluster \object{M~92} (\object{NGC~6341}). Two independent photometric reduction programs (SKICAT and DAOPHOT) were used to construct a color-magnitude diagram and a surface density profile for this cluster, based on J- and F-band DPOSS plates. A strong similarity has been found in the performance of the two programs in the low--crowded outermost cluster regions. After removing the background contribution, we obtained the cluster outer surface density profile down to a surface brightness magnitude of $\mu_{\mathrm V} \sim$ 31 mag arcsec$^{-2}$ and matched it with the inner profile of Trager et al. (\cite{Tra95}). The profile shapes match very well: since our data are uncalibrated, the shift in magnitudes between the profiles has been also used to calibrate our profile. The analysis shows that the cluster has an extra tidal halo extending out to $\sim 30\arcmin$ from the cluster center at a $3~\sigma$ level over the background noise. This halo is revealed to be almost circular. \keywords{globular clusters: general - globular clusters: individual: M~92 - Galaxy: kinematics and dynamics}
|
[
{
"name": "testa.tex",
"string": "\\documentclass{aa}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\usepackage{graphics}\n\\usepackage{times}\n\\usepackage{mathptm}\n%\\usepackage{amssymb}\n\\fontfamily{ptm}\n\\selectfont\n\n\\hbadness 10000\n\\vbadness 10000\n\n\\begin{document}\n\n\\thesaurus{05(10.07.2; 10.11.1; 10.07.03 \\object{M~92})}\n\\offprints{V. Testa, testa@coma.mporzio.astro.it}\n\n\\title{Use of DPOSS data to study globular cluster halos: an\napplication to \\object{M~92}}\n\n\\author{V. Testa \\inst{1}\\and S. R. Zaggia \\inst{2,3} \\and S. Andreon \\inst{2}\n\\and G. Longo \\inst{2} \\and R. Scaramella \\inst{1} \\and \nS.G. Djorgovski \\inst{4} \\and R. de Carvalho \\inst{5}}\n\n\\institute{ Osservatorio Astronomico di Roma, via Frascati, 33\n\tI-00040 Monteporzio Catone, Italy\n \\and Osservatorio Astronomico di Capodimonte, via Moiariello 16,\n\tI-80131 Napoli, Italy\n \\and European Southern Observatory, K. Schwarzschild Str. 2, \n\tD-85748, Garching, Germany \n \\and Department of Astronomy, California Institute of Technology, \n\tMS 105-24, Pasadena, CA 91125, USA\n \\and Observatorio Nacional de Rio de Janeiro, Rio de Janeiro,Brazil}\n\n\\date{Received 17 Aug 1999/ Accepted 25 Jan 2000}\n\n\\titlerunning{Extra-tidal halos in GCs: \\object{M~92}}\n\\authorrunning{V.~Testa et al.}\n\n\n\\maketitle\n\n\\begin{abstract} We exploited the large areal coverage offered by the\nDigitized Palomar Observatory Sky Survey to analyze the outermost regions \nof the galactic\nglobular cluster \\object{M~92} (\\object{NGC~6341}). Two independent\nphotometric reduction programs (SKICAT and DAOPHOT) were used to\nconstruct a color-magnitude diagram and a surface density \nprofile for this\ncluster, based on J- and F-band DPOSS plates. A strong similarity has \nbeen found in the performance of the two programs in the low--crowded\noutermost cluster regions. After removing the background contribution,\nwe obtained the cluster outer surface density profile\ndown to a surface brightness magnitude of \n$\\mu_{\\mathrm V} \\sim$ 31 mag arcsec$^{-2}$ and matched it with the \ninner profile of Trager et al. (\\cite{Tra95}). The profile shapes match \nvery well: since our data are uncalibrated, the shift in magnitudes \nbetween the profiles has been also used to calibrate our profile. The \nanalysis shows that the cluster has\nan extra tidal halo extending out to $\\sim 30\\arcmin$ from the cluster\ncenter at a $3~\\sigma$ level over the background noise. This halo is revealed\nto be almost circular.\n\n\\keywords{globular clusters: general - globular clusters: individual: M~92 - \nGalaxy: kinematics and dynamics}\n\\end{abstract}\n\n\\hbadness 10000\n\n\n%________________________________________________________________\n\n\\section{Introduction}\n\nThe tidal radii of globular clusters (GCs) are\nimportant tools for understanding the complex interactions of GCs with\nthe Galaxy. In fact, they have traditionally been used to study the\nmass distribution of the galactic halo (Innanen et al. \\cite{Inn83}), \nor to deduce GCs\norbital parameters (Freeman \\& Norris \\cite{Fre81}; Djorgovski et al.\n \\cite{DJ96}). Tidal radii have usually been\n{\\it estimated} (only in few cases {\\it directly} measured), by\nfitting King models to cluster density profiles rarely\nmeasured from the inner regions out to the tidal radius, because of\nthe nature of the photographic material, that prevented any measure in\nthe cluster center, and the small format of the first digital cameras.\n Only in the last few years, the advent of\ndeep digitized sky surveys and wide field digital detectors has allowed\nus to deal with the overwhelming problem of\ncontamination from field stars and to probe the outer region\nof GCs directly (Grillmair et al. \\cite{Gri95}, hereafter G95; \nZaggia et al. \\cite{Zag95}; Zaggia et al. \\cite{Zag97}; Lehman \\& \nScholz \\cite{LS97}). The study of tidal tails in\ngalactic satellites is gaining interest for many applications related\nto the derivation of the galactic structure and potential, the\nformation and evolution of the galactic halo, as well as the dynamical\nevolution of the clusters themselves. Recent determinations of \nproper motion for some globular clusters with HIPPARCOS have made it\npossible to estimate the orbital parameters of a good number of\nthem (Dinescu et al. \\cite{Din99}). This helps to clarify the\nnature and structure of tidal extensions in GCs. \n\nIn principle,\navailable tools to enhance cluster star counts against field stars\nrely on the color-magnitude diagram (CMD), proper motions, radial\nvelocities, or a combination of the three techniques. The application\nof these techniques to GCs have led to the discovery that tidal or\nextra-tidal material is a common feature: Grillmair (\\cite{Gri98}), for\ninstance, reported the discovery of tidal tails in 16 out of 21\nglobular clusters. Interestingly, signature of the presence of tidal\ntails in GCs has also been found in four GC's in M31 (Grillmair \n\\cite{Gri96}). For galactic clusters, the discovery was made by using \na selection in the CMD of cluster stars on catalogs extracted from \ndigitized photographic datasets. The CMD selection technique is an \neconomical and powerful method to detect GC tails, since it significantly \ndecreases the number of background and/or foreground objects.\n\n\\begin{figure*}[t]\n\\resizebox{10cm}{!}{\\includegraphics{testa_fig1.ps}} %\\hfill \n\\parbox[b]{55mm}{\n\\caption{A comparison of objects detected in the inner parts of\n\\object{M~92} by SKICAT (filled triangles) and DAOPHOT (dots) for the\ntwo different plates: $J$ ({\\it upper panel}) and $F$ ({\\it lower\npanel}). The inner circle (continuous) marks the circular aperture\nwhere plate detections cannot be used. The outer circle (short-dash)\nmarks the annular region where crowding correction is important. In\nboth panels North is up and East is to the right. The two diagonal\nbands in the lower panel indicate the satellite tracks where SKICAT\ndetects no objects.}\n\\label{fig1}}\n\\end{figure*}\n\n\nIn order to test the feasibility of a survey of most GCs present in\nthe Northern hemisphere, we applied the CMD technique to the galactic\nglobular cluster \\object{M~92} (NGC~6341), with the aim of \nmeasuring the tidal radius and searching for the possible presence of\nextra-tidal material. We used plates from the Digitized Second\nPalomar Sky Survey (hereafter DPOSS), in the framework of the CRoNaRio\n(Caltech-Roma-Napoli-Rio de Janeiro) collaboration\n(Djorgovski et al. \\cite{DJ97}, Andreon et al. \\cite{And97}, \nDjorgovski et al. \\cite{DJ99}). A previous account on this work was\ngiven in Zaggia et al. (\\cite{Zag98}). This is the first of a series \nof papers dedicated to the subject --an ideal application \nfor this kind of all-sky surveys.\n\n\\begin{figure*}[t]\n\\resizebox{10cm}{!}{\\includegraphics{testa_fig2.ps}} \\hfill \n\\parbox[b]{55mm}{\n\\caption{Comparison between SKICAT $M_{Core}$ and DAOPHOT aperture\nmagnitude in the filters $F$ ({\\it upper panel}) and $J$ ({\\it lower\npanel}).The histograms of the distributions, expressed in percentage of the\ntotal, are reported at the right edge of the plots.}\n\\label{fig2}}\n\\end{figure*}\n\n\\section{The Color$-$Magnitude Diagram}\n\nThe material used in this work are the $J$ and $F$ DPOSS plates of the\nfield 278. For each band, we extracted from the whole digitized plate\na sub-image (size: $8032 \\times 8032$ pixels), corresponding to an area\nof $136\\arcmin \\times 136\\arcmin$ , with a pixel size of $1\\arcsec$,\ncentered on \\object{M~92} at coordinates (Harris \\cite{Har96}):\n\n\\[\n\\alpha _{J2000}=17^{h}\\;17^{m}\\;07.3^{s}\n\\]\n\\[\n\\delta _{J2000}=+43^{o}\\;08{\\arcmin }\\;11.5{\\arcsec}\n\\]\n\n\\begin{figure*}[t]\n\\resizebox{12cm}{!}{\\includegraphics{testa_fig3.ps}} \\hfill \n\\parbox[b]{55mm}{\n\\caption{Color magnitude diagram of the stars detected in the field of\nthe globular cluster \\object{M~92}. {\\it Left panel:} CMD of \\object{M~92} \nin an annular region at $5' < r < 12'$. {\\it Right panel:} background field \nCMD in an annulus at $60' < r < 67'$.}\n\\label{fig3}}\n\\end{figure*}\n\nThe two images were linearized by using a density-to-intensity (DtoI)\ncalibration curve, provided by the sensitometric spots available on the\nDPOSS plates. The $F$ plate is contaminated by two very similar\nsatellite tracks (as an alternative, the two tracks come from a\nhigh altitude civil airplane) lying $\\sim 9\\arcmin$ and $\\sim\n13\\arcmin$ from the cluster center and crossing the field in a\nSouth-East/North-West direction. The effect of these tracks can be\nseen as empty strips on the lower panel of Fig.~\\ref{fig1}. Other\nthin, fainter tracks and some galaxies are present on the same\nplate, but at larger distances from the cluster core region. We\napplied the CMD technique to datasets obtained with different\nastronomical packages, in order to test the reliability of object\ndetection and photometry in crowded stellar fields. On the DPOSS\nplates containing \\object{M~92}, we used both the SKICAT and\nDAOPHOT packages. SKICAT, written at Caltech (see Weir et al. \n\\cite{Wei95a}, and refs. therein), is the standard software\nused by the CRoNaRio collaboration for the DPOSS plate processing and \ncatalog construction. DAOPHOT is a well-tested program for stellar photometry,\ndeveloped by Stetson (\\cite{Ste87}), and widely used by stellar astronomers. \nIn this work we have used DAOPHOT only to obtain aperture photometry,\nwith APPHOT, of objects detected with the DAOFIND algorithm on the\nDPOSS plates.\n\n\n\n\\subsection{The data set}\n\nThe SKICAT output catalog only contains objects classified as\nstars in both filters. For each object, we used\n$M_{\\mathrm{Core}}$ (the magnitude computed from the central\nnine pixels), because the other aperture magnitude is measured on an area\nfar too large for crowded regions. The final SKICAT catalog consists of\n108779 objects. Since SKICAT is optimized for the detection of faint\ngalaxies, in the present case we needed to test its performances in\ncrowded stellar fields to ensure that it properly detected the stellar\npopulation around the cluster.\n\nThus, SKICAT has been compared to DAOPHOT, which is\nspecifically designed for crowded fields stellar photometry and has\nbeen repeatedly tested in a variety of environments, including\nglobular clusters. The DAOPHOT dataset was built using aperture\nphotometry on the objects detected with the DAOFIND. The threshold was\nset at $3.5~\\sigma$, similar to the one used by SKICAT. Aperture\nphotometry was preferred to PSF fitting photometry, due to the large\nvariability of the DPOSS point-spread function which makes the\nPSF photometry less accurate than the aperture photometry. We used an\naperture of $1.69$ pixels of radius, corresponding to an area of\napproximately 9 pixels, i.e. equivalent to the area used by\nFOCAS/SKICAT to compute $M_{\\mathrm{Core}}$. Indeed, the\nadvantages of using PSF fitting are more evident in the central and\nmore crowded regions of the cluster, while we are mainly interested in\nthe outskirts, where crowding is less dramatic. Thus, we adopted the\nresults from the aperture photometry, and we refer to this dataset as\nthe DAOFIND+PHOT dataset.\n\nThe total number of objects detected in the $J$ and $F$ plates is,\nrespectively, 240138 and 253977. The larger number of objects detected\nby DAOFIND, compared to those from SKICAT, is mainly due to the better\ncapacity of DAOFIND in detecting objects in the crowded regions of the\ncore. In the case of DAOFIND, since the convolution kernel, which is set \nessentially by the pixel size and seeing value, is much smaller than\nin SKICAT, we also have objects measured near the satellite tracks.\n\n\\begin{figure*}[t]\n\\resizebox{12cm}{!}{\\includegraphics{testa_fig4.ps}} \\hfill \n\\parbox[b]{55mm}{\n\\caption{\\object{M~92} radial density profile. Open dots, \nTrager et al. (1995) data; filled dots, DPOSS SCs; crosses, crowding \nuncorrected SCs; solid line, isotropic King model.}\n\\label{fig4}}\n\\end{figure*}\n\nThe FOCAS/SKICAT and DAOFIND+PHOT aperture photometry were then\ncompared, and the results are shown in Fig.~\\ref{fig2} where the SKICAT\naperture magnitude is plotted versus the difference between itself and\n$M_{\\mathrm{Core}}$. The average difference is zero, with an\nerror distribution typical of this kind of tests, i.e. a\nfan-like shape with growing dispersion at fainter magnitudes. The\ndistribution of F magnitudes in Fig.~\\ref{fig2} clearly shows the effects of\nsaturation at the bright end, and in both plots there are several\noutliers, owing to the field crowding. In fact, these outliers\nare much more concentrated in the inner $12 \\arcmin$, where their\ndensity is 0.439 arcmin$^{-2}$, than at larger distances from the\ncenter, where the density drops to 0.022 arcmin$^{-2}$. \nThese objects are mostly classified as non stellar by SKICAT and DAOPHOT,\nsince they are either foreground galaxies or, more often, unresolved\nmultiple objects, and were rejected in the final catalogs. Their area\nis taken into account later on, when we compute the effective area of the\nannuli in the construction of the radial profile. The outliers show an\nasymmetric distribution with SKICAT magnitudes being brighter at\nbright magnitudes and viceversa at fainter magnitudes. This is due\nto two reasons: in the case of large objects, SKICAT splits them into\nmultiple entries, but keeps the $M_{\\mathrm{Core}}$ value of \nthe originally detected (big) object; at fainter magnitudes,\nwhere objects are small, $M_{\\mathrm{Core}}$ is computed on a\nnumber of pixels less than 9, while the aperture photometry of the\nobjects in the DAOFIND catalog are always computed on a circle of 1.69\npixel radius.However, the\ncontribution of these outliers to the counts is far below 1 percent\nof the total, as can be seen from the histogram plotted on the right hand\nside of fig. \\ref{fig2}.\n\nThe above analysis shows that SKICAT catalogs are, after a suitable\ncleaning, usable ``as they are'' also for studies of moderately\ncrowded stellar fields. We shall use the\nDPOSS-DAOPHOT dataset because it can better detect \nobjects in highly crowded fields, which allows us to probe into the\ninner ($200 \\arcsec < r < 400 \\arcsec$) regions of the cluster and \nmerge our star counts profile with the published one of Trager et al.\n(\\cite{Tra95}, hereafter T95).\n\n\n\\subsection{The color-magnitude diagram}\n\nIn order to build the CMD of the cluster, individual catalogs were\nmatched by adopting a searching radius of 5 $\\arcsec$, and keeping \nthe matched object with the smallest distance. The derived CMD \nis shown in Fig.~\\ref{fig3} for two annular\nregions: the inner one, between 5$\\arcmin$ and 12$\\arcmin$ from the center \n(left-hand panel) and the outer one, referring to the background, \nbetween 60$\\arcmin$ and 67$\\arcmin$ (right-hand panel). The \\object{M~92}\nturn-off region, as well as part of the horizontal branch, are clearly\nvisible. At bright magnitudes, the giant branch turns to the blue, due to \nplate saturation. At large angular distances\nfrom the center of \\object{M~92}, most objects are galactic stars with\nonly a small contribution from the cluster.\n\nFor reducing the background/foreground field contribution, we used an\napproach similar to that of Grillmair et al. \\cite{Gri95}. First of all,\nWe selected an annular region ($200 \\arcsec <r<300 \\arcsec$) around the \ncluster center to find the best fiducial CMD sequence of the cluster\nstars. Then, the CMD of this region was compared with the CMD of the\nfield at a distance greater than $\\simeq1^\\circ$ from the cluster\ncenter. The two CMD's were normalized by their area and then we\nbinned the CMD and computed the $S/N$ ratio of each element, just like \nin G95 (their Eq. 2). Finally, we then\nobtained the final contour of the best CMD region by cutting at a\n$S/N \\simeq 1$. Contours are shown in Fig.~\\ref{fig3}, on which a solid\nline marks the CMD region used to select the ``bona fide'' cluster\nstars as described above. We must say that this CMD selection\nis not aimed at finding all the stars in the cluster but only at\nthe best possible enhancement of the cluster stars as compared to the field\nstars. This is why the region of the sub-giant/giant branch is not\nincluded, since here the cluster stars are fewer than in the field. \nBy extracting objects at any distance\nfrom the center of the cluster, in the selected CMD region, the field\ncontamination is reduced by a factor of $\\sim 7$. In absence of strong\ncolor gradients, the fraction of lost stars does not depend on the\ndistance from the center.\n\n\\section{Extra-tidal excess in \\object{M~92}}\n\n\\subsection{Radial density profile}\n\nAs first step, we built a 2-D star density map by binning the\ncatalog in step of $1\\arcmin \\times 1\\arcmin$. Then, we fitted a polynomial\nsurface to the background, selecting only the outermost regions of the\nstudied area. The background correction is expressed in the same units\nof 2-D surface density counts, and can be direclty applied to the raw \ncounts.\nA tilted plane was sufficient to interpolate the background star\ncounts (SCs). Higher-order polynomials did not provide any\nsubstantial improvement over the adopted solution. We compared the\nfitted background with IRAS maps at 100$\\mu$, but we did not find any\ndirect signs of a correlation between the two. Rather, the direction of \nthe tilt is consistent with the direction of the galactic center. \nHence, the tilt of the background, which is however very small \n($\\sim 0.01 \\mathrm{mag/arcmin}$), can be considered as due to the \ngalactic gradient.\n\nThe cluster radial density profile was obtained from the background\nsubtracted SC's by counting stars in annuli of equal logarithmic\nsteps. The uncorrected surface density profile (hereafter SDP) is\nexpressed as:\n$$SDP_{i}^{\\mathrm{uncorr}}=-2.5*log(N_{i,i+1}/A_{i,i+1})+const,$$ \nwhere $N_{i,i+1}$ indicates the number of objects in the annulus\nbetween $r_{i}$ and $r_{i+1}$, and $A_{i,i+1}$ \n the area of the\nannulus. The constant was determined by matching the profile with the\npublished profile of T95 in the overlap range. \nThe effective radius at each point of the profile is given by:\n$$r_{i}^{\\mathrm{eff}}=\\sqrt{{1 \\over 2}\\times(r_{i}^2+r_{i+1}^2)}.$$\n\n\nThe SDP must now be corrected for crowding.\nWhen dealing with photographic material, it is not\npossible to apply the widely known artificial star\ntechnique used with CCD data. Therefore, we used a procedure similar\nto the ones described in Lehman \\& Scholz (\\cite{LS97}) and Garilli et al.\n(\\cite{Gar99}): we estimated the\narea occupied by the objects in each radial annulus by selecting all\nthe pixels brighter than the background noise level plus three sigmas,\nand considered as virtually uncrowded the external annuli in which the\npercentage (very small, $\\simeq0.5\\%$) of filled area did not vary\nwith the distance. The external region starts at $\\sim 1000\n\\arcsec$ from the cluster center with a filling factor smaller than\n$\\simeq 2\\%$. After correcting the area covered by non-stellar\nobjects, the ratio unfilled/filled area\ngives the crowding correction. This correction was computed at the\neffective radii of the surface brightness profile (hereafter SBP) and\nsmoothed using a spline function. The corrected surface brightness\nprofile was then computed as:\n$$SBP_{i}=SBP_{i}^{\\mathrm{uncorr}}+2.5\\times \\mathrm{log}(1.0-frac)$$\nwhere $frac$ is the crowding correction factor determined at the\ni$-th$ point on the profile. \n\\begin{figure*}\n\\resizebox{12cm}{!}{\\includegraphics{testa_fig5.ps}} \\hfill \n\\parbox[b]{55mm}{\n\\caption{Fit of a power law to the external profile of \\object{M~92},\nexpressed in number surface density to allow for an immediate comparison\nwith Johnston et al. (\\cite{Jon99}, hereafter J99), and binned to smooth \nout oscillations due to the small dimension of the annuli. Triangles \nindicate the profile of the extra-tidal halo. Diamonds represent \nthe binned and averaged profile within the tidal radius. The dashed line \nis the fitting power law with $\\gamma = -0.85 \\pm 0.08$.}\n\\label{fig5}}\n\\end{figure*}\n\nThe crowding corrected SBP of \\object{M~92} derived from DPOSS data is \nshown in Fig.~ \\ref{fig4} as filled dots and the uncorrected counts as \ncrosses. Table~\\ref{tab1} lists the measured surface brightness profile. \nWith a simple number counts normalization we joined our\nprofile to the one (open circles) derived by T95,\nin order to extend the profile to the inner regions. We then fitted a \nsingle-mass King model to our profile. The fitting profile is drawn on\nFig.~\\ref{fig4} as a continuous line. Our value for the tidal\nradius, $r_{\\mathrm t} = 740\\arcsec$, turned out to be similar to the \nvalue\ngiven in Brosche et al. (\\cite{Bro99}), $r_{\\mathrm t} = 802\\arcsec$ and \nslightly smaller than the one given in T95, \n$r_\\mathrm{t} =912\\arcsec$. As it can be seen from\nthe figure, DPOSS data extend at larger radial distances than the\nT95 compilation and reveal the existence \nof a noticeable deviation from the isotropic King model derived from the\ndirect fitting of the SBP. This deviation is a clear sign of the\npresence of extra tidal material. We also tried fitting anisotropic \nKing models to the SBP, but the fit was not as good as in the isotropic\ncase.\n\n\\begin{table}\n\\caption{Measured surface brightness profile}\n\\label{tab1}\n\\begin{tabular}{cccc}\n\\hline\nlog($r$) & $V_{SBP}^{uncorr.}$ & $V_{SBP}^{corr.}$ & $\\sigma(V_{SBP})$ \\\\\n\\hline\n2.307 & 24.09 & 21.84 & 0.09 \\\\\n2.348 & 23.90 & 22.39 & 0.06 \\\\\n2.389 & 23.96 & 23.10 & 0.09 \\\\\n2.431 & 23.83 & 23.22 & 0.05 \\\\\n2.472 & 24.00 & 23.62 & 0.07 \\\\\n2.514 & 24.17 & 23.89 & 0.06 \\\\\n2.555 & 24.50 & 24.36 & 0.06 \\\\\n2.596 & 24.89 & 24.79 & 0.07 \\\\\n2.638 & 25.26 & 25.19 & 0.07 \\\\\n2.679 & 25.87 & 25.82 & 0.10 \\\\\n2.720 & 26.25 & 26.21 & 0.09 \\\\\n2.762 & 26.79 & 26.75 & 0.13 \\\\\n2.803 & 27.38 & 27.34 & 0.14 \\\\\n2.845 & 27.97 & 27.93 & 0.19 \\\\\n2.886 & 28.70 & 28.66 & 0.30 \\\\\n2.927 & 28.90 & 28.86 & 0.28 \\\\\n2.969 & 29.76 & 29.72 & 0.54 \\\\\n3.010 & 29.61 & 29.56 & 0.41 \\\\\n3.052 & 29.75 & 29.71 & 0.41 \\\\\n3.093 & 29.73 & 29.69 & 0.38 \\\\\n3.134 & 30.03 & 29.98 & 0.43 \\\\\n3.176 & 29.91 & 29.87 & 0.36 \\\\\n3.217 & 30.46 & 30.42 & 0.51 \\\\\n3.300 & 31.28 & 31.23 & 0.85 \\\\\n3.341 & 31.02 & 30.97 & 0.62 \\\\\n3.383 & 30.87 & 30.82 & 0.50 \\\\\n3.424 & 31.26 & 31.21 & 0.63 \\\\\n3.466 & 31.24 & 31.19 & 0.57 \\\\\n\\hline\n\\end{tabular}\n\n\\end{table}\n\n\nAt what level is this deviation significant? The determination of the\ntidal radius of a cluster is still a moot case.\nWhile fitting a King model to a cluster density\nprofile, the determination of the tidal radius comes from a\nprocedure where the overall profile is considered, and internal\npoints weigh more than external ones. On the one hand, this is an\nadvantage since the population near the limiting radius is a mix of\nbound stars and stars on the verge of being stripped from the cluster\nby the Galaxy tidal potential. On the other hand, the tidal radius\nobtained in this way can be a poor approximation of the real one. \nIn the classical picture, and in presence of negligible diffusion, the\ncluster is truncated at its tidal radius at perigalacticon\n(see Aguilar et al. \\cite{Agu88}). Nevertheless, Lee \\& Ostriker \n(\\cite{Lee87}) pointed out that\nmass loss is not instantaneous at the tidal radius, and, for a given\ntidal field, they expect a globular cluster to be more populated \nthan in the corresponding King model. Moreover, a globular cluster along\nits orbit also suffers from dynamical shocks, due to the crossing of the \nGalaxy disk and, in case of eccentric orbits, to close passages near the\nbulge, giving rise to enhanced mass-loss and, later on, to\nthe destruction of the globular cluster itself. \nGnedin \\& Ostriker (\\cite{Gne97}) found that, after a gravitational shock,\nthe cluster expands as a whole, as a consequence of internal heating. \nIn this case, some stars move beyond\nthe tidal radius but are not necessarily lost, and are still\ngravitationally bound to the cluster. This could explain observed\ntidal radii larger than expected for orbits with a small value of the\nperigalacticon. Brosche et al. (\\cite{Bro99}) point out that the observed\nlimiting radii are too large to be compatible with perigalacticon \n$r_\\mathrm{t}$, and suggest\nthat the appropriate quantity to be considered is a proper average of\ninstantaneous tidal radii along the orbit. It can be seen from\nFig.~\\ref{fig4} that the cluster profile deviates from the\nsuperimposed King model before the estimated tidal radius, and has a\nbreak in the slope at about $r\\sim850\\arcsec$, after which the slope\nis constant. We shall come back later to this point. \n\nIn Fig.~\\ref{fig5} we show the surface density profile, expressed in \nnumber of stars to allow a direct comparison with J99, and binned in order to smooth out oscillations in the \nprofile, due to the small S/N ratio arising with small-sized annuli.\nJ99 predict that stars stripped from \na cluster, and forming a tidal stream, show a density profile described \nby a power law with exponent $\\gamma = -1$. We fitted a power law of \nthe type $\\Sigma(r) \\propto r^{\\gamma}$ to the extra-tidal profile \n(dashed line). The best fit gives a value $\\gamma = -0.85 \\pm 0.08$ \nand is shown as a dashed line in Fig. \\ref{fig5}. The errors on the\nprofile points include also the background uncertainty, in quadrature,\nso that the significance of the extra-tidal profile has been estimated in\nterms of the difference $f_i-3\\sigma_i$, where $f_i$ is \nthe number surface density profile at point $i$, and $\\sigma_i$ its\nerror, which includes the background and the signal Poissonian\nuncertainties. This quantity is positive for all the points except\nfor the outermost one. The fitted slope is consistent with the value\nproposed by J99 and in good accordance with literature values for other \nclusters (see G95 and Zaggia et al. \\cite{Zag97}).\n\nWe then fit an ellipse to the extra-tidal profile in\norder to derive a position angle of the tidal extension, and\nchecked whether the profile in that direction differs from the one\nobtained along the minor axis of the fitting ellipse, to\nconfirm that the extra-tidal material is a tail rather than a\nhalo. The best fitting ellipse, made on the ``isophote'' at the\n$2~\\sigma$ level from the background (approximately $1.5r_{\\mathrm t}$ \nfrom the center of the cluster), turned out to have a very low ellipticity,\n($e \\leq 0.05\\pm0.01$ at P.A.$ \\simeq 54^\\circ\\pm15^\\circ$). We have also\nmeasured the radial profiles along the major and minor axes, using an\naperture angle of $\\pm 45^\\circ$, in order to enhance the S/N ratio in\nthe counts. The two profiles turned out to be indistinguishable\nwithin our uncertainties. This result shows that the halo material has\na significantly different shape than the internal part of the cluster\nwhich shows an ellipticity of $0.10\\pm0.01$ at P.A. $141^\\circ\\pm1$ as\nfound by White \\& Shawl (\\cite{Whi87}).\n\n\n\\begin{figure*}[t]\n\\resizebox{12cm}{!}{\\includegraphics{testa_fig6.ps}} \\hfill \n\\parbox[b]{55mm}{\n\\caption{\\object{M~92} surface density map from background \nsubtracted star\ncounts. The black, thick circle is drawn at the estimated tidal radius\nof \\object{M~92}. The long, thicker arrow indicates the direction of the \ngalactic\ncenter, the thin arrow indicates the proper motion of the cluster as\nin Dinescu et al. (\\cite{Din99}). Contours are \n drawn at 1,2 and 3 $\\sigma$ of the background.}\n\\label{fig6}}\n\\end{figure*}\n\n\\subsection{Surface density map}\n\nIn the attempt to shed more light upon presence and \ncharacteristics of the extra-tidal extension, we used the 2-D star\ncounts map, as described at the beginning of the previous section. We\napplied a Gaussian smoothing algorithm to the map, in order to enhance\nthe low spatial frequencies and cut out the high frequency spatial\nvariations, which contribute strongly to the noise. We smoothed\nthe map using a Gaussian kernel of $6 \\arcmin$. The resulting smoothed\nsurface density map is shown in Fig.~\\ref{fig6}. Since the background\nabsolute level is zero, the darkest gray levels indicate negative star\ncounts. In this image, the probable tidal tail of \\object{M~92}\n(light-gray pixels around the cluster) is less prominent than in the\nradial density profile: this is because data are not\naveraged in azimuth. On the map we have drawn three ``isophotal''\ncontours at 1, 2 and 3$~\\sigma$ over the background. The fitted tidal\nradius is marked as a thick circle and the two arrows point toward the\ngalactic center (long one) and in the direction of the measured \nproper motion (see Dinescu et al. \\cite{Din99}). The tidal halo does not \nseem to have a preferred direction. A marginal sign of elongation is\npossibly visible along a direction almost orthogonal to that of\nthe galactic center.\n\nAs pointed out in the previous section, if we build the profile along\nthis direction and orthogonally to it, we do not derive clear signs of\nany difference in the star count profiles in one direction or the other,\nmainly because of the small number counts. \n\nOn the basis of these results, we can interpret the extra-tidal\nprofile of \\object{M~92} as follows: at radii just beyond the fitted King\nprofile tidal radius, the profile resembles a halo of stars --most likely \nstill tied up to the cluster or in the act of being stripped\naway. As the latter process is not instantaneous, these stars will\nstill be orbiting near the cluster for some time. We\ncannot say whether this is due to heating caused by tidal shocks,\nor to ordinary evaporation: a deep CCD photometry to study the mass\nfunction of extra-tidal stars would give some indications on this\nphenomenon. At larger radii, the 1 $\\sigma$ ``isophote'' shows a barely \napparent elongation of the profile in the direction\nSW to NE, with some possible features extending approximately towards \nS and E. Although the significance is only at 1 $\\sigma$ \nlevel, these structures are visible and might be made up by stars escaping \nthe cluster and forming a stream along the orbit. As pointed out in \nMeylan \\& Heggie (\\cite{Mey97}), stars escape from the cluster from the \nLagrangian points situated on the\nvector connecting the cluster with the center of the Galaxy, thus\nforming a two-sided lobe, which is then twisted by the Coriolis force.\nA clarifying picture of this effect is given in Fig. 3 of \nJohnston (\\cite{Jon98}). \n\n\n\\section{Summary and conclusions}\n\nWe investigated the presence and significance of a tidal extension of\nthe brightness profile of \\object{M~92}. The main results of our study are:\n\\begin{enumerate}\n\n\\item The presence of an extra-tidal profile extending out to\n$\\sim~0.5^{\\circ}$ from the cluster center, at a significance level of\n$3~\\sigma$ out to $r~\\sim~2000~\\arcsec$. We found no strong evidence\nfor preferential direction of elongation of the profile. This may\nimply that we are detecting the extra-tidal halo of evaporating stars,\nwhich will later form a tidal stream. Moreover, the tidal tail might be\ncompressed along the line of sight --see, for instance, Fig.~18\nof G95. In fact, G95 point out that tidal tails extend over enormous \ndistances ahead and behind the cluster orbit, and the volume density \nis subject to the open-orbit analogous of Kepler's third law: near \napogalacticon, stars in the tidal tail undergo differential slowing-down, \nso that the tail converges upon the\ncluster. Actually, most models (e.g., Murali \\& Dubinsky \\cite{Mur99})\npredict that the extra-tidal material should continue to follow the\ncluster orbit and thus take the shape of an elongated tail, or a\nstream. The stream has been already revealed in dwarf spheroidal\ngalaxies of the local group (Mateo et al. \\cite{Mat98}), but \nwhether the stream can also be visible in significantly smaller objects\nlike globular clusters is currently a moot point.\n\n\\item By constructing the surface density map and performing a\nGaussian smoothing, the low-frequency features are enhanced over the\nbackground. We find some marginal evidence for a possible elongation\nin the extra-tidal extention based on a visual inspection of this map.\nThis elongation may be aligned in a direction perdendicular\nto the Galactic center, although we already know that the significance of\nthis result is low; additional observations will be required to settle\nthe issue. A similar displacement is described in Fig.~3 of\nJohnston (\\cite{Jon98}).\n\n\\end{enumerate}\n\nFinally, we want to stress the power of the DPOSS material\nin conducting this kind of programs, either by using the standard output\ncatalogs, as they come out from the processing pipeline, or the\nspecific re-analysis of the digitized plate scans. In the future we\nwill extend this study to most of the globular clusters present on the\nDPOSS plates.\n\n\\begin{acknowledgements}\nSGD acknowledges support from the Norris Foundation. We thank the\nwhole POSS-II, DPOSS, and CRoNaRio teams for their efforts.\n\\end{acknowledgements}\n\n%\\bibliographystyle{plain}\n%\\bibliography{mnemonic,biball}\n\n\\begin{thebibliography}{}\n\\bibitem[1988]{Agu88} Aguilar L.,Hut P., Ostriker J.P., 1988, ApJ 335, 720\n\\bibitem[1997]{And97} Andreon S., Zaggia S.R., de Carvalho R. et al., 1997, \nin: Proceedings of the XVIIth Moriond astrophysics\nmeeting ``Extragalactic Astronomy in the Infrared'', eds. G. Mamon,\nT. X. Thuan, Y. T. Van, Editions Fronti\\`eres (Gif-sur-Yvette),\np. 409\n\\bibitem[1999]{Bro99} Brosche P., Odenkirchen M., Geffert M., 1999, \nNewAst 4, 133\n\\bibitem[1999]{Din99} Dinescu D.I., Girard T.M., van Altena W.F., 1999, \nAJ 117, 1792\n\\bibitem[1996]{DJ96} Djorgovski S.G., 1996, in: ``Dynamical evolution of \nStar Clusters - Confrontation of Theory and Observation'', IAU Symp. 174, \neds. P.Hut, J.Makino, Dordrecht: Kluwer, p. 9\n\\bibitem[1992]{DJ92} Djorgovski S.G., Lasker B.M., Weir W.M. et al., 1992, \nAAS Meeting 180, p. 1307\n\\bibitem[1997]{DJ97} Djorgovski S.G., de Carvalho R.R., Gal R. et al., 1997, \nin: ``New Horizons From Multi-Wavelength Sky Surveys'', IAU Symp. 179, \ned. B. McLean, Dordrecht: Kluwer, p. 424\n\\bibitem[1999]{DJ99} Djorgovski S.G., Gal R.R., Odewahn S.C. et al., 1999, \nThe Palomar Digital Sky Survey (DPOSS), in: ``Wide Field Surveys in \nCosmology'', eds. S. Colombi, Y. Mellier, B. Raban, \nGif-sur-Yvette: Editions Fronti\\`eres, p. 89\n\\bibitem[1981]{Fre81} Freeman K., Norris J., 1981, ARA\\&A 19, 319\n\\bibitem[1999]{Gar99} Garilli B., Maccagni D., Andreon S., 1999, \nA\\&A 342, 408\n\\bibitem[1997]{Gne97} Gnedin O., Ostriker J.P., 1997, ApJ, 474, 223\n\\bibitem[1998]{Gri98} Grillmair C. J., 1998, Probing the Galactic Halo with \nGlobular Cluster Tidal Tails, in: ASP Conf. Ser. 136: ``Galactic Halos: A UC \nSanta Cruz Workshop'', ed. D. Zaritsky, p. 45\n\\bibitem[1995]{Gri95} Grillmair C., Freeman K., Irwin M., Quinn P., 1995, \nAJ 109, 2553 (G95)\n\\bibitem[1996]{Gri96} Grillmair C.J., Ajhar E.A., Faber S.M. et al., \n1996, AJ 111, 2293\n\\bibitem[1996]{Har96} Harris W., 1996, AJ, 112, 1487 \n\\bibitem[1983]{Inn83} Innanen K.A., Harris W.E., Webbink R.F., 1983, \nAJ 88, 338\n\\bibitem[1998]{Jon98} Johnston K.V., 1998, ApJ 495, 297\n\\bibitem[1999]{Jon99} Johnston K.V., Sigurdsson S., Hernquist L., 1999, \nMNRAS 302, 771 (J99)\n\\bibitem[1987]{Lee87} Lee H.M., Ostriker J.P., 1987, ApJ 322, 123\n\\bibitem[1997]{LS97} Lehman I., Scholz R.D., 1997, A\\&A 320, 776\n\\bibitem[1998]{Mat98} Mateo M., Olszewski E.W., Morrison H.L., 1998, \nApJ 508, L55\n\\bibitem[1997]{Mey97} Meylan G., Heggie D.C., 1997, A\\&AR 8, 1\n\\bibitem[1999]{Mur99} Murali C., Dubinski J., 1999, AJ 118, 911\n\\bibitem[1987]{Ste87} Stetson P., 1987, PASP 99, 191\n\\bibitem[1995]{Tra95} Trager S., King I., Djorgovski S., 1995, \nAJ 109, 218 (T95)\n\\bibitem[1995a]{Wei95a} Weir N., Fayyad U., Djorgovski S., Roden J., \n1995, PASP 107, 1243\n\\bibitem[1982]{Val82} Valdez, F., 1982, in Instrumentation in Astronomy IV, \nSPIE, vol. 331, 465 \n\\bibitem[1987]{Whi87} White R. E., Shawl S. J. 1987, ApJ 317, 246\n\\bibitem[1995]{Zag95} Zaggia S. R., Piotto G., Capaccioli M., 1995, \nMem. Soc. Astron. It. 441, 667\n\\bibitem[1997]{Zag97} Zaggia S. R., Piotto G., Capaccioli M., 1997, \nA\\&A 327, 1004\n\\bibitem[1998]{Zag98} Zaggia S. R., Andreon S., Longo C. et al., 1998, \nUse of DPOSS Data to Study Globular Cluster Tidal Radii, \nin: ASP Conf. Ser. 136: ``Galactic Halos: A UC Santa Cruz Workshop'', ed. \nD. Zaritsky, p. 45\n\n\\end{thebibliography}\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002280.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[1988]{Agu88} Aguilar L.,Hut P., Ostriker J.P., 1988, ApJ 335, 720\n\\bibitem[1997]{And97} Andreon S., Zaggia S.R., de Carvalho R. et al., 1997, \nin: Proceedings of the XVIIth Moriond astrophysics\nmeeting ``Extragalactic Astronomy in the Infrared'', eds. G. Mamon,\nT. X. Thuan, Y. T. Van, Editions Fronti\\`eres (Gif-sur-Yvette),\np. 409\n\\bibitem[1999]{Bro99} Brosche P., Odenkirchen M., Geffert M., 1999, \nNewAst 4, 133\n\\bibitem[1999]{Din99} Dinescu D.I., Girard T.M., van Altena W.F., 1999, \nAJ 117, 1792\n\\bibitem[1996]{DJ96} Djorgovski S.G., 1996, in: ``Dynamical evolution of \nStar Clusters - Confrontation of Theory and Observation'', IAU Symp. 174, \neds. P.Hut, J.Makino, Dordrecht: Kluwer, p. 9\n\\bibitem[1992]{DJ92} Djorgovski S.G., Lasker B.M., Weir W.M. et al., 1992, \nAAS Meeting 180, p. 1307\n\\bibitem[1997]{DJ97} Djorgovski S.G., de Carvalho R.R., Gal R. et al., 1997, \nin: ``New Horizons From Multi-Wavelength Sky Surveys'', IAU Symp. 179, \ned. B. McLean, Dordrecht: Kluwer, p. 424\n\\bibitem[1999]{DJ99} Djorgovski S.G., Gal R.R., Odewahn S.C. et al., 1999, \nThe Palomar Digital Sky Survey (DPOSS), in: ``Wide Field Surveys in \nCosmology'', eds. S. Colombi, Y. Mellier, B. Raban, \nGif-sur-Yvette: Editions Fronti\\`eres, p. 89\n\\bibitem[1981]{Fre81} Freeman K., Norris J., 1981, ARA\\&A 19, 319\n\\bibitem[1999]{Gar99} Garilli B., Maccagni D., Andreon S., 1999, \nA\\&A 342, 408\n\\bibitem[1997]{Gne97} Gnedin O., Ostriker J.P., 1997, ApJ, 474, 223\n\\bibitem[1998]{Gri98} Grillmair C. J., 1998, Probing the Galactic Halo with \nGlobular Cluster Tidal Tails, in: ASP Conf. Ser. 136: ``Galactic Halos: A UC \nSanta Cruz Workshop'', ed. D. Zaritsky, p. 45\n\\bibitem[1995]{Gri95} Grillmair C., Freeman K., Irwin M., Quinn P., 1995, \nAJ 109, 2553 (G95)\n\\bibitem[1996]{Gri96} Grillmair C.J., Ajhar E.A., Faber S.M. et al., \n1996, AJ 111, 2293\n\\bibitem[1996]{Har96} Harris W., 1996, AJ, 112, 1487 \n\\bibitem[1983]{Inn83} Innanen K.A., Harris W.E., Webbink R.F., 1983, \nAJ 88, 338\n\\bibitem[1998]{Jon98} Johnston K.V., 1998, ApJ 495, 297\n\\bibitem[1999]{Jon99} Johnston K.V., Sigurdsson S., Hernquist L., 1999, \nMNRAS 302, 771 (J99)\n\\bibitem[1987]{Lee87} Lee H.M., Ostriker J.P., 1987, ApJ 322, 123\n\\bibitem[1997]{LS97} Lehman I., Scholz R.D., 1997, A\\&A 320, 776\n\\bibitem[1998]{Mat98} Mateo M., Olszewski E.W., Morrison H.L., 1998, \nApJ 508, L55\n\\bibitem[1997]{Mey97} Meylan G., Heggie D.C., 1997, A\\&AR 8, 1\n\\bibitem[1999]{Mur99} Murali C., Dubinski J., 1999, AJ 118, 911\n\\bibitem[1987]{Ste87} Stetson P., 1987, PASP 99, 191\n\\bibitem[1995]{Tra95} Trager S., King I., Djorgovski S., 1995, \nAJ 109, 218 (T95)\n\\bibitem[1995a]{Wei95a} Weir N., Fayyad U., Djorgovski S., Roden J., \n1995, PASP 107, 1243\n\\bibitem[1982]{Val82} Valdez, F., 1982, in Instrumentation in Astronomy IV, \nSPIE, vol. 331, 465 \n\\bibitem[1987]{Whi87} White R. E., Shawl S. J. 1987, ApJ 317, 246\n\\bibitem[1995]{Zag95} Zaggia S. R., Piotto G., Capaccioli M., 1995, \nMem. Soc. Astron. It. 441, 667\n\\bibitem[1997]{Zag97} Zaggia S. R., Piotto G., Capaccioli M., 1997, \nA\\&A 327, 1004\n\\bibitem[1998]{Zag98} Zaggia S. R., Andreon S., Longo C. et al., 1998, \nUse of DPOSS Data to Study Globular Cluster Tidal Radii, \nin: ASP Conf. Ser. 136: ``Galactic Halos: A UC Santa Cruz Workshop'', ed. \nD. Zaritsky, p. 45\n\n\\end{thebibliography}"
}
] |
astro-ph0002281
|
Geometric Gaussianity and Non-Gaussianity in the Cosmic Microwave Background
|
[
{
"author": "Kaiki Taro Inoue"
}
] |
In this paper, Gaussianity of eigenmodes and non-Gaussianity in the Cosmic Microwave Background (CMB) temperature fluctuations in two smallest compact hyperbolic (CH) models are investigated. First, it is numerically found that the expansion coefficients of low-lying eigenmodes on the two CH manifolds behave as if they are Gaussian random numbers at almost all the places. Next, non-Gaussianity of the temperature fluctuations in the ($l,m$) space in these models is studied. Assuming that the initial fluctuations are Gaussian, the real expansion coefficients $b_{l m}$ of the temperature fluctuations in the sky are found to be distinctively non-Gaussian. In particular, the cosmic variances are found to be much larger than that for Gaussian models. On the other hand, the anisotropic structure is vastly erased if one averages the fluctuations at a number of different observing points because of the Gaussian pseudo-randomness of the eigenmodes. Thus the dominant contribution to the two-point correlation functions comes from the isotropic terms described by the angular power spectra $C_l$. Finally, topological quantities: the total length and the genus of isotemperature contours are investigated. The variances of total length and genus at high and low threshold levels are found to be considerably larger than that of Gaussian models while the means almost agree with them.
|
[
{
"name": "paper3.tex",
"string": "%\\documentstyle[prl,aps,floats,psfig,amsfonts]{revtex}\n\\documentstyle[prd,aps,floats,psfig,amsfonts]{revtex}\n\\input epsf.sty\n%\\documentstyle[prd,aps,twocolumn]{revtex}\n%%% Math fonts %%%\n\\newcommand{\\del}{\\partial}\n\\newcommand{\\m}{\\mathbf}\n\\newcommand{\\x}{{\\mathbf{x}}}\n\\newcommand{\\y}{{\\mathbf{y}}}\n\\newcommand{\\z}{{\\mathbf{z}}}\n\\newcommand{\\n}{{\\mathbf{n}}}\n\\newcommand{\\U}{\\underline}\n%%%%%%%%%%%%%%%%%%%\n%%% Short Cuts %%%\n\\newcommand{\\f}{\\frac}\n\\newcommand{\\T}{\\tilde}\n\\newcommand{\\N}{\\nonumber}\n\\newcommand{\\bb}{\\bibitem}\n\\newcommand{\\BF}{\\begin{figure}}\n\\newcommand{\\EF}{\\end{figure}}\n\\newcommand{\\BE}{\\begin{equation}}\n\\newcommand{\\EE}{\\end{equation}}\n\\newcommand{\\BEA}{\\begin{eqnarray}}\n\\newcommand{\\EEA}{\\end{eqnarray}}\n%\\twocolumn[\\hsize\\textwidth\\columnwidth\\hsize\\csname\n%@twocolumnfalse\\endcsname\n%%\n%%\n\\tighten\n\\begin{document}\n\\draft\n%%\n\\title{Geometric Gaussianity and Non-Gaussianity in the Cosmic\nMicrowave Background}\n%%\n%%\n%%\n\\author{Kaiki Taro Inoue}\n\\address{Yukawa Institute for Theoretical Physics, Kyoto University,\nKyoto 606-8502, Japan}\n\\date{\\today}\n%%\n%%\n%%\n%%\n%%\n%%\n\\maketitle\n\\begin{abstract}\nIn this paper, Gaussianity of eigenmodes and \nnon-Gaussianity in the Cosmic Microwave Background (CMB)\ntemperature fluctuations in\ntwo smallest compact hyperbolic (CH) models are investigated. \nFirst, it is numerically found that the expansion coefficients of \nlow-lying eigenmodes on the two CH manifolds behave as if \nthey are Gaussian random numbers \nat almost all the places.\nNext, non-Gaussianity of the temperature fluctuations in the \n($l,m$) space in these models\nis studied. Assuming that the initial fluctuations are \nGaussian, the real expansion coefficients $b_{l m}$ of the temperature \nfluctuations in the sky are found to be \ndistinctively non-Gaussian. In particular, \nthe cosmic variances are found to be much larger than that\nfor Gaussian models. On the other hand, the \nanisotropic structure is vastly erased if one averages the \nfluctuations at a number of different observing points because of the \nGaussian pseudo-randomness of the eigenmodes. Thus the dominant\ncontribution to the two-point correlation functions comes from the\nisotropic terms described by the angular power spectra $C_l$. \nFinally, topological quantities: the total length and the genus \nof isotemperature contours are\ninvestigated. The variances of total length and genus\nat high and low threshold levels \nare found to be considerably larger than that of\nGaussian models while the means almost agree with them.\n\\end{abstract}\n\n\\pacs{PACS Numbers : 98.70.Vc, 98.80.Hw}\n\\begin{picture}(0,0)\n\\put(410,280)\n{YITP-00-11}\n\\end{picture}\n%%%%%%%%%%%%%%%% INTRODUCTION %%%%%%%%%%%%%%%%%%%\n\\section{introduction}\n\\indent\nIn recent years, locally isortopic and homogeneous \nFriedmann-Robertson-Walker (FRW) models with non-trivial\ntopology have attracted much attention. In the standard scenario, \nsimply-connectivity of the spatial hypersurface is assumed for\nsimplicity. However, the Einstein equations, being local equations, \ndo not fix the global topology of the spacetime. \nIn other words, a wide variety of \ntopologically distinct spacetimes with the same local geometry \ndescribed by a local metric element remain unspecified (see\n\\cite{Lachieze} for review on the cosmological topology). \nThe determination of the global\ntopology of the universe is one of the most important problem of the\nmodern observational cosmology. \n\\\\\n\\indent\nFor flat models without the cosmological constant,\nseverest constraints have been obtained by using the COBE\nDMR data. The suppression of the fluctuations on scales beyond the \ntopological identification scale $L$ leads to the decrease of the \nangular power spectra $C_l$ of the Cosmic Microwave Background (CMB)\ntemperature fluctuations on large angular scales \nwhich puts a lower bound $L\\!\\ge\\! 2400~ h^{-1}\n$Mpc (with $h\\!=\\!H_{0}/100~\\mathrm{kms^{-1}Mpc^{-1}\n}$) for a compact flat 3-torus model without the cosmological constant\n\\cite{Stevens,Oliveira}. Similar constraints have\nbeen obtained for other compact flat models \\cite{Levin}. \nThe maximum expected number\nof copies of the fundamental domain (cell) inside the last scattering\nsurface is approximately 8 for the 3-torus model. \n\\\\\n\\indent\nIn contrast, for low density models, the constraint could be\nconsiderably milder than the locally isotropic and homogeneous \nflat (Einstein-de-Sitter) models\nsince a bulk of large-angle CMB fluctuations \ncan be produced by the so-called (late) integrated Sachs-Wolfe effect\n(ISW) \\cite{HSS,Cornish2} which is the gravitational blueshift\neffect of the free streaming photons by the decay of the gravitational \npotential. As the gravitational potential decays in either \n$\\Lambda$-dominant epoch or curvature dominant epoch, \nthe free streaming photons \nwith large wavelength (the light travel time across the wavelength \nis greater than or comparable to\nthe decay time) that climbed a potential well at the last scattering \nexperience blueshifts due to the contraction of the comoving space\nalong the trajectories of the photons.\nBecause the angular sizes of the fluctuations produced at late time \nare large, the suppression of the fluctuations on scale larger than the \ntopological identification scale does not lead to a\nsignificant suppression of the large-angle power if the \nISW effect is dominant.\nRecent works \\cite{Aurich3,Inoue2,Inoue3,Cornish1} have shown that \nthe large-angle power ($2\\!\\le\\!l\\!\\le\\!20$) are completely consistent with\nthe COBE DMR data for compact hyperbolic (CH) models which \ninclude a small CH orbifold, the Weeks and the Thurston manifolds \nwith volume $0.72, 0.94$ and $0.98$ in unit of the cube of the\ncurvature radius, respectively. Note that the Weeks manifold is the\nsmallest and the Thurston manifolds is the second smallest \nin the known CH manifolds.\nFor instance, the number\nof copies of the fundamental domain inside the last scattering\nsurface at present is approximately 190 for a Weeks model \nwith $\\Omega_{0}\\!=\\!0.3$.\n\\\\\n\\indent\nIf the space is negatively curved, for a fixed number of\nthe copies of the fundamental domain inside the present horizon, \nthe large-angle fluctuations can be produced much effectively. \nIn negatively curved spaces (hyperbolic spaces), trajectories of \nphotons subtend a much\nsmaller angle in the sky for a given scale. In other words, \nfor a given angle of a pair\nof two photon trajectories, the physical distance of the \ntrajectories is much greater than\nthat in a flat space. Therefore, even if there is a number of copies\nof the fundamental domain which intersect the last scattering surface, \nthe number of copies which intersect the wave front (a sphere with\n$z\\!=\\!\\textrm{const.}$) \nof the free streaming photons is\nexponentially decreased at late time when the large-angle\nfluctuations are produced due to the ISW effect.\n\\\\\n\\indent\nHowever, one may not be satisfied with the constraints using only the \nangular power spectrum $C_{l}$ since it contains only isotropic\ninformation of the ensemble averaged temperature fluctuations \\cite{Bond}. \nIf they have anisotropic \nstructures, non-Gaussian signatures must be revealed.\nIn fact, the global isotropy \nof the locally isotropic and homogeneous \nFRW models is generally\nbroken. For instance, a flat 3-torus obtained by identifying\nthe opposite faces of a cube is obviously anisotropic \nat any points. Thus the temperature\nfluctuations averaged over the initial conditions \nin these multiply-connected FRW models are no \nlonger $SO(3)$ invariant at a certain point.\nThe temperature\nfluctuations on the sky are written in terms of (real) \nspherical harmonics $Q_{lm}(\\n)$ as \n\\BE\n\\f{\\Delta T}{T}(\\n)=\\sum_{l}~\\sum_{m=-l}^{l} b_{lm} Q_{lm}(\\n).\n\\EE\nIf the distribution functions of the real \nexpansion coefficients $b_{lm}$ are $SO(3)$ invariant, \nthe temperature fluctuations must be Gaussian provided that \n$b_{lm}$'s are independent random numbers \\cite{Mag1}. Therefore, the\ntemperature fluctuations at a certain point in the multiply-connected \nFRW models are not Gaussian if $b_{lm}$'s are independent. \n\\\\\n\\indent\nFor the simplest flat 3-torus models \n(without rotations in the identification maps) which are \nglobally homogeneous, it is sufficient to choose one observing \npoint and estimate how the power is distributed among the $m$'s for \na given angular scale $l$ in order to see the effect of the global\nanisotropy.\nHowever, in general, one must consider an ensemble of fluctuations\nat different observing points because of the spatial (global)\ninhomogeneity. Previous analyses have not fully investigated the \ndependence of the temperature fluctuations on choice of the \nobserving points.\n\\\\\n\\indent\nLack of analytical results on the eigenmodes \nmakes it difficult to investigate the nature of the temperature fluctuations\nin CH models.\nHowever, we may expect a high degree of complexity in the \neigenmodes since the corresponding\nclassical systems (geodesic flows) are strongly chaotic. \nIn fact, it has been numerically found that\nthe expansion coefficients of the low-lying eigenmodes on the \nThurston manifold at the point where the injectivity radius \nis maximal are Gaussian \npseudo-random numbers \\cite{Inoue1} \nwhich supports the previous analysis of the excited states (higher \nmodes) of a two-dimensional\nasymmetrical CH model \\cite{Aurich2}. We have put a prefix ''pseudo'' since \nthe eigenmodes are actually constrained by the periodic boundary conditions. \nThese results imply that the statistical properties of the eigenmodes\non CH spaces (orbifolds and manifolds) can be described \nby random-matrix theory (RMT)\\cite{Meh,Boh}. \nAn investigation of the dependence of the property on the observing\npoints is also important since CH spaces have symmetries (isometric\ngroups) which may veil the random feature of the eigenmodes. In this\npaper, a detailed analysis on the statistical property of low-lying \neigenmodes on the Weeks and the Thurston manifolds is conducted.\n\\\\\n\\indent\nAssuming that the eigenmodes are Gaussian, one can expect that \nthe anisotropic structure in the $(l,m)$ space is \nvastly erased when one averages the\nfluctuations over the space.\nThis seems to be a paradox since the CH spaces are actually globally\nanisotropic. However, one should consider a spatial average of \nfluctuations with different initial conditions if\none believes the Copernican principle that we are not in the center\nof the universe.\nEven if the space is anisotropic \nat a certain point, the averaged fluctuations may \nlook isotropic by considering\nan ensemble of fluctuations at all the possible observing points. \nNote that the eigenmodes on CH spaces\nhave no particular directions if they are Gaussian.\n\\\\\n\\indent\nIf the initial fluctuations are constant for each eigenmode, \nas we shall see, the Gaussian \nrandomness of the temperature fluctuations can be solely \nattributed to the Gaussian pseudo-randomness of the eigenmodes.\nIn this case, the Gaussian randomness of the temperature fluctuations has its\norigin in the geometrical property of the space\n(\\textit{Geometric Gaussianity}). Choosing an observing \npoint is equivalent to fixing a certain initial condition.\nHowever, it is much natural to assume that the initial fluctuations are\nalso random Gaussian as the standard inflationary scenarios predict.\nThen the temperature fluctuations may not obey the Gaussian statistics\nbecause they are written in terms of products of two different\nindependent Gaussian numbers rather than sums while they remain almost \nspatially isotropic if averaged over the space.\n\\\\\n\\indent\nIn this paper, Gaussianity of eigenmodes and non-Gaussianity in\nthe CMB for two smallest CH models (the Weeks and the Thurston models) \nare investigated. In Sec.~II, numerical results on Gaussianity of eigenmodes \nare shown and we discuss to what extent the results are generic.\nIn Sec.~III, we study the non-Gaussian behavior of the\ntemperature fluctuations in the ($l,m$) space. In Sec.~IV,\ntopological quantities (total length and genus) of isotemperature \ncontours are numerically simulated for studying the non-Gaussian behavior\nin the real space. Finally, we summarize our conclusions in Sec.~V.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\section{GEOMETRIC GAUSSIANITY}\nIn locally isotropic and homogeneous FRW background spaces, \neach type (scalar, vector and tensor) of\nfirst-order perturbations can be decomposed into a decoupled set of\nequations. In order to solve the decomposed linearly perturbed\nEinstein equations, it is useful to expand the \nperturbations in terms of eigenmodes\nof the Laplacian which satisfies the Helmholtz equation with certain\nboundary conditions,\n\\BE\n(\\nabla^2+k^2)u_{k}(x)=0,\n\\EE\nsince each eigenmode evolves independently in the linear approximation.\nThen one can easily see that the time evolution of the \nperturbations in the multiply-connected locally isotropic and\nhomogeneous FRW\nspaces coincide with that in the FRW spaces while \nthe global structure of the background space is described solely by these \neigenmodes. \n\\\\\n\\indent\nUnfortunately, no analytical expressions of eigenmodes on CH spaces\nhave been known. Nevertheless, the correspondence\nbetween classical and quantum mechanics may provide us a clue for\nunderstanding the generic property of the eigenmodes. If one\nrecognizes the Laplacian as the Hamiltonian in a quantum system, \neach eigenmode can be interpreted as a wavefunction in a stationary state. \nBecause classical dynamical systems (=geodesic \nflows) on CH spaces are strongly chaotic (or more precisely they are K-systems \nwith ergodicity, mixing and Bernoulli properties \\cite{Balazs}), one can expect\na high degree of complexity for each eigenstate. Imprint of the chaos \nin the classical systems may be hidden in the \nquantum counterparts.\nIn fact, in many cases, the short-range correlations observed\nin the eigenvalues (energy states) have been found to be consistent \nwith the universal prediction of RMT for three universality \nclasses:the Gaussian \northogonal ensemble(GOE), the Gaussian unitary ensemble(GUE) and the\nGaussian symplectic ensemble (GSE)\\cite{Meh,Boh}. \nIn our case the statistical properties are described by GOE (which\nconsist of real symmetric $N \\!\\times\\!N$ matrices $H$ which obey the\nGaussian distribution $\\propto \\exp{(-\\textrm{Tr}H^2/(4a^2))}$ \n(where $a$ is a constant) as the systems possess a time-reversal\nsymmetry. RMT also predicts that\nthe squared expansion coefficients of an eigenstate with respect to a \ngeneric basis are distributed as Gaussian random numbers \\cite{Bro}. \nUnfortunately, no analytic forms of generic bases(=eigenmodes) are\nknown for CH spaces which seems to be an intractable problem.\nHowever, if the eigenmodes are continued onto the universal covering\nspace by the periodic boundary conditions, they can be written in terms\nof a ''generic'' basis on the universal covering space (=3-hyperboloid\n$H^3$). In pseudospherical coordinates ($R,\\chi,\\theta,\\phi$), \nthe eigenmodes are written in terms of complex expansion \ncoefficients $\\xi_{\\nu l m}$\nand eigenmodes on the universal covering space, \n\\BE\nu_\\nu=\\sum_{l m} \\xi_{\\nu l m}\\,X_{\\nu l}(\\chi) Y_{l m}(\\theta,\\phi),\n\\label{eq:u}\n\\EE\nwhere $\\nu=\\sqrt{k^2-1}$, $X_{\\nu l}$ and $ Y_{l m}$ denote the\nradial eigenfunction and (complex) spherical harmonic on the pseudosphere \nwith radius $R$, respectively. Then the real expansion \ncoefficients $a_{\\nu l m}$ are given by\n\\begin{eqnarray}\n\\nonumber\na_{\\nu 0 0}&=&-\\textrm{Im}(\\xi_{\\nu 0 0}),~~~~\na_{\\nu l 0}=\\sqrt{c_{\\nu l}}\\textrm{Re}(\\xi_{\\nu l 0}),\n\\\\\n\\nonumber\na_{\\nu l m}&=&\\sqrt{2}\\textrm{Re}(\\xi_{\\nu l m}),~~m>0,\n\\\\\na_{\\nu l m}&=&-\\sqrt{2}\\textrm{Im}(\\xi_{\\nu l -m}),~~m<0,\n\\end{eqnarray}\nwhere\n\\begin{eqnarray}\n\\nonumber\nc_{\\nu l}&=&\\f{2}{(1+\\textrm{Re}(F(\\nu,l)))},\n\\\\\nF(\\nu, l)&=&\\f{\\Gamma(l+\\nu i+1)}{\\Gamma(\\nu i)}\n\\f{\\Gamma(-\\nu i)}{\\Gamma(l-\\nu i+1)}.\n\\end{eqnarray}\n\\\\\n\\indent\nIn this paper, the low-lying \neigenmodes ($k<13$) on the Weeks and Thurston\nmanifolds are numerically computed by the direct boundary \nelement method. The identification matrices of the Dirichlet domains \nare obtained by a computer program ``SnapPea'' by J. R. Weeks \\cite{Weeks1}. \nThe computed eigenvalues are \nwell consistent with that in the previous literature \n\\cite{Inoue1,Cornish3}. \nThe estimated errors in $k$ are within $0.01$. However, the\nlast digits in $k$ may be incorrect. \n$a_{\\nu l m}$ 's can be promptly obtained after the normalization and\northogonalization of these eigenmodes. The orthogonalization is\nachieved at the level of $10^{-3}$ to $10^{-4}$ (for the inner product\nof the normalized eigenmodes) which implies that each eigenmode is \ncomputed with relatively high accuracy.\n\\BF\n\\centerline{\\psfig{figure=k5.268W.eps,width=17cm}}\n\\caption{The lowest eigenmode $k\\!=\\!5.268$ on the Weeks manifold \ncontinued onto the Poincar$\\acute{\\textrm{e}}$ \nball and the boundaries of the copied Dirichlet domains (\\textit{solid\ncurves}) plotted on a slice $z\\!=\\!0$.}\n\\label{fig:EMW}\n\\EF\n\\BF\n\\centerline{\\psfig{figure=k5.404T.eps,width=17cm}}\n\\caption{The lowest eigenmode $k\\!=\\!5.404$ on the Thurston manifold \ncontinued onto the Poincar$\\acute{\\textrm{e}}$ \nball and the boundaries of the copied Dirichlet domains (\\textit{solid\ncurves}) plotted on a slice $z\\!=\\!0$.}\n\\label{fig:EMT}\n\\EF\nIn Fig.1 and Fig.2, one can see a high degree of complexity in the lowest \neigenmodes on the Poincar$\\acute{\\textrm{e}}$ ball which is isometric\nto the universal covering space $H^3$ whose coordinates are\ngiven by\n\\BE\nx=R \\tanh \\f{\\chi}{2} \\sin \\theta \\cos \\phi, ~~\ny=R \\tanh \\f{\\chi}{2} \\sin \\theta \\sin \\phi, ~~\nz=R \\tanh \\f{\\chi}{2} \\cos \\theta.\n\\EE\nReplacing $\\tanh \\f{\\chi}{2}$ by $\\tanh \\chi$ for each\ncoordinate, one obtains the Klein (projective) coordinates.\nIn the Poincar$\\acute{\\textrm{e}}$ coordinates, angles of \ngeodesics coincide with that of Euclidean ones. \nIn the Klein coordinates, all geodesics are straight \nlines while angles does not coincide with that of Euclidean ones.\n\\BF[tpb]\n\\centerline{\\psfig{figure=SqExpCoeffW.eps,width=17cm}}\n\\caption{Plots of $a_{\\nu l m}$'s which are ordered \nas $l(l+1)+m+1, 0\\le l \\le 20$ for eigenmodes \n$k\\!=\\!5.268$(left) and $k\\!=\\!12.789$(right) on the Weeks manifold\nat a point which is randomly chosen.}\n\\label{fig:anulmW}\n\\EF\nIn what follows $R$ is normalized to 1 without loss of generality.\n\\\\\n\\indent\nIn Fig.3, one can see that the distribution of \n$a_{\\nu l m}$'s which are ordered as $l(l+1)+m+1$ \nare qualitatively random.\nIn order to estimate the randomness \nquantitatively, we consider a cumulative distribution of \n\\begin{equation}\nb_{\\nu l m}=\\f{|a_{\\nu l m}-\\bar{a}_{\\nu}|^2}{\\sigma_{\\nu}^2}\n\\end{equation}\nwhere $\\bar{a}_{\\nu}$ is the mean of $a_{\\nu\nl m}$'s and $\\sigma_{\\nu}^2$ is the variance.\nIf $a_{\\nu l m}$'s are Gaussian then $b_{\\nu l m}$ 's obey\na $\\chi^2$ distribution $P(x)=(1/2)^{1/2}\\Gamma(1/2)x^{-1/2}e^{-x/2}$\nwith 1 degree of freedom. To test the goodness of fit between the\nthe theoretical cumulative distribution $I(x)$ and the empirical \ncumulative distribution function $I_N(x)$, we use \nthe Kolmogorov-Smirnov statistic $D_N$ which is the least upper bound\nof all pointwise differences $|I_N(x)-I(x)|$\n\\cite{Hog},\n\\begin{equation}\nD_N\\equiv \\sup_{x} |I_N(x)-I(x)|.\n\\end{equation}\n$I_N(x)$ is defined as\n\\begin{eqnarray}\n I_N(x)&=&\\left\\{ \\begin{array}{@{\\,}ll}\n0, & x<y_1,\n\\\\\nj/N,~~& y_j \\leq x < y_{j+1},~~~~j=1,2,\\ldots,N\\!-\\!1,\n\\\\\n1, & y_N \\leq x, \n\\end{array}\n\\right. \n\\end{eqnarray}\nwhere $y_1<y_2< \\ldots <y_N$ are the computed values of a random\nsample which consists of $N$ elements. \nFor random variables $D_N$ for any $z>0$, it can be shown that \nthe probability of $D_N\\!<\\!d$ is given by \\cite{Bir}\n\\begin{equation}\n\\lim_{N \\rightarrow \\infty} ~P(D_N<d=z N^{-1/2})=L(z),\\label{eq:P} \n\\end{equation} \nwhere\n\\begin{equation}\nL(z)=1-2 \\sum_{j=1}^{\\infty} (-1)^{j-1} e^{-2j^2 z^2}.\n\\end{equation}\nFrom the observed maximum difference $D_N\\!=\\!d$, we obtain \nthe significance level $\\alpha_D\\!=\\!1-P$ which is equal to the probability \nof $D_N\\!>\\!d$. If $\\alpha_D$ is found to be large enough, \nthe hypothesis $I_N(x)\\!\\neq\\! I(x)$ is not verified. \nThe significance levels $\\alpha_N$ for $0 \\!\\leq\\! l \\!\\leq\\! 20$ for\neigenmodes $k\\!<\\!13$ on the Thurston manifold are shown in table 1. \n\\begin{table}\n\\begin{center}\n\\begin{tabular}{cccc} \n\\multicolumn{1}{c}{k} &\n\\multicolumn{1}{c}{$\\alpha_D$} &\n\\multicolumn{1}{c}{k} &\n\\multicolumn{1}{c}{$\\alpha_D$} \n\\\\ \\hline\n5.404&0.98 &10.686b& $7.9\\times 10^{-4}$ \\\\ \\hline\n5.783&0.68 &10.737 & 0.96 \\\\ \\hline\n6.807a &0.52 &10.830 & 0.67 \\\\ \\hline\n6.807b & $7.1\\times 10^{-4}$ &11.103a & 0.041 \\\\ \\hline\n6.880&1.00 &11.103b & $8.8\\times 10^{-15}$ \\\\ \\hline\n7.118&0.79 &11.402 & 0.98 \\\\ \\hline\n7.686a&0.26 &11.710 & 0.92 \\\\ \\hline\n7.686b& $2.3\\times 10^{-8}$ &11.728 & 0.93 \\\\ \\hline\n8.294&0.45 &11.824 & 0.31 \\\\ \\hline\n8.591&0.91 &12.012a &0.52 \\\\ \\hline\n8.726&1.00 &12.012b &0.73 \\\\ \\hline \n9.246&0.28 &12.230 &0.032 \\\\ \\hline \n9.262&0.85 &12.500 &0.27 \\\\ \\hline \n9.754&0.39 &12.654 & 0.88 \\\\ \\hline \n9.904&0.99 &12.795 &0.76 \\\\ \\hline \n9.984&0.20 &12.806 &0.42 \\\\ \\hline \n10.358&0.40 &12.897a &0.87 \\\\ \\hline \n10.686a&0.76 &12.897b &$6.9 \\times 10^{-4}$\n\\end{tabular}\\caption{Eigenvalues $k$ and the corresponding \nsignificance levels $\\alpha_D$ for the test of the hypothesis\n $I_N(x) \\neq I(x)$ for the Thurston manifold. The injectivity radius \nis maximal at the base point.} \n\\label{tab:KScenter}\n\\end{center} \n\\end{table}\nThe agreement with the RMT prediction is\nfairly good for most of eigenmodes which is consistent with the\nprevious computation in \\cite{Inoue1}. However, for five degenerated modes, \nthe non-Gaussian signatures are prominent (in \\cite{Inoue1}, two modes \nin ($k\\!<\\!10$) have been missed). Where does this non-Gaussianity come\nfrom? \n\\\\\n\\indent\nFirst of all, we must pay attention to the fact that the\nexpansion coefficients $a_{\\nu l m}$ depend on the observing point.\nIn mathematical literature the point is called the \\textit{base point}. \nFor a given base point, it is possible to construct a particular\nclass of fundamental domain called the \\textit{Dirichlet}\n(\\textit{fundamental}) \\textit{domain} which is a convex polyhedron.\nA Dirichlet domain $\\Omega(x)$ centered at a base point $x$ is defined as\n\\BE\n\\Omega(x)=\\bigcap_{g} H(g,x)~~~,H(g,x)=\\{z|d(z,x)<d(g(z),x)\\},\n\\EE\nwhere $g$ is an element of a Kleinian group $\\Gamma$(a discrete isometry\n group of $PSL(2,{\\mathbb C})$) \nand $d(z,x)$ is the proper distance between $z$ and $x$. \n\\\\\n\\indent \nThe shape of the Dirichlet domain depends on the base point but the\nvolume is invariant. Although the base point can be chosen arbitrarily, \nit is a standard to choose a point $Q$ \nwhere the injective radius \\footnote{The injective radius of a point\n$p$ is equal to half the length of the shortest periodic geodesic at\n$p$.} is locally maximal. More intuitively, $Q$ is a center where one\ncan put a largest connected ball on the manifold. \nIf one chooses other point as the base point, the nearest copy of the base\npoint can be much nearer. The reason to choose $Q$ as a base point is \nthat one can expect the corresponding Dirichlet domain to have \nmany symmetries at $Q$ \\cite{Weeks2}.\n\\\\\n\\indent\n\\begin{figure}[tpb]\n\\centerline{\\psfig{figure=SYMFDT.eps,width=17cm}}\n\\caption{A Dirichlet domain of the Thurston manifold\nin the Klein coordinates viewed from opposite directions at $Q$\nwhere the injectivity radius is locally maximal. The Dirichlet domain\nhas a $Z2$ symmetry(invariant by $\\pi$-rotation)at $Q$.}\n\\label{fig:SYMFDT}\n\\end{figure}\nAs shown in Fig.4, the Dirichlet domain at $Q$ has \na $Z2$ symmetry (invariant by $\\pi$-rotation) \nif all the congruent faces are identified. Generally, \ncongruent faces \nare distinguished but it is found that these five modes have exactly the same\nvalues of eigenmodes on these congruent faces. Then one can no longer\nconsider $a_{\\nu l m}$'s as ''independent'' random numbers. Choosing \nthe invariant axis by the $\\pi$-rotation as the $z$-axis,\n$a_{\\nu l m}$'s are zero for odd $m$'s which leads\nto the observed non-Gaussian behavior.\nIt should be noted that the observed $Z2$ symmetry is not the subgroup\nof the isometry group (or \\textit{symmetry group} in mathematical literature)\n$D2$ (dihedral group with order $2$) of the Thurston manifold \nsince the congruent faces must be actually distinguished in the \nmanifold\\footnote{The observed $Z2$\nsymmetry is considered to be a ``hidden symmetry'' which is a symmetry\nof the finite sheeted cover of the manifold (which tessellates the\nmanifold as well as the universal covering space). \nFor instance, the Dirichlet domain of the Thurston manifold\ncan be tessellated by four pieces with three neighboring\nkite-like quadrilateral faces and one equilateral triangle \non the boundary and seven faces which contain the center as a vertex. \nBy identifying the four pieces (by a tetrahedral symmetry), one obtains an\norbifold which has a $Z2$ symmetry. } \n\\\\\n\\indent \nThus the observed non-Gaussianity is caused by a particular choice of the\nbase point. However, in general, the chance that we actually observe any\nsymmetries (elements of the isometry group of the manifold or the finite\nsheeted cover of the manifold) is expected to be \nvery low. Because a fixed point by an element of the isometric group\nis either a part of 1-dimensional line (for instance, an axis of a\nrotation) or an isolated point (for instance, a center of an antipodal map). \n\\\\\n\\indent\nIn order to confirm that the chance is actually low, the KS statistics\n$\\alpha_D$ of $a_{\\nu l m}$'s are computed at 300 base points which are \nrandomly chosen. \\begin{table}\n\\begin{center}\n\\begin{tabular}{cccp{22mm}|cccc} \n\\multicolumn{4}{c|}{Weeks}&\\multicolumn{4}{c}{Thurston} \n\\\\ \\hline\n\\multicolumn{1}{c}{k} &\n\\multicolumn{1}{c}{$<\\alpha_D>$} &\n\\multicolumn{1}{c}{k} &\n\\multicolumn{1}{p{22mm}|}{$<\\alpha_D>$} &\n\\multicolumn{1}{c}{k} &\n\\multicolumn{1}{c}{$<\\alpha_D>$} &\n\\multicolumn{1}{c}{k} &\n\\multicolumn{1}{c}{$<\\alpha_D>$} \n\\\\ \\hline\n5.268&0.58& 10.452b &~~0.62& 5.404&0.63 &10.686b& 0.62 \\\\ \\hline\n5.737a&0.61& 10.804&~~0.63&5.783&0.61 &10.737 & 0.62 \\\\ \\hline\n5.737b&0.61& 10.857&~~0.62&6.807a &0.62 &10.830 & 0.63\\\\ \\hline\n6.563&0.62 & 11.283&~~0.57&6.807b &0.62 &11.103a &0.59 \\\\ \\hline\n7.717&0.59& 11.515&~~0.61&6.880&0.63 &11.103b &0.60\\\\ \\hline\n8.162&0.61& 11.726a&~~0.63&7.118&0.61 &11.402 & 0.61 \\\\ \\hline\n8.207a&0.65& 11.726b&~~0.59&7.686a&0.61 &11.710 & 0.62 \\\\ \\hline\n8.207b&0.61& 11.726c&~~0.61&7.686b&0.63 &11.728 &0.64 \\\\ \\hline\n8.335a&0.59& 11.726d&~~0.61&8.294&0.60 &11.824 &0.62 \\\\ \\hline\n8,335b&0.62& 12.031a&~~0.60&8.591&0.60 &12.012a &0.63 \\\\ \\hline\n9.187&0.59& 12.031b&~~0.60&8.726&0.60 &12.012b &0.61 \\\\ \\hline \n9.514&0.56& 12.222a&~~0.61&9.246&0.60 &12.230 &0.60 \\\\ \\hline \n9.687&0.61& 12.222b&~~0.62&9.262&0.63 &12.500 &0.63 \\\\ \\hline \n9.881a&0.61& 12.648&~~0.59&9.754&0.62 &12.654 & 0.62 \\\\ \\hline \n9,881b&0.62& 12.789&~~0.59&9.904&0.60 &12.795 &0.62\\\\ \\hline \n10.335a&0.63& & & 9.984&0.60 &12.806 &0.62 \\\\ \\hline \n10.335b&0.60& & & 10.358&0.62 &12.897a &0.62 \\\\ \\hline \n10.452a&0.63& & & 10.686a&0.60 &12.897b &0.56\n\\end{tabular}\\caption{Eigenvalues $k$ and corresponding \naveraged significance levels $<\\alpha_D>$ based on 300 realizations\nof the base points for the test of the hypothesis\n $I_N(x) \\neq I(x)$ for the Weeks and the Thurston manifolds.} \n\\label{tab:KS}\n\\end{center} \n\\end{table}\nAs shown in table 2, the averaged significance levels $<\\!\\alpha_D\\!>$\nare remarkably consistent with the \nGaussian prediction. $1\\sigma$ \nof $\\alpha_D$ are found to be 0.26 to 0.30. \n\\\\\n\\indent\nNext, we apply the run test for testing the randomness of $a_{\\nu l\nm}$'s where each set of $a_{\\nu l m}$ 's are ordered as $l(l+1)+m+1$ \n(see \\cite{Hog}). Suppose that we have $n$ observations\nof the random variable $U$ which falls above the median and n \nobservations of the random variable\n$L$ which falls below the median. \nThe combination of those variables into $2 n$ observations\nplaced in ascending order of magnitude yields\n\\begin{center}\n\\large\\textit{\n\\U{UUU} \\U{LL} \\U{UU} \\U{LLL} \\U{U} \\U{L} \\U{UU} \\U{LL}},\n\\end{center}\nEach underlined group which consists of successive \nvalues of $U$ or $L$ is called \\textit{run}. The total number of \nrun is called the \\textit{run number}.\nThe run test is useful because the run number \nalways obeys the Gaussian statistics in the limit\n$n\\!\\rightarrow\\!\\infty$ regardless of the type of the\ndistribution function of the random variables.\n\\begin{table}\n\\begin{center}\n\\begin{tabular}{cccp{22mm}|cccc} \n\\multicolumn{4}{c|}{Weeks}&\\multicolumn{4}{c}{Thurston} \n\\\\ \\hline\n\\multicolumn{1}{c}{k} &\n\\multicolumn{1}{c}{$<\\alpha_r>$} &\n\\multicolumn{1}{c}{k} &\n\\multicolumn{1}{p{22mm}|}{$<\\alpha_r>$} &\n\\multicolumn{1}{c}{k} &\n\\multicolumn{1}{c}{$<\\alpha_r>$} &\n\\multicolumn{1}{c}{k} &\n\\multicolumn{1}{c}{$<\\alpha_r>$} \n\\\\ \\hline\n5.268&0.51& 10.452b &~~0.52& 5.404&0.48 &10.686b& 0.51 \\\\ \\hline\n5.737a&0.48& 10.804&~~0.52&5.783&0.45 &10.737 & 0.49 \\\\ \\hline\n5.737b&0.45& 10.857&~~0.53&6.807a &0.53 &10.830 &0.53\\\\ \\hline\n6.563&0.54 & 11.283&~~0.49&6.807b &0.50 &11.103a &0.52 \\\\ \\hline\n7.717&0.50& 11.515&~~0.51&6.880&0.47 &11.103b &0.53\\\\ \\hline\n8.162&0.54& 11.726a&~~0.51&7.118&0.50 &11.402 & 0.51 \\\\ \\hline\n8.207a&0.52& 11.726b&~~0.48&7.686a&0.49 &11.710 & 0.51 \\\\ \\hline\n8.207b&0.49& 11.726c&~~0.49&7.686b&0.52 &11.728 &0.49 \\\\ \\hline\n8.335a&0.53& 11.726d&~~0.48&8.294&0.50 &11.824 &0.54 \\\\ \\hline\n8,335b&0.50& 12.031a&~~0.54&8.591&0.50 &12.012a &0.51 \\\\ \\hline\n9.187&0.53& 12.031b&~~0.51&8.726&0.51 &12.012b &0.49 \\\\ \\hline \n9.514&0.55& 12.222a&~~0.54&9.246&0.43 &12.230 &0.51 \\\\ \\hline \n9.687&0.53& 12.222b&~~0.50&9.262&0.50 &12.500 &0.48 \\\\ \\hline \n9.881a&0.51& 12.648&~~0.54&9.754&0.54 &12.654 & 0.48 \\\\ \\hline \n9,881b&0.51& 12.789&~~0.48&9.904&0.52 &12.795 &0.50\\\\ \\hline \n10.335a&0.54& & & 9.984&0.49 &12.806 &0.51 \\\\ \\hline \n10.335b&0.51& & & 10.358&0.53 &12.897a &0.57 \\\\ \\hline \n10.452a&0.53& & & 10.686a&0.51 &12.897b &0.55\n\\end{tabular}\\caption{Eigenvalues $k$ and corresponding \naveraged significance levels $<\\!\\alpha_r\\!>$ for the test of the hypothesis\nthat the $a_{\\nu l m}$'s are not random numbers for the Weeks and\nThurston manifolds. $\\alpha_r$'s at 300 points which are randomly\nchosen are used for the computation.} \n\\label{tab:KS}\n\\end{center} \n\\end{table}\nAs shown in table 3, averaged significance levels $<\\!\\alpha_r\\!>$ are\nvery high (1$\\sigma$ is 0.25 to 0.31). \nThus each set of $a_{\\nu l m}$'s ordered as $l(l+1)+m+1$ can be\ninterpreted as a set of Gaussian pseudo-random numbers except for limited\nchoices of the base point where one can observe symmetries of \neigenmodes. \n\\\\\n\\indent\nUp to now, we have considered $l$ and $m$ as the index numbers of $a_{\\nu\nl m}$ at a fixed base point. However, for a fixed $(l,m)$, the\nstatistical property of a set of $a_{\\nu l m}$'s at a number of \ndifferent base points is also important since the temperature \nfluctuations must be averaged all over the places \nfor spatially inhomogeneous models. \nFrom Fig.5, one can see the behavior of m-averaged significance \nlevels \n\\BE\n\\alpha_D(\\nu, l)\\equiv \\sum_{m=-l}^{l} \\f{\\alpha_D(a_{\\nu l m})}{2l+1}\n\\EE\nwhich are calculated based on 300 realizations of the base points. \nIt should be noted that each $a_{\\nu l m}$ at a particular\nbase point is now considered to be ''one realization'' whereas\na choice of $l$ and $m$ is considered to be ''one realization'' in\nthe previous analysis (table 1).\nThe agreement with the RMT prediction is considerably good for \ncomponents $l\\!>\\!1$. For components $l\\!=\\!1$, the disagreement\noccurs for only several modes. However, the non-Gaussian \nbehavior is distinct in $l\\!=\\!0$ components. \nWhat is the reason of the non-Gaussian \nbehavior for $l\\!=\\!0$? \n\\begin{figure}[tpb]\n\\centerline{\\psfig{figure=KStest.eps,width=17cm}}\n\\caption{Plots of m-averaged significance \nlevels $\\alpha_D(\\nu, l)$ \nbased on 300 realizations for the Weeks and the Thurston manifolds\n($0 \\! \\le\\! l \\!\\le\\! 20$ and $k<13$). $n$ denotes the index number\nwhich corresponds to an eigenmode $u_k$ where the number of eigenmodes \nless than $k$ is equal to $n$ ($k(n\\!=\\!1)$ is the lowest non-zero\neigenvalue). The accompanying palettes show the \ncorrespondence between the level of the grey and the value.}\n\\label{fig:SYMFDT}\n\\end{figure}\nLet us estimate the values of the expansion coefficients for\n$l\\!=\\!0$. \nIn general, the complex expansion coefficients $\\xi_{\\nu l m}$ \ncan be written as,\n\\BE\n\\xi_{\\nu l m}(\\chi_0)=\\f{1}{X_{\\nu l}(\\chi_0)} \n\\int u_\\nu(\\chi_0,\\theta,\\phi)\\, \nY^*_{l m}(\\theta,\\phi) d \\Omega. \\label{eq:xi}\n\\EE \nFor $l\\!=\\!0$, the equation becomes\n\\BE\n\\xi_{\\nu 0 0}(\\chi_0)=-\\f{i}{2\\sqrt{2}} \\f{\\sinh{\\chi_0}}{\\sin{\\nu\n \\chi_0}} \\int u_\\nu(\\chi_0,\\theta,\\phi)\\, d \\Omega. \\label{eq:xi0}\n\\EE \nTaking the limit $\\chi_0 \\rightarrow 0$, one obtains,\n\\BE\n\\xi_{\\nu 0 0}=-\\f{2 \\pi u_\\nu(0) i}{\\nu}.\n\\EE\nThus $a_{\\nu 0 0}$ can be written in terms of the value of the\neigenmode at the base point. \nAs shown in Fig.1, the lowest eigenmodes have only \none ''wave'' on scale of the topological identification scale $L$ \n(which will be defined later on) \ninside a single Dirichlet domain which implies that the random\nbehavior within the domain may be not present. \nTherefore, for low-lying eigenmodes,\none would generally expect non-Gaussianity in a set of \n$a_{\\nu 0 0}$ 's. \nHowever, for high-lying eigenmodes, this may not be the case \nsince these modes have a number of ''waves'' on scale of $L$ \nand they may change their values locally in a almost random fashion.\n\\\\\n\\indent\nThe above argument cannot be applicable to $a_{\\nu l m}$ 's for \n$l \\!\\neq\\! 0$ where ${X_{\\nu l}}$ approaches zero in the limit \n$\\chi_0\\!\\rightarrow\\! 0$ while the integral term\n\\BE\n \\int u_\\nu(\\chi_0,\\theta,\\phi)\\, \nY^*_{l m}(\\theta,\\phi) d \\Omega \n\\EE \nalso goes to zero because of the symmetric property of the spherical\nharmonics. Therefore $a_{\\nu l m}$ 's cannot be written in terms of\nthe local value of the eigenmode for $l \\!\\neq\\! 0$. \nFor these modes, it is better to consider the opposite\nlimit $\\chi_0 \\rightarrow \\infty$. It is numerically found that \nthe sphere with very large radius $\\chi_0$ intersects each copy of \nthe Dirichlet domain almost randomly (the \npulled back surface into a single Dirichlet domain chaotically\nfills up the domain). Then the values of the eigenmodes\non the sphere with very large radius vary in an almost random\nfashion. For large $\\chi_0$, we have \n\\BE\nX_{\\nu l}(\\chi_0)\\!\\propto\\!e^{-2\n\\chi_0+\\phi(\\nu, l)i},\n\\EE\nwhere $\\phi(\\nu, l)$ describes the phase factor. Therefore, the order\nof the integrand in Eq. (\\ref{eq:xi}) is approximately $e^{-2\n\\chi_0}$ since Eq. (\\ref{eq:xi}) does not depend on the choice of\n$\\chi_0$. As the spherical harmonics do not have correlation with \nthe eigenmode $u_{\\nu}(\\chi_0,\\theta,\\phi)$, the integrand varies\nalmost randomly for different choices of $(l,m)$ or base points. \nThus we conjecture that Gaussianity of $a_{\\nu l m}$'s have their origins \nin the chaotic property of the sphere with large radius in CH spaces. \nThe property may be related to the \nclassical chaos in geodesic flows\\footnote{If one considers a great\ncircle on a sphere with large radius, the length of the circle is\nvery long except for rare cases in which the circle ``comes back'' \nbefore it wraps around in the universal covering space. Because the \nlong geodesics in CH spaces chaotically (with no particular direction \nand position) wrap through the manifold, it is natural to assume that \nthe great circles also have this chaotic property.} \n. \n\\\\\n\\indent\nSo far we have seen the Gaussian pseudo-randomness \nof the $a_{\\nu l m}$'s. Let us now consider the statistical properties\nof the expansion coefficients.\nAs the eigenmodes have oscillatory features, it is natural to expect\nthat the averages are equal to zero. In fact, the averages of\n$<\\!a_{\\nu l m}\\!>$ 's over $0\\!\\le\\! l\\!\\le\\! 20$ and $-l\\!\\le\\!\nm\\!\\le\\! -l$ and 300 realizations of base points for each $\\nu$-mode\nare numerically found to be $0.006\\pm 0.04-0.02$(1$\\sigma$) \nfor the Weeks manifold, \nand $0.003\\pm 0.04-0.02$(1$\\sigma$) for the Thurston\nmanifold. Let us next consider the $\\nu$-dependence ($k$-dependence) \nof the variances $Var(a_{\\nu l m})$. In order to crudely \nestimate the $\\nu$-dependence, \nwe need the angular size $\\delta \\theta $\nof the characteristic length of the eigenmode $u_{\\nu}$\nat $\\chi_0$\\cite{Inoue1}\n\\BE\n\\delta \\theta^2\\approx\n\\f{16 \\pi^2~V\\!o\\,l(M)} \n{k^2 (\\sinh(2(\\chi_o+r_{ave}))-\\sinh(2(\\chi_o-r_{ave}))-4 r_{ave})},\n\\label{eq:deltheta}\n\\EE\nwhere $V\\!o\\,l(M)$ denotes the volume of a manifold $M$ and $r_{ave}$\nis the averaged radius of the Dirichlet domain. There is an arbitrariness\nin the definition of $r_{ave}$. Here we define $r_{ave}$ as the radius \nof a sphere with volume equivalent to\nthe volume of the manifold, \n\\BE\nV\\!o\\,l(M)=\\pi(\\sinh(2 r_{ave})-2 r_{ave}),\n\\EE\nwhich does not depend on the choice of the base point.\nThe topological identification length $L$ is defined as $L\\!=\\!2r_{ave}$.\nFor the Weeks and the Thurston manifold, $L\\!=\\!1.19$ and \n$L\\!=\\!1.20$ respectively. From\nEq. (\\ref{eq:deltheta}), for large $\\chi_0$, one can approximate\n$u_{\\nu}(\\chi_o)\\sim u_\\nu'(\\chi'_o)$ by choosing an appropriate\nradius $\\chi'_o$ which satisfies \n$\\nu^{-2}\\exp(-2\\chi_o)=\\nu'^{-2}\\exp(-2\\chi'_o)$. \nAveraging Eq. (\\ref{eq:xi}) over $l$'s and $m$'s or the base\npoints, for large $\\chi_0$, one obtains,\n\\BE\n\\bigl <|\\xi_{\\nu' l m} |^2 \\bigr >\n\\sim \n\\f{\\exp(-2\\chi_o)}{\\exp(-2\\chi'_o)}\n\\bigl<|\\xi_{\\nu l m} |^2 \\bigr >,\n\\EE\nwhich gives $\\bigl<|\\xi_{\\nu l m}|^2 \\bigr> \\sim \\nu^{-2}$.\nThus the variance of $a_{\\nu l m}$'s is proportional to $\\nu^{-2}$.\nThe numerical results for the two CH manifolds shown in Fig.6\nclearly support the $\\nu^{-2}$ dependence of the variance. \n\\BF[tpb]\n\\centerline{\\psfig{figure=SqExpCoeff.eps,width=17cm}}\n\\caption{Averaged squared $a_{\\nu}$'s ($k\\!<\\!13$)\nbased on 300 realizations of the base points for the Weeks and the Thurston\nmanifold with $\\pm 1\\sigma$ run-to-run variations. \n $a_{\\nu}$ is defined to be $Var(a_{\\nu l m})$ averaged over $0\\! \\le\\! l\\!\n\\le\\!20$ and $-l\\! \\le\\! m\\!\\le\\!l$. \nThe best-fit curves for the Weeks and the Thurston manifolds are \n$21.0\\nu^{-2}$ and $20.3\\nu^{-2}$, respectively.} \n\\label{fig:SEC}\n\\EF\n\\\\\n\\indent\nAs we have seen, the property of eigenmodes on general CH manifolds is\nsummarized in the following conjecture:\n\\\\\n\\\\\n\\textit{Conjecture: Except for the base points which are too close to any\nfixed points by symmetries, for a fixed $\\nu$, a set of the expansion \ncoefficients $a_{\\nu l m}$ over $(l,m)$'s can be considered as \nGaussian pseudo-random numbers. For a fixed $(\\nu l m)~(l>0)$, \nthe expansion coefficients at different base points that are randomly chosen \ncan also be considered as Gaussian pseudo-random numbers. In either\ncase, the variance is proportional to $\\nu^{-2}$ and the average is zero.} \n%%\n%%\n\\section{NON-GAUSSIANITY IN OBSERVABLE ANGULAR POWER SPECTRA}\nAs mentioned in the last section, perturbations in CH models\nare written in terms of linear combinations of eigenmodes \nand the time evolution of the perturbations.\nBecause the time evolution of the perturbations coincides with that\nin open models, once the expansion coefficients $\\xi_{\\nu l m}$ (or \n$a_{\\nu l m}$) are given, the evolution of perturbations in \nCH models can be readily obtained.\n\\\\\n\\indent\nIf one assumes that the perturbation is \na adiabatic scalar type without anisotropic pressure, \nand the subhorizon effects\nsuch as acoustic oscillations of the temperature and the velocity\nof the bulk fluid, and the effect of the radiation contribution\nat high z are negligible, the time evolution of the \ngrowing mode of the Newtonian curvature $\\Phi$ is analytically given\nas (see e.g. \\cite{Kodama,Mukhanov})\n\\begin{equation}\n\\Phi(\\eta)=\n\\f{5(\\sinh^2 \\eta-3 \\eta\\sinh\\eta+4 \\cosh\\eta-4)}\n{(\\cosh\\eta-1)^3},\n\\end {equation} \nwhere $\\eta$ denotes the conformal time. In terms of $\\Phi$, \nthe temperature fluctuation in the sky are written as\n\\BEA\n\\f{\\Delta T(\\n)}{T}&=&\\sum_{lm}a_{lm}Y_{lm}(\\n)\n\\nonumber\n\\\\\n&=&\\sum_{\\nu l m} \\Phi_{\\nu}(0)\\xi_{\\nu l m}F_{\\nu l\n}(\\eta_0)Y_{lm}(\\n), \\label{eq:deltaT}\n\\EEA\nwhere\n\\BE\nF_{\\nu l}(\\eta_0)\n\\!\\!\\equiv -\\f{1}{3}\n\\Phi(\\eta_\\ast) X_{\\nu l}(\\eta_0\\!-\\!\\eta_\\ast)\n\\!-\\!\\! 2 \\!\\!\\int_{\\eta_\\ast}^\n{\\eta_0}\\!\\!\\!\\!\\!\\!d \\eta\\, \n\\f{d\\Phi}{d \\eta}X_{\\nu l}(\\eta_0\\!-\\!\\eta).\\label{eq:cor}\n\\EE \nHere $\\Phi_{\\nu}(0)$ is the initial value of the curvature\nperturbation and $\\eta_\\ast$ and $\\eta_0$ \nare the conformal time of the last scattering and the present \nconformal time, respectively. The angular power spectrum $ \nC_l $ is defined as\n\\BEA\n(2\\,l+1)\\, C_l\n&=&\\sum_{m=-l}^{l} \\langle |a_{lm}|^2 \\rangle\n\\nonumber\n\\\\\n&=&\\sum_{\\nu,m}\\f{4 \\pi^4~{\\cal P}_\\Phi(\\nu) }\n{\\nu(\\nu^2+1)\\textrm{Vol}(M)}~\\langle |\\xi_{\\nu l m}|^2 \\rangle \n|F_{\\nu l}(\\eta_0)|^2, \n\\EEA\nwhere ${\\cal P}_\\Phi(\\nu) $ is the initial power spectrum. It should\nbe noted that the above formula converges to that of open models\nin the short-wavelength limit (summation to integration) \nprovided that $<\\!|\\xi_{\\nu l m}|^2\\!>$ \nis proportional to $\\nu^{-2}$. The reason is as follows: Let us denote \nthe number of eigenmodes with eigenvalues equal to or less than\n$\\nu$ by $N(\\nu)$. In the short-wavelength limit $\\nu\\!>>\\!1$ \none can use Weyl's \nasymptotic formula which leads to\n\\BE\n\\f{d N(\\nu)}{d\\nu}=\\f{\\textrm{Vol}(M)}{2 \\pi^2}\\nu^2. \\label{eq:Weyl}\n\\EE \nThus the $\\nu^2$ dependence in Eq.(\\ref{eq:Weyl}) is exactly cancelled out \nby the $\\nu^{-2}$ dependence of eigenmodes. In what follows we assume \nthe extended Harrison-Zel'dovich \nspectrum, \\textit{i.e.} ${\\cal P}_\\Phi(\\nu)\\!=\\!Const.$\n(in the flat limit, it converges to the\nscale invariant Harrison-Zel'dovich spectrum) as the\ninitial power spectrum.\n\\\\\n\\indent\nIn estimating the temperature correlations, the non-diagonal\nterms ($l\\!\\neq\\!l'$ or $m\\!\\neq\\! m'$) may\nnot be negligible if the background spatial hypersurface is not\nisotropic, in other words, the angular power spectrum $C_l$\nmay not be sufficient in describing the temperature correlations\nsince $C_l$ provides us with only an isotropic information of \nstatistics of the correlations.\nHowever, this is not the case for CH models to which the conjecture\nproposed in Sec.~II is applicable.\nBased on the Copernican principle,\nit is not likely that we are at the center of any symmetries. \nTherefore, in order to statistically estimate the temperature \ncorrelations in the globally inhomogeneous background space, \none has to consider an ensemble of fluctuations with\ndifferent initial conditions at different places (or base points) \nwith different orientations. \nAlmost all the anisotropic\ninformation is lost in the spatial averaging process since\nthe eigenmodes are Gaussian.\n\\\\\n\\begin{figure}[tpb]\n\\centerline{\\psfig{figure=NonDiaT.eps,width=17cm}}\n\\caption{Contributions of non-diagonal terms in the temperature correlations \nin unit of diagonal terms which are defined as \n$f^{lm}_{l'm'}\\!=\\!|\\!<\\!a_{lm}a\\ast_{l'm'}\\!>\\!|\n~/\\sqrt{<|a_{lm}|^2><|a_{l'm'}|^2>}$ for the Thurston model with\n$\\Omega_0$=0.3. The four-dimensional space ($l,m,l',m'$) is\nrepresented in the two-dimensional space as \n$(n,n')\\!=\\!(l(l+1)+m+1,l'(l'+1)+m'+1)$ for $2\\!\\le\\!l\\!\\le\\!10,\n-l\\!\\le\\!m\\!\\le\\!l$ and $2\\!\\le\\!l'\\!\\le\\!10,\n-l'\\!\\le\\!m'\\!\\le\\!l'$. $f^{lm}_{l'm'}$'s\nare represented by the level of grey shown in the accompanying\npalettes. The left figure represents $f^{lm}_{l'm'}$'s averaged over\n300 realizations of the base points with infinite number of \ninitial conditions for the Newtonian curvature. The right figure \nrepresents $f^{lm}_{l'm'}$'s at a base point where the injective\nradius is maximal with infinite number of \ninitial conditions. The computation is based on 36\neigenmodes($k\\!<\\!13$) that are numerically obtained by using the\ndirect boundary element method. The averaged values of the \nnon-diagonal $f^{lm}_{l'm'}$'s ($l\\! \\neq\\! l'$ or $m\\! \\neq\\! m'$)are\n0.016(left) and 0.25(right).} \n\\label{eq:NonDiaT}\n\\end{figure}\n\\indent\nAs shown in Fig.7, for 300 realizations of observing points(left), \nthe averaged absolute values of the off-diagonal elements \nin unit of diagonal elements are very small ($\\sim0.016$)\nwhereas their contributions seem to be not negligible ($\\sim0.25$) at one\nparticular observing point(right) where one can observe a symmetry of\nthe Dirichlet domain. Thus the statistical property of\nthe temperature correlation can be estimated by using $C_l$'s provided \nthat the eigenmodes are Gaussian which validates the previous analyses\nusing $C_l$'s for constraining the CH models \n\\cite{Aurich3,Inoue2,Inoue3,Cornish1}. The\nspatial averaging process\\footnote{In general, one should include \nan averaging process over different choices of orientation of\ncoordinates as well as \nan averaging process over different choices of the observing point. \nNevertheless, the Gaussian conjecture in Sec.~II implies that the \neigenmodes on CH\nspaces are ``$SO(3)$ invariant'' \\cite{Mag1}\nif averaged all over the space. Therefore, omission of the \naveraging procedure for different orientations of coordinates \nmake no difference.}\nmust be taken into account since\nthere is no reason to believe that we are in the center of any symmetries.\n\\\\\n\\indent\nIf the initial conditions satisfy \n$(\\Phi_{\\nu}(0))^{-2}\\!\\propto\\!\\nu(\\nu^2+1)$ \nthat corresponds to the extended \nHarrison-Zel'dovich spectrum\n, then Eq.(\\ref{eq:deltaT}) tells us that the temperature fluctuation\nis Gaussian since it is equal to a sum\nof Gaussian (pseudo-)random numbers at almost all the observing points. \nIn this case, the Gaussian randomness of the temperature fluctuations \nin CH models can be solely attributed to the geometrical property of \nthe space (geometric Gaussianity) which may be related to the\ndeterministic chaos of the corresponding classical system. In other\nwords, the Gaussian randomness can be\nexplained in terms of the classical physical quantities \nwithout considering the initial quantum fluctuations provided that the above\nconditions are initially (deterministically) satisfied.\n\\\\\n\\indent\nHowever, it is much natural to assume that $\\Phi_{\\nu}(0)$'s are\nalso random Gaussian as\nin the inflationary scenarios in which Gaussianity \n(on large scales) of \nthe temperature fluctuations has its origin in Gaussianity of \nthe initial quantum fluctuations because the angular powers are\ngenerally similar\nto the extended Harisson-Zel'dovich spectrum. Then the statistical\nproperties of the temperature fluctuations are determined by the sum of the \nproducts of the two independent Gaussian random \nnumbers (the initial fluctuations and\nthe expansion coefficients of the eigenmodes).\n\\\\\n\\indent\nLet us calculate the distribution function $F(Z,\\sigma_Z)$ \nof a product of two independent random numbers $X$ and $Y$ \nthat obey the Gaussian (normal) distributions \n$N(X;0,\\sigma_X)$ and $N(Y;0,\\sigma_Y)$, respectively.\n\\BE\nN(X;\\mu,\\sigma)\\equiv \\f{1}{\\sqrt{2 \\pi} \\sigma}\n\\textrm{e}^{-(X-\\mu)^2/2\\sigma^2}.\n\\EE\nThen $F(Z\\!=\\!XY,\\sigma_Z)$ is readily given by\n\\BEA\nF(Z,\\sigma_Z)&=&2\\int_0^\\infty N(Z/Y,0,\\sigma_X)N(Y,0,\\sigma_Y)\n\\f{dY}{Y}\n\\nonumber\n\\\\\n&=& \\f{1}{\\pi \\sigma_X \\sigma_Y}K_{0}\\Bigl ( \\f{|Z|}{\\sigma_X \\sigma_Y}\n\\Bigr ),\n\\EEA\nwhere $K_{0}(z)$ is the modified Bessel function. The average of $Z$\nis zero and the standard deviation satisfies \n$\\sigma_Z=\\sigma_X \\sigma_Y$. As is well known,\n$K_{0}(z)$ is the Green function of the diffusion equation with \nsources distributed along an infinite line. Although $K_{0}(z)$ is \ndiverged at $z\\!=\\!0$ its integration over $(-\\infty,\\infty)$ is convergent. \n\\begin{figure}[tpb]\n\\centerline{\\psfig{figure=GtimesG.eps,width=17cm}}\n\\caption{On the left, the distribution function \n$F(Z,1)$ \nfor a product of two random Gaussian numbers is plotted in solid\ncurves. On the right, the distribution function \n$G(Z,1)$ (1$\\sigma\\!=\\!1$) \nof a sum of two random variables that obey \n$F(Z,1/\\sqrt{2})$. The dashed curves represent the\nGaussian distribution $N(Z;0,1)$.\n}\n\\label{eq:GtimesG}\n\\end{figure}\nFrom the asymptotic expansion of the modified\nBessel function\n\\BE\nK_0(z)\\sim \\sqrt{\\f{\\pi}{2 z}}\\textrm{e}^{-z}\\Biggl[1-\\f{1^2}{1!8z}\n+\\f{1^2\\cdot 3^2}{2!(8z)^2}-\\f{1^2\\cdot 3^2\\cdot 5^2}{3!(8z)^3}+\\ldots\n\\Biggr],~~~ z>>1,\n\\EE\none obtains in the lowest order approximation, \n\\BE\nF(Z,\\sigma)\\sim \\f{1}{\\sqrt{2 \\pi \\sigma\n|Z|}}\\textrm{e}^{-|Z|/\\sigma},~~~Z>>1.\n\\EE \nThus $F(Z,\\sigma)$ is slowly decreased than the Gaussian distribution \nfunction with the same variance in the large limit. \nOne can see the two non-Gaussian features in\nFig.8(left):the divergence at $Z\\rightarrow 0$ and the \nslow convergence to zero at $Z \\rightarrow \\infty$.\nThe slow convergence is an important feature, as we shall see, \nin distinguishing the non-Gaussian models with the Gaussian ones.\nIn the modest region $0.4\\!<\\!|Z|\\!<\\!2.4$,\n$F(Z,1)$ is much less than $N(Z,0,1)$. Generally, the temperature fluctuation\nis written as a sum of the random variables $Z_i$ which obeys the\ndistribution function $F(Z_i,\\sigma_{Z_{i}})$ for a fixed set of \ncosmological parameters. \nFor large-angle fluctuations, only the eigenmodes with large wavelength \n($\\!\\equiv\\!2 \\pi/k$)can contribute to the sum. Due to the finiteness of \nthe space, the number of eigenmodes which dominantly contribute to \nthe sum is finite. Therefore, the fluctuations are\ndistinctively non-Gaussian. For small-angle fluctuations, \nthe number of eigenmodes that contribute to the\nsum becomes so large that the distribution function converges to\nthe Gaussian distribution as the central limit theorem implies.\nOne can see from Fig.8 (right) that the distribution \nfunction $G(W,1)$ of $W\\!=\\!Z1+Z2$ where both $Z1$ and $Z2$ \nobey $F(Z,\\sqrt{2})$ is much similar to the Gaussian distribution $N(Z,0,1)$ \nthan $F(W,1)$ in the modest region. \n\\\\\n\\indent\nNow let us see the non-Gaussian features of the observable\nangular power spectrum \n$\\hat{C_l}$ assuming that the initial fluctuations are Gaussian. \nFirst of all, we define a statistic \n$\\tilde{\\chi}^2\\! \\equiv\\! (2l+1)\\hat {C_l}/C_l$ where \n\\BE\n(2l+1)\\hat{C_l}\\!=\\!\\sum_{m=-l}^{l}b_{lm}^2.\n\\EE \n\\begin{figure}[tpb]\n\\centerline{\\psfig{figure=DIS0.2W.eps,width=17cm}}\n\\caption{The distributions of $\\tilde{\\chi}^2\\! \\equiv\\!\n(2l+1)\\hat{C_l}/C_l$ \nfor the Weeks model with $\\Omega_0\\!=\\!0.2$, $l\\!=\\!5$(left) and $15$(right). \nThe horizontal axes represent the values of $\\tilde{\\chi}^2$.\nThe distributions are calculated using 33 eigenmodes ($k<13$)\nbased on 200 realizations of the \ninitial Gaussian fluctuations $\\Phi_{\\nu}(0)$,\nand 200 realizations of the base points. \nThe contribution of modes $k\\!>\\!13$ is approximately\nless than 8 percent for $l\\!\\le\\!15$. The solid curves\nrepresent the $\\chi^2$ distributions with $11$(left) and $31$(right) \ndegrees of freedom.}\n\\label{eq:GtimesG}\n\\end{figure}\nIf the expansion coefficients $b_{lm}$ of the temperature fluctuation in the\nsky are Gaussian, $\\tilde{\\chi}^2$ must obey \nthe $\\chi^2$ distribution with $2m\\!+\\!1$ degrees of freedom. \n\\begin{figure}[tpb]\n\\centerline{\\psfig{figure=DISPseudo.eps,width=17cm}}\n\\caption{The distributions of $\\tilde{\\chi}^2\\! \\equiv\\!\n(2l+1)\\hat{C_l}/C_l$ in an\napproximated model in which $b_{lm}$'s obey $G(Z,1)$ for $l\\!=\\!5$ and \n$l\\!=\\!15$\nbased on 40000 realizations for each $b_{lm}$. The horizontal axes\nrepresent the values of $\\tilde{\\chi}^2$. The solid curves\ncorrespond to the $\\chi^2$ distributions with $11$(left) and $31$(right) \ndegrees of freedom.}\n\\label{eq:DISPSEUDO}\n\\end{figure}\nFig.9 shows the two non-Gaussian features in the distribution of \n$b_{lm}$'s:a slight shift of the peak to the center(zero);\nslow convergence to zero for large $\\tilde{\\chi}^2$.\nAs shown in Fig.10, the distribution of $\\tilde{\\chi}^2$ is\napproximately obtained by assuming that $b_{lm}$'s obey \n$G(Z,1)$ (actually, the distribution functions of $b_{lm}$'s\nare slightly much similar to the Gaussian \ndistributions on large angular scales). \nThe two non-Gaussian features are attributed to\nthe nature of the distribution functions of each $b_{lm}$ \nwhich give large values at $b_{lm}\\!\\sim\\!0$ and decrease \nslowly at $b_{lm}>>1$ compared with the Gaussian distributions. \n\\begin{figure}[tpb]\n\\centerline{\\psfig{figure=Prob0.2W.eps,width=17cm}}\n\\caption{Plots of $1-P(Z)$ ($P(Z)$ is the cumulative \ndistribution function) which gives the probability of observing\n$X\\ge Z$. The solid curves correspond to \n$1-P(\\tilde{\\chi}^2)$ for the\nWeeks model $\\Omega_0\\!=\\!0.2$, $l\\!=\\!5$ (left) and $l\\!=\\!15$ (right). \nThe dashed curves correspond to $1-P(\\chi^2)$ of the Gaussian model.} \n\\label{eq:Prob0.2W}\n\\end{figure}\n\\\\\n\\indent\nThe slow decrease of the distribution of $\\tilde{\\chi}^2$ \nis important in discriminating the non-Gaussian models with the\nGaussian models. As shown in Fig.11, observing \n$\\tilde{\\chi}^2\\!\\sim\\!50$ are not improbable for the Weeks $\\Omega_0$\nmodel ($l\\!=\\!15$) whereas it is almost unlikely for the Gaussian model.\nBecause the distribution is slowly decreased for large\n$\\tilde{\\chi}$, the cosmic variances \n$(\\Delta C_l)^2$ \nare expected to be larger than that of the Gaussian models. \n\\begin{figure}[tpb]\n\\centerline{\\psfig{figure=Chioverchi.eps,width=18.5cm}}\n\\caption{Plots of $\\Delta C_l(\\textrm{CH})/\\Delta C_l\n(\\textrm{Gauss})$ for the two CH models based on 200 realizations\nof the initial perturbation $\\Phi_\\nu(0)$ and 200 realizations of \nthe base point. \n$\\Delta C_l$ denotes the standard deviation (1$\\sigma$) of $\\hat{C_l}$.} \n\\label{eq:Chioverchi}\n\\end{figure} \nFrom Fig.12, on large angular scales($2\\!\\le\\! l \\!\\le\\! 15$), \none can see that the standard deviations $\\Delta C_l$ of $\\hat{C_l}$ in\nthe two CH models are approximately 1-2 times of that for the\nGaussian models. \n\\\\\n\\indent\n\\section{TOPOLOGICAL QUANTITIES}\nTopological measures:total area of the excursion regions, total length \nand the genus of the isotemperature contours \nhave been used for testing Gaussianity \nof the temperature fluctuations in the COBE DMR\ndata\\cite{Colley,Kogut}. Let us first\nsummarize the known results for Gaussian fields (see \\cite{Gott,Adler}).\n\\\\\n\\indent\nThe genus $G$ of the excursion set for\na random temperature field on a connected and simply-connected 2-surface \ncan be loosely defined as \n\\BEA\nG&=&\\textrm{number of isolated high-temperature connected regions}\n\\\\\n\\nonumber\n&-& \\textrm{number of isolated low-temperature connected regions}. \n\\label{eq:G}\n\\EEA\nFor instance, for a certain threshold, a hot spot will contribute $+1$\nand a cold spot will contribute $-1$ to the genus. If a hot spot\ncontains a cold spot, the total contribution to the genus is zero.\nThe genus which is the global property of the\nrandom field can be related to the integration of the local properties\nof the field.\nFrom the Gauss-Bonnet theorem, the genus of a closed curve $C$\nbeing the boundary of a simply-connected region $\\Omega_C$ \nwhich consists of $N$ arcs with exterior angles \n$\\alpha_1,\\alpha_2,...\\alpha_N$ can be written in terms of\nthe geodesic curvature $\\kappa_s$ and the Gaussian curvature $K$ as \n\\BE\nG=\\f{1}{2 \\pi}\\Biggl[ \\int_C \\kappa_g ds+\\sum_{i=1}^N \\alpha_i+ \\int_{\\Omega_C}\nK dA \\Biggr ]. \\label{eq:GB}\n\\EE\nFor a random field on the 2-dimensional Euclidean space $E^2$\nwhere the N arcs are all geodesic segments (straight line segments),\n$K$ and $\\kappa_g$ vanish. Therefore, the genus is written as \n\\BE\nG_{E^2}=\\f{1}{2 \\pi}\\sum_{i=1}^N \\alpha_i \\Bigr. \\label{eq:F}\n\\EE\n\\\\\nThe above formula is applicable to the locally flat spaces\nsuch as $E^1\\times S^1$ and $T^2$ which have $E^2$ as the \nuniversal covering space since \n$K$ and $\\kappa_g$ also vanish in these spaces. In these \nmultiply-connected spaces, the naive \ndefinition Eq.(\\ref{eq:G}) is not correct for\nexcursion regions surrounded by a loop which cannot be contracted \nto a point. \n\\\\\n\\indent \nIn order to compute the genus for a random field on a sphere $S^2$ \nwith radius equal to 1, it is convenient to use \na map $\\psi$:$S^2-\\{p_1\\}-\\{p_2\\}\\!\\rightarrow\\! S^1\\times (0,\\pi)$\ndefined as \n\\BE\n\\psi:(\\sin\\theta \\cos\\phi,\\sin\\theta \\sin\\phi,\\cos\\theta)\n\\rightarrow (\\phi,\\theta),~~0\\le\\phi<2\\pi,0<\\theta<\\pi,\n\\EE\nwhere $p_1$ and $p_2$ denote the north pole and the south pole, respectively. \nBecause $S^1\\times (0,\\pi)$ can be considered as locally flat spaces\n($\\phi,\\theta$) with metric $ds^2=d\\theta^2+d\\phi^2$ which have \nboundaries $\\theta\\!=\\!0,\\pi$,\nthe genus for excursion regions that \ndo not contain the poles surrounded by straight segments\nin the locally flat ($\\phi,\\theta$) space is given\nby Eq.(\\ref{eq:F}). It should be noted that the straight segments do not \nnecessarily correspond to the geodesic segments in $S^2$. \nIf a pole is inside an excursion region \nand the pole temperature is above the threshold then the genus is \nincreased by one. If the pole temperature is below the threshold, it\ndoes not need any correction. Thus the genus for the excursions is \n\\BE\nG_{S^2}=\\f{1}{2 \\pi}\\sum_i \\alpha_i+N_p, \\label{eq:Gs}\n\\EE\nwhere $\\alpha_i$ is the exterior angles at the intersection of two \nstraight segments in the ($\\phi,\\theta$) space and $N_p$ is the number\nof poles above the threshold. \n\\\\\n\\indent\nNow consider an isotropic and homogeneous \nGaussian random temperature field on a sphere $S^2$\nwith radius 1. Let $(x,y)$ be the local Cartesian coordinates on $S^2$ and \nlet the temperature correlation function be\n$C(r)\\!=\\!<\\!(\\Delta T/T)_0(\\Delta T/T)_r\\!>\\!$ with $r\\!=\\!x^2+y^2$\nand $C_0\\!=\\!C(0)\\equiv \\sigma^2$, where $\\sigma$ is the standard\ndeviation and $C_2\\!=\\!-(d^2C/dr^2)_{r=0}$. Then the expectation\nvalue of the genus for a threshold $\\Delta T /T=\\nu\\sigma$ is given \nas \\cite{Adler}\n\\BE\n<G_{S^2}>=\\sqrt{\\f{2}{\\pi}}\\f{C_2}{C_0}\\nu\\textrm{e}^{-\\nu^2/2}+\\textrm{erfc}\n\\Biggl(\\f{\\nu}{\\sqrt{2}}\\Biggr ), \\label{eq:aveGs}\n\\EE \nwhere erfc($x$) is the complementary error function. The first term in \nEq.(\\ref{eq:aveGs}) is equal to the averaged contribution for the excursions\nwhich do not contain the poles while the second term in Eq.(\\ref{eq:aveGs})\nis the expectation value of $N_p$. \n\\\\\n\\indent\nThe mean contour length per unit area for an isotropic homogeneous \nGaussian random field is \\cite{Gott,Adler}\n\\BE\n<s>=\\f{1}{2}\\Biggl ( \\f{C_2}{C_0}\\Biggr)^{\\f{1}{2}}\\textrm{e}^{-\\nu^2/2},\n\\EE\nand the mean fractional area of excursion regions for the field is\nthe cumulative probability of a threshold level,\n\\BE\n<a>=\\f{1}{2}\\textrm{erfc}\\Biggl(\\f{\\nu}{\\sqrt{2}}\\Biggr),\n\\EE\nwhich gives the second term in Eq.(\\ref{eq:aveGs}).\n\\\\\n\\indent\n\\begin{figure}[tpb]\n\\centerline{\\psfig{figure=Sky.eps,width=18cm}}\n\\caption{Contour maps of the \nCMB (not smoothed by the DMR beam) for the Thurston model \n$\\Omega_0\\!=\\!0.4$ and \na flat (Einstein-de-Sitter) \nHarrison-Zel'dovich model $C_l \\propto\n1/(l(l+1))$ in which all multipoles $l\\!>\\!20$\nare removed.}\n\n\\label{eq:Sky}\n\\end{figure}\nAs in Sec.~III, the CMB anisotropy maps for the two CH\nadiabatic models are produced by using eigenmodes $k<13$ and angular \ncomponents $2\\!\\leq\\!l\\!\\leq\\!20$ for $\\Omega_0\\!=\\!0.2$ and $0.4$. The\ncontribution of higher modes are approximately 7 percent and 10\npercent for $\\Omega_0\\!=\\!0.2$ and $0.4$, respectively. The initial\npower spectrum is assumed to be the extended Harrison-Zel'dovich \nspectrum. The beam-smoothing effect is not included. \nFor comparison, sky maps for the Einstein-de-Sitter model with\nthe Harrison-Zel'dovich spectrum $C_l\\propto1/(l(l+1))$ are also\nsimulated. \n\\\\\n\\indent\nIn order to compute the genus and the contour length for each model,\n10000 CMB sky maps on a 400$\\times$200 grid in the $(\\phi,\\theta)$\nspace are produced. \nThe contours are approximated by oriented straight\nsegments. The genus comes from the sum of the exterior angles at the\nvertices of the contours and the number of poles at which the\ntemperature is above the threshold.\nThe total contour length is approximated by \nthe sum of all the straight segments. \nTypical realizations of the sky map are shown in Fig.13. \n\\\\\n\\indent\nFig.14 and Fig.15 clearly show that the mean genuses and the mean total\ncontours for the two CH models \nare well approximated by\nthe theoretical values for the Gaussian models. This is a natural\nresult since the distribution of the expansion coefficients $b_{lm}$ \nis very similar to\nthe Gaussian distribution in the modest range.\nOn the other hand, at high and low threshold levels,\nthe variances of the total contour lengths\nand the genuses are larger than that for the Gaussian models\nthat can be attributed to the nature of the distribution\nfunction of $b_{lm}$. \nOne can easily notice the non-Gaussian signatures from Fig.16 and Fig.17.\nThe excess variances for \nthe Weeks model $\\Omega_0\\!=\\!0.4$ compared with the Gaussian flat\nHarrison-Zel'dovich model are observed at the absolute \nthreshold level approximately $|\\nu|\\!>\\!1.4$ for genus and\n$|\\nu|\\!>\\!0.6$ for total contour length.\nIf one assumes that the initial fluctuations are \ngiven by $(\\Phi_{\\nu}(0))^{-2}\\!\\propto\\!\\nu(\\nu^2+1)$, the temperature\nfluctuations for CH models can be described as Gaussian pseudo-random fields.\nOne can see from Fig.18 that the behavior of the \nvariances of genus and total contour length for the Gaussian CH models\nis very similar to that for the flat Harrison-Zel'dovich model \nand the variances at high and low threshold levels are considerably \nsmaller than that for \nthe non-Gaussian models. \n\\\\\n\\indent\nBecause the mean behavior for the two non-Gaussian CH models is well described\nby the Gaussian models, the COBE DMR data \nwhich excludes grossly non-Gaussian models \\cite{Colley,Kogut} \ncannot constrain the two CH models by the topological measurements.\nHowever, one should take account of a fact that the signals in the\n$10^o$ smoothed COBE DMR 4-year sky maps are comparable to the noises\n\\cite{Bennett} that makes it hard to detect the non-Gaussian signals\nin the background fluctuations. In fact, some recent works \nusing different statistical tools have shown that the COBE DMR 4-year\nsky maps are non-Gaussian \\cite{Ferreira,Novikov,Pando} although \nsome authors cast \ndoubts upon the cosmological\norigin of the observed non-Gaussian signals \\cite{Bromley,Banday}. \nThus the \nevidence of Gaussianity in the CMB\nfluctuations is still not conclusive.\n\\begin{figure}\n\\centerline{\\psfig{figure=Genus0.2.eps,width=18cm}}\n\\caption{The mean genuses averaged over 100 realizations of the\ninitial fluctuations and 100 realizations of the base points\nand $\\pm 1 \\sigma$ run-to-run variations at 27 threshold levels \nfor the Weeks and the Thurston models with $\\Omega_0\\!=\\!0.2$.\nThe dashed curves denote the mean values for a Gaussian model \nwhere $C_0$ and $C_2$ are obtained by assuming that the expansion\ncoefficients of the eigenmodes are random Gaussian numbers (the mean\nis zero and the variance is proportional to $\\nu^{-2}$). The solid \ncurves denote the mean values for a Gaussian model that are \nbest-fitted to that for CH models.} \n\\label{eq:Genus0.2}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\psfig{figure=Length0.2.eps,width=18cm}}\n\\caption{The mean contour lengths averaged over 100 realizations of the\ninitial fluctuations and 100 realizations of the base points\nand $\\pm 1 \\sigma$ run-to-run variations at 27 threshold levels \nfor the Weeks and the Thurston models with $\\Omega_0\\!=\\!0.2$.\nThe dashed curves denote the mean values for a Gaussian model \nwhere $C_0$ and $C_2$ are obtained by assuming that the expansion\ncoefficients of the eigenmodes are random Gaussian numbers (the\nmean is zero and the variance is proportional to $\\nu^{-2})$. The solid \ncurves denote the mean values for a Gaussian model that are \nbest-fitted to that for CH models.} \n\\label{eq:Length0.2}\n\\end{figure}\n\n\\begin{figure}\n\\centerline{\\psfig{figure=Genus0.4WandF.eps,width=18cm}}\n\\caption{The mean genuses and $\\pm 1 \\sigma$ run-to-run variations at 27\nthreshold levels for a Weeks model with $\\Omega_0\\!=\\!0.4$\naveraged over 100 realizations of the\ninitial fluctuations and 100 realizations of the base points\nand that for a flat Harisson-Zel'dovich model averaged over\n10000 realizations.\nThe dashed curves denote the mean genuses for the corresponding \nGaussian models.}\n\\label{eq:Genus0.4WandF}\n\\end{figure}\n\n\\begin{figure}[tpb]\n\\centerline{\\psfig{figure=Length0.4WandF.eps,width=18cm}}\n\\caption{The mean total contour lengths and $\\pm 1 \\sigma$ \nrun-to-run variations at 27\nthreshold levels for a Weeks model \nwith $\\Omega_0\\!=\\!0.4$ averaged over 100 realizations of the\ninitial fluctuations and 100 realizations of the base points\nand that for a flat Harisson-Zel'dovich model averaged over\n10000 realizations.\nThe dashed curves denote the mean total contour lengths for the corresponding \nGaussian models.}\n\\label{eq:Length0.4WandF}\n\\end{figure}\n\n\\begin{figure}[tpb]\n\\centerline{\\psfig{figure=Phiconst0.4W.eps,width=18cm}}\n\\caption{The mean total contour lengths and genuses and $\\pm 1 \\sigma$ run-to-run variations at 27\nthreshold levels for a Weeks model \nwith $\\Omega_0\\!=\\!0.4$ averaged over 300 realizations of the base points.\nHere it is assumed that the initial fluctuations deterministically \nsatisfy $(\\Phi_{\\nu}(0))^{-2}\\!\\propto\\!\\nu(\\nu^2+1)$ so \nthat the fluctuations \nare described by the Gaussian statistics. \nThe dashed curves denote the mean total contour lengths and the mean\ngenuses for the corresponding Gaussian models.}\n\\label{eq:Phiconst0.4W}\n\\end{figure}\n\\pagebreak\n\\section{CONCLUSION}\nIn this paper, Gaussianity of the eigenmodes and \nnon-Gaussianity in the CMB\ntemperature fluctuations in\ntwo smallest CH(Weeks and Thurston) models are investigated. \nAs shown in Sec.~II, it is numerically shown that the \nexpansion coefficients of the two CH \nspaces behave as if they are random Gaussian numbers at\nalmost all the places. If one recognizes the Laplacian as the Hamiltonian \nof a free particle, each eigenmode is interpreted as a wavefunction\nin a stationary state. The observed behavior is consistent with a\nprediction of RMT which has been considered to be a good empirical\ntheory that describe the statistical properties of quantum mechanical \nsystems whose classical counterparts are strongly\nchaotic.\nHowever, as we have seen, the global symmetries in the system\ncan veil the generic properties. \nFor instance, some eigenmodes on the Thurston manifold \nhave a $Z2$ symmetry at a point where the injectivity radius is\nmaximal. For these eigenmodes, the expansion coefficients are\nstrongly correlated;hence they can no longer considered to be random\nGaussian numbers. \n\\\\\n\\indent\nBecause the eigenmodes actually satisfy the periodic boundary conditions,\nthere are points on a sphere $S^2$ which are identified\nwith different points on $S^2$. These points form pairs\nof circles which are identified by the periodic boundary conditions \n\\cite{Cornish4}. \nIf one could identify all the circles on a sphere, one would be able\nto construct the corresponding CH space \\cite{Weeks}. \nSimilarly, if one could identify all the fixed points and the\ncorresponding symmetries, one would be able to construct a CH space\nwhich have these symmetries.\nThe observed ``randomness'' in the eigenmodes is actually \ndetermined by these simple structures.\n\\\\\n\\indent\nIn order to understand the symmetric structures of the CH spaces,\nit is useful to choose an observing point (base point) at which\none enjoys symmetries as many as possible. However, in reality, \nthere is no natural reason to consider fluctuations at only \nthese particular points since the CH spaces are \nglobally inhomogeneous. \n\\\\\n\\indent\nSince the CMB fluctuations can be written in terms of a linear combination\nof eigenmodes, the fluctuations in CH models are almost spatially \n``isotropic'' if averaged all over the\nspace except for very\nlimited places at which the eigenmodes have certain symmetries\nprovided that the eigenmodes are Gaussian.\nThe spatial ``isotropy'' implies that \nthe contribution of non-diagonal terms in the two-point \ncorrelation functions are negligible. Thus the \nvalidity of the statistical tests using\nthe angular power spectrum $C_l$ \\cite{Aurich3,Inoue2,Inoue3,Cornish1} \ncannot be questioned\non the ground that the background space is anisotropic at a certain\npoint.\n\\\\\n\\indent\nIf one assumes that the initial fluctuations are Gaussian\nas in the standard inflationary scenarios, the temperature\nfluctuations are described by isotropic non-Gaussian random fields \nsince they are written in terms of a sum of products of two independent \nrandom Gaussian variables, namely the initial perturbations and the\nexpansion coefficients of the eigenmodes. \nThe distribution functions of the expansion\ncoefficients $b_{lm}$ for the sky maps at large values \nare slowly converged to zero than the\nGaussian distribution with the same variance and the cosmic\nvariances are found to be larger than that of the Gaussian models.\n\\\\\n\\indent\nThe increase in the variances are much conspicuous for topological\nquantities at large or small threshold levels. On the other hand,\nthe mean behavior is well approximated by the Gaussian predictions.\nTherefore, the obtained results agree with the COBE DMR 4-year maps \nanalyzed in\\cite{Colley,Kogut}. \nIn real observations one has to \ntackle with what obscure\nthe real signals such as pixel noises, galactic contaminations, \nbeam-smoothing effect and systematic calibration errors which have\nnot been considered in this paper.\nThe absence of large deviations from the mean \nvalues at large or small threshold levels in the current data\nmay be due to these effects, which will be much explored \nin the future work. \n\\\\\n\\indent\nAlthough the recent observations seem to prefer the flat FRW models\nwith the cosmological constant, the evidence is not perfectly conclusive.\nIf one includes the cosmological constant for a fixed curvature radius,\nthe radius of the last scattering surface (horizon) at present in \nunit of curvature radius becomes large. Therefore the observable\nimprints of the non-trivial topology of the\nbackground space become much prominent. \nFor instance, the number $N_f$ of copies of the fundamental domains inside\nthe last scattering at the present slice is approximately 27.9 \nfor a Weeks model with $\\Omega_\\Lambda\\!=\\!0.6$ and $\\Omega_m\\!=0.2\\!$ \nwhereas $N_f\\!=\\!4.3$ if $\\Omega_\\Lambda\\!=\\!0$ and $\\Omega_m\\!=0.8\\!$. \nThus we have still great possibilities in detecting the non-trivial\ntopology by the future satellite missions such as MAP and PLANCK which \nwill provide us much better information on the statistical properties of\nthe real signals. The large deviations of the topological\nquantities from the mean values would be the good signals that \nindicate the hyperbolicity (negative curvature) and the \nfiniteness (smallness) of the universe in addition to the direct \nobservation of the periodic structures peculiar to each non-trivial \ntopology (see \\cite{Luminet} for recent developments). \n\\\\\n\\indent\n\\vspace{3cm}\n\\section*{Acknowledgments}\nI would like to thank Jeff Weeks, Makoto Sakuma, Michihiko Fujii, and \nCraig Hodgson for answering many questions about symmetric\nstructures of compact hyperbolic 3-spaces and topology of 3-manifolds.\nI would also like to thank N.J. Cornish, Naoshi Sugiyama and Kenji\nTomita for their informative comments.\nThe numerical computation in this work was carried out \nat the Data Processing Center in Kyoto University and \nYukawa Institute Computer Facility. \nK.T. Inoue is supported by JSPS Research Fellowships \nfor Young Scientists, and this work is supported partially by \nGrant-in-Aid for Scientific Research Fund (No.9809834). \n\\vspace{-0.2cm}\n\\begin{thebibliography}{99}\n\n\\bb{Lachieze}\nM. Lachi$\\grave{\\textrm{e}}$ze-Rey and J.-P. Luminet, Phys. Rep. \n{\\bf 254}, 135 (1995)\n\n\\bb{Stevens}\nD. Stevens, D. Scott and J. Silk, Phys. Rev. Lett.\n{\\bf 71}, 20 (1993) \n\n\\bb{Oliveira}\nA. de Oliveira-Costa, G.F. Smoot and A.A. Starobinsky, Astrophys. J. \n{\\bf 468}, 457 (1996) \n\n\\bb{Levin}\nJ.L. Levin, E. Scannapieco and J Silk, Phys. Rev. D \n{\\bf 58}, 103516 (1998)\n\n\\bb{HSS}\nW. Hu, N. Sugiyama and J. Silk, Nature \n{\\bf 386}, 37 (1997) \n\n\\bb{Cornish2}\nN. Cornish and D. Spergel, Phys. Rev. \nD{\\bf 57}, 5982 (1998)\n\n\\bb{Aurich3}\nR. Aurich, Astrophys. J. {\\bf 524}, 497 (1999)\n\n\\bb{Inoue2}\nK.T. Inoue, in \n\\textit{AIP Conference Proceedings \"3K Cosmology\", 1998 Oct, Rome }\nedited by L. Maiani, F. Melchiorri and N. Vittorio \n(American Institute of Physics,1999) 343\n\n\\bb{Inoue3}\nK.T. Inoue, K. Tomita and N. Sugiyama, astro-ph/9906304\n\n\n\\bb{Cornish1} \nN.J. Cornish and D.N. Spergel, astro-ph/9906401\n\n\\bb{Bond}\nJ.R. Bond, D.Pogosyan and T.Souradeep, astro-ph/9912144\n\n\\bb{Mag1}\nJ.C.R. Magueijo, Phys. Lett. B{\\bf 342}, 32 (1995); \nErratum-ibid. B{\\bf 352}, 499 (1995)\n\n\\bb{Inoue1}\nK.T. Inoue, Class. Quantum. Grav. {\\bf 16}, 3071 (1999)\n\n\\bb{Aurich2}\nR. Aurich and F. Steiner, Physica D {\\bf 64}, 185 (1993)\n\n\\bb{Meh}\nM.L. Mehta, \\textit{Random Matrices} (Academic Press, New York, 1991) \n\n\\bb{Boh}\nO. Bohigas, ''Random Matrix Theories and Chaotic Dynamics'' in \n\\textit{Proceedings of the 1989 Les Houches School on Chaos and Quantum\nPhysics} edited by A. Giannoni \\textit{et al} (Elsevier,\nAmsterdam, 1989)\n\n\\bb{Balazs}\nN.L. Balazs and A. Voros, Phys. Rep. {\\bf 143}, 109 (1986)\n\n\\bb{Bro}\nT.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandy and S.S.M. Wong \n,Rev. Mod. Phys. {\\bf 53}, 385 (1981) \n\n\\bb{Weeks1}\nJ.R. Weeks, SnapPea \\textit{A Computer Program for Creating and Studying\nHyperbolic 3-manifolds}, available at: http://www.northnet.org/weeks\n\n\\bb{Cornish3}\nN.J. Cornish and D.N. Spergel, math.DG/9906017\n\n\\bb{Hog}\nR.V. Hogg and E.A. Tanis, \\textit{Probability and Statistical\nInference} (Macmillan Publishing Co., Inc., New York, 1977)\n\n\\bb{Bir}\nZ.W. Birnbaum, \\textit{Introduction to Probability and Mathematical \nStatistics} (Haper \\& Brothers, New York, 1962) \n\n\\bb{Weeks2} \nJ.R. Weeks, \\textit{private communication}\n\n\\bb{Kodama}\nH. Kodama and M. Sasaki, Prog. Theor. Phys. Supp. \n{\\bf 78}, 1 (1986)\n\n\\bb{Mukhanov} \nV.F. Mukhanov, H.A. Feldman and R.H. Brandenberger, Phys. Rep.\n{\\bf 215}, 203 (1992) \n\n\\bb{Colley}\nW.N. Colley, J.R. Gott III and C. Park, Mon. Not. R. Astron. Soc. \n{\\bf 281}, L82 (1996)\n\n\\bb{Kogut}\nA. Kogut, A.J. Banday, C.L. Bennett, K.M. G$\\acute{\\textrm{o}}$rski,\nG. Hinshaw, G.F. Smoot and E.L. Wright, Astrophys. J. {\\bf 464}, L29 (1996)\n\n\\bb{Gott}\nJ.R. Gott III and C. Park, Astrophys. J. {\\bf 352}, 1 (1990)\n\n\\bb{Adler}\nR.J. Adler, \\textit{The Geometry of Random Fields}\n (John Wiley \\& Sons, Chichester, 1981)\n\n\\bb{Bennett}\nC.L. Bennett \\textit{et al}., Astrophys. J. {\\bf 464}, L1 (1996) \n\n\\bb{Ferreira}\nP.G. Ferreira, J. Magueijo and K.M. G$\\acute{\\textrm{o}}$rski,\nAstrophys. J. {\\bf 503}, L1 (1998)\n\n\\bb{Novikov}\nD. Novikov, H. Feldmann, and S. Shandarin, astro-ph/9809238\n\n\\bb{Pando}\nJ. Pando, D. Valls-Gabaud and L.Z. Fang, Phys. Rev. Lett \n{\\bf 81}, 4568 (1998)\n\n\\bb{Bromley}\nB. Bromley, M. Tegmark, astro-ph/9904254\n\n\\bb{Banday}\nA.J. Banday, S, Zaroubi and K.M. G$\\acute{\\textrm{o}}$rski, \nastro-ph/9908070\n\n\\bb{Cornish4}\nN.J. Cornish, D. Spergel, \\& G. Starkman, Class. Quantum. Grav.\n{\\bf 15}, 2657 (1998); Proc. Nat. Acad. Sci. {\\bf 95}, 82 (1998) \n\n\\bb{Weeks}\nJ.R. Weeks, Class. Quantum. Grav. {\\bf 15}, 2599 (1998)\n\n\n\\bb{Luminet}\nJ.P. Luminet and B.F. Roukema, astro-ph/9901364 \n\\textit{proceedings of Cosmology School held at Cargese, Corsica,\nAugust 1998}\n\n\n\\end{thebibliography}\n\\end{document}\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n"
}
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[
{
"name": "astro-ph0002281.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n\\bb{Lachieze}\nM. Lachi$\\grave{\\textrm{e}}$ze-Rey and J.-P. Luminet, Phys. Rep. \n{\\bf 254}, 135 (1995)\n\n\\bb{Stevens}\nD. Stevens, D. Scott and J. Silk, Phys. Rev. Lett.\n{\\bf 71}, 20 (1993) \n\n\\bb{Oliveira}\nA. de Oliveira-Costa, G.F. Smoot and A.A. Starobinsky, Astrophys. J. \n{\\bf 468}, 457 (1996) \n\n\\bb{Levin}\nJ.L. Levin, E. Scannapieco and J Silk, Phys. Rev. D \n{\\bf 58}, 103516 (1998)\n\n\\bb{HSS}\nW. Hu, N. Sugiyama and J. Silk, Nature \n{\\bf 386}, 37 (1997) \n\n\\bb{Cornish2}\nN. Cornish and D. Spergel, Phys. Rev. \nD{\\bf 57}, 5982 (1998)\n\n\\bb{Aurich3}\nR. Aurich, Astrophys. J. {\\bf 524}, 497 (1999)\n\n\\bb{Inoue2}\nK.T. Inoue, in \n\\textit{AIP Conference Proceedings \"3K Cosmology\", 1998 Oct, Rome }\nedited by L. Maiani, F. Melchiorri and N. Vittorio \n(American Institute of Physics,1999) 343\n\n\\bb{Inoue3}\nK.T. Inoue, K. Tomita and N. Sugiyama, astro-ph/9906304\n\n\n\\bb{Cornish1} \nN.J. Cornish and D.N. Spergel, astro-ph/9906401\n\n\\bb{Bond}\nJ.R. Bond, D.Pogosyan and T.Souradeep, astro-ph/9912144\n\n\\bb{Mag1}\nJ.C.R. Magueijo, Phys. Lett. B{\\bf 342}, 32 (1995); \nErratum-ibid. B{\\bf 352}, 499 (1995)\n\n\\bb{Inoue1}\nK.T. Inoue, Class. Quantum. Grav. {\\bf 16}, 3071 (1999)\n\n\\bb{Aurich2}\nR. Aurich and F. Steiner, Physica D {\\bf 64}, 185 (1993)\n\n\\bb{Meh}\nM.L. Mehta, \\textit{Random Matrices} (Academic Press, New York, 1991) \n\n\\bb{Boh}\nO. Bohigas, ''Random Matrix Theories and Chaotic Dynamics'' in \n\\textit{Proceedings of the 1989 Les Houches School on Chaos and Quantum\nPhysics} edited by A. Giannoni \\textit{et al} (Elsevier,\nAmsterdam, 1989)\n\n\\bb{Balazs}\nN.L. Balazs and A. Voros, Phys. Rep. {\\bf 143}, 109 (1986)\n\n\\bb{Bro}\nT.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandy and S.S.M. Wong \n,Rev. Mod. Phys. {\\bf 53}, 385 (1981) \n\n\\bb{Weeks1}\nJ.R. Weeks, SnapPea \\textit{A Computer Program for Creating and Studying\nHyperbolic 3-manifolds}, available at: http://www.northnet.org/weeks\n\n\\bb{Cornish3}\nN.J. Cornish and D.N. Spergel, math.DG/9906017\n\n\\bb{Hog}\nR.V. Hogg and E.A. Tanis, \\textit{Probability and Statistical\nInference} (Macmillan Publishing Co., Inc., New York, 1977)\n\n\\bb{Bir}\nZ.W. Birnbaum, \\textit{Introduction to Probability and Mathematical \nStatistics} (Haper \\& Brothers, New York, 1962) \n\n\\bb{Weeks2} \nJ.R. Weeks, \\textit{private communication}\n\n\\bb{Kodama}\nH. Kodama and M. Sasaki, Prog. Theor. Phys. Supp. \n{\\bf 78}, 1 (1986)\n\n\\bb{Mukhanov} \nV.F. Mukhanov, H.A. Feldman and R.H. Brandenberger, Phys. Rep.\n{\\bf 215}, 203 (1992) \n\n\\bb{Colley}\nW.N. Colley, J.R. Gott III and C. Park, Mon. Not. R. Astron. Soc. \n{\\bf 281}, L82 (1996)\n\n\\bb{Kogut}\nA. Kogut, A.J. Banday, C.L. Bennett, K.M. G$\\acute{\\textrm{o}}$rski,\nG. Hinshaw, G.F. Smoot and E.L. Wright, Astrophys. J. {\\bf 464}, L29 (1996)\n\n\\bb{Gott}\nJ.R. Gott III and C. Park, Astrophys. J. {\\bf 352}, 1 (1990)\n\n\\bb{Adler}\nR.J. Adler, \\textit{The Geometry of Random Fields}\n (John Wiley \\& Sons, Chichester, 1981)\n\n\\bb{Bennett}\nC.L. Bennett \\textit{et al}., Astrophys. J. {\\bf 464}, L1 (1996) \n\n\\bb{Ferreira}\nP.G. Ferreira, J. Magueijo and K.M. G$\\acute{\\textrm{o}}$rski,\nAstrophys. J. {\\bf 503}, L1 (1998)\n\n\\bb{Novikov}\nD. Novikov, H. Feldmann, and S. Shandarin, astro-ph/9809238\n\n\\bb{Pando}\nJ. Pando, D. Valls-Gabaud and L.Z. Fang, Phys. Rev. Lett \n{\\bf 81}, 4568 (1998)\n\n\\bb{Bromley}\nB. Bromley, M. Tegmark, astro-ph/9904254\n\n\\bb{Banday}\nA.J. Banday, S, Zaroubi and K.M. G$\\acute{\\textrm{o}}$rski, \nastro-ph/9908070\n\n\\bb{Cornish4}\nN.J. Cornish, D. Spergel, \\& G. Starkman, Class. Quantum. Grav.\n{\\bf 15}, 2657 (1998); Proc. Nat. Acad. Sci. {\\bf 95}, 82 (1998) \n\n\\bb{Weeks}\nJ.R. Weeks, Class. Quantum. Grav. {\\bf 15}, 2599 (1998)\n\n\n\\bb{Luminet}\nJ.P. Luminet and B.F. Roukema, astro-ph/9901364 \n\\textit{proceedings of Cosmology School held at Cargese, Corsica,\nAugust 1998}\n\n\n\\end{thebibliography}"
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astro-ph0002282
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Silicate emission in Orion \thanks{Based on observations with ISO, an ESA project with instruments funded by ESA member states (especially the PI countries: France, Germany, the Netherlands and the United Kingdom) and with the participation of ISAS and NASA.}
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[
{
"author": "D. Cesarsky\\inst{1,2}"
},
{
"author": "A.P. Jones\\inst{1}"
},
{
"author": "J. Lequeux\\inst{3}"
},
{
"author": "L. Verstraete\\inst{1}"
}
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We present mid--infrared spectro--imagery and high--resolution spectroscopy of the Orion bar and of a region in the Orion nebula. These observations have been obtained in the Guaranteed Time with the Circular Variable Filters of the ISO camera (CAM-CVF) and with the Short Wavelength Spectrometer (SWS), on board the European Infrared Space Observatory (ISO). Our data shows emission from amorphous silicate grains from the entire \HII~ region and around the isolated O9.5V star $\theta^2$~Ori~A. The observed spectra can be reproduced by a mixture of interstellar silicate and carbon grains heated by the radiation of the hot stars present in the region. Crystalline silicates are also observed in the Orion nebula and suspected around $\theta^2$~Ori~A. They are probably of interstellar origin. The ionization structure and the distribution of the carriers of the Aromatic Infrared Bands (AIBs) are briefly discussed on the basis of the ISO observations. % \keywords {ISM: Orion nebula - ISM: Orion bar - ISM: \HII~ regions - stars: $\theta^2$~Ori~A - dust, extinction - Infrared: ISM: lines and bands} %
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{
"name": "orion_si.tex",
"string": "%\\documentstyle[epsfig]{l-aa}\n%\\documentstyle{l-aa}\n\\documentclass{aa}\n\\usepackage{psfig}\n%\n\\def\\mum{\\hbox{\\,$\\mu$m}}\n\\newcommand{\\etal}{et al.~}\n\\newcommand{\\eg}{e.g.~}\n\\newcommand{\\ie}{{\\it{ie.~}}}\n\\newcommand{\\Msun}{\\mbox{M$_{\\scriptsize \\odot}$}}\n\\newcommand{\\degrees}{$^{\\circ}$}\n\\newcommand{\\HI}{\\mbox{H\\,{\\sc i}}}\n\\newcommand{\\HII}{\\mbox{H\\,{\\sc ii}}}\n\\newcommand{\\NeII}{\\mbox{Ne\\,{\\sc ii}}}\n\\newcommand{\\NeIII}{\\mbox{Ne\\,{\\sc iii}}}\n\\newcommand{\\ArII}{\\mbox{Ar\\,{\\sc ii}}}\n\\newcommand{\\ArIII}{\\mbox{Ar\\,{\\sc iii}}}\n\\newcommand{\\ArIV}{\\mbox{Ar\\,{\\sc iv}}}\n\\newcommand{\\OII}{\\mbox{O\\,{\\sc ii}}}\n\\newcommand{\\OIII}{\\mbox{O\\,{\\sc iii}}}\n\\newcommand{\\SII}{\\mbox{S\\,{\\sc ii}}}\n\\newcommand{\\SIII}{\\mbox{S\\,{\\sc iii}}}\n\\newcommand{\\SIV}{\\mbox{S\\,{\\sc iv}}}\n\\newcommand{\\SiII}{\\mbox{Si\\,{\\sc ii}}}\n\\newcommand{\\CII}{\\mbox{C\\,{\\sc ii}}}\n\\newcommand{\\NII}{\\mbox{N\\,{\\sc ii}}}\n\\newcommand{\\flux}{{\\hbox{\\,erg\\,\\,s$^{-1}$\\,cm$^{-2}$\\,sr$^{-1}$}}}\n\\newcommand{\\fluxpm}{{\\hbox{\\,erg\\,\\,s$^{-1}$\\,cm$^{-2}$\\,\\mum$^{-1}$\\,sr$^{-1}$}}}\n%\n\\begin{document}\n\\thesaurus{08\t% Interstellar medium\n\t(09.09.1 Orion nebula; 09.09.1 Orion bar; 08.09.2 $\\theta^2$~Ori~A;\n\t09.08.1; 09.04.1; 13.09.4)}\n\\title {Silicate emission in Orion\n\\thanks{Based on observations with ISO, an ESA project with instruments\nfunded by ESA member states (especially the PI countries: France,\nGermany, the Netherlands and the United Kingdom) and with the\nparticipation of ISAS and NASA.}}\n\n\\author{D. Cesarsky\\inst{1,2}\\and\n A.P. Jones\\inst{1}\\and\n\tJ. Lequeux\\inst{3}\\and\n\tL. Verstraete\\inst{1}}\n\\offprints{james.lequeux@obspm.fr}\n\\institute{\t\nInstitut d'Astrophysique Spatiale, Bat. 121, Universit\\'e Paris\nXI, F-91405 Orsay CEDEX, France; \n{\\it ant@ias.fr; verstra@ias.fr}\n\\and\nMax Planck Institut f\\\"ur extraterrestrische Physik, D-85740 Garching,\nGermany; {\\it diego.cesarsky@mpe.mpg.de}\n\\and\nDEMIRM,Observatoire de Paris, 61 Avenue de l'Observatoire, F-75014\nParis, France; {\\it james.lequeux@obspm.fr}\n}\n\\date{Received 7 December 1999; accepted 26 January 2000}\n%\n\\maketitle\n%\n\\begin{abstract}\nWe present mid--infrared spectro--imagery and high--resolution\nspectroscopy of the Orion bar and of a region in the Orion\nnebula. These observations have been obtained in the Guaranteed Time\nwith the Circular Variable Filters of the ISO camera (CAM-CVF) and\nwith the Short Wavelength Spectrometer (SWS), on board the European\nInfrared Space Observatory (ISO). Our data shows emission from\namorphous silicate grains from the entire \\HII~ region and around the\nisolated O9.5V star $\\theta^2$~Ori~A. The observed spectra can be\nreproduced by a mixture of interstellar silicate and carbon grains\nheated by the radiation of the hot stars present in the\nregion. Crystalline silicates are also observed in the Orion nebula\nand suspected around $\\theta^2$~Ori~A. They are probably of\ninterstellar origin. The ionization structure and the distribution of\nthe carriers of the Aromatic Infrared Bands (AIBs) are briefly\ndiscussed on the basis of the ISO observations.\n%\n\\keywords\t{ISM: Orion nebula\t\t-\n\t\tISM: Orion bar \t\t-\n\t\tISM: \\HII~ regions\t\t-\n\t\tstars: $\\theta^2$~Ori~A\t\t-\n\t\tdust, extinction\t\t-\n\t\tInfrared: ISM: lines and bands} \n%\n\\end{abstract}\n%\n\\section{Introduction}\nThe Orion nebula is one of the most studied star--forming regions in\nthe Galaxy. The ionizing stars of the Orion nebula (the Trapezium\nstars, the hottest of which is $\\theta^1$~Ori~C, O6) have eroded a\nbowl--shaped \\HII~ region into the surface of the Orion molecular\ncloud. The Orion bar is the limb--brightened edge of this bowl where\nan ionization front is progressing into the molecular cloud. It is\nseen as an elongated structure at a position angle of approximately\n60\\degr. The Orion nebula extends to the North. The Trapezium stars\nare located at an angular distance of approximately 2.3 arc minutes\nfrom the bar, corresponding to 0.35 pc at a distance of 500 pc. The\nmolecular cloud extends to the other side of the bar, but also to the\nback of the Orion nebula. The bright star $\\theta^2$~Ori~A (O9.5Vpe)\nlies near the bar, and is clearly in front of the molecular cloud\nsince its color excess is only E(B--V) $\\simeq$ 0.2 mag.\n\n%FIGURE 1\n%\\begin{figure}[t!]\n\\begin{figure*}[t!]\n%\\picplace{8cm}\n%%\\vspace{-2.2cm}\n%\\hspace*{-0.5cm}\n{\\psfig{file=orion_minimosaic.ps,width=17cm,angle=00}}\n\\caption{Mosaic of six images of the Orion bar area (shown in\ndetector coordinates, a clockwise rotation of 10.4\\degr~ is needed to\ndisplay the real sky orientation; see Fig. 2 for the equatorial\ncoordinates). Top row: {\\it (left)} an image at 5.01\\mum,\n$\\theta^2$~Ori~A is visible in the middle left of the image; {\\it\n(centre)} the Orion bar at the AIB wavelength of 6.2\\mum; {\\it\n(right)} image at 9.5\\mum (the wavelength of one of the silicate\nfeatures), note that $\\theta^2$~Ori~A is again visible. Bottom row:\n{\\it (left)} image at the AIB wavelength of 11.3\\mum~ and {\\it\n(centre)} image at 12.7\\mum~(ISOCAM's CVF resolution blends [\\NeII]\nand the 12.7\\mum~AIB feature); image at 15.6\\mum {\\it (right)},\nwavelength of the [\\NeIII] forbidden line. }\n%\\end{figure}\n\\end{figure*}\n\nFigs. 1 and 2 illustrate the geometry of the region observed. Fig. 1\nshows six representative images of the region of the Orion bar (see\nthe figure caption for details). Fig. 2 shows the contours of the the\n[\\NeIII] 15.5\\mum~ fine-structure line emission which delineates the\n\\HII~ region. The emission in one of the mid-IR bands (hereafter\ncalled the Aromatic Infrared Bands, AIBs) at 6.2\\mum~ traces the Orion\nbar (an edge-on PhotoDissociation Region or PDR). The AIBs are usually\nstrongly emitted by PDRs. The Trapezium region was avoided because of\npossible detector saturation.\n\nPioneering infrared observations by Stein \\& Gillet (\\cite{Stein}) and\nNey \\etal (\\cite{Ney}) discovered interstellar silicate emission near\n10\\mum~ in the direction of the Trapezium. This was confirmed by\nBecklin \\etal (\\cite{Becklin}) who also noticed extended silicate\nemission around $\\theta^2$~Ori~A. Since that time, interstellar\nsilicate emission has been found by the Infrared Space Observatory\n(ISO) in the \\HII~ region N 66 of the Small Magellanic Cloud (Contursi\n\\etal in preparation) and in a few Galactic compact \\HII~ regions (Cox\n\\etal in preparation) and Photodissociation Regions (PDRs, Jones \\etal\nin preparation). The emission consists of two broad bands centered at\n9.7 and 18\\mum, which show little structure and are clearly dominated\nby amorphous silicates.\n\nWe report in the present article ISO observations of the Orion bar and\nof a part of the Orion nebula made with the Circular Variable Filter\nof the ISO camera (CAM-CVF) which allowed imaging spectrophotometry of\na field $3\\arcmin\\times3\\arcmin$ at low wavelength resolution (R\n$\\simeq$ 40). We also use an ISO Short--Wavelength Spectrometer (SWS)\nobservation which provides higher--resolution ($R\\simeq 1000$)\nspectroscopy at a position within the \\HII~ region (see Fig. 2). This\nspectrum was taken as part of the MPEWARM guaranteed-time program. We\nshow here that these new ISO data confirm and extend previous\nobservations of the amorphous silicate emission and also give evidence\nfor emission by crystalline silicates.\n\nSect. 2 of this paper describes the observations and data\nreduction. In Sect. 3, we discuss the emission of dust and gas. The\nsilicate emission is characterized in section 4 through modelling of\nthe observed continuum IR emission. Finally, conclusions are presented\nin Sect. 5. Our observations also give information on the\nfine--structure lines and on the AIBs. This will be presented in\nAppendices A and B respectively.\n\n\\section{Observations and data reduction}\n%\nImaging spectrophotometry was performed with the 32$\\times$32 element\nmid-IR camera (CAM) on board the ISO satellite, using the Circular\nVariable Filters (CVFs) (see Cesarsky et al. ~\\cite{CCesarsky} for a\ncomplete description). The observations employed the 6\\arcsec~ per\npixel field-of-view of CAM. Full scans of the two CVFs in the\nlong-wave channel of the camera were performed with both increasing\nand decreasing wavelength. The results of these two scans are almost\nidentical, showing that the transient response of the detector was\nonly a minor problem for these observations. The total wavelength\nrange covered is 5.15 to 16.5\\mum~ and the wavelength resolution\n$\\lambda/\\Delta\\lambda \\simeq 40$. 10$\\times$0.28 s exposures were\nadded for each step of the CVF, and 7 more at the first step in order\nto limit the effect of the transient response of the detectors. The\ntotal observing time was about 1 hour. The raw data were processed as\ndescribed in Cesarsky \\etal~(\\cite{M17}), with improvements described\nby Starck \\etal (\\cite{Starck}) using the CIA software\\footnote{CIA is\na joint development by the ESA Astrophysics Division and the ISOCAM\nConsortium led by the ISOCAM PI, C. Cesarsky, Direction des Sciences\nde la Mati\\`ere, C.E.A., France}. The new transient correction\ndescribed by Coulais \\& Abergel (\\cite{Coulais}) has been applied but\nthe corrections introduced are minimal, as mentioned above. The bright\nstar $\\theta^2$~Ori~A is visible in the maps of several spectral\ncomponents and has been used to re--position the data cube. This\ninvolved a shift of only 2\\arcsec. The final positions are likely to\nbe good to 3\\arcsec~ (half a pixel).\n\n%FIGURE 2\n\\begin{figure} %%[t!]\n%\\picplace{8cm}\n\\vspace{-1cm}\n%\\hspace*{-0.5cm}\n{\\psfig{file=orion_uib62neiii.ps,width=8.8cm,angle=00}}\n\\caption{[\\NeIII] map (contours) and 6.2\\mum~ Aromatic Infrared Band \n(AIB) map (grey scale). The grey scale corresponds to line intensities\nfrom 0.01 to 0.30 \\flux. The contours correspond to band intensities\nof 0.015 to 0.06 \\flux~ by steps of 0.05. The cross is at the position\nof the O9.5V star $\\theta^2$~Ori~A. The position of the hottest of the\nTrapezium stars ($\\theta^1$~Ori~C) is also indicated, outside the\nobserved field. The position of the SWS aperture in the direction of\nthe \\HII~ region is shown by a black cross. }\n\\end{figure}\n\nAll the maps presented here were obtained from the CVF data cube and\nhave approximately the same resolution: namely, 6\\arcsec~ pixels at\nthe short wavelengths increasing to about 8\\arcsec~ at 15\\mum; see\nAppendix C for more details.\n\nIn several of these maps a faint emission can be seen on the\nsouth--east part of the ISOCAM field of view. This feature does not\ncorrespond to anything conspicuous in published images of the region,\nin particular in the near--IR images of Marconi \\etal\n(\\cite{Marconi}). It is a spurious feature due to multiple reflections\nof the strong Trapezium between the detector and the CVF filter wheel,\nas shown by the ISOCAM ray tracing studies of Okumura (\\cite{koko}).\n\nThe complete SWS scan (2.4-46\\mum) was reduced with the latest version\nof SWS-IA running at the Institut d'Astrophysique\nSpatiale. Calibration files version CAL-030 were used.\n\nFig. 3 presents the SWS spectrum ($\\lambda/\\Delta\\lambda \\simeq 1000$)\nobtained inside the \\HII~ region at the position indicated on Fig. 2. Fig. 3\nalso shows the comparison of the SWS spectrum with that of the CAM-CVF pixels\naveraged in the SWS aperture. The agreement between these spectra is excellent,\nwell within 20 percent for the continuum. \n\n\n\\section{Gas and dust emission}\n\nThe spectra towards the \\HII~ region of the Orion nebula are shown in\nFigs. 3 and 4. The CAM-CVF spectrum of Fig. 3 is representative of\nthe whole field because CVF spectra obtained at different positions in\nthe \\HII~ region and around $\\theta^2$~Ori~A look qualitatively\nsimilar (compare Figs. 3 and 10 which show the CVF spectra of\ndifferent pixels; note particularly the rising long wavelength portion\nof the spectra). \\\\\n\nIn the SWS spectrum, a large number of unresolved lines from atoms,\nions and molecules are visible. We note the Pf$\\alpha$ recombination\nline of hydrogen (emitted by the warm, ionized gas of the \\HII~\nregion) and the molecular hydrogen pure rotation lines S(2) and very\nfaintly S(3) and S(5) (stemming from the cooler, molecular PDR gas).\nThe simultaneous presence of these lines reflects the variety of\nphysical conditions present along the line of sight. Clearly, we are\nlooking at emission from the \\HII~ region mixed with some emission\nfrom the background PDR. These unresolved lines are briefly discussed\nin Appendix A. \\\\\n\n%FIGURE 3\n\\begin{figure}[t!]\n%\\picplace{8cm}\n\\vspace{-0.5cm}\n%\\hspace*{-0.5cm}\n{\\psfig{file=orion_swscam.ps,width=8.8cm,angle=00}}\n\\caption{The SWS spectrum (full line) compared to the CAM-CVF spectrum\n(dotted line). In this latter case, all the CAM pixels falling in the\nSWS aperture have been co-added. }\n\\end{figure}\n\n\n%FIGURE 4\n\\begin{figure}[!t]\n%\\picplace{12.5cm}\n\\vspace{0.3cm}\n%\\hspace*{-0.5cm}\n%\\centerline{\\epsfig{figure={orion_sws.ps},width=8.8cm } }\n{\\psfig{figure={orion_sws.ps},width=8.8cm } }\n\\caption{SWS spectrum in the Orion nebula at the position shown in\nFig. 2. A fit to the spectrum (see Sect. 3 for details) is shown\nwhich uses amorphous astronomical silicate (130~K: bold dashed-dotted,\nand 80~K: light dashed-dotted), amorphous carbon (155~K: bold dashed,\nand 85~K: light dashed), and amorphous carbon VSGs (300~K: dotted).\nThe total calculated spectrum is given by the thin solid line. The\nidentification of the strongest spectral features is indicated. }\n\\end{figure}\n\n\nThe other striking fact of the SWS spectrum is the strong continuum\npeaking at about 25\\mum. It is emitted by warm dust in the \\HII~\nregion, but dust from the background PDR probably also\ncontributes. The broad emission bands of amorphous silicates centered\nat 10 and 18\\mum~ are visible. The classical AIBs at 6.2, 7.7, 8.6,\n11.3 and 12.7\\mum~ dominate the mid-IR part of the spectrum. As\ndiscussed by Boulanger \\etal \\cite{bbcr}, the mid-IR spectrum can be\ndecomposed into Lorentz profiles (the AIBs) and an underlying\npolynomial continuum. Maps of the various AIBs constructed in this way\nall show the same morphology originating mainly from the PDR gas in\nthe Orion bar (see Appendix B). We will hereafter use the 6.2\\mum-band\nas representative of the behaviour of the AIBs. \\\\\n\n\nIn Fig. 5 we compare the behaviour of the mid-IR continuum emission\nand of the AIBs. Clearly, the AIB emission is concentrated in the\nOrion bar whereas the 15.5\\mum-continuum emission extends throughout\nthe whole CAM field and shows a local peak around $\\theta^2$~Ori~A\n(note that the mid-IR emission around this star is foreground because\nthe star lies in front of the nebula). The continuum emission,\nhowever, appears to peak towards $\\theta^1$~Ori~C, outside the region\nobserved with ISOCAM.\n\nThe contrast in the emission morphology between the bands and\ncontinuum can be interpreted in terms of the photodestruction of the\nAIB carriers in the hard UV-radiation field of the \\HII~ region. The\nAIB carriers must be efficiently destroyed while the larger grains are\nmuch more resistant (\\eg Allain \\etal 1996). We detail the modelling\nof the dust thermal emission in the next section.\n \n%FIGURE 5\n\\begin{figure}[t!]\n%\\picplace{8cm}\n\\vspace{-1cm}\n%\\hspace*{-0.5cm}\n{\\psfig{file=orion_uib62cont16.ps,width=8.8cm,angle=00}}\n\\caption{Continuum emission at 15.5\\mum~ (contours) superimposed on the\nAIB 6.2\\mum~ map (grey scale). The continuum flux was taken to be the\naverage of the flux on each side of the [\\NeIII]15.5\\mum~ line. The\n6.2\\mum~feature strength was estimated as explained in the Appendix C.\nThe contours are from 10 to 80 Jy/pixel (1 pixel =\n$6\\arcsec\\times6\\arcsec$), by steps of 5 Jy/pixel; the grey scale map\nspans 0.01 to 0.3 \\flux. The position of $\\theta^2$~Ori~A is indicated\nby a cross. }\n\\end{figure}\n\n\n\\subsection{Modelling the dust emission}\n\nTo account for the observed SWS spectra, we have calculated the\nthermal equilibrium temperature of dust in the Orion \\HII~ region as a\nfunction of distance of the Orion bar from the Trapezium stars,\nassuming that $\\theta^1$ Ori C (an O6 star) dominates the local\nradiation field. We use the optical constants of the amorphous\nastronomical silicate of Draine (\\cite{Draine85}) and of the amorphous\ncarbon AC1 of Rouleau \\& Martin (\\cite{Rouleau}). Assuming typical\ninterstellar grain sizes (e.g. Draine \\& Lee \\cite{DandL84}), we find\na temperature range of 85--145~K for amorphous silicates and a range\nof 110--200~K for amorphous carbon, corresponding to grains of radius\n1500 and 100 \\AA~ respectively, at a distance of $\\sim 0.35$~pc from\n$\\theta^1$ Ori C (the distance of the Orion Bar to the Trapezium\nstars).\n\nUsing, for simplicity, discrete dust temperatures consistent with\nthose calculated above (T$_{\\rm silicate}$ = 80~K and 130~K, T$_{\\rm\ncarbon}$ = 85~K and 155~K) we are able to satisfactorily model the\ncontinuum emission spectrum from the dust in the Orion \\HII~ region at\nthe position of the ISO-SWS spectrum. In Fig. 4 we show the\ncalculated emission spectrum from our model where we adopt the\ncarbon/silicate dust mass ratios of Draine \\& Lee (\\cite{DandL84}). In\nthe calculated spectrum we have included the emission from carbon\ngrains at 300~K, containing $\\sim$ 1 percent. of the total carbon\ndust mass, in order to fit the short wavelength continuum\nemission. The hot carbon grain emission mimics that of the\nstochastically-heated Very Small Grains (VSGs, D\\'esert \\etal 1990).\nThe 300~K temperature represents a mean of the temperature\nfluctuations for these small particles in the radiation field of\n$\\theta^1$ Ori C, and therefore indicates a lower mass limit of $\\sim$\n1 percent for the mass of the available carbon in VSGs.\n\nThe results of our model show that the emission feature in the 10\\mum~\nregion is dominated by amorphous silicates at temperatures of the\norder of 130~K, but that there may also be a small contribution from\namorphous carbon grains in the 12\\mum~ region (Fig. 4). We also note\nbroad ``features'' in the SWS spectrum, above the modelled continuum\nin Fig. 4, at $\\sim 15-20$\\mum, $\\sim 20-28$\\mum~ and longward of\n32\\mum, that are not explained by our model. These features bear a\nresemblance to the major bands at 19.5, 23.7 and 33.6\\mum~ seen in the\ncrystalline forsterite spectra of Koike \\etal (\\cite{Koike}) and of\nJaeger \\etal (\\cite{Jaeger}). Bands in these same wavelength regions\nwere noted by Jones \\etal (\\cite{Jones}) in the SWS spectra of the\nM\\,17 \\HII~ region and were linked with the possible existence of\ncrystalline Mg-rich olivines in this object. Thus, similar broad\nemission bands are now observed in the 15--40\\mum~wavelength region of\nthe SWS spectra of two \\HII~ regions (Orion and M\\,17). These bands\nresemble those of the crystalline Mg-rich silicate forsterite. Another\nband at 9.6\\mum~ is probably due to some sort of crystalline silicate,\nand will be discussed in more details in the next section.\n\nThis dust model is simple--minded but emphasizes dust spectral\nsignatures in the mid-IR continuum which was the main aim here. More\ndetailed modelling treating temperature fluctuations and taking into\naccount the grain size distribution is underway (Jones \\etal in\npreparation).\n\n% ******************* NEW TEXT by Ant 9/2/00 ************************** \n%\nThe broad continua that lie above the model fit (i.e. $\\sim 20-28$\\mum~ and\n$>$~32\\mum, Fig. 4) can be associated with crystalline silicate emission bands.\nThis seems to be a robust conclusion of this study. The features are too narrow\nto be explained by single-temperature blackbody emission and are therefore\nlikely to be due to blended emission features from different materials.\nUnfortunately, having only one full SWS spectrum and CVF spectra that do not\nextend beyong 18\\mum, we are unable to say anything about the spatial variation\nof these broad bands in the Orion region.\n\nInterestingly, broad plateaux in the $\\sim 15-20$\\mum~ region have been\nassociated with large aromatic hydrocarbon species containing of the order of a\nthousand carbon atoms (van Kerckhoven \\etal \\cite{vanKerckhoven}). However, in\nthis study the integrated intensity of the $\\sim 15-20$\\mum~ plateaux do vary\nby a factor of up to 10 relative to the aromatic carbon features shortward of\n13\\mum. Thus, the origin of these broad emission features does remain\nsomething of an open question at this time.\n%\n% ********************************************************************* \n\n\n\\section{Tracing the silicate emission}\n\nTo delineate the spatial extent of the 10\\mum-silicate emission\nconspicuously visible in Fig. 3 and 4, we proceed as follows. We start\nwith the spectrum towards $\\theta^2$~Ori~A, which shows the most\nconspicuous silicate emission and we represent the AIBs by Lorentz\nprofiles, see Fig. 6 (top). Next we subtract them from the CVF\nspectra. The remaining continuum has the generic shape of a blackbody\non top of which we see the broad bands corresponding to the silicate\nemission, Fig. 6 (middle). Finally, we subtract a second order\npolynomial from the continuum thus obtaining the well known silicate\nemission profile at that position, Fig. 6 (bottom). The profile thus\nobtained is then used as a scalable template to estimate the emission\nelsewhere, see Appendix C for more details.\n\n%FIGURE 6\n\\begin{figure}[t!]\n%\\picplace{11cm}\n\\vspace{-0.5cm}\n%\\hspace*{-0.5cm}\n{\\psfig{file=orion_silfeature.ps,width=8.8cm,angle=00}}\n\\caption{{\\it Top panel:} CVF spectrum towards $\\theta^2$~Ori~A (solid\nline). The ordinates give fluxes in Jy per $6\\arcsec\\times6\\arcsec$\npixel. A Lorentz fit to the AIBs is shown as the dotted line. {\\it\nMiddle panel:} result of the subtraction of the AIBs from the CVF\nspectrum. The fit to the continuum is shown by the dotted line. {\\it\nBottom panel:} Residual from the middle figure, i.e. the suspected\namorphous silicate emission profile; notice the narrower bump near\n9.6\\mum. }\n\\end{figure}\n\nOn top of the broad band of amorphous silicate centered near 9.7\\mum~\nwe see a band centered at nearly 9.6\\mum, which we ascribe to\ncrystalline silicates (Jaeger \\etal \\cite{Jaeger}). This band was also\nused as a scalable template as explained above and in Appendix\nC. Finally, the S(5) rotation line of H$_2$ at 6.91\\mum~ is present\nand is probably blended with the [\\ArII] line at 6.99\\mum.\n\nIn Fig. 7, we see that the spatial distribution of the 9.7\\mum-feature\nof amorphous silicate is quite similar to that of the\n15.5\\mum-continuum. The 15.5\\mum~ continuum emission includes a\nstrong contribution from silicates (see Fig. 4), but a peak in the\nsilicate emission around $\\theta^2$~Ori~A is also evident. The\nsilicate emission is thus predominantly due to larger grains. The\nnarrower 9.6\\mum~feature is mapped in Fig. 8. We note its similarity\nto the distribution of the 9.7\\mum~broad band: this fact lends support\nto our assignation of this band to crystalline silicate. \\\\\n\n\n%FIGURE 7\n\\begin{figure}[t!]\n%\\picplace{8cm}\n\\vspace{-1cm}\n%\\hspace*{-0.5cm}\n{\\psfig{file=orion_silamcont16.ps,width=8.8cm,angle=00}}\n\\caption{Map of the intensity of the broad 9.7\\mum~ band of amorphous \nsilicates (contours) superimposed on the 15.5\\mum~ continuum map (grey\nscale). Note the bright silicate emission around $\\theta^2$~Ori~A\n(cross). The contours correspond to integrated band intensities from\n0.25 to 0.7 \\flux~ by steps of 0.05; the gray image spans from 1 to 80\nJy/pixel. }\n\\end{figure}\n\n%FIGURE 8\n\\begin{figure}[t!]\n%\\picplace{8cm}\n\\vspace{-1cm}\n%\\hspace*{-0.5cm}\n{\\psfig{file=orion_sil_am_cr.ps,width=8.8cm,angle=00}}\n\\caption{Map of the 9.6 micron feature map (contours) superimposed on\nthe map of the broad 9.7\\mum~ band of amorphous silicates (grey scale\nspanning 0.1 to 10 \\flux. The contours correspond to integrated band\nintensities from 0.02 to 0.11 \\flux~ by steps of 0.001. The shift with\nrespect to the position of $\\theta^2$~Ori~A (cross) is by less than\none pixel and may not be significant. }\n\\end{figure}\n\n%FIGURE 9\n\\begin{figure}[t!]\n%\\picplace{16cm}\n\\vspace{-1cm}\n%\\hspace*{-0.5cm}\n{\\psfig{file=orion_vdw_sil_cr.ps,width=8.8cm,angle=00}}\n\\vspace{0.3cm}\n{\\psfig{file=orion_vdw_sil_am.ps,width=8.8cm,angle=00}}\n\\caption{ The 9.6\\mum~ feature (top) and 6.2\\mum-AIB (bottom) both in\ncontours superimposed to the $v=1\\rightarrow 0$ S(1) line emission of\nmolecular hydrogen taken from van der Werf \\etal (\\cite{vanderwerf})\n(grey scale). The contours correspond to integrated band intensities\nfrom 0.02 to 0.11 by steps of 0.01 (top figure) and 0.045 to 0.27 by\nsteps of 0.025 (bottom figure) in units of \\flux. }\n\\end{figure}\n\n\nDue to the low spectral resolution of the CAM-CVF, however, the\n9.6\\mum~ feature will certainly blend with the S(3) pure rotational\nline of molecular hydrogen - if present. To check this we have\ncompared our 9.6\\mum~ map to that of molecular hydrogen in its\nfluorescent vibrational line 1$\\rightarrow 0$ S(1)\n(2.12\\mum). Courtesy of P.P. van der Werf (van der Werf \\etal\n\\cite{vanderwerf}), we reproduce in Fig. 9 the map of the fluorescent\nmolecular hydrogen emission. This latter correlates better with the\nAIB emission as traced by the 6.2\\mum-feature (bottom figure) than it\ndoes with the tentative crystalline silicate emission (top), namely\nthey both peak along the bar. This is not surprising because the H$_2$\nand AIB emitters require shielding from far-UV radiation to\nsurvive. Conversely, the 9.6\\mum~silicate feature is stronger where\nH$_2$ is weak as can be seen around $\\theta^2$~Ori~A. In addition, the\nH$_2$ S(3) rotational line at 9.66\\mum~ is detected in the ISO-SWS\nspectrum of the Orion bar presented in Verstraete \\etal (1999, in\npreparation) with an intensity of $6\\times 10^{-7}$ W m$^{-2}$\nsr$^{-1}$. This value is a factor of 16 below the median flux of the\n9.6\\mum~ feature in our map, namely $10^{-5}$ W m$^{-2}$ sr$^{-1}$. We\ncan thus safely conclude that our 9.6\\mum-emission predominantly\noriginate from silicates.\n% ******************* NEW TEXT by Ant 9/2/00 ************************** \n%\nA confirmation of the identification of the 9.6\\mum~ band with a\ncrystalline silicate dust component would be possible if a second\nsignature band were seen in our spectra. The SWS spectrum (Fig. 4)\nshows only broad emission bands that are difficult to characterise,\nand additionally, the chacteristic crystalline olivine band in the\n$11.2-11.4$\\mum~ region (\\eg Jaeger \\etal \\cite{Jaeger}), if present,\nis blended with the 11.2\\mum~ aromatic hydrocarbon\nfeature. Additionally, most of the chacteristic crystalline bands fall\nlongward of the CVF spectra. Thus, it is difficult to\nself-consistently confirm the 9.6\\mum~ band identification with the\npresented data.\n%\n% ********************************************************************* \n\nIn summary, emission in the 9.7\\mum~band of amorphous silicate\nemission exists everywhere inside the Orion \\HII~ region. Previously,\namorphous silicate emission had only been seen in the direction of the\nTrapezium (Stein \\& Gillett \\cite{Stein}; Forrest \\etal\n\\cite{Forrest}; Gehrz \\etal \\cite{Gehrz}). We may assume that the\n18\\mum~ band is also widely present in the region, as witnessed by the\nsingle SWS spectrum (Fig. 4) and by the generally rising long\nwavelength end of ISOCAM spectra; the two spectra shown, Figs. 3 and\n10 are quite representative of the steeply rising continuum longward\nof 15\\mum.\n\n\n\\subsection{ The interstellar silicate and H$_2$ emission around \n\t \\mbox{$\\theta^2$~Ori~A}}\n\nThe case of $\\theta^2$~Ori~A is particularly interesting because the\ngeometry is simple and therefore allows quantitative\ncalculations. Moreover, the thermal radio continuum, the recombination\nlines and the fine--structure lines are faint in the neighbourhood of\nthis star (Felli \\etal \\cite{Felli}; Pogge \\etal \\cite{Pogge}; Marconi\n\\etal \\cite{Marconi}, and the present paper, Fig. 2).\n$\\theta^2$~Ori~A is classified as an O9.5Vpe star and shows emission\nlines (see e.g. Weaver \\& Torres--Dodgen \\cite{Weaver}). It is a\nspectroscopic binary and an X-ray source. There is little gas left\naround the star and the observed silicate dust (Fig. 8) is almost all\nthat is visible of the interstellar material left over after its\nformation. Indeed, O stars are not known to produce dust in their\nwinds which are probably much too hot, so that the silicates we see\nhere must be of interstellar origin.\n \nThe mid--IR continuum observed towards $\\theta^2$~Ori~A can be\naccounted for by combining emission of warm silicate and carbon grains\n(see Fig. 10). The\n%% hand inserted from here\nmodel continuum was obtained in the same way as for the SWS\nobservation (see Fig. 4) and with the same assumptions. The grain\ntemperatures are consistent with the heating of interstellar grains by\nthe strong radiation field of the star.\n\n%FIGURE 9\n\\begin{figure}[t!]\n%\\picplace{11cm}\n\\vspace{0cm}\n%\\hspace*{-0.5cm}\n{\\psfig{figure={orion_fig9.ps},width=8.8cm }}\n\\caption{CVF spectrum towards $\\theta^2$ Ori A (heavy solid line).\nThe ordinates give fluxes in Jy per $6\\arcsec\\times6\\arcsec$ pixel.\nThe fit to the continuum is shown by the thin solid line.\nThe fit (see \\S3) to these data comprises, from top to bottom\non the right--hand axis: 100--K amorphous astronomical silicate\n(dot-dashed line), \n110--K amorphous carbon (dashed line ),\n235--K amorphous astronomical silicate (dot-dashed line) and \n330--K amorphous carbon emission (dashed line). }\n\\end{figure}\n\n\nAs discussed above, the band near 9.6 $\\mu$m (Fig. 6 bottom and\nFig. 8) may be due to crystalline silicates, any contribution of the\nS(3) H$_2$ line to this band is minor. Another band at 14 $\\mu$m (see\nFigs. 4 and 10) might also be due to crystalline silicates. Amongst\nthe crystalline silicates whose mid--IR absorption spectra are shown\nby Jaeger \\etal (\\cite{Jaeger}), synthetic enstatite (a form of\npyroxene) might perhaps match the $\\theta^2$ Ori A spectrum. The\ninterest in the possible presence of crystalline silicates around this\nstar is that they would almost certainly be of interstellar origin,\npre--dating the formation of the star. Observations at longer\nwavelengths are needed for a definitive check of the existence of\ncrystalline silicates and for confirming their nature. Such\nobservations do not exist in the ISO archives and should be obtained\nby a future space telescope facility.\n\n\n\\section{Conclusions}\n\nWe obtained a rather complete view of the infrared emission of the\nOrion nebula and its interface with the adjacent molecular cloud. The\nmost interesting results are the observation of amorphous, and\npossibly crystalline, silicates in emission over the entire \\HII~\nregion and in an extended region around the bright O9.5Vpe star\n$\\theta^2$ Ori A. We have fitted the mid--IR continuum of the \\HII~\nregion and around $\\theta^2$ Ori A with the emission from amorphous\nsilicate and amorphous carbon grains at the equilibrium temperatures\npredicted for the grains in the given radiation field. This shows\nthat both types of grains can survive in the harsh conditions of the\n\\HII~ region. A number of bands (the 9.6\\mum~bump seen in Fig. 6; the\nexcess 14\\mum~emission indicated in Figs. 4 and 10) suggest emission\nfrom crystalline silicates (essentially forsterite) in the \\HII~\nregion. Crystalline silicates may also exist around $\\theta^2$ Ori A,\nbut further, longer wavelength observations are required to confirm\ntheir presence. \\\\\n\nDo the observed crystalline silicates result from processing of\namorphous silicates in the \\HII~ region or in the environment of\n$\\theta^2$ Ori A? Silicate annealing into a crystalline form requires\ntemperatures of the order of 1000~K for extended periods (Hallenbeck\n\\etal \\cite{Hallenbeck}). The dust temperatures observed in the \\HII~\nregion and around $\\theta^2$ Ori A are considerably lower than this\nannealing temperature. One might however invoke grain heating\nfollowing grain--grain collisions in the shock waves that are likely\nto be present in the \\HII~ region. However, grain fragmentation rather\nthan melting is the more likely outcome of such collisions (Jones\n\\etal \\cite{JTH}). It is probable that the crystalline silicates observed here\nwere already present in the parent molecular cloud, and probably\noriginate from oxygen--rich red giants. \\\\\n\nEmission by both amorphous and crystalline silicates has been observed\nwith ISO around evolved stars (Waters \\etal \\cite{Waters}; Voors \\etal\n\\cite{Voors}). The crystalline silicates there must have been produced \nlocally by annealing of amorphous silicates. Gail \\& Sedlmayr\n(\\cite{Gail}) have shown that this is possible, and that both\namorphous and crystalline forms can be released into the interstellar\nmedium. However, there is no evidence for absorption by crystalline\nsilicates in the general interstellar medium in front of the deeply\nembedded objects for which amorphous silicate absorption is very\nstrong (Demyk \\etal 1999, Dartois \\etal \\cite{Dartois}).\nConsequently, crystalline silicates represent only a minor fraction\ncompared to amorphous silicates. It would be difficult to detect the\nemission from a small crystalline component of dust in the diffuse\ninterstellar medium because the dust is too cool (T$\\,\\sim 20\\,$K) to\nemit strongly in the $15-40\\,\\mu$m wavelength region. Observations of\n\\HII~ regions and bright stars provide the opportunity of observing\nthis emission due to the strong heating of dust. Emission from\namorphous and crystalline silicates is seen around young stars\n(Waelkens \\etal \\cite{Waelkens}; Malfait \\etal \\cite{Malfait}) as well\nas in comets (Crovisier \\etal \\cite{Crovisier}). There are also\nsilicates in meteorites, but their origin is difficult to determine\nbecause of secondary processing in the solar system. Crystalline\nsilicates in comets, and perhaps in interplanetary dust particles\nbelieved to come from comets (Bradley \\etal\n\\cite{Bradley}), must be interstellar since the material in comets never\nreached high temperatures. However, the silicates probably experienced changes\nduring their time in the interstellar medium. It is interesting to note that\nwhile very small grains of carbonaceous material exist, there seem to be no \nvery small silicate grains in the interstellar medium (D\\'esert \\etal 1986). \n\n\n%\n\\begin{acknowledgements}\nA.P. Jones is grateful to the Soci\\'et\\'e de Secours des Amis des Sciences\nfor funding during the course of this work. We are grateful to P.P. van der\nWerf for providing us with his map of molecular hydrogen emission. \n\\end{acknowledgements}\n%\n\n\\begin{flushleft}\n{\\bf Appendix A: the mid--IR line emission from the Orion nebula}\n\\end{flushleft}\n\nWe presented in Fig. 2 a map of the studied region in the [\\NeIII]\nline at 15.5 $\\mu$m. Fig. 11 displays the map of the [\\ArII] line at\n7.0 $\\mu$m superimposed on the map of the [\\ArIII]~9.0$\\mu$m line.\nThese maps illustrate the ionization structure of the Orion\nnebula. The spectral resolution of the CVF does not allow a separation\nof the the [\\ArII] line at 6.99 $\\mu$m from the S(5) pure rotation\nline of H$_2$ at 6.91 $\\mu$m. However, the bulk of the H$_2$ emission\ncome from deeper in the molecular cloud than that of [\\ArII], \\ie more\nto the south-west (see Fig. 9) and the contamination by the S(5) line\nis probably minor. The SWS spectrum shown here and that taken towards\nthe bar (Verstraete \\etal 1999, in preparation) in which the [\\ArII]\nand the H$_2$ S(5) line are well separated from each other, show that\nthe H$_2$ line is a factor 4 or 5 weaker and hence cannot seriously\ncontaminate the [\\ArII] map.\n\n%FIGURE 11\n\\begin{figure}[t!]\n\\vspace{-1cm}\n{\\psfig{file=orion_ariii_ii.ps,width=8.8cm,angle=00}}\n\\caption{Map in the line of [\\ArII] at 7.0 $\\mu$m (contours) superimposed\non the map of the [\\ArIII] 9.0 $\\mu$m line (grey scale spanning 0.01\nto 0.05 \\flux). The contours for [ArII] are from 10$^{-3}$ to\n10$^{-2}$ \\flux~ by steps of 10$^{-3}$. The position of $\\theta^2$ Ori\nA is indicated by a cross. The peak at 7 $\\mu$m at this position is\nprobably due to the S(5) line of H$_2$ rather than to [\\ArII] (see\ntext). }\n\\end{figure} \n\nThe emission by the singly--charged ion [\\ArII] is concentrated near\nthe ionization front on the inner side of the bar. This is very\nsimilar to what is seen in the visible lines of [\\NII] $\\lambda$6578\nand [\\SII] $\\lambda$6731 (Pogge \\etal \\cite{Pogge} Fig. $1c$ and\n$1d$). The detailed correspondence between the maps in these three\nions is excellent: note that the optical maps are not much affected by\nextinction. The ionization potentials for the formation of these ions\nare 15.8, 14.5 and 10.4 eV for \\ArII, \\NII~, \\SII~ respectively, and\nare thus not too different from each other.\n \nThe emission from the doubly--charged ions [\\NeIII] and [\\ArIII] shows\na very different spatial distribution, with little concentration near\nthe bar but increasing towards the Trapezium. The [\\NeIII] map\n(Fig. 2) is very similar to the [\\OIII]$\\lambda$5007 line map (Pogge\n\\etal \\cite{Pogge} Fig. $1e$), as expected from the similarity of the\nionization potentials of [\\NeII] and [\\OII], respectively 41.1 and\n35.1 eV. However, the distribution of the [\\ArIII] line (Fig. 11) is\nsomewhat different, with a trough where the [\\NeIII] and the [\\OIII]\nlines exhibit maxima. \\ArIII~ is ionized to \\ArIV~ at 40.9 eV, almost\nthe same ionization potential as that of \\NeII, so that \\ArIV~ (not\nobservable) should co--exist with \\NeIII~ and \\ArIII~ with \\NeII. A\nmap (not displayed) in the 12.7 $\\mu$m feature, which is a blend of\nthe 12.7 $\\mu$m AIB and of the [\\NeII] line at 12.8 $\\mu$m, is indeed\nqualitatively similar to the [\\ArIII] line map in the \\HII~ region. It\ndiffers in this region from the maps in the other AIBs, showing that\nit is dominated by the [\\NeII] line.\n\nAs expected, the dereddened distribution of the H$\\alpha$ line (Pogge\n\\etal \\cite{Pogge} Fig. $3b$), an indicator of density, is\nintermediate between that of the singly--ionized and doubly--ionized\nlines.\n\n\n\\begin{flushleft}\n{\\bf Appendix B: the AIB emission}\n\\end{flushleft}\n\nMaps of the emission of the 6.2 and 11.3$\\mu$m AIBs are shown in\nFig. 12. We do not display the distribution of the other AIBs because\nthey are very similar. All the spectra of Figs. 3, 4 and 6 show the\nclassical UIBs at 6.2, 7.7, 8.6, 11.3 and 12.7 $\\mu$m (in the CAM-CVF\ndata the latter is blended with the [\\NeII] line at 12.8\n$\\mu$m). There are fainter bands at 5.2, 5.6, 11.0,, 13.5 and 14.2\\mum\nvisible in the SWS spectrum of Fig. 3: they may be AIBs as well. All\nthe main bands visible in the CVF spectra are strongly concentrated\nnear the bar. Emission is observed everywhere, because of the\nextension of the PDR behind the Orion nebula and the presence of\nfainter interfaces to the South--East of the bar. We confirm the\ngeneral similarity between the distributions of the different AIBs\nthrough the Orion bar observed by Bregman\n\\etal (\\cite{Bregman}).\n\n%FIGURE 12\n\\begin{figure}[t!]\n\\vspace{-1cm}\n{\\psfig{file=orion_uib62_113.ps,width=8.8cm,angle=00}}\n\\caption{Map of the 11.3\\mum UIB (contours) superimposed on the\n6.2\\mum UIB map (grey scale from 0.05 to 0.3 \\flux). The contours\ncorrespond to integrated band intensities from 0.016 to 0.16 \\flux~ by\nsteps of 0.016. The distributions of the two UIBs are extremely\nsimilar. The position of $\\theta^2$ Ori A is indicated by a cross. }\n\\end{figure}\n\nWe thus conclude that, although the excitation conditions vary greatly\nfrom the Trapezium region towards the South--West of the bar, the\nmixing of fore-- and background material along the line of sight does\nnot allow us to observe spectroscopical changes in the AIB emission\nfeatures (due e.g. to ionization or dehydrogenation as in M17-SW,\nVerstraete \\etal \\cite{verstraete}).\n\n\\begin{flushleft}\n{\\bf Appendix C: Estimates of emission strengths}\n\\end{flushleft}\n\n%FIGURE 13\n\\begin{figure}[t]\n\\vspace{-0cm}\n{\\psfig{file=orion_template.ps,width=8.8cm,angle=00}}\n\\caption{The eleven line and band templates, normalized to unit peak\nintensity, used by the least square fitting code (first eleven panels;\nthe 12th panel, labeled Sum, shows the combined template). The low\nthree panels give examples of the fit goodness for three lines of\nsight (from left to right): towards $\\theta^2$ Ori A; towards a ``hot\nspot'' in the \\HII~ region; and towards a ``hot spot'' on the AIB\nemission. For all lines of sight the fit was stopped at 15\\mum~since a\nsimple parabola could not account for the steep rise at longer\nwavelengths. }\n\\end{figure}\n\nSpectral emission maps have been obtained using one or another of\nthree different methods. The emission from well defined and rather\nnarrow spectral features, viz. AIBs and ions, can be estimated either\nby numerical integration of the energy within the line and an ad--hoc\nbaseline ({\\it method 1}), or by simultaneous fit of Lorentz\n(Boulanger \\etal, \\cite{bbcr}) and/or gauss profiles, including a\nbaseline, determined by a least square fitting algorithm ({\\it method\n2}). The strength of features not amenable to an analytical\nexpression, like the suspected amorphous silicate emission (see\nFig. 6) has been estimated using the following method ({\\it method\n3}). We have constructed an emission template consisting of all the\nobserved emission features, each one arbitrarily normalised to unit\npeak intensity, see Fig. 13. A least square computer code was then\nused to obtain, for each of the $32\\times 32$ lines of sight, a set of\nmultiplying coefficients for each feature present in the template plus\na global parabolic baseline so as to minimize the distance between the\nmodel and the data points. The number of free parameters is then\neleven ``line intensities'' and three polynomial coefficients, for a\ntotal of 14 free parameters to be determined from 130 observed\nspectral points per line of sight. 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{
"name": "astro-ph0002282.extracted_bib",
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}
] |
astro-ph0002283
|
FIRBACK Source Counts and Cosmological Implications
|
[
{
"author": "H.~Dole\\inst{1}"
},
{
"author": "R.~Gispert\\inst{1}"
},
{
"author": "G.~Lagache\\inst{1}"
},
{
"author": "J-L.~Puget\\inst{1}"
},
{
"author": "H. Aussel\\inst{2,3}"
},
{
"author": "F.R. Bouchet\\inst{4}"
},
{
"author": "P. Ciliegi\\inst{5}"
},
{
"author": "D.L. Clements\\inst{6}"
},
{
"author": "C.J. Cesarsky\\inst{7}"
},
{
"author": "F.X. D\\'esert\\inst{8}"
},
{
"author": "D. Elbaz\\inst{2}"
},
{
"author": "A. Franceschini\\inst{3}"
},
{
"author": "B. Guiderdoni\\inst{4}"
},
{
"author": "M. Harwit\\inst{9}"
},
{
"author": "R. Laureijs\\inst{10}"
},
{
"author": "D. Lemke\\inst{11}"
},
{
"author": "R. McMahon\\inst{12}"
},
{
"author": "A.F.M. Moorwood\\inst{7}"
},
{
"author": "S. Oliver\\inst{13}"
},
{
"author": "W.T. Reach\\inst{14}"
},
{
"author": "M. Rowan-Robinson\\inst{13}"
},
{
"author": "M. Stickel\\inst{11}"
}
] |
FIRBACK is a one of the deepest surveys performed at 170 $\mu m$ with ISOPHOT onboard ISO, and is aimed at the study of cosmic far infrared background sources. About 300 galaxies are detected in an area of four square degrees, and source counts present a strong slope of 2.2 on an integral "logN-logS" plot, which cannot be due to cosmological evolution if no K-correction is present. The resolved sources account for less than 10\% of the Cosmic Infrared Background at 170 $\mu m$. In order to understand the nature of the sources contributing to the CIB, and to explain deep source counts at other wavelengths, we have developed a phenomenological model, which constrains in a simple way the luminosity function evolution with redshift, and fits all the existing deep source counts from the mid-infrared to the submillimetre range. %
|
[
{
"name": "dole_ringberg.tex",
"string": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%\n% This is a sample input file for your contribution to a multi-\n% author book to be published by Springer Verlag.\n%\n% Please use it as a template for your own input, and please\n% follow the instructions for the formal editing of your\n% manuscript as described in the file \"1readme\".\n%\n% Please send the Tex and figure files of your manuscript\n% together with any additional style files as well as the\n% PS file to the editor of your book.\n%\n% He or she will collect all contributions for the planned\n% book, possibly compile them all in one go and pass the\n% complete set of manuscripts on to Springer.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%\n\n\n\n%RECOMMENDED%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%\n\n\\documentclass[runningheads]{cl2emult}\n\n\\usepackage{makeidx} % allows index generation\n\\usepackage{graphicx} % standard LaTeX graphics tool\n % for including eps-figure files\n\\usepackage{subeqnar} % subnumbers individual equations\n % within an array\n\\usepackage{multicol} % used for the two-column index\n\\usepackage{cropmark} % cropmarks for pages without\n % pagenumbers\n\\usepackage{lnp} % placeholder for figures\n\\makeindex % used for the subject index\n % please use the style sprmidx.sty with\n % your makeindex program\n\n%upright Greek letters (example below: upright \"mu\")\n\\newcommand{\\euler}[1]{{\\usefont{U}{eur}{m}{n}#1}}\n\\newcommand{\\eulerbold}[1]{{\\usefont{U}{eur}{b}{n}#1}}\n\\newcommand{\\umu}{\\mbox{\\euler{\\char22}}}\n\\newcommand{\\umub}{\\mbox{\\eulerbold{\\char22}}}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%\n\n\n%OPTIONAL%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%\n%\n%\\usepackage{amstex} % useful for coding complex math\n%\\mathindent\\parindent % needed in case \"Amstex\" is used\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%\n\n%AUTHOR_STYLES_AND_DEFINITIONS%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%\n%\n%Please reduce your own definitions and macros to an absolute\n%minimum since otherwise it will become rather strenuous to\n%compile all individual contributions to a single book file\n%\n%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%\n\n\\begin{document}\n%\n\\title*{FIRBACK Source Counts and Cosmological Implications}\n%\n%\n\\toctitle{FIRBACK Source Counts Cosmological Implications}\n% allows explicit linebreak for the table of content\n%\n%\n\\titlerunning{FIRBACK Source Counts and Cosmological Implications}\n% allows abbreviation of title, if the full title is too long\n% to fit in the running head\n%\n\\author{H.~Dole\\inst{1}\n\\and R.~Gispert\\inst{1}\n\\and G.~Lagache\\inst{1}\n\\and J-L.~Puget\\inst{1}\n\\and H. Aussel\\inst{2,3}\n\\and F.R. Bouchet\\inst{4}\n\\and P. Ciliegi\\inst{5}\n\\and D.L. Clements\\inst{6}\n\\and C.J. Cesarsky\\inst{7}\n\\and F.X. D\\'esert\\inst{8}\n\\and D. Elbaz\\inst{2}\n\\and A. Franceschini\\inst{3}\n\\and B. Guiderdoni\\inst{4}\n\\and M. Harwit\\inst{9}\n\\and R. Laureijs\\inst{10}\n\\and D. Lemke\\inst{11}\n\\and R. McMahon\\inst{12}\n\\and A.F.M. Moorwood\\inst{7}\n\\and S. Oliver\\inst{13}\n\\and W.T. Reach\\inst{14}\n\\and M. Rowan-Robinson\\inst{13}\n\\and M. Stickel\\inst{11}\n}\n%\n\\authorrunning{Herv\\'e Dole \\it{et al.}}\n% if there are more than two authors,\n% please abbreviate author list for running head\n%\n%\n\\institute{Institut d'Astrophysique Spatiale, Orsay, France\n\\and Service d'Astrophysique, CEA/DSM/DAPNIA Saclay, France\n\\and Osservatorio Astronomico di Padova, Italy\n\\and Institut d'Astrophysique de Paris, France\n\\and Osservatorio Astronomico di Bologna, Italy\n\\and Cardiff University, UK\n\\and ESO, Garching, Germany\n\\and Laboratoire d'Astrophysique, Observatoire de Grenoble, France\n\\and 511 H.Street S.W., Washington, DC 20024-2725\n\\and ISOC ESA, VILSPA, Madrid, Spain\n\\and MPIA, Heidelberg, Germany\n\\and Institute for Astronomy, University of Cambridge, UK\n\\and Imperial College, London, UK\n\\and IPAC, Pasadena, CA, USA\n}\n\n\\maketitle % typesets the title of the contribution\n%\n\\vspace{-0.4cm}\n%\n\\begin{abstract}\nFIRBACK is a one of the deepest surveys performed at 170 $\\mu m$ with ISOPHOT onboard\nISO, and is aimed at the study of cosmic far infrared background sources. About 300 galaxies are\ndetected in an area of four square degrees, and source counts present a strong slope of 2.2 on an\nintegral \"logN-logS\" plot, which cannot be due to cosmological evolution if no K-correction is\npresent. The resolved sources account for less than 10\\% of the Cosmic Infrared Background at\n170 $\\mu m$.\nIn order to understand the nature of the sources contributing to the CIB, and to explain deep\nsource counts at other wavelengths, we have developed a phenomenological model, which\nconstrains in a simple way the luminosity function evolution with redshift, and fits all the\nexisting deep source counts from the mid-infrared to the submillimetre range.\n%\n\\end{abstract}\n%\n\\vspace{-0.8cm}\n%\n%________________________________________________________________\n\\section{Introduction}\nThe Cosmic Infrared Background (CIB), due to the accumulation of galaxy emission at all\nredshifts along the line of sight in an instrument beam, is a powerful tool for studying galaxy\nevolution. FIRBACK (\\cite{puget99a}, \\cite{dole99}), one of the deepest surveys performed at\n$170\\,\\mu m$, is aimed at the study of the CIB, in two complementary ways:\n\\begin{itemize}\n%\n\\vspace{-0.2cm}\n%\n\\item study the resolved sources (this paper)\n\\item study the background fluctuations (\\cite{lagache99a}, \\cite{lagache99b})\n\\end{itemize}\n\\vspace{-0.2cm}\nThroughout this paper we use a cosmology with $h=0.65$, $\\Omega=1$ and $\\Lambda=0$.\n%\n%________________________________________________________________\n\\section{The FIRBACK Survey}\nFIRBACK, is a survey of 4 square degrees in 3 high galactic latitude fields, chosen to have as\nlow an HI column-density as possible, typically \\- $N_H \\simeq 10^{20} cm^{-2}$, and if\npossible multiwavelength coverage.\nObservations were carried with ESA's Infrared Space Observatory (ISO, \\cite{kessler96}) with\nthe ISO\\-PHOT photometer \\cite{lemke96} in raster mode (AOT P22) with the \\verb+C200+\ncamera and \\verb+C_160+ broadband filter centered at $\\lambda = 170\\, \\mu m$. \nA detailed description of the reduction, data processing, and calibration will be discussed in\n\\cite{lagache2000}, whereas the analysis of the complete survey will be discussed in\n\\cite{dole2000}.\n%________________________________________________________________\n\\section{Source Counts at $170\\,\\mu m$}\nPreliminary FIRBACK integral source counts at $170\\,\\mu m$ (Fig.~\\ref{firback_count}), not\ncorrected for incompleteness, show a strong slope of 2.2 between 120 and 500 mJy. This strong\nslope is not explained by a K-correction or cosmological evolution alone: both must be present;\nthe K-correction is the ratio, at a given wavelength, of the emitted flux over the redshifted flux.\\\\\nNon (or low) evolution scenarii, or extrapolation of IRAS counts, are not able to reproduce the\nobserved counts. For illustration, we plot in Fig.~\\ref{firback_count} the non-evolution model\nfrom \\cite{franceschini98} and the evolution model A from \\cite{guiderdoni98}.\nOn the other hand, evolutionary models from \\cite{franceschini98} and from \\cite{guiderdoni98}\n(model E: evolution + ULIRGs) give a better agreement.\nAt this wavelength, FIRBACK sources account for only 3\\% of the background.\n%________________________________________________________________\n% FIGURE FIRBACK COUNTS\n\\begin{figure}\n\\centering\n\\includegraphics[width=.85\\textwidth]{figure1.eps}\n\\vspace{-0.3cm}\n\\caption[]{FIRBACK integral source counts at $170\\,\\mu m$ not corrected for incompleteness.\nModels from \\cite{guiderdoni98}: A (dot) with evolution, E (solid) with evolution + ULIRGs.\nModels from \\cite{franceschini98}: without evolution (dot-dash), with evolution (dash).}\n\\label{firback_count}\n\\end{figure}\n%\n%________________________________________________________________\n\\section{Modelling the Evolution of Galaxies}\n%\n%________________________________________________________________\n\\subsection{Method}\nOur philosophy is to make a phenomenological model that explains all the observed deep\nsource counts and reproduces the CIB in the mid-IR to submillimetre range.\nOne way to do this is to constrain the evolution with redshift of the luminosity function (LF) in\nthe infrared, given:\n\\begin{itemize}\n%\n%\\vspace{-0.2cm}\n%\n\\item templates of galaxy spectra\n\\item the energy density available at each redshift\n\\end{itemize}\nFor the first point, we used template galaxy spectra based on IRAS colors \\cite{maffei94}\nmodified to account for recent ISO observations, in particular the absorption feature near\n$10\\,\\mu m$ at high luminosity; PAH features are present in the mid-infrared \\cite{desert90},\neven if their strength seems larger than the observations: this is not a problem because the right\namount of energy is present in each peak, and we convolve the spectrum with the filter spectral\nresponse (Fig.~\\ref{template_spectra}).\nFor the second point, we used the inversion of the CIB spectrum by \\cite{gispert2000} and\n\\cite{puget99b}, which gives with good accuracy the energy density available at redshifts\nbetween 1 and 3. This energy density is the integral of the luminosity function at each redshift,\nbut there is no unique solution for the LF shape.\n%________________________________________________________________\n% FIGURE TEMPLATE SPECTRA\n\\begin{figure}\n\\centering\n\\includegraphics[width=.85\\textwidth]{figure2.eps}\n\\vspace{-0.2cm}\n\\caption[]{Template spectra used for simulating source counts; from bottom to top: $L =\n10^{9},\\, 10^{10},\\, 10^{11},\\, 10^{12},\\, 10^{13}\\, L_{\\odot}$.}\n\\label{template_spectra}\n\\end{figure}\n\\vspace{-0.3cm}\n%\n%________________________________________________________________\n\\subsection{Evolving Luminosity Function}\nThe question is: how to evolve the LF with redshift ? \\\\\nFig.~\\ref{lf_z0} represents the LF of \\cite{sanders96} at a redshift z=0, renormalized to\n$h=0.65$ and having the same integral as \\cite{soifer91}. Our constraint on the LF redshift\nvariation is the energy density available at each redshift \\cite{gispert2000}. Usually, authors\napply a pure density evolution to the LF as a function of redshift (i.e. a vertical shift), or a pure\nluminosity evolution (a horizontal shift). This does not work for FIRBACK source counts: There\nis no alternative other than adding the evolution to one part of the LF only. This part is\nconstrained by IR and submm observations: this is the bright end of the LF.\nFig.~\\ref{lf_z0} represents our decomposition of the local LF into two parts:\n\\begin{itemize}\n%\n\\vspace{-0.2cm}\n%\n\\item left part: ``normal'' galaxies\n\\item right part: ULIRG's, centered on a luminosity $L_{ULIRG} \\simeq 2.0 \\times 10^{11}\nL_{\\odot}$, where $L_{ULIRG}$ is the free parameter; we get the same value as \\cite{tan99}\n\\end{itemize}\nIn our model, \"without evolution\" means that the local LF (Fig.~\\ref{lf_z0}a) is taken, and is the\nsame at every redshift.\nIn the evolutionary scenario, only the ULIRG part moves, in such a way that the integral of the\nLF equals the constraint given by the CIB inversion at each redshift. The maximum is reached at\n$z \\simeq 2.5$, and Fig.~\\ref{lf_z0}b represents the LF at this redshift. We neglect at this stage\nthe evolution of ``normal'' galaxies, which do not play a crucial role in the mid-infrared to\nsubmillimetre wavelength range.\n%\n%________________________________________________________________\n% FIGURE LF Z=0 AND Z=2.5\n\\begin{figure}\n%\\begin{minipage}{5.5cm}\n\\centering\n\\includegraphics[width=0.95\\textwidth]{figure3.eps}\n\\vspace{-2.0cm}\n\\caption[]{a: Luminosity Function at z=0 (solid line); normal galaxy (dot-dash); ULIRG\n(dash-dash). b: Luminosity Function at z=2.5 (solid line); normal galaxy (dot-dash) ULIRG\n(dash-dash) and local LF (dots).}\n\\label{lf_z0}\n%\\end{minipage}\n%\\begin{minipage}{5.5cm}\n%\\centering\n%\\includegraphics[width=1.25\\textwidth]{luminosity_fct049.eps}\n%\\vspace{-2.cm}\n%\\caption[]{Luminosity Function at z=2.5 in solid line; normal galaxy (dot-dash) ULIRG (dash-dash) and local LF (dot)}\n%\\label{lf_z25}\n%\\end{minipage}\n\\end{figure}\n%________________________________________________________________\n% FIGURE LF Z=2.5\n%\\begin{figure}\n%\\centering\n%\\includegraphics[width=.45\\textwidth]{luminosity_fct049.ps}\n%\\vspace{-3.8cm}\n%\\caption[]{Luminosity Function at z=2.5}\n%\\label{lf_z25}\n%\\end{figure}\n%\n%________________________________________________________________\n\\vspace{-0.2cm}\n\\subsection{Model of Source Counts at $170\\,\\mu m$}\nThe model at $170\\,\\mu m$, together with our data, is presented in Fig.~\\ref{create_counts170}.\nThe brightest point of the observed counts is compatible with all our models, in particular the\nnon-evolutionary scenario, which is expected for local sources. We also show the effect of the\nK-correction, which steepens the integral source count slope. Our evolutionary scenario fits the\ndata within the error bars. Most of the background is expected to be resolved into sources once\nwe are able to detect sources at the mJy level. This wavelength region, in which evolutionary\neffects are particularly important and where there are good prospects for detecting higher redshift\nsources because of the K-correction, is nowadays probably the best-suited range for probing\ngalaxy evolution from space in the far-infrared. \n%\n%________________________________________________________________\n% FIGURE MODEL AT 170 MICRONS\n\\begin{figure}\n\\centering\n\\includegraphics[width=.85\\textwidth]{figure4.eps}\n\\vspace{-0.3cm}\n\\caption[]{Observed Counts and Models at $170\\,\\mu m$, with (solid line) and without (dashed\nline) evolution. The model with evolution and without K-correction is the dot-dash line.}\n\\label{create_counts170}\n\\end{figure}\n\\vspace{-1.0cm}\n%\n%________________________________________________________________\n\\subsection{Models of Source Counts at other wavelengths}\nData at $15\\,\\mu m$ \\cite{elbaz99}, $90\\,\\mu m$ \\cite{efstathiou99} and $850\\,\\mu m$\n\\cite{barger99}, with our models are presented\nin Fig.~\\ref{create_counts15}, Fig.~\\ref{create_counts90} and Fig.~\\ref{create_counts850}\nrespectively.\\\\\nAt $15\\,\\mu m$, both the slopes and the little ``waves'' in the counts appear in the models with\nthe combined effects of the K-correction and the evolution. At $90\\,\\mu m$, the K-correction\ndoes not emphasize the differences between the scenarii of evolution or non-evolution. At\n$850\\,\\mu m$, the ``non smooth'' appearance of our model is due to the discretization of the LF.\n%\n%________________________________________________________________\n% FIGURE MODEL AT 15 MICRONS\n\\begin{figure}\n\\centering\n\\includegraphics[width=.85\\textwidth]{figure5.eps}\n\\vspace{-0.3cm}\n\\caption[]{Models at $15\\,\\mu m$ with (solid line) and without (dashed line) evolution, and\nobserved counts from Elbaz et al. \\cite{elbaz99} (thin lines).}\n\\label{create_counts15}\n\\end{figure}\n%\n%________________________________________________________________\n% FIGURE MODEL AT 90 MICRONS\n\\begin{figure}\n\\centering\n\\includegraphics[width=.85\\textwidth]{figure6.eps}\n\\vspace{-0.3cm}\n\\caption[]{Models at $90\\,\\mu m$ with (solid line) and without (dashed line) evolution, and\nobserved counts from Efstathiou et al. \\cite{efstathiou99} (squares) and IRAS counts\n\\cite{efstathiou99} (solid area)}\n\\label{create_counts90}\n\\end{figure}\n%\\vspace{-1.0cm}\n%\n%________________________________________________________________\n% FIGURE MODEL AT 850 MICRONS\n\\begin{figure}\n\\centering\n\\includegraphics[width=.85\\textwidth]{figure7.eps}\n\\vspace{-0.3cm}\n\\caption[]{Models at $850\\,\\mu m$ with (solid line) and without (dashed line) evolution, and\nobserved counts from Barger et al. \\cite{barger99} (diamonds).}\n\\label{create_counts850}\n\\end{figure}\n%\\vspace{-1.0cm}\n%\n%________________________________________________________________\n\\section{Discussion}\n%\n%________________________________________________________________\n\\subsection{The bright end luminosity function evolution model}\nOur model of the evolving LF scenario fits most of the existing deep survey data from space (mid\nand far infrared) and ground (submillimetre).\nIt is also compatible with the observational estimate of the LF in \\cite{lilly99}.\nThe strong observational constrain of multiwavelength source counts is thus explainable by a\nsimple evolutionary law of the LF: \nthe Bright End Luminosity Function Evolution (BELFE) model. \n%the above-$11$ (in log $L_{\\odot}$)-luminosity-function evolution ($11$LiFE).\nOne simple model is in agreement with all up-to-date observables and reproduces the\nbackground.\n%\n%________________________________________________________________\n\\vspace{-0.2cm}\n\\subsection{Redshift and Nature of the sources}\nAnother crucial observational test for our\n%BELFE\n%11LiFE\nmodel is the predicted vs observed redshift distribution. Although the statistics are poor, we have\nsome evidence that most of the ISOCAM sources lie at redshift between 0 and 1.4 with a median\nat 0.8 \\cite{aussel99}, and that most of the SCUBA sources lie at redshifts greater than 2\n\\cite{barger99}.\nOur predicted redshift distributions at these two wavelengths are in agreement with the existing\nobservations.\\\\\nWhat about FIRBACK $170\\,\\mu m$ sources ? Our predicted redshift distribution shows that\nmost of the sources lie at redshifts below 1.5, with a median comparable to that of the ISOCAM\nsources. This means that we are sensitive both to local sources and sources beyond redshift $z\n=1$. All the FIRBACK sources with known redshifts (less than 10) \\cite{dennefeld99},\n\\cite{scott2000} are in this range. Two submillimetre sources are at $z > 1$, and a few visible\nsources are at $z \\simeq 0.2$.\\\\\nIt is difficult to address the question differences between PHOT and CAM sources, because their\nredshift distributions (both expected and observed) are similar. About half of the $170\\,\\mu m$\nsources have $15\\,\\mu m$ counterparts.\n%\n%________________________________________________________________\n\\vspace{-0.3cm}\n\\section{Conclusion}\nWe have presented results from the FIRBACK survey, one of the largest ISO programs, dealing\nwith resolved sources of the CIB: our source counts at $170\\,\\mu m$ show strong evolution. This\nevolution is explained by a simple law involving the redshift of the luminosity function, which\ndiffers from pure density or luminosity evolution: the \n%``11LiFE'' (above-$11$ (in log $L_{\\odot}$)-luminosity-function evolution).\n``Bright End Luminosity Function Evolution'' model.\nThe model fits all the existing source counts at 15, 90, 170 and 850 $\\mu m$, and also predicts a\nredshift distribution in agreement with the (sometimes sparse) observations. This powerful tool,\nbased on observational constraints on the CIB spectrum inversion and the local Luminosity\nFunction, and on assumed template galaxy spectra, not only agrees with existing data but also is\nable to make useful predictions on source counts or CIB fluctuations. These predictions may be\nuseful for planning the utilization of major telescopes of the future, such as SIRTF, Planck,\nFIRST and ALMA.\nAll the FIRBACK materials are available at: \\verb|http://wwwfirback.ias.fr|.\n%\n%________________________________________________________________\n\\vspace{-0.3cm}\n\\begin{thebibliography}{7}\n%\n\\addcontentsline{toc}{section}{References}\n\\bibitem{aussel99} Aussel, H., 1999, PHD Thesis Universit\\'e Paris VII\n\\bibitem{barger99} Barger A.J., Cowie L.L., Sanders, D.B., 1999 ApJ, 518, L5 \n\\bibitem{dennefeld99} Dennefeld, M., 1999, Private Communication\n\\bibitem{desert90} D\\'esert, F-X., Boulanger F., Puget, J.L., 1990, A\\&A, 237, 215\n\\bibitem{dole99} Dole H., Lagache G., Puget J-L., Gispert R., et al., 1999, ESA/SP-427, p1031,\nastro-ph/9902122\n\\bibitem{dole2000} Dole H., Gispert R., Lagache G., Puget J-L., et al., 2000, in preparation\n\\bibitem{elbaz99} Elbaz D., et al., 1999, A\\&A, 351, L37\n\\bibitem{efstathiou99} Efstathiou A., et al., 1999, MNRAS, submitted\n\\bibitem{franceschini98} Franceschini A., et al., 1998, MNRAS, 296, 709\n\\bibitem{gispert2000} Gispert R., Lagache G., Puget J-L., 2000, A\\&A, submitted\n\\bibitem{guiderdoni98} Guiderdoni B., et al., 1998, MNRAS, 295, 877\n\\bibitem{kessler96} Kessler M. F., et al., 1996, A\\&A, 315, L27\n\\bibitem{lagache99a} Lagache G., and Puget J-L., 1999, A\\&A, in press, astro-ph/9910255 \n\\bibitem{lagache99b} Lagache G., et al., 1999, this volume\n\\bibitem{lagache2000} Lagache G., and Dole, H., 2000, in preparation\n\\bibitem{lemke96} Lemke D., et al., 1996, A\\&A, 315, L64\n\\bibitem{lilly99} Lilly, Ss.J., et al, 1999, ApJ, 518, L641 \n\\bibitem{maffei94} Maffei B., 1994, PHD Thesis Universit\\'e Paris-Sud\n\\bibitem{puget99a} Puget J-L., et al., 1999, A\\&A, 345, 29 \n\\bibitem{puget99b} Puget J-L., et al., 1999, this volume\n\\bibitem{sanders96} Sanders D.B., and Mirabel I.F., 1996, ARAA, 34, 749\n\\bibitem{scott2000} Scott D., et al, 2000, A\\&A, in press, astro-ph/9910428\n\\bibitem{soifer91} Soifer B.T., and Neugeubauer G., 1991, AJ, 101, 354\n\\bibitem{tan99} Tan J.C., Silk J., Balland C., 1999, ApJ, 522, 579\n\\end{thebibliography}\n\n%INDEX%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%\n\\clearpage\n\\addcontentsline{toc}{section}{Index}\n\\flushbottom\n\\printindex\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%%%%%%%%%%%%%%%%%\n\n\\end{document}\n\n\n"
}
] |
[
{
"name": "astro-ph0002283.extracted_bib",
"string": "\\begin{thebibliography}{7}\n%\n\\addcontentsline{toc}{section}{References}\n\\bibitem{aussel99} Aussel, H., 1999, PHD Thesis Universit\\'e Paris VII\n\\bibitem{barger99} Barger A.J., Cowie L.L., Sanders, D.B., 1999 ApJ, 518, L5 \n\\bibitem{dennefeld99} Dennefeld, M., 1999, Private Communication\n\\bibitem{desert90} D\\'esert, F-X., Boulanger F., Puget, J.L., 1990, A\\&A, 237, 215\n\\bibitem{dole99} Dole H., Lagache G., Puget J-L., Gispert R., et al., 1999, ESA/SP-427, p1031,\nastro-ph/9902122\n\\bibitem{dole2000} Dole H., Gispert R., Lagache G., Puget J-L., et al., 2000, in preparation\n\\bibitem{elbaz99} Elbaz D., et al., 1999, A\\&A, 351, L37\n\\bibitem{efstathiou99} Efstathiou A., et al., 1999, MNRAS, submitted\n\\bibitem{franceschini98} Franceschini A., et al., 1998, MNRAS, 296, 709\n\\bibitem{gispert2000} Gispert R., Lagache G., Puget J-L., 2000, A\\&A, submitted\n\\bibitem{guiderdoni98} Guiderdoni B., et al., 1998, MNRAS, 295, 877\n\\bibitem{kessler96} Kessler M. F., et al., 1996, A\\&A, 315, L27\n\\bibitem{lagache99a} Lagache G., and Puget J-L., 1999, A\\&A, in press, astro-ph/9910255 \n\\bibitem{lagache99b} Lagache G., et al., 1999, this volume\n\\bibitem{lagache2000} Lagache G., and Dole, H., 2000, in preparation\n\\bibitem{lemke96} Lemke D., et al., 1996, A\\&A, 315, L64\n\\bibitem{lilly99} Lilly, Ss.J., et al, 1999, ApJ, 518, L641 \n\\bibitem{maffei94} Maffei B., 1994, PHD Thesis Universit\\'e Paris-Sud\n\\bibitem{puget99a} Puget J-L., et al., 1999, A\\&A, 345, 29 \n\\bibitem{puget99b} Puget J-L., et al., 1999, this volume\n\\bibitem{sanders96} Sanders D.B., and Mirabel I.F., 1996, ARAA, 34, 749\n\\bibitem{scott2000} Scott D., et al, 2000, A\\&A, in press, astro-ph/9910428\n\\bibitem{soifer91} Soifer B.T., and Neugeubauer G., 1991, AJ, 101, 354\n\\bibitem{tan99} Tan J.C., Silk J., Balland C., 1999, ApJ, 522, 579\n\\end{thebibliography}"
}
] |
astro-ph0002284
|
The extragalactic background and its fluctuations in the far-infrared wavelengths
|
[
{
"author": "G. Lagache\\inst{1}"
},
{
"author": "J-L. Puget\\inst{1}"
},
{
"author": "A. Abergel\\inst{1}"
},
{
"author": "F.R. Bouchet\\inst{3}"
},
{
"author": "F. Boulanger\\inst{1}"
},
{
"author": "P. Ciliegi\\inst{4}"
},
{
"author": "D.L. Clements\\inst{5}"
},
{
"author": "C.J. Cesarsky\\inst{6}"
},
{
"author": "F.X. D\\'esert\\inst{2}"
},
{
"author": "H. Dole\\inst{1}"
},
{
"author": "D. Elbaz\\inst{6}"
},
{
"author": "A. Franceschini\\inst{7}"
},
{
"author": "R. Gispert\\inst{1}"
},
{
"author": "B. Guiderdoni\\inst{3}"
},
{
"author": "L.M. Haffner\\inst{8}"
},
{
"author": "M. Harwit\\inst{9}"
},
{
"author": "R. Laureijs\\inst{10}"
},
{
"author": "D. Lemke\\inst{11}"
},
{
"author": "A.F.M. Moorwood\\inst{12}"
},
{
"author": "S. Oliver\\inst{13}"
},
{
"author": "W.T. Reach\\inst{14}"
},
{
"author": "R.J. Reynolds\\inst{8}"
},
{
"author": "M. Rowan-Robinson\\inst{13}"
},
{
"author": "M. Stickel\\inst{11}"
},
{
"author": "S.L. Tufte\\inst{15}"
}
] |
A Cosmic Far-InfraRed Background (CFIRB) has long been predicted that would traces the intial phases of galaxy formation. It has been first detected by~\cite{PUG96} using COBE data and has been later confirmed by several recent studies (~\cite{FIX98},~\cite{HAU98},~\cite{LAG99}). We will present a new determination of the CFIRB that uses for the first time, in addition to COBE data, two independent gas tracers: the HI survey of Leiden/Dwingeloo (~\cite{HAR98}) and the WHAM H$_{\alpha}$ survey (~\cite{REY99}). We will see that the CFIRB above 100 $\mu$m is now very well constrained. The next step is to see if we can detect its fluctuations. To search for the CFIRB fluctuations, we have used the FIRBACK observations. FIRBACK is a deep cosmological survey conducted at 170$\mu$m with ISOPHOT (~\cite{DOL00}). We show that the emission of unresolved extra-galactic sources clearly dominates, at arcminute scales, the background fluctuations in the lowest galactic emission regions. This is the first detection of the CFIRB fluctuations.
|
[
{
"name": "glagache.tex",
"string": "\\documentclass[runningheads]{cl2emult}\n\n\\usepackage{makeidx} % allows index generation\n\\usepackage{graphicx} % standard LaTeX graphics tool\n % for including eps-figure files\n\\usepackage{subeqnar} % subnumbers individual equations\n % within an array\n\\usepackage{multicol} % used for the two-column index\n\\usepackage{cropmark} % cropmarks for pages without\n % pagenumbers\n\\usepackage{lnp} % placeholder for figures\n\\makeindex % used for the subject index\n % please use the style sprmidx.sty with\n % your makeindex program\n\n\\begin{document}\n%\n\\title*{The extragalactic background and its fluctuations in the\nfar-infrared wavelengths}\n%\n%\n\\toctitle{The extra-Galactic background and its flucuations in the\nfar-infrared wavelengths}\n% allows explicit linebreak for the table of content\n%\n%\n\\titlerunning{The extra-Galactic background and its fluctuations in the\nfar-infrared}\n% allows abbreviation of title, if the full title is too long\n% to fit in the running head\n%\n\\author{G. Lagache\\inst{1}\n\\and J-L. Puget\\inst{1}\n\\and A. Abergel\\inst{1}\n\\and F.R. Bouchet\\inst{3} \n\\and F. Boulanger\\inst{1}\n\\and P. Ciliegi\\inst{4}\n\\and D.L. Clements\\inst{5} \n\\and C.J. Cesarsky\\inst{6} \n\\and F.X. D\\'esert\\inst{2}\n\\and H. Dole\\inst{1}\n\\and D. Elbaz\\inst{6} \n\\and A. Franceschini\\inst{7} \n\\and R. Gispert\\inst{1} \n\\and B. Guiderdoni\\inst{3} \n\\and L.M. Haffner\\inst{8}\n\\and M. Harwit\\inst{9} \n\\and R. Laureijs\\inst{10} \n\\and D. Lemke\\inst{11} \n\\and A.F.M. Moorwood\\inst{12} \n\\and S. Oliver\\inst{13}\n\\and W.T. Reach\\inst{14} \n\\and R.J. Reynolds\\inst{8}\n\\and M. Rowan-Robinson\\inst{13}\n\\and M. Stickel\\inst{11}\n\\and S.L. Tufte\\inst{15}}\n\n%\n\\authorrunning{G. Lagache, J-L. Puget et al.}\n% if there are more than two authors,\n% please abbreviate author list for running head\n%\n%\n\\institute{Institut d'Astrophysique Spatiale, Orsay, France\n\\and Laboratoire d'Astrophysique, Observatoire de Grenoble, France\n\\and Institut d'Astrophysique de Paris, France\n\\and Osservatorio Astronomico di Bologna, Italy\n\\and Cardiff University, UK\n\\and Service d'Astrophysique, CEA/DSM/DAPNIA Saclay, France \n\\and Osservatorio Astronomico di Padova, Italy\n\\and Astronomy Department, University of Wisconsin, Madison, USA\n\\and 511 H.Street S.W., Washington, DC 20024-2725\n\\and ISOC ESA, VILSPA, Madrid, Spain\n\\and MPIA, Heidelberg, Germany\n\\and ESO, Garching, Germany\n\\and Imperial College, London, UK\n\\and IPAC, Pasadena, CA, USA\n\\and Department of Physics, Lewis \\& Clark College, Portland, USA}\n\n\\maketitle % typesets the title of the contribution\n\n\\begin{abstract}\nA Cosmic Far-InfraRed Background (CFIRB) has long been predicted\nthat would traces the intial phases of galaxy formation.\nIt has been first detected by~\\cite{PUG96} using\nCOBE data and has been later confirmed by several recent studies \n(~\\cite{FIX98},~\\cite{HAU98},~\\cite{LAG99}).\nWe will present a new determination of the CFIRB that uses for the first time, \nin addition to COBE data, two independent gas tracers: the HI survey\nof Leiden/Dwingeloo (~\\cite{HAR98}) and the WHAM H$_{\\alpha}$ survey (~\\cite{REY99}). We will see that\nthe CFIRB above 100 $\\mu$m is now very well constrained.\nThe next step is to see if we can detect its fluctuations.\nTo search for the CFIRB fluctuations, we have used the FIRBACK observations. \nFIRBACK is a deep cosmological survey conducted at 170$\\mu$m with ISOPHOT\n(~\\cite{DOL00}). We show that \nthe emission of unresolved extra-galactic sources clearly dominates,\nat arcminute scales, the background fluctuations\nin the lowest galactic emission regions. This is the first\ndetection of the CFIRB fluctuations.\n\\end{abstract}\n\n\\section{Determination of the CFIRB above 100 $\\mu$m: an other approach}\n%\nIn very diffuse parts of the sky (no molecular clouds\nand HII regions), the far-IR emission \ncan be written as the sum of dust emission associated\nwith the neutral gas, dust associated with the ionised gas, \ninterplanetary dust emission and the CFIRB (and eventually \nthe cosmological dipole and\nCMB). In previous studies (~\\cite{PUG96},~\\cite{FIX98},~\\cite{HAU98}), \ndust emission associated with the ionised gas\nwhich was totally unknown has been either not subtracted\nproperly or neglected. \\\\\nWe have detected for the first time\ndust emission in the ionised gas (~\\cite{LAG99})\nand shown that the emissivity (which\nis the IR emission normalised to unit hydrogen column density)\nof dust in the ionised gas was nearly the same as that in the\nneutral gas. This has consequences on the determination of the CFIRB.\nFollowing this first detection, we have combined HI and \nWHAM H$_{\\alpha}$ data (~\\cite{REY99})\nwith far-IR COBE data in order to derive dust\nproperties in the diffuse ionised gas as well as to make a proper\ndetermination of the CFIRB.\nTechnically, after a careful pixel selection\n(see~\\cite{LAG00} for more details) we describe the \nfar-infrared dust emission as a function of the HI\nand H$^+$ column density by:\n\\begin{equation}\n\\label{main_EQ}\nIR= A \\times N(HI)_{20cm^{-2}} + B \\times N(H^+)_{20cm^{-2}} + C\n\\end{equation}\nwhere N(HI)$_{20cm^{-2}}$ and N(H$^+$)$_{20cm^{-2}}$ \nare the column densities normalised\nto 10$^{20}$ H cm$^{-2}$. The coefficients A, B\nand the constant term C are determined simultaneously using regression fits. \nWe show that about 25$\\%$ of the IR\nemission comes from dust associated with the ionised gas\nwhich is in very good agreement with the first determination\n(~\\cite{LAG99}). \nThe CFIRB spectrum obtained using this \nfar-infrared emission decomposition is shown in Fig.~\\ref{CFIRB_spec} \ntogether with the CFIRB FIRAS determination\nof~\\cite{LAG99} in the Lockman Hole region. We see a very\ngood agreement between the two spectra. These determinations are also\nin good agreement with~\\cite{FIX98}.\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=.8\\textwidth]{glagache_f1.ps}\n\\caption[]{CFIRB spectra obtained from the decomposition\nof the far-infrared sky (continuous line) and determined for the Lockman\nHole region (dashed line) by~\\cite{LAG99}. Also reported\nare DIRBE values at 100, 140 and 240 $\\mu$m.}\n\\label{CFIRB_spec}\n\\end{figure}\n\nAt 140 and 240 $\\mu$m, the values obtained for the CFIRB\nare 1.13$\\pm$0.54 MJy/sr and 0.88$\\pm$0.55 MJy/sr respectively \nFor each selected pixel, we compute\nthe residual emission, R = IR - A$\\times$N(HI) - B$\\times$N(H$^+$).\nUncertainties of the CFIRB have been derived from the width of the histogram\nof R (statistical uncertainties derived from the regression analysis are negligible). \nThe obtained CFIRB values, although much more noisy\n(due to the small fraction of the sky used), are in very\ngood agreement with the determination of ~\\cite{HAU98}.\nAt 140~$\\mu$m, the CFIRB value of~\\cite{LAG99} is smaller \nthan that derived here since the assumed WIM (Warm Ionised\ngas) dust spectrum\nwas overestimated (the WIM dust spectrum was\nvery noisy below 200~$\\mu$m and the estimated dust\ntemperature was too high).\\\\\n\nAt 100~$\\mu$m, \nassuming an accurate subtraction of the zodiacal emission,\nour decomposition gives:\nI$_{CFIRB}$(100)= 0.78$\\pm$0.21 MJy/sr. This is the first \ntime that two independent gas tracers for the HI and the\nH$^+$ have been used to determine the background at 100 \n$\\mu$m. One has to note that methods based on\nthe intercept of the far-IR/HI correlation\nfor the determination of the CFIRB \nare dangerous. For example, for our selected parts of the sky, \nthis intercept is about 0.91 MJy/sr, which is quite different from\nthe value of the CFIRB (0.78 MJy/sr). \nThe CFIRB value of 0.78 MJy/sr can be compared to the non-isotropic residual\nemission found by~\\cite{HAU98}. The average over three regions\nof the residual emission, equal\nto 0.73$\\pm$0.20 MJy/sr, is in very good agreement with our\ndetermination.\\\\\n\nSo we see, using different approaches, that we are now converging\non the shape and level of the CFIRB above 100 $\\mu$m.\nThe next step is to see if we can detect its fluctuations\nand study them.\n\n\\section{Why search for the CFIRB fluctuations?}\nThe CFIRB is made of sources with number counts as a function of flux which can\nbe represented, for the present discussion, by a simple power law:\n$$N(>S)= N_0 \\left( \\frac{S}{S_0} \\right)^{- \\alpha}$$\nObviously, these number counts need to flatten at low fluxes\nto insure a finite value of the background. Thus, we assume that $\\alpha$=0 \nfor $S<S^{\\ast}$.\\\\\n\nFor the simple Euclidian case ($\\alpha$=1.5), the CFIRB integral \nis dominated by sources near S$^{\\ast}$ and\nits fluctuations are dominated by sources which are just below the detection\nlimit S$_0$. It is well known that strong cosmological\nevolution, associated with a strong negative K-correction, could lead to a very steep\nnumber count distribution (see for example~\\cite{GUI98} and~\\cite{FRA98}). \nIn the far-IR present observations show a very steep slope of\n$\\alpha$=2.2 (~\\cite{DOL00}). In this case,\nthe CFIRB integral is still dominated by sources near S$^{\\ast}$ but\nits fluctuations are now also dominated by sources close to \nS$^{\\ast}$. Thus, it is essential to study the \nextra-galactic background fluctuations which are likely to be dominated\nby sources with a flux comparable to those dominating the\nCFIRB intensity.\\\\\n\nTo see if we can detect the CFIRB fluctuations, we need wide field\nfar-IR observations with high angular resolution and very high signal to noise ratio.\nThe FIRBACK project, which is a very deep cosmological survey\nwith ISOPHOT at 170 $\\mu$m (~\\cite{DOL00}), sustains all these conditions. \nTo search for CFIRB fluctuations, we have first used the so-called\n``Marano 1'' field for which we obtained 16 independent coadded\nmaps which allow us to determine very properly the instrumental noise.\nIn this field, we have a signal to noise ratio of about 300\nand we detect 24 sources (~\\cite{PUG99})\nthat we remove from the original map.\nWe then extend our first analysis to the other FIRBACK fields.\nDetails on the data reduction and calibration can be found\nin ~\\cite{LAG00b}.\\\\\n\nSource subtracted maps show background fluctuations which are\nmade of two components that we want to separate, \ngalactic cirrus fluctuations and if present the\nextra-galactic ones. \n\n\\section{Extra-galactic and galactic background fluctuation separation: detection of the CFIRB fluctuations}\nOur separation of the extra-galactic and galactic fluctuations\nis based on a power spectrum decomposition. This method\nallows us to discriminate the two components using the statistical\nproperties of their spatial behaviour. Fig. ~\\ref{fluc_Marano} \nshows the power spectrum of the ``Marano 1'' field.\nIn the plane of the detector, the power spectrum measured on the map \ncan be expressed in the form:\n\\begin{equation}\nP_{map}= P_{noise} + (P_{cirrus} + P_{sources}) \\times W_k \n\\label{Eq_Pk}\n\\end{equation}\nwhere P$_{noise}$ is the instrumental noise power spectrum measured\nusing the 16 independent maps of the Marano 1 field (~\\cite{LAG00c}), \nP$_{cirrus}$ and P$_{sources}$ are the cirrus and\nunresolved extra-galactic source power spectra respectively, \nand W$_k$ is the footprint power spectrum. For our analysis,\nwe remove P$_{noise}$ from P$_{map}$.\\\\\n\nWe know from previous work that the cirrus far-infrared \nemission power spectrum, P$_{cirrus}$,\nhas a steep slope in $\\sim k^{-3}$ \n(~\\cite{GAU92},~\\cite{KOG96},~\\cite{HER98},~\\cite{WRI98},~\\cite{SCH98}). \nThese observations\ncover the relevant spatial frequency range and have been recently extended\nup to 1 arcmin using very diffuse HI data (~\\cite{MAM99}). \nThe extra-galactic\ncomponent is unknown but certainly much flatter (see the discussion in~\\cite{LAG00c}). \nWe thus conclude\nthat the steep spectrum observed in our data at k$<$0.15 arcmin$^{-1}$ \n(Fig.~\\ref{fluc_Marano}) can only be due to cirrus emission. \nThe break in the power spectrum at k$\\sim$ 0.2 arcmin$^{-1}$ is \nvery unlikely to be due to the cirrus emission itself which is \nknown not to exhibit any prefered scale (~\\cite{FAL98}). \nThus, the normalisation of our cirrus power spectrum P$_{cirrus}$ is directly determined\nusing the low frequency data points and assuming a k$^{-3}$ dependence.\\\\\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=.8\\textwidth]{glagache_f3.ps}\n\\caption[]{Power spectrum of the source subtracted ``Marano 1'' field\n($\\ast$).\nThe instrumental noise power spectrum (dotted line) has been subtracted. The dashed line\nrepresents the cirrus power spectrum, multiplied by the footprint.}\n\\label{fluc_Marano}\n\\end{figure}\n\nWe clearly see in Fig.~\\ref{fluc_Marano} an excess over P$_{cirrus}$ between\nk=0.25 and 0.6 arcmin$^{-1}$ which is more than a factor of 10\nat k=0.4 arcmin$^{-1}$. Any reasonable power law spectrum\nfor the cirrus component multiplied by the footprint\nleads, as can be easily seen in Fig. ~\\ref{fluc_Marano}, to a very steep\nspectrum at spatial frequency k$>$0.2 arcmin$^{-1}$\nwhich is very different from the observed spectrum.\nMoreover, the excess is more than\n10 times larger than the measured instrumental noise power spectrum.\nTherefore, as no other major source of fluctuations\nis expected at this wavelength, the large excess observed between\nk=0.25 and 0.6 arcmin$^{-1}$ is interpreted as due\nto unresolved extra-galactic sources.\nThis is the first detection of the CFIRB fluctuations.\\\\\n\nThe Marano 1 field cannot be used to\nconstrain the clustering of galaxies due to it rather small size.\nHowever, the extra-galactic source power spectrum mean level can be determined.\nWe obtain P$_{sources}$~=~7400 Jy$^2$/sr, which is in very good\nagreement with the one predicted by~\\cite{GUI97}.\nThis gives CFIRB rms fluctuations around 0.07 MJy/sr (for\na range of spatial frequencies up to 5 arcmin$^{-1}$). \nThese fluctuations are at the $\\sim$9 percent level,\nwhich is very close to the predictions of~\\cite{HAI99}.\\\\\n\nThe same analysis can be done for the other and larger FIRBACK\nfields. From Eq. ~\\ref{Eq_Pk}, we deduce: \n$$P_{sources}= (P_{map} - P_{noise}) / W_k - P_{cirrus}$$\nFig. ~\\ref{fluc_N2} shows the extra-galactic fluctuation\npower spectrum (P$_{sources}$) obtained for the FIRBACK/ELAIS N2 field. \nIt is very well fitted with a constant CFIRB fluctuation power spectrum \nof about 5000 Jy$^2$/sr, which is in good agreement with that obtained\nin the ``Marano 1'' field. We obtain also exactly the same\nextra-galactic fluctuation power spectrum in the FIRBACK N1 field\nwith a value of about 5000 Jy$^2$/sr.\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=.8\\textwidth]{glagache_f4.ps}\n\\caption[]{Extra-galactic source power spectrum of the FIRBACK/ELAIS N2 field.\nThe vertical line shows the cut-off in angular resolution.}\n\\label{fluc_N2}\n\\end{figure}\n\n\\section{Conclusions}\nWe have shown in the FIRBACK fields that the extra-galactic background\nfluctuations lie well above the instrumental noise\nand the cirrus confusion noise. The observed power spectrum shows a flattening\nat high spatial frequencies which is due to unresolved extra-galactic \nsources.\nThe level of the extra-galactic power spectrum fluctuations\nis nearly the same in all FIRBACK fields.\nThe next step consists of removing the cirrus contribution using independent \ngas tracers (the H$_{\\alpha}$ and the 21cm emission lines)\nto isolate the extra-galactic fluctuation\nbrightness and try to constrain the IR large scale structures.\\\\\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{thebibliography}{7}\n%\\addcontentsline{toc}{section}{References}\n\n\\bibitem{PUG96} Puget J.L., Abergel A., Bernard J.P., et al. 1996, A\\&A 308, L5 \n\n\\bibitem{FIX98} Fixsen D.J., Dwek E., Mather J.C., et al. 1998, ApJ 508, 123\n\n\\bibitem{HAU98} Hauser M.G., Arendt R.G., Kelsall T., et al., 1998, ApJ 508, 25\n\n\\bibitem{LAG99} Lagache G., Abergel A., Boulanger F., et al., 1999, A\\&A 344, 322\n\n\\bibitem{HAR98} Hartmann D., Burton W.B., Atlas of Galactic neutral\nHydrogen, Cambridge University Press, 1997\n\n\\bibitem{REY99} Reynolds R.J., Tufte S.L., Haffner L.M., et al., 1998, PASA 15, 14\n\n\\bibitem{DOL00} Dole H., et al., this proceeding\n\n\\bibitem{LAG00} Lagache G., Haffner L.M., Reynolds R.J., Tufte S.L., A\\&A, in press (Astroph/9911355)\n\n\\bibitem{GUI98} Guiderdoni B., Hivon E., Bouchet F., Maffei B., 1998, MNRAS 295 , 877\n \n\\bibitem{FRA98} Franceschini A., Andreani P., Danese L. 1998, MNRAS 296, 709\n\n\\bibitem{PUG99} Puget J.L., Lagache G., Clements D.L. et al., 1999, A\\&A 354, 29\n\n\\bibitem{LAG00b} Lagache G., Dole H., to be submitted to A\\&A\n\n\\bibitem{LAG00c} Lagache G., J-L. Puget, A\\&A, in press (Astroph/9910255)\n\n\\bibitem{GAU92} Gautier T.N.III, Boulanger F., P\\'erault M., \nPuget J.L., 1992, AJ 103, 1313\n\n\\bibitem{KOG96} Kogut A., Banday A.J., Bennett C.L., et al., 1996, ApJ 460, 1\n\n\\bibitem{HER98} Herbstmeier U., Abraham P., Lemke D., et al., 1998, A\\&A 332, 739\n\n\\bibitem{WRI98} Wright E.L., 1998, ApJ 496, 1\n\n\\bibitem{SCH98} Schlegel D.J., Finkbeiner D.P., Davis M., 1998, ApJ 500, 525\n\n\\bibitem{MAM99} Miville-Desch\\^enes M.A., PhD thesis, Paris XI University \n\n\\bibitem{FAL98} Falgarone, E. in ``Starbursts: triggers, nature and evolution'',\nLes Houches School, 1998, Ed. B. Guiderdoni \\& A. Kembhavi\n\n\\bibitem{GUI97} Guiderdoni B., Bouchet B., Puget J.L., et al., 1997, Nature 390, 257\n\n\\bibitem{HAI99} Haiman Z., Knox L., 1999, ApJ in press (Astroph/9906399)\n\n\\end{thebibliography}\n\n%INDEX%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\clearpage\n\\addcontentsline{toc}{section}{Index}\n\\flushbottom\n\\printindex\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\end{document}\n\n"
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[
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"name": "astro-ph0002284.extracted_bib",
"string": "\\begin{thebibliography}{7}\n%\\addcontentsline{toc}{section}{References}\n\n\\bibitem{PUG96} Puget J.L., Abergel A., Bernard J.P., et al. 1996, A\\&A 308, L5 \n\n\\bibitem{FIX98} Fixsen D.J., Dwek E., Mather J.C., et al. 1998, ApJ 508, 123\n\n\\bibitem{HAU98} Hauser M.G., Arendt R.G., Kelsall T., et al., 1998, ApJ 508, 25\n\n\\bibitem{LAG99} Lagache G., Abergel A., Boulanger F., et al., 1999, A\\&A 344, 322\n\n\\bibitem{HAR98} Hartmann D., Burton W.B., Atlas of Galactic neutral\nHydrogen, Cambridge University Press, 1997\n\n\\bibitem{REY99} Reynolds R.J., Tufte S.L., Haffner L.M., et al., 1998, PASA 15, 14\n\n\\bibitem{DOL00} Dole H., et al., this proceeding\n\n\\bibitem{LAG00} Lagache G., Haffner L.M., Reynolds R.J., Tufte S.L., A\\&A, in press (Astroph/9911355)\n\n\\bibitem{GUI98} Guiderdoni B., Hivon E., Bouchet F., Maffei B., 1998, MNRAS 295 , 877\n \n\\bibitem{FRA98} Franceschini A., Andreani P., Danese L. 1998, MNRAS 296, 709\n\n\\bibitem{PUG99} Puget J.L., Lagache G., Clements D.L. et al., 1999, A\\&A 354, 29\n\n\\bibitem{LAG00b} Lagache G., Dole H., to be submitted to A\\&A\n\n\\bibitem{LAG00c} Lagache G., J-L. Puget, A\\&A, in press (Astroph/9910255)\n\n\\bibitem{GAU92} Gautier T.N.III, Boulanger F., P\\'erault M., \nPuget J.L., 1992, AJ 103, 1313\n\n\\bibitem{KOG96} Kogut A., Banday A.J., Bennett C.L., et al., 1996, ApJ 460, 1\n\n\\bibitem{HER98} Herbstmeier U., Abraham P., Lemke D., et al., 1998, A\\&A 332, 739\n\n\\bibitem{WRI98} Wright E.L., 1998, ApJ 496, 1\n\n\\bibitem{SCH98} Schlegel D.J., Finkbeiner D.P., Davis M., 1998, ApJ 500, 525\n\n\\bibitem{MAM99} Miville-Desch\\^enes M.A., PhD thesis, Paris XI University \n\n\\bibitem{FAL98} Falgarone, E. in ``Starbursts: triggers, nature and evolution'',\nLes Houches School, 1998, Ed. B. Guiderdoni \\& A. Kembhavi\n\n\\bibitem{GUI97} Guiderdoni B., Bouchet B., Puget J.L., et al., 1997, Nature 390, 257\n\n\\bibitem{HAI99} Haiman Z., Knox L., 1999, ApJ in press (Astroph/9906399)\n\n\\end{thebibliography}"
}
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astro-ph0002285
|
High Velocity Star Formation in the LMC
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[
{
"author": "David S. Graff and Andrew P. Gould"
}
] |
Light-echo measurements show that SN1987A is 425 pc behind the LMC disk. It is continuing to move away from the disk at $18\,\kms$. Thus, it has been suggested that SN1987A was ejected from the LMC disk. However, SN1987A is a member of a star cluster, so this entire cluster would have to have been ejected from the disk. We show that the cluster was formed in the LMC disk, with a velocity perpendicular to the disk of about $50\,\kms$. Such high velocity formation of a star cluster is unusual, having no known counterpart in the Milky Way.
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[
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"name": "astro-ph0002285.tex",
"string": "%% two-column preprint, use following\n%\\documentstyle[aas2pp4]{article}\n%% electronic submission, use following\n%\\documentstyle[12pt,aasms4]{article}\n%% apj format use following\n\\documentstyle[emulateapj]{article}\n%% draft preprint, use following\n%\\documentstyle[aaspp4]{article}\n%\\documentstyle[11pt]{article}\n%\\documentstyle[twocolumn,epsfig]{article}\n%\\def\\baselinestretch{0.9}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%these lines will fix the formatting for standard latex\n%%%%% comment them out for aastex\n%\\setlength{\\textwidth}{6.5 in}\n%\\setlength{\\oddsidemargin}{0 in}\n%\\setlength{\\evensidemargin}{0 in}\n%\\setlength{\\topskip}{0 in}\n%\\setlength{\\topmargin}{-.5 in}\n%\\setlength{\\headheight}{0 in}\n%\\setlength{\\columnsep}{0.85cm}\n%\\setlength{\\textheight}{9 in}\n%\\renewcommand{\\baselinestretch}{1.5} %this command adjusts the spacing\n %between lines\n\\def\\keywords{}\n\\def\\acknowledgements{}\n\\def\\apj{ApJ}\n\\def\\aj{A.J.}\n\\def\\baas{BAAS}\n\\def\\mnras{MNRAS}\n\\def\\pasp{PASP}\n\\def\\aap{A\\&A}\n\\def\\apjl{ApJ}\n\\def\\apjs{ApJS}\n\\def\\nat{Nature}\n\\def\\sigmahot{\\sigma_z^{\\rm hot}}\n\\def\\sigmacold{\\sigma_z^{\\rm cold}}\n\n%%%%%%%%%%%%%%%%%%\n%%%%comment out this line for standard latex, put in for aastex\n%\\slugcomment{submitted to ApJ Letters}\n%%%%%%%%%%%%%%%%%%%%%%%%%\n\n%%%%%%%%%%%%%%%%%%\n\\begin{document}\n\n\\def\\nth{n_{\\rm th}}\n\\def\\nobs{n_{\\rm obs}}\n\\def\\dmin{d_{\\rm min}}\n\\def\\macho{{\\sc macho}}\n\\def\\newpage{\\vfill\\eject}\n\\def\\vs{\\vskip 0.2truein}\n\\def\\gnu{\\Gamma_\\nu}\n\\def\\fnu {{\\cal F_\\nu}}\n\\def\\mass{m}\n\\def\\lum{{\\cal L}}\n\\def\\imf{\\xi(\\mass)}\n\\def\\ilf{\\psi(M)}\n\\def\\msun{M_\\odot}\n\\def\\zsun{Z_\\odot}\n\\def\\met{[M/H]}\n\\def\\vi{(V-I)}\n\\def\\mtot{M_{\\rm tot}}\n\\def\\mhalo{M_{\\rm halo}}\n\\def\\pp{\\parshape 2 0.0truecm 16.25truecm 2truecm 14.25truecm}\n\\def\\la{\\mathrel{\\mathpalette\\fun <}}\n\\def\\ga{\\mathrel{\\mathpalette\\fun >}}\n\\def\\fun#1#2{\\lower3.6pt\\vbox{\\baselineskip0pt\\lineskip.9pt\n \\ialign{$\\mathsurround=0pt#1\\hfil##\\hfil$\\crcr#2\\crcr\\sim\\crcr}}}\n\\def\\ie{{ i.e., }}\n\\def\\eg{{ e.g., }}\n\\def\\etal{{et al.\\ }}\n\\def\\etalc{{et al., }}\n\\def\\kpc{{\\rm kpc}}\n \\def\\Mpc{{\\rm Mpc}}\n\\def\\mh{\\mass_{\\rm H}}\n\\def\\mmax{\\mass_{\\rm u}}\n\\def\\ml{\\mass_{\\rm l}}\n\\def\\bc{f_{\\rm cmpct}}\n\\def\\br{f_{\\rm rd}}\n\\def\\kmsec{{\\rm km/sec}}\n\\def\\ibl{{\\cal I}(b,l)}\n\\def\\dmax{d_{\\rm max}}\n\\def\\dmin{d_{\\rm min}}\n\\def\\mbol{M_{\\rm bol}}\n\\def\\kms{{\\rm km}\\,{\\rm s}^{-1}}\n\n\\lefthead{Graff \\& Gould}\n\\righthead{High Velocity Star Formation in the LMC}\n%%%%%%%%%%%%%%%%%%%%%%%\n%%%%%%%electronic submission format\n\\submitted{Submitted to ApJL, 14 February 2000, Accepted 4 March 2000}\n\\title{High Velocity Star Formation in the LMC}\n\\author{David S. Graff and Andrew P. Gould}\n\\affil{Departments of Astronomy and Physics, The Ohio State University,\nColumbus, OH 43210, USA}\n\\authoremail{graff.25@osu.edu, gould@payne.mps.ohio-state.edu}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{abstract}\nLight-echo measurements show that SN1987A is 425 pc behind the LMC\ndisk. It is continuing to move away from the disk at $18\\,\\kms$.\nThus, it has been suggested that SN1987A was ejected from the LMC\ndisk. However, SN1987A is a member of a star cluster, so this entire\ncluster would have to have been ejected from the disk. We show that the\ncluster was formed in the LMC disk, with a velocity perpendicular to\nthe disk of about $50\\,\\kms$. Such high velocity formation of a star cluster is unusual,\nhaving no known counterpart in the Milky Way.\n\\end{abstract}\n\n\\keywords{Magellanic Clouds, Supernovae: Individual (SN1987A)}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\setcounter{footnote}{0}\n\\renewcommand{\\thefootnote}{\\arabic{footnote}}\n\n\\section{Introduction}\n\nThe Large Magellanic Cloud (LMC) shows a clear contrast between\nregular kinematics and irregular structure, with its offcenter bar and\nlack of any clear stellar spiral morphology. The velocities as traced\nby carbon star velocities (Graff \\etal 2000; Hardy \\etal 2000; Kunkel\n\\etal 1997) and by H$\\alpha$ emmision (Kim \\etal 1999) are well fit by\na rotating disk although there may be a non-disk component (Graff\n\\etal 2000; Luks \\& Rohlfs, 1992). The overall velocity dispersion of\nthe carbon stars $\\sim 20\\,\\kms$ is small compared to the rotational\nvelocity of the LMC $(60 - 70 \\,\\kms)$ indicating that the stellar\ncomponent of the LMC is relatively flat and rotationally supported.\nMoreover, Graff \\etal (2000) showed that the younger, metal rich\ncarbon stars in the inner $4^\\circ$ of the LMC have a much lower\nvelocity dispersion, only $8\\,\\kms$. This contrast suggests that\nthe LMC lies in a nearly face-on plane, but is irregular within\nthat plane.\n\nThe three-dimensional structure of LMC dust was measured using\nthe ``light-echo'' technique on SN1987A by Xu, Crotts \\& Kunkel\n(1996). They identified 12 seperate dust sheets. Most significantly, in this\nwork and in a follow up spectroscopic study (Xu \\& Crotts 1999), they\nidentified three components with the spherical shell N157C enclosing the OB \nassociation LH 90. This shell was found to lie 490 pc in\nfront of SN1987A. Including the LMC inclination of $\\sim 30^\\circ$, \nthe component of this distance perpendicular to the LMC plane\nis 425 pc.\n\nThis distance is much greater than the virial thickness of the young\nstellar population of the LMC in the location of SN1987A $\\sim 90$ pc\n(given the local surface density of 100 $\\msun/{\\rm pc}^2$ which we\ndetermine below). Thus, it is difficult to imagine how these two\nyoung stellar populations came to be so separated. Xu \\etal (1996)\nsuggest that SN1987A is a ``...runaway star behind the disk of the\nLarge Magellanic Cloud''.\n\nClassical runaway stars can be found high above the Milky Way plane\n(Conlon \\etal 1990). The runaway O and B stars are thought to be\nejected by one of two processes: supernova explosions in close binary\nsystems (Blaauw 1961) and strong dynamical interactions in star\nclusters (Poveda, Ruiz, \\& Allen 1967; Gies \\& Bolton 1986). Indeed, Hipparcos\nmeasurements of O and B stars have found several runaways that can be\nidentified as having been ejected from particular OB associations (de\nZeeuw \\etal 1999).\n\nHowever, Efremov (1991) and Panagia \\etal (2000) have identified\nSN1987A as belonging to KMK 80 (Kontizas, Metaxa \\& Kontizas 1988)\n``...a loose young cluster $12 \\pm 2$ Myr old....'' (Panagia \\etal\n2000). Thus, it cannot be a classic runaway star; any of the violent\nejection mechanisms discussed above would eject only the single star,\nand not its cluster.\n\n\n In the next section, we solve for the initial kinematics of SN1987A\nand its associated cluster, KMK 80. We find that the cluster {\\it\nformed} in the LMC plane, moving with a velocity of $50\\,\\kms$\nperpendicular to the LMC plane.\n\n\\section{Kinematics of SN1987A}\n\nWe begin by examining the velocities of these two young\nclusters relative to the LMC. The disk solution of Hardy et al.\\\n(2000) at the projected position of SN1987A is $271 \\pm 1\\,\\kms$.\n% (with the nearest clump of 23\n%measured carbon stars -- field 30 of Blanco \\& McCarthy 1990 -- \n%redshifted by $5\\,\\kms$ relative to the disk solution, i.e.,\n%$272\\pm 3\\,\\kms$).\n\n By comparison, SN1987A has a redshift of $286\\,\\kms$ (Meaburn,\nBryce \\& Holloway 1995) while the N157C complex containing LH 90 has a\nredshift of $270\\,\\kms$ (Xu \\& Crotts 1999). Thus, the velocity of LH 90\nis perfectly consistent with the LMC disk velocity at this point.\n\nOn the other hand, SN1987A is in two respects inconsistent with being\na member of the cold population: first, it is moving $15\\,\\kms$\nrelative to the disk, faster than the $8\\,\\kms$ typical of the cold\npopulation. Secondly, and more importantly, it lies far above the\nscale height of the cold population (and even above the scale height\nof the hot population).\n\nTo take account of both effects simultaneously, we define the\n``verticle energy'' of a star to be $E \\equiv v_z^2/2 + \\Phi(z)$ and\napproximate the potential energy to be $\\Phi(z) \\approx 2 \\pi G \\Sigma\n|z|$ for stars of height $z\\gg 150\\,$pc. An examination of the\nisophotal map of the LMC of de Vaucouleurs (1957) shows that the\nsurface brightness of the LMC in the neigborhood of SN1987A is about\n21.7 mag./arcsec$^2$, or 56 $L_\\odot {\\rm pc}^{-2}$. Assigning a\nPopulation I mass-luminosity ratio of 1.7, we derive a mass surface\ndensity of roughly $\\Sigma_{\\rm SN1987A} \\approx 100 M_\\odot {\\rm\npc}^{-2}$. We derive a total energy of $1300 \\,(\\kms)^2$\ncorresponding to a midplane velocity of $50\\,\\kms$. Thus, the total\ngravitational energy of the supernova is much too high for it to be a\nmember of the cold population (and somewhat high even for the hot\npopulation).\n \nWe note that the age of the star cluster containing the supernova is\nabout 12 Myr which is consitent with estimates of the age of the\nprecursor to the supernova. If the star cluster was formed at the LMC\nplane 12 Myr ago, with a velocity perpendicular to the plane of $50 \\\n\\kms$, and this velocity decreased with a gravitational acceleration\nof $-3\\,\\kms\\,\\rm Myr^{-1}$, it would today be $\\sim 400\\,$pc above\nthe plane moving at $14 \\ \\kms$, consitent with its measured distance\nof 425 pc above the plane and relative velocity of $15 \\ kms$.\n\n\n\\section{Discussion}\n\nThe match between these numbers is compelling, and we suggest that the\nentire KMK 80 star cluster was formed 12 Myr ago at the LMC plane, but\nwith an extraordinarily high velocity of $50\\,\\kms$ perpendicular to the \nplane. The agreement between age and flight time is typical of most runaway \nO and B stars in the halo of the Milky Way (Keenan, Brown \\& Lennon 1986).\n\nWe do not know what mechanism could create a star cluster moving at\nsuch high velocities. As far as we know, there is no counterpart in\nthe Milky Way. However, we can speculate on two possible mechanisms.\nFirst, the cluster might have formed as part of a galactic fountain\npushed out of the LMC by supernovae or stellar winds. Such a\nmechanism was put forward by Xu \\& Crotts who suggested that SN1987A\nwas formed on a shell of gas pushed out of the LMC by LH 90. These\nauthors noted that SN1987A is on the outskirts of the extremely\nviolent 30 Dor. region. \n\nSecond, a dense cloud of gas could have smashed through the LMC disk,\ntriggering star formation in the process with the resulting stars\ncarrying some of the initial momentum of the cloud. This cloud could\nhave been fountain material raining back down onto the LMC disk, or it\ncould have been a high velocity cloud orbiting either the LMC or the\nMilky Way.\n\nThere are a few systems in the Milky Way that might have been formed\nin processes similar to the KMK 80 cluster. In addition to runaway O\nstars, the Milky Way Halo also contains young, high velocity, high\nmetallicity A stars (Perry 1969; Rodgers 1971). These stars are all\nroughly the same age, $<650\\,$Myr (Lance 1988), which suggests that\nthey were created from the collsion of a Magellanic Cloud sized galaxy\nwith the Milky Way disk (Rodgers, Harding, \\& Sadler 1981; Lance\n1988). A similar recent collision in the LMC might generate high\nvelocity star formation without breaking up KMK 80.\n\nGould's belt (Gould 1874; P\\\"oppel 1997) contains several OB\nassociations in a roughly planar region oriented $18^\\circ$ from the\nplane of the Milky Way. Comer\\'on \\& Torra (1994) suggested that\nGould's belt arose from the glancing collision of a high velocity\ncloud with the Milky Way disk. Perhaps KMK 80 is part of a\nsimilar structure oriented more nearly perpendicular to the LMC plane.\n\nLogically, there are only two alternatives to our interpretation that\nKMK 80 formed at high vertical velocity. First, KMK 80 may actually\nlie in the LMC plane while the progenitor of SN1987A is simply seen\nprojected against this cluster, having been earlier ejected from a\nbinary. This appears to us to be a priori unlikely and can in any\nevent be tested by spectroscopic observations of KMK 80 members. In\naddition to confirming SN1987A as a radial-velocity member of this\ncluster, such measurements would yield the metallicity of the cluster\nand so of the SN1987A progenitor.\n\nSecond, SN1987A could actually lie in the LMC plane while N157C lies\n490 pc closer to us. Then, either LH 90 would still be at the center\nof N157C, or it would lie in the LMC plane and be seen by chance\nprojected against the center of this cloud. In the first case, one\nwould still have the same problem of an OB association lying far from\nthe LMC plane. As for the second case, the probability of a chance\nprojection of two such naturally associated structures seems\nincredibly low. In either case, KMK 80 would have to have\nbeen born with a vertical energy at least equal to its present\nkinetical energy of $(15\\,\\kms)^2$, which is still quite high.\nMoveover, the N157C cloud would have to have exactly the same radial\nvelocity as the LMC plane despite the fact that it lies $\\sim 400\\,$pc\nfrom it. Hence, the various alternatives to our interpretation, while\nnot actually ruled out, require extraordianry combinations of\ncoincidences.\n\n\n\\acknowledgements\n\nWe thank Arlin Crotts, Yuri Efremov and David Weinberg for useful discussions.\nThis work was supported in part by grant AST 97-27520 from the NSF.\n\n\n\\begin{thebibliography}{99}\n\n%\\bibitem[2000]{macho6yr} Alcock, C. \\etal 2000, ApJ submitted,\n%astro-ph/0001272\n\n\\bibitem[1990]{blaauw} Blaauw, A.\\ 1961, Bull. Astron. Inst. Netherlands, \n15, 265\n\n%\\bibitem[1990]{blanco} Blanco, V.M. \\& McCarthy, M.F. 1990, AJ, 100,\n%674\n\n\\bibitem[1994]{ct} Comer\\'on, F., \\& torra, J.\\ 1994, \\apj, 423, 652\n\n\\bibitem[1990]{conlon} Conlon, E.S., Dufton, P.L., Keenan, F.P., \\&\nLeonard, P.J.T.\\ 1990, A\\&A, 236, 357\n\n\\bibitem[1991]{efremov} Efremov, Yu.N. 1991, PAZh, 17, 404 (in Russian, translated into English in 1991, Sov. Astr. Lett., 17, 173)\n\n%\\bibitem[1996]{gn} Gardiner, L.T. \\& Noguchi, M. 1996, MNRAS, 278, 191\n\n\\bibitem[1986]{gies} Gies, D.R., \\& Bolton, C.T., 1986, \\apjs, 61, 419\n\n%\\bibitem[1999]{gfwp} Graff, D.S., Freese, K., Walker, T.P. \\&\n%Pinsonneault. M.H. 1999, ApJ, 523, 77\n\n\\bibitem[2000]{ggssh} Graff, D.S., Gould, A.P., Schommer, R.,\nSuntzeff, N. \\& Hardy, E. 2000, ApJ submitted (astro-ph 9910360)\n\n%\\bibitem[1995]{gouldvir} Gould, A. 1995, ApJ, 441, 77\n\n\\bibitem[1874]{gouldbelt} Gould, B.A. 1874, Proc. AAAS, 115\n\n%\\bibitem[1999]{gdg} Gyuk, G., Dalal, N. \\& Griest, K., ApJ submitted,\n%astro-ph/9907338\n\n\\bibitem[1999]{ssh} Hardy, E., Schommer, R.A. \\& Suntzeff, N.B. 2000,\nin preparation\n\n\\bibitem[1998]{kbl}Keenan, F.P., Brown, P.J.F., \\& Lennon, D.J.\\ 1986 \nA\\&A, 155, 333\n\n\\bibitem[1998]{kim} Kim, S. \\etal 1998, ApJ, 503, 674\n\n\\bibitem[1988]{kmk} Kontizas, E., Metaxa, M. \\& Kontizas, M. 1988, AJ, 96, 1625\n\n\\bibitem[1997]{kunkel} Kunkel, B.E., Demers, S., Irwin, M.J.,\nLo\\\"{i}c, A. 1997, ApJ, 488, 129\n\n\\bibitem[1988]{lance} Lance, C.M.\\ 1988, \\apj, 334, 927\n\n\\bibitem[1992]{lh} Luks, Th., \\& Rohlfs, K. 1992, A\\&A, 263, 41\n\n\\bibitem[1995]{mbh}Meaburn, J., Bryce, M. \\& Holloway, A.J. 1995,\nA\\&A, 299, 1\n\n\\bibitem[2000]{prsk} Panagia, N., Romaniello, M, Scuderi, S \\&\nKirshner, R.P. 2000, ApJ in press (astro-ph/0001476)\n\n\\bibitem[1969]{perry} Perry, C.L.\\ 1969, \\aj, 74, 139\n\n\\bibitem[1997]{poppel}P\\\"oppel, W.G.L.\\ 1997, Fund. Cosmic Phys., 18, 1\n\n\\bibitem[1967]{poveda}Poveda, A., Ruiz, J., \\& Allen, C.\\ 1967,\nBol. Obs. Tonantzintla y Tacubaya, 4, 860\n\n\\bibitem[1981]{rodgers} Rodgers, A.W.\\ 1971, \\apj, 165, 581\n\n\\bibitem[1981]{rhs} Rodgers, A.W., Harding, P., \\& Sadler, E.\\ 1981,\n\\apj, 244, 912\n\n%\\bibitem[1994]{sahu} Sahu, K.C. 1994, Nature, 370, 275\n\n\\bibitem[1994]{devauc} de Vaucouleurs, G.\\ 1957, \\aj, 62, 69\n\n%\\bibitem[1999]{mw} Weinberg, M. 1999, astro-ph/9905305\n\n%\\bibitem[1994]{wu} Wu, X.-P. 1994, ApJ, 435, 66\n\n\\bibitem[1999]{xc} Xu, J. \\& Crotts, A.P.S. 1999, ApJ, 511, 262\n\n\\bibitem[1996]{xck} Xu, J., Crotts, A.P.S. \\& Kunkel, W.E. 1996, ApJ,\n463, 391\n\n\\bibitem[1999]{deZeeuw} de Zeeuw, P.T., Hoogerwerf, R., de Bruijne,\nJ.H.J., Brown, A.G.A., \\& Blaauw, A. 1999, AJ, 117, 354\n\n\\end{thebibliography}\n\n\\end{document}\n\n\n\\pagebreak\n\n\\begin{tabular}{cccccc} \\hline\n\\multicolumn{6}{c}{Table 1. Rotation Curve Parameters}\\\\ \\hline\nV$_{sys}$ & dV/dr& V$_{circ}$ & $<\\Theta(PA)>$ & $\\sigma$ & V$_{tr}$ \\\\\n 50 km/s & 21.5 km/s/kpc & 75 km/s & --20$^{\\circ}$ & 18-22 km/s & 250\nkm/sec \\\\ \\hline\n\\end{tabular}\n\n\\pagebreak\n\n\\section*{Figure Captions}\n\n\\begin{figure}[ht]\n%\\plotone{twopop.eps}\n\\caption{The residuals of the carbon stars with respect to the LMC\ndisk fit. The grey line is the best fit single gaussian. The black\nline is the best fit two gaussian model of eq. (\\ref{twopop}).}\n\\label{residuals}\n\\end{figure}\n\n\n\\begin{figure}[ht]\n%\\plotone{threepop.eps}\n\\caption{A fit to the residuals with three gaussians. Although the\nthird peak is not significant in the fit to the residual, it is shown\nto be statistically significant when searched for in velocities, and\nshows the location of the KDP.}\n\\label{threepopfig}\n\\end{figure}\n\n\n\n\\begin{figure}[ht]\n%\\plotone{kdpfig.eps}\n\\caption{\nThe residuals of the stellar velocities with respect to the KDP. The\nKDP stands out as a strong peak near residual = 0.}\n\\label{kdpfig}\n\\end{figure}\n\n\n\n"
}
] |
[
{
"name": "astro-ph0002285.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\n%\\bibitem[2000]{macho6yr} Alcock, C. \\etal 2000, ApJ submitted,\n%astro-ph/0001272\n\n\\bibitem[1990]{blaauw} Blaauw, A.\\ 1961, Bull. Astron. Inst. Netherlands, \n15, 265\n\n%\\bibitem[1990]{blanco} Blanco, V.M. \\& McCarthy, M.F. 1990, AJ, 100,\n%674\n\n\\bibitem[1994]{ct} Comer\\'on, F., \\& torra, J.\\ 1994, \\apj, 423, 652\n\n\\bibitem[1990]{conlon} Conlon, E.S., Dufton, P.L., Keenan, F.P., \\&\nLeonard, P.J.T.\\ 1990, A\\&A, 236, 357\n\n\\bibitem[1991]{efremov} Efremov, Yu.N. 1991, PAZh, 17, 404 (in Russian, translated into English in 1991, Sov. Astr. Lett., 17, 173)\n\n%\\bibitem[1996]{gn} Gardiner, L.T. \\& Noguchi, M. 1996, MNRAS, 278, 191\n\n\\bibitem[1986]{gies} Gies, D.R., \\& Bolton, C.T., 1986, \\apjs, 61, 419\n\n%\\bibitem[1999]{gfwp} Graff, D.S., Freese, K., Walker, T.P. \\&\n%Pinsonneault. M.H. 1999, ApJ, 523, 77\n\n\\bibitem[2000]{ggssh} Graff, D.S., Gould, A.P., Schommer, R.,\nSuntzeff, N. \\& Hardy, E. 2000, ApJ submitted (astro-ph 9910360)\n\n%\\bibitem[1995]{gouldvir} Gould, A. 1995, ApJ, 441, 77\n\n\\bibitem[1874]{gouldbelt} Gould, B.A. 1874, Proc. AAAS, 115\n\n%\\bibitem[1999]{gdg} Gyuk, G., Dalal, N. \\& Griest, K., ApJ submitted,\n%astro-ph/9907338\n\n\\bibitem[1999]{ssh} Hardy, E., Schommer, R.A. \\& Suntzeff, N.B. 2000,\nin preparation\n\n\\bibitem[1998]{kbl}Keenan, F.P., Brown, P.J.F., \\& Lennon, D.J.\\ 1986 \nA\\&A, 155, 333\n\n\\bibitem[1998]{kim} Kim, S. \\etal 1998, ApJ, 503, 674\n\n\\bibitem[1988]{kmk} Kontizas, E., Metaxa, M. \\& Kontizas, M. 1988, AJ, 96, 1625\n\n\\bibitem[1997]{kunkel} Kunkel, B.E., Demers, S., Irwin, M.J.,\nLo\\\"{i}c, A. 1997, ApJ, 488, 129\n\n\\bibitem[1988]{lance} Lance, C.M.\\ 1988, \\apj, 334, 927\n\n\\bibitem[1992]{lh} Luks, Th., \\& Rohlfs, K. 1992, A\\&A, 263, 41\n\n\\bibitem[1995]{mbh}Meaburn, J., Bryce, M. \\& Holloway, A.J. 1995,\nA\\&A, 299, 1\n\n\\bibitem[2000]{prsk} Panagia, N., Romaniello, M, Scuderi, S \\&\nKirshner, R.P. 2000, ApJ in press (astro-ph/0001476)\n\n\\bibitem[1969]{perry} Perry, C.L.\\ 1969, \\aj, 74, 139\n\n\\bibitem[1997]{poppel}P\\\"oppel, W.G.L.\\ 1997, Fund. Cosmic Phys., 18, 1\n\n\\bibitem[1967]{poveda}Poveda, A., Ruiz, J., \\& Allen, C.\\ 1967,\nBol. Obs. Tonantzintla y Tacubaya, 4, 860\n\n\\bibitem[1981]{rodgers} Rodgers, A.W.\\ 1971, \\apj, 165, 581\n\n\\bibitem[1981]{rhs} Rodgers, A.W., Harding, P., \\& Sadler, E.\\ 1981,\n\\apj, 244, 912\n\n%\\bibitem[1994]{sahu} Sahu, K.C. 1994, Nature, 370, 275\n\n\\bibitem[1994]{devauc} de Vaucouleurs, G.\\ 1957, \\aj, 62, 69\n\n%\\bibitem[1999]{mw} Weinberg, M. 1999, astro-ph/9905305\n\n%\\bibitem[1994]{wu} Wu, X.-P. 1994, ApJ, 435, 66\n\n\\bibitem[1999]{xc} Xu, J. \\& Crotts, A.P.S. 1999, ApJ, 511, 262\n\n\\bibitem[1996]{xck} Xu, J., Crotts, A.P.S. \\& Kunkel, W.E. 1996, ApJ,\n463, 391\n\n\\bibitem[1999]{deZeeuw} de Zeeuw, P.T., Hoogerwerf, R., de Bruijne,\nJ.H.J., Brown, A.G.A., \\& Blaauw, A. 1999, AJ, 117, 354\n\n\\end{thebibliography}"
}
] |
astro-ph0002286
|
Black--Hole Transients and the Eddington Limit
|
[
{
"author": "A.R. King$^1$"
},
{
"author": "$^1$ Astronomy Group"
},
{
"author": "Leicester LE1 7RH"
},
{
"author": "U.K"
}
] |
I show that the Eddington limit implies a critical orbital period $P_{crit}({BH}) \simeq 2$~d beyond which black--hole LMXBs cannot appear as persistent systems. The unusual behaviour of GRO J1655-40 may result from its location close to this critical period.
|
[
{
"name": "astro-ph0002286.tex",
"string": "%\\documentstyle[epsf,referee]{mn}\n\\documentstyle[epsf]{mn}\n\\renewcommand{\\baselinestretch}{1}\n\\begin{document}\n\\def\\lsun{{\\rm L_{\\odot}}}\n\\def\\msun{{\\rm M_{\\odot}}}\n\\def\\rsun{{\\rm R_{\\odot}}}\n\\title{Black--Hole Transients and the Eddington Limit}\n\\author[A.R. King]{A.R. King$^1$\\\\ \n$^1$ Astronomy Group, University of Leicester, Leicester LE1\n7RH, U.K}\n\\maketitle \n\\begin{abstract}\nI show that the Eddington limit implies a critical orbital period \n$P_{\\rm crit}({\\rm BH}) \\simeq 2$~d beyond which black--hole \nLMXBs cannot appear as persistent systems. The unusual behaviour of\nGRO J1655-40 may result from its location close to this critical period.\n\\end{abstract}\n\n\\section{Introduction}\n%\nIt is now well understood that the accretion discs in low--mass X--ray\nbinaries (LMXBs) are strongly irradiated by the central X--rays, and\nthat this has a decisive effect on their thermal stability (van\nParadijs, 1996; King, Kolb \\& Burderi, 1996). Irradiation stabilizes\nLMXB discs compared with the otherwise similar ones in cataclysmic\nvariables (CVs) by removing their hydrogen ionization zones. In CVs\nthis instability causes dwarf nova outbursts, and in LMXBs it produces\ntransient outbursts rather than persistent accretion. The irradiation\neffect appears to be weaker if the accretor is a black hole rather\nthan a neutron star, possibly because of the lack of a hard surface\n(King, Kolb \\& Szuszkiewicz, 1997). The result is that neutron--star\nLMXBs with short ($\\sim$ hours) orbital periods tend to be persistent,\nwhile similar black--hole binaries are largely transient. Both types\nof LMXBs must be transient at sufficiently long orbital periods, since\na long period implies a large disc, so that a large X--ray luminosity\nwould be needed to keep the disc edge ionized and thus suppress\noutbursts. We can write this stability requirement as\n\\begin{equation}\n\\dot M_{\\rm crit}^{\\rm irr} \\sim R_{\\rm d}^2 \\sim P^{4/3},\n\\label{crit}\n\\end{equation}\nwhere $\\dot M_{\\rm crit}^{\\rm irr}$ is the minimum central accretion\nrate required to keep the disc stable, $R_{\\rm d}$ is the outer\ndisc radius, and $P$ is the orbital period, and we have used Kepler's\nlaw. Thus for large $P$, $\\dot M_{\\rm\ncrit}^{\\rm irr}$ will rise above any likely steady accretion\nrate, making long--period systems transient.\nThis simple prediction (King, Frank, Kolb \\& Ritter, 1997)\nseems to be borne out by the available evidence.\n\n\\section{The Critical Accretion Rate}\n%\nThe precise coefficient in (\\ref{crit}) depends on uncertainties\nin the vertical disc structure (see the discussion in Dubus, Lasota,\nHameury \\& Charles, 1999). Here I adopt the form derived by King, Kolb\n\\& Szuszkiewicz (1997). They argued that for a steady black--hole accretor,\nthe central irradiating source is likely to be the inner disc rather than a\nsolid spherical surface, as for a steady neutron--star accretor. (Note\nthat during an outburst of a {\\it transient} black--hole system such a\nspherical source may be present, as the central accretor may develop a\ncorona.) For a small source \nat the centre of the disc and lying in its plane, the irradiation temperature \n$T_{\\rm irr}(R)$ is given by\n\\begin{equation}\nT_{\\rm irr}(R)^4 = {\\eta \\dot Mc^2(1-\\beta)\\over 4\\pi \\sigma R^2}\n\\biggl({H\\over R}\\biggr)^2\n\\biggl({{\\rm d}\\ln H\\over {\\rm d}\\ln R} - 1\\biggr) \n\\label{eq3}\n\\end{equation}\n(Fukue, 1992). Here $\\eta$ is the efficiency of rest--mass energy\nconversion into X--ray heating, $\\beta$ is the X--ray albedo, and\n$H(R)$ is the local disc scale height. The minimum accretion rate\nrequired to keep the disc in the high state is given by setting\n$T_{\\rm irr}(R) = T_H$, where is $T_H$ is the hydrogen ionization\ntemperature. Since $T$ always decreases with $R$, the global minimum\nvalue $\\dot M_{\\rm crit}^{\\rm irr}$ is given by conditions at the\nouter edge $R_{\\rm d}$ of the disc. For the parametrization adopted by King,\nKolb \\& Szuszkiewicz (1997), and $\\eta = 0.2$, this leads to\n\\begin{equation}\n\\dot M_{\\rm crit}^{\\rm irr}(R) = 2.86\\times\n10^{-11}m_1^{5/6}m_2^{-1/2}f_{0.7}^2gP_h^{4/3}\\ \\msun\\ {\\rm yr}^{-1},\n\\label{crit2}\n\\end{equation}\nwhere \n$f_{0.7}$ is the disc filling fraction $f$\n(the ratio of $R_{\\rm d}$ to the accretor's\nRoche lobe) in units of 0.7; $m_1, m_2$ are the accretor and\ncompanion star mass in $\\msun$; and \n\\begin{eqnarray}\n\\lefteqn{g = } \\nonumber \\\\ \n\\lefteqn{\\biggl({1-\\beta\\over 0.1}\\biggr)^{-1}\\biggl({H\\over\n0.2R}\\biggr)^{-2}\n\\biggl({2/7\\over {\\rm d}\\ln H/{\\rm d}\\ln R - 1}\\biggr)\n\\biggl({T_H\\over 6500\\ {\\rm K}}\\biggr)^4}\n\\label{g}.\n\\end{eqnarray}\nEquation (\\ref{crit2}) is the same as eqn (12) of King, Kolb \\&\nSzuszkiewicz (1997) apart from the factors $f_{0.7}^2g$, there taken\nas unity. All of the uncertainties over disc thickness, warping,\nalbedo etc are lumped into the quantity $g$. With $g \\simeq f_{0.7}\n\\simeq 1$, equation (\\ref{crit2}) appears to be largely successful in\npredicting that systems with reasonably massive ($5 - 7\\msun$) black\nholes and main--sequence companions should be transient. By contrast,\nneutron star systems with main--sequence companions should be\npersistent, as the index of the ratio $H/R$ in (\\ref{eq3}) is unity,\nimplying more efficient disc irradiation. (Equation (\\ref{crit2}) also\nimplies that lower--mass black hole systems might be persistent.) These\nresults suggest that the quantity $g$ appearing in (\\ref{crit2})\ncannot be too far from unity.\n\n\\section{The Eddington Limit}\n%\nHere I concentrate an another aspect of eq. (\\ref{crit2}) which\ndoes not seem to have received much attention. Namely, for large\nenough $P$, $\\dot M_{\\rm crit}^{\\rm irr}$ must exceed the Eddington\naccretion rate\n\\begin{equation}\n\\dot M_{\\rm Edd} \\simeq 1\\times 10^{-8}m_1\\msun\\ {\\rm yr}^{-1}.\n\\label{edd}\n\\end{equation}\nThe obvious consequence of eqs. (\\ref{crit2}, \\ref{edd}) is that for\nsufficiently long orbital periods irradiation will be unable to\nsuppress outbursts, as the required central luminosity exceeds the\nEddington limit, and the system presumably cannot be both\nsuper--Eddington and persistent. Note that this conclusion holds\nwhatever the {\\it actual} value of the mass transfer rate in the\nparticular binary happens to be. Thus we should expect to find no\npersistent LMXBs above a certain critical orbital period $P_{\\rm\ncrit}$. For the neutron--star case this was recognised by Li \\& Wang\n(1998), who found $P_{\\rm crit}({\\rm NS}) \\simeq 20$~d, in agreement\nwith observation. For the black--hole case, combining (\\ref{crit2},\n\\ref{edd}) gives\n\\begin{equation}\nP_{\\rm crit}({\\rm BH}) \\simeq\n2.0f_{0.7}^{-1.5}g^{-0.75}\\biggl({\\dot M\\over 0.5\\dot M_{\\rm\nEdd}}\\biggr)^{0.75}m_1^{1/8}m_2^{1/8}~{\\rm d},\n\\label{pcrit}\n\\end{equation}\nwhere we have included a factor $(\\dot M/0.5\\dot M_{\\rm\nEdd})$ to allow for the fact that the radiation pressure limit for the\naccretion rate $\\dot M$ may in practice be below $\\dot M_{\\rm Edd}$.\nWe thus expect to find no persistent black--hole LMXBs above this\nperiod. This is indeed supported by the available data, but hardly\nsurprising in view of the difficulty in identifying black holes in\npersistent systems. Note that in {\\it high--mass} black--hole systems\nsuch as Cygnus X--1, the powerful UV luminosity of the companion star,\nas well as the small disc size expected in a wind--fed system, are\nboth likely to keep the disc hot and therefore give a persistent\nsystem.\n\n\n\\section{GRO~J1655-40}\n%\nWith $g \\sim 1$ as argued above, the value of $P_{\\rm crit}({\\rm BH})$\nfound above is close to the observed period $P = 2.62$~d of the\nblack--hole soft X--ray transient GRO J1655-40 (the nearest periods\namong alternative black--hole systems are $P = 6.47$~d for V404 Cyg\nand $P = 1.23$~d for 4U 1543--47). Indeed Kolb et al (1997) pointed\nout the system's proximity to the Eddington limit during outburst, and\nHynes et al. (1998) explicitly suggested that no globally steady disc\nsolution might be possible for this system with $\\dot M < \\dot M_{\\rm\nEdd}$. GRO~J1655-40 is unusual in at least two respects:\n\n1. The companion star has spectral type F3 -- F6IV and mass $M_2\n\\simeq 2.3\\msun$. On a conventional view, this places it in the\nHertzsprung gap. The companion star should therefore be expanding on a\nthermal timescale and thus driving a mass transfer rate $-\\dot M_2\n\\sim 10^{-7}\\msun~{\\rm yr}^{-1}$ (Kolb et al., 1997). This is well\nabove the appropriate value of $\\dot M_{\\rm crit}^{\\rm irr}$, making\nit puzzling that the system is nevertheless transient, and far above\nthe mean mass accretion rate of $\\dot M_{\\rm obs} = 1.26\\times\n10^{-10}\\msun~{\\rm yr}^{-1}$ deduced by van Paradijs (1996) from\nobservation. Reg\\\"os, Tout \\& Wickramasinghe (1998) appeal to\nconvective overshooting to increase the main--sequence radius of stars\nof $\\sim 2\\msun$. The companion might then be on the main sequence\nrather than in the Hertzsprung gap. This implies a slower evolutionary\nradius expansion, bringing the predicted mass transfer rate below\n$\\dot M_{\\rm crit}^{\\rm irr}$. However $-\\dot M_2$ is still predicted\nto lie uncomfortably far above $\\dot M_{\\rm obs}$.\n\n2. The system was first detected in an outburst in 1994, and had\nprobably been quiescent for at least 30~yr before that. Yet two more\noutbursts followed in the next two years.\n\nThe considerations given here offer explanations for both of these\nunusual features. First, if $P > P_{\\rm crit}({\\rm BH})$, the system\nmust be transient in some sense, regardless of the actual mass\ntransfer rate (cf Hynes et al., 1998). It would therefore not be\nnecessary to appeal to convective overshooting. Further, since the\nsystem is close to $P_{\\rm crit}({\\rm BH})$, it is evidently accreting\nat a value close to the Eddington rate during its quasi--steady states\n(see below), making it natural that $\\dot M_{\\rm obs}$ is much smaller\nthan the predicted mass transfer rate $-\\dot M_2$.\n\nSecond, assuming that the quantity $g$ has a relatively constant value\nclose to unity, as argued above, we see from (\\ref{pcrit}) that the\nvalue of $P_{\\rm crit}({\\rm BH})$ is most sensitive to the filling\nfactor $f$ (I consider the effect of dropping the assumption\n$g\\sim$~constant below). Thus if $f$ decreases, $P_{\\rm crit}({\\rm BH})$ can\nincrease above the actual orbital period, allowing irradiation to keep\nthe disc in the high state (prolong an outburst) for as long as $f$\nremains sufficiently small. Hence the unusual outburst behaviour of\nGRO~J1655-40 may be explicable in terms of the time evolution of the\ndisc size. Encouragingly there is some observational evidence (see the\ndiscussion in Orosz \\& Bailyn, 1997) that the grazing eclipses seen in\nthe optical are time--dependent, just as expected if the disc size\nvaries. Moreover Soria, Wu \\& Hunstead (1999) find evidence from the\nrotational velocities of double--peaked emission lines that the disc\nis at some epochs slightly larger than its tidal limit. The large\nresultant torques on the disc suggest that this state cannot persist\nand the disc must eventually shrink.\n\nIn fact we do expect $f$ to evolve systematically: in the early part\nof an outburst, the central accretion of low angular--momentum\nmaterial will raise the average disc angular momentum and thus cause\n$f$ to increase, hence lowering $P_{\\rm crit}({\\rm BH})$ and making\nthe system more vulnerable to a return to quiescence. However at some\nstage matter transferred from the companion will tend to reduce the\nangular momentum of the outer disc, thus decreasing $f$, raising\n$P_{\\rm crit}({\\rm BH})$ and allowing irradiation to stabilize the\ndisc in the high state. But eventually the disc must grow towards its\ntidal limit, increasing $f$ and thus lowering $P_{\\rm crit}({\\rm BH})$\nagain, finally enforcing a return to quiescence. Obviously a full\ndisc code is required to follow this sequence in detail and to check\nif it can account qualitatively for the unusual outburst behaviour of\nGRO~J1655--40. \n\nClearly, systematic evolution of one or more of the quantities\nappearing in $g$ during the outburst could have a similar effect in\nmaking $P_{\\rm crit}({\\rm BH})$ oscillate around the actual orbital\nperiod $P$. The most likely alternative candidate is the disc aspect\nratio $H/R$, which would appear explicitly with the power 1.5 if we\nsubstitute for $g$ in (\\ref{pcrit}). The aspect ratio could evolve\nsystematically on a viscous timescale because the disc may warp under\nradiative torques (Pringle, 1996). A warp presenting more of the disc\nsurface to the central source would tend to stabilize it against a\nreturn to quiescence even though the central luminosity was below the\nEddington limit. Again considerably more work is required to check\nthis possibility.\n\n\\section{Conclusions}\n%\nI have shown that the Eddington limit implies a critical orbital\nperiod $P_{\\rm crit}({\\rm BH})$ beyond which black--hole LMXBs cannot\nappear as persistent systems. The precise value of $P_{\\rm crit}({\\rm\nBH})$ is subject to uncertainties expressed by the quantity $g$ in\n(\\ref{crit2}). I have argued that $g$ cannot be very far from unity if\nwe are to understand the difference in the stability properties of\ndiscs in neutron--star and black--hole systems. In this case\nGRO~J1655-40 lies much closer to $P_{\\rm crit}({\\rm BH})$ than any\nother black--hole system.\n\nThe unusual behaviour of GRO~J1655-40 may result from its location\nvery close to $P_{\\rm crit}({\\rm BH})$; evolution of the disc size or\npossible radiative warping may move the system across the boundary\nwhere a sub--Eddington luminosity can keep the disc stably in the high\nstate. This system, and those at longer orbital periods, probably have\ncentral accretion rates which are highly super--Eddington during\noutbursts. Since observed radiative luminosities are mildly\nsub--Eddington, most of this mass must be expelled. Strong support for\nthis comes from the observation of P Cygni profiles in GRO~J1655--40\n(Hynes et al., 1998). The superluminal jets observed (Hjellming \\&\nRupen, 1995) in an outburst of this system may therefore simply\nrepresent the most dramatic part of this outflow.\n\n\\section{Acknowledgment}\nI gratefully acknowledge the support of a PPARC Senior Fellowship.\n\n\n\\begin{thebibliography}{} \n\n\\item{}\nDubus, G., Lasota J.--P., Hameury, J.--M., Charles, P.A., 1996, MNRAS,\n303, 139\n\\item{}\nFukue, J., PASJ, 44, 663\n\\item{}\nHjellming, R.M., Rupen, M.P., 1995, Nat, 375, 464\n\\item{}\nHynes, R.I., Haswell, C.A., Shrader, C.R., Chen, W., Horne, K.,\nHarlaftis, E.T., O'Brien, K., Hellier, C., Fender, R.P., 1998, MNRAS,\n300, 64\n\\item{}\nKing, A.R., Frank, J., Kolb, U., Ritter, H., 1997, ApJ, 484, 844\n\\item{}\nKing, A.R., Kolb, U., Burderi, L., 1996, ApJ, 464, L127\n\\item{}\nKing, A.R., Kolb, U., Szuszkiewicz, E., 1997, ApJ, 488, 89\n\\item{}\nKolb, U., King, A.R., Ritter, H., Frank, J., 1997, ApJ 485 L33\n\\item{}\nLi, X.--D., Wang, Z.--R., 1998, ApJ, 500, 935\n\\item{}\nOrosz, J.A., Bailyn, C.D., 1997, ApJ, 477, 876 \n\\item{}\nPringle, J.E., 1996, MNRAS, 281, 357\n\\item{}\nReg\\\"os, E., Tout, C.A., Wickramasinghe, D., 1998, ApJ, 509, 362\n\\item{}\nSoria, R., Wu, K., Hunstead, R., 1999, ApJ, in press (astro--ph\n9911318)\n\\item{}\nvan Paradijs, J., 1996, ApJ, 464, L139\n\\end{thebibliography}\n\n\n\\end{document}\n"
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{
"name": "astro-ph0002286.extracted_bib",
"string": "\\begin{thebibliography}{} \n\n\\item{}\nDubus, G., Lasota J.--P., Hameury, J.--M., Charles, P.A., 1996, MNRAS,\n303, 139\n\\item{}\nFukue, J., PASJ, 44, 663\n\\item{}\nHjellming, R.M., Rupen, M.P., 1995, Nat, 375, 464\n\\item{}\nHynes, R.I., Haswell, C.A., Shrader, C.R., Chen, W., Horne, K.,\nHarlaftis, E.T., O'Brien, K., Hellier, C., Fender, R.P., 1998, MNRAS,\n300, 64\n\\item{}\nKing, A.R., Frank, J., Kolb, U., Ritter, H., 1997, ApJ, 484, 844\n\\item{}\nKing, A.R., Kolb, U., Burderi, L., 1996, ApJ, 464, L127\n\\item{}\nKing, A.R., Kolb, U., Szuszkiewicz, E., 1997, ApJ, 488, 89\n\\item{}\nKolb, U., King, A.R., Ritter, H., Frank, J., 1997, ApJ 485 L33\n\\item{}\nLi, X.--D., Wang, Z.--R., 1998, ApJ, 500, 935\n\\item{}\nOrosz, J.A., Bailyn, C.D., 1997, ApJ, 477, 876 \n\\item{}\nPringle, J.E., 1996, MNRAS, 281, 357\n\\item{}\nReg\\\"os, E., Tout, C.A., Wickramasinghe, D., 1998, ApJ, 509, 362\n\\item{}\nSoria, R., Wu, K., Hunstead, R., 1999, ApJ, in press (astro--ph\n9911318)\n\\item{}\nvan Paradijs, J., 1996, ApJ, 464, L139\n\\end{thebibliography}"
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astro-ph0002287
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Secondary caustics in close multiple lenses
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We investigate the caustic structure of a lens composed by a discrete number of point--masses, having mutual distances smaller than the Einstein radius of the total mass of the system. Along with the main critical curve, it is known that the lens map is characterized by secondary critical curves producing small caustics far from the lens system. By exploiting perturbative methods, we derive the number, the position, the shape, the cusps and the area of these caustics for an arbitrary number of close multiple lenses. Very interesting geometries are created in some particular cases. Finally we review the binary lens case where our formulae assume a simple form. \keywords{Gravitational lensing; Close binary stars; % Clusters of galaxies; Quasars}%
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"name": "SECCAUS.TEX",
"string": "\n\\documentclass{aa}\n\\usepackage{graphicx}\n\\usepackage{amsmath}\n\n%\\input{tcilatex}\n\n\\begin{document}\n\\thesaurus{2(12.07.1; 08.02.1; 11.03.1; 11.17.3)}\n\n\\title{Secondary caustics in close multiple lenses}\n\\author{Valerio Bozza\\thanks{%\nE-mail valboz@sa.infn.it}} \\institute{Dipartimento di\nScienze Fisiche E.R. Caianiello,\\\\\n Universit\\`{a} di Salerno, I-84081 Baronissi, Salerno, Italy.\\\\\n Istituto Nazionale di Fisica Nucleare, sezione di Napoli.}\n\\date{Received / Accepted }\n\\maketitle\n\n\\begin{abstract}\nWe investigate the caustic structure of a lens composed by a\ndiscrete number of point--masses, having mutual distances smaller\nthan the Einstein radius of the total mass of the system. Along\nwith the main critical curve, it is known that the lens map is\ncharacterized by secondary critical curves producing small\ncaustics far from the lens system. By exploiting perturbative\nmethods, we derive the number, the position, the shape, the cusps\nand the area of these caustics for an arbitrary number of close\nmultiple lenses. Very interesting geometries are created in some\nparticular cases. Finally we review the binary lens case where our\nformulae assume a simple form.\n \\keywords{Gravitational lensing; Close binary stars; %\n Clusters of galaxies; Quasars}%\n\\end{abstract}\n\n\\section{Introduction}\n\nThe binary Schwarzschild lens is one of the most intensively\nstudied model. In fact, in a relatively simple way, it shows many\nfeatures that are observed in general gravitational lenses, such\nas the formation of multiple images, giant arcs and a not trivial\ncritical behaviour. The first study about the binary lens with\nequal masses was made by Schneider \\& Wei{\\ss} (1986). They\nderived the critical curves and the caustics showing that three\npossible topologies are present depending on the distance between\nthe two lenses. Erdl \\& Schneider (1993) extended these results to\na generic mass ratio of the two lenses. Witt \\& Petters (1993)\nreached the same results using complex notation. In some limits,\nDominik (1999) enlightened the connection between the caustics of\nthe binary lens and other models, such as the Chang--Refsdal lens\n(Chang \\& Refsdal 1979; 1984) and the quadrupole lens.\n\nThe critical curves and the caustics of multiple lenses can\ndevelop very complicated structures, so that the attempts to gain\nsome information about them have been very few. However there is a\ngreat interest in this problem for its applications in particular\nsituations, such as planetary systems (Gaudi et al. 1998), rich\nclusters of galaxies and microlensing of quasars by individual\nstars in the haloes of the lensing galaxies (Chang \\& Refsdal\n1979; Kayser et al. 1988).\n\nIn some special situations, the critical curves of multiple lenses\ncan be derived by perturbative methods, referring to the single\nSchwarzschild lens as the starting point for series expansions\n(Bozza 1999; Bozza 2000). These methods work very well in\nplanetary systems, for a lens very far from the others and systems\nwhere mutual distances are very small with respect to the total\nEinstein radius. In the first two cases, the complete caustic\nstructure has been derived and the connections with other models\nhave been showed. In the last case, only the central caustic\ncoming up from the deformation of the total Einstein ring has been\nstudied. Besides this main curve, there are many small critical\ncurves forming among the masses. The caustics generated by these\ncurves generally lie far from the centre of mass and can have some\ninfluence on sources distant from the mass distribution. Moreover,\nthey move very quickly as the parameters of the system change\n(Schramm et al. 1993) constituting the most problematic feature to\ncontrol in numerical simulations. For these reasons they are\nsometimes dubbed \\textit{ghost caustics}. In rapidly rotating\nbinaries they may have superluminal projected motion requiring a non--static\ntreatment of light deflection (Zheng \\& Gould 2000).\n\nIn this paper we use complex notation to face the problem of\nsecondary caustics of close multiple lenses. In this way we can\nstudy them as deeply as the other caustics, completing the previous\nworks. We shall see that different\nclasses of secondary caustics can be recognized, showing different\ngeometries.\n\nAfter some review of multiple lensing in Sect. 2, in Sect. 3 we\ncalculate the number and the position of secondary critical curves\nfor an arbitrary number and configuration of lenses. Then,\nin Sect. 4, we treat the\nsimple caustics and in Sect. 5 the multiple caustics (the\ndistinction will be explained at the end of Sect. 3). In Sect. 6\nwe specify our formulae for the binary case and in Sect. 7 we give\nthe summary.\n\n\\section{Basics of multiple lensing}\n\nWe shall study a system of n point--lenses placed at positions\n$\\mathbf{x}_i=\\left( x_{i1}; x_{i2} \\right)$ in coordinates\nnormalized to the Einstein radius\n\\begin{equation}\nR_{\\mathrm{E}}^{\\mathrm{0}}=\\sqrt{\\frac{4GM_0 }{c^{2}}\n\\frac{D_{\\mathrm{LS}}D_{\\mathrm{OL}}}{D_{\\mathrm{OS}}}},\n\\end{equation}\nwhere $M_0$ is a reference mass (it can be chosen to be the total\nmass, the typical mass of a single object or anything else). The\nsource coordinates $\\mathbf{y}=\\left( y_1; y_2 \\right)$ are\nnormalized to the scaled Einstein radius $R_{\\mathrm{E}}^0\n\\frac{D_{\\mathrm{OS}}}{D_{\\mathrm{OL}}}$. The masses $m_i$ of the\nlenses are measured in terms of $M_0$.\n\nWe introduce the complex coordinate in the lens plane $z=x_1+i\nx_2$ and the complex source coordinate $y=y_1+i y_2$. The\npositions of the masses will be denoted by $z_i=x_{i1}+i x_{i2}$.\nWe also introduce the functions\n\\begin{equation}\nS_k \\left(z \\right)=\\sum\\limits_{i=1}^n \\frac{m_i}{\\left(z-z_i\n\\right)^k}. %\n\\label{Sk}\n\\end{equation}\n\nThe lens equation for our system of n masses reads (Witt 1990)\n\\begin{equation}\ny=z-\\overline{S}_1 \\left(\\overline{z} \\right) .%\n\\label{Lens equation}\n\\end{equation}\nGiven a source at position $y$, the $z$'s solving this equation\nare the images produced by gravitational lensing.\n\nThis map is locally invertible where the determinant of the\nJacobian matrix\n\\begin{equation}\n\\det J =1-\\frac{\\partial y}{\\partial \\overline{z}}\n\\overline{\\frac{\\partial y}{\\partial \\overline{z}}} = 1-\\left| S_2\n\\left( z \\right) \\right|^2%\n\\label{General detJ}\n\\end{equation}\nis different from zero. The points where the Jacobian determinant\nvanishes are arranged in smooth closed curves called critical\ncurves. The images of these points through the lens map (\\ref{Lens\nequation}) in the source plane are called caustics. When a source\ncrosses a caustic, creation or destruction of pairs of images\noccurs and the magnification diverges (Schneider, Ehlers \\& Falco\n1992).\n\nThis is all we need to start our search for secondary caustics in\nclose multiple systems. The fundamental hypothesis we make is\n\\begin{equation}\n\\left|z_i \\right| \\ll \\sqrt{M} \\; \\; \\; \\forall i, %\n\\label{Perturbative hypothesis}\n\\end{equation}\nwhere $M$ is the total mass of the system. In this way, the\ndistances between pairs of lenses will be very small with respect\nto the Einstein radius of the lens that we would have if all the\nmasses were concentrated at the origin. This Einstein radius is\n$\\sqrt{M}$ in our notation. The relation (\\ref{Perturbative\nhypothesis}) allows us to consider the $z_i$'s as perturbative\nparameters in a series expansion. Then we can solve the equation\n$\\det J =0$ at each order, writing its solutions as series\nexpansions in powers of the perturbative parameters. In this way\nwe shall find the critical curves of this system and study their\nproperties analytically.\n\n\\section{Number and positions of secondary critical curves}\n\nClose multiple lenses have two classes of critical curves: the\nmain critical curve, resulting from the deformation of the\nEinstein ring of the total mass lens, and the secondary critical\ncurves, forming inside the distribution of the masses.\n\nEffectively, if we multiply the equation $\\det J=0$ by the\nquantity $\\prod\\limits_{i=1}^n \\left| z- z_i \\right|^4$, we get a\ncomplex equation in $z$ and $\\overline{z}$:\n\\begin{equation}\n\\prod\\limits_{i=1}^n \\left| z- z_i \\right|^4- \\left|\n\\sum\\limits_{i=1}^n m_i \\prod\\limits_{j \\neq i} \\left(z-z_j\n\\right)^2 \\right|^2=0. %\n\\label{Eq detJ}\n\\end{equation}\n\nAt the zero order, putting all $z_i$'s to zero, this equation\nbecomes\n\\begin{equation}\n\\left|z \\right|^{4n-4} \\left( \\left|z \\right|^4 - M^2 \\right)=0.\n\\end{equation}\nThis equation has the solution $\\left| z \\right|=\\sqrt{M}$, that\nis the Einstein ring of the total mass lens. Taking this solution\nas the starting point of a perturbative expansion, we get the main\ncaustic. The details of this calculation are in (Bozza 2000). But\nthe presence of the solution $z=0$ indicates that also this value\ncan be taken as the starting point for another expansion. This is\njust the value we shall take to find the secondary critical\ncurves.\n\nHaving observed the zero order situation, we can start our\nperturbative approach, searching for the first order solution.\nThen we write the solution $z$ as a series expansion:\n\\begin{equation}\nz=z_0+o \\left( \\left|z_i \\right| \\right),\n\\end{equation}\nwhere $z_0$ is of the first order in $\\left|z_i \\right|$. Stopping\nat the first order, we put $z=z_0$ in Eq. (\\ref{Eq detJ}). We see\nthat the first term becomes of order $4n$, while the second is of\norder $4n-4$. Then the latter dominates the first and Eq. (\\ref{Eq\ndetJ}) is equivalent to\n\\begin{equation}\n\\sum\\limits_{i=1}^n m_i \\prod\\limits_{j \\neq i} \\left(z_0-z_j\n\\right)^2=0. %\n\\label{Eq pos}\n\\end{equation}\n\nThis is a polynomial equation of degree $2n-2$. Then, for a system\nof n close lenses, there are, at most, $2n-2$ points where the\nJacobian determinant vanishes (at the first order in $z_i$),\ncorresponding to $2n-2$ secondary critical curves.\nThis is the first main result of our work. It is\nconsistent with the binary lens, since two secondary critical\ncurves are predicted by this formula.\n\nEq. (\\ref{Eq pos}) can be solved analytically for two and three\nlenses, otherwise we have to resort to simple numerical methods.\nIn Sect. 6, we shall specify these and the following results for\nthe binary lens where a manageable expression for the positions of\nthe critical curves is available. For the triple lens, the\nanalytical solutions are too cumbersome to allow a detailed study.\n\nNow, we have a straightforward way to calculate the positions of\nthe secondary critical curves for an arbitrary configuration of close\nmultiple lenses. Then, we can avoid the traditional blind\nsampling of the Jacobian determinant on the lens plane and\nreach, by this new method,\nthe full efficiency.\n\nWe take the generical solution $z_0$ of Eq. (\\ref{Eq pos}) as the\nfirst order term of our expansion. From now on, we use the\nnotation\n\\begin{equation}\nS_k^0=S_k \\left( z_0 \\right).\n\\end{equation}\nAs both $z_0$ and $z_i$ are of the first order, according to our\nperturbative expansion, $S_k^0$ has all denominators of order $k$\nand then it is of order $-k$.\n\nTo continue our study we do not need an analytical expression for\n$z_0$. We shall just use the fact that $z_0$ is a solution of Eq.\n(\\ref{Eq pos}), that is equivalent to say that\n\\begin{equation}\nS_2^0=0.%\n\\label{S20}\n\\end{equation}\n\nOf course, we have to distinguish between simple roots of Eq.\n(\\ref{Eq pos}) and roots of higher multiplicity. Remembering that\nthe $k^{\\mathrm{th}}$ derivative of $S_2 \\left( z\\right)$ is\nproportional to $S_{k+2} \\left(z \\right)$, we have the equivalence\nbetween the following statements:\n\\begin{equation}\nz_0\\text{ is a root of multiplicity }p \\Leftrightarrow S_{k+2}^0=0\n\\; \\; \\forall k<p. %\n\\label{Mult equivalence}\n\\end{equation}\n\nWe shall treat separately the caustics coming from simple roots\n(hereafter called simple caustics) and the caustics coming from\nmultiple roots (hereafter multiple caustics).\n\n\\section{Simple caustics}\n\nThese caustics are largely the most common as we explain in the\nnext section. So they surely have the most practical interest.\n\n\\subsection{Shape of the critical curves}\n\nOnce found the positions of the critical curves, we can carry on\nour perturbative expansion to discover the shape of these curves.\nSo we put\n\\begin{equation}\nz=z_0+\\epsilon_2+\\epsilon_3+\\ldots,\n\\end{equation}\nwhere $z_0$ is the position of one simple critical curve, found by\nEq. (\\ref{Eq pos}), and $\\epsilon_j$ are the corrections of order\n$\\left|z_i\\right|^j$. It is convenient to use the original\nequation $\\det J=0$, which can be written in the form\n\\begin{equation}\n1-S_2 \\left(z_0+\\epsilon_2+\\epsilon_3 \\right) \\overline{S}_2\n\\left(\\overline{z}_0+\\overline{\\epsilon}_2+\\overline{\\epsilon}_3 \\right)=0,%\n\\label{detJ=0}\n\\end{equation}\nstarting from Eq. (\\ref{General detJ})\n\nThe expansion of $S_2$ is\n\\begin{eqnarray}\n& S_2\\left(z_0+\\epsilon_2+\\epsilon_3 \\right)=&S_2^0+ \\nonumber \\\\%\n& & -2 \\epsilon_2 S_3^0+ \\nonumber \\\\%\n& & -2 \\epsilon_3 S_3^0+3 \\epsilon_2^2 S_4^0+ \\ldots.\n\\end{eqnarray}\nThe first row is the order $-2$ and is null according to Eq.\n(\\ref{S20}). The second row is the order $-1$ and the third row is\nthe order zero. Inserting this expansion in (\\ref{detJ=0}), the\nlowest order equation is of order $-2$:\n\\begin{equation}\n-4\\left| \\epsilon_2 \\right|^2 \\left| S_3^0 \\right|^2=0,\n\\end{equation}\nBeing $z_0$ a simple root, $S_3^0 \\neq 0$, so that $\\epsilon_2=0$.\n\nThe successive terms in the expansion of the equation\n(\\ref{detJ=0}) are of order zero:\n\\begin{equation}\n1-4\\left| \\epsilon_3 \\right|^2 \\left| S_3^0 \\right|^2=0.\n\\end{equation}\nFrom this equation we have\n\\begin{equation}\n\\left| \\epsilon_3 \\right|=\\frac{1}{2 \\left| S_3^0 \\right|}.\n\\label{Critical r eq}\n\\end{equation}\nThen the third order contains the first information on the shape\nof the critical curve. Eq. (\\ref{Critical r eq}) tells us that the\ncritical curve at position $z_0$ is a circle centered on $z_0$\nwith radius\n\\begin{equation}\nr=\\frac{1}{2 \\left| S_3^0 \\right|}. %\n\\label{Critical r}\n\\end{equation}\nFrom the form of $S_3^0$ (see Eq. (\\ref{Sk})), we see that the\ncloser the critical curve is to some mass, the higher the value of\n$S_3^0$, the smaller the radius of the circle.\n\nIf we multiply all masses by a factor $\\lambda$, the positions of\nthe critical curves do not change, because $\\lambda$ factors out\nfrom Eq. (\\ref{Eq pos}), but their radii change as $\\lambda^{-1}$.\nIf we do the same with the positions of the masses instead, the\npositions of the critical curves scale as $\\lambda$ and their\nradii scale as $\\lambda^3$.\n\n\\subsection{Caustics}\n\nTo find the caustics corresponding to the simple critical curves,\nwe just have to put the critical curve, in its obvious\nparameterization\n\\begin{equation}\nz\\left( \\theta \\right)=z_0+r e^{i\\theta} \\; \\; \\; 0\\leq \\theta < 2\n\\pi,\n\\end{equation}\ninto the lens equation (\\ref{Lens equation}) and expand to the\nthird order:\n\\begin{equation}\ny\\left( \\theta \\right)=-\\overline{S}_1^0+z_0+\\left( r\ne^{i\\theta}-\\frac{e^{-2i\\theta}}{S_3^0} \\right). %\n\\label{Simple caustic}\n\\end{equation}\n\nWe can observe that the lowest order is $-1$ and is independent on\n$\\theta$. It represents the position of the caustic. From the\norder of this term, we can deduce that these caustics can lie very\nfar from the origin of our system, going to infinity as the\ndistances among the masses are reduced to zero. The successive\nterm is $z_0$, which is of the first order and represents a\ncorrection to the position. Finally, the shape of the caustic is\ngiven by the third order.\n\nThe cusps of a caustic are characterized by the vanishing of the\ntangent vector. To find them, we have to require that\n\\begin{equation}\n\\frac{\\mathrm{d} y \\left( \\theta \\right)}{\\mathrm{d} \\theta}=0\n\\end{equation}\nand solve for $\\theta$. Taking $y \\left( \\theta \\right)$ from Eq.\n(\\ref{Simple caustic}), this equation can be simplified into\n\\begin{equation}\ne^{3i\\theta}+\\sqrt{\\frac{\\overline{S}_3^0}{S_3^0}}=0,\n\\end{equation}\nwhose solutions are\n\\begin{equation}\n\\theta_k=-\\frac{1}{3}\\arg \\left( S_3^0 \\right) +\\frac{2k \\pi}{3}\n\\; \\; k=0,1,2,\n\\end{equation}\nwhere $\\arg$ yields the argument of a complex number.\n\nWe have three cusps. So, in any close multiple system, having only\nsimple secondary caustics, these caustics have a triangular shape.\n\nFinally, we calculate the area of these caustics. This can be done\nby the integral\n\\begin{equation}\nA=\\int\\limits_\\gamma y_2 \\mathrm{d} y_1,\n\\end{equation}\nwhere $\\gamma$ is the caustic in its clockwise direction. We have\n\\begin{equation}\nA=-\\frac{1}{4i}\\int\\limits_0^{2\\pi} \\left[y \\left( \\theta \\right)\n-\\overline{y}\\left( \\theta \\right) \\right]\\partial_\\theta \\left[y\n\\left( \\theta \\right) +\\overline{y}\\left( \\theta \\right) \\right]\n\\mathrm{d} \\theta.\n\\end{equation}\nThe minus in the right member comes from the fact that our\nparameterization is counterclockwise. The integral only involves\ncomplex exponential functions and the result is\n\\begin{equation}\nA=\\frac{1}{2}\\pi r^2.\n\\end{equation}\nSo the extension of the simple caustics is of the sixth order in\nthe separations among the lenses, justifying the evasive nature of\nthese caustics.\n\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{SIMCRIT.EPS}}\n \\caption{Positions of the four secondary critical curves %\n (indicated by the small dots) for a triple system with %\n masses $m_1=0.25$, $m_2=0.25$, $m_3=0.5$ and positions %\n $z_1=0.1$, $z_2=-0.1$, $z_3=0.014+i0.089$ (indicated by %\n the three crosses).}\n \\label{Fig simple critical curves}\n\\end{figure}\n\n\\begin{figure*}\n \\resizebox{12cm}{!}{\\includegraphics{SIMCAUS.EPS}}\n \\hfill\n \\parbox[b]{55mm}{\n \\caption{Here are the four caustics produced by the critical curves %\n of Fig. \\ref{Fig simple critical curves} from left to right. The solid %\n curve is the perturbative caustic and the dashed line is the numerical\n one.}}\n \\label{Fig simple caustics}\n\\end{figure*}\n\nWith our expansions, we have attained considerable analytical information\nabout the secondary caustics establishing their shape, the area, the\nnumber of cusps in a completely general way. However, since these\nresults are the fruit of perturbative approximations, it is important\nto discuss their accuracy.\nSo we propose a comparison between our perturbative results and\nthe numerical ones in a typical situation.\nWe consider a system constituted by three\nlenses disposed as in Fig. \\ref{Fig simple critical curves}.\nAccording to our previous statement, this system can form, at\nmost, four simple secondary critical curves. For our choice of\nparameters, we display their positions in the same figure. The\ncaustics produced by these curves are shown in Fig. 2 where they\nare compared to the numerical ones. We have taken the distances\namong the masses of this distribution to be one tenth of the total\nEinstein radius. Even for this not too small value, the positions\nand the shapes of the secondary caustics are reproduced with a\nstriking accuracy. It is also to be noted that the quality of\nnumerical results is improved thanks to the guide provided by\nperturbative results.\n\nSo we see that the\nanalytical formulae derived in this section are very good\napproximations to the quantitative characteristics of the\nsecondary caustics, proving to be highly reliable.\n\n\\section{Multiple caustics}\n\nIn this section, we consider the case where $z_0$ is a multiple\nroot of Eq. (\\ref{Eq pos}). The parameters space of a system with\nn lenses is $3n-4$ dimensional, since each mass adds three\nparameters (its mass and its coordinates in the lens plane). Four\nparameters can be eliminated by considering equivalent those\nsystems differing by a global translation or rotation and/or by a\nglobal scale factor. Thus, for example, the binary lens is\ncompletely characterized by the mass ratio and the separation\nbetween the lenses.\n\nThe requirement of a double root in Eq. (\\ref{Eq pos}) translates\ninto the vanishing of the derivative of this equation with respect\nto $z$. This is one constraint equation, then the points of the\nparameters space producing multiple roots constitute a $3n-5$\ndimensional hypersurface, thus having measure zero. For this\nreason, the occurrence of multiple roots is relatively rare.\nAnyway, very interesting features emerge, justifying a detailed\nstudy of these particular cases.\n\n\\subsection{Critical curves}\n\nSuppose that $z_0$ is a root with multiplicity $p$. We have to\nfind the correct order of the perturbation to insert in the\nequation $\\det J =0$, representing the shape of our critical\ncurve. According to the equivalence (\\ref{Mult equivalence}), the\n$S_{k+2}^0$ with $k<p$ are null. Then, we put\n\\begin{equation}\nz=z_0+\\epsilon,\n\\end{equation}\nwith the order (that we shall indicate by $q$) of $\\epsilon$ to\nbe found. We only assume that $q$ be higher than one. Then, the\nexpansion of $S_2 \\left( z \\right)$ is\n\\begin{multline}\nS_2\\left( z_0+\\epsilon \\right)=S_2^0-2 \\epsilon S_3^0+3 \\epsilon\nS_4^0+ \\ldots \\\\ \\ldots +\\left(-1\\right)^k \\left( k+1 \\right)\n\\epsilon^k S_{k+2}^0+ \\ldots.\n\\end{multline}\n\nThe $k^\\mathrm{th}$ term is of order $q k-\\left(k+2\\right)$ and\nthe first term to be non--null is that for $k=p$. When we put this\nexpansion in the equation $\\det J=0 $, the first non--null term is\n\\begin{equation}\n-\\left( p+1 \\right)^2 \\left|\\epsilon^{p}S_{p+2}\\right|^2\n\\end{equation}\nhaving order $2q p-2\\left(p+2\\right)$. If this order is less than\nzero, we just get from $\\det J=0$ that $\\epsilon=0$, but if the\norder of this term is zero, then the zero order expansion of $\\det\nJ=0$ also involves another term (equal to $1$):\n\\begin{equation}\n1-\\left( p+1 \\right)^2 \\left|\\epsilon^{p}S_{p+2}\\right|^2=0\n\\end{equation}\nand the equation gives the non--trivial solution\n\\begin{equation}\n\\left|\\epsilon \\right|=\\frac{1}{\\left[\\left( p+1 \\right)\n\\left|S_{p+2}\\right|\\right]^{1/p}}.\n\\end{equation}\nThis happens when the order of $\\epsilon$ is $q=\\frac{2+p}{p}$.\nThis is consistent with the result of the previous section,\nbecause, for $p=1$, $q=3$. For $p=2$, we have that the first non\ntrivial order is the second and, for $p=3$, it is the order\n$\\frac{5}{3}$. When $p$ increases, the order of this perturbation\ndecreases, approaching 1 as a limit. This means that at high\nmultiplicities, the perturbative expansion becomes always less\naccurate, requiring ever more terms for an adequate description of\nthe caustics. Anyway, the main characteristics of the caustics can\nbe derived retaining just the first correction and that is what we\nshall do.\n\nThe critical curve just derived is again a circle with radius\n\\begin{equation}\nr=\\frac{1}{\\left[\\left( p+1 \\right)\n\\left|S_{p+2}\\right|\\right]^{1/p}}, %\n\\label{Mult critical r}\n\\end{equation}\nbecoming greater with the multiplicity.\n\n\\subsection{Caustics}\n\nWe take, as before, the parameterization\n\\begin{equation}\nz \\left(\\theta \\right)=z_0+ r e^{i\\theta}\n\\end{equation}\nfor the critical curve, with $r$ given by Eq. (\\ref{Mult critical\nr}). Putting this expression into the lens equation (\\ref{Lens\nequation}) and expanding to the $q^{\\mathrm{th}}$ order, we get\n\\begin{equation}\ny\\left( \\theta \\right)=-\\overline{S}_1^0+z_0+r \\left[\ne^{i\\theta}+\\left( -1 \\right)^p \\frac{e^{-\\left( p+1 \\right)\ni\\theta}}{ p+1 } \\sqrt{\\frac{\\overline{S}_{p+2}^0}{ S_{p+2}^0}}\n\\right].%\n\\label{Mult caustic}\n\\end{equation}\n\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{DOUCRIT.EPS}}\n \\caption{Critical curves in the event of a double root. %\n The masses are indicated by the crosses. The double critical %\n curve is the one at the bottom--center, while the other two %\n are on the top--left and top--right and are hardly visible in %\n this picture.}\n \\label{Fig Double critical curve}\n\\end{figure}\n\nThe $q^{\\mathrm{th}}$ order is the first depending on $\\theta$ and\ndetermines the shape of the caustic.\n\nTo understand this shape, we calculate the cusps as in the\nprevious section. The equation for the cusps is\n\\begin{equation}\ne^{\\left(p+2 \\right) i\\theta}+\\left( -1 \\right)^{p+1}\n\\sqrt{\\frac{\\overline{S}_{p+2}^0}{S_{p+2}^0}}=0\n\\end{equation}\nand its solutions are\n\\begin{equation}\n\\theta_k=\\frac{\\left(-1 \\right)^p}{p+2 }\\arg \\left(\nS_{p+2}^0\\right) +\\frac{2k \\pi}{p+2} \\; \\; \\; 0 \\leq k<p+2.\n\\end{equation}\n\nNow we have $p+2$ cusps. This is a very interesting result,\nbecause the caustic assumes the shape of a regular polygon with\n$p+2$ curved sides.\n\nThe area of the multiple caustic can be calculated in the same way\nas for the simple one. We just give the result:\n\\begin{equation}\nA= \\frac{p}{p+1}\\pi r^2.\n\\end{equation}\nIt is of order $2\\frac{2+p}{p}$. So, increasing the multiplicity\nfrom 1 to infinity, the order of the area lowers from 6 to 2 and\nthe extension of the caustic becomes ever more important.\n\nSome other consideration about the limit for $p\\rightarrow \\infty$\ncan be done. The number of cusps become infinite and, from Eq.\n(\\ref{Mult caustic}), we see that the caustic becomes a circle of\nradius $r$. In fact, the area becomes $\\pi r^2$.\n\n\\subsection{An example: a double caustic in a triple lens}\n\n\\begin{figure}\n \\resizebox{\\hsize}{!}{\\includegraphics{DOUCAUS.EPS}}\n \\caption{Caustic corresponding to the double critical curve %\n of Fig. \\ref{Fig Double critical curve}. The dashed curve is %\n the numerical caustic and the solid line is the perturbative %\n one.}\n \\label{Fig Double caustic}\n\\end{figure}\n\nNow we shall practically see how our formulae work in the case of\na multiple caustic. We consider three masses: $m_1=0.25$,\n$m_2=0.25$ and $m_3=0.5$. We fix the positions of the first two:\n$z_1=0.1$, $z_2=-0.1$; but we let the third free for the moment.\nWe simultaneously solve Eq. (\\ref{Eq pos}) and its derivative with\nrespect to $z_0$, for the two unknowns $z_0$ and $z_3$. We find\nsix possible positions of the third mass, giving rise to a double\nroot of the positions equation. None of them is a triple root. Two\nof these positions are on the $x_2$-axis. We choose one of them:\n$z_3=i 0.084263$. The double root is in $z_0=-i0.0299$. In Fig.\n\\ref{Fig Double critical curve}, we see that the critical curve in\nthis point is much greater than the other two. In fact, the radius\nof the double critical curve, calculated by Eq. (\\ref{Mult\ncritical r}), is $8.49 \\times 10^{-3}$, while the radius of the\ntwo simple critical curves is $6.13 \\times 10^{-4}$, according to\nEq. (\\ref{Critical r}).\n\nIn Fig. \\ref{Fig Double caustic}, we show the caustic generated by\nthis double critical curve. The geometry is correctly predicted by\nour perturbative expansion: there are four cusps in a double\ncaustic. We see that the approximation is less accurate than\nbefore, as we anticipated in our discussion about the order of the\nperturbation. However, for double caustics, it is not so difficult\nto add another term to the perturbative expansion and reach the\nsame accuracy of the simple caustics. The third order term in the\ncritical curve depends on $\\theta$:\n\\begin{equation}\n\\epsilon_3=6 r^2 \\mathrm{Re}\\left[ \\overline{S}_4^0 S_5^0 e^{i\n\\theta} \\right].\n\\end{equation}\nThe successive term in the caustic is\n\\begin{equation}\ne^{i \\theta} \\epsilon_3+3 e^{-3i \\theta} r^2 \\epsilon_3\n\\overline{S}_4^0- r^4 e^{-4i \\theta} \\overline{S}_5^0.\n\\end{equation}\n\nDouble caustics, and, more generally, multiple caustics, are\nformed by the union of small caustics, in some sense. Another\ninteresting question is: what happens if we change the parameters\nin the neighbourhood of our particular choice producing the double\nroot? We expect the double critical curve to separate into two\nsmaller ovals and the double quadrangular caustic to break into\ntwo triangular ones; but this can happen in different ways.\n\nIn this regime, the perturbative caustics are simple.\nHowever, as the parameters tend to give the\ndouble root, $S_3^0$ tends to zero, yielding a diverging $r$ for\nthe simple critical curves, according to Eq. (\\ref{Critical r}).\nThe transition with the formation of the double critical curve is\nthus not reproduced.\nGuided by perturbative approximations, the break of the double\ncaustic, when $z_3$ moves out from the position $i\n0.084263$, can be investigated numerically. The results are shown in\nFig. \\ref{Fig Double neighbourhood}.\n\n\\begin{figure*}\n \\resizebox{15cm}{!}{\\includegraphics{DOUNEIGH.EPS}}\n \\hfill\n \\parbox[b]{15cm}{\n \\caption{Critical curves and caustics for $z_3$ close to %\n $i 0.084263$. The left column shows the critical curves and %\n the right column the caustics. The thick lines are the numerical %\n curves and the thin lines are the perturbative ones. The choice of %\n $z_3$ in cases $a$, $b$ and $c$ are given in the text.}\n \\label{Fig Double neighbourhood}}\n\\end{figure*}\n\nIn case $a$, $z_3=i 0.082787$, i.e. we have moved the third mass\ntowards the others. The critical curve breaks in the horizontal\ndirection. Looking just at the thick line in Fig. \\ref{Fig Double\nneighbourhood}a2, representing the numerical caustic, we see that\nthe top cusp and the bottom cusp develop a butterfly geometry. At\nsome critical value, these butterflies touch and the two resulting\ntriangular caustics move away along the horizontal direction. We\nhave displayed in the same plot the perturbative caustics too.\nObviously, they are simple caustics, so they cannot show the\nbutterfly geometry but they can help in understanding how the\nseparation occurs. We also notice that the simple caustics\ncover the area of the\nnumerical transition double caustic very well constituting a significant\napproximation anyway.\n\nIn case $b$, $z_3=i 0.085759$, so that the third mass is farther\nfrom the others. Now the critical curve breaks in the vertical\ndirection and so does the caustic. The left and the right cusps\ntransform into butterflies. These butterflies are slightly\ndistorted by the fact that the resulting simple caustics have\ndifferent sizes: the one on the top is smaller than the other.\n\nIn case $c$, $z_3=0.00147+i 0.084263$. We have displaced the third\nmass in the horizontal direction. The critical curve breaks\ndiagonally and so does the caustic. But this time the transition\noccurs with a simple beak--to--beak singularity rather than with\nbutterflies. While in the previous situations the two simple\ncaustics in the last step of the separation touch with a fold,\nhere they touch with a cusp.\n\n\\section{Secondary caustics in binary lensing}\n\nIn this section, we specify our results for the binary case where\nsimple analytical formulae can be written. Let's consider two\nmasses placed on the horizontal axis and let's choose the origin\nin the centre of mass. We call the separation between the masses\n$a$, then we have $z_1=\\frac{m_2 a}{m_1+m_2}$ and $z_2=-\\frac{m_1\na}{m_1+m_2}$. Eq. (\\ref{Eq pos}) is of second degree. Its\nsolutions are\n\\begin{equation}\nz_0=a\\frac{m_2-m_1 \\pm i \\sqrt{m_1 m_2}}{m_1+m_2}.\n\\end{equation}\nThey are always simple and lie on a circle of radius $a/2$\ncentered in the middle of the two masses.\n\nThe radius of the two ovals is the same:\n\\begin{equation}\nr=\\frac{\\sqrt{m_1 m_2} a^3}{2 \\left( m_1+m_2 \\right)^2}.\n\\end{equation}\nIts maximum value $\\frac{a^3}{4 M_\\mathrm{tot}}$ is reached when\nthe two masses are equal, in fact, in this case, their distance\nfrom the two masses is maximum.\n\nThe two caustics are given by the following expression:\n\\begin{multline}\ny \\left( \\theta \\right)=\\frac{m_1-m_2}{a} \\mp i \\frac{2 \\sqrt{m_1\nm_2}}{a}+ \\\\ %\n+a\\frac{m_2-m_1}{m_1+m_2} \\pm i a \\frac{\\sqrt{m_1\nm_2}}{m_1+m_2} +\\\\ %\n+ a^3 \\sqrt{m_1 m_2}\\left[ \\frac{ e^{i \\theta}}{2 \\left( m_1+m_2\n\\right)^2} \\pm \\frac{i e^{-2 i \\theta}}{4 \\left( \\sqrt{m_1} \\pm i\n\\sqrt{m_2}\\right)^4} \\right].\n\\end{multline}\n\nTheir cusps are at positions\n\\begin{equation}\n\\theta_k=- \\arg \\left[\\pm i \\left(\\sqrt{m_1} \\pm i \\sqrt{m_2}\n\\right)^4 \\right] +\\frac{2k\\pi}{3} \\; \\; k=0,1,2.\n\\end{equation}\n\nTheir area is\n\\begin{equation}\nA=\\frac{\\pi m_1 m_2 a^6}{8 \\left( m_1+m_2 \\right)^4},\n\\end{equation}\nreaching the maximum value $\\frac{\\pi a^6}{32M^2_{\\mathrm{tot}}}$\nin the equal masses case.\n\n\\section{Summary}\n\nMultiple Schwarzschild lensing represents a very rich terrain for\nthe exploration of caustics in gravitational lensing. The\noccurrence of different kinds of singularities stimulates new\ninvestigations.\n\nIn this paper we have applied perturbative methods to secondary\ncaustics,\nforming when the masses are close each other with respect to the\ntotal Einstein radius. In this way we have been able to establish\nthe number of the caustics for any lens configuration, the positions\nand the shapes, with a complete characterization of the geometries\narising in all cases. Moreover, quantitative formulae for the area\nand other features of these objects have been given.\nAs we have seen, in the\nmost common case, the shape of the\nsimple caustics is always triangular. Anyway, multiple caustics exist\ndeveloping a great\nvariety of behaviours, giving rise, to curves having a number of cusps\nranging from four to\ninfinity. The breaking of multiple caustics can follow different\nways depending on how the parameters of the system change.\n\n\\begin{acknowledgements}\nI would like to thank Gaetano Scarpetta and Salvatore Capozziello\nfor their helpful comments on the manuscript.\n\nWork supported by fund ex 60\\% D.P.R. 382/80.\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\n\\bibitem{Bozza a} Bozza V., 1999, A\\&A 348, 311\n\n\\bibitem{Bozza b} Bozza V., 2000, A\\&A in press, astro-ph/9910535\n\n\\bibitem{Chang & Refsdal 1} Chang K., Refsdal S., 1979, Nat 282, 561\n\n\\bibitem{Chang & Refsdal 2} Chang K., Refsdal S., 1984, A\\&A 132, 168\n\n\\bibitem{Dominik} Dominik M., 1999, A\\&A 349, 108\n\n\\bibitem{Erdl & Schneider} Erdl H., Schneider P., 1993, A\\&A 268, 453\n\n\\bibitem{Gaudi et al.} Gaudi B.S., Naber R.M., Richard M., Sackett P.D.,\n1998, ApJ 502, 33\n\n\\bibitem{Kayser et al.} Kayser R., Wei{\\ss} A., Refsdal S.,\nSchneider P., 1988, A\\&A 214, 4\n\n\\bibitem{Schneider, Ehlers & Falco} Schneider P., Ehlers J., Falco\nE.E.,1992, Gravitational lenses. Springer-Verlag, Berlin\n\n\\bibitem{Schneider & Weiss} Schneider P., Wei{\\ss} A., 1986, A\\&A 164, 237\n\n\\bibitem{Schramm et al.} Schramm T., Kayser R., Chang K. et al.,\n1993, A\\&A 268, 350\n\n\\bibitem{Witt} Witt H.J., 1990, A\\&A 236, 311\n\n\\bibitem{Witt & Petters} Witt H.J., Petters A.O., 1993, J. Math. Phys.\n34, 4093\n\n\\bibitem{Zheng & Gould} Zheng Z., Gould A., 2000, submitted to\nApJ, astro-ph/0001199\n\n\\end{thebibliography}\n\n\\end{document}\n"
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[
{
"name": "astro-ph0002287.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem{Bozza a} Bozza V., 1999, A\\&A 348, 311\n\n\\bibitem{Bozza b} Bozza V., 2000, A\\&A in press, astro-ph/9910535\n\n\\bibitem{Chang & Refsdal 1} Chang K., Refsdal S., 1979, Nat 282, 561\n\n\\bibitem{Chang & Refsdal 2} Chang K., Refsdal S., 1984, A\\&A 132, 168\n\n\\bibitem{Dominik} Dominik M., 1999, A\\&A 349, 108\n\n\\bibitem{Erdl & Schneider} Erdl H., Schneider P., 1993, A\\&A 268, 453\n\n\\bibitem{Gaudi et al.} Gaudi B.S., Naber R.M., Richard M., Sackett P.D.,\n1998, ApJ 502, 33\n\n\\bibitem{Kayser et al.} Kayser R., Wei{\\ss} A., Refsdal S.,\nSchneider P., 1988, A\\&A 214, 4\n\n\\bibitem{Schneider, Ehlers & Falco} Schneider P., Ehlers J., Falco\nE.E.,1992, Gravitational lenses. Springer-Verlag, Berlin\n\n\\bibitem{Schneider & Weiss} Schneider P., Wei{\\ss} A., 1986, A\\&A 164, 237\n\n\\bibitem{Schramm et al.} Schramm T., Kayser R., Chang K. et al.,\n1993, A\\&A 268, 350\n\n\\bibitem{Witt} Witt H.J., 1990, A\\&A 236, 311\n\n\\bibitem{Witt & Petters} Witt H.J., Petters A.O., 1993, J. Math. Phys.\n34, 4093\n\n\\bibitem{Zheng & Gould} Zheng Z., Gould A., 2000, submitted to\nApJ, astro-ph/0001199\n\n\\end{thebibliography}"
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astro-ph0002288
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EVIDENCE FOR PRESSURE DRIVEN FLOWS AND TURBULENT DISSIPATION IN THE SERPENS NW CLUSTER
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[
{
"author": "Jonathan P. Williams\\altaffilmark{1}\\altaffilmark{2}"
}
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\rightskip = 0pt We have mapped the dense gas distribution and dynamics in the NW region of the Serpens molecular cloud in the CS(2--1) and \n2hp(1--0) lines and 3~mm continuum using the FCRAO telescope and BIMA interferometer. 7 continuum sources are found. The \n2hp\ spectra are optically thin and fits to the 7 hyperfine components are used to determine the distribution of velocity dispersion. 8 cores, 2 with continuum sources, 6 without, lie at a local linewidth minimum and optical depth maximum. The CS spectra are optically thick and generally self-absorbed over the full 0.2~pc extent of the map. We use the line wings to trace outflows around at least 3, and possibly 4, of the continuum sources, and the asymmetry in the self-absorption as a diagnostic of relative motions between core centers and envelopes. The quiescent regions with low \n2hp\ linewidth tend to have more asymmetric CS spectra than the spectra around the continuum sources indicating higher infall speeds. These regions have typical sizes $\sim 5000$~AU, linewidths $\sim 0.5$~\kms, and infall speeds $\sim 0.05$~\kms. The correlation of CS asymmetry with \n2hp\ velocity dispersion suggests that the inward flows of material that build up pre-protostellar cores are driven at least partly by a pressure gradient rather than by gravity alone. We discuss a scenario for core formation and eventual star forming collapse through the dissipation of turbulence.
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"name": "preprint.tex",
"string": "% 8/12/99 jpw bite the bullet and start writing\n% 10/17/99 jpw new figures, some comments from Phil: complete first draft\n% 11/02/99 jpw address comments from Phil; second draft\n% 12/05/99 jpw new analysis following error in hfs fitting; third draft\n% 12/28/99 jpw submitted\n% 2/03/00 jpw revised after referee comments\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\documentclass[preprint]{aastex}\n\\input psfig.sty\n%\\documentclass{aastex}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\newcommand{\\kms} {\\mbox{${\\rm km~s^{-1}}$}}\n\\newcommand{\\cc} {\\mbox{${\\rm cm^{-3}}$}}\n\\newcommand{\\etal} {et al.}\n\\newcommand{\\eg} {{\\it e.g.}}\n\\newcommand{\\ie} {{\\it i.e.}}\n\\newcommand{\\cf} {{\\it c.f.}}\n\\newcommand{\\etc} {{\\it etc.}}\n\\newcommand{\\e} {\\mbox{$^{-1}$}}\n\\newcommand{\\ee} {\\mbox{$^{-2}$}}\n\\newcommand{\\eee} {\\mbox{$^{-3}$}}\n\\newcommand{\\simgt} {\\gtrsim}\n\\newcommand{\\simlt} {\\lesssim}\n\\newcommand{\\degs} {\\mbox{$^{\\circ}$}}\n\\newcommand{\\Msun} {\\mbox{$M_\\odot$}}\n\\newcommand{\\Mlte} {\\mbox{$M_{\\rm LTE}$}}\n\\newcommand{\\Mvir} {\\mbox{$M_{\\rm vir}$}}\n\\newcommand{\\Mgrav} {\\mbox{$M_{\\rm grav}$}}\n\\newcommand{\\Lsun} {\\mbox{$L_\\odot$}}\n\\newcommand{\\Lir} {\\mbox{$L_{\\rm IR}$}}\n\\newcommand{\\LM} {\\mbox{$L_{\\rm IR}/M_{\\rm cloud}$}}\n\\newcommand{\\LMsun} {L_\\odot/M_\\odot}\n\\newcommand{\\D} {\\Delta}\n\\newcommand{\\Dv} {\\Delta V}\n\\newcommand{\\TK} {T_{\\rm K}}\n\\newcommand{\\X} {\\mbox{$N_{{\\rm H}_2}/W_{\\rm CO}$}}\n\\newcommand{\\Xunits} {\\mbox{cm$^{-2}$/K\\,km\\,s$^{-1}$}}\n\\newcommand{\\Nunits} {\\mbox{cm$^{-2}$/km\\,s$^{-1}$}}\n\\newcommand{\\Kkms} {\\mbox{${\\rm K\\,km\\,s}^{-1}$}}\n\\newcommand{\\Wco} {\\mbox{$W_{\\rm CO}$}}\n\\newcommand{\\iras} {{\\it IRAS}}\n\\newcommand{\\Trms} {T_{\\rm rms}}\n\\newcommand{\\Trstar} {\\mbox{$T_{\\rm R}^\\ast$}}\n\\newcommand{\\Tx} {\\mbox{$T_{\\rm ex}$}}\n\\newcommand{\\Txone} {\\mbox{$T_{{\\rm ex},1}$}}\n\\newcommand{\\Txtwo} {\\mbox{$T_{{\\rm ex},2}$}}\n\\newcommand{\\Tmb} {\\mbox{$T_{\\rm mb}$}}\n\\newcommand{\\JTbg} {\\mbox{$J(T_{\\rm bg})$}}\n\\newcommand{\\dtbr} {\\mbox{$\\Delta T_{\\rm b-r}$}}\n\\def\\cm2{\\mbox{${\\rm cm^{-2}}$}}\n\\def\\h2{\\mbox{${\\rm H}_2$}}\n\\def\\nh2{\\mbox{$n_{\\rm H_2}$}}\n\\def\\Nh2{\\mbox{$N_{{\\rm H}_2}$}}\n\\def\\Mh2{\\mbox{$M_{{\\rm H}_2}$}}\n\\def\\n2hp{\\mbox{N$_2$H$^+$}}\n\\def\\c34s{\\mbox{C$^{34}$S}}\n\\def\\fs{\\hbox{$.\\!\\!^{\\rm s}$}}\n\n\n\\slugcomment{Accepted by the Astrophysical Journal,\nFebruary 14$^{\\rm th}$, 1999}\n\\shorttitle{Pressure Flows and Turbulent Dissipation}\n\\shortauthors{Williams \\& Myers}\n\n\\begin{document}\n\n\\title{EVIDENCE FOR PRESSURE DRIVEN FLOWS AND TURBULENT DISSIPATION IN THE\nSERPENS NW CLUSTER}\n\\author{Jonathan P. Williams\\altaffilmark{1}\\altaffilmark{2}}\n\\altaffiltext{1}{National Radio Astronomy Observatory, 949 N. Cherry Ave.,\nTucson AZ 85721}\n\\altaffiltext{2}{Department of Astronomy, 211 Bryant Space Science Center,\nUniversity of Florida, Gainesville, FL 32611; williams@astro.ufl.edu}\n\\and\n\\author{Philip C. Myers\\altaffilmark{3}}\n\\altaffiltext{3}{Harvard--Smithsonian Center for Astrophysics,\n60 Garden Street, Cambridge, MA 02138; pmyers@cfa.harvard.edu}\n\n\n\\begin{abstract}\n\\rightskip = 0pt\nWe have mapped the dense gas distribution and dynamics in the NW region\nof the Serpens molecular cloud in the CS(2--1) and \\n2hp(1--0) lines and\n3~mm continuum using the FCRAO telescope and BIMA interferometer.\n7 continuum sources are found.\nThe \\n2hp\\ spectra are optically thin and fits to the 7 hyperfine\ncomponents are used to determine the distribution of velocity dispersion.\n8 cores, 2 with continuum sources, 6 without, lie at a local linewidth\nminimum and optical depth maximum.\nThe CS spectra are optically thick and generally self-absorbed\nover the full 0.2~pc extent of the map.\nWe use the line wings to trace outflows around at least 3,\nand possibly 4, of the continuum sources, and the asymmetry in\nthe self-absorption as a diagnostic of relative\nmotions between core centers and envelopes.\nThe quiescent regions with low \\n2hp\\ linewidth tend to have more\nasymmetric CS spectra than the spectra around the continuum sources\nindicating higher infall speeds. These regions have typical sizes\n$\\sim 5000$~AU, linewidths $\\sim 0.5$~\\kms,\nand infall speeds $\\sim 0.05$~\\kms. The correlation of CS asymmetry with\n\\n2hp\\ velocity dispersion suggests that the inward flows of material\nthat build up pre-protostellar cores are driven at least partly by a\npressure gradient rather than by gravity alone.\nWe discuss a scenario for core formation and eventual star forming\ncollapse through the dissipation of turbulence.\n\\end{abstract}\n\n\\keywords{ISM: individual(Serpens) --- ISM: kinematics and dynamics\n --- stars: formation --- turbulence} \n\n\n%\\clearpage\n\\rightskip = 0pt\n\\section{Introduction}\nStars form through the collapse of dense cores within molecular clouds.\nThe detection and measurement of the motions associated\nwith such star forming collapse appears to be secure\n(see reviews by Evans 2000; Myers, Evans, \\& Ohashi 2000).\nThe focus has primarily been on isolated, individual\nstar forming regions since these are the least complex cases to\nunderstand both observationally and theoretically.\nHowever, the majority of stars form in clusters\n(Zinnecker, McCaughrean, \\& Wilking 1993) so a broader\nunderstanding of star formation, including such fundamental\nissues as the origin of the IMF and the formation of massive stars,\nrequires the study of how stars form in groups.\n\nRelative to an individual star,\nthe deeper potential well of a stellar cluster should imply faster,\nand possibly easier to measure, inward motions, but observations are\ncomplicated by the generally greater distance to clusters than to individual\nstar forming regions studied so far, and by the overpowering luminosity\nof massive stars that limit the ability to image\nlower mass neighbors and thus to obtain a complete view\nof cluster birth. For example, observations of the massive cluster\nforming region, W49N, have produced evidence for a global\ncollapse of material onto the cluster as a whole (Welch et al. 1987)\nand, at higher resolution, for infall onto bright individual protostars\n(Zhang \\& Ho 1997). However, it has not been possible to explore\nthe formation of more moderate mass stars in these objects\nbecause of dynamic range limitations.\n\nIn this paper, we present millimeter line and continuum observations\nof a cluster forming region in the Serpens\nmolecular cloud. This region is well suited for an exploration into\nthe formation processes of stellar clusters because it is nearby\n(d=310~pc; de Lara, Chavarria-K, \\& Lopez-Molina 1991) and contains\na moderately dense embedded cluster\n(stellar density $\\simgt 450$~pc\\eee; Eiroa \\& Casali 1992)\nwith many highly embedded millimeter wavelength continuum sources\n(Testi \\& Sargent 1998) but no O or B stars.\n%This young embedded cluster has been well studied from optical\n%to millimeter wavelengths (see, for example, recent papers by\n%Davis et al. 1999; Kaas 1999; McMullin et al. 1999).\nIn addition, Williams \\& Myers (1997) and Mardones (1998)\nhave found signatures of widespread infall motions in this region.\n\nThe combination of proximity and low mass makes it possible to\nidentify individual star forming condensations and examine the\nstructure and dynamics of the cluster on a core by core basis.\nWith this goal, we mapped the cluster in the optically thick\nCS(2--1) and thin \\n2hp(1--0) lines with the FCRAO and BIMA telescopes.\nTheir different optical depths allow us to probe cloud velocities\nfrom an outer envelope to the center (Leung \\& Brown 1977).\nThe two species are also formed by different chemical pathways with\nabundances that depend on environment and time (Bergin et al. 1997)\nand thus their relative intensities offer information on the\nphysical conditions and chemical age of the cores.\nIn an earlier paper (Williams \\& Myers 1999a) we reported the discovery\nof a starless core that appears to be collapsing based on an analysis\nof a small part of the maps. Here, we report on the full dataset\nand investigate the dynamics of the dense gas across the whole cluster.\nWe find a number of new cores, some starless, others with continuum\nsources, suggesting that new stars are continually being added to\nthe group. There are spectroscopic signatures of outflow, infall,\nand localized dissipation of turbulence throughout the cloud\nwhich offer important clues about the physical processes involved\nin cluster formation.\nThe observations are outlined in \\S2 and the data displayed in \\S3.\nAn analysis of the data follows in \\S4, and we discuss our findings\nin \\S5, concluding in \\S6.\n\n\n\\section{Observations}\n\\label{sec:obs}\nSingledish maps of \\n2hp(1--0) (93.1762650~GHz, F$_1$F$=01-12$)\nand CS(2--1) (97.980968~GHz) were made at the\nFive College Radio Astronomy Observatory\\footnotemark\n\\footnotetext{FCRAO is supported in part by the\nNational Science Foundation under grant AST9420159 and is operated\nwith permission of the Metropolitan District Commission, Commonwealth\nof Massachusetts} (FCRAO) 14~m telescope in December 1996\nusing the QUARRY 15 beam array receiver and the FAAS backend\nconsisting of 15 autocorrelation spectrometers with\n1024 channels set to an effective resolution of 24~kHz (0.06~km/s).\nThe observations were taken in frequency switching mode and, after\nfolding, 3rd order baselines were subtracted. The pointing and focus\nwere checked every 3 hours on nearby SiO maser sources.\nThe FWHM of the telescope beam is $50''$, and a map covering\n$6'\\times 8'$ was made at Nyquist ($25''$) spacing.\nQUARRY was replaced with the SEQUOIA array in late 1997.\nThis 16 element array is built with low noise MMIC based amplifiers\nand has much improved sensitivity. This enabled us to map the weak\n\\c34s(2--1) (96.412982~GHz)\nline using the same backends and observing technique in March 1998.\n\nObservations were made with the 10\nantenna Berkeley-Illinois-Maryland array\\footnotemark\n\\footnotetext{Operated by the University of California at Berkeley,\nthe University of Illinois, and the University of Maryland,\nwith support from the National Science Foundation}\n(BIMA) for two 8 hour tracks in each line during\nApril 1997 (CS; C array)\nand October/November 1997 (\\n2hp; B and C array).\nA two field mosaic was made with phase center,\n$\\alpha(2000)=18^{\\rm h}29^{\\rm m}47\\fs 5,\n~\\delta(2000)=01^\\circ 16'51\\farcs 4$, centered close to S68N,\nand a second slightly overlapping pointing at\n$\\Delta\\alpha=33\\farcs 0, \\Delta\\delta=-91\\farcs 0$,\ncentered close to SMM1.\nAmplitude and phase were calibrated using 4 minute observations of\n1751+096 (4.4~Jy) interleaved with each 22 minute integration on source.\nThe correlator was configured with two sets of 256 channels at\na bandwidth of 12.5~MHz (0.16~\\kms\\ per channel) in each sideband\nand a total continuum bandwidth of 800~MHz.\n\nThe data were calibrated and maps produced using standard procedures in\nthe MIRIAD package. The two pointings were calibrated together but\ninverted from the $uv$ plane individually to avoid aliasing since\ntheir centers are separated by more than one primary beam FWHM.\nThe FCRAO data (after first scaling to common flux units using a\ngain of 43.7~Jy~K\\e) were then combined\nwith the BIMA data using maximum entropy deconvolution. The final maps\nwere produced by linearly mosaicking the two pointings in the $xy$ plane.\nThe combination of the single dish and interferometer data\nresults in maps that are fully sampled from the map size\ndown to the resolution limit (i.e., there is no ``missing flux'').\n\nIn addition, we obtained a map of continuum emission by summing\nover the line-free channels. This map showed a number of point\nsources corresponding to warm dusty envelopes around embedded\nprotostars. A similar map was obtained, over the entire Serpens\ncomplex, using the OVRO interferometer by Testi \\& Sargent (1998).\nOur map was of lower sensitivity and in order to make a better\ncomparison, we were awarded additional time from\nFebruary to April 1999 to map the continuum at 110~GHz in a mosaic\nconsisting of 3 fields overlapping at their primary beam FWHM\nover the same region.\n\nThe resolution of the final (naturally weighted) maps was\n$8\\farcs 1\\times 5\\farcs 6$ at p.a. $+2^\\circ$ for the continuum,\n$10\\farcs 0\\times 7\\farcs 8$ at p.a. $-72^\\circ$ for CS,\nand $8\\farcs 5\\times 4\\farcs 6$ at p.a. $+2^\\circ$ for \\n2hp.\nAdditional spectral line datasets were created by restoring to a\ncommon $10''$ (3100~AU) beam for analysis and comparison.\nThe velocity resolution of these maps was 0.16~\\kms.\n\n\n\\section{Analysis}\n\\label{sec:analysis}\n\\subsection{Continuum and integrated line maps}\n\\label{subsec:continuum}\nMaps of the continuum emission and integrated CS and \\n2hp\\ line\nintensities are presented in Figure~\\ref{fig:bima}.\nThe continuum map was obtained\nfrom the 3 field mosaic at 110~GHz (see above). The rms noise level\nwas 1.0~mJy~beam\\e\\ at the center, increasing toward the map edges\n(all maps are corrected for primary beam attenuation). Seven sources\nare labeled; S68N, SMM1 (also known as S68 FIRS1), SMM5, and SMM10\nwere mapped by Casali, Eiroa, \\& Duncan (1993) and Davis et al. (1999)\nand we have labeled the three others S68Nb through S68Nd\nbecause of their proximity to S68N.\nThese seven are also present in Testi \\& Sargent (1998)\nalthough we do not confirm several other sources in their map\nfor which our data have sufficient coverage, sensitivity,\nand resolution to detect.\nSingledish observations with the 1.3~mm facility bolometer\non the IRAM 30~m telescope should clarify the issue.\n\nSource positions and fluxes are listed in Table~1.\nS68Nc may be a double or multiple source since it is highly elongated\nbut we could not distinguish more than one significant peak,\nso it is listed in Table~1 as a single source.\nSMM1, with a peak flux of 165~mJy~beam\\e,\nis considerably brighter than the other sources,\nand it proved problematic to clean the map completely of its sidelobes.\nWright et al. (1999) pointed out that systematic errors including\nincomplete $uv$ coverage, calibration uncertainties, and pointing errors,\nlimit the fidelity of a mosaicked image to the true source brightness\ndistribution to $1-2$\\% at best.\nSuch errors would lie above the level of the noise and therefore may\nbe misinterpreted as detections.\nBoth clean and maximum entropy deconvolution methods\n(with varying parameters, and source modeling and replacement)\nproduced maps that all contained the seven labeled sources\nbut also created elongated features in the vicinity of SMM1\nthat varied in position and flux from map to map.\nTherefore we have a high confidence in the labeled sources\nin Figure~\\ref{fig:bima}\nbut we believe the unlabeled features to the southwest of SMM1\nto be artifacts of the data acquisition and reduction process\nand we disregard them.\nThe problems associated with this map illustrate the difficulties\nin obtaining a complete view of cluster formation in more massive\nand luminous star forming environments.\n\nThere are also some image artifacts present in the line maps.\nThe near-zero declination of the source resulted in strong\nnorth-south sidelobes even with the 45 baselines of the BIMA\ninterferometer. As with the continuum map, these proved difficult\nto clean away completely and thus there may be some small sidelobe\ncontamination from the brighter sources in each map.\nBased on experimenting with different deconvolution procedures,\nwe estimate this uncertainty in line strengths to be $20\\%$\nin addition to the thermal noise and flux calibration uncertainties.\n\nThe \\n2hp\\ and CS maps each show several condensations but\npresent a very different appearance. The \\n2hp\\ map follows\nthe distribution of the continuum sources much more closely\nthan the CS map which features a prominent starless core to\nthe west of S68N (Williams \\& Myers 1999a). These differences\nbetween the \\n2hp\\ and CS maps are probably due to a combination of\ndifferences in optical depth, protostellar outflows, and depletion.\nAs we show below, the \\n2hp\\ emission is optically thin but\nmost CS spectra are self-absorbed and have considerable optical\ndepth. Moreover, outflow wings are prominent in the CS line\nprofiles around SMM1 and S68N, but are almost entirely absent\nfrom the \\n2hp\\ spectra at the same positions.\nFinally, the time dependent chemical models of Bergin \\& Langer (1997)\nsuggest that CS should deplete onto\ngrains prior to star forming collapse but \\n2hp\\ should remain in\nthe gas phase even at high densities during the collapse phase.\nFor these reasons, in the following subsections we determine the\nphysical properties of the cluster forming gas and individual\nstar forming cores from the \\n2hp\\ data and measure\nmotions between core envelopes and centers using the CS data.\n\n\n\\subsection{\\n2hp(1--0)}\n\\label{subsec:n2hp}\nThe hyperfine structure of the $J=1-0$ transition of \\n2hp\\ spreads out\nthe emission into seven components (Caselli, Myers, \\& Thaddeus 1995),\neach with considerably lower intensity\nthan a single component line would have, but with the benefit\nof also spreading out the optical depth so that individual\ncomponents can be optically thin even when the sum of optical\ndepths over all components might exceed unity.\nBy fitting the seven hyperfine components simultaneously,\nwe maximize the information in the data while taking advantage\nof the individual low optical depths to determine the systemic\nvelocity and linewidth of the gas.\n\nWe fit the spectra using a function of the form,\n$$T_{\\rm B}(v)=\\Bigl[J(T_{\\rm ex})-J(T_{\\rm bg})\\Bigr]\n \\Bigl\\{1-{\\rm exp}[-\\sum_i g_i\\tau(v;v_i)]\\Bigr\\},\n\\eqno(1)$$\nwhere the measured brightness temperature $T_{\\rm B}$ is a\nfunction of velocity $v$,\n$T_{\\rm ex}$ is the excitation temperature,\n$T_{\\rm bg}=2.73$~K is the cosmic background temperature,\nand the sum is over hyperfine components $i=1,2,..7$.\nFor each component, $g_i$ is the statistical weight\n(Womack, Ziurys, \\& Wyckoff 1992) normalized so $\\sum_i g_i=1$,\nand $\\tau(v;v_i)$ is the total optical depth parameterized by $v_i$,\nthe relative centroid velocity of each component (Caselli et al. 1995),\n$$\\tau(v;v_i)=\\tau_0\\,{\\rm exp}[-(v-v_i-v_0)^2/2\\sigma^2].\n\\eqno(2)$$\nHere $\\tau_0$ is the peak optical depth (summed over all components),\n$v_0$ is the systemic velocity of the gas, and $\\sigma$ is the\nvelocity dispersion.\n\nSpectra were analyzed across the map after first restoring to a\ncircular $10''$ FWHM beam and sampling on a regular $10''$ square grid.\nThe fits to the spectra require four parameters,\n$T_{\\rm ex}, \\tau_0, v_0$, and $\\sigma$, but only the velocity\nand dispersion were tightly constrained by the data.\nThe fitted excitation temperature and optical depth are determined\nfrom the intensities of the 7 hyperfine components but the two are inversely\ncorrelated resulting in a wide range of pairs that fit any given peak with\nonly small changes in line shape that are indistinguishable given the\nmoderate signal-to-noise ratios in the data. Moreover, there appear to\nbe significant excitation anomalies analogous to the very low noise\nspectrum in Caselli et al. (1995). Because of the large uncertainties\nin $T_{\\rm ex}$ and $\\tau$, we do not discuss them further.\n\nWe also made three component, optically thin, gaussian fits,\n$T_{\\rm B}(v)=T_0\\sum_i g_i\\, {\\rm exp}[-(v-v_i-v_0)^2/2\\sigma^2]$,\nto the data. In most cases, the residuals were not significantly greater\nthan the four parameter fit demonstrating the degeneracy in\n$T_{\\rm ex}$ and $\\tau$. We also checked our fits with the hyperfine\nstructure fitting routine in the CLASS data reduction package. All 3\nmethods show good agreement in the velocity and dispersion.\n\nBy adding synthetic noise to very low noise \\n2hp\\ spectra\nwe tested the effect of varying signal-to-noise ratios on\nthe fits. The systemic velocity could be accurately determined\neven in very noisy spectra but the fitted linewidth systematically\nincreased as the signal-to-noise ratio decreased. The effect was\nnoticeable for peak ratios less than 10, and became severe for ratios\nless than 5. In the following analysis, only spectra with peak\nsignal-to-noise ratios greater than 5 are fit. For these spectra,\nwe derived $v_0$, and $\\sigma$ using the method described\nby equations (1) and (2). \n\nThe systemic velocity varies from 7.9 to 9.3~\\kms\\\nand away from the outflow around S68N (see \\S\\ref{subsec:cs})\nthere are no strong gradients.\nThe dispersion displayed a more interesting variation.\nFigure~\\ref{fig:sig_nt} plots the non-thermal velocity dispersion,\n$\\sigma_{\\rm NT}=[\\sigma^2-\\sigma_{\\rm T}^2]^{1/2}$,\nwhere $\\sigma_{\\rm T}=0.075$~\\kms\\ is the thermal velocity\ndispersion for \\n2hp\\ at $T_{\\rm kin}=20$~K (Wolf-Chase et al. 1998).\nThe greatest values, $\\sigma_{\\rm NT}>0.6$~\\kms\\ occur in the cores\ncontaining the S68N and SMM1 sources which both power strong outflows.\nThe minimum $\\sigma_{\\rm NT}$ is 0.16~\\kms\\ which is more than\ntwice $\\sigma_{\\rm T}$ and shows that internal motions\nin the cores are predominantly turbulent.\nHowever, there are a number of regions where the turbulent\nvelocity field drops to a local, confined, minimum.\nWe identify eight such regions and label them Q1 through Q8 (for quiescent).\n\nThree of the quiescent regions, Q1, Q2, and Q8, are coincident with\npeaks of integrated \\n2hp\\ intensity but the other five are not.\nNote that even in the low intensity regions, the signal-to-noise\nratio is strong enough to determine the dispersion quite accurately\nand that any bias would tend to {\\it increase} the dispersion.\nThe quiescent regions are not prominent in the map of integrated\nintensity because their linewidth is small.\nIndeed, our analysis of the data suggests to us that these\nquiescent ``cores'' are of greater interest than the cores of high\nintegrated intensity.\n\nThe eight quiescent cores tend to have higher peak temperatures than\ntheir immediate surroundings and are especially prominent in\nFigure~\\ref{fig:peaksig} which plots the peak \\n2hp\\ temperature divided\nby the total velocity dispersion. This is a measure of the optical depth\n(which was not well determined from the hyperfine fitting) and it rises\ntoward the quiescent cores which possess both relatively low dispersion\nand high peak temperatures.\n\nThe quiescent core Q2 is almost coincident with the continuum\nsource S68Nb and Q5 extends to encompass S68Nd but the\nother quiescent cores are apparently starless.\nQ6 lies $13''$ southeast of the strong CS core\nS68NW that was discussed in Williams \\& Myers (1999a).\nTable~2 lists the quiescent core locations, non-thermal velocity\ndispersion and the ratio of (thermal plus non-thermal) velocity\ndispersion as the data are smoothed from $10''$ to $50''$.\nThis ratio is discussed later in \\S\\ref{sec:turb} in the context\nof pressure gradients.\nSpectra toward the core centers at $15''$ and $50''$ resolution\nare shown in Figure~\\ref{fig:qspec_n2hp}.\nThe $15''$ spectra are slightly smoothed from the highest available\nresolution so as to achieve a higher signal-to-noise ratio and more\nclearly show fine features in the spectral profiles.\nThe lines are narrower and brighter at higher resolution and\nresemble the ``kernels'' in cluster forming cores described\nin Myers (1998). We discuss this point further in \\S\\ref{sec:turb}.\nThe red shoulders in Q1, Q5, and Q8 are also apparent in the other\nhyperfine components and may simply be velocity structure or possibly\nself-absorption. None of the quiescent core spectra show blue shoulders\nfrom high velocity infall.\n\nThe concomitant decrease in velocity dispersion and increase\nin optical depth as measured by the peak temperature divided by\nthe dispersion suggests that the quiescent cores have condensed\nout of the larger scale cluster forming cloud through\na localized reduction in turbulent pressure support.\nThe dissipation of turbulence as a means of core formation\nhas been alluded to previously but has only recently been\ndiscussed explicitly by Nakano (1998) and Myers \\& Lazarian (1998).\nA decrease in pressure support should result in an inward flow\nof material. The search for such a flow is the subject of the\nfollowing subsection.\n\n\n\\subsection{CS(2--1)}\n\\label{subsec:cs}\nA map of CS and \\c34s(2--1) spectra from FCRAO observations\nis shown in Figure~\\ref{fig:fcrao}.\nSince these two species share very similar chemical pathways, the\ndifferences in profiles are primarily due to their different optical depths.\nThe ratio of peak CS to \\c34s\\ temperatures ranges from of 4--8 indicating\nmoderate CS optical depths $\\tau\\simeq 1-3$ (Williams \\& Myers 1999b).\nWhereas the \\c34s\\ spectra present a single peak and are approximately\ngaussian, the CS spectra have low-level line wing emission and are\ngenerally double-peaked. The line wings are due to outflows from\nseveral cluster members, as we show below, and the two peaks result\nfrom self-absorption since the \\c34s\\ emission peaks at the dip\nof the CS spectra. Self-absorbed spectra from a static core\nwould be symmetric but here they are clearly asymmetric.\nWe use the asymmetries in the self-absorption to probe the\nvelocity differences between outer and inner regions of the cores,\nand thereby search for inward motions (e.g. Zhou 1995).\nA blue (low velocity) peak that is brighter than the red (high velocity)\nindicates that the (outer) absorbing layer is relatively red-shifted,\ni.e., infalling, whereas the opposite asymmetry implies outward motions.\nThe greater the blue-red difference, the greater the relative motions\nbetween the inner and outer regions of the core (Myers et al. 1996).\n\nThere is a preponderance of spectra with infall-type asymmetry\nand only a few spectra around S68N with the opposite symmetry\nin Figure~\\ref{fig:fcrao}. Moreover, the average spectrum over the cluster\n(not shown) is self-absorbed with a brighter blue than red peak.\nThis suggests that there is large scale contraction of the gas\naround the cluster.\nThe size of the contracting region is greater than 0.2~pc in diameter\nand extends well beyond the continuum sources.\nExtended asymmetrical self-absorption in this source in the\n$2_{12}-1_{10}$ line of H$_2$CO is also discussed in Mardones (1998).\nWe have observed a similarly sized infalling region in CS(2--1)\nin the Cepheus A cluster forming region (Williams \\& Myers 1999b).\nAt $50''$, the resolution of these data is too coarse to isolate the\ndynamics of individual cores but the addition of the interferometer\nmaps allows us to follow infall and outflow motions down to the scale of\nthe individual protostellar cores.\n\nThe Serpens cloud is known to contain a number of molecular outflows\n(White, Casali, \\& Eiroa 1995; Davis et al. 1999).\nFigure~\\ref{fig:outflows} maps the blue- and red-shifted emission\nfor the BIMA data only.\nBy analyzing the data prior to combining with the FCRAO data, the bulk of\nthe mostly uniform cloud emission is resolved out and small scale features,\nsuch as outflows, stand out. The resulting map shows outflows around\nS68N, SMM1, SMM10, and possibly S68Nb. The existence of an outflow\nfrom S68Nb is uncertain because of confusion with the extensive red\nlobe around S68N.\n\nCS spectra toward the quiescent cores and continuum sources are plotted\nin Figure~\\ref{fig:qspec_cs}. Here, we use the combined FCRAO/BIMA\ndataset since it is essential that all there be no missing flux if we\nare to interpret the spectra correctly.\nSpectra are centered on the position of minimum \\n2hp\\ linewidth\nfor the quiescent cores or the continuum source otherwise,\nand are at a slightly smoothed $15''$ resolution.\nThere are approximately symmetric line wings from the\nS68N, SMM1, and SMM10 outflows, a blue line wing from the\npossible outflow around Q2/S68Nb, and weak one-sided wings\nfrom the red lobe of the S68N outflow around Q5/S68Nd and Q7.\nThe \\n2hp\\ velocity and FWHM linewidth are indicated by the solid\nvertical line and shading respectively (spectra are shown in\nFigure~\\ref{fig:qspec_n2hp}).\nThe \\n2hp\\ velocity lies at the dip of the double-peaked\nCS spectra as for the \\c34s\\ spectra in Figure~\\ref{fig:fcrao}\nexcept for Q8.\n\nThe Q8 core, with the narrowest \\n2hp\\ linewidth in the map,\nlies at the edge of the cluster and is uncontaminated by CS outflow\nwings. The CS spectra around the core all have the classic\ninfall profile, but at the position of the linewidth minimum\nthe \\n2hp\\ velocity lines up with the blue CS peak and not the dip\nas would be expected for self-absorption. Given that all the other\ndouble-peaked spectra in the map are self-absorbed it seems unlikely\nthat the double-peaked spectra in this region are not also\nself-absorbed. However, the central \\n2hp\\ spectrum in\nFigure~\\ref{fig:qspec_n2hp} shows a second, red, peak at $15''$\nand a red shoulder at $50''$ and it may be that the \\n2hp\\ is also\nself-absorbed here.\nThe low resolution \\c34s\\ data in Figure~\\ref{fig:fcrao}\ndemonstrates that the CS spectra are self-absorbed in this region but\nto settle the issue in the Q8 core itself, sensitive higher resolution\nobservations of \\c34s\\ are necessary.\n\nAside from the uncertainty over the interpretation of the Q8 core,\nFigure~\\ref{fig:qspec_cs} shows an overall trend for the\nCS infall asymmetry to be greatest in those cores\nwith small \\n2hp\\ linewidths. That is, the CS spectra toward\nthe quiescent cores all have a greater blue\nthan red peak indicating a positive infall velocity,\nbut cores S68Nc, SMM10, and SMM1 present a very symmetric\nappearance indicating near-zero infall.\nThe extended red CS outflow lobe from S68N in Figure~\\ref{fig:outflows}\nmakes it difficult to isolate the Q5/S68Nd and Q7 cores and\nstudy their dynamics individually in this line, even though they\nare well separated in the \\n2hp\\ map.\nIt is particularly difficult to diagnose infall motions around\nS68N itself where the infall asymmetry abruptly reverses from one\nposition to another $10''$ away. Nevertheless, Figure~\\ref{fig:qspec_cs}\nsuggests a connection between the level of core turbulence and\nthe asymmetry of the CS profiles, in turn related to the infall speed.\nWe explore this in more detail in the following section.\n\n\n\\section{Pressure driven flows and turbulent dissipation}\n\\label{sec:turb}\nThe singledish spectra in Figure~\\ref{fig:fcrao} suggests\na global infall onto the cluster but the addition\nof the interferometer data allows a higher resolution view that\nreveal a wide range of spectral asymmetries\nthat present a patchwork of inward and outward flows.\nThe size of the region over which infall motions are observed\nis large, $\\sim 0.2$~pc in diameter, at least partly because\nthe cluster contains a number of collapsing cores.\nThe ($\\sim 3000$~AU) resolution of the combined dataset separates\nout the individual protostars and protostellar cores from each other,\nand permits an analysis of how the small scale inward and outward\nmotions are related to the local environment.\n\nDetailed modeling of line profiles enable the infall speed to\nbe determined (e.g., Zhou 1995; Williams et al. 1999)\nin isolated, low mass star forming cores\nbut there is a much greater range of spectral shapes in the CS data here.\nFor example, many are contaminated by outflows, either internal or\noverlapping from neighboring sources. Thus the modeling requires\nseveral additional parameters with the result that the uncertainty in\nthe determination of the infall speed at each point is large.\nTherefore, rather than try to fit the spectra directly,\nwe estimated the location of the main features\nin the CS spectra by eye using a simple cursor based routine.\nThis resulted in a catalog of positions and velocities where the CS\nspectra have local peaks and dips.\n\nThe simplest estimate of the CS spectral asymmetry is the difference in\nblue and red peak temperatures, $\\dtbr=T_{\\rm blue}-T_{\\rm red}$.\nWe consider the difference, rather than the\nratio of peak temperatures since it is determined with a smaller error.\nThis is obviously only defined for double-peaked spectra and we therefore\nexclude spectra with possible infall ``shoulders''.\nA second measure of asymmetry that has the advantage of being defined\nfor all spectral shapes is the velocity difference between the peak\nCS and \\n2hp\\ velocities. This is the unnormalized\n$\\delta v$ parameter introduced by Mardones et al. (1997).\nBased on simulations with simple two-layer infall models (Myers et al. 1996),\nwe find that the blue-red temperature difference correlates linearly\nwith the infall speed for a given optical depth and excitation temperature\nand that the scatter when a range of optical depths $\\tau=2-5$\nand excitation temperatures $T_{\\rm ex}=15-25$~K\nis considered is relatively small.\nThe velocity difference also correlates linearly with infall speed\nbut is more sensitive to optical depth variations.\nConsequently we use \\dtbr\\ as a measure of infall\nspeed and analyze its distribution across the cluster.\n\nTo test the hypothesis made in the previous section\nthat the CS asymmetries are large where\nthe \\n2hp\\ velocity dispersion is small, we simply plot \\dtbr\\\nagainst $\\sigma_{\\rm NT}(\\n2hp)$ in Figure~\\ref{fig:deltat}.\nThe points are very scattered and there is no significant correlation\nbetween the two quantities. However, when binned by $\\sigma_{\\rm NT}$, the\naverage \\dtbr\\ is greater than zero (implying a positive infall velocity).\nMoreover, $\\dtbr >0$~K for {\\it all} spectra with $\\sigma_{\\rm NT}<0.23$~\\kms.\nThe lack of direct correlation is because several different dynamical\nstates have been grouped together. By selecting individual regions,\nwe can isolate the different states.\n\nFigure~\\ref{fig:radial} plots the variation of CS asymmetry and \\n2hp\\\nvelocity dispersion against the distance from the center of a core\nfor two quiescent cores and two continuum sources.\nA similar behavior is found in the other cores:\nthe velocity dispersion tends to increase and the blue-red\ntemperature difference generally decreases with increasing\nradius from the center of the quiescent cores and vice versa\nfor the continuum sources.\nMoreover, the temperature difference is positive at the\ncenters of the quiescent cores but is small or negative\n(i.e., outflow) at the centers of the continuum cores.\n\nThe slopes of the least squares fits, or the radial gradients, of the\nCS blue-red temperature difference and \\n2hp\\ non-thermal velocity\ndispersion are tabulated in Table~3\nand plotted against each other in Figure~\\ref{fig:radgrad}.\nGenerally, the quiescent cores lie toward the lower right section\n(increasing \\n2hp\\ dispersion and decreasing CS asymmetry with radius)\nand the continuum sources lie in the upper right section\n(decreasing \\n2hp\\ dispersion and increasing CS asymmetry with radius).\nFor a constant density, a change in velocity dispersion implies\na change in pressure which results in a flow toward the lower\npressure (i.e., lower dispersion) regions.\nThe conversion from CS asymmetry to infall speed\ndepends not only on the blue-red temperature difference but also\nthe excitation temperature and optical depth. If these do not vary\ngreatly from core envelope to center then the observed increase in\n\\dtbr\\ as $\\sigma_{\\rm NT}$ decreases toward the centers of the\nquiescent cores implies an increase in infall speed.\n\nSince the pressure depends linearly on the density and quadratically\non the velocity dispersion, and since the infall speed is more\nsensitive to the blue-red temperature difference than the excitation\ntemperature and optical depth, the inverse correlation of \\dtbr\\\nwith $\\sigma_{\\rm NT}$ in Figure~\\ref{fig:radgrad}\nis evidence for pressure driven, inward, flows in the quiescent cores.\nThe correlation also extends to negative dispersion gradients and outflow\nmotions around the continuum sources illustrating the disruptive effect\nof young protostars on their parent cloud.\nFinally, we note that a fit through the\ndata points suggests a slightly negative CS asymmetry gradient\nat $d\\sigma_{\\rm NT}/dr=0$ which may indicate small, presumably\ngravitational, inward motions even when the pressure gradient is zero.\n\nUsing the two-layer model of Myers et al. (1996), we find that\nthe infall speed corresponding to a typical value, $\\dtbr =1$~K,\nfor $\\sigma_{\\rm NT}=0.3$~\\kms\\ is $v_{\\rm in}\\simeq 0.05$~\\kms.\nThis is quite small and similar to that expected for the quasistatic\ncontraction of a magnetically supported, isothermal core (Lizano \\& Shu 1989).\nHowever, the nature of the flow is very different \nfrom the predictions of such ambipolar diffusion models:\nall the cores, whether with or without continuum sources,\nhave highly non-thermal linewidths and the infall speed is\ngreatest in those cores with the smallest linewidths.\nThis inverse correlation is not expected in a purely gravitational\ncollapse and is more suggestive of a pressure driven flow.\nNakano (1998) and Myers \\& Lazarian (1998) describe how\ninward flows onto a core can occur through the dissipation\nof turbulence and consequent loss of pressure support.\nAs a core grows and its center becomes more opaque to ionizing\nradiation, its coupling to the magnetic field, and the range of\nMHD waves that propagate through it, decrease.\nWithout replenishment, the waves decay within a free-fall time\nand the turbulent pressure, $\\rho\\sigma_{\\rm NT}^2$, rapidly decreases\n(where $\\rho$ is the mass density).\nSince wave support is maintained in the lower opacity,\nmore highly ionized, core envelope, its pressure remains the same\nwith the result that there is a pressure gradient, leading to a flow,\nfrom core envelope to center. The magnitude of the flow\nwill be greatest where the pressure gradient is greatest,\nor equivalently where the central linewidths are smallest\nif the external pressure is approximately constant.\n\nThe magnitude of the inward speed depends on the pressure\ndifference between core center and envelope.\nThe observed inward motions are small, $v_{\\rm in}\\ll\\sigma_{\\rm NT}$,\nand therefore the pressure differences are small.\nSince the total (thermal plus non-thermal) velocity dispersion\nat $10''$ is a factor of $0.36-0.75$ less than at $50''$ (Table 2),\nthe density contrast between core centers and envelopes\nis inferred to lie in the range $2-8$.\nThis is comparable to the ratio of peak to average density for cores\nin the Ophiuchus cluster forming cloud (Motte, Andr\\'{e}, \\& Neri 1998).\n\nAs the core grows, the opacity increases further until the\nionization is dominated by cosmic rays ($A_V\\simeq 4$; McKee 1989).\nIn this case, Myers (1998) predicts the existence of ``kernels'',\n$\\sim 6000$~AU, in size that are completely cutoff from MHD waves.\nIf the external pressure is sufficiently large, as in massive\nstar forming regions, these kernels can be stable, supported\nby thermal pressure against their self-gravity.\nThe criterion for stability (Myers 1998 equation 3)\ncan be rewritten as $\\sigma_{\\rm NT}/\\sigma_{\\rm T}=1.5$\nwhich is satisfied in all the cores here where we have found\n$\\sigma_{\\rm NT}/\\sigma_{\\rm T}>2.1$.\nThe quiescent cores extend over $10''-20''$, which is close\nto the expected size of a kernel, and their velocity FWHM\nare $\\sim 0.5$~\\kms\\ similar to Myers' Figure~2, but there is\ninsufficient signal-to-noise to discern the predicted thermal ``spike''.\nThere are possible examples in the residuals\nto the hyperfine fits to the spectra but they are not consistent\nacross all the components and may be due to poorly cleaned sidelobes\nfrom other cores (the cleaning method is non-linear and varies\nin its effectiveness from channel to channel).\nHigh spatial and velocity resolution singledish observations of\nhigher transition lines such as \\n2hp(3--2) offer an independent\ntest for the presence of a thermal spike and may also be used to\nconstrain the density contrast in the cores.\n\nThe maps in Figures~\\ref{fig:bima},\\ref{fig:sig_nt}\nreveal a number of protostars and pre-protostellar collapsing cores.\nThe cluster did not form in a single event, therefore, but continues to\naccrue members through an ongoing process of individual star formation.\nHurt \\& Barsony (1996) analyzed the spectral energy distribution (SED)\nof several of the bright sources in this cluster and concluded that they\nwere Class 0 protostars. The IRAS data does not have the resolution to\nresolve the emission (and therefore to define their SED in the far-infrared)\nfrom the seven continuum sources that we have identified here\nbut if, following Hurt \\& Barsony, we divide up the IRAS fluxes\nevenly between all the objects, all seven would be classified as Class 0.\n\nThe discovery of the quiescent cores, and their association with\nhigh infall motions, suggests that they are the precursors to the \nClass 0 sources. Within the boundaries of the maps here, and at the\nsensitivity of the observations, we have found approximately equal\nnumbers of continuum sources and quiescent cores (7 and 8 respectively,\nwith 2 shared). If stars continue to form at a constant rate, then\nthe lifetime of the quiescent cores must be approximately the same\nas the lifetime of the Class 0 phase of protostellar evolution,\n$\\sim 3\\times 10^4$~yr (Andr\\'{e} \\& Montmerle 1994).\nSuch a short lifetime implies a dynamic evolution since\nthe free-fall timescale,\n$t_{\\rm ff}=(G\\rho)^{-1/2}\\simeq 6\\times 10^4$~yr,\nfor $\\nh2=10^6$~\\cc, approximately equal to the inferred\nvolume density of the quiescent cores and a factor of two greater\nthan the critical density of \\n2hp.\nThis rapid evolution is consistent with core growth through the decay\nof turbulence since this should occur on a free-fall timescale (Nakano 1998).\n\n\n\\section{Summary}\nThis paper presents millimeter wavelength continuum and spectral line\nobservations of a young, embedded, low mass cluster forming region\nin the Serpens molecular cloud. 7 continuum sources are found at the \nresolution and sensitivity of these data. The distribution of these\nsources corresponds well with the \\n2hp\\ emission but\nthe CS data presents a different appearance, with high velocity\nemission from outflows around 4 continuum sources, and central\ndips in spectral profiles from self-absorption (as shown on the\nlarge scale from singledish \\c34s\\ data and on the small scale\nfrom the \\n2hp). Away from the powerful outflow around S68N, the\nself-absorption is red-shifted which we interpret as indicating\ninward motions.\n\nThe \\n2hp\\ linewidth is dominated by non-thermal motions throughout\nthe cluster. However, there are 8 regions where the non-thermal velocity\ndispersion reaches a local minimum. 6 are starless and 2 contain continuum\nsources. They do not all coincide with peaks of the integrated intensity\nbut they all stand out in maps of the peak temperature divided by the\ndispersion, a measure of the optical depth.\nThe CS spectra toward these ``quiescent'' cores are particularly\nasymmetric, indicating relatively high infall speeds.\nGenerally, the \\n2hp\\ dispersion increases and the CS blue-red temperature\ndifference decreases with increasing distance from the core centers, and\nvice versa for the continuum sources. The correlation of CS asymmetry,\nrelated to infall speed, with \\n2hp\\ dispersion, related to the local\nturbulent pressure, suggests that the inward flows are at least partly\npressure driven and that the cores formed through the localized dissipation\nof turbulence as envisioned by Nakano (1998) and Myers \\& Lazarian (1998).\nSuch a scenario is consistent with the observed numbers of quiescent\ncores and Class 0 sources.\n\nThe singledish data alone shows a net inward motion onto the cluster.\nAlthough there is clearly considerable smearing of the detailed dynamics,\nthis suggests that it may be fruitful to search for infall signatures\nin more distant clusters at $\\sim 0.1-0.2$~pc resolution.\nIt will, of course, be important to observe other nearby cluster\nforming regions at higher resolution, $\\simlt 3000$~AU, to augment\nthis study. Ultimately, the comparison of conditions in many\nclusters will give a clearer picture of their formation,\nshow the effects of different environments, and, through an inventory\nof continuum sources and pre-protostellar cores, can be hoped to elucidate\nthe origins of the stellar IMF (Motte et al. 1998; Testi \\& Sargent 1998).\n\n\n\\acknowledgments\nJPW is supported by a Jansky fellowship. Partial support has also been\nprovided by the NASA Origins of Solar Systems Program, grant NAGW-3401.\nWe thank Leo Blitz and Dick Plambeck for generously assigning additional\nBIMA tracks to remap the continuum emission and Marc Pound and\nTamara Helfer for advice concerning the data reduction.\n\n\n%\\clearpage\n% ------------------------ REFERENCES --------------------\n\\begin{references}\n\\baselineskip=10pt\n\n\\reference{} Andr\\'{e}, P. \\& Montmerle, T. 1994, \\apj, 420, 837\n\n\\reference{} Bergin, E.A., Goldsmith, P.F., Snell, R.L., \\& Langer, W.D.\n 1997, \\apj, 482, 285\n\n\\reference{} Bergin, E.A., \\& Langer, W.D. 1997, \\apj, 486, 316\n\n\\reference{} Casali, M.M., Eiroa, C., \\& Duncan, W.D. 1993, \\aap, 275, 195\n\n\\reference{} Caselli, P., Myers P.C., \\& Thaddeus, P. 1995, \\apj, 455, L77\n\n%\\reference{} Curiel, S., Rodriguez, L.F., G\\'{o}mez, J.F.,\n% Torrelles, J.M., Ho, P.T.P., Eiroa, C. 1996, \\apj, 456, 677\n\n\\reference{} Davis, C.J., Matthews, H.E., Ray, T.P., Dent, W.R.F.,\n \\& Richer, J.S. 1999, \\mnras, in press\n\n\\reference{} Eiroa, C., \\& Casali M.M. 1992, \\aap, 262, 468\n\n\\reference{} Evans, N.J.II 2000, \\araa, in press\n\n\\reference{} Hurt, R.L., \\& Barsony, M. 1996, \\apj, 460, L45\n\n\\reference{} de Lara, E., Chavarria-K, C., \\& Lopez-Molina, G. 1991,\n \\aap, 243, 139\n\n\\reference{} Leung, C.M., \\& Brown, R.B. 1977, \\apj, 214, L73\n\n\\reference{} Lizano, S., \\& Shu, F.H. 1989, \\apj, 342, 834\n\n%\\reference{} Kaas, A.A. 1999, \\aj, 1999, in press\n\n\\reference{} Mardones, D., Myers, P.C., Tafalla, M., Wilner, D.J.,\n Bachiller, R., \\& Garay, G. 1997, \\apj, 489, 719\n\n\\reference{} Mardones, D. 1998, Ph.D. Thesis, Harvard University\n\n\\reference{} McKee, C.F. 1989, \\apj, 345, 782\n\n%\\reference{} McMullin, J.P., Mundy, L.G., Blake, G.A., Wilking, B.A.,\n% Mangum, J.G., \\& Latter, W.B. 1999, \\apj, in press\n\n\\reference{} Motte, F., Andr\\'{e}, Ph., \\& Neri, R. 1998, \\aap, 336, 150\n\n\\reference{} Myers, P.C., Evans, N.J.II, \\& Ohashi, N. 2000,\n in ``Protostars and Planets IV'',\n ed. V. Mannings, A.P. Boss \\& S.S. Russell\n (Tucson: University of Arizona Press), in press\n\n\\reference{} Myers, P.C., \\& Lazarian, A. 1999, \\apj, 507, L157\n\n\\reference{} Myers, P.C. 1998, \\apj, 496, L109\n\n\\reference{} Myers, P.C., Mardones, D., Tafalla, M., Williams, J.P.,\n Wilner, D.J. 1996, \\apj, 465, L133\n\n\\reference{} Nakano, T. 1998, \\apj, 494, 587\n\n%\\reference{} Rudolph, A., Welch, W.J., Palmer, P., \\& Dubrulle, B. 1990,\n% \\apj, 363, 528\n\n%\\reference{} Shu, F.H. 1977, \\apj, 214, 488\n\n\\reference{} Testi, L., \\& Sargent, A.I. 1998, \\apj, 508, L91\n\n\\reference{} Ungerechts, H., Bergin, E.A., Goldsmith, P.F., Irvine, W.M.,\n Schloerb, F.P., \\& Snell, R. L. 1997, \\apj, 482, 245\n\n%\\reference{} Ungerechts, H., \\& G\\\"{u}sten, R. 1984, \\aap, 131, 177\n\n\\reference{} Welch, W.J., Jackson, J.M., Dreher, J.W., Terebey, S.,\n \\& Vogel, S.N 1987, Science, 238, 1550\n\n\\reference{} White, G.J., Casali, M.M., \\& Eiroa, C. 1995, \\aap, 298, 594\n\n\\reference{} Williams, J.P., \\& Myers, P.C. 1999a, \\apj, 518, L37\n\n\\reference{} Williams, J.P., \\& Myers, P.C. 1999b, \\apj, 511, 208\n\n\\reference{} Williams, J.P., Myers, P.C., Wilner, D.J., \\& Di Francesco, J.\n 1999, \\apj, 513, L61\n\n\\reference{} Williams, J.P., \\& Myers, P.C. 1997,\n in ``Star Formation, Near and Far'',\n AIP Conference Proceedings 393, eds. S.S. Holt and L.G. Mundy, 387\n\n\\reference{} Wolf-Chase, G.A., Barsony, M., Wootten, H.A, Ward-Thompson, D.,\n Lowrance, P.J., Kastner, J.H., \\& McMullin, J.P. 1998, 501, L193\n\n\\reference{} Womack, M., Ziurys, L.M., \\& Wyckoff, S. 1992, \\apj, 387, 417\n\n\\reference{} Wright, M.C.H., Dickel, J., Koralesky, B., \\& Rudnick, L.\n 1999, \\apj, 518, 284\n\n\\reference{} Zhang, Q., \\& Ho, P.T.P. 1997, \\apj, 488, 241\n\n\\reference{} Zhou S. 1995, \\apj, 442, 685\n\n\\reference{} Zinnecker, H., McCaughrean, M.J., \\& Wilking, B.A. 1993,\n in Protostars and Planets III, eds. E. Levy, J.I. Lunine,\n \\& M.S. Matthews (Tucson: U. of Arizona Press), 429\n\n\\end{references}\n\n\\clearpage\n% ------------------------ END REFERENCES --------------------\n\n\n% ------------------------ TABLES --------------------\n\\begin{table}\n\\begin{center}\nTABLE 1\\\\\nContinuum Sources\\\\\n\\vskip 2mm\n\\begin{tabular}{lrrrr}\n\\hline\\\\[-2mm]\nSource & $\\Delta\\alpha^{\\rm a}$ & $\\Delta\\delta^{\\rm a}$\n & Flux density & Peak \\\\\n & ($''$) & ($''$) & (mJy) & (mJy~beam$^{-1}$)\\\\[1mm]\n\\hline\\hline\\\\[-3mm]\nSMM1 & 34.1 & --91.0 & 233.7 & 164.7 \\\\\nS68N & 9.0 & --7.8 & 36.1 & 20.2 \\\\\nS68Nd & 23.0 & --28.9 & 32.3 & 15.6 \\\\\nSMM10 & 66.9 & --60.4 & 25.3 & 22.1 \\\\\nSMM5 & 56.4 & --11.7 & 20.7 & 13.7 \\\\\nS68Nc$^{\\rm b}$ & 18.7 & 7.5 & 20.4 & 12.1 \\\\\nS68Nb & 30.6 & 19.4 & 17.7 & 15.1 \\\\[2mm]\n\\hline\\\\[-2mm]\n\\multicolumn{5}{l}{$^{\\rm a}$ location of peak relative to}\\\\\n\\multicolumn{5}{l}{$^{\\rm ~}$\n$\\alpha(2000)=18^{\\rm h}29^{\\rm m}47\\fs 5,\n\\delta(2000)=01^\\circ 16'51\\farcs 4$}\\\\\n\\multicolumn{5}{l}{$^{\\rm b}$ possibly multiple sources}\\\\\n\\end{tabular}\n\\end{center}\n\\label{tab:continuum}\n\\end{table}\n\n\\begin{table}\n\\begin{center}\nTABLE 2\\\\\nQuiescent Cores\\\\\n\\vskip 2mm\n\\begin{tabular}{lrrcccc}\n\\hline\\\\[-2mm]\nCore & $\\Delta\\alpha^{\\rm a}$ & $\\Delta\\delta^{\\rm a}$\n & $v_{\\rm LSR}$ & $\\sigma_{\\rm NT}$ ($10''$)\n & ${\\sigma_{\\rm tot}(10'')\\over\\sigma_{\\rm tot}(50'')}$\n & ${T_{\\rm peak}(10'')\\over T_{\\rm peak}(50'')}$ \\\\\n & ($''$) & ($''$) & (km s$^{-1}$) & (km s$^{-1}$) & & \\\\[1mm]\n\\hline\\hline\\\\[-3mm]\n Q1 & 17.4 & 39.0 & 8.482 & 0.17 & 0.52 & 2.9 \\\\\n Q2 & 28.2 & 18.6 & 8.757 & 0.20 & 0.68 & 1.7 \\\\\n Q3 & 41.4 & --1.8 & 8.514 & 0.19 & 0.68 & 1.6 \\\\\n Q4 & 43.8 & --18.6 & 8.353 & 0.21 & 0.69 & 1.4 \\\\\n Q5 & 15.0 & --35.4 & 8.189 & 0.23 & 0.52 & 1.2 \\\\\n Q6 & --42.6 & --29.4 & 8.601 & 0.24 & 0.75 & 1.6 \\\\\n Q7 & 10.2 & --66.6 & 8.311 & 0.20 & 0.52 & 1.1 \\\\\n Q8 & 83.4 & -91.8 & 7.964 & 0.16 & 0.36 & 1.9 \\\\[2mm]\n\\hline\\\\[-2mm]\n\\multicolumn{7}{l}{$^{\\rm a}$\nlocation of minimum $\\sigma_{\\rm NT}$ relative to}\\\\\n\\multicolumn{7}{l}{$^{\\rm ~}$\n$\\alpha(2000)=18^{\\rm h}29^{\\rm m}47\\fs 5,\n\\delta(2000)=01^\\circ 16'51\\farcs 4$}\\\\\n\\end{tabular}\n\\end{center}\n\\label{tab:quiescent}\n\\end{table}\n\\clearpage\n\n\\begin{table}\n\\begin{center}\nTABLE 3\\\\\nRadial Gradients\\\\\n\\vskip 2mm\n\\begin{tabular}{lrrrr}\n\\hline\\\\[-2mm]\nCore & $d\\Delta T_{\\rm b-r}/dr$ & err\n & $d\\sigma_{\\rm NT}/dr$ & err \\\\\n & \\multicolumn{2}{c}{(K pc$^{-1}$)}\n & \\multicolumn{2}{c}{(km s$^{-1}$ pc$^{-1}$)} \\\\[1mm]\n\\hline\\hline\\\\[-3mm]\nQ1 & --12.2 & 9.7 & --0.36 & 2.43 \\\\\nQ2/S68Nb & --11.1 & 18.5 & 5.52 & 2.74 \\\\\nQ3 & --32.2 & 16.7 & 5.02 & 1.67 \\\\\nQ4 & --23.7 & 17.3 & 4.87 & 1.38 \\\\\nQ5/S68Nd & --10.2 & 15.1 & 0.13 & 2.17 \\\\\nQ6 & --49.4 & 20.2 & 6.69 & 2.97 \\\\\nQ7 & --22.1 & 7.8 & 3.87 & 1.39 \\\\\nQ8 & --19.5 & 8.0 & 9.05 & 1.69 \\\\\nSMM1 & 4.0 & 7.1 & --2.71 & 1.51 \\\\\nS68N & 62.7 & 16.6 & --7.46 & 2.68 \\\\\nSMM10 & 28.8 & 7.2 & --3.32 & 1.51 \\\\\nSMM5 & --11.9 & 8.3 & 0.07 & 1.09 \\\\\nS68Nc & 7.4 & 10.2 & --1.54 & 2.27 \\\\[2mm]\n\\hline\\\\[-2mm]\n\\end{tabular}\n\\end{center}\n\\label{tab:radial}\n\\end{table}\n\\clearpage\n\n\n% ------------------------ FIGURES --------------------\n\\begin{figure}[htpb]\n\\vskip 0.0in\n\\centerline{\\psfig{figure=bima.ps,height=2.8in,angle=-90,silent=1}}\n\\vskip 0.0in\n\\figcaption[f1.ps]{Continuum and line emission in the Serpens cluster.\nThe left panel shows the continuum emission at 110~GHz in\na logarithmic greyscale ranging from 5 to 200~mJy~beam\\e,\nand contours at 7, 9, 11, 15, 20, 30, 50~mJy~beam\\e\\\n(dotted contours are their negative counterparts).\nThe seven labeled sources (other objects are believed to\nbe artifacts; see text) are indicated in the two other\npanels by the star-shaped symbols.\nThe center panel shows the combined BIMA+FCRAO \\n2hp(1-0) emission\nintegrated over all hyperfine components from $v=6.5$ to 10.0~\\kms.\nThe greyscale ranges linearly from 2.7 to 36~K~\\kms, with contours\nat 8.2, 10.9, 13.6, ...K~\\kms.\nThe right panel shows the combined BIMA+FCRAO CS(2--1) emission\nintegrated from $v=0.75$ to $10.5$~\\kms. The greyscale ranges\nlinearly from 5 to 40~K~\\kms, with contours at 10, 12.5, 15, ...K~\\kms.\nBoth line maps have been corrected for primary beam attenuation\nand masked beyond the dotted boundaries corresponding to the\n50\\% level of the two pointings. Synthesized beam sizes are\nindicated in the lower right corner for each map.\n\\label{fig:bima}}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}[htpb]\n\\vskip 0.0in\n\\centerline{\\psfig{figure=sig_nt.ps,height=6.5in,angle=0,silent=1}}\n\\vskip 0.0in\n\\figcaption[f2.ps]{The non-thermal velocity dispersion of \\n2hp\\ displayed\nin greyscale overlayed on a contour map of integrated\nemission as in Figure~1. The dispersion was only determined for\nthose spectra with a peak signal-to-noise ratio greater than 5 and lie\nwithin the boundary shown by the heavy solid line. The dashed line indicates\nthe FWHM of the mosaic. The resolution of this map is $10''$ indicated\nin the lower right corner. We identify eight regions where the velocity\ndispersion is a local minimum, labeled Q1 through Q8.\n\\label{fig:sig_nt}}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}[htpb]\n\\vskip 0.0in\n\\centerline{\\psfig{figure=peaksig.ps,height=6.5in,angle=0,silent=1}}\n\\vskip 0.0in\n\\figcaption[f3.ps]{The peak temperature divided by the velocity dispersion for\nthe \\n2hp\\ spectra, a measure of the optical depth, plotted in greyscale\nover a contour map of integrated emission.\nThe greyscale ranges linearly from 6 to 24~K~(km~s\\e)\\e.\nThe boundary and annotations are as in Figure~2.\nThe quiescent cores are most prominent in this map since they possess\nboth a locally small dispersion and high peak temperature.\n\\label{fig:peaksig}}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}[htpb]\n\\vskip 0.0in\n\\centerline{\\psfig{figure=qspec_n2hp.ps,height=5.5in,angle=90,silent=1}}\n\\vskip -1.8in\n\\figcaption[f4.ps]{\\n2hp\\ spectra at the center of the 8 quiescent cores Q1--Q8.\nThe upper panels show spectra at $15''$ resolution and the\nlower panels show spectra at the same positions at $50''$ resolution.\nOnly the isolated (F$_1$F$=01-12$) hyperfine component is shown.\nThe velocity and temperature scale is the same for all panels\nand is indicated in the lower left.\n\\label{fig:qspec_n2hp}}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}[htpb]\n\\vskip 0.0in\n\\centerline{\\psfig{figure=fcrao.ps,height=6.5in,angle=0,silent=1}}\n\\vskip 0.0in\n\\figcaption[f5.ps]{Map of CS and \\c34s(2--1) spectra from FCRAO observations\n(dark and light lines respectively).\nThe \\c34s\\ intensities have been multiplied by a factor of 2 for clarity.\nThe spectra are placed on a (Nyquist) $25''$ grid with a velocity\nrange 0 to 15~\\kms\\ and a temperature range $-1$ to 4~K ($T_R^\\ast$)\nfor each box shown by the dotted line and indicated by the axes for\nthe lower left box. The outline of the BIMA CS map and the seven\ncontinuum sources from Figure~1 are indicated. Offset coordinates\nare relative to $\\alpha(2000)=18^{\\rm h}29^{\\rm m}47\\fs 5,\n\\delta(2000)=01^\\circ 16'51\\farcs 4$.\n\\label{fig:fcrao}}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}[htpb]\n\\vskip 0.0in\n\\centerline{\\psfig{figure=outflows.ps,height=6.2in,angle=0,silent=1}}\n\\vskip 0.0in\n\\figcaption[f6.ps]{Blue- and red-shifted CS emission showing several protostellar\noutflows. The dotted contours show the integrated intensity from\n5.75 to 6.75~\\kms, the solid contours from 9.25 to 11.0~\\kms.\nStarting level and increment is 0.5~K~\\kms\\ in each case.\nThe map is made using BIMA data only restored to a circular\n$10''$ FWHM beam indicated in the lower right corner.\nThe locations of the continuum sources and quiescent cores are\nindicated by the star and triangle symbols respectively.\nThe S68N outflow dominates and its red lobe extends across the Q5/S68Nd core.\nThe SMM1 outflow is confined to a much smaller projected area\nand does not appear to be responsible for line wings around other cores.\nThere is a weak outflow around continuum core SMM10,\nand hints of an outflow around Q2/S68Nb.\n\\label{fig:outflows}}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}[htpb]\n\\vskip 0.0in\n\\centerline{\\psfig{figure=qspec_cs.ps,height=5.2in,angle=90,silent=1}}\n\\vskip 0.0in\n\\figcaption[f7.ps]{CS spectra toward the quiescent cores and continuum sources.\nSpectra have been slightly smoothed to $15''$ to better show the\nlineshapes. The velocity and temperature scale is the same for each\nspectrum. \\n2hp\\ velocities and FWHM linewidths are indicated by the\nsolid vertical line and gray shading respectively; spectra are ordered\nfrom lowest (top left) to highest (bottom right) \\n2hp\\ linewidth.\n\\label{fig:qspec_cs}}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}[htpb]\n\\vskip 0.0in\n\\centerline{\\psfig{figure=deltat.ps,height=6.8in,angle=0,silent=1}}\n\\vskip -0.1in\n\\figcaption[f8.ps]{The CS blue-red temperature difference plotted against the\n\\n2hp\\ non-thermal velocity dispersion\nfor all points in the dataset where both the CS spectra possess two peaks\nand the \\n2hp\\ spectra have a peak signal-to-noise ratio greater than 5.\nThe vertical dotted line is drawn at $\\sigma_{\\rm NT}=0.23$~\\kms. All\nspectra with lower values of dispersion have positive values of \\dtbr\\\nindicating a positive infall speed. The large open circles and error\nbars indicate the mean and standard deviation of the temperature\ndifference for five velocity dispersion bins.\n\\label{fig:deltat}}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}[htpb]\n\\vskip 0.0in\n\\centerline{\\psfig{figure=radial.ps,height=6.0in,angle=90,silent=1}}\n\\vskip -0.1in\n\\figcaption[f9.ps]{The radial variation of the CS blue-red temperature difference\nand \\n2hp\\ non-thermal velocity dispersion for two quiescent cores\nand two continuum sources. Points from individual spectra and a least\nsquares fit are shown.\n\\label{fig:radial}}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}[htpb]\n\\vskip 0.0in\n\\centerline{\\psfig{figure=radgrad.ps,height=5.4in,angle=90,silent=1}}\n\\vskip -0.1in\n\\figcaption[f10.ps]{The radial gradient of \\dtbr(CS) plotted against the radial\ngradient of $\\sigma_{\\rm NT}$(\\n2hp) for the continuum sources (stars)\nand quiescent cores (circles). The gradients are the slopes of\nleast squares fits as in Figure~\\ref{fig:radial}.\n\\label{fig:radgrad}}\n\\end{figure}\n\\clearpage\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002289
|
HST/NICMOS Imaging of the Planetary Nebula Hubble~12
|
[] |
Images of Hubble 12 were obtained with the HST/NICMOS instrument in the F110W, F164N, and F166N filters of NIC1, and the F160W, F187N, F190N, F212N, F215N filters of NIC2. The images show the structure of the inner ``torus" and lobes much clearer than previous ground-based images. In particular, the [Fe~II] lobes are clearly resolved and shown to be distinct from the H$_2$ emission structures. Apparent changes in the inner ionized and neutral bipolar shell implies periodic mass loss or changes in stellar wind shape or direction. The H$_2$ in the ``eye" is radiatively excited and shows a complex morphology that suggests that several mass ejection events are responsible for producing this structure. The position angle of the H$_2$ and [Fe~II] lobes differ, indicating a possible precession of the ejection axis.
|
[
{
"name": "hora.tex",
"string": "\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n\\markboth{Hora et al.}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n\n\\begin{document}\n\\title{HST/NICMOS Imaging of the Planetary Nebula Hubble~12}\n\\author{Joseph L. Hora \n\\affil{Harvard/Smithsonian Center for Astrophysics, 60 Garden St. MS-65,\nCambridge, MA 02138}\n\\author{William B. Latter}\n\\affil{ SIRTF Science Center, Caltech, MS 314-6, Pasadena, CA 91125 }\n\\author{Aditya Dayal}\n\\affil{ IPAC and JPL, Caltech, MS 100-22, Pasadena, CA 91125 }\n\\author{John Bieging \\& Douglas M. Kelly}\n\\affil{Steward Observatory, University of Arizona, Tucson, AZ 85721}\n\\author{A. G. G. M. Tielens}\n\\affil{Kapteyn Astronomical Institute, PO Box 800, NL-9700 AV Groningen,\nThe Netherlands}\n\\author{Susan R. Trammell}\n\\affil{University of North Carolina, Dept. of Physics, Charlotte, NC 28223}\n}\n \n\\begin{abstract}\nImages of Hubble 12 were obtained with the HST/NICMOS instrument \nin the F110W, F164N, and F166N filters of NIC1,\nand the F160W, F187N, F190N, F212N, F215N filters of NIC2.\nThe images show the structure of the inner ``torus\" and lobes much clearer than\nprevious ground-based images. In particular, the [Fe~II] lobes \nare clearly resolved and shown to be distinct from the H$_2$ emission\nstructures. \nApparent changes in the\ninner ionized and neutral bipolar shell implies periodic mass loss or\nchanges in stellar wind shape or direction.\nThe H$_2$ in the ``eye\"\nis radiatively excited and shows a complex morphology that suggests that several\nmass ejection events are responsible for producing this structure.\nThe position angle of the H$_2$ and [Fe~II] lobes differ, \nindicating a possible precession of\nthe ejection axis. \n\\end{abstract}\n\n\\section{Observations and Reductions}\nImages of Hubble 12 (Hb 12)\nwere obtained with the HST/NICMOS instrument on 13 Nov \n1997. The images in the F110W, F164N, and F166N were taken with NIC1,\nand the F160W, F187N, F190N, F212N, F215N images were obtained with NIC2.\nThe MULTIACCUM mode and spiral dither patterns were used. The NICMOS\nCALNICA and CALNICB pipelines were used to reduce the data. In general a\nfew dither sets were obtained in each filter; these were aligned and averaged\nto produce the final images.\nThe bright central star makes the region near the core difficult to see \nclearly, and adds a number of image artifacts. The lines that run approximately\nfrom corner to corner are part of the diffraction pattern of the instrument. \nThe horizontal and vertical lines that run through the star are array artifacts\ncaused when the central star saturates in the long integrations. In future\nreductions we will attempt to subtract the point source in the core to better\nstudy the region around it.\n\n\\begin{figure}\n\\plottwo{hora_fig1a.ps}{hora_fig1b.ps}\n\\caption{Hubble 12, in the F110W (left) and F164N filters (right). The field\nsize for each is $\\sim$ 13 arcsec square. The orientation of the images shown \nin the F110W image is the same for all images presented here. The F110W filter\nincludes contributions from\nthe bright Paschen $\\beta$ line and line emission from H$_2$, [Fe~II], and He~I\nlines within the bandpass. The F164N filter samples the [Fe~II] line\nat 1.64 $\\mu$m. }\n\\end{figure}\n\n\\begin{figure}\n\\plottwo{hora_fig2a.ps}{hora_fig2b.ps}\n\\caption{Hubble 12, in the F160W (left) and F187N filters (right). The\nfield size shown in each image is $\\sim$ 19 arcsec square. \nThe bandpass of the F160W filter includes lines from the\nBrackett series of H~I and line emission from H$_2$, [Fe~II], and He~I lines\nas well. The narrowband F187N filter samples the Paschen $\\alpha$ (H~I) line. }\n\\end{figure}\n\n\\section{Results and Discussion}\nHb 12 has been notable primarily because it represents one of\nthe clearest cases known of UV excited near-IR fluorescent H$_2$ emission\n(Dinerstein et al.\\ 1988; Ramsay et al.\\ 1993, Hora \\& Latter 1996, Luhman\n\\& Rieke 1996). \nDinerstein et al.\\ had mapped the inner structure and found it to be\nelliptical surrounding the central star; the deep H$_2$ images in\nHora \\& Latter (1996) showed the\nfaint bipolar lobes extending N-S, and the torus or ``eye\"-shaped strucure\nat the base of the lobes around the central star. \n The H$_2$ line ratios observed in the torus were in excellent\nagreement with predictions by theoretical H$_2$ fluorescence calculations\n(see also Luhman \\& Rieke 1996).\nHora \\& Latter also detected [Fe~II]\nline emission at 1.64 \\micron\\ in a position along the edge of the shell, but\nnot at the H$_2$ line peak emission location to the E of the central star.\n\n\\begin{figure}\n\\plottwo{hora_fig3a.ps}{hora_fig3b.ps}\n\\caption{Hubble 12, in the F212W (left) and F215N filters (right). The\nfield size shown in each image is approximately 19 arcsec square. \nThe F212N filter samples the H$_2$ line at 2.12 $\\mu$m, the F215N filter\nmeasures the nearby continuum (as well as a small contribution from the \nBrackett $\\gamma$ feature at 2.16 $\\mu$m.}\n\\end{figure}\n\nPrevious HST-WPC2 imaging by Sahai \\& Trauger (1998) in H$\\alpha$ showed the inner\nstructure to have an ``hourglass\" shape, and a small bipolar structure in\nthe core region, with lobes roughly E-W within a few tenths of an arcsec from\nthe star. \nWelch et al. (1999a,b) obtained ground-based images in the [Fe~II] line and\nnearby continuum and found that the line emission was also distributed along\nthe inner hourglass nebula. \nThe HST images presented here show the\nsymmetry axes of the hourglass and the H$_2$ eye and bipolar nebula \ndiffer in their alignment\nby $\\sim$ 5$^\\circ$. A comparison of these images with the inner\nbipolar structure found by Sahai \\& Trauger shows that \nits alignment\ndiffers by $\\sim 20^\\circ$ from the hourglass and outer H$_2$ lobes. The \ndifferent orientation of the structures suggests that the central source \nmay be precessing between discrete outflow events. Also, the structures seen \nin the H$_2$ image indicate other possible outflow events and remnants of \nother bipolar hourglass nebulae. Hb~12 may therefore be another example of\na PN with multiple nested bipolar bubbles.\n\nThe inner hourglass is bright in the Paschen $\\alpha$ and [Fe~II] lines, but\nthe outline of the ``eye'' appears only in the H$_2$ and the wide bandpass \nfilters (in continuum plus H$_2$ line emission). This \nimplies that the regions where only H$_2$ is detected\nare somehow shielded from what has ionized the inner \nhourglass.\nThere is no evidence for [Fe~II] emission from other regions in the \nnebula, and the density of the inner hourglass does not seem\nsufficient to provide effective shielding of the other regions from radiation\nfrom the central star, which might suggest shock excitation in an interacting\nwind. This hypothesis must be confirmed with investigation of the velocity\nstructure in the nebula. The strong influence of FUV photons elsewhere in\nthis object argues that the [Fe~II] emission is excited by FUV photons in the\nPDR. We will be investigating this possibility through detailed chemical\nmodeling.\n\nWe obtained high-resolution IR spectra of Hb~12 in the H$_2$ and [Fe~II] lines\nusing CSHELL at the IRTF (Kelly, Hora, \\&\nLatter 1999) which indicates that the N lobe is inclined towards us. We also\nhave additional medium-resolution spectra of the faint extended H$_2$ lobes to \ndetermine the excitation properties of the outer nebula. We\nare in the process of analyzing these data along with the optical and\nIR imagery to understand the structure of this interesting and complex nebula.\n\n\\begin{references}\n\\reference{Dinerstein, H. L., Lester, D. F., Carr, J. S., \\& Harvey, P. M.\n1988, ApJLett, 327, L27}\n\n\\reference{Hora, J. L., \\& Latter, W. B. 1996, ApJ, 461, 288}\n\n\\reference{Hora, J. L., Latter, W. B., \\& Deutsch, L. K. 1999, ApJSupp, in press}\n\n\\reference{Kelly, D. M., Hora, J. L., \\& Latter, W. B. 1999, in preparation}\n\n\\reference{Luhman, K., \\& Rieke, G. H. 1996, ApJ, 461, 298}\n\n\\reference{Ramsay, S. K., Chrysostomou, A., Geballe, T. R., Brand, P. W. J.\nL., \\& Mountain, M. 1993, MNRAS, 263, 695}\n\n\\reference{Sahai, R., \\& Trauger, J. T. 1998, AJ, 116, 1357}\n\n\\reference{Welch, C. A., Frank, A., Pipher, J. L., Forrest, W. J., \\& Woodward, C. E. \n1999a, ApJ, in press}\n\n\\reference{Welch, C. A., et al., 1999b, this conference}\n\n\\end{references}\n\n\\end{document}\n"
}
] |
[] |
astro-ph0002290
|
Evolution and surface abundances of red giants experiencing deep mixing\thanks{Accepted for publication in Astron.\ \& Astrophys.}
|
[
{
"author": "A.~Weiss\\inst{1}"
},
{
"author": "P.A.~Denissenkov\\inst{1,2}"
},
{
"author": "C.~Charbonnel\\inst{3}"
}
] |
We have calculated the evolution of low metallicity red giant stars under the assumption of deep mixing between the convective envelope and the hydrogen burning shell. We find that the extent of the observed abundance anomalies, and in particular the universal O-Na anticorrelation, can be totally explained by mixing which does not lead to significant helium enrichment of the envelope. On the other hand, models with extremely deep mixing and strong helium enrichment predict anomalies of sodium and oxygen, which are much larger than the observed ones. This latter result depends solely on the nucleosynthesis inside the hydrogen burning shell, but not on the details of the mixing descriptions. These, however, influence the evolution of surface abundances with brightness, which we compare with the limited observational material available. Our models allow, nevertheless, to infer details on the depth and speed of the mixing process in several clusters. Models with strong helium enrichment evolve to high luminosities and show an increased mass loss. However, under peculiar assumptions, red giants reach very high luminosities even without extreme helium mixing. Due to the consequently increased mass loss, such models could be candidates for blue horizontal branch stars, and, at the same time, would be consistent with the observed abundance anomalies. \keywords{Stars: abundances -- interiors -- evolution -- globular clusters: general }
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[
{
"name": "mixing.tex",
"string": "% deep mixing in red giants - final version Feb 14, 2000\n\n\\documentclass[referee]{aa-mpa}\n\\usepackage{graphicx}\n%\n% Journal names definitions:\n\\def\\apj{ApJ}\n\\def\\apjs{ApJS}\n\\def\\aap{A\\&A}\n\\def\\aas{A\\&AS}\n\\def\\aj{AJ}\n\\def\\mn{MNRAS}\n\\def\\pasp{PASP}\n%\n% BIBTEX MACROS\n\\makeatletter \n% copied from astron.sty\n\\let\\@internalcite\\cite\n\\def\\cite{\\@ifstar{\\citeyear}{\\citefull}}\n\\def\\citefull{\\def\\astroncite##1##2{##1 ##2}\\@internalcite}\n\\def\\citeyear{\\def\\astroncite##1##2{##2}\\@internalcite}\n% additional goodies\n\\def\\citeau{\\def\\astroncite##1##2{##1}\\@internalcite}\n\\def\\citen{\\def\\astroncite##1##2{##1 (##2)}\\@internalcite}\n\\def\\possesivcite{\\def\\astroncite##1##2{##1's (##2)}\\@internalcite}\n% strange, but necessary for correct line breaks (no over-full hboxes)\n\\def\\@citex[#1]#2{\\if@filesw\\immediate\\write\\@auxout{\\string\\citation{#2}}\\fi\n \\def\\@citea{}\\@cite{\\@for\\@citeb:=#2\\do\n {\\@citea\\def\\@citea{; }\\@ifundefined\n {b@\\@citeb}{{\\bf ?}\\@warning\n {Citation `\\@citeb' on page \\thepage \\space undefined}}%\n{\\csname b@\\@citeb\\endcsname}}}{#1}}\n%\n\\def\\@cite#1#2{#1\\if@tempswa , #2\\fi}\n\\def\\@biblabel#1{}\n\\makeatother\n%\n\n\n\\begin{document}\n\n\n\\thesaurus{06(08.01.1; 08.05.3; 08.09.3; 10.07.2)}\n\n\\title{Evolution and surface abundances of red giants experiencing\ndeep mixing\\thanks{Accepted for publication in Astron.\\ \\& Astrophys.}}\n\n\n\\author{A.~Weiss\\inst{1} \\and P.A.~Denissenkov\\inst{1,2} \\and\nC.~Charbonnel\\inst{3}}\n\n\\institute{Max-Planck-Institut f\\\"ur Astrophysik,\n Karl-Schwarzschild-Str.~1, 85748 Garching,\n Federal Republic of Germany\n \\and\n\t Astronomical Institute of the St. Petersburg University,\n\t Bibliotechnaja Pl.~2, Petrodvorets, 198904~St.\\,Petersburg,\n\t Russia\n \\and\n Observatoire Midi-Pyr{\\'e}n{\\'e}es, 14 Avenue Edouard\n Belin, 31400 Toulouse, France\n}\n\n\\offprints{A.~Weiss; (e-mail: weiss@mpa-garching.mpg.de)}\n%\\mail{A.~Weiss}\n\n\n\\authorrunning{Weiss, Denissenkov, Charbonnel}\n\\titlerunning{Deep mixing in red giants}\n\n\\maketitle\n\n\\begin{abstract}\nWe have calculated the evolution of low metallicity red giant stars\nunder the assumption of deep mixing between the convective envelope\nand the hydrogen burning shell. We find that the extent of the\nobserved abundance anomalies, and in particular the universal O-Na\nanticorrelation, can be totally explained by mixing which does not\nlead to significant helium enrichment of the envelope. On the other\nhand, models with extremely deep mixing and strong helium enrichment\npredict anomalies of sodium and oxygen, which are much larger than the\nobserved ones. This latter result depends solely on the\nnucleosynthesis inside the hydrogen burning shell, but not on the\ndetails of the mixing descriptions. These, however, influence the\nevolution of surface abundances with brightness, which we compare with\nthe limited observational material available. Our models allow,\nnevertheless, to infer details on the depth and speed of the mixing\nprocess in several clusters. Models with strong helium enrichment\nevolve to high luminosities and show an increased mass loss. However,\nunder peculiar assumptions, red giants reach very high luminosities\neven without extreme helium mixing. Due to the consequently increased\nmass loss, such models could be candidates for blue horizontal branch\nstars, and, at the same time, would be consistent with the\nobserved abundance anomalies.\n\n\\keywords{Stars: abundances -- interiors -- evolution \n -- globular clusters: general } \n\\end{abstract}\n\n\\newpage\n\n\\section{Introduction}\n\nThe observed anomalies in CNO-, NeNa- and MgAl- elements in globular\ncluster red giants (see \\cite{kra:94} and \\cite{daco:98} for reviews)\nare unexplained in canonical low-mass star evolution theory and\nindicate effects beyond the standard picture. At least for anomalies\nin those isotopes participating in the CNO-cycle models relying on the\nassumption of an additional, non-standard mixing process inside the\nstars have been presented, which explain convincingly the\nobservations, including the evolution of the carbon abundance along\nthe RGB, i.e.\\ with time (see \\cite{cchar:95}; \\cite{dw:96};\n\\cite{csb:98}).\nThis mixing is supposed to set in after the hydrogen burning shell has\nreached the composition discontinuity left behind by the first\ndredge-up on the red giant branch (RGB), i.e., after the so-called RGB\nbump (e.g. \\cite{sm:79}; \\cite{cchar:95}; \\cite{cbw:98}) where the\nmolecular weight barrier between hydrogen burning shell and envelope\nis at a minimum. It is usually described in terms of a diffusion\nprocess of certain efficiency and penetration depth. The CNO\nanomalies and their correlations with brightness and metallicity\n(which are expected qualitatively from nucleosynthesis arguments in\nstandard models, as discussed by \\cite{csb:98}) are thus explained by\na purely evolutionary picture (\\cite{st:92}; \\cite{dw:96};\n\\cite{bs:99b}). The physical origin of the mixing process is believed\nto be found in differential rotation of the star and the parameters\nused in some of the presently available calculations have been derived\nfrom existing theories (e.g.\\ \\cite{zahn:92}; \\cite{mz:98}), which\nare, however, far from being complete.\n\nA similar situation holds for oxygen and sodium, which are found to be\nanti-correlated in globular cluster red giants (\\cite{ksn:93}).\n\\citen{dd:90} and \\citen{lhs:93} showed that this could result from\nthe mixing of elements participating in the ONeNa-cycle, which\noperates at higher temperatures than the CNO-cycle and therefore\nrequires deeper mixing. \\citen{dw:96} demonstrated how all anomalies\nof the mentioned elements known at that time can be explained by the\ndeep mixing scenario. Their calculations were done by using canonical\nred giant models, which evolved along the RGB without any mixing, and\nperforming the mixing and nuclear reactions in a post-processing\nway. For this approach to be correct it is necessary that the\nevolution of the background models is not affected by the mixing\nprocess. In fact, the mixing necessary to reproduce the observed\nanomalies was always so shallow that only very small amounts of\nhydrogen/helium were mixed between envelope and shell, even in the\ncase of the O-Na-anti-correlation. This was taken as sufficient\njustification of the underlying basic assumption. Very similar\nconclusions were obtained by \\citen{csb:98}.\n\nWithin this approach, one cannot investigate the possibility or\nnecessity for even deeper mixing, which would affect the\nhydrogen/helium structure of the models. \\citen{swei:97} has renewed\nthe interest in such deep mixing by connecting the problem of\nhorizontal branch morphology with that of observed anomalies, as\npreviously suggested by \\citen{lh:95}. If the mixing leads to severe\nhelium enhancement in the envelope, increased luminosities and stellar\nwinds result, such that the star will populate the blue horizontal\nbranch (HB), while it remains a red HB star without the additional\nmixing.\n\nWhile \\citen{dw:96} did not investigate the effect of helium\ntransport, \\citen{swei:97} did not follow the evolution of the\nparticipating isotopes to compare with observations. In the present\npaper, we therefore attempt to close this gap by computing full\nevolutionary sequences which include deep diffusive mixing and by\ninvestigating abundance anomalies using these self-consistent models\nas background models. In particular, we want to answer the question\n{\\em how much helium enrichment of the envelope is necessary or\nallowed to achieve or to keep consistency with observations.}\n\nIn Sect.~2 we will discuss the nucleosynthesis aspects of the problem\nand review the observational status of the global O-Na anticorrelation, \nwhich is a powerful tracer of the transport processes in the red giants.\nIn Sect.~3 we will present and discuss the evolutionary models. \nAfter that, the predictions for the abundances based on our mixed models and \npost-processing nucleosynthesis will follow, before the conclusions close \nthe paper.\n\n\\section{The O-Na anticorrelation: \nobservational status and nucleosynthesis arguments}\n\n\\begin{figure}\n\\centerline{\\includegraphics[scale=0.40,draft=false]{fig1.eps}}\n\\caption[]{Observed [Na/Fe] vs.\\ [O/Fe] for galactic globular\ncluster and field giants. References for the data are:\nField: \\citen{shet:96a}, \\citen{shet:96b},\nM3: \\citen{ksl:92}, M13: \\citen{kss:97}, M15: \\citen{sks:97},\nM92: \\citen{shet:96a}, $\\omega$~Cen: \\citen{Norris95}. \nIn $\\omega$~Cen, black and white squares correspond to\nstars with [Fe/H] higher and lower than -1, respectively}\n\\protect\\label{f:obsano}\n\\end{figure}\n\nAmong the chemical anomalies observed in red giant atmospheres over\nthe past two decades, the variations in oxygen and sodium have a\nspecial status. Indeed, the so-called global oxygen-sodium\nanticorrelation appears to be a common feature to all the globular\nclusters in a wide range of metallicity \n(-2.5$\\leq$[Fe/H]$\\leq$-1), for which\ndetailed abundance analysis of the brightest giants have been carried\nout (\\cite{go:89}; \\cite{sneden91}; \\cite{drake92}; \\cite{bw:92};\n\\cite{ksn:93}; \\cite{Armosky94}; \\cite{mpgc:96}; \\cite{Pilachowski96};\n\\cite{kss:97}; \\cite{ksssf:98}). This pattern shows up in ``normal\"\nmonometallic clusters (M3, M4, M5, M10, M13, M15, M92, NGC 7002) as\nwell as in the multi-metallicity cluster $\\omega$ Cen\n(\\cite{Paltoglou89}; \\cite{Norris95}). Fig.~\\ref{f:obsano} summarizes\nthe present observational status concerning the O-Na-anticorrelation.\nBut more importantly, this feature, and the dependence of the Na\nenhancement and O depletion on the red giant evolutionary state\n(\\cite{Pilachowski96}; \\cite{kss:97}) can be explained\nstraightforwardly in the deep mixing scenario (\\cite{dw:96}).\n\nRegarding the Mg and Al anomalies, the situation is very different,\nand the observed Mg-Al anticorrelation (\\cite{shet:96a}) requires a\ncombination of the deep mixing and primordial scenarios\n(\\cite{dww:97}; \\cite{ddn:98}). {\\em Ad hoc} assumptions would be\nneeded to obtain the observed $^{24}$Mg depletion within the low mass\nAl-rich giants themselves (\\cite{shet:96b}). Since a low energy\nresonance in the $^{24}$Mg(p,$\\gamma)^{25}$Al reaction remains\nundetected (\\cite{Angulo99}) or even can be excluded (\\cite{Pow:99}),\n``exotic\" models are required to episodically increase the temperature\nof the hydrogen-burning shell up to values as high as $\\sim$ 70-85 MK\n(while canonical models reach a maximum temperature of only 55 MK) in\norder to deplete Mg at the expense of $^{24}$Mg (\\cite{lhz:97};\n\\cite{zl:97}; \\cite{fmk:99}) inside the low mass giants as apparently\nbeing the consequence of the results by \\citeau{shet:96a}\n(\\citeyear{shet:96a} and \\citeyear{shet:96b}) for M13. Lately,\nhowever, \\citen{isk:99} found that Mg and Al abundance variations in\nM4 can be explained completely by the idea that the Al-enhancement is\ndue to a destruction of the Mg-isotopes $^{25}{\\rm Mg}$ and $^{26}{\\rm\nMg}$ (cf.\\ Fig.~\\ref{f:abprof}). Even in this case, a significant\nincrease of the initial abundance of $^{25}$Mg is required\n(\\cite{ddn:98}). Since the Mg-Al anticorrelation cannot be explained\nby the deep mixing scenario alone, we do not consider it further in\nthis paper. In fact, all explanations brought forward up to now being\nrather exotic and complicated, one should also wait for additional\nobservational support for its existence (as well as for the isotopic\nratios) and relation to other stellar properties before advocating any\nexplanations.\n \n\\begin{figure}[ht]\n\\centerline{\\includegraphics[scale=0.45,draft=false,bb=60 220 580 750]{fig2.eps}}\n\\caption[]{Abundances of some isotopes participating in the\n \\mbox{CNO-,} NeNa- and MgAl-cycle as functions of the\n relative mass coordinate ($\\delta m = 0$ at the bottom of the\n hydrogen burning shell and $\\delta m = 1$ at the bottom of\n the convective envelope) in the red giant model from which detailed\n nucleosynthesis calculations with extra mixing\n start. $^{23}$Na is emphasized by a thick solid line. Also\n shown is the hydrogen abundance profile, normalized, however,\n to $10^{-3}$ to accomodate it on the same scale}\n\\protect\\label{f:abprof}\n\\end{figure}\n\nLast but not least, the morphology of the global O-Na anticorrelation\n(Fig.~\\ref{f:obsano}) bears crucial clues on the mixing process.\nFirst, its extension to very low oxygen abundances ([O/Fe] $\\leq\n-0.45$) is entirely due to the contribution of M13 red giants. It is\nthis ``second parameter'' globular cluster that has the fastest\nrotating blue horizontal branch (HB) stars. \\citen{prc:95} found six\nstars having $v\\sin i \\geq 30\\;{\\rm km}\\,{\\rm s}^{-1}$. In the same\npaper red HB stars in M3 (the cluster forming a classical ``second\nparameter''-pair with M13) have been found to possess smaller\nprojected rotational velocities, from 2 to 20~${\\rm km}\\,{\\rm\ns}^{-1}$. This indicates a relation between rotation and mixing.\n\nConcerning this extension along the horizontal axis, our experience in\nmodelling the global anticorrelation shows that it depends primarily\non the mixing rate $D_{\\rm mix}$ or, more precisely, on the product\n``mixing rate $\\times$ mixing time''. We will come back to these\narguments in Sect.~4, where our nucleosynthesis predictions in deeply\nmixed stars will be compared to the observations of [O/Fe] versus\n[Na/Fe].\n\nSecondly, the extension of the global anticorrelation along the\nvertical axis ($-0.4 \\leq $ [Na/Fe] $ \\leq 0.6$ in all clusters except\n$\\omega$ Cen) tells us mostly about the depth of the additional\nmixing. In \\citeau{dw:96} (\\citeyear{dw:96}, Fig.~4) and in\n\\citeau{ddn:98} (\\citeyear{ddn:98}, Fig.~1) it has been shown that on\napproaching the hydrogen burning shell the Na abundance displays two\nsuccessive rises (see Fig.~\\ref{f:abprof}). The first rise results\nfrom the reaction $^{22}$Ne(p,$\\gamma$)$^{23}$Na, whereas the deeper\none is produced in the NeNa-cycle by the partial consumption of\n$^{20}$Ne, which is much more abundant than both $^{22}$Ne and\n$^{23}$Na. The size of the vertical extension of the global\nanticorrelation implies that additional mixing, whatever it is, does\nnot penetrate the second step (rise) in the Na abundance profile where\nH starts to decrease. Otherwise, observed [Na/Fe] values would be\nmuch larger than they are\\footnote{Actually some metal-rich giants in\n$\\omega$ Cen show extremely high [Na/Fe] (up to 1 dex), probably\nindicating a penetration of the mixing to the second rise of Na. This\ncluster is the only one where some giants exhibit surface enrichment\nof Na produced from both $^{20}$Ne and $^{22}$Ne. It also has one of\nthe bluest horizontal branches (\\cite{wor:94}).}. \\citen{csb:98} have\ninvestigated the dependence of the abundance profiles on metallicity\n(and mass). Their results confirm our arguments completely. Only for\nstars of near-solar metallicity very deep mixing with significant\nhelium enrichment but without strong sodium enhancement could be\npossible (see also Fig.~5 of \\cite{dw:96}). However, the clusters\nunder discussion (e.g.\\ M13) are metal-poor. Let us note in\nFig.~\\ref{f:obsano} the different behavior of field stars\n(\\cite{shet:96a}, \\cite{shet:96b}). In this population, the\nO-Na-anticorrelation is not present (\\cite{gsc:00}). This indicates\nthat the deep mixing does not penetrate the region where ON-burning\noccurs, and may reveal possible environmental effects on its\nefficiency.\n\n\nTo prepare Fig.~\\ref{f:abprof} we applied a nucleosynthesis code to a\nred giant model with surface luminosity $\\log L/L_{\\odot} = 2.21$ from\nwhich our nucleosynthesis with additional deep mixing calculations\nstarted (Sect.~3). The considerable growth of the $^{27}$Al abundance\nwith depth is due to our ``non-standard'' assumption of an enhanced\ninitial abundance of the $^{25}{\\rm Mg}$ isotope ($[^{25}{\\rm Mg/Fe}]\n= 1.1$) and of the thousandfold enhanced rate of the reaction\n$^{26}{\\rm Al}^{\\rm g}(p,\\gamma)^{27}{\\rm Si}$ (for details see\n\\cite{ddn:98}). These ad hoc modifications were needed to explain the\nobserved Al enhancements (\\cite{ddn:98}), but have no influence on the\nresults of the present paper. {From} Fig.~\\ref{f:abprof}, we see\nimmediately that if extra mixing penetrates down to layers, say, at\n$\\delta m \\approx 0.06$, this will result in an enrichment of the red\ngiant's envelope in N, Na and Al and in its impoverishment in C, O,\nand $^{25}{\\rm Mg}$. Again, $^{24}{\\rm Mg}$ remains unchanged due to\nthe relatively low temperatures reached in such a star. These results\nwere recently confirmed by \\citen{plcf99} in models using the reaction\nrates recommended by NACRE (\\cite{Angulo99}).\n\n\\section{Red giant evolution with deep mixing}\n\nTo produce background models for the nucleosynthesis post-processing\nwe have evolved stellar models under the assumption of additional deep\nmixing after the RGB bump. All sequences were started at the same\ninitial model, which consisted of an $0.8\\,M_\\odot$ star \nof initial composition $Y=0.25$ and $Z=0.0003$, and which had been evolved\n(canonically) up to the luminosity of the bump, i.e., $\\log L/L_\\odot\n= 2.21$ (at this point, its mass is $0.798\\,M_\\odot$). \nThe envelope helium content has increased to 0.256 (in mass\nfraction) due to the first dredge-up. The input physics of the\nGarching stellar evolution code (used here) is up-to-date (for a\nsummary, see \\cite{ddn:98}), but atomic diffusion has not been\nincluded in the computations.\n\nThe additional deep mixing between the convective envelope and some\npoint inside the hydrogen shell has been implemented in the same general\nline as in our previous papers on this subject, that\nis, as a diffusive process with parameterized values for the\ndiffusive constant $D_{\\rm mix}$, which is the same for all elements,\nand for the penetration depth. \nThe values used for $D_{\\rm mix}$ are guided by the results of our\nearlier papers, and agree with estimates based on rotationally induced\nmixing theories. We refer the reader to \\citen{dw:96} for details of\nthis approach. We use the normalized mass coordinate $\\delta m$\nintroduced therein, which is 0 at the bottom of the hydrogen shell\n(usually, where $X=10^{-4}$) and 1 at the bottom of the convective\nenvelope. The choice of this mass coordinate allows accurate\ninterpolation between a small number of background models in the\nnucleosynthesis calculations (see \\cite{csb:98} for a similar\napproach). The shell, in this coordinate, is located below $\\delta m\n\\approx 0.10$. The depth, down to which the diffusive mixing should\noccur, we denote as $\\delta m_{\\rm mix}$. Obviously, due to the lack\nof solid theories, one could also choose, for example, purely\ngeometrical scales to define the penetration depth (\\cite{bs:99a}).\nContrary to our earlier papers, the criterion for penetration is not\ndetermined by a fixed value for $\\delta m_{\\rm mix}$ chosen before the\ncalculations, but is related to the decrease in hydrogen content\nwithin the shell (relative to the surface or convective envelope\nabundance $X_{\\rm env}$), expressed as a free parameter $\\triangle X$.\nWe have investigated several different prescriptions for the\npenetration criteria and found a great sensitivity of the mixing on\nthese prescriptions, which are\n\\begin{enumerate}\t\n\\item find that $\\delta m_{\\rm mix}$ in the initial model, where\n$X=X_{\\rm env}-\\triangle X$, and mix to the same $\\delta m_{\\rm mix}$\nin all subsequent models;\n\\item as 1., but $\\delta m=0$ is defined as the point where $X=X_{\\rm\nenv}/2$ (instead of $X=10^{-4}$);\n\\item as 1., but the diffusion constant $D_{\\rm mix}$ is decreasing\nexponentially from the maximum value $D_0$ for $\\delta m > 0.10$ to\n$D_{\\rm mix}\\approx 5\\cdot 10^{-5} D_0$ at $\\delta m_{\\rm mix}$\n\\item always mix to the point, where $X=X_{\\rm env}-\\triangle X$\n\\end{enumerate}\nExcept for method 3, these schemes were chosen to be as simple as\npossible and to be similar to the one by \\citen{swei:97}.\n\n\\begin{figure}[ht]\n\\centerline{\\includegraphics[scale=0.65,draft=false]{fig3.eps}}\n\\caption[]{Hydrogen profiles in the normalized $\\delta m$ coordinate\nin models with deep mixing during the evolution along the RGB. Mixing\nparameters were $D_{\\rm mix}=10^9\\,{\\rm cm}^2\\,{\\rm s}^{-1}$;\n$\\triangle X=0.20$, method 1. The vertical line is the mixing depth\n$\\delta m_{\\rm mix}$ as defined in the first model. See text for more\nexplanations}\n\\protect\\label{f:Xdmp24}\n\\end{figure}\n\nKeeping the relative mass coordinate fixed, up to which mixing should\noccur, implies that changes in the hydrogen profile in the shell\n(usually steepening in the course of evolution) or in the extend of\nthe convective envelope influence the mixing. As an illustration of\nthe ``movement'' of the profile in this coordinate we display in\nFig.~\\ref{f:Xdmp24} an example ($D_{\\rm mix}=10^9\\,{\\rm cm}^2\\,{\\rm\ns}^{-1}$; $\\triangle X=0.20$; method 1). The smooth solid line is the\ninitial model. The next model (at $\\log L/L_\\odot=2.288$) is the\nleft-most line. From there, the model profiles shift to the right\nagain. The solid line with clearly reduced hydrogen abundance\nthroughout the envelope corresponds to a model close to the RGB-tip\n($\\log L/L_\\odot=3.539$). In this phase the burning time at the bottom\nof the mixed region becomes short enough to lead to ``bottom-burning''\nof the envelope. An extended RGB-phase with luminosities drastically\nincreased above the canonical RGB-tip luminosity of $\\log L_{\\rm\ntip}/L_\\odot=3.33$ is the result; the final value being $\\log L_{\\rm\ntip}/L_\\odot=3.8$. Since mass loss (\\cite{r:75}, with $\\eta=0.3$) was\ntaken into account, the total mass at the tip decreases in such cases\nbelow $0.6\\, M_\\odot$. $\\delta m_{\\rm mix}$ is indicated by the\nvertical line and is $0.047$.\n\t\nUsing method 2 instead, $\\delta m =0$ is defined as the point where\nthe abundance of hydrogen has dropped to half the surface value of the\nsame model ($\\delta m_{\\rm mix} = 0.0066$ in this case). This\nprevents, obviously, any penetration to shell regions with lower\nhydrogen content. As in the previous case, the bottom of the envelope\nis burnt at the end of the RGB evolution. However, as soon as the\nhydrogen abundance approaches $X_{\\rm env}/2$ (guaranteed as long as\nmixing is not quasi-instantaneous), the mixing criterion inhibits\nfurther mixing. For this reason $X$ remains constant for $\\delta m <\n0$; in the final models $X_{\\rm env} = 0.6402$ and the hydrogen\nprofile always has a finite step in the shell. In this case, the\nluminosity rises to $\\log L_{\\rm tip}/L_\\odot=3.53$.\n\nThe steps visible in the chemical profiles of Fig.~\\ref{f:Xdmp24} are\ndue to the diffusion criterion applied to the numerical grid, because\nno interpolation to the exact value of $\\delta m_{\\rm mix}$ had been\ndone. We verified that the results do not depend on the grid\nresolution, which was increased by a factor of 10 in the shell in part\nof the calculations. Only the steps got smaller and more numerous. To\navoid such steps, we introduced a varying diffusion constant (method\n3) motivated by recent results of \\citen{dt:00}. They have proposed a\nphysical mechanism for extra mixing in red giants which quantitatively\ninterprets all the known star-to-star abundance variations in globular\nclusters. This is Zahn's mechanism (\\cite{zahn:92}; \\cite{mz:98})\nwhich considers extra mixing in a radiative zone of a rotating star as\na result of the joint operation of meridional circulation and\nturbulent diffusion. This process was already advocated by\n\\citen{cchar:95} to explain the low carbon isotopic ratios and lithium\nabundances in field Population II giants and to lower the $^3$He\nyields by low mass stars. Denissenkov \\& Tout report that the mixing\nrate does not vanish abruptly at a particular depth but instead it\ndies out gradually on a rather short depth range approximately between\n$\\delta m = 0.10$ and $\\delta m = 0.06\\sim 0.07$. This explains the\nfollowing choice of an exponential decline approach for $D_{\\rm mix}$:\n\\begin{eqnarray}\nD_{\\rm mix} & = & D_0; \\> \\delta m > \\delta m_0 \\nonumber \\\\\n & = & D_0 \\exp \\left[c_D \\left({\\delta m_0 - \\delta m \\over \\delta m_{\\rm mix} -\n\\delta m_0}\\right)\\right]; \\> 0\\le \\delta m \\le\\delta m_0\n\\label{e:Dexpo}\n\\end{eqnarray}\n\n\\noindent where $\\delta m_0=0.10$ was used for the beginning of the\ndecline and $\\delta m_{\\rm mix}$ is the mixing depth coordinate as\ndefined in method 1. Using $c_D=10$ ensures that $D_{\\rm mix}(\\delta\nm_{\\rm mix}) \\approx 5\\cdot10^{-5} D_0$. The resulting evolution\n(Fig.~\\ref{f:Xdme1}) is similar to that of the case shown in\nFig.~\\ref{f:Xdmp24}, but the profiles are smooth; mixing parameters\nare identical.\n\n\\begin{figure}[ht]\n\\centerline{\\includegraphics[scale=0.65,draft=false]{fig4.eps}}\n\\caption[]{As Fig.~\\ref{f:Xdmp24}, but for an exponentially declining\n diffusion coefficient $D_{\\rm mix}$ (Eq.~\\ref{e:Dexpo}). The results\n shown are from case D \n in Tab.~1}\n\\protect\\label{f:Xdme1}\n\\end{figure}\n\nWe finally note that method 4, applied straightforwardly, leads to a\ncomplete burning of the entire envelope for $D_{\\rm mix} \\ge 5\\cdot\n10^8$ and/or $\\triangle X \\ge 0.10$. However, this we consider to be\nan artefact, which is easy to understand: Since due to the mixing the\nhydrogen abundance in the envelope is reduced, the critical point down\nto which mixing should occur, is moving inwards. Therefore layers of\neven lower hydrogen content are mixed with the envelope, and the\ncritical point moves to even deeper regions. Only at the point where\nthe burning time-scale is shorter than the mixing time-scale and\ntherefore the surface hydrogen content no longer is able to adjust to\nthe burning, this process is stopped. A way out of this situation is\nto ensure that the mixing does not lead to a sharp step in the shell's\nhydrogen profile. This way, the critical point can be kept within the\nmixed layers. While the mixing procedure described in \\citen{swei:97}\nappears to follow the straightforward approach, Sweigart (private\ncommunication, 1999) in fact used a more complicated method to keep\nthe hydrogen profile even in the presence of mixing. Our method 3\nqualitatively has the same effect.\n\nTo summarize, method 4 appears to be unphysical; method 3 is based on\nthe physical picture by \\citen{dt:00}, but makes additional parameters\nnecessary. Methods 1 and 2 are the most straightforward choices\nleading to composition profiles similar to method 3; method 2 differs\nfrom 1 in that it avoids complete mixing and burning of the envelope\nduring the very last phases of RGB evolution.\n\n\\begin{table}\n\\caption{Parameters of calculations presented in\nFigs.~\\ref{f:hrdc}--\\ref{f:yt} and final values of the stellar mass\n($M_{\\rm f}/M_{\\odot}$) and luminosity ($\\log L_{\\rm f}/L_\\odot$), and\nof the helium mass fraction in the envelope ($Y_{\\rm env}$). The\nfinal luminosity $L_{\\rm f}$ is always very close or identical to the\nRGB-tip luminosity $L_{\\rm tip}$. The mass loss in sequences B and C'\nhas been reduced by a factor 20 compared to the other ones. The\npenetration depths, expressed in the normalized mass coordinate\n$\\delta m$ corresponding to the three $\\triangle X$ values are 0.060\n(0.05), 0.054 (0.10), and 0.047 (0.20). $D_{\\rm mix}$ is in units of\n${\\rm cm}^2\\,{\\rm s}^{-1}$}\n\\protect\\label{t:cases}\n\\begin{tabular}{l|rr|c|llc}\n\\hline\ncase & $D_{\\rm mix}$& $\\triangle X$ &\nmethod & $M_{\\rm f}$ & $Y_{\\rm env}$ & $\\log L_{\\rm f}$ \\\\\n\\hline\nS & 0.0 & --- & --- & 0.689 & 0.256 & 3.31\\\\\nA & $5\\cdot10^8$ & 0.05 & 3 & 0.586 & 0.270 & 3.79\\\\\nB & $5\\cdot10^8$ & 0.10 & 2 & 0.792 & 0.284 & 3.30\\\\\nC & $10^9$ & 0.20 & 2 & 0.567 & 0.360 & 3.53\\\\\nC'& $10^9$ & 0.20 & 2 & 0.771 & 0.360 & 3.56\\\\\nD & $10^9$ & 0.20 & 3 & 0.562 & 0.351 & 3.77\\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\nObviously the details of the mixing procedure influence the resulting\nevolution to quite a significant extent. Since at present we are far\nfrom providing a solid physical approach (which could allow, for\nexample, for a diffusion speed varying both in space and time), we\ncannot predict the true evolution of a star experiencing deep\nmixing. However, the calculations are needed only to provide\nbackground models with varying degrees of helium mixing into the\nenvelope, and it is of no importance how this is achieved in detail.\nWe have calculated 25 different sequences, varying method and\nparameters. The cases selected for Tab.~\\ref{t:cases} are\nrepresentative for the range of results we obtained, which are\nsummarized in Figs.~\\ref{f:hrdc}, \\ref{f:yl}, and \\ref{f:yt}. Case D\nof Tab.~\\ref{t:cases} is the one also shown in Fig.~\\ref{f:Xdme1}. We\nadd that the amount of mass loss has no influence on the mixing\nproperties. Neither does a gradual switching-on of the additional\nmixing during the first few models. We have performed some comparison\ncalculations with a completely different code (the Toulouse-Geneva\ncode; \\cite{cvz92}). While the results differ in details, the gross\nproperties are the same. The differences we ascribe to details in the\nmixing procedures and the implementation of diffusion.\n\nThe effects on the evolution, displayed in Figs.~\\ref{f:hrdc} --\n\\ref{f:yt}, are qualitatively as expected from the work by\n\\citen{swei:97}. The increase in the surface helium content is quite\ndramatic in cases C and D (fast and very deep mixing). However, it is\nnot as large as in \\citen{swei:97}, shown, for example, in his Fig.~2,\nwhere for $\\triangle X = 0.20$ a value of $Y\\ga 0.42$ was\nreached. Also, in contrast to Sweigart's result, in all our\ncalculations the helium enrichment of the outer envelope tends to\nlevel off with progressing evolution. This might be ascribed again to\ndifferences in the mixing scheme details, as we find these differences\nalso in the post-processing models presented in the next section\n(cf. Figs.~\\ref{f:naoyl2} and \\ref{f:naoyl1}). We also find that the\nluminosities can get extremely high (cases A and D) with high mass\nloss as the consequence and a beginning turn-away from the RGB before\nthe He-flash sets in. The beginning of such an evolution might be\nrecognised, too, in Fig.~3 of \\citen{sweip:97} in the case of deepest\nmixing. We also note that mixing method 2 (cases B and C) results in\nloops in the HRD, which depend on the occurrence of mixing\nepisodes. This is, for example, visible in the non-monotonic\nluminosity evolution in Fig.~\\ref{f:yl}.\n\n\\begin{figure}[ht]\n\\centerline{\\includegraphics[scale=0.65,draft=false]{fig5.eps}}\n\\caption[]{HRD of four mixed sequences of Tab.~\\ref{t:cases} and\nthe unmixed canonical one (S) for comparison. The linetypes refer to\nthe cases listed in \nTab.~\\ref{t:cases} and are given in the top-left corner. The large plot\nshows the upper RGB evolution only, the inset the complete evolution from\nthe ZAMS on.}\n\\protect\\label{f:hrdc}\n\\end{figure}\n\n\\begin{figure}[ht]\n\\centerline{\\includegraphics[scale=0.65,draft=false]{fig6.eps}}\n\\caption[]{Surface helium abundance (in mass fraction)\nas a function of luminosity for\nthe same sequences as in Fig.~\\ref{f:hrdc}. A coarseness of 0.001 is\ndue to the limited number of digits in the output}\n\\protect\\label{f:yl}\n\\end{figure}\n\n\\begin{figure}[ht]\n\\centerline{\\includegraphics[scale=0.65,draft=false]{fig7.eps}}\n\\caption[]{Surface helium abundance as a function of age for the same\nsequences as in Fig.~\\ref{f:hrdc}}\n\\protect\\label{f:yt}\n\\end{figure}\n\nThe lifetime on the RGB is in all cases prolonged (Fig.~\\ref{f:yt}) by\n1 or 2~Myr, in some cases up to 4 Myr (5--10\\% of the lifetime after\nthe bump). The evolutionary speed is influenced mainly immediately\nafter the onset of the additional mixing (after the bump). From the\ninitial model to one at $\\log L/L_\\odot \\approx 2.5$, the time\nincreases from 7~Myr (case S) to about 10~Myr (A \\& B) and 13~Myr (C\n\\& D). Thereafter, it is becoming comparable again in all cases. Such\nan effect could possibly be seen in luminosity functions, but it\nshould be most prominent only in a limited luminosity\nrange. \\citen{vlp:98} have argued that the luminosity function of M30\ncould be evidence for rapidly rotating cores of giants.\n\nIn some calculations, in particular those employing the exponentially\ndeclining diffusive speed (method 3), an interesting effect\nappeared. Although the mixing for moderate penetration depth and\nmixing speed remains small, the luminosity of the models rises to\nextreme values. As an example, in case A ($\\triangle X=0.05$, $D_{\\rm\nmix}=5\\cdot10^8\\,{\\rm cm}^2\\,{\\rm s}^{-1}$), $Y_{\\rm env} = 0.270$ (an\nenrichment of only $+0.014$) and $\\log L/L_\\odot = 3.79$ were reached\nat the tip of the RGB (see also Fig.~\\ref{f:hrdc}). An inspection of\nthe models shows that part of the extended region of almost\nhomogeneous composition, which is achieved due to the effect of the\nadditional diffusion, becomes hot enough for significant hydrogen\nburning. In Fig.~\\ref{f:mhil} we display the H-profiles of selected\nmodels in this phase. The first one (top line) is at $\\log L/L_\\odot =\n2.73$ ($Y_{\\rm env} = 0.265$). In this model, the point were the\nenergy production due to hydrogen burning exceeds $10^3\\,{\\rm\nerg}\\,{\\rm g}^{-1}\\,{\\rm sec}^{-1}$ for the first time, is very close\nto the composition step. In the next model ($\\log L/L_\\odot = 3.12$;\n$Y_{\\rm env} = 0.269$) this point has shifted to $\\delta m = 0.274$\nand is constantly progressing outward until it reaches $\\delta m =\n0.80$ in the most advanced models at the bottom of the figure ($\\log\nL/L_\\odot = 3.68$; $Y_{\\rm env} = 0.270$). This burning of the plateau\nconstitutes a broadening of the hydrogen shell and delivers extra\nluminosities. In fact, 50\\% of the total luminosity of the models with\nthe plateau value around $X=0.40$ are generated at $\\delta m > 0.06$,\nthat is outside the inner composition step. Therefore, the luminosity\nin excess of that of an ordinary star at the tip of the RGB (around\n$\\log L/L_\\odot = 3.30$) can completely be ascribed to the plateau\nburning (note that diffusion cannot keep the burning plateau\nhomogeneous with the outer regions). The effect we observe here is\nprobably due to our mixing description, which sets $D_{\\rm mix}$ to\nthe maximum value outside $\\delta m = 0.10$. If our mixing\ndescription is realistic, this would imply that one could get very\nhigh luminosities at the RGB-tip {\\em without} extreme helium mixing.\nThe time spent at luminosities above the standard TRGB brightness is\nonly $10^6$~yrs and therefore observation of such a superluminous star\nis rather unlikely. Due to the extreme overluminosities, the Reimers\nmass loss formula leads to stellar winds of order\n$10^{-7}\\,M_\\odot$/yr and a final mass of $0.58\\,M_\\odot$\n($M_c=0.517\\,M_\\odot$). After the helium flash, this star will\npopulate the blue part of the horizontal branch.\n\t\n\\begin{figure}[ht]\n\\centerline{\\includegraphics[scale=0.65,draft=false]{fig8.eps}}\n\\caption[]{Hydrogen profiles of selected models at the tip of \nsequence A ($\\triangle X=0.05$, $D_{\\rm mix}=5\\cdot10^8\\,{\\rm\ncm}^2\\,{\\rm s}^{-1}$, mixing method 3). \nThe point where energy generation by hydrogen burning exceeds\n$10^3\\,{\\rm erg/(gs)}$ first, is indicated in several models by symbols.}\n\\protect\\label{f:mhil}\n\\end{figure}\n\n\\newpage\n\n\\section{Nucleosynthesis in deeply mixed stars}\n\nThe detailed nucleosynthesis calculations we present now have been\nperformed in a post-processing way as in our previous works\n(\\cite{dw:96}; \\cite{ddn:98}). From an evolutionary sequence three red\ngiant models were selected. The starting one was the same one as for\nthe full evolutionary calculations discussed in the previous section,\ni.e.\\ a model at the bump ($\\log L/L_\\odot \\approx 2.2$) in which the\nhydrogen burning shell had recently crossed the H-He discontinuity\nleft by the base of the convective envelope on the first dredge-up\nphase. The final one was a model near the RGB tip ($\\log L/L_\\odot\n\\approx 3.3$), the second one having a luminosity intermediate to\nthose of the starting and finishing models. Distributions of $T$,\n$\\rho$ and $r$ with $\\delta m$ in these three ``background'' models\nwere used for interpolations in $\\log\\,L$ during the nucleosynthesis\ncalculations. Further details about our post-processing procedure can\nbe found in \\citen{dw:96}. The network of nuclear kinetics equations\nwas the smallest one of those considered in \\citen{ddn:98}. It takes\ninto account 26 particles coupled by 30 nuclear reactions from the\npp-chains, CNO-, NeNa- and MgAl-cycle. The additional mixing is\nmodelled by diffusion with a constant coefficient $D_{\\rm mix}$. We\nrecall that we allow for mixing prescriptions and parameters in these\ncalculations different from those for which the background models have\nbeen obtained.\n\n\\begin{figure}\n\\centerline{\\includegraphics[scale=0.46,bb= 0 220 540 700,draft=false]{fig9.eps}}\n\\caption[]{The global anticorrelation and three theoretical curves\n (labelled by the value of $D_{\\rm mix}$ used in the\n corresponding calculation);\n all three curves were calculated with the penetration\n criterion 1 and $\\triangle X = 0.2$; {\\em unmixed} red giant\n models were used as background. Observational data\n (omitting $\\omega~Cen$) are as in Fig.~\\ref{f:obsano}}\n\\protect\\label{f:naoanti2}\n\\end{figure}\n\nFor the comparison with observations we have preferred the ``global\nanticorrelation'' of [O/Fe] versus [Na/Fe] for the reasons detailed in\nSect.~2. In Fig.~\\ref{f:naoanti2} and Fig.~\\ref{f:naoanti1} it is\nplotted for globular clusters according to the latest observational\ndata.\n\n\\begin{figure}\n\\centerline{\\includegraphics[scale=0.46,draft=false,bb= 0 220 540 700]{fig10.eps}}\n\\caption[]{The same three curves as in Fig.~\\ref{f:naoanti2} in the\n$\\log L$ - $Y_{\\rm env}$ plane}\n\\protect\\label{f:naoyl2}\n\\end{figure}\n\nIn Fig.~\\ref{f:naoanti2} theoretical dependences of [Na/Fe] on [O/Fe]\nobtained in the post-processing way for three values of the diffusion\ncoefficient are shown. This first set of calculations was performed\nwith {\\em unmixed} background red giant models like in our previous\npapers but with mass loss taken into account. The depth of additional\nmixing was determined according to the penetration criterion 1\n(Sect.~2) with $\\triangle X = 0.2$. The mass loss rate $\\dot{M}$ was\nestimated with \\citen{r:75} formula in which the parameter value $\\eta\n= 0.3$ was adopted. In Fig.~\\ref{f:naoyl2} the resulting envelope He\nabundances are shown as functions of $\\log\\,L/L_\\odot$. The mixing\ndepth in the starting model which was kept constant during the\nnucleosynthesis calculations was $\\delta m_{\\rm mix} = 0.047$. Such a\nvalue of $\\delta m_{\\rm mix}$ allows some (modest) penetration of the\nsecond Na step (see Sect.~2) by the mixing which results in an upward\nsteepening of the theoretical dependences of [Na/Fe] on [O/Fe] by the\nend of the RGB evolution (Fig.~\\ref{f:naoanti2}). The maximum He\nenrichment achieved in the envelope in this set of calculations is\n$\\triangle Y_{\\rm env} \\approx 0.10$ (Fig.~\\ref{f:naoyl2}).\n\t\n\\begin{figure}\n\\centerline{\\includegraphics[scale=0.46,bb= 0 220 540 700,draft=false]{fig11.eps}}\n\\caption[]{As Fig.~\\ref{f:naoanti2}, but for calculations using {\\em\n mixed} red giant models as background.\n The solid curves were calculated with the penetration\n criterion 1 and $\\triangle X = 0.2$ and the dashed ones\n with constant mixing depth $\\delta m_{\\rm mix} = 0.04$}\n\\protect\\label{f:naoanti1}\n\\end{figure}\n\t\n\\begin{figure}\n\\centerline{\\includegraphics[scale=0.46,draft=false,bb= 0 220 540 700]{fig12.eps}}\n\\caption[]{The same five curves as in Fig.~\\ref{f:naoanti1} in the\n$\\log L$ - $Y_{\\rm env}$ plane}\n\\protect\\label{f:naoyl1}\n\\end{figure}\n\nIn the next nucleosynthesis calculations, the results of which are\npresented in Figs.~\\ref{f:naoanti1} and \\ref{f:naoyl1}, we have used\n{\\em mixed} background models from sequence C' of Tab.~\\ref{t:cases};\nfor this sequence the same mixing parameters as in case C\n(Tab.~\\ref{t:cases}) but a reduced mass loss rate has been used: the\nparameter $\\eta$ was divided by 20 in order to take into account a\nreduction of $\\dot{M}$ for low Z (\\cite{maed:92}). The reduced mass\nloss rate affects only the final mass, but not the helium enrichment.\nThese models were evolved along the RGB with effects of the He mixing\non stellar structure parameter distributions fully taken into account\nin the stellar evolution code (Sect.~3). Sequence C' was chosen\nbecause out of the sample cases listed in Tab.~\\ref{t:cases} it has\nthe highest degree of helium enrichment, in contrast to the previous,\nunmixed, background models. In this second set of nucleosynthesis\ncalculations we repeat the case of the first set\n(Fig.~\\ref{f:naoanti2}), i.e.\\ mixing down to $\\triangle X = 0.2$\n(solid lines), but also add two computer runs (dashed lines) in which\nthe mixing was chosen to be so deep that a high enrichment in He of\nthe envelope was guaranteed. We label these calculations by $\\delta\nm_{\\rm mix} = 0.04$, which is the penetration depth needed to mix down\nto $\\triangle X = 0.37$.\n\nComparison of the results obtained in the two sets of calculations\nallows to draw the following conclusions:\n\\begin{itemize}\n\\item mass loss is practically unimportant for this study (at least\nwithin the prescriptions and variations used in the various\ncalculations);\n\\item making use of mixed background models instead of unmixed ones\ndoes not seriously affect the theoretical dependences of [Na/Fe] on\n[O/Fe] (compare the solid curves in Figs.~\\ref{f:naoanti2} and\n\\ref{f:naoanti1}); therefore the details of the mixing prescription\nused for the background models are not significant for the\nnucleosynthesis results.\n\\item the total He enrichment of the convective envelope calculated\nin the post-processing way agrees very well with the final envelope He\nabundance obtained in the full evolutionary\ncalculations with additional deep mixing;\n\\item values $\\triangle Y_{\\rm env} > 0.15$ were obtained only in the two\ncomputer runs with the depth $\\delta m_{\\rm mix} = 0.04$, but in these\ncases additional mixing penetrated so deeply that it resulted in the\n[Na/Fe] on [O/Fe] dependences evidently inconsistent with the observations\n(dashed curves in Figs.~\\ref{f:naoanti1} and \\ref{f:naoyl1}).\n\\end{itemize}\n\nA simple inspection of Figs.~\\ref{f:naoanti2}-\\ref{f:naoyl1} allows\nthe conclusion that {\\em the global anticorrelation of [O/Fe]\nvs. [Na/Fe] as a whole and especially the [Na/Fe] values in its low\noxygen abundance tail certainly rule out any hypothesis about an\nincrease of more than $\\triangle Y_{\\rm env} \\approx 0.10$ in the\nenvelope He abundance of globular-cluster red giants.} A physical\nreason for this constraint is the above-mentioned inability of\nadditional mixing to penetrate the second Na abundance rise lying at\n$\\delta m \\leq 0.06 \\div 0.07$ as hinted by the observed global\nanticorrelation. In the starting models $\\delta m \\geq 0.07$\ncorresponds to $\\triangle X \\leq 0.05$ and, therefore, the envelope He\nenrichment is not expected to be much larger than $\\triangle Y_{\\rm\nenv} \\approx 0.05$.\n\n\\section{Discussion}\n\nIf the O-Na-anticorrelation observed in many globular cluster red\ngiants is indeed due to a deep mixing process beyond the standard\neffects taken into account in canonical stellar evolution theory, the\nquestion is justified whether this deep mixing might affect\nthe H-He-profile as well. In this case, consequences for the red\ngiant evolution including phases of enhanced luminosities and mass\nloss could result. We have, therefore, discussed both the\nevolutionary and nucleosynthetic effects quantitatively by performing\nstellar evolution calculations including deep mixing and\npost-processing nucleosynthesis models (the latter\nas we did in our earlier papers \\cite{dw:96}; \\cite{ddn:98}). \n\n{From} arguments depending only on nucleosynthesis we could already\ninfer that for temperature profiles typical of hydrogen-burning shells\nmixing of appreciable amounts of helium can only be achieved if the\nsecond Na rise is penetrated. This, however, leads to oxygen and\nsodium anomalies exceeding those observed (with the exception of a few\nstars in $\\omega$~Cen, a multi-metallicity, untypical cluster). In\nterms of our normalized mass coordinate (defined such that $\\delta m =\n0$ at $X = 10^{-4}$ at the bottom of the shell) this puts an\nobservationally constrained limit for the maximum mixing depth of\n$\\delta m_{\\rm mix} > 0.06 \\div 0.07$. Our complete models confirm\nthis argument: helium enrichment in excess of $\\triangle Y_{\\rm env}\n\\approx 0.05$ due to deep mixing can be ruled out for those stars with\nNa-O-anomalies as observed in clusters such as M15, M92, M3, and even\nM13 which presents one of the most extended blue horizontal branch.\n\n\\begin{figure}\n\\centerline{\\includegraphics[scale=0.45,draft=false]{fig13.eps}}\n\\caption[]{[Na/Fe] and [O/Fe] for giants in globular clusters. The\nsymbols identify individual clusters and have the same meaning as in\nFig.~\\ref{f:obsano}. Overlaid are the five theoretical predictions\nshown in Fig.~\\ref{f:naoanti1}, labeled by the values of $D_{\\rm\nmix}$. In the lower panel the two higher values relate to two lines\neach.}\n\\protect\\label{f:naomv}\n\\end{figure}\n\nThe details of the surface abundance history along the RGB depend on\nthe details of the deep mixing process and thus on its nature which we\ndid not attempt to specify here. In particular, the field-to-cluster\ndifferences must be understood (especially the fact that field giants\ndo not present the O-Na anticorrelation (\\cite{gsc:00}),\nindicating a deeper and more efficient mixing in their globular\ncluster counterparts) and seem to point out a non-negligible impact of\nenvironmental effects on the extra mixing efficiency.\n\nHowever, we can compare the observations with the histories of Na and\nO abundance anomalies predicted by our simple mixing prescriptions in\norder to get constraints for a solid physical model. This is done in\nFig.~\\ref{f:naomv}, which shows surface abundances for several\nclusters as a function of brightness, i.e.\\ progressing\nevolution. Also shown is the theoretical prediction of the five\ncalculations displayed in Fig.~\\ref{f:naoanti1}. Although the\nobservational data are very few (the uncertainty in the abundances is\nof order 0.2 dex), and information for stars before or at the bump is\navailable only for M13, some effects can be recognized, nevertheless.\n\nAll clusters show the whole spread of Na abundances between the\ncanonical case without extra mixing (they would lie on a horizontal\nline) and that as obtained from the calculations with less deep mixing\n(solid lines). As already mentioned, very low O abundances are only\nfound in M13 giants, and the observed spread for this element is a\nsignature of the mixing rate. For both elements the abundance\nanomalies are limited to values predicted by models with extra mixing\n{\\em not} penetrating the second $^{23}$Na rise in the hydrogen\nshell. Stars with intermediate anomalies we interpret as being due to\nmixing penetrating less deeply into the hydrogen shell. They could be\nreproduced with properly adjusted mixing parameters.\n\nOver the small brightness interval for which we have data (for all the\nclusters except M13 only the brightest giants are accessible), no\nsignificant abundance evolution is recognizable. The increase in $\\rm\n[Na/Fe]$ at the RGB tip obtained in all calculations labeled\n$\\triangle X=0.20$ is not visible in the observations, which may be\ntaken as indication that the physical reasons (e.g.\\ rotation) for the\nadditional mixing have lost their importance or even vanished. Such a\npossible time dependence of the extra mixing has not been taken into\naccount in our simple mixing prescriptions, but should result from\nmore physically motivated models. (We recall that in \\citen{dw:96} the\ncarbon evolution could be reproduced with constant mixing parameters,\nhowever.) We will therefore, in a forthcoming paper, use the model by\n\\citen{dt:00}, which includes temporal changes in the diffusion\nconstant due to angular momentum transport.\n\nIn our models, the largest abundance changes take place at the onset\nof the additional mixing, i.e., early on the RGB, after the bump\n(around $M_V\\approx -0.5$). This might be visible in the M13 data.\nThe low brightness group has normal abundances, but above $M_V\\approx\n-0.4$ strong anomalies already appear, reminiscent of the steep\nincrease in the calculations mixing deeper (dashed lines). In the case\nof Na no further enhancement is visible (the range of values does not\nvaries along the RGB), while O seems to get depleted further. In spite\nof the incomplete data at hand, the abundance anomalies seem to\ndevelop rather early and within a narrow brightness range, but then do\nnot increase any more. This general behaviour is consistent with our\ntheoretical predictions -- though not exactly reproduced -- and again\npoints to not too deep mixing at moderate speed. The calculations with\nextreme helium mixing would predict the largest O depletion and Na\nenhancement all along the RGB; the absence of such stars can therefore\nnot be explained with a selection effect working against the shortest\nlived stars at the tip of the RGB. The fact that M13 seems to show\nanomalies already before the bump has to be taken with care, because\nwe compare here only with one stellar model which has a metallicity\nalmost a factor of 10 smaller than that appropriate for M13. At that\nmetallicity, the bump would occur about 1~mag earlier (and our initial\nmodel is about 0.2~mag brighter than the end of the bump). We stress\nthe fact that the present observational data do not allow a detailed\ncomparison with the abundance evolution, but only rough qualitative\nstatements.\n\nAlthough Fig.~\\ref{f:naomv} again demonstrates how the abundance\nevolution depends on the assumption about the additional mixing\nprocess, our calculations also show that the nucleosynthesis argument\ngiven above is valid for {\\em all} mixing descriptions tested and\ntherefore model-independent. From this we predict that {\\sl red giants\nexhibiting the observed Na-O-anomalies do not have envelopes enriched\nin helium by much more than $\\triangle Y_{\\rm env} \\approx 0.05$,\nwhich is comparable to the general uncertainty in our knowledge about\nthe helium abundances in such stars.}\n\nConcerning the brightness reached during the RGB evolution, we showed\nthat for specific mixing prescriptions large excess luminosities can\nbe achieved at the end of the evolution without simultaneous mixing of\nlarge amounts of helium. As the reason we could identify the burning\nof the outer parts of the hydrogen shell where some H-He-mixing had\nhappened in earlier phases. These regions become hot enough for\nsignificant hydrogen burning on such short time-scales that the deep\nmixing process is not able to mix the products any longer into the\nconvective envelope. Such models experience very strong mass loss\nunder the assumption of the continuing validity of a Reimers-type\nstellar wind and finish the RGB phase with total masses below\n$0.6\\,M_\\odot$ and envelope masses of only 10\\% of this. They could be\ncandidates for blue HB stars and would link observed abundance\nanomalies, deep mixing and the second parameter problem, as suggested\nby \\citen{lh:95} and \\citen{swei:97}. They would avoid the problem of\noverproducing O-Na-anomalies as would result from the helium mixing\ninvestigated by \\citen{swei:97}.\n\nHowever, we repeat our warning that the details of the evolutionary\nconsequences of deep mixing depend crucially on the mixing process and\nhistory. Mixing speed and depth are both important for the amount of\nhelium mixed and for the result of the competing processes ``mixing''\nand ``burning'' and their time-scales. The mixing depth is also linked\nto the criterion for deep mixing, for which we have investigated\nseveral simple recipes.\n\nTo conclude, we need a solid physical picture for the deep mixing\nprocess in order to be able to investigate its effect on red giant\nevolution further. Presently, we can only point out some interesting\npossibilities -- such as the overluminosities -- and derive\nmodel-independent features, such as our main conclusion that the\nobserved anomalies of oxygen and sodium rule out strong helium\nenhancement and therefore very deep mixing.\n\n\n\\begin{acknowledgements}\nWe are grateful to A.~Sweigart for helpful discussions. This study\nwas partly done while CC and PAD visited the Max-Planck-Institut f\\\"ur\nAstrophysik in Garching. They express their gratitude to the staff for\nhospitality and support. We appreciate the very careful work of\nan anonymous referee, whose detailed and constructive comments helped\nto improve this paper.\n\\end{acknowledgements}\n\n\\newpage\n%\n%\\bibliographystyle{aa_weiss}\n%\\bibliography{mixing}\n\\begin{thebibliography}{50}\n\n\\bibitem[\\protect\\astroncite{Angulo et~al.}{1999}]{Angulo99}\nAngulo C., Arnould M., Rayet M., et~al., 1999, Nucl.Phys. 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"string": "\\begin{thebibliography}{50}\n\n\\bibitem[\\protect\\astroncite{Angulo et~al.}{1999}]{Angulo99}\nAngulo C., Arnould M., Rayet M., et~al., 1999, Nucl.Phys. A 656, 3\n\n\\bibitem[\\protect\\astroncite{Armosky et~al.}{1994}]{Armosky94}\nArmosky B.J., Sneden C., Langer G.E., Kraft R.P., 1994, AJ 108, 1364\n\n\\bibitem[\\protect\\astroncite{Boothroyd \\& Sackmann}{1999{a}}]{bs:99b}\nBoothroyd A.I., Sackmann I.J., 1999{a}, ApJ 510, 232\n\n\\bibitem[\\protect\\astroncite{Boothroyd \\& Sackmann}{1999{b}}]{bs:99a}\nBoothroyd A.I., Sackmann I.J., 1999{b}, ApJ 510, 217\n\n\\bibitem[\\protect\\astroncite{Brown \\& Wallerstein}{1992}]{bw:92}\nBrown J.A., Wallerstein G., 1992, AJ 104, 1818\n\n\\bibitem[\\protect\\astroncite{Cavallo et~al.}{1998}]{csb:98}\nCavallo R., Sweigart A., Bell R., 1998, ApJ 492, 575\n\n\\bibitem[\\protect\\astroncite{Charbonnel}{1995}]{cchar:95}\nCharbonnel C., 1995, ApJL 453, L41\n\n\\bibitem[\\protect\\astroncite{Charbonnel et~al.}{1998}]{cbw:98}\nCharbonnel C., Brown J.A., Wallerstein G., 1998, A\\&A 332, 204\n\n\\bibitem[\\protect\\astroncite{Charbonnel et~al.}{1992}]{cvz92}\nCharbonnel C., Vauclair S., Zahn J.P., 1992, A\\&A 255, 191\n\n\\bibitem[\\protect\\astroncite{{Da~Costa}}{1998}]{daco:98}\n{Da~Costa} G.S., 1998, in T.~R. Bedding, A.~J. Booth, and J. Bavis (eds.),\n Fundamental Stellar Properties: the interaction between observation and\n theory, no. 189 in IAU Symp. 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}
] |
astro-ph0002291
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The shock waves in decaying supersonic turbulence
|
[
{
"author": "Michael D. Smith$^{1}$"
},
{
"author": "Mordecai-Mark Mac Low$^{2,3}$ \\& Julia M. Zuev$^4$"
}
] |
%============================================================================== We here analyse numerical simulations of supersonic, hypersonic and magnetohydrodynamic turbulence that is free to decay. Our goals are to understand the dynamics of the decay and the characteristic properties of the shock waves produced. This will be useful for interpretation of observations of both motions in molecular clouds and sources of non-thermal radiation. We find that decaying hypersonic turbulence possesses an exponential tail of fast shocks and an exponential decay in time, i.e. the number of shocks is proportional to $t\,\exp (-ktv)$ for shock velocity jump $v$ and mean initial wavenumber $k$. In contrast to the velocity gradients, the velocity Probability Distribution Function remains Gaussian with a more complex decay law. The energy is dissipated not by fast shocks but by a large number of low Mach number shocks. The power loss peaks near a low-speed turn-over in an exponential distribution. An analytical extension of the mapping closure technique is able to predict the basic decay features. Our analytic description of the distribution of shock strengths should prove useful for direct modeling of observable emission. We note that an exponential distribution of shocks such as we find will, in general, generate very low excitation shock signatures. \keywords{Hydrodynamics -- Turbulence --Shock waves -- ISM: clouds -- ISM: kinematics and dynamics }
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[
{
"name": "final.tex",
"string": "\\documentstyle[amsmath,graphics,graphicx,rotate,pifont,psfig]{l-aa}\n\\input{epsf}\n\n%==============================================================================\n\\topmargin=3.0cm\n\\begin{document}\n \\thesaurus{08 \n (02.08.1; \n 02.19.1; \n 02.20.1;\n 09.03.1;\n 09.11.1 )}\n\n\\title{The shock waves in decaying supersonic turbulence}\n\n\\author{Michael D. Smith$^{1}$, Mordecai-Mark Mac Low$^{2,3}$ \\& \nJulia M. Zuev$^4$}\n\\offprints{M.D. Smith}\n\n\\institute{\n$^1$ Armagh Observatory, College Hill, Armagh BT61 9DG, Northern Ireland\\\\\n$^2$ Max-Planck-Institut f\\\"ur Astronomie, K\\\"onigstuhl 17,\nD-69117 Heidelberg, Germany\\\\ \n$^3$ Department of Astrophysics, American Museum of Natural History,\n79th St. at Central Park West, New York, New York, 10024-5192, USA\\\\\n$^4$ JILA, University of Colorado, Boulder, Campus Box 440, Boulder, CO 80309, USA\\\\ \nInternet: mds@star.arm.ac.uk, mordecai@amnh.org, julia.zuev@colorado.edu}\n\n\\date{Received; accepted}\n\n\\maketitle\n\\markboth{Smith, Mac Low \\& Zuev: Supersonic Turbulence}{}\n\n%==============================================================================\n\\begin{abstract} \n%==============================================================================\n\nWe here analyse numerical simulations of supersonic, hypersonic \nand magnetohydrodynamic turbulence that is free to decay. Our \ngoals are to understand the dynamics of the decay and the\ncharacteristic properties of the shock waves produced. This \nwill be useful for interpretation of observations of both \nmotions in molecular clouds and sources of non-thermal radiation. \n\nWe find that decaying hypersonic turbulence possesses an \nexponential tail of fast shocks and an exponential decay in time, \ni.e. the number of shocks is proportional to $t\\,\\exp (-ktv)$ for \nshock velocity jump $v$ and mean initial wavenumber $k$. In \ncontrast to the velocity gradients, the velocity Probability \nDistribution Function remains Gaussian with a more complex decay \nlaw. \n\nThe energy is dissipated not by fast shocks but by a large number of \nlow Mach number shocks. The power loss peaks near a low-speed\nturn-over in an exponential distribution. An analytical extension of \nthe mapping closure technique is able to predict the basic decay \nfeatures. Our analytic description of the distribution of shock \nstrengths should prove useful for direct modeling of observable \nemission. We note that an exponential distribution of shocks such as \nwe find will, in general, generate very low excitation shock \nsignatures. \n\n\\keywords{Hydrodynamics -- Turbulence --Shock waves -- ISM: clouds -- \n ISM: kinematics and dynamics }\n \n\\end{abstract}\n\n%====================== SECTION 1 ========================\n%==========================================================\n\\section{Introduction}\n%==========================================================\n\nMany structures we observe in the Universe have been shaped by fluid \nturbulence. In astronomy, we often observe high speed turbulence \ndriven by supersonic ordered motions such as jets, supernova shocks \nand stellar winds (e.g. Franco \\& Carraminana 1999). Hypersonic speeds, \nwith Mach numbers above 10, are commonly encountered. Clearly, to \nunderstand the structure, we require a theory for supersonic turbulence. \nHere, we concentrate on decaying turbulence, such as could be expected \nin the wakes of bow shocks, in the lobes of radio galaxies or following \nexplosive events. Two motivating questions are: how fast does \nsupersonic turbulence decay when not continuously replenished and how \ncan we distinguish decaying turbulence from other dynamical forms? The \nfirst question has been answered through recent numerical simulations \ndescribed below. The answer to the second question is sought here. We \nlook for a deep understanding of the dynamics and physics which control \ndecaying supersonic turbulence. From this, and a following study of \ndriven turbulence, we can derive the analytical characteristics and \nthe observational signatures pertaining to supersonic turbulence. \nWe caution that we specify to uniform three dimensional turbulence with \nan isothermal equation of state, an initially uniform magnetic field \nand periodic boundary conditions.\n\nNumerical studies of decaying supersonic turbulence in three dimensions \nhave revealed a power-law decay of the energy in time following a short \nlow-loss period (Mac Low et al. 1998; Stone et al. 1998).\nSimulations of decaying subsonic and incompressible turbulence show\nsimilar temporal behaviour (e.g. Galtier et al. 1997), as \ndiscussed by Mac Low et al. (1999). In the numerical experiments, random \nGaussian velocity fields were generated with small wavenumber \ndisturbances. Magnetic fields were included of various strengths. \nMac Low (1999) concluded that the decay is so rapid under all conditions \nthat the motions we observe in molecular clouds must be continuously \ndriven. In this work, we analyse the Mach 5 simulations from Mac Low et \nal. (1998) as well as a new Mach 50 simulation. The hypersonic run \nshould best illustrate the mechanisms behind the development and \nevolution of the shock field, possibly revealing asymptotic solutions.\n\nThe major goal is to derive the spectrum of shocks (the Shock \nProbability Distribution Function) generated by turbulence. Shocks \nare often responsible for detailed bright features, such as \nfilamentary and sheet structures, within which particles are highly \nexcited. An example of a region which appears to contain a chaotic \nmixture of shocks, termed a 'Supersonic Turbulent Reactor' is the \nDR\\,21 molecular hydrogen outflow, driven by a collimated wind \nfrom a high mass young star (Smith et al. 1998). The shock spectrum \nis related to the molecular excitation, with weak shocks being \nresponsible for rotational excitation and strong shocks for\nvibrational excitation.\n\nPrevious studies of compressible turbulence have concentrated on the \ndensity and velocity structure of the cold gas rather than the shocks. \nThree dimensional subsonic and transonic simulations (e.g. Porter \net al. 1994; Falgarone et al. 1994), two dimensional supersonic motions \n(V\\'azquez-Semadeni 1994) as well as three dimensional supersonic \nturbulence have been discussed (V\\'azquez-Semadeni et al. 1996, Padoan \net al. 1998). One attempts to describe and fit the density and \nvelocity structures observed in molecular clouds. This is often \nappropriate for the interpretation of clouds since, although the Mach \nnumber is still high, the shock speeds are too low to produce bright \nfeatures. The simulations analysed here are also being interpreted by \nMac Low \\& Ossenkopf (2000) in terms of density structure.\n\nDespite a diversity of theory, and an increase in analytical knowledge,\na succinct understanding of turbulence has not been attained (see\nLesieur 1997). Therefore, we need not apologise for not fully \ninterpreting the results for the supersonic case. We do not look for a \nKolmogorov-inspired theory for two reasons. First, fully developed \nturbulence becomes increasingly non-Gaussian towards small scales. \nThese intermittency effects dominate the statistics of velocity jumps \nin supersonic turbulence. Second: the strong compressibility implies \nthat a wavenumber analysis is irrelevant since the energy spectrum of \na shock or of a system of shocks is simply $k^{-2}$ (e.g. Gotoh \\& \nKraichnan 1993). Note that the Kolmogorov-like spectra found by Porter \net al. (1994) appeared at late times when the flow is clearly subsonic \n(and also note that even the initial RMS Mach number was only unity, \nwhich rather stretches the definition of supersonic turbulence).\n\nWe attempt here to construct a physical model to describe the non-Gaussian \nProbability Density Functions (PDFs) for the shock waves. We adapt \nthe mapping closure analysis, as applied to Navier-Stokes \n(incompressible) and Burgers (one dimensional and pressure free) turbulence \n(Kraichnan 1990), to compressible turbulence. Phenomenological \napproaches, such as multifractal models or the log-normal model, \nare avoided since they have limited connection to the underlying physical \nmechanisms. In contrast, mapping closure follows the stretching and \nsqueezing of the fluid, and the competition between ram pressure, \nviscosity and advection determines the spectral form.\n\nWe study here compressible turbulence without gravity, self-gravity\nor thermal conduction. No physical viscosity is modelled, but numerical \nviscosity remains present, and an artificial viscosity determines the \ndissipation in regions of strong convergence. By strong convergence, we mean\nhigh negative divergence of the velocity field, which thus \ncorrespond to the shock zones as shown in Fig.\\,\\ref{shockfield}.\nPeriodic boundary conditions were chosen for the finite difference \nZEUS code simulations, fully described by Mac Low et al. (1998). \n\nThe ZEUS code itself is a time-explicit second-order accurate \nfinite difference code (Stone \\& Norman 1992a,b). It is ideal for \nproblems involving supersonic flow and is versatile, robust and \nwell-tested. Although higher order codes are potentially more \naccurate, the high speed of the algorithms means that large \nproblems can be solved at high resolution. This enables us to \ntest for convergence of the energy dissipation rate (Mac Low \net al. 1998), shock distributions (Sect. 2.4) and numerical viscosity\n(Sect. 2.6). Furthermore, the basic hydrocode results have been confirmed on \nsolving the same problems with the contrasting method of smoothed\nparticle hydrodynamics (Mac Low et al. 1998). The constrained transport \nalgorithm (Evans \\& Hawley 1988) updated through use of the method of \ncharacteristics (Hawley \\& Stone 1995) is used to maintain a divergence-free \nmagnetic field to machine accuracy and to properly upwind the advection.\n \nWe begin by discussing the method used to count shocks from grid-based \nsimulations (Sect. 2.1-2.2). We then present the shock jump PDFs and provide \nanalytical fits for the hypersonic M = 50 case (Sect. 2.3-2.5). The \none-dimensional counting procedures are verified through a comparison \nwith full three-dimensional integrations of the dissipated energy (Sect. 2.6). \nSupersonic hydrodynamic M = 5 (Sect. 3) and magnetohydrodynamic (Alf\\'ven \nnumbers A = 1 and A = 5) simulations (Sect. 4) are then then likewise \nexplored. Note the definition of the Alfv\\'en Mach number \n$A = v_{\\rm rms}/v_{\\rm A}$, where $v_{\\rm A}^2 = B^2 / 4 \\pi \\rho$ \nwhere $v_{\\rm rms}$\nis the initial root mean square (RMS) velocity and $v_{\\rm A}$ is the\nAlfv\\'en speed. The evolution of the velocity PDFs are then presented and \nmodelled (Sect. 5). Finally, we interpret the results in terms of the \ndynamical models (Sect. 6).\n\n%====================== SECTION 2 ========================\n%=========================================================\n\\section{Hydrodynamic hypersonic turbulence}\n%===========================================================\n \n\\subsection{Model description}\n\nThe example we explore in detail is the decay of hypersonic hydrodynamic \nturbulence (Fig.\\,\\ref{shockfield}). The three dimensional numerical \nsimulation on a D$^3$ = 256$^3$ grid with periodic boundary conditions \nbegan with a root mean square Mach number of M = 50. The initial \ndensity is uniform and the initial velocity perturbations were drawn \nfrom a Gaussian random field, as described by Mac Low et al. (1998). \nThe power spectrum of the perturbations is flat and limited to the \nwavenumber range $1 < k < k_{max}$ with $k_{max} = 8$.\n%FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF1111111\n\\begin{figure*}[hbt]\n \\begin{center}\n \\leavevmode\n \\psfig{file=1812F1.ps,width=0.95\\textwidth,angle=0}\n\\caption{Four stages in the early development of the shock field. The \ndistribution of converging regions (i.e. the negative velocity divergence of \nthe velocity field) is displayed here for a cross-sectional plane of \nthe hydrodynamic M = 50 simulation. The displayed values are the \nnumerical equivalents of the divergence (i.e. the sum of the velocity\ndifferences) at each grid location. In order of increasing time, the \nminimum divergence (maximum convergence) and the average divergence \nwithin converging regions only in the displayed cross-sections are: \n(-178.4, -46.6), (-441.9, -48.0), (-146.7, -13.74) and (-99.9, -7.3).} \n\\label{shockfield}\n \\end{center}\n\\end{figure*} \n\nThe simulations employ a box of length 2L (hence L is equivalent to\n128 zones in this example) and a unit of speed, $u$. The gas is \nisothermal with a sound speed \nof $c_s = 0.1u$. Hence the sound crossing time is 20L/u. We take the time \nunit as $\\tau$ = L/u. Thus a wave of Mach 50 would laterally cross the box \nin a time 0.4$\\tau$ if unimpeded.\n\nCross-sections of the shock distribution are shown at four times in\nFig.\\,\\ref{shockfield}. We actually display a greyscale image,\nbiased to the high-convergence regions. An evolution is hardly \ndiscernable in snapshots showing all converging regions equally\nshaded (as displayed in Fig. 1 of Mac Low et al. 1999). \n\n\\subsection{Shock number distribution}\n\nIdeally, we would like to calculate the total surface area for each \nshock strength as a function of time. We introduce the shock number\ndistribution function $dN/dv$, which is the number of shock elements per unit \nshock speed as a function of time and shock speed. A shock\nelement is the surface area of a shock put into units of the grid cell area.\n\nTo simplify our numerical analysis, we calculate\ninstead the one dimensional shock jump function.\nThis is the number distribution of the total jump in speed across\neach converging region along a specific direction. This is written as\n$dN/dv_j$ where $v_j$ is the sum of the (negative) velocity gradients\n(i.e. $\\Sigma\\left[-{\\delta}v_x\\right]$ across a region being\ncompressed in the x-direction).\nWe employ the jump Mach number in the x-direction M$_j = v_j/c_s$ rather\nthan $v_j$ since this is the parameter relevant to the \ndynamics. Thus, each bounded region of convergence in the x-direction\ncounts as a single shock and the total jump in M$_j$ across this region\nis taken as its strength. \n\nNumerically, over the whole simulation grid \n(x,y,z), we calculate each shock jump through\n\\begin{equation}\nM_j = \\sum_{x=x_i}^{x=x_f} ({\\Delta}v_x/c_s)\n\\end{equation}\nwith the condition that ${\\Delta}v_x < 0$ in the range $x_i \\le x < x_f$.\nThis is then binned as a single shock element.\nThe shock number distribution $dN/dM_j$ is obviously dimensionless.\n\nThe 1D approach neglects both the shock angle and full shock \nstrength. The distribution of shock jumps, however, is found by \nadding up an enormous number of contributions over the whole grid. \nThis method has the advantage of being extremely robust, involving no model \nassumptions. To be a direct representation of the true shock \nstrength function, however, it requires a few assumptions to be \njustified: (1) a one-dimensional shock jump is\n related to the actual shock speed, \n(2) not too many shocks are excluded because their surfaces \nare aligned with the chosen direction, (3) the shock velocities are\ndistributed isotropically and (4) unsteepened compressional waves\ncan be distinguished from true shocks. \n\nFirst, we note that it is an extremely difficult task to calculate \nthe actual shock speed for each shock. It is, however, unnecessary \nsince the shock speed and one-dimensional shock jump are closely related \nstatistically. We also take the number of zones at which \ncompressive jumps are initiated as the number of shocks (where \nshocks are colliding, the method will be inaccurate). \nAssumption (3) will not hold for the magnetohydrodynamic \nturbulence which has a defined direction. In these cases, the jump \ndistributions must be calculated both parallel and transverse to the \noriginal magnetic field. Assumption (4) will not be made: we include \nall acoustic waves, but we have followed the\nwidth of the jumps and so can verify whether shocks or waves\nare being counted. This is important since broad compressional waves \nalso dissipate energy and become increasingly significant, of course, \nas the high-speed shocks decay and the flow eventually becomes subsonic.\n\nMany shock surfaces are distorted, occasionally bow-shaped. This does \nnot negate our counting procedure provided the curvature is not too \nstrong. Here the relevant lengths are the shock radius of curvature \nand the shock width. The latter is determined by our numerical method, \ninvolving von Neumann \\& Richtmyer (1950) artificial viscosity, which \nhere constrains strong shocks to just a few zones. As seen from \nFig.\\,\\ref{shockfield}, we can confidently take one-dimensional cuts \nacross the shock surfaces and equate the measured jump to the\nactual jump in speed of fluid elements to a good first approximation.\n\nIn Sect.\\,2.6, we check our method by demanding consistency with\nintegrated quantities derived directly from the numerical simulations.\n\n%ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss\n\\subsection{Hypersonic turbulence}\n%ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss\n\nThe random Gaussian field rapidly transforms into a shock field in the \nMach 50 case (Fig.\\,\\ref{shockfield}). The shock steepening is reflected \nin the initial increase in the minimum value of the divergence (see the \ncaption to Fig.\\,\\ref{shockfield}). Note that the {\\em average} value of \nthe divergence does not change i.e. the total number of converging zones \nonly falls from half to about one third, despite the steepening. The \nexplanation is that the shocks have time to form in the strongly \nconverging regions but the compression in most of the flow progresses \nslowly. After the time t = 0.1, the number of fast shocks decays and \nthe average convergence decreases. The total number of zones with \nconvergence, however, remains constant throughout. This fact, that the \ntotal shock surface area is roughly conserved, is verified in the \nfollowing analysis. \n\nThe one-dimensional distribution of the number of shock jumps as a\nfunction of time is presented in Fig.\\,\\ref{number} for the case with \nRMS Mach number M = 50. This demonstrates that the shock jump function \nboth decays and steepens. One can contrast this to the decay of\nincompressible turbulence where the distribution function, as\nmeasured by wavenumber, maintains the canonical Kolmogorov power-law in \nthe inertial range during the decay (Lesieur 1997). Here we remark that \na power-law fit is impossible (Fig.\\,\\ref{number}a) but stress that this \nresult applies only to the case at hand: {\\em decaying} turbulence.\n\n\n%FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF2222222\n\\begin{figure*}\n \\begin{center}\n \\leavevmode\n \\psfig{file=1812F2.ps,width=0.95\\textwidth,angle=0}\n\\caption{The jump velocity distribution. Two representations of the\nnumber of compressive layers in the x-direction as a function\nof the total x-speed change across the layer at 10 equally-spaced times\nbeginning at time $t = 0.5$ (solid line) and continuing, with a\nmonotonic decay of the high-speed jumps, in time steps of 0.5. \nThey demonstrate the decay and steepening and that (a) no power law can\nrepresent the behaviour at any stage, and (b) a series of exponentials of\nthe form ${\\exp}(-t(v_j-2)/2)$ fit the high velocities well. } \n\\label{number}\n \\end{center}\n\\end{figure*} \n\nThe jump distribution is very close to being exponential in both\nvelocity and time. This remarkably simple conclusion is based on the\ngood fits shown in Fig.\\,\\ref{number}b. Note that the\npure exponential only applies to the medium and strong shock regime.\nTo also account for the low Mach number regime, we fitted a further time\ndependence as shown in Fig.\\,\\ref{fitted}, yielding\n\\begin{equation}\n\\frac{dN}{dM_j} = 10^{5.72}\\,t\\,\\exp (-M_j\\,t/2.0)\n\\end{equation}\nin terms of the 1-D jump Mach number. Better fits can be obtained\nwith a somewhat more complex time dependence. We find excellent fits for\n\\begin{equation} \n\\frac{dN}{dM_j} = 10^{5.79}\\,t\\,{\\exp}\\left[-\\,{\\beta}\\,M_j\\,t^{\\alpha}\\right]\n\\end{equation}\nwith $\\alpha \\sim 0.88 \\pm 0.03$ and $\\beta \\sim 0.52 \\pm 0.03$. The\nvalues and errors are derived from parameter fitting of\n all the displayed curves to within a factor of $\\sim 1.5$.\nWe exclude in this process the phase where collisional\nequilibrium would not be expected: at early times and low Mach \nnumbers $t\\,M_j < 0.5$. Also, we exclude the jump speeds\nwhere the jump counts are low\n(shock numbers ${dN}/{dM_j} < 3000$). \n\n%FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF3333333\n\\begin{figure*}\n \\begin{center}\n \\leavevmode\n \\psfig{file=1812F3.ps,width=0.95\\textwidth,angle=0}\n\\caption{The jump velocity distribution extracted from the M = 50\nhydrodynamic simulation as a function of time, as in Fig.\\,\\ref{number}.\nThe fitted function is $dN/dM_j\\,=\\,10^{5.42}\\,t\\,{\\exp}(-tM_j/2)$. } \n\\label{fitted} \n \\end{center}\n\\end{figure*} \n\n%sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss\n\\subsection{Convergence and dependence on initial conditions}\n%ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss\n\nResolution studies are essential to confirm numerical results. One hopes \nthat the results demonstrate convergence. This is plausible for supersonic \nflow in which the decay does not depend on the details of the viscosity \nor the details of the shock transitions. This has been confirmed for the\nanalysis of the total energy (Mac Low et al. 1998).\n\nWe compare available simulations for the hypersonic study with 64$^3$ \nand 128$^3$. We also set the initial wavenumber range to $k_{max} = 2$ \nand can thus examine the dependence on the chosen initial state.\n\nThe results at the two different resolutions are in quite good agreement,\nespecially in the high Mach number regime (Fig.\\,\\ref{number2}). The density \n%FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF4444444444444444444\n\\begin{figure}[t]\n \\begin{center}\n \\leavevmode\n\\psfig{file=1812F4.ps,width=0.53\\textwidth,angle=0}\n\\caption{The evolution of the jump velocity distribution at two \nresolutions for M = 50 hydrodynamic simulation with k$_{max}$ = 2. The\nshock number for the 64$^3$ simulation has been multiplied by 4 to\nadjust for the larger zone sizes. } \n \\label{number2} \n \\end{center}\n\\end{figure}\nof high Mach number\nshocks is quite low and they are well resolved. At low Mach numbers, the lower\nresolution simulation fails, of course, to capture the vast quantities\nof weak compressional waves contained in the higher resolution example.\nIt is to be expected that shock turbulence configurations get \nextremely complex on small scales, through the interactions which produce\ntriple-point and slip-layer structures. To capture this structure\nrequires adaptive grid codes. This does not mean, however, that\nthe simulations are inaccurate for our purposes since energy dissipation is not\ncontrolled by the weak shocks until very late times, as verified in\nFig.\\,\\ref{power50}. \n%FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF555555555555555555555555\n\\begin{figure*}\n \\begin{center}\n \\leavevmode\n \\psfig{file=1812F5.ps,width=0.95\\textwidth,angle=0}\n\\caption{The power dissipated as a function of the jump velocity. The \npower is displayed per unit M$_j$ where M$_j$ = v$_j$/c$_s$, and the \ndata is extracted from the M = 50 hydrodynamic simulation for times \nt = 1,2,3,4 \\& 5. The fitted function is \n$d\\dot E/dM_j\\,=\\,0.016\\,t\\,M_j^{2.5}\\,{\\exp}(-tM_j/2)$.} \n\\label{power50}\n \\end{center}\n\\end{figure*} \n\nA similar formula for the shock jump function is found. The evolution, \nhowever, is three times slower. We show in Fig.\\,\\ref{fitted2} the model fit\n %FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF66666666666666666666666666666\n\\begin{figure}[hbt]\n \\begin{center}\n \\leavevmode\n \\psfig{file=1812F6.ps,width=0.53\\textwidth,angle=0}\n\\caption{The jump velocity distribution extracted from the 128$^3$ M = 50\nhydrodynamic simulation with k$_{max}$ = 2 as a function of time.\nThe fitted function is $dN/dM_j\\,=\\,10^{3.93}\\,t\\,{\\exp}(-tM_j/6)$. } \n\\label{fitted2} \n \\end{center}\n\\end{figure} \n\\begin{equation}\n\\frac{dN}{dM_j} = 10^{4.23}\\,t\\,\\exp (-M_j\\,t/6.0).\n\\end{equation}\n\nThis suggests that the rate of decay is proportional to the initial \nmean wavenumber of the wave distribution. The decay $k_{max} = 2$ \nsimulation is a factor of three slower than in the $k_{max} = 8$ \nsimulation. The mean wavenumber of the two simulations are $k_m = 1.5$ \nand $4.5$, with flat initial energy distributions. Hence, given that \n$M_j = v_x/c_s$ and t is in units of $L/10c_s$, the shock numbers\nare approximately $\\propto t\\,{\\exp}(-k_ot\\,v_j)$ where\n$k_o \\sim 1.1\\,k_m$. The dependence on the initial mean wavenumber is\nexpected since the box size should not influence the decay rate if\nwe are indeed, as we wish, following the unbounded decay.\n\nNote that two parameter fitting, as above, in this case yields\n\\begin{equation} \n \\frac{dN}{dM_j} = \n 10^{4.23}\\,t\\,{\\exp}\\left[-\\,{\\beta}\\,M_j\\,t^{\\alpha}\\right]\n\\end{equation}\nwith $\\alpha \\sim 1.02 \\pm 0.03$ and $\\beta \\sim 0.168 \\pm 0.008$.\n\n%=======================================================================\n\\subsection{Shock power distribution}\n%=======================================================================\n\nHow is the spectrum of shock jumps related to the decay of energy? Here\nwe show that the energy dissipation in the fast shocks is directly\ncorrelated with their number which is decreasing\nexponentially. Furthermore, the weakest shocks, which merge into\nan area of 'compressional waves', are ineffective in the overall\ndissipation. The result is that the moderately-supersonic part\nof the turbulence rapidly becomes and remains responsible for the \nenergy dissipation for an extended time. \n\nThe shock power distribution function is here defined as the energy\ndissipated per unit time per unit jump speed $v_j$ as a function of\njump speed. Here again we employ the uni-directional jump Mach number M$_j$.\nWe actually calculate the energy dissipated by artificial viscosity\nacting along a specific direction within the shocks as defined by \nconvergence along this direction. Hence we anticipate that in isotropic \nturbulence one third of the full loss will be obtained. The relative \ncontributions of artificial and numerical viscosity, which also confirms \nthe method employed here, are discussed in Sect.~2.5.\n\nThe jump {\\em number} distribution includes a high proportion of very \nweak compressional waves that dissipate little energy. The \none-dimensional shock power distribution, d$\\dot E$/dM$_j$, shown in \nFig.\\,\\ref{power50}, illustrates this. The functional fit is guided by \nthe above shock number distributions, which we would expect to remain \naccurate for the high Mach number jumps. We display the fit to:\n\\begin{equation}\n \\frac{d\\dot E}{dM_j} = 0.016\\,M_j^{2.5}\\,t\\, \\exp(-k\\,M_j\\,t)\n\\label{eqnpow}\n\\end{equation}\nwith k = 0.5, which is again remarkably accurate given the lack of \nadjustable parameters.\nHence ${d\\dot E}/{dM_j} \\propto M_j^{2.5}{d\\dot N}/{dM_j}$. Note that the\nenergy dissipated across an isothermal steady shock of Mach number M and \npre-shock density\n$\\rho$ is $\\dot E_s$ = (${\\rho}c_s^3$/2)\\,M$^3$(1\\,-\\,1/M$^2$) and that \nthe jump in Mach number is M$_J$ = M(1\\,-\\,1/M$^2$). This yields\n\\begin{equation}\n \\dot E_s = 0.5\\,{\\rho}c_s^3\\,M_J^3\\,\n \\left[1\\,+\\frac{\\surd(1+4/M_J^2)\\,-\\,1}{2}\\right].\n\\end{equation}\nTherefore, the numerical result suggests a (statistical) inverse\ncorrelation between density and shock strength.\n\nNote that Eq.\\,\\ref{eqnpow} yields $\\dot E \\propto t^{-2.5}$ (on \nintegrating over $M_j$ and substituting the variable $w = M_jt$) \nThus, one obtains a power-law decay in total energy of the form E \n$\\propto$ t$^{-1.5}$. This behaviour of the total energy decay and \nthe energy dissipation rate, is indeed found in the simulations, \nas shown in Fig.\\,\\ref{powertime}. Hence the results are fully \nconsistent with the simple fits.\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%777777777777777777777777777\n\\begin{figure}[hbt]\n \\begin{center}\n \\leavevmode\n \\psfig{file=1812F7.ps,width=0.53\\textwidth,angle=0}\n\\caption{The total energy as a function of time (full line) from data \nextracted from the M = 50 hydrodynamic simulation. For comparison, the \ndashed line is a power law with exponent -1.5.} \n\\label{powertime}\n \\end{center}\n\\end{figure} \nNote that the energy decay deviates from a pure power law: there is \nan early transition phase between times t = 0.1 - 0.5 during which \nthe decay is more rapid (Fig.\\,\\ref{powertime}). This was not found \nin simulations of moderate Mach number supersonic turbulence (Mac \nLow et al. 1998) but appears here and also in simulations in which \nthe supersonic turbulence is initially driven (Mac Low 1999). \n\n%=======================================================================\n\\subsection{Shock power and artificial viscosity}\n%=======================================================================\nIn order to check the approximations described in Sect.~2.2, we analyse\nhow the energy dissipated due to artificial viscosity\nvaries over time and with different parameters of the model. For \nnon-driven, or freely decaying runs, the following equation is \ntaken as a basic:\n\\begin{equation}\n \\frac{{dE}}{dt} = - (H_{\\nu} + H_{numerical})\\label{basic_h},\n\\end{equation}\nwhere $H_{\\nu}$ and $H_{numerical}$ are energy dissipation rates due\nto artificial viscosity and numerical viscosity respectively. \n\nWe follow Stone \\& Norman (1992) Eqs. (32)-(34), (134) in\ncomputing $H_{\\nu}$. The first step in computing derivatives is to realize that\nartificial viscosity operates on compression only, so points with positive\nderivatives in each direction are set to zero :\n\\begin{equation}\n {\\partial{v1}}_{i,j,k} = \\left\\{ \\begin{array}\n {l@{\\quad \\quad}l}\n 0 & {\\mbox{if } (v1_{i+1,j,k}-v1_{i,j,k})> 0} \\\\\n {v1_{i+1,j,k}-v1_{i,j,k}} & {\\mbox{otherwise}}.\n \\end{array} \\right. \n\\end{equation}\nThen scalar artificial pressures $q_i$ in all 3 directions are \ncomputed, with the uniform mesh ($\\Delta x$) :\n\\begin{equation}\n q_i = {l^2}{\\rho}{\\left( \\frac{\\partial{v_i}}{\\partial{x_i}} \n \\right)}^2 = {\\left[ \\frac{l}{\\Delta x}\\right] }^2 \n {\\rho} {({\\partial{v_i}})}^2\n\\end{equation}\nwhere ${(l/{\\Delta{x}})}^2$ is a dimensionless constant which\nmeasures the number of zones over which the artificial viscosity will\nspread a shock and was chosen to be 2 in these simulations. Then we \ncalculate the artificial viscosity tensor $h_{\\nu}$:\n\\begin{equation}\n {\\stackrel{\\longleftrightarrow}{h_{\\nu}}} = -{\\stackrel{\\longleftrightarrow}{\\nabla{v}}} : {\\stackrel{\\leftrightarrow}{Q}} = {(-1)}{\\left[{\\frac {\\partial{v1}}{\\partial {x1}}}{q1} + {\\frac {\\partial{v2}}{\\partial {x2}}}{q2} + {\\frac {\\partial{v3}}{\\partial {x3}}}{q3} \\right]} \n\\end{equation}\nand compute the artificial viscosity dissipation rate for the entire \ncube at each particular time dump as \n\\begin{equation}\n H_{\\nu} = \\int{\\stackrel{\\longleftrightarrow}{h_{\\nu}}} dx^3 \\sim\n \\sum_{ijk} (h_{\\nu,ijk}) \\delta x^3. \n\\end{equation}\nTo understand the convergence properties of the energy dissipation rate, \nwe performed a resolution study for resolutions of $64^3$, $128^3$,\nand $256^3$ zones for both hydrodynamic and MHD models. Fig.~\\ref{fig:g1} \n% ***********Figure 8888888888888888888888888888888888888888***************\n\\begin{figure}\n \\begin{center}\n \\includegraphics[width=0.485\\textwidth]{1812F8a.ps}\n \\includegraphics[width=0.485\\textwidth]{1812F8b.ps}\n \\end{center}\n\\caption{Resolution study for 3D models -- Energy dissipation rate due\nto artificial viscosity versus time. Top graph: model B (64$^3$,\ntriangle), model C (128$^3$, dashed line), and model D (256$^3$, solid\nline). Bottom graph: model N (64$^3$, triangle), model P (128$^3$,\ndashed line), and model Q (256$^3$, solid line). For hydrodynamic\nmodels we observe that the energy dissipation rate $H_{\\nu}$ has\nconverged to better than 35\\% moving from 64$^3$ to the 128$^3$\nmodels, and to better than 25\\% moving from the 128$^3$ to the 256$^3$\nmodels. These values are 37\\% and 23\\% for the MHD models. Thus,\nenergy dissipation rate due to artificial viscosity converges as we go\nto finer grids.}\n\\label{fig:g1} \n\\end{figure}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nshows that the energy dissipation rate $H_{\\nu}$ has converged to better \nthan 25\\% moving from the 128$^3$ to the 256$^3$ models.\n\nNow let us examine the fraction of the total kinetic energy lost to\ndissipation in shocks due to artificial viscosity $R = H_{\\nu}/ (dE/dt)$.\nWe avoid taking this ratio locally in time as variations of $H_{\\nu}$\nin time around the average lead to spurious results. A more robust way \nto compute this ratio is to integrate over the entire curve, thus \naveraging over the variations in $H_{\\nu}$ by computing\n\\begin{equation} \\label{ratio}\nR = \\frac {\\int H dt}{E_k(t_f) - E_k(t_0)}. \n\\end{equation}\nTable 1 shows these ratios for a set of models with $M=5$ and $k_{max}=8$. \n% *********************************TABLE***************\n\\begin{table*}\n\\begin{center}\n\\begin{tabular}{ccccccccc} \\hline\n\\multicolumn{9}{c}{\\bfseries Comparison of Ratios} \\\\ \\hline\nrun & B &C & D & N & P & Q & J & L \\\\\n\\hline \n grid &64$^3$ &128$^3$ &256$^3$ &64$^3$ &128$^3$ &256$^3$ &64$^3$ &256$^3$\\\\\n physics &Hydro &Hydro &Hydro &MHD &MHD &MHD &MHD &MHD\\\\\n A & $\\infty$ & $\\infty$ & $\\infty$ &1 &1 &1 &5 &5\\\\\n $R$ &0.62 &0.68 &0.68 &0.38 &0.36 &0.35 &0.59 &0.49\\\\\n \\hline \\end{tabular}\n \\caption{The fraction of the energy dissipated through artificial\n viscosity for models of supersonic turbulence. Ratio $R$ is defined\n by Eq.~(\\ref{ratio}). Model labels correspond to those of Table 1\n of Mac Low et al. (1998). A is the RMS Alfv\\'en Mach number.}\n\\end{center}\n\\end{table*}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\nThe table indicates that the energy dissipation ratio R has converged to \na few percent in the hydrodynamic case at the resolution of 128$^3$, and \neven in the MHD case is converged to better than 3\\% at $256^3$.\n\nWe find that the fraction of energy lost in shocks to artificial\nviscosity doubles when we go from MHD to hydrodynamic models. Mac Low\net al. (1998) speculated that runs with magnetic fields dissipating \nmuch of their energy via short-wavelength MHD waves. The factor of \ntwo difference in the dissipation rate due to artificial viscosity from\nhydrodynamic to MHD runs gives further evidence for this dissipation \nmechanism. This behavior appears well-converged, as discussed above.\n\n\n\n%==========================================================================\n\\section{Supersonic turbulence: M = 5}\n%==========================================================================\n\nModerate-speed hydrodynamic turbulence has been discussed by \nMac Low et al. (1998). They also found that the kinetic energy decreases\nwith time as a power law, but with a shallower exponent. For the M=5\nstudy (Model C) they recovered a E $\\propto t^{-1.0}$ law. \n\nThe shock jump distribution for M = 5 is shown in Fig.~\\ref{number5}. \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%9999999999999999999999999999999999\n\\begin{figure*}\n \\begin{center}\n \\leavevmode\n \\psfig{file=1812F9.ps,width=0.95\\textwidth,angle=0}\n\\caption{The jump velocity distribution extracted from the M = 5\nhydrodynamic simulation (Mac Low et al. 1998) as a function of time.\nThe fitted function is exponential in velocity but more complicated\nin time (see text) ($\\alpha = 0.67$ and $\\beta = 0.85$ displayed).\nThe time sequence shown is t = 1,2,3,5 and 10.} \n\\label{number5} \n \\end{center}\n\\end{figure*} \nExponential velocity distributions are again found even though the\nrange in Mach numbers over which we could expect a specific\nlaw is rather narrow (M$_j$ $\\sim 1 - 3$). Pure exponential\ntime fits, however, are not accurate. We display a suitable \nfit, of the form\n\\begin{equation} \n\\frac{dN}{dM_j} = 10^{6.07}\\,t^{\\alpha}\\,{\\exp}(-{\\beta}\\,M_jt^{\\alpha})\n\\end{equation}\nwith $\\alpha \\sim 0.67 \\pm 0.05$ and $\\beta \\sim 0.85 \\pm 0.1$.\nThe corresponding shock power distribution is shown in Fig.\\,\\ref{power5} \nalong with a best-fit family of curves calculated from\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%101010101010101010101010\n\\begin{figure*}\n \\begin{center}\n \\leavevmode\n \\psfig{file=1812F10.ps,width=0.95\\textwidth,angle=0}\n \\caption{The power dissipated as a function of the jump\n velocity. The power is displayed per unit M$_j$\n where M$_j$ = v$_j$/c$_s$, and the data is extracted \n from the M = 5 hydrodynamic simulation for times \n t = 1,2,3,4 \\& 5. The fitted function, given in the text,\n takes $\\alpha = 0.62$ and $\\beta = 1.6$.} \n \\label{power5}\n \\end{center}\n\\end{figure*} \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\begin{equation} \n\\frac{d\\dot E}{dM_j} = 0.10\\,M_j^{3.6}\\,t^{\\alpha}\\,\n {\\exp}(-{\\beta}\\,M_jt^{\\alpha})\n\\label{eqnpower}\n\\end{equation}\nwith $\\alpha = 0.62 \\pm 0.04$ and $\\beta = 1.6 \\pm 0.1$.Hence, an exponential velocity distribution is maintained. The decay,\nhowever, is slightly slower. Integrating over $M_j$, yields\n$E \\propto t^{-1.00}$.\n\n\nIntegrating over $M_j$, with the limits of integration from 0 to $\\infty$ (to\naccount for all the jumps), and with the substitution $x = M\nt^{\\alpha}$, we observe that the integral becomes\ntime-independent. Thus, integration of Eq.\\,\\ref{eqnpower} over $M_j$ yields\n${dE/dt} \\propto t^{-2.23}$. This yields $dE/dt \\propto\nt^{-1.23}$, which is quite close to the $E \\propto t^{-1}$ \nlaw found by Mac Low et al.\\ (1998). \n\nNow we want to compare how the two quantities vary with time: $dE/dt$\nfrom Eq.\\,\\ref{eqnpower} and the energy dissipation rate due to artificial \nviscosity $H_{\\nu}$, derived using the algorithm\ndiscussed in Sect. 2.6. Fig.~\\ref{fig:f1} shows that\nthe two methods indeed agree. Thus, the shock power distribution\nmethod (Sect. 2.6) confirms that the statistical approach works\nwith power calculations for each 1D converging region. \n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%11111111111111111111111111111111111111\n\\begin{figure}\n \\begin{center}\n \\includegraphics[width=0.485\\textwidth]{1812F11a.ps}\n \\includegraphics[width=0.485\\textwidth]{1812F11b.ps} \n \\end{center}\n\\caption{ Top: dE/dt versus time - the graph presents $H_{\\nu}$ for \nmodel C (grid 128, M=5, hydrodynamic) for 21 time dumps (rhombs), \nand integral of Eq. (8) over $dM_j$ (solid line). Both are energy \ndissipation rates due to artificial viscosity. We see a close fit of \nthe methods. For comparison, dashed line represents total kinetic \nenergy changes $dE/dt$ directly from the numerical simulation output. \nBottom: the absolute value of the relative error between $H_{\\nu}$ \nand integrated Eq. (\\ref{eqnpower}).} \n\\label{fig:f1} \n\\end{figure}\n\n%==========================================================================\n\\section{MHD turbulence: M = 5, A = 1 and 5}\n%==========================================================================\n\nAn analysis of simulations of MHD turbulence allows us to\ndetermine which wave modes are involved.\nThe time dependence of the kinetic energy of freely decaying\nMHD turbulence has been discussed by \nMac Low et al. (1998). Remarkably, the kinetic energy also decreases\nwith time as a power law, although with only a slightly shallower exponent\nthan the equivalent hydrodynamic simulation. We consider here\nthe high-field example in which the initial RMS Mach number M = 5\nand the initial RMS Alfv\\'en number A\nis unity and the low-field equivalent with A = 5. \nMac Low et al. recovered: E $\\propto t^{-0.87}$.\n(at the highest resolution of 256$^3$) for the high field case.\n\nThe initial field configuration is simply a uniform field aligned\nwith the z-axis. Thus the imposed velocity field controls the \nturbulent energy input, and some energy is subsequently transferred \ninto magnetic waves. We impose no turbulent diffusion here: magnetic energy\nmay, however, still be lost through numerical diffusion or MHD wave \nprocesses.\n\nThe jump number distribution function for these simulation \n(Fig. \\ref{numbermag})\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%1212121212121212121212121212121212\n\\begin{figure}\n \\begin{center}\n \\leavevmode\n \\psfig{file=1812F12a.ps,width=0.57\\textwidth,angle=0}\n \\psfig{file=1812F12b.ps,width=0.57\\textwidth,angle=0}\n\\caption{The jump velocity distribution extracted from the M = 5\nlow magnetic field (A = 5) and high field (A = 1) MHD 256$^3$ \nsimulations (Mac Low et al. 1998) as a function of time. The 5 \ntimes shown are t = 1,2,3,6 and 10. The two curves shown for\neach time are the velocity jumps transverse to the field (dashed) \nand parallel to the field (solid lines). The fitted exponentials \nare described in the text.} \n\\label{numbermag} \n \\end{center}\n\\end{figure} \npossesses exponential velocity distributions over a range in M$_j$. \nThe displayed fit to the high field case (Fig. \\ref{numbermagf}) is\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%1313131313131313131313131313131313131313\n\\begin{figure}\n \\begin{center}\n \\leavevmode\n \\psfig{file=1812F13.ps,width=0.57\\textwidth,angle=0}\n\\caption{Exponential fits to the jump velocity distributions\nfor the high magnetic field (M = 5, A = 1) MHD \n256$^3$ simulation. A mean value for the number of shocks in each\ndirection has been taken. The 5 times shown are t = 1,2,3,6 and 10. \nThe fitted exponentials are described in the text with $\\alpha = 0.66$\nand $\\beta = 0.62$.} \n\\label{numbermagf} \n \\end{center}\n\\end{figure} \n\\begin{equation} \n\\frac{dN}{dM_j} = 10^{5.94}\\,t^{\\alpha}\\,{\\exp}(-{\\beta}\\,M_jt^{\\alpha}).\n\\label{mhd-eqn}\n\\end{equation}\nwhere $\\alpha \\sim 0.66 \\pm 0.03$ and $\\beta \\sim 0.62 \\pm 0.03$. For the\nA = 5 case, $\\alpha \\sim 0.57 \\pm 0.03$ and $\\beta \\sim 1.01 \\pm 0.05$.\n\nThis analysis indicates that (1) supersonic MHD turbulence is, \n{\\em mathematically} at least, no different from hydrodynamic\nturbulence in that the shock distribution is exponential and (2) \nthe time dependencies are also similar to the hydrodynamic M = 5 case.\nFrom Fig.\\,\\ref{numbermag}, we conclude (1) that the distribution of \nhigh speed shocks remains unchanged and isotropic in the low-field \ncase, (2) the distribution of transverse waves is somewhat faster to \ndecay when a weak field is present, whereas in the strong field case \n(3) the high speed transverse waves survive significantly longer from \nthe outset and (4) the whole spectrum of parallel waves is suppressed \nby a factor $\\sim 2$.\n\nThe velocity jump distributions plotted here are a combination of \nshocks and waves. Due to the high Alfv\\'en speed, the shocks are \npredominantly slow shocks in the A = 1 case. These shocks\ncan propagate with wave vectors in all directions except\nprecisely transverse to the field. Their propagation speeds are \nrelatively slow since the (initially-uniform) Alfv\\'en speed is 5 times \nthe sound speed), and therefore their energy may be transferred into \nfaster waves via the turbulence raised in the magnetic field. In any \ncase, it appears from Fig.\\,\\ref{numbermag} that about two-thirds of \nthe compressional wave/shock energy is in transverse compression modes \nfor the case A = 1. The waves in this case, as measured here by regions \nof convergence along the axes, are fast magnetosonic waves (close to \ncompressional Alfv\\'en waves). The proportion of each can be estimated \nfrom the simulations by calculating the jump widths (in practice, we \nhere place the extra requirement that the one-dimensional jump across \neach individual zone exceeds 0.2\\,c$_s$, in order to distinguish the \nshocks from the waves). We then find that at M$_j$ = 1, just over half\nthe jumps are slow shocks (with an average resolution of $\\sim 3.0$ and 3.3\nzones transverse and parallel, respectively), while for M$_j$ $> 4$, \n76\\% of the 'jumps' are actually waves (an average of $\\sim 6.0$ and 7.7 \nzones in each converging region). This contrasts with the hydrodynamic\nsimulations where, quite uniformly, well over 90 \\% of the jumps are\nindeed narrow shocks, resolved only by the artificial viscosity.\nThese are of course estimates which ignore the possibility that many \nflow regions may be quite complex combinations of waves and shocks.\n\nAn explanation of why such different types of turbulence\ndecay in the same functional manner is offered in Sect. 6.5. \n\n%==========================================================================\n\\section{The probability distribution functions} %====================\n%==========================================================================\n\nA traditional aid to understanding numerically-created turbulence is\nthe probability distribution function (PDF) of the velocities. Here, \nwe determine the one-dimensional Mass Distribution Function by calculating \nthe mass per unit Mach number interval of the motion in the x-direction. \nNote all zones contribute here, whether in the shocks or not. \n\nWe recover Gaussian distributions in the velocity, as apparent \nin Fig.\\,\\ref{gauss}. This is clearly displayed on a Mass-log(M$^2$)\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%14141414141414141414141414141414\n\\begin{figure}\n \\begin{center}\n \\leavevmode\n \\psfig{file=1812F14.ps,width=0.58\\textwidth,angle=0}\n\\caption{The decay of the PDF for the M=50 simulation.\nThe distributions are shown for the 8 equal time steps from 0.5 to 4} \n\\label{gauss}\n \\end{center}\n\\end{figure} \nplot for the high-speed wings (Fig.\\,\\ref{gausslog}) where a Gaussian\nwould generate a linear relationship. Note\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%15151515151515151515151515151515\n\\begin{figure}\n \\begin{center}\n \\leavevmode\n \\psfig{file=1812F15.ps,width=0.58\\textwidth,angle=0}\n\\caption{A log-v$^2$ display of the decay of the PDF for the M=50 simulation\ndemonstrates the Gaussian nature of the PDFs.\nThe distributions for positive and negative absolute speeds\n are shown for the 8 equal time steps from 0.5 to 4, in descending order.} \n\\label{gausslog}\n \\end{center}\n\\end{figure}\nthat each time step produces two lines, one for positive and one\nfor negative absolute velocities. At early times, the imposed\nsymmetry is still dominant but later on, small asymmetries\nbecome more apparent. To estimate the time dependence we have \ntaken the mean mass fraction of each pair, on defining the\ninitial mass density to be unity (i.e. a unit mass is initially\ncontained in a box of size L$^3$)\nand found that a fit of the form\n\\begin{equation} \n\\frac{d(mass)}{dM} = 1.6\\,t^{0.75}\\,{\\exp}(-0.088\\,M^2t^{1.5})\n\\label{gausseqn}\n\\end{equation}\nis reasonable (Fig.\\,\\ref{gaussfit}). Interestingly, the \n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%161616161616161616161616161616\n\\begin{figure}\n \\begin{center}\n \\leavevmode\n \\psfig{file=1812F16.ps,width=0.58\\textwidth,angle=0}\n\\caption{Fits (dashed lines) to the decay of the PDF for the M=50 simulation.\nThe mean distributions (full lines) are shown for the 8 equal time steps \nfrom 0.5 to 4. The model fits are given by Eq.\\,\\ref{gausseqn},\nwhich is tailored so that the total mass in the box is conserved.} \n\\label{gaussfit}\n \\end{center}\n\\end{figure} \ndecay in time of the PDF is not exponential. It is a faster decay\nlaw than for the shocks. This is inherent to the nature of \ndecaying turbulence: in the beginning, closely-following\nshocks accelerate the fluid to high speeds. At late times, the \nfast shocks are quite evenly spread out and do not combine to \nproduce high acceleration.\n\n%=============================================================================\n\\section{Interpretation of shock number distribution}\n%==============================================================================\n\n%sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss\n\\subsection{The mapping closure method}\n%sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss\n\nA satisfying understanding of turbulence has been elusive. One can hope\nthat supersonic turbulence may possess some simplifying aspects. We\nhave thus devoted much time trying to interpret the above shock distributions\nof decaying turbulence. In this section, we first relate the numerical \nsimulations to theoretical models which have predicted exponential \nvelocity gradient PDFs for other forms of turbulence. We then\ninterpret the evolution of the shock PDFs with an extension of these\nmodels utilising the ballistic (ram pressure) principles behind \nhypersonic turbulence. \n\nWe require a model based on local interaction in physical space in\norder to model shock interactions. We adapt the heuristic `mapping\nclosure' model in the form presented by Kraichnan (1990), in which\nanalytical approximations were used to describe the evolution of Burgers\nturbulence. First, the initial competition between the squeezing and viscous \nprocesses is followed. An assumed Gaussian reference field is distorted \nnon-linearly in time into a dynamically evolving non-Gaussian field.\nVelocity amplitude and physical space are remapped by choosing\ntransformations of particular forms. The PDF of a \ntwo-point velocity difference changes smoothly from Gaussian at very \nlarge separations (relating independent points) to some function \n$\\xi$ at small distances. The mapping functions are then determined \nby matching the evolution equations with the dynamical equations. \nThe closure is obtained by limiting the form of the distortions to\nlocally determined transformations.\n\nThe model for Burgers turbulence provides our inspiration since, in the\nhypersonic flow simulations of isothermal gas,\nthermal pressure is only significant within the thin shock fronts.\nFurthermore, individual shock structures are predominantly one-dimensional. \nCare must be exercised, however, since regions of vorticity are created behind\ncurved shocks which are absent in the one-dimensional Burgers turbulence.\n\n\n%sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss\n\\subsection{Background formulation}\n%sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss\n\nWe assume a known {\\em reference field} for the initial velocity \n${\\bf u_o}({\\bf z})$ as a function of a {\\em reference} coordinate \nsystem ${\\bf z}$ (Gotoh \\& Kraichnan 1993). The 'surrogate' velocity \nfield is ${\\bf u}({\\bf x},t)$ and is related to ${\\bf u_o}$ and the \nreference coordinates by vector and tensor mapping functions X and J:\n\\begin{equation}\nu_i = X_i({\\bf u_o},t),\n\\end{equation}\n\\begin{equation}\n{\\partial}z_i/{\\partial}x_j = J_{ij}({\\bf u_o},{\\bf \\xi_{o}},t)\n\\end{equation}\nwhere reference velocity gradients are \n$\\xi_{ij,o} = \\partial{u_{i,o}}/\\partial{z_j}$ and \nvelocity gradients are $\\xi_{ij} = \\partial{u_{i}}/\\partial{x_j}$.\nThe goal is to find the distortions described by X and J for which \nthe surrogate velocity field is a valid approximation to the velocity \nfield as given by the equations of motion. The above transformations,\nhowever, constrain the allowed forms of higher order statistics and, hence,\nneglect some physics which affect the long-term evolution (Gotoh \\&\nKraichnan 1993).\n\nMapping closure also assumes that the velocity PDFs $P(u_o)$ and $P(u)$\nare related to multivariate-Gaussians through prescribed forms. The \njustification is simply the statistical mechanics argument, as applied \nto particle speeds in equilibrium thermodynamics. The velocity gradient \nPDF is written as $Q({\\xi},t)$ with $u$ and $\\xi$ taken to be statistically \nindependent. \n\nFor convenience, we concentrate on the component of the \nvelocity, $u_i$, in the $x_i$ direction. We rewrite the decay of velocity \namplitudes in the simpler form \n\\begin{equation}\nu_i = X_i({\\bf u_o},t) = r_i(t)\\, u_{i,o}(z_i),\n\\end{equation}\nand the velocity gradients then map through\n\\begin{equation}\n\\frac{\\partial{u_{i}}}{\\partial{x_i}} = \\xi_{ii} = \n r_{i}(t) \\xi_{ii,o}J_{ii}({\\bf u_o},{\\bf \\xi_o},t)\n = Y_{ii}(\\xi_o,t),\n\\label{eqnxi}\n\\end{equation}\nso defining Y. The velocity gradient PDF, which contains the shock PDF, \ncan now be written\n\\begin{equation}\nQ(\\xi_{ii}) = Q_o(\\xi_{ii,o})\\left[\\frac{\\xi_{ii}}{\\xi_{ii,o}}\\right]^{-1}\n \\frac{N}{J_{ii}}\n\\label{qpdf}\n\\end{equation}\nwhere $N(t)$ normalises the PDF. This is the framework in which we can \ndiscuss the statistical evolution of velocity gradients.\n\n%ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss\n\\subsection{Dynamical input}\n%ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss\n\nThe momentum equations being solved, with the pressure gradients \nneglected, are \n$Du_i/Dt = (1/{\\rho})({\\partial}/{\\partial}x_j)\\mu\\sigma_{i,j}$ \nwhere $Du_i/Dt = {\\partial}u_i/{\\partial}t + u_j{\\partial}u_i/{\\partial}x_j$,\n$\\sigma_{i,j}$ is the stress tensor and $\\mu$ is the viscosity. \nDifferentiation yields the velocity gradient equation:\n\\begin{equation} \n\\frac{D\\xi_{ii}}{Dt} + \\xi_{ik}\\xi_{ki} = \n- \\frac{1}{\\rho} \\frac{\\partial}{{\\partial}x_i}\n\\frac{\\partial}{{\\partial}x_j}(\\mu\\sigma_{i,j})\n\\label{etaij}\n\\end{equation}\nwhere the usual summation rule applies to j and k (but i is a chosen \ndirection). \n\nTo continue, we can derive the evolution of the functions J, by\nequating $Q({\\xi},t)$ as derived from these equations (yielding a\nrather complex form of the reduced Liouville equation, see Gotoh\n\\& Kraichnan 1993) with the Q derived from the mapping closure \napproximation (Eq.\\,\\ref{qpdf}). Then, however, the analysis becomes \nmathematically dense and numerical solutions are probably the best option.\n \nWe here revert to a simple heuristic form of mapping closure,\ntaking $\\xi$ to be any component of $\\xi_{ii}$ and the mapping \nfunction $J = J_{ii}$ to be determined by requiring the probability \nfunction $Q$ as derived from substituting for $D{\\xi}/Dt$ from the reduced \nEq.\\,\\ref{etaij} into the reduced Liouville equation,\n\\begin{equation}\n\\frac{\\partial Q}{\\partial t} + \\frac{\\partial }{\\partial \\xi}\n \\left(\\left[\\frac{D\\xi}{Dt}\\right]_{c:u,\\xi}Q\\right) = {\\xi}Q,\n\\end{equation}\n(where $[..]_{c:u,\\xi}$ denotes the ensemble mean\nconditional on given values of $u$ and $\\xi$) to be equal to the $Q$ derived \nfrom the equivalent for mapping closure (see Gotoh \\& Kraichnan 1993),\n\\begin{equation}\n\\frac{\\partial Q(\\xi,t)}{\\partial t} + \\frac{\\partial }{\\partial \\xi}\n \\left(\\frac{{\\partial}Y(\\xi_o,t)}{{\\partial}t}Q(\\xi,t)\\right) = {\\gamma}Q(\\xi,t),\n\\end{equation}\nwhere $\\gamma = ({\\partial}/{\\partial}t)\\,ln(N/J)$. After some manipulation, \nthis yields an equation for the evolution of J of the form (see also \nEq.\\,24 of Gotoh \\& Kraichnan (1993))\n\\begin{equation} \n\\frac{{\\partial}J}{{\\partial}t} = -r{\\xi_o}J^2 - {\\mu}k_d^2J^3 + D(J^3)\n\\label{jeqn}\n\\end{equation}\nwhere $k_d^2 = \n{\\langle}(\\partial{\\xi_o}/{\\partial}z)^2{\\rangle}/\\langle{\\xi_o^2}\\rangle$,\nangled brackets denoting the ensemble mean and $D(J^3)$ is a function \nconsisting of further non-linear derivative terms of the form $J^3$. \nAlso, an integral term involving $Q$ is neglected here, which {\\em a \nposteriori} limits the solutions to high jump Mach numbers\n$|{\\xi}| > r^2\\chi_o$ ($\\chi_o$ being defined below)\n\nNote that the left hand side and the first two terms on the right \nare close to the Navier-Stokes form given \nby Kraichnan (1990), with the addition of the function $r = r_i$ which \naccounts for compressibility. These terms provide the statistics of the \nfield through a non-linear transformation of the initial field with known \nstatistics. The final term combines together non-linear derivatives, a step \nwhich permits further manipulation but with the loss of information \nconcerning the constants of integration.\n\n\nThe evolution of $J$ begins rapidly by the steepening of large \nvelocity gradients (first term on the right), until balance with \nthe viscous term (second term on the right hand side) is achieved. \nEquating these two terms yields the form of the mapping function: \n$J = -r{\\xi_o}/({\\mu}k_d^2)$. Substitution into Eq.\\,\\ref{eqnxi} \nyields $\\xi = -r^2(t){\\xi_o}^2/({\\mu}k_d^2)$. We convert the initial \nGaussian PDF $Q_o(\\xi_o)$ into $Q_1(\\xi_1)$ by using Eq.\\,\\ref{qpdf} \nto yield the result that the velocity gradient PDF is transformed\ninto an exponential function:\n\\begin{equation}\n Q_1(\\xi_1) = \\left( \\frac{\\langle{\\xi_o^2}\\rangle}\n {8 \\pi r^2 \\chi_o^2}\\right)^\\frac{1}{2} \n \\frac{N(t)}{|\\xi_1|} \\exp \\left[ - \\frac{ |\\xi_1|}{2 r^2 \\chi_o} \\right]\n\\label{xixi}\n\\end{equation}\nwhere $\\chi_o = \\langle \\xi_o^2 \\rangle/(\\nu k_d^2)$. This function has \nbeen derived for the high gradients i.e. the shocks, consistent with the \nnumerical simulations.\n\nThe exponential being set up, the gradients are then determined by the\ninviscid terms. Thus, the continued evolution of $J$ is described by \nthe first two terms in Eq.\\,\\ref{jeqn} which, on substituting the \nmapping $J = {\\xi}/(r\\xi_1)$ yield\n\\begin{equation}\n\\frac{\\partial}{\\partial t}\\left( \\frac{\\xi/\\xi_1}{r}\\right) =\n \\xi_1\\frac{(\\xi/\\xi_1)^2}{r}.\n\\end{equation}\nThis has an asymptotic power law solution of the form\n$\\xi/\\xi_1 = 1/(1+t/(t_1))$, $t_1$ being a constant. \nHence, at large t, the velocity\ngradient associated with a fluid trajectory is inversely proportional to\ntime, as physically plausible for a high Mach number expanding flow. \nSubstituting $\\xi_1 = (1+t/t_1)\\xi$ for $\\xi_1$ in Eq.\\,\\ref{xixi}, \nand normalising the PDF through N, yields\n\\begin{equation}\nQ(\\xi) = k \\frac {\\xi_o}{\\xi}\n \\exp \\left[ - \\frac{ \\xi t}{\\chi\\xi_ot_o} \\right].\n\\end{equation}\nfor large t, where $\\chi = 2\\,r_o^2\\langle \\xi_o^2 {\\rangle}/(\\mu k_d^2\\xi_o)$\nand k is a constant.\nHence, mapping closure predicts, for zero-pressure hydrodynamic flow, \nthe same fast shock decay law as uncovered in the hypersonic simulations.\n\nThe above mapping closure technique provides insight into the rapid \nbuild up of velocity gradients and transformation to an exponential,\nas well as the evolution of the exponential term. The form of the prefactor\nexcludes an extension to low speeds.\n\n%ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss\n\\subsection{A direct physical model}\n%ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss\n\nThe interpretation we now present is an extension of the dynamic basis \nof the mapping closure model. First, we neglect viscosity since the \nlong term evolution must be derivable from purely inviscid\ntheory. The critical addition to the above analysis is a result of the \nsimulations: the total number of zones across which the gas is converging \nremains at approximately 30\\%, independent of time. This can also be \nderived from integrating Eqs. (2) and (4) over M$_j$ which yields \nconstant total shock surfaces of 1.05\\,10$^6$ and 0.10\\,10$^6$ zone \nsurface elements, respectively (the difference being mainly the factor \nof 8 more zones in the former 256$^3$ calculation). As can be seen \nfrom Fig.\\,\\ref{fitted}), the strong shocks disappear, being replaced by \nweak shocks. We interpret this empirical conservation law as due to the fluid\nbeing contained predominantly within the layers which drive the shocks\nand the looser-defined layers which drive the weaker compressional waves.\nThese layers interact, {\\em conserving the total shock area}. This is\nexpected from shock theory since the two driving layers merge but\nthe leading shock waves are both transmitted or reflected.\nThe need for layers to drive the shocks, as opposed to shocks to sweep\nup the layers, is a necessity in an isothermal flow where the\npressure behind a shock must be associated with enhanced density.\nNevertheless, a shock will sweep up and compress pre-existing density\nstructures ahead of it.\n\nThe decay of a single shock is controlled by the decay of the momentum \nof the driving layer. The decay of a driving layer is here modelled as due\nto the time-averaged interaction with numerous other layers. These layers \ncan be represented by an 'ensemble mean' with the average density $\\rho$. Thus\na shock is decelerated by the thrust of other shock layers, but its mass\nis not altered. Mass is not accumulated from the oncoming shock\nlayer, but instead remains associated with the oncoming layer. Then, a \nlayer of column density $\\Sigma$ will experience a deceleration of \n$\\Sigma$du/dt = -$C_d{\\rho}$u$^2$ where $C_d$ is a drag coefficient of \norder unity and u is the velocity jump (i.e the relative velocity of the \nlayer). Integration yields the result ut/L $\\sim \\Sigma$/(L$\\rho$) for \ntimes exceeding $\\Sigma$/$\\rho$u$_o$ where u$_o$ is the initial layer speed.\n\nWe impose three physical conditions on the shock distribution.\n\\begin{itemize} \n\\item At high speeds we take a standard decay law for a number of \nindependently-decaying layers. The decay rate of fast shocks is \nproportional to the number of shocks present. In this regime, \nsignificant numbers of new shocks are not generated.\n\\item Secondly, we shall require that the {\\em total} number of shocks \n(plus compressional waves, since there is no dividing line in the numerical \nsimulations) remains constant. The function which satisfies both these \nconditions clearly obeys, on integrating over all shocks with speed exceeding\n$v_1$,\n\\begin{equation}\n\\frac{d\\,\\,}{dt} \\int_{v_1}^{\\infty} \\frac{dN}{dv}dv =\n - \\kappa(v_1) \\int_{v_1}^{\\infty} \\frac{dN}{dv}dv\n\\label{condition1}\n\\end{equation}\nwith the decay rate function $\\kappa(v) \\rightarrow 0$ as \n$v \\rightarrow 0$, to conserve\nthe shock number. This has solutions\n\\begin{equation}\n\\frac{dN}{dv} = a\\, t\\frac{d\\kappa}{dv}e^{-{\\kappa}t}.\n\\end{equation}\nwhere a is a constant.\n\\item The third condition we invoke is based on the above functional \nform for individual shock deceleration for which vt is a constant. Then,\nthe number of shocks above any $v = v_o(t_o/t)$ should be conserved i.e.\n\\begin{equation}\n\\int_{v_o(t_o/t)}^{\\infty} \\frac{dN}{dv}dv = constant.\n\\end{equation}\nThis is similar to the result obtained for the velocity gradients\nin the mapping closure analysis. Integrating Eq.\\,\\ref{condition1} \nwith this condition then yields the jump distribution function \n\\begin{equation} \n\\frac{dN}{dv} = \\frac{N_o}{L_o} t e^{-vt/L_o},\n\\end{equation}\nwhere $N_o$ and $L_o$ are constants.\n\\end{itemize}\nThis implies that we have only two constants with which to fit, not a single\nline, but a whole family of lines! Yet, remarkably, this is quite well\nachieved, as shown in Fig.\\,\\ref{fitted}. Note that the exponential \ntime-dependence is indeed correct at high speeds, but there is a linear \ntime-dependence at low speeds, where the weak shocks accumulate.\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\\subsection{The MHD connection}\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\nWe have shown that the decaying MHD turbulence with M\\,=\\,5 possesses \nsimilar decay properties to the M\\,=\\,5 hydrodynamic case despite the \ndifferent wave phenomena involved. Slow shocks, however, possibly \ndominate the energy dissipation in the high-field A=1 case. The power \nis dissipated within shock jumps with Mach numbers in the range \n$M_j \\sim 1-2$. Alfv\\'en waves are an important ingredient in the \nexponential tail of the velocity jumps. In a uniform medium, Alfv\\'en \nwaves do not decay even when they posess non-linear amplitudes. \nHowever, the Alfv\\'en waves in a turbulent medium will interact \nnon-linearly with other Alfv\\'en waves, slow shocks, and density \nstructures. Each Alfv\\'en \nwave moves through a mean field of other waves. Similarly, each shock \nlayer propagates through the `mean field' of other shocked layers,\nthe basis utilised in the above physical model for the hydrodynamic case. \nHence, the MHD wave interactions could well lead to the decay of the velocity \njump distribution in the same manner as shocks.\n\n%==========================================================================\n\\section{Conclusions} %=================================\n%==========================================================================\n\nDiffuse gas under various guises is subject to supersonic turbulence. \nLarge-scale numerical simulations of 3D MHD now allow us to explore\nmany variants. Here, we have studied an isothermal gas in which \nlarge-scale Gaussian velocity perturbations are introduced and freely \ndecay within a 'periodic box'. Our main aim here is to analyse the \ndistribution of shocks, with the ensuing aim of determining the \nobservational signatures. For this purpose, we have supplemented the \noriginal RMS Mach 5 simulations (Mac Low et al. 1998) with hypersonic \nMach 50 runs. Indeed, we find that the hypersonic case leads to simple \nmathematical descriptions for the shock distribution function, from \nwhich the M = 5 runs deviate moderately. The Mach 50 runs obey a \nsteeper energy decay law and (hence) have a faster decay of the \nspectrum of shocks. The velocity PDFs remain near-Gaussian but with \nincreasing asymmetry at higher speeds and lower masses. \n\nIt should be remarked that the velocity PDFs distribution and shock \ndistributions decay at different rates. The mass fraction at high speeds \ndecreases faster than the number of shocks with similar speeds. This \nindicates that the turbulence is indeed decaying from its fully-developed \nstate, and the individual shock structures interfere less with each \nother as the flow evolves. That is, the saw teeth tend to become more \nregular with time. \n\nFurther conclusions are as follows.\n\\begin{itemize}\n\\item The magnetic field tends to slow down the spectral decay as well as the\noverall energy decay. Fast shocks survive longer.\n\\item Transverse waves of a given strength decay faster than waves\ntravelling parallel to the magnetic field.\n\\item Apart from a small initial period, the energy is not dissipated \nby the fast shocks but by the moderate shocks with jumps in the\nMach number from upstream to downstream approximately in the range \n$M_j\\,=\\,1\\,-\\,3$, even in the M = 50 simulation. This is due to the\nexponential fall in fast shock numbers, combined with the relatively \nineffective dissipation in the weakest shocks.\n\\end{itemize}\n\nOur studies show that for hydrodynamic models the ratio of $H_{\\nu}$ to\n$dE_{kin}/dt$ stays at about 65 percent through time, but this ratio\nvaries more with time and has a mean value of 30 percent for MHD\nmodels. We conclude that short wavelength MHD waves are present, and\nenergy loss is distributed rather than occuring primarily in thin\nlayers.\n\nIn the hypersonic case, we have found simple laws for the evolution\nand velocity distribution of shock speeds. The same basic exponential\nspectra are also found for the very closely related high negative \nvelocity gradients of Navier-Stokes and Burgers turbulence,\nin both simulations and analytical theory (e.g. Kraichnan 1990, Gotoh\n\\& Kraichnan 1993). We have extended their heuristic \n mapping closure model to the present case to reproduce our computed \nspectral forms, and thus demonstrated some of the dynamical properties which \nare inherent to supersonic turbulence. \n\nThe relevance of studies of decaying supersonic turbulence to\nstar-forming clouds was questioned by Mac Low et al. (1999). The\nrapid decay implies that such turbulence would be hard to catch\nin action within long-lived molecular clouds. Possible sites, however, \nwithin which decaying turbulence should prove relevant include the regions\ndownstream of bow shocks, clouds suffering a recent\nimpact and disrupted jets. An exponential distribution of shocks such \nas we find will generate very low excitation atomic and molecular spectra \nand inefficient electron scattering, leading to steep synchrotron spectra.\n\nIn a following paper, these shock spectra will be employed to calculate\nemission line spectra. On comparison with driven turbulence, we may then\nbegin to understand the type of turbulence we observe and what may\nbe producing the turbulence.\n\n\n\\acknowledgements\n\nMDS benefitted greatly from the hospitality of the Max-Planck-Institut f\\\"ur\nAstronomie. We thank E. Zweibel for advice and discussions. Computations \nwere performed at the MPG Rechenzentrum Garching. JMZ thanks the American \nMuseum of Natural History for hospitality. Partial support for this \nresearch was provided by the US National Science Foundation under grant \nAST-9800616.\n\n\\begin{thebibliography}{99}\n\\bibitem[] {}Evans C., Hawley J.F. 1988, ApJ 332, 659\n\\bibitem[] {}Falgarone E., Lis D.C., Phillips T.G. et al. 1994, ApJ 436, 728\n\\bibitem[] {}Franco J., Carraminana A., 1999, Interstellar Turbulence, \n CUP, Cambridge\n\\bibitem[] {}Galtier S., Politano H., Pouquet A., 1997, Phys. Rev. Lett.\n 79, 2807\n\\bibitem[] {}Gotoh T., Kraichnan R.H. 1993, Phys. 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{
"name": "astro-ph0002291.extracted_bib",
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}
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astro-ph0002292
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The Globular Cluster Systems in the Coma Ellipticals. III: The Unique Case of {\ic}
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[
{
"author": "Sean C.~Woodworth and William E.~Harris"
}
] |
IC 4051 is a giant E galaxy on the outskirts of the Coma cluster core. Using archival \hst\ WFPC2 data, we derive the metallicity distribution, luminosity function, and spatial structure of its globular cluster system (GCS). The metallicity distribution derived from the $(V-I)$ colors has a mean $\langle$Fe/H$\rangle \simeq -0.3$, a near-complete lack of metal-poor clusters, and only a small metallicity gradient with radius. We tentatively suggest that the GCS has two roughly equal metallicity subcomponents, one centered at [Fe/H] $\sim 0.0$ and the second at [Fe/H] $\sim -1.0$, although their identification is blurred by the photometric uncertainties. The luminosity distribution (GCLF) has the standard Gaussian-like form observed in all other giant E galaxies, with a peak (turnover) at $V^0 = 27.8$, consistent with a Coma distance of 100 Mpc. The radial profiles of both the GCS and the halo light show an unusually steep falloff which may indicate that the halo of this galaxy has been tidally truncated. Lastly, the specific frequency of the GCS is remarkably large: we find $S_N = 11 \pm 2$, at a level which rivals M87 and most others in the central cD-type category, even though IC 4051 is not a cD or brightest cluster elliptical. This galaxy exhibits a combination of GCS characteristics found nowhere else. A formation model consistent with most of the observations would be that this galaxy was subjected to removal of a large fraction of its protogalactic gas shortly after its main phase of globular cluster formation, probably by its first passage through the Coma core. Since then, no significant additions due to accretions or mergers have taken place, in strong contrast to the central Coma galaxy NGC 4874.
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[
{
"name": "Woodworth.tex",
"string": "\\documentstyle[12pt,aaspp4,epsf]{article}\n\n\n%\\def\\Deg{${}^{\\circ}$\\llap{.}}\n%\\def\\Min{${}^{\\prime}$\\llap{.}}\n%\\def\\Deg{\\hbox{${}^{\\circ}$\\llap{.}}}\n%\\def\\Min{\\hbox{${}^{\\prime}$\\llap{.}}}\n%\\def\\Sec{\\hbox{${}^{\\prime\\prime}$\\llap{.}}}\n\\def\\ltsim{ \\,{}^<_\\sim\\, }\n\\def\\gtsim{ \\,{}^>_\\sim\\, }\n\\def\\ie{i.e.}\n\\def\\eg{e.g.}\n\\def\\cf{cf.}\n\\def\\etal{et al.}\n\\def\\hst{{\\it HST}}\n\\def\\ic{IC~4051}\n%\\def\\hr{\\hbox{${}^{\\hbox{\\scriptsize h}}$}}\n%\\def\\mn{\\hbox{${}^{\\hbox{\\scriptsize m}}$}}\n\n\\lefthead{Woodworth \\etal }\n\\righthead{{\\ic} Globular Clusters}\n\n\\begin{document}\n\n\\title{The Globular Cluster Systems in the Coma Ellipticals. III: \nThe Unique Case of {\\ic}}\n\n\\author{Sean C.~Woodworth and William E.~Harris}\n\\affil{Department of Physics \\& Astronomy, \nMcMaster University, Hamilton, Ontario L8S 4M1\n\\\\Electronic mail: woodwrth, harris@physics.mcmaster.ca}\n\n%\\clearpage\n\n\\begin{abstract}\nIC 4051 is a giant E galaxy on the outskirts of the Coma cluster core.\nUsing archival \\hst\\ WFPC2 data, we derive\nthe metallicity distribution, luminosity\nfunction, and spatial structure of its globular cluster system (GCS).\nThe metallicity distribution derived from the $(V-I)$\ncolors has a mean $\\langle$Fe/H$\\rangle \\simeq -0.3$, \na near-complete lack of\nmetal-poor clusters, and only a small metallicity gradient with radius.\nWe tentatively suggest that the GCS has two \nroughly equal metallicity subcomponents,\none centered at [Fe/H] $\\sim 0.0$ and the second at [Fe/H] $\\sim -1.0$,\nalthough their identification is blurred by the photometric\nuncertainties.\nThe luminosity distribution (GCLF) has the standard Gaussian-like\nform observed in all other giant E galaxies, with a peak (turnover)\nat $V^0 = 27.8$, consistent with a Coma distance of 100 Mpc.\nThe radial profiles of both the GCS and the halo light\nshow an unusually steep falloff which may indicate that the halo\nof this galaxy has been tidally truncated.\nLastly, the specific frequency\nof the GCS is remarkably large: we find $S_N = 11 \\pm 2$, at a level\nwhich rivals M87 and most others in the central cD-type category, even\nthough IC 4051 is not a cD or brightest cluster elliptical.\nThis galaxy exhibits a combination of GCS characteristics\nfound nowhere else. A formation model consistent\nwith most of the observations would be that this galaxy was subjected to \nremoval of a large fraction of its protogalactic gas shortly after\nits main phase of globular cluster formation, probably by its first\npassage through the Coma core. Since then, no significant additions\ndue to accretions or mergers have taken place, in strong contrast\nto the central Coma galaxy NGC 4874.\n\n\\end{abstract}\n\n\\keywords{Galaxies: Star Clusters; Structure; Evolution; Elliptical;\nInvidual}\n\n\\clearpage\n\n\n\\section{INTRODUCTION}\n\nThe Coma Cluster ($d \\sim 100$ Mpc), as a rich Abell cluster, is the \nhost environment for a huge range of E/S0 galaxies. Its two\ncentral supergiants, NGC 4874 and 4889, are among the very most luminous\ngalaxies known, and the cluster has many other large ellipticals\nscattered throughout its $\\sim 1-$Mpc core region and well beyond. \nThe globular cluster systems (GCSs) around these galaxies \nare well within reach\nof the HST cameras, and thus give us an extraordinarily rich range\nof target galaxies for comparative GCS studies.\nComa also has important implications \nfor the determination of the Hubble constant\n$H_0$, since its large recession velocity\n($\\sim 7100$ km s$^{-1}$) greatly exceeds any anticipated local peculiar \nmotions, and it is situated at high galactic\nlatitude ($b = +87\\fdg7$) nearly unaffected by foreground absorption,\n\n{\\ic} is a giant E2 galaxy located \n$\\simeq 14'$ east in projection from the center of Coma\nand has no luminous neighbors.\nWith an integrated magnitude \n$V_T^0 = 13.20$, it is the fifth brightest elliptical\ngalaxy within the $1\\arcdeg$ central region of Coma. \nThus, {\\ic} presents a good opportunity to study the GCS of a\nmore-or-less ``normal'' large elliptical.\n\\cite{baum97} obtained the first \ndeep WFPC2 exposures of \\ic\\ with exactly this purpose in mind, \nbut they limited\ntheir published analysis to only the photometry from the\nPC1 frame on which the galaxy was centered. However, considerably more\ninformation on the radial structure of the GCS, its specific\nfrequency, and radial metallicity gradient are potentially \navailable from the outer sections of the WFPC2 field.\nIn this paper, we re-analyze the archival HST/WFPC2 frames from\nthe \\cite{baum97} program and discuss the global properties of\nthe \\ic\\ GCS using the entire body of data available in the\nraw exposures. \n\n\\section{DATA ANALYSIS}\n\nThe raw database comprises {\\hst}/WFPC2 \nobservations taken on 1995 July 20/21 (Baum {\\etal} 1997).\nEight images totalling 20500 s (essentially, a sequence of\nfull-orbit exposures) were taken through the $F606W$ (wide\n$V$) filter, and two\nimages totalling 5200 s were taken through the $F814W$ ($I$) filter.\nThe techniques in our data analysis are similar to those\nin Papers I and II of this series (\\cite{kav99}; \\cite{hk99}), in which we\nanalyzed the GCS around NGC 4874, the central cD giant.\nThe first step was to register\nand combine the images to produce a master $V$ and master $I$\nframe free of cosmic rays. An excellent color composite image \nconstructed from the combined frames is published by Baum et al.\nFor the PC1 frame, we produced a ``flattened'' \nimage in which the overall elliptical contours of the central\ngalaxy were modelled and then subtracted. In the WF2,3,4 fields,\nwe generated an empirical model of the galaxy light by median\nfiltering each frame and subtracting the smoothed image from the\noriginal picture (after a preliminary star-finding and removal).\n\nOur photometry was then carried out on the flattened master \nframes with the DAOPHOT II and ALLSTAR codes \n(\\cite{ste92}). \nThe instrumental magnitudes returned by ALLSTAR were transformed to the\nstandard $V$,$I$ system via the equations derived by \\cite{holtzman95},\n\\begin{equation}\nV = m(F606W) - {\\overline {\\Delta m}} + 22.093 + 0.254(V - I) + 0.012(V - I)^2 + 2.5\\log(GR_i),\n\\end{equation}\n\\begin{equation}\nI = m(F814W) - {\\overline {\\Delta m}} + 20.839 - 0.062(V - I) + 0.025(V - I)^2 + 2.5\\log(GR_i),\n\\end{equation}\nwhere $m(F606W,F814W)$ are the instrumental magnitudes returned\nby ALLSTAR, and the $\\overline {\\Delta m}$ are constants\nwhich shifts these ALLSTAR psf\nmagnitudes to the equivalent magnitude of the light within a \n$0\\farcs5$ aperture. The mean value of $\\Delta m$ \nwas determined empirically for each of the four WFPC2 fields\nfrom roughly ten moderately bright, isolated stars in each CCD,\nand applied to all our detected starlike images. The typical internal\nuncertainties in the mean $\\Delta m$ values were $\\pm 0.02$ mag.\n\nIt should be noted that at the distance\nof Coma, all globular clusters are easily starlike in appearance\nand thus these transformation\nequations normalized to the $0\\farcs5$ aperture \ncan strictly be applied to them.\nThe calibration equation for $V$ quoted above is the synthetic model\ntransformation from Table 10 of \\cite{holtzman95}, while the equation\nfor $I$ is the observationally based one from their Table 7. If, instead,\nwe had chosen their Table 10 model transformation for $I$, our\nresulting $(V-I)$ color indices would have ended up bluer by roughly\n0.02 mag at the average color $(V-I) \\simeq 1.2$ of the \\ic\\ globular\nclusters (see below; this shift would have the effect of reducing the\ndeduced cluster metallicities by \n$\\Delta$[Fe/H] = 0.1).\\footnote{\\cite{baum97} adopted the synthetic\ntransformation for $I$ from Table 10 of Holtzman \\etal, but used the\nspecific curve for the color range $(V-I) < 1.0$. \nHowever, the majority of the\nglobular clusters are somewhat redder than this, so that the transformation\nfor $(V-I) > 1.0$ would have been preferable. The net result is to\nincrease the small $(V-I)$ difference between their scale and ours \nby a further $\\sim 0.02 - 0.03$ mag, although\nour {\\it instrumental} color scale $(F606W-F814W)$ agrees quite closely\nwith theirs.} When we add the internal uncertainties in\nthe aperture corrections $\\Delta m$, we\nestimate that the zeropoints of either the magnitude or color scales\nare uncertain to at least $\\pm 0.03$ mag.\n\nFinally, as an internal check on the relative zeropoints of the $V$ and $I$\nscales between the PC1 chip and the three WF chips, we inspected the\nmean $(V-I)$ color indices of the measured globular clusters in the\nannulus around the center of IC 4051 ($R \\sim\n10'' - 20''$) that overlapped the PC/WF boundary. We enforced the WF2,3,4\ndata in this annulus to have the same mean color as those in the PC1\nregion by adjusting the $I$ magnitudes (which are from \nmuch shorter exposures than $V$, thus \ninternally more uncertain). The final result places our $(V-I)$ scale\nin agreement with the \\cite{baum97} scale to within 0.03 mag, \na level entirely consistent with the combined photometric uncertainties.\n\nAs was already evident from the \\cite{baum97} study, \\ic\\ has a\npopulous GCS, which appears as a very obvious swarm of faint objects\nacross the whole WFPC2 field. The main source of sample\ncontamination is from very faint, compact background galaxies, with\na (nearly negligible) contribution from Galactic foreground stars.\nA high proportion of the background galaxies can be eliminated\nthrough conventional radial-moment image analysis.\nFor this purpose we used the $r_1$ radial moment as implemented\nin \\cite{hapv91}, \n\\noindent\n\\begin{equation}\nr_{1} = \\left(\\frac{\\sum rI}{\\sum I}\\right),\n\\end{equation}\nwhich is an intensity-weighted mean radius for the object calculated\nover all pixels brighter than the detection threshold (see Harris\n\\etal\\ 1991). A straightforward plot of $r_1$ against magnitude\nthen shows a well defined stellar sequence, with nonstellar objects\nscattering to larger $r_1$. These classification\ngraphs for the four CCDs in $V$ are shown in\nFigure \\ref{fig1}. The dashed lines indicate the adopted\ncutoffs applied to the measurements. Similar object\nclassifications were applied to the $I$ data (which, however,\nhave shallower limits), with \nthe final culled data lists containing\n4058 objects in $V$ and 1672 objects in $(V-I)$.\n\nThe faint-end completeness of our photometry was\ninvestigated through an extensive series of artificial-star \ntests on the master images. The procedure performed here\nwas to add 500 artificial stars \nto each frame over a range of input magnitudes, measure these\nframes through the normal DAOPHOT sequence, and find out how\nmany were recovered. Fifteen of these trials were carried out,\nwith average resulting completeness fractions as \ndisplayed in Figure \\ref{fig2}.\nConvenient fits to the raw points are provided by the Pritchet\ninterpolation function,\n\\begin{equation}\nf = \\frac{1}{2} \\left[{1 - \n\t \\frac{{\\alpha}(R-R_{lim})}{\\sqrt{1+{\\alpha}^2(R-R_{lim})^2}}}\\right].\n\\label{compeq}\n\\end{equation}\nTable \\ref{tab1} summarizes the best-fit parameters to Equation \n\\ref{compeq} for each CCD and bandpass. In the Table,\n($V_{lim}, I_{lim}$) are the magnitudes at which $f$ drops to 0.5, and the \nparameter $\\alpha$ controls the steepness of the falloff. \nThe curves for all three of the outer chips (WF2,3,4) are nearly\nidentical; for the inner PC1 chip, the limiting magnitudes are brighter,\ndriven by the spread of the PSF over many more pixels and (for $R \\ltsim\n10''$) the brighter background light.\n\nLastly, Figure \\ref{fig3} shows how the photometric measurement\nuncertainties (also derived from the ADDSTAR completeness tests) increase\nwith magnitude. At the formal limiting ($f=0.5$) magnitude, \nthe rms uncertainty in the photometry reaches 0.15 mag.\nWherever possible, we avoid dealing with any features of the data\nbelow that limit.\n\n\\section{COLOR AND METALLICITY DISTRIBUTIONS}\n\nThe distribution in colour of the globular clusters \ncan be used to gain insight into the existence of\nmultiple sub-populations in the GCS. Bimodal color distributions\nare found about half the time in gE galaxies (e.g., \\cite{kw99};\n\\cite{neil99}) and are often interpreted as relics of\nat least two major phases of star formation in the early\nhistory of the galaxy, whether by merger, accretion, or \n{\\it in situ} processes. With the conventional\n``null hypothesis'' for giant ellipticals that the clusters \nare all old ($\\gtsim 10$ Gy), the color index is primarily a tracer\nof cluster metallicity. \nThe colour-magnitude distribution for the 1672\nobjects measured in both $V$ and $I$ is shown in Figure \\ref{fig4}.\nAt projected galactocentric radii larger than about $80 \\arcsec$,\nwe found (see below) that the residual numbers of clusters dropped\nnearly to zero, so we adopt this outer region as defining a\nsuitable ``background'' population.\n\nTo eliminate a few more contaminating objects, we reject\nobjects bluer than $(V-I) = 0.74$ or redder than\n$(V-I) = 1.46$ (vertical dashed lines in Fig.~\\ref{fig4}).\nThese colour limits generously include the range \nin colours of the \nknown globular clusters in large galaxies (e.g., \\cite{har96};\n\\cite{whi95}; \\cite{neil99}). We also further limited the color sample\nto objects brighter than $V=26.0$ to ensure high completeness\nat all colors. \n\nA ``clean'' color distribution for the GCS was then obtained \nby subtraction\nof the background ($R > 80''$) color distribution, normalized\nto the same total area as the inner population.\nThis procedure left a final total of 479 objects within the magnitude\nand color limits given above, with a net distribution over $(V-I)$\nas shown in the histogram of Figure \\ref{fig5}.\nThe mean color of the sample is \n$\\langle V - I \\rangle = 1.12 \\pm 0.01$ (internal uncertainty of the\nmean), with a dispersion\nof $\\sigma_{V-I} = 0.13$. \nSubtracting an adopted foreground reddening $E(V-I) = 0.014$ and\nusing the calibration of $(V-I)_0$ in terms of metallicity\ngiven in Paper II, \n$$ (V-I)_0 = 0.17 \\, {\\rm [Fe/H]} \\, + \\, 1.15 \\, , $$\nwe then estimate that the IC 4051 GCS as a whole has \n$\\langle$Fe/H$\\rangle \\simeq -0.3$. The peak position of this\ncolor distribution is quite similar to the metal-{\\it rich} components\nin other giant ellipticals such as NGC 4472 (\\cite{geisler96}), M87\n(\\cite{whi95}; \\cite{kun99}), and other Virgo members (\\cite{neil99}).\nHowever, the metal-{\\it poor} component which is usually found in\nthese same galaxies at a mean color $(V-I) \\sim 0.95$ \nor [Fe/H] $\\sim -1.5$ (and which we\nfound in the Coma cD NGC 4874; see Paper II) is entirely missing\nin IC 4051, or at very most is a fringe component buried in the\nwings of the main distribution.\n\nWe cannot place firm\nlimits on the intrinsic dispersion $\\sigma$[Fe/H], since the mean\nobservational measurement scatter over the sample is $\\sigma_{V-I} \n\\simeq 0.11$, comparable with the observed sample dispersion of $\\pm0.13$.\nNevertheless, subtracting off the observational scatter in quadrature,\nwe estimate roughly $\\sigma_0$[Fe/H] $\\simeq 0.4$, which\nis in close agreement (for example) with the value $\\sigma$[Fe/H] = 0.38\nfound by Geisler \\etal\\ (1996) \\nocite{geisler96} \nto fit each of the metal-rich and\nmetal-poor components in NGC 4472. In the Milky Way, the well known\nbimodal MDF has been found to be fit by Gaussian functions with\ndispersions near $ 0.3$ dex (\\cite{zin85}; \\cite{armandroff88};\n\\cite{har99}).\nFor IC 4051, a single Gaussian with the same mean and\nstandard deviation as the sample (Fig.~\\ref{fig5}) matches\nthe MDF with a $\\chi^2 \\simeq 14.6$ over 14 degrees of freedom, \nwhich provides no strong evidence for bimodality (but see below).\n\nTrends of mean color with either galactocentric distance or\nmagnitude were also searched for.\nTable \\ref{tab2} shows the mean color and dispersion in 0.5-magnitude bins\nfrom $V = 22.5$ to 26.0. These binned means reveal\nno significant change in color with luminosity.\nHowever, slightly more interesting features emerge in the graph\nof color versus radius (Figure \\ref{fig6}).\nBinned mean colors, listed in Table \\ref{tab3}, indicate no \nsystematic change in color for $R \\gtsim 10''$, but within $10''$\nthe clusters are indeed slightly redder\nthan the overall mean. The distribution\nin its entirety is barely suggestive of two sub-populations: one\ncentered on $(V-I) \\sim 1.2$ which is found at all radii; and a second,\nslightly bluer one centered near $(V-I) \\sim 1.0$. The lack of bluer\nclusters within $R \\ltsim 10''$ is then largely responsible for the\ninner color gradient of the whole sample mentioned above.\nMuch stronger versions of this same effect have shown up in \nsome other giant E or cD galaxies\nwith far more obvious bimodal MDFs\n(e.g., \\cite{secker95};\n\\cite{geisler96}; \\cite{lee98}; \\cite{ostrov98}).\nIn these, the different central concentrations of the metal-rich\nand metal-poor subsystems produce a steady outward change in\nthe relative proportions of blue-to-red clusters with radius\nand thus a mean metallicity gradient.\n\nUsing Fig.~\\ref{fig6} as a guide, we divided the sample of objects\nat $(V-I) = 1.07$ and tested the radial distributions of the\nbluer and redder halves. A standard Kolmogorov-Smirnov two-sample\ntest indicated that their spatial distributions are significantly\ndifferent (the redder half is more centrally concentrated) at\nthe 99\\% level, suggesting to us that the inner gradient is indeed\na real effect.\n\nWe therefore {\\it very tentatively suggest} that the IC 4051 system\nmay contain a bimodal MDF in which the two modes are rather closely\nspaced in mean metallicity, thus heavily blurred out by the raw\nphotometric measurement uncertainty. Numerical experiments with various\ntwo-component fittings of the entire MDF lead to models of the form shown\nin Figure \\ref{fig7}. Here, a sample twin-Gaussian fit is shown in\nwhich the bluer (metal-poor) component is centered at $(V-I)=1.00$\nor [Fe/H] $\\simeq -0.96$,\nthe redder (metal-rich) one at $(V-I)=1.17$ or [Fe/H] $\\simeq +0.04$, \nboth have dispersions\n$\\sigma(V-I) = 0.10$, and the redder one contains about 55\\%\nof the total sample. The combined components now represent the \ntotal shape of the MDF better, with its modest skewness toward the red\nside (the total $\\chi^2$ is 12.6). The relative proportions of blue\nand red components, however, are quite uncertain (the formal\nuncertainties are $\\pm0.1$, but variations of factors\nof two in the proportions give scarcely different overall fits).\n\nClearly, this particular two-component \nmodel is only illustrative of the range of possibilities:\nthe moderately small difference in color between the two components, and the\nvery significant broadening of the MDF by photometric measurement\nuncertainty, do not justify more extensive analysis.\nHowever, it would clearly be of value to\nmeasure the MDF of this populous globular cluster system with a\nphotometric index much more sensitive to metallicity than $(V-I)$,\nin which the subpopulations would be far more clearly revealed.\nA more sensitive color index would also permit establishment of the\ntrue mean [Fe/H] with much less zeropoint uncertainty.\n\nLastly, it is worth comparing the mean colors of\nthe GCS components to that of the halo {\\it light} of\nthe central galaxy. \\cite{meh98} find $(V-I) \\simeq 1.30$\nat a projected radius $R = 10''$, increasing inward to $(V-I) = 1.35$\nat the very center. This color range is distinctly redder than\nthe typical levels $(V-I) \\simeq 1.20 \\pm 0.03$ \nfor giant E galaxies (\\cite{but95}; \\cite{pru98}). \nThe measured absorption line indices (Mg, Fe, H$\\beta$) \nlead \\cite{meh98} to conclude, in line with the integrated\ncolor, that the core of IC 4051 is extremely old and very metal-rich,\nperhaps as high as [Fe/H] $=+0.25$. However, the \ndeduced metallicity from the line indices becomes\nlower at larger radii, dropping to an equivalent [Fe/H] $\\sim -0.5$\nfor $R \\gtsim 20''$ (the effective radius $r_e$ of the light profile),\nsimilar to the inner GCS.\nMehlert \\etal\\ find that IC 4051 harbors\nan old, co-rotating core with an unusually large ``break radius'' (it is\ndetectable out to $5''$ or 3.4 kpc) but which contributes $\\ltsim$ 1\\%\nof the total light of the galaxy. If this inner stellar disk\nis a signature of a dissipational merging event, it is likely to have\noccurred at early times.\n\n\\section{THE LUMINOSITY DISTRIBUTION}\n\nAs \\cite{baum97} showed, the $V$ photometry reaches faint\nenough to reveal the ``turnover point'' (peak frequency)\nin the globular cluster luminosity function (GCLF).\nBy adding in the photometry from the WF chips, we have been\nable to double the total sample of clusters and thus improve\nthe definition of the GCLF.\n\nThe distribution of all the detected objects classified\nas ``starlike'' and used to define the GCLF is shown in Figure \\ref{fig8}.\nThese are, quite evidently, strongly concentrated to the\ncenter of IC 4051 (much more so than in the GCS of\nthe Coma supergiant NGC 4874; see Papers I and II). \nMore or less arbitrarily, we take the region $R > 80''$\nmarked by the outer dashed line in Fig.~\\ref{fig8},\nas defining the luminosity function of the background population,\nto be subtracted statistically from the inner ($10'' < R < 80''$)\nzone after correction for photometric incompleteness.\n\nThe results of this exercise for each of the four CCD chips\nseparately are shown in Figure \\ref{fig9}. Aside from the\nnoticeably brighter completeness limit for the PC1 zone,\nno significant differences in the GCLF shape or turnover from\nplace to place are evident. (The GCLF peak for the PC1 region\nshows an apparent peak fainter than $V \\sim 28$, but this\nis fainter than\nthe 50\\% completeness limit and so cannot be given much weight.)\nWe therefore add all four sectors\nto form the composite GCLF shown in Figure \\ref{fig10}.\nThe numerical results in 0.3-mag bins are listed in Table \\ref{tab4}:\nhere, successive columns give (1) the $V$ magnitude range of\nthe bin (2) the number of detected starlike objects in the\ninner ($10''-80''$) zone (3) the number in the outer ($> 80''$)\nbackground zone (4) the number in the inner zone corrected for\ncompleteness, and (5) the net GCLF, after subtraction of the\narea-normalized background counts.\n\nTo estimate the turnover level and shape of the GCLF, we fit \na standard Gaussian interpolation function (\\cite{har91}; \\cite{jac92})\nto the data shown in Fig.~\\ref{fig10}, setting the \nstandard deviation $\\sigma_V$ of the curve and then solving for\nthe best-fit turnover level $V^0$. Trials with different\nadopted $\\sigma_V$'s gave the results summarized in Table \\ref{tab5}.\nThe reduced $\\widetilde{\\chi}^2$ values favor a solution in the\nbroad range $\\sigma_V \\sim 1.4 - 1.8$, with little to choose\namong values in this range \nin a formal sense. However, it is well known that both\n$\\sigma_V$ and $V^0$ tend to be overestimated in situations like\nthese where the magnitude limit of the data reaches barely past the\nactual turnover (e.g., \\cite{han87}; Paper I) since the solutions\nfor the two parameters are correlated. For this reason, we favor\na choice in the narrower range $\\sigma_V \\simeq 1.4 - 1.6$ and\n$V^0 \\simeq 27.6 - 28.0$. Sample Gaussian curves for the extremes\nof this range are shown in Fig.~\\ref{fig10}.\n\nOur final adopted pair of parameters is $V^0 = 27.8 \\pm 0.2$, \n$\\sigma_V = 1.5 \\pm 0.1$. For comparison, \\cite{baum97} found\n$V^0 = 27.72$ employing a different and more complex fitting function.\nAs is discussed more extensively\nin Paper I, this turnover level is also similar to what we found in\nthe central cD NGC 4874. Using both of them combined, along with\na calibration of the absolute magnitude of the turnover point based\non the Virgo ellipticals, we find $d \\sim 100$ Mpc for Coma along\nwith a Hubble constant $H_0 \\simeq 70$ (see Paper I).\n\nA second and more physically oriented way to display the same material\nis as the {\\it luminosity distribution function} (LDF), or number\nof clusters per unit (linear) luminosity. (The relation between\nthe GCLF and LDF forms is exhaustively discussed by \\cite{mcl94}.)\nThe LDF is shown in \nFigure \\ref{fig11}. At levels brighter than the GCLF ``turnover''\n(which in turn is only slightly brighter than the photometric\ncompleteness limit), the LDF clearly approximates a power-law\nfalloff toward higher luminosity, $N(L) dL \\sim L^{-\\alpha}$.\nTo second order, however, the slope $\\alpha = -d$log($N$)/$d$log($L$)\nappears to steepen slightly at the upper end:\nan unweighted least-squares fit to all bins brighter than the\nturnover yields $\\alpha = 2.05$, while exclusion of the half-dozen\nvery brightest bins yields $\\alpha = 1.75$.\n\nThese power-law forms -- as well as logarithmic slope values $\\alpha \\sim 2$ --\nare entirely similar to what has been found in a wide range of\nother galaxies from dwarf ellipticals to spirals (\\cite{hp94};\n\\cite{dur96}). However, in most giant ellipticals studied to date, the\nslopes tend to be somewhat flatter at $\\alpha \\sim 1.5 \\pm 0.3$ (\\cite{hp94}).\nThe total shape for log $(L/L_{\\odot}) \\gtsim 5$, complete with\nits progressive steepening toward higher luminosity, \ncan be well matched by a formation model\nin which protocluster clouds build up by collisional agglomeration\nand in which the more massive clouds have shorter lifetimes against\nstar formation (\\cite{mp96}; \\cite{har99}). \nOur data for IC 4051 add further to the general body of material\nwhich indicates a remarkable place-to-place similarity in the\nluminosities of old globular clusters, and thus a quasi-universal\nformation process.\n\n\\section{RADIAL DISTRIBUTION AND SPECIFIC FREQUENCY}\n\nBecause the GCS around IC 4051 is quite centrally concentrated\n(see Fig.~\\ref{fig8}), we can use the complete WFPC2 data to\ndefine the spatial distribution outward nearly to its limits.\nThe radial profile of the raw counts for all starlike objects\nbrighter than $V = 27.0$, for which the data are highly complete\nnearly in to the central core of the galaxy, is shown in Figure \\ref{fig12}.\nThe inner core ($R \\ltsim 5''$), in which the projected density of\nclusters is nearly flat, continues outward to a steep power-law\nfalloff which covers most of our survey area. Finally,\nfor $R > 80''$, the number density $\\sigma$ begins to level off\ntowards its eventual far-field background level; more or less\narbitrarily, we set this background at $\\sigma_b = (0.02 \\pm 0.01)$\narcsec$^{-2}$ as representing\nnearly the average of the outermost two points.\n(As will be seen below, small\ndifferences in the adopted $\\sigma_b$ \nwill not have major effects on any of our subsequent conclusions.)\n\nThe complete profile data broken into circular annuli are listed\nin Table \\ref{tab6}, giving the number of objects in each bin, the surface\narea of the annulus, and the projected density $\\sigma$.\nThe residual number density of clusters, $\\sigma_{cl} = \\sigma-\\sigma_b$, \nis plotted in Figure \\ref{fig13}. Simple \\cite{king66} models can\nbe fitted to the $\\sigma_{cl}$ data points to give rough estimates\nof the GCS core radius and central concentration: performing a weighted\nfit in the manner described in Paper II, and ignoring the very uncertain\noutermost three points, we find a formal best-fit\ncore radius $R_c = 10\\farcs25$ (equivalent to 5.1 kpc at the adopted\nComa distance) as well as a concentration index $c = 1.45$ for a dimensionless\ncentral potential $W_0 = 6.26$. The core radius is four times\nsmaller in IC 4051 than the $\\sim 22$ kpc\nvalue we found in the much more extended NGC 4874 (Paper II).\n\nA second comparison can be made with the halo {\\it light} of the galaxy.\nIt is conventionally found in giant ellipticals\nthat the GCS is a more spatially extended\nsystem as a whole than the halo (\\cite{har91}, 1999). IC 4051 is no\nexception, despite its overall compact structure. \nIn Fig.~\\ref{fig13}, we show the \nwide-field surface intensity profiles\nin $\\mu_R$ measured by \\cite{str78} and \\cite{jfk92}. Although the\nStrom data are photographically measured, their profile agrees tolerably with\nthe more recent CCD measurements of \\cite{jfk92} over their region\nof overlap.\n\nThe bulk of the GCS profile is more extended than the halo light,\nexcept possibly for the outer ($R \\gtsim 30''$) regions where their\nslopes are more nearly similar. For $R \\gtsim 20''$,\nthe GCS profile behaves as $\\sigma_{cl} \\sim R^{-2}$, although\nat the largest radii little weight can be placed on\nthe very uncertain outermost half-dozen points. There is a strong\nhint from the halo light profile that the galaxy may be truncated\npast $R \\sim 60''$ (about 30 kpc), though here again the profile\nis very sensitive to slight differences in the adopted background level,\nso not much meaning can be ascribed to the slope differences \nbetween the GCS and the halo there.\nFor giant E galaxies in general, a rough mean relation between\ngalaxy luminosity $M_V^T$ and the radial falloff outside the\ncentral core is (\\cite{kai96}) $d$log$\\sigma$/$d$log$R$ $\\simeq -0.29 M_V^T\n- 8.00$. For IC 4051, this relation would predict $\\sigma_{cl} \\sim\nR^{-1.65}$, somewhat flatter than the observed $R^{-2}$ trend.\n\nCalculating the total GCS population and specific frequency is now\na straightforward matter. From Table \\ref{tab6}, we multiply $\\sigma_{cl}(R)$ \nby the area of each annulus, then sum the annuli to get the total cluster\npopulation out to the limits of our survey. We find\n$N = (1845 \\pm 165)$ for $V \\leq 27.0$ and $R \\ltsim 130''$.\nIf the true GCLF turnover magnitude is at $V^0 = 27.8 \\pm 0.2$ (see above),\nthen we must multiply this raw total by $\\simeq (3.35 \\pm 0.52)$ to\nestimate the total cluster population over all magnitudes, giving\n$N_{cl} = 6180 \\pm 1100$. The integrated luminosity of the galaxy\nis $V^T = 13.20$ (RC3 catalog value), corresponding to $M_V^T = -21.9$\nfor our adopted Coma distance. Thus, the specific frequency is\n$$ S_N = N_{cl} \\cdot 10^{0.4(M_V^T + 15)} = 10.8 \\pm 1.9 \\, .$$\n\nIn strict terms this is a {\\it lower limit} to the true global\n$S_N$, since we have not accounted for any cluster population outside\nthe $\\simeq 120''$ radial limit of our WFPC2 field. However, given\nthat the halo is clearly declining quite steeply in this region\n(Fig.~\\ref{fig13}), any such population correction is likely to be\nsmall. A generous but reasonable \n{\\it upper limit} estimate to the total population can\nbe made if we assume that the GCS profile continues as $\\sigma_{cl}\n\\sim R^{-2}$ outward to the nominal tidal radius at $R_t \\sim 230''$.\nThis assumption gives an additional $\\sim 380 \\pm 300$ clusters brighter than\n$V = 27$, which then translates to $S_N = 12.6 \\pm 2.6$.\n\nPlacing more weight on the lower limit -- which reflects \nthe steep falloff of the system near the radial limit of\nour data -- we adopt a final estimate\n$$S_N{\\rm (final)} = 11 \\pm 2 \\, .$$\n\nRemarkably, this GCS population ratio is\nseveral times higher than the $S_N \\ltsim 2$ value found in\nNGC 4881 (\\cite{baum95}), a galaxy which is quite comparable with\nIC 4051 in luminosity, structure, and location on the outskirts\nof the Coma core. This high $S_N$, in fact, \nplaces IC 4051 in the range which\nis conventionally reserved for the central-giant cD galaxies\nlike M87 and many other BCGs (\\cite{har98}; \\cite{bla97}, \\nocite{bla99}\n1999).\nIt is, perhaps, particularly noteworthy that IC 4051 has a specific\nfrequency three times higher than the central cD {\\it in its\nown host galaxy cluster}, NGC 4874 (see Paper II). No other instance\nof such a large contrast between a low$-S_N$ central cD and \na higher$-S_N$ outlying\nelliptical is known. IC 4051 provides striking evidence that a central\nlocation in a rich cluster environment is {\\it not} required to form\na high population of globular clusters.\n\n\\section{DISCUSSION}\n\nA brief summary of our findings for IC 4051 is that its GCS is\n(a) almost entirely metal-rich, albeit possibly with two narrowly\nseparated subcomponents;\n(b) relatively compact in radial structure; and (c) a ``high specific\nfrequency'' system despite that fact that its host galaxy is not a\ncentral giant elliptical nor one with a cD-type envelope.\n\nJust as in Paper II for NGC 4874, we now attempt to use the integrated\ncharacteristics to reconstruct a partial history of the system.\nFormation scenarios for giant ellipticals tend to fall into three\nbasic camps: (a) ``in situ'' formation, whereby the galaxy\ncondenses by dissipative collapse of gas clouds in its immediate\nvicinity, in one or more major bursts; (b) later mergers of pre-existing\ndisk-type galaxies with both gas and stars; or (c) successive mergers\nor accretions of smaller gas-poor satellites. Various combinations of\nthese extremes are, of course, possible, and even likely.\n\nFor IC 4051, the lack of {\\it low-}metallicity clusters already places\nfairly strong constraints on the range of possible formation events.\nFor example, the mechanism investigated by \\cite{cot98} -- in \nwhich an original metal-rich ``seed'' gE accretes dozens or hundreds of\nsmaller satellites -- is unlikely, since these dwarf satellites would\nhave brought in a population of hundreds or even thousands of \nlow-metallicity clusters, which we do not see. \n\nSimilarly, merger-formation \nmodels in which gas-rich disk galaxies combine to build a composite\nelliptical (\\cite{ash92}) would predict a strong component of metal-poor \nclusters in the resulting MDF from the globular clusters that were\npresent in the pre-merger galaxies. These merger models also have\nsevere difficulty in generating high specific frequency products,\nsince increasing the cluster population {\\it relative to the field stars}\nby a large enough amount to produce high $S_N$ requires \nvery large ($> 10^{10} M_{\\odot}$)\ninput gas masses, more than is routinely available in disk galaxies today.\nThe normal merger route does appear to be quite effective as a logical\nsource for low$-S_N$ field ellipticals (see \\cite{har99} or \\cite{whi95a}\nfor much more extensive discussion). \n\nHowever, if either the merger or accretion \nprocesses are taken to an extreme form\nin which {\\it the merging objects are almost completely gaseous}, then they\nbecome closely similar to the {\\it in situ} route, and the conundrum\nof the missing low-metallicity clusters can be more easily circumvented.\nIf the gas supply -- however it was assembled -- underwent most or all\nof its star formation in the high-pressure, high-density environment\nof the protoelliptical, then the conversion of gas to stars\nwould have run much further to completion\nand built up the metallicity to the high levels that we now observe.\nLater gaseous mergers are, of course, not ruled out: the central\ncorotating disk in the core of IC 4051 (Mehlert \\etal\\ 1998)\n\\nocite{meh98} with its very high metallicity is a likely signature\nof such an event, though at its $\\ltsim 1$\\% contribution to the\npresent-day luminosity, it probably did not form more than a few dozen\nglobular clusters along with it, and even these would have mostly\ndisrupted by now if they resided in the central few kpc of the core.\n\nThe relatively compact structure of the galaxy may be the result of\ntidal trimming (``harrassment'') from the Coma potential well (e.g.,\n\\cite{moo96}).\nThe radial velocity of IC 4051 (4940 km s$^{-1}$) is almost two standard\ndeviations away from the\nComa centroid (6850 km s$^{-1}$; see \\cite{col96}), \nindicating that this galaxy\noscillates back and forth through the cluster and \nis now passing through the dense Coma core at high speed.\n\nThese elements of an evolutionary scenario for IC 4051 are in strong\ncontrast to NGC 4874, for which we argued (Paper II) that \na large fraction of its clusters (which are\nalmost entirely low-metallicity) could\nhave been acquired by accretions of smaller satellites.\nIn IC 4051, we are forced to argue that the bulk of its clusters\nformed {\\it in situ}. The globular clusters in these two galaxies\nprovide unique evidence for the view that large E galaxies can form by\nradically different evolutionary routes.\n\nOne of the most challenging elements of IC 4051 to interpret \nis certainly the high specific frequency of its GCS.\nIn the previous literature (\\cite{har91}, 2000; \\cite{bla97}, 1999;\n\\cite{har98}; \\cite{mcl99}) it has become conventional to associate\nhigh $S_N$ with giant galaxies at the centers of rich clusters.\nThese central BCG's or cD's can have had histories\nof star and cluster formation through inflowing gas clouds and filaments,\nmergers, and accretions (e.g., \\cite{dub98}) that were much more\nextended than for normal outlying ellipticals. Recently, the view\nhas been developed that such high$-S_N$ galaxies should be regarded\nnot as ``cluster-rich'' but rather as ``star-poor''\n(\\cite{bla97}, 1999; \\cite{har98}; \\cite{mcl99}). In this scheme,\nwe postulate that \nthe protogalactic gas started forming globular clusters at early times\nat a normal efficiency rate,\nbut was then disrupted (perhaps by supernova-driven \ngalactic winds, or by tidal shredding during infall;\ncf.~the papers cited above) before its star formation\ncould run to completion. The leftover gas now remains around these\ngalaxies as their hot X-ray halos. This picture, however, assumes \nthat the globular clusters form earlier than the bulk of the field stars\nin any given round of star formation -- not an implausible requirement\ngiven the bulk of the observational evidence for starburst systems\n(see Harris 2000) and given that globular clusters emerge from the densest,\nmost massive protocluster clouds.\n\nMcLaughlin (1999) \\nocite{mcl99} defines a globular\ncluster formation efficiency, measured empirically as the mass ratio\n$$ \\epsilon = {M_{cl} \\over {M_{\\star} + M_{gas}} } $$\nwhere $M_{\\star}$ and $M_{gas}$ are the masses \nwithin the galaxy in the form of visible stars and\nin the X-ray gas respectively. He finds that $\\epsilon$ is essentially\nidentical in the well studied Virgo and Fornax\nsystems M87, NGC 4472, and NGC 1399 (despite their very different\n$S_N$), providing evidence for a\n``universal'' globular cluster formation efficiency $\\epsilon \\simeq\n0.26$\\% relative to the\n{\\it initial protogalactic gas supply}. The total mass ratio\n$\\epsilon$ is a more important indicator of cluster formation\nthan $S_N$, which is only a measure\nof the cluster numbers (or equivalently total mass) relative to \nthe galaxy light. In other words, $S_N$ is a measure of\nonly the gas mass $M_{\\star}$ that got converted to stars.\nAdditional support for the near-universality of \n$\\epsilon$ in several other BCG's is found by Blakeslee (1999) \\nocite{bla99}.\n\nIn this view, {\\it any high$-S_N$ galaxy\nshould then be surrounded by a massive X-ray gaseous component}\nwhether or not it is a centrally dominant giant. \nNotably, IC 4051 is indeed one of the\nfew Coma ellipticals with an individually detected X-ray halo.\nDow \\& White (1995), \\nocite{dow95} \nfrom ROSAT observations of the Coma core region, find\nthat IC 4051 is detectable at the $2-\\sigma$ level in the soft\nX-ray range $0.2 - 0.4$ keV, but not in the higher $0.4 - 2.4$ keV range. \nIf it were at the $\\sim 6.3$ times closer distance of Virgo, IC 4051 \nwould have a total $L_X \\simeq 5 \\times 10^{41}$ erg s$^{-1}$. This\nlevel makes it quite comparable with the\nVirgo giant NGC 4472, which has $L_X \\simeq 6 \\times 10^{41}$ erg s$^{-1}$\nin the soft X-ray regime (\\cite{fab92}; \\cite{irw96}; \\cite{mat97};\n\\cite{buo98}). However, this amount of X-ray gas corresponds to only\n$\\sim 5$\\% of the stellar mass (\\cite{mcl99}) and NGC 4472, as expected,\nhas only a ``normal'' specific frequency level $S_N \\simeq 5$.\n\nWith our adopted distance ratios for Virgo and Coma, we find that\nIC 4051 is about half as luminous as NGC 4472, so if it has a roughly\nsimilar amount of X-ray gas mass, this gas would only make up\n$\\sim 10$\\% of its stellar mass. Along with $S_N \\simeq 11$,\nwe find that these parameters convert to\na {\\it present-day} value for the mass ratio in IC 4051 of\n$\\epsilon \\sim 0.005$, twice as large as McLaughlin's (1999)\n\\nocite{mcl99} fiducial value.\n\nNominally, it therefore seems that IC 4051 acts against the\nparadigm of a universal globular cluster formation efficiency.\nAn obvious possibility, however, is that IC 4051 originally\ndid possess much more gas shortly after its main era of\nglobular cluster formation, but that most of this unused material was\nquickly stripped away \nas IC 4051 went through its first few passages of the Coma core.\nThis gas would have joined the general reservoir \nof hot gas spread throughout the Coma potential well.\nThe same mechanism which resulted in this galaxy's compact structure\nmight then have plausibly left it with the unusual combination of \nhigh $S_N$ and modest amount of X-ray gas that we now see.\n\nA situation which would act much more strongly to falsify \nMcLaughlin's case for a\nuniversal $\\epsilon$ would be the opposite one:\nthat is, a galaxy with a massive X-ray halo but a ``normal''\nor subnormal $S_N \\ltsim 4$. In such a case it would be much\nharder to avoid the conclusion that the formation efficiency\nof globular clusters was genuinely different (and low).\nDoes the central Coma giant NGC 4874 present us with such a case?\nAs we found in Paper II, \nNGC 4874 is {\\it not} a high-$S_N$ system and is embedded within\na very massive X-ray envelope. This X-ray gas is, however, so extended\nthat must belong to the general Coma potential well as a whole, with no\ndetectable concentrated component that \ncan be associated with NGC 4874 itself\n(\\cite{dow95}). Thus there are ambiguities in\nthe interpretation that are hard to circumvent. Better candidates\nwould be E galaxies with massive X-ray halos that are not at\nthe centers of rich clusters.\n\nFinally, we may compare the interesting case of IC 4051 with that\nof its Coma neighbor NGC 4881 (\\cite{baum95}), a giant E galaxy\nof similar location, size, and structure. Curiously, NGC 4881 holds a\nGCS of {\\it low} specific frequency ($S_N \\ltsim 2$) which appears\nto be almost entirely metal-{\\it poor}, just the opposite of\nIC 4051. It has no significant amounts of X-ray gas (\\cite{dow95}).\nWe speculate that NGC 4881 may have resulted from the\nmerger of smaller galaxies in which these metal-poor globulars had\nalready formed. These mergers should have been rather gas-poor to\nprevent the formation of newer and more metal-rich clusters.\nThis is, however, an extremely sketchy interpretation, and there is an\nobvious problem with the much higher metallicity of the host galaxy\nlight (how did the bulk of the giant E galaxy form at higher metallicity\nwithout leaving behind some metal-rich globular clusters? See Paper II\nfor additional discussion). \n\nThe Coma ellipticals clearly present a wide range of GCS characteristics\nthat strongly challenge the array of current galaxy formation models.\n\n\n\\acknowledgments\n\nThis research was supported through a grant to WEH from\nthe Natural Sciences and Engineering Research Council of Canada.\nWe thank Peter Macdonald of Ichthus Data Systems and the Department of\nMathematics and Statistics at McMaster \nfor providing the MIX multicomponent fitting code.\nBill Baum provided several constructive comments on the first version\nof the text.\n\n\\clearpage \n\n\\begin{thebibliography}{}\n\n\n\\bibitem[Armandroff \\& Zinn 1988]{armandroff88} Armandroff, T. 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E. 1995, \\aj, 109, 1019\n\n\\bibitem[Stetson 1992]{ste92} Stetson, P.~B. 1992, in Astronomical \nData Analysis Software and Systems I, ASP Conf.~Ser.~8, \nedited by G.~H.~Jacoby (ASP, San Francisco), p. 289\n\n\\bibitem[Strom \\& Strom (1978)]{str78} Strom, K.~M., \\& Strom, S.~E.\n1978, \\aj, 83, 73\n\n\\bibitem[Whitmore \\& Schweizer 1995]{whi95a}\nWhitmore, B.~C., \\& Schweizer, F. 1995, \\aj, 109, 960\n\n\\bibitem[Whitmore \\etal\\ 1995]{whi95} Whitmore, B.~C., Sparks, W.~B.,\nLucas, R.~A., Macchetto, F.~D., \\& Biretta, J.~A. 1995, \\apjl, 454, L73\n\n\\bibitem[Zinn 1985]{zin85} Zinn, R. 1985, \\apj, 293, 424\n\n\\end{thebibliography}\n\n\n\n\n\n\n\\clearpage\n\n\n%%%%%%%%%%%%%%% TABLES\n\n\n\\begin{deluxetable}{ccccc}\n\\tablenum{1}\n\\tablecaption{Completeness Function Parameters \\label{tab1}}\n\\tablewidth{0pt}\n\\tablecolumns{5}\n\\tablehead{\n\\colhead{CCD} & \\colhead{$F606W (V)$} & \\colhead{ } &\n\\colhead{$F814W (I)$} & \\colhead{ } \\nl\n\\colhead{ } & \\colhead{$\\alpha$} & \\colhead{$V_{lim}$} & \\colhead{$\\alpha$} & \\colhead{$I_{lim}$ }\n}\n\\startdata\nPC1 & 3.508 & 27.85 & 3.682 & 25.70 \\nl\nWF2 & 3.141 & 28.39 & 3.078 & 26.13\\nl\nWF3 & 3.123 & 28.46 & 3.157 & 26.24\\nl\nWF4 & 3.154 & 28.39 & 3.530 & 26.18\\nl\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\n\n\\begin{deluxetable}{crcc}\n\\tablenum{2}\n\\tablecaption{Mean Color vs. $V$ Magnitude \\label{tab2}}\n\\tablewidth{0pt}\n\\tablecolumns{4}\n\\tablehead{\n\\colhead{$V$} & \\colhead{N } & \\colhead{$\\langle V - I \\rangle$} & \n\\colhead{$\\sigma_{(V-I)}$} \n}\n\\startdata\n\n$ 22.5 \\!-\\! 23.0 $ & 7 & 1.058 & 0.031 \\nl\n$ 23.0 \\!-\\! 23.5 $ & 7 & 1.136 & 0.053 \\nl\n$ 23.5 \\!-\\! 24.0 $ & 20 & 1.101 & 0.018 \\nl\n$ 24.0 \\!-\\! 24.5 $ & 43 & 1.111 & 0.016 \\nl\n$ 24.5 \\!-\\! 25.0 $ & 77 & 1.128 & 0.012 \\nl\n$ 25.0 \\!-\\! 25.5 $ & 145 & 1.113 & 0.010 \\nl\n$ 25.5 \\!-\\! 26.0 $ & 180 & 1.119 & 0.010 \\nl\n\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\n\n\n\\begin{deluxetable}{lrcccc}\n\\tablenum{3}\n\\tablecaption{Mean Color vs. Radius \\label{tab3}}\n\\tablewidth{0pt}\n\\tablecolumns{6}\n\\tablehead{\n\\colhead{R (arcsec) } & \\colhead{ N } & \\colhead{$\\langle V - I \\rangle$ } & \n\\colhead{$\\pm$ } & \n\\colhead{$\\langle {\\rm Fe/H} \\rangle$ } & \\colhead{$\\pm$ }\n}\n\\startdata\n$\\phn0.0 \\!-\\!\\phn 8.0$ & 79&1.170 & 0.013 & $ +0.04 $ & 0.08 \\nl\n$\\phn8.0 \\!-\\! 12.0$ & 80 & 1.141 & 0.011 & $ -0.14 $& 0.07 \\nl\n$12.0 \\!-\\! 16.0$ & 61 & 1.116 & 0.014 & $ -0.28 $ & 0.08 \\nl\n$16.0 \\!-\\! 26.0$ & 68 & 1.083 & 0.015 & $ -0.48 $ & 0.09 \\nl\n$26.0 \\!-\\! 40.0$ & 75 & 1.120 & 0.013 & $ -0.26 $ & 0.08 \\nl\n$40.0 \\!-\\! 55.0$ & 51 & 1.120 & 0.017 & $ -0.26 $ & 0.10 \\nl\n$55.0 \\!-\\! 80.0$ & 65 & 1.050 & 0.015 & $ -0.67 $ & 0.09 \\nl\n\n\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\n\n\n\n\n\\begin{deluxetable}{cllll}\n\\tablenum{4}\n\\tablecaption{Binned GCLF Data \\label{tab4}}\n\\tablewidth{0pt}\n\\tablecolumns{4}\n\\tablehead{\n\\colhead{$V$} & \\colhead{N$_{in}$}& \\colhead{N$_{out}$ } & \\colhead{N$_{in,corr}$} \n& \\colhead{N$_{final}$}\n}\n\\startdata\n$ 22.1 \\!-\\! 22.4$ & \\phn\\phn 1.0 $\\pm$ 1.0 & \\phn 0.0 $ \\pm$ 0.0 & \\phn\\phn 1.0 $\\pm$ 1.0 & \\phn\\phn 1.0 $\\pm$ 1.0 \\nl\n$ 22.4 \\!-\\! 22.7$ & \\phn\\phn 1.0 $\\pm$ 1.0 & \\phn 1.0 $ \\pm$ 1.0 & \\phn\\phn 1.0 $\\pm$ 1.0 &\\phn\\phn \\llap{$-$}0.9 $\\pm$ 1.5 \\nl\n$ 22.7 \\!-\\! 23.0$ & \\phn\\phn 5.0 $\\pm$ 2.2 & \\phn 1.0 $ \\pm$ 1.0 & \\phn\\phn 5.0 $\\pm$ 2.2 & \\phn\\phn 3.1 $\\pm$ 2.5 \\nl\n$ 23.0 \\!-\\! 23.3$ & \\phn\\phn 1.0 $\\pm$ 1.0 & \\phn 0.0 $ \\pm$ 0.0 & \\phn\\phn 1.0 $\\pm$ 1.0 & \\phn\\phn 1.0 $\\pm$ 1.0 \\nl\n$ 23.3 \\!-\\! 23.6$ & \\phn\\phn 7.0 $\\pm$ 2.6 & \\phn 2.0 $ \\pm$ 1.4 & \\phn\\phn 7.0 $\\pm$ 2.6 & \\phn\\phn 3.1 $\\pm$ 3.0 \\nl\n$ 23.6 \\!-\\! 23.9$ & \\phn 13.0 $\\pm$ 3.6 & \\phn 1.0 $ \\pm$ 1.0 &\\phn 13.0 $\\pm$ 3.6 & \\phn 11.1 $\\pm$ 3.8 \\nl\n$ 23.9 \\!-\\! 24.2$ & \\phn 11.0 $\\pm$ 3.3 & \\phn 1.0 $ \\pm$ 1.0 &\\phn 11.0 $\\pm$ 3.3 & \\phn\\phn 9.1 $\\pm$ 3.5 \\nl\n$ 24.2 \\!-\\! 24.5$ & \\phn 22.0 $\\pm$ 4.7 & \\phn 2.0 $ \\pm$ 1.4 &\\phn 22.0 $\\pm$ 4.7 & \\phn 18.2 $\\pm$ 4.9 \\nl\n$ 24.5 \\!-\\! 24.8$ & \\phn 36.0 $\\pm$ 6.0 & \\phn 2.0 $ \\pm$ 1.4 &\\phn 36.1 $\\pm$ 6.0 & \\phn 32.2 $\\pm$ 6.2 \\nl\n$ 24.8 \\!-\\! 25.1$ & \\phn 53.0 $\\pm$ 7.3 & \\phn 1.0 $ \\pm$ 1.0 &\\phn 53.1 $\\pm$ 7.3 & \\phn 51.2 $\\pm$ 7.4 \\nl\n$ 25.1 \\!-\\! 25.4$ & \\phn 81.0 $\\pm$ 9.0 & \\phn 7.0 $ \\pm$ 2.6 &\\phn 81.2 $\\pm$ 9.0 & \\phn 67.7 $\\pm$ 9.5 \\nl\n$ 25.4 \\!-\\! 25.7$ & 115.0 $\\pm$ 10.7 & 12.0 $ \\pm$ 3.5 & 115.4 $\\pm$ 10.8 & \\phn 92.2 $\\pm$ 11.4 \\nl\n$ 25.7 \\!-\\! 26.0$ & 108.0 $\\pm$ 10.4 & 17.0 $ \\pm$ 4.1 & 108.5 $\\pm$ 10.4 & \\phn 75.5 $\\pm$ 11.3 \\nl\n$ 26.0 \\!-\\! 26.3$ & 159.0 $\\pm$ 12.6 & 23.0 $ \\pm$ 4.8 & 159.9 $\\pm$ 12.7 & 115.3 $\\pm$ 13.7 \\nl\n$ 26.3 \\!-\\! 26.6$ & 229.0 $\\pm$ 15.1 & 43.0 $\\pm$ 6.6 & 230.8 $\\pm$ 15.3 & 147.4 $\\pm$ 16.8 \\nl\n$ 26.6 \\!-\\! 26.9$ & 263.0 $\\pm$ 16.2 & 44.0 $ \\pm$ 6.6 & 266.2 $\\pm$ 16.4 & 180.5 $\\pm$ 17.9 \\nl\n$ 26.9 \\!-\\! 27.2$ & 320.0 $\\pm$ 17.9 & 42.0 $ \\pm$ 6.5 & 326.1 $\\pm$ 18.2 & 244.1 $\\pm$ 19.5 \\nl\n$ 27.2 \\!-\\! 27.5$ & 312.0 $\\pm$ 17.7 & 66.0 $ \\pm$ 8.1 & 324.2 $\\pm$ 18.4 & 194.2 $\\pm$ 20.4 \\nl\n$ 27.5 \\!-\\! 27.8$ & 305.0 $\\pm$ 17.5 & 57.0 $ \\pm$ 7.5 & 343.4 $\\pm$ 19.9 & 229.0 $\\pm$ 21.6 \\nl\n$ 27.8 \\!-\\! 28.1$ & 292.0 $\\pm$ 17.1 & 66.0 $ \\pm$ 8.1 & 408.8 $\\pm$ 27.5 & 268.0 $\\pm$ 29.1 \\nl\n$ 28.1 \\!-\\! 28.4$ & 220.0 $\\pm$ 14.8 & 81.0 $ \\pm$ 9.0 & 436.7 $\\pm$ 44.0 & 216.9 $\\pm$ 46.1 \\nl\n$ 28.4 \\!-\\! 28.7$ & 150.0 $\\pm$ 12.2 & 66.0 $ \\pm$ 8.1 & 690.7 $\\pm$ 87.7 & 291.9 $\\pm$ 92.2 \\nl\n$ 28.7 \\!-\\! 29.0$ & \\phn 97.0 $\\pm$ 9.8 & 46.0 $ \\pm$ 6.8 & \\llap{1}076.5 $\\pm$131.4 & 363.7 $\\pm$144.4 \\nl\n$ 29.0 \\!-\\! 29.3$ & \\phn\\phn 8.0 $\\pm$ 2.8 & \\phn 3.0 $ \\pm$ 1.7 & 159.9 $\\pm$ 57.2 &\\phn 45.9 $\\pm$ 68.4 \\nl\n\n\n\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\n\n\n\n\\begin{deluxetable}{cccc}\n\\tablenum{5}\n\\tablecaption{GCLF $\\widetilde{\\chi}^2$ Fitting Results \\label{tab5}}\n\\tablewidth{0pt}\n\\tablecolumns{3}\n\\tablehead{\n\\colhead{$\\sigma_V$ } & \\colhead{$\\widetilde{\\chi}^2$ } & \n\\colhead{$V_0$ } \n}\n\\startdata\n1.3 & 2.17 & 27.44 \\nl\n1.4 & 1.62 & 27.59 \\nl\n1.5 & 1.37 & 27.77 \\nl\n1.6 & 1.32 & 27.97 \\nl\n1.7 & 1.42 & 28.21 \\nl\n1.8 & 1.62 & 28.46 \\nl\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\n\n\n\n\\begin{deluxetable}{lrll}\n\\tablenum{6}\n\\tablecaption{Radial Density Profile \\label{tab6}}\n\\tablewidth{0pt}\n\\tablecolumns{5}\n\\tablehead{\n\\colhead{R (arcsec) } & \\colhead{N } & \\colhead{A (arcsec$^2$) } & \n\\colhead{$\\sigma$(n/arcsec$^2$) } \n}\n\\startdata\n$ \\phn \\phn 0.0 \\!-\\! 2.0 $& 16 & \\phn \\phn 12.533& $1.277 \\pm 0.319$ \\nl\n$ \\phn \\phn 2.0 \\!-\\! 4.0 $& 56 & \\phn \\phn 37.687& $1.486 \\pm 0.199$ \\nl\n$ \\phn \\phn 4.0 \\!-\\! 6.0 $& 86 & \\phn \\phn 62.845& $1.368 \\pm 0.148$ \\nl\n$ \\phn \\phn 6.0 \\!-\\! 8.0 $& 107& \\phn \\phn 87.989 & $1.216 \\pm 0.118$ \\nl\n$ \\phn \\phn 8.0 \\!-\\! 10.0$& 113& \\phn 113.069& $0.999 \\pm 0.094$ \\nl\n$ \\phn 10.0 \\!-\\! 15.0 $& 268& \\phn 392.731& $0.682 \\pm 0.042$ \\nl\n$ \\phn 15.0 \\!-\\! 20.0 $& 172& \\phn 442.020& $0.389 \\pm 0.030$ \\nl\n$ \\phn 20.0 \\!-\\! 25.0 $& 98 & \\phn 373.326& $0.263 \\pm 0.027$ \\nl\n$ \\phn 25.0 \\!-\\! 30.0 $& 91 & \\phn 459.581& $0.198 \\pm 0.021$ \\nl\n$ \\phn 30.0 \\!-\\! 35.0 $& 92 & \\phn 582.352& $0.158 \\pm 0.017$ \\nl\n$ \\phn 35.0 \\!-\\! 40.0 $& 68 & \\phn 702.702& $0.097 \\pm 0.012$ \\nl\n$ \\phn 40.0 \\!-\\! 50.0 $& 146& 1762.469& $0.083 \\pm 0.007$ \\nl\n$ \\phn 50.0 \\!-\\! 60.0 $& 104& 2235.922& $0.047 \\pm 0.005$ \\nl\n$ \\phn 60.0 \\!-\\! 70.0 $& 90 & 2431.022& $0.037 \\pm 0.004$ \\nl\n$ \\phn 70.0 \\!-\\! 80.0 $& 88 & 2484.612& $0.035 \\pm 0.004$ \\nl\n$ \\phn 80.0 \\!-\\! 90.0 $& 81 & 2594.925& $0.031 \\pm 0.004$ \\nl\n$ \\phn 90.0 \\!-\\! 100.0$& 57 & 2124.154& $0.027 \\pm 0.004$ \\nl\n$ 100.0 \\!-\\! 110.0 $& 23 & \\phn 898.649& $0.026 \\pm 0.005$ \\nl\n$ 110.0 \\!-\\! 130.0 $& 9 & \\phn 521.199& $0.017 \\pm 0.006$ \\nl\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{Woodworth.fig1.ps}\n\\caption{Image classification plots for all\ndetected objects on the deep $V$ exposures. The radial image moment\n$r_1$ (see text) is plotted against $V$ for each of the four WFPC2\nCCDs. The dashed lines show the adopted boundaries separating\nstar-like objects (below the line) from nonstellar ones (above). \nThe vast majority of the starlike objects are globular \nclusters around IC 4051.}\n\\label{fig1}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{Woodworth.fig2.ps}\n\\caption{\nCompleteness functions for the $V$ (F606W) and $I$ (F814W) photometry.\nThe solid dots (leftmost curve) represent the PC1 data, \nsolid squares represent WF2, solid triangles WF3, and open circles WF4.\nThe lines through each set of points show the Pritchet interpolation\nfunction curves described in the text and parametrized in Table 1.\nThe PC1 photometry has a noticeably brighter limiting magnitude.}\n\\label{fig2}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{Woodworth.fig3.ps}\n\\caption{\nMean photometric uncertainty as a function\nof magnitude, derived from the artificial-star tests. The dashed\nline represents the PC1, while the solid lines are for the WF2,3,4\nchips. Here and in the completeness functions, there are no\nsignificant differences among the three WF chips.}\n\\label{fig3}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{Woodworth.fig4.ps}\n\\caption{\nColor-magnitude distribution for all measured starlike objects with\n$(V-I)$ colors. The vast majority of these are globular clusters in\nIC 4051. Objects within $80\\arcsec$\nof the center of IC 4051 are plotted in the left panel, and\nobjects lying beyond $80\\arcsec$ in the right panel.\nThe solid line shows the 50\\% detection completeness limit in $I$.}\n\\label{fig4}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{Woodworth.fig5.ps}\n\\caption{\nThe metallicity distribution function (MDF)\nfor the globular cluster system in {\\ic}.\nNumber of objects per 0.05-mag bin, after subtraction of\nbackground (see text), is plotted against $(V-I)$.\nThe [Fe/H] scale at top follows the linear conversion\nrelation given in the text, and should be taken only\nas schematic for [Fe/H] $\\gtsim 0$.\nThe best-fit single Gaussian function is shown, with\n$\\langle V-I \\rangle = 1.12$ and $\\sigma(V-I) = 0.13$.\nThe {\\it dashed line} shows the color distribution for the\nglobular clusters in the Virgo giant M87 (\\protect\\cite{kun99}).}\n\\label{fig5}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{Woodworth.fig6.ps}\n\\caption{\n$V-I$ colour plotted against projected galactocentric distance,\nfor bright objects ($V < 26.0$) for which the photometry is\nhighly complete at all radii and the measurement uncertainties\nare smallest. Horizontal lines at $(V-I) = 1.17, 1.00$ are drawn\nat the suggested two subpopulations; the bluer of the two\ncomponents is almost absent within $10''$.}\n\\label{fig6}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{Woodworth.fig7.ps}\n\\caption{\nThe color distribution of the clusters, fitted by a two-component\nGaussian model as described in the text. The two subcomponents,\ncentered at $(V-I) = 1.00, 1.17$ and each with $\\sigma = 0.10$,\nare shown as the dashed lines, and their sum as the smooth\nsolid line.}\n\\label{fig7}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{Woodworth.fig8.ps}\n\\caption{\nSpatial distribution of the globular clusters\nused to define the GCLF. Dotted lines outline the boundaries\nof the four CCDs.\nThe zone outside the outer dashed circle at $R = 80''$ is\nused to define the ``background'' number density of objects.\nNo data within $R = 10''$ (inner dashed circle) were used\nfor the GCLF analysis. Note the obvious high \nconcentration of the GC population toward the center of IC 4051.}\n\\label{fig8}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{Woodworth.fig9.ps}\n\\caption{\nGCLFs (number of objects per 0.3-mag bin, after correction\nfor incompleteness and subtraction of background)\nfor the four separate WFPC2 chips. \nThe dashed line in each graph represents the 50\\% completeness \nlimit of the photometry, while the solid line shows the best-fit Gaussian \nfunction (see next Figure).}\n\\label{fig9}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{Woodworth.fig10.ps}\n\\caption{\nThe GCLF for all combined $V$ data (the sum of the four\nplots in the previous figure).\nThe dotted and dashed vertical lines represent \nthe $50\\%$ completeness \nlimit of the PC1 and WF data respectively.\nThe solid line is the best-fit Gaussian \nfunction to the binned data for an assumed GCLF dispersion\n$\\sigma_V = 1.6$, while the dashed line is the best-fit Gaussian\nfor $\\sigma_V = 1.4$.}\n\\label{fig10}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{Woodworth.fig11.ps}\n\\caption{\nThe luminosity distribution function (LDF, or number of clusters\nper unit luminosity $L/L_{\\odot}$).\nThe vertical dashed line shows the luminosity at which the\nGCLF (from the previous figure) reaches its peak or ``turnover'',\nequivalent to log$(L/L_{\\odot}) \\sim 4.8$.\nThe dotted line is a weighted best-fit power-law\nfunction $N \\sim L^{-\\alpha}$ for the restricted\nrange $4.8 \\lesssim \\log(L/L_{\\odot})\n\\lesssim 6.5$, yielding $\\alpha = 1.75$. \nAn unweighted fit to all the data (dot-dashed line)\nyields a somewhat steeper slope $\\alpha \\simeq 2.05$ affected\nby the downturn at the bright end.}\n\\label{fig11}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{Woodworth.fig12.ps}\n\\caption{\nRadial surface density profile for all detected objects with $V \\leq 27.0$. \nFor $R \\gtsim 80''$ (vertical dashed line), the \nnumber density $\\sigma$ begins flattening\noff to its asymptotic background level, which we adopt as\n$\\sigma_b = 0.02$ arcsec$^{-2}$ (horizontal dashed line).}\n\\label{fig12}\n\\end{figure}\n\\clearpage\n\n\\begin{figure}\n\\epsscale{1.0}\n\\plotone{Woodworth.fig13.ps}\n\\caption{\nThe radial projected density profile of the globular cluster\nsystem. {\\it Solid dots} with error bars are taken from \nTable 7 and assume a background density $\\sigma_b = 0.02$ arcsec$^{-2}$.\nThe solid line is the $R-$band photographic\nsurface intensity profile of the halo\nlight, from Strom \\& Strom (1978), while the dotted line is the\n$R-$band CCD profile from Jorgensen \\etal\\ (1992). Both\nare shifted vertically arbitrarily to match to the GCS profile.\nThe dashed line is the best-fit King model discussed in the text,\nwith core radius $R \\simeq 10''$ and $c = 1.45$.}\n\\label{fig13}\n\\end{figure}\n\\clearpage\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002292.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\n\\bibitem[Armandroff \\& Zinn 1988]{armandroff88} Armandroff, T. E., \\&\nZinn, R. 1988, \\aj, 96, 92\n\n\\bibitem[Ashman \\& Zepf 1992]{ash92} Ashman, K.~M., \\& Zepf, S.~E. 1992,\n\\apj, 384, 50\n\n\\bibitem[Baum \\etal\\ 1995]{baum95} Baum, W.~A. et al.~1995,\n\\aj, 110, 2537\n\n\\bibitem[Baum \\etal\\ (1997)]{baum97} Baum, W.~A. et al.~1997,\n\\aj, 113, 1483\n\n\\bibitem[Blakeslee 1997]{bla97} Blakeslee, J.~P. 1997, \\apjl, 481, L59 (B97)\n\n\\bibitem[Blakeslee 1999]{bla99} Blakeslee, J.~P. 1999, \\aj, 118, 1506\n\n\\bibitem[Buote \\& Fabian 1998]{buo98} Buote, D.~A., \\& Fabian, A.~C.\n1998, \\mnras, 296, 977\n\n\\bibitem[Buta \\& Williams 1995]{but95}\nButa, R., \\& Williams, K.~L. 1995, \\aj, 109, 543\n\n\\bibitem[Colless \\& Dunn 1996]{col96}\nColless, M., \\& Dunn, A.~M. 1996, \\apj, 458, 435\n\n\\bibitem[C\\^ot\\'e \\etal\\ (1998)]{cot98} C\\^ot\\'e, P.,\nMarzke, R., \\& West, M.~J. 1998, ApJ, 501, 554\n\n\\bibitem[Dow \\& White 1995]{dow95} Dow, K.~L., \\& White, S.~D.~M.\n1995, \\apj, 439, 113\n\n\\bibitem[Dubinski 1998]{dub98} Dubinski, J. 1998, \\apj, 502, 141\n\n\\bibitem[Durrell \\etal\\ 1996]{dur96} Durrell, P.~R., Harris, W.~E.,\nGeisler, D., \\& Pudritz, R.~E. 1996, \\aj, 112, 972\n\n\\bibitem[Fabbiano \\etal\\ 1992]{fab92} Fabbiano, G., Kim, D.-W.,\n\\& Trinchieri, G. 1992, \\apjs, 80, 531\n\n\\bibitem[Geisler \\etal\\ 1996]{geisler96} Geisler, D., Lee, M.~G.,\n\\& Kim, E. 1996, \\aj, 111, 1529\n\n\\bibitem[Hanes \\& Whittaker 1987]{han87} Hanes, D.~A., \\& Whittaker,\nD.~G. 1987, \\aj, 94, 906\n\n\\bibitem[Harris 1991]{har91} Harris, W.~E. 1991, \\araa, 29, 543\n\n\\bibitem[Harris 1996]{har96} Harris, W.~E. 1996, \\aj, 112, 1487\n\n\\bibitem[Harris 2000]{har99}\nHarris, W.~E. 2000, Lectures for 1998 Saas-Fee Advanced School on\nStar Clusters, in press\n\n\\bibitem[Harris \\etal\\ (1991)]{hapv91} Harris, W.~E., Allwright, J.~W.~B.,\nPritchet, C.~J., \\& van den Bergh, S. 1991, \\apjs, 76, 115\n\n\\bibitem[Harris \\etal\\ 1998]{har98} Harris, W.~E., Harris, G. L. H., \n\\& McLaughlin, D. E. 1998, \\aj, 115, 1801\n\n\\bibitem[Harris \\etal\\ 2000]{hk99} Harris, W.~E., Kavelaars, J.~J.,\nHanes, D.~A., Hesser, J.~E., \\& Pritchet, C.~J. 2000, \\apj, 533, in press\n(Paper II)\n\n\\bibitem[Harris \\& Pudritz 1994]{hp94} Harris, W.~E., \\& Pudritz, R.~E.\n1994, \\apj, 429, 177 \n\n\\bibitem[Holtzman \\etal\\ (1995)]{holtzman95} Holtzman, J.~A. et al.~1995,\n\\pasp, 107, 1065\n\n\\bibitem[Irwin \\& Sarazin 1996]{irw96} Irwin, J.~A., \\& Sarazin, C. \n1996, \\apj, 471, 683\n\n\\bibitem[Jacoby \\etal\\ 1992]{jac92} Jacoby, G.~H. \\etal\\ 1992,\n\\pasp, 104, 599\n\n\\bibitem[Jorgensen \\etal\\ (1992)]{jfk92} Jorgensen, I.,\nFranx, M., \\& Kjaergaard, P. 1992, AApS, 95, 489\n\n\\bibitem[Kaisler \\etal\\ 1996]{kai96} Kaisler, D., Harris, W.~E.,\nCrabtree, D.~R., \\& Richer, H.~B. 1996, \\aj, 111, 2224\n\n\\bibitem[Kavelaars \\etal\\ 2000]{kav99}\nKavelaars, J.~J., Harris, W.~E., Hanes, D.~A., Hesser, J.~E.,\n\\& Pritchet, C.~J. 2000, \\apj, 533, in press (Paper I)\n\n\\bibitem[King (1966)]{king66} King, I.~R. 1966, \\aj, 71, 64\n\n\\bibitem[Kundu \\& Whitmore 1999]{kw99}\nKundu, A., \\& Whitmore, B.~C. 1999, Bull.AAS, 31, 874\n\n\\bibitem[Kundu \\etal\\ 1999]{kun99}\nKundu, A., Whitmore, B.~C., Sparks, W.~B., Macchetto, F.~D.,\nZepf, S.~E., \\& Ashman, K.~M. 1999, \\apj, 513, 733\n\n\\bibitem[Lee \\etal\\ 1998]{lee98} Lee, M.~G., Kim, E., \\&\nGeisler, D. 1998, AJ, 115, 947\n\n\\bibitem[Matsumoto \\etal\\ 1997]{mat97} Matsumoto, H., Koyama, K.,\nAwaki, H., \\& Tsuru, T. 1997, \\apj, 482, 133\n\n\\bibitem[McLaughlin 1994]{mcl94} McLaughlin, D.~E. 1994, \\pasp, 106, 47\n\n\\bibitem[McLaughlin 1999]{mcl99} McLaughlin, D.~E. 1999, \\aj, 117, 2398\n\n\\bibitem[McLaughlin \\& Pudritz 1996]{mp96} McLaughlin, D.~E., \\& Pudritz,\nR.~E. 1996, \\apj, 457, 578\n\n\\bibitem[Mehlert \\etal\\ (1998)]{meh98} Mehlert, D., Saglia, R.~P.,\nBender, R., \\& Wegner, G. 1998, \\aap, 332, 33\n\n\\bibitem[Moore \\etal\\ 1996]{moo96} Moore, B., Katz, N.,\nLake, G., Dressler, A., \\& Oemler, A.~Jr 1996, Nature, 379, 613\n\n\\bibitem[Neilsen \\& Tsvetanov 1999]{neil99}\nNeilsen, E.~H., \\& Tsvetanov, Z.~I. 1999, \\apjl, 515, L13\n\n\\bibitem[Ostrov \\& Forte 1998]{ostrov98} Ostrov, P., \\& Forte, J.~C. 1998,\n\\aj, 116, 2854\n\n\\bibitem[Prugniel \\& H\\'eraudeau 1998]{pru98}\nPrugniel, Ph., \\& H\\'eraudeau, Ph. 1998, AApS, 128, 299\n\n\\bibitem[Secker \\etal\\ 1995]{secker95} Secker, J., Geisler, D., \nMcLaughlin, D.~E., \\& Harris, W. E. 1995, \\aj, 109, 1019\n\n\\bibitem[Stetson 1992]{ste92} Stetson, P.~B. 1992, in Astronomical \nData Analysis Software and Systems I, ASP Conf.~Ser.~8, \nedited by G.~H.~Jacoby (ASP, San Francisco), p. 289\n\n\\bibitem[Strom \\& Strom (1978)]{str78} Strom, K.~M., \\& Strom, S.~E.\n1978, \\aj, 83, 73\n\n\\bibitem[Whitmore \\& Schweizer 1995]{whi95a}\nWhitmore, B.~C., \\& Schweizer, F. 1995, \\aj, 109, 960\n\n\\bibitem[Whitmore \\etal\\ 1995]{whi95} Whitmore, B.~C., Sparks, W.~B.,\nLucas, R.~A., Macchetto, F.~D., \\& Biretta, J.~A. 1995, \\apjl, 454, L73\n\n\\bibitem[Zinn 1985]{zin85} Zinn, R. 1985, \\apj, 293, 424\n\n\\end{thebibliography}"
}
] |
astro-ph0002294
|
Studying the Pulsation of Mira Variables in the Ultraviolet
|
[
{
"author": "B. E. Wood\\altaffilmark{1}"
},
{
"author": "M. Karovska"
}
] |
We present results from an empirical study of the Mg~II h \& k emission lines of selected Mira variable stars, using spectra from the {\em International Ultraviolet Explorer} (IUE). The stars all exhibit similar Mg~II behavior during the course of their pulsation cycles. The Mg~II flux always peaks after optical maximum near pulsation phase $\phi=0.2-0.5$, although the Mg~II flux can vary greatly from one cycle to the next. The lines are highly blueshifted, with the magnitude of the blueshift decreasing with phase. The widths of the Mg~II lines are also phase-dependent, decreasing from about 70 km~s$^{-1}$ to 40 km~s$^{-1}$ between $\phi=0.2$ and $\phi=0.6$. We also study other UV emission lines apparent in the IUE spectra, most of them Fe~II lines. These lines are much narrower and not nearly as blueshifted as the Mg~II lines. They exhibit the same phase-dependent flux behavior as Mg~II, but they do not show similar velocity or width variations.
|
[
{
"name": "iuemira1.tex",
"string": "\\documentclass[preprint]{aastex}\n\\usepackage{mkfig}\n\n\\begin{document}\n\n\\title{\\bf Studying the Pulsation of Mira Variables in the Ultraviolet}\n\n\\author{B. E. Wood\\altaffilmark{1}, M. Karovska}\n\\affil{Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge,\n MA 02138.}\n\\email{wood@head-cfa.harvard.edu, karovska@head-cfa.harvard.edu}\n\n\\altaffiltext{1}\n {Present address: JILA, University of Colorado, Boulder, CO 80309-0440.}\n\n\\begin{abstract}\n\n We present results from an empirical study of the Mg~II h \\& k emission\nlines of selected Mira variable stars, using spectra from the\n{\\em International Ultraviolet Explorer} (IUE). The stars all exhibit similar\nMg~II behavior during the course of their pulsation cycles. The Mg~II flux\nalways peaks after optical maximum near pulsation phase $\\phi=0.2-0.5$,\nalthough the Mg~II flux can vary greatly from one cycle to the next.\nThe lines are highly blueshifted, with the magnitude of the blueshift\ndecreasing with phase. The widths of the Mg~II lines are also\nphase-dependent, decreasing from about 70 km~s$^{-1}$ to 40 km~s$^{-1}$\nbetween $\\phi=0.2$ and $\\phi=0.6$. We also study other UV\nemission lines apparent in the IUE spectra, most of them Fe~II lines.\nThese lines are much narrower and not nearly as blueshifted as\nthe Mg~II lines. They exhibit the same phase-dependent flux behavior as\nMg~II, but they do not show similar velocity or width variations.\n\n\\end{abstract}\n\n\\keywords{stars: AGB and post-AGB --- stars: variables: other --- stars:\n oscillations --- ultraviolet: stars --- line: profiles}\n\n\\section{Introduction}\n\n At some point in their lives, many if not most stars go through an\nunstable phase which leads to pulsation. There are many classes of these\npulsating stars. Perhaps the most famous are the Cepheid variables, which\nare popular mostly because of their well-defined relationship between\nstellar luminosity and pulsation period (typically 5--50 days) that\nmakes these stars very useful as distance indicators.\n%RR~Lyrae and $\\delta$~Scuti variables are two other examples of\n%short-period pulsating stars.\n\n Mira variables are another important class of stellar pulsators, having\nlong periods of 150--500 days and luminosities that vary by as\nmuch as 6--7 magnitudes from minimum to maximum. Miras are asymptotic\ngiant branch (AGB) stars with masses similar to that of the Sun.\n%As such, %they are important for tracing the final stages in the life of a\n%Sun-like star before it becomes a planetary nebula. With typical radii of\n%1--3 AU, Miras are so large that they are among the few stars that can be\n%at least crudely resolved by telescopes on or in orbit around the Earth\n%(e.g.\\ Burns et al.\\ 1998; Karovska et al.\\ 1991, 1997).\nThey have very massive, slow, cool winds, which produce a complex\ncircumstellar environment. Observations of molecular CO lines show that\nMiras are often surrounded by molecular envelopes thousands of AU in\ndiameter. These observations yield estimates of the wind termination\nvelocity and total mass loss rate, which are typically of order 5 km~s$^{-1}$\nand $10^{-7}$ M$_{\\odot}$ yr$^{-1}$, respectively \\citep{ky95}.\nThe circumstellar envelopes are rich sites for dust formation and are often\nfound to be sources of SiO, OH, and H$_{2}$O maser emission\n\\citep{pjd94,bl97}.\n\n The massive winds of Miras are believed to be driven by a combination\nof shocks induced by stellar pulsation, and dust formation\n\\citep{ghb88}. The shocks lift a substantial amount of\nmaterial up to 1--2 stellar radii above the surface of the star. Radiation\npressure on dust formed in this material then pushes it away from the star.\nThe pulsation-induced shocks not only assist in generating the massive winds\nof Miras, but they also determine the atmospheric structure of these stars\nto a large extent. Thus, understanding the nature of the shocks and\nmeasuring their properties is essential to understanding the physics of\npulsation and mass loss from pulsating stars.\n\n The ultraviolet spectral regime is an ideal place to study radiation\nfrom the shocks. Many UV emission lines are generated from\nimmediately behind the shocks, which are potentially very useful diagnostics\nfor various characteristics of the shocks. Foremost among these lines\nare the strong Mg~II h \\& k lines at 2800 \\AA.\n\n A large number of UV spectra of Miras have been taken by the\n{\\it International Ultraviolet Explorer} (IUE) over the years, and\nsome of the basic characteristics of the Mg~II h \\& k lines have been\nnoted. It is known, for example, that the Mg~II lines are not visible\nthroughout part of the pulsation cycle. They typically appear at about\npulsation phase $\\phi=0.1$, well after optical maximum ($\\phi=0.0$). The\nMg~II fluxes peak around $\\phi=0.3-0.45$ and then decrease until becoming\nundetectable at about $\\phi=0.7$ \\citep{ewb86,dgl96}.\n\n For a set of LW-HI observations of S~Car and R~Car, \\citet{jab89}\nshowed that the Mg~II h \\& k lines are blueshifted\nrelative to the stellar rest frame by as much as 100 km~s$^{-1}$, and the h\nline is significantly stronger than the k line. Both of these properties\nare very difficult to explain, as the shock speeds should be much lower than\n100 km~s$^{-1}$, and for other astronomical targets the k line is almost\nalways found to be stronger than the h line \\citep[e.g.][]{rdr95}.\n\n Clearly the unusual behavior of the Mg~II lines of Miras\nshould be looked at in more detail to understand\nthe pulsation process. In this paper, we utilize the extensive IUE\ndata sets that exist for 5 Miras to fully characterize the behavior\nof the ultraviolet emission of these stars. Many pulsation cycles are\nsampled for each star, allowing us to see how the UV emission lines behave\nfrom one cycle to the next.\n\n\\section{The IUE Archival Data}\n\n We have searched the IUE database for Miras that have been extensively\nobserved by the satellite. In this paper, we are only interested in\nMiras without companion stars that may be contaminating the UV spectrum.\nWe are particularly interested in high resolution spectra taken with\nIUE's long-wavelength cameras (i.e.\\ LW-HI spectra). With these spectra,\nfully resolved profiles of detected emission lines (especially Mg~II) can be\nanalyzed. However, we also include low resolution, long-wavelength\ncamera spectra (i.e.\\ LW-LO spectra) in our analysis, which can at least be\nused to measure accurate fluxes of the Mg~II lines and the background.\nWe only consider large aperture data to ensure that our measured fluxes are\naccurate. Except for the Lyman-$\\alpha$ line, which is blended with\ngeocoronal emission, no emission lines are typically seen in Mira spectra\ntaken with IUE's short-wavelength SWP camera, so we are not interested in\nthose data.\n\n Table 1 lists the five Miras with the most extensive sets of IUE\nobservations. (Actually, L$^{2}$~Pup is a semi-regular variable star\nrather than a Mira, but it is a long-period pulsating star similar to Miras\nand it has a very large IUE dataset so we include it in our analysis.) The\ntable gives the position, distance, center-of-mass radial velocity ($V_{rad}$),\nand pulsation period of each star. The distances were taken from the\nHipparcos catalog \\citep{macp97}.\n\n The center-of-mass radial velocities of these stars were taken from the\nSIMBAD database. However, deriving true systemic center-of-mass velocities is\ndifficult for the pulsating Miras, because different spectral features\nobserved for these stars exhibit different velocities, and these velocities\nare often found to vary during the pulsation cycle. The velocities in\nTable 1 are based on measurements of optical absorption lines of neutral\natoms, which provide plausible values for $V_{rad}$. Other potential\nmeasures, such as various optical emission lines, molecular radio emission\nlines, and maser lines, are generally blueshifted relative to the neutral\natomic absorption lines by roughly 5--10 km~s$^{-1}$. These features are\nprobably formed either behind an outward moving shock or in the outer regions\nof the stellar atmosphere where the massive wind of the star is being\naccelerated \\citep{ahj54,pwm60,gw75,dh88}. Note that infrared CO emission\nlines, which can also be used to estimate stellar center-of-mass radial\nvelocities, generally suggest velocities that are blueshifted relative to the\noptical velocities by $\\sim 5$ km~s$^{-1}$ \\citep{khh78,khh96,khh97}.\n\n In order to determine how UV emission varies during the pulsation cycle\nit is necessary to derive accurate pulsation phases, which requires knowledge\nof the pulsation period and a zero-phase date. All of the Miras in\nTable 1 have been monitored for many decades, and their average periods are\nwell known. However, the periods of Miras can sometimes differ from this\naverage. Therefore, in order to derive the most accurate phases, we sought\nto determine the average period and zero-phase of our Miras during IUE's\nlifetime only (1978--1996).\n\n The American Association of Variable Star Observers (AAVSO) has a\nlong-term program to monitor hundreds of Miras using observations from\namateur astronomers around the world \\citep{jam97}.\nUsing AAVSO data obtained from the World Wide Web, we derived the pulsation\nperiods listed in Table 1. The derived periods of S~Car, R~Car, and R~Leo\nare within a day of the accepted long-term average values\n\\citep[see, e.g.,][]{ah85}, but the derived period of\nL$^{2}$~Pup is 4 days shorter and that of T~Cep is 11 days longer. For these\ntwo stars, the accuracy of the computed pulsation phases is improved\nsignificantly with the use of the derived periods in Table 1. As mentioned\nabove, L$^{2}$~Pup is a semi-regular variable rather than a traditional Mira,\nbut it is similar to Miras in other respects so it is included in our sample.\nBecause of the irregularity of its period, the accuracy of the pulsation\nphases we derive is limited to about $\\pm 0.2$. The pulsation of the\nother stars on our list is far more regular, and we estimate that the phases\nwe use for these stars are accurate to within about $\\pm 0.05$.\n\n Table 1 lists the number of LW-HI and LW-LO\nspectra available for each star. In each case, the available data provide\nreasonably good coverage of at least 2--3 different pulsation cycles.\nThe data were extracted from the IUE Final Archive. The spectra in\nthe archive were processed using the NEWSIPS software, which became available\nnear the end of the IUE's 18-year lifetime in the mid-1990s. This software\ncorrects the fixed pattern noise problem that plagued spectra processed with\nthe older IUESIPS software, and improves signal-to-noise by up to a factor\nof 2 for high resolution spectra. The NEWSIPS software is described in\ndetail by \\citet{jsn96}.\n\n\\section{Data Analysis}\n\n\\subsection{The LW-LO Spectra}\n\n Figure 1 illustrates the behavior of the near UV spectrum of the Mira\nR~Car during a typical pulsation cycle in 1986--1987. The primary spectral\nfeature visible in the LW-LO spectra is the Mg~II h \\& k feature at 2800~\\AA,\nwhich appears shortly after optical maximum, achieves a maximum flux around\n$\\phi=0.4-0.5$, and then declines. The Fe~II UV1 multiplet lines at\n2620~\\AA\\ are also visible when Mg~II is at its brightest.\n\n We developed a semi-automated routine to measure the Mg~II fluxes from\nthe LW-LO spectra of our stars. For each spectrum, the underlying background\nflux is estimated using the flux in the surrounding spectral region.\nThe reasonableness of this computed background is verified visually. After\nsubtracting the background from the spectrum, the Mg~II flux is then computed\nby direct integration. The error vector provided by the NEWSIPS software\nthen allows us to estimate the 1~$\\sigma$ uncertainty for this flux. Three\nspectra from R~Leo show substantial background emission at an unexpected\nphase, which we believe indicates contamination by scattered solar light, so\nthese spectra are not used.\n\n In Figure 2, we plot the Mg~II fluxes as a function of pulsation phase\nfor all the stars in our sample. We use thick symbols to indicate Mg~II\nlines with 3 or more pixels that have been flagged by NEWSIPS as being\npotentially inaccurate, usually due to overexposure. These fluxes\nshould be considered more uncertain than the plotted 1~$\\sigma$ error bars\nwould suggest. In general, however, these fluxes are not wildly discrepant\nfrom fluxes of better exposed lines measured closely in time. Dashed lines\nconnect points that are within the same pulsation cycle, excluding cases\nwhere the points are separated by over 0.4 phase.\n\n Figure 2 shows that the pulsation cycles of each star are all consistent\nwith the general rule of a flux maximum around $\\phi=0.2-0.5$. However,\nthere are substantial flux differences from one cycle to the next. The R~Car\ndata set shows the most extreme such variability, with the Mg~II fluxes\nreaching only about $1\\times 10^{-13}$ ergs cm$^{-2}$ s$^{-1}$ in one cycle\nand approaching $1\\times 10^{-10}$ ergs cm$^{-2}$ s$^{-1}$ during another.\nIn contrast, the Mg~II fluxes of S~Car differ by less than an order of\nmagnitude from one cycle to the next, this despite the fact that S~Car has\none of the largest IUE LW-LO databases. The other relatively short period\npulsator in our sample, L$^{2}$~Pup, seems to behave similarly. The data\npoints show more scatter for L$^{2}$~Pup, but this is probably due to\ninaccuracies in the estimated pulsation phases caused by the irregular\nperiod of this star (see \\S 2). A comparison of L$^{2}$~Pup's Mg~II\nand optical variability has been presented by \\citet{ewb90}.\n\n The phase of maximum Mg~II flux differs somewhat for the five\nstars, with S~Car appearing to have the earliest maximum and R~Leo the\nlatest. One of the brighter Mg~II cycles of R~Leo is particularly\ninteresting for showing substantial Mg~II flux very near optical maximum at\n$\\phi=0.04$ (observations LWP21679 and LWP21680). We generally do not detect\nsignificant Mg~II flux this close to $\\phi=0.0$ for any of our stars\n(excluding L$^{2}$~Pup because of its uncertain phases), but apparently there\ncan be exceptions to this rule. By inspecting the AAVSO light curve we\nconfirmed that the strong Mg~II lines had in fact been observed very near\noptical maximum.\n\n\\subsection{The LW-HI Spectra}\n\n\\subsubsection{The Mg~II h \\& k Lines}\n\n Turning our attention to the LW-HI spectra, in Figures 3--7 we display\nthe observed Mg~II h \\& k line profiles for the five stars in our sample.\nThe k line is shown as a solid line and the h line is represented by a\ndotted line. The spectra are shown on a velocity scale in the stellar rest\nframe, assuming the stellar center-of-mass velocities listed in Table 1, and\nassuming rest wavelengths in air of 2802.705~\\AA\\ and 2795.528~\\AA\\ for\nthe h and k lines, respectively. The date, time, and pulsation phase of\neach observation are indicated in the figures. Cosmic ray hits, which are\napparent in the original spectra as very narrow, bright spectral features\nnot observed in other spectra, have been identified and removed manually.\nOne S~Car spectrum with wildly discrepant properties (LWP12197) was removed\nfrom the analysis and is therefore not shown in Figure 5.\n\n Many of the S~Car spectra were taken with the star deliberately offset\nwithin IUE's large aperture. This results in an inaccurate wavelength\ncalibration. Fortunately, there is a set of nine observations taken on 1991\nMarch 9--13 with different offsets (see Fig.\\ 5). After measuring the\ncentroids of the Mg~II h line (see below), we were able to see from these\ndata how the offsets affected the h line centroid and we used this\ninformation to correct the wavelengths of all the S~Car spectra obtained\nwith aperture offsets. The spectra in Figure 5 are the corrected spectra.\n\n In almost every spectrum in Figures 3--7, the k line is contaminated by\nsubstantial absorption centered at a stellar rest frame velocity of about\n$-70$ km~s$^{-1}$. This absorption is due to lines of Fe~I and Mn~I with\nrest wavelengths in air of 2795.005~\\AA\\ and 2794.816~\\AA, respectively\n\\citep{dgl89,dgl98}.\nBecause the mutilation of the k line by these overlying neutral\nabsorbers is generally severe, we focus most of our attention on the more\npristine h line.\n\n Another concern is interstellar absorption, which should affect both\nthe h and k lines at the same velocity. The one star whose spectrum we know\nwill {\\em not} be affected by the ISM is S~Car, because its extremely large\n$+289$ km~s$^{-1}$ center-of-mass velocity will shift the Mg~II lines well\naway from any ISM absorption. The h line of L$^{2}$~Pup shows absorption at\nabout $-40$ km~s$^{-1}$ (see Fig.\\ 7). The ISM velocity predicted for this\nline of sight by the local ISM flow vector of \\citet{rl95}\nis $-43$ km~s$^{-1}$ after shifting to the stellar\nrest frame. Thus, it seems likely that this is indeed interstellar\nabsorption, although for lines of sight as long as those towards the stars\nin our sample, ISM components could potentially be present with\nsignificantly different velocities than that predicted by the local flow\nvector.\n\n The h lines of R~Leo, R~Car, and T~Cep do not appear to be contaminated\nby any obvious ISM absorption features. For R~Leo and T~Cep, the ISM\nvelocities predicted by the local flow vector ($-4$ and $+14$ km~s$^{-1}$,\nrespectively) suggest that the ISM absorption may lie outside of the observed\nMg~II emission (see Figs.\\ 3 and 6). For the R~Car line of sight,\nthe local flow vector predicts ISM absorption at $-30$ km~s$^{-1}$, which\nfalls just within the red side of the h line. No obvious absorption is seen,\nhowever, suggesting that the ISM column density for this particular line of\nsight may be quite low. This is not necessarily unusual, as other lines of\nsight with distances of $\\gtrsim 100$ pc have been found to have very low H~I\ncolumn densities of $\\sim 10^{18}$ cm$^{-2}$ \\citep{cg95,np97}.\n\n We will assume that the Mg~II h line profiles of R~Leo, R~Car, and T~Cep\nare at most only mildly affected by ISM absorption, meaning that for these\nthree stars and S~Car we can be reasonably confident that any substantial\nline profile differences we might find are due to intrinsic differences in\nthe stellar spectra. The Mg~II h line profiles of these four stars often\nappear to be slightly asymmetric, with a red side that is steeper than the\nblue side. Nevertheless, the profiles can be represented reasonably well\nas a Gaussian, and can therefore be quantified with Gaussian fits.\nWe developed a semi-automated procedure to fit all Mg~II h lines\ndetected with enough signal-to-noise (S/N) for a meaningful fit to be\nperformed. The quality of all fits was verified visually. For spectra\nwithout strong Mg~II h lines, we estimated a line\nflux by direct integration as we did for the LW-LO spectra. For\nL$^{2}$~Pup, we measured h line fluxes for {\\em all} the spectra in this\nmanner, since we could not accurately fit Gaussians to the ISM-contaminated \nline profiles observed for this star.\n\n In Figures 8--10, we plot versus pulsation phase the Mg~II h line\nfluxes, centroid velocities, and widths measured from the LW-HI spectra of\nthe stars in our sample. As in Figure 2, dotted lines connect points within\nthe same pulsation cycle, and thick data points indicate h lines with three\nor more pixels flagged as being overexposed. The 1~$\\sigma$ uncertainties\nshown in the figure were estimated using the procedures outlined by\n\\citet{ddl92}. The flux variations seen in Figure 8\nare essentially the same as those seen in the LW-LO data (see Fig.\\ 2).\nNote once again how much the Mg~II fluxes vary from one cycle to the next\nfor R~Car.\n\n \\citet*{jab89} found that the Mg~II lines in\nselected observations of S~Car and R~Car were substantially blueshifted.\nFigure 9 demonstrates that this behavior is common to all the Mg~II lines\nobserved by IUE for all the Miras in our sample. Furthermore, Figure 9 also\nreveals a strong correlation between line velocity and pulsation phase, in\nwhich the magnitude of the line blueshifts decreases with pulsation phase.\nFor example, between $\\phi=0.2$ and $\\phi=0.6$ the line velocities of S~Car\nchange from about $-100$ km~s$^{-1}$ to $-50$ km~s$^{-1}$, and those of\nT~Cep change from $-50$ km~s$^{-1}$ to $-30$ km~s$^{-1}$. Note that even\nthough we are using Gaussians to fit the Mg~II profiles, this does {\\em not}\nimply that Mg~II h \\& k are optically thin or that the large blueshifts of\nthese lines actually represent gas velocities (see \\S 3.2.2).\n\n This velocity behavior exactly mimics the behavior of the optical Ca~II\nH \\& K lines of Miras, which also have blueshifted velocities that typically\nchange from about $-100$ km~s$^{-1}$ to $-40$ km~s$^{-1}$ between $\\phi=0.2$\nand $\\phi=0.6$ \\citep{pwm52,wb52}. Thus, opacity effects and atmospheric\nflow fields appear to induce the same line behavior in both the Mg~II and\nCa~II lines. Furthermore, many Cepheid variables appear to exhibit\nsimilar behavior, suggesting that these phase-dependent velocity variations\nmay be typical for stellar pulsators in general \\citep{pwm60}.\n\n The data in Figure 9 suggest a possible correlation between pulsation\nperiod and line velocity, with the shortest period Mira in our sample (S~Car)\nhaving the largest blueshifts, and the longest period star (T~Cep) having the\nsmallest. The R~Car data suggest another possible correlation.\nFor the pulsation cycle with the largest Mg~II fluxes, the Mg~II h lines of\nR~Car are more blueshifted than they are during the\nweaker cycles. Unfortunately, our sample of stars and the number of\nwell-sampled pulsation cycles per star is very small, making it difficult to\ntruly establish these correlations.\n\n Figure 10 demonstrates that a well-defined phase dependence also exists\nfor the line widths, which are quantified in Figure 10 as\nfull-widths-at-half-maxima (FWHM). The line width behavior is very similar\nfor all the stars, with a decrease from about 70 km~s$^{-1}$ to 40 km~s$^{-1}$\nbetween $\\phi=0.2$ and $\\phi=0.6$.\n\n\\subsubsection{Other Lines in the IUE LW-HI Spectra}\n\n The Mg~II h \\& k lines are by far the brightest lines that appear in\nthe LW-HI spectra of Miras, but they are not the only lines present. During\npulsation cycles that produce strong Mg~II lines, other lines\nalso appear out of the background noise of the LW-HI spectra.\n\n The largest Mg~II fluxes observed for any star in our sample were\nobserved during the 1989--90 pulsation cycle of R~Car, during which Mg~II h\nline fluxes reached up to $5\\times 10^{-11}$ ergs cm$^{-2}$ s$^{-1}$ (see\nFigs.\\ 4 and 8). Figure 11 shows three sections of an LW-HI spectrum taken\nduring this period. These sections contain all of the obvious real\nemission features apparent in the full spectrum. The expected line locations\nof several multiplets are indicated in the figure, which accounts for most of\nthe observed emission features. The spectrum is dominated by several\nmultiplets of Fe~II lines (UV1, UV32, UV60, UV62, and UV63). The\nMg~II h \\& k (UV1) lines are of course apparent, as perhaps are two much\nweaker Mg~II lines of the UV3 multiplet. The intersystem Al~II] (UV1) line\nat 2669.155~\\AA\\ is easily visible. \\citet{dgl98}\nobserved the feature at 2823~\\AA\\ in an HST/GHRS\nspectrum of the Mira R~Hya, and identified it as an Fe~I (UV44) 2823.276~\\AA\\\nline which is fluoresced by the Mg~II k line. A couple other emission\nfeatures in Figure 11 can also be identified with Fe~I (UV44) lines.\n\n The lines seen in Figure 11 have previously been\nobserved in many IUE and HST/GHRS spectra of red giant stars\n\\citep{pgj91,kgc95,rdr98}.\nThe Al~II] line and most of the Fe~II lines are formed by collisional\nexcitation, as are the Mg~II h \\& k lines, but \\citet{pgj92}\nfind that the UV62 and UV63 multiplet lines of Fe~II\nare excited by a combination of collisional excitation and photoexcitation\nby photospheric emission at optical wavelengths.\n\n The flux behavior of all the lines in Figure 11 parallels that of Mg~II,\nincreasing to a maximum near $\\phi=0.3-0.4$ and then decreasing. Thus, the\nFe~II and Al~II] lines presumably originate in atmospheric locations similar\nto Mg~II h \\& k. Note that many of the lines apparent in Figure 11 were\nonly observed during this one particularly bright cycle of R~Car, presumably\nbeing too weak to be detected during weaker cycles on R~Car and the other\nstars. For a selection of the brightest emission lines, we used an automated\nfitting procedure like that described in \\S 3.2.1 to fit Gaussians to the\nlines of all the stars in our sample, whenever the lines are clearly\ndetected. The lines measured in this manner are listed in Table 2.\nFor L$^{2}$~Pup, no observed cycle was bright enough to detect any of these\nlines, and for S~Car only the brightest Fe~II line at 2625.667~\\AA\\ could\never be clearly detected.\n\n For the observations in which the lines are observed, we find that\nline flux ratios among the various Fe~II lines are always similar to those\nseen in Figure 11, as are Mg~II/Fe~II flux ratios. For example, the\n(Mg~II $\\lambda$2803)/(Fe~II $\\lambda$2626) ratio is always about 20.\nThe Fe~II and Mg~II/Fe~II flux ratios found for the Miras are somewhat\ndifferent from those observed in red giants, but not radically so.\n\n However, the Fe~II line {\\em profiles} are very different.\nFor normal red giant stars, most of the Fe~II lines are clearly\nopacity broadened and have profiles very different from that of a simple\nGaussian \\citep*{pgj91,kgc95}. In contrast, the Fe~II lines of\nMiras are very narrow, Gaussian-shaped emission features, with widths at or\nnear the IUE's instrumental resolution of $\\sim 0.2$ \\AA. This is why we\ncould accurately fit the lines with single Gaussians. The exception is the\nbroader Fe~II 2599.394~\\AA\\ line, which should have the highest opacity of\nall the Fe~II lines.\n\n The widths and velocities of the lines listed in Table 2 do not\nappear to exhibit any substantial phase dependent behavior, in contrast to\nMg~II h \\& k. As an example, in Figure 12 we plot the velocities of the\nFe~II 2625.667~\\AA\\ line as a function of pulsation phase for the four Miras\nin which this line was occasionally detected. Only S~Car has a hint\nof phase dependence, with some evidence for a small increase in velocity\nwith phase. Much of the scatter seen in Figure 12 could be due to\nuncertainties in target centering, which can induce systematic velocity\nerrors of $\\pm5$ km~s$^{-1}$ \\citep{bew95}.\n\n Since there is little if any phase dependence in the velocities of the\nlines listed in Table 2, we compute a weighted average and standard deviation\nfor all the measurements of all the lines \\citep{prb92}, and in Table 2\nthese velocities are listed for each Mira in\nour sample. For R~Leo, R~Car, and S~Car, all of the lines are blueshifted\n$5-15$ km~s$^{-1}$. The Fe~II 2599.394~\\AA\\ line is once again an exception,\nshowing significantly larger blueshifts.\n\n The lines of T~Cep behave differently, as they do not show systematic\nblueshifts relative to the star. The Mg~II lines of T~Cep are also not as\nblueshifted as the other stars (see \\S 3.2.1 and Fig.\\ 9). It is difficult\nto identify a reason for this difference in behavior, but\nperhaps the center-of-mass velocity we are assuming for this star is off by\n$\\sim 10$ km~s$^{-1}$. The difficulties in defining center-of-mass\nvelocities for Miras have already been discussed in \\S 2.\n\n The large blueshifts observed for the Mg~II lines are unlikely to be\ndirect measurements of outflow velocities. The shock velocities present\nin Miras are expected to be of order $10-20$ km~s$^{-1}$, although this issue\nis still a matter of debate \\citep*{ghb88,dh88,khh97}. Thus, the\n$5-15$ km~s$^{-1}$ blueshifts seen for most of the Fe~II and Al~II] lines of\nR~Leo, R~Car, and S~Car are more likely to be measuring the true outflow\nvelocities of shocked material. The larger widths and blueshifts of the\nMg~II lines are probably due to opacity effects, similar to the findings of\n\\citet{pgj93} for non-Mira M-type giants. The similar behavior of the\nFe~II $\\lambda$2599 line suggests that this line is influenced by similar\nopacity effects, which is reasonable since this line should have the highest\nopacity of any of the Fe~II lines.\n\n The other Fe~II lines will have substantially lower\noptical depths than Mg~II h \\& k and Fe~II $\\lambda$2599, and some may even\nbe optically thin. The Al~II] $\\lambda$2669 line should also have very low\nopacity, since it is a semi-forbidden transition. Thus, the Fe~II and\nAl~II] line centroids should be more indicative of the true outflow\nvelocities of the shocked material, and the line widths (which are actually\nunresolved) should be more indicative of turbulent velocities within the\nshocked material.\n\n Interpreting the difference between the behavior of the Mg~II lines and\nthat of the less opaque lines could be very important for understanding the\nstructure of the shocks propagating through Mira atmospheres. In\nfuture work, we hope to explore possible reasons why the Mg~II lines are\nbroader and more blueshifted than the less optically thick lines.\n\n\\section{Summary}\n\n We have compiled IUE observations of 5 Mira variables with substantial\nIUE data sets in order to study the properties of emission lines seen in the\nUV spectra of these stars, which are believed to be formed behind outwardly\npropagating shocks in the atmospheres of these pulsating stars. Our\nfindings are summarized as follows:\n\\begin{description}\n\\item[1.] We confirm the phase-dependent Mg~II flux behavior previously\n reported for Mira variables \\citep*[e.g.][]{ewb86},\n which is observed for all the pulsation cycles that we study: the Mg~II\n flux rises after optical maximum, peaks near $\\phi=0.2-0.5$, and then\n decreases. For some Miras (e.g.\\ R~Car) the amount of Mg~II flux produced\n during a pulsation cycle can vary by 2--3 orders of magnitude from one\n cycle to the next, while for others (e.g.\\ S~Car) the flux behavior is\n more consistent.\n\\item[2.] The Mg~II k lines are almost always contaminated with circumstellar\n absorption lines of Fe~I and Mn~I, making analysis of the line profile very\n difficult.\n\\item[3.] The Mg~II h line is always blueshifted, with the magnitude of the\n blueshift decreasing with pulsation phase. The blueshifts vary somewhat\n from star to star and cycle to cycle, but typical velocity changes are from\n $-70$ km~s$^{-1}$ to $-40$ km~s$^{-1}$ from $\\phi=0.2$ to $\\phi=0.6$. Note,\n however, that these line shifts do not represent the actual gas velocities\n at the formation depths of these lines, because of the high opacity of\n Mg~II h \\& k. These velocity variations are very similar to those of the\n optical Ca~II H \\& K lines.\n\\item[4.] The width of the Mg~II h line decreases from about 70 km~s$^{-1}$\n to 40 km~s$^{-1}$ between $\\phi=0.2$ and $\\phi=0.6$.\n\\item[5.] In addition to the Mg~II lines, other lines of Fe~II, Fe~I, and\n Al~II] are also observed in IUE LW-HI spectra. The fluxes of these lines\n show the same phase-dependent behavior as the Mg~II lines.\n\\item[6.] Unlike Mg~II, these other emission lines tend to be very narrow\n and do not show phase-dependent velocity and width variations. Except\n for Fe~II $\\lambda$2599, the Fe~II and Al~II] lines of most of the Miras\n show blueshifts of $5-15$ km~s$^{-1}$, which may indicate the flow velocity\n of the shocked material. In contrast, the lines of T~Cep do not show any\n significant line shifts, although we speculate that perhaps this\n is due to an uncertain center-of-mass velocity for this star.\n\\end{description}\n\n\\acknowledgments\n\n We would like to thank the referee, Dr.\\ D.\\ Luttermoser, for many\nuseful comments on the manuscript. MK is a member of the Chandra X-ray\nCenter, which is operated under contract NAS-839073, and is partially\nsupported by NASA. In this research, we have used, and acknowledge with\nthanks, data from the AAVSO International Database, based on observations\nsubmitted to the AAVSO by variable star observers worldwide.\n\n\\clearpage\n\n\\begin{thebibliography}{}\n\\bibitem[Bevington \\& Robinson(1992)]{prb92}\nBevington, P. R., \\& Robinson, D. 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Dupree (San Fransisco: ASP Conf.\n Ser., Vol. 109), 535\n\\bibitem[Luttermoser et al.(1989)]{dgl89}\nLuttermoser, D. G., Johnson, H. R., Avrett, E. H., \\& Loeser, R. 1989, ApJ,\n 345, 543\n\\bibitem[Luttermoser \\& Mahar(1998)]{dgl98}\nLuttermoser, D. G., \\& Mahar, S. 1998, in Cool Stars, Stellar Systems, and\n the Sun, Tenth Workshop, ed. R. A. Donahue \\& J. A. Bookbinder\n (San Francisco: ASP Conf.\\ Ser., Vol.\\ 154), 1613\n\\bibitem[Mattei \\& Foster(1997)]{jam97}\nMattei, J. A., \\& Foster, G. 1997, BAAS, 29, 1284\n\\bibitem[Merrill(1952)]{pwm52}\nMerrill, P. W. 1952, ApJ, 116, 337\n\\bibitem[Merrill(1960)]{pwm60}\nMerrill, P. W. 1960, in Stellar Atmospheres, ed. J. L. Greenstein\n (Chicago: The Univ. of Chicago Press), 509\n\\bibitem[Nichols \\& Linsky(1996)]{jsn96}\nNichols, J. S., \\& Linsky, J. L. 1996, PASP, 111, 517\n\\bibitem[Perryman et al.(1997)]{macp97}\nPerryman, M. A. C., et al.\\ 1997, A\\&A, 323, L49\n\\bibitem[Piskunov et al.(1997)]{np97}\nPiskunov, N., Wood, B. E., Linsky, J. L., Dempsey, R. C., \\& Ayres, T. R.\n 1997, ApJ, 474, 315\n\\bibitem[Robinson \\& Carpenter(1995)]{rdr95}\nRobinson, R. D., \\& Carpenter, K. G. 1995, ApJ, 442, 328\n\\bibitem[\\protect\\citeauthoryear{Robinson et al.}{Robinson, Carpenter, \\& Brown}{1998}]{rdr98}\nRobinson, R. D., Carpenter, K. G., \\& Brown, A. 1998, ApJ, 503, 396\n\\bibitem[Wallerstein(1975)]{gw75}\nWallerstein, G. W. 1975, ApJS, 29, 375\n\\bibitem[Wood \\& Ayres(1995)]{bew95}\nWood, B. E., \\& Ayres, T. R. 1995, ApJ, 443, 329\n\\bibitem[Young(1995)]{ky95}\nYoung, K. 1995, ApJ, 445, 872\n\\end{thebibliography}\n\n\\clearpage\n\n\\begin{deluxetable}{lccccccc}\n\\tablecaption{Mira Variables with Large IUE Data Sets}\n\\tablecolumns{8}\n\\tablehead{\n \\colhead{Star} & \\colhead{RA} & \\colhead{DEC} & \\colhead{Distance} &\n \\colhead{$V_{rad}$} & \\colhead{Period} & \\multicolumn{2}{c}{\\# of\n IUE Spectra} \\\\\n \\cline{7-8} \\\\\n \\colhead{} & \\colhead{(J2000)} & \\colhead{(J2000)} & \\colhead{(pc)} &\n \\colhead{(km s$^{-1}$)} & \\colhead{(days)} & \\colhead{(LW-HI)} &\n \\colhead{(LW-LO)}}\n\\startdata\nS Car &10:09:22 &$-61^{\\circ}32^{\\prime}57^{\\prime\\prime}$ &\n $405\\pm103$ &+289 & 150 & 42 & 67 \\\\\nR Car & 9:32:15 &$-62^{\\circ}47^{\\prime}20^{\\prime\\prime}$ &\n $128\\pm14$ & +28 & 308 & 28 & 45 \\\\\nL$^{2}$ Pup & 7:13:32 &$-44^{\\circ}38^{\\prime}39^{\\prime\\prime}$ &\n $61\\pm5$ & +53 & 136 & 15 & 68 \\\\\nT Cep &21:09:32 & $68^{\\circ}29^{\\prime}27^{\\prime\\prime}$ &\n $210\\pm33$ &$-12$& 399 & 15 & 32 \\\\\nR Leo & 9:47:33 & $11^{\\circ}25^{\\prime}44^{\\prime\\prime}$ &\n $101\\pm21$ & +13 & 313 & 13 & 58 \\\\\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{lcccccc}\n\\small\n\\tablecaption{Line Velocities}\n\\tablecolumns{7}\n\\tablehead{\n \\colhead{Ion} & \\colhead{Wavelength} & \\colhead{Multiplet} & \n \\multicolumn{4}{c}{Velocity (km s$^{-1}$)} \\\\\n \\cline{4-7} \\\\\n \\colhead{} & \\colhead{} & \\colhead{} & \\colhead{R Leo} &\n \\colhead{R Car} & \\colhead{S Car} & \\colhead{T Cep}}\n\\startdata\nAl II]&2669.155&1&$-7.1\\pm8.7$ & $-4.7\\pm3.3$ & \\nodata & $1.5\\pm4.7$ \\\\\nFe I &2823.276&44&$-5.6\\pm9.6$ & $-3.9\\pm5.0$ & \\nodata & $3.2\\pm4.0$ \\\\\nFe II&2598.368&1 &$-14.5\\pm9.1$ & $-10.7\\pm1.4$& \\nodata & $3.8\\pm8.7$ \\\\\nFe II&2599.394&1 &$-24.8\\pm4.8$ & $-36.1\\pm2.6$& \\nodata &$-16.3\\pm5.2$ \\\\\nFe II&2607.085&1 &$-14.4\\pm5.9$ & $-10.0\\pm2.8$& \\nodata & \\nodata \\\\\nFe II&2611.873&1 &$-12.9\\pm2.5$ & $-8.5\\pm2.1$ & \\nodata &$-3.8\\pm10.0$ \\\\\nFe II&2617.616&1 &$-15.9\\pm6.1$ & $-9.6\\pm2.8$ & \\nodata &$-11.5\\pm3.3$ \\\\\nFe II&2620.408&1 &$-9.5\\pm8.4$ & $-5.9\\pm2.7$ & \\nodata & $4.8\\pm2.6$ \\\\\nFe II&2625.667&1 &$-12.8\\pm6.0$ & $-10.7\\pm2.7$&$-15.9\\pm4.9$& $-2.7\\pm1.8$ \\\\\nFe II&2628.292&1 &$-15.6\\pm6.5$ & $-9.2\\pm2.5$ & \\nodata & $-3.7\\pm3.4$ \\\\\nFe II&2732.440&32&$-13.2\\pm4.8$ & $-3.5\\pm1.8$ & \\nodata & $3.0\\pm3.7$ \\\\\nFe II&2759.334&32&$-9.1\\pm4.3$ & $-5.6\\pm1.9$ & \\nodata & $3.2\\pm3.6$ \\\\\nFe II&2926.587&60&$-12.7\\pm6.8$ & $-8.2\\pm4.4$ & \\nodata & $1.5\\pm4.2$ \\\\\nFe II&2953.773&60&$-9.0\\pm3.5$ & $-4.1\\pm3.8$ & \\nodata & $-2.0\\pm4.8$ \\\\\nFe II&2730.734&62&$-18.2\\pm10.4$& $-6.9\\pm3.8$ & \\nodata & \\nodata \\\\\nFe II&2743.197&62&$-5.2\\pm6.4$ & $-4.6\\pm3.4$ & \\nodata & $6.2\\pm4.1$ \\\\\nFe II&2755.735&62&$-9.3\\pm6.3$ & $-8.1\\pm2.6$ & \\nodata & $0.6\\pm4.2$ \\\\\nFe II&2727.538&63&$-18.6\\pm9.6$ & $-14.3\\pm4.7$& \\nodata & \\nodata \\\\\nFe II&2739.547&63&$-12.8\\pm8.3$ & $-7.2\\pm3.4$ & \\nodata & $5.2\\pm2.7$ \\\\\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{figure}\n\\plotone{fig1.eps}\n\\caption{Six low resolution IUE spectra of R~Car, illustrating\n the variation in Mg~II h \\& k line flux as a function of pulsation phase\n for one pulsation cycle.}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\plotfiddle{fig2.eps}{3.5in}{90}{75}{75}{300}{0}\n\\caption{The Mg~II line fluxes measured from IUE LW-LO spectra, plotted\n versus pulsation phase. Dotted lines connect points within the same\n pulsation cycle. Thick symbols identify potentially inaccurate data\n points (usually due to overexposure), as indicated by NEWSIPS data quality\n flags.}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\plotfiddle{fig3.eps}{3.5in}{90}{75}{75}{300}{0}\n\\caption{The IUE LW-HI observations of the Mg~II h (dotted lines) and k\n (solid lines) line profiles of R~Leo. The pulsation phase, date, and UT\n time of observation are indicated in each panel. The spectra\n are plotted on a velocity scale in the stellar rest frame.}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\plotfiddle{fig4.eps}{3.5in}{90}{75}{75}{300}{0}\n\\caption{Same as Fig.\\ 3, for R~Car.}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\plotfiddle{fig5.eps}{3.5in}{90}{75}{75}{300}{0}\n\\caption{Same as Fig.\\ 3, for S~Car.}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\plotfiddle{fig6.eps}{3.5in}{90}{75}{75}{300}{0}\n\\caption{Same as Fig.\\ 3, for T~Cep.}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\plotfiddle{fig7.eps}{3.5in}{90}{75}{75}{300}{0}\n\\caption{Same as Fig.\\ 3, for L$^{2}$~Pup.}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\plotfiddle{fig8.eps}{3.5in}{90}{75}{75}{300}{0}\n\\caption{The Mg~II h line fluxes measured from IUE LW-HI spectra, plotted\n versus pulsation phase. Dotted lines connect points within the same\n pulsation cycle. Thick symbols identify potentially inaccurate data\n points due to overexposure, as indicated by NEWSIPS data quality flags.}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\plotfiddle{fig9.eps}{3.5in}{90}{75}{75}{300}{0}\n\\caption{The Mg~II h line centroid velocities measured from IUE LW-HI spectra\n in the stellar rest frame, plotted versus pulsation phase. Dotted lines\n connect points within the same pulsation cycle. Thick symbols identify\n potentially inaccurate data points due to overexposure, as indicated by\n NEWSIPS data quality flags.}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\plotfiddle{fig10.eps}{3.5in}{90}{75}{75}{300}{0}\n\\caption{The Mg~II h line widths measured from IUE LW-HI spectra, plotted\n versus pulsation phase. Dotted lines connect points within the same\n pulsation cycle. Thick symbols identify potentially inaccurate data\n points due to overexposure, as indicated by NEWSIPS data quality flags.}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\plotfiddle{fig11.eps}{3.5in}{90}{75}{75}{300}{0}\n\\caption{Sections of an IUE LW-HI spectrum (LWP17263) of R~Car obtained\n on 1990 January 30. Expected line locations are displayed for several\n multiplets, which account for most of the lines seen in the spectrum.}\n\\end{figure}\n\n\\clearpage\n\n\\begin{figure}\n\\plotfiddle{fig12.eps}{3.5in}{90}{75}{75}{300}{0}\n\\caption{The centroid velocities of the Fe~II 2625.667~\\AA\\ line in the\n stellar rest frame, measured from IUE LW-HI spectra and plotted versus\n pulsation phase. Dotted lines connect points within the same pulsation\n cycle.}\n\\end{figure}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002294.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[Bevington \\& Robinson(1992)]{prb92}\nBevington, P. R., \\& Robinson, D. K. 1992, Data Reduction and Error Analysis\n for the Physical Sciences (New York: McGraw-Hill)\n\\bibitem[\\protect\\citeauthoryear{Bookbinder et al.}{Bookbinder, Brugel, \\& Brown}{1990}]{jab89}\nBookbinder, J. A., Brugel, E. W., \\& Brown, A. 1989, ApJ, 342, 516\n\\bibitem[Bowen(1988)]{ghb88}\nBowen, G. H. 1988, ApJ, 329, 299\n\\bibitem[\\protect\\citeauthoryear{Brugel et al.}{Brugel, Willson, \\& Bowen}{1990}]{ewb90}\nBrugel, E. W., Willson, L. A., \\& Bowen, G. 1990, in Evolution in\n Astrophysics: IUE Astronomy in the Era of New Space Missions, (Noordwijk:\n ESA SP-310), 241\n\\bibitem[\\protect\\citeauthoryear{Brugel et al.}{Brugel, Willson, \\& Cadmus}{1986}]{ewb86}\nBrugel, E. W., Willson, L. A., \\& Cadmus, R. 1986, in New Insights in\n Astrophysics: Eight Years of UV Astronomy with IUE, (Noordwijk:\n ESA SP-263), 213\n\\bibitem[Buscombe \\& Merrill(1952)]{wb52}\nBuscombe, W., \\& Merrill, P. W. 1952, ApJ, 116, 525\n\\bibitem[\\protect\\citeauthoryear{Carpenter et al.}{Carpenter, Robinson, \\& Judge}{1995}]{kgc95}\nCarpenter, K. G., Robinson, R. D., \\& Judge, P. G. 1995, ApJ, 444, 424\n\\bibitem[Diamond et al.(1994)]{pjd94}\nDiamond, P. J., Kemball, A. J., Junor, W., Zensus, A., Benson, J., \\&\n Dhawan, V. 1994, ApJ, 430, L61\n\\bibitem[Gillet(1988)]{dh88}\nGillet, D. 1988, A\\&A, 190, 200\n\\bibitem[Gry et al.(1995)]{cg95}\nGry, C., Lemonon, L., Vidal-Madjar, A., Lemoine, M., \\& Ferlet, R. 1995,\n A\\&A, 302, 497\n\\bibitem[Hinkle(1978)]{khh78}\nHinkle, K. H. 1978, ApJ, 220, 210\n\\bibitem[Hinkle \\& Barnbaum(1996)]{khh96}\nHinkle, K. H., \\& Barnbaum, C. 1996, AJ, 111, 913\n\\bibitem[\\protect\\citeauthoryear{Hinkle et al.}{Hinkle, Lebzelter, \\& Scharlach}{1997}]{khh97}\nHinkle, K. H., Lebzelter, T., \\& Scharlach, W. W. G. 1997, AJ, 114, 2686\n\\bibitem[Hirshfeld \\& Sinnott(1985)]{ah85}\nHirshfeld, A., \\& Sinnott, R. W. 1985, Sky Catalogue 2000.0, Vol. 2\n (Cambridge: Sky Publishing Corporation)\n\\bibitem[Joy(1954)]{ahj54}\nJoy, A. H. 1954, ApJS, 1, 39\n\\bibitem[Judge \\& Jordan(1991)]{pgj91}\nJudge, P. G., \\& Jordan, C. 1991, ApJS, 77, 75\n\\bibitem[\\protect\\citeauthoryear{Judge et al.}{Judge, Jordan, \\& Feldman}{1992}]{pgj92}\nJudge, P. G., Jordan, C., \\& Feldman, U. 1992, ApJ, 384, 613\n\\bibitem[Judge et al.(1993)]{pgj93}\nJudge, P. G., Luttermoser, D. G., Neff, D. H., Cuntz, M., \\& Stencel, R. E.\n 1993, AJ, 105, 1973\n\\bibitem[Lallement et al.(1995)]{rl95}\nLallement, R. L., Ferlet, R., Lagrange, A. M., Lemoine, M., \\& Vidal-Madjar,\n A. 1995, A\\&A, 304, 461\n\\bibitem[Lenz \\& Ayres(1992)]{ddl92}\nLenz, D. D., \\& Ayres, T. R. 1992, PASP, 104, 1104\n\\bibitem[Lopez et al.(1997)]{bl97}\nLopez, B., et al.\\ 1997, ApJ, 488, 807\n\\bibitem[Luttermoser(1996)]{dgl96}\nLuttermoser, D. G. 1996, in Cool Stars, Stellar Systems, and the Sun, Ninth\n Workshop, ed. R. Pallavicini \\& A. K. Dupree (San Fransisco: ASP Conf.\n Ser., Vol. 109), 535\n\\bibitem[Luttermoser et al.(1989)]{dgl89}\nLuttermoser, D. G., Johnson, H. R., Avrett, E. H., \\& Loeser, R. 1989, ApJ,\n 345, 543\n\\bibitem[Luttermoser \\& Mahar(1998)]{dgl98}\nLuttermoser, D. G., \\& Mahar, S. 1998, in Cool Stars, Stellar Systems, and\n the Sun, Tenth Workshop, ed. R. A. Donahue \\& J. A. Bookbinder\n (San Francisco: ASP Conf.\\ Ser., Vol.\\ 154), 1613\n\\bibitem[Mattei \\& Foster(1997)]{jam97}\nMattei, J. A., \\& Foster, G. 1997, BAAS, 29, 1284\n\\bibitem[Merrill(1952)]{pwm52}\nMerrill, P. W. 1952, ApJ, 116, 337\n\\bibitem[Merrill(1960)]{pwm60}\nMerrill, P. W. 1960, in Stellar Atmospheres, ed. J. L. Greenstein\n (Chicago: The Univ. of Chicago Press), 509\n\\bibitem[Nichols \\& Linsky(1996)]{jsn96}\nNichols, J. S., \\& Linsky, J. L. 1996, PASP, 111, 517\n\\bibitem[Perryman et al.(1997)]{macp97}\nPerryman, M. A. C., et al.\\ 1997, A\\&A, 323, L49\n\\bibitem[Piskunov et al.(1997)]{np97}\nPiskunov, N., Wood, B. E., Linsky, J. L., Dempsey, R. C., \\& Ayres, T. R.\n 1997, ApJ, 474, 315\n\\bibitem[Robinson \\& Carpenter(1995)]{rdr95}\nRobinson, R. D., \\& Carpenter, K. G. 1995, ApJ, 442, 328\n\\bibitem[\\protect\\citeauthoryear{Robinson et al.}{Robinson, Carpenter, \\& Brown}{1998}]{rdr98}\nRobinson, R. D., Carpenter, K. G., \\& Brown, A. 1998, ApJ, 503, 396\n\\bibitem[Wallerstein(1975)]{gw75}\nWallerstein, G. W. 1975, ApJS, 29, 375\n\\bibitem[Wood \\& Ayres(1995)]{bew95}\nWood, B. E., \\& Ayres, T. R. 1995, ApJ, 443, 329\n\\bibitem[Young(1995)]{ky95}\nYoung, K. 1995, ApJ, 445, 872\n\\end{thebibliography}"
}
] |
astro-ph0002295
|
The Power Spectrum of Rich Clusters on Near-Gigaparsec Scales
|
[
{
"author": "Christopher J. Miller and David J. Batuski"
}
] |
Recently, there have been numerous analyses of the redshift space power spectrum of rich clusters of galaxies. Some of these analyses indicate a \lq\lq bump\rq\rq~ in the Abell/ACO cluster power spectrum around $k = 0.05h$Mpc$^{-1}$. Such a feature in the power spectrum excludes most standard formation models and indicates possible periodicity in the distribution of large-scale structure. However, the data used in detecting this peak include clusters with estimated redshifts and/or clusters outside of Abell's (1958) statistical sample, {i.e.} $R = 0$ clusters. Here, we present estimates of the redshift-space power spectrum for a newly expanded sample of 637 $R \ge 1$ Abell/ACO clusters which has a constant number density to z = 0.10 in the Southern Hemisphere and a nearly constant number density to z = 0.14 in the Northern Hemisphere. The volume sampled, $\sim 10^8h^{-3}$Mpc$^{3}$, is large enough to accurately calculate the power per mode to scales approaching $10^3h^{-1}$Mpc. We find the shape of the power spectrum is a power-law on scales $0.02 \le k \le 0.10h$Mpc$^{-1}$, with enhanced power over less rare clusters such as APM clusters. The power-law here follows $n = -1.4$. The power spectrum is essentially featureless, although we do see a dip near $k = 0.04h$Mpc$^{-1}$ which cannot be considered statistically significant based on this data alone. We do not detect a narrow peak at $k \sim 0.05h$Mpc$^{-1}$ and there is no evidence for a turn-over in the power spectrum as has been previously reported. We compare the shape of the Abell/ACO rich cluster power spectrum to various linear models.
|
[
{
"name": "power2.tex",
"string": "\\documentstyle[emulateapj]{article}\n\\begin{document}\n\\title{\\bf The Power Spectrum of Rich Clusters on Near-Gigaparsec Scales}\n\n\\author{Christopher J. Miller and David J. Batuski}\n\\affil{Department of Physics \\& Astronomy, University of Maine}\n\n\\begin{abstract} \nRecently, there have been numerous analyses of the redshift space power spectrum\nof rich clusters of galaxies. Some of these analyses indicate a \\lq\\lq bump\\rq\\rq~\nin the Abell/ACO cluster power spectrum around $k = 0.05h$Mpc$^{-1}$.\nSuch a\nfeature in the power spectrum excludes most standard formation models and indicates\npossible periodicity in the distribution of large-scale structure. \nHowever,\nthe data used in detecting this peak include clusters with estimated redshifts\nand/or clusters outside of Abell's (1958) statistical sample, {\\it i.e.} $R = 0$ clusters. \nHere, we present estimates of the redshift-space power spectrum for a newly expanded\nsample of 637 $R \\ge 1$ \nAbell/ACO clusters which has a constant number density to z = 0.10 in the Southern Hemisphere\nand a nearly constant number density to z = 0.14 in the Northern Hemisphere. \nThe volume sampled, $\\sim 10^8h^{-3}$Mpc$^{3}$, is large\nenough to accurately calculate the power per mode to scales approaching $10^3h^{-1}$Mpc.\nWe find the shape of the power spectrum is a power-law on scales $0.02 \\le k \\le 0.10h$Mpc$^{-1}$,\nwith\nenhanced power over less rare clusters such as APM clusters. The power-law here follows $n = -1.4$.\nThe power spectrum is essentially featureless, \nalthough we do see a dip near $k = 0.04h$Mpc$^{-1}$ which cannot be considered\nstatistically significant based on this data alone.\nWe do not detect a narrow peak at $k \\sim 0.05h$Mpc$^{-1}$ and\nthere is no evidence for a turn-over in the power spectrum as has been previously reported. \nWe compare the\nshape of the Abell/ACO rich cluster power spectrum to various linear models.\n\n\\end{abstract}\n\n\\section{Introduction}\nThere has recently been a renewed interest in accurately determining the\npower spectrum of matter distribution scales greater than 100$h^{-1}$Mpc;\nin part due to the increased\nnumber of clusters with measured redshifts and the large volumes they trace.\nThe power spectrum for\nthe galaxy distribution has been determined many times for many different classes\nof galaxies. However, most galaxy surveys lack the volume necessary for the\naccurate quantification of power on large-scales ({\\it e.g.} the Las Campanas Redshift Survey \n(Lin {\\it et al.} 1996-hereafter LCRS) or the Stromlo-APM survey (Tadros \\& Efstathiou 1996).\nA summary of the results from these analyses is that the redshift-space\npower spectra roughly agree on scales $\\lambda$ ($ = 2\\pi/k$) $< 100 h^{-1}$Mpc.\nIn this region, $P(k) \\propto k^n$ and $n \\sim -2$. (Of course, the amplitude of the\npower spectra depends on the samples of galaxy examined which provides strong evidence for\na luminosity bias (see e.g. Vogeley et al. 1992 and Park et al. 1994)).\nHowever, on scales $\\lambda > 100h^{-1}$Mpc, there is much less\nagreement. For example, some galaxy samples, such as from the LCRS\nand the Automated Plate Machine (APM) 2d and 3d surveys \nshow a broad flattening\naround $k = 0.05 h$Mpc$^{-1}$ although no distinct maximum can be found within\nconvincing statistical bounds (LCRS;\nTadros and Efstathiou 1996; Peacock 1997; Gatzanaga \\& Baugh 1998).\nHowever, Landy {\\it et al.} (1996) find a distinct peak in $P(k)$ for a 2 dimensional\nanalysis of the LCRS and Broadhurst {\\it et al.} (1990)\nfind a peak near $\\lambda = 130h^{-1}$Mpc in\na deep pencil beam survey.\n\nSome Abell/ACO cluster analyses \nalso show a peak around\n$ k \\sim 0.05 h$Mpc$^{-1}$ (Retzlaff {\\it et al.} 1998; Einasto {\\it et al.} 1997-hereafter E97).\nYet other cluster analyses only show a smooth turnover\nin the power spectrum to its scale-invariant ($n = 1$) form. For instance,\nthe APM clusters, examined by Tadros, Efstathiou and Dalton (1998-hereafter TED98)\nshow a maximum in $P(k)$ at the smaller value of\n$k \\sim 0.03h$Mpc$^{-1}$ and no distinct \\lq\\lq bump\\rq\\rq~ at $k = 0.05h$Mpc$^{-1}$.\nAlso, Peacock \\& West (1992) and Jing \\& Valdarnini (1993) find a break in the Abell cluster\npower spectrum near $k = 0.05h$Mpc$^{-1}$, but no distinct peak in power.\nAn excellent review of the power spectra for different galaxy species can be found in \nEinasto {\\it et al.} (1999-hereafter E99). E99 determine a mean\npower spectrum for all galaxies for a large range in wavenumber. They do this by \nusing the APM 2d power spectra on small scales, and by \naveraging over numerous samples on large scales and then normalizing to the APM 2d power. \n\nIf a narrow peak in power near $k \\sim 0.05h$Mpc$^{-1}$ is a real feature of the power spectrum\nin general, most current models of structure formation (in the quasi-linear regime) become invalid\n(E99). While baryonic signatures can produce features in the power spectrum,\nthose features are oscillatory and they do not produce a singular, narrow peak as seen\nin some of the current data. Eisenstein et al. (1998) examined this prospect and found\nthat no selection of cosmological parameters reproduces the power spectrum as seen in E97.\nHowever, Gramann \\& Suhhonenko (1999) suggest that an inflationary scenario with a scalar field\nhaving a localized step-like feature can reproduce the power spectrum of clusters.\nHowever, in this work, we show that the peak in the cluster power spectrum is not\npresent in larger (in volume and in number)\ncluster samples after excluding less reliable data (such as $R=0$ Abell/ACO clusters\nand clusters with estimated redshifts).\n\nOur aim in this paper is to provide an estimate for the power spectrum of Abell/ACO\nclusters that is based on a complete and fair sample. Both Retzlaff {\\it et al.} and\nE97 use $R =0$ clusters in their determination of $P(k)$. \nEinasto {\\it et al.} (1994) have argued that $R =0$ clusters\ndo not contaminate studies of large-scale structure because the multiplicity of\nsuperclusters is independent of richness and the mean separation distances for\n$R =0$ and $R \\ge 1$ clusters are very similar.\nHowever, $R = 0$ clusters were not cataloged in a systematic way and were never \nmeant to be examined in a statistical manner due to their incompleteness (Abell 1958).\nIn addition, many researchers have found line-of-sight anisotropies in $R = 0$ cluster\nsamples (Sutherland 1988; Efstathiou {\\it et al.} 1992; Peacock \\& West 1992).\nTherefore, the use of $R =0$ clusters in the determination of $P(k)$\nis highly suspect. E97 have also used a large\nnumber (435 out of 1305 clusters) of estimated redshifts in their\ndetermination of $P(k)$. We also suspect that\nE97 used a large number of cluster redshifts with only one measured galaxy. Miller {\\it et al.}\n(1999a) show that cluster velocities with one measured galaxy are in error by more than $2500$ km s$^{-1}$\n14\\% of the time.\nOf course, estimated redshifts are only\naccurate to at best 25\\%. Thus, the statistical certainty of any large-scale structure\nanalyses based on the cluster samples with a large number of estimated or poorly determined\nredshifts must also be taken with caution.\n\n\\section{The Cluster Sample}\nWe examine Abell/ACO clusters across the entire sky excluding the galactic plane \n{\\it i.e.} $|b| > 30^{\\circ}$. We only consider $R \\ge 1$ clusters (with\nmeasured redshifts) since they\nwere defined by Abell (1958) as members of his statistically complete sample.\nRecently, Miller {\\it et al.} (1999a,b) examined similar subsets of $R \\ge 1$ clusters\nfor projection effects, line-of-sight anisotropies, and spatial correlations. We\nsummarize their results below.\n\nThe Abell/ACO $R \\ge 1$ cluster dataset has significant advantages over other cluster\nsamples (including those with $R =0$ clusters as well as APM clusters). With the\nadvent of multi-fiber spectroscopy, nearly all rich Abell/ACO clusters within $z=0.10$ now have\nmultiple galaxy determined redshifts (Slinglend {\\it et al.} 1998; Katgert {\\it et al.}\n1996). Multiple redshifts have allowed for more accurate determinations of the extent\nof projection effects and Miller {\\it et al.} 1999a report that at most, 10\\% of\nAbell/ACO clusters suffer from moderate to severe foreground/background contamination.\nThe lack of projection effects\nfor $R \\ge 1$ clusters is also apparent from the 89\\% X-ray emission\ndetection rate by Voges {\\it et al.} 1999.\nMiller {\\it et al.} (1999a,b) also show that there is very little line-of-sight anisotropy\nin the $R \\ge 1$ Abell/ACO cluster samples - comparable to the APM cluster\ncatalog (Dalton {\\it et al.} 1994)\nThis is in sharp contrast to $R \\ge 0$\nsamples and even some modern X-ray selected/confirmed cluster samples (see e.g. Efstathiou\net al. 1992, Peacock \\& West 1992, and Miller et al. 1999b).\n\nVogeley (1998) recently pointed out how Galactic extinction could\nadd ``false'' power to structure analyses based on large galaxy\nsamples (such as the Sloan Digital Sky Survey). While clusters should\nnot affected as strongly as individual galaxies, it is still worth examining\nextinction effects within our cluster sample.\nIn 1996, Nichol and Connolly used the Stark {\\it et al.} 1992 HI maps to report\nthat some samples of Abell clusters significantly anti-correlate with\nregions of high galactic neutral hydrogen density. \nRecently, Schlegel, Finkbeiner, and Davis (1998) have\ncreated HI extinction maps of the entire sky with much greater resolution than the Stark HI\nmaps. We use these new maps to re-examine\nand confirm the Nichol and Connolly results. We also examine a volume-limited ($z=0.10$) sample\nof Abell/ACO clusters.\nUsing a Kolmogorov-Smirnov (K-S) test, we compare the E(B-V) extinctions for positions\ncentered on the Abell/ACO clusters to E(B-V) extinctions for several thousand randomly\nselection positions. We find that the probability that our clusters were drawn\nfrom a random selection of E(B-V) extinctions is 10\\%. \nIn other words, the average extinction\nwithin our Abell/ACO clusters is smaller than for the random positions, but\nnot significantly so. For comparison, Nichol and Connolly found only a 2\\% probability that the\nPostman, Huchra, and Geller (1992) Abell/ACO clusters (with $|b| \\ge 30^o$ and $R \\ge 1$) were\ndrawn from a random sampling of E(B-V) extinctions. \nThe effect that galactic extinction would have on a power spectrum should not be \nas strong for clusters as it would be for galaxies. Cluster galaxies have\na wide range of magnitudes, and while some dimmer galaxies within a cluster may be missed due\nto extinction, the majority of bright galaxies will still be counted. When we created\nour volume-limited samples, we are including those clusters that appear dim as a result of\ngalactic extinction (as opposed to a magnitude-limited survey which would exclude those\nclusters). The lack of statistically significant evidence that our clusters\nare corrupted by extinction, and the use of a volume-limited sample (with $|b| \\ge 30^o$),\nconvinces us that\nwe can ignore any extinction effects in our analyses.\nHowever, to be certain that extinction is not altering the shape or amplitude of\nour redshift-space power spectrum, we will model the extinction distribution\nof our clusters in our random catalogs for one of our two PS estimation methods (see method (b) below).\n\nAn additional argument for the completeness of $R \\ge 1$ Abell/ACO clusters is\nprovided by their spatial number density as shown in Figure 1. \nWe use clusters of all magnitudes and use the same methods \nas Miller {\\it et al.} (1999a) to calculate and\nbin the cluster number densities. \nNotice in Figure 1 that the sample\nhas a nearly constant density out to $z = 0.10$\nand that the density\nonly drops by a factor of $0.58$ out to $z = 0.14$. \n[Note: The bump in the density at $z \\sim 0.07$ is mostly due to\nthe Corona Borealis Supercluster.]\nIn Figure 1, we fit three different functions to the number density:\na three-parameter number function (as in FKP), a power-law for $z \\ge 0.10$,\nand a step-function. The best-fit produces $\\chi^2_{red} = 2$ for the number function. \n\nUsing cluster redshifts from the literature as well as $\\sim 100$ as yet unpublished\nredshifts from the MX Survey Extension (Miller {\\it et al.} 2000),\nwe have created a sample of 637 $R \\ge 1$ Abell/ACO clusters with $|b| \\ge 30^{\\circ}$.\nThe MX Survey provides a much deeper (in both magnitude and in redshift) catalog\nof Northern Hemisphere cluster redshifts than is currently available for the Southern Hemisphere ACO clusters\n(see e.g. Miller et al. 1999; Katgert et al. 1996).\nTherefore, we exclude any cluster\nbeyond $z = 0.10$ in the south ($\\delta \\le -27^{\\circ}$) and beyond $z = 0.14$ in the\nnorth ($\\delta \\ge -27^{\\circ}$).\nSeveral researchers have noted discrepancies between the richness counts of\nthe Abell and ACO catalogs (see Miller et al. (1999) for a discussion).\nTherefore, we also measure $P(k)$ for a subset of our data that\nexcludes all ACO clusters with\n$N_{gal} < 55 $ (where $N_{gal}$ is the number of galaxies used to determine the richness as\ngiven in ACO and $N_{gal} \\ge 50$ corresponds to $R \\ge 1$). This richness cut excludes\n30 ACO clusters from our sample.\n\nThis is the largest cluster sample compiled to date for large-scale structure analyses.\nThe survey volume covers $1.2\\times10^8h^{-3}$Mpc$^3$ and is nearly four times larger than\nthe APM cluster survey (Dalton {\\it et al.} 1994)\nand the Retzlaff {\\it et al.} (1998) Abell/ACO survey.\nAdditionally, only $\\sim$ 10\\% of our cluster redshifts are\nbased on one measured galaxy redshift.\nWe calculate distances to the clusters using\na Friedmann Universe with $q_0 = 0$ and $H_0 = 100$ km s$^{-1}$ Mpc$^{-1}$. \nThe choice of $q_o$ makes little difference in\nour results (see also Retzlaff {\\it et al.} 1998).\n\n\nWhen a cluster dataset goes as deep as the one used here, and has been\ncreated in a somewhat piecemeal fashion, we must be very \nconfident that the cluster observations used in this sample are more or less isotropic in volume, and that\nwe are not including large sections of the sky that go deeper (in magnitude) than others.\nWe address this concern \nfiguratively in Figure 2, by examining the fraction of observed to total cataloged clusters.\nIn this sky plot (in galactic coordinates), we\nshow Abell clusters with $z=0.10$ (filled circles), Abell clusters within\n$0.10 < z \\le 0.14$ (open circles), and ACO clusters within $z=0.10$ (stars).\nWe can divide the sky into quadrants with two sections in the north\nand two in the south (each separated at $l = 180^{o}$) and examine\nnearby ($z \\le 0.10$) and distant ($0.10 < z \\le 0.14$) clusters\nseparately. From Figure 2, we see\nreasonably fair coverage throughout the entire sky in both redshift\nranges (recall that\nthe southern right quadrant only goes to $z=0.10$).\nQuantitatively, we present in Table 1 the number of clusters available in each\nquadrant cataloged by Abell/ACO, and the number\nof clusters observed in each quadrant. Note that the fractional\ncoverages in each of the sections are very similar. The mean fractional coverage\n(including both near and far quadrants) is $0.138\\pm{0.019}$, so that the\nnumber of clusters within the more distant,\nnorthern right quadrant is only $1.5\\sigma$ smaller than the mean.\nTable 1 provides clear evidence that the sky coverage for our cluster sample is\nnot observationally biased towards certain regions.\n\nAfter accounting for projection effects, line-of-sight anisotropies, X-ray identifications,\nHI column density variations, a constant number density, and fair sky coverage,\nthis is the largest, \nmost complete, and fairly sampled distribution of matter in the local\nUniverse. We assume that clusters are biased tracers of mass (Kaiser 1986; Peacock \\& Dodds 1994) and\nthat in the end, we may compare the shape of our power spectrum to those of typical cosmological models.\n\n\\section{Methods and Analyses}\nWe utilize two different methods to estimate $P(k)$ in redshift-space. Both methods follow\nthe same basic idea: directly sum the plane wave contributions from each cluster, account for\nappropriate weights and the shape of the volume, compute the square of the modulus of each\nmode and subtract off the shot noise. The resultant power spectrum is the estimated variance\nof the density contrast $|\\delta(k)|^2$.\nThe power spectrum is accurate only to some limiting scale, specified by $k_{min}$,\nwhich is constrained by the size and shape of the volume examined.\nThe differences between the two methods arise\nwhen accounting for the weighting scheme and the shape of the volume.\nWe also point out that Tegmark {\\it et al.} (1998) have recently presented\nan alternative method for measuring $P(k)$ for large datasets (such as the Sloan\nDigital Sky Survey). As discussed in detail in Tegmark {\\it et al.}, they\nadvocate the use of standard Fourier techniques on small scales, a pixelized quadratic\nmatrix method on large-scales, and also a Karhunen - Loeve (KL) eigenmode analysis to\nprobe redshift-space anisotropies. While the Tegmark {\\it et al.} power spectrum\nestimation method is undoubtedly\nmore refined than the methods used here, we are more interested in comparing results\nfrom the most commonly used techniques (and also allowing our results to be compared\nto previous cluster $P(k)$ measurements). Also, the methods described in Tegmark et al.\nare designed for large datasets (e.g. several 100,000 points) and we would not expect\na large advantage in our smaller samples.\n\nThe first method we use was originally applied by Vogeley et al. (1992),\nPark et al. (1994) and da Costa et al. (1994) \nto the CfA2 redshift survey (Geller \\& Huchra 1989). This method is also\ndescribed in LCRS and Fisher {\\it et al.} 1993.\nMost recently, this method was used and described by Retzlaff {\\it et al.} (1998) on a \nsample of Abell/ACO clusters. \nBriefly, the estimated power spectrum convolved with\nthe window function can be written as follows:\n\\begin{equation}\n\\hat{P}_{a}(k) = {\\frac{V}{1-|\\hat{W}(k)|^2}}[\\hat{\\Pi}(k) - \\hat{S}].\n\\end{equation}\nThe first factor in Equation 1 accounts for the systematic under-estimation of $P(k)$ at\nsmall values of $k$ due to normalization biases and \nthe shape of the window, also known as large-scale power damping (Peacock \\& Nicholson 1991). \nThe first term in brackets, $\\hat{\\Pi}$ is the squared-modulus of the Fourier transform of the \ndensity contrast, $\\delta(\\bf{r})$, minus the Window Function,\nor the estimated power. $\\hat{\\Pi}$ is a discrete quantity that\nincludes shot noise $\\hat{S}$ which we must subtract off.\nThe estimate of the power, $\\hat{P}_{a}(k)$, is convolved with the\nWindow function, $\\hat{W}(k)$.\n\nIn practice, we calculate $\\hat{W}(k)$ separately for as many points as is feasible (in this case \n$3\\times 10^5$ random points) and average over 1000 directions of $k$. \nThe window function is presented in Figure 3. We calculate $|\\hat{W}(k)|^2$ using points\nrandomly distributed in our volume and also with the same redshift and extinction\ndistribution as our real data (the redshift distribution is smoothed with a Gaussian to remove any\nlarge-scale structure). Figure 3 shows that the shape of $|\\hat{W}(k)|^2$ changes\nvery little as we adjust the random distribution within our volume.\nWe also calculate $|\\hat{W}(k)|^2$ for a volume that\nencompasses only one hemisphere out to $z = 0.14$. We see that, as the volume becomes more asymmetric,\nsignificant\ndifferences betweem the window functions appear.\nThe ``bumps'' seen in $|\\hat{W}(k)|^2$ are a direct result\nof a volume-limited, spherically symmteric survey, and have little effect on the PS estimation,\nso long as their relative heights are much smaller than the largest $|\\hat{W}(k)|^2$ used. \nThese ``bumps'' are an indicator that the survey window is spherically symmetric\nand that averaging over all directions of ${\\bf k}$ is appropriate.\nThis is not typically the case in previous (non-Abell/ACO)\n$P(k)$ analyses (see Tegark (1995) for a good discussion of window functions).\n\nThe smallest $k$ that can be accurately probed depends on the value of $|\\hat{W}(k)|^2$ and\nhow it convolves with the real power spectrum (see Lin et al. 1996). Recall, \n\\begin{equation}\n\\langle P_{estimated}(k) \\rangle \\propto \\int |\\hat{W}({\\bf k} - {\\bf k'})|^2 P_{true}({\\bf k'}) k'^2 dk'.\n\\end{equation}\nIdeally, for all values of $k$ probed, the integrand of Equation (2) will be sharply peaked at $k = k'$.\nIn Figure 4, we plot the integrand of Equation (2) assuming a constant $P(k)$. We find that the\nshape of our volume does not affect our analyses for $k >\\sim 0.015h$Mpc$^{-1}$. For $k$ smaller\nthan this limit, we see that ``leakage'' occurs and power from larger $k$ slips into our measurements.\nFigure 4 also shows that if uncorrelated modes of $P(k)$ are required, we should separate\nour bins by $\\delta k = 0.015$. \nOur choice of $k_{min} =0.015 h$Mpc$^{-1}$ is a conservative\nlimit, since most past analyses of $P(k)$ have stopped where\n$|\\hat{W}(k)|^2 = 0.1$ (e.g. Peacock and Nicholson 1991; Vogeley et al. 1992; Retzlaff et al. 1998).\nThe value of $|\\hat{W}(k)|^2$ for our analysis at $k_{min}$ is only $ 0.05h$Mpc$^{-1}$.\n\nThe weights for each cluster\noriginate in the estimation of the density contrast,\n\\begin {equation}\n\\hat{\\delta}(r)=\\frac{1}{N}\\sum_i{\\frac{\\delta^{3}(\\bf{r}-\\bf{r}_i)}{\\phi(r_i)}} - 1\n\\end{equation}\nwhere $\\phi({\\bf r}) = \\psi(b)\\varphi(z)$ is the selection function which accounts for galactic\nobscuration and redshift selection.\nWe use $\\psi(b) = 10^{\\gamma(1-csc|b|)}$ with $\\gamma = 0.32$ for the latitude selection\nfunction (see Postman, Huchra, and Geller 1992). \n%We use $\\varphi(z) = 1$ for clusters within $z=0.10$ and\n%and $\\varphi = 0.58$ for clusters with $0.10 < z \\le 0.14$.\nThe selection function in $z$ is determined separately for the three different number density models\nused in Figure 1. We find that the choice of number-density fit\nhas little on the PS estimation.\n\nThe second method we use was derived by Feldman, Kaiser, \\& Peacock (1994-hereafter FKP).\nTED96 use a very similar approach in their analysis of APM clusters.\nHere, the\npower spectrum is:\n\\begin{equation}\n\\hat{P}_b(k) = |F({\\bf k})|^2 - P_{shot}\n\\end{equation}\nwhere $F(k)$ is the Fourier transform of the normalized and weighted galaxy fluctuation field:\n\\begin{equation}\nF(\\bf{r})=\\frac{w(r)[n_c(r)-{\\alpha}n_s(r)]}{[\\int d^3r\\bar{n}^2(r)w^2(r)]^{1/2}}\n\\end{equation}\nIn these equations, $n_c$ and $n_s$ represent the number densities of the cluster sample\nand a randomly generated synthetic catalog respectively. \nThe number of\npoints we use in the random catalog is 500 times that of the real data so $\\alpha = \\frac{1}{500}$\n(we note\nthat there is no difference in the power spectrum results for random catalogs with 100\ntimes as many points). $P_{shot}$ is again, the power due to shot noise from a discrete sample and\nis determined as in FKP.\nIn this method, we model the redshift selection of our random catalogs from\nthe redshifts of the real data, smoothed with a Gaussian of width $3000$ km s$^{-1}$.\nThe weights for the individual clusters (real and synthetic) are determined from\n\\begin{equation}\nw_o(r) = \\frac{1}{1+n(r)P_{init}(k)}.\n\\end{equation}\nTo create the extinction adjusted random catalogs, we draw from regions in\nthe sky that have the same extinction distribution as our real data using the Schlegel et al. (1998)\nmaps. We find little difference in our $P(k)$ when we apply no extinction correction.\nTo determine $n(r)$ used in the weighting factor, we use the three different number density\nfits\n(as given in Figure 1). Again, we find that the choice of number density fit has little\neffect on the PS estimation. \n\nThe weighting scheme for $P_{b}(k)$ depends on {\\it a priori} knowledge of $P(k)$ at all\nscales. We choose different values of \n$P_{init}(k)$ ( 5, 10, 30, 60$\\times 10^4h^{-3}$Mpc$^{3}$)\nfor the cluster weights and\nfind that there is little difference in the amplitude ($\\sim 1.5 $ times) \nof $P_{b}(k)$ between\n$P_{init} = 5$ and $60\\times 10^4 h^{-3}$Mpc$^{3}$ and so we adopt \n$P_{init} = 30\\times 10^4 h^{-3}$Mpc$^{3}$ in all further $P_{b}(k)$ results.\nWe calculate errors on $P_{b}(k)$ using those methods of FKP (equation 2.4.6).\n\nIn Figure 5, we compare all of our calculations of $P(k)$.\nIn the top panel of Figure 5, we plot $P_a(k)$ using the three different number density functions.\nWe also measure $P(k)$ for the richness adjusted sample.\nWe plot the same for\n$P_{b}(k)$ in the middle panel of Figure 5. In all cases, we find very little difference in our $P(k)$ estimations.\nIn the bottom panel of Figure 5 we compare $P_a(k)$ to $P_b(k)$ using the number function as our density fit.\nHere, we do see some small differences in the measured power at $k$ less than $0.02h$Mpc$^{-1}$, however\nboth spectra estimates are within the 1 $\\sigma$ error. \nThe lack of difference between $P_a(k)$ and $P_b(k)$ \nis a direct result of the stability of the methods and the\nwell defined number density and \nsymmetric volume of the cluster sample.\n\n\\section{Discussion}\n\nThere are two striking results regarding the power spectrum of rich Abell/ACO clusters. (1) While\nwe do see a dip in power near $k = 0.4h$ Mpc$^{-1}$, it is not statistically significant. \nThe measured power spectrum is essentially featureless and there is \nno narrow peak in the power spectrum as has been\nreported in E97 and Retzlaff {\\it et al.} (1998). (2) The other difference\nis that there is increasing power to very large scales ($k = 0.015h$Mpc$^{-1}$ or $\\sim 400h^{-1}$Mpc).\nIn past analyses of the power spectrum, most\nauthors have reported the (weak) detection of a turnover in the power spectrum (see section 1). However,\nthe turnover has always occurred very near the largest scales accessible in their volumes. \n[Note: other preliminary analyses of the PS on scales $k < 0.05h$Mpc$^{-1}$ are also showing\nthis increase in power (Guzzo et al. 1999; Hamilton and Tegmark 2000; Efstathiou and Moody 2000)].\nThe power spectrum is roughly a power-law on scales $0.02 \\le k < 0.10 h$Mpc$^{-1}$ with $P(k) \\propto k^{-1.4}$.\n\nIn Figure 6, we compare our results to two other cluster sample power spectrum analyses,\nthe APM cluster sample of TED98, and the $R \\ge 0$ Abell/ACO sample of Retzlaff et al. (1998).\nFigure 6 shows that the shapes of $P(k)$ for\nthese three different cluster samples\nare remarkably\nsimilar in the range $ 0.04 \\le k \\le 0.15 h$Mpc$^{-1}$.\nThe higher amplitude for our sample of $R \\ge 1$ clusters is expected according to\nhierarchical clustering schemes (Kaiser 1986) and larger bias found in richer clusters (see\nPeacock and Dodds 1994).\nWe have recalculated the Retzlaff {\\it et al.}\n(1998) Abell/ACO cluster sample using the methods for $P_a(k)$. We do this in part as a check on\nour methods and also to independently confirm their results of a peak near $k = 0.05h$Mpc$^{-1}$\nand a turnover thereafter. The Retzlaff {\\it et al.} sample includes all Abell/ACO clusters\nwithin $240 h^{-1}$Mpc and outside $|b| \\ge 30^{\\circ}$. We find 412 clusters which meet this\ncriteria (compared to their 417 clusters- the difference we attribute to minor variations in\na few cluster redshifts near the survey boundaries). Our results, not surprisingly, are identical\nto those published in Retzlaff {\\it et al.} (1998) since our method for determining $P_a(k)$ is\nidentical to theirs. For this determination of $P_a(k)$ ({\\it i.e.} using $R =0$ clusters and\na much smaller volume), we also see a peak in the power spectrum at $k = 0.05h$Mpc$^{-1}$\nand a turnover thereafter. As pointed out by Retzlaff {\\it et al.}, this peak\nis not statistically significant. As a further examination of this issue, we plot in Figure 6 \n$P_b(k)$ for a smaller cluster sample,\nvolume-limited in the north and south to $z = 0.10$. For this sample, we can only detect power to\n$k_{min} \\sim 0.035h$Mpc$^{-1}$. For $k$ greater than $0.035h$Mpc$^{-1}$\nwe find little difference between this sample and the larger one. But\nwe can no longer probe on the scales where we expect $P(k)$ to continue its rise.\nThus, one could conclude that a turn-over has been found, when in fact a larger (in size and number) sample\nshows that the power continues to rise for $k < 0.03h$Mpc$^{-1}$.\n\n\\subsection{Comparisions to Linear Theory}\nWe also compare our power spectrum results to those of linear theory created by CMBFAST \n(Seljak \\& Zaldarriaga 1996). We consider three Cold Dark Matter (CDM) variants, flat, open and\nwith a vacuum density ($\\Lambda$CDM), and a Mixed Dark Matter (MDM) model.\nFor the CDM cases, we choose $\\Omega_b = 0.02$, in accordance with\nSchramm \\& Turner (1998). For the open case, we choose\n$\\Omega_0=\\Omega_b + \\Omega_{CDM} = 0.2$ in accordance with Bahcall (1997). For the $\\Lambda$CDM\nmodel, we choose $\\Omega_{CDM} = 0.18$ and $\\Omega_{vacuum} = 0.80$ so that\n$\\Omega_b + \\Omega_{CDM} + \\Omega_{vacuum} = 1$. For the MDM model,\nwe choose $H_0 = 50 $km s$^{-1}$Mpc$^{-1}$\nwith $\\Omega_b =0.05$, $\\Omega_{CDM}=0.35$ and $\\Omega_{\\nu}=0.3$\n(where $\\Omega_{\\nu}$ is the massive neutrino density).\nThe CMBFAST package normalizes\nthe amplitude of generated spectra to the Bunn and White (1997) four-year COBE normalization. \nHowever, in this work, we are only concerned with the {\\it shape} of the power spectrum.\nWe are motivated by our assumption that clusters are biased tracers of the mass distribution\nand therefore the shape of the cluster power spectrum should be similar to that of the matter\npower spectrum.\nIn Figure 7, we present the amplitude shifted\nlinear models in comparison to our empirically determined \npower spectra.\nAs a result of the known similarities in the shapes of the $\\Lambda$CDM models and low matter density\nopen CDM models, we find that both fit the shape of the rich\nAbell/ACO cluster power spectrum to $k_{min} = 0.015h$Mpc$^{-1}$ or $400h^{-1}$Mpc extremely\nwell (see Table 2).\nOn the largest scales, the \nMDM model lacks power over a wide range of $k$ ($0.015 \\le $k$ \\le 0.03h$Mpc$^{-1}$) to match\nour cluster data.\nTED98 found that $\\Lambda$CDM linear models did not have\nenough power on large scales to match the APM cluster power spectrum. Instead, they find a much\nbetter fit for\na mixed dark matter (MDM) model.\nWe\npoint out that the $\\Lambda$CDM model in Figure 7 of TED98 does provide an excellent\nfit to the APM cluster data if their last data point at $k = 0.02h$Mpc$^{-1}$ (where\nthe error is rather large) is excluded.\n\n\\section{Conclusion}\nThe agreement between\nthe shapes of $P(k)$ for the four different samples shown in Figure 6 (from $k = 0.05$ to $0.15 $h Mpc$^{-1}$),\nprovides further evidence that clusters are\ntracers of the peaks of the underlying luminous \nmass distribution. While there is a\ngreat deal of volume-overlap in these four samples, they are made up of significantly\ndifferent luminous objects (from very poor APM clusters to the richest Abell clusters).\nFor instance, the Retzlaff et al. (1998) Abell/ACO sample\ncontains at most 253 $R \\ge 1$ clusters, while the remaining 218 are $R \\ge 0$. \nOur sample contains 637 $R \\ge 1$ clusters. The APM sample of 364 clusters, \ncontains even fewer $R \\ge 1$ Abell clusters ($\\sim 40$).\nIf all groups and clusters\ntrace the underlying mass distribution in a similar way, then the we would expect their respective\npower spectra to be similar in shape, and only the amplitude to vary.\n \nPrevious analyses of the cluster power spectrum have been plagued\nby three major problems: (1) uncertainties in the number density, (2) small volumes,\nand (3) irregularly shaped volumes. The sample analyzed in this work greatly improves\nupon each of these difficulties. \nOur Abell/ACO sample has a nearly constant number\ndensity throughout the entire volume. This is in stark contrast to most\nother sparse tracer surveys (such as the QDOT {\\it IRAS} survey power spectrum\nof FKP and the Retzlaff {\\it et al.} Abell/ACO cluster sample).\nAlong with the number density, the large size of the volume\nand the semi-regular shape of the double-cone geometry, all contribute significantly\nto a more accurate determination of $P(k)$ on the largest scales.\nThe reality of the power on scales $200 - 300h^{-1}$Mpc is also becoming evident\nobservationally. Batuski {\\it et al.} 1999\nhave recently discovered two filamentary superclusters in the constellation of Aquarius\nthat are as long as $75h^{-1}$Mpc and $150h^{-1}$Mpc. As we peer out further into the\nlocal Universe, we continue to find structures on very large scales. \n\n\nWe have presented the redshift-space power spectrum for the largest galaxy cluster sample\ncompiled to date. This sample has been examined extensively for projection effects, anisotropies,\nand observational selection effects and found to be a fair and complete sampling of biased\nmatter in the local Universe. The volume and shape of the survey provide accurate and robust\nmeasurements of $P(k)$ over the wavenumber range $0.015 \\le k \\le 0.15 h$Mpc$^{-1}$. From\n$k= 0.15$ down to $k = 0.05 h$Mpc$^{-1}$, we\nfind a similar shape to the power spectrum compared to other cluster samples such as\nthe APM cluster survey and a smaller sample of $R \\ge 0$ Abell/ACO clusters studied by\nRetzlaff {\\it et al.} (1998). At smaller $k$, we do not find\nany statistically significant features in $P(k)$. \nUnlike previous cluster $P(k)$ analyses, we do not find\nany strong evidence for a turnover.\nWe find that $\\Lambda$CDM and\nlow $\\Omega_0$ CDM linear models provide excellent fits to the rich cluster power spectrum.\n\n{\\bf Acknowledgments} The authors wish to thank Adrian Melott and Daniel Eisenstein\nfor helpful conversations. We also would like to acknowledge the role of the\nthe referee, Michael S. Vogeley, for his suggestions on improving the original manuscript. \nWe also thank H. Tadros for supplying the APM cluster PS in electronic form.\nCM was funded in part by NASA-EPSCoR through the\nMaine Science and Technology Foundation.\n\n\\begin{deluxetable}{cccccc}\n%\\tablefontsize{\\footnotesize}\n\\tablenum{1}\n\\tablewidth{0pt}\n\\tablecaption{\\bf Sky Coverage}\n\\tablehead{\n\\colhead{$\\ell$ range} & \\colhead{ $b$ range} & \\colhead{ $z$ range} & \n\\colhead{Number (all z)} & \\colhead{ Number with} & \\colhead{Fraction{\\tablenotemark{a}}} \\nl\n\\colhead{ } & \\colhead{ } & \\colhead{ } &\n\\colhead{cataloged} & \\colhead{observed redshifts} & \\colhead{}}\n\\startdata\n$0^o \\le \\ell < 180^o$ & $30^o \\le b \\le 90^o$ & $z \\le 0.10$ & 636 & 80 & 0.1257 \\nl\n$0^o \\le \\ell < 180^o$ & $30^o \\le b \\le 90^o$ & $0.10 < z \\le 0.14$ & 636 & 86 & 0.1352 \\nl\n$180^o \\le \\ell < 360^o$ & $30^o \\le b \\le 90^o$ &$z \\le 0.10$ & 503 & 78 & 0.1550 \\nl\n$180^o \\le \\ell < 360^o$ & $30^o \\le b \\le 90^o$ &$0.10 < z \\le 0.14$ & 503 & 52 & 0.1034 \\nl\n$0^o \\le \\ell < 180^o$ & $-90^o \\le b \\le -30^o$ &$z \\le 0.10$ &608 & 95 & 0.1563 \\nl\n$0^o \\le \\ell < 180^o$ & $-90^o \\le b \\le -30^o$ &$0.10 < z \\le 0.14$ & 608 & 84 & 0.1382 \\nl\n$180^o \\le \\ell < 360^o$ & $-90^o \\le b \\le -30^o$ &$z \\le 0.10$ & 492 & 75 & 0.1524 \\nl\n\\tablenotetext{a}{Fraction is the Number observed/ Number cataloged.}\n\\enddata\n\\end{deluxetable}\n\n \n\\begin{deluxetable}{ccc}\n%\\tablefontsize{\\footnotesize}\n\\tablenum{2}\n\\tablewidth{0pt}\n\\tablecaption{\\bf Goodness-of-Fit to Linear Models}\n\\tablehead{\n\\colhead{Model} & \\colhead{$\\chi_{reduced}^2$} & \\colhead{DOF}}\n\\startdata\n$\\Lambda$CDM ($H_o = 100$km s$^{-1}$) & 0.65 & 8 \\nl\nOpen CDM ($H_o = 100$km s$^{-1}$) & 0.66 & 8 \\nl\nCDM ($H_o = 100$km s$^{-1}$) & 4.55 & 8 \\nl\nMDM ($H_o = 50$km s$^{-1}$) & 2.19 & 8 \\nl\n\\enddata\n\\end{deluxetable}\n\n\\begin{thebibliography}{}\n\\bibitem[(Abell 1958)]{abe58} Abell, G. O. 1958, \\apjsupp, ~ 3, 211\n\\bibitem[(Abell et al. 1989)]{aco89} Abell, G. O.,\n Corwin, H. G., Olowin, R. P. 1989, \\apjsupp, ~70, 1 (ACO)\n\\bibitem[(Bahcall 1997)]{bah97} Bahcall, N. 1997, in {\\it Critical Dialogues in Cosmology}, ed. N. Turok,\n World Scientific, Singapore, 221\n\\bibitem[(Batuski {\\it et al.} 1999)]{bat99} Batuski, D.J., Miller, C.J., Slinglend, K.A.,\n Balkowski, C., Maurogordato, S., Cayatte, V., Felenbok, P., and Olowin, R. 1999, \\apj, 520, 491\n\\bibitem[(Broadhurst {\\it et al.} 1990)]{brd90} Broadhurst, T.J., Ellis, R.S., Koo, D.C., \\& \n Szalay, A.S. 1990, Nature, 343, 726\n\\bibitem[(Bunn \\& White 1997)]{bun97} Bunn, E.F. \\& White, M. 1997, \\apj, 480, 6\n\\bibitem[(da Costa et al. 1994)]{dac94} da Costa, L.N., Vogeley, M.S., Geller, M.J., Huchra, J.P.,\n \\& Park, C. 1994, \\apj, 437, L1\n\\bibitem[(Dalton {\\it et al.} 1994)]{dal94} Dalton, G.B., Croft, R.A.C.,\n Efstathiou, G., Sutherland, W.J., Maddox, S.J., and Davis, M. 1994, \\mnras,\n 271, 47\n\\bibitem[(Efstathiou {\\it et al.} 1992)]{eft92} Efstathiou, G., Dalton, G.B.,\n Maddox, S.J., \\& Sutherland, W. 1992, \\mnras, ~257, 125\n\\bibitem[(Efstahiou and Moody 2000)]{eft00} Efstathiou, G. and Moody, S.J. 2000, preprint\n ~astro-ph/0010478\n\\bibitem[(Einasto {\\it et al.} 1997)]{ein97} Einasto, J., Einasto, M., Gottl\\\"{o}ber, S.,\n M\\\"{u}ller, V., Saar, V., Starobinsky, A.A., Tago, E., Tucker, D., Andernach, H., \\& \n Frisch, P. 1997, Nature, 385, 139 (E97)\n\\bibitem[(Einasto {\\it et al.} 1999)]{ein99} Einasto, J., Einasto, M., Tago, E.,\n Starobinsky, A.A., Atrio-Barandela, F.,\n M\\\"{u}ller, V., Knebe, A, \\& Cen, R. 1999, \\apj, 519, 469 (E99) \n Frisch, P. 1997, Nature, 385, 139 (E97)\n\\bibitem[(Einasto {\\it et al.} 1994)]{ein94} Einasto, M., Einasto, J., Tago, E., Dalton, G.B.,\n \\& Andernach, H. 1994, \\mnras, 269, 301\n\\bibitem[(Eisenstein and Hu 1998)]{eis98} Eisenstein, D.J., Hu, W., Silk, J., and Szalay, A.S.\n 1998,\\apj, 494, L1\n\\bibitem[(Feldman, Kaiser, \\& Peacock 1994)]{fel94} Feldman, H.A., Kaiser, N. \\& Peacock, J.A.\n 1994, \\apj, 426, 23 (FKP)\n\\bibitem[(Fisher {\\it et al.} 1993)]{fis93} Fisher, K.B., Davis, M., Strauss, M.A.,\n Yahil, A., \\& Huchra, J.P. 1993, \\apj, 402, 42\n\\bibitem[(Gatza\\~{n}aga, \\& Baugh)]{gat98} Gatza\\~{n}aga, E. \\& Baugh, C.M. 1998, \\mnras, 294, 229\n\\bibitem[Geller \\& Huchra(1989)]{1989Sci...246..897G} Geller, M.\\ J.\\ \\& \nHuchra, J.\\ P.\\ 1989, Science, 246, 897 \n\\bibitem[(Gramann \\& Suhhonenko 1999)]{suh99} Gramann, M. \\& Suhhonenko, I. 1999, \\apj, 519, 433\n\\bibitem[(Hamilton and Tegmark 2000)]{hal00} Hamilton, A.J.S. and Tegmark, M. 2000, submitted to \\mnras,\nastroph/0008392\n\\bibitem[(Guzzo 1999)]{guz99} Guzzo, L. 1999, presented at {\\it The Second Coral Sea Cosmology Conference}\n\\bibitem[(Hoyle et al. 1999)]{hoy99} Hoyle, F., Baugh, C. M., Shanks, T., Ratcliffe, A. 1999, \\mnras,\n 309, 659\n\\bibitem[(Jing and Valdarnini 1993)]{jin93} Jing, Y.P. and Valdarnini, R. 1993, \\apj, 406,6\n\\bibitem[(Kaiser 1994)]{kai94} Kaiser, N. 1986, \\mnras, 222,323\n\\bibitem[(Katgert {\\it et al.} 1996)]{kat96} Katgert,P., Mazure, A., Perea, J.,\n den Hartog, R., Moles, M., Le Fevre, O., Dubath, P., Focardi, P., Rhee, G.,\n Jones, B., Escalera, E., Biviano, A., Gerbal, D., Giuricin, G. 1996,\n A \\& A, ~310, 8\n\\bibitem[(Landy {\\it et al.} 1996)]{lan96} Landy, S.D., Shectman, S.A., Lin, H., Kirshner, R.P.,\n Oemler, A.A., \\& Tucker, D. 1996, \\apj, 456, L1\n\\bibitem[(Lin {\\it et al.} 1996)]{lin96} Lin, H., Kirshner, R.P., Shectman, S.A., Landy, S.D.,\n Oemler, A., Tucker, D.L., \\& Schecter, P.L. 1996, \\apj 471, 617 (LCRS)\n\\bibitem[(Miller {\\it et al.} 1999a)]{mi99a} Miller, C.J., Batuski, D.J., Slinglend, K.A., \\&\n Hill, J.M. 1999a, \\apj, 523, 492\n\\bibitem[(Miller {\\it et al.} 1999b)]{mi99b} Miller, C.J., Ledlow, M.J. \\& Batuski, D.J. 1999b,\n \\mnras, submitted\n\\bibitem[(Miller {\\it et al.} 1999c)]{mic99} Miller, C.J., Krughoff, K.S., Slinglend, K.A.,\n Batuski, D.J., \\& Hill, J.M. 1999c (in preparation)\n\\bibitem[(Nichol \\& Connolly 1996)]{nic96} Nichol, R.C. \\& Connolly, A.J. 1996, \\mnras, 279, 521\n\\bibitem[(Park et al. 1994)]{par94} Park, C., Vogeley, M.S., Geller, M.J., \\& Huchra, J.P. 1994,\\apj,431,561\n\\bibitem[(Peacock 1997)]{pea97} Peacock, J.A. 1997, \\mnras, 285, 885\n\\bibitem[(Peacock \\& Dodds 1994)]{pea94} Peacock, J.A. \\& Dodds, S.J. 1994, \\mnras, 267, 1020\n\\bibitem[(Peacock and Nicholson 1991)]{pea91} Peacock, J.A. \\& Nicholson, D. 1991, \\mnras, 253, 307\n\\bibitem[(Peacock \\& West 1992)]{pew92} Peacock, J.A. \\& West, M.J. 1992,\n \\mnras, 259, 494\n\\bibitem[(Postman et al. 1992)]{pos92} Postman, M.,\n Huchra, J. P., \\& Geller, M. J. 1992, \\apj, ~384, 404\n\\bibitem[(Retzlaff {\\it et al.} 1998)]{ret98} Retzlaff, J., Borgani, S., Gottl\\\"{o}ber, S., \n Klypin, A., \\& M\\\"{u}ller, V. 1998, NewA, 3, 631\n\\bibitem[(Schlegel {\\it et al.} 1998)]{sch98} Schlegel, D.J., Finkbeiner, D.P., \\& Davis, M.\n 1998, \\apj, 500, 525\n\\bibitem[(Schramm \\& Turner 1998)]{sch98} Schramm, D.N. \\& Turner, M.S. 1998, Rev. Mod. Phys., 70, 303\n\\bibitem[(Seljak \\& Zaldarriaga 1996)]{sel96} Seljak, U. \\& Zaldarriaga, M. 1996, \\apj, 469, 437\n\\bibitem[(Slinglend {\\it et al.} 1998)]{sli98} Slinglend, K.A., Batuski, D.J,\n Miller, C.M., Haase. S., Michaud, K., \\& Hill, J.M. 1998, \\apjsupp, 115,1\n\\bibitem[(Stark {\\it et al.} 1992)]{sta92} Stark, A.A., Gammie, C.F., Wilson, R.W.,\n Bally, J.L., Linke, R.A., Heiles, C., \\& Hurwitz, M. 1992, \\apjsupp, 79, 77\n\\bibitem[(Sutherland 1988)]{sut88} Sutherland, W. 1988, \\mnras, ~234, 159\n\\bibitem[(Tadros \\& Efstathiou 1996)]{tad96} Tadros, H., \\& Efstathiou, G. 1996, \n \\mnras, 282, 1381 (TE96)\n\\bibitem[(Tadros, Efstathiou \\& Dalton 1998)]{tad98} Tadros, H.,Efstathiou, G., \\& Dalton, G.\n 1998, \\mnras, 296, 995 (TED98)\n\\bibitem[(Tegmark 1995)]{teg95} Tegmark, M. 1995, \\apj, 455, 429\n\\bibitem[(Vogeley 1998)]{vog98} Vogeley, M.S. 1998, in {\\it The Evolving Universe}, \n Kluwer Academic Publishers, p. 395\n\\bibitem[(Vogeley et al. 1992)]{vog92} Vogeley, M.S., Park, C., Geller, M.J., \\& Huchra, J.P. 1992,\n \\apj, 391, L5\n\\bibitem[(Voges, {\\rm et al.} 1999)]{vog99} Voges, W., Ledlow, M.J., Owen, F.N.,\n \\& Burns J.O. 1999, \\aj, submitted \n\n\n\n\\end{thebibliography}\n\n\\begin{figure*}[hl]\n\\plotone{f1.eps}\n\\caption[]{The proper number density as a function of redshift is presented for the Abell/ACO cluster\nsample. The lines are various fits to the data. The solid-line (having the lowest $\\chi^2$) is\na three parameter number function. The dotted-line is for a power-law beyond $z =0.01$. The dashed-line\nis for a step function. We find no significant differences in our PS analysis as a function of\nthe number density function utilized.}\n\\end{figure*}\n\n\\begin{figure*}\n\\plotone{f2.eps}\n\\caption[]{ A Hammer-Aitoff projection sky-plot of all clusters used in the\npower spectrum analysis. Closed circles denote Abell (1958) clusters within $z=0.10$,\nopen circles denote Abell clusters with $0.10 < z \\le 0.14$, and stars indicate\nACO (1989) clusters within $z=0.10$. We have divided our sample into four quadrants\nin latitude/longitude and two bins in $z$, to show that the clusters in our sample\nhave been observed evenly throughout the sky (see Table 1).}\n\\end{figure*}\n\n\n\n\\begin{figure*}\n\\plotone{f3.eps}\n\\caption[]{This is the Fourier window function, $\\langle|\\hat{W}({\\bf k})|^2 \\rangle$ used to calculate $P_a(k)$. We use 300000 points\nand 1000 random directions for each $|k|$ to estimate the Fourier transform of the window function. $k$ is in\nunits of $h$Mpc$^{-1}$. The dashed-line is for a random distribution of points. The solid-line is after\nwe apply the same redshift and extinction distribution as our real data. The dotted-line is for a highly asymmetric\nsurvey (i.e. one hemisphere to $z = 0.14$).\nThe hatched region\nindicates where our window function prevents an accurate determination of $P(k)$.}\n\\end{figure*}\n\n\n\\begin{figure*}[hl]\n\\plotone{f4.eps}\n\\caption[]{The integrand of Equation (2) for constant $P(k)$ with arbitrary normalization.\nWe show three values of $k = 0.01, 0.02, 0.05h$Mpc$^{-1}$. We see that for $ k = 0.01h$Mpc$^{-1}$ there\nis ``leakage'' from large $k$. At $k = 0.02h$Mpc$^{-1}$ this leakage is no longer evident, and\nso we choose $k_{min} = 0.015h$Mpc$^{-1}$ as the largest-scales we can accurately probe.}\n\\end{figure*}\n\n\\begin{figure*}\n\\plotone{f5.eps}\n\\caption[]{In the {\\bf top} panel we show $P_a(k)$ calculated using the three different number density\nfunctions used in Figure 1. Circles are for the step-function, stars are for the power-law fit,\nand squares are for the number function fit. The open circles include all $R \\ge 1$ ACO clusters\nwhile the filled symbols are for ACO clusters with $N_{gal} \\ge 56$. We use a window function\nthat models the real data (e.g. in density and extinction). The errors are estimates based\non scaling the errors from $P_b(k)$.\nIn the {\\bf middle} panel we show $P_b(k)$ using the same symbols as the top panel. We use random\ncatalogs with the same extinction and density distribution as the real data. The error bars\nare determined using the FKP method as mentioned in the text.\nIn the {\\bf bottom} panel, we plot $P_a(k)$ (circles) and $P_b(k)$ (squares). The hatched region\nindicates where our window function prevents an accurate determination of $P(k)$.\n}\n\\end{figure*}\n\n\\begin{figure*}\n\\plotone{f6.eps}\n\\caption[]{We compare $P_b(k)$ for Abell/ACO clusters calculated in this work (solid circles) to the smaller\nAbell/ACO sample used by Retzlaff {\\it et al.} (1998) (triangles) and the APM cluster sample power spectrum\ncalculated by Tadros {\\it et al.} (1998) (stars). The open circles are $R \\ge 1$ Abell/ACO clusters within \n$z=0.10$ (north and south). \n}\n\\end{figure*}\n\n\\begin{figure*}\n\\plotone{f7.eps}\n\\caption[]{\nWe compare $P_b(k)$ to model liner power spectra for a flat CDM \n($\\Omega_b=0.02, \\Omega_{CDM}=0.98$ with $H_0 = 100 $km s$^{-1}$ Mpc$^{-1}$ {\\bf dashed-dot}),\nmixed dark matter\n($\\Omega_b=0.05, \\Omega_{CDM} = 0.65$ and $\\Omega_{\\nu} = 0.3$ with $H_0=50 $km s$^{-1}$ Mpc$^{-1}$\n{\\bf dashed-dot-dot}),\nopen ($\\Omega_b=0.02, \\Omega_{CDM}=0.18$ with $H_0 = 100 $km s$^{-1}$ Mpc$^{-1}$ {\\bf dashed}),\nand lambda \n($\\Omega_b=0.02, \\Omega_{CDM} = 0.18, \\Omega_{vacuum}=0.80$ {\\bf solid}) CDM models. }\n\\end{figure*}\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002295.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[(Abell 1958)]{abe58} Abell, G. O. 1958, \\apjsupp, ~ 3, 211\n\\bibitem[(Abell et al. 1989)]{aco89} Abell, G. O.,\n Corwin, H. G., Olowin, R. P. 1989, \\apjsupp, ~70, 1 (ACO)\n\\bibitem[(Bahcall 1997)]{bah97} Bahcall, N. 1997, in {\\it Critical Dialogues in Cosmology}, ed. N. Turok,\n World Scientific, Singapore, 221\n\\bibitem[(Batuski {\\it et al.} 1999)]{bat99} Batuski, D.J., Miller, C.J., Slinglend, K.A.,\n Balkowski, C., Maurogordato, S., Cayatte, V., Felenbok, P., and Olowin, R. 1999, \\apj, 520, 491\n\\bibitem[(Broadhurst {\\it et al.} 1990)]{brd90} Broadhurst, T.J., Ellis, R.S., Koo, D.C., \\& \n Szalay, A.S. 1990, Nature, 343, 726\n\\bibitem[(Bunn \\& White 1997)]{bun97} Bunn, E.F. \\& White, M. 1997, \\apj, 480, 6\n\\bibitem[(da Costa et al. 1994)]{dac94} da Costa, L.N., Vogeley, M.S., Geller, M.J., Huchra, J.P.,\n \\& Park, C. 1994, \\apj, 437, L1\n\\bibitem[(Dalton {\\it et al.} 1994)]{dal94} Dalton, G.B., Croft, R.A.C.,\n Efstathiou, G., Sutherland, W.J., Maddox, S.J., and Davis, M. 1994, \\mnras,\n 271, 47\n\\bibitem[(Efstathiou {\\it et al.} 1992)]{eft92} Efstathiou, G., Dalton, G.B.,\n Maddox, S.J., \\& Sutherland, W. 1992, \\mnras, ~257, 125\n\\bibitem[(Efstahiou and Moody 2000)]{eft00} Efstathiou, G. and Moody, S.J. 2000, preprint\n ~astro-ph/0010478\n\\bibitem[(Einasto {\\it et al.} 1997)]{ein97} Einasto, J., Einasto, M., Gottl\\\"{o}ber, S.,\n M\\\"{u}ller, V., Saar, V., Starobinsky, A.A., Tago, E., Tucker, D., Andernach, H., \\& \n Frisch, P. 1997, Nature, 385, 139 (E97)\n\\bibitem[(Einasto {\\it et al.} 1999)]{ein99} Einasto, J., Einasto, M., Tago, E.,\n Starobinsky, A.A., Atrio-Barandela, F.,\n M\\\"{u}ller, V., Knebe, A, \\& Cen, R. 1999, \\apj, 519, 469 (E99) \n Frisch, P. 1997, Nature, 385, 139 (E97)\n\\bibitem[(Einasto {\\it et al.} 1994)]{ein94} Einasto, M., Einasto, J., Tago, E., Dalton, G.B.,\n \\& Andernach, H. 1994, \\mnras, 269, 301\n\\bibitem[(Eisenstein and Hu 1998)]{eis98} Eisenstein, D.J., Hu, W., Silk, J., and Szalay, A.S.\n 1998,\\apj, 494, L1\n\\bibitem[(Feldman, Kaiser, \\& Peacock 1994)]{fel94} Feldman, H.A., Kaiser, N. \\& Peacock, J.A.\n 1994, \\apj, 426, 23 (FKP)\n\\bibitem[(Fisher {\\it et al.} 1993)]{fis93} Fisher, K.B., Davis, M., Strauss, M.A.,\n Yahil, A., \\& Huchra, J.P. 1993, \\apj, 402, 42\n\\bibitem[(Gatza\\~{n}aga, \\& Baugh)]{gat98} Gatza\\~{n}aga, E. \\& Baugh, C.M. 1998, \\mnras, 294, 229\n\\bibitem[Geller \\& Huchra(1989)]{1989Sci...246..897G} Geller, M.\\ J.\\ \\& \nHuchra, J.\\ P.\\ 1989, Science, 246, 897 \n\\bibitem[(Gramann \\& Suhhonenko 1999)]{suh99} Gramann, M. \\& Suhhonenko, I. 1999, \\apj, 519, 433\n\\bibitem[(Hamilton and Tegmark 2000)]{hal00} Hamilton, A.J.S. and Tegmark, M. 2000, submitted to \\mnras,\nastroph/0008392\n\\bibitem[(Guzzo 1999)]{guz99} Guzzo, L. 1999, presented at {\\it The Second Coral Sea Cosmology Conference}\n\\bibitem[(Hoyle et al. 1999)]{hoy99} Hoyle, F., Baugh, C. M., Shanks, T., Ratcliffe, A. 1999, \\mnras,\n 309, 659\n\\bibitem[(Jing and Valdarnini 1993)]{jin93} Jing, Y.P. and Valdarnini, R. 1993, \\apj, 406,6\n\\bibitem[(Kaiser 1994)]{kai94} Kaiser, N. 1986, \\mnras, 222,323\n\\bibitem[(Katgert {\\it et al.} 1996)]{kat96} Katgert,P., Mazure, A., Perea, J.,\n den Hartog, R., Moles, M., Le Fevre, O., Dubath, P., Focardi, P., Rhee, G.,\n Jones, B., Escalera, E., Biviano, A., Gerbal, D., Giuricin, G. 1996,\n A \\& A, ~310, 8\n\\bibitem[(Landy {\\it et al.} 1996)]{lan96} Landy, S.D., Shectman, S.A., Lin, H., Kirshner, R.P.,\n Oemler, A.A., \\& Tucker, D. 1996, \\apj, 456, L1\n\\bibitem[(Lin {\\it et al.} 1996)]{lin96} Lin, H., Kirshner, R.P., Shectman, S.A., Landy, S.D.,\n Oemler, A., Tucker, D.L., \\& Schecter, P.L. 1996, \\apj 471, 617 (LCRS)\n\\bibitem[(Miller {\\it et al.} 1999a)]{mi99a} Miller, C.J., Batuski, D.J., Slinglend, K.A., \\&\n Hill, J.M. 1999a, \\apj, 523, 492\n\\bibitem[(Miller {\\it et al.} 1999b)]{mi99b} Miller, C.J., Ledlow, M.J. \\& Batuski, D.J. 1999b,\n \\mnras, submitted\n\\bibitem[(Miller {\\it et al.} 1999c)]{mic99} Miller, C.J., Krughoff, K.S., Slinglend, K.A.,\n Batuski, D.J., \\& Hill, J.M. 1999c (in preparation)\n\\bibitem[(Nichol \\& Connolly 1996)]{nic96} Nichol, R.C. \\& Connolly, A.J. 1996, \\mnras, 279, 521\n\\bibitem[(Park et al. 1994)]{par94} Park, C., Vogeley, M.S., Geller, M.J., \\& Huchra, J.P. 1994,\\apj,431,561\n\\bibitem[(Peacock 1997)]{pea97} Peacock, J.A. 1997, \\mnras, 285, 885\n\\bibitem[(Peacock \\& Dodds 1994)]{pea94} Peacock, J.A. \\& Dodds, S.J. 1994, \\mnras, 267, 1020\n\\bibitem[(Peacock and Nicholson 1991)]{pea91} Peacock, J.A. \\& Nicholson, D. 1991, \\mnras, 253, 307\n\\bibitem[(Peacock \\& West 1992)]{pew92} Peacock, J.A. \\& West, M.J. 1992,\n \\mnras, 259, 494\n\\bibitem[(Postman et al. 1992)]{pos92} Postman, M.,\n Huchra, J. P., \\& Geller, M. J. 1992, \\apj, ~384, 404\n\\bibitem[(Retzlaff {\\it et al.} 1998)]{ret98} Retzlaff, J., Borgani, S., Gottl\\\"{o}ber, S., \n Klypin, A., \\& M\\\"{u}ller, V. 1998, NewA, 3, 631\n\\bibitem[(Schlegel {\\it et al.} 1998)]{sch98} Schlegel, D.J., Finkbeiner, D.P., \\& Davis, M.\n 1998, \\apj, 500, 525\n\\bibitem[(Schramm \\& Turner 1998)]{sch98} Schramm, D.N. \\& Turner, M.S. 1998, Rev. Mod. Phys., 70, 303\n\\bibitem[(Seljak \\& Zaldarriaga 1996)]{sel96} Seljak, U. \\& Zaldarriaga, M. 1996, \\apj, 469, 437\n\\bibitem[(Slinglend {\\it et al.} 1998)]{sli98} Slinglend, K.A., Batuski, D.J,\n Miller, C.M., Haase. S., Michaud, K., \\& Hill, J.M. 1998, \\apjsupp, 115,1\n\\bibitem[(Stark {\\it et al.} 1992)]{sta92} Stark, A.A., Gammie, C.F., Wilson, R.W.,\n Bally, J.L., Linke, R.A., Heiles, C., \\& Hurwitz, M. 1992, \\apjsupp, 79, 77\n\\bibitem[(Sutherland 1988)]{sut88} Sutherland, W. 1988, \\mnras, ~234, 159\n\\bibitem[(Tadros \\& Efstathiou 1996)]{tad96} Tadros, H., \\& Efstathiou, G. 1996, \n \\mnras, 282, 1381 (TE96)\n\\bibitem[(Tadros, Efstathiou \\& Dalton 1998)]{tad98} Tadros, H.,Efstathiou, G., \\& Dalton, G.\n 1998, \\mnras, 296, 995 (TED98)\n\\bibitem[(Tegmark 1995)]{teg95} Tegmark, M. 1995, \\apj, 455, 429\n\\bibitem[(Vogeley 1998)]{vog98} Vogeley, M.S. 1998, in {\\it The Evolving Universe}, \n Kluwer Academic Publishers, p. 395\n\\bibitem[(Vogeley et al. 1992)]{vog92} Vogeley, M.S., Park, C., Geller, M.J., \\& Huchra, J.P. 1992,\n \\apj, 391, L5\n\\bibitem[(Voges, {\\rm et al.} 1999)]{vog99} Voges, W., Ledlow, M.J., Owen, F.N.,\n \\& Burns J.O. 1999, \\aj, submitted \n\n\n\n\\end{thebibliography}"
}
] |
astro-ph0002296
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Primordial Nucleosynthesis For The New Millennium
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[
{
"author": "G. Steigman"
}
] |
The physics of the standard hot big bang cosmology ensures that the early Universe was a primordial nuclear reactor, synthesizing the light nuclides (D, \3he, \4he, and \7li) in the first 20 minutes of its evolution. After an overview of nucleosynthesis in the standard model (SBBN), the primordial abundance yields will be presented, followed by a status report (intended to stimulate further discussion during this symposium) on the progress along the road from observational data to inferred primordial abundances. Theory will be confronted with observations to assess the consistency of SBBN and to constrain cosmology and particle physics. Some of the issues/problems key to SBBN in the new millenium will be highlighted, along with a wish list to challenge theorists and observers alike.
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[
{
"name": "paper.tex",
"string": "%\\documentstyle[11pt,newpasp,twoside]{article}\n\\documentstyle[11pt,newpasp,twoside,epsf]{article}\n%\\documentstyle[12pt]{article}\n%\\input terry.tex\n\\markboth{G. Steigman}{APS Conf. Ser. Style}\n\\pagestyle{myheadings}\n\\nofiles\n\n% Some definitions I use in these instructions.\n\n\\def\\emphasize#1{{\\sl#1\\/}}\n\\def\\arg#1{{\\it#1\\/}}\n\\let\\prog=\\arg\n\n\\def\\edcomment#1{\\iffalse\\marginpar{\\raggedright\\sl#1\\/}\\else\\relax\\fi}\n\\marginparwidth 1.25in\n\\marginparsep .125in\n\\marginparpush .25in\n\\reversemarginpar\n% definitions\n%\\def\\la{\\lower0.6ex\\vbox{\\hbox{$ \\buildrel{\\textstyle \n%<}\\over{\\sim}\\ $}}}\n%\\def\\ga{\\lower0.6ex\\vbox{\\hbox{$ \\buildrel{\\textstyle \n%>}\\over{\\sim}\\ $}}}\n\\def\\sun{${\\,_\\odot}$}\n\\def\\msun{${\\,M_\\odot}$}\n\\def\\hii{H\\thinspace{$\\scriptstyle{\\rm II}$}~}\n\\def\\Oii{O\\thinspace{$\\scriptstyle{\\rm II}$}}\n\\def\\Oiii{O\\thinspace{$\\scriptstyle{\\rm III}$}}\n\\def\\Nii{N\\thinspace{$\\scriptstyle{\\rm II}$}}\n\\def\\Sii{S\\thinspace{$\\scriptstyle{\\rm II}$}}\n\\def\\etal{{\\it et al.}~}\n\\def\\ie{{\\it i.e.},~}\n\\def\\eg{{\\it e.g.},~}\n\\def\\3he{$^3$He}\n\\def\\4he{$^4$He}\n\\def\\6li{$^6$Li}\n\\def\\7li{$^7$Li}\n\\def\\3h{$^3$H}\n\\def\\Yp{Y$_{\\rm P}$~}\n\n\n\\begin{document}\n\\title{Primordial Nucleosynthesis For The New Millennium}\n\\author{G. Steigman}\n\\affil{Departments of Physics and Astronomy; The Ohio State University; \n174 West 18th Avenue; Columbus, OH 43210 USA}\n\n\\begin{abstract}\nThe physics of the standard hot big bang cosmology ensures that the early \nUniverse was a primordial nuclear reactor, synthesizing the light nuclides \n(D, \\3he, \\4he, and \\7li) in the first 20 minutes of its evolution. After \nan overview of nucleosynthesis in the standard model (SBBN), the primordial \nabundance yields will be presented, followed by a status report (intended \nto stimulate further discussion during this symposium) on the progress along \nthe road from observational data to inferred primordial abundances. Theory \nwill be confronted with observations to assess the consistency of SBBN and \nto constrain cosmology and particle physics. Some of the issues/problems \nkey to SBBN in the new millenium will be highlighted, along with a wish \nlist to challenge theorists and observers alike.\n\\end{abstract}\n\n\\section{Introduction}\n\nAmong the quantitative, ``hard\" sciences, astronomy has traditionally \nbeen scorned, with particular disdain reserved for cosmology. No more. \nIn the decade of the nineties the combination of an avalanche of high \nquality observational data and theoretical advances driven by enhaced \ncomputer (and brain) power, have succeeded in transforming cosmology to \na precise science. In this introductory lecture to IAU Symposium 198 \non The Light Elements and Their Evolution it is my intent to describe \nprimordial nucleosynthesis in this precision era of cosmology and to \nhighlight the challenges, along with some goals, for the new millennium. \nAfter a brief review of the important physics during the era of primordial \nnucleosynthesis in the standard, hot big bang cosmological model (SBBN), \nI will present an overview of the predicted primordial abundances, \nemphasizing the generally very small theoretical uncertainties. These \nwill then be compared to the present best estimates (including their \nuncertainties) of the primordial abundances inferred from current \nobservational data. After assessing the consistency of SBBN, I will \nexplore what SBBN has to offer to Cosmology and to Particle Physics \nand, what Cosmology may teach us about SBBN. I will conclude with a \nsummary of the key issues/problems confronting SBBN and with a wish \nlist of topics I hope will be addressed during this meeting -- and beyond.\n\n\\section{An Early Universe Chronology}\n\nOur story begins when the Universe is a few tenths of a second old and \nthe temperature of the cosmic background radiation has dropped to a few \nMeV as the Universe expanded and cooled from its denser, hotter infancy. \nAt this time (and earlier) the density and average energy of colliding \nparticles is so high that even the weak interactions occur sufficiently \nrapidly to establish equilibrium. In particular, at this stage all flavors \nof neutrinos ($e, \\mu, \\tau$) are in thermal equilibrium with the cosmic \nbackground radiation (CBR) photons and with the copius electron-position \npairs present ($\\nu_{i} + \\bar{\\nu}_{i} \\leftrightarrow e^{+} + e^{-} \n\\leftrightarrow \\gamma + \\gamma$). However, as the Universe ages beyond \na few tenths of a second and the temperature drops below a few MeV, these \nweak interactions become too slow to keep pace with the rapid expansion of \nthe Universe and the neutrinos decouple from the CBR. The electron-type \nneutrinos continue to play a role in transforming neutrons into protons \nand, vice-versa ($p + e^{-} \\leftrightarrow n + \\nu_{e}$, $n + e^{+} \n\\leftrightarrow p + \\bar{\\nu}_{e}$, $n \\leftrightarrow p + e^{-} + \\bar\n{\\nu}_{e}$). As the temperature continues to drop, less massive protons \nare favored over the more massive neutrons and the $n/p$ ratio falls (roughly \nas $e^{-\\Delta m/kT}$, where $\\Delta m$ is the neutron -- proton mass \ndifference $\\sim 1.3$~MeV). After the temperature drops below 800~keV \nor so, when the Universe is a few seconds old, even these weak interactions \nbecome too slow to keep pace with the expansion and the neutron-to-proton \nratio ``freezes out\" (in fact, the ratio continues to decrease, albeit \nvery slowly). All the while, neutrons and protons have been colliding, \noccasionally forming deuterons ($p + n \\rightarrow D + \\gamma$). However, \nthe deuterons find themselves bathed in a high density background of \nenergetic CBR photons which quickly photodissociate them ($D + \\gamma \n\\rightarrow p + n$) before they can find a proton or neutron and form \nthe more tightly bound, less fragile, \\3h or \\3he nuclei. Since, as we \nshall see, there are roughly nine to ten orders of magnitude more CBR \nphotons than nucleons in the Universe, the deuteron ``stepping-stone\" to \nfurther nucleosynthesis is absent until the temperature drops sufficiently \nlow so that even in the high-energy tail of the black-body spectrum there \nare too few photons to prevent the deuteron from acting as a catalyst for \nprimordial nucleosynthesis. This critical temperature, which is weakly \n(logarithmically) dependent on the nucleon abundance (the nucleon-to-photon \nratio $\\eta$), is roughly 80~keV. Now, at last, when the Universe is a \nfew minutes old, Big Bang Nucleosynthesis finally commences. However, \nthe Universe was a fatally flawed nuclear reactor, cooling and diluting \nrapidly as it aged. When the Universe is some 10 -- 20 minutes old \n($\\sim 1000$~sec) and the temperature has dropped below 30~keV or so, \nthe coulomb barriers preventing nuclear reactions between charged nuclei \nand protons and among charged nuclei become insurmountable (in the short \namount of time available) and primordial nucleosynthesis comes to an \nabrupt end. In this all too brief but shining era there has been time \nto synthesize (in abundances comparable to those observed or observable) \nonly the lightest nuclides: D, \\3he, \\4he, and \\7li. In ``standard\" (a \nhomogeneous Universe, expanding isotropically with the particle content \nof the standard model of particle physics in which there are three flavors \nof light ($m \\ll $~MeV) or massless neutrinos) big bang nucleosynthesis \n(SBBN) the abundances (relative to protons $\\equiv$~ hydrogen) of these \nfour nuclides are determined by only one free parameter, the present epoch \nnucleon-to-photon ratio $\\eta$ ($\\eta \\equiv (n_{\\rm N}/n_{\\gamma})_{0}, \n~\\eta_{10} \\equiv 10^{10}\\eta$).\n\n\\section{SBBN-Predicted Primordial Abundances}\n\nOnce the deuterium photodissociation bottleneck is breached primordial \nnucleosynthesis begins in earnest, quickly burning D to \\3h, \\3he and \n\\4he. The higher the nucleon density, the faster D is destroyed. The \nsame is true of \\3h (which, if it survives will decay to \\3he) and \\3he. \nThus, the primordial abundances of D and \\3he are determined by the \ncompetition between the nuclear reaction rates and the universal expansion \nrate. The former rate depends on the overall density of the reactants -- \nthe nucleon density. Since all densities decrease as the Universe expands, \nit is convenient to quantify the nucleon density by specifying the {\\it \nratio} of the nucleon density to the photon density (measured after $e^{+}\ne^{-}$ annihilation which enhances the Universe's photon budget) $\\eta$. \nSince observations of the cosmic background radiation (CBR) temperature \n(T = 2.73~K) determine the present density of CBR photons, a knowledge \nof $\\eta$ is equivalent to a determination of the present mass density \nin nucleons (``baryons\" $\\equiv $~B). In terms of the density parameter\n$\\Omega_{\\rm B}$ (the ratio of the mass density to the critical mass density)\nand the present value of the Hubble parameter (H$_{0} \\equiv 100h$~km/s/Mpc),\n$\\eta_{10} = 273\\Omega_{\\rm B}h^{2}$. As $\\eta$ increases the surviving \nabundances of D and \\3he decrease; since the \\3he nucleus is more tightly \nbound than the deuteron, the decrease of the \\3he/H ratio with $\\eta$ is \nless rapid than that of D/H. \n\nIn contrast to D and \\3he, the primordial abundance of \\4he is not reaction \nrate limited since the nuclear reactions building helium-4 are so rapid \nthat virtually all neutrons available when BBN commences are incorporated \ninto \\4he. As a result the \\4he abundance, conventionally presented as \nthe mass fraction of all nucleons which are in \\4he, Y$_{\\rm P}$, is {\\it \nneutron limited}. Since the neutron-to-proton ratio is determined by the \ncompetition between the (charged-current) weak interactions which mediate \nthe transformation of neutrons into protons (and, vice-versa) and the \nuniversal expansion rate, \\Yp is sensitive to the universal expansion \nrate at the time the $n/p$ ratio ``freezes\" and when the deuterium \nphotodissociation barrier disappears. Since the universal expansion rate \nis controlled by the total energy density, \\Yp provides an important test \nof cosmology and of particle physics in the early Universe (Steigman, \nSchramm \\& Gunn 1977). It should be noted that \\Yp is not entirely \ninsensitive to the nucleon density since the higher $\\eta$, the earlier \nthe photodissociation barrier is overcome. At earlier times when the \ntemperature is higher, fewer neutrons have been transformed into protons \nand are available for incorporation into \\4he. As a result, \\Yp increases \nlogarithmically with $\\eta$.\n\nThere is no stable nucleus at mass-5 and this presents a gap in the \nroad to the synthesis of nuclei heavier than \\4he. In order to bridge \nthe gap nuclear reactions must occur among nuclei with two or more \nnucleons. But, the abundances of D, \\3h, and \\3he are small and the \ncoulomb barriers (especially between \\3he and \\4he and between \\4he \nand \\4he) suppress these reactions as the Universe expands and cools. \nAs a result, there is very little ``leakage\" to nuclei beyond mass-4; \nas a corollary, virtually all the \\4he formed, survives. The only \nheavier nucleus produced primordially in an abundance comparable to \nthat observed (or, even, observable with current technology) is \\7li, \nwhose BBN abundance is some 4 -- 5 orders of magnitude smaller than \nthat of D and \\3he. The absence of a stable nucleus at mass-8 provides \nanother gap preventing the production of astrophysically interesting \nabundances of any heavier nuclei.\n\nAs will become clear in our subsequent discussion, the ``interesting\" \nrange of $\\eta$ is $\\eta_{10} = 1 - 10$ ($\\Omega_{\\rm B}h^{2} = 0.004 \n- 0.037$), so we focus our discussion here on values of $\\eta$ in this \nrange. In the current precision era of BBN {\\it most} of the nuclear\nreactions relevant to the synthesis of the light elements have been\nmeasured to reasonable accuracy at energies directly comparable to the\nthermal energies at the time of primordial nucleosynthesis (\\eg see \nNollett, this volume). As a result, the theoretical uncertainties in\nthe BBN-predicted abundances are generally quite small. For $\\eta$ in\nthe above range, the 1$\\sigma$ uncertainties in D/H and \\3he/H vary\nfrom 8 -- 10\\%. Since \\4he is most sensitive to the very well measured\nweak interaction rates, the error in SBBN-predicted \\Yp is very small \n(0.2 -- 0.5\\% or, $\\sigma_{\\rm Y}$ = 0.0005 -- 0.0011). In contrast,\nlarger uncertainties, of order 12 -- 21\\%, afflict the predicted \nprimordial abundance of \\7li. \n\nSince this Symposium devoted much discussion to \\7li, and space-limitations\nhere prevent me from discussing all the light elements in detail, I will\nconcentrate in the following on the two key light elements, deuterium and \nhelium-4. In Figure 1 is shown the relation between the BBN-predicted\nabundances of D and \\4he. The band going from upper left to lower right\nrepresents the $\\pm 2\\sigma$ range of uncertainties in the primordial \nabundances ((D/H)$_{\\rm P}$ and Y$_{\\rm P}$). Low D/H (high $\\eta$) \ncorresponds to high \\Yp and high D/H (low $\\eta$) corresponds to low \nY$_{\\rm P}$. This anticorrelation will be very important when we \nconfront the predictions of SBBN with the observational data.\n\n\\section{Precise (Accurate?) Primordial Abundances}\n\nTo test SBBN and fully exploit the opportunities it offers to constrain\ncosmology (e.g., the baryon density) and particle physics (e.g., new\nparticles with weak or weaker-than-weak interactions) requires that \nobservational data be used to pin down the primordial abundances of the\nlight elements to precisions as good as (or, better than) those of the\nSBBN predictions. As we approach the new millennium there is good news\nalong with some bad news. The good news is that new detectors on ever\nlarger telescopes which cover the spectrum from radio to x-ray energies\nand beyond are providing very high quality data, leading to inferred\nabundances of high statistical accuracy. Furthermore, the abundances \nof the light elements are determined from observations which differ \nfrom element to element in the telescopes and techniques employed as \nwell as in the astrophysical sites explored. As a result, insidious \ncorrelated errors between and among the various element abundances are \nunlikely to be a problem. The good news is also responsible for the \nbad news. Since the statistical errors have become so small, systematic \nerrors now tend to dominate the uncertainties in the derived primordial \nabundances. As Bob Rood has said during this Symposium, estimating \nsystematic errors is an oxymoron. When a potential source of systematic \nerror is identified, observations can (and should) be designed to \neliminate or bound its contribution to the error budget. It is a \npointless and potentially misleading exercise to ``estimate\" the magnitude \nof unidentified systematic errors. In part to remind us that our precise \nabundance determinations may not be accurate, and in part to challenge \nour observational colleagues who have done such a magnificent job of \nreducing the statistical errors, I will try to focus on the potential \nsources of systematic uncertainty (when I can identify them) in the \nfollowing overview of the current observational status.\n\n\\subsection{Deuterium}\n\nAs J. Linsky (this volume) has reminded us, the deuterium abundance \nin the local interstellar medium (the local interstellar cloud: LIC) \nis known very accurately: (D/H)$_{\\rm LIC} = 1.5 \\pm 0.1 \\times \n10^{-5}$ (Linsky 1998). Since deuterium is only destroyed during \nthe evolution of the Galaxy (Epstein, Lattimer \\& Schramm 1976), the \nLIC abundance provides a lower bound to its primordial (pre-Galactic) \nvalue. This bound is strong enough to bound the nucleon density from \nabove ($\\eta_{10} \\la 10$; $\\Omega_{\\rm B}h^{2} \\la 0.04$), ensuring \nthat baryons cannot ``close\" the Universe ($\\Omega_{\\rm B} \\ll 1$), \nnor even dominate its present mass density ($\\Omega_{\\rm B} \\ll \n\\Omega_{\\rm M} \\approx 0.3 - 0.4$). Thus, local observations of \ndeuterium, combined with the {\\it assumption} of the correctness \nof SBBN (which we must test), already reaps great rewards: the \nmass-energy density of the Universe must be dominated by unseen \n(``dark\") non-baryonic matter. To go beyond (in the quest for the \nprimordial deuterium abundance) we must look for observing targets \nwhich are less evolved than the LIC. The presolar nebula is one such \nsite. From solar system observations of \\3he reported by G. Gloeckler \n(this volume), it is possible to infer the presolar deuterium abundance \n(Geiss \\& Reeves 1972; Geiss \\& Gloecker 1998): (D/H)$_{\\odot} = 1.9 \n\\pm 0.5 \\times 10^{-5}$. Although marginally higher than the LIC \nabundance, the larger errors prevent us from using this determination \nto improve on our previous bounds from the LIC. What this result does \nindicate is that there has been very little (if any) evolution in the \nD-abundance in the solar vicinity of the Galaxy in the last 4.5~Gyr. \nThis is consistent with a large class of Galactic chemical evolution \nmodels discussed by M. Tosi (this volume) which point to only a modest \noverall destruction of primordial deuterium by a factor of 2 -- 3 \n(Tosi et al. 1998). If this theoretical estimate is combined with the \nLIC abundance, we may estimate the primordial abundance: (D/H)$_{\\rm P} \n\\approx 2.6 - 5.1 \\times 10^{-5}$ ($\\sim 2\\sigma$). Although possibly \nmodel dependent, this estimate is in remarkable agreement with the \n2 -- 3 determinations of D/H in high-redshift, low-metallicity (hence \nvery nearly primordial) Ly-$\\alpha$ absorbers illuminated by background \nQSOs described by D. Tytler and S. Levshakov (this volume). The \ndata and analysis of Burles \\& Tytler (1998a,b: BT) suggests that \n(D/H)$_{\\rm P} = 2.9 - 4.0 \\times 10^{-5}$ ($\\sim 2\\sigma$). Notice \nthat the 1$\\sigma$ uncertainty in the observationally determined \nprimordial abundance, $\\sim 8$\\%, is impedance-matched to the \n$\\sim 8$\\% SBBN theoretical uncertainty cited earlier. However, \nlest we risk dislocating a shoulder while patting ourselves on the \nback at the triumph of such wonderful data, we should not ignore \nthe claim (Webb et al. 1997; Tytler et al. 1999) that the deuterium \nabundance in at least one Ly-$\\alpha$ absorption system may be much \nhigher. This is a reminder that while any determination of the \ndeuterium abundance anywhere in the Universe (LIC, solar system, \nLy-$\\alpha$ absorbers, etc.) provides a {\\it lower} bound to primordial \ndeuterium, finding an upper bound is more problematic. Indeed, in \nsome absorbing systems it may be impossible to distinguish D-absorption \nfrom that due to hydrogen in an interloping, low column density, \n``wrong-velocity\" system. Thus, the deuterium abundance inferred \nfrom absorption-line data may only provide an {\\it upper} bound to \nthe true deuterium abundance. Since the low-Z, high-z QSO absorbing \nsystems hold the greatest promise of revealing for us nearly unevolved, \nnearly primordial material, we look forward to the time when we can \nuse the {\\it distribution} of D/H values from more than a handful of \nsuch systems to eliminate -- statistically -- the uninvited contribution \nto the inferred primordial deuterium abundance from such interlopers. \nKeeping this in mind, in the following I will, nevertheless, use the \nBT determination when confronting theory with data. \n\n\\subsection{Helium-4}\n\nIn contrast to deuterium whose primordial abundance only decreases \nas pristine gas is incorporated into stars, stars burn hydrogen to \nhelium. As a result, the \\4he observed anywhere in the Universe is \nan unknown mixture of primordial and stellar-produced helium. It has \nlong been appreciated that to minimize the uncertain correction due \nto the debris of stellar evolution, it is best to concentrate on \\4he \nabundance determinations in the lowest-metallicity regions available. \nThese are the low-Z, extragalactic \\hii regions which have been discussed \nby K. Olive, T. Thuan, and S. M. Viegas at this Symposium (this volume). \nThe reader is urged to consult their papers for details; here I will \nmerely summarize my view of the current status of the determination \nof the primordial \\4he mass fraction Y$_{\\rm P}$. Several years ago \nOlive \\& Steigman (1995: OS) gathered together the data from the literature \n(dominated by the data assembled by Pagel et al. 1992). More recently \nOlive, Skillman \\& Steigman (1997: OSS) supplemented this with newer \ndata (some of it, unfortunately, still unpublished). Using a variety \nof approaches such as the regression of Y on the oxygen and/or nitrogen\nabundances and the weighted means of Y in the lowest metal-abundance \n\\hii regions, OSS concluded that \\Yp = 0.234 $\\pm$ 0.003 (note that, \nin contrast to the published (OSS) result, this value is obtained when \nthe NW region of IZw18, suspected of being contaminated by underlying \nstellar absorption, is excluded from the fit, and the newer data of \nIzotov, Thuan and collaborators is not included). Izotov, Thuan \nand their collaborators (Izotov, Thuan, \\& Lipovetsky 1994, 1997; \nIzotov \\& Thuan 1998(IT); Thuan, this volume) have been systematically \nobserving a mostly independent set of \\hii regions. Although, as \nwith the data employed in the OS and OSS studies, they ignore the \nionization correction ($icf \\equiv 1$), they take special care with \nthe correction for collisional excitation. IT (also Thuan, this volume) \nfind Y$_{\\rm P}({\\rm IT}) = 0.244~\\pm$ 0.002. Comparing the IT and OSS \nestimates of \\Yp we find that difference between the two \\Yp estimates \nfar exceeds the statistical errors, suggesting systematic differences \nin the acquisition and/or analysis of the data samples. In a recent \ndiscussion which attempted to account for these unidentified systematic \ndifferences, Olive, Steigman \\& Walker (1999: OSW) combined the 2$\\sigma$ \nranges for each determination to conclude: \\Yp = 0.238 $\\pm$ 0.005; at \nthe 2$\\sigma$ level, \\Yp $\\leq 0.248$. Note, that this is also the \n2$\\sigma$ upper bound to the IT data alone. Since, as we shall see \nshortly, it is the upper bound which is crucial to testing the consistency \nof SBBN, in the following we shall adopt the IT value (and error estimate) \nfor the primordial abundance of \\4he. \n\nRecently, Viegas, Gruenwald \\& Steigman (1999: VGS; see Viegas \\& \nGruenwald, this volume) have emphasized the importance of the ionization \ncorrection which has heretofore been ignored. VGS suggest that the \nIT helium abundance (Y$_{\\rm P}$) should be reduced by 0.003 to account \nfor unseen neutral hydrogen in regions where the helium is still ionized \nin \\hii regions ionized by young, hot, metal-poor stars. In subsequent \ncomparisons I shall explore the implications of adopting Y$_{\\rm P}({\\rm \nVGS}) = 0.241~\\pm$ 0.002.\n\n\\subsection{Helium-3 and Lithium-7}\n\nThe cosmic history of the two other light nuclides produced in\nastrophysically interesting abundances during SBBN, \\3he and \n\\7li, is considerably more complex than that of D or \\4he, which \nlimits their utility as probes of the consistency of SBBN. \\3he \nis destroyed in the hotter interiors of all stars, but some \\3he \ndoes survive in the cooler, outer layers. For lower mass stars \nthis \\3he survival layer increases and, indeed, newly synthesized \n\\3he is produced by incomplete hydrogen burning. The competition \nbetween destruction, survival, and synthesis complicates the Galactic\nhistory of the \\3he abundance. Nonetheless, since any deuterium \nincorporated into stars is first burned to \\3he, the apparent lack \nof enhanced \\3he (see Bania \\& Rood, this volume) argues against \na very large pre-Galactic abundance of deuterium (Steigman \\& Tosi \n1995). For further discussion of the evolution of \\3he see Bania \n\\& Rood (this volume).\n\nAs with \\3he, any \\7li incorporated into stars is quickly burned \naway. However, fusion and spallation reactions between cosmic ray \nnuclei and those in the interstellar medium are a potent source of \n\\7li (as well as of \\6li, $^7$Be, $^{10}$B, and $^{11}$B). It is\nalso likely that there are stellar sources of \\7li as indicated \nby the sample of lithium-rich red giants (V. Smith, this volume). \nSince the abundance of lithium in the solar system and in the \ninterstellar medium (``here and now\") greatly exceeds that in the \nvery metal-poor halo stars (T. Beers \\& S. Ryan, this volume), the \nlatter likely provide the closest approach to a nearly primordial \nsample. Since a significant fraction of this Symposium is devoted \nto lithium, I will defer here to those other discussions except to \ncomment that, within the theoretical and observational uncertainties, \nthe primordial abundances inferred from the observational data are \nconsistent with SBBN constrained by the confrontation with D and \\4he.\n\n\\section{Confrontation Of SBBN With Data}\n\nAlthough SBBN does lead to the prediction of the abundances of D, \n\\3he, \\4he, and \\7li, the currently best-constrained primordial \nabundances are those of deuterium and helium-4 which we are \nconcentrating on in this status report. For each value of $\\eta$, \nSBBN predicts a pair of (D/H)$_{\\rm P}$ and \\Yp values. Therefore, \nin SBBN there is a unique connection between (D/H)$_{\\rm P}$ and \n\\Yp which, allowing for the theoretical uncertainties discussed \nabove, is shown as the band (solid lines) in Figure 1 going from \nthe upper left to the lower right (2$\\sigma$ uncertainties). Note \nthat high-helium correlates with low-deuterium and, vice-versa. \nAlso shown as the dotted ellipse in Figure 1 is the contour of the \n(independent) 2$\\sigma$ uncertainties in the BT deuterium abundance \nand the IT helium-4 mass fraction. \n\n\\begin{figure}\n\\vspace{1.in}\n%\\plotone{fig1.eps}\n\\plotfiddle{fig1.eps}{1in}{0}{30}{30}{-100}{-50}\n\\caption{The SBBN-predicted \\4he mass fraction \\Yp as a function \nof the SBBN-predicted primordial deuterium-to-hydrogen ratio D/H \nis shown (at the $\\pm 2\\sigma$ level) by the solid lines. The \ndotted ellipse is the 95\\% contour of the BT deuterium abundance \nand the IT \\4he mass fraction (see the text).}\n\\end{figure}\n\nAlthough the overlap between theory and data is not complete, \nFigure 1 shows that, at the $\\sim 2\\sigma$ level, the predictions \nof SBBN are consistent with current observational data. This is \na dramatic success for the standard hot, big bang cosmological \nmodel. Of course it is not at all surprising that some value \nof $\\eta$ may be found to provide consistency with the inferred \nprimordial deuterium abundance. But there was no guarantee at \nall that the helium-4 abundance corresponding to this choice would \nbear any relation to its inferred primordial value. Consistency \nwith the BT D-abundance limits the nucleon abundance to the range \n(2$\\sigma$) $\\eta_{10} = 4.4 - 5.9$ or, $\\Omega_{\\rm B}h^{2} = \n0.016 - 0.022$. For $\\eta$ in this range there is consistency, \nwithin the theoretical and observational uncertainties, between \nthe SBBN-predicted and observationally inferred primordial abundances \nof \\3he and \\7li as well. Four for the price of one! There is, \nof course, one more test -- and opportunity -- offered by this \nresult. This SBBN-inferred nucleon abundance must also be \nconsistent with present epoch estimates of the baryon density. \nIndeed, the SBBN-determined value of $\\Omega_{\\rm B}$ is {\\it \nlarger} than estimates (Persic \\& Salucci 1992) of the ``luminous\" \nmatter in the Universe suggesting that the majority of baryons \nare ``dark\". This is good ($\\Omega_{\\rm B} > \\Omega_{\\rm LUM}$); \nthe opposite would have been a disaster. This early-Universe \nestimate of the baryon density is in good agreement with that \ninferred from the X-ray cluster baryon fraction (Steigman, Hata \n\\& Felten 1999) and with the independent estimate from the \nLy-$\\alpha$ forest (Weinberg et al. 1997) discussed below.\n\n\\subsection{What BBN May Do For Cosmology}\n\nX-ray clusters likely provide a ``fair\" sample of the universal\nbaryon {\\it fraction} $f_{\\rm B}$ (White et al. 1993; Steigman \n\\& Felten 1995; Evrard, Metzler, \\& Navarro 1996) which, when \ncombined with the SBBN-inferred baryon density $\\Omega_{\\rm B}$, \nleads to a ``clean\" prediction, independent of detailed cosmological \nmodels, of the overall matter density $\\Omega_{\\rm M}$. If the \nresults presented here are combined with the determination of \n$f_{\\rm B}$ from Evrard (1997), and with a Hubble parameter $h \n= 0.70 \\pm 0.07$ (Mould et al. 1999), we predict $\\Omega_{\\rm M} \n= 0.35 \\pm 0.08$, in excellent agreement with several other recent, \nindependent determinations. For example, a lower bound to the cosmic \nbaryon density follows from the requirement that the high-redshift \nintergalactic medium contain enough neutral hydrogen to produce\nthe Ly-$\\alpha$ absorption observed in quasar spectra. According\nto Weinberg et al. (1997), depending on estimates of the quasar\nUV background intensity, this lower bound corresponds to $\\eta_{10}\n\\ga 3.4 - 4.9$, in excellent agreement with the SBBN prediction\nbased on the BT deuterium determination. Note that this lower\nbound from the Ly-$\\alpha$ absorption forbids (in the context of\nSBBN) the primordial deuterium abundance to be any larger than\n$\\sim 8 \\times 10^{-5}$, largely excluding the one surviving\nclaim of high D (Webb et al. 1997).\n\nIndeed, if the SBBN results are combined with the magnitude-redshift \ndata from surveys of high-redshift Type Ia supernovae (Garnavich et \nal. 1998; Perlmutter et al. 1999) which bound a linear combination \nof $\\Omega_{\\rm M}$ and the cosmological constant $\\Omega_{\\Lambda} \n\\equiv \\Lambda/3$H$_{0}^{2}$, we may also constrain the cosmological \nconstant ($\\Omega_{\\Lambda} = 0.80 \\pm 0.20$), the curvature \n($\\Omega_{k} \\equiv 1 - (\\Omega_{\\rm M} + \\Omega_{\\Lambda}) = \n-0.15 \\pm 0.25$), and the deceleration parameter ($q_{0} = \n\\Omega_{\\rm M}/2 - \\Omega_{\\Lambda} = -0.62 \\pm 0.18$).\n\n\\subsection{What Cosmology May Do For BBN}\n\nAs we have just seen, the SBBN-determined baryon density is \nconsistent with that determined or constrained by observations \nof the Universe during its present or recent evolution. We \nmay turn the argument around and ask what baryon density is \nsuggested by non-BBN contraints, and then compare the light \nelement abundances which correspond to that density with those \ninferred from the observational data. As an exercise of this \nsort, suppose (for reasons of ``naturalness\" or inflation) that \nthe Universe is ``flat\": $\\Omega_{\\rm M} + \\Omega_{\\Lambda} \n= 1$. When combined with the SN Ia magnitude-redshift data \n(Perlmutter et al. 1999), this suggests that $\\Omega_{\\rm M} \n= 0.29 \\pm 0.07$ (and $\\Omega_{\\Lambda} = 0.71 \\pm 0.07$).\nNow, if this mass density estimate ($\\Omega_{\\rm M}$) is \ncombined with with the X-ray determined cluster baryon fraction \n$f_{\\rm B}$ (Evrard 1997; Steigman, Hata \\& Felten 1999), \nthe resulting nucleon abundance is $\\eta_{10} = 4.5 \\pm 1.5$. \nAlthough the uncertainty is large, it is reassuring that this \nnon-BBN estimate has significant overlap with our SBBN estimate.\nIndeed, for the baryon density in this range SBBN predicts:\n(D/H)$_{\\rm P} = 4.3 \\pm 2.3 \\times 10^{-5}$ and Y$_{\\rm P} \n= 0.245 \\pm 0.004$. \n\n\\subsection{What SBBN May Do For Particle Physics}\n\nThe expansion rate of the early Universe is controlled by the\ndensity of the relativistic particles present. In the standard\nmodel at the time of BBN these are: photons, electron-positron\npairs (when T $ \\ga m_{e}$) and three ``flavors\" of neutrinos\n($\\nu_{e}$, $\\nu_{\\mu}$, $\\nu_{\\tau}$) which, if ``light\" ($m_{\\nu}\n\\ll 1$~MeV), are relativistic at BBN even if one or more of them\nmay contribute to the present density of non-relativistic (``hot\")\ndark matter. If ``new\" particles were to contribute to the energy \ndensity at BBN, the increase in the density would result in an\nincrease in the universal expansion rate, leaving less time for\nneutrons to transform into protons. The higher $n/p$ ratio at BBN\nwould result in the production of more primordial \\4he (Steigman,\nSchramm \\& Gunn 1977). It is convenient (and conventional) to\ncharacterize such additional contributions to the energy density\nby comparing their effects to that of an additional ``flavor\" of\n(light) neutrino: $\\Delta\\rho \\equiv \\Delta N_{\\nu}\\rho_{\\nu}$.\nFor $\\Delta N_{\\nu}$ small, $\\Delta $Y $ \\approx 0.01\\Delta N_{\\nu}$.\nNotice in Figure 1 that the predicted \\4he abundance is a little\nhigh for perfect overlap with the observations. If $\\Delta N_{\\nu}$ \nwere $ < 0$, (N$_{\\nu} \\approx 2.8$) the overlap would improve (e.g., \nHata et al. 1995), while if $\\Delta N_{\\nu} > 0$, the overlap would \nbe reduced until it disappeared. This is illustrated in Figure 2 \nwhich shows the Y versus D/H BBN band that would result if $\\Delta \nN_{\\nu} = 0.2$ (i.e., $N_{\\nu} = 3.2$, in contrast to the SBBN value \nof 3.0). Notice that due to the faster expansion, more deuterium \nsurvives being burnt away so that, for fixed $\\eta$, the D-abundance \nalso increases; however since D/H is a much more sensitive function \nof $\\eta$, this has a much smaller effect on the Y versus D/H relation \nthan does the increase in Y.\n\n\\begin{figure}\n\\vspace{1.in}\n%\\plotone{fig2.eps}\n\\plotfiddle{fig2.eps}{1in}{0}{30}{30}{-100}{-50}\n\\caption{As Figure 1, but for $N_{\\nu} = 3.2$}\n\\end{figure}\n\n\\section{Conclusions And Outlook}\n\nThe study of the early evolution of the Universe and, in\nparticular primordial nucleosynthesis, has truly entered\nthe precision era of cosmology. Precise abundances of the \nlight nuclides are predicted and inferred from observations\nand the two are -- apparently -- in excellent agreement.\nAs pleased as we may be at this success, it behooves us\nto avoid the temptation to rest on our laurels and to\ntest this consistency ever more carefully. To this end,\nit doesn't take much contemplation to identify several\nclouds looming on the horizon. What follows is my\npersonal list of some problems/issues I would like \nto see addressed at this Symposium and beyond.\n\n\\subsection{Problems/Issues}\n\nFirst consider deuterium. On the one hand, any determination\nof the D/H ratio anywhere, anytime provides a {\\it lower}\nbound to the primordial abundance. On the other hand, since\n``wrong\" velocity hydrogen can masquerade as deuterium, any\nobservation of ``deuterium\" is really an {\\it upper} bound \nto its true abundance. More data tracking the velocity\nstructure of the absorbing features used to identify D \nand H and exploring variations in D/H in material with \nsimilar histories will be very valuable. More data at \nhigh-redshift and low-metallicity will be very valuable. \nAfter all, at present we are drawing profound conclusions \non the basis of only two such systems.\n\nMuch remains to be done concerning the primordial abundance\nof \\4he. For the most part, the \\hii regions from which\nthe helium abundance is inferred have been modelled as\nhomogeneous spheres or plane-parallel slabs. A glance at \nthe beautiful HST images of real \\hii regions reveals that \nthey are anything but such idealizations. What are the effects \nof temperature and/or density inhomogeneities, and how large \nmay they be? What of underlying stellar absorption which, if \npresent but neglected, would lead to an {\\it under}estimate \nof the helium abundance. And, what of the usually neglected\nionization correction for neutral hydrogen and helium (Viegas, \nGruenwald \\& Steigman 1999; see Viegas \\& Gruenwald, this \nvolume)? Considering this latter work, where models of \\hii \nregions ionized by realistic spectra of young star clusters \nwere used in a reanalysis of the IT data, a {\\it reduction} \nin \\Yp of order 0.003 was suggested. A comparison with Figure \n1 shows that if \\Yp were reduced by this amount, the overlap \nbetween theory and data would, in fact, disappear.\n\n\\subsection{Wish List}\n\nGiven the setting of this Symposium (Natal) and the proximity\nto the Christmas season, I'd like to conclude with my personal\nwish list. To avoid being greedy, I'll only ask for two gifts.\n\nA half-dozen or so observations of deuterium in high-z, low-Z \nsystems along the lines-of-sight to distant quasars, with D/H \ndetermined in each (on average) to 10\\% or better. With such \na gift, I could determine $\\eta$ to better than 4\\%, predict\n\\Yp to $\\la 0.0007$, and constrain $\\Delta N_{\\nu}$ to an \nuncertainty less than $\\pm$~0.05. I'd be a very happy \ncosmologist indeed.\n\nMy second wish is for \\4he measured to 3\\% accuracy (or better)\nin each of about a dozen low-metallicity, extragalactic \\hii \nregions, with care taken to address the several problems outlined \nabove. With such data, \\Yp could be fixed to better than the \ncurrent level of $\\pm 0.002$, permitting \\4he to be used as a \nbaryometer ($\\Delta\\eta/\\eta~\\la 20\\%$).\n\n%\\end{document} \n\n\\acknowledgments\n\nMuch of what I know about this subject I have learned from my \ncollaborators and I would be remiss if I failed to thank them \nfor their contributions. In particular, I wish to acknowledge\nR. Gruenwald, K. Olive, E. Skillman, M. Tosi, and S. M. Viegas \nand, of course, my late friend Dave Schramm. L. da Silva, M. \nSpite and the Scientific and Local Organizing committees deserve \ngreat credit for their efficient organization of a very enjoyable \nand successful meeting. In part, this work is supported at The \nOhio State University by DOE grant DE--AC02--76ER--01545. \n\n\\begin{references}\n\n\\reference Burles, S., \\& Tytler, D. 1998a, \\apj, 499, 699 (BT)\n\n\\reference Burles, S., \\& Tytler, D. 1998b, \\apj, 507, 732 (BT)\n\n\\reference Epstein, R. Lattimer, J., \\& Schramm, D. N. 1976, \nNature, 263, 198\n\n\\reference Evrard, A. E. 1997, \\mnras, 292, 289 \n\n\\reference Evrard, A. E., Metzler, C. A., \\& Navarro, J. F. 1996,\n\\apj, 469, 494\n\n\\reference Garnavich, P. M. et al. 1998, \\apj, 509, 74\n \n\\reference Geiss, J., \\& Reeves, H. 1972, \\aap, 18, 126\n\n\\reference Geiss, J., \\& Gloeckler, G. 1998, \\ssr, 84, 239\n\n\\reference Hata, N., Scherrer, R. J., Steigman, G., Thomas, D., \nWalker, T. P., Bludman, S., \\& Langacker P. 1995, \\prl, 75, 3977\n\n\\reference Linsky, J. L. 1998, \\ssr, 84, 285\n \n\\reference Izotov, Y. I., Thuan, T. X., \\& Lipovetsky, V. A. 1994, \n\\apj, 435, 647\n\n\\reference Izotov, Y. I., Thuan, T. X., \\& Lipovetsky, V. A. 1997, \n\\apjs, 108, 1\n\n\\reference Izotov, Y. I., \\& Thuan, T. X. 1998, \\apj, 500, 188 (IT)\n\n\\reference Mould, J. R. et al. 1999, \\apj, submitted (astro-ph/9909260)\n\n\\reference Olive, K. A., Skillman, E., \\& Steigman, G. 1997, \\apj, 483, \n788 (OSS)\n\n\\reference Olive, K. A., \\&, Steigman, G. 1995, \\apjs, 97, 49 (OS)\n\n\\reference Olive, K. A., \\&, Steigman, G., \\& Walker, T. P. 1999, Physics\nReports, in press (astro-ph/9905320) (OSW)\n\n\\reference Pagel, B. E. J., Simonson, E. A., Terlevich, R. J. \\& Edmunds, \nM. 1992, \\mnras, 255, 325\n\n\\reference Perlmutter, S. et al. 1999, \\apj, 517, 565 \n\n\\reference Persic, M., \\& Salucci, P. 1992, \\mnras, 258, 14P\n\n\\reference Steigman, G., Schramm, D. N., \\& Gunn, J. E. 1977, Phys. Lett.,\nB66, 202\n\n\\reference Steigman, G., \\& Felten, J. E. 1995, \\ssr, 74, 245\n\n\\reference Steigman, G., Hata, N., \\& Felten, J. E. 1999, \\apj, 510, 564\n\n\\reference Steigman, G., \\& Tosi, M. 1995, \\apj, 453, 173\n\n\\reference Tosi, M., Steigman, G., Matteucci, F., \\& Chiappini, C. 1998,\n\\apj, 498, 226\n\n\\reference Tytler, D., Burles, S., Lu, L., Fan, X. M., Wolfe, A., \\&\nSavage, B. D. 1999, \\aj, 117, 63\n \n\\reference Viegas, S.M., Gruenwald, R., \\& Steigman, G. 1999, \\apj, 532 \n(in press, March 20, 2000; astro-ph/9909213)\n\n%\\reference Vilchez, J.M. \\& Pagel, B.E.J. 1988, MNRAS, 231, 257\n\n\\reference Webb, J. K., Carswell, R. F., Lanzetta, K. M., Ferlet, R., \nLemoine, M., Vidal-Madjar, A., \\& Bowen, D. V. 1997, Nature, 388, 250\n\n\\reference Weinberg, D. H., Miralda-Escud$\\acute{\\rm e}$, J., Hernquist, \nL., \\& Katz, N. 1997, \\apj 490, 564\n\n\\reference White, S. D. M., Navarro, J. F., Evrard, A. E., \\& Frenk,\nC. S. 1993, Nature, 366, 429\n\n\\end{references}\n\n\n\\end{document}\n\n\n\n"
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astro-ph0002297
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A Sample of 669 Ultra Steep Spectrum Radio Sources to Find High Redshift Radio Galaxies \thanks{Tables A.1, A.2 and A.3 are also and appendices B, C and D are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html }
|
[
{
"author": "Carlos De Breuck \\inst{1,2}"
},
{
"author": "Wil van Breugel \\inst{2}"
},
{
"author": "Huub J. A. R\\\"ottgering \\inst{1}"
},
{
"author": "George Miley \\inst{1}"
}
] |
Since radio sources with Ultra Steep Spectra (USS; $\alpha \lesssim -1.30; S \propto \nu^{\alpha}$) are efficient tracers of high redshift radio galaxies (HzRGs), we have defined three samples of such USS sources using the recently completed WENSS, TEXAS, MRC, NVSS and PMN radio-surveys. Our combined sample contains 669 sources with $S_{1400} > 10$~mJy and covers virtually the entire sky outside the Galactic plane ($|b|>15$\arcdeg). For our 2 largest samples, covering $\delta > -35\arcdeg$, we selected only sources with angular sizes $\Theta < 1\arcmin$. For 410 sources, we present radio-maps with 0\farcs3 to $\sim$5\arcsec\ resolution from VLA and ATCA observations or from the FIRST survey, which allows the optical identification of these radio sources. Comparison with spectrally unbiased samples at similar flux density levels, shows that our spectral index, flux density, and angular size selections do not affect the angular size distribution of the sample, but do avoid significant contributions by faint foreground spiral galaxies. We find that the spectral index distribution of 143,000 sources from the WENSS and NVSS consists of a steep spectrum galaxy and a flat spectrum quasar population, with the relative contribution of flat spectrum sources doubling from $S_{1400}>0.1$~Jy to $S_{1400}>2.5$~Jy. The identification fraction of our USS sources on the POSS ($R \lesssim 20$) is as low as 15\%, independent of spectral index $\alpha < -1.30$. We further show that 85\% of the USS sources that can be identified with an X-ray source are probably contained in galaxy clusters, and that $\alpha < -1.6$ sources are excellent Galactic pulsar candidates, because the percentage of these sources is four times higher in the Galactic plane. Our sample has been constructed to start an intensive campaign to obtain a large sample of high redshift objects ($z>3$) that is selected in a way that does not suffer from dust extinction or any other optical bias. \keywords{Surveys --- Galaxies: active --- Radio continuum: galaxies}
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[
{
"name": "ds1811.tex",
"string": "%\\documentclass[referee]{aa} % for a referee version\n%\n\\documentclass{aa}\n\\usepackage{psfig}\n%\n \n\\newcommand\\eg{{\\it e.g.} }\n\\newcommand\\etal{et~al.}\n\\newcommand\\ie{{\\it i.e.~}\\ }\n\\newcommand\\lya{Ly$\\alpha$}\n\\newcommand\\Lya{Ly$\\alpha$}\n\\font\\aipsfont = cmsy9 scaled\\magstep1\n\\font\\smallaipsfont = cmsy5 scaled\\magstep1\n\\newcommand\\aips {{\\aipsfont AIPS}}\n\\newcommand\\Lh {{\\aipsfont L$\\;$}}\n\\newcommand\\minpoint{$^{\\prime}\\mskip-4.7mu.\\mskip0.8mu$}\n\\newcommand\\araa{{ARA\\&A}}\n\\newcommand\\aap{{A\\&A}}\n\\newcommand\\aasup{{A\\&AS}}\n\\newcommand\\aaps{{A\\&AS}}\n\\newcommand\\aj{{AJ}}\n\\newcommand\\apj{{ApJ}}\n\\newcommand\\apjl{{ApJ}}\n\\newcommand\\apjs{{ApJS}}\n\\newcommand\\iaucirc{{IAU Circ.}}\n\\newcommand\\mnras{{MNRAS}}\n\\newcommand\\nature{{Nature}}\n\\newcommand\\nat{{Nature}}\n\\newcommand\\pasp{{PASP}}\n\\def\\spose#1{\\hbox to 0pt{#1\\hss}}\n\\newcommand\\simlt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}}\n\\newcommand\\lesssim{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13C$}}}\n\\newcommand\\simgt{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}}\n\\newcommand\\gtrsim{\\mathrel{\\spose{\\lower 3pt\\hbox{$\\mathchar\"218$}}\n \\raise 2.0pt\\hbox{$\\mathchar\"13E$}}}\n\\newcommand\\arcdeg{\\degr}\n\\newcommand\\nodata{...}\n\\includeonly{wntable,tnmptable}\n\n\\begin{document}\n\n\\thesaurus{04.19.1; 11.01.2; 13.18.1}\n\n\\title{A Sample of 669 Ultra Steep Spectrum Radio Sources to Find High Redshift Radio Galaxies \\thanks{Tables A.1, A.2 and A.3 are also and appendices B, C and D are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html }}\n\\subtitle{}\n\\titlerunning{A sample of 669 USS sources}\n\n\\author{Carlos De Breuck \\inst{1,2} \\and Wil van Breugel \\inst{2} \\and Huub J. A. R\\\"ottgering \\inst{1} \\and George Miley \\inst{1}}\n\n\\authorrunning{Carlos De Breuck \\etal}\n\n\\offprints{Carlos De Breuck}\n\n\\institute{Sterrewacht Leiden, Postbus 9513, 2300 RA Leiden, The\n Netherlands; debreuck,miley,rottgeri@strw.leidenuniv.nl\n \\and Institute of Geophysics and Planetary Physics,\n Lawrence Livermore National Laboratory, L-413, Livermore,\n CA 94550, U.S.A.; wil@igpp.llnl.gov}\n\n\\date{Received 1999 November 5; accepted 2000 February 10}\n\n\\maketitle\n\n\\begin{abstract}\nSince radio sources with Ultra Steep Spectra (USS; $\\alpha \\lesssim -1.30; S \\propto \\nu^{\\alpha}$) are efficient tracers of high redshift radio galaxies (HzRGs), we have defined three samples of such USS sources using the recently completed WENSS, TEXAS, MRC, NVSS and PMN radio-surveys. Our combined sample contains 669 sources with $S_{1400} > 10$~mJy and covers virtually the entire sky outside the Galactic plane ($|b|>15$\\arcdeg). For our 2 largest samples, covering $\\delta > -35\\arcdeg$, we selected only sources with angular sizes $\\Theta < 1\\arcmin$. For 410 sources, we present radio-maps with 0\\farcs3 to $\\sim$5\\arcsec\\ resolution from VLA and ATCA observations or from the FIRST survey, which allows the optical identification of these radio sources.\n\nComparison with spectrally unbiased samples at similar flux density levels, shows that our spectral index, flux density, and angular size selections do not affect the angular size distribution of the sample, but do avoid significant contributions by faint foreground spiral galaxies.\nWe find that the spectral index distribution of 143,000 sources from the WENSS and NVSS consists of a steep spectrum galaxy and a flat spectrum quasar population, with the relative contribution of flat spectrum sources doubling from $S_{1400}>0.1$~Jy to $S_{1400}>2.5$~Jy.\nThe identification fraction of our USS sources on the POSS ($R \\lesssim 20$) is as low as 15\\%, independent of spectral index $\\alpha < -1.30$. We further show that 85\\% of the USS sources that can be identified with an X-ray source are probably contained in galaxy clusters, and that $\\alpha < -1.6$ sources are excellent Galactic pulsar candidates, because the percentage of these sources is four times higher in the Galactic plane.\n\nOur sample has been constructed to start an intensive campaign to obtain a large sample of high redshift objects ($z>3$) that is selected in a way that does not suffer from dust extinction or any other optical bias.\n\n\\keywords{Surveys --- Galaxies: active --- Radio continuum: galaxies}\n\n\\end{abstract}\n \n\\section{Introduction}\nRadio galaxies have now been found out to redshifts of $z=5.19$ (\\cite{wvb99b}) and radio-loud quasars out to $z=4.72$ (\\cite{hoo98}). Although new optical selection techniques such as color-dropouts, deep spectroscopy of blank fields, and narrow-band \\Lya\\ imaging have now found galaxies at similar (\\cite{ste99}) and even higher redshifts (up to $z \\sim 5.75$; \\cite{dey98}; \\cite{wey98}; \\cite{spi98}, \\cite{hu99}), radio sources are still the only objects that can be selected uniformly over all redshift ranges, and in a way that does not suffer from optical biases such as dust extinction, which is known to be important at these high redshifts (\\eg\\ \\cite{hug98}; \\cite{ivi98}; \\cite{dic98}).\n\nAt low to moderate redshift ($z \\lesssim 1$), powerful radio sources are uniquely identified with massive ellipticals (\\cite{lil84}; \\cite{owe89}; \\cite{bes98}; \\cite{mcl00}). The strongest indications that this is also true at higher redshifts comes from the near-IR Hubble $K-z$ diagram of radio galaxies which shows a remarkably close correlation from the present out to $z=5.19$ (\\cite{lil89}; \\cite{eal97}; \\cite{wvb98}, \\cite{wvb99b}). This suggests that we can use radio galaxies to study the formation and evolution of the most massive galaxies, which, by their implied star-formation history, can put important constraints on galaxy formation models, and even on cosmological parameters (\\eg \\cite{dun96}; \\cite{spi97}).\nAlthough the unification model for radio galaxies and quasars (\\eg \\cite{bar89}) suggests we could also use quasars as tracers, a detailed stellar population study of quasar host galaxies is almost impossible due to the extreme luminosity of the AGN. Furthermore, samples of radio sources designed to find large quantities of quasars require additional optical selections (\\eg\\ \\cite{gre96}, \\cite{hoo98}, \\cite{whi00}).\n\n%---------------------------------------------------------- zalpha\n\\begin{figure}\n\\psfig{file=ds1811f1.eps,width=8.8cm}\n\\caption[zalpha.ps]{$\\alpha_{1400}^{325}$ against $z$ for 2 samples\nwithout spectral index selection (3CR, \\cite{spi85} and MRC,\n\\cite{mcc96}), and 2 USS samples (4C, \\cite{cha96a} and our new WN/TN\nsamples, as defined in this paper). Note that the correlation is\npresent in the spectrally unbiased 3CR and MRC, and that the 4C and\nour new USS samples are finding three to five times more $z>2$ radio\ngalaxies than the MRC. The horizontal dotted line indicates the\n$\\alpha_{1400}^{325} < -1.3$ cutoff used in our USS\nsample. \\label{zalpha}}\n\\end{figure}\n%______________________________________________________________\n\nConsiderable effort has been spent over the last decade to find these high redshift radio galaxies (HzRGs), which has lead to the discovery of more than 140 radio galaxies at redshifts $z>2$ (see \\eg \\cite{deb98a} for a recent summary). However by $z>3$, their numbers become increasingly sparse, and using flux limited radio surveys such as the 3CR ($S_{178} > 10$~Jy; \\cite{lai83}), or the MRC strip ($S_{408} > 0.95$~Jy; \\cite{mcc96}), the highest redshift radio galaxy found so far is at $z\\sim 3.2$ (Fig. \\ref{zalpha}; \\cite{raw90}; \\cite{mcc96}). This redshift limit arises because radio power is correlated with redshift in bright flux limited samples, and an upper limit exists in the radio luminosity. Lowering the flux limit would not only substantially increase the number of sources in these samples, but at the same time the fraction of luminous very high redshift radio galaxies would decrease (\\cite{blu98}, \\cite{jar99}). This fractional decrease would arise even if there is no decrease in co-moving space density at $z \\sim 2.5$. Such a redshift cutoff has been suggested by Bremer \\etal (1998), but recently Jarvis \\etal (1999) rule out a break at $z\\lesssim 2.5$. To efficiently find large numbers of HzRGs in acceptable observing times, it is therefore necessary to apply additional selection criteria, at the expense of completeness.\n\nBy far the most successful selection criterion has been the ultra steep spectrum criterion (\\eg \\cite{rot94}; \\cite{cha96a}; \\cite{blu98}). Selecting sources with very steep radio spectra increases dramatically the chance of finding $z>2$ radio galaxies (Fig. \\ref{zalpha}). This technique is based on the results of Tielens \\etal\\ (1979) \\nocite{tie79} and Blumenthal \\& Miley (1979)\\nocite{blu79}, who found that the identification fraction on the POSS ($R \\lesssim 20$) decreases with steepening spectral index, consistent with the steeper sources being at higher redshifts. It is now getting clear that this correlation can be explained by a combination of a K-correction of a concave radio spectrum and an increasing spectral curvature with redshift (\\cite{kro91}, \\cite{car99}; \\cite{wvb99a}). To further investigate the $z - \\alpha$ correlation, we have calculated spectral indices using the flux densities from the WENSS (\\cite{ren97}) and NVSS (\\cite{con98}) catalogs for four different samples: the flux density limited 3CR (\\cite{spi85}) and MRC (\\cite{mcc96}) surveys, and the USS samples from the 4C (\\cite{cha96a}) and the one presented in this paper.\nThe results (Fig. \\ref{zalpha}) show a trend for steeper spectral index sources to have higher redshifts in flux limited, spectrally unbiased samples, confirming the empirical relation out to the highest redshifts. The efficiency of the USS criterion is clearly illustrated by the fact that the 4C USS sample (\\cite{cha96a}) contains 50\\% $z>2$ sources, and by the early spectroscopic results on the USS samples presented in this paper, which indicate that $\\sim$2/3 of our sources have $z>2$. It is even more impressive to note that 13 of the 14 radio galaxies at $z>3.5$ we know of have been found from samples with a steep spectral index selection\\footnote{The only exception is VLA J123642+6213 (\\cite{wad99}), which has been identified in the HDF, but it does have a steep spectral index ($\\alpha_{1400}^{8500}=-0.94$).}! The limitation of this technique is that the steepest spectrum sources are rare, comprising typically only 0.5\\% (at $\\alpha < -1.30$) of a complete low frequency sample; therefore, large and deep all sky surveys are needed to obtain a significant sample of USS sources.\n\nWith the advent of several new deep all-sky surveys (\\S 2), it is now possible for the first time to construct a well defined all-sky USS sample with optimized selection criteria to find large numbers of $z>3$ radio galaxies. In this paper, we describe the construction of such a sample, and present high resolution radio observations needed to determine accurate positions and morphologies. This information is essential for the optical and near-IR identifications, and subsequent optical spectroscopy of a significant sub-set of our sample, which will be described in a future papers. \nThe organization of the paper is as follows: we describe the radio surveys we used in \\S 2 and define our samples in \\S 3. We present and discuss our radio observations in \\S 4, and present our conclusions in \\S 5. \n%Throughout the paper, we use $H_0 = 50$ km s$^{-1}$ Mpc$^{-1}$, $q_0 = 0$ and $\\Lambda = 0$.\n\\begin{table*}\n\\centerline{\\bf Table 1: Radio Surveys}\n\n\\footnotesize\n\\begin{tabular}{lccc}\n\\hline\n\\\\\n & WENSS & TEXAS & MRC \\\\\n\\\\\n\\hline\n\\\\\nFrequency (MHz) & 325 & 365 & 408 \\\\\nSky region (J2000) & $\\delta >$ +29\\arcdeg & $-$35\\fdg7 $< \\delta <$ +71\\fdg5 & $-$85\\arcdeg $< \\delta <$ +18\\fdg5 \\\\\n\\# of sources & 229,576 & 67,551 & 12,141 \\\\\nResolution & $ 54\\arcsec \\times$ 54\\arcsec cosec$\\delta$ & 10\\arcsec$^a$ & $2\\farcm62 \\times 2\\farcm86 \\sec (\\delta - 35\\fdg5)$ \\\\\nPosition uncertainty & 1\\farcs5 & 0\\farcs5---1\\arcsec & 8\\arcsec \\\\\n(strong sources) & & & \\\\\nRMS noise & $\\sim$4 mJy & 20 mJy & 70 mJy \\\\\nFlux density limit & 18 mJy & 150 mJy & 670 mJy \\\\\nReference & \\cite{ren97} & \\cite{dou96} & \\cite{lar81} \\\\\n\\\\\n\\hline\n\\hline\n\\\\\n & NVSS & FIRST & PMN \\\\\n\\\\\n\\hline\n\\\\\nFrequency (MHz) & 1400 & 1400 & 4850 \\\\\nSky region (J2000) & $\\delta > -$40\\arcdeg$^b$ & $7^h20^m < \\alpha < 17^h20^m$; +22\\fdg2 $< \\delta <$ +57\\fdg5 & $-$87\\fdg5 $< \\delta <$ +10\\arcdeg \\\\\n & & $21^h20^m < \\alpha < 3^h20^m$; $-$2\\fdg5 $< \\delta <$ +1\\fdg6 \\\\\n\\# of sources & 1,689,515 & 437,429 & 50,814 \\\\\nResolution & 45\\arcsec $\\times$ 45\\arcsec & 5\\arcsec $\\times$ 5\\arcsec & 4\\minpoint2 \\\\\nPosition uncertainty & 1\\arcsec & 0\\farcs1 & $\\sim$45\\arcsec \\\\\n(strong sources) & & & \\\\\nRMS noise & 0.5 mJy & 0.15 mJy & $\\sim$8 mJy \\\\\nFlux density limit & 2.5 mJy & 1 mJy & 20 mJy \\\\\nReference & \\cite{con98} & \\cite{bec95} & \\cite{gri93} \\\\\n\\hline\n\\end{tabular}\n\n$^a$ The Texas interferometer has a complicated beam. However, sources with separations between 10\\arcsec\\ and 2\\arcmin\\ can be successfully modeled as doubles, and will have a single entry in the catalog. See \\cite{dou96} for details.\n\n$^b$ Some small gaps are not covered. They are listed on the NVSS homepage (1998 January 19 version).\n\\end{table*}\n\n\n\\section{Description of the Radio Surveys}\n\n%---------------------------------------------------------- surveylimits\n\\begin{figure}[t]\n\\psfig{file=ds1811f2.eps,width=8.6cm}\n\\caption[surveylimits.ps]{Limiting flux density plotted for all major radio surveys. Lines are of constant spectral indices of $-1.3$. Note that WENSS, NVSS and FIRST have flux density limits $\\sim 100$ times deeper than previous surveys at comparable wavelengths. \\label{surveylimits}}\n\\end{figure}\n%______________________________________________________________\n\nDuring the past years, several all-sky radio-surveys have become available (Table 1), which are 1--2 orders of magnitude more sensitive than previous surveys at similar frequencies (Fig.\\ \\ref{surveylimits}). The combination of these new surveys allows us to define for the first time a large sample of USS sources that covers the whole sky\\footnote{To facilitate optical follow-up, we will exclude the Galactic plane at $|b|<15$\\degr} in both hemispheres. We list the main survey parameters in Table 1. In this section, we will briefly discuss the usefulness of these new radio surveys for the construction of USS samples. \n\n\\subsection{WENSS}\nThe Westerbork Northern Sky Survey (WENSS; \\cite{ren97}) at 325~MHz is the deepest low-frequency survey with a large sky coverage (3.14 sr). We used the WENSS to define the largest, and most complete USS sample to date, covering the entire sky North of declination 29\\arcdeg. We used version 1.0 of the main and polar WENSS catalogs. A small area is covered by both these catalogs; we selected only the sources from the main catalog in this overlapping area.\n\n\\subsection{Texas}\n%---------------------------------------------------------- texasppp\n\\begin{figure}\n\\psfig{file=ds1811f3.eps,width=9cm}\n\\caption[texasppp.ps]{Fraction of sources with '+++'\\ flag in the Texas catalog (see text) as a function of Texas $S_{365}$ flux density. Note that the selection of '+++' sources excludes primarily sources with $S_{365} \\lesssim 700$~mJy. \\label{texasppp}}\n\\end{figure}\n%______________________________________________________________\n\nThe Texas survey, made with the Texas interferometer from 1974 to 1983 (\\cite{dou96}), covers 9.63 steradians at a frequency of 365~MHz with a limiting flux density about ten times higher than that of the WENSS. The Texas interferometer's 3.5~km maximum baseline provides $<$1\\arcsec\\ positional accuracy, but its poor uv-coverage leads to irregular beamshapes and lobe-shifts, hampering accurate modeling of extended sources. A detailed discussion of these complications can be found in Douglas \\etal\\ (1996).\nTo minimize these problems, we have selected only the 40.9\\% sources that are well modeled (listed with a '+++' flag in the catalog). This selection excludes primarily $S_{365} \\lesssim 700$~mJy sources (Fig. \\ref{texasppp}), but even at $S_{365} \\gtrsim 700$~mJy, one out of three sources is excluded by this criterion.\n\\cite{dou96} have calculated the completeness above flux density S of the Texas catalog (defined as the fraction of sources with true flux density greater than S which appear in the catalog) by comparing the Texas with the MRC (\\cite{lar81}) and a variety of other low-frequency catalogs. They found that the completeness varies with declination (because the survey was done in declination strips over a large time span), and an expected increase in completeness at higher flux densities. In Table 2, we reproduce their completeness table, extended with the values after the '+++' selection.\n\n\\begin{table}\n\\centerline{\\bf Table 2: Completeness of the Texas survey}\n\\begin{tabular}{lcc}\n\\hline\nLimiting flux density & all sources & '+++' sources \\\\\n\\hline\n250 mJy & 0.8 & 0.2 \\\\\n350 mJy & 0.88 & 0.28 \\\\\n500 mJy & 0.92 & 0.40 \\\\\n750 mJy & 0.96 & 0.51 \\\\\n1 Jy & 0.96 & 0.50 \\\\\n\\hline\n\\end{tabular}\n\\end{table}\n\n%---------------------------------------------------------- wtratio\n\\begin{figure}\n\\psfig{file=ds1811f4.eps,width=8.6cm}\n\\caption[wtratio.ps]{Ratio of integrated Texas over WENSS flux density against integrated WENSS flux density. Only Texas '+++' sources are plotted. The horizontal line is the expected ratio 0.865 due to the 40 MHz difference in central frequency, and assuming a spectral index of $\\alpha_{365}^{1400}=-0.88$. The curved line indicates a 150 mJy flux density limit in the Texas catalog. Note the increasing amount of overestimated Texas flux densities with decreasing flux density $S_{WENSS} < 400$~mJy. \\label{wtratio}}\n\\end{figure}\n%______________________________________________________________\n\nTo examine the reliability of the listed flux densities, and to check to what extent the '+++' selection has removed the spurious sources from the catalog, we have correlated the Texas '+++' sources with WENSS, NVSS and FIRST.\nIn Figure \\ref{wtratio}, we compare the Texas flux densities with those of the WENSS. At $S_{325} \\gtrsim 500$~mJy, the ratio of the flux densities is closely distributed around 0.9. This ratio is what we expect due to the 40 MHz central frequency difference between the two surveys and assuming a spectral index $\\alpha_{365}^{1400} = -0.879$ (the median of the Texas-NVSS spectral indices).\nAt $S_{325} \\lesssim 500$~mJy, the number of sources in the Texas catalog which are brighter than in WENSS catalog increases with decreasing flux density. This can be explained by the 'up-scattering' of sources near the flux limit of the Texas catalog (\\ie only sources intrinsically brighter than $S_{365} = 150$~mJy will be detected, but no $S_{365} < 150$~mJy sources with a large positive flux density measurement error). The result of this on a USS sample based on the Texas survey and correlated with a higher frequency survey (such as the NVSS), will be that with lower $S_{365}$, we will find more sources whose spectral indices appear steeper than they really are.\n\nWe also examined the dependence of the ratio Texas/WENSS flux density on angular size, determined from the FIRST survey (see \\S 2.1.4). We found no significant residual variation of the flux density ratio at sizes between 5\\arcsec\\ and 2\\arcmin.\n\nIn Figure \\ref{usssr}b, we plot the density of NVSS sources around a Texas source (see also \\S 2.2.5). The width of the over-density peak ($\\sim 10$\\arcsec) is due to the positional inaccuracies in the Texas and NVSS catalogues. However, the very broad tail of sources between 20\\arcsec\\ and 110\\arcsec\\ and the secondary peak coinciding with the fringe separation at 73\\arcsec\\ indicates that the '+++' selection did not remove all spurious sources from the catalog.\n\nIn summary, after the selection of '+++' sources, the Texas catalog still contains $<5$\\% spurious sources (\\cite{dou96}), probably due to residual lobe-shifted sources. Our comparison of the Texas flux densities with those of the WENSS survey shows that the differences are consistent with the errors quoted in the catalog. The selection of the Texas catalog with only '+++' sources is thus $>$95\\% reliable, but only $\\sim$40\\% complete.\n\n\\subsection{NVSS}\nThe NRAO VLA Sky Survey (NVSS; \\cite{con98}) covers the 10.3 steradians north of $-$40\\arcdeg\\ at 1.4~GHz, and reaches a 50 times lower limiting flux density than previous large area 1.4~GHz surveys. At the flux density levels we are using ($S_{1400}>10$~mJy), the catalog is virtually complete.\nBecause the NVSS resolution is comparable to that of the WENSS and Texas surveys, and its sky coverage is large, we use the NVSS to determine the spectral indices in our USS samples based on the WENSS and Texas surveys.\nThe final NVSS catalog was not yet completed at the time of our USS sample construction. For our final sample, presented in this paper, we use the 1998 January 19 version. This version still lacks data in a small number of regions of the sky (listed on the NVSS homepage). As a result, the sky coverage of the area listed in Table 3 is only 99.77\\%.\n\n\\subsection{FIRST}\nThe Faint Images of Radio Sky at Twenty centimeters (FIRST, \\cite{bec95}) survey is currently being made with the VLA in the B-array at 1.4~GHz, and has a limiting flux density three times deeper than the NVSS. We used the 1998 February 4 version of the catalog, covering 1.45~steradians. As noted by Becker \\etal\\ (1995), the photometry for extended sources in FIRST might be less reliable than that of the NVSS, due to the $9 \\times$ higher resolution, which could underestimate large-scale diffuse radio emission. As the FIRST area is completely covered by the NVSS, we will consistently use NVSS flux densities for our spectral index calculation. The main advantages of FIRST over NVSS for our purposes are the much better positional accuracy ($<$~0\\farcs5) and the higher (5\\arcsec) resolution. This combination allows the identification of even the very faint ($R > 20$) optical counterparts of radio sources. Additionally, the fainter detection limit of the FIRST allows an extra check on the flux densities of compact sources.\n\n\\subsection{MRC}\nThe Molonglo Reference Catalog of radio sources (\\cite{lar81}) at 408~MHz is presently the most sensitive low-frequency catalog with reasonable positional accuracy that covers the deep southern hemisphere, $\\delta < -35$\\arcdeg. We will use this catalog in combination with the PMN survey (see below) to define the first USS sample at $\\delta < -40\\arcdeg$.\n\n\\subsection{PMN}\nThe Parkes-MIT-NRAO (PMN) survey is a combination of 4 strips observed with the Parkes telescope at 4.85~GHz. The strips cover different parts of the sky, each with a slightly different limiting flux density. The regions are: southern ($-87\\fdg5 < \\delta < -37\\arcdeg$, \\cite{wri94}), zenith ($-37\\arcdeg < \\delta < -29\\arcdeg$, \\cite{wri96}), tropical ($-29\\arcdeg < \\delta < -9\\fdg5$, \\cite{gri94}), and equatorial ($-9\\fdg5 < \\delta < +10\\arcdeg$, \\cite{gri95}). For our southern hemisphere sample, we have used the southern and zenith catalogs to find USS sources at $\\delta < -30\\arcdeg$.\n\n%---------------------------------------------------------- usssky\n\\begin{figure}\n\\psfig{file=ds1811f6.eps,width=8.8cm}\n\\caption[usssky.ps]{Sky coverage of our 3 USS samples. Constant declination lines denote the boundaries between our the WN and TN and between the TN and MP samples, as indicated on the right. Note the difference in source density and the exclusion of the Galactic Plane. \\label{usssky}}\n\\end{figure}\n%______________________________________________________________\n\n\\section{USS Samples}\n\n%---------------------------------------------------------- usssr\n\\begin{figure*}\n\\psfig{file=ds1811f5.eps,width=18cm}\n\\caption[usssr.ps]{The density of sources from the high frequency catalog used in the correlation (NVSS or PMN) around sources from the low frequency catalog (WENSS, Texas or MRC) as a function of search radius. The dotted line represents the distribution of confusion sources (see text). The apparent under-density of WENSS--NVSS sources at search radii $\\simgt 60\\arcsec$ is due to the grouping of multiple component sources in the $\\sim$1\\arcmin\\ resolution WENSS. Note the plateau and secondary peak around the 73\\arcsec\\ Texas fringe separation in the Texas--NVSS correlation and the much larger uncertainty in the MRC--PMN correlation.\\label{usssr}}\n\\end{figure*}\n%______________________________________________________________\n\nFigure \\ref{surveylimits} shows that the surveys described above have very compatible flux density limits for defining samples of USS sources. At the same time, their sky coverage is larger and more uniform than previous surveys used for USS sample construction (\\cite{wie92}, \\cite{rot94}; \\cite{cha96a}, \\cite{blu98}; \\cite{ren98}, \\cite{pur99}, \\cite{ped99}, \\cite{and00}). We selected the deepest low and high frequency survey available at each part of the sky. For a small region $-35\\arcdeg < \\delta < -30\\arcdeg$ which is covered by both Texas and MRC, we used both surveys. This resulted in a more complete samples since the lower sensitivity of the PMN survey in the zenith strip (see \\S2.6) is partly compensated by the (albeit incomplete) Texas survey.\nTo avoid problems with high Galactic extinction during optical imaging and spectroscopy, all regions at Galactic latitude $|b| <$ 15\\arcdeg\\ were excluded\\footnote{This also reduces the number of Galactic pulsars in our sample (see \\S4.7.2).}, as well as the area within 7\\arcdeg of the LMC and SMC. This resulted in three USS samples that cover a total of 9.4 steradians (Fig. \\ref{usssky}).\n\nWe designate the USS samples by a two-letter name, using the first letter of their low- and high-frequency contributing surveys. Sources from these samples are named with this 2-letter prefix followed by their IAU J2000-names using the positions from the NVSS catalog (WN and TN samples) or the MRC catalog (MP sample). We did not rename the sources after a more accurate position from our radio observations or from the FIRST survey. The sample definitions are summarized in Table 3.\n\n\\subsection{Survey combination issues}\nWe first discuss the problems that arise when combining radio surveys with different resolutions and positional uncertainties.\n\\subsubsection{Correlation search radius}\nDue to the positional uncertainties and resolution differences between radio surveys, in general the same source will be listed with slightly different positions in the catalogs.\n\nTo empirically determine the search radius within which to accept sources in 2 catalogs to be the same, we compared the density of objects around the position listed in the low-frequency survey (which has lower resolution) with the expected number of random correlations in each sample ($\\equiv$ confusion sources). To determine this number as a function of distance from the position in the most accurate catalog, we created a random position catalog by shifting one of the input catalogs by 1\\arcdeg\\ in declination, and made a correlation with this shifted catalog. The density of sources as a function of distance from the un-shifted catalog then represents the expected number of confusing sources as a function of radial distance. In Figure \\ref{usssr}, we plot for each of our three samples the observed density around these sources with this confusing distribution over-plotted. The correlation search radius should thus be chosen at a distance small enough for the density of confusion sources to be negligible.\n\nWe decided to adopt the radius where the density of real sources is at least ten times higher that the density of confusion sources as the search radius for our sample construction, except for the WN sample (would be 15\\arcsec) where we chose the same radius as for the TN sample (10\\arcsec). The later was done for consistency between both samples. Because of the five times lower resolution and source densities in the MRC and PMN surveys, the search radius of the MP sample is eight times larger. Summarized, the search radii we used are 10\\arcsec\\ for WN and TN, and 80\\arcsec\\ for MP.\n\\begin{table*}\n\\centerline{\\bf Table 3: USS samples}\n\\scriptsize\n\\begin{tabular}{lrccccccc}\n\\hline\nSample & Sky Area$\\qquad\\quad$ & Density & Spectral Index & Search Radius & Flux Limit & C$^a$ & R$^a$ & \\# of Sources \\\\\n & & sr$^{-1}$ & & & mJy & &\\\\\n\\hline\nWN & 29\\arcdeg $< \\delta <$ 75\\arcdeg, $|b| >$ 15\\arcdeg$^b$ & 151 & $\\alpha_{325}^{1400} \\le -1.30$ & 10\\arcsec & $S_{1400} >$ 10 & 96\\% & 90\\% & 343 \\\\\nTN & $-$35\\arcdeg $< \\delta <$ 29\\arcdeg, $|b| >$ 15\\arcdeg$^b$ & 48$^c$ & $\\alpha_{365}^{1400} \\le -1.30$ & 10\\arcsec & $S_{1400} >$ 10 & 97\\%$^c$ & 93\\% & 268 \\\\\nMP & $\\delta < -$30\\arcdeg, $|b| >$ 15\\arcdeg & 26 & $\\alpha_{408}^{4800} \\le -1.20$ & 80\\arcsec & S$_{408} > 700$; S$_{4850} > 35$ & 100\\% & 100\\% & 58 \\\\\n\\hline\n\\end{tabular}\n\n$^a$ C=completeness and R=reliability accounting only for scattering across the spectral index limit (see \\S3.3.1).\n\n$^b$ coverage is only 99.7\\% because some small patches of sky we not covered at the time of writing. They are listed on the NVSS homepage \\\\(1998 January 19 version).\n\n$^c$ Because we selected only problem free sources from the Texas survey, the effective completness of the TN sample is $\\sim 30\\%$.\n\\end{table*}\n\n\\subsubsection{Angular size}\nIn order to minimize errors in the spectral indices due to different resolutions and missing flux on large angular scales in the composing surveys, we have only considered sources which are not resolved into different components in the composing surveys. Effectively, this imposes an angular size cutoff of $\\sim$1\\arcmin\\ to the WN, $\\sim$2\\arcmin\\ to the TN sample and $\\sim$4\\arcmin\\ to the MP sample.\nWe deliberately did not choose a smaller angular size cutoff (as \\eg Blundell \\etal\\ (1998) did for the 6C$^*$ sample), because (1) higher resolution angular size information is only available in the area covered by the FIRST survey, and (2) even a 15\\arcsec\\ cutoff would only reduce the number of sources by 30\\%, while it would definitely exclude several HzRGs from the sample. For example, in the 4C USS sample (\\cite{cha96b}), three out of eight $z>2$ radio galaxies have angular sizes $>$15\\arcsec.\n\nWe think that our $\\sim$1\\arcmin\\ angular size cutoff will exclude almost no HzRGs, because the largest angular size for $z > 2$ radio galaxies in the literature is 53\\arcsec\\ (4C~23.56 at $z = 2.479$; \\cite{cha96a}, \\cite{car97}), while all 45 $z > 2.5$ radio galaxies with good radio maps are $<$~35\\arcsec\\ (\\cite{car97}). Although the sample of known $z>2$ radio galaxies is affected by angular size selection effects, very few HzRGs larger than 1\\arcmin\\ would be expected.\n\nThe main incompleteness of our USS sample stems from the spectral index cutoff and the flux limit (\\S3.2). However, our flux limit ($S_{1400}$=10~mJy) is low enough to break most of the redshift-radio power degeneracy at $z>2$. To achieve this with flux limited samples, multiple samples are needed (\\eg \\cite{blu99}).\n\n\\subsection{Sample definition}\n\n\\subsubsection{WENSS-NVSS (WN) sample}\nA correlation of the WENSS and NVSS catalogs with a search radius of 10\\arcsec\\ centered on the WENSS position (see \\S 3.1.1) provides spectral indices for $\\sim 143,000$ sources. Even with a very steep $\\alpha_{325}^{1400} \\le -1.30$ spectral index criterion, we would still have 768 sources in our sample.\nTo facilitate follow-up radio observations, and to increase the accuracy of the derived spectral indices (see \\S 3.3.1), we have selected only NVSS sources with $S_{1400} > 10$~mJy. Because the space density of the highest redshift galaxies is low, it is important not to limit the sample area (see \\eg \\cite{raw98}) to further reduce the number of sources in our sample.\nBecause the NVSS has a slightly higher resolution than the WENSS (45\\arcsec\\ compared to $54\\arcsec \\times 54\\arcsec $cosec$~\\delta$), some WENSS sources have more than one associated NVSS source. We have rejected the 11 WN sources that have a second NVSS source within one WENSS beam. Instead of the nominal WENSS beam ($54\\arcsec \\times 54\\arcsec$cosec$\\delta$), we have used a circular 72\\arcsec\\ WENSS beam, corresponding to the major axis of the beam at $\\delta = 48\\arcdeg$, the position that divides the WN sample into equal numbers to the North and South. \nThe final WN sample contains 343 sources.\n\n\\subsubsection{Texas-NVSS (TN) sample}\nBecause the Texas and NVSS both have a large sky-coverage, the area covered by the TN sample includes 90\\% of the WN area. In the region $\\delta >29\\arcdeg$, we have based our sample on the WENSS, since it does not suffer from lobe-shift problems and reaches ten times lower flux densities than the Texas survey (\\S 2.2).\nIn the remaining 5.28 steradians South of declination +29\\arcdeg, we have spectral indices for $\\sim 25,200$ sources. Again, we used a 10\\arcsec\\ search radius (see \\S 3.1.1), and for the same reason as in the WN sample we selected only NVSS sources with $S_{1400} > 10$~mJy. Combined with the $\\alpha_{365}^{1400} \\le -1.30$ criterion, the number of USS TN sources is 285.\nAs for the WN sample, we further excluded sources with more than one $S_{1400}>$10~mJy NVSS source within 60\\arcsec\\ around the TEXAS position, leaving 268 sources in the final TN sample. We remind (see \\S 2.2) that the selection of the TEXAS survey we used is only $\\sim$40\\% complete with a strong dependence on flux density. Using the values from table 2, we estimate that the completeness of our TN sample is $\\sim$30\\%.\n\n\\subsubsection{MRC-PMN (MP) sample}\nIn the overlapping area, we preferred the TN over the MP sample for the superior positional accuracies and resolutions of both Texas and NVSS compared to MRC or PMN. Because the MRC survey has a low source density, we would have only 13 MP sources with $\\alpha_{408}^{4850} \\le -1.30$. We therefore relaxed this selection criterion to $\\alpha_{408}^{4850} \\le -1.20$, yielding a total sample of 58 sources in the deep South ($\\delta < -30$\\arcdeg).\n%---------------------------------------------------------- wn3spixhis\n\\begin{figure*}\n\\centerline{\\psfig{file=ds1811f7.eps,width=15cm}}\n\\caption[wn3his.ps]{Spectral index distributions from the WENSS-NVSS correlation. The left and right panels show the variation with 325~MHz and 1.4~GHz flux density. A low frequency selected sample is more appropriate to study the steep-spectrum population. The parameters of a two-component Gaussian fit (dotted line = steep, dashed line = flat) are shown in each panel. The solid line is the sum of both Gaussians. \\label{wn3spixhis}}\n\\end{figure*}\n%______________________________________________________________\n\n\\subsection{Discussion}\n\n\\subsubsection{Spectral index errors}\nWe have listed the errors in the spectral indices due to flux density errors in the catalogs in Tables A.1 to A.3. The WN and TN samples have the most accurate spectral indices: the median spectral index errors are $\\Delta\\bar{\\alpha}_{325}^{1400} = 0.04$ for WN sources and $\\Delta\\bar{\\alpha}_{365}^{1400} = 0.04$ ($S_{365} >$ 1~Jy) to 0.07 ($S_{365} >$ 150~mJy) for TN sources. For the MP sample, $\\Delta\\bar{\\alpha}_{408}^{4850} \\approx 0.1$, with little dependence on flux density (S$_{408} > 750$mJy).\n\nBecause our sample selects the sources in the steep tail of the spectral index distribution (Fig. \\ref{wn3spixhis} and \\ref{spixhis}), there will be more sources with an intrinsic spectral index flatter than our cutoff spectral index that get scattered into our sample by measurement errors than there will be sources with intrinsic spectral index steeper than the cutoff that get scattered out of our sample. \n\nFollowing the method of \\cite{ren98}, we fitted the steep tail between $-1.60 < \\alpha < -1.0$ with a Gaussian function. For each of our three samples, we generated a mock sample drawn from this distribution, and added measurement errors by convolving this true spectral index distribution with a Gaussian distribution with as standard deviation the mean error of the spectral indices. The WN mock sample predicts that 13 $\\alpha_{325}^{1400} < -1.30$ sources get scattered out of the sample while 36 $\\alpha_{325}^{1400} > -1.30$ sources get scattered into the USS sample.\nThus, the WN sample is 96\\% complete and 90\\% reliable. For the TN sample, we expect to loose 7 $\\alpha_{365}^{1400} < -1.30$ sources\\footnote{only due to the spectral index cutoff, the sample has more important incompleteness factors; see \\S 2.2}, and have 18 contaminating $\\alpha_{365}^{1400} > -1.30$ sources. The completeness is thus 97\\% and the reliability 93\\%. For the MP sample, this spectral index scattering is negligible, because there are too few sources in the steep spectral index tail.\n\nOur reliability and completeness are significantly better than the values of $\\sim$75\\% and $\\sim$50\\% of \\cite{ren98} because (1) our spectral indices are more accurate because they were determined from a wider frequency interval than the 325--610~MHz used by \\cite{ren98}, and (2) our sample has a steeper cutoff spectral index, where the spectral index distribution function contains fewer sources and has a shallower slope, leading to fewer sources that can scatter in or out of the sample.\n\n\\subsubsection{Spectral index distributions}\nUsing the 143,000 spectral indices from the WENSS-NVSS correlation, we examined the flux density dependence of the steep and flat spectrum sources. Selecting sources with $S_{325}>50$~mJy or $S_{1400}>100$~mJy assures that we will detect all sources with $\\alpha_{325}^{1400}>{\\frac{\\ln(S_{NVSS}^{lim}/50)}{\\ln(325/1400)}}=-1.82$ or $\\alpha_{325}^{1400}<{\\frac{\\ln(S_{WENSS}^{lim}/100)}{\\ln(325/1400)}}=0.82$ respectively, where $S_{NVSS}^{lim}=3.5$~mJy and $S_{WENSS}^{lim}=30$~mJy are the lowest flux densities where the NVSS and WENSS are complete (\\cite{con98}, \\cite{ren97}). The results shown in Figure \\ref{wn3spixhis} therefore reflect only the effect of a different selection frequency. Two populations are present in both the $S_{325}$ and $S_{1400}$ selected distributions. The peaks of the steep and flat populations at $\\bar{\\alpha}_{325}^{1400} \\approx -0.8$ and $\\bar{\\alpha}_{325}^{1400} \\approx -0.4$ do not show significant shifts over three orders of magnitude in flux density. This is consistent with the results that have been found at 4.8~GHz (\\cite{wit79}, \\cite{mac81}, \\cite{owe83}), with the exception that their $\\bar{\\alpha}_{1400}^{4800} \\approx 0.0$ for the flat spectrum component is flatter than the $\\bar{\\alpha}_{325}^{1400} \\approx -0.4$ we found. However, we find that the relative contribution of the flat spectrum component increases from 25\\% at $S_{1400}>0.1$~Jy to 50\\% at $S_{1400}>2.5$~Jy\n\nBecause the steep- and flat-spectrum populations are best separated in the $S_{1400}>$2.5~Jy bin, we have searched the literature for identifications of all 58 $S_{1400} > 2.5$~Jy sources to determine the nature of both populations. All but one (3C 399, \\cite{mar98}) of the objects outside of the Galactic plane ($|b| > 15\\arcdeg$) were optically identified. Of the 30 steep spectrum ($\\alpha_{325}^{1400} < -0.6$) sources, two thirds were galaxies, while the rest were quasars. Half of the flat spectrum ($\\alpha_{325}^{1400} > -0.6$) sources were quasars, 20\\% blazars, and 30\\% galaxies. Figure \\ref{wn3spixhis} therefore confirms that the steep and flat spectral index populations are dominated by radio galaxies and quasars respectively. We also find that while the relative strength between the steep and flat spectrum populations changes due to the selection frequency, the median spectral index and width of the population does not change significantly over three orders in magnitude of flux density. Even fainter studies would eventually start to get contamination from the faint blue galaxy population (see \\eg\\ \\cite{win85}).\n%---------------------------------------------------------- spixhis\n\\begin{figure}\n\\psfig{file=ds1811f8.eps,width=9cm}\n\\caption[spixhis.ps]{ Logarithmic spectral index distribution for WENSS-NVSS (full line), Texas-NVSS (dot-dash line) and MRC-PMN (dotted line). The vertical line indicates the -1.3 cutoff used in our spectral index selection. Note the difference in number density and the sharper fall-off on the flat-end part of the TN and MP compared to the WN. \\label{spixhis}}\n\\end{figure}\n%______________________________________________________________\n\n\\begin{table*}\n\\centerline{\\bf Table 4: Radio Observations}\n\\begin{center}\n\\begin{tabular}{lrrrcr}\n\\hline\nUT Date & Telescope & Config. & Frequency & Resolution & \\# of sources \\\\\n\\hline\n1996 October 28 & VLA & A & 4.86 GHz & 0\\farcs3 & 90 WN, 25 TN \\\\\n1997 January 25 & VLA & BnA& 4.86 GHz & 0\\farcs6 & 29 TN \\\\\n1997 March 10 & VLA & BnA & 4.885 GHz & 0\\farcs6 & 8 TN \\\\\n1997 December 15 & ATCA & 6C & 1.420 GHz & 6\\arcsec $\\times$ 6\\arcsec\\ cosec$\\delta$ & 41 MP, 32 TN \\\\\n1998 August 12+17 & VLA & B & 4.86 GHz & 1\\farcs0 & 151 WN \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\subsubsection{Consistency of the three USS samples}\nWe compare the spectral index distributions of our three USS samples in logarithmic histograms (Fig. \\ref{spixhis}). The distributions are different in two ways. First, the WENSS-NVSS correlation contains nine times more sources than the Texas-NVSS, and 14 times more than the MRC-PMN correlation. Second, the shapes of the distributions are different: while the steep side of the TN sample coincides with that of the WN, its flat end part falls off much faster. The effect is so strong that it even shifts the TN peak steep-wards by $\\sim0.15$. For the MP sample, the same effect is less pronounced, though still present.\n\nBoth effects are due to the different flux density limits of the catalogs. The deeper WENSS catalog obviously contains more sources than the TEXAS or MRC catalogs, shifting the distributions vertically in Figure \\ref{surveylimits}. The relative 'shortage' of flat spectrum sources in the Texas-NVSS and MRC-PMN correlations can be explained as follows. A source at the flux density limit in both WENSS and NVSS would have a spectral index of $\\alpha_{325}^{1400} = -1.3$, while for Texas and NVSS this would be $\\alpha_{365}^{1400} = -1.7$ (see Fig. \\ref{surveylimits}). Faint NVSS sources with spectral indices flatter than these limits will thus more often get missed in the TEXAS catalog than in the WENSS catalog. This effect is even strengthened by the lower completeness at low flux densities of the Texas catalog. However, very few USS sources will be missed in either the WENSS-NVSS or Texas-NVSS correlations\\footnote{The TN sample will have more spurious sources at low flux density levels; see \\S2.2}. The parallel slope also indicates that the USS sources from both the WENSS-NVSS and Texas-NVSS correlations were drawn from the same population of radio sources. We therefore expect a similar efficiency in finding HzRGs from both samples.\n\nThe MP sample has been defined using a spectral index with a much wider frequency difference. However, the observed ATCA 1.420 GHz flux densities can be used to construct $\\alpha_{408}^{1420}$. An 'a posteriori' selection using $\\alpha_{408}^{1420} \\le -1.30$ from out ATCA observations (see \\S 4.2) would keep $\\sim$60\\% of the MP sources in a WN/TN USS sample.\n\n\\section{Radio Observations}\nOf all the major radio surveys described in \\S 2, only FIRST has sufficient positional accuracy and resolution for the optical identification of $R > 20$ objects. We present FIRST maps of 139 WN and 8 TN sources in appendices B.2 and B.4.\n\nOutside the area covered by FIRST, we have observed all the remaining WN sources, 30\\% of the TN sample, and 71\\% of the MP sources at 0\\farcs3 to 5\\arcsec\\ resolution using the Very Large Array (VLA; \\cite{nap83}) and Australia Telescope Compact Array (ATCA; \\cite{fra92}) telescopes.\nA log of the radio observations is given in Table 4. We observed targets for our VLA runs on the basis of declination (A-array for $\\delta >$ 0\\arcdeg\\ and BnA-array for $\\delta <$ 0\\arcdeg) and sky coverage of the WN and TN samples, which were still incomplete at the time of the 1996 observations. We observed all WN, and most TN sources with the VLA, and all MP sources with the ATCA. We observed TN sources between $-31$\\arcdeg $< \\delta < -10$\\arcdeg\\ with either VLA or ATCA, depending on the progress of the NVSS at the time of the observations.\n\n\\subsection{VLA observations and data reduction}\n\nWe observed all sources in the standard 4.86 GHz C-band with a 50 MHz bandwidth, resulting in a resolution of $\\sim$0\\farcs3 in the A-array and $\\sim$1\\arcsec\\ in the BnA-array. We spent 5 minutes on each source, implying a theoretical rms level of 75 $\\mu$Jy, or a ratio of total integrated signal over map noise of 110 for the weakest sources, assuming no spectral curvature beyond 1.4 GHz.\nWe performed calibration and data editing in \\aips, the Astronomical Image Processing System from NRAO.\nWe used 3C286 as the primary flux calibrator in all runs. Comparison of the flux density of 3C48 with the predicted values indicated the absolute flux density scale was accurate up to 2\\%. We observed nearby (within 15\\arcdeg) secondary flux calibrators every 15 to 20 minutes to calibrate the phases. After flagging of bad data, we spilt the uv-data up into separate data sets for imaging and self-calibration in DIFMAP, the Caltech difference mapping program (\\cite{she97}).\nWe used field sizes of 164\\arcsec\\ (A$-$array) or 256\\arcsec\\ (BnA$-$array) with pixel scales of 0\\farcs08 / pixel (A$-$array) or 0\\farcs25 / pixel (BnA$-$array). Even the smallest field of view is still four times larger than the resolution of the NVSS, so all components of an unresolved NVSS source will be covered.\n\nWe cleaned each source brighter than the 5$\\sigma$ level, followed by a phase-only self-calibration. We repeated the latter for all sources in the field of a source. Next, we made a new model from the (self-calibrated) uv-data, and subsequently cleaned to the level reached before. The last stage in the mapping routine was a deep clean with a 1\\% gain factor over the entire field. Most of the resulting maps have noise levels in the range 75 to 100 $\\mu$Jy, as expected.\n\n\\subsection{ATCA observations and data reduction}\nWe used the ATCA in the 6C configuration, which has a largest baseline of 6km. We observed at a central frequency of 1.384 GHz, which was selected to avoid local interference. We used 21 of the 30 frequency channels that had high enough signal, which resulted in an effective central frequency of 1.420 GHz, with a 84 MHz bandwidth. In order to obtain a good uv-coverage, we observed each source eight to ten times for three minutes, spread in hour angle. The primary flux calibrator was the source 1934-648; we used secondary flux calibrators within 20\\arcdeg\\ of the sources to calibrate the phases.\nWe performed editing and calibration in \\aips, following standard procedures. We made maps using the automated mapping/self-calibration procedure MAPIT in \\aips. The resulting 1.420 GHz maps (Fig. \\ref{mpatca}) have noise levels of $\\sim$5 mJy.\n\n\\subsection{Results}\nOf all 343 WN sources, 139 have FIRST maps (appendix B.2). All remaining 204 sources were observed, and 141 were detected. The remaining 30\\% were too faint at 4.86~GHz to be detected in 5~min snapshots, because their high frequency spectral index steepens more than expected, or they were over-resolved. Because they are significantly brighter, all the observed 89 TN and 41 MP sources were detected.\nWe present contour maps of all the detections in Appendices B.1, B.3, B.5, and B.6 and list the source parameters in Tables A.1 to A.3.\n\nWe have subdivided our sources into 5 morphological classes, using a classification similar to that used by R\\\"ottgering \\etal\\ (1994). Note that this classification is inevitably a strong function of the resolution, which varies by a factor of 20 between the VLA A-array and the ATCA observations. \n\nWe have determined the source parameters by fitting two-dimensional Gaussian profile to all the components of a source. The results are listed in Tables A.1 to A.3 which contain:\n\n\\begin{description}\n\\item[Col 1:]{Name of the source in IAU J2000 format. The 2-letter prefix indicates the sample: WN: WENSS--NVSS, TN: Texas--NVSS, MP: MRC--PMN.}\n\\item[Col 2:]{The integrated flux density from the low-frequency catalog.}\n\\item[Col 3:]{The integrated flux density at the intermediate frequency, determined from the NVSS for WN and TN, or from the 1.420~GHz ATCA observations for the MP sample.}\n\\item[Col 4:]{The integrated flux density at 4.86 GHz, determined from the VLA observations for WN and TN, and from the PMN survey for the MP sample.}\n\\item[Col 5:]{The lower frequency two-point spectral index. This is the spectral index used to define the WN and TN samples.}\n\\item[Col 6:]{The higher frequency two-point spectral index. This is the spectral index used to define the MP sample.}\n\\item[Col 7:]{Morphological classification code: single (S), double (D), triple (T) and multiple (M) component sources, and irregularly shaped diffuse (DF) sources.}\n\\item[Col 8:]{Largest angular size. For single component sources, this is the de-convolved major axis of the elliptical Gaussian, or, for unresolved sources (preceded with $<$), an upper limit is given by the resolution. For double, triple and multiple component sources, this is the largest separation between their components. For diffuse sources this is the maximum distance between the source boundaries defined by three times the map rms noise.}\n\\item[Col 9:]{De-convolved position angle of the radio structure, measured North through East}\n\\item[Col 10 -- 11:]{J2000 coordinates, determined from the map with position code listed in col. 12. The positions in the VLA and ATCA maps have been fitted with a single two-dimensional elliptical Gaussian. For double (D) sources, the geometric midpoint is given; for triples (T) and multiples (M), the core position is listed. For diffuse (DF) sources we list the center as determined by eye.}\n\\item[Col 12:]{Position code, indicating the origin of the morphological and positional data in column 7 to 11: A=ATCA, F=FIRST, M=MRC, N=NVSS, and V=VLA}.\n\\end{description}\n\n\\subsection{Notes on individual sources}\n\\noindent{\\bf WN~J0043+4719:} The source 18\\arcsec\\ north of the NVSS position is not detected in the NVSS. This is therefore not a real USS source because the NVSS flux density was underestimated.\n\n\\noindent{\\bf WN~J0048+4137:} Our VLA map probably doesn't go deep enough to detect all the flux of this source.\n\n\\noindent{\\bf WN~J0727+3020:} The higher resolution FIRST map shows that both components of this object are indeed identified on the POSS, even though the NVSS position is too far off to satisfy our identification criterion.\n\n\\noindent{\\bf WN~J0717+4611:} Optical and near-IR spectroscopy revealed this object as a red quasar at $z=1.462$ (\\cite{deb98b}).\n\n\\noindent{\\bf WN~J0725+4123:} The extended POSS identification suggest this source is located in a galaxy cluster.\n\n\\noindent{\\bf WN~J0829+3834:} The NVSS position of this unresolved source is 7\\arcsec\\ ($3\\sigma$) from the FIRST position, which itself is only at 2\\arcsec\\ from the WENSS position.\n\n\\noindent{\\bf WN~J0850+4830:} The difference with the NVSS position indicates that our VLA observations are not deep enough to detect a probable north-eastern component.\n\n\\noindent{\\bf WN~J0901+6547:} This 38\\arcsec\\ large source is over-resolved in our VLA observations, and probably even misses flux in the NVSS, and is therefore not a real USS source.\n\n\\noindent{\\bf WN~J1012+3334:} The bend morphology and bright optical sources to the east indicate this object is probably located in a galaxy cluster.\n\n\\noindent{\\bf WN~J1101+3520:} The faint FIRST component 20\\arcsec\\ north of the brighter Southern component is not listed in the FIRST catalog, but is within 1\\arcsec\\ of a faint optical object. This might be the core of a 70\\arcsec\\ triple source.\n\n\\noindent{\\bf WN~J1152+3732:} The distorted radio morphology and bright, extended POSS identification suggest this source is located in a galaxy cluster.\n\n\\noindent{\\bf WN~J1232+4621:} This optically identified and diffuse radio source suggest this source is located in a galaxy cluster.\n\n\\noindent{\\bf WN~J1314+3515:} The diffuse radio source appears marginally detected on the POSS.\n\n\\noindent{\\bf WN~J1329+3046A,B, WN~J1330+3037, WN~J1332+3009 \\& WN~J1333+3037:} The noise in the FIRST image is almost ten times higher than average due to the proximity of the $S_{1400}$=15~Jy source 3C~286.\n\n\\noindent{\\bf WN~J1330+5344:} The difference with the NVSS position indicates that our VLA observations are not deep enough to detect a probable south-eastern component.\n\n\\noindent{\\bf WN~J1335+3222:} Although the source appears much like the hotspot of a larger source with the core 90\\arcsec\\ to the east, no other hotspot is detected in the FIRST within 5\\arcmin.\n\n\\noindent{\\bf WN~J1359+7446:} The extended POSS identification suggests this source is located in a galaxy cluster.\n\n\\noindent{\\bf WN~J1440+3707:} The equally bright galaxy 30\\arcsec\\ south of the POSS identification suggests that this source is located in a galaxy cluster.\n\n\\noindent{\\bf WN~J1509+5905:} The difference with the NVSS position indicates that our VLA observations are not deep enough to detect a probable western component.\n\n\\noindent{\\bf WN~J1628+3932:} This is the well studied galaxy NGC~6166 in the galaxy cluster Abell 2199 (\\eg \\cite{zab93}.\n\n\\noindent{\\bf WN~J1509+5905:} The difference with the NVSS position indicates that our VLA observations are not deep enough to detect a probable west-south-western component.\n\n\\noindent{\\bf WN~J1821+3601:} The source 35\\arcsec\\ south-west of the NVSS position is not detected in the NVSS. This is therefore not a real USS source because the NVSS flux density was underestimated.\n\n\\noindent{\\bf WN~J1832+5354:} The source 19\\arcsec\\ north-east of the NVSS position is not detected in the NVSS. This is therefore not a real USS source because the NVSS flux density was underestimated.\n\n\\noindent{\\bf WN~J1852+5711:} The extended POSS identification suggests this source is located in a galaxy cluster.\n\n\\noindent{\\bf WN~J2313+3842:} The extended POSS identification suggests this source is located in a galaxy cluster.\n\n\\noindent{\\bf TN~J0233+2349:} This is probably the north-western hotspot of a 35\\arcsec\\ source, with the south-eastern component barely detected in our VLA map. \n\n\\noindent{\\bf TN~J0309-2425:} We have classified this source as a 13\\arcsec\\ double, but the western component might also be the core of a 45\\arcsec\\ source, with the other hotspot around $\\alpha = 3^h9^m10^s, \\delta=-24\\arcdeg25\\arcmin50\\arcsec$.\n\n\\noindent{\\bf TN~J0349-1207:} The core-dominated structure is reminiscent of the red quasar WN~J0717+4611.\n\n\\noindent{\\bf TN~J0352-0355:} This is probably the south-western hotspot of a 30\\arcsec\\ source.\n\n\\noindent{\\bf TN~J0837-1053:} Given the 10\\arcsec\\ difference between the positions of the NVSS and diffuse VLA source, this is probably the northern component of a larger source.\n\n\\noindent{\\bf TN~J0408-2418:} This is the z=2.44 source MRC 0406-244 (\\cite{mcc96}). The bright object on the POSS is a foreground star to the north-east of the R=22.7 galaxy.\n\n\\noindent{\\bf TN~J0443-1212:} Using the higher resolution VLA image, we can identify this radio source with a faint object on the POSS.\n\n\\noindent{\\bf TN~J2106-2405:} This is the z=2.491 source MRC 2104-242 (\\cite{mcc96}). The identification is an R=22.7 object, not the star to the north-north-west of the NVSS position.\n%---------------------------------------------------------- wnspeccurv\n\\begin{figure}\n\\psfig{file=ds1811f9.eps,width=9cm,angle=90}\n\\caption[wnspeccurv]{Radio ``color-color'' plots for the WN sample. The abscissa is the $\\alpha_{325}^{1400}$ spectral index used to construct the sample. The ordinates are the low-frequency spectral indices determined from the 8C (38 MHz, \\cite{ree90}) or 6C (151 MHz, \\cite{hal93}) and the 325~MHz WENSS (left panel), and the high frequency spectral index determined between the 1.4~GHz NVSS and our 4.86~GHz VLA observations (right panel). The line in each panel indicates a straight power law spectrum. Note the unequal number of points on either side of these lines, indicating substantial spectral curvature. \\label{wnspeccurv}}\n\\end{figure}\n%______________________________________________________________\n\n\\subsection{Radio spectra and spectral curvature}\n\nWe have used the CATS database at the Special Astronomical Observatory (\\cite{ver97}) to search for all published radio measurements of the sources in our samples. In Appendix C, we show the radio spectra for all sources with flux density information for more than two frequencies (the $S_{4860}$ points from our VLA observations are also included). These figures show that most radio spectra have curved spectra, with flatter spectral indices below our selection frequencies, as has been seen in previous USS studies (see \\eg\\ \\cite{rot94}, \\cite{blu98}). \n\nThis low frequency flattening and high frequency steepening is obvious in the radio 'color-color diagrams' of the WN sample (Fig. \\ref{wnspeccurv}). The median spectral index at low frequencies ($\\nu < 325$~MHz) is $-1.16$, while the median $\\bar{\\alpha}_{325}^{1400} = -1.38$. At higher frequencies ($\\nu > 1400$~MHz), the steepening continues to a median $\\bar{\\alpha}_{1400}^{4850} = -1.44$. Note that the real value of the latter is probably even steeper, as 30\\% of the WN sources were not detected in our 4.86~GHz VLA observations, and may therefore have even more steepened high-frequency spectral indices.\n\n\\subsection{Radio source properties}\n\\subsubsection{Radio source structure and angular size}\n\nIn Table 5, we give the distribution of the radio structures of the 410 USS sources for which we have good radio-maps. At first sight, all three our samples have basically the same percentage of resolved sources, but the similar value for the MP sample is misleading, as it was observed at much lower resolution.\n\n\\begin{table}\n\\centerline{\\bf Table 5: Radio Structure Distribution}\n\\tiny\n\\begin{center}\n\\begin{tabular}{lrrrr}\n\\\\\n & \\multicolumn{4}{c}{USS Samples} \\\\\n\\cline{2-5} \\\\\nMorphology & WN$\\qquad$ & TN$\\qquad$ & MP$\\qquad$ & Combined$\\quad$\\\\\n\\hline\nSingle & 157 (56$\\pm$4\\%) & 43 (48$\\pm$7\\%) & 23 (56$\\pm$12\\%) & 223 (54$\\pm$4\\%) \\\\\nDouble & 81 (29$\\pm$3\\%) & 28 (31$\\pm$6\\%) & 16 (39$\\pm$10\\%) & 125 (31$\\pm$3\\%) \\\\\nTriple & 22 ( 8$\\pm$2\\%) & 9 (10$\\pm$3\\%) & 0 ( 0$\\pm$ 0\\%) & 31 ( 8$\\pm$1\\%) \\\\\nMultiple & 2 ( 1$\\pm$1\\%) & 4 ( 5$\\pm$2\\%) & 0 ( 0$\\pm$ 0\\%) & 6 ( 1$\\pm$1\\%) \\\\\nDiffuse & 18 ( 6$\\pm$2\\%) & 5 ( 6$\\pm$3\\%) & 2 ( 5$\\pm$ 3\\%) & 25 ( 6$\\pm$1\\%) \\\\\n\\hline\n\\# Observed & 280 & 89 & 41 & 410 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n%---------------------------------------------------------- slas\n\\begin{figure}\n\\psfig{file=ds1811f10.eps,width=9cm}\n\\caption[slas]{Median angular size for the flux density limited, spectrally unbiased WSRT samples of \\cite{oor88} (open triangles), and for our combined USS samples (filled squares). The sources have been binned in equal number bins, and errors represent the 35\\% and 65\\% levels of the distribution. Note that our USS selection does not affect the value of the median, and that our USS samples also exclude sources that fall below the break at $S_{1400} \\lesssim 10$~mJy. \\label{slas}}\n\\end{figure}\n%______________________________________________________________\n\nOur results are different from the USS sample of R\\\"ottgering \\etal\\ (1994), which contains only 18\\% unresolved sources at comparable resolution (1\\farcs5). To check if this effect is due to the fainter sources in our sample, we compared our sample with the deep high resolution VLA observations of spectrally unbiased sources (\\cite{oor88}; \\cite{col85}).\nThe resolution of our observations is significantly better than the median angular size for $S_{1400} > 1$~mJy sources, allowing us to accurately determine the median angular sizes in our samples.\nWe find that our USS sources have a constant median angular size of $\\sim6$\\arcsec\\ between 10~mJy and 1~Jy (Fig. \\ref{slas}). This is indistinguishable from the results from samples without spectral index selection. It indicates that our USS selection of sources with $\\alpha < -1.3$ and $\\Theta < 1\\arcmin$ does not bias the angular size distribution in the resulting sample. The 'downturn' in angular sizes that occurs at $\\sim$1~mJy is probably due to a different radio source population, which consist of lower redshift sources in spiral galaxies (see \\eg, \\cite{col85}, \\cite{oor87}, \\cite{ben93}). By selecting only sources with $S_{1400} > 10$~mJy, we have avoided ``contamination'' of our sample by these foreground sources.\n\nWe have searched for further correlations between spectral index or spectral curvatures and angular size or flux density, but found no significant results, except for a trend for more extended sources to have lower than expected 4.86~GHz flux densities, but this effect can be explained by missing flux at large scales in our VLA observations.\n\n\\subsection{Identifications}\n\\subsubsection{POSS}\nWe have searched for optical identifications of our USS sources on the digitized POSS-I. We used the likelihood ratio identification criterion as described by \\eg de Ruiter \\etal\\ (1977). In short, this criterion compares the probability that a radio and optical source with a certain positional difference are really associated with the probability that this positional difference is due to confusion with a field object (mostly a foreground star), thereby incorporating positional uncertainties in both radio and optical positions. The ratio of these probabilities is expressed as the likelihood ratio $LR$. \nIn the calculation, we have assumed a density of POSS objects $\\rho = 4 \\times 10^{-4}$ \\arcsec$^{-2}$, independent of galactic latitude $b$. \nWe have adopted a likelihood ratio cutoff \\Lh=1.0, slightly lower than the values used by de Ruiter \\etal\\ (1977) and R\\\"ottgering \\etal\\ (1994). We list sources with $LR >$ 1.0 for our USS samples in Tables A.4 to A.6. We have included four WN sources (WN~J0704+6318, WN~J1259+3121, WN~J1628+3932 and WN~J2313+3842), two TN sources (TN~J0510-1838 and TN~J1521+0741) and four MP sources (MP~J0003-3556, MP~J1921-5431, MP~J1943-4030 and MP~J2357-3445) as identifications because both their optical and radio morphologies are diffuse and overlapping, making it impossible to measure a common radio and optical component, while they are very likely to be associated.\n\n%---------------------------------------------------------- idfraction\n\\begin{figure}\n\\psfig{file=ds1811f11.eps,width=9cm}\n\\caption[idfraction]{Identification fraction on the POSS as a function of spectral index for the combined WN and TN sample. Note the absence of a further decrease in the identification fraction with steepening spectral index. \\label{idfraction}}\n\\end{figure}\n%______________________________________________________________\n\nFigure \\ref{idfraction} shows the identification fraction of USS sources on the POSS ($R \\lesssim 20$). Because the distributions for the WN and TN are very similar, we have combined both samples to calculate the identification fraction. Unlike the results for 4C USS (\\cite{tie79,blu79}), we do not detect a decrease of the identification fraction with steepening spectral index\\footnote{In the Westerbork faint USS (\\cite{wie92}) or the USS sample from R\\\"ottgering \\etal\\ (1994), there is also a decrease in the identification fraction, even at limiting magnitudes of $R=22.5$ and $R=23.7$, indicating that this trend continues out to fainter magnitudes and radio fluxes}. We interpret the constant $\\sim$15\\% identification fraction from our sample as a combined population of foreground objects, primarily consisting of clusters (see next section). Our extremely steep spectral index criterion would then selected only radio galaxies too distant to be detected on the POSS ($R \\simgt 20.0$).\n\n\\subsubsection{Literature}\nUsing the NASA Extragalactic Database (NED), the SIMBAD database and the W$^3$Browse at the High Energy Astrophysics Science Archive Research Center, we have searched for known optical and X-ray identifications of sources in our samples (see appendices A.7 to A.9). Of the bright optical ($R \\lesssim 20$) identifications, only one source is a known as a K0-star, three (TN~J0055$+$2624, TN~J0102$-$2152, and TN~J1521$+$0742) are ``Relic radio galaxies'' (\\cite{kom94}, \\cite{gio99}), while all others are known galaxy clusters. \n\nAll optical cluster identifications, except MP~J1943-4030, are also detected in the ROSAT All-Sky survey Bright Source Catalogue (RASS-BSC; \\cite{vog99}). Conversely, of the 23 X-ray sources, seven are known galaxy clusters, and three known galaxies. The remaining 13 sources are good galaxy cluster candidates because they either show a clear over-density of galaxies on the POSS (eight sources), or they have low X-ray count rates ($<$ 0.02 counts s$^{-1}$), suggesting that these might be more distant galaxy clusters too faint to be detected on the POSS. We conclude that probably $>$3\\% of our USS sources are associated with galaxy clusters, and that the combined USS + X-ray selection is an efficient (up to 85\\%) selection technique to find galaxy clusters\\footnote{In the RASS-BSC, only 14\\% of the extra-galactic sources are identified with galaxy clusters (\\cite{vog99}).}.\n\nThree of our USS sources (WN~J2313+4253, TN~J0630-2834 and TN~J1136+1551) are previously known pulsars (\\cite{kap98}). It is worth noting that two out of nine sources in our USS samples with $\\alpha < -2$ are known pulsars. Because Lorimer \\etal\\ (1995) \\nocite{lor95} found the median spectral index of pulsars to be $\\sim -1.6$, we examined the distribution of spectral indices as a function of Galactic latitude. In figure \\ref{pulsargb}, we plot the percentage of $\\alpha_{325}^{1400} < -1.60$ pulsar candidates as a function of Galactic latitude. The four times higher density near the Galactic plane strongly suggests that the majority of these $\\alpha_{325}^{1400} < -1.60$ sources are indeed pulsars, which are confined to our Galaxy. A sample of such $\\alpha_{325}^{1400} < -1.60$ sources at $|b|<15$\\degr\\ would be an efficient pulsar search method.\n\n%---------------------------------------------------------- pulsargb\n\\begin{figure}\n\\psfig{file=ds1811f12.eps,width=9cm}\n\\caption[pulsargb]{Percentage of $\\alpha_{325}^{1400} < -1.60$ radio sources from a WENSS--NVSS correlation as a function of Galactic latitude. Note the clear peak near the Galactic plane, indicating that these $\\alpha_{325}^{1400} < -1.60$ objects might well be Galactic pulsars. \\label{pulsargb}}\n\\end{figure}\n%______________________________________________________________\n\nWe also note that no known quasars are present in our sample. Preliminary results from our optical spectroscopy campaign (De Breuck \\etal\\ 1998b, 2000) indicate that $\\sim$10\\% of our sample are quasars. We interpret this lack of previously known quasars are a selection bias in quasar samples against USS sources.\n\nAt $R \\simgt 20$, all five USS sources with known redshift are HzRGs, indicating a selection of sources without detections on the POSS strongly increases our chances of finding HzRGs.\n\n\\section{Conclusions}\nWe have constructed three spatially separated samples of USS sources containing a total of 669 objects. High-resolution radio observations of more than half of these show that the median size is $\\sim$6\\arcsec, independent of 1.4 GHz flux density, which is consistent with results of similar resolution surveys of samples without spectral index selection. The absence of a downturn in angular size at the lowest fluxes indicates that we do not include significant numbers of spiral galaxies in our sample. A USS sample fainter than ours would therefore include more of these foreground sources, and be less efficient to find HzRGs. \n\nThe identification fraction on the POSS is $\\sim$15\\%, with no clear dependence on spectral index, indicating that the HzRGs in the sample are all too distant to be detected, and the POSS detections consist of different classes of objects. A correlation of our USS samples with X-ray catalogs showed that at least 85\\% of the X-ray identifications seem to be galaxy clusters known from the literature or by inspection of the POSS. We conclude that (1) the majority of the 'non HzRG' USS sources in our sample are clusters, and (2) the combined selection of USS and X-ray sources is an extremely efficient technique to select galaxy clusters.\n\nThe above results indicate that up to 85\\% of our USS sample might be HzRGs. To identify these objects, we have started an intensive program of R- and K-band imaging on 3--10m class telescopes.\nInitial results from optical spectroscopy indicate that 2/3 are indeed $z>2$ radio galaxies (\\cite{deb98a}), and K-band imaging of optically undetected ($R > 25$) sources (see \\eg, \\cite{wvb99a}) has already lead to the discovery of the first radio galaxy at $z>5$ (\\cite{wvb99b}). \n\n\\begin{acknowledgements}\n\nWe are grateful for the excellent help provided by the staff of the\nVLA and ATCA observatories, with special thanks to Chris Carilli and\nGreg Taylor (NRAO), and Ray Norris and Kate Brooks (ATNF) for help in\nwith observation planning and data reduction. We thank Hien ``Napkin''\nTran for his comments on the manuscript. The VLA is a facility of the\nNational Radio Astronomy Observatory, which is operated by Associated\nUniversities Inc. under cooperative agreement with the National\nScience Foundation. The Australia Telescope is funded by the\nCommonwealth of Australia for operation as a National Facility managed\nby CSIRO. The authors made use of the database CATS (\\cite{ver97}) of\nthe Special Astrophysical Observatory, the NASA/IPAC Extragalactic\nDatabase (NED) which is operated by the Jet Propulsion Laboratory,\nCalifornia Institute of Technology, under contract with the National\nAeronautics and Space Administration, and the High Energy Astrophysics\nScience Archive Research Center Online Service, provided by the\nNASA/Goddard Space Flight Center. Work performed at the Lawrence\nLivermore National Laboratory is supported by the DOE under contract\nW7405-ENG-48.\n\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\\bibitem[Abell \\etal\\ 1989]{abe89} Abell, G. O., Corwin, H. G. Jr., \\& Olowin, R. 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Morganti, Sydney, p.\\ 236\n\\bibitem[van Breugel \\etal\\ 1999b]{wvb99b} van Breugel, W., De Breuck, C., Stanford\n, S. A., Stern, D., R\\\"ottgering, H., \\& Miley, G. 1999, \\apj, 518, 61\n\\bibitem[Verkhodanov \\etal\\ 1997]{ver97} Verkhodanov O. V., Trushkin S. A., Andernach H., Chernenkov V. N. 1997, in \"Astronomical Data Analysis Software and Systems VI\", ed.: G. Hunt and H. E. Payne, ASP Conference Series, Vol. 125, p.\\ 322-325.\n\\bibitem[Vigotti \\etal\\ 1989]{vig89} Vigotti, M., Grueff, G., Perley, R., Clark, B. G., \\& Bridle, A. 1989, \\aj, 98, 419\n\\bibitem[Voges \\etal\\ 1999]{vog99} Voges, W., \\etal\\ 1999, \\aap, 349, 389 \n\\bibitem[Waddington \\etal\\ 1999]{wad99} Waddington, I., Windhorst, R., Cohen, S., Partridge, R., Spinrad, H., \\& Stern, D. 1999, \\apjl, 526, L77 \n\\bibitem[Weymann et al. 1998]{wey98} Weymann, R. \\etal\\ 1998, \\apjl, 505, L95 \n\\bibitem[White, Giommi \\& Angelini 1994]{whi94} White, N. E., Giommi, P. \\& Angelini, L. 1994, \\iaucirc, 6100, 1\n\\bibitem[White \\etal\\ 1997]{whi97} White, R. L., Becker, R. H., Helfand, D. J., \\& Gregg, M. D. 1997, \\apj, 475, 479\n\\bibitem[White \\etal\\ 2000]{whi00} White, R. L. \\etal 2000, \\apjs, in press, astro-ph/9912215\n\\bibitem[Wieringa 1991]{wie91} Wieringa, M. H., Ph. D. thesis, Rijksuniversiteit Leiden\n\\bibitem[Wieringa \\& Katgert 1992]{wie92} Wieringa, M. H., \\& Katgert, P. 1992, \\aasup, 93, 399\n\\bibitem[Windhorst \\etal\\ 1985]{win85} Windhorst, R. A., Miley, G. K., Owen, F. N., Kron, R. G., \\& Koo, D. C. 1985, \\apj, 289, 494\n\\bibitem[Witzel \\etal\\ 1979]{wit79} Witzel, A., Schmidt, J., Pauliny-Toth, I. I. K., \\& Nauber, U. 1979, \\aj, 84, 942\n\\bibitem[Wright \\etal\\ 1994]{wri94} Wright, A. E., Griffith, M. R., Burke, B. F., \\& Ekers, R. D. 1994, \\apjs, 91, 111\n\\bibitem[Wright \\etal\\ 1996]{wri96} Wright, A. E., Griffith, M. R., Troup, E., Hunt, A., Burke, B. F., \\& Ekers, R. D. 1996, \\apjs, 103, 145\n\\bibitem[Zabludoff \\etal\\ 1993]{zab93} Zabuldoff, A. I., Geller, M. J., Huchra, J. P., \\& Vogeley, M. S. 1993, \\aj, 106, 1273\n\\end{thebibliography}\n\n\\appendix\n\\section{Source Lists}\n\\include{wntable}\n\\include{tnmptable}\n\n\\begin{table}\n\\footnotesize\n\\centerline{\\bf Table A.4: WN POSS identifications}\n\\begin{tabular}{rrrrr}\nName & $S_{1400}$ & $\\alpha_{325}^{1400}$ & LAS & LR$^a$ \\\\\n & mJy & & \\arcsec & \\\\\n\\hline\nWN J0029$+$3439 & 40.9 & $-$1.34 & 12.8 & 4.2 \\\\\nWN J0121$+$4305 & 50.8 & $-$1.39 & \\nodata & 7.1 \\\\\nWN J0315$+$3757 & 13.3 & $-$1.35 & 1.7 & 14.8 \\\\\nWN J0559$+$6926 & 12.9 & $-$1.31 & 0.3 & 4.6 \\\\\nWN J0641$+$4325 & 15.6 & $-$1.57 & \\nodata & 195.6 \\\\\nWN J0725$+$4123 & 35.5 & $-$1.39 & 8.3 & 183.0 \\\\\nWN J0756$+$5010 & 29.9 & $-$1.31 & 1.7 & 127.3 \\\\\nWN J0830$+$3018 & 13.9 & $-$1.41 & 3.5 & 27.3 \\\\\nWN J0835$+$3439 & 19.1 & $-$1.38 & 58.0 & 24.6 \\\\\nWN J0923$+$4602 & 12.1 & $-$1.49 & 21.6 & 17.0 \\\\\nWN J0952$+$5153 & 16.1 & $-$1.76 & 2.7 & 194.1 \\\\\nWN J0955$+$6023 & 10.9 & $-$1.54 & 3.1 & 1.0 \\\\\nWN J1014$+$7407 & 21.8 & $-$1.41 & 2.2 & 147.7 \\\\\nWN J1026$+$2943 & 12.0 & $-$1.31 & 11.9 & 136.5 \\\\\nWN J1030$+$5415 & 29.2 & $-$1.39 & 6.1 & 16.4 \\\\\nWN J1052$+$4826 & 154.2 & $-$1.31 & 10.0 & 38.1 \\\\\nWN J1124$+$3228 & 38.9 & $-$1.31 & 5.7 & 101.2 \\\\\nWN J1130$+$4911 & 18.9 & $-$1.34 & 37.0 & 18.9 \\\\\nWN J1141$+$6924 & 11.8 & $-$1.32 & \\nodata & 1.4 \\\\\nWN J1148$+$5116 & 20.5 & $-$1.35 & 6.7 & 1.0 \\\\\nWN J1152$+$3732 & 17.1 & $-$2.18 & 15.0 & 159.9 \\\\\nWN J1232$+$4621 & 19.8 & $-$1.30 & 12.5 & 42.9 \\\\\nWN J1258$+$5041 & 28.8 & $-$1.42 & 44.9 & 3.7 \\\\\nWN J1259$+$3121 & 34.0 & $-$1.41 & 20.6 & 0.0 \\\\\nWN J1330$+$6505 & 10.5 & $-$1.34 & 1.8 & 21.5 \\\\\nWN J1353$+$3336 & 15.9 & $-$1.31 & \\nodata & 3.3 \\\\\nWN J1400$+$4348 & 20.2 & $-$1.49 & 6.4 & 29.2 \\\\\nWN J1403$+$3109 & 45.7 & $-$1.35 & 11.0 & 148.5 \\\\\nWN J1410$+$4615 & 14.2 & $-$1.36 & 4.4 & 42.5 \\\\\nWN J1440$+$3707 & 16.7 & $-$1.76 & 7.4 & 182.0 \\\\\nWN J1459$+$4947 & 18.7 & $-$1.53 & 3.0 & 47.2 \\\\\nWN J1558$+$7028 & 15.7 & $-$1.36 & 2.1 & 2.8 \\\\\nWN J1624$+$4202 & 11.0 & $-$1.31 & 24.4 & 182.2 \\\\\nWN J1628$+$3932 & 3680.7 & $-$1.36 & 48.8 & 0.0 \\\\\nWN J1717$+$3828 & 35.8 & $-$1.60 & 33.6 & 141.4 \\\\\nWN J1752$+$2949 & 16.9 & $-$1.42 & 3.2 & 3.4 \\\\\nWN J1801$+$3336 & 11.6 & $-$1.69 & 2.5 & 1.5 \\\\\nWN J1815$+$3656 & 17.6 & $-$1.34 & 1.6 & 195.0 \\\\\nWN J1819$+$6213 & 12.7 & $-$1.45 & 1.6 & 122.9 \\\\\nWN J1852$+$5711 & 53.4 & $-$1.36 & \\nodata & 145.4 \\\\\nWN J1927$+$6436 & 80.3 & $-$1.44 & 20.1 & 6.2 \\\\\nWN J1944$+$6552 & 147.2 & $-$1.53 & 1.8 & 147.5 \\\\\nWN J2146$+$3330 & 10.8 & $-$1.56 & \\nodata & 4.6 \\\\\nWN J2147$+$3137 & 25.4 & $-$1.46 & \\nodata & 31.9 \\\\\nWN J2313$+$3842 & 11.3 & $-$1.50 & \\nodata & 0.0 \\\\\nWN J2313$+$4053 & 40.2 & $-$1.42 & 1.5 & 36.4 \\\\\n\\hline\n\\end{tabular}\n\n$^a$ Likelihood Ratio, see text\n\\vspace{1cm}\n\\end{table}\n\n\\begin{table}\n\\footnotesize\n\\centerline{\\bf Table A.5: TN POSS identifications}\n\\begin{tabular}{rrrrr}\nName & $S_{1400}$ & $\\alpha_{365}^{1400}$ & LAS & LR$^a$ \\\\\n & mJy & & \\arcsec & \\\\\n\\hline\nTN J0244$+$0327 & 84.8 & $-$1.38 & \\nodata & 6.9 \\\\\nTN J0245$+$2700 & 54.0 & $-$1.47 & \\nodata & 30.5 \\\\\nTN J0250$+$0130 & 39.1 & $-$1.45 & \\nodata & 14.7 \\\\\nTN J0256$-$2717 & 177.9 & $-$1.32 & \\nodata & 126.6 \\\\\nTN J0301$+$0155 & 402.7 & $-$1.70 & \\nodata & 21.3 \\\\\nTN J0433$+$0717 & 33.1 & $-$1.44 & \\nodata & 29.9 \\\\\nTN J0443$-$1212 & 56.8 & $-$1.47 & 20.2 & 162.1 \\\\\nTN J0510$-$1838 & 641.3 & $-$1.76 & 36.1 & 0.0 \\\\\nTN J0729$+$2436 & 68.9 & $-$2.03 & 19.4 & 129.0 \\\\\nTN J0812$+$0915 & 43.4 & $-$1.38 & \\nodata & 37.7 \\\\\nTN J0818$-$0741 & 59.3 & $-$1.38 & \\nodata & 96.5 \\\\\nTN J0958$-$1103 & 70.6 & $-$1.35 & \\nodata & 181.8 \\\\\nTN J1043$+$2404 & 52.0 & $-$1.59 & 3.7 & 167.8 \\\\\nTN J1053$-$1518 & 63.7 & $-$1.33 & \\nodata & 1.8 \\\\\nTN J1117$-$1409 & 134.5 & $-$1.31 & \\nodata & 128.0 \\\\\nTN J1220$+$0604 & 65.1 & $-$1.50 & \\nodata & 189.4 \\\\\nTN J1239$+$1005 & 79.3 & $-$1.75 & \\nodata & 180.7 \\\\\nTN J1245$-$1127 & 88.0 & $-$1.32 & \\nodata & 146.1 \\\\\nTN J1326$-$2330 & 83.2 & $-$1.37 & \\nodata & 190.1 \\\\\nTN J1408$-$0855 & 114.3 & $-$1.34 & \\nodata & 160.9 \\\\\nTN J1418$-$2256 & 82.0 & $-$1.38 & 7.6 & 85.4 \\\\\nTN J1513$-$2417 & 83.6 & $-$1.34 & \\nodata & 2.5 \\\\\nTN J1521$+$0741 & 105.6 & $-$2.10 & \\nodata & 0.0 \\\\\nTN J1531$-$3234 & 80.6 & $-$1.39 & 4.8 & 172.5 \\\\\nTN J1547$-$2218 & 72.4 & $-$1.32 & \\nodata & 7.1 \\\\\nTN J1556$-$2759 & 66.4 & $-$1.65 & \\nodata & 9.2 \\\\\nTN J1628$+$1604 & 55.5 & $-$1.77 & \\nodata & 153.7 \\\\\nTN J1646$-$1328 & 102.5 & $-$1.32 & \\nodata & 119.7 \\\\\nTN J1701$+$0252 & 57.1 & $-$1.36 & \\nodata & 19.4 \\\\\nTN J1707$-$1120 & 54.2 & $-$1.53 & \\nodata & 85.5 \\\\\nTN J1710$-$0826 & 69.2 & $-$1.38 & \\nodata & 8.8 \\\\\nTN J1953$-$0541 & 59.0 & $-$1.56 & \\nodata & 71.3 \\\\\nTN J2028$+$0811 & 74.8 & $-$1.34 & \\nodata & 33.1 \\\\\nTN J2155$-$2109 & 77.2 & $-$1.31 & \\nodata & 184.6 \\\\\nTN J2335$+$0634 & 84.3 & $-$1.33 & \\nodata & 189.2 \\\\\n\\hline\n\\end{tabular}\n\n$^a$ Likelihood Ratio, see text\n\\vspace{1cm}\n\\end{table}\n\n\\begin{table}\n\\footnotesize\n\\centerline{\\bf Table A.6: MP UKST identifications}\n\\begin{tabular}{rrrrr}\nName & $S_{408}$ & $\\alpha_{408}^{4850}$ & LAS & LR$^a$ \\\\\n & mJy & & \\arcsec & \\\\\n\\hline\nMP J0003$-$3556 & 2440 & $-$1.28 & \\nodata & 0.0 \\\\\nMP J0103$-$3225 & 2290 & $-$1.29 & \\nodata & 88.1 \\\\\nMP J0618$-$7340 & 750 & $-$1.37 & \\nodata & 7.5 \\\\\nMP J1033$-$3418 & 5590 & $-$1.23 & \\nodata & 81.7 \\\\\nMP J1250$-$4026 & 1350 & $-$1.24 & 7.4 & 131.0 \\\\\nMP J1921$-$5431 & 4590 & $-$1.71 & \\nodata & 0.0 \\\\\nMP J1943$-$4030 & 4400 & $-$1.36 & \\nodata & 0.0 \\\\\nMP J2313$-$4243 & 1390 & $-$1.28 & \\nodata & 95.5 \\\\\nMP J2357$-$3445 & 8700 & $-$1.74 & \\nodata & 0.0 \\\\\n\\hline\n\\end{tabular}\n\n$^a$ Likelihood Ratio, see text\n\\vspace{1cm}\n\\end{table}\n\n\\begin{table*}\n\\centerline{\\bf Table A.7: WN identifications from the literature}\n\\begin{tabular}{rrrrrr}\nName & $z$ & $R$[mag] & $F_X^a$ & Identification & Reference \\\\\n\\hline\nWN J0633$+$4653 & \\nodata & 23.6 & \\nodata & 4C +46.12 & \\cite{cha96a} \\\\\nWN J0648$+$4309 & \\nodata & 23.0 & \\nodata & B3 0644+432 & \\cite{wie92} \\\\\nWN J0658$+$4444 & \\nodata & 23.4 & \\nodata & B3 0654+448 & \\cite{wie92} \\\\\nWN J0717$+$4611 & 1.462 & 21.6 & \\nodata & B3 0714+462 & \\cite{deb98b} \\\\\nWN J0725$+$4123 & \\nodata & \\nodata & 0.1137 & 1RXS J072600.0+4 & \\cite{vog99} \\\\\nWN J0923$+$4602 & \\nodata & \\nodata & 0.0242 & 1WGA J0923.1+460 & \\cite{whi94}\\\\\nWN J0952$+$5153 & 0.214 & \\nodata & 0.2413 & ZwCl 0949.6+5207 & \\cite{vog99} \\\\\nWN J1148$+$5116 & \\nodata & \\nodata & 0.0508 & 1RXS J114802.7+5 & \\cite{vog99} \\\\\nWN J1152$+$3732 & \\nodata & \\nodata & 0.0192 & 1WGA J1152.5+373 & \\cite{whi94} \\\\\nWN J1259$+$3121 & \\nodata & 16.2 & \\nodata & NGP9 F323-0140639 & \\cite{ode96} \\\\\nWN J1332$+$3009 & \\nodata & 19.8 & \\nodata & NGP9 F324-0235590 & \\cite{ode96} \\\\\nWN J1352$+$4259 & \\nodata & 21.7 & \\nodata & 4C +43.31 & \\cite{vig89} \\\\\nWN J1359$+$7447 & \\nodata & \\nodata & 0.07485 & 1RXS J135916.0+7 & \\cite{vog99} \\\\\nWN J1400$+$4348 & \\nodata & 8.2 & & HD122441 & SIMBAD \\\\\nWN J1410$+$4615 & \\nodata & \\nodata & & SHK 010 & \\cite{sha73} \\\\\nWN J1436$+$6319 & 4.261 & 24.1 & \\nodata & 4C +63.20 & \\cite{lac94} \\\\\nWN J1440$+$3707 & \\nodata & \\nodata & 0.07944 & 1RXS J144005.4+3 & \\cite{vog99} \\\\\nWN J1628$+$3932 & 0.031 & 13.1 & 4.5 & NGC 6166 & \\cite{zab93} \\\\\nWN J1736$+$6502 & \\nodata & 22.2 & \\nodata & 8C 1736+650 & \\cite{lac93} \\\\\nWN J1829$+$6913 & \\nodata & \\nodata & 0.05765 & 1RXS J182903.8+6 & \\cite{vog99} \\\\\nWN J1852$+$5711 & \\nodata & \\nodata & 0.1466 & 1RXS J185209.4+5 & \\cite{vog99} \\\\\nWN J1944$+$6552 & \\nodata & \\nodata & 0.1118 & 1RXS J194423.1+6 & \\cite{vog99} \\\\\nWN J2319$+$4251 & \\nodata & \\nodata & 0.1255 & 1RXS J231947.4+4 & \\cite{vog99} \\\\\n\\hline\n\\end{tabular}\n\n$^a$F$_X$ is the number of X-ray counts s$^{-1}$ as listed in the cited catalogs.\n\n\\vspace{1cm}\n\\end{table*}\n\n\\begin{table*}\n\\centerline{\\bf Table A.8: TN identifications from the literature}\n\\begin{tabular}{rrrrrr}\nName & $z$ & $R$[mag] & $F_X^a$ & Identification & Reference \\\\\n\\hline\nTN J0055$+$2624 & 0.1971 & \\nodata & \\nodata & ABELL 85 & \\cite{gio99} \\\\\nTN J0102$-$2152 & 0.0604 & \\nodata & \\nodata & ABELL 133 & \\cite{kom94} \\\\\nTN J0245$+$2700 & \\nodata & \\nodata & 0.0782 & 1RXS J024521.0+2 & \\cite{bad98} \\\\\nTN J0256$-$2717 & 0.480 & 19.2 & \\nodata & MRC 0254-27 & \\cite{mcc96} \\\\\nTN J0301$+$0155 & 0.170 & \\nodata & 0.2053 & ZwCl 0258.9+0142 & \\cite{cra95} \\\\\nTN J0408$-$2418 & 2.440 & 22.7 & \\nodata & MRC 0406-244 & \\cite{mcc96} \\\\\nTN J0510$-$1838 & \\nodata & 19.5 & 0.00314 & 1RXS J051032.4-1 & \\cite{vog99} \\\\\nTN J0630$-$2834 & \\nodata & \\nodata & 0.00314 & 1WGA J0630.8-283 & \\cite{whi94} \\\\\nTN J0729$+$2436 & \\nodata & \\nodata & 0.1752 & 1RXS J072927.4+2 & \\cite{vog99} \\\\\nTN J0936$-$2243 & 1.339 & 23.0 & \\nodata & 3C 222 & \\cite{hec94} \\\\\nTN J0958$-$1103 & 0.153 & \\nodata & 1.64 & ABELL 0907 & \\cite{mcc96} \\\\\nTN J1521$+$0742 & 0.045 & 14.5 & 1.64 & NGC 5920 & \\cite{kom94} \\\\\nTN J2106$-$2405 & 2.491 & 22.7 & \\nodata & MRC 2104-242 & \\cite{mcc96} \\\\\nTN J2239$-$0429 & \\nodata & 18.8 & \\nodata & 4C -04.85 & \\cite{rot95} \\\\\nTN J2320$+$1222 & \\nodata & 22.9 & \\nodata & MRC 2317+120 & \\cite{rot95} \\\\\n\\hline\n\\end{tabular}\n\n$^a$F$_X$ is the number of X-ray counts s$^{-1}$ as listed in the cited catalogs.\n\n\\vspace{1cm}\n\\end{table*}\n\n\\begin{table*}\n\\centerline{\\bf Table A.9: MP identifications from the literature}\n\\begin{tabular}{rrrrrr}\nName & $z$ & $R$[mag] & $F_X^a$ & Identification & Reference \\\\\n\\hline\nMP J0003$-$3556 & 0.0497 & 13.2 & 0.5206 & ABELL 2717 & \\cite{col95} \\\\\nMP J0103$-$3225 & \\nodata & 19.0 & & IRAS F01009-3241 & \\cite{con95} \\\\\nMP J1250$-$4026 & \\nodata & \\nodata & 0.000595 & 1RXP J125006-402 & \\cite{vog99} \\\\\nMP J1943$-$4030 & \\nodata & 17.3 & & ABELL 3646 & \\cite{abe89} \\\\\nMP J2313$-$4243 & 0.0564 & 14.6 & 2.024 & ABELL S1101 & \\cite{sto91} \\\\\nMP J2357$-$3445 & 0.0490 & 13.7 & 2.27 & ABELL 4059 & \\cite{pos95} \\\\\n\\hline\n\\end{tabular}\n\n$^a$F$_X$ is the number of X-ray counts s$^{-1}$ as listed in the cited catalogs.\n\n\\end{table*}\n\n\\clearpage\n\n\\section{Radio Maps}\n\\subsection{VLA Maps of the WN Sample}\n\n\\small{VLA maps of the WN sample. The contour scheme is a geometric progression in $\\sqrt 2$, which implies a factor 2 change in surface brightness every 2 contours. The first contour level, indicated above each plot, is at $3\\sigma_{rms}$, where $\\sigma_{rms}$ is the rms noise determined around the sources. The restoring beams are indicated in the lower left corner of the plots. Two maps are given for each source, one showing a 6\\arcmin\\ field of view to show possible related components, and a smaller blow-up of the source to show its morphology. The open cross indicates the NVSS position. Sources identified on the POSS have been marked in the top right corner. \\label{wnvla}}\n\n\\subsection{FIRST Maps of the WN Sample}\n\n\\small{FIRST maps of the WN sample.Contours are as in section \\ref{wnvla} \\label{wnfirst}}\n\n\\subsection{VLA Maps of the TN Sample}\n\n\\small{VLA maps of the TN sample. Contours are as in section \\ref{wnvla} \\label{tnvla}}\n \n\\subsection{FIRST Maps of the TN Sample}\n\n\\small{FIRST maps of the TN sample. Contours are as in section \\ref{wnvla}. \\label{tnfirst}}\n\n\\subsection{ATCA Maps of the TN Sample}\n\n\\small{ATCA maps of the TN sample. Contours are as in section \\ref{wnvla}. \\label{tnatca}}\n\n\\subsection{ATCA Maps of the MP Sample}\n\n\\small{ATCA maps of the MP sample. Contours are as in section \\ref{wnvla}. \\label{mpatca}}\n\n\\section{Radio Spectra}\n\\subsection{Radio Spectra for the WN Sample}\n\n\\small{Radio spectra of the WN sample using data from the literature. The two connected flux points indicate the spectral index used to select the source in the USS sample. Note the steeper spectra with higher frequency in most objects. \\label{wnradiospectra}}\n\n\\subsection{Radio Spectra for the TN Sample}\n\n\\small{Radio spectra of the TN sample using data from the literature. The two connected flux points indicate the spectral index used to select the source in the USS sample. Note the steeper spectra with higher frequency in most objects. \\label{tnradiospectra}}\n\n\\subsection{Radio Spectra for the MP Sample}\n\n\\small{Radio spectra of the MP sample using data from the literature and our ATCA observations (diamonds). The two connected flux points indicate the spectral index used to select the source in the USS sample. Note the steeper spectra with higher frequency in most objects. \\label{mpradiospectra}}\n\n\\section{POSS Finding Charts}\n\\subsection{POSS Finding Charts for the WN Sample}\n\n\\small{POSS finding charts of the WN sample. The open cross indicates the NVSS position.}\n\n\\subsection{POSS Finding Charts for the TN Sample}\n\n\\small{POSS finding charts of the TN sample. The open cross indicates the NVSS position.}\n\n\\subsection{POSS Finding Charts for the MP Sample}\n\n\\small{POSS finding charts of the MP sample. The open cross indicates the MRC position.}\n\n\\end{document}\n"
},
{
"name": "tnmptable.tex",
"string": "\\begin{table*}\n\\centerline{\\bf Table A.2: TN sample}\n\\tiny\n\\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{365}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{365}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nTN J0008-0912 & 638$\\pm$ 64 & 100.2$\\pm$ 4.4 & \\nodata & $-1.38\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 00 08 52.43 & $-$09 12 01.4 & N \\\\\nTN J0018+1904 & 498$\\pm$ 30 & 84.5$\\pm$ 3.8 & \\nodata & $-1.32\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 00 18 07.35 & $+$19 04 50.0 & N \\\\\nTN J0026+1501 & 241$\\pm$ 26 & 39.4$\\pm$ 2.0 & \\nodata & $-1.35\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 00 26 03.31 & $+$15 01 29.2 & N \\\\\nTN J0027+0059 & 735$\\pm$ 55 & 98.0$\\pm$ 4.4 & \\nodata & $-1.50\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 00 27 39.36 & $+$00 59 53.6 & N \\\\\nTN J0033-2731 & 512$\\pm$ 41 & 66.1$\\pm$ 3.0 & \\nodata & $-1.52\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 00 33 24.28 & $-$27 31 48.1 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0037+2629 & 442$\\pm$ 35 & 70.8$\\pm$ 3.2 & \\nodata & $-1.36\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 00 37 10.05 & $+$26 29 42.3 & N \\\\\nTN J0038-1540 & 471$\\pm$ 33 & 63.9$\\pm$ 1.4 & $10.8\\pm0.6$ & $-1.49\\pm$0.06 & $-1.43\\pm0.05$ & D & 3.2 & 18 & 00 38 47.19 & $-$15 40 06.6 & V \\\\\nTN J0040+1417 & 435$\\pm$ 41 & 71.1$\\pm$ 1.5 & \\nodata & $-1.35\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 00 40 37.04 & $+$14 17 14.6 & N \\\\\nTN J0041+1250 & 451$\\pm$ 65 & 71.0$\\pm$ 3.3 & $21.0\\pm1.1$ & $-1.38\\pm$0.11 & $-0.98\\pm0.06$ & D & 10.7 & 103 & 00 41 31.27 & $+$12 50 32.3 & V \\\\\nTN J0042+2649 & 484$\\pm$ 57 & 69.6$\\pm$ 3.2 & \\nodata & $-1.44\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 00 42 32.46 & $+$26 49 06.2 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0055+2624 & 8670$\\pm$457 & 1375.5$\\pm$56.2 & \\nodata & $-1.37\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 00 55 50.38 & $+$26 24 35.8 & N \\\\\nTN J0102-1055 & 775$\\pm$ 41 & 110.4$\\pm$ 4.9 & $16.4\\pm0.9$ & $-1.45\\pm$0.05 & $-1.53\\pm0.06$ & D & 1.5 & 136 & 01 01 59.99 & $-$10 55 56.0 & V \\\\\nTN J0102-2152 & 1900$\\pm$ 88 & 168.3$\\pm$ 6.7 & \\nodata & $-1.80\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 01 02 41.09 & $-$21 52 30.2 & N \\\\\nTN J0114-0333 & 367$\\pm$ 36 & 54.7$\\pm$ 2.6 & $12.9\\pm0.7$ & $-1.42\\pm$0.08 & $-1.16\\pm0.06$ & T & 2.4 & 146 & 01 14 42.50 & $-$03 33 58.8 & V \\\\\nTN J0119-2054 & 522$\\pm$ 60 & 87.8$\\pm$ 4.0 & \\nodata & $-1.33\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 01 19 47.65 & $-$20 54 46.8 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0121+1320 & 348$\\pm$ 33 & 57.3$\\pm$ 2.7 & $ 8.4\\pm0.5$ & $-1.34\\pm$0.08 & $-1.55\\pm0.06$ & S & 0.3 & 89 & 01 21 42.74 & $+$13 20 58.3 & V \\\\\nTN J0154+0044 & 465$\\pm$ 29 & 78.6$\\pm$ 3.6 & \\nodata & $-1.32\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 01 54 38.48 & $+$00 44 37.7 & N \\\\\nTN J0156+1619 & 437$\\pm$ 45 & 62.9$\\pm$ 2.9 & \\nodata & $-1.44\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 01 56 18.01 & $+$16 19 52.5 & N \\\\\nTN J0201-1302 & 360$\\pm$ 33 & 57.0$\\pm$ 2.7 & $11.0\\pm0.6$ & $-1.37\\pm$0.08 & $-1.32\\pm0.06$ & S & $<$ 1.3 & 0 & 02 01 15.80 & $-$13 02 19.4 & V \\\\\nTN J0205+2242 & 381$\\pm$ 26 & 60.4$\\pm$ 2.8 & $ 8.8\\pm0.5$ & $-1.37\\pm$0.06 & $-1.55\\pm0.06$ & D & 2.7 & 148 & 02 05 10.69 & $+$22 42 50.2 & V \\\\\n&&&&&&&&&&&\\\\\nTN J0208+1305 & 403$\\pm$ 61 & 68.3$\\pm$ 3.1 & \\nodata & $-1.32\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 02 08 32.45 & $+$13 05 53.0 & N \\\\\nTN J0215+2651 & 431$\\pm$ 49 & 69.3$\\pm$ 3.2 & \\nodata & $-1.36\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 02 15 45.31 & $+$26 51 12.3 & N \\\\\nTN J0218+0844 & 395$\\pm$ 32 & 61.8$\\pm$ 1.3 & $ 8.8\\pm0.5$ & $-1.38\\pm$0.06 & $-1.56\\pm0.05$ & S & 0.4 & 169 & 02 18 25.56 & $+$08 44 31.3 & V \\\\\nTN J0230-0255 & 573$\\pm$ 56 & 90.1$\\pm$ 4.0 & $22.5\\pm1.2$ & $-1.38\\pm$0.08 & $-1.12\\pm0.06$ & M & 6.7 & 156 & 02 30 21.97 & $-$02 55 05.1 & V \\\\\nTN J0230-2001 & 380$\\pm$ 33 & 57.8$\\pm$ 2.7 & \\nodata & $-1.40\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 02 30 45.73 & $-$20 01 19.0 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0233+2349$^*$ & 1075$\\pm$ 86 & 176.8$\\pm$ 7.8 & $43.5\\pm2.3$ & $-1.34\\pm$0.07 & $-1.13\\pm0.06$ & DF & 4.0 & 116 & 02 33 10.32 & $+$23 49 52.2 & V \\\\\nTN J0234-1215 & 451$\\pm$ 46 & 64.2$\\pm$ 2.9 & \\nodata & $-1.45\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 02 34 57.31 & $-$12 15 21.7 & N \\\\\nTN J0243+1405 & 395$\\pm$ 51 & 58.4$\\pm$ 1.3 & $26.2\\pm1.4$ & $-1.42\\pm$0.10 & $-0.64\\pm0.05$ & T & 3.1 & 126 & 02 43 10.52 & $+$14 05 36.9 & V \\\\\nTN J0244+0327 & 542$\\pm$ 62 & 84.8$\\pm$ 3.8 & \\nodata & $-1.38\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 02 44 53.97 & $+$03 27 46.8 & N \\\\\nTN J0245+2700 & 388$\\pm$ 53 & 54.0$\\pm$ 2.5 & \\nodata & $-1.47\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 02 45 22.27 & $+$27 00 06.3 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0250+0130 & 275$\\pm$ 25 & 39.1$\\pm$ 2.0 & \\nodata & $-1.45\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 02 50 20.94 & $+$01 30 24.9 & N \\\\\nTN J0254-1039 & 421$\\pm$ 60 & 68.1$\\pm$ 3.1 & $25.5\\pm1.4$ & $-1.36\\pm$0.11 & $-0.79\\pm0.06$ & D & 11.7 & 129 & 02 54 59.89 & $-$10 39 49.2 & V \\\\\nTN J0256-2717 & 1045$\\pm$ 70 & 177.9$\\pm$ 7.4 & \\nodata & $-1.32\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 02 56 51.44 & $-$27 17 56.5 & N \\\\\nTN J0301+0155 & 3950$\\pm$180 & 402.7$\\pm$17.3 & \\nodata & $-1.70\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 03 01 38.49 & $+$01 55 14.9 & N \\\\\nTN J0306+0524 & 909$\\pm$ 76 & 155.1$\\pm$ 6.3 & \\nodata & $-1.32\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 03 06 08.10 & $+$05 24 23.8 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0309-2425$^*$ & 483$\\pm$ 53 & 62.6$\\pm$ 2.9 & $14.8\\pm0.9$ & $-1.52\\pm$0.09 & $-1.16\\pm0.06$ & D & 12.9 & 23 & 03 09 09.26 & $-$24 25 11.7 & V \\\\\nTN J0310+0814 & 593$\\pm$ 67 & 96.8$\\pm$ 4.3 & \\nodata & $-1.35\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 03 10 37.37 & $+$08 14 59.2 & N \\\\\nTN J0311-2553 & 1102$\\pm$ 66 & 174.1$\\pm$ 7.5 & \\nodata & $-1.37\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 03 11 47.40 & $-$25 53 21.1 & N \\\\\nTN J0312-2622 & 442$\\pm$ 41 & 46.4$\\pm$ 2.3 & \\nodata & $-1.68\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 03 12 34.19 & $-$26 22 23.9 & N \\\\\nTN J0316-0815 & 1950$\\pm$ 92 & 305.1$\\pm$13.4 & $42.2\\pm2.2$ & $-1.38\\pm$0.05 & $-1.59\\pm0.05$ & T & 3.2 & 34 & 03 16 18.59 & $-$08 15 54.8 & V \\\\\n&&&&&&&&&&&\\\\\nTN J0321+1631 & 1084$\\pm$ 85 & 175.7$\\pm$ 7.7 & \\nodata & $-1.35\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 03 21 36.86 & $+$16 31 55.8 & N \\\\\nTN J0327-0948 & 281$\\pm$ 30 & 39.0$\\pm$ 2.0 & \\nodata & $-1.47\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 03 27 00.55 & $-$09 48 05.2 & N \\\\\nTN J0344+1903 & 297$\\pm$ 22 & 50.7$\\pm$ 2.4 & \\nodata & $-1.32\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 03 44 00.12 & $+$19 03 53.1 & N \\\\\nTN J0344-2029 & 538$\\pm$ 71 & 74.0$\\pm$ 1.6 & $19.2\\pm1.1$ & $-1.48\\pm$0.10 & $-1.08\\pm0.05$ & D & 6.5 & 42 & 03 44 37.88 & $-$20 29 03.8 & V \\\\\nTN J0349-1207$^*$ & 460$\\pm$ 61 & 77.5$\\pm$ 3.5 & $23.3\\pm1.3$ & $-1.32\\pm$0.11 & $-0.97\\pm0.06$ & T & 9.4 & 101 & 03 49 49.22 & $-$12 07 10.6 & V \\\\\n&&&&&&&&&&&\\\\\nTN J0351-1947 & 642$\\pm$ 86 & 111.4$\\pm$ 4.9 & \\nodata & $-1.30\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 03 51 33.13 & $-$19 47 10.5 & N \\\\\nTN J0352-0355$^*$ & 681$\\pm$ 63 & 114.9$\\pm$ 4.8 & $13.5\\pm0.8$ & $-1.32\\pm$0.08 & $-1.65\\pm0.06$ & DF & \\nodata & 0 & 03 52 32.04 & $-$03 55 47.2 & V \\\\\nTN J0355+0440 & 2015$\\pm$119 & 262.0$\\pm$11.5 & \\nodata & $-1.52\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 03 55 12.79 & $+$04 40 41.0 & N \\\\\nTN J0356-3028 & 1030$\\pm$ 65 & 167.5$\\pm$ 7.3 & $34.1\\pm1.8$ & $-1.35\\pm$0.06 & $-1.28\\pm0.06$ & D & 3.1 & 86 & 03 56 45.54 & $-$30 28 36.9 & V \\\\\nTN J0401-0156 & 1001$\\pm$ 65 & 172.8$\\pm$ 7.1 & \\nodata & $-1.31\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 04 01 08.43 & $-$01 56 08.9 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0402+1007 & 479$\\pm$ 54 & 74.6$\\pm$ 3.4 & $13.4\\pm0.8$ & $-1.38\\pm$0.09 & $-1.38\\pm0.06$ & D & 0.8 & 67 & 04 02 34.44 & $+$10 07 14.9 & V \\\\\nTN J0404-0541 & 666$\\pm$ 69 & 114.1$\\pm$ 5.1 & \\nodata & $-1.31\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 04 04 09.66 & $-$05 41 07.3 & N \\\\\nTN J0408-2418$^*$ & 3881$\\pm$172 & 647.7$\\pm$28.1 & \\nodata & $-1.33\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 04 08 51.38 & $-$24 18 15.5 & N \\\\\nTN J0410+1019 & 1185$\\pm$ 88 & 166.9$\\pm$ 3.4 & $26.5\\pm1.4$ & $-1.46\\pm$0.06 & $-1.26\\pm0.05$ & S & 0.2 & 109 & 04 10 40.52 & $+$10 19 13.6 & V \\\\\nTN J0429-2118 & 561$\\pm$ 58 & 95.5$\\pm$ 4.3 & \\nodata & $-1.32\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 04 29 39.79 & $-$21 18 01.7 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0431+0725 & 175$\\pm$ 24 & 30.4$\\pm$ 0.7 & \\nodata & $-1.30\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 04 31 54.21 & $+$07 25 13.8 & N \\\\\nTN J0433+0717 & 229$\\pm$ 27 & 33.1$\\pm$ 1.8 & \\nodata & $-1.44\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 04 33 05.61 & $+$07 17 55.2 & N \\\\\nTN J0435-0736 & 358$\\pm$ 71 & 47.0$\\pm$ 2.3 & $16.6\\pm0.9$ & $-1.51\\pm$0.15 & $-0.84\\pm0.06$ & T & 11.9 & 59 & 04 35 32.20 & $-$07 36 12.3 & V \\\\\nTN J0437+0259 & 410$\\pm$ 54 & 71.1$\\pm$ 3.3 & \\nodata & $-1.30\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 04 37 33.04 & $+$02 59 06.2 & N \\\\\nTN J0443-1212$^*$ & 412$\\pm$ 59 & 56.8$\\pm$ 2.7 & $14.6\\pm0.8$ & $-1.47\\pm$0.11 & $-1.09\\pm0.06$ & M & 20.2 & 25 & 04 43 53.72 & $-$12 12 46.7 & V \\\\\n&&&&&&&&&&&\\\\\nTN J0452-1737 & 747$\\pm$ 73 & 118.1$\\pm$ 2.5 & $23.7\\pm1.3$ & $-1.37\\pm$0.07 & $-1.29\\pm0.05$ & D & 2.4 & 176 & 04 52 26.66 & $-$17 37 54.0 & V \\\\\nTN J0510-1838 & 6801$\\pm$325 & 641.3$\\pm$25.6 & \\nodata & $-1.76\\pm$0.05 & \\nodata & D & 36.1 & 63 & 05 10 32.30 & $-$18 38 41.4 & A \\\\\nTN J0515-3410 & 589$\\pm$ 52 & 97.4$\\pm$ 4.4 & \\nodata & $-1.34\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 05 15 18.86 & $-$34 10 09.5 & N \\\\\nTN J0517-0641 & 285$\\pm$ 30 & 40.0$\\pm$ 0.9 & $ 6.8\\pm0.4$ & $-1.46\\pm$0.08 & $-1.43\\pm0.05$ & S & 1.0 & 0 & 05 17 36.89 & $-$06 41 14.6 & V \\\\\nTN J0525-1832 & 549$\\pm$ 73 & 86.4$\\pm$ 3.9 & $24.1\\pm1.3$ & $-1.38\\pm$0.11 & $-1.02\\pm0.06$ & T & 8.1 & 172 & 05 25 54.85 & $-$18 32 32.5 & V \\\\\n&&&&&&&&&&&\\\\\nTN J0547-0706 & 2552$\\pm$156 & 362.6$\\pm$16.0 & \\nodata & $-1.45\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 05 47 27.57 & $-$07 06 35.0 & N \\\\\nTN J0549-2459 & 427$\\pm$ 55 & 58.0$\\pm$ 1.3 & \\nodata & $-1.49\\pm$0.10 & \\nodata & S & 23.5 & 8 & 05 49 28.61 & $-$24 59 15.2 & A \\\\\nTN J0551-0756 & 473$\\pm$ 71 & 68.5$\\pm$ 3.2 & \\nodata & $-1.44\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 05 51 30.37 & $-$07 56 17.5 & N \\\\\nTN J0552-0433 & 1618$\\pm$ 83 & 269.7$\\pm$11.8 & $37.7\\pm2.0$ & $-1.33\\pm$0.05 & $-1.56\\pm0.06$ & D & 4.3 & 152 & 05 52 14.38 & $-$04 33 28.8 & V \\\\\nTN J0553-2033 & 887$\\pm$ 80 & 148.0$\\pm$ 6.2 & \\nodata & $-1.33\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 05 53 37.24 & $-$20 33 07.6 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0558-1358 & 425$\\pm$ 54 & 73.4$\\pm$ 3.4 & \\nodata & $-1.31\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 05 58 39.43 & $-$13 58 45.5 & N \\\\\nTN J0559-3406 & 773$\\pm$ 69 & 123.5$\\pm$ 5.4 & \\nodata & $-1.36\\pm$0.07 & \\nodata & S & 4.6 & 8 & 05 59 14.30 & $-$34 06 51.0 & A \\\\\nTN J0602-2741 & 810$\\pm$ 54 & 117.2$\\pm$ 5.2 & $20.7\\pm1.2$ & $-1.44\\pm$0.06 & $-1.39\\pm0.06$ & T & 4.3 & 88 & 06 02 41.32 & $-$27 41 10.1 & V \\\\\nTN J0630-2834 & 343$\\pm$ 29 & 14.3$\\pm$ 0.5 & \\nodata & $-2.36\\pm$0.07 & \\nodata & S & 13.5 & 2 & 06 30 49.49 & $-$28 34 40.4 & A \\\\\nTN J0634-3232 & 394$\\pm$ 63 & 67.7$\\pm$ 3.1 & \\nodata & $-1.31\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 06 34 17.10 & $-$32 32 34.1 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0729+2436 & 1062$\\pm$ 87 & 68.9$\\pm$ 3.1 & \\nodata & $-2.03\\pm$0.07 & \\nodata & D & 19.4 & 72 & 07 29 28.65 & $+$24 36 26.2 & F \\\\\nTN J0733+1753 & 291$\\pm$ 45 & 46.1$\\pm$ 2.3 & \\nodata & $-1.37\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 07 33 17.53 & $+$17 53 28.4 & N \\\\\nTN J0805+2738 & 987$\\pm$ 79 & 153.0$\\pm$ 6.7 & \\nodata & $-1.39\\pm$0.07 & \\nodata & T & 71.3 & 119 & 08 05 15.50 & $+$27 38 01.2 & F \\\\\nTN J0806+0401 & 560$\\pm$ 53 & 92.1$\\pm$ 2.0 & \\nodata & $-1.34\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 08 06 32.25 & $+$04 01 37.7 & N \\\\\nTN J0812+0915 & 277$\\pm$ 46 & 43.4$\\pm$ 2.2 & \\nodata & $-1.38\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 08 12 16.84 & $+$09 15 43.7 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0818-0741 & 381$\\pm$ 48 & 59.3$\\pm$ 2.8 & \\nodata & $-1.38\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 08 18 51.89 & $-$07 41 48.2 & N \\\\\nTN J0831+0046 & 451$\\pm$ 55 & 72.8$\\pm$ 3.3 & \\nodata & $-1.36\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 08 31 39.92 & $+$00 46 56.5 & N \\\\\nTN J0831+0851 & 567$\\pm$ 53 & 83.8$\\pm$ 3.8 & $98.3\\pm5.2$ & $-1.42\\pm$0.08 & $ 0.13\\pm0.06$ & DF & 3.0 & 2 & 08 31 52.74 & $+$08 51 14.1 & V \\\\\nTN J0837-1053$^*$ & 450$\\pm$ 81 & 69.2$\\pm$ 3.1 & $11.6\\pm0.7$ & $-1.39\\pm$0.14 & $-1.43\\pm0.06$ & D & 23.5 & 11 & 08 37 41.62 & $-$10 53 46.0 & V \\\\\nTN J0855-0000 & 416$\\pm$ 57 & 65.9$\\pm$ 3.0 & $13.8\\pm0.8$ & $-1.37\\pm$0.11 & $-1.26\\pm0.06$ & D & 3.8 & 85 & 08 55 57.26 & $-$00 00 58.2 & V \\\\\n\\end{tabular}\n\\end{table*}\n\\begin{table*}\n\\tiny\n\\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{365}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{365}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nTN J0856-1510 & 469$\\pm$ 68 & 70.0$\\pm$ 3.2 & $ 3.7\\pm0.3$ & $-1.41\\pm$0.11 & $-2.01\\pm0.07$ & S & 1.0 & 14 & 08 56 12.44 & $-$15 10 35.7 & V \\\\\nTN J0902+1809 & 491$\\pm$ 37 & 55.5$\\pm$ 2.6 & \\nodata & $-1.62\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 09 02 00.00 & $+$18 09 03.4 & N \\\\\nTN J0906-0701 & 939$\\pm$101 & 142.5$\\pm$ 5.8 & \\nodata & $-1.40\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 09 06 40.23 & $-$07 01 12.4 & N \\\\\nTN J0910-2228 & 465$\\pm$ 32 & 55.3$\\pm$ 2.6 & $ 4.0\\pm0.3$ & $-1.58\\pm$0.06 & $-2.11\\pm0.07$ & S & 2.0 & 0 & 09 10 34.15 & $-$22 28 47.4 & V \\\\\nTN J0914+1119 & 343$\\pm$ 53 & 49.5$\\pm$ 1.1 & \\nodata & $-1.44\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 09 14 30.81 & $+$11 19 08.0 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0919+1845 & 522$\\pm$ 50 & 90.0$\\pm$ 4.0 & \\nodata & $-1.31\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 09 19 33.25 & $+$18 45 51.2 & N \\\\\nTN J0920-0712 & 760$\\pm$ 53 & 100.4$\\pm$ 4.5 & $16.3\\pm0.9$ & $-1.51\\pm$0.06 & $-1.46\\pm0.06$ & S & 1.4 & 135 & 09 20 22.43 & $-$07 12 17.6 & V \\\\\nTN J0920-1405 & 842$\\pm$ 88 & 133.6$\\pm$ 5.5 & \\nodata & $-1.37\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 09 20 37.77 & $-$14 05 56.3 & N \\\\\nTN J0924-2201 & 656$\\pm$ 72 & 73.3$\\pm$ 1.5 & $ 8.6\\pm0.5$ & $-1.63\\pm$0.08 & $-1.72\\pm0.05$ & D & 1.2 & 74 & 09 24 19.92 & $-$22 01 41.5 & V \\\\\nTN J0936+0422 & 6025$\\pm$362 & 992.0$\\pm$42.5 & \\nodata & $-1.34\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 09 36 32.02 & $+$04 22 10.7 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0936-2243 & 488$\\pm$ 63 & 69.1$\\pm$ 3.2 & $18.5\\pm1.0$ & $-1.45\\pm$0.10 & $-1.06\\pm0.06$ & D & 8.1 & 77 & 09 36 32.53 & $-$22 43 04.9 & V \\\\\nTN J0941-1628 & 1810$\\pm$115 & 304.4$\\pm$13.4 & $64.7\\pm3.8$ & $-1.33\\pm$0.06 & $-1.24\\pm0.06$ & D & 1.9 & 175 & 09 41 07.43 & $-$16 28 02.5 & V \\\\\nTN J0946-0306 & 238$\\pm$ 24 & 38.2$\\pm$ 2.0 & \\nodata & $-1.36\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 09 46 00.88 & $-$03 06 26.2 & N \\\\\nTN J0954-1635 & 1531$\\pm$ 98 & 260.0$\\pm$11.4 & \\nodata & $-1.32\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 09 54 52.30 & $-$16 35 35.1 & N \\\\\nTN J0956-1500 & 505$\\pm$ 49 & 68.9$\\pm$ 1.5 & \\nodata & $-1.48\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 09 56 01.46 & $-$15 00 21.6 & N \\\\\n&&&&&&&&&&&\\\\\nTN J0958-1103 & 431$\\pm$ 63 & 70.6$\\pm$ 3.2 & \\nodata & $-1.35\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 09 58 21.84 & $-$11 03 47.5 & N \\\\\nTN J1000+0549 & 410$\\pm$ 55 & 67.3$\\pm$ 3.1 & \\nodata & $-1.34\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 10 00 44.58 & $+$05 49 31.1 & N \\\\\nTN J1002+2225 & 343$\\pm$ 41 & 54.2$\\pm$ 2.6 & $12.2\\pm0.7$ & $-1.37\\pm$0.10 & $-1.20\\pm0.06$ & D & 11.2 & 10 & 10 02 54.08 & $+$22 25 21.9 & V \\\\\nTN J1026-2116 & 399$\\pm$ 29 & 61.5$\\pm$ 1.3 & $ 8.5\\pm0.5$ & $-1.39\\pm$0.06 & $-1.59\\pm0.05$ & S & 1.0 & 0 & 10 26 22.37 & $-$21 16 07.7 & V \\\\\nTN J1028+1114 & 459$\\pm$ 56 & 79.7$\\pm$ 3.6 & \\nodata & $-1.30\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 10 28 24.31 & $+$11 14 52.4 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1031+0259 & 416$\\pm$ 62 & 60.0$\\pm$ 1.3 & \\nodata & $-1.44\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 10 31 13.36 & $+$02 59 05.3 & N \\\\\nTN J1033-1339 & 981$\\pm$ 75 & 153.8$\\pm$ 6.8 & $26.0\\pm1.4$ & $-1.38\\pm$0.07 & $-1.43\\pm0.06$ & S & 2.0 & 107 & 10 33 10.70 & $-$13 39 52.0 & V \\\\\nTN J1043-1718 & 578$\\pm$ 70 & 91.0$\\pm$ 3.9 & $18.9\\pm1.0$ & $-1.38\\pm$0.10 & $-1.26\\pm0.06$ & D & 34.7 & 63 & 10 43 19.42 & $-$17 18 53.5 & V \\\\\nTN J1043+2404 & 439$\\pm$ 34 & 52.0$\\pm$ 2.5 & \\nodata & $-1.59\\pm$0.07 & \\nodata & S & 3.7 & 90 & 10 43 43.28 & $+$24 04 47.3 & F \\\\\nTN J1045+1832 & 348$\\pm$ 27 & 53.6$\\pm$ 1.2 & \\nodata & $-1.39\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 10 45 42.93 & $+$18 32 37.5 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1049-1258 & 818$\\pm$ 56 & 112.2$\\pm$ 5.0 & $17.2\\pm0.9$ & $-1.48\\pm$0.06 & $-1.50\\pm0.06$ & M & 10.1 & 104 & 10 49 06.22 & $-$12 58 18.3 & V \\\\\nTN J1053-1518 & 383$\\pm$ 62 & 63.7$\\pm$ 2.9 & \\nodata & $-1.33\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 10 53 44.52 & $-$15 18 29.8 & N \\\\\nTN J1056-0400 & 449$\\pm$ 57 & 57.2$\\pm$ 2.7 & \\nodata & $-1.53\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 10 56 52.64 & $-$04 00 15.9 & N \\\\\nTN J1102+1029 & 3713$\\pm$224 & 633.6$\\pm$27.8 & \\nodata & $-1.32\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 11 02 17.47 & $+$10 29 08.0 & N \\\\\nTN J1102-1651 & 688$\\pm$ 68 & 112.5$\\pm$ 5.0 & $20.2\\pm1.1$ & $-1.35\\pm$0.08 & $-1.38\\pm0.06$ & D & 3.0 & 70 & 11 02 47.13 & $-$16 51 34.4 & V \\\\\n&&&&&&&&&&&\\\\\nTN J1112-2948 & 663$\\pm$ 51 & 101.0$\\pm$ 4.5 & $16.6\\pm0.9$ & $-1.40\\pm$0.07 & $-1.45\\pm0.06$ & D & 9.1 & 119 & 11 12 23.86 & $-$29 48 06.4 & V \\\\\nTN J1114-2221 & 386$\\pm$ 53 & 64.9$\\pm$ 3.0 & \\nodata & $-1.33\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 11 14 04.82 & $-$22 21 26.6 & N \\\\\nTN J1117-1409 & 785$\\pm$ 69 & 134.5$\\pm$ 5.9 & \\nodata & $-1.31\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 11 17 23.00 & $-$14 09 09.5 & N \\\\\nTN J1118-2612 & 514$\\pm$ 44 & 62.3$\\pm$ 2.9 & \\nodata & $-1.57\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 11 18 54.08 & $-$26 12 20.6 & N \\\\\nTN J1121-1155 & 332$\\pm$ 65 & 50.1$\\pm$ 2.4 & \\nodata & $-1.41\\pm$0.15 & \\nodata & \\nodata & \\nodata & \\nodata & 11 21 32.75 & $-$11 55 03.2 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1121+1706 & 1156$\\pm$ 83 & 196.8$\\pm$ 8.4 & \\nodata & $-1.32\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 11 21 39.89 & $+$17 06 14.8 & N \\\\\nTN J1123-2154 & 407$\\pm$ 64 & 50.6$\\pm$ 2.4 & $ 8.5\\pm0.5$ & $-1.55\\pm$0.12 & $-1.43\\pm0.06$ & S & 0.8 & 29 & 11 23 10.15 & $-$21 54 05.3 & V \\\\\nTN J1125-0342 & 354$\\pm$ 52 & 61.4$\\pm$ 2.9 & \\nodata & $-1.30\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 11 25 57.41 & $-$03 42 04.0 & N \\\\\nTN J1133-2715 & 2938$\\pm$125 & 447.9$\\pm$ 9.2 & \\nodata & $-1.40\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 11 33 31.53 & $-$27 15 22.9 & N \\\\\nTN J1136+1551 & 384$\\pm$ 33 & 21.7$\\pm$ 0.6 & \\nodata & $-2.14\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 11 36 03.28 & $+$15 51 06.7 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1136+0610 & 698$\\pm$ 50 & 118.8$\\pm$ 5.3 & \\nodata & $-1.32\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 11 36 38.91 & $+$06 10 26.8 & N \\\\\nTN J1139+0935 & 508$\\pm$ 58 & 87.3$\\pm$ 3.9 & \\nodata & $-1.31\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 11 39 22.75 & $+$09 35 26.1 & N \\\\\nTN J1146-1052 & 843$\\pm$ 79 & 120.9$\\pm$ 5.4 & \\nodata & $-1.44\\pm$0.08 & \\nodata & S & 8.8 & 1 & 11 46 07.21 & $-$10 52 08.6 & A \\\\\nTN J1148-0901 & 571$\\pm$ 67 & 80.4$\\pm$ 3.7 & \\nodata & $-1.46\\pm$0.09 & \\nodata & S & $<$ 6.0 & 5 & 11 48 39.90 & $-$09 01 48.8 & A \\\\\nTN J1149+1844 & 457$\\pm$ 39 & 77.6$\\pm$ 1.6 & \\nodata & $-1.32\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 11 49 36.78 & $+$18 44 21.5 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1151-3013 & 435$\\pm$ 28 & 52.7$\\pm$ 1.2 & $ 7.0\\pm0.4$ & $-1.57\\pm$0.05 & $-1.62\\pm0.05$ & S & 1.0 & 0 & 11 51 59.42 & $-$30 13 40.8 & V \\\\\nTN J1156-3105 & 317$\\pm$ 48 & 48.3$\\pm$ 2.3 & \\nodata & $-1.40\\pm$0.12 & \\nodata & S & 10.7 & 167 & 11 56 25.60 & $-$31 05 40.0 & A \\\\\nTN J1159-1629 & 324$\\pm$ 34 & 52.9$\\pm$ 1.2 & $10.4\\pm0.6$ & $-1.35\\pm$0.08 & $-1.30\\pm0.05$ & D & 1.4 & 38 & 11 59 53.25 & $-$16 29 48.2 & V \\\\\nTN J1204+1630 & 804$\\pm$ 56 & 129.7$\\pm$ 5.8 & \\nodata & $-1.36\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 12 04 20.49 & $+$16 30 49.5 & N \\\\\nTN J1210+1738 & 397$\\pm$ 50 & 68.1$\\pm$ 3.2 & \\nodata & $-1.31\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 12 10 36.00 & $+$17 38 27.8 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1216+1944 & 546$\\pm$ 44 & 91.7$\\pm$ 4.1 & \\nodata & $-1.33\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 12 16 01.76 & $+$19 44 43.3 & N \\\\\nTN J1216-2850 & 870$\\pm$ 43 & 145.2$\\pm$ 6.4 & \\nodata & $-1.33\\pm$0.05 & \\nodata & S & $<$ 7.0 & 163 & 12 16 17.38 & $-$28 50 48.7 & A \\\\\nTN J1220+0604 & 491$\\pm$ 61 & 65.1$\\pm$ 3.0 & \\nodata & $-1.50\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 12 20 07.82 & $+$06 04 16.5 & N \\\\\nTN J1221-2646 & 1403$\\pm$ 82 & 217.1$\\pm$ 9.5 & \\nodata & $-1.39\\pm$0.05 & \\nodata & S & 8.3 & 162 & 12 21 42.91 & $-$26 46 37.7 & A \\\\\nTN J1227-2255 & 271$\\pm$ 27 & 44.0$\\pm$ 2.2 & \\nodata & $-1.35\\pm$0.08 & \\nodata & S & $<$ 7.0 & 158 & 12 27 47.23 & $-$22 55 35.1 & A \\\\\n&&&&&&&&&&&\\\\\nTN J1239+1005 & 830$\\pm$ 89 & 79.3$\\pm$ 1.7 & \\nodata & $-1.75\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 12 39 02.08 & $+$10 05 49.2 & N \\\\\nTN J1239+1043 & 569$\\pm$ 63 & 87.1$\\pm$ 3.8 & \\nodata & $-1.40\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 12 39 31.67 & $+$10 43 22.9 & N \\\\\nTN J1239-0319 & 1629$\\pm$ 74 & 277.3$\\pm$12.2 & \\nodata & $-1.32\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 12 39 38.91 & $-$03 19 02.2 & N \\\\\nTN J1245-1127 & 518$\\pm$ 62 & 88.0$\\pm$ 4.0 & \\nodata & $-1.32\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 12 45 02.47 & $-$11 27 25.9 & N \\\\\nTN J1247+1547 & 405$\\pm$ 44 & 70.1$\\pm$ 3.2 & \\nodata & $-1.30\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 12 47 04.84 & $+$15 47 38.9 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1251-2714 & 609$\\pm$ 53 & 96.5$\\pm$ 4.3 & \\nodata & $-1.37\\pm$0.07 & \\nodata & S & $<$ 7.0 & 158 & 12 51 14.86 & $-$27 14 19.9 & A \\\\\nTN J1256-0911 & 457$\\pm$ 38 & 76.4$\\pm$ 3.5 & \\nodata & $-1.33\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 12 56 19.48 & $-$09 11 24.8 & N \\\\\nTN J1303-3349 & 2431$\\pm$108 & 360.8$\\pm$ 7.7 & \\nodata & $-1.42\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 13 03 02.67 & $-$33 49 15.5 & N \\\\\nTN J1306-0436 & 331$\\pm$ 57 & 55.2$\\pm$ 2.6 & \\nodata & $-1.33\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 13 06 36.11 & $-$04 36 17.4 & N \\\\\nTN J1313-0459 & 369$\\pm$ 34 & 58.1$\\pm$ 2.7 & \\nodata & $-1.38\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 13 13 34.37 & $-$04 59 30.0 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1317+0339 & 399$\\pm$ 62 & 39.8$\\pm$ 2.0 & \\nodata & $-1.71\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 13 17 48.12 & $+$03 39 12.3 & N \\\\\nTN J1323-2604 & 564$\\pm$ 60 & 97.3$\\pm$ 2.0 & \\nodata & $-1.31\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 13 23 32.43 & $-$26 04 04.7 & N \\\\\nTN J1326-2330 & 523$\\pm$ 33 & 83.2$\\pm$ 3.8 & \\nodata & $-1.37\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 13 26 25.24 & $-$23 30 23.5 & N \\\\\nTN J1327+1437 & 788$\\pm$ 68 & 115.0$\\pm$ 5.1 & \\nodata & $-1.43\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 13 27 23.93 & $+$14 37 00.4 & N \\\\\nTN J1336+2450 & 358$\\pm$ 71 & 51.3$\\pm$ 2.5 & \\nodata & $-1.45\\pm$0.15 & \\nodata & M & 54.4 & 100 & 13 36 15.12 & $+$24 50 05.4 & F \\\\\n&&&&&&&&&&&\\\\\nTN J1338-1942 & 718$\\pm$ 63 & 122.9$\\pm$ 5.4 & $22.1\\pm1.2$ & $-1.31\\pm$0.07 & $-1.34\\pm0.06$ & S & 1.4 & 152 & 13 38 26.06 & $-$19 42 30.1 & V \\\\\nTN J1339-0114 & 349$\\pm$ 51 & 59.5$\\pm$ 1.3 & \\nodata & $-1.32\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 13 39 55.26 & $-$01 14 10.8 & N \\\\\nTN J1340+2723 & 827$\\pm$ 93 & 137.8$\\pm$ 6.1 & $24.8\\pm1.4$ & $-1.33\\pm$0.09 & $-1.38\\pm0.06$ & DF & 1.7 & 0 & 13 40 29.38 & $+$27 23 25.0 & V \\\\\nTN J1346-1004 & 363$\\pm$ 59 & 49.6$\\pm$ 2.4 & \\nodata & $-1.48\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 13 46 16.84 & $-$10 04 57.2 & N \\\\\nTN J1351+1328 & 662$\\pm$ 54 & 93.8$\\pm$ 4.2 & \\nodata & $-1.45\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 13 51 54.72 & $+$13 28 38.1 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1352-0800 & 554$\\pm$ 88 & 95.6$\\pm$ 4.3 & \\nodata & $-1.31\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 13 52 55.32 & $-$08 00 14.1 & N \\\\\nTN J1353+2302 & 403$\\pm$ 38 & 59.5$\\pm$ 1.3 & $23.3\\pm1.3$ & $-1.42\\pm$0.07 & $-0.75\\pm0.05$ & DF & 2.5 & 44 & 13 53 42.26 & $+$23 02 50.9 & V \\\\\nTN J1358+2003 & 227$\\pm$ 42 & 35.0$\\pm$ 1.8 & \\nodata & $-1.39\\pm$0.14 & \\nodata & \\nodata & \\nodata & \\nodata & 13 58 29.63 & $+$20 03 13.4 & N \\\\\nTN J1403-1223 & 396$\\pm$ 69 & 65.8$\\pm$ 3.0 & \\nodata & $-1.34\\pm$0.14 & \\nodata & S & 30.6 & 169 & 14 03 37.33 & $-$12 23 57.3 & A \\\\\nTN J1408-0855 & 694$\\pm$ 73 & 114.3$\\pm$ 5.1 & \\nodata & $-1.34\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 14 08 18.46 & $-$08 55 38.5 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1411-0824 & 542$\\pm$ 71 & 76.1$\\pm$ 3.5 & \\nodata & $-1.46\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 14 11 53.33 & $-$08 24 02.9 & N \\\\\nTN J1412-2548 & 452$\\pm$ 59 & 78.0$\\pm$ 3.6 & \\nodata & $-1.31\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 14 12 51.27 & $-$25 48 05.5 & N \\\\\nTN J1418-2256 & 527$\\pm$ 59 & 82.0$\\pm$ 3.7 & \\nodata & $-1.38\\pm$0.09 & \\nodata & S & 7.6 & 148 & 14 18 16.65 & $-$22 56 58.6 & A \\\\\nTN J1428+2425 & 411$\\pm$ 34 & 69.1$\\pm$ 1.5 & \\nodata & $-1.33\\pm$0.07 & \\nodata & S & 1.0 & 0 & 14 28 10.20 & $+$24 25 11.3 & F \\\\\nTN J1438+2334 & 564$\\pm$ 69 & 96.5$\\pm$ 4.2 & \\nodata & $-1.31\\pm$0.10 & \\nodata & D & 21.1 & 157 & 14 38 56.52 & $+$23 34 25.6 & F \\\\\n\\end{tabular}\n\\end{table*}\n\\begin{table*}\n\\tiny\n\\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{365}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{365}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nTN J1439-3226 & 622$\\pm$ 65 & 90.7$\\pm$ 1.9 & \\nodata & $-1.43\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 14 39 02.87 & $-$32 26 46.6 & N \\\\\nTN J1449+1440 & 464$\\pm$ 50 & 80.3$\\pm$ 3.7 & \\nodata & $-1.30\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 14 49 02.50 & $+$14 40 42.2 & N \\\\\nTN J1451+2351 & 595$\\pm$ 44 & 93.2$\\pm$ 4.2 & \\nodata & $-1.38\\pm$0.07 & \\nodata & D & 12.6 & 109 & 14 51 10.71 & $+$23 51 38.8 & F \\\\\nTN J1452-1113 & 344$\\pm$ 55 & 53.9$\\pm$ 2.6 & \\nodata & $-1.38\\pm$0.13 & \\nodata & S & $<$ 7.5 & 2 & 14 52 04.88 & $-$11 13 35.7 & A \\\\\nTN J1452+2013 & 291$\\pm$ 40 & 43.4$\\pm$ 1.0 & \\nodata & $-1.42\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 14 52 22.93 & $+$20 13 09.8 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1453+1106 & 833$\\pm$ 56 & 144.9$\\pm$ 6.4 & \\nodata & $-1.30\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 14 53 21.97 & $+$11 06 04.9 & N \\\\\nTN J1454+0017 & 1309$\\pm$ 88 & 214.8$\\pm$ 9.2 & \\nodata & $-1.34\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 14 54 40.87 & $+$00 17 41.9 & N \\\\\nTN J1459-2730 & 321$\\pm$ 40 & 52.5$\\pm$ 2.5 & \\nodata & $-1.35\\pm$0.10 & \\nodata & S & 6.5 & 143 & 14 59 34.96 & $-$27 30 08.3 & A \\\\\nTN J1506+2728 & 360$\\pm$ 58 & 60.7$\\pm$ 1.3 & $15.9\\pm0.9$ & $-1.32\\pm$0.12 & $-1.07\\pm0.05$ & D & 1.1 & 131 & 15 06 35.41 & $+$27 28 55.6 & V \\\\\nTN J1513-2417 & 504$\\pm$ 33 & 83.6$\\pm$ 3.7 & \\nodata & $-1.34\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 15 13 31.67 & $-$24 17 55.3 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1513-1801 & 534$\\pm$ 36 & 85.3$\\pm$ 3.9 & \\nodata & $-1.36\\pm$0.06 & \\nodata & S & $<$ 7.5 & 4 & 15 13 55.31 & $-$18 01 07.9 & A \\\\\nTN J1515-2651 & 352$\\pm$ 44 & 58.0$\\pm$ 2.7 & \\nodata & $-1.34\\pm$0.10 & \\nodata & S & 6.5 & 9 & 15 15 59.29 & $-$26 51 14.9 & A \\\\\nTN J1520+1410 & 478$\\pm$ 55 & 66.0$\\pm$ 1.4 & \\nodata & $-1.47\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 15 20 53.36 & $+$14 10 45.5 & N \\\\\nTN J1521+0741 & 1777$\\pm$123 & 105.6$\\pm$ 4.5 & \\nodata & $-2.10\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 15 21 50.75 & $+$07 41 41.1 & N \\\\\nTN J1522-2540 & 464$\\pm$ 63 & 54.1$\\pm$ 2.6 & \\nodata & $-1.60\\pm$0.11 & \\nodata & S & 8.2 & 10 & 15 22 23.28 & $-$25 40 07.1 & A \\\\\n&&&&&&&&&&&\\\\\nTN J1524+0642 & 479$\\pm$ 55 & 82.9$\\pm$ 1.7 & \\nodata & $-1.30\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 15 24 06.39 & $+$06 42 15.9 & N \\\\\nTN J1531-3234 & 522$\\pm$ 59 & 80.6$\\pm$ 3.6 & \\nodata & $-1.39\\pm$0.09 & \\nodata & S & 4.8 & 27 & 15 31 33.59 & $-$32 34 01.7 & A \\\\\nTN J1547-2218 & 427$\\pm$ 62 & 72.4$\\pm$ 3.3 & \\nodata & $-1.32\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 15 47 49.95 & $-$22 18 25.6 & N \\\\\nTN J1556-2759 & 612$\\pm$ 56 & 66.4$\\pm$ 3.1 & \\nodata & $-1.65\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 15 56 43.63 & $-$27 59 43.1 & N \\\\\nTN J1559-1727 & 575$\\pm$ 71 & 97.4$\\pm$ 4.3 & \\nodata & $-1.32\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 15 59 34.08 & $-$17 27 41.6 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1604-0248 & 345$\\pm$ 33 & 46.8$\\pm$ 1.0 & \\nodata & $-1.49\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 16 04 59.59 & $-$02 48 47.9 & N \\\\\nTN J1621+2043 & 539$\\pm$ 48 & 61.4$\\pm$ 2.9 & \\nodata & $-1.62\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 16 21 06.18 & $+$20 43 36.4 & N \\\\\nTN J1628+1604 & 602$\\pm$ 44 & 55.5$\\pm$ 2.6 & \\nodata & $-1.77\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 16 28 19.16 & $+$16 04 00.0 & N \\\\\nTN J1634-2222 & 4714$\\pm$214 & 809.2$\\pm$35.4 & \\nodata & $-1.31\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 16 34 49.79 & $-$22 22 12.7 & N \\\\\nTN J1637-1931 & 432$\\pm$ 40 & 36.8$\\pm$ 0.9 & \\nodata & $-1.83\\pm$0.07 & \\nodata & S & 10.8 & 6 & 16 37 44.80 & $-$19 31 24.8 & A \\\\\n&&&&&&&&&&&\\\\\nTN J1646-1328 & 608$\\pm$ 63 & 102.5$\\pm$ 4.6 & \\nodata & $-1.32\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 16 46 51.67 & $-$13 28 49.1 & N \\\\\nTN J1652-1339 & 328$\\pm$ 33 & 56.5$\\pm$ 1.3 & \\nodata & $-1.31\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 16 52 24.29 & $-$13 39 04.3 & N \\\\\nTN J1653-1155 & 1131$\\pm$ 60 & 197.0$\\pm$ 8.7 & \\nodata & $-1.30\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 16 53 52.81 & $-$11 55 59.2 & N \\\\\nTN J1656-1521 & 587$\\pm$ 79 & 93.9$\\pm$ 4.2 & \\nodata & $-1.36\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 16 56 03.77 & $-$15 21 23.3 & N \\\\\nTN J1701-0101 & 999$\\pm$ 55 & 172.2$\\pm$ 7.6 & \\nodata & $-1.31\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 17 01 37.58 & $-$01 01 13.6 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1701+0252 & 356$\\pm$ 38 & 57.1$\\pm$ 2.7 & \\nodata & $-1.36\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 17 01 54.89 & $+$02 52 13.4 & N \\\\\nTN J1702-0811 & 436$\\pm$ 38 & 69.9$\\pm$ 3.2 & \\nodata & $-1.36\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 17 02 04.71 & $-$08 11 07.5 & N \\\\\nTN J1702+2015 & 322$\\pm$ 48 & 43.4$\\pm$ 2.1 & \\nodata & $-1.49\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 17 02 23.02 & $+$20 15 34.2 & N \\\\\nTN J1702-0145 & 808$\\pm$ 74 & 135.6$\\pm$ 6.0 & \\nodata & $-1.33\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 17 02 43.11 & $-$01 45 54.0 & N \\\\\nTN J1707-1120 & 425$\\pm$ 72 & 54.2$\\pm$ 2.6 & \\nodata & $-1.53\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 17 07 51.37 & $-$11 20 21.0 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1710-0826 & 445$\\pm$ 74 & 69.2$\\pm$ 3.2 & \\nodata & $-1.38\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 17 10 20.36 & $-$08 26 40.3 & N \\\\\nTN J1714+2226 & 285$\\pm$ 48 & 43.3$\\pm$ 1.0 & \\nodata & $-1.40\\pm$0.13 & \\nodata & S & 1.6 & 38 & 17 14 53.42 & $+$22 26 18.5 & F \\\\\nTN J1821+2433 & 1416$\\pm$ 95 & 227.5$\\pm$ 4.7 & \\nodata & $-1.36\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 18 21 37.07 & $+$24 33 13.8 & N \\\\\nTN J1855-3430 & 654$\\pm$ 85 & 87.8$\\pm$ 3.8 & \\nodata & $-1.49\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 18 55 24.12 & $-$34 30 27.7 & N \\\\\nTN J1905-3520 & 799$\\pm$ 75 & 131.3$\\pm$ 5.4 & \\nodata & $-1.34\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 19 05 22.67 & $-$35 20 50.9 & N \\\\\n&&&&&&&&&&&\\\\\nTN J1932-1931 & 5678$\\pm$335 & 813.6$\\pm$35.5 & \\nodata & $-1.45\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 19 32 07.22 & $-$19 31 49.7 & N \\\\\nTN J1941-1952 & 1194$\\pm$103 & 183.0$\\pm$ 3.8 & \\nodata & $-1.40\\pm$0.07 & \\nodata & S & 7.9 & 164 & 19 41 00.07 & $-$19 52 14.0 & A \\\\\nTN J1953-0541 & 478$\\pm$ 83 & 59.0$\\pm$ 2.8 & \\nodata & $-1.56\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 19 53 27.04 & $-$05 41 28.5 & N \\\\\nTN J1954-1207 & 657$\\pm$ 67 & 102.8$\\pm$ 4.6 & \\nodata & $-1.38\\pm$0.08 & \\nodata & S & $<$ 7.0 & 177 & 19 54 24.15 & $-$12 07 48.7 & A \\\\\nTN J2007-1316 & 777$\\pm$ 46 & 115.4$\\pm$ 5.2 & \\nodata & $-1.42\\pm$0.06 & \\nodata & S & 7.2 & 174 & 20 07 53.23 & $-$13 16 43.6 & A \\\\\n&&&&&&&&&&&\\\\\nTN J2008-1344 & 798$\\pm$ 71 & 132.3$\\pm$ 2.7 & \\nodata & $-1.34\\pm$0.07 & \\nodata & S & 8.2 & 176 & 20 08 07.48 & $-$13 44 17.8 & A \\\\\nTN J2009-3040 & 409$\\pm$ 65 & 65.3$\\pm$ 3.0 & \\nodata & $-1.36\\pm$0.12 & \\nodata & S & $<$ 7.0 & 144 & 20 09 48.13 & $-$30 40 07.0 & A \\\\\nTN J2014-2115 & 348$\\pm$ 33 & 48.0$\\pm$ 1.1 & \\nodata & $-1.47\\pm$0.07 & \\nodata & D & 56.4 & 11 & 20 14 31.96 & $-$21 14 36.7 & A \\\\\nTN J2021+0839 & 880$\\pm$ 72 & 145.4$\\pm$ 6.4 & \\nodata & $-1.34\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 20 21 33.11 & $+$08 39 09.2 & N \\\\\nTN J2028+0811 & 455$\\pm$ 58 & 74.8$\\pm$ 1.6 & \\nodata & $-1.34\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 20 28 37.12 & $+$08 11 21.4 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2028-1934 & 814$\\pm$ 88 & 134.4$\\pm$ 5.8 & \\nodata & $-1.34\\pm$0.09 & \\nodata & S & 19.2 & 169 & 20 28 48.57 & $-$19 34 03.2 & A \\\\\nTN J2029-0858 & 396$\\pm$ 34 & 47.2$\\pm$ 2.3 & \\nodata & $-1.58\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 20 29 49.60 & $-$08 58 48.5 & N \\\\\nTN J2034-2735 & 510$\\pm$ 70 & 67.4$\\pm$ 1.5 & \\nodata & $-1.51\\pm$0.10 & \\nodata & S & $<$ 8.0 & 163 & 20 34 15.74 & $-$27 35 45.6 & A \\\\\nTN J2042+1354 & 281$\\pm$ 45 & 42.0$\\pm$ 1.0 & \\nodata & $-1.41\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 20 42 07.25 & $+$13 54 16.6 & N \\\\\nTN J2048-0618 & 881$\\pm$ 99 & 150.7$\\pm$ 6.6 & \\nodata & $-1.31\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 20 48 06.24 & $-$06 18 40.5 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2049-2223 & 823$\\pm$ 86 & 126.1$\\pm$ 5.6 & \\nodata & $-1.40\\pm$0.08 & \\nodata & D & 95.0 & 97 & 20 49 43.04 & $-$22 22 56.3 & A \\\\\nTN J2051-0527 & 377$\\pm$ 79 & 54.7$\\pm$ 1.2 & \\nodata & $-1.44\\pm$0.16 & \\nodata & \\nodata & \\nodata & \\nodata & 20 51 13.39 & $-$05 27 06.1 & N \\\\\nTN J2051+0133 & 391$\\pm$ 33 & 66.6$\\pm$ 3.1 & \\nodata & $-1.32\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 20 51 32.31 & $+$01 33 34.9 & N \\\\\nTN J2052-0555 & 321$\\pm$ 35 & 41.5$\\pm$ 0.9 & \\nodata & $-1.52\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 20 52 49.93 & $-$05 55 49.1 & N \\\\\nTN J2102+2158 & 483$\\pm$ 52 & 73.5$\\pm$ 1.6 & \\nodata & $-1.40\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 21 02 52.80 & $+$21 58 35.1 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2103-1917 & 1410$\\pm$109 & 228.6$\\pm$10.1 & \\nodata & $-1.35\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 21 03 42.91 & $-$19 17 47.7 & N \\\\\nTN J2106-2405$^*$ & 2232$\\pm$150 & 366.3$\\pm$15.9 & \\nodata & $-1.34\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 21 06 58.42 & $-$24 05 04.2 & N \\\\\nTN J2107+0933 & 476$\\pm$ 56 & 68.0$\\pm$ 3.1 & \\nodata & $-1.45\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 21 07 10.61 & $+$09 33 32.5 & N \\\\\nTN J2108+0249 & 573$\\pm$ 41 & 65.8$\\pm$ 3.1 & \\nodata & $-1.61\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 21 08 26.75 & $+$02 49 46.3 & N \\\\\nTN J2113+0111 & 553$\\pm$ 68 & 90.8$\\pm$ 4.1 & \\nodata & $-1.34\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 21 13 50.43 & $+$01 11 22.3 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2125+2013 & 352$\\pm$ 45 & 51.9$\\pm$ 2.5 & \\nodata & $-1.42\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 21 25 51.74 & $+$20 13 39.8 & N \\\\\nTN J2133+1629 & 1737$\\pm$123 & 283.4$\\pm$12.4 & \\nodata & $-1.35\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 21 33 29.32 & $+$16 29 19.4 & N \\\\\nTN J2134+0946 & 351$\\pm$ 47 & 48.0$\\pm$ 2.3 & \\nodata & $-1.48\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 21 34 42.85 & $+$09 46 56.6 & N \\\\\nTN J2136+0947 & 426$\\pm$ 60 & 66.9$\\pm$ 3.1 & \\nodata & $-1.38\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 21 36 36.29 & $+$09 47 22.8 & N \\\\\nTN J2147-0645 & 382$\\pm$ 63 & 57.3$\\pm$ 2.7 & \\nodata & $-1.41\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 21 47 57.13 & $-$06 45 48.8 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2155-2109 & 449$\\pm$ 87 & 77.2$\\pm$ 1.6 & \\nodata & $-1.31\\pm$0.15 & \\nodata & \\nodata & \\nodata & \\nodata & 21 55 50.90 & $-$21 09 30.0 & N \\\\\nTN J2158-2516 & 1225$\\pm$ 59 & 200.9$\\pm$ 8.9 & \\nodata & $-1.34\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 21 58 11.14 & $-$25 16 01.5 & N \\\\\nTN J2201-2822 & 703$\\pm$ 54 & 120.5$\\pm$ 5.1 & \\nodata & $-1.31\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 22 01 22.94 & $-$28 22 14.0 & N \\\\\nTN J2204+1621 & 381$\\pm$ 42 & 57.3$\\pm$ 2.7 & \\nodata & $-1.41\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 22 04 14.18 & $+$16 21 43.7 & N \\\\\nTN J2205-3201 & 430$\\pm$ 60 & 65.7$\\pm$ 3.1 & \\nodata & $-1.40\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 22 05 27.56 & $-$32 01 23.9 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2217-1913 & 321$\\pm$ 34 & 40.5$\\pm$ 2.0 & \\nodata & $-1.54\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 22 17 28.22 & $-$19 13 21.1 & N \\\\\nTN J2219-1648 & 301$\\pm$ 53 & 32.0$\\pm$ 0.8 & \\nodata & $-1.67\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 22 19 40.06 & $-$16 48 03.1 & N \\\\\nTN J2232-2917 & 528$\\pm$ 59 & 91.7$\\pm$ 1.9 & \\nodata & $-1.30\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 22 32 57.25 & $-$29 17 56.5 & N \\\\\nTN J2237-0242 & 727$\\pm$ 48 & 125.0$\\pm$ 2.6 & \\nodata & $-1.31\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 22 37 22.60 & $-$02 42 23.0 & N \\\\\nTN J2239-0429 & 3807$\\pm$177 & 571.4$\\pm$24.9 & \\nodata & $-1.41\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 22 39 32.85 & $-$04 29 33.9 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2245+0007 & 297$\\pm$ 53 & 51.6$\\pm$ 1.1 & \\nodata & $-1.30\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 22 45 44.99 & $+$00 07 11.3 & N \\\\\nTN J2251-1634 & 551$\\pm$ 64 & 60.6$\\pm$ 1.3 & \\nodata & $-1.64\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 22 51 14.06 & $-$16 34 03.2 & N \\\\\nTN J2251-1034 & 862$\\pm$ 72 & 138.8$\\pm$ 5.9 & \\nodata & $-1.36\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 22 51 22.01 & $-$10 34 18.0 & N \\\\\nTN J2252-1618 & 397$\\pm$ 60 & 51.6$\\pm$ 2.5 & \\nodata & $-1.52\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 22 52 20.15 & $-$16 18 14.9 & N \\\\\nTN J2253-2156 & 425$\\pm$ 72 & 59.3$\\pm$ 2.8 & \\nodata & $-1.47\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 22 53 17.03 & $-$21 56 38.0 & N \\\\\n\\end{tabular}\n\\end{table*}\n\\begin{table*}\n\\tiny\n\\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{365}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{365}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nTN J2301+0555 & 484$\\pm$ 62 & 74.1$\\pm$ 3.3 & \\nodata & $-1.40\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 23 01 18.11 & $+$05 55 01.0 & N \\\\\nTN J2303-0251 & 405$\\pm$ 56 & 66.5$\\pm$ 3.1 & \\nodata & $-1.34\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 23 03 55.67 & $-$02 51 08.6 & N \\\\\nTN J2310+1358 & 1497$\\pm$102 & 251.9$\\pm$ 5.2 & \\nodata & $-1.33\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 23 10 52.32 & $+$13 58 20.5 & N \\\\\nTN J2312-0040 & 293$\\pm$ 25 & 45.5$\\pm$ 1.0 & \\nodata & $-1.39\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 23 12 46.90 & $-$00 40 53.0 & N \\\\\nTN J2312-0208 & 1295$\\pm$ 80 & 194.8$\\pm$ 8.6 & \\nodata & $-1.41\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 23 12 55.71 & $-$02 08 39.9 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2314+2053 & 386$\\pm$ 27 & 46.8$\\pm$ 2.3 & $ 5.9\\pm0.4$ & $-1.57\\pm$0.06 & $-1.67\\pm0.07$ & S & 0.3 & 129 & 23 14 56.04 & $+$20 53 37.4 & V \\\\\nTN J2320+1222 & 1566$\\pm$ 93 & 264.3$\\pm$ 5.4 & \\nodata & $-1.32\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 23 20 07.79 & $+$12 22 06.6 & N \\\\\nTN J2333-1508 & 504$\\pm$ 68 & 70.2$\\pm$ 3.3 & \\nodata & $-1.47\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 23 33 06.99 & $-$15 08 12.8 & N \\\\\nTN J2335+0634 & 507$\\pm$ 58 & 84.3$\\pm$ 3.8 & \\nodata & $-1.33\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 23 35 06.42 & $+$06 34 38.8 & N \\\\\nTN J2350-1321 & 419$\\pm$ 35 & 56.1$\\pm$ 1.2 & \\nodata & $-1.50\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 23 50 15.92 & $-$13 21 16.0 & N \\\\\n&&&&&&&&&&&\\\\\nTN J2352+0814 & 498$\\pm$ 50 & 71.0$\\pm$ 3.2 & \\nodata & $-1.45\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 23 52 10.44 & $+$08 14 50.0 & N \\\\\nTN J2352+0450 & 398$\\pm$ 59 & 60.5$\\pm$ 2.8 & \\nodata & $-1.40\\pm$0.12 & \\nodata & \\nodata & \\nodata & \\nodata & 23 52 32.20 & $+$04 50 30.1 & N \\\\\nTN J2352-3139 & 573$\\pm$ 87 & 85.8$\\pm$ 3.8 & $29.0\\pm1.5$ & $-1.41\\pm$0.12 & $-0.87\\pm0.06$ & T & 21.1 & 170 & 23 52 46.79 & $-$31 39 36.9 & V \\\\\n\\hline\n\\end{tabular}\n\n$^{\\dag}$ Not a real USS source; see notes\n\n$^*$ See notes\n\\vspace{1cm}\n\\end{table*}\n\\begin{table*}\n\\centerline{\\bf Table A.3: MP sample}\n\\tiny\n\\begin{tabular}{rrrrrrrrrrrrr}\nName & $S_{408}$ & $S_{1420}$ & $S_{4850}$ & $\\alpha_{408}^{1420}$ & $\\alpha_{408}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos\\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$\\arcsec$\\;$ & \\\\\n\\hline\nMP J0003-3556 & 2440$\\pm$ 80 & \\nodata & 103.0$\\pm$13.0 & \\nodata & $-1.28\\pm$0.05 & \\nodata & \\nodata & \\nodata & 00 03 13.11 & $-$35 56 33.8 & M \\\\\nMP J0028-5523 & 1910$\\pm$ 80 & $ 389\\pm 38$ & 86.0$\\pm$ 9.0 & $-1.28\\pm0.10$ & $-1.25\\pm$0.05 & S & 3.7 & 57 & 00 28 53.76 & $-$55 23 28.5 & A \\\\\nMP J0100-6403 & 1410$\\pm$150 & $ 247\\pm 24$ & 56.0$\\pm$ 7.0 & $-1.40\\pm0.11$ & $-1.30\\pm$0.07 & S & 4.2 & 100 & 01 00 32.42 & $-$64 03 13.6 & A \\\\\nMP J0103-3225 & 2290$\\pm$ 80 & \\nodata & 93.0$\\pm$13.0 & \\nodata & $-1.29\\pm$0.06 & \\nodata & \\nodata & \\nodata & 01 03 17.10 & $-$32 25 53.3 & M \\\\\nMP J0114-3302 & 1590$\\pm$ 90 & $ 396\\pm 39$ & 76.0$\\pm$12.0 & $-1.11\\pm0.14$ & $-1.23\\pm$0.07 & D & 22.0 & 119 & 01 14 37.06 & $-$33 02 10.2 & A \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J0118-6331 & 1040$\\pm$ 90 & $ 264\\pm 26$ & 50.0$\\pm$ 7.0 & $-1.10\\pm0.09$ & $-1.23\\pm$0.07 & S & 4.1 & 48 & 01 18 07.54 & $-$63 31 43.2 & A \\\\\nMP J0130-8352 & 950$\\pm$ 50 & $ 159\\pm 15$ & 23.0$\\pm$ 5.0 & $-1.43\\pm0.11$ & $-1.50\\pm$0.09 & S & 3.2 & 66 & 01 30 07.45 & $-$83 52 29.6 & A \\\\\nMP J0141-4421 & 1400$\\pm$ 60 & $ 295\\pm 29$ & 56.0$\\pm$ 9.0 & $-1.25\\pm0.10$ & $-1.30\\pm$0.07 & D & 29.9 & 95 & 01 41 13.57 & $-$44 21 10.8 & A \\\\\nMP J0141-6941 & 3980$\\pm$320 & $ 755\\pm 75$ & 179.0$\\pm$11.0 & $-1.33\\pm0.09$ & $-1.25\\pm$0.04 & D & 16.1 & 153 & 01 41 55.18 & $-$69 41 33.1 & A \\\\\nMP J0155-8521 & 830$\\pm$ 70 & \\nodata & 38.0$\\pm$ 5.0 & \\nodata & $-1.25\\pm$0.06 & \\nodata & \\nodata & \\nodata & 01 55 16.98 & $-$85 21 07.4 & M \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J0202-5425 & 820$\\pm$ 70 & $ 186\\pm 18$ & 41.0$\\pm$ 8.0 & $-1.19\\pm0.09$ & $-1.21\\pm$0.09 & D & 14.5 & 5 & 02 02 56.25 & $-$54 25 13.3 & A \\\\\nMP J0211-5146 & 900$\\pm$ 40 & $ 160\\pm 16$ & 43.0$\\pm$ 8.0 & $-1.38\\pm0.08$ & $-1.23\\pm$0.08 & S & 11.1 & 50 & 02 11 44.92 & $-$51 46 47.0 & A \\\\\nMP J0249-4145 & 1100$\\pm$ 50 & $ 242\\pm 24$ & 48.0$\\pm$ 9.0 & $-1.21\\pm0.08$ & $-1.27\\pm$0.08 & S & 8.2 & 49 & 02 49 10.08 & $-$41 45 36.3 & A \\\\\nMP J0339-4018 & 3610$\\pm$140 & $ 759\\pm 75$ & 174.0$\\pm$13.0 & $-1.25\\pm0.09$ & $-1.22\\pm$0.03 & S & 5.6 & 33 & 03 39 48.18 & $-$40 18 22.1 & A \\\\\nMP J0340-6507 & 1640$\\pm$ 50 & $ 383\\pm 38$ & 81.0$\\pm$ 8.0 & $-1.17\\pm0.10$ & $-1.22\\pm$0.04 & D & 14.0 & 18 & 03 40 44.92 & $-$65 07 07.3 & A \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J0446-3305 & 1910$\\pm$100 & $ 448\\pm 44$ & 82.0$\\pm$12.0 & $-1.16\\pm0.10$ & $-1.27\\pm$0.06 & D & 58.8 & 6 & 04 46 00.21 & $-$33 05 18.3 & A \\\\\nMP J0449-5449 & 900$\\pm$ 70 & $ 200\\pm 20$ & 46.0$\\pm$ 8.0 & $-1.20\\pm0.09$ & $-1.20\\pm$0.08 & S & 4.3 & 56 & 04 49 04.66 & $-$54 49 10.1 & A \\\\\nMP J0601-3926 & 2270$\\pm$320 & $ 451\\pm 45$ & 97.0$\\pm$10.0 & $-1.29\\pm0.09$ & $-1.27\\pm$0.07 & S & 6.2 & 43 & 06 01 00.77 & $-$39 26 18.1 & A \\\\\nMP J0605-5036 & 1040$\\pm$ 70 & $ 358\\pm 35$ & 43.0$\\pm$ 8.0 & $-0.85\\pm0.10$ & $-1.29\\pm$0.08 & D & 9.4 & 105 & 06 05 47.25 & $-$50 36 41.7 & A \\\\\nMP J0618-7340 & 750$\\pm$ 50 & \\nodata & 25.0$\\pm$ 6.0 & \\nodata & $-1.37\\pm$0.10 & \\nodata & \\nodata & \\nodata & 06 18 47.54 & $-$73 40 40.8 & M \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J0648-7118 & 1000$\\pm$ 50 & $ 300\\pm 30$ & 42.0$\\pm$ 7.0 & $-0.96\\pm0.09$ & $-1.28\\pm$0.07 & S & 2.5 & 45 & 06 48 37.38 & $-$71 18 26.4 & A \\\\\nMP J0731-6621 & 870$\\pm$ 40 & \\nodata & 40.0$\\pm$ 7.0 & \\nodata & $-1.24\\pm$0.07 & \\nodata & \\nodata & \\nodata & 07 31 47.00 & $-$66 21 30.3 & M \\\\\nMP J0839-7359 & 1450$\\pm$ 60 & \\nodata & 69.0$\\pm$ 7.0 & \\nodata & $-1.23\\pm$0.04 & DF & \\nodata & \\nodata & 08 39 33.28 & $-$73 59 37.4 & M \\\\\nMP J1033-3418 & 5590$\\pm$250 & \\nodata & 268.0$\\pm$22.0 & \\nodata & $-1.23\\pm$0.04 & \\nodata & \\nodata & \\nodata & 10 33 13.04 & $-$34 18 48.4 & M \\\\\nMP J1119-3631 & 2440$\\pm$ 70 & $ 542\\pm 54$ & 113.0$\\pm$14.0 & $-1.21\\pm0.10$ & $-1.24\\pm$0.05 & S & 4.8 & 166 & 11 19 21.81 & $-$36 31 39.5 & A \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J1208-3403 & 4650$\\pm$210 & \\nodata & 198.0$\\pm$18.0 & \\nodata & $-1.28\\pm$0.04 & \\nodata & \\nodata & \\nodata & 12 08 39.17 & $-$34 03 10.7 & M \\\\\nMP J1250-4026 & 6030$\\pm$180 & \\nodata & 299.0$\\pm$18.0 & \\nodata & $-1.21\\pm$0.03 & \\nodata & \\nodata & \\nodata & 12 50 05.68 & $-$40 26 28.7 & M \\\\\nMP J1250-4119 & 1350$\\pm$ 60 & $ 167\\pm 16$ & 63.0$\\pm$ 9.0 & $-1.67\\pm0.09$ & $-1.24\\pm$0.06 & S & 7.4 & 123 & 12 50 46.49 & $-$41 19 35.7 & A \\\\\nMP J1355-7806 & 1690$\\pm$ 90 & \\nodata & 44.0$\\pm$ 6.0 & \\nodata & $-1.47\\pm$0.06 & DF & \\nodata & \\nodata & 13 55 35.57 & $-$78 06 43.7 & M \\\\\nMP J1657-7423 & 1080$\\pm$ 50 & \\nodata & 50.0$\\pm$ 7.0 & \\nodata & $-1.24\\pm$0.06 & \\nodata & \\nodata & \\nodata & 16 57 44.73 & $-$74 23 09.3 & M \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J1710-7343 & 910$\\pm$ 70 & $ 47\\pm 4$ & 26.0$\\pm$ 6.0 & $-2.37\\pm0.10$ & $-1.44\\pm$0.10 & S & \\nodata & 149 & 17 10 17.73 & $-$73 43 19.1 & A \\\\\nMP J1733-8342 & 4630$\\pm$210 & \\nodata & 198.0$\\pm$12.0 & \\nodata & $-1.27\\pm$0.03 & \\nodata & \\nodata & \\nodata & 17 33 55.38 & $-$83 42 48.0 & M \\\\\nMP J1755-6916 & 1580$\\pm$ 90 & $ 486\\pm 48$ & 71.0$\\pm$ 7.0 & $-0.94\\pm0.09$ & $-1.25\\pm$0.05 & D & 0.5 & 90 & 17 55 30.23 & $-$69 16 49.8 & A \\\\\nMP J1758-6738 & 3000$\\pm$140 & $ 478\\pm 47$ & 112.0$\\pm$ 9.0 & $-1.47\\pm0.09$ & $-1.33\\pm$0.04 & D & 31.2 & 119 & 17 58 51.25 & $-$67 38 30.5 & A \\\\\nMP J1821-7457 & 2190$\\pm$110 & \\nodata & 77.0$\\pm$ 7.0 & \\nodata & $-1.35\\pm$0.04 & \\nodata & \\nodata & \\nodata & 18 21 59.83 & $-$74 57 47.5 & M \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J1909-7755 & 900$\\pm$ 70 & $ 182\\pm 18$ & 41.0$\\pm$ 6.0 & $-1.28\\pm0.09$ & $-1.25\\pm$0.07 & D & 27.9 & 81 & 19 09 57.19 & $-$77 56 01.5 & A \\\\\nMP J1912-5349 & 1110$\\pm$ 70 & $ 441\\pm 44$ & 56.0$\\pm$ 8.0 & $-0.74\\pm0.09$ & $-1.21\\pm$0.06 & D & 17.0 & 45 & 19 12 20.77 & $-$53 49 01.3 & A \\\\\nMP J1921-6217 & 2110$\\pm$ 40 & $ 400\\pm 40$ & 79.0$\\pm$ 8.0 & $-1.33\\pm0.08$ & $-1.33\\pm$0.04 & S & 3.4 & 113 & 19 21 03.06 & $-$62 17 25.2 & A \\\\\nMP J1921-5431 & 4590$\\pm$210 & \\nodata & 66.0$\\pm$ 8.0 & \\nodata & $-1.71\\pm$0.05 & \\nodata & \\nodata & \\nodata & 19 21 52.92 & $-$54 31 51.8 & M \\\\\nMP J1929-3732 & 3260$\\pm$110 & $ 806\\pm 80$ & 135.0$\\pm$12.0 & $-1.12\\pm0.09$ & $-1.29\\pm$0.04 & S & 3.7 & 14 & 19 29 08.51 & $-$37 32 48.8 & A \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J1940-4236 & 1340$\\pm$ 70 & \\nodata & 64.0$\\pm$ 9.0 & \\nodata & $-1.23\\pm$0.06 & \\nodata & \\nodata & \\nodata & 19 40 58.04 & $-$42 36 49.5 & M \\\\\nMP J1942-5553 & 2120$\\pm$110 & $ 385\\pm 38$ & 74.0$\\pm$ 8.0 & $-1.37\\pm0.08$ & $-1.36\\pm$0.05 & S & 6.7 & 176 & 19 42 06.97 & $-$55 53 32.6 & A \\\\\nMP J1943-4030 & 4400$\\pm$140 & \\nodata & 153.0$\\pm$12.0 & \\nodata & $-1.36\\pm$0.03 & DF & \\nodata & \\nodata & 19 43 52.33 & $-$40 30 10.9 & M \\\\\nMP J1953-4852 & 860$\\pm$ 30 & $ 143\\pm 14$ & 42.0$\\pm$ 8.0 & $-1.44\\pm0.09$ & $-1.22\\pm$0.08 & S & 4.7 & 115 & 19 53 39.88 & $-$48 52 13.8 & A \\\\\nMP J2002-5252 & 2730$\\pm$130 & $ 411\\pm 41$ & 76.0$\\pm$ 9.0 & $-1.52\\pm0.09$ & $-1.45\\pm$0.05 & S & 4.5 & 29 & 20 02 22.89 & $-$52 52 51.8 & A \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J2003-8340 & 1600$\\pm$ 80 & $ 253\\pm 25$ & 67.0$\\pm$ 6.0 & $-1.48\\pm0.09$ & $-1.28\\pm$0.04 & S & 3.5 & 106 & 20 03 30.73 & $-$83 41 00.0 & A \\\\\nMP J2017-5747 & 1860$\\pm$160 & $ 287\\pm 28$ & 79.0$\\pm$ 8.0 & $-1.50\\pm0.08$ & $-1.28\\pm$0.05 & S & 11.8 & 28 & 20 17 48.11 & $-$57 47 11.9 & A \\\\\nMP J2045-6018 & 11160$\\pm$340 & $2105\\pm210$ & 447.0$\\pm$24.0 & $-1.34\\pm0.09$ & $-1.30\\pm$0.02 & D & 41.6 & 44 & 20 45 21.82 & $-$60 18 51.5 & A \\\\\nMP J2048-5750 & 2810$\\pm$130 & $ 494\\pm 49$ & 137.0$\\pm$10.0 & $-1.39\\pm0.09$ & $-1.22\\pm$0.03 & S & 5.7 & 18 & 20 48 36.64 & $-$57 50 47.6 & A \\\\\nMP J2126-5439 & 1180$\\pm$ 80 & $ 282\\pm 28$ & 57.0$\\pm$ 8.0 & $-1.15\\pm0.12$ & $-1.22\\pm$0.06 & D & 17.1 & 147 & 21 26 53.65 & $-$54 39 36.0 & A \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J2204-5831 & 900$\\pm$ 70 & $ 148\\pm 14$ & 44.0$\\pm$ 8.0 & $-1.45\\pm0.08$ & $-1.22\\pm$0.08 & S & 10.5 & 11 & 22 04 05.48 & $-$58 31 38.3 & A \\\\\nMP J2222-4723 & 910$\\pm$ 70 & $ 509\\pm 50$ & 45.0$\\pm$ 9.0 & $-0.47\\pm0.09$ & $-1.21\\pm$0.09 & D & 9.1 & 148 & 22 22 53.71 & $-$47 23 12.1 & A \\\\\nMP J2226-7654 & 900$\\pm$ 60 & $ 203\\pm 20$ & 35.0$\\pm$ 6.0 & $-1.19\\pm0.09$ & $-1.31\\pm$0.07 & S & 4.1 & 107 & 22 26 56.90 & $-$76 54 48.0 & A \\\\\nMP J2229-3824 & 8210$\\pm$210 & \\nodata & 412.0$\\pm$23.0 & \\nodata & $-1.21\\pm$0.02 & \\nodata & \\nodata & \\nodata & 22 29 46.94 & $-$38 24 02.9 & M \\\\\nMP J2308-6423 & 1750$\\pm$ 90 & $ 301\\pm 30$ & 39.0$\\pm$ 7.0 & $-1.41\\pm0.09$ & $-1.54\\pm$0.08 & D & 14.3 & 7 & 23 08 45.21 & $-$64 23 33.3 & A \\\\\n&&&&&&&&&&&\\\\\t\t \nMP J2313-4243 & 1390$\\pm$ 60 & \\nodata & 58.0$\\pm$ 9.0 & \\nodata & $-1.28\\pm$0.07 & \\nodata & \\nodata & \\nodata & 23 13 58.76 & $-$42 43 38.1 & M \\\\\nMP J2352-6154 & 1450$\\pm$ 40 & $ 311\\pm 31$ & 69.0$\\pm$ 8.0 & $-1.23\\pm0.10$ & $-1.23\\pm$0.05 & D & 56.1 & 148 & 23 52 55.52 & $-$61 54 06.9 & A \\\\\nMP J2357-3445 & 8700$\\pm$350 & \\nodata & 117.0$\\pm$14.0 & \\nodata & $-1.74\\pm$0.05 & \\nodata & \\nodata & \\nodata & 23 57 01.09 & $-$34 45 38.9 & M \\\\\n\\hline\n\\end{tabular}\n\\end{table*}\n"
},
{
"name": "wntable.tex",
"string": "\\begin{table*}\n\\centerline{\\bf Table A.1: WN sample}\n\\tiny\n \\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{325}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{325}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nWN J0000+4654 & 204$\\pm$ 9 & 21.1$\\pm$ 1.4 & $ 2.97\\pm0.13$ & $-1.55\\pm$0.06 & $-1.58\\pm0.06$ & D & 3.6 & 173 & 00 00 28.88 & +46 54 40.7 & V \\\\\nWN J0007+3641 & 447$\\pm$18 & 28.8$\\pm$ 1.7 & $ 2.51\\pm0.11$ & $-1.88\\pm$0.05 & $-1.96\\pm0.06$ & S & 1.7 & 67 & 00 07 02.92 & +36 41 55.9 & V \\\\\nWN J0007+4615 & 144$\\pm$ 7 & 16.9$\\pm$ 0.5 & \\nodata & $-1.47\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 00 07 15.05 & +46 15 40.8 & N \\\\\nWN J0016+4311 & 105$\\pm$ 6 & 15.7$\\pm$ 1.5 & \\nodata & $-1.30\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 00 16 40.63 & +43 11 03.5 & N \\\\\nWN J0029+3439 & 288$\\pm$12 & 40.9$\\pm$ 2.0 & $ 44.76\\pm1.05$ & $-1.34\\pm$0.04 & $ 0.07\\pm0.04$ & DF & 12.8 & 80 & 00 29 01.61 & +34 39 34.7 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0034+4142 & 84$\\pm$ 6 & 11.0$\\pm$ 0.5 & $ 2.50\\pm0.12$ & $-1.39\\pm$0.05 & $-1.19\\pm0.05$ & D & 23.7 & 154 & 00 34 29.21 & +41 42 09.5 & V \\\\\nWN J0034+3238 & 120$\\pm$ 9 & 16.4$\\pm$ 0.5 & \\nodata & $-1.36\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 00 34 56.36 & +32 38 36.4 & N \\\\\nWN J0038+7859 & 109$\\pm$ 6 & 15.1$\\pm$ 0.5 & $ 1.30\\pm0.09$ & $-1.35\\pm$0.04 & $-1.97\\pm0.06$ & S & 2.5 & 159 & 00 38 01.96 & +78 59 51.5 & V \\\\\nWN J0040+3857 & 127$\\pm$ 7 & 17.5$\\pm$ 0.5 & $ 3.13\\pm0.14$ & $-1.36\\pm$0.04 & $-1.38\\pm0.04$ & S & 1.4 & 31 & 00 40 56.23 & +38 57 30.0 & V \\\\\nWN J0043+4719$^{\\dag}$ & 99$\\pm$ 6 & 14.2$\\pm$ 1.3 & $ 41.81\\pm1.01$ & $-1.33\\pm$0.08 & $ 0.87\\pm0.08$ & T & 18.5 & 157 & 00 43 53.13 & +47 19 48.3 & V \\\\\n&&&&&&&&&&&\\\\\nWN J0048+4137$^*$ & 277$\\pm$11 & 34.5$\\pm$ 1.9 & $ 1.75\\pm0.10$ & $-1.43\\pm$0.05 & $-2.40\\pm0.06$ & S & 2.5 & 17 & 00 48 46.34 & +41 37 20.8 & V \\\\\nWN J0059+3958 & 152$\\pm$ 7 & 11.4$\\pm$ 1.4 & \\nodata & $-1.77\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 00 59 51.07 & +39 58 46.5 & N \\\\\nWN J0112+4039 & 111$\\pm$ 7 & 15.4$\\pm$ 0.5 & \\nodata & $-1.35\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 01 12 26.31 & +40 39 30.1 & N \\\\\nWN J0117+3715 & 165$\\pm$ 8 & 22.5$\\pm$ 0.6 & $ 6.62\\pm0.21$ & $-1.36\\pm$0.04 & $-0.98\\pm0.03$ & S & 1.4 & 71 & 01 17 10.02 & +37 15 16.3 & V \\\\\nWN J0121+4305 & 389$\\pm$16 & 50.8$\\pm$ 2.5 & \\nodata & $-1.39\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 01 21 10.71 & +43 05 18.3 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0135+3303 & 94$\\pm$ 6 & 12.1$\\pm$ 0.5 & $ 10.22\\pm0.28$ & $-1.40\\pm$0.06 & $-0.14\\pm0.04$ & T & 1.8 & 18 & 01 35 07.24 & +33 03 47.4 & V \\\\\nWN J0137+3250 & 177$\\pm$ 9 & 23.8$\\pm$ 1.6 & $ 16.06\\pm0.40$ & $-1.37\\pm$0.06 & $-0.32\\pm0.06$ & T & 27.9 & 104 & 01 36 59.85 & +32 50 40.7 & V \\\\\nWN J0155+8036 & 338$\\pm$14 & 38.0$\\pm$ 0.9 & $ 6.87\\pm0.21$ & $-1.50\\pm$0.03 & $-1.38\\pm0.03$ & D & 4.6 & 159 & 01 55 43.77 & +80 36 48.1 & V \\\\\nWN J0207+3655 & 118$\\pm$ 6 & 17.5$\\pm$ 1.4 & \\nodata & $-1.31\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 02 07 22.59 & +36 55 16.0 & N \\\\\nWN J0231+3600 & 303$\\pm$13 & 45.2$\\pm$ 2.2 & $ 7.66\\pm0.22$ & $-1.30\\pm$0.04 & $-1.43\\pm0.05$ & D & 14.8 & 59 & 02 31 11.48 & +36 00 26.6 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0240+3526 & 79$\\pm$ 5 & 10.2$\\pm$ 0.5 & \\nodata & $-1.40\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 02 40 31.10 & +35 26 55.1 & N \\\\\nWN J0303+3733 & 1071$\\pm$43 & 127.9$\\pm$ 5.7 & $ 17.32\\pm0.43$ & $-1.46\\pm$0.04 & $-1.61\\pm0.04$ & D & 4.4 & 3 & 03 03 26.01 & +37 33 41.6 & V \\\\\nWN J0303+3629 & 117$\\pm$ 6 & 17.1$\\pm$ 0.5 & \\nodata & $-1.32\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 03 03 29.87 & +36 29 56.1 & N \\\\\nWN J0305+3525 & 110$\\pm$ 6 & 15.8$\\pm$ 1.3 & $ 3.74\\pm0.15$ & $-1.33\\pm$0.07 & $-1.16\\pm0.07$ & S & 1.9 & 64 & 03 05 47.42 & +35 25 13.4 & V \\\\\nWN J0310+3644 & 289$\\pm$11 & 24.2$\\pm$ 0.6 & $ 2.45\\pm0.12$ & $-1.70\\pm$0.03 & $-1.84\\pm0.05$ & S & 2.0 & 118 & 03 10 54.80 & +36 44 02.5 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0315+3757 & 95$\\pm$ 5 & 13.3$\\pm$ 0.5 & $ 4.74\\pm0.17$ & $-1.35\\pm$0.05 & $-0.83\\pm0.04$ & S & 1.7 & 53 & 03 15 17.29 & +37 57 05.0 & V \\\\\nWN J0323+3738 & 205$\\pm$ 9 & 22.6$\\pm$ 1.5 & $ 8.11\\pm0.25$ & $-1.51\\pm$0.06 & $-0.83\\pm0.06$ & DF & 9.7 & 100 & 03 23 38.24 & +37 38 39.3 & V \\\\\nWN J0343+7540 & 118$\\pm$ 6 & 12.5$\\pm$ 1.6 & \\nodata & $-1.54\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 03 43 39.77 & +75 40 43.2 & N \\\\\nWN J0346+3039 & 286$\\pm$12 & 35.6$\\pm$ 1.9 & $ 4.95\\pm0.18$ & $-1.43\\pm$0.05 & $-1.59\\pm0.05$ & D & 0.4 & 89 & 03 46 42.60 & +30 39 51.0 & V \\\\\nWN J0352+3143 & 154$\\pm$ 7 & 21.8$\\pm$ 1.5 & \\nodata & $-1.34\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 03 52 24.49 & +31 43 03.1 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0359+3000 & 88$\\pm$ 6 & 12.1$\\pm$ 0.5 & \\nodata & $-1.36\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 03 59 12.86 & +30 00 51.7 & N \\\\\nWN J0528+6549 & 96$\\pm$ 6 & 10.6$\\pm$ 2.4 & $ 1.08\\pm0.09$ & $-1.51\\pm$0.16 & $-1.84\\pm0.19$ & S & 1.9 & 108 & 05 28 46.07 & +65 49 57.3 & V \\\\\nWN J0533+7205 & 117$\\pm$ 7 & 17.4$\\pm$ 1.6 & $ 2.42\\pm0.12$ & $-1.30\\pm$0.08 & $-1.59\\pm0.08$ & D & 2.9 & 140 & 05 33 38.64 & +72 05 52.7 & V \\\\\nWN J0538+7348 & 132$\\pm$ 7 & 18.1$\\pm$ 0.5 & $ 3.20\\pm0.14$ & $-1.36\\pm$0.04 & $-1.39\\pm0.04$ & S & 2.1 & 113 & 05 38 25.59 & +73 48 39.6 & V \\\\\nWN J0559+6926 & 87$\\pm$ 5 & 12.9$\\pm$ 0.5 & $ 1.88\\pm0.13$ & $-1.31\\pm$0.06 & $-1.55\\pm0.06$ & S & 0.3 & 85 & 05 59 06.04 & +69 26 37.8 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0610+6611 & 98$\\pm$ 6 & 12.5$\\pm$ 1.9 & $ 1.19\\pm0.09$ & $-1.41\\pm$0.11 & $-1.89\\pm0.14$ & S & 2.2 & 114 & 06 10 08.59 & +66 11 43.1 & V \\\\\nWN J0617+5012 & 196$\\pm$ 9 & 26.5$\\pm$ 0.7 & $ 6.80\\pm0.23$ & $-1.37\\pm$0.04 & $-1.09\\pm0.03$ & D & 3.4 & 11 & 06 17 39.37 & +50 12 54.7 & V \\\\\nWN J0625+5708 & 71$\\pm$ 4 & 10.3$\\pm$ 0.5 & $ 1.54\\pm0.10$ & $-1.32\\pm$0.07 & $-1.53\\pm0.06$ & D & 7.3 & 18 & 06 25 01.67 & +57 08 26.1 & V \\\\\nWN J0627+7311 & 470$\\pm$19 & 61.9$\\pm$ 2.9 & $ 4.00\\pm0.17$ & $-1.39\\pm$0.04 & $-2.20\\pm0.05$ & S & $<0.3$ & 0 & 06 27 03.64 & +73 11 54.2 & V \\\\\nWN J0633+6024 & 115$\\pm$ 6 & 13.4$\\pm$ 2.8 & $ 2.07\\pm0.11$ & $-1.47\\pm$0.15 & $-1.50\\pm0.17$ & S & 2.2 & 118 & 06 33 19.70 & +60 24 37.1 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0633+4653 & 3661$\\pm$146 & 520.1$\\pm$22.8 & $ 80.88\\pm1.74$ & $-1.34\\pm$0.04 & $-1.50\\pm0.04$ & T & 4.0 & 19 & 06 33 52.18 & +46 53 40.5 & V \\\\\nWN J0641+4325 & 154$\\pm$ 7 & 15.6$\\pm$ 0.5 & \\nodata & $-1.57\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 06 41 08.23 & +43 25 00.3 & N \\\\\nWN J0646+3912 & 166$\\pm$ 8 & 20.5$\\pm$ 2.4 & \\nodata & $-1.43\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 06 46 34.97 & +39 12 00.3 & N \\\\\nWN J0648+4309 & 215$\\pm$ 9 & 30.4$\\pm$ 1.7 & $ 5.00\\pm0.19$ & $-1.34\\pm$0.05 & $-1.45\\pm0.05$ & DF & 1.5 & 151 & 06 48 01.10 & +43 09 47.8 & V \\\\\nWN J0648+4137 & 91$\\pm$ 5 & 10.9$\\pm$ 1.5 & $ 1.69\\pm0.11$ & $-1.45\\pm$0.11 & $-1.50\\pm0.12$ & S & 13.2 & 94 & 06 48 14.58 & +41 37 18.8 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0650+4106 & 393$\\pm$16 & 53.5$\\pm$ 1.2 & $ 15.04\\pm0.41$ & $-1.37\\pm$0.03 & $-1.02\\pm0.03$ & DF & 3.0 & 26 & 06 50 41.66 & +41 06 39.1 & V \\\\\nWN J0653+4434 & 115$\\pm$ 6 & 13.1$\\pm$ 0.5 & \\nodata & $-1.49\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 06 53 23.84 & +44 34 55.4 & N \\\\\nWN J0656+5301 & 137$\\pm$ 7 & 18.7$\\pm$ 1.5 & \\nodata & $-1.36\\pm$0.07 & \\nodata & D & 56.1 & 88 & 06 56 38.40 & +53 01 18.1 & F \\\\\nWN J0658+4444 & 407$\\pm$17 & 50.6$\\pm$ 2.4 & $ 13.91\\pm0.35$ & $-1.43\\pm$0.04 & $-1.04\\pm0.04$ & S & 1.7 & 73 & 06 58 27.43 & +44 44 16.4 & V \\\\\nWN J0702+4448 & 147$\\pm$ 7 & 17.0$\\pm$ 0.5 & \\nodata & $-1.48\\pm$0.04 & \\nodata & S & 7.8 & 119 & 07 02 16.79 & +44 48 59.7 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0711+4242 & 140$\\pm$ 6 & 16.0$\\pm$ 0.5 & \\nodata & $-1.49\\pm$0.04 & \\nodata & S & 3.3 & 17 & 07 11 40.25 & +42 42 09.6 & F \\\\\nWN J0715+4655 & 89$\\pm$ 6 & 10.4$\\pm$ 0.5 & $ 1.86\\pm0.13$ & $-1.47\\pm$0.06 & $-1.38\\pm0.07$ & S & 0.2 & 114 & 07 15 02.03 & +46 55 26.3 & V \\\\\nWN J0716+5107 & 204$\\pm$ 9 & 28.4$\\pm$ 0.7 & $ 4.54\\pm0.18$ & $-1.35\\pm$0.04 & $-1.47\\pm0.04$ & D & 1.2 & 8 & 07 16 40.50 & +51 07 04.7 & V \\\\\nWN J0717+4611$^*$ & 724$\\pm$29 & 107.8$\\pm$ 4.8 & $ 45.30\\pm1.00$ & $-1.30\\pm$0.04 & $-0.70\\pm0.04$ & T & 6.2 & 16 & 07 17 58.49 & +46 11 39.1 & V \\\\\nWN J0720+5140 & 95$\\pm$ 6 & 11.6$\\pm$ 0.5 & \\nodata & $-1.44\\pm$0.05 & \\nodata & S & 3.2 & 101 & 07 20 00.20 & +51 40 28.5 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0720+5758 & 93$\\pm$ 7 & 13.9$\\pm$ 0.5 & $ 2.37\\pm0.12$ & $-1.30\\pm$0.05 & $-1.42\\pm0.05$ & S & 2.0 & 109 & 07 20 09.56 & +57 58 32.9 & V \\\\\nWN J0721+3324 & 313$\\pm$13 & 36.8$\\pm$ 1.9 & $ 2.35\\pm0.13$ & $-1.47\\pm$0.05 & $-2.21\\pm0.06$ & DF & 2.0 & 143 & 07 21 56.85 & +33 24 53.8 & V \\\\\nWN J0725+4123$^*$ & 272$\\pm$12 & 35.5$\\pm$ 1.9 & \\nodata & $-1.39\\pm$0.05 & \\nodata & S & 8.3 & 156 & 07 25 57.08 & +41 23 05.1 & F \\\\\nWN J0727+3020$^*$ & 93$\\pm$ 6 & 12.8$\\pm$ 1.9 & \\nodata & $-1.36\\pm$0.11 & \\nodata & D & 34.8 & 103 & 07 27 48.50 & +30 21 00.7 & F \\\\\nWN J0736+6845 & 84$\\pm$ 5 & 12.4$\\pm$ 0.5 & \\nodata & $-1.31\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 07 36 36.42 & +68 45 56.8 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0737+7146 & 79$\\pm$ 5 & 10.3$\\pm$ 0.5 & \\nodata & $-1.40\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 07 37 09.93 & +71 46 29.3 & N \\\\\nWN J0740+6319 & 254$\\pm$11 & 26.1$\\pm$ 1.7 & \\nodata & $-1.56\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 07 40 27.01 & +63 19 55.2 & N \\\\\nWN J0741+5611 & 313$\\pm$13 & 44.4$\\pm$ 1.0 & $ 7.08\\pm0.24$ & $-1.34\\pm$0.03 & $-1.48\\pm0.03$ & S & 0.5 & 20 & 07 41 15.38 & +56 11 35.9 & V \\\\\nWN J0747+3654 & 289$\\pm$12 & 36.8$\\pm$ 0.8 & \\nodata & $-1.41\\pm$0.03 & \\nodata & S & 2.1 & 2 & 07 47 29.38 & +36 54 38.1 & F \\\\\nWN J0747+4527 & 138$\\pm$ 7 & 19.1$\\pm$ 2.2 & \\nodata & $-1.35\\pm$0.09 & \\nodata & S & 3.5 & 109 & 07 47 29.56 & +45 27 16.3 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0751+3300 & 98$\\pm$ 7 & 11.5$\\pm$ 0.5 & $ 1.90\\pm0.12$ & $-1.47\\pm$0.05 & $-1.44\\pm0.06$ & S & 0.4 & 139 & 07 51 48.04 & +33 00 07.1 & V \\\\\nWN J0756+5010 & 204$\\pm$ 9 & 29.9$\\pm$ 0.7 & \\nodata & $-1.31\\pm$0.04 & \\nodata & S & 1.7 & 93 & 07 56 24.63 & +50 10 12.5 & F \\\\\nWN J0801+7134 & 120$\\pm$ 6 & 13.5$\\pm$ 2.3 & \\nodata & $-1.50\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 08 01 18.68 & +71 34 01.6 & N \\\\\nWN J0809+6624 & 257$\\pm$11 & 32.2$\\pm$ 2.3 & \\nodata & $-1.42\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 08 09 19.28 & +66 24 09.5 & N \\\\\nWN J0810+4948 & 146$\\pm$ 7 & 18.1$\\pm$ 1.4 & $ 2.16\\pm0.13$ & $-1.43\\pm$0.07 & $-1.74\\pm0.08$ & S & $<0.3$ & 0 & 08 10 34.92 & +49 48 37.5 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0812+3424 & 160$\\pm$ 8 & 19.9$\\pm$ 1.4 & \\nodata & $-1.43\\pm$0.06 & \\nodata & D & 6.6 & 58 & 08 12 14.43 & +34 24 09.3 & F \\\\\nWN J0813+4828 & 184$\\pm$ 9 & 23.3$\\pm$ 1.7 & $ 15.20\\pm0.40$ & $-1.42\\pm$0.06 & $-0.32\\pm0.06$ & D & 0.9 & 173 & 08 13 38.10 & +48 28 41.5 & V \\\\\nWN J0819+5628 & 95$\\pm$ 6 & 11.7$\\pm$ 0.5 & \\nodata & $-1.43\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 08 19 33.65 & +56 28 38.1 & N \\\\\nWN J0829+3834$^*$ & 112$\\pm$ 6 & 12.7$\\pm$ 1.3 & \\nodata & $-1.49\\pm$0.08 & \\nodata & S & 1.6 & 0 & 08 29 17.35 & +38 34 52.6 & F \\\\\nWN J0830+3018 & 109$\\pm$ 6 & 13.9$\\pm$ 1.2 & \\nodata & $-1.41\\pm$0.07 & \\nodata & S & 3.5 & 89 & 08 30 36.91 & +30 18 11.8 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0834+4820 & 128$\\pm$ 7 & 17.9$\\pm$ 0.5 & $ 3.65\\pm0.18$ & $-1.35\\pm$0.04 & $-1.27\\pm0.04$ & S & 0.4 & 99 & 08 34 25.85 & +48 20 00.8 & V \\\\\nWN J0835+3439 & 143$\\pm$ 7 & 19.1$\\pm$ 1.3 & \\nodata & $-1.38\\pm$0.06 & \\nodata & D & 58.0 & 168 & 08 35 22.92 & +34 39 49.8 & F \\\\\nWN J0842+3540 & 110$\\pm$ 6 & 15.0$\\pm$ 0.5 & \\nodata & $-1.36\\pm$0.04 & \\nodata & S & 1.1 & 0 & 08 42 10.82 & +35 40 42.2 & F \\\\\nWN J0842+3101 & 76$\\pm$ 5 & 10.5$\\pm$ 3.6 & \\nodata & $-1.36\\pm$0.24 & \\nodata & \\nodata & \\nodata & \\nodata & 08 42 16.35 & +31 01 11.6 & N \\\\\nWN J0843+3723 & 290$\\pm$13 & 35.8$\\pm$ 1.9 & \\nodata & $-1.43\\pm$0.05 & \\nodata & S & 1.1 & 5 & 08 43 02.09 & +37 23 18.1 & F \\\\\n&&&&&&&&&&&\\\\\nWN J0850+4830$^*$ & 192$\\pm$ 9 & 18.9$\\pm$ 1.4 & $ 1.53\\pm0.13$ & $-1.59\\pm$0.06 & $-2.02\\pm0.09$ & S & 0.3 & 52 & 08 50 56.50 & +48 30 46.2 & V \\\\\nWN J0852+3311 & 179$\\pm$ 8 & 24.6$\\pm$ 1.5 & \\nodata & $-1.36\\pm$0.05 & \\nodata & D & 6.1 & 13 & 08 52 50.55 & +33 11 41.0 & F \\\\\nWN J0901+6547$^{\\dag}$ & 140$\\pm$ 7 & 19.0$\\pm$ 0.5 & $ 71.60\\pm1.57$ & $-1.37\\pm$0.04 & $ 1.07\\pm0.03$ & D & 37.6 & 117 & 09 01 27.69 & +65 47 25.8 & V \\\\\nWN J0901+3151 & 135$\\pm$ 8 & 20.1$\\pm$ 1.4 & \\nodata & $-1.30\\pm$0.06 & \\nodata & D & 20.1 & 109 & 09 01 48.50 & +31 51 59.4 & F \\\\\nWN J0903+8246 & 112$\\pm$ 6 & 15.5$\\pm$ 0.5 & \\nodata & $-1.35\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 09 03 44.81 & +82 46 02.0 & N \\\\\n\\end{tabular}\n\\end{table*}\n\n\\begin{table*}\n\\tiny\n\\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{325}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{325}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nWN J0911+6306 & 118$\\pm$ 6 & 12.9$\\pm$ 1.3 & \\nodata & $-1.52\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 09 11 34.24 & +63 06 21.7 & N \\\\\nWN J0913+6104 & 297$\\pm$12 & 33.8$\\pm$ 1.8 & \\nodata & $-1.49\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 09 13 05.21 & +61 04 11.7 & N \\\\\nWN J0915+8133 & 127$\\pm$ 5 & 18.6$\\pm$ 0.6 & $ 2.99\\pm0.13$ & $-1.32\\pm$0.04 & $-1.47\\pm0.04$ & S & 2.3 & 127 & 09 15 09.29 & +81 33 34.1 & V \\\\\nWN J0920+5544 & 142$\\pm$ 7 & 13.5$\\pm$ 1.2 & \\nodata & $-1.61\\pm$0.07 & \\nodata & D & 8.9 & 129 & 09 20 46.78 & +55 44 21.8 & F \\\\\nWN J0923+4602 & 107$\\pm$ 5 & 12.1$\\pm$ 0.5 & \\nodata & $-1.49\\pm$0.06 & \\nodata & D & 21.6 & 172 & 09 23 10.44 & +46 02 59.0 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0928+6003 & 119$\\pm$ 6 & 11.0$\\pm$ 0.5 & $ 2.14\\pm0.11$ & $-1.63\\pm$0.05 & $-1.32\\pm0.06$ & S & 3.4 & 128 & 09 28 44.58 & +60 03 01.7 & V \\\\\nWN J0930+4358 & 118$\\pm$ 7 & 12.0$\\pm$ 0.5 & \\nodata & $-1.57\\pm$0.05 & \\nodata & S & 3.1 & 88 & 09 30 12.14 & +43 58 27.2 & F \\\\\nWN J0930+3207 & 218$\\pm$ 9 & 31.1$\\pm$ 1.7 & \\nodata & $-1.33\\pm$0.05 & \\nodata & S & 11.7 & 58 & 09 30 53.32 & +32 07 20.8 & F \\\\\nWN J0939+6323 & 268$\\pm$11 & 39.7$\\pm$ 2.0 & $ 10.86\\pm0.29$ & $-1.31\\pm$0.05 & $-1.04\\pm0.05$ & T & 30.3 & 27 & 09 39 54.89 & +63 23 31.9 & V \\\\\nWN J0940+3838 & 108$\\pm$ 6 & 11.8$\\pm$ 1.6 & \\nodata & $-1.52\\pm$0.10 & \\nodata & \\nodata & \\nodata & \\nodata & 09 40 26.15 & +38 38 35.0 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J0946+6726 & 632$\\pm$25 & 84.7$\\pm$ 3.7 & $ 40.19\\pm0.88$ & $-1.38\\pm$0.04 & $-0.60\\pm0.04$ & T & 44.8 & 114 & 09 46 44.25 & +67 26 41.8 & V \\\\\nWN J0948+6305 & 731$\\pm$29 & 90.5$\\pm$ 1.9 & $ 14.46\\pm0.38$ & $-1.43\\pm$0.03 & $-1.48\\pm0.03$ & D & 3.1 & 134 & 09 48 40.83 & +63 05 42.0 & V \\\\\nWN J0952+5153 & 211$\\pm$10 & 16.1$\\pm$ 1.3 & \\nodata & $-1.76\\pm$0.06 & \\nodata & S & 2.7 & 166 & 09 52 49.14 & +51 53 05.0 & F \\\\\nWN J0955+6023 & 103$\\pm$ 6 & 10.9$\\pm$ 1.6 & $ 4.32\\pm0.15$ & $-1.54\\pm$0.11 & $-0.75\\pm0.12$ & DF & 3.1 & 129 & 09 55 30.01 & +60 23 17.1 & V \\\\\nWN J1002+5512 & 119$\\pm$ 5 & 17.7$\\pm$ 0.5 & \\nodata & $-1.30\\pm$0.05 & \\nodata & S & 10.4 & 58 & 10 02 39.24 & +55 12 55.5 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1003+4448 & 94$\\pm$ 5 & 13.9$\\pm$ 2.0 & \\nodata & $-1.31\\pm$0.11 & \\nodata & DF & 17.2 & 93 & 10 03 30.22 & +44 48 16.2 & F \\\\\nWN J1012+3334$^*$ & 168$\\pm$ 8 & 16.4$\\pm$ 1.6 & \\nodata & $-1.59\\pm$0.07 & \\nodata & D & 22.1 & 6 & 10 12 00.43 & +33 35 00.9 & F \\\\\nWN J1013+3254 & 102$\\pm$ 7 & 14.2$\\pm$ 0.5 & \\nodata & $-1.35\\pm$0.05 & \\nodata & S & $<0.3$ & 89 & 10 13 06.54 & +32 54 33.2 & F \\\\\nWN J1014+7407 & 170$\\pm$ 8 & 21.8$\\pm$ 0.6 & $ 3.76\\pm0.14$ & $-1.41\\pm$0.04 & $-1.41\\pm0.04$ & S & 2.2 & 150 & 10 14 15.75 & +74 07 56.2 & V \\\\\nWN J1015+3038 & 285$\\pm$12 & 38.0$\\pm$ 1.9 & \\nodata & $-1.38\\pm$0.04 & \\nodata & D & 12.8 & 151 & 10 15 08.92 & +30 38 02.0 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1015+7432 & 146$\\pm$ 7 & 21.4$\\pm$ 0.6 & \\nodata & $-1.31\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 10 15 52.49 & +74 32 20.0 & N \\\\\nWN J1018+3634 & 137$\\pm$ 7 & 20.0$\\pm$ 1.4 & \\nodata & $-1.32\\pm$0.06 & \\nodata & S & $<0.3$ & 180 & 10 18 03.13 & +36 34 43.2 & F \\\\\nWN J1019+5244 & 85$\\pm$ 5 & 10.5$\\pm$ 0.4 & \\nodata & $-1.43\\pm$0.06 & \\nodata & D & 16.5 & 145 & 10 19 20.59 & +52 44 33.2 & F \\\\\nWN J1022+3308 & 90$\\pm$ 5 & 10.1$\\pm$ 0.4 & \\nodata & $-1.50\\pm$0.05 & \\nodata & S & 7.8 & 136 & 10 22 37.44 & +33 08 43.6 & F \\\\\nWN J1026+2943 & 81$\\pm$ 6 & 12.0$\\pm$ 1.2 & \\nodata & $-1.31\\pm$0.08 & \\nodata & S & 11.9 & 20 & 10 26 12.04 & +29 43 48.0 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1029+4838 & 118$\\pm$ 8 & 17.2$\\pm$ 1.4 & $ 2.80\\pm0.16$ & $-1.32\\pm$0.07 & $-1.46\\pm0.08$ & S & 2.0 & 131 & 10 29 32.99 & +48 38 09.0 & V \\\\\nWN J1030+5415 & 223$\\pm$10 & 29.2$\\pm$ 1.6 & \\nodata & $-1.39\\pm$0.05 & \\nodata & S & 6.1 & 44 & 10 30 42.94 & +54 15 35.9 & F \\\\\nWN J1036+3936 & 153$\\pm$ 7 & 16.7$\\pm$ 0.5 & \\nodata & $-1.52\\pm$0.04 & \\nodata & T & 17.5 & 107 & 10 36 21.29 & +39 36 59.4 & F \\\\\nWN J1038+4229 & 816$\\pm$33 & 114.0$\\pm$ 5.1 & \\nodata & $-1.35\\pm$0.04 & \\nodata & S & 1.2 & 3 & 10 38 41.04 & +42 29 51.5 & F \\\\\nWN J1041+5859 & 193$\\pm$ 9 & 25.2$\\pm$ 0.6 & $ 6.96\\pm0.22$ & $-1.39\\pm$0.04 & $-1.04\\pm0.03$ & D & 11.2 & 119 & 10 41 29.64 & +58 59 23.5 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1043+3953 & 95$\\pm$ 8 & 13.9$\\pm$ 0.5 & \\nodata & $-1.32\\pm$0.05 & \\nodata & S & $<0.3$ & 79 & 10 43 32.24 & +39 53 46.8 & F \\\\\nWN J1052+4826 & 1039$\\pm$41 & 154.2$\\pm$ 6.8 & \\nodata & $-1.31\\pm$0.04 & \\nodata & D & 10.0 & 108 & 10 52 53.05 & +48 26 33.8 & F \\\\\nWN J1053+5424 & 467$\\pm$20 & 66.4$\\pm$ 1.4 & $ 7.94\\pm0.25$ & $-1.34\\pm$0.03 & $-1.70\\pm0.03$ & D & 1.1 & 34 & 10 53 36.31 & +54 24 42.1 & V \\\\\nWN J1055+3047 & 342$\\pm$14 & 39.0$\\pm$ 2.0 & \\nodata & $-1.49\\pm$0.05 & \\nodata & S & 7.1 & 147 & 10 55 18.52 & +30 47 23.2 & F \\\\\nWN J1057+3156 & 221$\\pm$10 & 22.2$\\pm$ 1.5 & \\nodata & $-1.57\\pm$0.06 & \\nodata & T & 28.7 & 20 & 10 57 56.56 & +31 56 21.0 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1057+3007 & 276$\\pm$12 & 39.5$\\pm$ 2.0 & \\nodata & $-1.33\\pm$0.05 & \\nodata & D & 24.6 & 90 & 10 57 57.45 & +30 07 02.9 & F \\\\\nWN J1058+3506 & 205$\\pm$10 & 24.0$\\pm$ 1.5 & \\nodata & $-1.47\\pm$0.05 & \\nodata & S & 1.3 & 126 & 10 58 14.74 & +35 06 40.9 & F \\\\\nWN J1058+7003 & 82$\\pm$ 4 & 10.5$\\pm$ 0.5 & \\nodata & $-1.41\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 10 58 34.95 & +70 03 17.6 & N \\\\\nWN J1059+4341 & 99$\\pm$ 8 & 12.3$\\pm$ 1.6 & \\nodata & $-1.43\\pm$0.10 & \\nodata & D & 29.1 & 66 & 10 59 43.88 & +43 41 05.2 & F \\\\\nWN J1101+3520$^*$ & 120$\\pm$ 7 & 17.5$\\pm$ 2.1 & \\nodata & $-1.32\\pm$0.09 & \\nodata & S & 8.1 & 1 & 11 01 14.35 & +35 20 12.7 & F \\\\\n&&&&&&&&&&&\\\\\nWN J1111+3311 & 92$\\pm$ 6 & 13.3$\\pm$ 0.5 & \\nodata & $-1.32\\pm$0.05 & \\nodata & S & 6.7 & 16 & 11 11 40.79 & +33 12 00.9 & F \\\\\nWN J1115+5016 & 232$\\pm$10 & 33.9$\\pm$ 0.8 & $ 5.47\\pm0.22$ & $-1.32\\pm$0.03 & $-1.46\\pm0.04$ & D & 0.2 & 117 & 11 15 06.87 & +50 16 23.9 & V \\\\\nWN J1117+5251 & 1439$\\pm$57 & 198.7$\\pm$ 8.7 & \\nodata & $-1.36\\pm$0.04 & \\nodata & D & 9.5 & 6 & 11 17 24.37 & +52 51 54.6 & F \\\\\nWN J1122+3239 & 143$\\pm$ 7 & 19.5$\\pm$ 1.4 & \\nodata & $-1.36\\pm$0.06 & \\nodata & S & 4.2 & 89 & 11 22 33.53 & +32 39 40.9 & F \\\\\nWN J1123+3141 & 623$\\pm$25 & 74.0$\\pm$ 3.3 & \\nodata & $-1.46\\pm$0.04 & \\nodata & T & 25.8 & 83 & 11 23 55.85 & +31 41 26.1 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1124+3228 & 263$\\pm$11 & 38.9$\\pm$ 0.9 & \\nodata & $-1.31\\pm$0.03 & \\nodata & S & 5.7 & 165 & 11 24 34.17 & +32 28 19.6 & F \\\\\nWN J1126+8318 & 175$\\pm$ 8 & 25.8$\\pm$ 1.6 & \\nodata & $-1.31\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 11 26 26.48 & +83 18 23.8 & N \\\\\nWN J1128+4822 & 280$\\pm$12 & 29.9$\\pm$ 0.7 & \\nodata & $-1.53\\pm$0.03 & \\nodata & S & 1.2 & 171 & 11 28 05.19 & +48 22 56.6 & F \\\\\nWN J1128+6416 & 257$\\pm$11 & 31.0$\\pm$ 1.7 & $ 3.20\\pm0.17$ & $-1.45\\pm$0.05 & $-1.82\\pm0.06$ & S & 0.8 & 116 & 11 28 12.10 & +64 16 25.3 & V \\\\\nWN J1130+4911 & 134$\\pm$ 6 & 18.9$\\pm$ 1.5 & \\nodata & $-1.34\\pm$0.07 & \\nodata & T & 37.0 & 145 & 11 30 17.53 & +49 11 17.7 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1139+3048 & 819$\\pm$33 & 119.6$\\pm$ 5.3 & \\nodata & $-1.32\\pm$0.04 & \\nodata & D & 9.0 & 40 & 11 39 14.34 & +30 48 50.7 & F \\\\\nWN J1139+3706 & 139$\\pm$ 8 & 16.7$\\pm$ 1.4 & \\nodata & $-1.45\\pm$0.07 & \\nodata & S & 3.5 & 32 & 11 39 43.04 & +37 06 55.7 & F \\\\\nWN J1141+6924 & 81$\\pm$ 5 & 11.8$\\pm$ 0.5 & \\nodata & $-1.32\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 11 41 09.71 & +69 24 16.3 & N \\\\\nWN J1148+5116 & 148$\\pm$ 7 & 20.5$\\pm$ 1.7 & \\nodata & $-1.35\\pm$0.07 & \\nodata & D & 6.7 & 50 & 11 48 01.92 & +51 16 29.6 & F \\\\\nWN J1148+6233 & 98$\\pm$ 5 & 14.1$\\pm$ 0.5 & $ 1.37\\pm0.09$ & $-1.33\\pm$0.05 & $-1.88\\pm0.06$ & S & 2.4 & 144 & 11 48 44.42 & +62 33 24.6 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1148+3519 & 114$\\pm$ 7 & 13.9$\\pm$ 1.7 & \\nodata & $-1.44\\pm$0.09 & \\nodata & D & 20.0 & 7 & 11 48 54.29 & +35 19 10.1 & F \\\\\nWN J1151+4436 & 78$\\pm$ 5 & 11.1$\\pm$ 0.5 & \\nodata & $-1.34\\pm$0.06 & \\nodata & D & 15.1 & 20 & 11 51 16.80 & +44 36 10.0 & F \\\\\nWN J1152+3732$^*$ & 414$\\pm$17 & 17.1$\\pm$ 1.4 & \\nodata & $-2.18\\pm$0.06 & \\nodata & S & 15.0 & 119 & 11 52 36.34 & +37 32 43.9 & F \\\\\nWN J1154+5415 & 153$\\pm$ 7 & 19.1$\\pm$ 0.5 & $ 1.05\\pm0.10$ & $-1.42\\pm$0.04 & $-2.33\\pm0.08$ & S & $<0.3$ & 0 & 11 54 18.97 & +54 15 11.4 & V \\\\\nWN J1203+8350 & 132$\\pm$ 6 & 18.5$\\pm$ 0.5 & \\nodata & $-1.35\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 12 03 30.63 & +83 50 37.1 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1204+5014 & 94$\\pm$ 5 & 11.3$\\pm$ 1.7 & \\nodata & $-1.45\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 12 04 31.11 & +50 14 49.8 & N \\\\\nWN J1206+3136 & 167$\\pm$ 9 & 22.2$\\pm$ 1.5 & \\nodata & $-1.38\\pm$0.06 & \\nodata & D & 16.6 & 53 & 12 06 48.10 & +31 36 50.9 & F \\\\\nWN J1208+4301 & 162$\\pm$ 8 & 13.9$\\pm$ 1.4 & \\nodata & $-1.68\\pm$0.08 & \\nodata & T & 8.0 & 27 & 12 08 42.77 & +43 01 42.3 & F \\\\\nWN J1216+4446 & 191$\\pm$ 8 & 13.6$\\pm$ 0.5 & \\nodata & $-1.81\\pm$0.04 & \\nodata & S & 6.1 & 98 & 12 16 46.84 & +44 46 51.3 & F \\\\\nWN J1218+3143 & 1906$\\pm$76 & 281.5$\\pm$12.4 & \\nodata & $-1.31\\pm$0.04 & \\nodata & S & 5.6 & 65 & 12 18 31.47 & +31 43 41.7 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1219+4644 & 140$\\pm$ 8 & 20.9$\\pm$ 0.6 & $ 2.84\\pm0.14$ & $-1.30\\pm$0.04 & $-1.59\\pm0.05$ & S & 0.2 & 157 & 12 19 31.79 & +46 44 49.6 & V \\\\\nWN J1223+4256 & 116$\\pm$ 6 & 17.2$\\pm$ 0.5 & \\nodata & $-1.31\\pm$0.04 & \\nodata & S & 4.3 & 179 & 12 23 11.32 & +42 56 57.3 & F \\\\\nWN J1224+4956 & 145$\\pm$ 7 & 21.4$\\pm$ 1.6 & \\nodata & $-1.31\\pm$0.06 & \\nodata & T & 39.6 & 66 & 12 24 21.03 & +49 56 49.2 & F \\\\\nWN J1224+5436 & 790$\\pm$31 & 69.1$\\pm$ 1.5 & $ 6.30\\pm0.20$ & $-1.67\\pm$0.03 & $-1.92\\pm0.03$ & D & 0.9 & 16 & 12 24 52.35 & +54 36 39.9 & V \\\\\nWN J1226+4836 & 155$\\pm$ 8 & 17.0$\\pm$ 0.5 & \\nodata & $-1.51\\pm$0.04 & \\nodata & S & 4.8 & 115 & 12 26 22.45 & +48 36 39.6 & F \\\\\n&&&&&&&&&&&\\\\\nWN J1232+4621$^*$ & 133$\\pm$ 6 & 19.8$\\pm$ 1.8 & \\nodata & $-1.30\\pm$0.07 & \\nodata & DF & 12.5 & 156 & 12 32 39.79 & +46 21 48.1 & F \\\\\nWN J1242+3915 & 549$\\pm$22 & 78.4$\\pm$ 1.7 & \\nodata & $-1.33\\pm$0.03 & \\nodata & D & 11.2 & 51 & 12 42 53.09 & +39 15 48.6 & F \\\\\nWN J1247+6121 & 103$\\pm$ 5 & 15.4$\\pm$ 2.4 & \\nodata & $-1.30\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 12 47 45.31 & +61 21 23.3 & N \\\\\nWN J1249+4043 & 160$\\pm$ 7 & 22.8$\\pm$ 1.4 & \\nodata & $-1.33\\pm$0.05 & \\nodata & D & 37.0 & 80 & 12 49 27.43 & +40 43 49.3 & F \\\\\nWN J1258+3212 & 182$\\pm$12 & 19.9$\\pm$ 1.5 & \\nodata & $-1.52\\pm$0.06 & \\nodata & S & 6.7 & 131 & 12 58 23.62 & +32 12 42.4 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1258+5041 & 230$\\pm$11 & 28.8$\\pm$ 2.0 & \\nodata & $-1.42\\pm$0.06 & \\nodata & T & 44.9 & 58 & 12 58 50.96 & +50 41 42.3 & F \\\\\nWN J1259+3121 & 268$\\pm$11 & 34.0$\\pm$ 1.8 & \\nodata & $-1.41\\pm$0.05 & \\nodata & DF & 20.6 & 1 & 12 59 51.96 & +31 21 05.6 & F \\\\\nWN J1300+5311 & 157$\\pm$ 7 & 19.2$\\pm$ 0.5 & $ 2.70\\pm0.16$ & $-1.44\\pm$0.04 & $-1.58\\pm0.05$ & S & 0.3 & 7 & 13 00 36.25 & +53 11 52.4 & V \\\\\nWN J1302+3206 & 383$\\pm$16 & 54.0$\\pm$ 1.2 & \\nodata & $-1.34\\pm$0.03 & \\nodata & S & 4.7 & 102 & 13 02 03.07 & +32 06 35.6 & F \\\\\nWN J1303+8024 & 165$\\pm$ 7 & 22.2$\\pm$ 0.6 & $ 5.05\\pm0.18$ & $-1.37\\pm$0.03 & $-1.19\\pm0.04$ & D & 4.1 & 145 & 13 03 33.92 & +80 24 42.2 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1303+5437 & 145$\\pm$ 7 & 15.4$\\pm$ 1.4 & \\nodata & $-1.54\\pm$0.07 & \\nodata & D & 16.5 & 88 & 13 03 45.48 & +54 37 28.9 & F \\\\\nWN J1306+4726 & 100$\\pm$ 7 & 13.1$\\pm$ 0.5 & \\nodata & $-1.39\\pm$0.05 & \\nodata & S & 10.2 & 40 & 13 06 35.99 & +47 26 10.1 & F \\\\\nWN J1310+5706 & 112$\\pm$ 6 & 15.9$\\pm$ 0.5 & \\nodata & $-1.34\\pm$0.04 & \\nodata & S & 4.2 & 99 & 13 10 22.96 & +57 06 57.9 & F \\\\\nWN J1310+3820 & 69$\\pm$ 4 & 10.3$\\pm$ 1.5 & \\nodata & $-1.30\\pm$0.12 & \\nodata & S & 4.4 & 18 & 13 10 24.08 & +38 20 44.1 & F \\\\\nWN J1312+6646 & 291$\\pm$12 & 41.6$\\pm$ 0.9 & $ 8.56\\pm0.24$ & $-1.33\\pm$0.03 & $-1.27\\pm0.03$ & D & 6.3 & 118 & 13 12 45.59 & +66 46 36.1 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1314+3649 & 286$\\pm$11 & 36.4$\\pm$ 0.8 & \\nodata & $-1.41\\pm$0.03 & \\nodata & S & 1.3 & 90 & 13 14 17.86 & +36 49 14.6 & F \\\\\nWN J1314+3515$^*$ & 169$\\pm$ 7 & 20.2$\\pm$ 1.7 & \\nodata & $-1.45\\pm$0.07 & \\nodata & DF & 34.2 & 47 & 13 14 25.00 & +35 15 53.9 & F \\\\\nWN J1315+4337 & 149$\\pm$ 8 & 16.3$\\pm$ 0.5 & \\nodata & $-1.52\\pm$0.04 & \\nodata & S & 1.3 & 152 & 13 15 19.05 & +43 37 57.1 & F \\\\\nWN J1321+3311 & 141$\\pm$ 8 & 19.0$\\pm$ 0.6 & \\nodata & $-1.37\\pm$0.04 & \\nodata & D & 14.7 & 63 & 13 21 13.55 & +33 11 31.2 & F \\\\\nWN J1323+4713 & 106$\\pm$ 5 & 14.9$\\pm$ 0.5 & \\nodata & $-1.34\\pm$0.04 & \\nodata & S & 2.5 & 139 & 13 23 08.31 & +47 13 10.7 & F \\\\\n\\end{tabular}\n\\end{table*}\n\n\\begin{table*}\n\\tiny\n\\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{325}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{325}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nWN J1327+5341 & 196$\\pm$ 9 & 27.4$\\pm$ 0.7 & \\nodata & $-1.35\\pm$0.04 & \\nodata & S & 0.6 & 162 & 13 27 12.77 & +53 41 20.6 & F \\\\\nWN J1327+5332 & 163$\\pm$ 7 & 20.5$\\pm$ 0.6 & $ 2.70\\pm0.17$ & $-1.42\\pm$0.04 & $-1.61\\pm0.06$ & D & 0.3 & 89 & 13 27 37.86 & +53 32 10.8 & V \\\\\nWN J1329+3046$^*$ & 86$\\pm$ 5 & 11.7$\\pm$ 1.7 & \\nodata & $-1.37\\pm$0.11 & \\nodata & S & 1.6 & 6 & 13 29 31.75 & +30 46 13.6 & F \\\\\nWN J1329+3046$^*$ & 88$\\pm$ 5 & 12.1$\\pm$ 2.0 & \\nodata & $-1.36\\pm$0.13 & \\nodata & S & 3.6 & 129 & 13 29 55.12 & +30 46 51.2 & F \\\\\nWN J1330+6505 & 74$\\pm$ 6 & 10.5$\\pm$ 0.5 & $ 2.34\\pm0.12$ & $-1.34\\pm$0.06 & $-1.21\\pm0.06$ & S & 1.8 & 5 & 13 30 02.77 & +65 04 59.3 & V \\\\\n&&&&&&&&&&&\\\\\nWN J1330+3037$^*$ & 496$\\pm$20 & 64.5$\\pm$ 2.9 & \\nodata & $-1.40\\pm$0.04 & \\nodata & D & 25.5 & 140 & 13 30 53.67 & +30 37 59.1 & F \\\\\nWN J1330+3604 & 103$\\pm$ 5 & 15.1$\\pm$ 0.5 & \\nodata & $-1.31\\pm$0.05 & \\nodata & D & 9.6 & 0 & 13 30 56.83 & +36 04 01.6 & F \\\\\nWN J1330+5344$^*$ & 525$\\pm$21 & 71.0$\\pm$ 3.2 & $ 8.10\\pm0.29$ & $-1.37\\pm$0.04 & $-1.74\\pm0.05$ & DF & 2.5 & 173 & 13 30 58.90 & +53 44 07.8 & V \\\\\nWN J1331+2937 & 93$\\pm$ 5 & 12.5$\\pm$ 1.3 & $ 3.44\\pm0.13$ & $-1.37\\pm$0.09 & $-1.04\\pm0.09$ & S & 2.7 & 40 & 13 31 21.58 & +29 37 12.6 & V \\\\\nWN J1332+3009$^*$ & 239$\\pm$10 & 35.3$\\pm$ 2.0 & \\nodata & $-1.31\\pm$0.05 & \\nodata & D & 39.2 & 161 & 13 32 45.73 & +30 09 59.9 & F \\\\\n&&&&&&&&&&&\\\\\nWN J1333+3037$^*$ & 423$\\pm$17 & 21.5$\\pm$ 0.6 & \\nodata & $-2.04\\pm$0.03 & \\nodata & S & 0.4 & 179 & 13 33 21.20 & +30 37 35.1 & F \\\\\nWN J1333+4913 & 149$\\pm$ 7 & 22.2$\\pm$ 0.6 & $ 4.78\\pm0.23$ & $-1.30\\pm$0.04 & $-1.22\\pm0.04$ & T & 5.4 & 40 & 13 33 56.42 & +49 13 27.1 & V \\\\\nWN J1335+3222$^*$ & 150$\\pm$ 7 & 18.3$\\pm$ 1.4 & \\nodata & $-1.44\\pm$0.06 & \\nodata & D & 8.8 & 85 & 13 35 35.44 & +32 22 48.7 & F \\\\\nWN J1336+3820 & 116$\\pm$ 6 & 15.6$\\pm$ 0.5 & \\nodata & $-1.37\\pm$0.04 & \\nodata & S & 3.4 & 61 & 13 36 40.88 & +38 20 02.2 & F \\\\\nWN J1337+3149 & 142$\\pm$ 7 & 19.6$\\pm$ 1.9 & \\nodata & $-1.36\\pm$0.08 & \\nodata & D & 35.2 & 21 & 13 37 02.46 & +31 49 49.2 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1337+3401 & 109$\\pm$ 8 & 14.3$\\pm$ 0.5 & \\nodata & $-1.39\\pm$0.04 & \\nodata & S & 3.5 & 56 & 13 37 10.50 & +34 01 26.8 & F \\\\\nWN J1339+5320 & 104$\\pm$ 5 & 13.9$\\pm$ 0.5 & $ 1.80\\pm0.15$ & $-1.38\\pm$0.05 & $-1.63\\pm0.07$ & D & 0.1 & 138 & 13 39 59.25 & +53 20 07.8 & V \\\\\nWN J1341+4953 & 153$\\pm$ 8 & 16.4$\\pm$ 1.4 & \\nodata & $-1.53\\pm$0.07 & \\nodata & D & 18.6 & 160 & 13 41 25.70 & +49 53 41.8 & F \\\\\nWN J1346+6736 & 107$\\pm$ 6 & 14.5$\\pm$ 0.5 & $ 2.82\\pm0.16$ & $-1.37\\pm$0.04 & $-1.32\\pm0.05$ & S & $<0.3$ & 0 & 13 46 37.02 & +67 36 21.7 & V \\\\\nWN J1347+3033 & 341$\\pm$14 & 42.4$\\pm$ 2.2 & \\nodata & $-1.43\\pm$0.05 & \\nodata & D & 37.3 & 151 & 13 47 16.09 & +30 33 07.6 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1352+4259 & 1213$\\pm$48 & 173.9$\\pm$ 7.7 & \\nodata & $-1.33\\pm$0.04 & \\nodata & D & 12.1 & 19 & 13 52 28.39 & +42 59 18.1 & F \\\\\nWN J1353+3336 & 107$\\pm$ 6 & 15.9$\\pm$ 1.9 & \\nodata & $-1.31\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 13 53 07.46 & +33 36 24.6 & N \\\\\nWN J1355+3848 & 204$\\pm$ 8 & 25.6$\\pm$ 0.6 & \\nodata & $-1.42\\pm$0.03 & \\nodata & S & 2.3 & 59 & 13 55 29.50 & +38 48 11.1 & F \\\\\nWN J1359+7446$^*$ & 214$\\pm$ 9 & 12.9$\\pm$ 0.5 & $ 1.26\\pm0.10$ & $-1.92\\pm$0.05 & $-1.87\\pm0.07$ & S & 2.5 & 12 & 13 59 16.90 & +74 46 42.6 & V \\\\\nWN J1400+4348 & 178$\\pm$ 7 & 20.2$\\pm$ 1.5 & \\nodata & $-1.49\\pm$0.06 & \\nodata & S & 6.4 & 93 & 14 00 51.84 & +43 48 07.2 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1403+3109 & 328$\\pm$13 & 45.7$\\pm$ 2.2 & \\nodata & $-1.35\\pm$0.04 & \\nodata & S & 11.0 & 25 & 14 03 39.47 & +31 09 11.4 & F \\\\\nWN J1410+4615 & 103$\\pm$ 5 & 14.2$\\pm$ 1.4 & \\nodata & $-1.36\\pm$0.08 & \\nodata & S & 4.4 & 79 & 14 10 48.17 & +46 15 57.5 & F \\\\\nWN J1416+3821 & 94$\\pm$ 6 & 13.1$\\pm$ 0.5 & \\nodata & $-1.35\\pm$0.05 & \\nodata & D & 7.6 & 14 & 14 16 13.21 & +38 21 56.7 & F \\\\\nWN J1418+4546 & 186$\\pm$ 8 & 17.9$\\pm$ 0.5 & $ 2.70\\pm0.14$ & $-1.60\\pm$0.04 & $-1.52\\pm0.05$ & S & 0.5 & 18 & 14 18 38.40 & +45 46 38.4 & V \\\\\nWN J1420+6735 & 382$\\pm$15 & 33.1$\\pm$ 1.7 & $ 1.22\\pm0.09$ & $-1.67\\pm$0.05 & $-2.65\\pm0.07$ & S & 2.0 & 173 & 14 20 03.34 & +67 35 07.5 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1420+4126 & 128$\\pm$ 6 & 18.7$\\pm$ 0.6 & \\nodata & $-1.32\\pm$0.04 & \\nodata & S & 5.3 & 65 & 14 20 50.23 & +41 26 26.1 & F \\\\\nWN J1421+3103 & 110$\\pm$ 5 & 13.6$\\pm$ 0.5 & \\nodata & $-1.43\\pm$0.05 & \\nodata & S & 0.4 & 127 & 14 21 07.69 & +31 03 03.9 & F \\\\\nWN J1422+3452 & 163$\\pm$ 7 & 10.7$\\pm$ 1.3 & \\nodata & $-1.86\\pm$0.09 & \\nodata & S & 13.3 & 151 & 14 22 05.17 & +34 52 14.4 & F \\\\\nWN J1422+4212 & 258$\\pm$10 & 35.4$\\pm$ 1.8 & \\nodata & $-1.36\\pm$0.05 & \\nodata & S & 5.1 & 164 & 14 22 44.38 & +42 12 00.2 & F \\\\\nWN J1426+3522 & 89$\\pm$ 5 & 11.5$\\pm$ 1.6 & \\nodata & $-1.40\\pm$0.11 & \\nodata & \\nodata & \\nodata & \\nodata & 14 26 56.32 & +35 22 34.7 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1431+3015 & 101$\\pm$ 5 & 14.3$\\pm$ 1.5 & \\nodata & $-1.34\\pm$0.09 & \\nodata & D & 28.9 & 158 & 14 31 17.77 & +30 15 00.2 & F \\\\\nWN J1431+7317 & 129$\\pm$ 6 & 17.9$\\pm$ 1.3 & $ 4.65\\pm0.19$ & $-1.35\\pm$0.06 & $-1.08\\pm0.07$ & D & 11.2 & 47 & 14 31 28.01 & +73 17 29.7 & V \\\\\nWN J1433+3044 & 144$\\pm$ 6 & 16.7$\\pm$ 1.3 & \\nodata & $-1.48\\pm$0.06 & \\nodata & D & 14.5 & 100 & 14 33 56.51 & +30 44 25.5 & F \\\\\nWN J1435+3523 & 160$\\pm$ 7 & 22.3$\\pm$ 1.6 & \\nodata & $-1.35\\pm$0.06 & \\nodata & S & 8.0 & 64 & 14 35 53.99 & +35 24 06.8 & F \\\\\nWN J1436+6319 & 3507$\\pm$140 & 514.0$\\pm$22.4 & $ 64.84\\pm1.39$ & $-1.31\\pm$0.04 & $-1.67\\pm0.04$ & D & 3.8 & 154 & 14 36 37.28 & +63 19 13.9 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1437+7409 & 111$\\pm$ 5 & 16.4$\\pm$ 0.5 & $ 1.32\\pm0.11$ & $-1.31\\pm$0.05 & $-2.02\\pm0.07$ & S & $<0.3$ & 0 & 14 37 35.89 & +74 09 22.2 & V \\\\\nWN J1439+3729 & 142$\\pm$ 7 & 17.1$\\pm$ 0.5 & \\nodata & $-1.45\\pm$0.04 & \\nodata & D & 7.2 & 157 & 14 39 49.99 & +37 29 03.4 & F \\\\\nWN J1440+3707$^*$ & 219$\\pm$ 9 & 16.7$\\pm$ 1.3 & \\nodata & $-1.76\\pm$0.06 & \\nodata & S & 7.4 & 61 & 14 40 03.63 & +37 07 27.4 & F \\\\\nWN J1444+4114 & 97$\\pm$ 5 & 13.2$\\pm$ 1.4 & \\nodata & $-1.37\\pm$0.09 & \\nodata & D & 30.1 & 151 & 14 44 27.65 & +41 14 38.3 & F \\\\\nWN J1444+4112 & 109$\\pm$ 6 & 13.1$\\pm$ 0.5 & \\nodata & $-1.45\\pm$0.05 & \\nodata & D & 12.6 & 96 & 14 44 48.82 & +41 12 25.5 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1447+5423 & 97$\\pm$ 6 & 13.3$\\pm$ 0.5 & \\nodata & $-1.36\\pm$0.05 & \\nodata & S & 11.0 & 174 & 14 47 54.36 & +54 23 25.2 & F \\\\\nWN J1450+3534 & 95$\\pm$ 5 & 10.2$\\pm$ 0.4 & \\nodata & $-1.53\\pm$0.05 & \\nodata & S & 3.3 & 62 & 14 50 20.69 & +35 34 46.5 & F \\\\\nWN J1451+3649 & 254$\\pm$10 & 29.8$\\pm$ 2.3 & \\nodata & $-1.47\\pm$0.06 & \\nodata & T & 50.7 & 101 & 14 51 11.62 & +36 49 34.4 & F \\\\\nWN J1454+3210 & 264$\\pm$11 & 37.6$\\pm$ 0.9 & \\nodata & $-1.33\\pm$0.03 & \\nodata & S & 3.0 & 22 & 14 54 11.64 & +32 10 16.8 & F \\\\\nWN J1459+6405 & 339$\\pm$14 & 40.0$\\pm$ 3.6 & \\nodata & $-1.46\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 14 59 33.34 & +64 05 58.0 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1459+4947 & 175$\\pm$ 8 & 18.7$\\pm$ 0.5 & \\nodata & $-1.53\\pm$0.04 & \\nodata & S & 3.0 & 109 & 14 59 43.19 & +49 47 15.9 & F \\\\\nWN J1500+3613 & 390$\\pm$16 & 52.9$\\pm$ 2.5 & \\nodata & $-1.37\\pm$0.04 & \\nodata & S & 2.2 & 76 & 15 00 09.01 & +36 13 25.8 & F \\\\\nWN J1502+4756 & 221$\\pm$ 9 & 19.1$\\pm$ 1.5 & \\nodata & $-1.68\\pm$0.06 & \\nodata & D & 12.3 & 37 & 15 02 03.58 & +47 56 34.7 & F \\\\\nWN J1508+5839 & 122$\\pm$ 6 & 12.5$\\pm$ 0.5 & $ 1.37\\pm0.09$ & $-1.56\\pm$0.05 & $-1.78\\pm0.06$ & D & 35.2 & 128 & 15 08 08.17 & +58 39 13.3 & V \\\\\nWN J1509+5905$^*$ & 752$\\pm$30 & 107.3$\\pm$ 4.6 & $ 8.60\\pm0.26$ & $-1.33\\pm$0.04 & $-2.03\\pm0.04$ & DF & 1.8 & 74 & 15 09 32.34 & +59 05 24.5 & V \\\\\n&&&&&&&&&&&\\\\\nWN J1525+3010 & 145$\\pm$ 7 & 17.2$\\pm$ 0.5 & \\nodata & $-1.46\\pm$0.04 & \\nodata & S & 1.2 & 123 & 15 25 01.21 & +30 10 30.2 & F \\\\\nWN J1525+5130 & 94$\\pm$ 5 & 10.7$\\pm$ 0.5 & $ 2.02\\pm0.13$ & $-1.49\\pm$0.06 & $-1.34\\pm0.06$ & S & 0.8 & 7 & 15 25 12.93 & +51 30 06.1 & V \\\\\nWN J1528+6317 & 332$\\pm$14 & 40.0$\\pm$ 2.0 & $ 20.80\\pm0.52$ & $-1.45\\pm$0.04 & $-0.53\\pm0.05$ & DF & 6.0 & 121 & 15 28 06.47 & +63 17 40.2 & V \\\\\nWN J1529+3454 & 124$\\pm$ 6 & 13.0$\\pm$ 0.5 & \\nodata & $-1.54\\pm$0.05 & \\nodata & S & 2.3 & 35 & 15 29 41.52 & +34 54 31.3 & F \\\\\nWN J1537+3402 & 83$\\pm$ 5 & 11.6$\\pm$ 0.5 & \\nodata & $-1.35\\pm$0.05 & \\nodata & S & 1.7 & 31 & 15 37 50.57 & +34 02 33.3 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1543+3512 & 231$\\pm$10 & 23.6$\\pm$ 1.5 & \\nodata & $-1.56\\pm$0.05 & \\nodata & D & 9.2 & 0 & 15 43 29.49 & +35 12 29.7 & F \\\\\nWN J1546+3935 & 155$\\pm$ 7 & 13.7$\\pm$ 0.5 & \\nodata & $-1.66\\pm$0.04 & \\nodata & D & 8.5 & 102 & 15 46 41.95 & +39 35 52.7 & F \\\\\nWN J1546+3005 & 92$\\pm$ 6 & 13.0$\\pm$ 0.5 & \\nodata & $-1.34\\pm$0.05 & \\nodata & S & 2.3 & 144 & 15 46 57.65 & +30 05 38.1 & F \\\\\nWN J1550+3830 & 229$\\pm$10 & 32.9$\\pm$ 1.7 & \\nodata & $-1.33\\pm$0.05 & \\nodata & S & 4.2 & 178 & 15 50 19.42 & +38 30 14.8 & F \\\\\nWN J1552+3715 & 546$\\pm$22 & 27.3$\\pm$ 1.6 & \\nodata & $-2.05\\pm$0.05 & \\nodata & D & 18.6 & 120 & 15 52 07.07 & +37 15 07.1 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1555+4011 & 359$\\pm$14 & 50.9$\\pm$ 2.4 & \\nodata & $-1.34\\pm$0.04 & \\nodata & S & 1.1 & 90 & 15 55 02.50 & +40 11 58.2 & F \\\\\nWN J1558+7028 & 114$\\pm$ 6 & 15.7$\\pm$ 2.1 & $ 1.68\\pm0.11$ & $-1.36\\pm$0.11 & $-1.80\\pm0.12$ & S & 2.1 & 38 & 15 58 37.92 & +70 28 11.2 & V \\\\\nWN J1559+6110 & 130$\\pm$ 6 & 18.3$\\pm$ 1.3 & $ 3.47\\pm0.14$ & $-1.34\\pm$0.06 & $-1.34\\pm0.07$ & S & 0.3 & 20 & 15 59 50.65 & +61 10 57.8 & V \\\\\nWN J1559+5926 & 116$\\pm$ 6 & 15.3$\\pm$ 1.3 & $ 41.70\\pm0.92$ & $-1.39\\pm$0.07 & \\nodata & D & 31.0 & 60 & 15 59 54.42 & +59 26 35.3 & V \\\\\nWN J1604+5505 & 142$\\pm$ 7 & 20.7$\\pm$ 0.6 & \\nodata & $-1.32\\pm$0.04 & \\nodata & S & 1.1 & 15 & 16 04 21.91 & +55 05 45.4 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1606+6346 & 130$\\pm$ 6 & 19.0$\\pm$ 0.6 & $ 5.60\\pm0.19$ & $-1.32\\pm$0.04 & $-0.98\\pm0.04$ & D & 5.6 & 14 & 16 06 12.44 & +63 47 06.1 & V \\\\\nWN J1606+4142 & 83$\\pm$ 5 & 12.3$\\pm$ 0.5 & \\nodata & $-1.31\\pm$0.05 & \\nodata & S & 3.2 & 145 & 16 06 30.58 & +41 42 10.8 & F \\\\\nWN J1609+5725 & 70$\\pm$ 5 & 10.2$\\pm$ 0.5 & $ 2.13\\pm0.11$ & $-1.32\\pm$0.07 & $-1.26\\pm0.06$ & S & 1.7 & 60 & 16 09 28.14 & +57 25 02.8 & V \\\\\nWN J1618+5736 & 233$\\pm$10 & 33.5$\\pm$ 1.8 & $ 6.38\\pm0.20$ & $-1.33\\pm$0.05 & $-1.34\\pm0.05$ & S & 2.1 & 102 & 16 18 07.35 & +57 36 11.7 & V \\\\\nWN J1622+3447 & 156$\\pm$ 7 & 21.1$\\pm$ 0.6 & \\nodata & $-1.37\\pm$0.04 & \\nodata & S & 1.6 & 0 & 16 22 10.93 & +34 47 44.6 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1623+8213 & 166$\\pm$ 7 & 19.8$\\pm$ 0.6 & \\nodata & $-1.46\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 16 23 01.71 & +82 13 17.4 & N \\\\\nWN J1624+4202 & 75$\\pm$ 5 & 11.0$\\pm$ 1.7 & \\nodata & $-1.31\\pm$0.12 & \\nodata & D & 24.4 & 19 & 16 24 37.86 & +42 02 10.5 & F \\\\\nWN J1627+5430 & 146$\\pm$ 7 & 20.9$\\pm$ 0.6 & \\nodata & $-1.33\\pm$0.04 & \\nodata & S & 1.6 & 176 & 16 27 24.09 & +54 30 55.2 & F \\\\\nWN J1628+3932 & 26737$\\pm$1069 & 3680.7$\\pm$35.1 & \\nodata & $-1.36\\pm$0.03 & \\nodata & M & 48.8 & 77 & 16 28 38.56 & +39 33 00.1 & F \\\\\nWN J1633+7351 & 75$\\pm$ 5 & 10.1$\\pm$ 1.3 & $ 23.88\\pm0.55$ & $-1.37\\pm$0.11 & $ 0.69\\pm0.11$ & DF & 21.8 & 90 & 16 33 07.45 & +73 51 38.1 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1645+4413 & 135$\\pm$ 6 & 18.9$\\pm$ 0.6 & \\nodata & $-1.35\\pm$0.04 & \\nodata & S & 1.1 & 56 & 16 45 35.69 & +44 13 42.1 & F \\\\\nWN J1704+3839 & 335$\\pm$14 & 34.5$\\pm$ 1.8 & \\nodata & $-1.56\\pm$0.05 & \\nodata & D & 23.8 & 145 & 17 04 00.50 & +38 39 56.7 & F \\\\\nWN J1713+3656 & 116$\\pm$ 6 & 14.8$\\pm$ 0.5 & \\nodata & $-1.41\\pm$0.04 & \\nodata & S & 1.1 & 169 & 17 13 55.63 & +36 56 34.5 & F \\\\\nWN J1714+7031 & 132$\\pm$ 6 & 14.2$\\pm$ 1.4 & $ 0.95\\pm0.09$ & $-1.53\\pm$0.08 & $-2.18\\pm0.11$ & S & 2.4 & 46 & 17 14 35.18 & +70 31 30.7 & V \\\\\nWN J1714+5251 & 262$\\pm$11 & 37.9$\\pm$ 2.0 & \\nodata & $-1.32\\pm$0.05 & \\nodata & D & 26.6 & 80 & 17 14 37.93 & +52 51 30.1 & F \\\\\n\\end{tabular}\n\\end{table*}\n\n\\begin{table*}\n\\tiny\n\\begin{tabular}{lrrrrrrrrrrrr}\nName & $S_{325}$ & $S_{1400}$ & S$_{4850}$ & $\\alpha_{325}^{1400}$ & $\\alpha_{1400}^{4850}$ & Str & LAS & PA & $\\alpha_{J2000}$ & $\\delta_{J2000}$ & Pos \\\\\n & mJy & mJy & mJy & & & & \\arcsec & $\\arcdeg$ & $^h\\;\\;$$^m\\;\\;\\;\\;$$^s\\;\\;\\,$ & \\arcdeg$\\;\\;\\;$ \\arcmin$\\;\\;\\;$ \\arcsec$\\;$ & \\\\\n\\hline\nWN J1717+3828 & 368$\\pm$15 & 35.8$\\pm$ 2.0 & \\nodata & $-1.60\\pm$0.05 & \\nodata & M & 33.6 & 156 & 17 17 16.22 & +38 28 16.5 & F \\\\\nWN J1718+5823 & 1098$\\pm$44 & 133.2$\\pm$ 2.7 & $ 11.26\\pm0.32$ & $-1.44\\pm$0.03 & $-1.98\\pm0.03$ & S & 0.3 & 107 & 17 18 18.51 & +58 23 21.8 & V \\\\\nWN J1723+5822 & 88$\\pm$ 6 & 10.4$\\pm$ 0.5 & $ 2.27\\pm0.11$ & $-1.46\\pm$0.06 & $-1.23\\pm0.06$ & S & 4.7 & 103 & 17 23 01.98 & +58 22 44.0 & V \\\\\nWN J1723+6844 & 105$\\pm$ 6 & 15.7$\\pm$ 1.3 & \\nodata & $-1.30\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 17 23 05.64 & +68 44 17.7 & N \\\\\nWN J1731+4640 & 200$\\pm$ 9 & 15.7$\\pm$ 0.5 & \\nodata & $-1.74\\pm$0.04 & \\nodata & D & 11.6 & 106 & 17 31 46.10 & +46 40 03.1 & F \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1731+4654 & 323$\\pm$13 & 42.0$\\pm$ 2.1 & \\nodata & $-1.40\\pm$0.05 & \\nodata & S & 1.9 & 176 & 17 31 59.63 & +46 54 00.2 & F \\\\\nWN J1732+6757 & 85$\\pm$ 5 & 11.9$\\pm$ 0.5 & $ 2.31\\pm0.11$ & $-1.35\\pm$0.05 & $-1.32\\pm0.05$ & D & 1.5 & 178 & 17 32 30.61 & +67 57 02.5 & V \\\\\nWN J1733+4037 & 80$\\pm$ 5 & 11.2$\\pm$ 2.0 & \\nodata & $-1.35\\pm$0.13 & \\nodata & \\nodata & \\nodata & \\nodata & 17 33 31.13 & +40 37 00.6 & N \\\\\nWN J1734+4527 & 87$\\pm$ 5 & 11.0$\\pm$ 0.5 & \\nodata & $-1.42\\pm$0.06 & \\nodata & D & 10.4 & 174 & 17 34 07.58 & +45 27 25.6 & F \\\\\nWN J1734+3606 & 69$\\pm$ 3 & 10.2$\\pm$ 3.2 & $ 3.12\\pm0.13$ & $-1.31\\pm$0.22 & $-0.95\\pm0.25$ & S & 2.1 & 137 & 17 34 24.13 & +36 06 38.8 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1736+6502 & 193$\\pm$ 8 & 27.4$\\pm$ 1.6 & $ 4.40\\pm0.16$ & $-1.34\\pm$0.05 & $-1.47\\pm0.06$ & D & 16.0 & 159 & 17 36 37.50 & +65 02 28.7 & V \\\\\nWN J1739+5309 & 78$\\pm$ 5 & 11.3$\\pm$ 0.5 & \\nodata & $-1.32\\pm$0.06 & \\nodata & S & 7.3 & 114 & 17 39 28.39 & +53 09 41.8 & F \\\\\nWN J1749+5659 & 124$\\pm$ 7 & 15.9$\\pm$ 1.6 & \\nodata & $-1.41\\pm$0.08 & \\nodata & \\nodata & \\nodata & \\nodata & 17 49 21.19 & +56 59 59.6 & N \\\\\nWN J1749+6248 & 104$\\pm$ 6 & 13.3$\\pm$ 0.5 & $ 2.93\\pm0.12$ & $-1.41\\pm$0.05 & $-1.22\\pm0.05$ & S & 1.7 & 48 & 17 49 27.04 & +62 48 54.0 & V \\\\\nWN J1752+2949 & 135$\\pm$ 6 & 16.9$\\pm$ 0.5 & $ 2.29\\pm0.14$ & $-1.42\\pm$0.04 & $-1.61\\pm0.05$ & S & 3.2 & 102 & 17 52 56.67 & +29 49 28.3 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1801+3336 & 136$\\pm$ 6 & 11.6$\\pm$ 0.5 & $ 1.26\\pm0.12$ & $-1.69\\pm$0.05 & $-1.78\\pm0.08$ & S & 2.5 & 34 & 18 01 07.26 & +33 36 40.4 & V \\\\\nWN J1802+3948 & 1102$\\pm$44 & 157.3$\\pm$ 6.8 & $ 27.67\\pm0.62$ & $-1.33\\pm$0.04 & $-1.40\\pm0.04$ & T & 19.2 & 13 & 18 02 31.65 & +39 48 59.6 & V \\\\\nWN J1804+5547 & 173$\\pm$ 8 & 22.9$\\pm$ 1.7 & \\nodata & $-1.38\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 18 04 15.35 & +55 47 16.3 & N \\\\\nWN J1804+3048 & 192$\\pm$ 8 & 27.7$\\pm$ 0.7 & $ 5.88\\pm0.18$ & $-1.33\\pm$0.04 & $-1.25\\pm0.03$ & S & 2.0 & 84 & 18 04 42.01 & +30 48 45.0 & V \\\\\nWN J1806+6332 & 138$\\pm$ 7 & 17.7$\\pm$ 0.5 & \\nodata & $-1.41\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 18 06 23.66 & +63 32 07.9 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1807+5027 & 483$\\pm$19 & 71.4$\\pm$ 3.3 & $ 11.67\\pm0.31$ & $-1.31\\pm$0.04 & $-1.46\\pm0.04$ & D & 3.7 & 173 & 18 07 07.39 & +50 27 25.8 & V \\\\\nWN J1807+6628 & 76$\\pm$ 5 & 10.9$\\pm$ 1.4 & $ 1.20\\pm0.11$ & $-1.33\\pm$0.10 & $-1.78\\pm0.13$ & S & 0.3 & 103 & 18 07 29.75 & +66 28 33.4 & V \\\\\nWN J1810+6635 & 115$\\pm$ 8 & 14.1$\\pm$ 0.5 & $ 2.62\\pm0.12$ & $-1.44\\pm$0.04 & $-1.36\\pm0.05$ & S & 1.6 & 15 & 18 10 28.41 & +66 35 15.1 & V \\\\\nWN J1811+6008 & 160$\\pm$ 7 & 17.8$\\pm$ 0.5 & $ 7.87\\pm0.24$ & $-1.50\\pm$0.04 & $-0.66\\pm0.03$ & DF & 3.5 & 31 & 18 11 18.38 & +60 08 42.9 & V \\\\\nWN J1813+4847 & 92$\\pm$ 5 & 12.1$\\pm$ 0.5 & \\nodata & $-1.39\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 18 13 16.68 & +48 47 50.1 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1814+5009 & 120$\\pm$ 7 & 16.7$\\pm$ 0.5 & \\nodata & $-1.35\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 18 14 01.40 & +50 09 58.0 & N \\\\\nWN J1815+3656 & 124$\\pm$ 6 & 17.6$\\pm$ 0.6 & $ 2.96\\pm0.14$ & $-1.34\\pm$0.04 & $-1.43\\pm0.05$ & S & 1.6 & 48 & 18 15 23.11 & +36 56 00.9 & V \\\\\nWN J1816+3840 & 186$\\pm$ 8 & 27.3$\\pm$ 1.6 & \\nodata & $-1.31\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 18 16 26.11 & +38 40 53.0 & N \\\\\nWN J1818+7042 & 1624$\\pm$65 & 199.6$\\pm$ 8.8 & $ 30.50\\pm0.74$ & $-1.44\\pm$0.04 & $-1.51\\pm0.04$ & D & 1.4 & 10 & 18 18 04.24 & +70 42 59.5 & V \\\\\nWN J1818+3852 & 105$\\pm$ 6 & 12.6$\\pm$ 0.5 & $ 1.29\\pm0.09$ & $-1.45\\pm$0.05 & $-1.84\\pm0.07$ & S & 2.6 & 64 & 18 18 42.17 & +38 52 20.4 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1818+3428 & 167$\\pm$ 7 & 23.7$\\pm$ 0.6 & $ 5.68\\pm0.19$ & $-1.34\\pm$0.04 & $-1.15\\pm0.03$ & T & 7.5 & 103 & 18 18 47.90 & +34 28 24.0 & V \\\\\nWN J1818+6144 & 149$\\pm$ 6 & 21.9$\\pm$ 1.5 & $ 1.11\\pm0.10$ & $-1.31\\pm$0.06 & $-2.40\\pm0.09$ & S & 1.6 & 11 & 18 18 50.55 & +61 44 18.4 & V \\\\\nWN J1819+3122 & 77$\\pm$ 5 & 10.5$\\pm$ 0.5 & \\nodata & $-1.36\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 18 19 28.60 & +31 22 19.3 & N \\\\\nWN J1819+6213 & 106$\\pm$ 6 & 12.7$\\pm$ 0.5 & $ 0.47\\pm0.08$ & $-1.45\\pm$0.05 & $-2.66\\pm0.14$ & S & 1.6 & 41 & 18 19 52.26 & +62 13 58.0 & V \\\\\nWN J1820+5711 & 136$\\pm$ 7 & 20.3$\\pm$ 1.5 & \\nodata & $-1.30\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 18 20 51.14 & +57 11 06.5 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1821+3602 & 3398$\\pm$136 & 99.0$\\pm$ 4.2 & $233.33\\pm4.90$ & $-2.42\\pm$0.04 & $ 0.69\\pm0.04$ & T & 35.0 & 55 & 18 21 02.20 & +36 02 15.7 & V \\\\\nWN J1821+3601$^{\\dag}$ & 151$\\pm$ 6 & 10.2$\\pm$ 1.5 & $105.26\\pm2.53$ & $-1.85\\pm$0.11 & $ 1.88\\pm0.12$ & D & 34.9 & 55 & 18 21 22.59 & +36 01 03.3 & V \\\\\nWN J1829+6914 & 207$\\pm$ 9 & 13.0$\\pm$ 1.3 & $ 2.25\\pm0.12$ & $-1.90\\pm$0.08 & $-1.41\\pm0.09$ & S & 1.8 & 22 & 18 29 05.68 & +69 14 06.1 & V \\\\\nWN J1829+4919 & 98$\\pm$ 6 & 14.2$\\pm$ 0.5 & $ 7.95\\pm0.24$ & $-1.32\\pm$0.06 & $-0.47\\pm0.04$ & D & 12.5 & 173 & 18 29 33.74 & +49 19 55.6 & V \\\\\nWN J1829+5945 & 346$\\pm$14 & 50.4$\\pm$ 2.4 & $ 8.82\\pm0.25$ & $-1.32\\pm$0.04 & $-1.40\\pm0.04$ & S & 1.7 & 26 & 18 29 57.26 & +59 45 03.2 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1830+6422 & 70$\\pm$ 3 & 10.3$\\pm$ 0.5 & \\nodata & $-1.31\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 18 30 45.82 & +64 22 26.3 & N \\\\\nWN J1832+5354$^{\\dag}$ & 226$\\pm$10 & 28.7$\\pm$ 1.6 & $ 23.82\\pm0.59$ & $-1.41\\pm$0.05 & $-0.15\\pm0.05$ & D & 19.4 & 56 & 18 32 41.16 & +53 54 34.0 & V \\\\\nWN J1836+5210 & 191$\\pm$ 9 & 24.2$\\pm$ 1.5 & $ 3.54\\pm0.15$ & $-1.41\\pm$0.05 & $-1.55\\pm0.06$ & S & 1.4 & 10 & 18 36 23.22 & +52 10 28.4 & V \\\\\nWN J1839+4710 & 176$\\pm$ 8 & 22.8$\\pm$ 1.6 & \\nodata & $-1.40\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 18 39 14.54 & +47 10 59.4 & N \\\\\nWN J1843+5932 & 998$\\pm$40 & 148.2$\\pm$ 6.6 & $ 30.87\\pm0.70$ & $-1.31\\pm$0.04 & $-1.26\\pm0.04$ & T & 7.7 & 64 & 18 43 31.70 & +59 32 59.3 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1847+5423 & 108$\\pm$ 6 & 15.8$\\pm$ 1.3 & $ 6.67\\pm0.23$ & $-1.32\\pm$0.07 & $-0.69\\pm0.07$ & DF & 2.9 & 67 & 18 47 04.03 & +54 23 06.6 & V \\\\\nWN J1852+5711$^*$ & 387$\\pm$16 & 53.4$\\pm$ 2.5 & \\nodata & $-1.36\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 18 52 08.35 & +57 11 42.7 & N \\\\\nWN J1857+7411 & 160$\\pm$ 7 & 19.9$\\pm$ 0.6 & \\nodata & $-1.43\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 18 57 03.60 & +74 11 31.2 & N \\\\\nWN J1859+5900 & 98$\\pm$ 6 & 11.7$\\pm$ 0.5 & $ 1.64\\pm0.12$ & $-1.46\\pm$0.06 & $-1.56\\pm0.07$ & S & 0.5 & 171 & 18 59 40.34 & +59 00 36.8 & V \\\\\nWN J1859+5416 & 81$\\pm$ 4 & 10.1$\\pm$ 1.6 & $ 2.70\\pm0.14$ & $-1.43\\pm$0.12 & $-1.06\\pm0.13$ & S & 1.7 & 17 & 18 59 57.65 & +54 16 21.8 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1907+8532 & 69$\\pm$ 4 & 10.2$\\pm$ 0.4 & \\nodata & $-1.31\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 19 07 26.54 & +85 32 35.2 & N \\\\\nWN J1911+6342 & 185$\\pm$10 & 23.3$\\pm$ 1.5 & $ 3.37\\pm0.14$ & $-1.42\\pm$0.05 & $-1.56\\pm0.06$ & S & 1.8 & 7 & 19 11 49.54 & +63 42 09.6 & V \\\\\nWN J1912+8627 & 126$\\pm$ 7 & 18.8$\\pm$ 1.2 & $ 2.55\\pm0.13$ & $-1.30\\pm$0.05 & $-1.61\\pm0.07$ & S & 2.4 & 178 & 19 12 06.26 & +86 27 10.1 & V \\\\\nWN J1917+6635 & 75$\\pm$ 5 & 11.2$\\pm$ 0.5 & $ 2.37\\pm0.12$ & $-1.30\\pm$0.06 & $-1.25\\pm0.06$ & S & 1.9 & 152 & 19 17 35.50 & +66 35 38.5 & V \\\\\nWN J1917+7149 & 280$\\pm$12 & 40.4$\\pm$ 2.1 & \\nodata & $-1.33\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 19 17 56.11 & +71 49 19.7 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1923+6047 & 83$\\pm$ 5 & 12.4$\\pm$ 0.5 & $ 2.56\\pm0.13$ & $-1.30\\pm$0.06 & $-1.27\\pm0.05$ & S & 2.4 & 91 & 19 23 33.18 & +60 47 56.8 & V \\\\\nWN J1925+5203 & 199$\\pm$ 9 & 27.5$\\pm$ 1.7 & $ 4.30\\pm0.16$ & $-1.36\\pm$0.05 & $-1.49\\pm0.06$ & D & 8.6 & 52 & 19 25 16.97 & +52 03 34.4 & V \\\\\nWN J1925+5742 & 100$\\pm$ 6 & 14.5$\\pm$ 0.5 & $ 1.58\\pm0.11$ & $-1.32\\pm$0.06 & $-1.78\\pm0.06$ & S & 2.0 & 9 & 19 25 22.22 & +57 42 27.3 & V \\\\\nWN J1926+5710 & 136$\\pm$ 7 & 20.2$\\pm$ 0.6 & $ 4.55\\pm0.18$ & $-1.31\\pm$0.04 & $-1.20\\pm0.04$ & S & 1.8 & 161 & 19 26 43.85 & +57 10 00.5 & V \\\\\nWN J1927+6436 & 661$\\pm$26 & 80.3$\\pm$ 3.5 & $ 6.62\\pm0.21$ & $-1.44\\pm$0.04 & $-2.01\\pm0.04$ & D & 20.1 & 120 & 19 27 22.83 & +64 36 02.6 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J1944+6552 & 1367$\\pm$55 & 147.2$\\pm$ 6.5 & $ 19.45\\pm0.47$ & $-1.53\\pm$0.04 & $-1.63\\pm0.04$ & S & 1.8 & 165 & 19 44 23.99 & +65 52 23.8 & V \\\\\nWN J1953+7052 & 75$\\pm$ 7 & 10.3$\\pm$ 0.5 & $ 3.22\\pm0.15$ & $-1.36\\pm$0.07 & $-0.94\\pm0.05$ & D & 14.4 & 150 & 19 53 21.10 & +70 52 19.8 & V \\\\\nWN J1954+7011 & 460$\\pm$19 & 63.4$\\pm$ 2.9 & \\nodata & $-1.36\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 19 54 30.53 & +70 11 33.5 & N \\\\\nWN J2044+7044 & 311$\\pm$13 & 41.7$\\pm$ 0.9 & $ 7.18\\pm0.22$ & $-1.38\\pm$0.03 & $-1.42\\pm0.03$ & D & 1.3 & 83 & 20 44 57.80 & +70 44 03.8 & V \\\\\nWN J2052+6925 & 113$\\pm$ 6 & 16.1$\\pm$ 1.3 & \\nodata & $-1.33\\pm$0.07 & \\nodata & \\nodata & \\nodata & \\nodata & 20 52 33.78 & +69 25 09.3 & N \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J2053+6849 & 109$\\pm$ 5 & 15.8$\\pm$ 0.5 & $ 2.59\\pm0.13$ & $-1.32\\pm$0.05 & $-1.45\\pm0.05$ & S & 2.8 & 13 & 20 53 38.68 & +68 48 54.7 & V \\\\\nWN J2139+3125 & 249$\\pm$10 & 28.0$\\pm$ 0.7 & \\nodata & $-1.50\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 21 39 32.31 & +31 25 18.7 & N \\\\\nWN J2146+3330 & 105$\\pm$ 6 & 10.8$\\pm$ 0.5 & \\nodata & $-1.56\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 21 46 55.47 & +33 30 01.7 & N \\\\\nWN J2147+3137 & 215$\\pm$ 9 & 25.4$\\pm$ 1.6 & \\nodata & $-1.46\\pm$0.05 & \\nodata & \\nodata & \\nodata & \\nodata & 21 47 35.21 & +31 37 58.9 & N \\\\\nWN J2158+3424 & 182$\\pm$ 8 & 25.3$\\pm$ 0.7 & $ 4.48\\pm0.17$ & $-1.35\\pm$0.04 & $-1.39\\pm0.04$ & T & 7.9 & 163 & 21 58 54.14 & +34 24 47.8 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J2213+3411 & 320$\\pm$13 & 29.8$\\pm$ 2.2 & \\nodata & $-1.63\\pm$0.06 & \\nodata & \\nodata & \\nodata & \\nodata & 22 13 12.48 & +34 11 42.8 & N \\\\\nWN J2219+2951 & 151$\\pm$10 & 13.2$\\pm$ 0.5 & \\nodata & $-1.67\\pm$0.04 & \\nodata & \\nodata & \\nodata & \\nodata & 22 19 28.65 & +29 51 57.4 & N \\\\\nWN J2221+3800 & 99$\\pm$ 6 & 14.4$\\pm$ 0.5 & $ 2.18\\pm0.11$ & $-1.32\\pm$0.05 & $-1.52\\pm0.05$ & S & 1.4 & 5 & 22 21 49.53 & +38 00 38.4 & V \\\\\nWN J2222+3305 & 232$\\pm$10 & 30.4$\\pm$ 1.7 & $ 3.53\\pm0.14$ & $-1.39\\pm$0.05 & $-1.73\\pm0.05$ & S & 1.4 & 13 & 22 22 15.19 & +33 05 44.1 & V \\\\\nWN J2245+3937 & 204$\\pm$ 8 & 15.5$\\pm$ 1.3 & $ 5.65\\pm0.21$ & $-1.76\\pm$0.07 & $-0.81\\pm0.07$ & DF & 4.0 & 168 & 22 45 02.74 & +39 37 27.9 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J2250+4131 & 128$\\pm$ 7 & 15.2$\\pm$ 1.4 & $ 2.03\\pm0.11$ & $-1.46\\pm$0.07 & $-1.62\\pm0.09$ & S & 1.5 & 25 & 22 50 51.16 & +41 31 16.4 & V \\\\\nWN J2313+4053 & 101$\\pm$ 6 & 11.3$\\pm$ 1.4 & \\nodata & $-1.50\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 23 13 06.34 & +40 53 40.6 & N \\\\\nWN J2313+4253 & 94$\\pm$ 7 & 13.4$\\pm$ 1.5 & $ 3.41\\pm0.14$ & $-1.33\\pm$0.09 & $-1.10\\pm0.10$ & S & 1.4 & 13 & 23 13 08.62 & +42 53 13.0 & V \\\\\nWN J2313+3842$^*$ & 304$\\pm$13 & 13.2$\\pm$ 2.6 & \\nodata & $-2.15\\pm$0.14 & \\nodata & \\nodata & \\nodata & \\nodata & 23 13 47.75 & +38 42 26.2 & N \\\\\nWN J2319+4251 & 321$\\pm$14 & 40.2$\\pm$ 2.9 & $ 3.88\\pm0.14$ & $-1.42\\pm$0.06 & $-1.88\\pm0.07$ & S & 1.5 & 20 & 23 19 47.25 & +42 51 09.2 & V \\\\\n&&&&&&&&&&&\\\\\t\t \nWN J2337+3421 & 84$\\pm$ 4 & 12.4$\\pm$ 1.3 & \\nodata & $-1.31\\pm$0.09 & \\nodata & \\nodata & \\nodata & \\nodata & 23 37 23.43 & +34 21 51.5 & N \\\\\nWN J2338+4047 & 115$\\pm$ 6 & 16.9$\\pm$ 0.5 & $ 5.06\\pm0.18$ & $-1.31\\pm$0.04 & $-0.97\\pm0.04$ & D & 15.7 & 8 & 23 38 11.10 & +40 47 19.6 & V \\\\\nWN J2350+3631 & 196$\\pm$ 8 & 22.8$\\pm$ 0.6 & $ 2.20\\pm0.11$ & $-1.47\\pm$0.04 & $-1.88\\pm0.04$ & DF & 2.7 & 165 & 23 50 25.69 & +36 31 27.6 & V \\\\\n\\hline\n\\end{tabular}\n\n$^{\\dag}$ Not a real USS source; see notes\n\n$^*$ See notes\n\n\\end{table*}\n"
}
] |
[
{
"name": "astro-ph0002297.extracted_bib",
"string": "\\begin{thebibliography}{}\n\\bibitem[Abell \\etal\\ 1989]{abe89} Abell, G. O., Corwin, H. G. Jr., \\& Olowin, R. P. 1989, \\apjs, 70, 1\n\\bibitem[Andernach \\etal 2000]{and00} Andernach, H., Verkhodanov, O. \\& Verkhodanova, N. 2000, IAU Symp. 199, in press, astro-ph/0001473\n\\bibitem[Bade \\etal\\ 1998]{bad98} Bade, N. \\etal\\ 1998, \\aasup, 127, 145\n\\bibitem[Barthel 1989]{bar89} Barthel, P. D. 1989, \\apj, 336, 606\n\\bibitem[Becker \\etal\\ 1995]{bec95} Becker, R. H., White, R. L., \\& Helfand, D. J. 1995, \\apj, 450, 559\n\\bibitem[Benn \\etal\\ 1993]{ben93} Benn, C. 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}
] |
astro-ph0002298
|
X--ray variability and prediction of TeV emission in the HBL 1ES~1101--232
|
[
{
"author": "A. Wolter"
},
{
"author": "\\inst{1} F. Tavecchio"
},
{
"author": "\\inst{1} A. Caccianiga"
},
{
"author": "\\inst{2} G. Ghisellini"
},
{
"author": "\\inst{1} G. Tagliaferri \\inst{1}"
}
] |
1ES~1101--232 is a bright BL Lac of the High frequency peak class. We present here the results of two \sax\ observations in which the source has shown a variation of about 30\% in flux with a corresponding spectral variability. We interpret the overall spectral energy distribution in terms of an homogeneous SSC model and, by using also the TeV upper limit from a short Mark 6 pointing, derive constraints on the physical parameters of the source, in particular on the magnetic field strength. The overall Spectral Energy Distribution makes 1ES~1101--232 a very promising candidate for TeV detection. \keywords{(Galaxies:) BL Lacertae objects: general -- X--rays: galaxies -- BL Lacertae objects: individual: 1ES~1101--232 }
|
[
{
"name": "9325.tex",
"string": "\\documentclass{aa}\n%%\\documentclass[referee]{aa}\n\n\n\\include{psfig}\n\n\\def\\doublespace{\\baselineskip 24pt}\n\\def\\singlespace{\\baselineskip 15pt}\n\\def\\e20{\\times 10^{20} {\\rm cm}^{-2} }\n\\def\\sax{{\\it Beppo}SAX}\n\\def\\NH{N_{\\rm H}}\n\\def\\ecs{\\rm \\,erg~ cm^{-2}\\,s^{-1} }\n\\def\\mincir{\\ \\raise -2.truept\\hbox{\\rlap{\\hbox{$\\sim$}}\\raise5.truept \n\\hbox{$<$}\\ }} % minore o circa uguale\n\n\\begin{document}\n\n\\thesaurus{03(11.02.1; 13.25.3)}\t\n%A\\&A Section 03: (Extragalactic Astronomy)\n%%(11.02.1; % {\\it (Galaxies:)} BL Lacertae objects: general\n%%13.25.3 %X--rays: general)\n\n\n\n\\title{X--ray variability and prediction of TeV emission in the HBL 1ES~1101--232}\n\\author{A. Wolter,\n\\inst{1} \nF. Tavecchio, \\inst{1} A. Caccianiga,\\inst{2} G. Ghisellini,\\inst{1} G. Tagliaferri \\inst{1}\n}\n\n\\offprints{A. Wolter: anna@brera.mi.astro.it}\n\n\\institute{Osservatorio Astronomico di Brera,\n\t\tVia Brera, 28\n\t\t20121 MILANO, Italy\n\\and Observatorio Astronomico de Lisboa, Tapada da Ajuda, P-1300 Lisboa, Portugal\n}\n\n\\date{Received ....; accepted ....}\n\\maketitle\n\\markboth{A. Wolter et al.}{The HBL 1ES~1101--232}{}\n\n\\begin{abstract}\n\n1ES~1101--232 is a bright BL Lac of the High frequency peak class. \nWe present here the results of two \\sax\\ observations in which the\nsource has shown a variation of about 30\\% in flux with a corresponding\nspectral variability.\nWe interpret the overall spectral energy distribution in terms\nof an homogeneous SSC model and, by using also the TeV upper limit\nfrom a short Mark 6 pointing, derive constraints\non the physical parameters of the source, in particular on the magnetic \nfield strength.\nThe overall Spectral Energy Distribution makes\n1ES~1101--232 a very promising candidate for TeV detection. \n\n\\keywords{(Galaxies:) BL Lacertae objects: general --\n\t X--rays: galaxies -- BL Lacertae objects: individual: 1ES~1101--232\n }\n\\end{abstract}\n\n\\section{Introduction}\n\\noindent\n\nBL Lac objects form a minority class of active nuclei (see e.g. Urry \\& \nPadovani, 1995), but nevertheless their high luminosities and extreme \nvariability in all bands \nmake them an interesting subclass to study intrinsic properties of\nnuclear emission. Furthermore, it is matter of discussion the position of\nBL Lacs with respect to other active nuclei in the framework of Unification\nModels. The current picture claims that BL Lacs are the fraction of \nFanaroff-Riley I galaxies that point their jet towards us, but many\ndetails still need to be worked out. Often, BL Lacs are studied together\nwith other classes of flat radio spectrum sources, to form the class of blazars.\n\nRecently a sequence has been proposed for the subclass of gamma ray\nbright blazars, and possibly valid for all blazars, based on their \nbolometric luminosity\n(Ghisellini et al. 1998, Fossati et al. 1998). \nThe overall spectral energy distribution has two peaks \n(in $\\nu F_\\nu$ representation), \nthe one at lower energies due to synchrotron radiation and the higher energy \none to Inverse Compton scattering. \nIt is proposed that the value of the peak frequency is the result\nof the balance between radiative cooling and acceleration of the \ncorresponding electrons (see e.g. Ghisellini, 1999):\nin less luminous objects the radiative cooling is less efficient, allowing\nthe accelerated electrons to reach higher energies.\nAs a consequence, both the synchrotron and the inverse Compton peaks\nshift to higher frequencies as the bolometric intrinsic\nluminosity decreases.\nIn this view, the class of BL Lacertae objects known as HBL \n(High frequency peak BL Lacs)\nhas a smaller bolometric luminosity and a higher synchrotron peak frequency\nthan the class of LBL (Low frequency peak BL Lacs).\nHBL are mostly found in X--ray selected samples, since they are expected to \nproduce most of their synchrotron emission in the X--ray band. \nIf the emission peak (as in the LBL objects) is\nat frequencies smaller than the observed X--ray band, the X--ray spectrum is \nsteep (i.e. the steepening part above the peak), while HBL with a flat \nX--ray spectrum should have their peak in the observed X--ray band.\n\nAs part of a program aimed at a spectral survey of soft X--ray selected \nBL Lacs with \\sax\\ (Wolter et al. 1998), \nwe have studied also 1ES~1101--232 (z=0.186), \na bright BL Lac selected from the Slew Survey (Perlman et al. 1996) \nthat shows an extreme behavior with a very flat X--ray spectrum.\nThe object was detected, besides in the 0.1-10 keV energy band, also\nup to $\\sim$ 100 keV in only $\\sim 6000$ sec. \nThe best fit of the source in the 0.1-100 keV band is given by a broken \npower law, with Galactic low energy absorption, that has a break energy\nE$_0$=1.36 (1.11--1.65) keV.\nThe spectral slope (energy index) derived from the PDS is consistent\nwith the one derived from the MECS above the break energy E$_0$:\n$\\alpha_x$ = 1.03 (0.99--1.08) (Wolter et al. 1998).\n\nWe have constructed also the Spectral Energy Distribution (SED) for this\nobject, using flux measurements collected from the literature, from radio to\nX--rays.\nWe have fitted a cubic polynomial to the \ndistribution in order to find the peak of the SED, that indeed \nfalls in the \\sax\\ band (log $\\nu_{peak} \\sim$ 17.48, corresponding to \n$\\sim 1.3$ keV).\nFor this object, therefore, the break energy derived from\nthe spectral fit in the X--ray band is consistent, albeit within its\nlarge indetermination, with the position of the synchrotron \npeak as derived from the overall distribution (SED). \n\nThe SED of 1ES~1101--232 is similar to that of the flaring state\nof Mkn 501 (Pian et al. 1998) and 1ES~2344+514 (Catanese et al. 1998; \nGiommi et al. 2000), \nand therefore we could expect a strong TeV emission. \nA quasi--simultaneous X--ray and TeV observation has been\ntherefore scheduled, to confirm the X--ray spectrum of the source, and\nits overall shape,\nto detect possible variations in flux, that could constrain the physical\nparameters of the source, and to monitor the TeV emission to search\nfor possible detection. \n\n%__________________________________________________ Two col. table\n\\begin{table*}\n \\caption{Fit results for 1ES~1101--232 LECS+MECS data OBS. 19/06/98 {\\bf Low state}}\n\\begin{tabular}[h]{| l l c c c r r r|}\n \\hline\nModel & $N_{\\rm H}^a$ & $\\alpha_1$ & $\\alpha_2$ & $E_0$ & $F^{\\rm b}$ & $\\chi^2(dof)$ & Prob. \\\\\n & & & & keV & & & \\\\\n(1) & 5.76 & -- & 1.19(1.16-1.22) & -- & 2.60 & 267.1(195) & $<$ 0.5\\%\\\\\n(2) & 8.3(7.1-10.4) & -- & 1.25(1.22-1.29) & -- & 2.57 & 240.5(195) & 1.5\\%\\\\\n(3) & 5.76 &0.80(0.58-0.96)& 1.29(1.25-1.33) & 1.34(1.08-1.82) &2.55 & 216.2(194) & 13\\% \\\\\n\\hline\n\\end{tabular}\n\\begin{list}{}{}\n\\item (1) Single p.l., $N_{\\rm H}$=$N_{\\rm H}^{\\rm Gal}$, LECS/MECS ratio free; \n(2) Single p.l., $N_{\\rm H}$ free, LECS/MECS ratio=0.7 ; \n(3) Broken p.l., $N_{\\rm H}=N_{\\rm H}^{\\rm Gal}$, LECS/MECS ratio = 0.7. \nErrors quoted are 90\\% confidence intervals. \\\\\n$^{\\rm a}$ Column density in $\\e20$. \\\\\n$^{\\rm b}$ Unabsorbed [2--10 keV] flux in $10^{-11} \\ecs$. \\\\\n\\end{list}\n\\label{broken_n}\n\\end{table*}\n%__________________________________________________ Two col. table\n\\begin{table*}\n \\caption{Fit results for 1ES~1101--232 LECS+MECS data OBS. 04/01/97 {\\bf High state} } \n\\begin{tabular}[h]{| l l c c c r r r|}\n \\hline\nModel & $N_{\\rm H}^{\\rm a}$ & $\\alpha_1$ & $\\alpha_2$ & $E_0$ & $F^{\\rm b}$ & $\\chi^2(dof)$ & Prob. \\\\\n & & & & keV & & & \\\\\n(1) & 5.76 & -- & 0.97(0.95-1.00) & -- & 3.81 & 224.0 (182) & $<$ 2\\%\\\\\n(2) & 8.9(7.2-12.6) & -- & 1.03(0.99-1.08) & -- & 3.79 & 205.1 (182) & 11 \\%\\\\\n(3) & 5.76 &0.59(0.35-0.74) & 1.05(1.01-1.08) & 1.36(1.11-1.65) &3.76 & 191.6 (181) & 28 \\%\\\\\n\\hline\n\\end{tabular}\n\\begin{list}{}{}\n\\item \n(1) Single p.l., $N_{\\rm H}$=$N_{\\rm H}^{\\rm Gal}$, LECS/MECS ratio free; \n(2) Single p.l., $N_{\\rm H}$ free, LECS/MECS ratio=0.7; \n(3) Broken p.l., $N_{\\rm H}$=$N_{\\rm H}^{\\rm Gal}$, LECS/MECS ratio = 0.7.\nErrors quoted are 90\\% confidence intervals. \\\\\n$^{\\rm a}$ Column density in $\\e20$. \\\\\n$^{\\rm b}$ Unabsorbed [2-10 keV] flux in $10^{-11} \\ecs$. \\\\\n\\end{list}\n \\label{broken_o}\n\\end{table*}\n\n\nThe \\sax\\ data are presented here. The TeV observation, conducted in \nnon--optimal weather condition, did not yield a detection, but we will use\nthe upper limit (Chadwick et al. 1999a) to derive useful information on\nthe physical mechanisms at work in this source.\nThe plan of the paper is as follows: in Section 2 we describe the observational\ndata obtained with \\sax\\ in the two epochs, in Section 3 we summarize the TeV\npredictions and observations, that help constraining the parameters of the\nsource, by using the SED and theoretical models of emission as explained in\nSection 4. Section 5 presents our results and conclusions.\n\n\nThroughout the paper a Hubble constant H$_0$=50 $km\\, s^{-1}\\, Mpc^{-1}$ \nand a Friedman universe with a deceleration parameter $q_0$=0 are assumed.\n\n\n \n\\section{ \\sax\\ data}\n\nThe X--ray astronomy satellite \\sax\\ is a project of the Italian\nSpace Agency (ASI) with a participation of the Netherlands Agency for \nAerospace Programs (NIVR).\nThe scientific payload comprises four Narrow Field Instruments [NFI:\nLow Energy Concentrator Spectrometer (LECS), Medium Energy Concentrator\nSpectrometer (MECS), High Pressure Gas Scintillation Proportional Counter\n(HPGSPC), and Phoswich Detector System (PDS)], all pointing in the\nsame direction, and two Wide Field Cameras (WFC), pointing in\nopposite directions perpendicular to the NFI common axis. A detailed\ndescription of the entire \\sax\\ mission can be found in Butler \\& Scarsi (1990)\nand Boella et al. (1997a). \n\nThe MECS consists of three equal units, each composed of a grazing\nincidence mirror unit and of a position sensitive gas scintillation \nproportional counter, with a field of view of\n56 arcmin diameter, working range 1.3--10 keV, energy resolution $\\sim 8\\%$\nand angular resolution $\\sim 0.7$ arcmin (FWHM) at 6 keV.\nThe effective area at 6 keV is 155 cm$^2$ (Boella et al. 1997b)\n\nThe LECS is a unit similar to the MECS, with a thinner window that\ngrants a lower energy cut-off (sensitive in the energy range 0.1-10.0 keV)\nbut also reduces the FOV to 37 arcmin diameter (Parmar et al. 1997). \nThe LECS energy resolution is a factor $\\sim 2.4$ better\nthan that of the ROSAT PSPC ($\\sim 32\\%$ at 0.28 keV), while the \neffective area is smaller: 22 cm$^{2}$ at 0.28 and and 50 cm$^{2}$ at 6 keV.\n\nThe PDS is a system of four crystals, sensitive in the 13--200~keV band and\nmounted on a couple of rocking collimators, which points two units on the\ntargets and two units $3.5^{\\circ}$ aside respectively, to monitor the\nbackground.\nThe position of the collimators flips every 96 seconds.\nThanks to the stability of the instrumental background, the PDS has shown \nan unprecedented sensitivity in its energy range, allowing 3$\\sigma$ detection \nof $\\alpha \\sim 1$ sources as faint as 10 m Crab \nwith 10 ks of effective exposure time (Guainazzi \\& Matteuzzi, 1997).\n\nThe source is not detected by the HPGSPC, so we will not discuss this \ninstrument.\n\n\n\\subsection{Observation of June 1998}\n\n\\begin{figure}\n\\psfig{file=9325.f1,width=8truecm,height=6truecm,angle=-90}\n\\caption{X--ray spectrum (LECS+MECS+PDS) of June 1998, with broken power law fit\n(model 3 from Table~\\ref{broken_n})}\n\\label{fignew}\n\\end{figure}\n\nThe object has been observed in AO2 on 19 June 1998 for a total of \n8958 sec (LECS -- 3167 net counts); \n24895 sec (MECS(2+3) -- 10612 net counts) and \n10792 sec (PDS on source -- 1320 net counts).\nThe AO2 observation has been performed with only 2 MECS (MECS2 and MECS3)\nsince MECS1 was no longer active.\nThe source has been observed almost in the same period (May 1998) by the \nMark6 telescope (working in the GeV-TeV range). \n\nThe extraction of the \\sax\\ data has been performed with FTOOLS v4.0 and the\nspectral analysis with XSPEC v9.0, using the most recently available matrices\n(September 1997 release).\nThe data analysis has been performed on the same guidelines as outlined\nby the \\sax\\ Cookbook ({\\small\\verb+http://www.sdc.asi.it/software/cookbook/+})\nand described e.g. in Wolter et al. (1998).\nWe summarize here that counts are extracted in a circular region of 8.5'/4' \n(LECS/MECS) radius, and the background is taken from the blank \nsky images distributed by the \\sax\\ Data Center, in a region corresponding \nto the one used to extract\nsource counts. Counts are binned so as to have at least 30 total counts \nin each bin to ensure applicability of the $\\chi^2$ statistics.\nFit to LECS data are performed only up to 4 keV, as the\nresponse matrix of LECS is not well calibrated above this\nenergy (see Orr et al. 1998).\nAll confidence levels are computed using $\\Delta \\chi^2$ = 2.7 (corresponding\nto 90\\% for 1 interesting parameter), unless otherwise stated. \n\nFor the LECS+MECS combined data, \na single power law is not acceptable ($> 3 \\sigma$) with $N_{\\rm H}$\nfixed at the Galactic value.\nIf $N_{\\rm H}$ is left free, the fit with a single power law is acceptable only\nat about $3 \\sigma$ (Prob $\\sim 1.5\\%$). The residuals are however \nskewed, showing that the fit is not good.\nThe fit is significantly improved (F--test at $>$ 99.99 \\% probability) by\nusing a broken power law shape. \nResults for the three models for LECS and MECS data are listed in \nTable~\\ref{broken_n}.\n\nFor each observation, in the first fit \n(single power-law model with Galactic $N_{\\rm H}$) we left the \nLECS normalization free\nwith respect to the MECS normalization to account for the residual \nerrors in intensity cross-calibration (see Cusumano, Mineo, Guainazzi\net al. in preparation). The fitted value \nof 0.696 (1997) and 0.701 (1998) fall in the range\nexpected given the current knowledge of the cross-calibration\n(F. Fiore, private communication; see also \n{\\small\\verb+http://www.sdc.asi.it/software/cookbook/cross_cal.html+}).\nSince the ratio of the two normalizations depends\non the position of the source in the detector, and not on the model\nchosen, we fix the LECS/MECS normalization to 0.7 also for the\nother subsequent models. \n\n\nThe PDS exposure time is not even twice than in AO1 (10.8 ks vs. 6.4 ks). \nSince the spectrum is steeper and the source is \nfainter than in the AO1 observation, the PDS detection is \nnot more significant than the AO1 detection ($2.6 \\sigma$). \nIn order to fit the PDS data alone we rebin them to 6 data points. \nWe fix the absorbing column to the Galactic value (N$_H = 5.76 \\times \n10^{20}$ cm$^{-2}$) while the normalization with respect to the MECS\nand index are left free.\nThe best fit slope is\n$\\alpha_{PDS}$ = 1.02 [$<$ 2.65], and the PDS/MECS ratio is 0.90, consistent\nwith what expected on the basis of cross-calibration of the instruments,\nwith a $\\chi^2$ = 2.2(4 dof), for\na probability of 70\\%, therefore statistically acceptable.\nHowever, given the low statistical \nsignificance of the PDS data, the uncertainty on the slope is high. \nWe therefore fit the total spectrum, from 0.1 keV to $\\sim $50 keV, using \nLECS, MECS and PDS data together: the result of the broken power law fit\nis shown in Figure~\\ref{fignew}. \nIt yields an unabsorbed flux in the [2--10 keV] band of\n$F_X=2.54 \\times 10^{-11}$ erg cm$^{-2}$ s$^{-1}$, \nand a corresponding luminosity in the same band of\n$L_X = 4.7\\times 10^{45}$ erg s$^{-1}$.\nThe PDS data are consistent with the LECS+MECS extrapolation.\n\n\n\\subsection {Comparison of the 1997 and 1998 observations}\n\nFor ease of comparison, we report in Table~\\ref{broken_o} the AO1 observation \nresults of 1ES~1101--232, from Wolter et al. (1998).\nThe LECS exposure was 5195 sec (2484 net counts), the MECS exposure\nwas 13830 (9509 net counts) and the PDS on-source exposure was 6410 sec (1996 \nnet counts).\nThe best fit models of the LECS+MECS spectra for various spectral \nshapes are listed in Table~\\ref{broken_o}, while in Figure~\\ref{figold} \nthe LECS+MECS+PDS \nspectrum is plotted, with the best fit of model (3).\n\n\\begin{figure}\n\\psfig{file=9325.f2,width=8truecm,height=6truecm}\n\\caption{X--ray spectrum (LECS+MECS+PDS) of Jan 1997, with broken power law fit\n(model 3 from Table~\\ref{broken_o}).}\n\\label{figold}\n\\end{figure}\n\n\nIn order to compare the two observations, we first check directly the count\nrates in the two epochs. The best representation is the ratio of\nthe two observed spectra, that does not depend on the choice of models\nand parameters. We therefore bin the two spectra, the relative \nbackground and response matrices in 32 channels, in order to avoid having \nempty bins after background subtraction. We then divide the two \nbackground-subtracted count rates and plot the results (after having \nflagged out the energy ranges that are not well calibrated in the matrices) \nin Fig.~\\ref{figrap}. \nThe ratio is consistent with being flat up to $\\sim 2$ keV, and steepening \nafter it, showing that a change in the spectrum occurred above $\\sim 2$ keV. \nThe two instruments, LECS and MECS, give a consistent ratio\nin the overlapping energy range. A fit with a constant in the interval \n0.5--10 keV is not statistically acceptable.\n\n\n\\begin{figure}\n\\psfig{file=9325.f3,width=8truecm,height=6truecm,angle=-90}\n\\caption{Ratio of data point from the Jun 1998 and Jan 1997 observations. \nStars indicate data points from the LECS instrument, crosses data points\nfrom the MECS instrument.\nThe trend in the data, with a drop above $\\sim$2 keV, is evident.}\n\\label{figrap}\n\\end{figure}\n\nAlso comparing the fit results for the two observations of Jan 1997 and \nJun 1998, we see that the high energy slope\n($\\alpha_2$) is steeper in the second one. The flux, with all the\nthree best fit models reported in the tables, is a factor of $\\sim$ 32\\% \nlower in the second than in the first one. \nThe low energy slope ($\\alpha_1$) and the break energy ($E_0$) are\ninstead consistent within the errors between the two observations.\n\nWe can make therefore the hypothesis that the different fluxes and \nspectra between the two epochs are \nexplained by a change in the spectral slope above the peak of the synchrotron\nemission. Hence we fit all the data (1997+1998) simultaneously, keeping the low\nenergy slope and break energy tied (equal one to each other, but free to \nvary) between the two observations. \nOn the contrary, the high energy slopes in the two observations are left \nindependent.\nThe $N_{\\rm H}$ is fixed to the galactic value, that fits well both \nobservations. The PDS data are not used for the comparison, being of \nlow statistical significance; the LECS and MECS data are re-binned to\n100 total counts for each bin, to improve the significance of the individual\ndata points, since no small range feature is present. The LECS/MECS \nnormalization is again fixed to 0.7.\n\n\\begin{figure}\n\\psfig{file=9325.f4a,width=7truecm,height=5.5truecm,angle=-90}\n\\psfig{file=9325.f4b,width=7truecm,height=5.5truecm,angle=-90}\n\\caption{LECS+MECS spectrum and broken power law fit for Jan 1997 (Upper Panel)\nand Jun 1998 (Lower Panel) observations. The broken power law fit of the two\nobservations combined is given in the text.}\n\\label{figcom}\n\\end{figure}\n\n\n\\begin{table}\n\\caption{Unabsorbed Fluxes and Rest--Frame Luminosities for the two \nobservations in the (0.1--2) and (2--10) keV energy bands.}\n\\begin{tabular}[htb]{| l c c c c |}\n \\hline\nDate & $F$[0.1-2] & $F$[2-10] & $L$[0.1-2] & $L$[2-10] \\\\\n & \\multicolumn{2}{c}{$\\times 10^{-11} \\ecs$}&\\multicolumn{2}{c|}{$\\times 10^{45}$ erg s$^{-1}$} \\\\\n\\hline \n04/01/97 & 3.46 & 3.85 & 5.4 & 6.8 \\\\\n19/06/98 & 3.32 & 2.53 & 5.3 & 4.7 \\\\\n\\hline\n\\end{tabular}\n\\label{fluxes}\n\\end{table}\n\n\nThe resulting values of $\\alpha_1$ and $E_0$ are consistent with those of both\nsingle observations: $\\alpha_1$=0.72 [0.44, 0.88]; \n$E_0=1.17 [0.93, 1.43]$ keV.\nThe high energy slope is \n$\\alpha_2^{1998}$ = 1.26 [1.19, 1.32], vs. \n$\\alpha_2^{1997}$ = 1.01 [0.95, 1.07], confirming that the slope indeed\nsteepened significantly. The $\\chi^2$ of the fit is 184.4 with 178 dof, \ncorresponding to a probability of 36\\%.\nThe errors quoted here are 90\\% confidence for \n4 parameters of interest ($\\Delta\\chi^2 = 7.76$).\nThe combined spectra (LECS and MECS) for both \nobservations with the best fit model are shown in Figure~\\ref{figcom}.\nWe report in Table~\\ref{fluxes} the unabsorbed fluxes and rest-frame\nluminosities in the \n0.1--2 and 2--10 keV bands for the two observations using the combined \nfit results.\n\n\nThe fluxes derived using the combined model are consistent with the\nfluxes derived from the two independent fits to the observations. We can\ntherefore attribute the observed flux variation entirely to a steepening\nof the high energy ($>$2 keV) portion of the spectrum. There is no\nevidence, within the statistical uncertainties, of a change in $\\alpha_1$\nor $E_0$, although in other well known sources (Mkn501, Mkn421, PKS2155--304) \nan increase in flux seems to be linked to an increase in $E_0$ and/or the \nhigh energy slope.\n\n\n\\section{The TeV band }\n\nBlazars as a class have been shown to emit a large fraction of their power\nat high energies, in the MeV--TeV band.\nThe current models assume that the high energy emission is produced by\nInverse Compton scattering (e.g. the SSC model or the EC model, see Ghisellini\net al. (1998) for the relevance of the two mechanisms), and the location of \nthe peak of the Compton component depends mainly on the lower energy peak due \nto the Synchrotron component. \n\nIn particular, objects of the LBL kind, that have the synchrotron peak\nat soft energies,\nshow their second peak at energies in the MeV--GeV range, and are in fact \ndetected by EGRET on board CGRO (see Mukherjee et al. 1997).\nObjects of the HBL kind, that have their synchrotron peak at UV--X--ray frequencies,\ninstead, should show the Compton peak in an even higher energy band. In fact,\nup to now, the only sources of VHE gamma rays (in the TeV band, by using\n$\\check{\\rm C}$erenkov detectors) are HBL: \nMkn 421 (Punch et al. 1992), Mkn 501 (Quinn et al. 1996), \n1ES~2344+514 (Catanese et al. 1998), \nPKS 2155--304 (Chadwick et al. 1999b).\n\nThe new $\\check{\\rm C}$erenkov arrays allow the detection of bright sources \nin relatively short exposure times, and therefore it has been possible to \nmonitor their variability:\nsome of these objects have in fact shown periods of flaring activity on \ntime-scales as short as 15 minutes (Gaidos et al. 1996, Aharonian et al. 1999).\n\nAnother point of debate is the amount of absorption of VHE photons due to \nthe cosmic infra--red background. The aforementioned detected objects in fact\nare all nearby.\nDetection of sources that lie further away can therefore help in constraining\nthe amount of the IR background (e.g. Stecker and De Jager, 1998).\n\nThe simultaneous detection of X--ray and TeV emission allows us to estimate\na number of physical parameters of the source, such as the magnetic field and\nthe Doppler factor (see e.g. Tavecchio et al. 1998). \nWe will show in Section 4 that a number of interesting constraints can be \nderived also by using the upper limit derived in the TeV band, together \nwith the X--ray band information.\n\n\\subsection {Predictions of TeV emission in 1ES~1101--232 from phenomenological\nconstraints.}\n\nA very simple prediction of the TeV emission can be made by following \nthe scheme presented e.g. in Fossati et al. (1998).\nIn this model a) the ratio of the frequencies of the high (Compton) and low \n(synchrotron) energy peaks is constant and equal to $5\\times 10^{8}$ and\nb) the high energy peak and the radio luminosity have a fixed ratio, \n$\\nu_\\gamma L_{peak,\\gamma} \\over \\nu_{5GHz} L_{5GHz}$ =$3 \\times 10^{3}$. \nThis model represents the average SED observed for \nthe various classes, while single sources can deviate from\nthis average phenomenological parameterization.\nThis very simple relationship, however, allows us to make order of magnitude\nprediction even not knowing the physical conditions at the source. From \nthe two expressions above we can derive both the expected frequency\nof the second peak and its intensity.\nThe peak of the synchrotron emission is measured (this paper and Wolter \net al. 1998) at\n$\\nu_s = 3 \\times 10^{17}$ Hz: the Compton peak is therefore expected\nat $\\nu_C = 1.5 \\times 10^{26}$ Hz which corresponds to $\\sim$0.6 TeV.\nThe measured radio flux at 5 GHz is $5 \\times 10^{-15}$ erg \ncm$^{-2}$ s$^{-1}$ (see references in Table~\\ref{refere}).\nThe expected flux at the Compton peak (0.6 TeV) is therefore\n$\\sim 8. \\times 10^{-12}$ photon cm$^{-2}$ s$^{-1}$. \n\nAnother prediction can be made from the observed X--ray flux, by using the\nrecipe of Stecker, De Jager \\& Salamon (1996). Within an SSC scenario they\nuse simple scaling arguments to predict the TeV fluxes for HBL, based on the \nX--ray flux and the assumption that the properties of the emission are similar \nto those observed for Mkn 421. Their argument is partially\nsupported by the actual detection of (a few) other sources\nfor which they predicted possible detectability.\nThe factor of increase between the synchrotron and Compton \ncomponent is $10^9$, and, assuming $L_C/L_s \\sim 1$,\nthey derive $\\nu_{TeV} F_{TeV} \\sim \\nu_{X} F_{X}$.\nTherefore, from the observed X--ray properties for 1ES~1101--232 (peak around\n1 keV and flux of 2.5--3.8 $\\times 10^{-11} \\ecs$), we infer that the expected\nCompton peak is around 1 TeV with a flux of $1.5$--$2.5 \\times 10^{-11}$ \nphoton cm$^{-2}$ s$^{-1}$.\n\nThese estimates make 1ES 1101--232 a good TeV candidate, at the border\nof current sensitivities, and possibly well above it\nduring flaring activities.\n\n\n\\subsection{TeV Observations}\n\n1ES~1101--232 has been observed on the nights of 19--27 May 1998\nwith the Durham University Mark 6 atmospheric $\\check{\\rm C}$erenkov telescope.\nWe summarize here the data analysis and the results presented in \nChadwick et al. (1999a). \nThe telescope uses the imaging technique to separate VHE gamma rays from the \ncosmic ray background, together with a robust noise-free trigger (Armstrong\net al. 1999). Data are taken in 15 minutes segments, alternating \nON-source with an equal number of OFF-source observations. \nAfter removal of cloud--affected data, there are a total of\n10.5 hours ON-source data and the same amount of OFF-source data.\nData are screened for ``good\" events by the selection criteria listed in\nTable 2 of Chadwick et al. (1999a).\nThe source was not detected and an upper limit of \n$F_{TeV}$ [$> 300$ GeV] = 3.7$\\times 10^{-11}$ photons cm$^{-2}$ s$^{-1}$ \nhas been derived.\n\nThe data have been investigated for time variability on time-scales of days \n(at a flux limit of $\\sim 1 \\times 10^{-10}$ cm$^{-2}$ s$^{-1}$) \nand 15 min intervals. There is no evidence for any bursting behavior\n(Chadwick, private communication).\n\n\n\\section {SED construction and TeV predictions from theoretical models.}\n\n\nWe have constructed the overall Spectral Energy Distribution (SED), using\nboth data from literature and the \\sax\\ spectra from the two observations. \nWe construct two different SED, one for each \\sax\\ observation, that are\nclearly modeled by a different synchrotron state.\nThe two SED are presented in Fig.~\\ref{figsedb}.\n\n\\begin{table}\n\\caption{References for the data points of Fig~\\ref{figsedb}.}\n\\begin{tabular}[h]{|l l|}\n\\hline\nBand \t& Reference\t\\\\\n\\hline\nRadio 1.4GHz & NVSS: Condon et al. 1998 AJ 115, 1693 \\\\\nRadio 1.4GHz & Remillard et al. 1989 ApJ 345, 140 \\\\\nRadio 5 GHz & Perlman et al. 1996 ApJS 104, 251 \\\\\nRadio 5 GHz & Giommi et al. 1995 A\\&AS 109, 267 \\\\\nOptical V \t& Pesce et al. 1994 AJ 107, 494 \\\\\nOptical V & Lanzetta et al. 1995 ApJ 440, 435 \\\\\nOptical V & Giommi et al. 1995 A\\&AS 109, 267 \\\\\nOptical V & Jannuzi et al. 1994 ApJ 428, 130 \\\\\nOptical V & Falomo et al. 1994 ApJS 93, 125 \\\\\nIR J,H,K & Bersanelli et al. 1992 AJ 104, 28 \\\\\nIR K\t\t& Falomo et al. 1993 AJ 106, 11 \\\\\nUV 1400A \t& Pian \\& Treves 1993 ApJ 416, 130 \\\\\nUV 1400A \t& Edelson et al. 1992 ApJS 83, 1 \\\\\nX--ray 2 keV & Perlman et al. 1996 ApJS 104, 251 \\\\\nX--ray 2 keV & Giommi et al. 1995 A\\&AS 109, 267 \\\\\nEGRET \t\t& Fichtel et al. 1994 ApJS 94, 551 \\\\\n\\hline\n\\end{tabular}\n\\label{refere}\n\\end{table}\n\n\n\\begin{figure}\n\\psfig{file=9325.f5a,width=9.5truecm}\n\\psfig{file=9325.f5b,width=9.5truecm}\n\\caption{SED of the two \\sax\\ epoch observations {\\it Top:} 04/01/97 -- \nhigh state; {\\it Bottom:} 19/06/98 -- low state, plus models.\nLarge empty circles represent historical data from literature, while arrows\nindicate upper limits from EGRET (MeV) and Mark6 (GeV-TeV) experiments\nrespectively\n(see Table~\\ref{refere} for references). Small dots with error-bars are \nthe unfolded X--ray spectra discussed in this work.\nLines represent the spectra computed with the SSC model (see text for\ndetails) with different model parameters, reported in Table~\\ref{params}:\ndashed lines represent spectra calculated with $\\delta=10$ and two different \nvalues for the magnetic field $B$; similarly, solid lines represent spectra \ncalculated with $\\delta=20$ and two different values for the magnetic \nfield $B$. \n}\n\\label{figsedb}\n\\end{figure}\n\n\\begin{table}\n\\caption{Input parameters for the models of Fig.~\\ref{figsedb}}\n\n\\begin{tabular}[h]{| r r c c c c c c|}\n\\hline\n\\multicolumn{3}{|l}{High State} & & & & & \\\\\n\\hline\n \\# &$\\delta$ &$B$ &$\\gamma_b$ &$R$ &$K$ &$n_1$ &$n_2$ \\\\\n & &(G) &$\\times10^4$ &cm &cm$^{-3}$ & & \\\\\n\\hline\n1 & 10 & 0.3 & 15.8 &1$\\times10^{16}$ & 1.7$\\times10^4$ & 2 & 3.5\\\\\n2 & 10 & 0.6 & 11.2 &1$\\times10^{16}$ & 5.9$\\times10^4$ & 2 & 3.5\\\\\n3 & 20 & 0.1 & 19.3 &1$\\times10^{16}$ & 7.9$\\times10^3$ & 2 & 3.5\\\\\n4 & 20 & 0.2 & 13.5 &1$\\times10^{16}$ & 2.8$\\times10^4$ & 2 & 3.5\\\\\n\\hline\n\\hline\n\\multicolumn{3}{|l}{Low State} & & & & & \\\\\n\\hline\n \\# &$\\delta$ &$B$ &$\\gamma_b$ &$R$ &$K$ &$n_1$ &$n_2$ \\\\\n & &(G) &$\\times10^4$ &cm &cm$^{-3}$ & & \\\\\n\\hline\n1 & 10 & 0.5 & 8.45 & 1$\\times10^{16}$ & 2.5$\\times10^4$ & 2 & 3.9\\\\\n2 & 10 & 1.0 & 5.98 & 1$\\times10^{16}$ & 8.9$\\times10^3$ & 2 & 3.9\\\\\n3 & 20 & 0.1 & 13.3 & 1$\\times10^{16}$ & 6.3$\\times10^3$ & 2 & 3.9\\\\\n4 & 20 & 0.2 & 9.40 & 1$\\times10^{16}$ & 2.2$\\times10^3$ & 2 & 3.9\\\\\n\\hline\n\\end{tabular}\n\\label{params}\n\\end{table}\n\n\nWe have reproduced the SED in both X--ray states with a simple homogeneous SSC \nmodel.\nThe source is modeled as a spherical region with size $R$, uniform and\ntangled magnetic field $B$, in motion toward the observer with a bulk \nLorentz factor $\\Gamma$.\nThe region is filled by a population of relativistic electrons with a\ndistribution of Lorentz factors given by:\n$N(\\gamma )=K\\gamma^{-n_1}(1+\\gamma/\\gamma_{b})^{n_1-n_2}$, \nwhere the asymptotic slopes are $n_1$ and $n_2$, the break point\nis $\\gamma_{b}$ and $K$ is a normalization factor.\nThe self--Compton emission is derived taking into account the full \nKlein--Nishina (KN) cross section, computed using the relations reported in \nJones (1968; see also Blumenthal \\& Gould 1970). \nWe do not take into account absorption of IR photons by the infrared\nbackground, whose emission level is still uncertain. \nThis implies that in principle the derived curves are upper limits to the\ndetectable VHE emission, also because the redshift of 1ES~1101--232 is only\nslightly smaller\nthan the limit ($z=0.2$) chosen to monitor blazar emission in the TeV band\nby the HEGRA experiment (Rhode \\& Meyer, 1997).\nOn the other hand, a detection of the source in this band would provide also a\nmeasure of the density of IR background photons.\n\nAlthough the complete determination of the set of physical parameters for the\nSSC model requires the knowledge of the positions of both the synchrotron peak \nand the Inverse Compton peak (as discussed in Tavecchio et al. 1998), \nwe can put strong constraints to the parameters using the informations\nprovided by the X--ray spectrum and the TeV upper limit\nsuggesting that the condition $L_C/L_s\\leq 1$ applies.\n\nWe note here that the analytical relations discussed in Tavecchio et al. (1998)\nin the KN regime are obtained with a step approximation for the KN \ncross--section. \nIn the extreme KN regime the numerical values given by this \napproximation might differ from the results of the numerical model derived\nwith the full KN treatment, but we can use the analytical discussion as a \nguideline for the numerical model.\n\nTypical variability time-scales observed in HBLs \n($t_{var}\\sim\\,10^{3-4}$ s, see e.g\nZhang et al. 2000, Giommi et al. 1999, 2000) suggest Doppler factors \n$\\delta$ in the range 10--20 and sizes of $R \\leq 10^{16}$ cm. \nWe fixed the radius to $R=10^{16}$ cm. This choice directly puts a lower \nlimit to the value of the magnetic field:\n\n\\footnotesize\n\\begin{equation}\nB\\delta^{2+\\alpha _1} > A \\times\n (1+z)^{\\alpha _1} \\left[ \\frac{g} \n{\\nu_c\\nu_s} \\right] ^{(1-\\alpha _1)/2} \n\\left( \\frac {L_s}\n{ t_{var} L_C^{1/2}} \\right)\n\\label{ulower} \n\\end{equation} \n\\normalsize\n\n\\noindent\nwhere $g(\\alpha _1,\\alpha _2)$ is a constant related to\nthe spectral indices $\\alpha_1$ and $\\alpha _2$ and A is the\nappropriate constant\n(see Tavecchio et al. 1998 for details on (\\ref{ulower})).\nFrom this relation we can infer that an upper limit\non $L_C$ and an estimate of $t_{var}$ directly puts a lower \nlimit for $B$. The physical reason for this lower limit is related to the \nfact that the synchrotron peak Luminosity is proportional to the product\n$N_eB^2$ (where $N_e$ is the number of emitting electrons), while the ratio\nbetween the Compton peak Luminosity and the synchrotron peak Luminosity is \nproportional to $N_e$: therefore an upper limit to $L_C/L_s$ gives an upper \nlimit to $N_e$ and this, together with the synchrotron Luminosity, provides \nthe lower limit for the magnetic field $B$.\nAnother way of describing the effect, assuming that\nthe scattering is in the Thomson regime, is that in this case\nrequiring $L_C/L_s<1$ corresponds to require that the\nratio between the synchrotron and the magnetic energy densities \n$U_{syn}/U_B<1$.\nFor a given source size and Doppler factor the synchrotron radiation \nenergy density is fixed, and the above relation then corresponds to a \nlower limit on the value of the magnetic field.\n\n \nIn Fig.~\\ref{figsedb} we plot the spectrum of both states computed for \ntwo different values of $\\delta$ ($\\delta=10$ for the dashed lines,\n$\\delta=20$ for the solid lines), and for two different values of the magnetic\nfield $B$, as listed in Table~\\ref{params}.\nThe lowest value of $B$ has been determined by requiring\nnot to over-produce the high energy (TeV) emission, since, for a given\nsynchrotron luminosity, size and Doppler factor, the ratio\nbetween the self Compton and the synchrotron powers depends only on the\nmagnetic field.\n\nWe take this value, listed in Table~\\ref{params},\nfor the models 1 and 3 shown in Fig. 5.\nFor models 2 and 4 we have doubled the B value, and decreased the\nrelativistic electron density and $\\gamma_b$ accordingly, in order to produce\nthe same amount of synchrotron flux and about the same synchrotron peak\nfrequency.\nIn this case the self--Compton flux decreases, due to the decreased\nelectron density.\n\nThe transition from the high to the low state is consistent with a change\nof the second slope $n_2$ and with a decrease of $\\gamma_b$ by a factor\nof 1.5--2. This behavior is similar to what observed in the other well\nknown TeV BL Lac, such as PKS 2155--304 (see e.g. Chiappetti et al. 1999),\nMkn 501 (e.g. Pian et al 1998) and Mkn 421 (Maraschi et al. 1999), where\nhigh X-ray states are interpreted as states with either higher \n$\\gamma _b$ and/or higher magnetic field.\n\n\nIt is evident from Fig.~\\ref{figsedb} that a small change in the magnetic\nfield, while still consistent with the X--ray (\\sax) observations,\nproduces a dramatically different amount of TeV photons. Assuming that\nthe size of the source and the Doppler factor do not vary substantially\nwith time, variations of the synchrotron flux can be attributed to\nchanges of the density of electrons and/or the magnetic field. If this\nis the case, we expect that the TeV emission can be easily detected,\neither for X--ray fluxes slightly brighter than what observed up to now,\nor by longer TeV exposure times.\n\n\\section{Results and Conclusions}\n \nThe X--ray spectrum of 1ES~1101--232 as measured by \\sax\\ is fitted \nonly by a broken power law (a single power law or an absorbed \npower law are not statistically acceptable)\nwith a break at 1.3 - 1.9 keV. From the first to the second observation, \nthe spectrum varied at high energies, becoming softer (steeper). \nThe flux decrease, by about 32\\%, has occurred in the 2--10 keV band.\nThe PDS observation are not of statistical significance sufficient\nto put a real constraint on the spectrum.\n\nEven if the variation in the X--ray band is not dramatic, we can clearly\ndistinguish between the two states, that are modeled by different parameters\nof the synchrotron component.\n\nBy using the TeV upper limit and the two \\sax\\ observations we model also the\nhigher energy portion of the spectrum as a self--Compton component, by\nusing the model described e.g. in Tavecchio et al. (1998) that assumes a simple\nhomogeneous SSC model in the KN regime, in which the relativistic electrons\nhave a broken power law energy distribution. \n\nThe two X-ray states of the source are described by varying this\ndistribution, assuming that the other relevant parameters ($R$ and\n$\\delta$) are nearly constant.\n\n\nWe can compare these results with what found for the few TeV detected sources.\nThe choice of Doppler factor of 10 and 20 made here is in the interval of\nthe values of $\\delta$ found by other authors for Mkn 421, \nPKS2155--304 and Mkn501, that range\nfrom $\\delta \\sim 5$ (e.g. Takahashi, 1999; Mkn 421, Catanese et al. \n1998: Mkn 501) \nto $\\delta \\sim 30$ (e.g. Bednarek \\& Protheroe 1999: Mkn501; \nKataoka et al 2000: PKS2155--304;\nBednarek \\& Protheroe 1997: Mkn 421).\nAt the same time, values of $B$ in excess of 0.03 G and up to 1 G \n(Chiappetti et al. 1999) are found for the same sources.\n\nOf the three above mentioned objects, the most similar to 1ES~1101--232 \nis Mkn 501, for which different measures have been produced: e.g.\n$\\delta \\geq 15$ \\& $B=0.8 $G (Pian et al. 1998);\n$\\delta = 15$ \\& $B=0.2 $G (Kataoka et al. 1999);\n$\\delta = 30$ \\& $B=0.7 $G (Bednarek \\& Protheroe 1999),\nin good agreement with the values of Table~\\ref{params}.\n\n\nEven if based, besides the accurate X-ray spectral determination up \nto $\\sim 50$ keV, only on a TeV upper limit we can infer that\nthe physical conditions in 1ES~1101--232 are similar to the\nbrightest TeV sources, making it a very promising candidate for \nTeV observations, and a testbed for the SSC model.\nFurthermore, since the redshift of 1ES~1101--232 is intermediate,\na detection of this source in the VHE range would pose constraints\non the density of the IR background photons that is still at the moment\nvery uncertain.\n\n\\begin{acknowledgements}\nThis work has received partial financial support from the Italian \nSpace Agency. \nWe would like to thank Paula Chadwick and S.J. McQueen for informing us\nabout their VHE results in advance of publication, Paolo Giommi and Roberto\nDella Ceca for helpful discussion and comments, and an anonymous referee\nfor useful suggestions that improved the readability of the paper.\n\n\\end{acknowledgements}\n \n\\begin{thebibliography}{}\n\n\\bibitem{} Aharonian, F.A. et al., 1999, A\\&A, 341, 69\n\n\\bibitem{} Armstrong, P. et al., 1999, Experimental Astronomy, v. 9, 51\n\n\\bibitem{} Bednarek, W., \\& Protheroe, R.J., 1997, MNRAS, 290, 139 %(mkn421)\n\n\\bibitem{} Bednarek, W., \\& Protheroe, R.J., 1999, MNRAS, 310, 577\n%%astro-ph/9902050 %(mkn501)\n\n\\bibitem{} Blumenthal \\& Gould, 1970, Rev. of Modern Phys., 42, 237\n\n\\bibitem{} Boella G., Butler R.C., Perola G.C., et al., \n 1997a, A\\&AS 122, 299\n\n\\bibitem{} Boella G., Chiappetti L., Conti G., et al., \n 1997b, A\\&AS 122, 327\n\n\\bibitem{} Butler C., Scarsi L., 1990, SPIE 1344, 46\n\n\\bibitem{} Catanese M. et al., 1998, ApJ, 501, 616\n\n\\bibitem{} Chadwick, P.M., Lyons, K., McComb, T.J.L., Orford, K.J., Osborne, \nJ.L., Rayner, S.M., Shaw, S.E., and Turver, K.E., 1999a, ApJ, 521, 547\n\n\\bibitem{} Chadwick, P.M., Lyons, K., McComb, T.J.L., Orford, K.J., Osborne, \nJ.L., Rayner, S.M., Shaw, S.E., Turver, K.E., Wieczorek, G.J., 1999b, \nApJ, 513, 161\n\n\\bibitem{} Chiappetti, L., et al., 1999, ApJ, 521, 552\n\n\\bibitem{} Fossati, G., Maraschi, L., Celotti, A., Comastri, A., and\nGhisellini, G., 1998, MNRAS, 299, 433\n\n\\bibitem{} Gaidos, J.A., et al, 1996, Nature, 383, 319\n\n\\bibitem{} Ghisellini, G., 1999, in ``The BL Lac Phenomenon\",\nEd. L. Takalo, ASP conf. series, 159, 311. \n\n\\bibitem{} Ghisellini, G., Celotti, A., Fossati, G., Maraschi, L., and\nComastri, A., 1998, MNRAS, 301, 451\n\n\\bibitem{} Giommi, P., Padovani, P., Perlman, E., 2000, MNRAS, in press,\nastro-ph/9907377\n\n\\bibitem{} Giommi, P., et al., 1999, A\\&A, 51, 59\n\n\\bibitem{} Guainazzi M. \\& Matteuzzi A., 1997, SDC-TR 011\n\n\\bibitem{} Jones, 1968, Phys. Rev, 167, 1159\n\n\\bibitem{} Kataoka, J., et al. 2000, ApJ, 528, 243 %(2155)\n\n\\bibitem{} Kataoka, J., et al. 1999, ApJ, 514, 138 %(mkn 501)\n\n\\bibitem{} Maraschi, L., et al., 1999, ApJL, 526, L81\n\n\\bibitem{} Mukherjee, R., et al. 1997, ApJ, 490, 116\n\n\\bibitem{} Orr, A. et al. 1998, Nuclear Physics B Proceedings\nSupplements, L. Scarsi, H. Bradt, P. Giommi and F. Fiore (eds.), Elsevier\nScience B.V\n\n\\bibitem{} Parmar A.N., Martin D.D.E., Bavdaz M., et al., \n 1997, A\\&AS 122, 309\n\n\\bibitem{} Perlman E.S., Stocke J.T., Schachter, J.F., Elvis, M.,\nEllingson, E., Urry, C.M., Potter M., Impey C.D., Kolchinsky, P. 1996, \nApJS, 104, 251 \n\n\\bibitem{} Pian, E., et al. 1998, ApJ, 492, L17\n\n\\bibitem{} Punch, M., et al., 1992, Nature, 358, 477\n\n\\bibitem{} Quinn J., et al., ApJ, 1996, 456, L83\n\n\\bibitem{} Rhode, W., Meyer, H., 1997, Proceedings of the International \nConference on ``Relativistic Jets in AGNs\", p.223-227\n\n\\bibitem{} Stecker, F.W., De Jager, O.C. \\& Salamon, M.H.,\n1996, Ap.J. 473, L75\n\n\\bibitem{} Stecker F.W., \\& De Jager, O.C. 1998, A\\&A, 334, L85\n\n\\bibitem{} Takahashi, T., et al. 1999, Astropart. Phys., 11, 173 \n\n\\bibitem{} Tavecchio, F., et al., 1998, ApJ, 509, 608\n\n\\bibitem{} Urry, C. M., \\& Padovani, P. 1995, PASP, 107, 803\n\n\\bibitem{} Wolter A., et al., 1998, A\\&A, 335, 899\n\n\\bibitem{} Zhang, Y.H., et al., 1999, ApJ, 527, 719\n%%astro-ph/9907325\n\\end{thebibliography}\n\n\n\\end{document}\n\n"
}
] |
[
{
"name": "astro-ph0002298.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem{} Aharonian, F.A. et al., 1999, A\\&A, 341, 69\n\n\\bibitem{} Armstrong, P. et al., 1999, Experimental Astronomy, v. 9, 51\n\n\\bibitem{} Bednarek, W., \\& Protheroe, R.J., 1997, MNRAS, 290, 139 %(mkn421)\n\n\\bibitem{} Bednarek, W., \\& Protheroe, R.J., 1999, MNRAS, 310, 577\n%%astro-ph/9902050 %(mkn501)\n\n\\bibitem{} Blumenthal \\& Gould, 1970, Rev. of Modern Phys., 42, 237\n\n\\bibitem{} Boella G., Butler R.C., Perola G.C., et al., \n 1997a, A\\&AS 122, 299\n\n\\bibitem{} Boella G., Chiappetti L., Conti G., et al., \n 1997b, A\\&AS 122, 327\n\n\\bibitem{} Butler C., Scarsi L., 1990, SPIE 1344, 46\n\n\\bibitem{} Catanese M. et al., 1998, ApJ, 501, 616\n\n\\bibitem{} Chadwick, P.M., Lyons, K., McComb, T.J.L., Orford, K.J., Osborne, \nJ.L., Rayner, S.M., Shaw, S.E., and Turver, K.E., 1999a, ApJ, 521, 547\n\n\\bibitem{} Chadwick, P.M., Lyons, K., McComb, T.J.L., Orford, K.J., Osborne, \nJ.L., Rayner, S.M., Shaw, S.E., Turver, K.E., Wieczorek, G.J., 1999b, \nApJ, 513, 161\n\n\\bibitem{} Chiappetti, L., et al., 1999, ApJ, 521, 552\n\n\\bibitem{} Fossati, G., Maraschi, L., Celotti, A., Comastri, A., and\nGhisellini, G., 1998, MNRAS, 299, 433\n\n\\bibitem{} Gaidos, J.A., et al, 1996, Nature, 383, 319\n\n\\bibitem{} Ghisellini, G., 1999, in ``The BL Lac Phenomenon\",\nEd. L. Takalo, ASP conf. series, 159, 311. \n\n\\bibitem{} Ghisellini, G., Celotti, A., Fossati, G., Maraschi, L., and\nComastri, A., 1998, MNRAS, 301, 451\n\n\\bibitem{} Giommi, P., Padovani, P., Perlman, E., 2000, MNRAS, in press,\nastro-ph/9907377\n\n\\bibitem{} Giommi, P., et al., 1999, A\\&A, 51, 59\n\n\\bibitem{} Guainazzi M. \\& Matteuzzi A., 1997, SDC-TR 011\n\n\\bibitem{} Jones, 1968, Phys. Rev, 167, 1159\n\n\\bibitem{} Kataoka, J., et al. 2000, ApJ, 528, 243 %(2155)\n\n\\bibitem{} Kataoka, J., et al. 1999, ApJ, 514, 138 %(mkn 501)\n\n\\bibitem{} Maraschi, L., et al., 1999, ApJL, 526, L81\n\n\\bibitem{} Mukherjee, R., et al. 1997, ApJ, 490, 116\n\n\\bibitem{} Orr, A. et al. 1998, Nuclear Physics B Proceedings\nSupplements, L. Scarsi, H. Bradt, P. Giommi and F. Fiore (eds.), Elsevier\nScience B.V\n\n\\bibitem{} Parmar A.N., Martin D.D.E., Bavdaz M., et al., \n 1997, A\\&AS 122, 309\n\n\\bibitem{} Perlman E.S., Stocke J.T., Schachter, J.F., Elvis, M.,\nEllingson, E., Urry, C.M., Potter M., Impey C.D., Kolchinsky, P. 1996, \nApJS, 104, 251 \n\n\\bibitem{} Pian, E., et al. 1998, ApJ, 492, L17\n\n\\bibitem{} Punch, M., et al., 1992, Nature, 358, 477\n\n\\bibitem{} Quinn J., et al., ApJ, 1996, 456, L83\n\n\\bibitem{} Rhode, W., Meyer, H., 1997, Proceedings of the International \nConference on ``Relativistic Jets in AGNs\", p.223-227\n\n\\bibitem{} Stecker, F.W., De Jager, O.C. \\& Salamon, M.H.,\n1996, Ap.J. 473, L75\n\n\\bibitem{} Stecker F.W., \\& De Jager, O.C. 1998, A\\&A, 334, L85\n\n\\bibitem{} Takahashi, T., et al. 1999, Astropart. Phys., 11, 173 \n\n\\bibitem{} Tavecchio, F., et al., 1998, ApJ, 509, 608\n\n\\bibitem{} Urry, C. M., \\& Padovani, P. 1995, PASP, 107, 803\n\n\\bibitem{} Wolter A., et al., 1998, A\\&A, 335, 899\n\n\\bibitem{} Zhang, Y.H., et al., 1999, ApJ, 527, 719\n%%astro-ph/9907325\n\\end{thebibliography}"
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astro-ph0002299
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astro-ph0002300
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Rotational modes of non-isentropic stars and the gravitational radiation driven instability
|
[
{
"author": "Shijun Yoshida and Umin Lee"
}
] |
We investigate the properties of $r$-mode and inertial mode of slowly rotating, non-isentropic, Newtonian stars, by taking account of the effects of the Coriolis force and the centrifugal force. The Coriolis force is the dominant restoring force for both $r$-mode and inertial mode, which are also called rotational mode in this paper. For the velocity field produced by the oscillation modes the $r$-mode has the dominant toroidal component over the spheroidal component, while the inertial mode has the comparable toroidal and spheroidal components. In non-isentropic stars the specific entropy of the fluid depends on the radial distance from the center, and the interior structure is in general divided into two kinds of layers of fluid stratification that is stable or unstable against convection. Because of the non-isentropic structure, low frequency oscillations of the star are affected by the buoyant force, which has no effects on oscillations of isentropic stars. In this paper we employ simple polytropic models with the polytropic index $n=1$ as the background neutron star models for the modal analysis. For the non-isentropic models we consider only two cases, that is, the models with the stable fluid stratification in the whole interior and the models that are fully convective. For simplicity we call these two kinds of models ``radiative'' and ``convective'' models in this paper. For both cases, we assume the deviation of the models from isentropic structure is small. Examining the dissipation timescales due to the gravitational radiation and several viscous processes for the polytropic neutron star models, we find that the gravitational radiation driven instability of the nodeless $r$-modes associated with $l'=|m|$ remains strong even in the non-isentropic models, where $l'$ and $m$ are the indices of the spherical harmonic function representing the angular dependence of the eigenfunction. Calculating the rotational modes of the radiative models as functions of the angular rotation frequency $\Omega$, we find that the inertial modes are strongly modified by the buoyant force at small $\Omega$, where the buoyant force as a dominant restoring force becomes comparable with or stronger than the Coriolis force. Because of this property we obtain the mode sequences in which the inertial modes at large $\Omega$ are identified as $g$-modes or the $r$-modes with $l'=|m|$ at small $\Omega$. We also note that as $\Omega$ increases from $\Omega=0$ the retrograde $g$-modes become retrograde inertial modes, which are unstable against the gravitational radiation reaction.
|
[
{
"name": "ms.tex",
"string": "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n% %\n% Rotational modes of non-isentropic stars and %\n% the gravitational radiation driven instability %\n% %\n% S. YOSHIDA and U. LEE %\n% %\n% Astronomical Institute, %\n% Graduate School of Science, Tohoku University, % \n% Sendai 980-8578, Japan %\n% %\n% yoshida@astr.tohoku.ac.jp %\n% %\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\documentstyle[aaspp4]{article}\n\n\\received{}\n\\accepted{}\n\\journalid{VOL}{JOURNAL DATE}\n\\articleid{START PAGE}{END PAGE}\n\\paperid{MANUSCRIPT ID}\n\n\\slugcomment{}\n\\lefthead{Yoshida, Lee}\n\\righthead{}\n\n\\begin{document}\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% O. FRONT MATTER %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\title{Rotational modes of non-isentropic stars and the gravitational radiation \n driven instability }\n%\n\\author{Shijun Yoshida and Umin Lee}\n%\n\\affil{Astronomical Institute, Graduate School of Science, \nTohoku University, Sendai 980-8578, \nJapan \\\\ yoshida@astr.tohoku.ac.jp, lee@astr.tohoku.ac.jp}\n\n\n\\begin{abstract}\nWe investigate the properties of\n$r$-mode and inertial mode of slowly rotating, non-isentropic, \nNewtonian stars, by taking account of the effects of \nthe Coriolis force and the centrifugal force.\nThe Coriolis force is the dominant restoring force \nfor both $r$-mode and inertial mode, which are also called rotational mode \nin this paper. \nFor the velocity field produced by the oscillation modes\nthe $r$-mode has the dominant toroidal component over the \nspheroidal component, while the inertial mode has\nthe comparable toroidal and spheroidal components.\nIn non-isentropic stars the specific entropy of the fluid\ndepends on the radial distance from the center, and\nthe interior structure is in general divided into\ntwo kinds of layers of fluid stratification that is\nstable or unstable against convection.\nBecause of the non-isentropic structure, low frequency\noscillations of the star are affected by the buoyant force, which\nhas no effects on oscillations of isentropic stars.\nIn this paper we employ simple polytropic models with the polytropic index $n=1$\nas the background neutron star models for the modal analysis.\nFor the non-isentropic models we consider only two cases, that is,\nthe models with the stable fluid stratification in the whole interior\nand the models that are fully convective.\nFor simplicity we call these two kinds of models ``radiative'' and ``convective''\nmodels in this paper.\nFor both cases, we assume the deviation of the models from isentropic \nstructure is small.\nExamining the dissipation timescales due to \nthe gravitational radiation and \nseveral viscous processes for the polytropic neutron star models,\nwe find that the gravitational radiation driven instability of \nthe nodeless $r$-modes associated with $l'=|m|$ remains strong \neven in the non-isentropic models,\nwhere $l'$ and $m$ are the indices \nof the spherical harmonic function representing the angular dependence\nof the eigenfunction.\nCalculating the rotational modes of the radiative models \nas functions of the angular rotation frequency $\\Omega$, we find that\nthe inertial modes are strongly modified \nby the buoyant force at small $\\Omega$, where the buoyant force\nas a dominant restoring force becomes\ncomparable with or stronger than the Coriolis force.\nBecause of this property we obtain the mode sequences \nin which the inertial modes at large $\\Omega$\nare identified as $g$-modes or the $r$-modes with $l'=|m|$ at small $\\Omega$.\nWe also note that as $\\Omega$ increases from $\\Omega=0$\nthe retrograde $g$-modes become retrograde inertial modes,\nwhich are unstable against the gravitational radiation reaction.\n\\end{abstract}\n\n\n\\keywords{instabilities --- stars: neutron --- \nstars: oscillations --- stars: rotation}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% I. INTRODUCTION %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\section{Introduction}\n\n\nSince the recent discovery of the gravitational radiation driven instability of\nthe $r$-modes by Andersson (1998) and Friedman \\& Morsink (1998),\na large number of papers have been published on the properties of the \nrotational modes of rotating stars because of their possible importance \nin astrophysics\n(e.g., Kojima 1998, Andersson, Kokkotas \\& Schutz 1998, \nKokkotas \\& Stergioulas 1998, Lindblom \\& Isper 1998, Beyer \\& Kokkotas \n1999, Lindblom, Mendell \\& Owen 1999, Kojima \\& Hosonuma 1999, \nLockitch \\& Friedman 1999, Yoshida \\& Lee 2000, Lockitch 1999, Yoshida \net al 1999).\nHere, we have used the term of ``rotational mode'' to refer to both $r$-mode and \ninertial mode of rotating stars.\nAs an important consequence of the instability, for example, Lindblom, Owen \n\\& Morsink (1998) argued that due to the instability, \nthe maximum angular rotation velocity of hot neutron stars is \nstrongly restricted. \nOwen et al. (1998) also suggested that\nthe gravitational radiation emitted from hot young neutron stars due to\nthe $r$-mode instability would be one of the potential sources\nfor the gravitational wave detectors, e.g. LIGO.\n\n\n\nThe dominant restoring force for the rotational modes\nis the Coriolis force and the characteristic frequency \nis comparable to the angular rotation frequency $\\Omega$ of the star \n(e.g., Greenspan 1964, Pedlosky 1987). \nThe $r$-modes are characterized by the properties that\nthe toroidal motion dominates the spheroidal motion in the velocity field, and that \nthe oscillation frequency $\\omega$ observed in the corotating frame of the star \nis given by $\\omega=2m\\Omega/(l'(l'+1))$ \nin the limit of $\\Omega\\rightarrow0$, \nwhere $m$ and $l'$ are the indices of the spherical harmonic function $Y_{l'}^m$ \nrepresenting the toroidal component of the velocity field of the mode\n(e.g., Papaloizou \\& Pringle 1978 , Provost, Berthomieu \\& Rocca 1981, \nSaio 1982). \nOn the other hand, the inertial modes have the comparable toroidal and\nspheroidal components of the velocity field and therefore they are not necessarily\nrepresented by a single spherical harmonic function\n(e.g, Lee, Strohmayer \\& Van Horn 1992, Yoshida \\& Lee 2000). \nNote that the inertial mode of this kind is also called ``rotation mode'' or \n``generalized $r$-mode'' (Lindblom \\& Ipser 1998, Lockitch \\& Friedman 1999). \n\n\n\nMost of the recent studies on the $r$-mode instability\ndriven by the gravitational radiation reaction are restricted to \nthe case of neutron stars with isentropic structure, since the barotropic\n(one-parameter) equation of state, $p=p(\\rho)$ is usually assumed for\nboth the interior structure and the small amplitude oscillation.\nIn isentropic stars\nthe specific entropy of the fluid in the interior is constant and\nthe buoyant force has no effects on the oscillation.\nHowever, stars in general have non-isentropic interior structure, \nwhich may be divided into\ntwo kinds of layers with fluid stratification \nstable or unstable against convection.\nIt is well know that the property of the oscillation modes of\nnon-isentropic stars is substantially different from that of isentropic stars,\nsince the buoyant force comes into play as a restoring force for \nlow frequency oscillations like $g$-mode propagating in the layers with the stable \nstratification (see, e.g., Unno et al 1989).\nThis is also the case for rotational modes, which have low oscillation\nfrequencies comparable to the spin rate $\\Omega$ of the star.\nFor example, we note that\nthe $r$-mode associated with $l'=|m|$ having the nodeless eigenfunction in the\nradial direction is the only $r$-mode permitted in an isentropic star for a given $m$\n(e.g, Lockitch \\& Friedman 1999, Yoshida \\& Lee 2000), \nbut in non-isentropic stars with the stable fluid stratification all\nthe $r$-modes with $l'\\ge |m|$ are possible for a given $m$, and there are\nin principle an infinite number of $r$-modes for given $l'$ and $m$\n(e.g., Provost et al 1981, Saio 1982, Lee \\& Saio 1997). \nWe therefore consider it important to investigate the modal properties of \nthe rotational modes in non-isentropic stars, particularly in order to\nanswer the question whether the property of \nthe $r$-mode instability for neutron star models with non-isentropic structure\nremains the same as that for isentropic neutron star models.\n\n\n\n\nIn this paper, we study the $r$-mode and the inertial mode oscillations\nof slowly rotating, non-isentropic, Newtonian stars, where\nuniform rotation and adiabatic oscillation are assumed\nto simplify the mathematical treatments. \nThe effects of the rotational deformation of the equilibrium structure \non the eigenfunction and eigenfrequency are included in the analysis, \nusing the formulation by Yoshida \\& Lee (2000) \n(see also Lee \\& Saio 1986, Lee 1993).\nWe employ simple polytropic models \nwith the polytropic index $n=1$\nas the background neutron star models.\nFor the non-isentropic models we consider only two cases, that is,\nthe models that have stable fluid stratification in the whole interior\nand those that are in convective equilibrium.\nIn this paper, following the conventions used \nin the field of stellar evolution and pulsation, \nwe simply call these two kinds of models\n``radiative'' and ``convective'' models, respectively, although\nno energy transport in the interior is considered.\nThe plan of this paper is as follows. \nIn \\S 2, we briefly describe the basic equations employed in the linear modal analysis\nof slowly rotating stars.\nIn \\S 3, we show numerical results for the rotational modes of non-isentropic \nstars, and discuss the properties of the eigenfrequency and eigenfunction of the modes.\nIn \\S 4, we examine the stability of simple neutron star models\nagainst the $r$-modes, computing their growth or damping timescales due \nto the gravitational radiation reaction and some viscous damping processes.\n\\S 5 is for conclusions.\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% II. Method of Solutions %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\section{Method of Solutions}\n\n\nThe method of solutions used in this paper is exactly the same as that \napplied in Yoshida \\& Lee (2000). Here, therefore, we briefly describe \nthe basic equations and the method of calculation. \nThe details are given in Yoshida \\& Lee (2000). \n\n\\subsection{Equilibrium Configurations}\n\n\nWe consider oscillations of uniformly rotating Newtonian stars. \nThus the angular rotation frequency of the star, $\\Omega$ is constant.\nWe assume the polytropic relation for the equilibrium structure of the model, \nand the relation between the pressure $p$ and the mass density $\\rho$ is given by\n%\n\\begin{equation}\np = K \\, \\rho^{1 + \\frac{1}{n}} \\, ,\n\\end{equation}\n%\nwhere $n$ and $K$ are the polytropic index and the structure constant determined by\ngiving the mass and the radius of the model, \nrespectively. \nIn this investigation, assuming slow rotation, we employ \nthe Chandrasekhar-Milne expansion (see, e.g, Tassoul 1978) to obtain \nthe equilibrium structure of rotating stars. \nIn this technique the effects of the \ncentrifugal force and the equilibrium deformation are treated \nas small perturbations to the non-rotating spherical symmetric structure \nof the star. \nThe small expansion parameter due to rotation is chosen as \n$\\bar{\\Omega}=\\Omega (R^3/G M)^{1/2}$, where $R$ and $M$ are \nthe radius and the mass of the non-rotating star, respectively. \nThe equilibrium configurations are constructed with accuracy up to the order of \n${\\bar{\\Omega}}^2$. For simplicity, we consider a sequence of slowly \nrotating stars whose central density is the same as that of the \nnon-rotating star. \n\n\n\\subsection{Perturbation Equations}\n\n\n\nIn the perturbation analysis, we introduce a parameter $a$ that is \nconstant on the distorted effective potential surface of the star. In practice, \nthe parameter $a$ is defined such that\n%\n\\begin{equation}\n\\Psi (r,\\theta) = \\Psi_0 (a) \\, , \\label{ep-co}\n\\end{equation}\n%\nwhere $\\Psi_0$ and $\\Psi$ are the effective potentials for the non-rotating \nand slowly rotating models, respectively. Note that $\\Psi_0$ is equal to \nthe gravitational potential and $\\Psi$ is the sum of the gravitational \npotential and the centrifugal potential. With this parameter $a$, \nthe distorted equi-potential surface may be given by\n%\n\\begin{equation}\nr = a \\lbrace 1 + \\epsilon (a,\\theta,\\varphi) \\rbrace \\, ,\n\\label{def-a}\n\\end{equation}\n%\nwhere $\\epsilon$ is the function of the order of \n${\\bar{\\Omega}}^2$, and is obtained by giving the functional forms\nof $\\Psi$ and $\\Psi_0$ using the Chandrasekhar-Milne expansion (Yoshida \\& Lee 2000). \nHere we have used spherical polar coordinates $(r,\\theta,\\varphi)$. \nHowever, we employ hereafter the parameter $a$ as the radial coordinate, \nin stead of the polar radial coordinate $r$.\n\n\nThe governing equations of nonradial oscillations of a rotating star are \nobtained by linearizing the basic equations used in fluid mechanics\n(e.g., Unno et al 1989). \nIn the following, we use $\\delta$ and $\\Delta$ to denote the Eulerian and \nthe Lagrangian changes of physical quantities, respectively.\nSince the equilibrium state is assumed to be stationary and axisymmetric, \nthe perturbations may be\nrepresented by a Fourier component proportional to \n$e^{i(\\sigma t + m \\varphi)}$, where $\\sigma$ is the frequency observed in \nan inertial frame and $m$ is the azimuthal quantum number. \nThe continuity equation may be linearized to be\n%\n\\begin{equation}\n\\delta \\rho = - \\nabla_i (\\rho \\xi^i), \\label{del_rho} \\label{mass_con} \n\\end{equation}\n%\nwhere $\\xi^i$ is the Lagrangian displacement vector, and we have made use of\n$\\delta v^i = i(\\sigma + m \\Omega) \\xi^i \\equiv i \\omega \\xi^i$\nwith $\\omega$ being the oscillation frequency observed in the corotating \nframe of the star. \nHere $\\nabla_i$ denotes the covariant derivative derived from the metric\n$g_{ij}$. \n\nIn this study, we consider only adiabatic oscillations. \nThus, the perturbed equation of state is given by\n\\begin{equation}\n\\delta p = \\Gamma p \\left( \\frac{\\delta \\rho}{\\rho} +\n\\xi^i A_i \\right) \\, , \\label{del_p} \n\\end{equation}\n%\nwhere\n$\\Gamma$ is the adiabatic exponent defined as\n%\n\\begin{equation}\n\\Gamma = \\left( \\frac{ \\partial \\ln p}{\\partial \\ln \\rho} \\right)_{ad} \\, ,\n\\end{equation}\n%\nand $A_i$ is the generalized Schwarzschild discriminant\\footnote{Since \nthe Schwarzschild discriminant $A_i$ is proportional to $\\nabla_i s$ with $s$\nbeing the specific entropy, a model with $A_i=0$ \nthroughout the interior is called isentropic model in this paper.\nUsing the same barotropic \n(one-parameter) equation of state, $p=p(\\rho)$ for both\nthe equilibrium structure and the perturbation leads to isentropic models.} given by\n%\n\\begin{equation}\nA_i \\equiv \\frac{1}{\\rho} \\nabla_i \\rho - \\frac{1}{\\Gamma p} \\nabla_i p \\, ,\n\\label{def_A}\n\\end{equation}\n%\nand the positive and negative values of $A_i$ indicate the fluid stratification\nunstable and stable against convection, respectively.\n\n\nThe linearized Euler's equation is\n\\begin{equation}\n-\\omega^2 \\xi_i + \\nabla_i \n\\left( \\frac{\\delta p}{\\rho} + \\delta \\Phi \\right) + \n\\left(\\frac{\\delta p}{\\rho} \\, g_{ij}+\\xi_j \\frac{1}{\\rho} \\nabla_i p\n\\right) \\, A^j + \n2 i \\omega \\Omega \\xi^j \\nabla_j \\varphi_i \n= 0 \\, , \\label{pert_Euler}\n\\end{equation}\n%\nwhere $\\Phi$ denotes the gravitational potential, \nand $\\varphi^i$ is the rotational Killing vector, with which the 3-velocity\nof the equilibrium fluid of a rotating star is given as \n$v^i=\\Omega\\varphi^i$. The perturbed Poisson equation is\n%\n\\begin{equation}\n\\nabla_i \\nabla^i \\delta \\Phi = 4\\pi G\\delta \\rho \\, ,\n\\label{pert_Poisson}\n\\end{equation}\n%\nwhere $G$ is the gravitational constant. \n\n\n\n\nPhysically acceptable solutions of the linear differential equations are \nobtained by imposing boundary conditions at the inner and outer \nboundaries of the star. The inner boundary conditions are the regularity \ncondition of the perturbed quantities at the stellar center. \nThe outer boundary conditions at the surface of the star are \n$\\Delta p/\\rho=0$\nand the continuity of the perturbed gravitational potential at the surface to\nthe solution of $\\nabla_i\\nabla^i\\delta\\Phi=0$ that vanishes at the infinity.\n\n\nIn order to solve the system of partial differential equations given above, \nwe employ the series expansion in terms of spherical harmonics to\nrepresent the angular dependence of the perturbed quantities.\nThe Lagrangian displacement vector, $\\xi^i$ is expanded in terms of the \nvector spherical harmonics as\n%\n\\begin{equation} \n\\xi^a = \\sum_{l\\geq\\vert m \\vert}^{\\infty} a \\, S_l(a) \nY_l^m (\\theta,\\varphi) e^{i \\sigma t} \\, , \\label{v_a}\n\\end{equation}\n%\n\\begin{equation}\n\\xi^\\theta = \\sum_{l,l'\\geq\\vert m \\vert}^{\\infty} \n\\left\\{ H_l (a) {Y_l^m}_{,\\theta} + T_{l'} (a) \\frac{1}{\\sin \\theta} \\, \n{Y_{l'}^m}_{,\\varphi} \\right\\} e^{i \\sigma t} \\, , \\label{v_t}\n\\end{equation}\n%\n\\begin{equation}\n\\xi^\\varphi = \\frac{1}{\\sin^2 \\theta} \n\\sum_{l,l'\\geq\\vert m \\vert}^{\\infty} \\left\\{ H_l (a) {Y_l^m}_{,\\varphi}\n - T_{l'} (a) {\\sin \\theta} \\, {Y_{l'}^m}_{,\\theta}\n \\right\\} e^{i \\sigma t} \\, \\label{v_p} \n\\end{equation}\n%\n(Regge \\& Wheeler 1957, see also Thorne 1980). \nThe perturbed scalar quantity such as $\\delta \\Phi$ is expressed as\n%\n\\begin{equation} \n\\delta \\Phi = \\sum_{l\\geq\\vert m \\vert}^{\\infty} \\delta \\Phi_l (a) \\, \nY_l^m (\\theta,\\varphi) e^{i \\sigma t} \\, . \\label{d_phi}\n\\end{equation}\n%\nHere, the expansion coefficients $T_{l'}$ are called ``axial'' \n(or ``toroidal'') and the other coefficients are called \n``polar'' (or ``spheroidal''). It is known that\nthese two set of components are decoupled when $\\Omega=0$.\n\n\nSubstituting the perturbed quantities expanded in terms of the spherical \nharmonics into the linearized basic \nequations ($\\ref{del_rho}$), ($\\ref{del_p}$), ($\\ref{pert_Euler}$) \nand ($\\ref{pert_Poisson}$), we obtain an infinite system of coupled linear \nordinary differential equations for the expansion coefficients. \nNotice that the system of differential equations employed in this paper\nis arranged to give\neigenfunctions and eigenfrequencies consistent up to the order of $\\bar\\Omega^3$ \nfor slow rotation.\nThe explicit expressions for the governing equations are given in Appendix of \nYoshida \\& Lee (2000). \n\n\nSince the equilibrium state of a rotating star is invariant under \nthe parity transformation defined by $\\theta \\to \\pi - \\theta$, \nthe linear perturbations have definite parity for that transformation. \nIn this paper, a set of modes whose scalar perturbations such as \n$\\delta \\Phi$ are symmetric with respect to the equator is called ``even'' \nmodes, while the other set of modes whose scalar perturbations are antisymmetric \nwith respect to the equator is called ``odd'' modes \n(see, e.g., Berthomieu et al. 1978).\nFor positive integers $j=1,~2,~3,~\\cdots$, we have $l=|m|+2j-2$ and \n$l'=l+1$ for even modes, and $l=|m|+2j-1$ and $l'=l-1$ for odd modes, \nwhere the symbols $l$ and $l'$ have been used to denote the spheroidal \nand toroidal components of the displacement vector $\\xi^i$, \nrespectively (see equations (\\ref{v_a})--(\\ref{d_phi})). \nNote that we do not use the term of the even (the odd) parity mode to refer to\nthe polar (the axial) mode, although this terminology is used traditionally in \nrelativistic perturbation theory (e.g., Regge \\& Wheeler 1957). \n\n\nOscillations of rotating stars are also divided into prograde and retrograde modes.\nWhen observed in the corotating frame of the star,\nwave patterns of the prograde modes are propagating\nin the same direction as rotation of the star, \nwhereas those of the retrograde modes are\npropagating in the opposite direction to the rotation.\nFor positive values of $m$, the prograde and retrograde modes have negative and positive\n$\\omega$, respectively.\n\n\n\nFor numerical calculations, we truncate the infinite set of linear \nordinary differential equations to obtain a finite set by discarding all \nthe expansion coefficients associated with $l$ higher than $l_{max}$. \nThis truncation determines the number of the expansion coefficients \nkept in the spherical harmonic expansion of each perturbed quantity. \nWe denote this number as $k_{max}$. Our basic equation becomes a \nsystem of $4\\times k_{max}$-th order linear ordinary differential equations, which,\ntogether with the boundary conditions, are numerically solved as an \neigenvalue problem of $\\omega\\equiv \\sigma+m\\Omega$ by using a Henyey type \nrelaxation method (e.g., Unno et al . 1989, see also Press et al. 1992).\n\n\n\nWe cannot determine a priori $k_{max}$,\nthe number of the expansion coefficients kept in the eigenfunctions. \nIn this paper, we start with an appropriate trial \nvalue of $k_{\\mbox{\\tiny max}}$ to compute an oscillation mode \nat a given value of $\\bar\\Omega$. \nThen, we increase the \nvalue of $k_{\\mbox{\\tiny max}}$, until the eigenfrequency converges within \nan appropriate numerical error, where the mode identification is done\nby examining the form and the number of nodes of the dominant expansion coefficients.\nWe consider that the mode thus obtained\nwith the sufficient number of the expansion coefficients\nis the correct oscillation mode we want for the rotating model at $\\bar\\Omega$.\n\n\n\nIn order to check our numerical code, we calculate eigenfrequencies of \nthe $r$-modes of the $n=3$ and $\\Gamma=5/3$ polytropic model \nat $\\bar{\\Omega}=0.1$. In Table 1, our \nresults are tabulated together with those calculated by Saio (1982) \nby using a semi-analytical \nperturbative approach. As shown by Table 1, our results are in good \nagreement with Saio's results. \n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% III. Rotational Modes of Non-isentropic.... %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\section{Rotational Modes of Slowly Rotating Non-isentropic Stars}\n\n\nBecause it is believed that \nisentropic structure is a good approximation for young and hot neutron stars,\nin this study we concentrate our attention to the case that \nthe deviation of the non-isentropic models from isentropic structure \nis sufficiently small.\nIn this case, we may assume that the adiabatic exponent $\\Gamma$ is given by\n% \n\\begin{eqnarray} \n\\frac{1}{\\Gamma} = \\frac{n}{n+1} + \\gamma \\, ,\n\\label{def-gamma}\n\\end{eqnarray}\n%\nwhere $\\gamma$ is a constant giving the deviation from the isentropic structure.\nBy substituting equation (\\ref{def-gamma}) into equation (\\ref{def_A}), \nwe obtain an explicit form of $A_i$ as:\n%\n\\begin{eqnarray}\nA_i &=& - \\, \\gamma \\, \\nabla_i \\ln p \\, .\n\\end{eqnarray}\n%\nIn this study, we only consider oscillations of polytropic models with the index $n=1$.\nPositive and negative values of $\\gamma$ are respectively for convective and radiative\nmodels.\nIsentropic models are given by $\\gamma=0$.\nSince our formulation for stellar oscillations of rotating stars is \naccurate only up to the order of $\\bar{\\Omega}^3$, we shall apply our method \nto the oscillation modes in the range of $\\bar\\Omega\\le 0.1$.\n \n\nFor convenience of later discussions, it may be useful to review\nthe properties of $r$-modes and inertial modes\nof isentropic models with $\\gamma=0$ (see, e.g., Yoshida \\& Lee 2000). \nBecause of \nthe asymptotic behavior of the eigenfrequency of the rotational modes\nin the limit of $\\Omega\\rightarrow 0$, it is \nconvenient to introduce a non-dimensional frequency $\\kappa$ as follows:\n%\n\\begin{equation}\n\\frac{\\omega}{\\Omega} = \\kappa \\, . \\label{def-kappa}\n\\end{equation}\n%\nSince the rotational deformation is of the order of $\\bar\\Omega^2$,\nthe effects on the frequency of the rotational modes appear as the terms of \nthe order of $\\bar\\Omega^3$. \nTherefore, we may expand the dimensionless \neigenfrequency $\\kappa$ of the rotational modes in powers of $\\bar\\Omega$ as follows: \n%\n\\begin{equation}\n\\kappa = \\kappa_0 + \\kappa_2 \\, \\bar{\\Omega}^2 \n + O(\\bar{\\Omega}^4) \\, , \\label{def-kappa0}\n\\end{equation}\n%\nwhere\n%\n\\begin{equation}\n\\kappa_0 = \\frac{2 m}{l'(l'+1)} \\, \n\\label{r-fre}\n\\end{equation}\n%\nfor the $r$-modes associated with the indices \n$l'$ and $m$ of vector harmonics with the axial \nparity (see, e.g. Papaloizou \\& Pringle 1978).\nFor the inertial modes, there is no analytic expression for $\\kappa_0$ in general.\n\n\n\nAs suggested by Provost et al. (1981) and Saio (1982),\nthe $r$-mode associated with $l'=|m|$\nhaving the nodeless eigenfunction $T_{l'}(r)$ is the only $r$-mode permitted\nfor isentropic stars for a given $m$.\nIn the limit of $\\Omega\\rightarrow 0$, we have \n$\\kappa\\rightarrow\\kappa_0=2m/l'(l'+1)$.\nAmong the expansion coefficients of the eigenfunctions \nthe toroidal component $T_{l'=|m|}$ is dominating.\nFor the inertial modes,\nthe value of $\\kappa$ in the limit of $\\Omega\\rightarrow 0$\nis also finite but different from \n$\\kappa_0 = {2 m}/{l'(l'+1)}$. \n\nThe inertial modes are characterized by the two angular \nquantum numbers $l_0$ and $m$, where the value of $l_0$ is \nthe maximum index $l$ of spherical harmonics associated with \nthe dominant expansion coefficients \nof the eigenfunctions (see Lockitch \\& Friedman 1999, Yoshida \\& Lee 2000). \nNote that our definition of $l_0$ is not the same as that of Lockitch \\& \nFriedman (1999), but the same as that of Lindblom \\& Ipser (1998) and \nYoshida \\& Lee (2000).\nNote also that odd (even) parity modes have odd (even) values\nof $l_0-|m|$, and that\nthe odd parity mode having $l_0-|m|=1$ is the $r$-mode associated with $l'=|m|$.\nThe value of $\\kappa_0$ for the inertial modes depends not only on the\nindices $m$ and $l_0$, but also on the equilibrium structure \nof stars (e.g., Yoshida \\& Lee 2000). \nFor given values of $l_0$ and $m$, the number of different inertial modes is\nequal to $l_0 - \\vert m\\vert(\\ge 2)$. \nHowever, there seems to be no good quantum number to classify the different inertial\nmodes associated with the same $l_0$ and $m$.\nWe here introduce an ordering integer $n$ to use the labellings such as \n$i_n$ and $\\omega_n$ for these inertial modes.\nSince the frequencies of the inertial modes with the same $l_0$ and $m$\nare found in a sequence given by, in the case of $m>0$,\n%\n\\begin{equation}\n\\omega_{-(l_0 - \\vert m\\vert-1)/2} < \\cdots < \\omega_{-1} < 0 \\leq \n\\omega_{0} < \\omega_{1} < \\cdots < \n\\omega_{(l_0 - \\vert m\\vert-1)/2}\\, \n\\end{equation}\n% \nfor odd parity modes, and\n%\n\\begin{equation}\n\\omega_{-(l_0 - \\vert m\\vert)/2} < \\cdots < \\omega_{-1} < 0 < \n\\omega_{1} < \\cdots < \n\\omega_{(l_0 - \\vert m\\vert)/2}\\, \n\\end{equation}\n%\nfor even parity modes, we may define \nthe ordering number $n$ as an integer that satisfies\nthe inequality $|l_0-|m|-1|/2\\ge |n| \\ge 0$ for odd parity inertial modes, and\n$|l_0-|m||/2\\ge |n| >0$ for even parity inertial modes\n(see Lockitch \\& Friedman 1998, Yoshida \\& Lee 2000).\nWe apply this classification to the inertial modes of both isentropic and \nnon-isentropic stars in the following discussions.\n\n\n\n\\subsection{$r$-modes}\n\n\n\nFor the radiative models, all the\n$r$-modes associated with $l'\\ge |m|$ are possible for a given $m$, \nand there are in principle \na countable infinite number of $r$-modes for given $l'$ and $m$. \nThe $r$-modes with the same $l'$ and $m$ may be classified by counting\nthe number of nodes\nof the axial components $T_{l'}$ in the radial direction.\nFor them the values of $\\kappa_2$ are different, but the values of $\\kappa_0$\nare the same and equal to $2m/l'(l'+1)$.\nIt is important to note that this classification \nof the $r$-modes is applicable only in the limit of $\\bar\\Omega\\rightarrow 0$\nand $\\kappa\\rightarrow \\kappa_0=2m/l'(l'+1)$, \nsince \nthe components associated with the other values of $l'$ will come into play \nfor large $\\bar\\Omega$\n(see, e.g. Provost et al. 1981, Saio 1982).\nLet us introduce an integer $k$ to denote\nthe number of nodes of the toroidal eigenfunction $T_{l'}$,\nwhere the node at the center of the \nstar is excluded from the count.\nThen, the $r$-modes are \ncompletely specified by the three quantum numbers $m$, $l'$ and $k$. \nIn this paper, for given $l'$ and $m$,\nwe employ the notation of $r_k$ to denote the $r$-mode whose \ntoroidal eigenfunction $T_{l'}(r)$ has $k$ nodes in the radial direction.\n\n\nIn Figures 1 to 3, the dimensionless eigenvalues $\\kappa$ are given versus \n$\\bar{\\Omega}$ for several \nlow-radial-order $r$-modes with $m=1$, 2, and 3\nfor the $n=1$ polytropic model with $\\gamma=-10^{-4}$, where\nthe $r$-modes with $l'= |m|$, $l'= |m| + 1$ and \n$l'= |m| + 2$ are given in each figure.\nModes with $l'= |m| + 1$ \nare even parity modes, and those with $l'=|m|$ and $l'=|m|+2$ are odd parity modes. \nIn the figures, the eigenvalues $\\kappa$ of the $i_0$-modes with $l_0=|m|+2 k+1$,\ncalculated at $\\bar{\\Omega}=0.1$ \nfor the $n=1$ isentropic model, are designated by\nthe filled circles, where the integer $k$ corresponds to the number in the subscript \nof the notation $r_k$.\nFigures 1 to 3 clearly show that\nthe qualitative behavior of the eigenfrequencies as functions of $\\bar\\Omega$\nis not strongly dependent on the azimuthal quantum number $m$. \nFrom these figures we also understand that\nthe $r$-modes of the radiative model with $\\gamma < 0$\nare divided into three distinctive classes according to the asymptotic \nbehavior of the eigenvalues at large $\\bar\\Omega$.\n%\nThe first class of the $r$-modes consists of the nodeless $r_0$-modes \nassociated with $l'=|m|$. \nThe eigenvalue $\\kappa$ of the $r$-modes of this class is well approximated by \nequations (17) and (18) at any values of $\\bar\\Omega$ examined in this paper.\nNote that the $r_0$-mode with $m=l'=1$ is a \npeculiar mode in the sense that $\\kappa$ is almost constant since\n$\\kappa_2=0$ and $\\kappa=\\kappa_0+O(\\bar\\Omega^4)$ (see Saio 1982, Greenspan 1964). \n%\nThe second class consists of the $r_k$-modes with \n$l'=\\vert m \\vert$ and $k>0$. \nEquations (\\ref{def-kappa0}) and (\\ref{r-fre}) can give good values for \nthe eigenvalue $\\kappa$ of the $r$-modes of this class\nonly when $\\bar{\\Omega}$ is sufficiently small.\nAs $\\bar\\Omega$ increases, $\\kappa$ tends to\nthe $i_0$ inertial modes with $l_0=|m|+2 k+1$ of the isentropic model. \nNote that the $i_0$-modes are odd parity inertial modes \n(see equations (19) and (20)).\nWe therefore consider that at large $\\bar\\Omega$ \nthe $r_k$-modes of this class become\nidentical with the $i_0$-modes with $l_0=|m|+2 k+1$, for which $\\kappa$\nis almost constant.\n%\nThe third class of the $r$-modes consists of the $r_k$-modes with \n$l' > \\vert m \\vert$ and $k\\ge0$.\nThe eigenvalue $\\kappa$ of the $r$-modes of this class is well represented by\nequations (17) and (18) only when $\\bar\\Omega$ is sufficiently small, and\nit becomes small monotonically as $\\bar\\Omega$ increases.\nThe $r$-modes of this class may have no corresponding inertial modes\nof the isentropic model.\n\n\nAs proved by Friedman \\& Schutz (1978), oscillation modes whose frequency $\\sigma$\nobserved in an inertial frame\nsatisfies the condition $\\sigma(\\sigma+m\\Omega)=\\sigma\\omega<0$ \nare unstable to the gravitational radiation reaction. \nThe condition for the instability\nmay be rewritten as $0 < \\kappa < m$ for retrograde modes with $\\omega>0$ and $m>0$. \nFigures 1 to 3 show that the $r$-mode with $l'\\geq2$ \nsatisfies the inequality $0 < \\kappa < m$ for the range of $\\bar\\Omega$\nexamined in this paper.\nIt is also found that the $r_k$-modes with $l'=1$ \nand $k>0$ also satisfy the inequality $0 < \\kappa < m$ for $\\bar\\Omega>0$.\nThe reason for the instability of the $r_k$-modes with $l'=1$ and $k>0$ may be\nunderstood by noting that the \npolar components with the index $l=2$ can be responsible for the emission \nof gravitational radiation. \nWe may conclude that the $r_0$-mode with $l'=\\vert m\\vert=1$ is \nthe only $r$-mode that is stable against \nthe gravitational radiation reaction. \n \n\n \nIn Figure 4, the eigenfrequencies $\\kappa$ of three $r$-modes with $m=2$\nare plotted as functions of $|\\gamma|$, where\nwe have assumed $\\bar\\Omega=0.01$. \nThe three modes are respectively the $r_0$-mode with $l'=m=2$, \nthe $r_1$-mode with $l'=m=2$, and the $r_0$-mode with $l'=3$ and $m=2$.\nThese three $r$-modes belong to the first, second, and third classes of the $r$-modes\ndiscussed in the previous paragraph.\nThe solid lines and the dotted \nlines are used to denote the cases of negative and positive $\\gamma$, \nrespectively.\nNote that although we can obtain the three $r$-modes without any difficulty\nfor the radiative models with negative $\\gamma$, \nwe cannot always calculate the $r$-modes of the second and the third classes\nfor the convective models with positive $\\gamma$.\nLet us first discuss the case of the radiative models.\nAs shown by Figure 4, the eigenvalue $\\kappa$ of the $r_0$-mode with $l'=|m|=2$ \nis practically independent of $|\\gamma|$ and has values approximately equal to\n$\\kappa_0=2m/l'(l'+1)=2/3$.\nHowever, $\\kappa$ of the $r_1$-mode with $l'=|m|=2$ \nis dependent on $|\\gamma|$.\nAt small $|\\gamma|$, the $r_1$-mode has the eigenvalue close to $\\kappa_0=0.517$, \nwhich corresponds to \nthe inertial mode with $l_0-\\vert m \\vert = 3$ of the isentropic model, but \nit tends to $2m/l'(l'+1)=2/3$ as $|\\gamma|$ increases.\nThe $r_0$-mode with $l'=3$ and $m=2$ also has the eigenfrequency $\\kappa$\nwhich depends on $|\\gamma|$.\nAlthough the value of $\\kappa$ is close to $\\kappa_0=2m/l'(l'+1)=1/3$ \nat large $|\\gamma|$, it tends to zero as $|\\gamma|\\rightarrow 0$.\nThis behavior of $\\kappa\\rightarrow 0$ in the limit of $|\\gamma|\\rightarrow 0$\nis consistent with the fact that the $r$-modes associated with \n$l'> \\vert m\\vert$ do not exist in isentropic stars, for which $\\gamma=0$. \nLet us next discuss the case of the convective models with $\\gamma>0$.\nThe eigenvalue $\\kappa$ of the $r_0$-mode with $l'=|m|=2$ is only weakly dependent on\n$\\gamma$, as in the case of the radiative models.\nNote that the curves for the $r_0$-mode with $l'=|m|=2$ for negative and positive $\\gamma$\nare almost indistinguishable in Figure 4.\nThe $r_1$-mode with $l'=|m|=2$ for the convective models behaves differently than \nthat for the radiative models as $|\\gamma|$ increases.\nIn fact, the value of $\\kappa$ decreases\nrapidly with increasing $\\gamma$ and \nthe $r_1$-mode cannot be found at large values of $\\gamma>0$.\nNo $r_0$-mode with $l'=3$ and $m=2$ are found for the convective models.\n\n\n\nLet us discuss the properties of the eigenfunctions of the $r$-modes \nfor the radiative models.\nSince the amplitude of the displacement vector\nis much larger than that of the scalar perturbations, in the following discussions\nwe may show only the displacement vector of the modes.\nIn Figures 5 to 7, we show the expansion coefficients \n$S_l$, $H_l$ and ${\\it i} T_{l'}$ as functions of the fractional radius $a/R$\nfor the $r$-modes with $m=2$, where we have assumed $\\gamma=-10^{-4}$, and\nthe amplitude is normalized at the surface such that $iT_{l'}=1$. \nHere, $l=|m|$ and $l'=l+1$ for even modes, and $l=|m|+1$ and $l'=l-1$ for odd modes.\nThe modes given in Figures 5 to 7 are respectively\nthe $r_0$-mode with $l'=2$, the $r_1$-mode with $l'=2$, and the $r_0$-mode with $l'=3$. \nIn each figure, the eigenfunctions for the cases of \n$\\bar{\\Omega}= 10^{-3}$ and $\\bar{\\Omega}= 10^{-1}$ \nare shown in panels $(a)$ and $(b)$, respectively. \nThe panels $(a)$ of Figures 5 to 7 show that \nthe toroidal component $iT_{l'}$ of the $r$-modes is dominating the other expansion \ncoefficients when $\\bar\\Omega$ is small. \nHowever, as shown by the panels (b), although $iT_{l'}$\nof the $r_0$-mode with $l'=2$ remains dominant even at \n$\\bar{\\Omega}= 0.1$, the toroidal components $iT_{l'}$\nof the $r_1$-mode with $l'=2$ and the $r_0$-mode with $l'=3$\nare not necessarily dominating any more at $\\bar{\\Omega}= 0.1$.\nThe properties of the eigenfunctions of the $r_1$-mode with $l'=m=2$ \nat large $\\bar\\Omega$ may be regarded as those of the inertial modes. \n%\nIt is interesting to note that\nthe displacement vector of the $r_0$-mode with $l'=3$ has large amplitude \nin the deep interior and almost vanishing amplitude near the stellar \nsurface at large $\\bar\\Omega$. \nThis suggests that because of the low frequencies $\\omega$ in the corotating frame\nthe buoyant force is as important as the Coriolis force to determine the\nmode character at large $\\bar\\Omega$.\n \n\n\\subsection{Inertial modes}\n\n\nFor the radiative models with the polytropic index $n=1$ and $\\gamma = -10^{-4}$,\nthe eigenfrequencies $\\bar{\\omega}\\equiv\\omega/(GM/R^3)^{1/2}$ \nof low frequency oscillations\nare shown as functions of $\\bar\\Omega$\nfor $m=1$, 2, and 3 in Figures 8 to 10,\nwhere even and odd parity modes are displayed in panels (a) and (b), respectively.\nThe straight dashed lines drawn in the figures are given by\n$\\bar{\\omega}=0$ and $\\bar{\\omega}= m \\bar{\\Omega}$ (see below).\nIn the figures, the inertial modes of the $n=1$ isentropic model \ncomputed at $\\bar\\Omega=0.1$ are designated by the filled circles.\nWe note that the oscillation modes in a mode sequence\nare regarded as inertial modes when $\\bar\\Omega$ is large, and\nas internal gravity ($g$-) modes when $\\bar\\Omega$ is small.\nIf we follow one of the continuous mode sequences from large $\\bar\\Omega$ \nto small $\\bar\\Omega$,\nwe may physically understand the behavior of the low frequency oscillation \nin the radiative models as a function of $\\bar\\Omega$.\nAt large $\\bar\\Omega$, the Coriolis force is dominating as the restoring force\nand the oscillation mode is identified as an inertial mode.\nAs $\\bar\\Omega$ decreases, however, the buoyant force \nbecomes dominating the Coriolis force\nand the mode becomes identical with a $g$-mode \nin the limit of $\\bar\\Omega\\rightarrow 0$.\nBecause of the effects of the buoyant force in the radiative model,\nthe frequency $\\bar\\omega$ of the inertial modes deviates from that\nof the inertial modes of the isentropic model as $\\bar\\Omega$ decreases.\n\n\nThe modes within the two straight dashed lines depicted in Figures 8, 9 \nand 10 are\nunstable against the gravitational radiation driven instability \nin the sense that they satisfy the frequency condition\n$\\sigma(\\sigma+m\\Omega) < 0$ (Friedman \\& Schutz 1978).\nWe can see from Figure 8 that the $i_k$-modes with $k\\neq0$ and \n$m=1$ are stable against the instability for all $\\bar{\\Omega}$. \nFigures 9 and 10 show that as $\\bar\\Omega$ increases\nall the retrograde $g$-modes with $|m|\\geq 2$, which are stable \nagainst the instability when $\\bar\\Omega\\sim0$, \nbecome retrograde inertial modes, which are unstable against the instability \nat large $\\bar{\\Omega}$.\n\n\n\nThere are several cases where we find it practically impossible to\nobtain completely continuous mode sequences \nbetween the $g$-modes at small $\\bar\\Omega$ and\nthe inertial modes at large $\\bar\\Omega$.\nIn such sequences, there exist a domain of $\\bar\\Omega$, in which \nthere appear a lot of modes having a large number of nodes\nof the dominant expansion coefficients, and it is difficult to identify the\nsame oscillation modes as those computed in the previous steps in $\\bar\\Omega$.\nIn Figures 8 to 10, the domains of $\\bar\\Omega$ with this difficulty are indicated by\nthe dotted lines in the mode sequences.\nUnfortunately, we cannot remove the difficulty by increasing $k_{max}$.\nOne of the reasons for the difficulty may be attributed to the method of\ncalculation we employ in this paper.\nAs discussed in Unno et al (1989), since we have truncated \nthe infinite system of differential equations to obtain a finite system of equations,\nthe numerical procedure used here inevitably contains\na process of inverting matrices which are singular at some value of the ratio\n$2\\Omega/\\omega\\sim 1$, depending on the oscillation mode we are interested in.\nIn this paper, we assume that there always exist a continuous mode sequence\nbetween the $g$-mode and inertial mode as a function of $\\bar\\Omega$, \neven if the mode sequence contains\na domain of $\\bar\\Omega$ in which the modes we are interested in cannot be\nobtained numerically.\n\n\n\\subsection{Connection rules between the $g$-modes, $r$-modes and inertial modes}\n\n\n\nIn order to find \nthe connection rule between the $g$-modes at small $\\bar\\Omega$ and \nthe inertial modes at large $\\bar\\Omega$, we tabulate first the\nfrequencies of the $g$-modes at $\\bar\\Omega=0$ \nfor the radiative model with the index $n=1$ and $\\gamma=-10^{-4}$ in Table 2.\nTo obtain a clear understanding of the global correspondence between \nthe $g$-, $r$-, and inertial modes, with the help of Table 2 and Figures 8 to 10, \nwe give schematic diagrams\nfor the connection rules between the several low-radial-order modes as follows: \n\n\\noindent\nFor odd parity modes we have\n%\n\\begin{eqnarray}\n\\footnotesize\n&\\left[\n\\begin{array}{llll}\n & & &\\cdots\\\\\n & &\ni_{2\\phm{-}}(l_0=\\vert m\\vert+5)&\\cdots\\\\ \n &i_{1\\phm{-}}(l_0=\\vert m\\vert+3)&\ni_{1\\phm{-}}(l_0=\\vert m\\vert+5)&\\cdots\\\\\ni_{0\\phm{-}}(l_0=\\vert m\\vert +1)&i_{0\\phm{-}}(l_0=\\vert m\\vert+3)&\ni_{0\\phm{-}}(l_0=\\vert m\\vert+5)&\\cdots\\\\ \n &i_{-1}(l_0=\\vert m\\vert +3) &\ni_{-1}(l_0=\\vert m\\vert +5) &\\cdots\\\\\n & &\ni_{-2}(l_0=\\vert m\\vert +5) &\\cdots\\\\\n & & &\\cdots\\\\\n\\end{array} \n\\right]& \\label{ina-odd}\\\\\n& & \\nonumber\\\\\n&\\Updownarrow& \\nonumber\\\\\n& & \\nonumber\\\\\n&\\left[\n\\begin{array}{llll}\n & & &\\cdots\\\\\n & &g_{1\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert+3)&\\cdots\\\\ \n &g_{1\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert+1)&\ng_{2\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert+1)&\\cdots\\\\\nr_{0\\phm{-}}(l'_{\\phm{0}}=\\vert m\\vert)\\phm{+1}& \nr_{1\\phm{-}}(l'_{\\phm{0}}=\\vert m\\vert)\\phm{+3}&\nr_{2\\phm{-}}(l'_{\\phm{0}}=\\vert m\\vert)\\phm{+5}&\\cdots\\\\\n &g_{-1}(l_{\\phm{0}}=\\vert m\\vert+1)&\ng_{-2}(l_{\\phm{0}}=\\vert m\\vert+1)&\\cdots\\\\\n & &g_{-1}(l_{\\phm{0}}=\\vert m\\vert+3)&\\cdots\\\\\n & & &\\cdots\\\\\n\\end{array}\n\\right]& \\ , \\label{gra-odd}\n\\end{eqnarray}\n%\nand for even parity modes we have\n%\n\\begin{eqnarray}\n\\footnotesize\n&\\left[\n\\begin{array}{llll}\n & & &\\cdots\\\\\n & &i_{3\\phm{-}}(l_0=\\vert m\\vert+6)&\\cdots\\\\ \n &i_{2\\phm{-}}(l_0=\\vert m\\vert+4)&\ni_{2\\phm{-}}(l_0=\\vert m\\vert+6)&\\cdots\\\\\ni_{1\\phm{-}}(l_0=\\vert m\\vert+2)&i_{1\\phm{-}}(l_0=\\vert m\\vert+4)&\ni_{1\\phm{-}}(l_0=\\vert m\\vert+6)&\\cdots\\\\\ni_{-1}(l_0=\\vert m\\vert+2) &i_{-1}(l_0=\\vert m\\vert+4) &\ni_{-1}(l_0=\\vert m\\vert+6)&\\cdots\\\\\n &i_{-2}(l_0=\\vert m\\vert+4) &\ni_{-2}(l_0=\\vert m\\vert+6)&\\cdots\\\\\n & &i_{-3}(l_0=\\vert m\\vert+6)&\\cdots\\\\\n & & &\\cdots\\\\\n\\end{array} \n\\right]& \\label{ina}\\\\\n& & \\nonumber\\\\\n&\\Updownarrow& \\nonumber\\\\\n& & \\nonumber\\\\\n&\\left[\n\\begin{array}{llll}\n & & &\\cdots\\\\\n & &g_{1\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert+4) &\\cdots\\\\ \n &g_{1\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert+2)&\n g_{2\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert+2)&\\cdots\\\\\ng_{1\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert)\\phm{+2}& \ng_{2\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert)\\phm{+4}&\ng_{3\\phm{-}}(l_{\\phm{0}}=\\vert m\\vert)\\phm{+6}&\\cdots\\\\\ng_{-1}(l_{\\phm{0}}=\\vert m\\vert)\\phm{+2} & \ng_{-2}(l_{\\phm{0}}=\\vert m\\vert)\\phm{+4} &\ng_{-3}(l_{\\phm{0}}=\\vert m\\vert)\\phm{+6} &\\cdots\\\\\n &g_{-1}(l_{\\phm{0}}=\\vert m\\vert+2) &\n g_{-2}(l_{\\phm{0}}=\\vert m\\vert+2) &\\cdots\\\\\n & &g_{-1}(l_{\\phm{0}}=\\vert m\\vert+4) &\\cdots\\\\\n & & &\\cdots\\\\\n\\end{array}\n\\right]& \\ , \\label{gra}\n\\end{eqnarray}\n%\nwhere the two corresponding modes occupy the same position \nin the two matrices connected with an arrow. \n\n\nFrom the diagrams,\nwe may find the connection rule between the $g_{\\pm k}$-modes with $l$ and $m$ and \nthe inertial modes $i_{\\pm j}$ with $l_0$ and $m$: \n\\begin{equation}\ng_{\\pm k}(l=l^j)\\longleftrightarrow i_{\\pm j}(l_0=l^j+2k), \\label{g-i}\n\\end{equation}\nwhere $l^j=|m|+2j-2$ for even modes and $l^j=|m|+2j-1$ for odd modes,\nand $j$ and $k$ are positive integers.\n%\nThe symbol $g_{\\pm k}$ denotes the $g$-mode\nwith $k$ radial nodes of the expansion coefficient $S_l$, \nhaving positive and negative frequencies $\\omega$\nobserved in the corotating frame of the star when $\\bar\\Omega\\not=0$.\n\n\nThe connection rule between the $r$-modes\nassociated with $l'=|m|$ and the inertial modes $i_0$ with $l_0$ and $m$ may be given by\n%\n\\begin{equation}\nr_{j-1} ( l' = \\vert m \\vert ) \\longleftrightarrow i_0 \n(l_0 = |m| + 2 j -1) \\, ,\n\\label{r-i-odd}\n\\end{equation}\n%\nwhere $j$ is a positive integer.\nNote that the \n$i_0$-mode with $l_0 = \\vert m \\vert +1$ is exactly the same as \nthe $r_0$-modes with $l'=\\vert m \\vert$. \nTo establish the connection rules given above, we have neglected the effects of\navoided crossings between the modes associated with different values of $l$ and/or $k$, since\nthe mode property is carried over at the crossings.\n\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% V. DISSIPATION TIMESCALES ..... %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\section{Dissipation Timescales for $r$-modes of Non-isentropic Stars}\n\n\nFor the rotational modes of non-isentropic models, we have found that\nall the $r$-modes except the $r_0$-mode with $l'=|m|=1$ \nare unstable to the gravitational radiation reaction \nin the sense that the frequency $\\sigma$ satisfies the condition \n$\\sigma(\\sigma+m\\Omega)<0$.\nLet us determine the stability of the $r$-modes of the non-isentropic models\nagainst the gravitational radiation driven instability, taking account of\nthe dissipative processes due to the shear and bulk viscosity, where\nwe will follow the method of calculation almost the same as that employed\nin the previous stability analyses of the $r_0$-mode with $l'=|m|$ and the\ninertial modes for isentropic models\n(Lindblom et al 1998, Owen et al 1998, Andersson et al 1998, \nKokkotas \\& Stergioulas 1998, Lindblom et al 1999, Lockitch \\& Friedman 1999,\nYoshida \\& Lee 2000).\n\n\n\n\n\nThe damping timescale of the $r_0$-mode associated with $l'=|m|$\nfor sufficiently small $\\bar{\\Omega}$ may be estimated by (Lindblom et al 1998)\n%\n\\begin{eqnarray}\n\\frac{1}{\\tau} &=& \\frac{1}{\\tilde \\tau_S} \\left( \\frac{10^9 K}{T} \\right)^2\n+ \\frac{1}{\\tilde \\tau_B} \\left( \\frac{T}{10^9 K} \\right)^6\n\\left( \\frac{\\Omega^2}{\\pi G \\bar{\\rho}} \\right) \\nonumber \\\\\n&+& \\sum_{l=2}^{\\infty} \\frac{1}{\\tilde \\tau_{J,l}} \n\\left( \\frac{\\Omega^2}{\\pi G \\bar{\\rho}} \\right)^{l+1}\n+ \\sum_{l=2}^{\\infty} \\frac{1}{\\tilde \\tau_{D,l}} \n\\left( \\frac{\\Omega^2}{\\pi G \\bar{\\rho}} \\right)^{l+2} \\, ,\n \\label{tau2}\n\\end{eqnarray}\n%\nwhere $\\bar{\\rho}$ is the average density of the star.\nThe dissipative timescales $\\tilde\\tau$ are calculated for each oscillation mode\nin the limit of $\\bar\\Omega\\rightarrow 0$ so that\nthey are independent of the rotation frequency $\\Omega$.\nHere, the first, second, third and fourth terms in the right-hand side of \nequation (\\ref{tau2}) are contributions from the shear viscosity, \nthe bulk viscosity, the current multipole radiation and the mass \nmultipole radiation, respectively. \nThe expression (\\ref{tau2}) of the damping timescales has been derived on the assumptions that\nthe frequency of the modes is well represented by a linear function of $\\Omega$ and the\ntoroidal component of the displacement vector is dominating.\nAlthough the assumptions are reasonable for the $r_0$-modes with $l'=|m|$ \n(see Yoshida and Lee 2000),\nthey are not necessarily correct for the $r_k$-modes with $l'=|m|$ and $k>0$, \nfor which we use\n%\n\\begin{eqnarray}\n\\frac{1}{\\tau} &=& \\frac{1}{\\tilde \\tau_S} \\left( \\frac{10^9 K}{T} \\right)^2\n+ \\frac{1}{\\tilde \\tau_B} \\left( \\frac{T}{10^9 K} \\right)^6\n\\left( \\frac{\\pi G \\bar{\\rho}}{\\Omega^2} \\right) \\nonumber \\\\\n&+& \\sum_{l=2}^{\\infty} \\frac{1}{\\tilde \\tau_{J,l}} \n\\left( \\frac{\\Omega^2}{\\pi G \\bar{\\rho}} \\right)^{l+1}\n+ \\sum_{l=2}^{\\infty} \\frac{1}{\\tilde \\tau_{D,l}} \n\\left( \\frac{\\Omega^2}{\\pi G \\bar{\\rho}} \\right)^{l+2} \\, ,\n \\label{tau2b}\n\\end{eqnarray}\n%\nbecause these $r$-modes become inertial modes at large $\\bar\\Omega$.\nThe difference between these two expressions is found\nin the second terms in the right-hand side of the two equations. \nWhen $\\bar\\Omega$ is small, equation (\\ref{tau2b}) gives the correct \nexpression of $\\tau^{-1}$ for inertial modes of isentropic stars\n(See, Lockitch \\& Friedman 1999, Yoshida \\& Lee 2000).\nTo determine the damping timescales $\\tilde\\tau$ in (\\ref{tau2b}) in the limit of \n$\\bar\\Omega\\rightarrow 0$,\nwe assume that the dissipative timescale $\\tilde\\tau^{-1}$ \ndepends on $\\bar\\Omega$ as $a\\bar\\Omega^2+b$ for each dissipative process, where\nthe two unknown constants $a$ and $b$ are\ndetermined by calculating $\\tilde\\tau^{-1}$ and $d\\tilde\\tau^{-1}/d\\bar\\Omega$\nat $\\bar\\Omega=0.1$.\nThe $\\tilde\\tau^{-1}$ in the limit of $\\bar\\Omega\\rightarrow0$ is given by\n$\\tilde\\tau^{-1}=b$.\nWe note that equation (\\ref{tau2b}) is not necessarily a correct approximation for \nnon-isentropic stars. \nWe use the expression (\\ref{tau2b}) simply \nbecause we want to give rough \nestimates of the dissipative timescales, in order to compare the timescales \nwith those of the isentropic case.\n\n \nIn Table 3, we tabulate the dissipation timescales $\\tilde\\tau$ in the unit of second for \nthe various dissipative processes for the $r_k$-modes with $l'=\\vert m \\vert$, \nwhere the radius and the mass of the $n=1$ polytropic neutron star model\nat $\\Omega=0$ are chosen to be $R=12.57\\mbox{km}$ and $M=1.4M_{\\sun}$, \nrespectively. \nNote that in Table 3 we have not included the $r_k$-modes with $l'>|m|$,\nsince the frequency $\\omega$ becomes vanishingly small at large $\\bar\\Omega$ \n(see Figures 1 to 3) \nand hence the magnitude of the gravitational radiation driven\ninstability, which is proportional to $\\omega$, becomes quite small.\nFor the $r_0$-modes with $l'=|m|$,\nin order to see the effects of the buoyancy force on \nthe stability, the results for the four different values of $\\gamma$ are tabulated. \nAs shown by Table 3, the gravitational radiation driven instability \nfor the $r_0$-modes with $l'=\\vert m \\vert$ \nis not affected by introducing the deviation from isentropic structure and remains\nstrong even for the non-isentropic models.\nAs for the $r_k$-modes with $l'=|m|$ and $k> 0$, it is found that \nthe dissipative timescales are comparable to those of the corresponding inertial \nmodes (compare Table 4 of Yoshida \\& Lee 2000). Thus, we may conclude that the $r$-mode \ninstability driven by the gravitational radiation reaction is dominated by \nthe $r_0$-mode with $l'=\\vert m \\vert = 2$ both in isentropic and in non-isentropic stars. \n\n\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% CONCLUSIONS %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\section{Conclusions}\n\n \nIn this paper, we have numerically investigated the properties of rotational \nmodes for slowly rotating, \nnon-isentropic, Newtonian stars, where the effects of \nthe centrifugal force are taken into consideration to calculate the modes\nwith accuracy up to the order of $\\bar\\Omega^3$.\nEstimating the dissipation timescales due to the \ngravitational radiation and the shear and bulk viscosity\nfor simple polytropic neutron star models with the index $n=1$,\nwe have shown that the gravitational radiation driven instability\nof the $r_0$-mode with $l'=|m|$ is hardly \naffected by introducing the deviation from the\nisentropic structure, and that the instability of the $r_0$-modes with $l'=|m|=2$\nremains strongest even for the non-isentropic models.\nNote that the $r_0$-modes with $l'=|m|$ are the only $r$-modes possible in\nisentropic stars and their modal property does not very much depend on $\\Omega$ and \nthe deviation from isentropic structure.\nWe thus conclude that \nthe result of the stability analysis of the $r_0$-modes with $l'=|m|$\nfor isentropic stars remains valid even for non-isentropic stars.\n\n\nWe have numerically found that for the radiative models\nthe inertial modes at large $\\bar\\Omega$ \nbecome identical with the $r_k$-modes with $l'=|m|$ and $k>0$ and $g$-modes\nin the limit of $\\bar\\Omega\\rightarrow 0$ because of the effect of the buoyant force, \nwhere the integer $k$ denotes the number of node of the \neigenfunction with dominant amplitude.\nThis behavior of the $g$-modes or the inertial modes as functions of $\\Omega$\nhas been suggested by, for example,\nSaio (1999) and Lockitch \\& Friedman (1999).\nWe find the connection rules between the $r_k$-modes with $l'=|m|$ and $k>0$ and\n$g$-modes at small $\\bar\\Omega$ and\nthe inertial modes at large $\\bar\\Omega$.\nWe also suggest that the $r_k$-modes with $l'>|m|$ and $k\\ge 0$, \nwhose frequency in the corotating frame\nbecomes vanishingly small as $\\bar\\Omega$ increases, \nhave at large $\\bar\\Omega$ no corresponding inertial\nmodes of the isentropic models.\n\n\nGood progress has been made in the understanding of\nthe properties of the $r$-mode instability \ndue to the gravitational radiation since its discovery.\nRecently, for example, Yoshida et al (1999) have shown that the results \nof the $r$-mode instability obtained by using the slow rotation approximation,\nas employed in this paper,\nare consistent with the results obtained \nby calculating directly the $r$-mode oscillations \nof rotating stars without the approximation. \nKojima (1998) and Kojima \\& Hosonuma (1999) have studied the time evolutional \nbehavior of $r$-modes by using the Laplace transformation technique\nfor slowly rotating relativistic models. \nLockitch (1999) also obtained $r$-modes and \nrotation modes for slowly rotating, incompressible, relativistic stars. \nHowever, we believe it necessary to show\nthat the gravitational radiation driven instability\nof $r$-modes remains sufficiently robust in more realistic and unrestricted situations,\ntaking account of the effects of differential rotation, magnetic field \nand general relativity, for example.\nTo investigate the $r$-mode instability in more general situations is one of\nour future studies.\n\n\n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% END OF MAIN BODY OF PAPER %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\acknowledgements\n\n\nWe would like to thank Prof. H. Saio for useful comments and discussions. \nS.Y. was supported by Research Fellowship of the Japan Society for \nthe Promotion of Science for Young Scientists. \n\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% BIBLIOGRAPHY %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\begin{thebibliography}{}\n\n\\bibitem[Andersson 1998]{nils97}\n Andersson, N. 1998, \\apj, 502, 708\n%\n\\bibitem[Andersson et al.\\ 1998]{aks98}\n Andersson, N., Kokkotas, K., \\& Schutz B. F. 1998, \\apj, 510, 846\n%\n\\bibitem[Berthomieu et al. 1978]{be78}\nBerthomieu, G., Gonczi, G., Graff, Ph., Provost, J., \\& Rocca, A. 1978, \n\\aap, 70, 597 \n%\n\\bibitem[Beyer \\& Kokkotas 1999]{bk99}\n Beyer, H. R., \\& Kokkotas, K. D. 1999, \\mnras, 308, 745\n%\n\\bibitem[Friedman \\& Morsink 1998]{jfs97} \n Friedman, J. L., \\& Morsink, S. M. 1998, \\apj, 502, 714\n%\n\\bibitem[Friedman \\& Schutz 1978]{fs87} \n Friedman, J. L., \\& Schutz, B. F. 1978, \\apj, 222, 281\n%\n\\bibitem[Greenspan 1964]{g64}\n Greenspan, H. P. 1964, The Theory of Rotating Fluids (Cambridge: Cambridge \nUniv. Press)\n%\n\\bibitem[Kojima 1998]{k98}\n Kojima, Y. 1998, \\mnras, 293, 49\n%\n\\bibitem[Kojima \\& Hosonuma 1999]{kh99}\n Kojima, Y., \\& Hosonuma, M. 1999, \\apj, 520, 788\n%\n\\bibitem[Kokkotas \\& Stergioulas 1998]{ks98}\n Kokkotas, K., \\& Stergioulas, N. 1998, \\aap, 341, 110\n%\n\\bibitem[Lee 1993]{l93}\n Lee, U. 1993, \\apj, 405, 359\n%\n\\bibitem[Lee \\& Saio 1986]{ls86}\n Lee, U., \\& Saio, H. 1986, \\mnras, 221, 365\n%\n\\bibitem[Lee \\& Saio 1997]{ls97}\n Lee, U., \\& Saio, H. 1997, \\apj, 491, 839\n%\n\\bibitem[Lee et al.\\ 1992]{lsvh92}\n Lee, U., Strohmayer, T. D., \\& Van Horn, H. M. 1992, \\apj, 397, 647\n%\n\\bibitem[Lindblom \\& Ipser 1998]{li98}\n Lindblom, L., \\& Ipser, J. R. 1998, \\prd, 59, 044009\n%\n\\bibitem[Lindblom et al.\\ 1999]{lmo99}\n Lindblom, L., Mendell, G., \\& Owen, B. J. 1999, \\prd, 60, 064006\n%\n\\bibitem[Lindblom et al.\\ 1998]{lom98}\n Lindblom, L., Owen, B. J., \\& Morsink, S. M. 1998, \\prl, 80, 4843\n%\n\\bibitem[Lockitch \\ 1999]{lo99}\n Lockitch, K. H. 1999, Ph.D. Thesis (University of Wisconsin-Milwaukee), \n(gr-qc/9909029) \n%\n\\bibitem[Lockitch \\& Friedman\\ 1999]{lf99}\n Lockitch, K. H., \\& Friedman J. L. 1999, \\apj, 521, 764\n%\n\\bibitem[Owen et al.\\ 1998]{o98}\n Owen, B. J., Lindblom, L., Cutler, C., Schutz, B. F., Vecchio, A., \\&\n Andersson, N. 1998, \\prd, 58, 084020\n%\n\\bibitem[Papaloizou \\& Pringle 1978]{pp78}\n Papaloizou, J., \\& Pringle, J. E. 1978, \\mnras, 182, 423\n%\n\\bibitem[Pedlosky 1987]{pe87}\n Pedlosky, J. 1987, Geophysical Fluid Dynamics, Second Edition \n(Berlin: Springer-Verlag)\n%\n\\bibitem[Press et al. 1992]{pr92}\n Press, W. H., Teukolsky, S. A., Vetterling, W. T., \\& Flannery, B. P. \n1992, Numerical Recipes: The Art of Scientific Computing, Second Edition \n(Cambridge: Cambridge Univ. Press)\n%\n\\bibitem[Provost et al. 1981]{pea81}\n Provost, J., Berthomieu, G., \\& Rocca, A. 1981, \\aap, 94, 126\n%\n\\bibitem[Regge \\& Wheeler 1957]{rw57}\n Regge, T., \\& Wheeler, J. A. 1957, Phys. Rev., 108, 1063\n%\n\\bibitem[Saio 1982]{s82}\n Saio, H. 1982, \\apj, 256, 717\n%\n\\bibitem[Saio 1999]{s99}\n Saio, H. 1999, private communication. \n%\n\\bibitem[Tassoul 1978]{t78}\n Tassoul, J.-L. 1978, Theory of Rotating Stars (Princeton: Princeton Univ.\nPress)\n%\n\\bibitem[Thorne 1980]{th80}\n Thorne, K. S. 1980, Rev. Mod. Phys., 52, 299\n%\n\\bibitem[Unno et al. 1989]{u89}\n Unno, W., Osaki, Y., Ando, H., Saio, H., \\& Shibahashi, H. 1989, \n Nonradial Oscillations of Stars, Second Edition (Tokyo: Univ. Tokyo Press) \n%\n\\bibitem[Yoshida et al 1999]{ykye99}\n Yoshida, S'i., Karino, S., Yoshida, S., \\& Eriguchi, Y. 1999, \n Submitted to \\mnras (astro-ph/9910532)\n%\n\\bibitem[Yoshida \\& Lee 2000]{yl00}\n Yoshida, S., \\& Lee, U. 2000, \\apj, in press. (astro-ph/9908197)\n%\n\\end{thebibliography}\n%\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% FIGURES %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\n\\begin{figure}\n\\epsscale{.6}\n\\plotone{fig1.eps}\n\\caption{Dimensionless frequencies $\\kappa=\\omega/\\Omega$ for the\nlow-radial-order $r$-modes with $m=1$ are plotted as functions of the dimensionless \nangular rotation frequency $\\bar{\\Omega}=\\Omega/(GM/R^3)^{1/2}$, \nfor the $n=1$ polytropic model with $\\gamma=-10^{-4}$. \nThe solid, the dotted and the dashed curves are\nfor the $r_0$, $r_1$, and $r_2$-modes, respectively. \nThe attached label $l'$ \ndenotes the angular quantum number $l'$ associated with the spherical harmonic function\nrepresenting the toroidal component of the displacement vector.\nNote that the eigenvalue of the \n$r$-modes is given by $\\kappa_0=2 m/(l'(l'+1))$ in the limit of $\\bar\\Omega\\rightarrow 0$. \nThe filled circles at $\\bar{\\Omega}=0.1$ denote the eigenvalues $\\kappa$ of \nthe inertial modes calculated for the isentropic model \nwith the index $n=1$ and $\\gamma=0$ at $\\bar{\\Omega}=0.1$. }\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.6}\n\\plotone{fig2.eps}\n\\caption{Same as Figure 1, but for $m=2$.}\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.6}\n\\plotone{fig3.eps}\n\\caption{Same as Figure 2, but for $m=3$.}\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.6}\n\\plotone{fig4.eps}\n\\caption{Dimensionless frequencies $\\kappa$ for the low-radial-order \n$r$-modes with $m=2$ are plotted as functions of $|\\gamma|$ for the $n=1$ polytropic model \nat $\\bar{\\Omega}=10^{-2}$. \nThe attached label $l'$ denotes the index of the spherical harmonic function for \nthe toroidal component of the displacement vector.\nThe number of nodes of $iT_{l'}$ in the radial direction \nis indicated by the subscript in the notation $r_k$ attached to the mode sequences. \nThe solid line and the dotted line are given for negative \nand positive values of $\\gamma$, respectively.} \n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.4}\n\\plottwo{fig5a.eps}{fig5b.eps}\n\\caption{The first expansion coefficients $S_l$, $H_l$, $iT_{l'}$ for \nthe $r_0$ mode with $l'=m=2$ are plotted against $a/R$ for \nthe polytropic model with the index $n=1$ and $\\gamma=-10^{-4}$. \nPanels $(a)$ and $(b)$ are for the cases of\n$\\bar{\\Omega}=10^{-3}$ and $\\bar{\\Omega}=10^{-1}$, respectively. \nThe eigenfunctions are normalized so that $T_{l'}(a=R)=1$. \nThe attached labels $S_l$, $H_l$, and $iT_{l'}$ denote the expansion coefficients \nof the displacement vector.}\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.4}\n\\plottwo{fig6a.eps}{fig6b.eps}\n\\caption{Same as Figure 5, but for the $r_1$-mode with $l'=2$.}\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.4}\n\\plottwo{fig7a.eps}{fig7b.eps}\n\\caption{Same as Figure 5, but for the $r_0$-mode with $l'=3$.}\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.4}\n\\plottwo{fig8a.eps}{fig8b.eps}\n\\caption{Dimensionless frequencies \n$\\bar{\\omega}=\\omega/(GM/R^3)^{1/2}$ for the low-radial-order \n$g$- and inertial modes with $m=1$ are plotted as functions of \n$\\bar{\\Omega}=\\Omega/(GM/R^3)^{1/2}$, \nfor the $n=1$ polytropic model with $\\gamma=-10^{-4}$. \nThe even and the odd parity modes are shown in panels $(a)$ and $(b)$, \nrespectively. \nThe attached labels \n$g_{\\pm k}(l)\\longleftrightarrow i_{\\pm j}(l_0-\\vert m\\vert)$ \nindicates the connection rule between the $g$-modes and inertial modes.\nThe filled circles at $\\bar{\\Omega}=0.1$ denote the eigenfrequencies $\\bar\\omega$\nof the inertial modes for the $n=1$ isentropic model at $\\bar{\\Omega}=0.1$.\nThe part indicated by the dotted line in the mode sequence is the domain\nof $\\bar\\Omega$, in which the modes belonging to the sequence cannot be \ncalculated. The two dashed lines are given by $\\bar{\\omega}=0$ \nand $\\bar{\\omega}= m \\bar{\\Omega}$.} \n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.4}\n\\plottwo{fig9a.eps}{fig9b.eps}\n\\caption{Same as Figure 8, but for $m=2$.}\n\\end{figure}\n\n\\begin{figure}\n\\epsscale{.4}\n\\plottwo{fig10a.eps}{fig10b.eps}\n\\caption{Same as Figure 9, but for $m=3$.}\n\\end{figure}\n\n\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n%% TABLES %%\n%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n\n\\clearpage\n\n\\begin{deluxetable}{ccccc}\n\\footnotesize\n\\tablecaption{$(\\omega/\\Omega-\\kappa_0)/{\\bar{\\Omega}}^2\\ \n$\\tablenotemark{a} \\ \nfor $r$-modes of the $n=3$ polytrope with $\\Gamma=5/3$ \\label{code-check}}\n\\tablewidth{250pt}\n\\tablehead{\n\\colhead{$m$} & \\colhead{$l'$} & \\colhead{Mode} & \n\\colhead{Present} & \\colhead{Saio 1982} \n}\n\\startdata\n 1 & 1 & $r_0$ & \\phm{-}0.000 & \\phm{-}0.000 \\nl\n & & $r_1$ & -0.040 & -0.040 \\nl\n & & $r_2$ & -0.115 & -0.114 \\nl\n & 2 & $r_0$ & -0.100 & -0.099 \\nl\n & & $r_1$ & -0.191 & -0.190 \\nl\n & & $r_2$ & -0.315 & -0.312 \\nl\n & 3 & $r_0$ & -0.037 & -0.037 \\nl\n & & $r_1$ & -0.063 & -0.061 \\nl\n & & $r_2$ & -0.097 & -0.096 \\nl\n 2 & 2 & $r_0$ & \\phm{-}0.121 & \\phm{-}0.120 \\nl\n & & $r_1$ & \\phm{-}0.024 & \\phm{-}0.024 \\nl\n & & $r_2$ & -0.001 & -0.001 \\nl\n & 3 & $r_0$ & -0.037 & -0.037 \\nl\n & & $r_1$ & -0.071 & -0.070 \\nl\n & & $r_2$ & -0.115 & -0.114 \\nl\n 3 & 3 & $r_0$ & \\phm{-}0.174 & \\phm{-}0.173 \\nl\n & & $r_1$ & \\phm{-}0.064 & \\phm{-}0.063 \\nl\n & & $r_2$ & \\phm{-}0.028 & \\phm{-}0.027 \\nl\n\\enddata\n\\tablenotetext{a}{$\\kappa_0$ is defined as $\\kappa_0=2 m/(l' (l'+1))$. \nThe eigenfrequencies are calculated at $\\bar{\\Omega}=0.1$. }\n\\end{deluxetable}\n\n\\begin{deluxetable}{ccc}\n\\footnotesize\n\\tablecaption{The eigenfrequency $\\bar{\\omega}$ \nfor low-radial-order $g$-modes of the $n=1$ polytrope\nwith $\\gamma=-10^{-4}$ at $\\Omega=0$ \\label{g-mode}}\n\\tablewidth{250pt}\n\\tablehead{\n\\colhead{$l$} & \\colhead{$g_1$} & \\colhead{$g_2$} \n}\n\\startdata\n 1 & $1.20\\times 10^{-2}$ & $7.69\\times 10^{-3}$ \\nl\n 2 & $1.68\\times 10^{-2}$ & $1.15\\times 10^{-2}$ \\nl\n 3 & $2.01\\times 10^{-2}$ & $1.44\\times 10^{-2}$ \\nl\n 4 & $2.26\\times 10^{-2}$ & $1.68\\times 10^{-2}$ \\nl\n 5 & $2.47\\times 10^{-2}$ & $1.88\\times 10^{-2}$ \\nl\n 6 & $2.65\\times 10^{-2}$ & $2.05\\times 10^{-2}$ \\nl\n\\enddata\n\\end{deluxetable}\n\n\\clearpage\n\n\\begin{deluxetable}{cccccccccc}\n\\footnotesize\n\\tablecaption{Dissipative timescales $\\tilde\\tau$ of $r$-modes\\tablenotemark{a} \n\\ for the polytropic neutron star models with the index $n=1$. }\n\\tablewidth{0pt}\n\\tablehead{\n\\colhead{$m$} & \\colhead{mode} & \\colhead{$\\gamma$} \n & \\colhead{$\\kappa_0$}\n & \\colhead{$\\tilde \\tau_B$(s)} & \\colhead{$\\tilde \\tau_S$(s)} \n & \\colhead{$\\tilde \\tau_{J,\\vert m\\vert}$(s)\\tablenotemark{b}} \n & \\colhead{$\\tilde \\tau_{D,\\vert m\\vert+1}$(s)} \n & \\colhead{$\\tilde \\tau_{J,\\vert m\\vert+2}$(s)}\n} \n\\startdata\n1&$r_1$&\n$0$\n & 0.691 &$ 5.89\\times 10^{9} $&$ 9.23\\times 10^{7} $\n &$ \\cdots$&$ -2.46\\times 10^{5} $&$ -1.27\\times 10^{8} $\n\\nl\n & &\n$-10^{-4}$\n & 1.000 &$ 6.08\\times 10^{9} $&$ 9.04\\times 10^{7} $\n &$ \\cdots$&$ -2.31\\times 10^{5} $&$ -1.58\\times 10^{8} $\n\\nl\n & & & & & & & & \\nl\n2&$r_0$&\n$\\phm{-}10^{-4}$\n &0.667 &$ 2.03\\times 10^{11} $&$ 2.50\\times 10^{8} $\n &$ -3.31\\times 10^{0} $&$ -3.49\\times 10^{2}$&$ \\cdots$\n\\nl\n & &\n$0$\n &0.667 &$ 2.03\\times 10^{11} $&$ 2.50\\times 10^{8} $\n &$ -3.31\\times 10^{0} $&$ -3.49\\times 10^{2}$&$ \\cdots$\n\\nl\n & &\n$-10^{-4}$\n &0.667 &$ 2.03\\times 10^{11} $&$ 2.50\\times 10^{8} $\n &$ -3.31\\times 10^{0} $&$ -3.49\\times 10^{2}$&$ \\cdots$\n\\nl\n & &\n$-10^{-2}$\n &0.667 &$ 2.10\\times 10^{11} $&$ 2.54\\times 10^{8} $\n &$ -3.31\\times 10^{0} $&$ -3.49\\times 10^{2}$&$ \\cdots$\n\\nl\n & & & & & & & & \\nl\n &$r_1$& \n$0$\n &0.517 &$ 6.47\\times 10^{9} $&$ 6.18\\times 10^{7} $\n &$ -1.31\\times 10^{8} $&$ -8.39\\times 10^{4} $\n &$ -1.88\\times 10^{6} $\n\\nl\n & &\n$-10^{-4}$\n &0.667 &$ 6.79\\times 10^{9} $&$ 6.01\\times 10^{7} $\n &$\\phm{-}2.18\\times 10^{7}\\ \\tablenotemark{c} $\n &$ -7.05\\times 10^{4} $&$ -2.06\\times 10^{6} $\n\\nl\n & & & & & & & & \\nl\n3&$r_0$&\n$\\phm{-}10^{-4}$\n &0.500 &$ 6.64\\times 10^{10} $&$ 1.43\\times 10^{8} $\n &$ -3.17\\times 10^{1} $&$ -1.88\\times 10^{3}$&$\\dots$\n\\nl\n & &\n$0$\n &0.500 &$ 6.63\\times 10^{10} $&$ 1.43\\times 10^{8} $\n &$ -3.17\\times 10^{1} $&$ -1.88\\times 10^{3}$&$\\dots$\n\\nl\n & &\n$-10^{-4}$\n &0.500 &$ 6.64\\times 10^{10} $&$ 1.43\\times 10^{8} $\n &$ -3.17\\times 10^{1} $&$ -1.88\\times 10^{3}$&$\\dots$\n\\nl\n & &\n$-10^{-2}$\n &0.500 &$ 6.97\\times 10^{10} $&$ 1.46\\times 10^{8} $\n &$ -3.17\\times 10^{1} $&$ -1.87\\times 10^{3}$&$\\dots$\n\\nl\n & & & & & & & & \\nl\n &$r_1$& \n$0$\n &0.413 &$ 6.97\\times 10^{9} $&$ 4.78\\times 10^{7} $\n &$ -1.86\\times 10^{10} $&$ -5.30\\times 10^{5}$\n &$ -4.07\\times 10^{6} $\n\\nl\n & &\n$-10^{-4}$\n &0.500 &$ 7.42\\times 10^{9} $&$ 4.63\\times 10^{7} $\n &$\\phm{-}2.39\\times 10^{5}\\ \\tablenotemark{c} $\n &$ -4.37\\times 10^{5} $&$ -4.48\\times 10^{6} $ \n\\nl\n\\enddata\n\\tablenotetext{a}{We present dissipative timescales only for those \nthat are unstable to gravitational radiation reaction.}\n\\tablenotetext{b}{We present dissipative timescales $\\tilde{\\tau}_l$ due to \nthe gravitational radiation reaction only for\nthe dominant multipole moments.}\n\\tablenotetext{c}{For these dissipative timescales, we obtain positive\nvalues, which should be negative by definition. The reason for the\ninconsistent result may be because the extrapolation formula (\\ref{tau2b}) \nfor $\\tau^{-1}$, which is obtained at $\\bar\\Omega=0$, does not necessarily work well\nfor arbitrary values of $\\bar\\Omega$. \nFor instance, we find that\n$\\tilde{\\tau}_{J,\\vert m\\vert}/\\tilde{\\tau}_{D,\\vert m\\vert+1} \\sim 10^{3}$ \nfor $m=2$ and \n$\\tilde{\\tau}_{J,\\vert m\\vert}/\\tilde{\\tau}_{D,\\vert m\\vert+1} \\sim 10^{2}$ \nfor $m=3$, where the dissipative timescales are estimated at \n$\\bar{\\Omega}=0.1$. \nThis may suggest that \nthe mass multipole radiation dominates the current one \nfor the $r_1$-modes for large $\\bar\\Omega$. \nThus, our conclusions on the stability of the $r_1$-modes \nextrapolated for large $\\bar\\Omega$\nare not altered at all.}\n\\end{deluxetable}\n\n\n\\end{document}\n\n\n"
}
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{
"name": "astro-ph0002300.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem[Andersson 1998]{nils97}\n Andersson, N. 1998, \\apj, 502, 708\n%\n\\bibitem[Andersson et al.\\ 1998]{aks98}\n Andersson, N., Kokkotas, K., \\& Schutz B. F. 1998, \\apj, 510, 846\n%\n\\bibitem[Berthomieu et al. 1978]{be78}\nBerthomieu, G., Gonczi, G., Graff, Ph., Provost, J., \\& Rocca, A. 1978, \n\\aap, 70, 597 \n%\n\\bibitem[Beyer \\& Kokkotas 1999]{bk99}\n Beyer, H. R., \\& Kokkotas, K. D. 1999, \\mnras, 308, 745\n%\n\\bibitem[Friedman \\& Morsink 1998]{jfs97} \n Friedman, J. L., \\& Morsink, S. M. 1998, \\apj, 502, 714\n%\n\\bibitem[Friedman \\& Schutz 1978]{fs87} \n Friedman, J. L., \\& Schutz, B. F. 1978, \\apj, 222, 281\n%\n\\bibitem[Greenspan 1964]{g64}\n Greenspan, H. P. 1964, The Theory of Rotating Fluids (Cambridge: Cambridge \nUniv. Press)\n%\n\\bibitem[Kojima 1998]{k98}\n Kojima, Y. 1998, \\mnras, 293, 49\n%\n\\bibitem[Kojima \\& Hosonuma 1999]{kh99}\n Kojima, Y., \\& Hosonuma, M. 1999, \\apj, 520, 788\n%\n\\bibitem[Kokkotas \\& Stergioulas 1998]{ks98}\n Kokkotas, K., \\& Stergioulas, N. 1998, \\aap, 341, 110\n%\n\\bibitem[Lee 1993]{l93}\n Lee, U. 1993, \\apj, 405, 359\n%\n\\bibitem[Lee \\& Saio 1986]{ls86}\n Lee, U., \\& Saio, H. 1986, \\mnras, 221, 365\n%\n\\bibitem[Lee \\& Saio 1997]{ls97}\n Lee, U., \\& Saio, H. 1997, \\apj, 491, 839\n%\n\\bibitem[Lee et al.\\ 1992]{lsvh92}\n Lee, U., Strohmayer, T. D., \\& Van Horn, H. M. 1992, \\apj, 397, 647\n%\n\\bibitem[Lindblom \\& Ipser 1998]{li98}\n Lindblom, L., \\& Ipser, J. R. 1998, \\prd, 59, 044009\n%\n\\bibitem[Lindblom et al.\\ 1999]{lmo99}\n Lindblom, L., Mendell, G., \\& Owen, B. J. 1999, \\prd, 60, 064006\n%\n\\bibitem[Lindblom et al.\\ 1998]{lom98}\n Lindblom, L., Owen, B. J., \\& Morsink, S. M. 1998, \\prl, 80, 4843\n%\n\\bibitem[Lockitch \\ 1999]{lo99}\n Lockitch, K. H. 1999, Ph.D. Thesis (University of Wisconsin-Milwaukee), \n(gr-qc/9909029) \n%\n\\bibitem[Lockitch \\& Friedman\\ 1999]{lf99}\n Lockitch, K. H., \\& Friedman J. L. 1999, \\apj, 521, 764\n%\n\\bibitem[Owen et al.\\ 1998]{o98}\n Owen, B. J., Lindblom, L., Cutler, C., Schutz, B. F., Vecchio, A., \\&\n Andersson, N. 1998, \\prd, 58, 084020\n%\n\\bibitem[Papaloizou \\& Pringle 1978]{pp78}\n Papaloizou, J., \\& Pringle, J. E. 1978, \\mnras, 182, 423\n%\n\\bibitem[Pedlosky 1987]{pe87}\n Pedlosky, J. 1987, Geophysical Fluid Dynamics, Second Edition \n(Berlin: Springer-Verlag)\n%\n\\bibitem[Press et al. 1992]{pr92}\n Press, W. H., Teukolsky, S. A., Vetterling, W. T., \\& Flannery, B. P. \n1992, Numerical Recipes: The Art of Scientific Computing, Second Edition \n(Cambridge: Cambridge Univ. Press)\n%\n\\bibitem[Provost et al. 1981]{pea81}\n Provost, J., Berthomieu, G., \\& Rocca, A. 1981, \\aap, 94, 126\n%\n\\bibitem[Regge \\& Wheeler 1957]{rw57}\n Regge, T., \\& Wheeler, J. A. 1957, Phys. Rev., 108, 1063\n%\n\\bibitem[Saio 1982]{s82}\n Saio, H. 1982, \\apj, 256, 717\n%\n\\bibitem[Saio 1999]{s99}\n Saio, H. 1999, private communication. \n%\n\\bibitem[Tassoul 1978]{t78}\n Tassoul, J.-L. 1978, Theory of Rotating Stars (Princeton: Princeton Univ.\nPress)\n%\n\\bibitem[Thorne 1980]{th80}\n Thorne, K. S. 1980, Rev. Mod. Phys., 52, 299\n%\n\\bibitem[Unno et al. 1989]{u89}\n Unno, W., Osaki, Y., Ando, H., Saio, H., \\& Shibahashi, H. 1989, \n Nonradial Oscillations of Stars, Second Edition (Tokyo: Univ. Tokyo Press) \n%\n\\bibitem[Yoshida et al 1999]{ykye99}\n Yoshida, S'i., Karino, S., Yoshida, S., \\& Eriguchi, Y. 1999, \n Submitted to \\mnras (astro-ph/9910532)\n%\n\\bibitem[Yoshida \\& Lee 2000]{yl00}\n Yoshida, S., \\& Lee, U. 2000, \\apj, in press. (astro-ph/9908197)\n%\n\\end{thebibliography}"
}
] |
astro-ph0002301
|
[] |
Cartan torsion contribution to Sachs-Wolfe effect in the inflationary phase of the Universe is discussed.From the COBE data of the microwave anisotropy is possible to compute the spin-density in the Universe as $10^{16}$ mks units.The spin-density fluctuations at the hadron era is shown to coincide with the anisotropy temperature fluctuations.
|
[
{
"name": "astro-ph0002301.tex",
"string": "\\documentstyle[12pt]{article}\n\\begin{document}\n\\thispagestyle{empty}\n\n\\begin{center}\n\\LARGE \\tt \\bf{Sachs-Wolfe effect in Spacetimes with Torsion}\n\\end{center}\n\n\\vspace{2.5cm}\n\n\\begin{center} {\\large L.C. Garcia de Andrade\\footnote{Departamento de\nF\\'{\\i}sica Te\\'{o}rica - Instituto de F\\'{\\i}sica - UERJ\n\nRua S\\~{a}o Fco. Xavier 524, Rio de Janeiro, RJ\n\nMaracan\\~{a}, CEP:20550-003 , Brasil.\n\nE-mail : GARCIA@DFT.IF.UERJ.BR}}\n\\end{center}\n\n\\vspace{2.0cm}\n\n\\begin{abstract}\nCartan torsion contribution to Sachs-Wolfe effect in the inflationary phase of the Universe is discussed.From the COBE data of the microwave anisotropy is possible to compute the spin-density in the Universe as $10^{16}$ mks units.The spin-density fluctuations at the hadron era is shown to coincide with the anisotropy temperature fluctuations.\n\\end{abstract}\n\n\\vspace{1.0cm}\n\n\\begin{center}\n\\large{PACS number(s) : 0420,0450}\n\\end{center}\n\n\\newpage\nThe Sachs-Wolfe effect \\cite{1,2,3} is given by\n\\begin{equation}\n\\frac{{\\delta}T}{T}=-{\\Phi}\n\\label{1}\n\\end{equation}\nwhere ${\\Phi}$ is the Newtonian gravitational potential.Since there vis no restriction on the origin of the gravitational potential in this expression one may extend this expression to allow for alternative theories of gravity.Thus one is able to compute the anisotropy fluctuations in the CMB temperatures.In this letter we shall be concerned with the computation of the temperature fluctuations in the context of weak field limit approximation of the Einstein-Cartan gravity.In Newtonian approximation the Einstein-Cartan field equation may be expressed as\n\\begin{equation}\n\\frac{1}{c^{2}}{\\frac{{\\partial}^{2}{\\Phi}}{{{\\partial}t}^{2}}}-{{\\nabla}^{2}}{\\Phi}=-4{\\pi}G({\\rho}-G{\\sigma}^{2})\n\\label{2}\n\\end{equation}\nwhere ${\\sigma}^{2}$ is the spin-torsion energy density and ${\\rho}$ is the usual matter density.Since the cosmological spacetime used is of the form\n\\begin{equation}\nds^{2}=dt^{2}-(1-2{\\Phi})(dx^{2}+dy^{2}+dz^{2})\n\\label{3}\n\\end{equation}\nis homogeneous ${{\\nabla}^{2}}{\\Phi}=0$ equation (\\ref{2}) reduces to\n\\begin{equation}\n\\ddot{\\Phi}=-4{\\pi}Gc^{2}({\\rho}-G{\\sigma}^{2})\n\\label{4}\n\\end{equation}\nSolution of this expression can be easily obtained obtained by considering the RHS of (\\ref{4}) is constant in the average, thus\n\\begin{equation}\n{\\Phi}(t)=-4{\\pi}Gc^{2}({\\rho}-G{\\sigma}^{2})t^{2}+Bt+C\n\\label{5}\n\\end{equation}\nwhere $B$ and $C$ are integration constants.Therefore spin-torsion effects contribute to the temperature fluctuations through the term\n\\begin{equation}\n{\\frac{{\\delta}T}{T}}_{torsion}=4{\\pi}G^{2}c^{2}{\\sigma}^{2}t^{2}\n\\label{6}\n\\end{equation}\nSince at the inflation era $t=10^{-35}s$ and from COBE data $\\frac{{\\delta}T}{T}<10^{-5}$ one may obtain an expression for the spin-torsion density at the inflation era as\n\\begin{equation}\n{\\sigma}^{2}=\\frac{1}{4{\\pi}}(G^{-2}c^{-2}t^{-2}){\\frac{{\\delta}T}{T}}_{torsion}\n\\label{7}\n\\end{equation}\nwhich yields ${\\sigma}=10^{16}$ mks-units.Notice that this value is much weaker than the value obtained by de Sabbata and Sivaram \\cite{4} for the maximum spin-torsion density at the Planck era of the Universe which is ${\\sigma}_{Pl}=10^{71}$.In the hadron era \\cite{4} for example $G^{2}{\\sigma}^{2}=T^{2}$ and one may obtain the classical density fluctuation as \n\\begin{equation}\n\\frac{{\\delta}T}{T}=\\frac{{\\delta}{\\sigma}}{\\sigma}\n\\label{8}\n\\end{equation}\nThis amazing result shows that the spin-torsion density fluctuation coincides with the matter density fluctuation which allow us to obtain the spin-torsion density fluctuation from the COBE data.Similar results in the Relativistic Einstein-Cartan gravity with dilaton fields has been recently obtained by Palle \\cite{5} and myself \\cite{6}.\n\\section*{Acknowledgement}\nI am very much indebt to Prof.I.Shapiro and Prof.R.Ramos for helpful discussions on the subject of this paper. Financial support from CNPq. and FAPESP is gratefully acknowledged.\n\\begin{thebibliography}{6}\n\\bibitem{1} Sachs,R.K.and Wolfe,A.M.1967,ApJ,147,73\n\\bibitem{2} Peebles,J.Principles of Physical Cosmology,1993,Princeton University Press.\n\\bibitem{3} White,M.and Hu,W.Astronomy and Astrophysics,1999,astro-ph/9609105\n\\bibitem{4} de Sabbata,V. and Sivaram,C.Spin and Torsion and Gravitation,1995,World Scientific\n\\bibitem{5} Palle,D.,On Primordial density fluctuation in the Einstein-Cartan Gravity,1999,gr-qc Los Alamos archives.\n\\bibitem{6} Garcia de Andrade,L.C.,Phys.Lett.B468,1999,28.\n\\end{thebibliography}\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002301.extracted_bib",
"string": "\\begin{thebibliography}{6}\n\\bibitem{1} Sachs,R.K.and Wolfe,A.M.1967,ApJ,147,73\n\\bibitem{2} Peebles,J.Principles of Physical Cosmology,1993,Princeton University Press.\n\\bibitem{3} White,M.and Hu,W.Astronomy and Astrophysics,1999,astro-ph/9609105\n\\bibitem{4} de Sabbata,V. and Sivaram,C.Spin and Torsion and Gravitation,1995,World Scientific\n\\bibitem{5} Palle,D.,On Primordial density fluctuation in the Einstein-Cartan Gravity,1999,gr-qc Los Alamos archives.\n\\bibitem{6} Garcia de Andrade,L.C.,Phys.Lett.B468,1999,28.\n\\end{thebibliography}"
}
] |
|
astro-ph0002302
|
Spirals and the size of the disk in EX\,Dra
|
[
{
"author": "V. Joergens \\inst{1,2}"
},
{
"author": "H.C. Spruit \\inst{1}"
},
{
"author": "R.G.M. Rutten \\inst{3,4}"
}
] |
Observations at high spectral and temporal resolution are presented of the dwarf nova EX\,Dra in outburst. The disk seen in the \ion{He}{i} line reconstructed by Doppler tomography shows a clear two-armed spiral pattern pointing to spiral shocks in the disk. The Balmer and \ion{He}{ii} maps also give evidence for the presence of spirals. The eclipse as seen in the red continuum indicates a disk radius of 0.31 times the orbital separation, which might be large enough to explain the observed spiral shocks through excitation by the tidal field of the secondary. The eclipse in the Balmer line profiles, well resolved in our observations, indicates a somewhat smaller disk size (0.25). We discuss the possibility that this is related to an optical depth effect in the lines. \keywords{accretion disks -- hydrodynamics -- Cataclysmic Variables -- stars: EX\,Dra}
|
[
{
"name": "bh033.tex",
"string": "\n%\\documentstyle[epsf]{l-aa}\n\\documentclass{aa}\n\\newcommand{\\be}{\\begin{equation}}\n\\newcommand{\\ee}{\\end{equation}}\n\\newcommand{\\bd}{\\begin{displaymath}}\n\\newcommand{\\ed}{\\end{displaymath}}\n\\newcommand{\\gapprox}{\\;\\rlap{\\lower 2.5pt \n \\hbox{$\\sim$}}\\raise 1.5pt\\hbox{$>$}\\;} \n\\newcommand{\\lapprox}{\\;\\rlap{\\lower 2.5pt \n \\hbox{$\\sim$}}\\raise 1.5pt\\hbox{$<$}\\;} \n\\newcommand{\\pr}{\\prime}\n\\newcommand{\\p}{\\partial}\n\\newcommand{\\rd}{{\\rm d}} \n\n%\\newcommand{\\mk}{\\bf} % temporary markup by boldface\n\\newcommand{\\mk}{} % udno temporary markup\n\n\\usepackage{graphicx}\n\\begin{document}\n \\thesaurus{06 % A&A Section 6: Form. struct. and evolut. of stars\n 02.01.2 %accretion\n 02.08.1 %hydro\n 08.02.2 %ecl binaries\n 08.09.2 EX\\,Dra\n }\n%\n \\title{Spirals and the size of the disk in EX\\,Dra}\n% \\subtitle{}\n\n% \n \\author{V. Joergens \\inst{1,2} \\and H.C. Spruit \\inst{1}\n \\and R.G.M. Rutten \\inst{3,4}}\n\n% \\offprints{}\n \n \\institute{Max-Planck-Institut f\\\"ur Astrophysik, Postfach 1523, \n D-85740 Garching bei M\\\"unchen, Germany \\and\n Max-Planck-Institut f\\\"ur Extraterrestrische Physik, \n Postfach 1603, D-85740 Garching bei M\\\"unchen, Germany \\and\n Netherlands Foundation for Research in Astronomy \\and\n Royal Greenwich Observatory, Apartado de Correos 321, \n 38780 Santa Cruz de La Palma, Canary Islands, Spain\n }\n\n \\date{Received }\n\n \\maketitle\n\n% \\maintitlerunninghead{}\n\n% \\authorrunninghead{}\n\n\\begin{abstract}\nObservations at high spectral and temporal resolution are presented of\nthe dwarf nova EX\\,Dra in outburst. \nThe disk seen in the \\ion{He}{i} line reconstructed by Doppler tomography\nshows a clear two-armed spiral pattern pointing to spiral shocks in the disk.\nThe Balmer and \\ion{He}{ii} maps also give evidence for \nthe presence of spirals. \nThe eclipse as seen in the red continuum indicates a disk radius of 0.31 times\nthe orbital separation, which might be\nlarge enough to explain the observed spiral shocks through\nexcitation by the tidal field of the secondary. \nThe eclipse in the Balmer line profiles, well \nresolved in our observations, indicates a somewhat smaller disk size (0.25).\nWe discuss the possibility that this is related to an optical depth effect \nin the lines.\n\\keywords{accretion disks -- hydrodynamics -- Cataclysmic Variables -- stars: \nEX\\,Dra}\n\\end{abstract}\n\n\\section{Introduction}\n\nSpiral shocks in accretion disks have been predicted from numerical \nsimulations (Sawada et al. 1986, 1987, R\\'o\\.zyczka \\& Spruit 1993, Yukawa et \nal. 1997), and analytic considerations (Spruit 1987, Spruit et al. 1987, \nLarson 1990). They are excited by the tidal field of the secondary if the \ndisk extends \nfar enough into the Roche lobe and can result in two prominent spiral arms.\nIf shock dissipation is the main mechanism damping the wave, it extends over \nthe entire disk and causes accretion at an effective $\\alpha$-value of \n$0.01(H/r)^{3/2}$ (Spruit 1987, Larson 1990, Godon 1997). \n\nThe first observational evidence for shock waves in accretion disks of \ncataclysmic variables (CVs) was the detection of a clear two-armed \nstructure in the disk of IP\\,Peg during rise to outburst (Steeghs et \nal. 1997). The spiral pattern, interpreted as evidence for shock waves,\nhas also been seen during outburst maximum (Harlaftis et al. 1999) and early \ndecline of outburst (Morales-Rueda et al. 2000).\n\nAt the temperatures expected from dwarf nova disks models, whether in outburst \nor in quiescence, the predicted spirals are tightly wound and would be hard to \ndetect observationally (Bunk et al. 1990), so that their presence in the \nobservations is somewhat unexpected.\nSpirals this strong are most naturally explained if the disk\ntemporarily extends rather far into the primary Roche lobe, so that\nthe tidal force of the secondary causes a strong disturbance. A strong\nnon-axisymmetric disturbance, however, would also cause the gas to\nloose angular momentum quickly (transfered to the secondary), so that\nthe disk would shrink to a smaller radius where the tidal force is\nweaker. Spirals in disks of CVs would then be understandable if they are a\ntemporary phenomenon, perhaps restricted to\noutbursts. To test this, more observations of different systems at\nsufficient spectral resolution and signal-to-noise are needed\n(Steeghs \\& Stehle 1999). \n\nWith high quality spectroscopic studies of different CVs it should also be \npossible to answer the question if spiral shocks in CV accretion disks are a \ncommon phenomenon. Systems suitable for this purpose would be bright and \nhave frequent outbursts, such as SS\\,Cyg and EX\\,Dra. \n\nEX\\,Dra is a double--eclipsing dwarf nova with a 5-hour orbit \n(Barwig et al. 1993, Billington et al. 1996, system parameters by \nFiedler et al. 1997).\nThere is suggestive evidence for asymmetric structures in the \\ion{He}{i}\nDoppler map reconstructed from outburst data taken in 1993 (Joergens et al. \n2000). From eclipse maps obtained at various stages in the outburst cycle Baptista \\& \nCatalan (1999) claim that spiral waves form at the early stages of an \noutburst. We report in this paper on observations at high spectral and temporal\nresolution during an outburst in 1996.\n\n\\section{Observations and reduction}\nEX\\,Dra was observed on the nights of July 27\nand 28 1996, with the ISIS spectrograph on the 4.2\\,m William\nHerschel Telescope. \nThe red ISIS arm was equipped with the TEK\\,5 CCD,\nthe blue arm with TEK\\,1 CCD, covering the \nwavelength ranges 6375-6778\\,{\\AA} and\n4585-4993\\,{\\AA} respectively, at a dispersion of\n0.4\\,{\\AA}/pixel. \nThe spectra were observed during seeing of 1.4 -- 1.7 arc sec, \nusing an exposure time of 60s.\n%, corresponding to 0.3\\% of the binary orbit. \nThe spectra were optimally-extracted, including the elimination of \ncosmic ray hits but not the correction of Pixel-to-pixel variations of the \ndetector sensitivity. \nSlit losses due to variable atmospheric conditions were \ncorrected using a faint comparison star on the slit.\nThe red spectra, but not the blue spectra, were flux calibrated. \n\nOur spectra were taken roughly in the middle of an outburst. Photometric \nobservation at the Wendelstein observatory showed that the system was already \nin outburst on 26 July, and in quiescence on 4 August (Barwig, private comm.). \nVSNET (1998) records show that the system was in quiescence on 24 July \nand in outburst one day later and in quiescence again on 1 August. The outburst \ntherefore started on 25 August, three days before our observations.\n\n\n\\section{Interpretation of the Doppler maps}\n\\label{interpret}\n\nDoppler maps were computed from the phase-folded spectra of 28 July, using the IDL-based \nfast-maximum entropy package described by Spruit (1998)\\footnote{available \nat http:www.mpa-garching.mpg.de/$\\sim$henk}. \nFor further details on Doppler tomography see Marsh \\& Horne (1988). \n{\\mk The eclipsed part of the data (phases -0.12 to 0.12) has been \nexcluded from the reconstruction process, and does not affect the maps produced.\nFor information, however, these parts of the data are included in the spectra\nshown in Fig.~1. \nThey were used separately to derive disk sizes in the lines and\nthe continuum.}\n\nFig. \\ref{colla} shows the results for the four strongest lines in the spectra,\nH$_\\alpha$, H$_\\beta$, \\ion{He}{i}\\,$\\lambda 6678$ and \\ion{He}{ii}\\,$\\lambda \n4686$. The phase-folded spectra are shown in the left column, the \ncorresponding Doppler maps in the right and in the middle the spectra \nreconstructed from the maps. The theoretical\ntrajectory of the mass transfering stream\nhas been plotted in the \\ion{He}{ii} image, together with the Keplerian \nvelocity along the stream path (cp. Marsh\\,\\&\\,Horne 1988). Bars\nconnecting the two arcs indicate correspondence in physical space, and are \nannotated with radius r/a and the azimuth $\\Phi$ relative to the primary.\nThe system parameters \n%($\\mbox{M}_1=0.75,\\mbox{q}=0.75,\\mbox{i}=84.2$) \nand the ephemeris are from Fiedler et al. (1997).\n\n\\begin{figure*}\n\\vbox{\n%row 1: H-alpha spectrum , reco, map.\n\\hbox{\\mbox{}\\hfill\n \\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f1}\n \\hfill\\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f2}\n \\hfill\\includegraphics[height=5.4cm]{bh033.f3}\\hfill\\mbox{}}\n%row 2: H-beta , reco, map.\n\\hbox{\\mbox{}\\hfill\\includegraphics[width=5.3cm,height=3.5cm,angle=90]\n{bh033.f4}\n \\hfill\\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f5}\n \\hfill\\includegraphics[height=5.4cm]{bh033.f6}\\hfill\\mbox{}}\n% row 3: He I 6678 , reco, map.\n\\hbox{\\mbox{}\\hfill\\includegraphics[width=5.3cm,height=3.5cm,angle=90]\n{bh033.f7}\n \\hfill\\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f8}\n \\hfill\\includegraphics[height=5.4cm]{bh033.f9}\\hfill\\mbox{}}\n% row 4: He II , reco, map.\n\\hbox{\\mbox{}\\hfill\\includegraphics[width=5.3cm,height=3.5cm,angle=90]\n{bh033.f10}\n \\hfill\\includegraphics[width=5.3cm,height=3.5cm,angle=90]{bh033.f11}\n \\hfill\\includegraphics[height=5.4cm]{bh033.f12}\\hfill\\mbox{}}\n}\n\\caption{\\label{colla} Phase-folded spectra of EX\\,Dra in outburst on 28 July \n1996 \n(left column), corresponding Doppler maps (right column), and the spectra \nreconstructed from the maps (middle). Top to bottom: H$_\\alpha$, H$_\\beta$,\n\\ion{He}{i}, \\ion{He}{ii}. The mass transferring stream (see text) and\nthe Doppler \nimage of the Roche lobe of the secondary star are over plotted on the \n\\ion{He}{ii} \nimage. Upper and lower intensity cuts of the Doppler maps have been adjusted \nsuch that the disk emission has roughly the same contrast in each image.\n}\n\\end{figure*}\n\nThe \\ion{He}{i} image shows the spirals clearest:\nasymmetric disk emission is concentrated \nin two arms in the first and third quadrant. \nWe interpret this deviation from a Keplerian disk\nas indication of the presence of spiral shock waves in the accretion \ndisk. The image looks quite similar to\nthe \\ion{He}{i} map of IP\\,Peg published by Steeghs et al. (1997). \nAs in the case of IP\\,Peg, the arms do not follow a circle centered on the white \ndwarf, but are somewhat elongated along the V$_y$-axis. \nThis is the pattern expected from spiral shocks (Steeghs \n\\& Stehle 1999). The asymmetry of the spirals in the EX\\,Dra disk \nis smaller than in the IP\\,Peg observations\n(Steeghs et al. 1997, Harlaftis et al. 1999, Morales-Rueda et al. 2000), \nperhaps indicating that the shocks are weaker.\nThe spiral arm in the upper right is stronger in intensity as well as in\nasymmetry than that one in the lower left. This pattern is also seen in the \nDoppler maps of IP\\,Peg. \nAs in the case of IP\\,Peg, the Balmer lines show similar, \nbut less clearly defined structures.\n\nThe Doppler images, with the exception of \\ion{He}{ii}, \nshow strong emission from the secondary star, also visible during the \noutburst in 1993 (Joergens et al. 2000). This indicates \nheating of the secondary by radiation from the inner disk. \nThe temperatures are obviously \nnot high enough to excite the \\ion{He}{ii} line. \nThe \\ion{He}{ii} line also differs \nfrom the other lines by the presence of a prominent emission patch \nat the theoretical gas stream trajectory.\nThe center of this hot spot emission is somewhat below the trajectory,\nconsistent with quiescence observations of EX\\,Dra (Billington et al.\n1996, Joergens et al. 2000). \n\n\\section{The disk radius}\n\\label{disk}\nThe large width of the \\ion{He}{ii} line is as expected for a high\nexcitation line produced near the center of a disk in outburst. The\neclipse of the \\ion{He}{ii} line is visible in the spectrum up to a velocity\nof about 1500\\,km/s. The orbital velocity at the disk edge is about 4.3\ntimes lower than this. Assuming Keplerian rotation, the disk region\neclipsed at 1500\\,km/s \nis about 20 times smaller in radius than the outer radius \nof the disk. At our phase resolution, the 1500 km/s emission is thus \npoint-like, \nand can be used to measure the width of the secondary's shadow on the orbital \nplane, $\\Delta\\phi=0.08\\pm0.005$. From the position of the hot spot in the \\ion{He}{ii}\nmap, we can estimate a disk size of $r/a=0.32 \\pm 0.04$. \n\nThe eclipse of the Balmer and \\ion{He}{i} lines shows that the blue\ndisk emission reappears (at V$\\approx 350$km/s) at the same phase as\nthe last red emission disappears, within \nthe measurement uncertainty. The size of the disk as seen in these lines is thus,\nby a coincidence, nearly as wide as the occulting shadow of the secondary. \nHence the disk radius as seen in the Balmer lines is \n$r_{\\rm dB}/a\\approx 2\\pi\\Delta\\phi/2=0.25\\pm0.02$. \n\nWe can compare this with the disk size as measured from the eclipse in the\ncontinuum. The light curve in the continuum between 6400 and 6500{\\AA}, \nextracted from our spectra, is shown in Fig. 2. The width of the eclipse is \n$w=0.17\\pm 0.005$ orbits. With $\\Delta\\phi=0.08$, this implies a disk radius \n$r_{\\rm d}/a=0.31\\pm 0.01$.\n\nFiedler et al. (1997) find a value of 0.11 for the eclipse width of\nthe white dwarf, from analysis of a mean blue light curve in quiescence. The \ndisk as seen in the continuum thus appears to be larger in outburst than in \nquiescence, as expected. \nThe eclipse width values of 0.17 in outburst and 0.11 in \nquiescence are also compatible with the eclipse light curves of Baptista \\& \nCatalan (1999). These authors measured the eclipses of EX\\,Dra\nat various stages in the \noutburst cycle.\n\n\\begin{figure}\n \\includegraphics[height=0.49\\textwidth,angle=270]\n{bh033.f13}\n\\caption{Spectrophotometric light curve of the wavelength range \n6400--6500{\\AA}.}\n\\end{figure}\n\n\\section{Discussion and conclusions}\nWe find evidence for spiral structures in the outburst accretion disk\nof EX\\,Dra similar to those found in IP\\,Peg by Steeghs\\,et\\,al. (1997). \nThe pattern of intensity and velocity perturbations agrees with that predicted \nfrom numerical simulations of spiral shock waves (Steeghs\\,\\&\\,Stehle 1999). It\nis best seen in the \\ion{He}{i} line, somewhat less clearly in the Balmer and \n\\ion{He}{ii} lines. \nIn EX Dra the pattern appears somewhat less clearly and\nasymmetric than in IP\\,Peg.\n\nIn particular, it is less clear in the \n\\ion{He}{ii} line, suggesting lower temperatures and shock strengths\nof the spirals of EX\\,Dra. \nPossibly the observability of spirals in the \\ion{He}{ii} map \nis hampered by strong hot spot emission visible in this line.\n\nWe derive a disk radius \nof $r/a=0.31\\pm0.01$ from the red continuum eclipse light curve.\nFrom numerical simulations, Steeghs \\&\nStehle find that disk sizes \\mbox{$r_{\\rm d}/a\\,=\\,0.3-0.4$} \nare needed to excite \nspirals that are strong enough to generate an observable pattern in the \nspectra.\n(Transformation from $r_{\\rm d}/a$ to $r_{\\rm d}/R_{L_1}$ is given by\nR$_{L_1}=0.53\\,a$ for q=0.75, cp. Plavec \\& Kratochvil 1964.)\nSince the tidal force is a very steep function of $r/a$, the \nspirals rapidly become weak at smaller disk sizes. The {\\mk disk \nsize we find here in EX\\,Dra} is at the lower limit of the required size. \n\nFurther evidence for the size of the disk in EX\\,Dra in outburst was\nobtained by Baptista \\& Catalan (1999). \nRadial intensity distributions presented there\nshow disk radii of 0.30\\,$a$ in quiescence\nand 0.49\\,$a$ in outburst. The authors see hints of spirals in their \neclipse maps, during the early outburst stages.\nThis may be compared with the \nobservations presented here, which show spirals and a \ndisk size of 0.31\\,$a$ three days after the beginning of an outburst.\n \nThe eclipses of the Balmer lines in our spectra yield significantly {\\em smaller} \ndisks sizes than the continuum eclipse, $r_{\\rm dB}/a=0.25\\pm 0.02$.\nSince it is known that the line emission is produced primarily in the outer\nparts of the disk (e.g. Rutten et al. 1994), one might have expected the disk \nas seen in the lines to be larger, if anything, than in the continuum. \n\nA possible resolution of this conflict may lie in the optical depth effects \naffecting the emission lines in systems seen at high inclination. {\\mk The low central \nintensity of the Balmer lines in high-inclination CVs (often below the continuum)\nshows that such effects are strong. As shown by Horne \\& Marsh (1986),\nthe effects are strongest for lines of sight parallel and perpendicular\nto the orbital motion, leading to reduced line emission from these directions\ncompared to intermediate lines of sight (near $45^\\circ$ to the orbit).\nThe bias towards intermediate angles will give the appearance of a somewhat\nsmaller disk size. It is still to be determined if this suggestion also\nworks quantitatively.}\n\n%As shown by\n%Horne \\& Marsh (1986), the low central intensity of the Balmer lines\n%in dwarf nova disks at high orbital inclination are the result of\n%self-absorption in the lines. The self-absorption is strong along\n%lines of sight perpendicular and tangential to the orbits of the gas,\n%where the velocity gradient is small. The effect is weakest along\n%lines of sight at intermediate angles to the orbit, where the gradient\n%of the orbital velocity (projected along the line of sight) is\n%largest. At the very high inclination of EX\\,Dra, the effect could be\n%strong. The outer parts of the disk that determine the eclipse\n%width are seen with the line of sight nearly parallel to the orbital\n%motion. We may expect the emission in these regions to be weakened by \n%self-absorption, thus mimicking a somewhat smaller disk. \n%A more detailed comparison of the Horne \\& Marsh \n%optical depth effect with observations is needed to establish if this\n%explanation is quantitatively adequate.\n\n\\begin{acknowledgements}\nWe thank Dr.\\ Heinz Barwig for providing the photometric information on\nEX\\,Dra. We thank the anonymous referee \nfor the comments, which helped to improve the presentation of the data and to \ncorrect an error. This work was done in the context of the research network \n`Accretion onto black holes, compact objects and protostars' (TMR Grant \nERB-FMRX-CT98-0195). The Isaac Newton \nTelescope is operated on the island of La Palma by the Isaac Newton Group of \nTelescopes in the Spanish Observatorio del Roque de los Muchachos of the \nInstituto de Astrofisica de Canarias.\n\\end{acknowledgements}\n\n\\begin{thebibliography}{}\n\n\\bibitem{} Baptista R., Catalan M.S., 1999, astro-ph/9905096\n\n\\bibitem{} Barwig H., Fiedler H., Reimers D., Bade N., 1993, \n in: Compact Stars in Binary Systems,\n eds.\\ H. van Woerden, Abstracts of IAU Symp.\\ 165, p.\\ 89\n\n\\bibitem{} Billington I., Marsh T.R., Dhillon V.S., 1996, MNRAS 278, 673 \n\n\\bibitem{} Bunk, W., Verbunt, F.; Livio, M., 1990, A\\&A 232, 371\n\n\\bibitem{} Fiedler H., Barwig H., Mantel K.H., 1997 A\\&A, 327, 173\n\n\\bibitem{} Godon P., 1997, ApJ 480, 329\n\n\\bibitem{} Harlaftis E. T., Steeghs D., Horne K., Martin E., Magazzu A.,\n1999, MNRAS 306, 348\n\n\\bibitem{} Horne K., Marsh T., 1986, MNRAS 218, 761\n\n\\bibitem{} Joergens V., Mantel K.H., Barwig H., B\\\"arnbantner O., Fiedler H.,\n 2000 A\\&A, in press\n\n\\bibitem{} Larson R.B., 1990, MNRAS 243, 588\n\n\\bibitem{} Marsh T., Horne K., 1988, MNRAS 235, 269\n\n\\bibitem{} Morales-Rueda L., Marsh T. R., Billington I., 2000, MNRAS, in press \n\n\\bibitem{} Plavec M., Kratochvil P., 1964, Bulletin of the Astronomical \nInstitute of Czechoslovakia 15, 165\n\n\\bibitem{} R\\'o\\.zyczka M., Spruit H.C.,1993, ApJ 417, 677 \n\n\\bibitem{} Rutten R.G.M, Dhillon V.S., Horne K., Kuulkers E., 1994, A\\&A 283, 441\n\n\\bibitem{} Sawada, K., Matsuda, T., Hachisu, I., 1986, MNRAS 219, 75\n\n\\bibitem{} Sawada, K., Matsuda, T., Inoue M., Hachisu, I., 1987, MNRAS, 224, 307\n\n\\bibitem{} Spruit H.C., 1987, A\\&A 184, 173 \n\n\\bibitem{} Spruit H.C., 1998, astro-ph/9806141\n\n\\bibitem{} Spruit H.C., Matsuda T., Inoue M. and Sawada K., 1987, MNRAS 229, \n517 \n \n\\bibitem{} Steeghs D., Harlaftis E.T., Horne K., 1997 MNRAS 290, 28,\nerratum in 1998 MNRAS 296, 463\n\n\\bibitem{} Steeghs D., Horne K., Stehle R., Harlaftis E.T., 1998, AAS 193, 520\n\n\\bibitem{} Steeghs D., Stehle R., 1999, MNRAS 307, 99 \n\n\\bibitem{} Yukawa H., Boffin H. M. J., Matsuda T., 1997, MNRAS 292, 321\n\n\\bibitem{} VSNET, 1998, http://www.kusastro.kyoto-u.ac.jp/vsnet\n\n\\end{thebibliography}\n\n\\end{document}\n"
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[
{
"name": "astro-ph0002302.extracted_bib",
"string": "\\begin{thebibliography}{}\n\n\\bibitem{} Baptista R., Catalan M.S., 1999, astro-ph/9905096\n\n\\bibitem{} Barwig H., Fiedler H., Reimers D., Bade N., 1993, \n in: Compact Stars in Binary Systems,\n eds.\\ H. van Woerden, Abstracts of IAU Symp.\\ 165, p.\\ 89\n\n\\bibitem{} Billington I., Marsh T.R., Dhillon V.S., 1996, MNRAS 278, 673 \n\n\\bibitem{} Bunk, W., Verbunt, F.; Livio, M., 1990, A\\&A 232, 371\n\n\\bibitem{} Fiedler H., Barwig H., Mantel K.H., 1997 A\\&A, 327, 173\n\n\\bibitem{} Godon P., 1997, ApJ 480, 329\n\n\\bibitem{} Harlaftis E. T., Steeghs D., Horne K., Martin E., Magazzu A.,\n1999, MNRAS 306, 348\n\n\\bibitem{} Horne K., Marsh T., 1986, MNRAS 218, 761\n\n\\bibitem{} Joergens V., Mantel K.H., Barwig H., B\\\"arnbantner O., Fiedler H.,\n 2000 A\\&A, in press\n\n\\bibitem{} Larson R.B., 1990, MNRAS 243, 588\n\n\\bibitem{} Marsh T., Horne K., 1988, MNRAS 235, 269\n\n\\bibitem{} Morales-Rueda L., Marsh T. R., Billington I., 2000, MNRAS, in press \n\n\\bibitem{} Plavec M., Kratochvil P., 1964, Bulletin of the Astronomical \nInstitute of Czechoslovakia 15, 165\n\n\\bibitem{} R\\'o\\.zyczka M., Spruit H.C.,1993, ApJ 417, 677 \n\n\\bibitem{} Rutten R.G.M, Dhillon V.S., Horne K., Kuulkers E., 1994, A\\&A 283, 441\n\n\\bibitem{} Sawada, K., Matsuda, T., Hachisu, I., 1986, MNRAS 219, 75\n\n\\bibitem{} Sawada, K., Matsuda, T., Inoue M., Hachisu, I., 1987, MNRAS, 224, 307\n\n\\bibitem{} Spruit H.C., 1987, A\\&A 184, 173 \n\n\\bibitem{} Spruit H.C., 1998, astro-ph/9806141\n\n\\bibitem{} Spruit H.C., Matsuda T., Inoue M. and Sawada K., 1987, MNRAS 229, \n517 \n \n\\bibitem{} Steeghs D., Harlaftis E.T., Horne K., 1997 MNRAS 290, 28,\nerratum in 1998 MNRAS 296, 463\n\n\\bibitem{} Steeghs D., Horne K., Stehle R., Harlaftis E.T., 1998, AAS 193, 520\n\n\\bibitem{} Steeghs D., Stehle R., 1999, MNRAS 307, 99 \n\n\\bibitem{} Yukawa H., Boffin H. M. J., Matsuda T., 1997, MNRAS 292, 321\n\n\\bibitem{} VSNET, 1998, http://www.kusastro.kyoto-u.ac.jp/vsnet\n\n\\end{thebibliography}"
}
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astro-ph0002303
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Design optimization of MACHe3,\\ a project of superfuid \hetrois detector for direct Dark Matter search.
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[
{
"author": "F. Mayet $^{a,}\\!$\\thanksref{corr}"
}
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MACHe3 (MAtrix of Cells of superfluid \hetro) is a project of a new detector for direct Dark Matter (DM) search. A cell of superfluid \hetrois has been developed and the idea of using a large number of such cells in a high granularity detector is proposed. \noindent This paper presents, after a brief description of the superfluid \hetrois cell, the simulation of the response of different matrix configurations allowing to define an optimum design as a function of the number of cells and the volume of each cell. The background rejection, for several configurations, is presented both for neutrons and \gams of various kinetic energies.
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"name": "mac3new.tex",
"string": "\\documentclass{elsart}\n\\usepackage{graphicx}\n\\usepackage{amsmath}\n\\usepackage{amssymb}\n%\n%\n%\n\\newcommand{\\GeVc} {\\mbox{$ {\\mathrm{GeV}}/c $}}\n\\newcommand{\\GeVcc} {\\mbox{$ {\\mathrm{GeV}}/c^2 $}}\n\\newcommand{\\MeVc} {\\mbox{$ {\\mathrm{MeV}}/c $}}\n\\newcommand{\\hetrois} {\\mbox{$ ^{3}{\\mathrm{He}} $}~}\n\\newcommand{\\hetro} {\\mbox{$ ^{3}{\\mathrm{He}} $}}\n\\newcommand{\\tritium} {\\mbox{$ ^{3}{\\mathrm{H}} $}~}\n\\newcommand{\\hequatre} {\\mbox{$ ^{4}{\\mathrm{He}}}}\n\\newcommand{\\citeup}{\\cite}\n\\newcommand{\\cher}{\\u{C}erenkov }\n\\newcommand{\\Cher}{\\u{C}ERENKOV }\n\\newcommand{\\neut}{$\\tilde{\\chi}$~}\n\\newcommand{\\neutt}{$\\tilde{\\chi}$}\n\\newcommand{\\mydeg} {\\mbox{$ ^\\circ $}}\n\\newcommand{\\DM} {Dark Matter}\n\\newcommand{\\gam} {{$\\gamma$-ray}~} \n\\newcommand{\\gams} {{$\\gamma$-rays}~} \n\n\n\n\n\n%\n%\n% A useful Journal macro\n\\def\\Journal#1#2#3#4{{#1} {\\bf #2}, #3 (#4)}\n%\n% Some useful journal names\n\\def\\NCA{\\em Nuovo Cimento}\n\\def\\NIM{\\em Nucl. Instrum. Methods}\n%\\def\\NIMA{{\\em Nucl. Instrum. Methods} A}\n\\def\\NIMA#1#2#3{{\\rm Nucl.~Instr.~and~Meth.} {\\bf#1} (19#2) #3}\n\\def\\NPB{{\\em Nucl. Phys.} B}\n\\def\\PLB{{\\em Phys. Lett.} B}\n%\\def\\PRL{\\em Phys. Rev. Lett.}\n\\def\\PRD{{\\em Phys. Rev.} D}\n\\def\\PRB#1#2#3{{\\rm Phys. Rev.} {\\bf{B#1}} (19#2) #3}\n\\def\\ZPC{{\\em Z. Phys.} C}\n\\def\\PRL#1#2#3{{\\rm Phys.~Rev.~Lett.} {\\bf{#1}} (19#2) #3}\n%\n%\n%\n\\begin{document}\n\\runauthor{ }\n\\begin{frontmatter}\n\\title{Design optimization of MACHe3,\\\\ a project of superfuid \\hetrois detector for direct Dark Matter search.}\n\\author{F. Mayet $^{a,}\\!$\\thanksref{corr}}\n\\author{, D. Santos $^{a,}\\!$\\thanksref{corr}}\n\\author{, G. Perrin $^{a}$,}\n\\author{ Yu. M. Bunkov $^{b}$, H. Godfrin $^{b}$}\n\\thanks[corr]{corresponding authors : Frederic.Mayet@isn.in2p3.fr, santos@isn.in2p3.fr, tel: +33 4-76-28-40-21, fax: +33\n4-76-28-40-04}\n\\address{$^{a}$ Institut des Sciences Nucl\\'eaires, \\\\\n CNRS/IN2P3 and Universit\\'e Joseph Fourier, \\\\\n 53, avenue des Martyrs, 38026 Grenoble cedex, France}\n\\address{$^{b}$ Centre de Recherche sur les Tr\\`es Basses Temp\\'eratures, \\\\\n CNRS, BP166, 38042 Grenoble cedex 9, France} \n\\begin{abstract}\nMACHe3 (MAtrix of Cells of superfluid \\hetro) is a project of a new detector for direct Dark Matter (DM) search. A cell of superfluid \\hetrois\nhas been developed and the idea of using a large number of such cells in a high granularity detector is proposed.\n\\noindent\nThis paper presents, after a brief description of the superfluid \\hetrois cell, the simulation of the response \n of different matrix configurations allowing to define an optimum design as a function of the number of cells and the volume\n of each cell. The background rejection, for several configurations, is presented both for neutrons and \\gams of various kinetic\n energies.\n\\end{abstract}\n\\begin{keyword}\nDark Matter, Supersymmetry, Superfluid Helium-3, Bolometer.\\\\ {\\it PACS : }95.35; 67.57; 07.57.K; 11.30.P\n\\end{keyword}\n\\end{frontmatter}\n\\newpage\n\\section{Introduction to MACHe3}\nAs previously suggested \\cite{vieux1,vieux2}, superfluid \\hetrois provides a suitable working medium for the detection of low energy \nrecoil interactions. Recent studies \\cite{prl95} have shown the possibility to use a superfluid \\hetrois cell at ultra low temperatures\n(T$\\simeq$100 $\\mu$K).\nThe primary device consisted of a small copper cubic box (V$\\simeq$ 0.125 cm$^{3}$) filled with \\hetro. It is immersed in a larger\nvolume containing liquid \\hetrois and thin plates of copper nuclear-cooling refrigerant, see fig. \\ref{fig:design}. \nTwo vibrating wires are placed inside the cell, forming a Lancaster type bolometer\\cite{prl95}. A small hole on one \nof the box walls connects the box to the main \\hetrois volume, thus allowing the diffusion of the thermal excitations of the \\hetrois generated \nby the energy deposited in the bolometer by the interacting particle.\\\\\nThis high sensitivity device is used as follows : the incoming particle deposits an amount of energy in the cell, which is converted into \n\\hetrois quasiparticles. These are detected by their damping effect on the vibrating wire. It must be pointed out that the size of the\nhole governs the relaxing time (quasiparticles escape time) and the Q factor of the resonator governs the rising time, see figure \n\\ref{fig:signal}. The present device has a rather high Q factor (Q $\\simeq 10^{4}$), giving a rising time of the order of one second.\nAlthough the primary experiment was still rudimentary, it has allowed to detect signals down to a threshold of 1 keV \\cite{prl95}.\nMany ideas are under study to improve the sensitivity of such a cell. Recently, the fabrication of \nmicromechanical silicon resonators has been reported \\cite{trique} and the possibility to use such wires at\nultra-low temperatures is under study.\\\\\nThe aim of the present article is to show that, by using a large number of these cells, a \nhigh granularity superfluid \\hetrois detector could be used for direct Dark Matter (DM) search\\footnote{It should be noticed that such a device need \nto be placed in an underground site to \nreduce cosmic rays (mainly muons) background. It should also be surrounded by neutron and \\gam shieldings.}. \nFor this purpose we have evaluated, by simulation of different kind of background events, the rejection coefficients that may be achieved with such a device.\n%\n\\section{Particle interactions in \\hetrois}\nAs other direct DM search detectors (Edelweiss\\cite{edel}, CRESST\\cite{cresst}, CUORE\\cite{cuore}), the identification of \nWIMPs (\\neutt)\\footnote{In particular, we shall suppose all through this work a neutralino (\\neutt), the lightest supersymmetric\nparticle, as the particle making up the bulk of galactic cold DM.} may be obtained by detecting \ntheir elastic scaterring on a nucleus of a sensitive medium. \nIn the case of \\hetro, the \\neut is expected to transfer \\cite{next} up to 6 keV. The maximum \\hetrois recoil energy is given by :\n\\begin{center}\n$\\mathrm{E}^{max}_{recoil}=2\\times \\frac{mM^{2}}{(m+M)^2}\\times v^2$\n\\end{center}\n\\noindent\nwhere $m$ is the mass of the \\hetrois nucleus, $M$ the mass of the \\neut and $v$ is the relative speed of the \\neut.\nAssuming that $M \\gg m$, as the accelerator experiments claim , this relation yields to $\\mathrm{E}^{max}_{recoil}=2mv^2$, which gives for $v \\simeq 300 km.s^{-1}$, \na maximum recoil energy of $\\sim$ 6 keV.\\\\\nHence, in order to evaluate the\nexpected background for such a detection, it is necessary to know the proportion of events releasing less than 6 keV in the \n\\hetrois cell.\nThe main background components for direct DM search are : thermal and fast neutrons, muons and gamma rays.\n%\n%\n%\n\\subsection{Neutron interaction in \\hetrois}\n\\label{sec:intera}\nThe total cross-section interaction for a neutron in \\hetrois ranges from $\\sigma_{tot} \\simeq 1000$ barns, \nfor low energy neutrons(E$_{n} \\simeq$ 1 eV), down to $\\sigma_{tot} \\simeq 1$ barn\nfor 1 MeV neutrons. The main processes are : elastic scattering which starts being predominant above 600 keV, and neutron \ncapture: \\hetro(n,p)\\tritium , which is largely predominant for low energy neutrons ($E_{n} \\leq 10$ keV) :\n\\begin{center}\nn+ $^{3}$He $\\rightarrow$ p+$^{3}$H +764 keV\n\\end{center}\n\\noindent\nThe energy released by the neutron capture is shared by the recoil ions : the tritium $^{3}$H with kinetic energy 191 keV \nand the proton with kinetic energy 573 keV. The range \\cite{ltemp} for these two particles\nis fairly short : typically 12 $\\mu$m for tritium and 67 $\\mu$m for proton; consequently neutrons undergoing capture in \\hetrois are expected \nto produce 764 keV within the cell, \nthus being clearly separated from the expected \\neut signal (E $\\leq $ 6keV). The tritium produced by neutron capture\nwill eventually decay with a half-life of 12 years by $\\beta$-decay with an end-point electron spectrum at 18 keV. It \nmeans that the number of neutrons capture per cell must be counted to estimate the contribution of this kind of events\non the false \\neut rate.\\\\\nThe capture cross-section decreases with increasing neutron kinetic energy, but on the other hand, the energy released in \nthe \\hetrois cell by the elastic scattering is getting larger, thus\ndiminishing the probability to leave less than 6 keV. From this, it is clear that the worst case will be 8 keV neutrons for which the capture \nprocess is\nless predominant, and the energy left by (n,n) interaction is always less or equal to 6 keV.\\\\\nIn order to reduce contamination from neutron background, the idea is either to have a correlation among the cells, which means a large number \nof \\hetrois cells, or to have a cell large enough for the neutron to be slowed down until it is captured.\n%\n%\n%\n\\subsection{$\\gamma$-ray interaction in \\hetrois}\nAs \\hetrois presents the property to have a low\nphotoelectric cross-section, Compton scaterring is largely predominant between 100 keV and 10 MeV (for 100 keV \\gams : \n$\\sigma_{comp}/\\sigma_{phot} \\simeq$ 10). Consequently, the strategy to\nseparate a \\neut event from a $\\gamma$-ray event is two fold : either the cell is large enough for the $\\gamma$-ray to undergo multi-Compton \nscattering within one cell \\footnote{This will of course be efficient for an energy greater than 10 keV.}, or the number of cells in the \nmatrix is large enough so that there could be an\ninteraction in more than one cell (this will be referred to as a correlated event or a multi-cell event). It will be shown, in the next\nsection, that having a relatively large cell in a large matrix presents the best rejection against $\\gamma$-ray events.\\\\\nThe copper used to build the cells must be produced by a controlled procedure with respect to the radioactive contaminations. Nevertheless, the interaction\nof \\gams with the copper will produce X-rays and scaterred electrons by Compton and photo-electric interactions. These kind of interactions have been\ntaken into account in our simulations and they enhance the correlation among the different cells fired by an incoming \\gam.\n%\n%\n% \n\\section{Simulation of the response of MACHe3 to background events.}\n\\label{simumatrix}\nThe aim of this simulation is to evaluate the capability of a superfluid \\hetrois matrix to reject background events, by taking advantage \nboth on correlation among the cells (multi-cell events) and energy loss measurement. The simulation has been done with a complete Monte-Carlo \nsimulation using GEANT3.21 \\cite{geant} package and in particular the GCALOR-MICAP(1.04/10) \\cite{micap} package for slow neutrons.\nThe simulated detector consists of a cube containing a variable number of cubic \\hetrois cells, as it can be seen on figure \\ref{fig:10kev}. It is immersed in a large volume containing \\hetrois\n($\\rho_{SF}$=0.08 $g.cm^{-3}$). Each\ncell is surrounded by a thin copper layer and it is separated from the others by a gap of 2 $mm$ (filled with \\hetro). The events are generated \nin a direction perpendicular\\footnote{It has been checked that this procedure does\nnot affect the values and general behaviour of the matrix parameters, keeping the calculation time short.} to one of the matrix faces. The number of\nevents per simulation is of the order of 200$\\times10^{3}$.\nThe idea is to find the best matrix design (number of cubic cells and the size of each cell) for which\n the rejection power, taking into account the correlation among the cells and the energy loss measurement, is the highest. \n\n\\noindent\nAs said previously, a typical \\neut is expected to release less than 6 keV in the \\hetrois cell. As the elastic \ncross-section between a \\neut and \\hetrois is fairly small ($\\sigma \\lesssim\n10^{-3} pb$), a\n\\neut event is expected to be characterized by a single-cell event, with equal probability among all the cells of the matrix.\\\\\nConsequently, the rejection against background events will be achieved by choosing only events having the following characteristics :\n\\begin{itemize}\n{\n\\item Only one cell fired (single-cell event). The quality parameter related to this selection will be defined below as C$_{geo}$.\n\\item Energy measurement in this cell below 6 keV and above a threshold of 0.5 keV (quality parameter : R$_{ener}$).\n\\item An additional constraint can be imposed : the fired cell is in the inner part of the matrix (quality parameter : C$_{veto}$). This condition, which considers the outermost cell layer\nas a veto, will allow to reject low energy neutrons interacting elastically, as shown below.\n}\n\\end{itemize}\nLet N be the number of events giving a signal in the matrix (any energy, any number of cells), N$_{1}$ the number of single-cell events \n(any energy) and N$_{6}$ the number of single-cell events with an energy measurement below 6 keV. M$_{1}$ and M$_{6}$ will be referred with\nthe same meaning as N$_{1}$ and N$_{6}$, but for events firing a cell in the inner part of the detector (out of the veto).\\\\\nThen, we may define the following parameters as :\n\\begin{itemize}\n{\n\\item C$_{geo}$$=\\frac{\\mathrm{N}_{1}}{\\mathrm{N}}$ ; the correlation coefficient (proportion of single-cell events).\n\\item R$_{ener}=\\frac{\\mathrm{N}_{1}}{\\mathrm{N}_{6}}$ ; the rejection by energy measurement.\n\\item C$_{veto}=\\frac{\\mathrm{N}_{1}}{\\mathrm{M}_{1}}$ ; the veto coefficient.\n\\item R$_{int}=\\frac{\\mathrm{N}}{\\mathrm{M}_{6}}$ ; the intrinsic rejection.}\n\\end{itemize}\n\n\\subsection{Design optimization.}\nIn order to define the optimimum matrix design (number of cubic cells and size of the cells), a complete simulation has been done.\nThe results concerning three types of background are presented : 10 keV\nneutrons, 1 MeV neutrons and 2.6 MeV $\\gamma$-rays. For each sample, the four parameters defined above are evaluated in various configurations : cell size\nof 0.5, 1.0, 2.5 and 5.0 $cm$ and matrix containing $3^{3}$, $5^{3}$, $7^{3}$, $10^{3}$ ($20^{3}$) cells. The best design will be the one for which C$_{geo}$\n is the lowest (thus minimizing the proportion of single-cell background events) and R$_{ener}$ is the highest (meaning a low proportion of background events\n with an energy measurement below 6 keV).\n%\n\\subsection{$\\gamma$-ray background.} \nDue to the fact that it is a simulation without any constraint on the detector volume, the correlation coefficient depends\nstrongly on the size of the matrix, with a small dependence on the cell size, as shown on figure \\ref{fig:cgeo26m}. \nThe best correlation is obtained for 8000 cells of size\n2.5 $cm$ (C$_{geo} \\simeq 45 \\%$). In order to keep a reasonable number of cells, it can be noticed that a matrix \nof same volume (1000 cells of 5.0 $cm$ side) presents also a good correlation \n(C$_{geo} \\simeq 55 \\%$). A multi-cell event can either be a multi-Compton event, or a single-Compton event for which the \nelectron is escaping the cell and firing a neighbouring cell. This last process depends mainly on the cell size and explains the fact that C$_{geo}$ \nremains constant for cell sides larger than 1 $cm$, see fig. \\ref{fig:cgeo26m}.\\\\\nIt has been found that the energy rejection (R$_{ener}$) depends mainly on the size of the cell.\nFor a large cell (5 $cm$ side), a rejection R$_{ener} \\simeq 90 $ is obtained, allowing to reject 98 \\%\nof the 2.6 MeV $\\gamma$-rays.\nThe total rejection (see fig. \\ref{fig:rejall}), which take into account the correlation and energy selection, together with \nveto selection and interaction probability, is R$\\simeq$700 for 1000 cells of size 5.0 $cm$ (for 2.6 MeV \\gams).\\\\\nConsequently, for \\gam background rejection purpose, a cell of 5.0 $cm$ side presents the best energy rejection and a matrix of 1000 cells \nof this size allows to obtain a good correlation coefficient. In section \\ref{gamrejsec}, the rejection of such a matrix as a function\nof the \\gam energy will be presented.\n% \n%\n\\subsection{Low energy neutron background.}\nFigures \\ref{fig:cgeon10} and \\ref{fig:cenern10} present the correlation coefficient (C$_{geo}$) and the energy rejection \n(R$_{ener}$) as a function of the cell size, for different matrix sizes and an incident neutron energy of 10 keV. \nThe correlation coefficient depends both on the size of the cell\nand of the matrix, since the neutron capture is the predominant process at this energy. \nThe best correlation is obtained for 8000 cells of size\n2.5 $cm$ (C$_{geo} \\simeq 85 \\%$), but a larger cell (5 $cm$ side), with only 1000 cells presents also a similar correlation \n(C$_{geo} \\simeq 86 \\%$). The energy rejection (R$_{ener}$) depends not only on the size of the cell, but also on the size \nof the matrix. \nThe best rejection (R$_{ener}\\simeq 22$) is achieved for a large cell (5 $cm$ side) and a large matrix (1000 cells). \nThe total rejection, shown on fig.\\ref{fig:rejall}, is R$\\simeq$80 for 1000 cells of 5 $cm$ side, meaning that only 1.25 \\% of the incoming\n10 keV neutrons may simulate a \\neut event. It must be pointed out that 10 keV represent the worst case for rejection purpose, as it can be\nseen on figure \\ref{fig:rejall}. \n\n\\subsection{Fast neutron background.}\nFigures \\ref{fig:cgeon1} and \\ref{fig:cenern1} show the correlation coefficient (C$_{geo}$) and the energy rejection \n(R$_{ener}$) as a function of the cell size, for different matrix sizes and an incident neutron energy of 1 MeV. As well as \nfor low energy neutrons, the\ncorrelation coefficient depends on the matrix and cell sizes. A correlation of $\\sim$ 65 \\% is achieved for a\nlarge \\hetrois volume (1000 cells of 5 $cm$ or 8000 cells of 2.5 $cm$). \nA large matrix of big cells (1000 cells of 5 $cm$) allows to obtain a rather large energy rejection (R$_{ener} \\simeq 500$),\nleading to a total rejection of the order of 1000 (see fig.\\ref{fig:rejall}), meaning that 99.9\\% of 1 MeV neutrons arriving on\nthe \\hetrois matrix may be discriminated from a \\neut event.\\\\\n\\noindent\nFor these three particle samples, the simulation has shown that a large cell (125 $cm^3$) allows to obtain \na large energy rejection, and a large matrix (1000 cells or more) allows to have a good correlation among cells, \nthus rejecting efficiently \\gams and neutrons of kinetic energy E$\\simeq$1 MeV. Hence, for background \nrejection consideration the optimum configuration is a matrix of 1000 cells of 5 $cm$ side.\n\n\\subsection{Rejection power of a superfluid \\hetrois matrix.}\nAs shown previously, a matrix of $10^{3}$ large cells (125 $cm^{3}$ each) presents the best rejection power, both for neutrons and\n$\\gamma$-rays. This section presents the various coefficients, as defined in section \\ref{sec:intera}, as a function of the energy of the \nincoming particle.\\\\\n\\subsubsection{Rejection against \\gam background.}\n\\label{gamrejsec}\nFigure \\ref{fig:coeffgam} shows the correlation coefficient, the veto coefficient, the energy rejection and the total rejection as a function of\nthe $\\gamma$-ray energy. A good correlation is achieved for high energy $\\gamma$-rays ($E_{\\gamma} \\geq $1 MeV), whereas low\nenergy $\\gamma$-rays are mainly rejected by the veto. In fact, 80 keV X-rays undergo photoelectric effect in\nthe copper layer ($\\sigma_{phot} \\simeq 10^{4}$barn)\nsurrounding the cell; the scaterred electrons may escape the copper layer and leave a few keV in the cell. This will mainly happen\nin the outermost cells.\\\\\nFigure \\ref{fig:rejall} presents the total rejection as a function of the $\\gamma$-ray energy. It can be concluded that an \\hetrois\nmatrix provides a rejection ranging between 10 and 1000, depending on the $\\gamma$-ray energy. It must be pointed out that this is\nthe rejection power of the matrix itself. For instance, 90\\% of X-rays will be rejected by the matrix, but the flux of\nsuch particles will be reduced substantially by an inner and outer copper shielding.\n\\subsubsection{Rejection against neutron background.}\nFigure \\ref{fig:coeffneut} presents the four matrix parameters as a function of the neutron energy. A correlation better than 70 \\% is \nachieved for neutrons\nof energy greater than 100 keV (fig. \\ref{fig:coeffneut}, upper left), while low energy neutrons are mainly rejected by the veto. Indeed, 60 \\% of 10 keV neutrons are captured in\nthe first layer (fig. \\ref{fig:coeffneut}, upper right). The energy measurement constitute an efficient selection for low energy \nneutron (R$_{ener}\\simeq$ 100 for 1 keV neutrons) and for\nfast neutrons (R$_{ener}\\simeq$ 1000 for 1 MeV neutrons). As expected 10 keV neutrons have the worst energy rejection (R$_{ener}\\simeq$ 15).\\\\\nThe total rejection\\footnote{This coefficient takes into account the interaction probability and will be used to evaluate the \nfalse event rate.} (ratio between number of incoming particles and number of false \\neut events), shown on figure \\ref{fig:rejall},\nindicates that only one 1 keV\nneutron out of 2000 may simulate a \\neut event. The rejection falls down to 75 for 10 keV neutrons (mainly rejected by the veto) and is of the\norder of 1000 for 1 MeV neutrons.\n\n\\noindent \nIt must be pointed out that the evaluated rejection is for a \"naked matrix\", i.e. without taking into account any lead or paraffin shielding\n or any separation between electron and ion recoils. It represents the capability of the \\hetrois matrix to reject background events by means of energy loss\nmeasurements and correlation considerations. As a conclusion, it can be said that the \\hetrois matrix presents a rejection power ranging between 75 and 2000 for\nneutrons, and between 10 and 800 for $\\gamma$-rays,depending on their kinetic energies.\n\n\\subsection{An evaluation of the neutron-induced false event rate.}\nAs neutrons recoiling off nuclei may easily simulate a \\neut event, it is crucial to evaluate the neutron-induced false event rate.\\\\\nIn contrast to most DM detectors, MACHe3 may be sensitive to rather low energy neutrons, and its response depends strongly on their kinetic\nenergies. For this purpose, a simulation \nof a paraffin neutron shielding has been done, in order to evaluate the expected neutron spectrum trough this shielding.\\\\\nThe simulated device is a large ($1m\\times 1m$) paraffin block ($\\rho$=0.95 g.cm$^{-3}$) with a width of 30 $cm$. \nIn order to be conservative, as well as keeping the calculation times short, we choose to generate the events in a direction perpendicular \nto the face of the paraffin block and considering that all neutrons crossing the block are supposed to enter the matrix volume.\\\\\nA benchmark study has been done, to compare MCNP calculation code\\cite{mcnp} and GEANT3.21. We found that these two codes give similar results, \nexcept for thermal neutrons (below 1 eV) for which GEANT underevaluate the flux. Again, to be conservative, we choose the one giving \nthe highest flux (MCNP)\\footnote{MCNP is much faster than GEANT, in this case, allowing shorter calculation times.}.\\\\\nWe have used the measured neutron spectrum \\cite{Chazal:1998qn} in Laboratoire Souterrain de Modane (LSM), between 2 and 6 MeV \\footnote{The thermal neutron flux, evaluated \nin \\cite{Chazal:1998qn} to be (1.6$\\pm0.1)\\times 10^{-6} cm^{-2}s^{-1}$, will be highly suppressed by the 30 $cm$ paraffin shielding}, with an\nintegrated flux of $\\Phi_{n}\\simeq 4\\times 10^{-6} cm^{-2}s^{-1}$. We found an overall neutron flux through the shielding of 5.1$\\times 10^{-8} cm^{-2}s^{-1}$, with the \nneutron kinetic energy ranging between\n$10^{-2}$ eV and 6 MeV (see the upper curve on fig. \\ref{fig:neutfalse}).\\\\\nUsing this flux and the expected rejection factor (fig. \\ref{fig:rejall}), we evaluated the false\n\\neut rate induced by neutron background, see fig. \\ref{fig:neutfalse}. We \nfound a rate of $\\sim$0.1 false event per day through the\n1.5$m^{2}$ surface detector (1000 cells of 125 $cm^{3}$). Even with such a conservative approach, this contamination is much lower than the expected \\neut rate (of the order of \n$\\sim$1 day$^{-1}$\nin a detector of this size \\cite{next}). \n\\subsection{An evaluation of the muon-induced false event rate.}\nThe muon background flux in an underground laboratory (Gran Sasso) has been measured by \\cite{muons}. They found a mean flux of \n$\\Phi_{\\mu}=2.3\\times 10^{-4} m^{-2}s^{-1}$\nfor an average kinetic energy $<\\!$$E$$>$=200 GeV.\\\\\nAn evaluation of the $\\mu$-induced event rate has been done. The same procedure as above (see section \\ref{simumatrix}) has been used, \nwithout paraffin shielding; i.e. the events are\ngenerated in a direction perpendicular to one of the matrix faces. This is a conservative approach because the worst case is in which muons are \npassing in between 2 cell layers. As expected, most of the $\\mu$-events interact in all the crossed cells (75\\%\ninteract in 10 cells, with an average energy left of $\\sim$ 1 MeV). The correlation coefficient is C$_{geo}\n\\simeq 2.1\\%$ (meaning 97.9$\\%$ of $\\mu$-events are rejected), with an energy rejection R$_{ener} \\simeq 40$, leading to an overall rejection \nof R$\\simeq 2100$. This lead to a\n$\\mu$-induced false \\neut rate of the order of 0.0095 day$^{-1}$m$^{-2}$, which is more than two orders of magnitude below the\nexpected \\neut rate. The layers may be shifted, thus allowing a much higher rejection against muon background\nevents.\n\\subsection{\\gam background.}\nAs shown in section \\ref{gamrejsec}, a high granularity superfluid \\hetrois detector provides an intrinsic rejection ranging \nbetween 10 and 800 for $\\gamma$-rays, depending on their kinetic energies. This selection, based on the correlation among the cells \nand energy loss measurement, may be improved by adding a discrimination between\nrecoils and electrons. Different experimental approaches should be tested. A complete study of an inner and outer cryostat shielding is also\nneeded, as well as an evaluation of natural radioactivity of materials. Nevertheless, this simulation indicates that an important intrinsic rejection can be achieved.\n\n\\section{Conclusion}\nIn this prospective paper, we have demonstrate that a large matrix ($\\sim$ 1000 cells) of large cells (125 $cm^{3}$) is the\npreferred design for a superfluid \\hetrois detector searching for DM, as far as background rejection is concerned. \nAn experimental work needs to be done to demonstrate the possibility to use such a large volume of superfluid $ ^{3}{\\mathrm{He}}$-B at ultra-low temperatures. This work has evaluated the background\nrejection of a high granularity superfluid \\hetrois detector for a large range of kinetic energies,\nboth for neutrons and $\\gamma$-rays. It has been shown that, by means of\ncorrelation among the cells and energy loss measurement, a high rejection may be obtained for $\\gamma$-ray, neutron and muon background. Using the\nmeasured muon and neutron flux in an underground laboratory, we have evaluated the contamination to be one order of \nmagnitude (two orders\nfor muons) less than the expected \\neut rate. For background rejection purpose, the main advantage of a superfluid \\hetrois detector is to present a high \nrejection against neutron background, mainly because of the\nhigh capture cross-section at low energy. As neutrons interact {\\it a priori} like \\neutt, they are the\nultimate background noise for DM detectors.\\\\\n\n\\textbf{Acknowledgements}\\\\\nThe authors are grateful to D. Kerdraon and L. Perrot for the help concerning the use of MCNP calculation code, and also\nF. Ohlsson-Malek for the fruitful discussions on the GEANT code. \n\n\\begin{thebibliography}{99}\n\\bibitem{vieux1}G. R. Pickett, in {\\em Proc. of the European Workshop on Low Temperature Devices for \nthe Detection of Low Energy Neutrinos and Dark Matter (1988 Annecy, France)}, edited by L. Gonzales-Mestres and D. Perret-Gallix (Ed.\nFrontieres).\n\n\\bibitem{vieux2}Yu. M. Bunkov \\textit{et al.}, in {\\em Proc. of the International Workshop on Superconductivity and Particle Detection (1994 Toledo,\nSpain) eds. T.A. Girard, A. Morales and G. Waysand, World Scientific, p.21 (1995)}\n\n\\bibitem{prl95}D. I. Bradley \\textit{et al.}, \\PRL{75}{95}{1887}.\\\\\nC. B\\\"{a}uerle \\textit{et al.}, \\PRB{57}{98}{22}.\n\\bibitem{trique}S. Triqueneaux \\textit{et al.}, in {\\em Proc. of the 22nd International Conf. on Low Temperature Physics},\nAugust 1999, Physica B (in print).\n\\bibitem{next}D. Santos, F. Mayet, G. Perrin \\textit{et al., to be submitted to Phys. Rev. D}.\n\\bibitem{edel}L. Berge \\textit{et al.}, astro-ph/9801199\n\\bibitem{cresst}M. Bravin \\textit{et al.}, hep-ex/9904005 \n\\bibitem{cuore}A. Alessandrello \\textit{et al.}, in {\\em Proc. Dark matter in astrophysics and particle physics 1998.}\n\\bibitem{ltemp}J. S. Meyer and T. Sloan, J. of Low Temp. Phys. (108) 1997.\n\\bibitem{geant}R. Brun, F. Carminati, {\\em GEANT Detector Description and Simulation Tool}, CERN \nProgam Library Long Writeup W5013, September 1993.\n\\bibitem{micap}J. O. Johnson, T. A. Gabriel, {\\em A user's guide to MICAP}, ORNL/TM-10340, January 1988\\\\\nC. Zeitniz and T. A. Gabriel, \\NIMA{349}{94}{106}.\n\\bibitem{mcnp}J. F. Briesmeister, {\\em MCNP $^{TM}$, A general Monte Carlo N-particle transport code}, LANL Report LA-12625-M(93)\n%\\cite{Chazal:1998qn}\n\\bibitem{Chazal:1998qn}\nV.~Chazal {\\it et al.},\n%``Neutron background measurements in the underground laboratory of Modane,''\nAstropart.\\ Phys.\\ {\\bf 9}, 163 (1998).\n\\bibitem{muons}\nC.~Arpesella,\n%``Background measurements at GRAN SASSO laboratory,''\nLNGS-92-28\n{\\it Contribution to TAUP '91 Workshop, Toledo, Spain, Sep 9-13, 1991}.\\\\\nH. V. Klapdor-Kleingrothaus {\\it et al.}, hep-ph/9910205.\n\\end{thebibliography}\n\\newpage\n\\listoffigures\n\n\n%******************************************************\n% \n\\newpage\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{Fig2BPRB.eps}\n{\\noindent\n\\caption{Ultra-low temperature nuclear stage and bolometer cell.\n\\label{fig:design}}}\n\\end{center}\n\\end{figure}\n%\n\\newpage\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{henri_background.eps}\n{\\noindent\n\\caption{Temperature recorded inside the bolometer as a function of time.\n\\label{fig:signal}}}\n\\end{center}\n\\end{figure}\n%\n\\newpage\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.40]{10kev.matrix.epsi}\n{\\noindent\n\\caption{2-dimensionnal view of a proposed matrix of 1000 cells (125 $cm^{3}$ each). The events generated in a direction \nperpendicular to the upper face, are 10 keV neutrons. It can be noticed that most of\nneutrons of this energy are captured in the first layer.\n\\label{fig:10kev}}}\n\\end{center}\n\\end{figure}\n%\n%\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{cgeo.g26.epsi}\n\\caption{Correlation coefficient (C$_{geo}$) as a function of the size of the \\hetrois cell for 2.6 MeV $\\gamma$-rays. \nThe different curves correspond to different matrix sizes as indicated by the labels. \n\\label{fig:cgeo26m}}\n\\end{center}\n\\end{figure}\n%\n%\n\\newpage\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{cgeo.n10k.epsi}\n\\caption{Correlation coefficient (C$_{geo}$) as a function of the size of the \\hetrois cell for 10 keV neutrons. The different curves\ncorrespond to different matrix sizes as indicated by the labels.\n\\label{fig:cgeon10}}\n\\end{center}\n\\end{figure}\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{cener.n10k.epsi}\n\\caption{Energy Rejection (R$_{ener}$) as a function of the size of the \\hetrois cell for 10 keV neutrons. The different curves\ncorrespond to different matrix sizes as indicated by the labels. \n\\label{fig:cenern10}}\n\\end{center}\n\\end{figure}\n\n\\newpage\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{cgeo.n1m.epsi}\n\\caption{Correlation coefficient (C$_{geo}$) as a function of the size of the \\hetrois cell for 1 MeV neutrons. The different curves\ncorrespond to different matrix sizes as indicated by the labels. \n\\label{fig:cgeon1}}\n\\end{center}\n\\end{figure}\n\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{cener.n1m.epsi}\n\\caption{Energy Rejection (R$_{ener}$) as a function of the size of the \\hetrois cell for 1 MeV neutrons. The different curves\ncorrespond to different matrix sizes as indicated by the labels. \n\\label{fig:cenern1}}\n\\end{center}\n\\end{figure}\n\n\\newpage\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{coeffneut.epsi}\n{\\noindent\n\\caption{Neutrons interacting in MACHe3 : The four matrix parameters, defined in sec. \\ref{simumatrix}, as a function of the neutron energy, for a matrix of 1000 cells (125 $cm^{3}$ each).\n\\label{fig:coeffneut}}}\n\\end{center}\n\\end{figure}\n%\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.55]{coeffgam.epsi}\n{\\noindent\n\\caption{\\gams interacting in MACHe3 : The four matrix parameters, defined in sec. \\ref{simumatrix}, as a function of the $\\gamma$-ray energy, for a matrix of 1000 cells (125\n$cm^{3}$ each).\n\\label{fig:coeffgam}}}\n\\end{center}\n\\end{figure}\n%\n\\newpage\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.8]{rejall.epsi}\n{\\noindent\n\\caption{Total Rejection as a function of the incident particle energy, for a matrix of 1000 cells (125\n$cm^{3}$ each). The different set of points correspond to \\gams (squares) and neutrons (circles). The total rejection is defined as the ratio \nbetween the number of incoming particles and the number of false \\neut events (less than 6 keV in one non-peripheric cell).\n\\label{fig:rejall}}}\n\\end{center}\n\\end{figure}\n\\newpage\n%\n\\begin{figure}\n\\begin{center}\n\\includegraphics[scale=0.60]{neutronfinal.epsi}\n{\\noindent\n\\caption{The upper curve is the simulated neutron spectrum through a 30 $cm$ wide paraffin \nshielding, the measured spectrum at LSM being the input. Comparing with the measured neutron flux, this shielding allows \nan overall reduction factor of $\\sim$ 50. The lowest curve represents the neutron induced false \\neut rate \nin MACHe3. This spectrum has been obtained by combining the upper curve with the total rejection \n(fig. \\ref{fig:rejall}), with a threshold of 500 eV. The overall counting rate, due to neutron background, is \nevaluated to be $\\sim$ 0.1 day$^{-1}$ in a 1000 cells detector.\n\\label{fig:neutfalse}}}\n\\end{center}\n\\end{figure}\n\n\n\n\n\n\\end{document}\n"
}
] |
[
{
"name": "astro-ph0002303.extracted_bib",
"string": "\\begin{thebibliography}{99}\n\\bibitem{vieux1}G. R. Pickett, in {\\em Proc. of the European Workshop on Low Temperature Devices for \nthe Detection of Low Energy Neutrinos and Dark Matter (1988 Annecy, France)}, edited by L. Gonzales-Mestres and D. Perret-Gallix (Ed.\nFrontieres).\n\n\\bibitem{vieux2}Yu. M. Bunkov \\textit{et al.}, in {\\em Proc. of the International Workshop on Superconductivity and Particle Detection (1994 Toledo,\nSpain) eds. T.A. Girard, A. Morales and G. Waysand, World Scientific, p.21 (1995)}\n\n\\bibitem{prl95}D. I. Bradley \\textit{et al.}, \\PRL{75}{95}{1887}.\\\\\nC. B\\\"{a}uerle \\textit{et al.}, \\PRB{57}{98}{22}.\n\\bibitem{trique}S. Triqueneaux \\textit{et al.}, in {\\em Proc. of the 22nd International Conf. on Low Temperature Physics},\nAugust 1999, Physica B (in print).\n\\bibitem{next}D. Santos, F. Mayet, G. Perrin \\textit{et al., to be submitted to Phys. Rev. D}.\n\\bibitem{edel}L. Berge \\textit{et al.}, astro-ph/9801199\n\\bibitem{cresst}M. Bravin \\textit{et al.}, hep-ex/9904005 \n\\bibitem{cuore}A. Alessandrello \\textit{et al.}, in {\\em Proc. Dark matter in astrophysics and particle physics 1998.}\n\\bibitem{ltemp}J. S. Meyer and T. Sloan, J. of Low Temp. Phys. (108) 1997.\n\\bibitem{geant}R. Brun, F. Carminati, {\\em GEANT Detector Description and Simulation Tool}, CERN \nProgam Library Long Writeup W5013, September 1993.\n\\bibitem{micap}J. O. Johnson, T. A. Gabriel, {\\em A user's guide to MICAP}, ORNL/TM-10340, January 1988\\\\\nC. Zeitniz and T. A. Gabriel, \\NIMA{349}{94}{106}.\n\\bibitem{mcnp}J. F. Briesmeister, {\\em MCNP $^{TM}$, A general Monte Carlo N-particle transport code}, LANL Report LA-12625-M(93)\n%\\cite{Chazal:1998qn}\n\\bibitem{Chazal:1998qn}\nV.~Chazal {\\it et al.},\n%``Neutron background measurements in the underground laboratory of Modane,''\nAstropart.\\ Phys.\\ {\\bf 9}, 163 (1998).\n\\bibitem{muons}\nC.~Arpesella,\n%``Background measurements at GRAN SASSO laboratory,''\nLNGS-92-28\n{\\it Contribution to TAUP '91 Workshop, Toledo, Spain, Sep 9-13, 1991}.\\\\\nH. V. Klapdor-Kleingrothaus {\\it et al.}, hep-ph/9910205.\n\\end{thebibliography}"
}
] |
astro-ph0002304
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The frequency content of $\delta$ Sct stars as determined by photometry
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[
{
"author": "Ennio Poretti"
}
] |
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[
{
"name": "eporetti.tex",
"string": "%\\documentstyle[11pt,paspconf,epsf]{article}\n\\documentstyle[11pt,newpasp,twoside,epsfig]{article}\n\\markboth{E. Poretti}{Photometry of $\\delta$ Sct stars}\n\\setcounter{page}{1}\n\n\n\\begin{document}\n\n\\title{The frequency content of $\\delta$ Sct stars as\ndetermined by photometry}\n\n\\author{Ennio Poretti}\n\\affil{Osservatorio Astronomico di Brera, Via E.~Bianchi 46, 23807 Merate, Italy}\n\n\n% The abstract is entered in a LaTeX \"environment\", designated with paired\n% \\begin{abstract} -- \\end{abstract} commands. Other environments are\n% identified by the name in the curly braces.\n\n\n\\begin{abstract}\nThe results obtained by means of the photometric approach to the study of\n$\\delta$ Sct stars are extensively discussed. The different frequency contents of\nthe three best candidates for asteroseismological studies (FG Vir, 4 CVn\nand XX Pyx) are presented and compared; the importance of the amplitude\nvariations and of the combination terms is emphasized. \nThe analysis of other multiperiodic variables shows how a large variety\nof nonradial modes are excited; in some cases, modifications of\nthe power spectrum can be\nobserved over a few years and new modes can be seen to grow. Among monoperiodic\npulsators, constant as well as variable amplitudes can be observed. \nThe difficulty of identifying an \noscillation yielding quantum numbers is emphasized; the possibilities offered by\n$\\delta$ Sct stars belonging to binary systems and open clusters are\ndiscussed. In this respect, combining the photometric and the spectroscopic\napproaches could lead to a solution. A comparison is also made between low- and\nhigh-amplitude pulsators, finding similarities.\n\nThe use of a reliable Period--Luminosity--Colour relationships toward\nthe shortest periods can greatly help \nmode identification in the galactic stars; moreover, it could provide an independent\nverification of extragalactic distances. \n\n\\end{abstract}\n\n% Keywords should be included, but they are not printed in the hardcopy.\n\n\\keywords{photometry, pulsating stars, $\\delta$ Sct stars, data analysis}\n\n\n\\section{Introduction}\n$\\delta$ Sct variables are now a well-defined class of stars.\nThey are located on or just above the zero-age main sequence,\nin the lowest part of the classical instability strip. $\\delta$\nSct stars have masses between 1.5 and 2.5 M$_{\\sun}$ and they are\nclose to the end of the core hydrogen burning phase (Breger \\&\nPamyatnykh 1998). The presence of convective\nzones and related phenomena such as convective overshooting, make them\nvery interesting objects for the understanding of stellar evolution. \nThe investigation of pulsational properties of pre-main sequence stars\nallowed their instability strip in the H-R diagram to be defined\n(Marconi \\& Palla 1998); some of these stars showing $\\delta$ Sct variability\nwere discovered (Kurtz \\& Muller 1999).\n\nPhotometric monitoring is the most practiced approach to study\nthe properties of $\\delta$ Sct stars and several stars have been\ndeeply investigated. However, the spectroscopic approach tells us that\nmany modes that are not photometrically detectable are actually excited.\nRotation acts as an important factor in the increase of the number of\nexcited modes.\n\nThe observed frequencies are between 5 and 35~cd$^{-1}$ and \nmultiperiodicity is very common; only a few stars show a monoperiodic\nbehaviour above the current limit of the detectable amplitude from\nground, i.e., $\\sim$1~mmag. The observed modes are in the domain\nof pressure ($p$) modes; there is no observational evidence that\ngravity ($g$) modes are excited in $\\delta$ Sct stars, even if some cases \nare suggested. At the moment, $g$-modes seem to be present only in\nthe $\\gamma$ Dor stars, which in turn do not show $p$-modes.\n\nThe great observational effort made by several teams allows us to\nhandle a well-defined phenomenological scenario of the $\\delta$\nSct variability. This contribution tries to summarize the results\nobtained in the past years by means of extended photometric time\nseries. The paper is structured as follows:\n\\begin{list} { } { }\n\\item 2.~The best candidates for asteroseismological studies\n\\begin{list} { } { }\n\\item 2.1~FG Vir: 24 independent modes\n\\item 2.2~XX Pyx: strong and rapid amplitude changes \n\\item 2.3~4 CVn: presence of combination terms and amplitude variations\n\\item 2.4~Comparison between FG Vir, XX Pyx and 4 CVn\n\\end{list}\n\\item 3.~Other stars studied by the Merate Group\n\\begin{list} { } { }\n\\item 3.1~44 Tau: variable amplitude and recurrent ratio 0.77\n\\item 3.2~BH Psc: variable amplitude and rich pulsational content\n\\item 3.3~V663 Cas: growth of new modes\n\\item 3.4~The help of the spectroscopic approach\n\\end{list}\n\\item 4.~Monoperiodic pulsators\n\\item 5.~$\\delta$ Sct stars in binary systems\n\\item 6.~$\\delta$ Sct stars in open clusters\n\\item 7.~The frequency content of high amplitude $\\delta$ Sct stars\n\\item 8.~Summing-up and Conclusions\n\\item 9.~The future: the exportation of the results on galactic stars\n to \\\\ \\hspace*{4truemm} extragalactic research\n\\end{list}\n In what manner\nthe photometric results can be used to identify modes (i.e., to\nclassify the oscillation in terms of quantum numbers $n$, $\\ell$ and $m$)\nis discussed by Garrido (2000). Some\nimprovements, both observational and theoretical, are probably\nnecessary to make new, substantial steps forward.\nA better connection between theory and observation will allow us\nto really progress in the asteroseismology of these stars.\n\n\n\\section{The best candidates for asteroseismological studies}\nThe studies and the related papers on $\\delta$ Sct stars\n follow a recurrent paradigm in the process of the\ndetermination of the frequency content. \nIn most cases a first solution, often wrongly considered a ``good'' solution, \nis obtained on the basis of a few, fragmented nights. At this stage, the\nobservations are hardly useful for a significant analysis.\nHowever, since the complicated light behaviour of our stars always\nleaves some unclear facts, the same authors or another team plan a second\nrun. As a consequence, it appears that the solution proposed in the first\npaper was indeed preliminary.\n A very interesting result often obtained while doing this refinement\nis the detection of variations in amplitude and/or in frequency for the excited\nmodes. Therefore, more observations are requested and, in general, they are\nnever sufficient \\ldots\\@ We can however obtain more and more satisfactory results from\nthe observational works on $\\delta$ Sct stars by delving deeper and deeper in this\nprocess, even if it involves stronger and stronger efforts.\nThe three cases reported below are probably the best examples that the \n$\\delta$ Sct community can offer.\n\n\n\\subsection{FG Vir: 24 independent modes} \\label{fg}\n\nFG Vir can be considered a cornerstone in the development of our knowledge\nof $\\delta$ Sct stars. After a few nights of observations by L\\'opez de Coca\net al. (1984), it was studied first by Mantegazza, Poretti, \\& Bossi (1994)\non the basis of a single-site campaign carried out at the European Southern\nObservatory, Chile. These authors proposed seven certain frequencies and a \npossible eighth one; they also claimed the presence of undetected terms,\nowing to the relatively high level of noise in some parts of the power\nspectrum. A successive multisite campaign (Breger et al. 1998)\nconfirmed the seven frequencies,\ndemonstrating how a single site observing run can be successful in the\ndetection of the main components of a multiperiodic pulsator. However, the eighth,\nsmall-amplitude frequency was an alias and the misidentification originated\nfrom the combination of the spectral window with the noise. A search for the\npresence of the hitherto previously undetectable terms was undertaken and the number of\nfrequencies increased to at least 24. However, new campaigns on this star\nare considered necessary to improve the frequency resolution\nand a time baseline of several months is requested.\n\n\n\\begin{figure}[ht]\n\\setlength{\\textwidth}{5.3in}\n\\plotone{eporetti1.eps}\n\\caption{Roughly a half of the $y$ (filled circles) and $v$ (open circles)\nmeasurements obtained during the 1995 multisite campaign on FG Vir are shown.\nThe fits of the 24 frequency solutions\nderived by Breger et al. (1998) are represented as solid curves}\n\\label{multi}\n\\end{figure}\n\nThe light curves obtained in a multisite campaign look quite fine and they\nbear witness to the efforts made by the $\\delta$ Sct researchers to\nimprove the quality and the quantity of the data; Fig.~\\ref{multi} shows the \nvery dense $v$ and $y$ light curves obtained on a baseline spanning 20 days, a subset\nof the 1995 campaign. \nConsidering all the frequencies now known in the light curve, it seems that\nthe pulsation of FG Vir is much more stable than that of XX Pyx and 4 CVn:\nthe amplitude variability is very limited and the frequency values \nseem to be stable over a baseline of decades. The frequencies are mainly \ndistributed in two subgroups: the first ranges from 9.2 to 11.1~cd$^{-1}$,\nthe second from 19.2 to 24.2~cd$^{-1}$. An isolated peak is found at\n 16.1~cd$^{-1}$ and a few between 28.1 to 34.1~cd$^{-1}$. Contrasting with\nthe 22 independent frequencies found, only 2 combination terms have been detected.\n It should be noted that\nthe identification was accepted at an amplitude S/N limit of 4.0 for an\nindependent term and 3.5 for a combination frequency. Kuschnig et al. (1997)\nsupply a theoretical basis for these assumptions. The combination terms are related\nto the $f_1$ term, which has an amplitude 5 times larger than the other ones.\nThis term also displays an asymmetric shape, since the 2$f_1$ harmonic \nis also observed ($R_{21}=A_{\\rm 2f}/A_{\\rm f}=0.04$).\n\nPhotometric measurements are adequate to perform mode identification by\nmeans of the phase shifts in different colours. Viskum et al. (1998) and\nBreger et al. (1999a) agree \nthat the dominant mode can be identified with $\\ell$=1 and the \n12.15~cd$^{-1}$ mode with the radial fundamental. \nConsidering the sophisticated pulsational modeling proposed by Breger et al.\n(1999a),\nFG Vir looks as a very good candidate to match theory and observations.\n\n\\subsection{XX Pyx: strong and rapid amplitude changes} \\label{xx}\n\nOur knowledge on XX Pyx has rapidly grown in the last years, following the\nparadigm described above.\nIts variability was discovered with the Whole\nEarth Telescope (Handler et al. 1996) and then\nthe first solution of the light curve (based on 116.7 hours of photometry)\nwas already very good: 7 frequencies between 27.01 and 38.11~cd$^{-1}$ were\nunambiguously found. However, a second campaign was planned \nto match the requirements of stellar seismology. Not\nonly was the number of frequencies increased to 13 (Handler et al. 1997), but,\nas noted above, the possibility\nof comparing different observing seasons immediately evidenced \nthe variability of the amplitudes. The three dominating modes change their\nphotometric amplitude within one month at certain times, while the amplitudes\ncan remain constant at other times (Handler et al. 1998): Fig.~\\ref{xxamp}\nshows the behaviour of these modes. The investigation about the nature of these\nvariations considered various hypotheses: oblique pulsator, precession of the pulsational\naxis, beating of closely spaced frequencies. However, none of them \n can explain satisfactorily the amplitude changes.\nIt is important to note that no change in the pulse shape of the $f_1$ mode seems\nto accompany the amplitude variations, \nwhile changes are expected in case of frequency beating. In the\nsame way, evolutionary effects, binarity, magnetic field cannot explain period changes.\n\n\\begin{figure}[t]\n\\setlength{\\textwidth}{4.3in}\n\\vspace*{1.5em}\n\\plotone{eporetti2.eps}\n\\caption{The three main pulsation modes of XX Pyx. The rapid variability of their\n amplitude is detected by subdividing the\nmeasurements in different subsets. White histograms indicate upper limit values\nfor the amplitude.}\n\\label{xxamp}\n\\end{figure}\nThe distribution of the frequencies is clearly shifted toward high values. \nA 2$f_1$ harmonic term is observed; Handler et al.\n(1996) suggested the presence of very small combination terms as a representation of \nnonlinearities originating in the outer part of the star's envelope, but \nthey are very close to the significance limit. \n\n\nAs a last step, a pulsational model of XX Pyx was undertaken, but a\nunique solution could not be proposed (Pamyatnykh et al. 1998).\nThe presence of a frequency spacing of $\\approx$$\\,26\\, \\mu$Hz was used\nto analyze different possibilities, but \n the seismic modeling\nwas unable to match the observed frequencies since the mean departures exceed the\nmean observational frequency by at least one order of magnitude.\nUnfortunately,\nthis star is very faint ($V$=11.5) and line-profile variations, which could help\nin the mode identifications, are very difficult to measure with the requested\naccuracy. An improvement is expected from the results of a new multisite\ncampaign (Arentoft et al. 2000), perpetuating the observational paradigm\nof $\\delta$ Sct stars.\n\\subsection{4 CVn: presence of combinations terms and amplitude variations} \\label{ai} \n\nSeveral campaigns were organized on this bright ($V$=6.1) star, allowing the\ndetermination of a set of reliable frequencies on nine occasions over 30\nyears. They are mostly free from the 1~cd$^{-1}$ alias problem and are \naccurate to 0.001 cd$^{-1}$. Breger et al. (1999b) propose a\nsolution of the light curve composed of 18 independent frequencies and 16\ncombination terms $f_i\\pm f_j$; the residual rms is decreased to the level\nexpected for the noise.\n\nThe frequency content of 4 CVn is characterized by the grouping of all\nthe 18 independent frequencies in the interval 4.749--8.595 cd$^{-1}$.\nIn the 1996 campaign, 5 have an amplitude larger than 9 mmag; 5 others \nhave an amplitude between 6.4 and 3.2 mmag. After a single peak at 1.6\nmmag, the other terms (also including the combination terms) have an\namplitude smaller than 1 mmag. However, the main result of the survey\nof 4 CVn is the large variability of the amplitude. This is surely not\nan effect of the noise distribution, since the most relevant changes\nalso occur in the largest amplitude terms. Fig.~\\ref{figcvn} shows 6 cases\nof such variations: note\nthe decrease in the amplitude of the 5.05~cd$^{-1}$ term and the \ncorresponding increase in that of the 8.59~cd$^{-1}$ term. Other terms,\nsuch as the 6.98~cd$^{-1}$ term, show a more stable value for the amplitude.\nIt is quite impossible to discern a rule in the behaviour of the \namplitudes. A complete discussion of the amplitude changes in the light\ncurves of 4 CVn is given by Breger (2000a).\n\nThe presence of a large number of combination terms is another important\naspect; they flank the set of the independent frequencies. The sums\n$f_i+f_j$ are more numerous than the differences $f_i-f_j$: this should be\na selection effect since the signal at low frequencies is more difficult\nto detect owing to the presence of a higher level of noise.\n\nThe pulsational modes of 4 CVn have also been investigated for the variability\nof the period: some results have been obtained (Breger \\& Pamyatnykh 1998), but\nthe matter has to be investigated further, probably considering also the \nhigh-amplitude $\\delta$ Sct stars (Szeidl 2000). The lack of a\nwell-defined trend in the observed changes is the main difficulty to face\nwhen proposing an explanation. \n\n\\begin{figure}[ht]\n\\setlength{\\textwidth}{4.3in}\n\\plotone{eporetti3.eps}\n\\caption{4 CVn: the variability of the amplitude is evident for several modes.\nAll the available datasets are shown here}\n\\label{figcvn}\n\\end{figure}\n%\\smallskip\n%\\smallskip\n\nFrom a methodological point of view, it is important to notice the relevant\ncontribution of the measurements performed by the 0.75 m Automatic Photometric\nTelescope ``Wolfgang'' located at Washington Camp in Arizona, USA\n(Breger \\& Hiesberger 1999). As a matter of\nfact, the data are of excellent quality (standard deviation 3 mmag in\n$B$ and $V$ light), even if a variation in the brightness differences \nbetween the two comparison stars (about 2 mmag) was observed. It\ncoincides with the two subsets (each lasting 4 weeks) in which the\nmeasurements are separated by a gap of two weeks. According to the\nauthors, the sudden variation is probably a consequence of instrumental\nproblems of the APT and it is not due to the variation of the comparison stars. \nThe solution of this kind of problem can in the future ensure the\ncollection of a large quantity of good-quality data by means of robotic\ntelescopes, a new frontier for the study of $\\delta$ Sct stars.\n\n\\newpage\n\n\\subsection{Comparison between FG Vir, XX Pyx and 4 CVn}\nFigure~\\ref{figfre} shows the frequency content of the well-studied pulsators\ndescribed in this section; the combination terms are omitted. At first glance,\nit also appears that their content is completely different: high frequencies only\nfor XX Pyx, low frequencies only for 4 CVn, two groups of intermediate \nfrequency values for FG Vir. The obvious conclusion is that $\\delta$ Sct stars are\nvery complicated pulsators and that a general recipe cannot be used to predict\ntheir mode excitation.\n\n\nAs regards the similarities between $\\delta$ Sct stars it should be noted\nthat the frequency content of 4 CVn matches very closely that of HD~2724\n(Mantegazza \\& Poretti 1999): at least 7 frequencies have almost the same\nvalue. Among the high-amplitude terms in 4 CVn, only the 5.05~cd$^{-1}$\nterm has no correspondence in HD 2724. The combination frequencies, very\nnumerous in 4 CVn, are not seen in the light curve of HD 2724. This\ncan be due both to the smaller amplitude of the modes excited in HD\n2724 and to the lack of a powerful tool such as a multisite campaign, not yet\nexploited on HD 2724. The physical parameters of the two stars are very similar,\ntoo.\nSo, it seems that we can have the possibility to group stars and not\nonly to observe a different behaviour for every star.\n\n\\begin{figure}[ht]\n\\setlength{\\textwidth}{4.3in}\n\\plotone{eporetti4.eps}\n\\caption{The different distribution of the frequencies is evident in\nthe cases of XX Pyx, 4 CVn and FG Vir. Amplitudes are in mmag; combination\nterms and harmonics are not shown.}\n\\label{figfre}\n\\end{figure}\n\nThe variations of the amplitudes are a further complication, even if we can\nargue that the disappearance or the damping of some terms can enhance or\nmake discernible other modes, increasing the number of known frequencies. The\ncause of the amplitude variability is not clear: it can either be intrinsic or\noriginate from the beating of two close frequencies. Both in the case of\nXX Pyx and 4 CVn the intrinsic damping is considered by the respective authors\nas a more satisfactory explanation since the other hypothesis could not match\nsome observations.\n\n\\section{Other stars studied by the Merate Group}\nIn our effort to reveal the pulsational behaviour of\n$\\delta$ Sct stars the Merate group regularly performed some campaigns on selected objects.\nAt the beginning (second half of the eighties) there was no well-studied\nobject and the main goal of our studies was to monitor different variables\nand try to solve the light curves as satisfactorily as possible. As a matter\nof fact, the history of the worldwide observations of FG Vir started with\nour campaign in 1992 (Mantegazza et al. 1994). \n\nOur contribution to the field was guaranteed by the extensive campaigns carried\nout in Merate (as a rule one target was observed for several weeks) and at\nESO, in both cases using a 0.5-m telescope. Breger (2000b) reports on\nthe list of our campaigns.\nHere we would like to discuss some interesting cases.\n\n\\subsection{44 Tau: variable amplitude and recurrent ratio 0.77} \\label{ff}\n\nThis star has an important place in the development of the studies\nperformed by the Merate group. The intensive survey carried out in 1989\nallowed us to verify for the first time the variability of the amplitude\nof some modes; this fact drove a change in our approach\nto the study of $\\delta$ Sct stars. It was realized that a few nights on an\nobject cannot constitute a significant improvement on the knowledge of the\npulsational behaviour and therefore the planning of an observational \ncampaign must satisfy critical parameters such as frequency resolution (i.e.,\na long baseline), alias damping (long nights or, better, multisite \nobservations), evaluation of observational errors and spectral window\neffects, \\ldots\n\nSeveral datasets were available on 44 Tau and a comparison among them\nled to the detection of amplitude variations (Poretti, Mantegazza, \\&\nRiboni 1992). \nHowever, this bright star ($V$=5.5) was considered a good target \nfor other teams also; Akan (1993) and Park \\& Lee (1995) provided other intensive\ndatasets and the verification of the amplitude variations was an important\ngoal of their studies. Figure~\\ref{fff} summarizes the results: the\nthree papers quoted above supply the three values around 1990.\nThe 6.90~cd$^{-1}$ term is always the dominant one even if a slight decrease\nhas been observed in the last years, in correspondence with an increase in\nthe amplitude of the 7.01~cd$^{-1}$ term. Note also the similar behaviour of\nthe 9.12 and 9.56~cd$^{-1}$ terms and the stability of the other ones.\nThe general look of Fig.~\\ref{fff} suggests a real variation in the\namplitudes rather than the effect of uncertainties in the amplitude \ndetermination.\n\nThe frequency detected in the light curve of 44 Tau also emphasizes\nhow complicated it is to type the modes. In several old papers the\n0.77 ratio between two modes was considered as a clear fingerprint of\nthe pulsation in the fundamental and first overtone radial modes, as\nhappens in high-amplitude $\\delta$ Sct stars. However, \nseveral examples of ratios in the range 0.76-0.78 can be found among the seven\nterms: 6.90/8.96, 7.01/8.96, 6.90/9.12, 7.01/9.12, 7.30/9.56, 8.96/11.52 \n\\ldots \\@ As a consequence, it is quite evident that nonradial modes can also\nshow the same ratio even in a small bunch of terms (only seven here) \nand that trying to find two frequencies showing\na 0.77 ratio to type them as radial modes is naive and misleading.\n\nAs a final remark, it should be noted that 44 Tau is probably \na unique case in the $\\delta$ Sct scenario owing to the very\nsmall $v\\sin i$ value, i.e., 4 km~s$^{-1}$. In a certain sense,\nit proves that a multimode pulsation can be found in a slow \nrotator or in a pole-on star.\n\n\\begin{figure}[ht]\n\\setlength{\\textwidth}{4.3in}\n\\plotone{eporetti5.eps}\n\\caption{44 Tau: the values of the amplitudes are reported for all\nthe available datasets and for all the 7 detected modes. Note the\nopposite trend of the 7.01 and 9.56~cd$^{-1}$ terms. Amplitudes\nare in mag.} \n\\label{fff}\n\\end{figure}\n\n\\subsection{BH Psc: variable amplitude and rich pulsational content}\n\nBH Psc was observed by our group in 1989, 1991, 1994 and 1995 at the\nEuropean Southern Observatory, Chile. The analysis of the first two\ncampaigns showed a very complex light variability resulting from\nthe superposition of more than 10 pulsation modes with frequencies\nbetween 5 and 12~cd$^{-1}$ and semi-amplitudes between 17 and 3 mmag\n(Mantegazza, Poretti, \\& Zerbi 1995).\nThe fit left a high r.m.s.\\ residual 2.3 times greater than that\nmeasured between the two comparison stars. A second photometric campaign\nwas carried out in October and November 1994; we hoped to reveal more\nterms and to check the stability of their amplitudes. The analysis of \nthe new data allowed us to single out 13 frequencies (Mantegazza, Poretti,\n\\& Bossi 1996). They are concentrated\nin the region 5--11.5~cd$^{-1}$: this distribution is slightly larger than that\nobserved for 4 CVn, but they can be considered very similar. However, more\nterms should be present, with an amplitude below 3 mmag, since a good 15\\%\nof the variance could not be explained with the detected terms and the noise.\nMoreover, the standard deviation around the mean value was considerably\nhigher in 1991 than in 1994 (26 mmag against 18 mmag); considerations about\nthe amplitudes of the modes confirmed that the pulsation energy in 1994\nwas lower than in 1991. BH Psc constitutes another example of a $\\delta$\nSct star showing strong amplitude variations.\n\nFigure~\\ref{bhpsc} shows the fit of the 13-term solution to the $B$\nmeasurements in some nights: undetected terms are the more\nprobable explanations for the systematic deviations which\nappear on some occasions. According to the paradigm discussed in Sect.~2 and\nlooking at Fig.~\\ref{bhpsc}, we were at the point where deeper observations\nare needed and we organized \na multisite campaign in September and October 1995.\n The analysis of the 1174 $B$ and 1251 $V$ measurements \nstrengthens the hypothesis of a strong amplitude variation, probably\nas rapid as in the case of XX Pyx (Mantegazza et al., in preparation).\n\n\n\\begin{figure}[t]\n\\setlength{\\textwidth}{4.8in}\n\\plotone{eporetti6.eps}\n\\caption{BH Psc: $\\Delta B$ differential magnitudes obtained in\n1994 (dots) and their least-squares fit with the 13-sinusoid\nmodel (solid lines): note in some parts the deviations of the points from the\ncalculated light curve, which suggest the presence of undetected terms.} \n\\label{bhpsc}\n\\end{figure}\n\n\\subsection{V663 Cas: growth of new modes} \nThe solution of the light curve of V663 Cas$\\equiv$HD~16439$\\equiv$SAO~4710\nwas not an\neasy task. At the beginning it was considered as a monoperiodic pulsator with\n$f_1$=17.13~cd$^{-1}$ \n(Sedano, Rodr\\'{\\i}guez, \\& L\\'opez de Coca 1987), but an observing \ncampaign in the winter of 1988--89 \nevidenced a second peak at 10.13~cd$^{-1}$ (Mantegazza \\& Poretti\n1990). The\namplitude of this second peak is only 3 mmag, so we considered that this\nterm was not detected by Sedano et al. owing to their limited dataset.\nThe panels in the left column of Fig.~\\ref{sao} show the detection of \nthese terms in the 1988--89 dataset. The analysis of the original data\nallowed us to identify the $f_1$ term (top panel). Then the frequency\nof this term (but neither its amplitude or its phase) was introduced\nas a known constituent (k.c.) in the subsequent iteration, in which the\n$f_2$ term was detected (middle panel). Once more, these two terms were\nintroduced as k.c.'s: in this case no significant third term was revealed\n(bottom panel).\n\nStill following the paradigm of the study of the $\\delta$ Sct stars,\na second intensive campaign was performed in the winter of 1994--95 \n(Poretti, Mantegazza, \\& Bossi 1996). The\nresults of the frequency analysis are shown in the panels of the right\ncolumn of Fig.~\\ref{sao}. After the easy detection of the $f_1$ term \n(top panel), the second spectrum looks different: the structure\nat about 10~cd$^{-1}$ is more complex than the one observed in the\n1988--89 dataset (to compare the two middle panels). Indeed, after\nconsidering the $f_2$ term, a new $f_3$ term was revealed at\n10.48~cd$^{-1}$ and the noise around 18~cd$^{-1}$ was higher than\nin the 1988--89 dataset (bottom panel).\n\nSince the time\nbaseline, the number, and the standard deviation of the measurements are the\nsame for the two observing seasons, this fact cannot be related to a sampling\nproblem. Moreover, the amplitude of the $f_1$ term has slightly decreased \nfrom 15.9 to 14.0 mmag in $B$ light. By comparing the two observing\nseasons we can discern the growth of new modes in the light curve\nof V663 Cas.\n\n\\begin{figure}[t]\n\\setlength{\\textwidth}{4.3in}\n\\plotone{eporetti7.eps}\n\\caption{V663 Cas: comparison between the power spectra obtained\nin the analysis of the 1988--89 data (left column) and of the 1994--95\nones (right column). Each spectrum is obtained by considering the\nterms detected in the previous ones as known constituents (k.c.).\nThe appearance of a new term is clearly visible\ncomparing the two bottom panels.}\n\\label{sao}\n\\end{figure}\n\n\\subsection{The help of the spectroscopic approach} \\label {syn}\n\nIt is quite evident that every star carries a brick with which to\nbuild our castle of knowledge about $\\delta$ Sct pulsations, and\nresults on one star have consequences for the analysis of the next\none. However, mode identification from photometric data always leaves\nsome uncertainties. For this reason we turned toward spectroscopy:\nindependent constraints on mode typing and detection of low and high\ndegree $\\ell$ modes can be obtained from the analysis of the time\nseries of the individual pixels defining the line profiles. Moreover,\ntrying to fill the gap between the output of the observations and\nthe inputs for a reliable pulsational model, we tried to discriminate\nbetween different modes through a direct fit of pulsational model to\nspectroscopic and photometric data. Such a {\\it synergic} approach is\ndescribed by Mantegazza (2000).\n\n\n\\section{Monoperiodic pulsators}\n\nIt is a quite accepted concept that detecting as many frequencies as\npossible in the light curves is mandatory in order to make progress\nin the field of asteroseismology. Only in this way is it possible to\ncompare the values predicted by the theoretical models with the observed\nones. Consequently, the observation of monoperiodic stars has been put\naside in the last decade. However, even these variables display a wide\nvariety of intriguing behaviour. \n\n\\subsubsection{Beta Cas:} It is probably the best known monoperiodic\npulsator, also included in the secondary target list of the MONS\nsatellite. Riboni, Poretti, \\& Galli (1994) proved that a constant value\nof the frequency cannot fit the times of maximum brightness collected\nsince 1965; on the other hand, a constant value (9.897396~cd$^{-1}$)\ncan fit all the datasets since 1983. Hence, a probable variation of the\nperiod occurred between 1965 and 1983. On the other hand, the amplitude\nhas remained stable ($\\Delta V$~=~0.03 mag) over a 25-year baseline since\nno significant variation could be inferred. Considering the value of\nthe period (0.101 d), this behaviour is typical for a high-amplitude\n$\\delta$ Sct star rather than for a small amplitude one.\n\n\\subsubsection{\\it AZ CMi:} The light curve of AZ CMi is asymmetrical\n($R_{21}$=0.13 in $V$ light; Poretti 2000) and very stable in shape and\namplitude ($\\Delta V$=0.055 mag); hints of a possible decreasing value\nof the amplitude need more observations to be confirmed. $B$ and $V$\nphotometry is available: the measured phase shift is $\\phi_{B-V}-\\phi_V$=\n--9$\\pm$9 degrees. Since it is negative, such a value slightly suggests\na nonradial mode, but the error bar hampers a definite identification\n(Poretti et al. 1996).\n\n\\smallskip\n\nThe examples reported above seem to suggest that monoperiodic stars are\nsimple and stable pulsators even if the ambiguity\nbetween radial or nonradial modes cannot be solved. However, the analysis of \nother cases complicates the scenario a little:\n\\smallskip\n\n\\subsubsection{\\it BF Phe:} All the measurements available on this star\nare well satisfied by the single term $f$=16.0166 ~cd$^{-1}$ (Poretti et\nal. 1996). The reality of a secondary peak was discussed and, at the end,\nrejected. The amplitude observed in 1991 in $V$ light is very similar to\nthat observed in 1993 in $y$ light. However, in $b$ light the amplitude\nobserved in 1989 (25 mmag) is larger than that observed in 1993 (16 mmag)\nand this discrepancy cannot be explained by errors in the measurements;\nunfortunately BF Phe was measured in 1989 in the $b$-light only. Hence,\nthis monoperiodic pulsator shows an amplitude that has changed by a\nfactor of 1.7 in two years, if we consider the amplitude was the same\nin 1991 and 1993.\n\n\\subsubsection{\\it 28 And:} Rodr\\'\\i guez et al. (1993) demonstrated\nthat 28 And$\\equiv$GN And is a monoperiodic pulsator. They carried out\na frequency analysis on the datasets available in the literature and when\nthe main frequency is prewhitened the resulting periodograms do not show\nany trace of another significant peak. New $uvby$ photometric data were\nacquired in 1996 (Rodr\\'\\i guez et al. 1998); the observed amplitude\nof the light curves is very small compared with any other previous\ndataset. More precisely, the amplitude was about 19 times smaller than\nthat observed five years before. In this new dataset a second term was\ndetected; however, the reality of this term is not well-established,\nsince it is marginally significant (S/N=4.1 and other smaller peaks are\nvisible in the power spectrum). Further observations are requested to\nverify if 28 And will display a pulsational behaviour similar to that\nof V663 Cas, with new frequencies slowly growing to a detectable level.\n\nThe cases of genuine monoperiodic $\\delta$ Sct stars as BF Phe and\n(probably) 28~And yield the observational evidence that in\nthese pulsators also the amplitudes of the excited modes are affected\nby variations. Moreover, a multiperiodic pulsator as V663 Cas can show \na different pulsational content in different seasons, greatly complicating\nobservational investigation. \nAs a matter of fact we proved that the changing amplitude is not\na prerogative of pulsators with a large number of excited modes (as observed\nin XX Pyx, 4 CVn and 44 Tau). It is also possible to find a $\\delta$ Sct\npulsator displaying a single period with a very small amplitude:\nthe light curve of HD~19279 has a full amplitude of only 4.2 mmag\n(Mantegazza \\& Poretti 1993).\n\nMoreover, the detection of a single frequency in the light curve is not\nan indication of radial pulsation for $\\delta$ Sct stars of low amplitude.\nTable \\ref{tabmono} lists the physical parameters as determined\n by means of Hipparcos parallaxes and Str\\\"omgren\nphotometry: as can be noticed, these stars display a large variety of \npulsational constants $Q$'s and, hence, different excited modes.\n\\vspace*{-1.0em}\n\n\n\\begin{table}[b!]\n\\caption{Determination of the pulsational constant $Q$ for the monoperiodic\n$\\delta$ Sct stars discussed here. M$_{\\rm bol}$ values were determined by\nusing the Hipparcos parallaxes} \\label {tabmono}\n\\begin{center}\n%\\scriptsize\n\\small\n\\begin{tabular}{llr c r r r r}\n\\tableline\n \\multicolumn{2}{c}{Star} & HIP & & \\multicolumn{1}{c}{T$_{\\rm eff}$} &\n \\multicolumn{1}{c}{$\\log$ g} & \\multicolumn{1}{c}{M$_{\\rm bol}$} &\n \\multicolumn{1}{c}{$Q$} \\\\\n \\multicolumn{2}{c}{ } & & & \\multicolumn{1}{c}{[K]} &\n \\multicolumn{1}{c}{} & \\multicolumn{1}{c}{} &\n \\multicolumn{1}{c}{[d$^{-1}$]} \\\\\n%\\hline\n\\tableline \n\\noalign{\\smallskip}\nAZ & CMi & 37705 & & 7800 & 3.6 & 0.8 & 0.020 \\\\\nBF & Phe & 117515& & 7500 & 4.1 & 2.5 & 0.034 \\\\\n28 & And & 2355 & & 7500 & 3.7 & 1.4 & 0.018 \\\\\n$\\beta$ & Cas & 746 & & 7000 & 3.6 & 1.2 & 0.020 \\\\\n%$\\tau$ & Peg & & 8180 & 3.8 & 1.0 & 0.016 \\\\\n\\noalign{\\smallskip}\n\\tableline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\section{$\\delta$ Sct stars in binary systems}\nIn principle, the study of $\\delta$ Sct stars belonging to binary\nsystems can supply useful suggestions to understand the physics\nof the pulsation driving. The complications introduced by the \ncompanion are much less important than the measurable parameters we can\nattain. Lampens \\& Boffin (2000) provide a review on\n$\\delta$ Sct stars in stellar systems. Here we would like \nto draw attention to a few binary systems:\n\\smallskip\n\n\\subsubsection{$\\theta^2$ {\\it Tau}:} It is the component of a wide binary\n($P$=140.728~d) and there is no interaction between the two\nstars. However, it is a well-studied pulsator. Breger et al. (1989)\ndetermined five frequencies, very close to each other (from 13.23 to\n14.62~cd$^{-1}$), without regular spacing among them. Such a very close\n(much closer than in the case of 4 CVn), isolated multiplet is not usual\nin the solution of light curves. The amplitudes of the modes seem to be\nvery stable, even if recently Zhiping, Aiying, \\& Dawei (1997) claimed\nto have evidence of amplitude variations; further campaigns could be useful\nto clarify the matter.\n\n\\subsubsection{$\\theta$ {\\it Tuc:}} This double line spectroscopic\nbinary is located near the South Celestial Pole, which makes it very\nsuitable for long-term monitoring. The orbital period is 7.1036 d;\na regular spacing is observed among the 10 detected frequencies, which\ntake place in the interval 15.8--20.3~cd$^{-1}$ (Papar\\'o et al. 1996).\nLow-frequency terms have been observed and they are ascribed to the\norbital period. The mode identification was performed by Sterken (1997)\nusing the Str\\\"omgren photometry: the results are not conclusive for\nmost of the frequencies, but the $f$=20.28~cd$^{-1}$ is reconcilable with\na radial mode. De Mey, Daems, \\& Sterken (1998) confirmed this result\nand they also found that the system has a very low mass ratio, $q$=0.09.\nThe possibility that the regular spacing is related to the slow rotation\nof the $\\delta$ Sct star deserves further attention. De Mey et al. (1998)\nalso found 1.7$\\,$$<R_1$$\\,$$<2.7\\, R_{\\sun}$ for the radius $R_1$ of the\n$\\delta$ Sct star. A rotational period of 7.1036~d is not plausible since\nit should imply 12$\\,$$< v_1$$\\,$$<19$~km~s$^{-1}$ for the rotational\nvelocity $v_1$, a value irreconcilable with the observed $v_1 \\sin i$:\n35~km~s$^{-1}$ (Mantegazza 2000); even higher values are reported in\nthe literature, see Sterken (1997).\n\n\\subsubsection{{\\it AB Cas}:} AB Cas is an eclipsing binary with $P_{\\it\norb}$=1.367 d; the primary component is also a monoperiodic pulsator with\n$P_{\\it puls}$=0.058 d (Fig.\\ref{ab}); there is no connection between the\ntwo periods (Rodr\\'{\\i}guez et al. 1998). The light and colour curves\nare quite normal for this variable: perhaps its main peculiarity is\nits monoperiodicity. It should be noted that the pulsational period is\namong the shortest observed in $\\delta$ Sct stars. The pulsation seems\nto disappear when the secondary star transits across the disk of the\nprimary: this is due to the large depth of the primary eclipse. However,\nwhen the curve due to binarity is removed, the pulsation is visible in\nthe residuals. In fact, during the primary eclipse we can see about 20\\%\nof the disk of the pulsating star. Unfortunately, the observational\nuncertainties do not allow one to discriminate between radial and\nnonradial modes by using the changes in the amplitude caused by the\nprogress of the eclipse. Other considerations suggest a fundamental\nradial mode.\n\n\\begin{figure}[ht]\n\\setlength{\\textwidth}{4.3in}\n\\plotone{eporetti8.eps}\n\\caption{The pulsation of the primary component of AB Cas is superimposed\non the light curve caused by eclipses}\n\\label{ab}\n\\end{figure}\n\n\\subsubsection{{\\it 57 Tau}:} Papar\\'o et al. (2000) indicated 57 Tau as a \npulsator showing simultaneously gravity and pressure modes.\n However, the discovery of its duplicity (Kaye\n1999) explains the low-frequency terms as due to the orbital effect\n($P_{\\it orb}$=2.4860 d); the first example of a pulsator combining the\n$\\gamma$ Dor (gravity) and $\\delta$ Sct (pressure) modes has so far not been\nfound. The promising case of BI CMi (Mantegazza \\& Poretti 1994) \nis still awaiting closer investigation.\n\\smallskip\n\\smallskip\n\nAs a concluding remark on this subject, the connection between\npulsation and duplicity does not seem to be well-exploited in current\nresearch on $\\delta$ Sct stars. It is quite obvious that simultaneous\nphotometry and spectroscopy of a pulsator in an eclipsing system can\nhelp mode typing. One of the main difficulties met in the combined\nuse of photometric and spectroscopic data on $\\delta$ Sct stars (the\nsynergic approach described in Sect.~\\ref{syn}) is to put constraints\non the inclination angle. The possibility of determining this angle and\nthe rotational period (as obtained from the orbital solution, assuming\nsynchronous rotation and equatorial orbits) greatly simplifies mode\nidentification by reducing the number of admissible modes. Lampens \\&\nBoffin (2000) report on many other candidates to study the connection\nbetween duplicity and pulsation.\n\n\\section{$\\delta$ Sct stars in open clusters}\n$\\delta$ Sct stars belonging to an open cluster offer a very good\nopportunity to delve deep into the models thanks to the more precise\ninformation available on metallicity, distance and age. The common\norigin of all the stars allows closer comparisons between the\nresults found on each of them. Interesting results were found by Hern\\'andez\n(1998) by analyzing the data collected by the STEPHI observational\nnetwork on $\\delta$ Sct stars located in the Praesepe cluster.\nUnfortunately all these stars are very complicated pulsators and \nit is very difficult to define a clear picture of their frequency\ncontent.\n\nAlvarez et al. (1998) discussed a set of frequencies for two of\nthem, BQ and BW Cnc. In particular, BW Cnc displays two pairs of very\nclose frequencies; inspection of the light curves showed how two close\nfrequencies can disappear or be misidentified in the presence of bad time\nresolution. These authors recommend long time baselines for campaigns\non $\\delta$ Sct stars, i.e., much longer than 1 week. Also considering\nthe results described below, this requirement has to be considered\nas mandatory for further works. BQ Cnc is a binary system, but only\nthree frequencies were identified; one of them could be a $g$-mode\nand further investigations are requested. Interesting results on the\nPraesepe pulsating stars were also obtained by Arentoft et al. (1998),\nwho successfully used defocussed CCD images. The number of detected\nfrequencies was limited, but the possibility of using the Praesepe\nmetallicity leads the analysis toward deriving reliable physical stellar\nparameters. Pe\\~{n}a et al. (1998) also re-analyzed photometric time\nseries of $\\delta$ Sct stars in Praesepe proposing mode identifications on\nthe basis of the physical properties of the cluster. Unfortunately, the\nuncertainties due to the effects of rotation and convective overshooting\nlimit these conclusions somewhat.\n\nThe STACC network monitored some northern open clusters\n(NGC~7245, NGC~7062, NGC~7226, NGC~7654) searching for $\\delta$\n Sct stars (Viskum et al. 1997). As a result, they found\nthat the fraction of these variables is much lower than\namong field stars and in other open clusters. This \nobservational fact suggests that some parameters are\nworking in the selection of the pulsation excitation\nand future efforts should be undertaken to discover\nwhat they are.\n\n\\section{The frequency content of high amplitude $\\delta$ Sct stars}\n\nAfter examining the complex phenomenological scenario of low amplitude\n$\\delta$ Sct stars, it is interesting to verify what happens in the domain\nof the high amplitude $\\delta$ Sct stars (HADS). Rodr\\'\\i guez et al. (1996)\nanalyzed the multicolour data (Str\\\"omgren and Johnson systems) for\nmonoperiodic HADS. The results indicate that all these stars, both\nPop.~I and Pop.~II objects, are fundamental radial pulsators. This\nconclusion was obtained on the basis of the phase shifts and amplitude\nratios between light and colour variations.\n\nMoreover, Rodr\\'{\\i}guez (1999) analyzed all the reliable photometric\ndatasets of a selected sample of monoperiodic HADS to study the\nstability of the light curves. In this manner more than 22000\nmeasurements were scrutinized for seven stars (ZZ Mic, EH Lib,\nBE Lyn, YZ Boo, SZ Lyn, AD CMi, DY Her). The conclusion was that no\nsignificant long-term changes of amplitude occurred for any of\nthese stars.\n\\smallskip\n\nThe impression is that the HADS are very stable fundamental radial\npulsators, with a few exceptions represented by double-mode HADS.\nCan such an idyllic scenario resist the observational effort made in the\nlast few years? It seems it does, since a large homogeneity was found\nby Morgan, Simet, \\& Bargenquast (1998) analyzing the HADS contained\nin the OGLE database. We note here that the subgroup with an anomalous\n$\\phi_{31}$ parameter seems to be an artifact (Poretti, in preparation).\n\nHowever, we can single out a few interesting cases among the HADS.\n\n%\\smallskip\n\n\\subsubsection{V1162 Ori:} Arentoft \\& Sterken (2000) discuss the time\nseries collected on V1162 Ori. After a period break and a significant\ndecrease in amplitude (about 50\\%; Hintz, Joner, \\& Kim 1998), they\nalso found that the period was no longer valid in early 1998 and that\nthe period changed again during March--April 1998. The latter change\nwas accompanied by an increase in amplitude of the order of 10\\%; such a\nphenomenology calls to mind the behaviour of some low-amplitude $\\delta$~Sct\nstars. A new campaign is in progress to clarify the reasons for\nthese changes.\n\n%\\smallskip\n\n\\subsubsection{\\it V974 Oph:}\nThe case of V974 Oph is more intriguing. This faint ($V$=11.8) variable\nwas observed twice at ESO (July 1987 and April 1989). It was first\nconsidered a HADS similar to V1719 Cyg (Poretti \\& Antonello 1988), but\nthe second run clearly demonstrated that it is a multiperiodic star:\nat least 4 independent frequencies were detected ranging from 5.23 to\n6.66~cd$^{-1}$. Three of them have a half-amplitude larger than 0.04 mag;\nharmonic and combination terms are also observed. The latter result ruled\nout the simple model of a binary star composed of two HADSs. The strong\nchanges in the shape are the largest observed in the amplitude of a HADS\n(Poretti 2000). Maybe V974 Oph can be considered as a link between the\nmultiperiodic low amplitude $\\delta$~Sct stars and the stable fundamental\nradial HADS pulsators.\n\n\\section{Summing-up and Conclusions}\nIn our travel through the observational scenario we met many objects which\nteach us something about the pulsation of $\\delta$ Sct stars. The high\nfrequencies shown by XX Pyx, the intermediate frequencies displayed by FG Vir\nand the low frequencies found in the case of\n4 CVn are leading toward the idea that the mode excitation is really\ncomplex and unpredictable. In this respect, the close similarity between \n4 CVn and HD~2724 is comfortable. Probably the multiperiodic behaviour\nof the high-amplitude $\\delta$ Sct star V974 Oph can also be seen as a \nsimplification of the phenomenology, demonstrating that we can observe a \nmultimode excitation even when a large pulsational energy is involved.\nTo complete the similarities in the opposite direction,\nwe observe monoperiodic pulsators with a very small amplitude \n(HD 19279 and $\\beta$ Cas). What the excited mode is should be\n investigated in order to\nunderstand if a selection effect acts for these low-amplitude monoperiodic\nstars and what difference there is with a star such as AZ CMi, which displays an\nasymmetrical light curve.\n\nThe amplitude variations are observed in a large variety of stars, both\nmultiperiodic (XX Pyx, 4 CVn, 44 Tau) and monoperiodic (28 And and BF\nPhe). The observations of mode growth in the light curve of a relatively\nsimple pulsator such as V663 Cas clarifies what can happen in much more\ncomplicated ones: some modes can be damped and then re-excited. There\nare some observational facts which make this explanation preferable even\nif the model of a beating between two close frequencies with similar,\nconstant amplitude cannot be ruled out. In this context the continuous\nsurvey of $\\delta$ Sct stars which will be performed by space missions\ncould greatly improve the situation; in the case of intrinsic variations,\nthe time-scale of such variations could be determined. \\smallskip\n\nThe better focusing of the phenomenological scenario is not the only\nresult. The effort made by the observers in the last years allowed us\nto detect a large number of frequencies in stars such as FG Vir, XX Pyx,\n4 CVn and BH Psc. By means of multisite campaigns we are able to detect\nterms with amplitudes less than 1 mmag; in these conditions ground-based\nobservations can be successfully complementary to space missions. The\nmode identification techniques are based on both the phase shifts and\namplitude ratios of the light and colour curves and the synergic approach\nperformed by considering spectroscopic curves. Their full exploitation\nshould guarantee an important role for our researche in stellar physics.\n\n\n\\section{The future: the exportation of the results on galactic stars to\nextragalactic research}\n\n\\begin{figure}[ht]\n\\setlength{\\textwidth}{4.3in}\n\\plotone{eporetti9.eps}\n\\caption{The short-period variable stars in the Carina dwarf Spheroidal\ngalaxy. The Period--Luminosity--Metallicity relationships for fundamental\nmode (lower line) and first overtone (upper line) pulsators are shown together\nwith the frequency values. Dashed lines indicate error bars.}\n\\label{carina}\n\\end{figure}\n\n\nThere is always a bit of confusion about the taxonomy of short-period\npulsating stars: in the Galaxy they are called $\\delta$ Sct stars if\nPop.~I objects and SX Phe stars if Pop.~II objects. The old definitions\n``dwarf Cepheids'' or RRs or AI Vel stars are currently avoided in the\ndedicated literature, but they turn up again in papers on extragalactic\nresearches. However, the definition currently used by stellar researchers,\ni.e., high-amplitude $\\delta$ Sct stars (HADS), seems to be irrespective\nof which Population they belong to and we are coming back to old\ndefinitions with new names. Moreover, the phenomenology previously\ndescribed warns us that the separation between high-- and low-amplitude\n$\\delta$ Sct stars is not so obvious and that the amplitude cannot be\nconsidered a good physical criterion to separate variable stars.\n\nMateo, Hurley-Keller, \\& Nemec (1998) reported on the discovery of 20\npulsating stars in the\nCarina dwarf Spheroidal Galaxy. Their periods range from 0.048~d to\n0.077~d and their amplitude is below 0.30 mag in $V$-light.\nPoretti (1999) improved the period values first determined by Mateo et al.\n(1998), obtaining a more clear picture of the Period--Luminosity--Metallicity\nrelationships (Fig.~\\ref{carina}).\n\nThe observed stars are monoperiodic and their periods are usually shorter\nthan the periods observed in galactic HADS. An extended effort was made\nto understand the properties of the Fourier parameters of galactic HADS\n(Morgan et al. 1998), particularly to use them as a mode discriminant. In\nthe case of an external galaxy the approach to the analysis of HADS\nlight curves is the opposite: the Period--Luminosity relationships\nallow us to separate in a straightforward way the pulsation modes. Then\nwe could have the tool to investigate the differences thus driven,\nalways using the\nFourier decomposition. In this direction, the results described by\nPoretti (1999) are quite preliminary, but we can be confident that in\nthe near future we will be able to expand the horizon of HADS studies\nto extragalactic topics.\n\n\\acknowledgments\nThe author wishes to thank M.~Breger, G.~Handler, M.~Papar\\'o,\nE.~Rodr\\`{\\i}guez, and C.~Sterken for comments on the first draft,\nL.~Mantegazza for useful discussions, and J.~Vialle for checking the\nEnglish form.\n\n\\begin{references}\n\n\\reference Akan C. 1993, A\\&A, 278, 150\n\\reference Alvarez, M., Hern\\'andez, M.M., Michel, E., et al. 1998,\n\\aap, 340, 149\n\\reference Arentoft, T., Handler, G., Shobbrook, R.R. et al. 2000,\nin ASP Conf. Ser., The impact of large-scale surveys on pulsation\nstar research, ed. 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